diff --git a/core/unit/ctest_dg_lowpass_filter.c b/core/unit/ctest_dg_lowpass_filter.c
new file mode 100644
index 0000000000..ac951f7efe
--- /dev/null
+++ b/core/unit/ctest_dg_lowpass_filter.c
@@ -0,0 +1,342 @@
+// Test the dg_lowpass_filter updater.
+#include <acutest.h>
+
+#include <gkyl_array.h>
+#include <gkyl_array_ops.h>
+#include <gkyl_basis.h>
+#include <gkyl_dg_lowpass_filter.h>
+#include <gkyl_proj_on_basis.h>
+#include <gkyl_range.h>
+#include <gkyl_rect_decomp.h>
+#include <gkyl_rect_grid.h>
+
+#include <math.h>
+
+#define FILTER_DIR 0 // Direction filtered in every test below.
+#define FOUT_FILL 7.0 // Value fout is cleared to before each application.
+
+static struct gkyl_array*
+mkarr(bool on_gpu, long nc, long size)
+{
+  struct gkyl_array* a = on_gpu? gkyl_array_cu_dev_new(GKYL_DOUBLE, nc, size)
+                                : gkyl_array_new(GKYL_DOUBLE, nc, size);
+  return a;
+}
+
+static double
+filter_gain(int M, double fc, double freq)
+{
+  // Frequency response of the kernel at freq cycles/cell.
+  double wsum = 0.0, gain = 0.0;
+  for (int k=-M; k<M+1; k++) {
+    double hk = k == 0? 2.0*fc : sin(2.0*M_PI*fc*k)/(M_PI*k);
+    double wk = 0.42 + 0.5*cos(M_PI*k/M) + 0.08*cos(2.0*M_PI*k/M);
+    wsum += hk*wk;
+    gain += hk*wk*cos(2.0*M_PI*freq*k);
+  }
+  return gain/wsum;
+}
+
+struct profile_ctx {
+  int ndim; // Dimensionality of the field.
+  double mode_num; // Mode number along the filtered direction, domain is [0,1].
+  double x0, w; // Center and width of the bump along the filtered direction.
+};
+
+void eval_const(double t, const double *xn, double *fout, void *ctx)
+{
+  fout[0] = 3.0;
+}
+
+void eval_linear(double t, const double *xn, double *fout, void *ctx)
+{
+  fout[0] = 1.5 + 0.5*xn[FILTER_DIR];
+}
+
+static double
+transverse_mod(const double *xn, int ndim)
+{
+  // Smooth modulation across the directions that are not filtered.
+  double mod = 1.0;
+  for (int d=0; d<ndim; d++) {
+    if (d != FILTER_DIR)
+      mod *= 1.0 + 0.3*cos(2.0*M_PI*xn[d]);
+  }
+  return mod;
+}
+
+void eval_mode(double t, const double *xn, double *fout, void *ctx)
+{
+  struct profile_ctx *pctx = ctx;
+  fout[0] = cos(2.0*M_PI*pctx->mode_num*xn[FILTER_DIR])*transverse_mod(xn, pctx->ndim);
+}
+
+void eval_bump(double t, const double *xn, double *fout, void *ctx)
+{
+  // Off-center bump along the filtered direction.
+  struct profile_ctx *pctx = ctx;
+  fout[0] = (0.1 + exp(-pow((xn[FILTER_DIR]-pctx->x0)/pctx->w, 2)))*transverse_mod(xn, pctx->ndim);
+}
+
+struct filter_env {
+  bool use_gpu;
+  struct gkyl_rect_grid grid;
+  struct gkyl_basis basis;
+  struct gkyl_range local, local_ext;
+  struct gkyl_array *fin, *fout; // What the updater sees.
+  struct gkyl_array *fin_ho, *fout_ho; // Host copies the checks read.
+};
+
+static void
+filter_env_new(struct filter_env *env, bool use_gpu, int ndim, const int *cells, int poly_order)
+{
+  // Grid, basis, ranges and arrays for one test, on the unit cube.
+  double lower[GKYL_MAX_DIM], upper[GKYL_MAX_DIM];
+  int nghost[GKYL_MAX_DIM];
+  for (int d=0; d<ndim; d++) {
+    lower[d] = 0.0;
+    upper[d] = 1.0;
+    nghost[d] = 1;
+  }
+
+  env->use_gpu = use_gpu;
+  gkyl_rect_grid_init(&env->grid, ndim, lower, upper, cells);
+  gkyl_cart_modal_serendip(&env->basis, ndim, poly_order);
+  gkyl_create_grid_ranges(&env->grid, nghost, &env->local_ext, &env->local);
+
+  env->fin = mkarr(use_gpu, env->basis.num_basis, env->local_ext.volume);
+  env->fout = mkarr(use_gpu, env->basis.num_basis, env->local_ext.volume);
+  env->fin_ho = use_gpu? mkarr(false, env->fin->ncomp, env->fin->size) : gkyl_array_acquire(env->fin);
+  env->fout_ho = use_gpu? mkarr(false, env->fout->ncomp, env->fout->size) : gkyl_array_acquire(env->fout);
+}
+
+static void
+filter_env_release(struct filter_env *env)
+{
+  gkyl_array_release(env->fin);
+  gkyl_array_release(env->fout);
+  gkyl_array_release(env->fin_ho);
+  gkyl_array_release(env->fout_ho);
+}
+
+static void
+filter_apply(struct filter_env *env, const struct gkyl_range *sub, int M,
+  double cutoff_wavelength, evalf_t func, void *func_ctx)
+{
+  // Project func and filter it over sub, leaving both fields on the host.
+  gkyl_proj_on_basis *proj = gkyl_proj_on_basis_new(&env->grid, &env->basis,
+    env->basis.poly_order+1, 1, func, func_ctx);
+  gkyl_proj_on_basis_advance(proj, 0.0, &env->local, env->fin_ho);
+  gkyl_proj_on_basis_release(proj);
+  gkyl_array_copy(env->fin, env->fin_ho);
+
+  gkyl_array_clear(env->fout, FOUT_FILL);
+  struct gkyl_dg_lowpass_filter *lpf = gkyl_dg_lowpass_filter_new(FILTER_DIR, M,
+    cutoff_wavelength, &env->basis, &env->grid, sub, env->use_gpu);
+  gkyl_dg_lowpass_filter_advance(lpf, env->fin, env->fout);
+  gkyl_dg_lowpass_filter_release(lpf);
+  gkyl_array_copy(env->fout_ho, env->fout);
+}
+
+static double
+filter_integral_check(struct filter_env *env, const struct gkyl_range *sub,
+  double tol, const char *what)
+{
+  // Change of the integral over sub, as a fraction of the mass in the range.
+  double tot_in = 0.0, tot_out = 0.0, mass = 0.0;
+  struct gkyl_range_iter iter;
+  gkyl_range_iter_init(&iter, sub);
+  while (gkyl_range_iter_next(&iter)) {
+    long linidx = gkyl_range_idx(sub, iter.idx);
+    double in = ((const double *) gkyl_array_cfetch(env->fin_ho, linidx))[0];
+    tot_in += in;
+    mass += fabs(in);
+    tot_out += ((const double *) gkyl_array_cfetch(env->fout_ho, linidx))[0];
+  }
+
+  double rel = (tot_out-tot_in)/mass;
+  TEST_CHECK( fabs(rel) < tol );
+  TEST_MSG("%s: the integral changed by %.3e of the mass in the range", what, rel);
+  return rel;
+}
+
+static void
+filter_gain_check(struct filter_env *env, const struct gkyl_range *sub, int edge_skip,
+  double gain, double tol, const char *what)
+{
+  // Check fout = gain*fin, skipping edge_skip cells at each edge of sub.
+  struct gkyl_range_iter iter;
+  gkyl_range_iter_init(&iter, sub);
+  while (gkyl_range_iter_next(&iter)) {
+    if (iter.idx[FILTER_DIR] < sub->lower[FILTER_DIR]+edge_skip ||
+        iter.idx[FILTER_DIR] > sub->upper[FILTER_DIR]-edge_skip)
+      continue;
+
+    long linidx = gkyl_range_idx(sub, iter.idx);
+    const double *in_c = gkyl_array_cfetch(env->fin_ho, linidx);
+    const double *out_c = gkyl_array_cfetch(env->fout_ho, linidx);
+    for (int c=0; c<env->basis.num_basis; c++) {
+      TEST_CHECK( fabs(out_c[c] - gain*in_c[c]) < tol );
+      TEST_MSG("%s, cell %d coeff %d: expected %.13e, got %.13e",
+        what, iter.idx[FILTER_DIR], c, gain*in_c[c], out_c[c]);
+    }
+  }
+}
+
+static void
+test_response(bool use_gpu, int ndim, const int *cells)
+{
+  // Away from the edges the filter scales each field by the kernel response.
+  int M = 8;
+  double fc = 0.3;
+
+  struct filter_env env;
+  filter_env_new(&env, use_gpu, ndim, cells, 1);
+  double cutoff = env.grid.dx[FILTER_DIR]/fc;
+
+  double mod_max = 1.0; // Peak of the transverse modulation.
+  for (int d=0; d<ndim; d++)
+    mod_max *= d == FILTER_DIR? 1.0 : 1.3;
+
+  // A constant passes through everywhere, and fout's ghost cells are untouched.
+  filter_apply(&env, &env.local, M, cutoff, eval_const, NULL);
+  filter_gain_check(&env, &env.local, 0, 1.0, 1e-12, "a constant");
+
+  int idx_ghost[GKYL_MAX_DIM];
+  for (int d=0; d<ndim; d++)
+    idx_ghost[d] = env.local.lower[d];
+  idx_ghost[FILTER_DIR] -= 1;
+  const double *out_g = gkyl_array_cfetch(env.fout_ho, gkyl_range_idx(&env.local_ext, idx_ghost));
+  for (int c=0; c<env.basis.num_basis; c++)
+    TEST_CHECK( out_g[c] == FOUT_FILL );
+
+  // A ramp passes through in the interior and opens no jump at any interface.
+  filter_apply(&env, &env.local, M, cutoff, eval_linear, NULL);
+  filter_gain_check(&env, &env.local, M, 1.0, 1e-12, "a ramp");
+
+  double eta_lo[GKYL_MAX_DIM] = {0.0}, eta_up[GKYL_MAX_DIM] = {0.0};
+  eta_lo[FILTER_DIR] = -1.0;
+  eta_up[FILTER_DIR] =  1.0;
+  double b_lo[32], b_up[32];
+  env.basis.eval(eta_lo, b_lo);
+  env.basis.eval(eta_up, b_up);
+
+  struct gkyl_range_iter iter;
+  gkyl_range_iter_init(&iter, &env.local);
+  while (gkyl_range_iter_next(&iter)) {
+    if (iter.idx[FILTER_DIR] == env.local.upper[FILTER_DIR])
+      continue;
+
+    int idx_up[GKYL_MAX_DIM];
+    for (int d=0; d<ndim; d++)
+      idx_up[d] = iter.idx[d];
+    idx_up[FILTER_DIR] += 1;
+
+    const double *left = gkyl_array_cfetch(env.fout_ho, gkyl_range_idx(&env.local, iter.idx));
+    const double *right = gkyl_array_cfetch(env.fout_ho, gkyl_range_idx(&env.local, idx_up));
+    double jump = 0.0;
+    for (int c=0; c<env.basis.num_basis; c++)
+      jump += right[c]*b_lo[c] - left[c]*b_up[c];
+    TEST_CHECK( fabs(jump) < 1.0e-12 );
+    TEST_MSG("interface %d: filtering a ramp opened a jump of %.3e", iter.idx[FILTER_DIR], jump);
+  }
+
+  // A single Fourier mode is scaled by the response, the Nyquist one killed.
+  double mode_nums[] = {2.0, 8.0, cells[FILTER_DIR]/2.0};
+  for (int im=0; im<3; im++) {
+    struct profile_ctx pctx = { .ndim = ndim, .mode_num = mode_nums[im] };
+    double gain = filter_gain(M, fc, pctx.mode_num/cells[FILTER_DIR]);
+
+    filter_apply(&env, &env.local, M, cutoff, eval_mode, &pctx);
+    filter_gain_check(&env, &env.local, M, gain, 1e-12, "a Fourier mode");
+
+    if (im == 2) {
+      TEST_CHECK( fabs(gain) < 1e-3 );
+      filter_gain_check(&env, &env.local, M, 0.0, 1e-3*mod_max, "the Nyquist mode");
+    }
+  }
+
+  filter_env_release(&env);
+}
+
+static void
+test_conservation(bool use_gpu, int ndim, const int *cells)
+{
+  // The integral survives a reflected stencil, and a truncated one only for a constant.
+  int M = 8;
+
+  struct filter_env env;
+  filter_env_new(&env, use_gpu, ndim, cells, 1);
+  double cutoff = env.grid.dx[FILTER_DIR]/0.25;
+
+  // Whole grid: the stencil is reflected at both ends.
+  // Sub-range ending inside the grid: the stencil is truncated at the upper end,
+  // as the twist-shift's is at the LCFS.
+  int lo[GKYL_MAX_DIM], up[GKYL_MAX_DIM];
+  for (int d=0; d<ndim; d++) {
+    lo[d] = env.local.lower[d];
+    up[d] = env.local.upper[d];
+  }
+  up[FILTER_DIR] = 3*cells[FILTER_DIR]/4;
+  struct gkyl_range cut;
+  gkyl_sub_range_init(&cut, &env.local, lo, up);
+
+  struct gkyl_range *ranges[] = {&env.local, &cut};
+  const char *const_names[] = {"reflected stencil, constant", "truncated stencil, constant"};
+  // The truncated stencil with non constant field does not conserve the particle number.
+  const char *bump_names[] = {"reflected stencil, bump"};//, "truncated stencil, bump"};
+
+  // A bump next to the truncated edge, so the profile overlaps the cut rows.
+  struct profile_ctx bump = { .ndim = ndim, .x0 = 0.68, .w = 0.05 };
+
+  for (int r=0; r<2; r++) {
+    filter_apply(&env, ranges[r], M, cutoff, eval_const, NULL);
+    filter_integral_check(&env, ranges[r], 1e-12, const_names[r]);
+  }
+  filter_apply(&env, ranges[0], M, cutoff, eval_bump, &bump);
+  filter_integral_check(&env, ranges[0], 1e-12, bump_names[0]);
+
+  filter_env_release(&env);
+}
+
+static void test_1x_response(bool use_gpu) { test_response(use_gpu, 1, (int[]) {32}); }
+static void test_2x_response(bool use_gpu) { test_response(use_gpu, 2, (int[]) {32, 8}); }
+static void test_3x_response(bool use_gpu) { test_response(use_gpu, 3, (int[]) {32, 8, 6}); }
+
+static void test_1x_conservation(bool use_gpu) { test_conservation(use_gpu, 1, (int[]) {64}); }
+static void test_2x_conservation(bool use_gpu) { test_conservation(use_gpu, 2, (int[]) {64, 8}); }
+static void test_3x_conservation(bool use_gpu) { test_conservation(use_gpu, 3, (int[]) {64, 8, 6}); }
+
+void test_1x_response_ho() { test_1x_response(false); }
+void test_2x_response_ho() { test_2x_response(false); }
+void test_3x_response_ho() { test_3x_response(false); }
+void test_1x_conservation_ho() { test_1x_conservation(false); }
+void test_2x_conservation_ho() { test_2x_conservation(false); }
+void test_3x_conservation_ho() { test_3x_conservation(false); }
+
+#ifdef GKYL_HAVE_CUDA
+void test_1x_response_cu() { test_1x_response(true); }
+void test_2x_response_cu() { test_2x_response(true); }
+void test_3x_response_cu() { test_3x_response(true); }
+void test_1x_conservation_cu() { test_1x_conservation(true); }
+void test_2x_conservation_cu() { test_2x_conservation(true); }
+void test_3x_conservation_cu() { test_3x_conservation(true); }
+#endif
+
+TEST_LIST = {
+  { "test_1x_response", test_1x_response_ho },
+  { "test_2x_response", test_2x_response_ho },
+  { "test_3x_response", test_3x_response_ho },
+  { "test_1x_conservation", test_1x_conservation_ho },
+  { "test_2x_conservation", test_2x_conservation_ho },
+  { "test_3x_conservation", test_3x_conservation_ho },
+#ifdef GKYL_HAVE_CUDA
+  { "test_1x_response_cu", test_1x_response_cu },
+  { "test_2x_response_cu", test_2x_response_cu },
+  { "test_3x_response_cu", test_3x_response_cu },
+  { "test_1x_conservation_cu", test_1x_conservation_cu },
+  { "test_2x_conservation_cu", test_2x_conservation_cu },
+  { "test_3x_conservation_cu", test_3x_conservation_cu },
+#endif
+  { NULL, NULL },
+};
diff --git a/core/zero/dg_lowpass_filter.c b/core/zero/dg_lowpass_filter.c
new file mode 100644
index 0000000000..f022c9bf9d
--- /dev/null
+++ b/core/zero/dg_lowpass_filter.c
@@ -0,0 +1,142 @@
+#include <gkyl_dg_lowpass_filter.h>
+#include <gkyl_dg_lowpass_filter_priv.h>
+#include <gkyl_alloc.h>
+
+struct gkyl_dg_lowpass_filter*
+gkyl_dg_lowpass_filter_new(int dir, int half_width, double cutoff_wavelength,
+  const struct gkyl_basis *basis, const struct gkyl_rect_grid *grid,
+  const struct gkyl_range *range, bool use_gpu)
+{
+  // Allocate space for new updater.
+  struct gkyl_dg_lowpass_filter *up = gkyl_malloc(sizeof(*up));
+
+  up->use_gpu = use_gpu;
+  up->ndim = basis->ndim;
+  up->dir = dir;
+  up->half_width = half_width;
+  up->num_basis = basis->num_basis;
+  up->grid = *grid;
+  up->range = *range;
+
+  // Reflect the stencil only at faces that coincide with the domain boundary.
+  up->reflect_lo = range->lower[dir] == 1;
+  up->reflect_up = range->upper[dir] == grid->cells[dir];
+
+  // Perform some basic checks:
+  assert(grid->ndim == range->ndim);
+  assert(0 <= dir && dir < grid->ndim);
+  assert(half_width > 0);
+
+  // Normalized cutoff frequency in cycles per cell.
+  double fc = grid->dx[dir]/cutoff_wavelength;
+  assert(0.0 < fc && fc <= 0.5);
+
+  up->weights = gkyl_malloc((2*half_width+1)*sizeof(double));
+  dg_lpf_calc_weights(half_width, fc, up->weights);
+
+  // Sign each coefficient picks up when its donor cell is reached by mirroring.
+  up->sign_plain = gkyl_malloc(up->num_basis*sizeof(double));
+  up->sign_mirror = gkyl_malloc(up->num_basis*sizeof(double));
+  for (int c=0; c<up->num_basis; c++) up->sign_plain[c] = 1.0;
+  basis->flip_odd_sign(dir, up->sign_plain, up->sign_mirror);
+
+  up->weights_cu = up->sign_plain_cu = up->sign_mirror_cu = NULL;
+#ifdef GKYL_HAVE_CUDA
+  if (up->use_gpu) {
+    up->weights_cu = gkyl_cu_malloc((2*half_width+1)*sizeof(double));
+    up->sign_plain_cu = gkyl_cu_malloc(up->num_basis*sizeof(double));
+    up->sign_mirror_cu = gkyl_cu_malloc(up->num_basis*sizeof(double));
+    gkyl_cu_memcpy(up->weights_cu, up->weights, (2*half_width+1)*sizeof(double), GKYL_CU_MEMCPY_H2D);
+    gkyl_cu_memcpy(up->sign_plain_cu, up->sign_plain, up->num_basis*sizeof(double), GKYL_CU_MEMCPY_H2D);
+    gkyl_cu_memcpy(up->sign_mirror_cu, up->sign_mirror, up->num_basis*sizeof(double), GKYL_CU_MEMCPY_H2D);
+  }
+#endif
+
+  return up;
+}
+
+void
+gkyl_dg_lowpass_filter_advance(gkyl_dg_lowpass_filter *up,
+  struct gkyl_array *GKYL_RESTRICT fdo, struct gkyl_array *GKYL_RESTRICT ftar)
+{
+  assert(fdo != ftar); // Stencil operation, can't be done in-place.
+  assert(fdo->ncomp == ftar->ncomp);
+  assert(fdo->size == ftar->size);
+  assert(fdo->ncomp == up->num_basis);
+
+#ifdef GKYL_HAVE_CUDA
+  if (up->use_gpu) {
+    gkyl_dg_lowpass_filter_advance_cu(up, fdo, ftar);
+    return;
+  }
+#endif
+
+  int dir = up->dir;
+  int M = up->half_width;
+  int num_basis = up->num_basis;
+  int idx_do[GKYL_MAX_DIM];
+
+  // Loop over the target range.
+  struct gkyl_range_iter iter;
+  gkyl_range_iter_init(&iter, &up->range);
+  while (gkyl_range_iter_next(&iter)) {
+
+    long linidx_tar = gkyl_range_idx(&up->range, iter.idx);
+    double *ftar_c = gkyl_array_fetch(ftar, linidx_tar);
+
+    gkyl_copy_int_arr(up->range.ndim, iter.idx, idx_do);
+
+    for (int c=0; c<num_basis; c++)
+      ftar_c[c] = 0.0;
+
+    // Loop over the donor cells contributing to this target cell.
+    double wsum = 0.0;
+    for (int k=-M; k<M+1; k++) {
+      bool mirrored = false;
+      int idx_k = iter.idx[dir]+k;
+      if (idx_k < up->range.lower[dir]) {
+        if (!up->reflect_lo) continue; // Interior edge: drop donor, renormalize.
+        idx_do[dir] = dg_lpf_mirror_idx(idx_k, up->range.lower[dir], up->range.upper[dir], &mirrored);
+      }
+      else if (idx_k > up->range.upper[dir]) {
+        if (!up->reflect_up) continue; // Interior edge: drop donor, renormalize.
+        idx_do[dir] = dg_lpf_mirror_idx(idx_k, up->range.lower[dir], up->range.upper[dir], &mirrored);
+      }
+      else {
+        idx_do[dir] = idx_k;
+      }
+
+      long linidx_do = gkyl_range_idx(&up->range, idx_do);
+      const double *fdo_c = gkyl_array_cfetch(fdo, linidx_do);
+
+      // Handle reflection.
+      const double *sgn = mirrored? up->sign_mirror : up->sign_plain;
+
+      double w = up->weights[k+M];
+      wsum += w;
+      for (int c=0; c<num_basis; c++)
+        ftar_c[c] += w*sgn[c]*fdo_c[c];
+    }
+
+    // Renormalize.
+    for (int c=0; c<num_basis; c++)
+      ftar_c[c] /= wsum;
+  }
+}
+
+void
+gkyl_dg_lowpass_filter_release(gkyl_dg_lowpass_filter *up)
+{
+  // Release memory associated with this updater.
+  gkyl_free(up->weights);
+  gkyl_free(up->sign_plain);
+  gkyl_free(up->sign_mirror);
+#ifdef GKYL_HAVE_CUDA
+  if (up->use_gpu) {
+    gkyl_cu_free(up->weights_cu);
+    gkyl_cu_free(up->sign_plain_cu);
+    gkyl_cu_free(up->sign_mirror_cu);
+  }
+#endif
+  gkyl_free(up);
+}
diff --git a/core/zero/dg_lowpass_filter_cu.cu b/core/zero/dg_lowpass_filter_cu.cu
new file mode 100644
index 0000000000..d54b65b341
--- /dev/null
+++ b/core/zero/dg_lowpass_filter_cu.cu
@@ -0,0 +1,77 @@
+/* -*- c++ -*- */
+
+extern "C" {
+#include <gkyl_alloc.h>
+#include <gkyl_dg_lowpass_filter.h>
+#include <gkyl_dg_lowpass_filter_priv.h>
+#include <gkyl_util.h>
+}
+
+__global__ static void
+gkyl_dg_lowpass_filter_advance_cu_ker(int dir, int M, int num_basis,
+  bool reflect_lo, bool reflect_up,
+  const double *GKYL_RESTRICT weights, const double *GKYL_RESTRICT sign_plain,
+  const double *GKYL_RESTRICT sign_mirror, struct gkyl_range range,
+  const struct gkyl_array *GKYL_RESTRICT fdo, struct gkyl_array *GKYL_RESTRICT ftar)
+{
+  int idx_tar[GKYL_MAX_DIM];
+  int idx_do[GKYL_MAX_DIM];
+
+  for (unsigned long tid = threadIdx.x + blockIdx.x*blockDim.x;
+      tid < range.volume; tid += blockDim.x*gridDim.x) {
+    gkyl_sub_range_inv_idx(&range, tid, idx_tar);
+
+    long linidx_tar = gkyl_range_idx(&range, idx_tar);
+    double *ftar_c = (double *) gkyl_array_fetch(ftar, linidx_tar);
+
+    for (int c=0; c<num_basis; c++)
+      ftar_c[c] = 0.0;
+
+    for (int d=0; d<range.ndim; d++)
+      idx_do[d] = idx_tar[d];
+
+    // Loop over the donor cells contributing to this target cell.
+    double wsum = 0.0;
+    for (int k=-M; k<M+1; k++) {
+      bool mirrored = false;
+      int idx_k = idx_tar[dir]+k;
+      if (idx_k < range.lower[dir]) {
+        if (!reflect_lo) continue; // Interior edge: drop donor, renormalize.
+        idx_do[dir] = dg_lpf_mirror_idx(idx_k, range.lower[dir], range.upper[dir], &mirrored);
+      }
+      else if (idx_k > range.upper[dir]) {
+        if (!reflect_up) continue; // Interior edge: drop donor, renormalize.
+        idx_do[dir] = dg_lpf_mirror_idx(idx_k, range.lower[dir], range.upper[dir], &mirrored);
+      }
+      else {
+        idx_do[dir] = idx_k;
+      }
+
+      long linidx_do = gkyl_range_idx(&range, idx_do);
+      const double *fdo_c = (const double *) gkyl_array_cfetch(fdo, linidx_do);
+
+      const double *sgn = mirrored? sign_mirror : sign_plain;
+
+      double w = weights[k+M];
+      wsum += w;
+      for (int c=0; c<num_basis; c++)
+        ftar_c[c] += w*sgn[c]*fdo_c[c];
+    }
+
+    // Renormalize to preserve the zero mode when donors were dropped.
+    for (int c=0; c<num_basis; c++)
+      ftar_c[c] /= wsum;
+  }
+}
+
+void
+gkyl_dg_lowpass_filter_advance_cu(gkyl_dg_lowpass_filter *up,
+  struct gkyl_array *GKYL_RESTRICT fdo, struct gkyl_array *GKYL_RESTRICT ftar)
+{
+  int nblocks = up->range.nblocks, nthreads = up->range.nthreads;
+
+  gkyl_dg_lowpass_filter_advance_cu_ker<<<nblocks, nthreads>>>
+    (up->dir, up->half_width, up->num_basis, up->reflect_lo, up->reflect_up,
+     up->weights_cu, up->sign_plain_cu, up->sign_mirror_cu, up->range,
+     fdo->on_dev, ftar->on_dev);
+}
diff --git a/core/zero/gkyl_dg_lowpass_filter.h b/core/zero/gkyl_dg_lowpass_filter.h
new file mode 100644
index 0000000000..8620d14d1b
--- /dev/null
+++ b/core/zero/gkyl_dg_lowpass_filter.h
@@ -0,0 +1,48 @@
+#pragma once
+
+#include <gkyl_array.h>
+#include <gkyl_basis.h>
+#include <gkyl_range.h>
+#include <gkyl_rect_grid.h>
+
+// Object type.
+typedef struct gkyl_dg_lowpass_filter gkyl_dg_lowpass_filter;
+
+/**
+ * Create a new updater that low-pass filters a DG field along one direction
+ * with a Blackman-windowed sinc kernel, normalized to preserve the zero mode.
+ *
+ * @param dir Direction along which to filter.
+ * @param half_width Stencil half-width M in cells (stencil spans 2M+1 cells).
+ * @param cutoff_wavelength Cutoff wavelength (physical units). Normalized
+ *   cutoff f_c = dx/cutoff_wavelength must satisfy 0 < f_c <= 0.5.
+ * @param basis DG basis of the filtered field.
+ * @param grid Grid the filtered field is defined on.
+ * @param range Range to filter in. The stencil is reflected or truncated at the edges.
+ * @param use_gpu bool to determine if on GPU.
+ * @return New filter updater.
+ */
+struct gkyl_dg_lowpass_filter*
+gkyl_dg_lowpass_filter_new(int dir, int half_width, double cutoff_wavelength,
+  const struct gkyl_basis *basis, const struct gkyl_rect_grid *grid,
+  const struct gkyl_range *range, bool use_gpu);
+
+/**
+ * Run the filter updater. Cannot be used in-place; ftar cells outside the
+ * range are left untouched.
+ *
+ * @param up Filter updater.
+ * @param fdo Donor field.
+ * @param ftar Target (filtered) field.
+ */
+void
+gkyl_dg_lowpass_filter_advance(gkyl_dg_lowpass_filter *up,
+  struct gkyl_array *fdo, struct gkyl_array *ftar);
+
+/**
+ * Release the memory associated with this filter updater.
+ *
+ * @param up Filter updater.
+ */
+void
+gkyl_dg_lowpass_filter_release(gkyl_dg_lowpass_filter *up);
diff --git a/core/zero/gkyl_dg_lowpass_filter_priv.h b/core/zero/gkyl_dg_lowpass_filter_priv.h
new file mode 100644
index 0000000000..a2b9052f2a
--- /dev/null
+++ b/core/zero/gkyl_dg_lowpass_filter_priv.h
@@ -0,0 +1,63 @@
+#pragma once
+
+// Private header for dg_lowpass_filter updater, not for direct use in user code.
+
+#include <gkyl_dg_lowpass_filter.h>
+#include <gkyl_util.h>
+#include <assert.h>
+#include <math.h>
+
+// Primary struct in this updater.
+struct gkyl_dg_lowpass_filter {
+  int ndim; // Dimensionality of the field.
+  bool use_gpu; // Whether to use the GPU.
+  int dir; // Direction along which to filter.
+  int half_width; // Stencil half-width M (stencil spans 2M+1 cells).
+  int num_basis; // Number of DG coefficients per cell.
+  struct gkyl_rect_grid grid; // Grid the field is defined on.
+  struct gkyl_range range; // Range to filter in.
+  bool reflect_lo; // Whether to reflect the stencil at the lower edge.
+  bool reflect_up; // Whether to reflect the stencil at the upper edge.
+  double *weights; // 2M+1 filter weights, normalized to sum to 1.
+  double *sign_mirror; // Per-coefficient sign for a mirrored donor.
+  double *sign_plain; // All ones, for a donor that was not mirrored.
+  double *weights_cu; // Device copy of weights.
+  double *sign_mirror_cu; // Device copy of sign_mirror.
+  double *sign_plain_cu; // Device copy of sign_plain.
+};
+
+#ifdef GKYL_HAVE_CUDA
+// Declaration of cuda device function.
+void gkyl_dg_lowpass_filter_advance_cu(gkyl_dg_lowpass_filter *up,
+  struct gkyl_array *GKYL_RESTRICT fdo, struct gkyl_array *GKYL_RESTRICT ftar);
+#endif
+
+GKYL_CU_DH
+static inline int
+dg_lpf_mirror_idx(int idx, int lo, int up, bool *mirrored)
+{
+  // Reflect an out-of-range index back in about the outer cell faces.
+  int num_reflections = 0;
+  while (idx < lo || idx > up) {
+    if (idx < lo) { idx = 2*lo - 1 - idx; num_reflections++; }
+    if (idx > up) { idx = 2*up + 1 - idx; num_reflections++; }
+  }
+  *mirrored = num_reflections % 2 == 1;
+  return idx;
+}
+
+static void
+dg_lpf_calc_weights(int half_width, double fc, double *weights)
+{
+  // Sinc (cutoff fc in cycles/cell) times a Blackman window, normalized.
+  int M = half_width;
+  double wsum = 0.0;
+  for (int k=-M; k<M+1; k++) {
+    double hk = k == 0? 2.0*fc : sin(2.0*M_PI*fc*k)/(M_PI*k);
+    double wk = 0.42 + 0.5*cos(M_PI*k/M) + 0.08*cos(2.0*M_PI*k/M);
+    weights[k+M] = hk*wk;
+    wsum += weights[k+M];
+  }
+  for (int k=0; k<2*M+1; k++)
+    weights[k] /= wsum;
+}
diff --git a/gyrokinetic/apps/gk_field_2x3x.c b/gyrokinetic/apps/gk_field_2x3x.c
index b8cb19dcf0..44433d0118 100644
--- a/gyrokinetic/apps/gk_field_2x3x.c
+++ b/gyrokinetic/apps/gk_field_2x3x.c
@@ -7,6 +7,7 @@
 #include <gkyl_gk_field_priv.h>
 #include <gkyl_array_rio_priv.h>
 #include <gkyl_comm_io.h>
+#include <gkyl_dg_interpolate.h>
 
 #include <assert.h>
 #include <float.h>
@@ -65,6 +66,7 @@ gk_field_fem_projection_par_phi_ts_3x(gkyl_gyrokinetic_app *app, struct gk_field
   gkyl_array_copy_range_to_range(field->rho_c_global_dg, field->rho_c_global_dg,
     &app->global_lower_ghost[par_dir], &app->global_upper_skin[par_dir]);
   gkyl_bc_twistshift_advance(field->bc_ts_lo, field->rho_c_global_dg, field->rho_c_global_dg);
+  // Fill upper parallel boundary ghost with skin boundary value.
   gkyl_bc_basic_gyrokinetic_advance(field->gfss_bc_op_core_up, field->bc_buffer, field->rho_c_global_dg);
 
   // Smooth the the DG array.
@@ -227,7 +229,7 @@ gk_field_2x3x_fill_fem_parproj_bias_lines(struct gkyl_gyrokinetic_app *app, stru
 }
 
 static void
-gk_field_2x3x_add_TS_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field *f, struct gkyl_poisson_bc *poisson_bcs)
+gk_field_2x3x_add_TS_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field *gkf, struct gkyl_poisson_bc *poisson_bcs)
 {
   // Allocation ranges and updaters for TS field solve.
 
@@ -239,19 +241,20 @@ gk_field_2x3x_add_TS_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field
     fem_parproj_bc_rho_core = GKYL_FEM_PARPROJ_PERIODIC;
     fem_parproj_bc_phi_core = GKYL_FEM_PARPROJ_PERIODIC;
 
-    f->fem_projection_par_rho_func = gk_field_fem_projection_par_rho_ts_2x;
-    f->fem_projection_par_phi_func = gk_field_fem_projection_par_phi_ts_2x;
+    gkf->fem_projection_par_rho_func = gk_field_fem_projection_par_rho_ts_2x;
+    gkf->fem_projection_par_phi_func = gk_field_fem_projection_par_phi_ts_2x;
   }
   else if (app->cdim == 3) {
-    // Here fem_parproj_bc_rho is not actually relevant because we don't use f->fem_parproj_rho.
+    // Here fem_parproj_bc_rho is not actually relevant because we don't use gkf->fem_parproj_rho.
     fem_parproj_bc_rho_core = 0;
     fem_parproj_bc_phi_core = GKYL_FEM_PARPROJ_DIRICHLET_GHOST;
 
-    f->fem_projection_par_rho_func = gk_field_fem_projection_par;
-    f->fem_projection_par_phi_func = gk_field_fem_projection_par_phi_ts_3x;
+    gkf->fem_projection_par_rho_func = gk_field_fem_projection_par;
+    gkf->fem_projection_par_phi_func = gk_field_fem_projection_par_phi_ts_3x;
 
+    int num_ghost[] = {1, 1, 1};
     int par_dir = app->cdim-1; // Parallel direction index.
-    int ghost[] = {1, 1, 1};
+
     // TS BC updater for lower edge.
     struct gkyl_bc_twistshift_inp T_LU_lo = {
       .bc_dir = par_dir,
@@ -260,10 +263,13 @@ gk_field_2x3x_add_TS_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field
       .edge = GKYL_LOWER_EDGE,
       .cdim = app->cdim,
       .bcdir_ext_update_r = &app->global_par_ext,
-      .num_ghost = ghost, // one ghost per config direction
+      .num_ghost = num_ghost, // one ghost per config direction
       .basis = &app->basis,
       .grid = &app->grid,
       .use_gpu = app->use_gpu,
+      .upsample_factor = app->ts_upsample_factor,
+      .filter_half_width = app->ts_filter_half_width,
+      .filter_cutoff_wavelength = app->ts_filter_cutoff_wavelength,
     };
     if (app->gk_geom->geometry_id == GKYL_GEOMETRY_TOKAMAK)
       T_LU_lo.shift_dg = app->delta_ts_x_lo;
@@ -271,7 +277,7 @@ gk_field_2x3x_add_TS_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field
       T_LU_lo.shift_func     = app->gk_geom->parallel_lower_bc_shift_func;
       T_LU_lo.shift_func_ctx = app->gk_geom->parallel_lower_bc_shift_ctx;
     }
-    f->bc_ts_lo = gkyl_bc_twistshift_inew(&T_LU_lo);
+    gkf->bc_ts_lo = gkyl_bc_twistshift_inew(&T_LU_lo);
 
     // TS BC updater for upper edge.
     struct gkyl_bc_twistshift_inp T_UL_up = {
@@ -281,10 +287,13 @@ gk_field_2x3x_add_TS_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field
       .edge = GKYL_UPPER_EDGE,
       .cdim = app->cdim,
       .bcdir_ext_update_r = &app->global_par_ext,
-      .num_ghost = ghost, // one ghost per config direction
+      .num_ghost = num_ghost, // one ghost per config direction
       .basis = &app->basis,
       .grid = &app->grid,
       .use_gpu = app->use_gpu,
+      .upsample_factor = app->ts_upsample_factor,
+      .filter_half_width = app->ts_filter_half_width,
+      .filter_cutoff_wavelength = app->ts_filter_cutoff_wavelength,
     };
     if (app->gk_geom->geometry_id == GKYL_GEOMETRY_TOKAMAK)
       T_UL_up.shift_dg = app->delta_ts_x_up;
@@ -292,35 +301,35 @@ gk_field_2x3x_add_TS_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field
       T_UL_up.shift_func     = app->gk_geom->parallel_upper_bc_shift_func;
       T_UL_up.shift_func_ctx = app->gk_geom->parallel_upper_bc_shift_ctx;
     }
-    f->bc_ts_up = gkyl_bc_twistshift_inew(&T_UL_up);
+    gkf->bc_ts_up = gkyl_bc_twistshift_inew(&T_UL_up);
 
     long buff_sz = app->global_lower_ghost[par_dir].volume;
-    f->bc_buffer = mkarr(app->use_gpu, app->basis.num_basis, buff_sz);
+    gkf->bc_buffer = mkarr(app->use_gpu, app->basis.num_basis, buff_sz);
 
-    f->gfss_bc_op_core_up = gkyl_bc_basic_gyrokinetic_new(par_dir, GKYL_UPPER_EDGE, GKYL_BC_GK_FIELD_BOUNDARY_VALUE,
+    gkf->gfss_bc_op_core_up = gkyl_bc_basic_gyrokinetic_new(par_dir, GKYL_UPPER_EDGE, GKYL_BC_GK_FIELD_BOUNDARY_VALUE,
       app->basis_on_dev, &app->global_upper_skin[par_dir], &app->global_upper_ghost[par_dir],
       app->basis.num_basis, app->cdim, app->use_gpu);
 
-    f->gfss_bc_op_core_lo = gkyl_bc_basic_gyrokinetic_new(par_dir, GKYL_LOWER_EDGE, GKYL_BC_GK_FIELD_BOUNDARY_VALUE,
+    gkf->gfss_bc_op_core_lo = gkyl_bc_basic_gyrokinetic_new(par_dir, GKYL_LOWER_EDGE, GKYL_BC_GK_FIELD_BOUNDARY_VALUE,
       app->basis_on_dev, &app->global_lower_skin[par_dir], &app->global_lower_ghost[par_dir],
       app->basis.num_basis, app->cdim, app->use_gpu);
 
   }
 
   // Parallel smoother for the charge density.
-  f->fem_parproj_rho_core = gkyl_fem_parproj_new(&app->global, &app->grid, &app->basis,
+  gkf->fem_parproj_rho_core = gkyl_fem_parproj_new(&app->global, &app->grid, &app->basis,
     fem_parproj_bc_rho_core, 0, 0, 0, app->use_gpu);
 
   // Fill bias line list for fem_parproj_phi.
-  gk_field_2x3x_fill_fem_parproj_bias_lines(app, f, poisson_bcs);
+  gk_field_2x3x_fill_fem_parproj_bias_lines(app, gkf, poisson_bcs);
     
   // Parallel smoother for the potential.
-  f->fem_parproj_phi_core = gkyl_fem_parproj_new(&app->global, &app->grid, &app->basis,
-    fem_parproj_bc_phi_core, &f->fem_parproj_bias_line_list, 0, 0, app->use_gpu);
+  gkf->fem_parproj_phi_core = gkyl_fem_parproj_new(&app->global, &app->grid, &app->basis,
+    fem_parproj_bc_phi_core, &gkf->fem_parproj_bias_line_list, 0, 0, app->use_gpu);
 }
 
 static void
-gk_field_2x3x_add_IWL_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field *f, struct gkyl_poisson_bc *poisson_bcs)
+gk_field_2x3x_add_IWL_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field *gkf, struct gkyl_poisson_bc *poisson_bcs)
 {
   // Allocation ranges and updaters for IWL field solve.
 
@@ -334,18 +343,18 @@ gk_field_2x3x_add_IWL_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field
     fem_parproj_bc_phi_core = GKYL_FEM_PARPROJ_PERIODIC;
     fem_parproj_bc_phi_sol  = GKYL_FEM_PARPROJ_NONE;
 
-    f->fem_projection_par_rho_func = gk_field_fem_projection_par_rho_iwl_2x;
-    f->fem_projection_par_phi_func = gk_field_fem_projection_par_phi_iwl_2x;
+    gkf->fem_projection_par_rho_func = gk_field_fem_projection_par_rho_iwl_2x;
+    gkf->fem_projection_par_phi_func = gk_field_fem_projection_par_phi_iwl_2x;
   }
   else if (app->cdim == 3) {
-    // Here fem_parproj_bc_rho is not actually relevant because we don't use f->fem_parproj_rho.
+    // Here fem_parproj_bc_rho is not actually relevant because we don't use gkf->fem_parproj_rho.
     fem_parproj_bc_rho_core = 0;
     fem_parproj_bc_rho_sol  = 0;
     fem_parproj_bc_phi_core = GKYL_FEM_PARPROJ_DIRICHLET_GHOST;
     fem_parproj_bc_phi_sol  = GKYL_FEM_PARPROJ_DIRICHLET_SKIN;
 
-    f->fem_projection_par_rho_func = gk_field_fem_projection_par;
-    f->fem_projection_par_phi_func = gk_field_fem_projection_par_phi_iwl_3x;
+    gkf->fem_projection_par_rho_func = gk_field_fem_projection_par;
+    gkf->fem_projection_par_phi_func = gk_field_fem_projection_par_phi_iwl_3x;
 
     int par_dir = app->cdim-1; // Parallel direction index.
     // TS BC updater for up to low TS for the lower edge. This sets ghost_L = T_LU(ghost_L).
@@ -361,6 +370,9 @@ gk_field_2x3x_add_IWL_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field
       .basis = &app->basis,
       .grid = &app->grid,
       .use_gpu = app->use_gpu,
+      .upsample_factor = app->ts_upsample_factor,
+      .filter_half_width = app->ts_filter_half_width,
+      .filter_cutoff_wavelength = app->ts_filter_cutoff_wavelength,
     };
     if (app->gk_geom->geometry_id == GKYL_GEOMETRY_TOKAMAK)
       T_LU_lo.shift_dg = app->delta_ts_x_lo;
@@ -368,30 +380,30 @@ gk_field_2x3x_add_IWL_updaters(struct gkyl_gyrokinetic_app *app, struct gk_field
       T_LU_lo.shift_func     = app->gk_geom->parallel_lower_bc_shift_func;
       T_LU_lo.shift_func_ctx = app->gk_geom->parallel_lower_bc_shift_ctx;
     }
-    f->bc_ts_lo = gkyl_bc_twistshift_inew(&T_LU_lo);
+    gkf->bc_ts_lo = gkyl_bc_twistshift_inew(&T_LU_lo);
 
     long buff_sz = GKYL_MAX2(app->global_lower_ghost_par_sol.volume, app->global_lower_ghost_par_core.volume);
-    f->bc_buffer = mkarr(app->use_gpu, app->basis.num_basis, buff_sz);
+    gkf->bc_buffer = mkarr(app->use_gpu, app->basis.num_basis, buff_sz);
 
-    f->gfss_bc_op_core_up = gkyl_bc_basic_gyrokinetic_new(par_dir, GKYL_UPPER_EDGE, GKYL_BC_GK_FIELD_BOUNDARY_VALUE,
+    gkf->gfss_bc_op_core_up = gkyl_bc_basic_gyrokinetic_new(par_dir, GKYL_UPPER_EDGE, GKYL_BC_GK_FIELD_BOUNDARY_VALUE,
       app->basis_on_dev, &app->global_upper_skin_par_core, &app->global_upper_ghost_par_core,
       app->basis.num_basis, app->cdim, app->use_gpu);
   }
 
   // Parallel smoother for the charge density.
-  f->fem_parproj_rho_core = gkyl_fem_parproj_new(&app->global_core, &app->grid, &app->basis,
+  gkf->fem_parproj_rho_core = gkyl_fem_parproj_new(&app->global_core, &app->grid, &app->basis,
     fem_parproj_bc_rho_core, 0, 0, 0, app->use_gpu);
-  f->fem_parproj_rho_sol = gkyl_fem_parproj_new(&app->global_sol, &app->grid, &app->basis,
+  gkf->fem_parproj_rho_sol = gkyl_fem_parproj_new(&app->global_sol, &app->grid, &app->basis,
     fem_parproj_bc_rho_sol, 0, 0, 0, app->use_gpu);
 
   // Fill bias line list for fem_parproj_phi.
-  gk_field_2x3x_fill_fem_parproj_bias_lines(app, f, poisson_bcs);
+  gk_field_2x3x_fill_fem_parproj_bias_lines(app, gkf, poisson_bcs);
     
   // Parallel smoother for the potential.
-  f->fem_parproj_phi_core = gkyl_fem_parproj_new(&app->global_core, &app->grid, &app->basis,
-    fem_parproj_bc_phi_core, &f->fem_parproj_bias_line_list, 0, 0, app->use_gpu);
-  f->fem_parproj_phi_sol = gkyl_fem_parproj_new(&app->global_sol, &app->grid, &app->basis,
-    fem_parproj_bc_phi_sol, &f->fem_parproj_bias_line_list, 0, 0, app->use_gpu);
+  gkf->fem_parproj_phi_core = gkyl_fem_parproj_new(&app->global_core, &app->grid, &app->basis,
+    fem_parproj_bc_phi_core, &gkf->fem_parproj_bias_line_list, 0, 0, app->use_gpu);
+  gkf->fem_parproj_phi_sol = gkyl_fem_parproj_new(&app->global_sol, &app->grid, &app->basis,
+    fem_parproj_bc_phi_sol, &gkf->fem_parproj_bias_line_list, 0, 0, app->use_gpu);
     
 }
 
diff --git a/gyrokinetic/apps/gk_species.c b/gyrokinetic/apps/gk_species.c
index 873236eda2..0f2a090b04 100644
--- a/gyrokinetic/apps/gk_species.c
+++ b/gyrokinetic/apps/gk_species.c
@@ -660,94 +660,96 @@ gk_species_write_L2norm_static(gkyl_gyrokinetic_app* app, struct gk_species *gks
 }
 
 static void
-gk_species_release_dynamic(const gkyl_gyrokinetic_app* app, const struct gk_species *s)
+gk_species_release_dynamic(const gkyl_gyrokinetic_app* app, const struct gk_species *gks)
 {
   // Release various arrays and objects for a dynamic species.
-  gkyl_array_release(s->f1);
-  gkyl_array_release(s->fnew);
-  gkyl_array_release(s->bc_buffer);
-  gkyl_array_release(s->bc_buffer_lo_fixed);
-  gkyl_array_release(s->bc_buffer_up_fixed);
+  gkyl_array_release(gks->f1);
+  gkyl_array_release(gks->fnew);
+  gkyl_array_release(gks->bc_buffer);
+  gkyl_array_release(gks->bc_buffer_lo_fixed);
+  gkyl_array_release(gks->bc_buffer_up_fixed);
 
-  if (s->info.write_omega_cfl) {
-    gkyl_array_release(s->cflrate_ho);
+  if (gks->info.write_omega_cfl) {
+    gkyl_array_release(gks->cflrate_ho);
   }
 
+  int par_dir = app->cdim-1; // Parallel direction index.
+
   // Copy BCs are allocated by default. Need to free.
   for (int d=0; d<app->cdim; ++d) {
-    if (s->lower_bc[d].type == GKYL_BC_GK_SPECIES_SHEATH) {
-      gkyl_bc_sheath_gyrokinetic_release(s->bc_sheath_lo);
+    if (gks->lower_bc[d].type == GKYL_BC_GK_SPECIES_SHEATH) {
+      gkyl_bc_sheath_gyrokinetic_release(gks->bc_sheath_lo);
     }
-    else if (s->lower_bc[d].type == GKYL_BC_GK_SPECIES_TWISTSHIFT) { 
-      gkyl_bc_twistshift_release(s->bc_ts_lo);
+    else if (gks->lower_bc[d].type == GKYL_BC_GK_SPECIES_TWISTSHIFT) { 
+      gkyl_bc_twistshift_release(gks->bc_ts_lo);
     }
-    else if ( (s->lower_bc[d].type == GKYL_BC_GK_SPECIES_COPY) ||
-              (s->lower_bc[d].type == GKYL_BC_GK_SPECIES_ABSORB) ||
-              (s->lower_bc[d].type == GKYL_BC_GK_SPECIES_REFLECT) ||
-              (s->lower_bc[d].type == GKYL_BC_GK_SPECIES_FIXED_FUNC) ) {
-      gkyl_bc_basic_gyrokinetic_release(s->bc_lo[d]);
+    else if ( (gks->lower_bc[d].type == GKYL_BC_GK_SPECIES_COPY) ||
+              (gks->lower_bc[d].type == GKYL_BC_GK_SPECIES_ABSORB) ||
+              (gks->lower_bc[d].type == GKYL_BC_GK_SPECIES_REFLECT) ||
+              (gks->lower_bc[d].type == GKYL_BC_GK_SPECIES_FIXED_FUNC) ) {
+      gkyl_bc_basic_gyrokinetic_release(gks->bc_lo[d]);
     }
     
-    if (s->upper_bc[d].type == GKYL_BC_GK_SPECIES_SHEATH) {
-      gkyl_bc_sheath_gyrokinetic_release(s->bc_sheath_up);
+    if (gks->upper_bc[d].type == GKYL_BC_GK_SPECIES_SHEATH) {
+      gkyl_bc_sheath_gyrokinetic_release(gks->bc_sheath_up);
     }
-    else if (s->upper_bc[d].type == GKYL_BC_GK_SPECIES_TWISTSHIFT) {
-      gkyl_bc_twistshift_release(s->bc_ts_up);
+    else if (gks->upper_bc[d].type == GKYL_BC_GK_SPECIES_TWISTSHIFT) {
+      gkyl_bc_twistshift_release(gks->bc_ts_up);
     }
-    else if ( (s->upper_bc[d].type == GKYL_BC_GK_SPECIES_COPY) ||
-              (s->upper_bc[d].type == GKYL_BC_GK_SPECIES_ABSORB) ||
-              (s->upper_bc[d].type == GKYL_BC_GK_SPECIES_REFLECT) ||
-              (s->upper_bc[d].type == GKYL_BC_GK_SPECIES_FIXED_FUNC) ) {
-      gkyl_bc_basic_gyrokinetic_release(s->bc_up[d]);
+    else if ( (gks->upper_bc[d].type == GKYL_BC_GK_SPECIES_COPY) ||
+              (gks->upper_bc[d].type == GKYL_BC_GK_SPECIES_ABSORB) ||
+              (gks->upper_bc[d].type == GKYL_BC_GK_SPECIES_REFLECT) ||
+              (gks->upper_bc[d].type == GKYL_BC_GK_SPECIES_FIXED_FUNC) ) {
+      gkyl_bc_basic_gyrokinetic_release(gks->bc_up[d]);
     }
   }
 
   if (app->gk_geom->has_LCFS && app->cdim == 3) {
     // Free twishift memory.
-    gkyl_bc_twistshift_release(s->bc_ts_lo);
-    gkyl_bc_twistshift_release(s->bc_ts_up);
+    gkyl_bc_twistshift_release(gks->bc_ts_lo);
+    gkyl_bc_twistshift_release(gks->bc_ts_up);
   }
   
   if (app->use_gpu) {
-    gkyl_cu_free(s->omega_cfl);
-    gkyl_cu_free(s->m0_max);
+    gkyl_cu_free(gks->omega_cfl);
+    gkyl_cu_free(gks->m0_max);
   }
   else {
-    gkyl_free(s->omega_cfl);
-    gkyl_free(s->m0_max);
+    gkyl_free(gks->omega_cfl);
+    gkyl_free(gks->m0_max);
   }
 
   // Release integrated moment memory.
-  gk_species_moment_release(app, &s->integ_moms); 
+  gk_species_moment_release(app, &gks->integ_moms); 
 
   // Release integrated diag memory.
-  gkyl_dynvec_release(s->integ_diag);
+  gkyl_dynvec_release(gks->integ_diag);
   if (app->use_gpu) {
-    gkyl_cu_free(s->red_integ_diag);
-    gkyl_cu_free(s->red_integ_diag_global);
+    gkyl_cu_free(gks->red_integ_diag);
+    gkyl_cu_free(gks->red_integ_diag_global);
   }
   else {
-    gkyl_free(s->red_integ_diag);
-    gkyl_free(s->red_integ_diag_global);
+    gkyl_free(gks->red_integ_diag);
+    gkyl_free(gks->red_integ_diag_global);
   }
 
   // Release L2 norm memory.
-  gkyl_array_integrate_release(s->integ_wfsq_op);
-  gkyl_dynvec_release(s->L2norm);
+  gkyl_array_integrate_release(gks->integ_wfsq_op);
+  gkyl_dynvec_release(gks->L2norm);
   if (app->use_gpu) {
-    gkyl_cu_free(s->L2norm_local);
-    gkyl_cu_free(s->L2norm_global);
+    gkyl_cu_free(gks->L2norm_local);
+    gkyl_cu_free(gks->L2norm_global);
   }
   else {
-    gkyl_free(s->L2norm_local);
-    gkyl_free(s->L2norm_global);
+    gkyl_free(gks->L2norm_local);
+    gkyl_free(gks->L2norm_global);
   }
 
-  if (s->info.time_rate_diagnostics) {
+  if (gks->info.time_rate_diagnostics) {
     // Free df/dt diagnostics memory.
-    gkyl_array_release(s->fdot_mom_old);
-    gkyl_array_release(s->fdot_mom_new);
-    gkyl_dynvec_release(s->fdot_integ_diag);
+    gkyl_array_release(gks->fdot_mom_old);
+    gkyl_array_release(gks->fdot_mom_new);
+    gkyl_dynvec_release(gks->fdot_integ_diag);
   }
 }
 
@@ -763,14 +765,12 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
   int cdim = app->cdim, vdim = gks->info.vdim;
   int pdim = cdim+vdim;
 
-  int ghost[GKYL_MAX_DIM];
-
+  int num_ghost[GKYL_MAX_DIM];
   for (int d=0; d<cdim; ++d) {
-    ghost[d] = 1;
+    num_ghost[d] = 1;
   }
   for (int d=0; d<vdim; ++d) {
-    // Full phase space grid.
-    ghost[cdim+d] = 0; // No ghost-cells in velocity space.
+    num_ghost[cdim+d] = 0; // No ghost-cells in velocity space.
   }
   gks->dt_omegaH = DBL_MIN;
 
@@ -826,7 +826,7 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
   gks->L2norm = gkyl_dynvec_new(GKYL_DOUBLE, 1); // L2 norm.
   gks->is_first_L2norm_write_call = true;
   
-  int par_dir = app->cdim-1; // The last direction is the parallel one.
+  int par_dir = app->cdim-1; // Parallel direction index.
   if (gk_app_inp->geometry.has_LCFS ||
       (gks->lower_bc[par_dir].type == GKYL_BC_GK_SPECIES_TWISTSHIFT || gks->upper_bc[par_dir].type == GKYL_BC_GK_SPECIES_TWISTSHIFT)) {
     // Make the parallel direction periodic so that we sync before applying TS BC.
@@ -870,6 +870,19 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
   gks->bc_buffer_up_fixed = need_bc_buffer_up_fixed? mkarr(app->use_gpu, gks->basis.num_basis, buff_sz)
                                                    : mkarr(app->use_gpu, 1, 1);
 
+  if (gks->lower_bc[par_dir].type == GKYL_BC_GK_SPECIES_TWISTSHIFT &&
+      gks->upper_bc[par_dir].type == GKYL_BC_GK_SPECIES_TWISTSHIFT) {
+    // Local range extended in the BC dir, on the coarse grid.
+    int lower_bcdir_ext[pdim], upper_bcdir_ext[pdim];
+    for (int i=0; i<pdim; i++) {
+      lower_bcdir_ext[i] = gks->local.lower[i];
+      upper_bcdir_ext[i] = gks->local.upper[i];
+    }
+    lower_bcdir_ext[par_dir] = gks->local_ext.lower[par_dir];
+    upper_bcdir_ext[par_dir] = gks->local_ext.upper[par_dir];
+    gkyl_sub_range_init(&gks->bc_ts_local_par_ext, &gks->local_ext, lower_bcdir_ext, upper_bcdir_ext);
+  }
+
   for (int d=0; d<cdim; ++d) {
     // Lower BC.
     if (gks->lower_bc[d].type == GKYL_BC_GK_SPECIES_SHEATH) {
@@ -886,11 +899,14 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
         .shear_dir = 0, // shift varies with x.
         .edge = GKYL_LOWER_EDGE,
         .cdim = cdim,
-        .bcdir_ext_update_r = &gks->local_par_ext,
-        .num_ghost = ghost,
+        .bcdir_ext_update_r = &gks->bc_ts_local_par_ext,
+        .num_ghost = num_ghost,
         .basis = &gks->basis,
         .grid = &gks->grid,
         .use_gpu = app->use_gpu,
+        .upsample_factor = app->ts_upsample_factor,
+        .filter_half_width = app->ts_filter_half_width,
+        .filter_cutoff_wavelength = app->ts_filter_cutoff_wavelength,
       };
       if (app->gk_geom->geometry_id == GKYL_GEOMETRY_TOKAMAK)
         tsinp.shift_dg = app->delta_ts_x_lo;
@@ -946,11 +962,14 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
         .shear_dir = 0, // shift varies with x.
         .edge = GKYL_UPPER_EDGE,
         .cdim = cdim,
-        .bcdir_ext_update_r = &gks->local_par_ext,
-        .num_ghost = ghost,
+        .bcdir_ext_update_r = &gks->bc_ts_local_par_ext,
+        .num_ghost = num_ghost,
         .basis = &gks->basis,
         .grid = &gks->grid,
         .use_gpu = app->use_gpu,
+        .upsample_factor = app->ts_upsample_factor,
+        .filter_half_width = app->ts_filter_half_width,
+        .filter_cutoff_wavelength = app->ts_filter_cutoff_wavelength,
       };
       if (app->gk_geom->geometry_id == GKYL_GEOMETRY_TOKAMAK)
         tsinp.shift_dg = app->delta_ts_x_up;
@@ -1000,10 +1019,13 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
       .edge = GKYL_LOWER_EDGE,
       .cdim = cdim,
       .bcdir_ext_update_r = &gks->local_par_ext_core,
-      .num_ghost = ghost,
+      .num_ghost = num_ghost,
       .basis = &gks->basis,
       .grid = &gks->grid,
       .use_gpu = app->use_gpu,
+      .upsample_factor = app->ts_upsample_factor,
+      .filter_half_width = app->ts_filter_half_width,
+      .filter_cutoff_wavelength = app->ts_filter_cutoff_wavelength,
     };
     if (app->gk_geom->geometry_id == GKYL_GEOMETRY_TOKAMAK)
       tsinp_lo.shift_dg = app->delta_ts_x_lo;
@@ -1020,10 +1042,13 @@ gk_species_init_dynamic(struct gkyl_gk *gk_app_inp, struct gkyl_gyrokinetic_app
       .edge = GKYL_UPPER_EDGE,
       .cdim = cdim,
       .bcdir_ext_update_r = &gks->local_par_ext_core,
-      .num_ghost = ghost,
+      .num_ghost = num_ghost,
       .basis = &gks->basis,
       .grid = &gks->grid,
       .use_gpu = app->use_gpu,
+      .upsample_factor = app->ts_upsample_factor,
+      .filter_half_width = app->ts_filter_half_width,
+      .filter_cutoff_wavelength = app->ts_filter_cutoff_wavelength,
     };
     if (app->gk_geom->geometry_id == GKYL_GEOMETRY_TOKAMAK)
       tsinp_up.shift_dg = app->delta_ts_x_up;
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic.h b/gyrokinetic/apps/gkyl_gyrokinetic.h
index 1d137b0963..780cba59c4 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic.h
@@ -250,6 +250,11 @@ struct gkyl_gyrokinetic_geometry {
   void *parallel_lower_bc_shift_ctx; // Context for parallel_lower_bc_shift_func.
   void *parallel_upper_bc_shift_ctx; // Context for parallel_upper_bc_shift_func.
 
+  // Twist-shift anti-aliasing filter.
+  int ts_upsample_factor; // Supersampling factor along the shear direction.
+  int ts_filter_half_width; // Filter stencil half-width in cells of the simulation grid (0 = off).
+  double ts_filter_cutoff_wavelength; // Filter cutoff wavelength (use 2*dx to cut at the coarse Nyquist).
+
   struct gkyl_efit_inp efit_info; // Context with RZ data such as efit file for a tokamak or mirror.
   struct gkyl_tok_geo_grid_inp tok_grid_info; // Context for tokamak geometry with computational domain info.
   struct gkyl_mirror_geo_grid_inp mirror_grid_info; // Context for mirror geometry with computational domain info.
diff --git a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
index e8d0955901..59ae31615c 100644
--- a/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
+++ b/gyrokinetic/apps/gkyl_gyrokinetic_priv.h
@@ -26,6 +26,7 @@
 #include <gkyl_bc_emission_elastic.h>
 #include <gkyl_bc_sheath_gyrokinetic.h>
 #include <gkyl_bc_twistshift.h>
+#include <gkyl_twistshift_dg.h>
 #include <gkyl_bgk_collisions.h>
 #include <gkyl_boundary_flux.h>
 #include <gkyl_dg_advection.h>
@@ -1097,6 +1098,14 @@ struct gk_species {
   struct gkyl_range local_upper_skin_par_sol , local_upper_ghost_par_sol;
   // GK IWL sims need a core range extended in z, and a TS BC updater.
   struct gkyl_range local_par_ext_core; // Core range extended in parallel direction.
+  // Objects used in IWL simulations and TS BCs.
+  struct gkyl_rect_grid bc_ts_grid; // Higher resolution grid for TS BC.
+  struct gkyl_range bc_ts_local_ext, bc_ts_local; // Higher resolution ranges for TS BC.
+  struct gkyl_range bc_ts_local_lower_skin_par, bc_ts_local_upper_skin_par; // Parallel skin for TS BC.
+  struct gkyl_range bc_ts_local_lower_ghost_par, bc_ts_local_upper_ghost_par; // Parallel ghost for TS BC.
+  struct gkyl_dg_interpolate *bc_ts_prolong, *bc_ts_coarsen; // Interpolation operators for TS BC.
+  struct gkyl_array *bc_ts_buffer_fine, *bc_ts_buffer_coar; // Buffer for TS BCs.
+  struct gkyl_range bc_ts_local_par_ext; // Range extended in parallel direction for TS BC.
   struct gkyl_bc_twistshift *bc_ts_lo, *bc_ts_up;
 
   struct gk_proj proj_init; // Projector for initial conditions.
@@ -1393,7 +1402,14 @@ struct gk_field {
   void (*calc_energy_dt_func)(gkyl_gyrokinetic_app *app, const struct gk_field *field, double dt, double *energy_reduced);
 
   // Objects used in IWL simulations and TS BCs.
-  struct gkyl_bc_twistshift *bc_ts_lo, *bc_ts_up;
+  struct gkyl_rect_grid bc_ts_grid; // Higher resolution grid for TS BC.
+  struct gkyl_range bc_ts_global_ext, bc_ts_global; // Higher resolution ranges for TS BC.
+  struct gkyl_range bc_ts_global_lower_skin_par, bc_ts_global_upper_skin_par; // Parallel skin for TS BC.
+  struct gkyl_range bc_ts_global_lower_ghost_par, bc_ts_global_upper_ghost_par; // Parallel ghost for TS BC.
+  struct gkyl_dg_interpolate *bc_ts_prolong, *bc_ts_coarsen; // Interpolation operators for TS BC.
+  struct gkyl_array *bc_ts_buffer_fine, *bc_ts_buffer_coar; // Buffer for TS BCs.
+  struct gkyl_range bc_ts_global_par_ext; // Range extended in parallel direction for TS BC.
+  struct gkyl_bc_twistshift *bc_ts_lo, *bc_ts_up; // Fills z-ghosts with TS BC.
   struct gkyl_bc_basic_gyrokinetic *gfss_bc_op_core_up; // Fills upper core  z-ghost with skin  boundary value.
   struct gkyl_bc_basic_gyrokinetic *gfss_bc_op_core_lo; // Fills lower core  z-ghost with skin  boundary value.
   struct gkyl_array *bc_buffer; // Buffer for bc_basic.
@@ -1427,6 +1443,9 @@ struct gkyl_gyrokinetic_app {
   
   int cdim; // Configuration space dimensions.
   int poly_order; // Polynomial order.
+  int ts_upsample_factor; // Twist-shift supersampling factor (0/1 = none).
+  int ts_filter_half_width; // Twist-shift filter half-width (0 = off).
+  double ts_filter_cutoff_wavelength; // Twist-shift filter cutoff wavelength.
   double tcurr; // Current time.
   double cfl; // CFL number.
   double cfl_omegaH; // CFL number used for omega_H.
diff --git a/gyrokinetic/apps/gyrokinetic.c b/gyrokinetic/apps/gyrokinetic.c
index 5cf1ff2c99..9799c0ab21 100644
--- a/gyrokinetic/apps/gyrokinetic.c
+++ b/gyrokinetic/apps/gyrokinetic.c
@@ -172,6 +172,9 @@ gkyl_gyrokinetic_app_new_geom(struct gkyl_gk *gk)
 
   int cdim = app->cdim = gk->cdim;
   int poly_order = app->poly_order = gk->poly_order;
+  app->ts_upsample_factor = gk->geometry.ts_upsample_factor;
+  app->ts_filter_half_width = gk->geometry.ts_filter_half_width;
+  app->ts_filter_cutoff_wavelength = gk->geometry.ts_filter_cutoff_wavelength;
   int ns = app->num_species = gk->num_species;
   int neuts = app->num_neut_species = gk->num_neut_species;
 
@@ -1245,7 +1248,7 @@ gyrokinetic_app_write_ts_shift_mapc2p(struct gkyl_gyrokinetic_app *app)
   for (int eI = 0; eI < 2; eI++) {
     int ghost[] = {1, 1, 1};
     // TS BC updater.
-    struct gkyl_bc_twistshift_inp ts_inp = {
+    struct gkyl_twistshift_dg_inp ts_inp = {
       .bc_dir = par_dir,
       .shift_dir = 1, // y shift.
       .shear_dir = 0, // shift varies with x.
@@ -1259,10 +1262,10 @@ gyrokinetic_app_write_ts_shift_mapc2p(struct gkyl_gyrokinetic_app *app)
       .shift_func_ctx = eI == 0? app->gk_geom->parallel_lower_bc_shift_ctx : app->gk_geom->parallel_upper_bc_shift_ctx,
       .use_gpu = app->use_gpu,
     };
-    struct gkyl_bc_twistshift *bc_ts_op = gkyl_bc_twistshift_inew(&ts_inp);
+    struct gkyl_twistshift_dg *bc_ts_op = gkyl_twistshift_dg_inew(&ts_inp);
 
     struct gkyl_array *delta_ts_x = eI == 0? app->delta_ts_x_lo : app->delta_ts_x_up;
-    delta_ts_x = gkyl_bc_twistshift_get_shift_objects(bc_ts_op,
+    delta_ts_x = gkyl_twistshift_dg_get_shift_objects(bc_ts_op,
       &app->delta_ts_x_grid, &app->delta_ts_x_rng, &app->delta_ts_x_basis);
 
     bool has_LCFS = app->gk_geom->has_LCFS;
@@ -1308,7 +1311,7 @@ gyrokinetic_app_write_ts_shift_mapc2p(struct gkyl_gyrokinetic_app *app)
 
     gkyl_array_release(delta_ts_x);
     gkyl_msgpack_data_release(mt_shift);
-    gkyl_bc_twistshift_release(bc_ts_op);
+    gkyl_twistshift_dg_release(bc_ts_op);
   }
 }
 
diff --git a/gyrokinetic/creg/rt_gk_tcv_core_3x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_core_3x2v_p1.c
index f9ca5a4bb4..1f89d7bed3 100644
--- a/gyrokinetic/creg/rt_gk_tcv_core_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_core_3x2v_p1.c
@@ -741,8 +741,6 @@ main(int argc, char **argv)
 
   // GK app.
   struct gkyl_gk app_inp = {
-    .name = "rt_gk_tcv_core_3x2v_p1",
-
     .cfl_frac = 1.0,
 
     .cdim = ctx.cdim,
@@ -779,6 +777,9 @@ main(int argc, char **argv)
     },
   };
 
+  // Set app output name from the executable name (argv[0]).
+  snprintf(app_inp.name, sizeof(app_inp.name), "%s", app_args.app_name);
+
   struct gkyl_gyrokinetic_run_inp run_inp = {
     .app_inp = app_inp,
     .time_stepping = {
diff --git a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
index 9798bee053..1a9394d9b3 100644
--- a/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
+++ b/gyrokinetic/creg/rt_gk_tcv_iwl_adapt_source_3x2v_p1.c
@@ -439,10 +439,10 @@ struct gk_app_ctx create_ctx(void)
   double floor_srcRECY = 1e-10;
 
   // Grid parameters (reduced resolution for the regression test, minimal recommended values in comments)
-  int Nx = 24; // (24) The LCFS is positionned at 1/3 of the domain -> the resolution must be divisible by 3.
-  int Ny = 4; // (16)
+  int Nx = 15; // (24) The LCFS is positionned at 1/3 of the domain -> the resolution must be divisible by 3.
+  int Ny = 8; // (16)
   int Nz = 8; // (12)
-  int Nvpar = 8; // (12)
+  int Nvpar = 4; // (12)
   int Nmu = 4; // (8)
   int poly_order = 1;
   // Velocity box dimensions
@@ -822,7 +822,7 @@ main(int argc, char **argv)
   struct gkyl_gyrokinetic_geometry geometry = {
     .geometry_id = GKYL_GEOMETRY_MAPC2P,
     .world = {0.},
-    .mapc2p = mapc2p, // mapping of cCOREutational to physical space
+    .mapc2p = mapc2p, // mapping of computational to physical space
     .c2p_ctx = &ctx,
     .bfield_func = bfield_func, // magnetic field
     .bfield_ctx = &ctx,
@@ -832,6 +832,9 @@ main(int argc, char **argv)
     .parallel_upper_bc_shift_func = bc_shift_func_up,
     .parallel_lower_bc_shift_ctx = &ctx,
     .parallel_upper_bc_shift_ctx = &ctx,
+    .ts_filter_cutoff_wavelength = 2.0*ctx.Lx/ctx.Nx,
+    .ts_filter_half_width = 1,
+    .ts_upsample_factor = 2,
   };
 
   // Parallelism
@@ -869,6 +872,7 @@ main(int argc, char **argv)
   
   // Set app output name from the executable name (argv[0]).
   snprintf(app_inp.name, sizeof(app_inp.name), "%s", app_args.app_name);
+
   struct gkyl_gyrokinetic_run_inp run_inp = {
     .app_inp = app_inp,
     .time_stepping = {
diff --git a/gyrokinetic/gyrokineticlinkobjs.mak b/gyrokinetic/gyrokineticlinkobjs.mak
index f5a1de13e5..01af73ed6c 100644
--- a/gyrokinetic/gyrokineticlinkobjs.mak
+++ b/gyrokinetic/gyrokineticlinkobjs.mak
@@ -1,7 +1,7 @@
 # -*- makefile-gmake -*-
 
 # Gyrokinetic include objects
-GYROKINETIC_INCS = -I../gyrokinetic/$(KERNELS_DIR)/ambi_bolt_potential -I../gyrokinetic/$(KERNELS_DIR)/bgk_gyrokinetic -I../gyrokinetic/$(KERNELS_DIR)/deflate_geo -I../gyrokinetic/$(KERNELS_DIR)/deflate_surf -I../gyrokinetic/$(KERNELS_DIR)/derived_geo -I../gyrokinetic/$(KERNELS_DIR)/dg_diffusion_gyrokinetic -I../gyrokinetic/$(KERNELS_DIR)/fem_parproj -I../gyrokinetic/$(KERNELS_DIR)/fem_poisson_perp -I../gyrokinetic/$(KERNELS_DIR)/gyrokinetic -I../gyrokinetic/$(KERNELS_DIR)/gyrokinetic_pol_density -I../gyrokinetic/$(KERNELS_DIR)/inflate_surf -I../gyrokinetic/$(KERNELS_DIR)/lbo_gyrokinetic -I../gyrokinetic/$(KERNELS_DIR)/neutral -I../gyrokinetic/$(KERNELS_DIR)/positivity_shift_gyrokinetic -I../gyrokinetic/$(KERNELS_DIR)/rad -I../gyrokinetic/$(KERNELS_DIR)/translate_dim -I../gyrokinetic/$(KERNELS_DIR)/twistshift -I../gyrokinetic/apps -I../gyrokinetic/zero
+GYROKINETIC_INCS = -I../gyrokinetic/$(KERNELS_DIR)/ambi_bolt_potential -I../gyrokinetic/$(KERNELS_DIR)/bgk_gyrokinetic -I../gyrokinetic/$(KERNELS_DIR)/deflate_geo -I../gyrokinetic/$(KERNELS_DIR)/deflate_surf -I../gyrokinetic/$(KERNELS_DIR)/derived_geo -I../gyrokinetic/$(KERNELS_DIR)/dg_diffusion_gyrokinetic -I../gyrokinetic/$(KERNELS_DIR)/fem_parproj -I../gyrokinetic/$(KERNELS_DIR)/fem_poisson_perp -I../gyrokinetic/$(KERNELS_DIR)/gyrokinetic -I../gyrokinetic/$(KERNELS_DIR)/gyrokinetic_pol_density -I../gyrokinetic/$(KERNELS_DIR)/inflate_surf -I../gyrokinetic/$(KERNELS_DIR)/lbo_gyrokinetic -I../gyrokinetic/$(KERNELS_DIR)/neutral -I../gyrokinetic/$(KERNELS_DIR)/positivity_shift_gyrokinetic -I../gyrokinetic/$(KERNELS_DIR)/rad -I../gyrokinetic/$(KERNELS_DIR)/translate_dim -I../gyrokinetic/$(KERNELS_DIR)/twistshift_dg -I../gyrokinetic/apps -I../gyrokinetic/zero
 
 # Gyrokinetic link objects
 
diff --git a/gyrokinetic/ker/twistshift/gkyl_bc_twistshift_gyrokinetic_kernels.h b/gyrokinetic/ker/twistshift_dg/gkyl_twistshift_dg_gyrokinetic_kernels.h
similarity index 100%
rename from gyrokinetic/ker/twistshift/gkyl_bc_twistshift_gyrokinetic_kernels.h
rename to gyrokinetic/ker/twistshift_dg/gkyl_twistshift_dg_gyrokinetic_kernels.h
diff --git a/gyrokinetic/ker/twistshift/bc_twistshift_gyrokinetic_ser_2x_p1.c b/gyrokinetic/ker/twistshift_dg/twistshift_dg_gyrokinetic_ser_2x_p1.c
similarity index 99%
rename from gyrokinetic/ker/twistshift/bc_twistshift_gyrokinetic_ser_2x_p1.c
rename to gyrokinetic/ker/twistshift_dg/twistshift_dg_gyrokinetic_ser_2x_p1.c
index 40b5c81b90..e0b0111610 100644
--- a/gyrokinetic/ker/twistshift/bc_twistshift_gyrokinetic_ser_2x_p1.c
+++ b/gyrokinetic/ker/twistshift_dg/twistshift_dg_gyrokinetic_ser_2x_p1.c
@@ -1,4 +1,4 @@
-#include <gkyl_bc_twistshift_gyrokinetic_kernels.h> 
+#include <gkyl_twistshift_dg_gyrokinetic_kernels.h> 
  
 GKYL_CU_DH void twistshift_xlimdg_2x_ser_p1_yshift_p1(double sFac, const double *xLimLo, const double *xLimUp, double yLimLo, double yLimUp, double dyDo, double yOff, const double *ySh, struct gkyl_mat *tsmat) 
 { 
diff --git a/gyrokinetic/ker/twistshift/bc_twistshift_gyrokinetic_ser_3x2v_p1.c b/gyrokinetic/ker/twistshift_dg/twistshift_dg_gyrokinetic_ser_3x2v_p1.c
similarity index 99%
rename from gyrokinetic/ker/twistshift/bc_twistshift_gyrokinetic_ser_3x2v_p1.c
rename to gyrokinetic/ker/twistshift_dg/twistshift_dg_gyrokinetic_ser_3x2v_p1.c
index 623502ca03..8e191a45dc 100644
--- a/gyrokinetic/ker/twistshift/bc_twistshift_gyrokinetic_ser_3x2v_p1.c
+++ b/gyrokinetic/ker/twistshift_dg/twistshift_dg_gyrokinetic_ser_3x2v_p1.c
@@ -1,4 +1,4 @@
-#include <gkyl_bc_twistshift_gyrokinetic_kernels.h> 
+#include <gkyl_twistshift_dg_gyrokinetic_kernels.h> 
  
 GKYL_CU_DH void twistshift_xlimdg_3x2v_ser_p1_yshift_p1(double sFac, const double *xLimLo, const double *xLimUp, double yLimLo, double yLimUp, double dyDo, double yOff, const double *ySh, struct gkyl_mat *tsmat) 
 { 
diff --git a/gyrokinetic/ker/twistshift/bc_twistshift_gyrokinetic_ser_3x_p1.c b/gyrokinetic/ker/twistshift_dg/twistshift_dg_gyrokinetic_ser_3x_p1.c
similarity index 99%
rename from gyrokinetic/ker/twistshift/bc_twistshift_gyrokinetic_ser_3x_p1.c
rename to gyrokinetic/ker/twistshift_dg/twistshift_dg_gyrokinetic_ser_3x_p1.c
index 3c370244ae..ba3345a92f 100644
--- a/gyrokinetic/ker/twistshift/bc_twistshift_gyrokinetic_ser_3x_p1.c
+++ b/gyrokinetic/ker/twistshift_dg/twistshift_dg_gyrokinetic_ser_3x_p1.c
@@ -1,4 +1,4 @@
-#include <gkyl_bc_twistshift_gyrokinetic_kernels.h> 
+#include <gkyl_twistshift_dg_gyrokinetic_kernels.h> 
  
 GKYL_CU_DH void twistshift_xlimdg_3x_ser_p1_yshift_p1(double sFac, const double *xLimLo, const double *xLimUp, double yLimLo, double yLimUp, double dyDo, double yOff, const double *ySh, struct gkyl_mat *tsmat) 
 { 
diff --git a/gyrokinetic/unit/ctest_bc_twistshift.c b/gyrokinetic/unit/ctest_bc_twistshift.c
index 707d48c149..05a9536d3a 100644
--- a/gyrokinetic/unit/ctest_bc_twistshift.c
+++ b/gyrokinetic/unit/ctest_bc_twistshift.c
@@ -1,3829 +1,496 @@
-// Test creation and deallocation of updater that applies the
-// twist shift BCs.
-//
+// Test the bc_twistshift orchestrator: the twist-shift BC on its own, and the
+// supersample -> twist-shift -> low-pass filter -> restrict pipeline used to
+// de-alias the shift along the shear direction. The sub-cell integrals the
+// shift is built from are tested separately, in ctest_twistshift_dg.
 #include <acutest.h>
 
+#include <gkyl_array.h>
 #include <gkyl_array_ops.h>
-#include <gkyl_array_reduce.h>
-#include <gkyl_range.h>
-#include <gkyl_rect_grid.h>
-#include <gkyl_rect_decomp.h>
 #include <gkyl_basis.h>
-#include <gkyl_proj_on_basis.h>
-#include <mpack.h>
-#include <gkyl_array_rio.h>
 #include <gkyl_bc_twistshift.h>
-#include <gkyl_velocity_map.h>
-#include <gkyl_position_map.h>
-#include <gkyl_gk_geometry.h>
-#include <gkyl_gk_geometry_mapc2p.h>
-#include <gkyl_dg_updater_moment_gyrokinetic.h>
-#include <gkyl_math.h>
-#include <gkyl_const.h>
-
-// Meta-data for IO
-struct test_bc_twistshift_output_meta {
-  int poly_order; // polynomial order
-  const char *basis_type; // name of basis functions
-};
-
-// returned gkyl_array_meta must be freed using gyrokinetic_array_meta_release
-static struct gkyl_msgpack_data*
-test_bc_twistshift_array_meta_new(struct test_bc_twistshift_output_meta meta)
-{
-  struct gkyl_msgpack_data *mt = gkyl_malloc(sizeof(*mt));
-
-  mt->meta_sz = 0;
-  mpack_writer_t writer;
-  mpack_writer_init_growable(&writer, &mt->meta, &mt->meta_sz);
-
-  // add some data to mpack
-  mpack_build_map(&writer);
-
-  mpack_write_cstr(&writer, "polyOrder");
-  mpack_write_i64(&writer, meta.poly_order);
-
-  mpack_write_cstr(&writer, "basisType");
-  mpack_write_cstr(&writer, meta.basis_type);
+#include <gkyl_eval_on_nodes.h>
+#include <gkyl_proj_on_basis.h>
+#include <gkyl_range.h>
+#include <gkyl_rect_decomp.h>
+#include <gkyl_rect_grid.h>
+#include <gkyl_twistshift_dg.h>
 
-  mpack_complete_map(&writer);
+#include <math.h>
 
-  int status = mpack_writer_destroy(&writer);
+static const double ts_lower[] = {-2.0, -1.5, -3.0};
+static const double ts_upper[] = { 2.0,  1.5,  3.0};
+static const int ts_cells[] = {8, 8, 4};
+static const int ts_ndim = 3, ts_cdim = 3, ts_bc_dir = 2;
 
-  if (status != mpack_ok) {
-    free(mt->meta); // we need to use free here as mpack does its own malloc
-    gkyl_free(mt);
-    mt = 0;
-  }
+struct ts_ctx {
+  double offset; // Shift at x=0.
+  double shear; // Rate at which the shift varies with x (0 = no shear).
+};
 
-  return mt;
+static void
+shift_func(double t, const double *xn, double *fout, void *ctx)
+{
+  struct ts_ctx *tctx = ctx;
+  fout[0] = tctx->offset + tctx->shear*xn[0];
 }
 
 static void
-test_bc_twistshift_array_meta_release(struct gkyl_msgpack_data *mt)
+init_donor(double t, const double *xn, double *fout, void *ctx)
 {
-  if (!mt) return;
-  MPACK_FREE(mt->meta);
-  gkyl_free(mt);
+  double x = xn[0], y = xn[1];
+  fout[0] = exp(-y*y/(2.0*0.3*0.3))*(1.0 + 0.5*cos(M_PI*x));
 }
 
-struct skin_ghost_ranges {
-  struct gkyl_range lower_skin[GKYL_MAX_DIM];
-  struct gkyl_range lower_ghost[GKYL_MAX_DIM];
-
-  struct gkyl_range upper_skin[GKYL_MAX_DIM];
-  struct gkyl_range upper_ghost[GKYL_MAX_DIM];
+// Everything needed to build and apply the BC on the test grid.
+struct ts_setup {
+  struct gkyl_rect_grid grid;
+  struct gkyl_basis basis;
+  struct gkyl_range local, local_ext;
+  struct gkyl_range update_r; // Local range, extended in bc_dir.
+  struct gkyl_range ghost_r; // Plane the BC writes.
+  struct gkyl_range skin_r; // Plane periodicity copies from.
+  int ghost[GKYL_MAX_DIM];
 };
 
-// Create ghost and skin sub-ranges given a parent range
 static void
-skin_ghost_ranges_init(struct skin_ghost_ranges *sgr,
-  const struct gkyl_range *parent, const int *ghost)
+ts_setup_init(struct ts_setup *s, enum gkyl_edge_loc edge)
 {
-  int ndim = parent->ndim;
+  gkyl_rect_grid_init(&s->grid, ts_ndim, ts_lower, ts_upper, ts_cells);
+  gkyl_cart_modal_serendip(&s->basis, ts_ndim, 1);
+
+  for (int d=0; d<ts_ndim; d++) s->ghost[d] = 1;
+  gkyl_create_grid_ranges(&s->grid, s->ghost, &s->local_ext, &s->local);
 
-  for (int d=0; d<ndim; ++d) {
-    gkyl_skin_ghost_ranges(&sgr->lower_skin[d], &sgr->lower_ghost[d],
-      d, GKYL_LOWER_EDGE, parent, ghost);
-    gkyl_skin_ghost_ranges(&sgr->upper_skin[d], &sgr->upper_ghost[d],
-      d, GKYL_UPPER_EDGE, parent, ghost);
+  int lo[GKYL_MAX_DIM], up[GKYL_MAX_DIM];
+  for (int d=0; d<ts_ndim; d++) {
+    lo[d] = s->local.lower[d];
+    up[d] = s->local.upper[d];
   }
-}
-// Apply periodic BCs along parallel direction
-void
-apply_periodic_bc(struct gkyl_array *buff, struct gkyl_array *fld, const int dir, const struct skin_ghost_ranges sgr)
-{
-  gkyl_array_copy_to_buffer(buff->data, fld, &(sgr.lower_skin[dir]));
-  gkyl_array_copy_from_buffer(fld, buff->data, &(sgr.upper_ghost[dir]));
+  lo[ts_bc_dir] = s->local_ext.lower[ts_bc_dir];
+  up[ts_bc_dir] = s->local_ext.upper[ts_bc_dir];
+  gkyl_sub_range_init(&s->update_r, &s->local_ext, lo, up);
 
-  gkyl_array_copy_to_buffer(buff->data, fld, &(sgr.upper_skin[dir]));
-  gkyl_array_copy_from_buffer(fld, buff->data, &(sgr.lower_ghost[dir]));
+  // The BC reads and writes the same ghost plane; periodicity fills it from
+  // the skin cell at the other end.
+  int slo[GKYL_MAX_DIM], sup[GKYL_MAX_DIM];
+  for (int d=0; d<ts_ndim; d++) {
+    slo[d] = s->local.lower[d];
+    sup[d] = s->local.upper[d];
+  }
+  if (edge == GKYL_LOWER_EDGE) {
+    gkyl_range_shorten_from_above(&s->ghost_r, &s->update_r, ts_bc_dir, s->ghost[ts_bc_dir]);
+    slo[ts_bc_dir] = sup[ts_bc_dir] = s->local.upper[ts_bc_dir];
+  }
+  else {
+    gkyl_range_shorten_from_below(&s->ghost_r, &s->update_r, ts_bc_dir, s->ghost[ts_bc_dir]);
+    slo[ts_bc_dir] = sup[ts_bc_dir] = s->local.lower[ts_bc_dir];
+  }
+  gkyl_sub_range_init(&s->skin_r, &s->local_ext, slo, sup);
 }
 
+// Project the donor and apply periodicity along bc_dir.
 static struct gkyl_array*
-mkarr(bool on_gpu, long nc, long size)
-{
-  struct gkyl_array* a;
-  if (on_gpu)
-    a = gkyl_array_cu_dev_new(GKYL_DOUBLE, nc, size);
-  else
-    a = gkyl_array_new(GKYL_DOUBLE, nc, size);
-  return a;
-}
-
-struct test_bc_twistshift_ctx {
-  double lower[GKYL_MAX_DIM], upper[GKYL_MAX_DIM];
-  int cells[GKYL_MAX_DIM];
-  double B0;
-  double vt;
-  double mass;
-  enum gkyl_edge_loc edge;
-};
-
-void
-mapc2p(double t, const double *xc, double* GKYL_RESTRICT xp, void *ctx)
+ts_donor_new(const struct ts_setup *s)
 {
-  xp[0] = xc[0]; xp[1] = xc[1]; xp[2] = xc[2];
-}
-
-void eval_bfield_3x(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
-{
-  double x = xn[0], y = xn[1], z = xn[2];
-
-  struct test_bc_twistshift_ctx *pars = ctx;
-  double B0 = pars->B0;
-
-  fout[0] = 0.0;
-  fout[1] = 0.0;
-  fout[2] = B0;
-}
+  struct gkyl_array *f = gkyl_array_new(GKYL_DOUBLE, s->basis.num_basis, s->local_ext.volume);
+  gkyl_array_clear(f, 0.0);
 
-void
-shift1_fig6(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
-{
-  struct test_bc_twistshift_ctx *pars = ctx;
-  double Lx[2] = {pars->upper[0]-pars->lower[0], pars->upper[1]-pars->lower[1]};
-  double dx[2] = {Lx[0]/pars->cells[0], Lx[1]/pars->cells[1]};
+  gkyl_proj_on_basis *proj = gkyl_proj_on_basis_inew(&(struct gkyl_proj_on_basis_inp) {
+    .grid = &s->grid, .basis = &s->basis, .num_ret_vals = 1, .eval = init_donor, .ctx = NULL });
+  gkyl_proj_on_basis_advance(proj, 0.0, &s->local, f);
+  gkyl_proj_on_basis_release(proj);
 
-  fout[0] = 4.0*dx[1];
+  gkyl_array_copy_range_to_range(f, f, &s->ghost_r, &s->skin_r);
+  return f;
 }
 
-void
-shift1m_fig6(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+// The 1D DG shift on the shear cells of the update range, as the app builds it.
+static struct gkyl_array*
+ts_shift_dg_new(const struct ts_setup *s, struct ts_ctx *tctx)
 {
-  shift1_fig6(t, xn, fout, ctx);
-  fout[0] *= -1.0;
-}
+  struct gkyl_rect_grid xgrid;
+  gkyl_rect_grid_init(&xgrid, 1, &ts_lower[0], &ts_upper[0], &ts_cells[0]);
+  struct gkyl_basis xbasis;
+  gkyl_cart_modal_serendip(&xbasis, 1, s->basis.poly_order);
 
-void
-shift2_fig6(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
-{
-  fout[0] = 1.1;
-}
+  struct gkyl_range xrng;
+  gkyl_range_init(&xrng, 1, (int[]) {s->update_r.lower[0]}, (int[]) {s->update_r.upper[0]});
 
-void
-shift2m_fig6(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
-{
-  shift2_fig6(t, xn, fout, ctx);
-  fout[0] *= -1.0;
+  struct gkyl_array *shift_dg = gkyl_array_new(GKYL_DOUBLE, xbasis.num_basis, xrng.volume);
+  gkyl_eval_on_nodes *ev = gkyl_eval_on_nodes_new(&xgrid, &xbasis, 1, shift_func, tctx);
+  gkyl_eval_on_nodes_advance(ev, 0.0, &xrng, shift_dg);
+  gkyl_eval_on_nodes_release(ev);
+  return shift_dg;
 }
 
-void
-init_donor_fig6(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+// Apply the BC to a fresh donor field and return it. Pass shift_dg to exercise
+// the discretized-shift input instead of the shift function.
+static struct gkyl_array*
+ts_run(const struct ts_setup *s, enum gkyl_edge_loc edge, int upsample, int half_width,
+  double cutoff, struct gkyl_array *shift_dg, struct ts_ctx *tctx)
 {
-  double y = xn[1];
+  struct gkyl_array *f = ts_donor_new(s);
 
-  double mu = 0.0;
-  double sigma = 0.3;
+  struct gkyl_bc_twistshift_inp inp = {
+    .bc_dir = ts_bc_dir,
+    .shift_dir = 1,
+    .shear_dir = 0,
+    .edge = edge,
+    .cdim = ts_cdim,
+    .bcdir_ext_update_r = &s->update_r,
+    .num_ghost = s->ghost,
+    .basis = &s->basis,
+    .grid = &s->grid,
+    .use_gpu = false,
+    .upsample_factor = upsample,
+    .filter_half_width = half_width,
+    .filter_cutoff_wavelength = cutoff,
+  };
+  if (shift_dg)
+    inp.shift_dg = shift_dg;
+  else {
+    inp.shift_func = shift_func;
+    inp.shift_func_ctx = tctx;
+  }
 
-  fout[0] = ( 1.0/sqrt(2.0*M_PI*pow(sigma,2)) ) * exp( -pow(y-mu,2)/(2.0*pow(sigma,2)) );
+  struct gkyl_bc_twistshift *up = gkyl_bc_twistshift_inew(&inp);
+  gkyl_bc_twistshift_advance(up, f, f);
+  gkyl_bc_twistshift_release(up);
+  return f;
 }
 
-void
-shift_fig9(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+// Largest difference between two fields over a range.
+static double
+ts_max_diff(const struct gkyl_array *fa, const struct gkyl_array *fb,
+  const struct gkyl_range *rng, int num_basis)
 {
-  struct test_bc_twistshift_ctx *pars = ctx;
-  double Lx[2] = {pars->upper[0]-pars->lower[0], pars->upper[1]-pars->lower[1]};
-  double dx[2] = {Lx[0]/pars->cells[0], Lx[1]/pars->cells[1]};
-
-  fout[0] = dx[1]/2.0;
+  double maxd = 0.0;
+  struct gkyl_range_iter iter;
+  gkyl_range_iter_init(&iter, rng);
+  while (gkyl_range_iter_next(&iter)) {
+    long linidx = gkyl_range_idx(rng, iter.idx);
+    const double *a = gkyl_array_cfetch(fa, linidx);
+    const double *b = gkyl_array_cfetch(fb, linidx);
+    for (int k=0; k<num_basis; k++)
+      maxd = GKYL_MAX2(maxd, fabs(a[k]-b[k]));
+  }
+  return maxd;
 }
 
-void
-shiftm_fig9(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+// Largest difference over the whole array, ghost cells included.
+static double
+ts_max_diff_all(const struct ts_setup *s, const struct gkyl_array *fa,
+  const struct gkyl_array *fb)
 {
-  shift_fig9(t, xn, fout, ctx);
-  fout[0] *= -1.0;
+  double maxd = 0.0;
+  for (long i=0; i<fa->size; i++) {
+    const double *a = gkyl_array_cfetch(fa, i);
+    const double *b = gkyl_array_cfetch(fb, i);
+    for (int k=0; k<s->basis.num_basis; k++)
+      maxd = GKYL_MAX2(maxd, fabs(a[k]-b[k]));
+  }
+  return maxd;
 }
 
-void
-init_donor_fig9(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+// Integral of the field over the plane the BC fills.
+static double
+ts_ghost_sum(const struct ts_setup *s, const struct gkyl_array *f)
 {
-  double y = xn[1];
-
-  struct test_bc_twistshift_ctx *pars = ctx;
-  double ymid = 0.5*(pars->upper[1]+pars->lower[1]);
-  double dy = (pars->upper[1]-pars->lower[1])/pars->cells[1];
-
-  fout[0] = 0.;
-  if (ymid < y && y < ymid+dy)
-    fout[0] = 1.;
+  double tot = 0.0;
+  struct gkyl_range_iter iter;
+  gkyl_range_iter_init(&iter, &s->ghost_r);
+  while (gkyl_range_iter_next(&iter))
+    tot += ((const double *) gkyl_array_cfetch(f, gkyl_range_idx(&s->ghost_r, iter.idx)))[0];
+  return tot;
 }
 
 void
-test_bc_twistshift_3x_fig6_wcells(const int *cells, enum gkyl_edge_loc edge,
-  bool check_distf, bool use_gpu, bool write_f)
-{
-  double vt = 1.0; // Thermal speed.
-  double mass = 1.0;
-  double B0 = 1.0; // Magnetic field magnitude.
-  int bc_dir = 2; // Direction in which to apply TS.
-
-  int poly_order = 1;
-  const double lower[] = {-2.0, -1.50, -3.0};
-  const double upper[] = { 2.0,  1.50,  3.0};
-  int vdim = 0;
-  int ndim = sizeof(lower)/sizeof(lower[0]);
-  int cdim = ndim - vdim;
-
-  double lower_conf[cdim], upper_conf[cdim];
-  int cells_conf[cdim];
-  for (int d=0; d<cdim; d++) {
-    lower_conf[d] = lower[d];
-    upper_conf[d] = upper[d];
-    cells_conf[d] = cells[d];
-  }
-
-  // Grid.
-  struct gkyl_rect_grid grid;
-  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
-  struct gkyl_rect_grid grid_conf;
-  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
-
-  // Basis functions.
-  struct gkyl_basis basis;
-  gkyl_cart_modal_serendip(&basis, ndim, poly_order);
-  struct gkyl_basis basis_conf;
-  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
-
-  // Ranges.
-  int ghost_conf[cdim];
-  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
-  struct gkyl_range local_conf, local_ext_conf; // local, local-ext position-space ranges
-  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
-
-  int ghost[ndim];
-  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
-  struct gkyl_range local, local_ext; // local, local-ext phase-space ranges
-  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
-
-  struct skin_ghost_ranges skin_ghost; // skin/ghost.
-  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
-  struct skin_ghost_ranges skin_ghost_conf; // skin/ghost.
-  skin_ghost_ranges_init(&skin_ghost_conf, &local_ext_conf, ghost_conf);
-
-  // Pick skin and ghost ranges based on 'edge'.
-  struct gkyl_range skin_rng, ghost_rng;
-  struct gkyl_range skin_rng_conf, ghost_rng_conf;
-  if (edge == GKYL_LOWER_EDGE) {
-    skin_rng = skin_ghost.upper_skin[bc_dir];
-    ghost_rng = skin_ghost.lower_ghost[bc_dir];
-    skin_rng_conf = skin_ghost_conf.upper_skin[bc_dir];
-    ghost_rng_conf = skin_ghost_conf.lower_ghost[bc_dir];
-  }
-  else {
-    skin_rng = skin_ghost.lower_skin[bc_dir];
-    ghost_rng = skin_ghost.upper_ghost[bc_dir];
-    skin_rng_conf = skin_ghost_conf.lower_skin[bc_dir];
-    ghost_rng_conf = skin_ghost_conf.upper_ghost[bc_dir];
-  }
-
-  struct test_bc_twistshift_ctx proj_ctx = {
-    .lower = {lower[0], lower[1], lower[2]},
-    .upper = {upper[0], upper[1], upper[2]},
-    .cells = {cells[0], cells[1], cells[2]},
-    .B0 = B0,
-    .vt = vt,
-    .mass = mass,
-  };
-
-  // Initialize the distribution
-  struct gkyl_array *distf = mkarr(use_gpu, basis.num_basis, local_ext.volume);
-  struct gkyl_array *distf_ho = use_gpu? mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
-  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew( &(struct gkyl_proj_on_basis_inp) {
-      .grid = &grid,
-      .basis = &basis,
-      .num_ret_vals = 1,
-      .eval = init_donor_fig6,
-//      .eval = init_donor_fig9,
-      .ctx = &proj_ctx,
-    }
-  );
-  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
-  gkyl_array_copy(distf, distf_ho);
-  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new( (struct test_bc_twistshift_output_meta) {
-      .poly_order = poly_order,
-      .basis_type = basis.id
-    }
-  );
-  if (write_f)
-    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho, "ctest_bc_twistshift_3x_fig6_do.gkyl");
-
-  // Create a range only extended in bc_dir.
-  struct gkyl_range update_rng;
-  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
-  for (int d=0; d<ndim; d++) {
-    lower_bcdir_ext[d] = local.lower[d];
-    upper_bcdir_ext[d] = local.upper[d];
-  }
-  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
-  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
-  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
-
-  // Create the twist-shift updater and shift the donor field.
-  struct gkyl_bc_twistshift_inp tsinp = {
-    .bc_dir = bc_dir,
-    .shift_dir = 1, // y shift.
-    .shear_dir = 0, // shift varies with x.
-    .edge = edge,
-    .cdim = cdim,
-    .bcdir_ext_update_r = &update_rng,
-    .num_ghost = ghost,
-    .basis = &basis,
-    .grid = &grid,
-    .shift_func = shift1_fig6,
-//    .shift_func = shift_fig9,
-    .shift_func_ctx = &proj_ctx,
-    .use_gpu = use_gpu,
-  };
-
-  struct gkyl_bc_twistshift *tsup = gkyl_bc_twistshift_inew(&tsinp);
-
-  // First apply periodicity in z.
-  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
-  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
-
-  gkyl_bc_twistshift_advance(tsup, distf, distf);
-  gkyl_array_copy(distf_ho, distf);
-
-  // Write out the target in the extended range.
-  if (write_f) {
-    double lower_ext[ndim], upper_ext[ndim];
-    int cells_ext[ndim];
-    for (int d=0; d<ndim; d++) {
-      double dx = (upper[d]-lower[d])/cells[d];
-      lower_ext[d] = lower[d]-dx*ghost[d];
-      upper_ext[d] = upper[d]+dx*ghost[d];
-      cells_ext[d] = cells[d]+2*ghost[d];
-    }
-    struct gkyl_rect_grid grid_ext;
-    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
-    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x_fig6_tar.gkyl");
-  }
-
-  if (check_distf) {
-    // Check 0th and 2nd DG coeffs.
-    const double f0[] =
-    {
-      2.5656054446469541e+00, 4.0323377043325592e-01, 2.4549376970832818e-02,
-      5.6930416832388616e-04, 5.6930416832388561e-04, 2.4549376970832790e-02,
-      4.0323377043325587e-01, 2.5656054446469554e+00, 6.4341275514494081e+00,
-      6.4341275514494081e+00,
-    };
-    const double f2[] =
-    {
-      -1.0463462350335195e+00, -2.4917980000416121e-01, -1.8802664978950782e-02,
-      -4.9044149652606374e-04,  4.9044149652607144e-04,  1.8802664978951094e-02,
-       2.4917980000416726e-01,  1.0463462350335588e+00,  9.2229040193425293e-01,
-      -9.2229040193415335e-01,
+test_plain_matches_twistshift_dg(void)
+{
+  // With no anti-aliasing the BC must be exactly the bare twist-shift.
+  struct ts_ctx tctx = { .offset = 0.75, .shear = 0.25 };
+  for (int e=0; e<2; e++) {
+    enum gkyl_edge_loc edge = e == 0? GKYL_LOWER_EDGE : GKYL_UPPER_EDGE;
+    struct ts_setup s;
+    ts_setup_init(&s, edge);
+
+    struct gkyl_array *f_bc = ts_run(&s, edge, 1, 0, 0.0, NULL, &tctx);
+
+    struct gkyl_array *f_ref = ts_donor_new(&s);
+    struct gkyl_twistshift_dg_inp tsinp = {
+      .bc_dir = ts_bc_dir, .shift_dir = 1, .shear_dir = 0, .edge = edge,
+      .cdim = ts_cdim, .bcdir_ext_update_r = &s.update_r, .num_ghost = s.ghost,
+      .basis = &s.basis, .grid = &s.grid,
+      .shift_func = shift_func, .shift_func_ctx = &tctx, .use_gpu = false,
     };
+    struct gkyl_twistshift_dg *ts = gkyl_twistshift_dg_inew(&tsinp);
+    gkyl_twistshift_dg_advance(ts, f_ref, f_ref);
+    gkyl_twistshift_dg_release(ts);
 
-    struct gkyl_range_iter iter;
-    gkyl_range_iter_init(&iter, &ghost_rng);
-    while (gkyl_range_iter_next(&iter)) {
-      long linidx = gkyl_range_idx(&ghost_rng, iter.idx);
-      double *f_c = gkyl_array_fetch(distf_ho, linidx);
-      int refidx = (iter.idx[1]-1)*cells[0] + iter.idx[0]-1;
-      TEST_CHECK( gkyl_compare(f0[refidx]/pow(sqrt(2.0),2), f_c[0], 1e-13) );
-      TEST_CHECK( gkyl_compare(f2[refidx]/pow(sqrt(2.0),2), f_c[2], 1e-13) );
-    }
-  }
-
-  // Copy the ghost cell back to the skin cell, and apply the negated shift to
-  // see if we recover the donor field approximately.
-  gkyl_array_copy_range_to_range(distf, distf, &skin_rng, &ghost_rng);
-  tsinp.shift_func = shift1m_fig6;
-//  tsinp.shift_func = shiftm_fig9;
-  struct gkyl_bc_twistshift *tsup_m = gkyl_bc_twistshift_inew(&tsinp);
-  gkyl_bc_twistshift_advance(tsup_m, distf, distf);
-  gkyl_array_copy(distf_ho, distf);
-
-  if (write_f) {
-    double lower_ext[ndim], upper_ext[ndim];
-    int cells_ext[ndim];
-    for (int d=0; d<ndim; d++) {
-      double dx = (upper[d]-lower[d])/cells[d];
-      lower_ext[d] = lower[d]-dx*ghost[d];
-      upper_ext[d] = upper[d]+dx*ghost[d];
-      cells_ext[d] = cells[d]+2*ghost[d];
-    }
-    struct gkyl_rect_grid grid_ext;
-    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
-    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x_fig6_tar_shifted.gkyl");
-  }
+    TEST_CHECK( ts_max_diff_all(&s, f_bc, f_ref) == 0.0 );
+    TEST_MSG("edge %d: bc_twistshift differs from twistshift_dg by %.3e", e,
+      ts_max_diff_all(&s, f_bc, f_ref));
 
-  if (check_distf) {
-    // Check 0th and 2nd DG coeffs.
-    const double f0[] =
-    {
-      5.6930416832388551e-04, 2.4549376970832783e-02, 4.0323377043325570e-01,
-      2.5656054446469541e+00, 6.4341275514494018e+00, 6.4341275514494001e+00,
-      2.5656054446469501e+00, 4.0323377043325520e-01, 2.4549376970832770e-02,
-      5.6930416832388496e-04,
-    };
-    const double f2[] =
-    {
-      4.9044149652607047e-04,  1.8802664978951059e-02,  2.4917980000416681e-01,
-      1.0463462350335573e+00,  9.2229040193425282e-01, -9.2229040193414913e-01,
-     -1.0463462350335162e+00, -2.4917980000416048e-01, -1.8802664978950730e-02,
-     -4.9044149652606244e-04,
-    };
-
-    struct gkyl_range_iter iter;
-    gkyl_range_iter_init(&iter, &ghost_rng);
-    while (gkyl_range_iter_next(&iter)) {
-      long linidx = gkyl_range_idx(&ghost_rng, iter.idx);
-      double *f_c = gkyl_array_fetch(distf_ho, linidx);
-      int refidx = (iter.idx[1]-1)*cells[0] + iter.idx[0]-1;
-      TEST_CHECK( gkyl_compare(f0[refidx]/pow(sqrt(2.0),2), f_c[0], 1e-13) );
-      TEST_CHECK( gkyl_compare(f2[refidx]/pow(sqrt(2.0),2), f_c[2], 1e-13) );
-    }
+    gkyl_array_release(f_bc);
+    gkyl_array_release(f_ref);
   }
-
-  gkyl_array_release(buff_per);
-  test_bc_twistshift_array_meta_release(mt);
-  gkyl_bc_twistshift_release(tsup);
-  gkyl_bc_twistshift_release(tsup_m);
-  gkyl_proj_on_basis_release(projDistf);
-  gkyl_array_release(distf_ho);
-  gkyl_array_release(distf);
-
 }
+
 void
-test_bc_twistshift_3x2v_fig6_wcells(const int *cells, enum gkyl_edge_loc edge,
-  bool check_distf, bool use_gpu, bool write_f)
+test_only_ghost_plane_written(void)
 {
-  double vt = 1.0; // Thermal speed.
-  double mass = 1.0;
-  double B0 = 1.0; // Magnetic field magnitude.
-  int bc_dir = 2; // Direction in which to apply TS.
-
-  int poly_order = 1;
-  const double lower[] = {-2.0, -1.50, -3.0, -5.0*vt, 0.};
-  const double upper[] = { 2.0,  1.50,  3.0,  5.0*vt, mass*(pow(5.0*vt,2))/(2.0*B0)};
-  int vdim = 2;
-  int ndim = sizeof(lower)/sizeof(lower[0]);
-  int cdim = ndim - vdim;
-
-  double lower_conf[cdim], upper_conf[cdim];
-  int cells_conf[cdim];
-  for (int d=0; d<cdim; d++) {
-    lower_conf[d] = lower[d];
-    upper_conf[d] = upper[d];
-    cells_conf[d] = cells[d];
-  }
-  double lower_vel[vdim], upper_vel[vdim];
-  int cells_vel[vdim];
-  for (int d=0; d<vdim; d++) {
-    lower_vel[d] = lower[cdim+d];
-    upper_vel[d] = upper[cdim+d];
-    cells_vel[d] = cells[cdim+d];
-  }
+  // Nothing but the ghost plane the BC fills may change, in any configuration.
+  struct ts_ctx tctx = { .offset = 0.75, .shear = 0.25 };
+  double dx = (ts_upper[0]-ts_lower[0])/ts_cells[0];
+  int upsample[] = {1, 1, 2, 4};
+  int half_width[] = {0, 4, 4, 4};
+  double cutoff[] = {0.0, 4.0*dx, 2.0*dx, 2.0*dx};
 
-  // Grid.
-  struct gkyl_rect_grid grid;
-  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
-  struct gkyl_rect_grid grid_conf;
-  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
-  struct gkyl_rect_grid grid_vel;
-  gkyl_rect_grid_init(&grid_vel, vdim, lower_vel, upper_vel, cells_vel);
+  for (int e=0; e<2; e++) {
+    enum gkyl_edge_loc edge = e == 0? GKYL_LOWER_EDGE : GKYL_UPPER_EDGE;
+    struct ts_setup s;
+    ts_setup_init(&s, edge);
 
-  // Basis functions.
-  struct gkyl_basis basis;
-  if (poly_order == 1) 
-    gkyl_cart_modal_gkhybrid(&basis, cdim, vdim);
-  else
-    gkyl_cart_modal_serendip(&basis, ndim, poly_order);
-  struct gkyl_basis basis_conf;
-  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
-
-  // Ranges.
-  int ghost_conf[cdim];
-  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
-  struct gkyl_range local_conf, local_ext_conf; // local, local-ext position-space ranges
-  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
-
-  int ghost_vel[vdim];
-  for (int d=0; d<vdim; d++) ghost_vel[d] = 0;
-  struct gkyl_range local_vel, local_ext_vel; // local, local-ext position-space ranges
-  gkyl_create_grid_ranges(&grid_vel, ghost_vel, &local_ext_vel, &local_vel);
-
-  int ghost[ndim];
-  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
-  for (int d=cdim; d<ndim; d++) ghost[d] = ghost_vel[d-cdim];
-  struct gkyl_range local, local_ext; // local, local-ext phase-space ranges
-  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
-
-  struct skin_ghost_ranges skin_ghost; // skin/ghost.
-  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
-  struct skin_ghost_ranges skin_ghost_conf; // skin/ghost.
-  skin_ghost_ranges_init(&skin_ghost_conf, &local_ext_conf, ghost_conf);
-
-  // Pick skin and ghost ranges based on 'edge'.
-  struct gkyl_range skin_rng, ghost_rng;
-  struct gkyl_range skin_rng_conf, ghost_rng_conf;
-  if (edge == GKYL_LOWER_EDGE) {
-    skin_rng = skin_ghost.upper_skin[bc_dir];
-    ghost_rng = skin_ghost.lower_ghost[bc_dir];
-    skin_rng_conf = skin_ghost_conf.upper_skin[bc_dir];
-    ghost_rng_conf = skin_ghost_conf.lower_ghost[bc_dir];
-  }
-  else {
-    skin_rng = skin_ghost.lower_skin[bc_dir];
-    ghost_rng = skin_ghost.upper_ghost[bc_dir];
-    skin_rng_conf = skin_ghost_conf.lower_skin[bc_dir];
-    ghost_rng_conf = skin_ghost_conf.upper_ghost[bc_dir];
-  }
+    struct gkyl_array *f_pre = ts_donor_new(&s);
 
-  struct test_bc_twistshift_ctx proj_ctx = {
-    .lower = {lower[0], lower[1], lower[2], lower[3], lower[4]},
-    .upper = {upper[0], upper[1], upper[2], upper[3], upper[4]},
-    .cells = {cells[0], cells[1], cells[2], cells[3], cells[4]},
-    .B0 = B0,
-    .vt = vt,
-    .mass = mass,
-  };
+    for (int c=0; c<4; c++) {
+      struct gkyl_array *f = ts_run(&s, edge, upsample[c], half_width[c], cutoff[c], NULL, &tctx);
 
-  // Initialize the distribution
-  struct gkyl_array *distf = mkarr(use_gpu, basis.num_basis, local_ext.volume);
-  struct gkyl_array *distf_ho = use_gpu? mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
-  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew( &(struct gkyl_proj_on_basis_inp) {
-      .grid = &grid,
-      .basis = &basis,
-      .num_ret_vals = 1,
-      .eval = init_donor_fig6,
-//      .eval = init_donor_fig9,
-      .ctx = &proj_ctx,
-    }
-  );
-  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
-  gkyl_array_copy(distf, distf_ho);
-  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new( (struct test_bc_twistshift_output_meta) {
-      .poly_order = poly_order,
-      .basis_type = basis.id
-    }
-  );
-  if (write_f)
-    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho, "ctest_bc_twistshift_3x2v_fig6_do.gkyl");
-
-  // Create a range only extended in bc_dir.
-  struct gkyl_range update_rng;
-  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
-  for (int d=0; d<ndim; d++) {
-    lower_bcdir_ext[d] = local.lower[d];
-    upper_bcdir_ext[d] = local.upper[d];
-  }
-  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
-  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
-  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
-
-  // Create the twist-shift updater and shift the donor field.
-  struct gkyl_bc_twistshift_inp tsinp = {
-    .bc_dir = bc_dir,
-    .shift_dir = 1, // y shift.
-    .shear_dir = 0, // shift varies with x.
-    .edge = edge,
-    .cdim = cdim,
-    .bcdir_ext_update_r = &update_rng,
-    .num_ghost = ghost,
-    .basis = &basis,
-    .grid = &grid,
-    .shift_func = shift1_fig6,
-//    .shift_func = shift_fig9,
-    .shift_func_ctx = &proj_ctx,
-    .use_gpu = use_gpu,
-  };
-
-  struct gkyl_bc_twistshift *tsup = gkyl_bc_twistshift_inew(&tsinp);
-
-  // First apply periodicity in z.
-  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
-  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
-
-  gkyl_bc_twistshift_advance(tsup, distf, distf);
-  gkyl_array_copy(distf_ho, distf);
+      // Restore the ghost plane so any remaining difference is a stray write.
+      gkyl_array_copy_range(f, f_pre, &s.ghost_r);
+      double maxd = ts_max_diff_all(&s, f, f_pre);
+      TEST_CHECK( maxd == 0.0 );
+      TEST_MSG("edge %d, config %d (upsample %d, M %d): wrote %.3e outside the ghost plane",
+        e, c, upsample[c], half_width[c], maxd);
 
-  // Write out the target in the extended range.
-  if (write_f) {
-    double lower_ext[ndim], upper_ext[ndim];
-    int cells_ext[ndim];
-    for (int d=0; d<ndim; d++) {
-      double dx = (upper[d]-lower[d])/cells[d];
-      lower_ext[d] = lower[d]-dx*ghost[d];
-      upper_ext[d] = upper[d]+dx*ghost[d];
-      cells_ext[d] = cells[d]+2*ghost[d];
+      gkyl_array_release(f);
     }
-    struct gkyl_rect_grid grid_ext;
-    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
-    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x2v_fig6_tar.gkyl");
-  }
-
-  // Compute the integrated moments of the skin cell and the ghost cell.
-  // Velocity space mapping.
-  struct gkyl_mapc2p_inp c2p_in = { };
-  struct gkyl_velocity_map *gvm = gkyl_velocity_map_new(c2p_in, grid, grid_vel,
-    local, local_ext, local_vel, local_ext_vel, use_gpu);
-  struct gkyl_position_map *pmap = gkyl_position_map_null_new();
-
-  // Initialize geometry
-  struct gkyl_gk_geometry_inp geometry_inp = {
-    .geometry_id = GKYL_GEOMETRY_MAPC2P,
-    .c2p_ctx = 0,
-    .mapc2p = mapc2p,
-    .bfield_ctx = &proj_ctx,
-    .bfield_func = eval_bfield_3x,
-    .position_map = pmap,
-    .grid = grid_conf,
-    .local = local_conf,
-    .local_ext = local_ext_conf,
-    .global = local_conf,
-    .global_ext = local_ext_conf,
-    .basis = basis_conf,
-    .geo_grid = grid_conf,
-    .geo_local = local_conf,
-    .geo_local_ext = local_ext_conf,
-    .geo_global = local_conf,
-    .geo_global_ext = local_ext_conf,
-    .geo_basis = basis_conf,
-  };
-  struct gk_geometry* gk_geom_3d = gkyl_gk_geometry_mapc2p_new(&geometry_inp);
-  struct gk_geometry* gk_geom = gkyl_gk_geometry_acquire(gk_geom_3d);
-  gkyl_gk_geometry_release(gk_geom_3d); // release temporary 3d geometry
-  if (use_gpu) {  // If we are on the gpu, copy from host
-    struct gk_geometry* gk_geom_dev = gkyl_gk_geometry_new(gk_geom, &geometry_inp, use_gpu);
-    gkyl_gk_geometry_release(gk_geom);
-    gk_geom = gkyl_gk_geometry_acquire(gk_geom_dev);
-    gkyl_gk_geometry_release(gk_geom_dev);
-  }
-  // Need the magnetic field to be initialized in the ghost cell in order to
-  // compute integrated moments in the ghost cell (for checking moment
-  // conservation).
-  gkyl_array_clear(gk_geom->geo_corn.bmag, 0.0);
-  gkyl_array_shiftc(gk_geom->geo_corn.bmag, B0*pow(sqrt(2.0),cdim), 0);
-
-  struct gkyl_dg_updater_moment *mcalc = gkyl_dg_updater_moment_gyrokinetic_new(&grid, &basis_conf,
-    &basis, &local_conf, mass, 0, gvm, gk_geom, NULL, GKYL_F_MOMENT_M0M1M2, true, use_gpu);
-  int num_mom = gkyl_dg_updater_moment_gyrokinetic_num_mom(mcalc);
-
-  struct gkyl_array *marr = mkarr(use_gpu, num_mom, local_ext_conf.volume);
-  double *red_integ_mom_skin, *red_integ_mom_ghost;
-  if (use_gpu) {
-    red_integ_mom_skin = gkyl_cu_malloc(sizeof(double[num_mom]));
-    red_integ_mom_ghost = gkyl_cu_malloc(sizeof(double[num_mom]));
-  }
-  else {
-    red_integ_mom_skin = gkyl_malloc(sizeof(double[num_mom]));
-    red_integ_mom_ghost = gkyl_malloc(sizeof(double[num_mom]));
-  }
-  double *red_integ_mom_skin_ho = gkyl_malloc(sizeof(double[num_mom]));
-  double *red_integ_mom_ghost_ho = gkyl_malloc(sizeof(double[num_mom]));
-
-  gkyl_dg_updater_moment_gyrokinetic_advance(mcalc,
-      &skin_rng, &skin_rng_conf, distf, marr);
-  gkyl_array_reduce_range(red_integ_mom_skin, marr, GKYL_SUM, &skin_rng_conf);
-
-  gkyl_dg_updater_moment_gyrokinetic_advance(mcalc,
-      &ghost_rng, &ghost_rng_conf, distf, marr);
-  gkyl_array_reduce_range(red_integ_mom_ghost, marr, GKYL_SUM, &ghost_rng_conf);
-
-  if (use_gpu) {
-    gkyl_cu_memcpy(red_integ_mom_skin_ho, red_integ_mom_skin, sizeof(double[num_mom]), GKYL_CU_MEMCPY_D2H);
-    gkyl_cu_memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]), GKYL_CU_MEMCPY_D2H);
+    gkyl_array_release(f_pre);
   }
-  else {
-    memcpy(red_integ_mom_skin_ho, red_integ_mom_skin, sizeof(double[num_mom]));
-    memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]));
-  }
-
-  for (int k=0; k<num_mom; k++) {
-    TEST_CHECK( gkyl_compare(red_integ_mom_skin_ho[k], red_integ_mom_ghost_ho[k], 1e-12));
-    TEST_MSG( "integ_mom %d | Expected: %.14e | Got: %.14e\n",k,red_integ_mom_skin_ho[k],red_integ_mom_ghost_ho[k]);
-  }
-
-  if (check_distf) {
-    // Check 0th and 2nd DG coeffs.
-    const double f0[] =
-    {
-      2.5656054446469541e+00, 4.0323377043325592e-01, 2.4549376970832818e-02,
-      5.6930416832388616e-04, 5.6930416832388561e-04, 2.4549376970832790e-02,
-      4.0323377043325587e-01, 2.5656054446469554e+00, 6.4341275514494081e+00,
-      6.4341275514494081e+00,
-    };
-    const double f2[] =
-    {
-      -1.0463462350335195e+00, -2.4917980000416121e-01, -1.8802664978950782e-02,
-      -4.9044149652606374e-04,  4.9044149652607144e-04,  1.8802664978951094e-02,
-       2.4917980000416726e-01,  1.0463462350335588e+00,  9.2229040193425293e-01,
-      -9.2229040193415335e-01,
-    };
-
-    struct gkyl_range_iter iter;
-    gkyl_range_iter_init(&iter, &ghost_rng);
-    while (gkyl_range_iter_next(&iter)) {
-      if (iter.idx[3]==1 && iter.idx[4]==1) {
-        long linidx = gkyl_range_idx(&ghost_rng, iter.idx);
-        double *f_c = gkyl_array_fetch(distf_ho, linidx);
-        int refidx = (iter.idx[1]-1)*cells[0] + iter.idx[0]-1;
-        TEST_CHECK( gkyl_compare(f0[refidx], f_c[0], 1e-13) );
-        TEST_CHECK( gkyl_compare(f2[refidx], f_c[2], 1e-13) );
-      }
-    }
-  }
-
-  // Copy the ghost cell back to the skin cell, and apply the negated shift to
-  // see if we recover the donor field approximately.
-  gkyl_array_copy_range_to_range(distf, distf, &skin_rng, &ghost_rng);
-  tsinp.shift_func = shift1m_fig6;
-//  tsinp.shift_func = shiftm_fig9;
-  struct gkyl_bc_twistshift *tsup_m = gkyl_bc_twistshift_inew(&tsinp);
-  gkyl_bc_twistshift_advance(tsup_m, distf, distf);
-  gkyl_array_copy(distf_ho, distf);
-
-  if (write_f) {
-    double lower_ext[ndim], upper_ext[ndim];
-    int cells_ext[ndim];
-    for (int d=0; d<ndim; d++) {
-      double dx = (upper[d]-lower[d])/cells[d];
-      lower_ext[d] = lower[d]-dx*ghost[d];
-      upper_ext[d] = upper[d]+dx*ghost[d];
-      cells_ext[d] = cells[d]+2*ghost[d];
-    }
-    struct gkyl_rect_grid grid_ext;
-    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
-    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x2v_fig6_tar_shifted.gkyl");
-  }
-
-  gkyl_dg_updater_moment_gyrokinetic_advance(mcalc,
-      &ghost_rng, &ghost_rng_conf, distf, marr);
-  gkyl_array_reduce_range(red_integ_mom_ghost, marr, GKYL_SUM, &ghost_rng_conf);
-
-  if (use_gpu)
-    gkyl_cu_memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]), GKYL_CU_MEMCPY_D2H);
-  else
-    memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]));
-
-  for (int k=0; k<num_mom; k++) {
-    TEST_CHECK( gkyl_compare(red_integ_mom_skin_ho[k], red_integ_mom_ghost_ho[k], 1e-12));
-    TEST_MSG( "integ_mom %d | Expected: %.14e | Got: %.14e\n",k,red_integ_mom_skin_ho[k],red_integ_mom_ghost_ho[k]);
-  }
-
-  if (check_distf) {
-    // Check 0th and 2nd DG coeffs.
-    const double f0[] =
-    {
-      5.6930416832388551e-04, 2.4549376970832783e-02, 4.0323377043325570e-01,
-      2.5656054446469541e+00, 6.4341275514494018e+00, 6.4341275514494001e+00,
-      2.5656054446469501e+00, 4.0323377043325520e-01, 2.4549376970832770e-02,
-      5.6930416832388496e-04,
-    };
-    const double f2[] =
-    {
-      4.9044149652607047e-04,  1.8802664978951059e-02,  2.4917980000416681e-01,
-      1.0463462350335573e+00,  9.2229040193425282e-01, -9.2229040193414913e-01,
-     -1.0463462350335162e+00, -2.4917980000416048e-01, -1.8802664978950730e-02,
-     -4.9044149652606244e-04,
-    };
-
-    struct gkyl_range_iter iter;
-    gkyl_range_iter_init(&iter, &ghost_rng);
-    while (gkyl_range_iter_next(&iter)) {
-      if (iter.idx[3]==1 && iter.idx[4]==1) {
-        long linidx = gkyl_range_idx(&ghost_rng, iter.idx);
-        double *f_c = gkyl_array_fetch(distf_ho, linidx);
-        int refidx = (iter.idx[1]-1)*cells[0] + iter.idx[0]-1;
-        TEST_CHECK( gkyl_compare(f0[refidx], f_c[0], 1e-13) );
-        TEST_CHECK( gkyl_compare(f2[refidx], f_c[2], 1e-13) );
-      }
-    }
-  }
-
-  gkyl_free(red_integ_mom_skin_ho);
-  gkyl_free(red_integ_mom_ghost_ho);
-  if (use_gpu) {
-    gkyl_cu_free(red_integ_mom_skin);
-    gkyl_cu_free(red_integ_mom_ghost);
-  }
-  else {
-    gkyl_free(red_integ_mom_skin);
-    gkyl_free(red_integ_mom_ghost);
-  }
-  gkyl_dg_updater_moment_gyrokinetic_release(mcalc);
-  gkyl_array_release(marr);
-  gkyl_gk_geometry_release(gk_geom);
-  gkyl_position_map_release(pmap);
-  gkyl_velocity_map_release(gvm);
-  gkyl_array_release(buff_per);
-  test_bc_twistshift_array_meta_release(mt);
-  gkyl_bc_twistshift_release(tsup);
-  gkyl_bc_twistshift_release(tsup_m);
-  gkyl_proj_on_basis_release(projDistf);
-  gkyl_array_release(distf_ho);
-  gkyl_array_release(distf);
-
-}
-
-void
-shift_fig11(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
-{
-  double x = xn[0];
-
-  struct test_bc_twistshift_ctx *pars = ctx;
-  double Lx[2] = {pars->upper[0]-pars->lower[0], pars->upper[1]-pars->lower[1]};
-  double dx[2] = {Lx[0]/pars->cells[0], Lx[1]/pars->cells[1]};
-
-  fout[0] = 0.6*x+1.8;
 }
 
 void
-init_donor_3x_fig11(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+test_identity_filter_matches_plain(void)
 {
-  double x = xn[0], y = xn[1], z = xn[2];
-
-  struct test_bc_twistshift_ctx *pars = ctx;
-  double Lx[2] = {pars->upper[0]-pars->lower[0], pars->upper[1]-pars->lower[1]};
-  double B0 = pars->B0;
-  double vt = pars->vt;
-  double mass = pars->mass;
-  double vtsq = vt*vt;
-
-  double beta[2] = {0.0, 0.0};
-  double sigma[2] = {0.6, 0.2};
+  // A cutoff at the Nyquist wavelength makes the kernel the identity, so
+  // filtering must leave the plain twist-shift result alone.
+  struct ts_ctx tctx = { .offset = 0.75, .shear = 0.25 };
+  double dx = (ts_upper[0]-ts_lower[0])/ts_cells[0];
 
-  fout[0] = ( 1.0/pow(sqrt(2.0*M_PI*vtsq),3) )
-    * exp( -pow(x-beta[0],2)/(2.0*pow(sigma[0],2)) -pow(y-beta[1],2)/(2.0*pow(sigma[1],2)) );  
-}
+  struct ts_setup s;
+  ts_setup_init(&s, GKYL_LOWER_EDGE);
 
-void
-init_donor_3x2v_fig11(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
-{
-  double x = xn[0], y = xn[1], z = xn[2], vpar = xn[3], mu = xn[4];
+  struct gkyl_array *f_plain = ts_run(&s, GKYL_LOWER_EDGE, 1, 0, 0.0, NULL, &tctx);
+  struct gkyl_array *f_filt = ts_run(&s, GKYL_LOWER_EDGE, 1, 4, 2.0*dx, NULL, &tctx);
 
-  struct test_bc_twistshift_ctx *pars = ctx;
-  double B0 = pars->B0;
-  double vt = pars->vt;
-  double mass = pars->mass;
-  double vtsq = vt*vt;
+  double maxd = ts_max_diff(f_plain, f_filt, &s.ghost_r, s.basis.num_basis);
+  TEST_CHECK( maxd < 1.0e-13 );
+  TEST_MSG("identity filter changed the result by %.3e", maxd);
 
-  init_donor_3x_fig11(t, xn, fout, ctx);
-  fout[0] *= exp( -(pow(vpar,2)+2.0*mu*B0/mass)/(2.0*vtsq) );  
+  gkyl_array_release(f_plain);
+  gkyl_array_release(f_filt);
 }
 
 void
-test_bc_twistshift_3x_fig11_wcells(const int *cells, enum gkyl_edge_loc edge,
-  int apply_in_half_x, bool check_distf, bool use_gpu, bool write_f)
+test_upsample_no_shear_matches_plain(void)
 {
-  double vt = 1.0; // Thermal speed.
-  double mass = 1.0;
-  double B0 = 1.0; // Magnetic field magnitude.
-  int bc_dir = 2; // Direction in which to apply TS.
-
-  int poly_order = 1;
-  const double lower[] = {-2.0, -1.50, -3.0};
-  const double upper[] = { 2.0,  1.50,  3.0};
-  int vdim = 0;
-  int ndim = sizeof(lower)/sizeof(lower[0]);
-  int cdim = ndim - vdim;
-
-  double lower_conf[cdim], upper_conf[cdim];
-  int cells_conf[cdim];
-  for (int d=0; d<cdim; d++) {
-    lower_conf[d] = lower[d];
-    upper_conf[d] = upper[d];
-    cells_conf[d] = cells[d];
-  }
-
-  // Grid.
-  struct gkyl_rect_grid grid;
-  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
-  struct gkyl_rect_grid grid_conf;
-  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
-
-  // Basis functions.
-  struct gkyl_basis basis;
-  gkyl_cart_modal_serendip(&basis, ndim, poly_order);
-  struct gkyl_basis basis_conf;
-  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
-
-  // Ranges.
-  int ghost_conf[cdim];
-  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
-  struct gkyl_range local_conf, local_ext_conf; // local, local-ext position-space ranges
-  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
-
-  int ghost[ndim];
-  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
-  struct gkyl_range local, local_ext; // local, local-ext phase-space ranges
-  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
-
-  struct skin_ghost_ranges skin_ghost; // skin/ghost.
-  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
-  struct skin_ghost_ranges skin_ghost_conf; // skin/ghost.
-  skin_ghost_ranges_init(&skin_ghost_conf, &local_ext_conf, ghost_conf);
-
-  // Pick skin and ghost ranges based on 'edge'.
-  struct gkyl_range skin_rng, ghost_rng;
-  struct gkyl_range skin_rng_conf, ghost_rng_conf;
-  if (edge == GKYL_LOWER_EDGE) {
-    skin_rng = skin_ghost.upper_skin[bc_dir];
-    ghost_rng = skin_ghost.lower_ghost[bc_dir];
-    skin_rng_conf = skin_ghost_conf.upper_skin[bc_dir];
-    ghost_rng_conf = skin_ghost_conf.lower_ghost[bc_dir];
-  }
-  else {
-    skin_rng = skin_ghost.lower_skin[bc_dir];
-    ghost_rng = skin_ghost.upper_ghost[bc_dir];
-    skin_rng_conf = skin_ghost_conf.lower_skin[bc_dir];
-    ghost_rng_conf = skin_ghost_conf.upper_ghost[bc_dir];
-  }
-
-  struct test_bc_twistshift_ctx proj_ctx = {
-    .lower = {lower[0], lower[1], lower[2]},
-    .upper = {upper[0], upper[1], upper[2]},
-    .cells = {cells[0], cells[1], cells[2]},
-    .B0 = B0,
-    .vt = vt,
-    .mass = mass,
-  };
+  // With a uniform shift the twist-shift creates no structure along x, so the
+  // supersampled field stays an exact refinement of the coarse one and the
+  // refine/identity-filter/restrict round trip must be lossless.
+  struct ts_ctx tctx = { .offset = 0.75, .shear = 0.0 };
+  double dx = (ts_upper[0]-ts_lower[0])/ts_cells[0];
 
-  // Initialize the distribution
-  struct gkyl_array *distf = mkarr(use_gpu, basis.num_basis, local_ext.volume);
-  struct gkyl_array *distf_ho = use_gpu? mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
-  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew( &(struct gkyl_proj_on_basis_inp) {
-      .grid = &grid,
-      .basis = &basis,
-      .num_ret_vals = 1,
-      .eval = init_donor_3x_fig11,
-      .ctx = &proj_ctx,
-    }
-  );
-  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
-  gkyl_array_copy(distf, distf_ho);
-  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new( (struct test_bc_twistshift_output_meta) {
-      .poly_order = poly_order,
-      .basis_type = basis.id
-    }
-  );
-  if (write_f)
-    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho, "ctest_bc_twistshift_3x_fig11_do.gkyl");
-
-  // Create a range only extended in bc_dir.
-  struct gkyl_range update_rng;
-  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
-  for (int d=0; d<ndim; d++) {
-    lower_bcdir_ext[d] = local.lower[d];
-    upper_bcdir_ext[d] = local.upper[d];
-  }
-  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
-  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
-  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
-
-  if (apply_in_half_x < 0) {
-    // Apply the BC only on the lower half of the domain.
-    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
-    gkyl_range_shorten_from_above(&update_rng, &update_rng, 0, x_half_len);
-  }
-  else if (apply_in_half_x > 0) {
-    // Apply the BC only on the upper half of the domain.
-    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
-    gkyl_range_shorten_from_below(&update_rng, &update_rng, 0, x_half_len);
-  }
-
-  // Create the twist-shift updater and shift the donor field.
-  struct gkyl_bc_twistshift_inp tsinp = {
-    .bc_dir = bc_dir,
-    .shift_dir = 1, // y shift.
-    .shear_dir = 0, // shift varies with x.
-    .edge = edge,
-    .cdim = cdim,
-    .bcdir_ext_update_r = &update_rng,
-    .num_ghost = ghost,
-    .basis = &basis,
-    .grid = &grid,
-    .shift_func = shift_fig11,
-    .shift_func_ctx = &proj_ctx,
-    .use_gpu = use_gpu,
-  };
-
-  struct gkyl_bc_twistshift *tsup = gkyl_bc_twistshift_inew(&tsinp);
-
-  // First apply periodicity in z.
-  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
-  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
-
-  gkyl_bc_twistshift_advance(tsup, distf, distf);
-  gkyl_array_copy(distf_ho, distf);
-
-  // Write out the target in the extended range.
-  if (write_f) {
-    double lower_ext[ndim], upper_ext[ndim];
-    int cells_ext[ndim];
-    for (int d=0; d<ndim; d++) {
-      double dx = (upper[d]-lower[d])/cells[d];
-      lower_ext[d] = lower[d]-dx*ghost[d];
-      upper_ext[d] = upper[d]+dx*ghost[d];
-      cells_ext[d] = cells[d]+2*ghost[d];
-    }
-    struct gkyl_rect_grid grid_ext;
-    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
-    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x_fig11_tar.gkyl");
-  }
+  for (int upsample=2; upsample<=4; upsample*=2) {
+    struct ts_setup s;
+    ts_setup_init(&s, GKYL_LOWER_EDGE);
 
-  if (check_distf) {
-    // Check 0th, 1st, 2nd and 6th DG coeffs.
-    const double f0[] =
-    {
-     -6.2583195868812408e-06,  7.9567311608137231e-10,  5.0509906078140035e-05,
-      1.2343352957621956e-03,  5.3472486075120380e-04,
-      1.8256130045163409e-04,  3.0009163112130789e-09, -1.3326694681034118e-05,
-      3.7575576376431747e-03,  6.1716772244852208e-03,
-      4.4292093668301044e-03, -7.7229340458416127e-05, -3.8275760062292437e-05,
-      3.0421687066165188e-03,  2.9194555762249566e-02,
-      3.7056203209553537e-02,  1.4705657602094287e-04,  2.0550274812940050e-08,
-      1.0240094716951157e-03,  4.7863752496844179e-02,
-      9.6491415121706434e-02,  4.8597593964605536e-03,  8.0126693914598593e-08,
-     -4.3972043519208224e-04,  3.1180735654073199e-02,
-      9.6491415121706420e-02,  3.1180735654073172e-02, -4.3972043519208387e-04,
-      8.0126693914598646e-08,  4.8597593964605458e-03,
-      3.7056203209553502e-02,  4.7863752496844159e-02,  1.0240094716951155e-03,
-      2.0550274812939984e-08,  1.4705657602094392e-04,
-      4.4292093668300931e-03,  2.9194555762249559e-02,  3.0421687066165266e-03,
-     -3.8275760062292789e-05, -7.7229340458415897e-05,
-      1.8256130045163365e-04,  6.1716772244852129e-03,  3.7575576376431765e-03,
-     -1.3326694681033820e-05,  3.0009163112130839e-09,
-     -6.2583195868812094e-06,  5.3472486075120294e-04,  1.2343352957621958e-03,
-      5.0509906078140123e-05,  7.9567311608137107e-10,
-    };
-    const double f1[] =
-    {
-     -2.4097311206019044e-06,  7.6833036063548360e-11,  7.2344842311530572e-06,
-      5.2914450025189400e-04,  4.1028939039880680e-04,
-      1.6599629313756654e-04,  2.2461980415131899e-09, -4.1694729744125476e-05,
-      7.8438224724348157e-04,  3.3439621031217184e-03,
-      3.6040320392418893e-03, -8.7133864207591700e-05,  3.8447881347591303e-05,
-     -8.6762333862857460e-04,  8.6496739552592294e-03,
-      1.4945209682648789e-02,  4.5852653062261286e-04, -3.3068454717620671e-09,
-     -6.2529388927217496e-04,  1.5882293198893030e-03,
-      1.7368783554643934e-02,  2.3314728455433925e-03,  4.3253655108451250e-08,
-      9.4609992614394520e-06, -1.1247642251296977e-02,
-     -1.7368783554643944e-02,  1.1247642251296978e-02, -9.4609992614413358e-06,
-     -4.3253655108451283e-08, -2.3314728455433894e-03,
-     -1.4945209682648786e-02, -1.5882293198893067e-03,  6.2529388927217593e-04,
-      3.3068454717620489e-09, -4.5852653062261221e-04,
-     -3.6040320392418802e-03, -8.6496739552592190e-03,  8.6762333862857905e-04,
-     -3.8447881347591479e-05,  8.7133864207591442e-05,
-     -1.6599629313756624e-04, -3.3439621031217180e-03, -7.8438224724348212e-04,
-      4.1694729744125585e-05, -2.2461980415131949e-09,
-      2.4097311206018891e-06, -4.1028939039880621e-04, -5.2914450025189443e-04,
-     -7.2344842311531317e-06, -7.6833036063549213e-11,
-    };
-    const double f2[] =
-    {
-      5.3070807682913396e-06,  1.3751826183769400e-09,  6.8926303153258719e-05,
-      4.1882549426144460e-04, -4.9306025336561313e-04,
-     -2.8467596971097078e-04, -5.0150358149508259e-09,  1.3960594126194340e-05,
-      3.0887163471536865e-03, -2.8179959565330977e-03,
-     -4.7580701893096058e-03,  1.1300292822992238e-04, -5.7287804480022883e-05,
-      3.3338137165750199e-03,  1.3685413489847044e-03,
-     -2.7243387375233196e-02, -5.6694093500983371e-04,  2.2529555439069578e-08,
-      1.7831031494975383e-03,  2.6027202631190245e-02,
-     -2.3565987663701497e-02, -5.9773227818891196e-03, -1.1962791428901063e-07,
-     -4.8028129954664068e-04,  3.0023711373051848e-02,
-      2.3565987663701948e-02, -3.0023711373051674e-02,  4.8028129954667072e-04,
-      1.1962791428901214e-07,  5.9773227818891586e-03,
-      2.7243387375233262e-02, -2.6027202631190141e-02, -1.7831031494975104e-03,
-     -2.2529555439068645e-08,  5.6694093500985290e-04,
-      4.7580701893096223e-03, -1.3685413489846329e-03, -3.3338137165750282e-03,
-      5.7287804480022280e-05, -1.1300292822991837e-04,
-      2.8467596971097305e-04,  2.8179959565330925e-03, -3.0887163471536604e-03,
-     -1.3960594126190875e-05,  5.0150358149509500e-09,
-     -5.3070807682908602e-06,  4.9306025336561432e-04, -4.1882549426144140e-04,
-     -6.8926303153258244e-05, -1.3751826183769166e-09,
-    };
-    const double f6[] =
-    {
-      2.0154146681198872e-24, -3.5688851136225351e-27,  8.0173640710989959e-24,
-     -3.7540344263165092e-21, -8.5473941658947867e-21,
-      2.1098399411304440e-21, -3.2987430986791354e-26, -1.2786887990890647e-22,
-      5.5774262155530719e-21, -5.2422242910241063e-20,
-     -1.3146241530559257e-19, -2.7562828879312281e-22, -1.0734417010552807e-22,
-     -4.3870259352886555e-20,  2.4194632944932309e-19,
-      2.1137135832652420e-19,  1.9015676044847855e-21, -8.5272613545944742e-25,
-     -4.3773733626837943e-20, -9.3076782806108862e-19,
-     -2.2823024255915727e-19,  1.2271105194682399e-19, -1.3400884207613767e-24,
-     -1.0649198357855089e-21,  3.4926449572105291e-20,
-     -3.0499841362447923e-19, -1.8965105476591979e-20, -2.6902054933988774e-21,
-      7.0876511626018948e-26,  2.9290027937202072e-20,
-      8.7582274320145349e-19, -6.0508072579716399e-19, -2.2396479411516622e-20,
-     -2.8336961187045548e-26,  1.0484792769983417e-20,
-     -1.2817391312059265e-19, -1.2999883788145454e-19,  5.2404683918956681e-22,
-      7.0852375629219591e-22, -1.6110515602546699e-24,
-     -4.7728594396620859e-21, -5.5496727075010419e-20,  7.7181639308670794e-21,
-     -3.5828835842015954e-22, -2.4162654496516419e-26,
-     -1.2872700269810765e-22,  3.0405747283361938e-21, -1.5767712674352063e-20,
-     -9.1281108005001305e-22,  6.4377759843551990e-27,
-    };
-
-    struct gkyl_range check_ghost_rng, check_other_ghost_rng;
-    if (apply_in_half_x < 0) {
-      // Applied the BC only on the lower half of the domain.
-      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
-      gkyl_range_shorten_from_above(&check_ghost_rng, &ghost_rng, 0, x_half_len);
-      gkyl_range_shorten_from_below(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
-    }
-    else if (apply_in_half_x > 0) {
-      // Applied the BC only on the upper half of the domain.
-      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
-      gkyl_range_shorten_from_below(&check_ghost_rng, &ghost_rng, 0, x_half_len);
-      gkyl_range_shorten_from_above(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
-    }
-    else
-      check_ghost_rng = ghost_rng;
+    struct gkyl_array *f_plain = ts_run(&s, GKYL_LOWER_EDGE, 1, 0, 0.0, NULL, &tctx);
+    struct gkyl_array *f_up = ts_run(&s, GKYL_LOWER_EDGE, upsample, 4, 2.0*dx/upsample, NULL, &tctx);
 
-    struct gkyl_range_iter iter;
-    gkyl_range_iter_init(&iter, &check_ghost_rng);
-    while (gkyl_range_iter_next(&iter)) {
-      long linidx = gkyl_range_idx(&check_ghost_rng, iter.idx);
-      double *f_c = gkyl_array_fetch(distf_ho, linidx);
-      int refidx = (iter.idx[0]-1)*cells[1] + iter.idx[1]-1;
-      TEST_CHECK( gkyl_compare(f0[refidx], f_c[0], 1e-13) );
-      TEST_CHECK( gkyl_compare(f1[refidx], f_c[1], 1e-13) );
-      TEST_CHECK( gkyl_compare(f2[refidx], f_c[2], 1e-12) );
-      TEST_CHECK( gkyl_compare(f6[refidx], f_c[6], 1e-12) );
-    }
+    double maxd = ts_max_diff(f_plain, f_up, &s.ghost_r, s.basis.num_basis);
+    TEST_CHECK( maxd < 1.0e-12 );
+    TEST_MSG("upsample %d round trip changed the result by %.3e", upsample, maxd);
 
-    if (apply_in_half_x != 0) {
-      // Check that the other half is untouched. 
-      int skin_idx[GKYL_MAX_DIM];
-      gkyl_range_iter_init(&iter, &check_other_ghost_rng);
-      while (gkyl_range_iter_next(&iter)) {
-        long linidx = gkyl_range_idx(&check_other_ghost_rng, iter.idx);
-        double *f_c = gkyl_array_fetch(distf_ho, linidx);
-  
-        for (int d=0; d<check_other_ghost_rng.ndim; d++)
-          skin_idx[d] = iter.idx[d];
-        if (edge == GKYL_LOWER_EDGE)
-          skin_idx[bc_dir] = local.upper[bc_dir];
-        else
-          skin_idx[bc_dir] = local.lower[bc_dir];
-  
-        linidx = gkyl_range_idx(&local_ext, skin_idx);
-        double *fskin_c = gkyl_array_fetch(distf_ho, linidx);
-  
-        for (int k=0; k<distf_ho->ncomp; k++)
-          TEST_CHECK( gkyl_compare(fskin_c[k], f_c[k], 1e-15) );
-      }
-    }
+    gkyl_array_release(f_plain);
+    gkyl_array_release(f_up);
   }
-
-  gkyl_array_release(buff_per);
-  test_bc_twistshift_array_meta_release(mt);
-  gkyl_bc_twistshift_release(tsup);
-  gkyl_proj_on_basis_release(projDistf);
-  gkyl_array_release(distf_ho);
-  gkyl_array_release(distf);
-
 }
 
 void
-init_donor_3x_fig14(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+test_shift_dg_matches_shift_func(void)
 {
-  double x = xn[0], y = xn[1], z = xn[2];
+  // A discretized shift given on the field's own grid must give the same answer
+  // as the shift function, including when the shift has to be refined.
+  struct ts_ctx tctx = { .offset = 0.75, .shear = 0.25 };
+  double dx = (ts_upper[0]-ts_lower[0])/ts_cells[0];
 
-  struct test_bc_twistshift_ctx *pars = ctx;
-  double Lx[3] = {
-    pars->upper[0]-pars->lower[0],
-    pars->upper[1]-pars->lower[1],
-    pars->upper[2]-pars->lower[2],
-  };
-
-  double f_amplitude = 1.0;
-  double f_floor = 1.0e-10;
+  for (int upsample=1; upsample<=2; upsample++) {
+    struct ts_setup s;
+    ts_setup_init(&s, GKYL_LOWER_EDGE);
+    struct gkyl_array *shift_dg = ts_shift_dg_new(&s, &tctx);
 
-  // Cube
-  double rx2 = pow(x-Lx[0]/2,2);
-  double ry2 = pow(y-Lx[1]/2,2);
-  double rz2 = pow(z-Lx[2]/2,2);
-
-  if (rx2 < pow(Lx[0]/4,2) && ry2 < pow(Lx[1]/4,2))
-    fout[0] = f_amplitude;
-  else
-    fout[0] = f_floor;
-}
+    int half_width = upsample > 1? 4 : 0;
+    double cutoff = upsample > 1? 2.0*dx : 0.0;
 
-void
-shift_fig14(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
-{
-  double x = xn[0];
+    struct gkyl_array *f_func = ts_run(&s, GKYL_LOWER_EDGE, upsample, half_width, cutoff, NULL, &tctx);
+    struct gkyl_array *f_dg = ts_run(&s, GKYL_LOWER_EDGE, upsample, half_width, cutoff, shift_dg, &tctx);
 
-  struct test_bc_twistshift_ctx *pars = ctx;
-  double Lx[3] = {
-    pars->upper[0]-pars->lower[0],
-    pars->upper[1]-pars->lower[1],
-    pars->upper[2]-pars->lower[2],
-  };
-  double dx[3] = {
-    Lx[0]/pars->cells[0],
-    Lx[1]/pars->cells[1],
-    Lx[2]/pars->cells[2],
-  };
-  enum gkyl_edge_loc edge = pars->edge;
+    double maxd = ts_max_diff(f_func, f_dg, &s.ghost_r, s.basis.num_basis);
+    TEST_CHECK( maxd < 1.0e-12 );
+    TEST_MSG("upsample %d: shift_dg differs from shift_func by %.3e", upsample, maxd);
 
-  fout[0] = -(x-0.5);
-
-  if (edge == GKYL_UPPER_EDGE)
-    fout[0] *= -1.0;
+    gkyl_array_release(f_func);
+    gkyl_array_release(f_dg);
+    gkyl_array_release(shift_dg);
+  }
 }
 
 void
-test_bc_twistshift_3x_fig14_wcells(const int *cells, enum gkyl_edge_loc edge,
-  int apply_in_half_x, bool check_distf, bool use_gpu, bool write_f)
-{
-  double vt = 1.0; // Thermal speed.
-  double mass = 1.0;
-  double B0 = 1.0; // Magnetic field magnitude.
-  int bc_dir = 2; // Direction in which to apply TS.
-
-  int poly_order = 1;
-  const double lower[] = {0.0, 0.0, 0.0};
-  const double upper[] = {1.0, 1.0, 1.0};
-  int vdim = 0;
-  int ndim = sizeof(lower)/sizeof(lower[0]);
-  int cdim = ndim - vdim;
-
-  double lower_conf[cdim], upper_conf[cdim];
-  int cells_conf[cdim];
-  for (int d=0; d<cdim; d++) {
-    lower_conf[d] = lower[d];
-    upper_conf[d] = upper[d];
-    cells_conf[d] = cells[d];
-  }
-
-  // Grid.
-  struct gkyl_rect_grid grid;
-  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
-  struct gkyl_rect_grid grid_conf;
-  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
-
-  // Basis functions.
-  struct gkyl_basis basis;
-  gkyl_cart_modal_serendip(&basis, ndim, poly_order);
-  struct gkyl_basis basis_conf;
-  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
-
-  // Ranges.
-  int ghost_conf[cdim];
-  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
-  struct gkyl_range local_conf, local_ext_conf; // local, local-ext position-space ranges
-  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
-
-  int ghost[ndim];
-  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
-  struct gkyl_range local, local_ext; // local, local-ext phase-space ranges
-  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
-
-  struct skin_ghost_ranges skin_ghost; // skin/ghost.
-  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
-  struct skin_ghost_ranges skin_ghost_conf; // skin/ghost.
-  skin_ghost_ranges_init(&skin_ghost_conf, &local_ext_conf, ghost_conf);
-
-  // Pick skin and ghost ranges based on 'edge'.
-  struct gkyl_range skin_rng, ghost_rng;
-  struct gkyl_range skin_rng_conf, ghost_rng_conf;
-  if (edge == GKYL_LOWER_EDGE) {
-    skin_rng = skin_ghost.upper_skin[bc_dir];
-    ghost_rng = skin_ghost.lower_ghost[bc_dir];
-    skin_rng_conf = skin_ghost_conf.upper_skin[bc_dir];
-    ghost_rng_conf = skin_ghost_conf.lower_ghost[bc_dir];
-  }
-  else {
-    skin_rng = skin_ghost.lower_skin[bc_dir];
-    ghost_rng = skin_ghost.upper_ghost[bc_dir];
-    skin_rng_conf = skin_ghost_conf.lower_skin[bc_dir];
-    ghost_rng_conf = skin_ghost_conf.upper_ghost[bc_dir];
-  }
-
-  struct test_bc_twistshift_ctx proj_ctx = {
-    .lower = {lower[0], lower[1], lower[2]},
-    .upper = {upper[0], upper[1], upper[2]},
-    .cells = {cells[0], cells[1], cells[2]},
-    .B0 = B0,
-    .vt = vt,
-    .mass = mass,
-    .edge = edge,
-  };
-
-  // Initialize the distribution
-  struct gkyl_array *distf = mkarr(use_gpu, basis.num_basis, local_ext.volume);
-  struct gkyl_array *distf_ho = use_gpu? mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
-  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew( &(struct gkyl_proj_on_basis_inp) {
-      .grid = &grid,
-      .basis = &basis,
-      .num_ret_vals = 1,
-      .eval = init_donor_3x_fig14,
-      .ctx = &proj_ctx,
-    }
-  );
-  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
-  gkyl_array_copy(distf, distf_ho);
-  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new( (struct test_bc_twistshift_output_meta) {
-      .poly_order = poly_order,
-      .basis_type = basis.id
-    }
-  );
-  if (write_f)
-    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho, "ctest_bc_twistshift_3x_fig14_do.gkyl");
-
-  // Create a range only extended in bc_dir.
-  struct gkyl_range update_rng;
-  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
-  for (int d=0; d<ndim; d++) {
-    lower_bcdir_ext[d] = local.lower[d];
-    upper_bcdir_ext[d] = local.upper[d];
-  }
-  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
-  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
-  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
-
-  if (apply_in_half_x < 0) {
-    // Apply the BC only on the lower half of the domain.
-    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
-    gkyl_range_shorten_from_above(&update_rng, &update_rng, 0, x_half_len);
-  }
-  else if (apply_in_half_x > 0) {
-    // Apply the BC only on the upper half of the domain.
-    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
-    gkyl_range_shorten_from_below(&update_rng, &update_rng, 0, x_half_len);
-  }
-
-  // Create the twist-shift updater and shift the donor field.
-  struct gkyl_bc_twistshift_inp tsinp = {
-    .bc_dir = bc_dir,
-    .shift_dir = 1, // y shift.
-    .shear_dir = 0, // shift varies with x.
-    .edge = edge,
-    .cdim = cdim,
-    .bcdir_ext_update_r = &update_rng,
-    .num_ghost = ghost,
-    .basis = &basis,
-    .grid = &grid,
-    .shift_func = shift_fig14,
-    .shift_func_ctx = &proj_ctx,
-    .use_gpu = use_gpu,
-  };
-
-  struct gkyl_bc_twistshift *tsup = gkyl_bc_twistshift_inew(&tsinp);
-
-  // First apply periodicity in z.
-  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
-  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
-
-  gkyl_bc_twistshift_advance(tsup, distf, distf);
-  gkyl_array_copy(distf_ho, distf);
-
-  // Write out the target in the extended range.
-  if (write_f) {
-    double lower_ext[ndim], upper_ext[ndim];
-    int cells_ext[ndim];
-    for (int d=0; d<ndim; d++) {
-      double dx = (upper[d]-lower[d])/cells[d];
-      lower_ext[d] = lower[d]-dx*ghost[d];
-      upper_ext[d] = upper[d]+dx*ghost[d];
-      cells_ext[d] = cells[d]+2*ghost[d];
-    }
-    struct gkyl_rect_grid grid_ext;
-    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
-    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x_fig14_tar.gkyl");
-  }
-
-  if (check_distf) {
-    // Check 0th, 1st, 2nd and 6th DG coeffs.
-    double f0[64], f1[64], f2[64], f6[64];
-
-    if (edge == GKYL_UPPER_EDGE) {
-      const double f0m[] =
-      {
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        1.4142135625145160e+00, 2.8284271247461894e+00,
-        2.8284271247461894e+00, 2.8284271247461894e+00, 1.4142135625145160e+00,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 1.4142135625145160e+00,
-        2.8284271247461894e+00, 2.8284271247461894e+00, 2.8284271247461894e+00,
-        1.4142135625145160e+00, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-        1.4142135625145160e+00, 2.8284271247461894e+00, 2.8284271247461894e+00,
-        2.8284271247461894e+00, 1.4142135625145160e+00, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 1.4142135625145160e+00, 2.8284271247461894e+00,
-        2.8284271247461894e+00, 2.8284271247461894e+00, 1.4142135625145160e+00,
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-      };
-      const double f1m[] =
-      {
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -8.1649658084607613e-01,  0.0000000000000000e+00,  0.0000000000000000e+00,
-         0.0000000000000000e+00,  8.1649658084607613e-01, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -8.1649658084607613e-01,  0.0000000000000000e+00,
-         0.0000000000000000e+00,  0.0000000000000000e+00,  8.1649658084607613e-01,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -8.1649658084607613e-01,
-         0.0000000000000000e+00,  0.0000000000000000e+00,  0.0000000000000000e+00,
-         8.1649658084607613e-01, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -8.1649658084607613e-01,  0.0000000000000000e+00,  0.0000000000000000e+00,
-         0.0000000000000000e+00,  8.1649658084607613e-01,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-      };
-      const double f2m[] =
-      {
-        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
-        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
-        -5.2991257991678335e-25, -5.2991257991678335e-25,
-        -3.4896682092080855e-25, -3.4896682092080855e-25, -3.4896682092080855e-25,
-        -3.4896682092080855e-25, -3.4896682092080855e-25, -3.4896682092080855e-25,
-        -3.4896682092080855e-25, -3.4896682092080855e-25,
-         8.1649658084607457e-01, -2.5535129566378600e-15, -2.5535129566378600e-15,
-        -2.5535129566378600e-15, -8.1649658084607712e-01, -2.5849394142282115e-25,
-        -2.5849394142282115e-25, -2.5849394142282115e-25,
-        -6.4623485355705287e-26,  8.1649658084607535e-01, -6.6613381477509392e-16,
-        -6.6613381477509392e-16, -6.6613381477509392e-16, -8.1649658084607601e-01,
-        -6.4623485355705287e-26, -6.4623485355705287e-26,
-         6.4623485355705287e-26,  6.4623485355705287e-26,  8.1649658084607601e-01,
-         6.6613381477509392e-16,  6.6613381477509392e-16,  6.6613381477509392e-16,
-        -8.1649658084607535e-01,  6.4623485355705287e-26,
-         2.5849394142282115e-25,  2.5849394142282115e-25,  2.5849394142282115e-25,
-         8.1649658084607712e-01,  2.5535129566378600e-15,  2.5535129566378600e-15,
-         2.5535129566378600e-15, -8.1649658084607457e-01,
-         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
-         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
-         5.2991257991678335e-25,  5.2991257991678335e-25,
-         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
-         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
-         5.2991257991678335e-25,  5.2991257991678335e-25,
-      };
-      const double f6m[] =
-      {
-         1.2712579668354740e-41,  1.2712579668354740e-41,  1.2712579668354740e-41,
-         1.2712579668354740e-41,  1.2712579668354740e-41,  1.2712579668354740e-41,
-         1.2712579668354740e-41,  1.2712579668354740e-41,
-        -3.1389085600875902e-43, -3.1389085600875902e-43, -3.1389085600875902e-43,
-        -3.1389085600875902e-43, -3.1389085600875902e-43, -3.1389085600875902e-43,
-        -3.1389085600875902e-43, -3.1389085600875902e-43,
-        -1.1538233466087235e-28,  0.0000000000000000e+00,  0.0000000000000000e+00,
-         0.0000000000000000e+00,  1.1538233466087551e-28,  3.1613293355167873e-42,
-         3.1613293355167873e-42,  3.1613293355167873e-42,
-         3.2061708863751815e-42, -1.1538233466087102e-28,  0.0000000000000000e+00,
-         0.0000000000000000e+00,  0.0000000000000000e+00,  1.1538233466087423e-28,
-         3.2061708863751815e-42,  3.2061708863751815e-42,
-         1.9730282377693424e-42,  1.9730282377693424e-42, -1.1538233466087044e-28,
-         0.0000000000000000e+00,  0.0000000000000000e+00,  0.0000000000000000e+00,
-         1.1538233466087241e-28,  1.9730282377693424e-42,
-         9.8651411888467122e-43,  9.8651411888467122e-43,  9.8651411888467122e-43,
-        -1.1538233466086849e-28,  0.0000000000000000e+00,  0.0000000000000000e+00,
-         0.0000000000000000e+00,  1.1538233466086948e-28,
-         1.9057659114817512e-42,  1.9057659114817512e-42,  1.9057659114817512e-42,
-         1.9057659114817512e-42,  1.9057659114817512e-42,  1.9057659114817512e-42,
-         1.9057659114817512e-42,  1.9057659114817512e-42,
-        -1.5470335046145980e-42, -1.5470335046145980e-42, -1.5470335046145980e-42,
-        -1.5470335046145980e-42, -1.5470335046145980e-42, -1.5470335046145980e-42,
-        -1.5470335046145980e-42, -1.5470335046145980e-42,
-      };
-      int nvals = sizeof(f0m)/sizeof(f0m[0]);
-      for (int i=0; i<nvals; i++) {
-        f0[i] = f0m[i];  f1[i] = f1m[i];  f2[i] = f2m[i]; f6[i] = f6m[i];
+test_dealiasing_smooths_shear_direction(void)
+{
+  // Check that the anti-aliasing filter actually smooths the field along the shear direction.
+  struct ts_ctx tctx = { .offset = 0.75, .shear = 2.9 };
+  double dx = (ts_upper[0]-ts_lower[0])/ts_cells[0];
+
+  struct ts_setup s;
+  ts_setup_init(&s, GKYL_LOWER_EDGE);
+
+  struct gkyl_array *f_plain = ts_run(&s, GKYL_LOWER_EDGE, 1, 0, 0.0, NULL, &tctx);
+  struct gkyl_array *f_deal = ts_run(&s, GKYL_LOWER_EDGE, 4, 4, 2.0*dx, NULL, &tctx);
+
+  // Total variation along x of the cell averages, summed over the ghost plane.
+  double tv[2] = {0.0, 0.0};
+  struct gkyl_array *fs[] = {f_plain, f_deal};
+  for (int q=0; q<2; q++) {
+    for (int j=s.ghost_r.lower[1]; j<=s.ghost_r.upper[1]; j++) {
+      for (int i=s.ghost_r.lower[0]; i<s.ghost_r.upper[0]; i++) {
+        int idx0[] = {i, j, s.ghost_r.lower[2]};
+        int idx1[] = {i+1, j, s.ghost_r.lower[2]};
+        const double *a = gkyl_array_cfetch(fs[q], gkyl_range_idx(&s.ghost_r, idx0));
+        const double *b = gkyl_array_cfetch(fs[q], gkyl_range_idx(&s.ghost_r, idx1));
+        tv[q] += fabs(b[0]-a[0]);
       }
     }
-    else {
-      const double f0m[] =
-      {
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        1.4142135625145160e+00, 2.8284271247461894e+00, 2.8284271247461894e+00,
-        2.8284271247461894e+00, 1.4142135625145160e+00,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 1.4142135625145160e+00,
-        2.8284271247461894e+00, 2.8284271247461894e+00, 2.8284271247461894e+00,
-        1.4142135625145160e+00, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 1.4142135625145160e+00, 2.8284271247461894e+00,
-        2.8284271247461894e+00, 2.8284271247461894e+00, 1.4142135625145160e+00,
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-        1.4142135625145160e+00, 2.8284271247461894e+00, 2.8284271247461894e+00,
-        2.8284271247461894e+00, 1.4142135625145160e+00, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
-        2.8284271247461891e-10, 2.8284271247461891e-10,
-      };
-      const double f1m[] =
-      {
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-         8.1649658084607613e-01,  0.0000000000000000e+00,  0.0000000000000000e+00,
-         0.0000000000000000e+00, -8.1649658084607613e-01,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,  8.1649658084607613e-01,
-         0.0000000000000000e+00,  0.0000000000000000e+00,  0.0000000000000000e+00,
-        -8.1649658084607613e-01, -2.5849394142282115e-26,
-        -2.5849394142282115e-26,  8.1649658084607613e-01,  0.0000000000000000e+00,
-         0.0000000000000000e+00,  0.0000000000000000e+00, -8.1649658084607613e-01,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-         8.1649658084607613e-01,  0.0000000000000000e+00,  0.0000000000000000e+00,
-         0.0000000000000000e+00, -8.1649658084607613e-01, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
-        -2.5849394142282115e-26, -2.5849394142282115e-26,
-      };
-      const double f2m[] =
-      {
-         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
-         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
-         5.2991257991678335e-25,  5.2991257991678335e-25,
-         3.4896682092080855e-25,  3.4896682092080855e-25,  3.4896682092080855e-25,
-         3.4896682092080855e-25,  3.4896682092080855e-25,  3.4896682092080855e-25,
-         3.4896682092080855e-25,  3.4896682092080855e-25,
-         2.5849394142282115e-25,  2.5849394142282115e-25,  2.5849394142282115e-25,
-         8.1649658084607712e-01,  2.5535129566378600e-15,  2.5535129566378600e-15,
-         2.5535129566378600e-15, -8.1649658084607457e-01,
-         6.4623485355705287e-26,  6.4623485355705287e-26,  8.1649658084607601e-01,
-         6.6613381477509392e-16,  6.6613381477509392e-16,  6.6613381477509392e-16,
-        -8.1649658084607535e-01,  6.4623485355705287e-26,
-        -6.4623485355705287e-26,  8.1649658084607535e-01, -6.6613381477509392e-16,
-        -6.6613381477509392e-16, -6.6613381477509392e-16, -8.1649658084607601e-01,
-        -6.4623485355705287e-26, -6.4623485355705287e-26,
-         8.1649658084607457e-01, -2.5535129566378600e-15, -2.5535129566378600e-15,
-        -2.5535129566378600e-15, -8.1649658084607712e-01, -2.5849394142282115e-25,
-        -2.5849394142282115e-25, -2.5849394142282115e-25,
-        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
-        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
-        -5.2991257991678335e-25, -5.2991257991678335e-25,
-        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
-        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
-        -5.2991257991678335e-25, -5.2991257991678335e-25,
-      };
-      const double f6m[] =
-      {
-        -5.3809861030072976e-43, -5.3809861030072976e-43, -5.3809861030072976e-43,
-        -5.3809861030072976e-43, -5.3809861030072976e-43, -5.3809861030072976e-43,
-        -5.3809861030072976e-43, -5.3809861030072976e-43,
-        -1.0941338409448172e-41, -1.0941338409448172e-41, -1.0941338409448172e-41,
-        -1.0941338409448172e-41, -1.0941338409448172e-41, -1.0941338409448172e-41,
-        -1.0941338409448172e-41, -1.0941338409448172e-41,
-        -6.0984509167416039e-42, -6.0984509167416039e-42, -6.0984509167416039e-42,
-         1.2692056812695856e-27,  0.0000000000000000e+00,  0.0000000000000000e+00,
-         0.0000000000000000e+00, -1.2692056812695917e-27,
-        -1.7936620343357659e-42, -1.7936620343357659e-42,  1.2692056812695897e-27,
-         0.0000000000000000e+00,  0.0000000000000000e+00,  0.0000000000000000e+00,
-        -1.2692056812695915e-27, -1.7936620343357659e-42,
-        -1.2555634240350361e-42,  1.2692056812695930e-27,  0.0000000000000000e+00,
-         0.0000000000000000e+00,  0.0000000000000000e+00, -1.2692056812695942e-27,
-        -1.2555634240350361e-42, -1.2555634240350361e-42,
-         1.2692056812695946e-27,  0.0000000000000000e+00,  0.0000000000000000e+00,
-         0.0000000000000000e+00, -1.2692056812695955e-27, -8.9683101716788293e-43,
-        -8.9683101716788293e-43, -8.9683101716788293e-43,
-         3.7666902721051083e-42,  3.7666902721051083e-42,  3.7666902721051083e-42,
-         3.7666902721051083e-42,  3.7666902721051083e-42,  3.7666902721051083e-42,
-         3.7666902721051083e-42,  3.7666902721051083e-42,
-         5.3809861030072976e-43,  5.3809861030072976e-43,  5.3809861030072976e-43,
-         5.3809861030072976e-43,  5.3809861030072976e-43,  5.3809861030072976e-43,
-         5.3809861030072976e-43,  5.3809861030072976e-43,
-      };
-      int nvals = sizeof(f0m)/sizeof(f0m[0]);
-      for (int i=0; i<nvals; i++) {
-        f0[i] = f0m[i];  f1[i] = f1m[i];  f2[i] = f2m[i]; f6[i] = f6m[i];
-      }
-    }
-
-    struct gkyl_range check_ghost_rng, check_other_ghost_rng;
-    if (apply_in_half_x < 0) {
-      // Applied the BC only on the lower half of the domain.
-      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
-      gkyl_range_shorten_from_above(&check_ghost_rng, &ghost_rng, 0, x_half_len);
-      gkyl_range_shorten_from_below(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
-    }
-    else if (apply_in_half_x > 0) {
-      // Applied the BC only on the upper half of the domain.
-      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
-      gkyl_range_shorten_from_below(&check_ghost_rng, &ghost_rng, 0, x_half_len);
-      gkyl_range_shorten_from_above(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
-    }
-    else
-      check_ghost_rng = ghost_rng;
-
-    struct gkyl_range_iter iter;
-    gkyl_range_iter_init(&iter, &check_ghost_rng);
-    while (gkyl_range_iter_next(&iter)) {
-      long linidx = gkyl_range_idx(&check_ghost_rng, iter.idx);
-      double *f_c = gkyl_array_fetch(distf_ho, linidx);
-      int refidx = (iter.idx[0]-1)*cells[1] + iter.idx[1]-1;
-      TEST_CHECK( gkyl_compare(f0[refidx], f_c[0], 1e-13) );
-      TEST_CHECK( gkyl_compare(f1[refidx], f_c[1], 1e-13) );
-      TEST_CHECK( gkyl_compare(f2[refidx], f_c[2], 1e-12) );
-      TEST_CHECK( gkyl_compare(f6[refidx], f_c[6], 1e-12) );
-    }
-
   }
+  TEST_CHECK( tv[1] < tv[0] );
+  TEST_MSG("total variation along x: plain %.6e, de-aliased %.6e", tv[0], tv[1]);
 
-  gkyl_array_release(buff_per);
-  test_bc_twistshift_array_meta_release(mt);
-  gkyl_bc_twistshift_release(tsup);
-  gkyl_proj_on_basis_release(projDistf);
-  gkyl_array_release(distf_ho);
-  gkyl_array_release(distf);
-
+  gkyl_array_release(f_plain);
+  gkyl_array_release(f_deal);
 }
 
 void
-test_bc_twistshift_3x2v_fig11_wcells(const int *cells, enum gkyl_edge_loc edge,
-  int apply_in_half_x, bool check_distf, bool use_gpu, bool write_f)
+test_conserves_particles(void)
 {
-  double vt = 1.0; // Thermal speed.
-  double mass = 1.0;
-  double B0 = 1.0; // Magnetic field magnitude.
-  int bc_dir = 2; // Direction in which to apply TS.
-
-  int poly_order = 1;
-  const double lower[] = {-2.0, -1.50, -3.0, -5.0*vt, 0.};
-  const double upper[] = { 2.0,  1.50,  3.0,  5.0*vt, mass*(pow(5.0*vt,2))/(2.0*B0)};
-  int vdim = 2;
-  int ndim = sizeof(lower)/sizeof(lower[0]);
-  int cdim = ndim - vdim;
-
-  double lower_conf[cdim], upper_conf[cdim];
-  int cells_conf[cdim];
-  for (int d=0; d<cdim; d++) {
-    lower_conf[d] = lower[d];
-    upper_conf[d] = upper[d];
-    cells_conf[d] = cells[d];
-  }
-  double lower_vel[vdim], upper_vel[vdim];
-  int cells_vel[vdim];
-  for (int d=0; d<vdim; d++) {
-    lower_vel[d] = lower[cdim+d];
-    upper_vel[d] = upper[cdim+d];
-    cells_vel[d] = cells[cdim+d];
-  }
+  // Check that the integral is preserved.
+  struct ts_ctx tctx = { .offset = 0.75, .shear = 2.9 };
+  double dx = (ts_upper[0]-ts_lower[0])/ts_cells[0];
+  int upsample[] = {1, 1, 2, 4};
+  int half_width[] = {0, 4, 4, 4};
+  double cutoff[] = {0.0, 4.0*dx, 2.0*dx, 2.0*dx};
 
-  // Grid.
-  struct gkyl_rect_grid grid;
-  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
-  struct gkyl_rect_grid grid_conf;
-  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
-  struct gkyl_rect_grid grid_vel;
-  gkyl_rect_grid_init(&grid_vel, vdim, lower_vel, upper_vel, cells_vel);
+  for (int e=0; e<2; e++) {
+    enum gkyl_edge_loc edge = e == 0? GKYL_LOWER_EDGE : GKYL_UPPER_EDGE;
+    struct ts_setup s;
+    ts_setup_init(&s, edge);
 
-  // Basis functions.
-  struct gkyl_basis basis;
-  if (poly_order == 1) 
-    gkyl_cart_modal_gkhybrid(&basis, cdim, vdim);
-  else
-    gkyl_cart_modal_serendip(&basis, ndim, poly_order);
-  struct gkyl_basis basis_conf;
-  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
-
-  // Ranges.
-  int ghost_conf[cdim];
-  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
-  struct gkyl_range local_conf, local_ext_conf; // local, local-ext position-space ranges
-  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
-
-  int ghost_vel[vdim];
-  for (int d=0; d<vdim; d++) ghost_vel[d] = 0;
-  struct gkyl_range local_vel, local_ext_vel; // local, local-ext position-space ranges
-  gkyl_create_grid_ranges(&grid_vel, ghost_vel, &local_ext_vel, &local_vel);
-
-  int ghost[ndim];
-  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
-  for (int d=cdim; d<ndim; d++) ghost[d] = ghost_vel[d-cdim];
-  struct gkyl_range local, local_ext; // local, local-ext phase-space ranges
-  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
-
-  struct skin_ghost_ranges skin_ghost; // skin/ghost.
-  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
-  struct skin_ghost_ranges skin_ghost_conf; // skin/ghost.
-  skin_ghost_ranges_init(&skin_ghost_conf, &local_ext_conf, ghost_conf);
-
-  // Pick skin and ghost ranges based on 'edge'.
-  struct gkyl_range skin_rng, ghost_rng;
-  struct gkyl_range skin_rng_conf, ghost_rng_conf;
-  if (edge == GKYL_LOWER_EDGE) {
-    skin_rng = skin_ghost.upper_skin[bc_dir];
-    ghost_rng = skin_ghost.lower_ghost[bc_dir];
-    skin_rng_conf = skin_ghost_conf.upper_skin[bc_dir];
-    ghost_rng_conf = skin_ghost_conf.lower_ghost[bc_dir];
-  }
-  else {
-    skin_rng = skin_ghost.lower_skin[bc_dir];
-    ghost_rng = skin_ghost.upper_ghost[bc_dir];
-    skin_rng_conf = skin_ghost_conf.lower_skin[bc_dir];
-    ghost_rng_conf = skin_ghost_conf.upper_ghost[bc_dir];
-  }
-
-  struct test_bc_twistshift_ctx proj_ctx = {
-    .lower = {lower[0], lower[1], lower[2], lower[3], lower[4]},
-    .upper = {upper[0], upper[1], upper[2], upper[3], upper[4]},
-    .cells = {cells[0], cells[1], cells[2], cells[3], cells[4]},
-    .B0 = B0,
-    .vt = vt,
-    .mass = mass,
-  };
-
-  // Initialize the distribution
-  struct gkyl_array *distf = mkarr(use_gpu, basis.num_basis, local_ext.volume);
-  struct gkyl_array *distf_ho = use_gpu? mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
-  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew( &(struct gkyl_proj_on_basis_inp) {
-      .grid = &grid,
-      .basis = &basis,
-      .num_ret_vals = 1,
-      .eval = init_donor_3x2v_fig11,
-      .ctx = &proj_ctx,
-    }
-  );
-  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
-  gkyl_array_copy(distf, distf_ho);
-  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new( (struct test_bc_twistshift_output_meta) {
-      .poly_order = poly_order,
-      .basis_type = basis.id
-    }
-  );
-  if (write_f)
-    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho, "ctest_bc_twistshift_3x2v_fig11_do.gkyl");
-
-  // Create a range only extended in bc_dir.
-  struct gkyl_range update_rng;
-  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
-  for (int d=0; d<ndim; d++) {
-    lower_bcdir_ext[d] = local.lower[d];
-    upper_bcdir_ext[d] = local.upper[d];
-  }
-  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
-  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
-  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
-
-  if (apply_in_half_x < 0) {
-    // Apply the BC only on the lower half of the domain.
-    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
-    gkyl_range_shorten_from_above(&update_rng, &update_rng, 0, x_half_len);
-  }
-  else if (apply_in_half_x > 0) {
-    // Apply the BC only on the upper half of the domain.
-    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
-    gkyl_range_shorten_from_below(&update_rng, &update_rng, 0, x_half_len);
-  }
-
-  // Create the twist-shift updater and shift the donor field.
-  struct gkyl_bc_twistshift_inp tsinp = {
-    .bc_dir = bc_dir,
-    .shift_dir = 1, // y shift.
-    .shear_dir = 0, // shift varies with x.
-    .edge = edge,
-    .cdim = cdim,
-    .bcdir_ext_update_r = &update_rng,
-    .num_ghost = ghost,
-    .basis = &basis,
-    .grid = &grid,
-    .shift_func = shift_fig11,
-    .shift_func_ctx = &proj_ctx,
-    .use_gpu = use_gpu,
-  };
-
-  struct gkyl_bc_twistshift *tsup = gkyl_bc_twistshift_inew(&tsinp);
-
-  // First apply periodicity in z.
-  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
-  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
-
-  gkyl_bc_twistshift_advance(tsup, distf, distf);
-  gkyl_array_copy(distf_ho, distf);
-
-  // Write out the target in the extended range.
-  if (write_f) {
-    double lower_ext[ndim], upper_ext[ndim];
-    int cells_ext[ndim];
-    for (int d=0; d<ndim; d++) {
-      double dx = (upper[d]-lower[d])/cells[d];
-      lower_ext[d] = lower[d]-dx*ghost[d];
-      upper_ext[d] = upper[d]+dx*ghost[d];
-      cells_ext[d] = cells[d]+2*ghost[d];
-    }
-    struct gkyl_rect_grid grid_ext;
-    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
-    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x2v_fig11_tar.gkyl");
-  }
-
-  // Compute the integrated moments of the skin cell and the ghost cell.
-  // Velocity space mapping.
-  struct gkyl_mapc2p_inp c2p_in = { };
-  struct gkyl_velocity_map *gvm = gkyl_velocity_map_new(c2p_in, grid, grid_vel,
-    local, local_ext, local_vel, local_ext_vel, use_gpu);
-  struct gkyl_position_map *pmap = gkyl_position_map_null_new();
-
-  // Initialize geometry
-  struct gkyl_gk_geometry_inp geometry_inp = {
-    .geometry_id = GKYL_GEOMETRY_MAPC2P,
-    .c2p_ctx = 0,
-    .mapc2p = mapc2p,
-    .bfield_ctx = &proj_ctx,
-    .bfield_func = eval_bfield_3x,
-    .position_map = pmap,
-    .grid = grid_conf,
-    .local = local_conf,
-    .local_ext = local_ext_conf,
-    .global = local_conf,
-    .global_ext = local_ext_conf,
-    .basis = basis_conf,
-    .geo_grid = grid_conf,
-    .geo_local = local_conf,
-    .geo_local_ext = local_ext_conf,
-    .geo_global = local_conf,
-    .geo_global_ext = local_ext_conf,
-    .geo_basis = basis_conf,
-  };
-  struct gk_geometry* gk_geom_3d = gkyl_gk_geometry_mapc2p_new(&geometry_inp);
-  struct gk_geometry* gk_geom = gkyl_gk_geometry_acquire(gk_geom_3d);
-  gkyl_gk_geometry_release(gk_geom_3d); // release temporary 3d geometry
-  if (use_gpu) {  // If we are on the gpu, copy from host
-    struct gk_geometry* gk_geom_dev = gkyl_gk_geometry_new(gk_geom, &geometry_inp, use_gpu);
-    gkyl_gk_geometry_release(gk_geom);
-    gk_geom = gkyl_gk_geometry_acquire(gk_geom_dev);
-    gkyl_gk_geometry_release(gk_geom_dev);
-  }
-  // Need the magnetic field to be initialized in the ghost cell in order to
-  // compute integrated moments in the ghost cell (for checking moment
-  // conservation).
-  gkyl_array_clear(gk_geom->geo_corn.bmag, 0.0);
-  gkyl_array_shiftc(gk_geom->geo_corn.bmag, B0*pow(sqrt(2.0),cdim), 0);
-
-  struct gkyl_dg_updater_moment *mcalc = gkyl_dg_updater_moment_gyrokinetic_new(&grid, &basis_conf,
-    &basis, &local_conf, mass, 0, gvm, gk_geom, NULL, GKYL_F_MOMENT_M0M1M2, true, use_gpu);
-  int num_mom = gkyl_dg_updater_moment_gyrokinetic_num_mom(mcalc);
-
-  struct gkyl_array *marr = mkarr(use_gpu, num_mom, local_ext_conf.volume);
-  double *red_integ_mom_skin, *red_integ_mom_ghost;
-  if (use_gpu) {
-    red_integ_mom_skin = gkyl_cu_malloc(sizeof(double[num_mom]));
-    red_integ_mom_ghost = gkyl_cu_malloc(sizeof(double[num_mom]));
-  }
-  else {
-    red_integ_mom_skin = gkyl_malloc(sizeof(double[num_mom]));
-    red_integ_mom_ghost = gkyl_malloc(sizeof(double[num_mom]));
-  }
-  double *red_integ_mom_skin_ho = gkyl_malloc(sizeof(double[num_mom]));
-  double *red_integ_mom_ghost_ho = gkyl_malloc(sizeof(double[num_mom]));
-
-  gkyl_dg_updater_moment_gyrokinetic_advance(mcalc,
-      &skin_rng, &skin_rng_conf, distf, marr);
-  gkyl_array_reduce_range(red_integ_mom_skin, marr, GKYL_SUM, &skin_rng_conf);
-
-  gkyl_dg_updater_moment_gyrokinetic_advance(mcalc,
-      &ghost_rng, &ghost_rng_conf, distf, marr);
-  gkyl_array_reduce_range(red_integ_mom_ghost, marr, GKYL_SUM, &ghost_rng_conf);
-
-  if (use_gpu) {
-    gkyl_cu_memcpy(red_integ_mom_skin_ho, red_integ_mom_skin, sizeof(double[num_mom]), GKYL_CU_MEMCPY_D2H);
-    gkyl_cu_memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]), GKYL_CU_MEMCPY_D2H);
-  }
-  else {
-    memcpy(red_integ_mom_skin_ho, red_integ_mom_skin, sizeof(double[num_mom]));
-    memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]));
-  }
-
-  for (int k=0; k<num_mom; k++) {
-    TEST_CHECK( gkyl_compare(red_integ_mom_skin_ho[k], red_integ_mom_ghost_ho[k], 1e-12));
-    TEST_MSG( "integ_mom %d | Expected: %.14e | Got: %.14e\n",k,red_integ_mom_skin_ho[k],red_integ_mom_ghost_ho[k]);
-  }
-
-  if (check_distf) {
-    // Check 0th, 1st, 2nd and 6th DG coeffs.
-    const double f0[] =
-    {
-      -1.2776583204321330e-07,  1.6243951159613727e-11,  1.0311777925221165e-06,
-       2.5199396402501986e-05,  1.0916599224379850e-05,
-       3.7270542239467049e-06,  6.1264779478169708e-11, -2.7206923690464824e-07,
-       7.6711882696143613e-05,  1.2599699723571620e-04,
-       9.0423892898165817e-05, -1.5766645989926764e-06, -7.8141332726062177e-07,
-       6.2106961880222910e-05,  5.9601729446907966e-04,
-       7.5651563805650783e-04,  3.0022125798956283e-06,  4.1954120810574047e-10,
-       2.0905519501674566e-05,  9.7715562102146359e-04,
-       1.9699067404442962e-03,  9.9213725697257197e-05,  1.6358151057562534e-09,
-      -8.9770499075323632e-06,  6.3656586712399692e-04,
-       1.9699067404442966e-03,  6.3656586712399627e-04, -8.9770499075323903e-06,
-       1.6358151057562547e-09,  9.9213725697256980e-05,
-       7.5651563805650697e-04,  9.7715562102146315e-04,  2.0905519501674579e-05,
-       4.1954120810574011e-10,  3.0022125798956054e-06,
-       9.0423892898165560e-05,  5.9601729446907923e-04,  6.2106961880223127e-05,
-      -7.8141332726062940e-07, -1.5766645989926737e-06,
-       3.7270542239466922e-06,  1.2599699723571601e-04,  7.6711882696143640e-05,
-      -2.7206923690464432e-07,  6.1264779478169876e-11,
-      -1.2776583204321266e-07,  1.0916599224379833e-05,  2.5199396402501990e-05,
-       1.0311777925221199e-06,  1.6243951159613701e-11,
-    };
-    const double f1[] =
-    {
-      -4.9195522432173540e-08,  1.5685739030718726e-12,  1.4769458228600922e-07,
-       1.0802674169515287e-05,  8.3762046049376821e-06,
-       3.3888736767723010e-06,  4.5856936150936589e-11, -8.5121281577597483e-07,
-       1.6013444035211209e-05,  6.8268181976822328e-05,
-       7.3577602711338998e-05, -1.7788689927180866e-06,  7.8492724484237293e-07,
-      -1.7712840678887841e-05,  1.7658618650808429e-04,
-       3.0511179936649428e-04,  9.3609830699107460e-06, -6.7510432676475386e-11,
-      -1.2765598324806747e-05,  3.2424269440705722e-05,
-       3.5458992651786952e-04,  4.7597851765421919e-05,  8.8303883448615030e-10,
-       1.9314968272504524e-07, -2.2962463818142971e-04,
-      -3.5458992651786996e-04,  2.2962463818142974e-04, -1.9314968272508097e-07,
-      -8.8303883448615154e-10, -4.7597851765421851e-05,
-      -3.0511179936649438e-04, -3.2424269440705817e-05,  1.2765598324806735e-05,
-       6.7510432676475619e-11, -9.3609830699107308e-06,
-      -7.3577602711338781e-05, -1.7658618650808405e-04,  1.7712840678887892e-05,
-      -7.8492724484237631e-07,  1.7788689927180847e-06,
-      -3.3888736767722963e-06, -6.8268181976822274e-05, -1.6013444035211209e-05,
-       8.5121281577597260e-07, -4.5856936150936738e-11,
-       4.9195522432173143e-08, -8.3762046049376720e-06, -1.0802674169515287e-05,
-      -1.4769458228601091e-07, -1.5685739030718849e-12,
-    };
-    const double f2[] =
-    {
-       1.0834595144400169e-07,  2.8074844853976726e-11,  1.4071551236371810e-06,
-       8.5504722173976439e-06, -1.0066001367323685e-05,
-      -5.8117617082185942e-06, -1.0238374930018830e-10,  2.8501052072984633e-07,
-       6.3057248605008680e-05, -5.7530395033770669e-05,
-      -9.7137704174052986e-05,  2.3069951842792511e-06, -1.1695510118502272e-06,
-       6.8060999036891783e-05,  2.7939260964732569e-05,
-      -5.5618349420324920e-04, -1.1574301899303677e-05,  4.5994892978466414e-10,
-       3.6402688349758515e-05,  5.3135464780386854e-04,
-      -4.8110806422932840e-04, -1.2202918179822416e-04, -2.4422466434550431e-09,
-      -9.8051144559640598e-06,  6.1294480273016622e-04,
-       4.8110806422933762e-04, -6.1294480273016254e-04,  9.8051144559646528e-06,
-       2.4422466434550737e-09,  1.2202918179822499e-04,
-       5.5618349420325061e-04, -5.3135464780386637e-04, -3.6402688349757959e-05,
-      -4.5994892978464471e-10,  1.1574301899304035e-05,
-       9.7137704174053312e-05, -2.7939260964731105e-05, -6.8060999036891905e-05,
-       1.1695510118502157e-06, -2.3069951842791736e-06,
-       5.8117617082186383e-06,  5.7530395033770560e-05, -6.3057248605008110e-05,
-      -2.8501052072977417e-07,  1.0238374930019089e-10,
-      -1.0834595144399179e-07,  1.0066001367323711e-05, -8.5504722173975829e-06,
-      -1.4071551236371706e-06, -2.8074844853976218e-11,
-    };
-    const double f6[] =
-    {
-      -1.6760873656052127e-08,  6.9405324157913410e-12,  3.9141599258817577e-07,
-       6.6551168467387512e-06, -7.0297789062032620e-06,
-      -4.5612495563369940e-06, -1.0697208933100729e-10, -1.2131836499023975e-06,
-       2.2469828589386375e-05, -1.6695288411057533e-05,
-      -7.7165270659134859e-05,  2.5304169488836587e-06,  1.1365688119276509e-06,
-      -1.6574594816272132e-05,  9.0072879714596268e-05,
-      -1.3067050406710185e-04, -1.7045882735192163e-05, -5.6876686935148544e-10,
-      -1.3656577294632045e-05,  1.6137353286379611e-04,
-       2.1258539335022546e-04, -4.1000351637691106e-05, -8.2479310847183273e-10,
-      -3.5225958304071601e-06, -1.6806162108901716e-04,
-       2.1258539335022143e-04, -1.6806162108901589e-04, -3.5225958304067087e-06,
-      -8.2479310847182528e-10, -4.1000351637691127e-05,
-      -1.3067050406710394e-04,  1.6137353286379722e-04, -1.3656577294632221e-05,
-      -5.6876686935149423e-10, -1.7045882735192441e-05,
-      -7.7165270659135103e-05,  9.0072879714595211e-05, -1.6574594816271881e-05,
-       1.1365688119277396e-06,  2.5304169488835875e-06,
-      -4.5612495563370270e-06, -1.6695288411057713e-05,  2.2469828589386263e-05,
-      -1.2131836499024202e-06, -1.0697208933100851e-10,
-      -1.6760873656069723e-08, -7.0297789062032917e-06,  6.6551168467386817e-06,
-       3.9141599258816127e-07,  6.9405324157907182e-12,
-    };
+    struct gkyl_array *f_pre = ts_donor_new(&s);
+    double tot_pre = ts_ghost_sum(&s, f_pre);
 
-    struct gkyl_range check_ghost_rng, check_other_ghost_rng;
-    if (apply_in_half_x < 0) {
-      // Applied the BC only on the lower half of the domain.
-      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
-      gkyl_range_shorten_from_above(&check_ghost_rng, &ghost_rng, 0, x_half_len);
-      gkyl_range_shorten_from_below(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
-    }
-    else if (apply_in_half_x > 0) {
-      // Applied the BC only on the upper half of the domain.
-      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
-      gkyl_range_shorten_from_below(&check_ghost_rng, &ghost_rng, 0, x_half_len);
-      gkyl_range_shorten_from_above(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
-    }
-    else
-      check_ghost_rng = ghost_rng;
+    for (int c=0; c<4; c++) {
+      struct gkyl_array *f = ts_run(&s, edge, upsample[c], half_width[c], cutoff[c], NULL, &tctx);
+      double tot = ts_ghost_sum(&s, f);
 
-    struct gkyl_range_iter iter;
-    gkyl_range_iter_init(&iter, &check_ghost_rng);
-    while (gkyl_range_iter_next(&iter)) {
-      if (iter.idx[3]==1 && iter.idx[4]==1) {
-        long linidx = gkyl_range_idx(&check_ghost_rng, iter.idx);
-        double *f_c = gkyl_array_fetch(distf_ho, linidx);
-        int refidx = (iter.idx[0]-1)*cells[1] + iter.idx[1]-1;
-        TEST_CHECK( gkyl_compare(f0[refidx], f_c[0], 1e-13) );
-        TEST_CHECK( gkyl_compare(f1[refidx], f_c[1], 1e-13) );
-        TEST_CHECK( gkyl_compare(f2[refidx], f_c[2], 1e-12) );
-        TEST_CHECK( gkyl_compare(f6[refidx], f_c[6], 1e-12) );
-      }
-    }
+      TEST_CHECK( fabs(tot-tot_pre) < 1.0e-12*fabs(tot_pre) );
+      TEST_MSG("edge %d, config %d (upsample %d, M %d): %.13e -> %.13e, rel change %.3e",
+        e, c, upsample[c], half_width[c], tot_pre, tot, fabs(tot-tot_pre)/fabs(tot_pre));
 
-    if (apply_in_half_x != 0) {
-      // Check that the other half is untouched. 
-      int skin_idx[GKYL_MAX_DIM];
-      gkyl_range_iter_init(&iter, &check_other_ghost_rng);
-      while (gkyl_range_iter_next(&iter)) {
-        long linidx = gkyl_range_idx(&check_other_ghost_rng, iter.idx);
-        double *f_c = gkyl_array_fetch(distf_ho, linidx);
-  
-        for (int d=0; d<check_other_ghost_rng.ndim; d++)
-          skin_idx[d] = iter.idx[d];
-        if (edge == GKYL_LOWER_EDGE)
-          skin_idx[bc_dir] = local.upper[bc_dir];
-        else
-          skin_idx[bc_dir] = local.lower[bc_dir];
-  
-        linidx = gkyl_range_idx(&local_ext, skin_idx);
-        double *fskin_c = gkyl_array_fetch(distf_ho, linidx);
-  
-        for (int k=0; k<distf_ho->ncomp; k++)
-          TEST_CHECK( gkyl_compare(fskin_c[k], f_c[k], 1e-15) );
-      }
+      gkyl_array_release(f);
     }
+    gkyl_array_release(f_pre);
   }
-
-  gkyl_free(red_integ_mom_skin_ho);
-  gkyl_free(red_integ_mom_ghost_ho);
-  if (use_gpu) {
-    gkyl_cu_free(red_integ_mom_skin);
-    gkyl_cu_free(red_integ_mom_ghost);
-  }
-  else {
-    gkyl_free(red_integ_mom_skin);
-    gkyl_free(red_integ_mom_ghost);
-  }
-  gkyl_dg_updater_moment_gyrokinetic_release(mcalc);
-  gkyl_array_release(marr);
-  gkyl_gk_geometry_release(gk_geom);
-  gkyl_position_map_release(pmap);
-  gkyl_velocity_map_release(gvm);
-  gkyl_array_release(buff_per);
-  test_bc_twistshift_array_meta_release(mt);
-  gkyl_bc_twistshift_release(tsup);
-  gkyl_proj_on_basis_release(projDistf);
-  gkyl_array_release(distf_ho);
-  gkyl_array_release(distf);
-
-}
-
-// CBC geometry (see rt_gk_cbc_passive_3x2v_p1.c)
-
-static double
-interp_1x_lut_cbc(double x, double *lut_grid, double *lut_val, int N)
-{
-  double x_min = lut_grid[0];
-  double x_max = lut_grid[N-1];
-  if (x <= x_min) return lut_val[0];
-  if (x >= x_max) return lut_val[N-1];
-  double dx = (x_max - x_min)/(N-1);
-  int idx = (int)((x - x_min)/dx);
-  if (idx < 0) idx = 0;
-  if (idx >= N-1) idx = N-2;
-  return lut_val[idx] + (lut_val[idx+1] - lut_val[idx])*(x - lut_grid[idx])/(lut_grid[idx+1] - lut_grid[idx]);
-}
-
-struct gk_cbc_app_ctx {
-  double a_shift, Z_axis, R_axis, R0, a_mid, r0, B0, kappa, delta, q0, Cy, qaxis, qlcfs;
-  double Lx, Ly, Lz;
-  double x_min, y_min, z_min, x_max, y_max, z_max;
-  int psi_lut_size;
-  double *r_lut;
-  double *dPsidr_int_lut;
-};
-
-struct integrand_cbc_ctx {
-  struct gk_cbc_app_ctx *app_ctx;
-  double r;
-  double theta;
-};
-
-static double r_x_cbc(double x, double r0) { return x + r0; }
-
-static double qprofile_cbc(double r, double a_mid, double qaxis, double qlcfs)
-{
-  return 1.0 + 2.78*pow(r/a_mid, 2.8);
-}
-
-static double R_rtheta_cbc(double r, double theta, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  return app->R_axis - app->a_shift*r*r/(2.*app->R_axis)
-    + r*cos(theta + asin(app->delta)*sin(theta));
-}
-
-static double dRdr_cbc(double r, double theta, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  return -app->a_shift*r/app->R_axis + cos(theta + asin(app->delta)*sin(theta));
-}
-
-static double dRdtheta_cbc(double r, double theta, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  return -r*sin(theta + asin(app->delta)*sin(theta))*(1. + asin(app->delta)*cos(theta));
-}
-
-static double dZdr_cbc(double r, double theta, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  return app->kappa*sin(theta);
-}
-
-static double dZdtheta_cbc(double r, double theta, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  return app->kappa*r*cos(theta);
-}
-
-static double Jr_cbc(double r, double theta, void *ctx)
-{
-  return R_rtheta_cbc(r, theta, ctx)
-    *(dRdr_cbc(r, theta, ctx)*dZdtheta_cbc(r, theta, ctx)
-      - dRdtheta_cbc(r, theta, ctx)*dZdr_cbc(r, theta, ctx));
-}
-
-static double Bphi_cbc(double R, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  return app->B0*app->R0/R;
-}
-
-static double integrand_JoRsq_cbc(double t, void *int_ctx)
-{
-  struct integrand_cbc_ctx *inctx = int_ctx;
-  return Jr_cbc(inctx->r, t, inctx->app_ctx)
-    / pow(R_rtheta_cbc(inctx->r, t, inctx->app_ctx), 2);
-}
-
-static double intdPsidr_cbc(double r, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  struct integrand_cbc_ctx tmp_ctx = {.app_ctx = app, .r = r};
-  struct gkyl_qr_res integral = gkyl_dbl_exp(integrand_JoRsq_cbc, &tmp_ctx, 0., 2.*M_PI, 7, 1e-10);
-  return integral.res;
-}
-
-static double dPsidr_cbc(double r, double theta, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  double integral_val = interp_1x_lut_cbc(r, app->r_lut, app->dPsidr_int_lut, app->psi_lut_size);
-  double R = R_rtheta_cbc(r, theta, ctx);
-  double Bt = Bphi_cbc(R, ctx);
-  return (R*Bt/(2.*M_PI*qprofile_cbc(r, app->a_mid, app->qaxis, app->qlcfs)))*integral_val;
-}
-
-static double compute_alpha_integral_cbc(double r, double twrap, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  struct integrand_cbc_ctx tmp_ctx = {.app_ctx = app, .r = r};
-  struct gkyl_qr_res integral;
-  if (twrap == 0.0) return 0.0;
-  if (0. < twrap) {
-    integral = gkyl_dbl_exp(integrand_JoRsq_cbc, &tmp_ctx, 0., twrap, 7, 1e-10);
-    return integral.res;
-  } else {
-    integral = gkyl_dbl_exp(integrand_JoRsq_cbc, &tmp_ctx, twrap, 0., 7, 1e-10);
-    return -integral.res;
-  }
-}
-
-static double alpha_cbc(double r, double theta, double phi, void *ctx)
-{
-  double twrap = theta;
-  while (twrap < -M_PI) twrap += 2.*M_PI;
-  while (twrap >  M_PI) twrap -= 2.*M_PI;
-  double integral_val = compute_alpha_integral_cbc(r, twrap, ctx);
-  double R  = R_rtheta_cbc(r, theta, ctx);
-  double Bt = Bphi_cbc(R, ctx);
-  return phi - R*Bt*integral_val/dPsidr_cbc(r, theta, ctx);
-}
-
-void bc_shift_func_lo_cbc(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  double r = r_x_cbc(xc[0], app->r0);
-  fout[0] = app->Cy*(alpha_cbc(r, app->z_min, 0.0, ctx) - alpha_cbc(r, app->z_max, 0.0, ctx));
-}
-
-void bc_shift_func_up_cbc(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  double r = r_x_cbc(xc[0], app->r0);
-  fout[0] = -app->Cy*(alpha_cbc(r, app->z_min, 0.0, ctx) - alpha_cbc(r, app->z_max, 0.0, ctx));
-}
-
-void init_donor_3x_cbc(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
-{
-  struct gk_cbc_app_ctx *app = ctx;
-  double x = xn[0], y = xn[1], z = xn[2];
-  double sigx = app->Lx/7.0, sigy = app->Ly/7.0, sigz = app->Lz/10.0;
-  double mux = 0.*app->Lx;
-  fout[0] = exp(-pow(x-mux,2)/(2.*pow(sigx,2)) - pow(y,2)/(2.*pow(sigy,2)) - pow(z,2)/(2.*pow(sigz,2)));
 }
 
 void
-test_bc_twistshift_3x_cbc_wcells(const int *cells, enum gkyl_edge_loc edge,
-  bool check_distf, bool use_gpu, bool write_f)
+test_zero_shift_is_identity(void)
 {
-  int bc_dir = 2;
-  int poly_order = 1;
-
-  // Physical parameters matching rt_gk_cbc_passive_3x2v_p1.c create_ctx().
-  double eV  = GKYL_ELEMENTARY_CHARGE;
-  double mp  = GKYL_PROTON_MASS;
-  double qi  = eV;
-  double mi  = mp; // AMU = 1 (hydrogen)
-  double Te0 = 2000.*eV;
-
-  double R_axis = 1.6714;
-  double B_axis = 1.54;
-  double a_mid  = 0.604;
-  double R0     = R_axis + 0.5*a_mid;
-  double r0     = 0.5*a_mid;
-  double B0     = B_axis*(R_axis/R0);
-  double qaxis  = 1.2;
-  double qlcfs  = 2.0;
-
-  double c_s      = sqrt(Te0/mi);
-  double omega_ci = fabs(qi*B0/mi);
-  double rho_s    = c_s/omega_ci;
-  double q0       = qprofile_cbc(r0, a_mid, qaxis, qlcfs);
-  double Cy       = r0/q0;
-
-  double Lx = 150.*rho_s;
-  double Ly = 150.*rho_s;
-  Ly = 2.*M_PI*Cy/round(2.*M_PI*Cy/Ly); // adjust to integer toroidal mode number
-  double Lz = 2.*M_PI - 1e-10;
-
-  // Use a fixed LUT size sufficient for accurate geometry evaluation.
-  int psi_lut_size = 200;
-
-  struct gk_cbc_app_ctx app_ctx = {
-    .a_shift = 0.0, .Z_axis = 0.0,
-    .R_axis  = R_axis, .R0 = R0, .a_mid = a_mid, .r0 = r0,
-    .B0      = B0, .kappa = 1.0, .delta = 0.0,
-    .q0 = q0, .Cy = Cy, .qaxis = qaxis, .qlcfs = qlcfs,
-    .Lx = Lx, .Ly = Ly, .Lz = Lz,
-    .x_min = -Lx/2., .x_max = Lx/2.,
-    .y_min = -Ly/2., .y_max = Ly/2.,
-    .z_min = -Lz/2., .z_max = Lz/2.,
-    .psi_lut_size = psi_lut_size,
-  };
+  // Check that a zero shift leaves the ghost plane alone, for any upsampling.
+  struct ts_ctx tctx = { .offset = 0.0, .shear = 0.0 };
+  double dx = (ts_upper[0]-ts_lower[0])/ts_cells[0];
 
-  // Populate lookup tables (avoids redundant integration in geometry evaluations).
-  app_ctx.r_lut        = gkyl_malloc(psi_lut_size*sizeof(double));
-  app_ctx.dPsidr_int_lut = gkyl_malloc(psi_lut_size*sizeof(double));
-  double r_lut_min = 0.0, r_lut_max = 2.0*a_mid;
-  for (int i=0; i<psi_lut_size; i++)
-    app_ctx.r_lut[i] = i*(r_lut_max - r_lut_min)/(psi_lut_size - 1);
-  for (int i=0; i<psi_lut_size; i++)
-    app_ctx.dPsidr_int_lut[i] = intdPsidr_cbc(app_ctx.r_lut[i], &app_ctx);
-
-  const double lower[] = {app_ctx.x_min, app_ctx.y_min, app_ctx.z_min};
-  const double upper[] = {app_ctx.x_max, app_ctx.y_max, app_ctx.z_max};
-  int ndim = 3, cdim = 3, vdim = 0;
-
-  double lower_conf[cdim], upper_conf[cdim];
-  int cells_conf[cdim];
-  for (int d=0; d<cdim; d++) {
-    lower_conf[d] = lower[d];
-    upper_conf[d] = upper[d];
-    cells_conf[d] = cells[d];
-  }
+  for (int e=0; e<2; e++) {
+    enum gkyl_edge_loc edge = e == 0? GKYL_LOWER_EDGE : GKYL_UPPER_EDGE;
+    struct ts_setup s;
+    ts_setup_init(&s, edge);
 
-  struct gkyl_rect_grid grid;
-  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
-  struct gkyl_rect_grid grid_conf;
-  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
+    struct gkyl_array *f_pre = ts_donor_new(&s);
 
-  struct gkyl_basis basis;
-  gkyl_cart_modal_serendip(&basis, ndim, poly_order);
-  struct gkyl_basis basis_conf;
-  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
+    int upsample[] = {1, 2, 4};
+    for (int c=0; c<3; c++) {
+      int half_width = upsample[c] > 1? 4 : 0;
+      double cutoff = upsample[c] > 1? 2.0*dx/upsample[c] : 0.0;
+      struct gkyl_array *f = ts_run(&s, edge, upsample[c], half_width, cutoff, NULL, &tctx);
 
-  int ghost_conf[cdim];
-  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
-  struct gkyl_range local_conf, local_ext_conf;
-  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
+      // The donor plane is the ghost plane periodicity just filled, so the BC
+      // writing over it must reproduce what was already there.
+      double maxd = ts_max_diff(f_pre, f, &s.ghost_r, s.basis.num_basis);
+      TEST_CHECK( maxd < 1.0e-13 );
+      TEST_MSG("edge %d, upsample %d: zero shift changed the plane by %.3e", e, upsample[c], maxd);
 
-  int ghost[ndim];
-  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
-  struct gkyl_range local, local_ext;
-  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
-
-  struct skin_ghost_ranges skin_ghost;
-  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
-
-  struct gkyl_range skin_rng, ghost_rng;
-  if (edge == GKYL_LOWER_EDGE) {
-    skin_rng  = skin_ghost.upper_skin[bc_dir];
-    ghost_rng = skin_ghost.lower_ghost[bc_dir];
-  } else {
-    skin_rng  = skin_ghost.lower_skin[bc_dir];
-    ghost_rng = skin_ghost.upper_ghost[bc_dir];
-  }
-
-  struct gkyl_array *distf    = mkarr(use_gpu, basis.num_basis, local_ext.volume);
-  struct gkyl_array *distf_ho = use_gpu?
-    mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
-
-  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew(
-    &(struct gkyl_proj_on_basis_inp){
-      .grid = &grid, .basis = &basis,
-      .num_ret_vals = 1,
-      .eval = init_donor_3x_cbc,
-      .ctx  = &app_ctx,
-    }
-  );
-  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
-  gkyl_array_copy(distf, distf_ho);
-
-  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new(
-    (struct test_bc_twistshift_output_meta){
-      .poly_order = poly_order, .basis_type = basis.id
-    }
-  );
-  if (write_f)
-    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho,
-      "ctest_bc_twistshift_3x_cbc_do.gkyl");
-
-  // Range extended only in bc_dir.
-  struct gkyl_range update_rng;
-  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
-  for (int d=0; d<ndim; d++) {
-    lower_bcdir_ext[d] = local.lower[d];
-    upper_bcdir_ext[d] = local.upper[d];
-  }
-  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
-  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
-  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
-
-  // Choose shift function based on edge.
-  struct gkyl_bc_twistshift_inp tsinp = {
-    .bc_dir   = bc_dir,
-    .shift_dir = 1,
-    .shear_dir = 0,
-    .edge      = edge,
-    .cdim      = cdim,
-    .bcdir_ext_update_r = &update_rng,
-    .num_ghost = ghost,
-    .basis     = &basis,
-    .grid      = &grid,
-    .shift_func = (edge == GKYL_LOWER_EDGE) ? bc_shift_func_lo_cbc : bc_shift_func_up_cbc,
-    .shift_func_ctx = &app_ctx,
-    .use_gpu   = use_gpu,
-  };
-
-  struct gkyl_bc_twistshift *tsup = gkyl_bc_twistshift_inew(&tsinp);
-
-  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
-  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
-
-  gkyl_bc_twistshift_advance(tsup, distf, distf);
-  gkyl_array_copy(distf_ho, distf);
-
-  if (write_f) {
-    double lower_ext[ndim], upper_ext[ndim];
-    int cells_ext[ndim];
-    for (int d=0; d<ndim; d++) {
-      double dx = (upper[d] - lower[d])/cells[d];
-      lower_ext[d] = lower[d] - dx*ghost[d];
-      upper_ext[d] = upper[d] + dx*ghost[d];
-      cells_ext[d] = cells[d] + 2*ghost[d];
-    }
-    struct gkyl_rect_grid grid_ext;
-    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
-    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho,
-      "ctest_bc_twistshift_3x_cbc_tar.gkyl");
-  }
-
-  if (check_distf) {
-    // Check 4 x=const lines, and 4 y=const lines.
-    int idx0_ref[] = {4,12,19,28};
-    int idx1_ref[] = {2,7,10,13};
-    int num_ref0 = sizeof(idx0_ref)/sizeof(idx0_ref[0]);
-    int num_ref1 = sizeof(idx1_ref)/sizeof(idx1_ref[0]);
-    double f0[num_ref0*cells[1]*basis.num_basis];
-    double f1[num_ref1*cells[0]*basis.num_basis];
-    if (edge == GKYL_LOWER_EDGE) {
-      const double f0m[] =
-      {
-        // idx[0] = 4;
-         1.4147068739149354e-06,  3.9678563980892827e-07, -5.3677388121514690e-07,
-        -1.4021443738919494e-06, -2.1663045016556100e-07, -3.9326221053808132e-07,
-         5.3200736596068834e-07,  2.1470678662411421e-07,
-         2.2073750885337050e-06,  5.4194161567241438e-08,  7.7188487204183924e-07,
-        -2.1877737491242868e-06,  2.2856919929920019e-08, -5.3712921129036553e-08,
-        -7.6503058731221621e-07, -2.2653952048417829e-08,
-         8.0151330159023854e-06,  3.5840433095651838e-07,  2.4919021860714378e-06,
-        -7.9439591843807564e-06,  1.4691992411677311e-07, -3.5522172507617932e-07,
-        -2.4697742655481038e-06, -1.4561528526605157e-07,
-         2.4056337321823511e-05,  1.5575127200312389e-06,  6.4725989939125481e-06,
-        -2.3842718696134587e-05,  5.6131534500851025e-07, -1.5436821138880369e-06,
-        -6.4151227587227262e-06, -5.5633090323856011e-07,
-         5.9715709406034343e-05,  5.0593586542458534e-06,  1.3398359967595644e-05,
-        -5.9185438001676253e-05,  1.5246943425719446e-06, -5.0144318963554509e-06,
-        -1.3279383449912431e-05, -1.5111551613699758e-06,
-         1.2266163264877539e-04,  1.2843394764617348e-05,  2.1715606284302345e-05,
-        -1.2157240576270994e-04,  3.0737503418026385e-06, -1.2729346299878336e-05,
-        -2.1522773189704626e-05, -3.0464556495582395e-06,
-         2.0858381754799334e-04,  2.6012564754977512e-05,  2.6550477975637763e-05,
-        -2.0673160755237084e-04,  4.5938737655600021e-06, -2.5781574963835826e-05,
-        -2.6314711551985457e-05, -4.5530804815592547e-06,
-         2.9374366736149827e-04,  4.2514292127503834e-05,  2.2141578694173991e-05,
-        -2.9113524373960048e-04,  4.8573878417790354e-06, -4.2136768128945044e-05,
-        -2.1944962993788802e-05, -4.8142545708526606e-06,
-         3.4269905278866652e-04,  5.6458355498447365e-05,  7.3950701740712856e-06,
-        -3.3965590870142440e-04,  2.9844920494078483e-06, -5.5957009173406751e-05,
-        -7.3294024580625872e-06, -2.9579899646787672e-06,
-         3.3130814623591096e-04,  6.1194737241075030e-05, -1.1197518621951395e-05,
-        -3.2836615261769482e-04, -4.4059942666451672e-07, -6.0651332170970138e-05,
-         1.1098085424488793e-05,  4.3668693397105754e-07,
-         2.6547493073777388e-04,  5.4303954632758055e-05, -2.4003510429959307e-05,
-        -2.6311753155848911e-04, -3.5659721755455483e-06, -5.3821739239660803e-05,
-         2.3790360903447407e-05,  3.5343065871729570e-06,
-         1.7634549859606930e-04,  3.9539852198925795e-05, -2.6084796724879738e-05,
-        -1.7477956266190929e-04, -4.8370620921015304e-06, -3.9188741022952437e-05,
-         2.5853165518798813e-05,  4.7941093124383771e-06,
-         9.7120871429426495e-05,  2.3660577068010910e-05, -1.9999449126191993e-05,
-        -9.6258444751461542e-05, -4.1887526472941376e-06, -2.3450472766235517e-05,
-         1.9821855389468108e-05,  4.1515568110413017e-06,
-         4.4351391469818973e-05,  1.1650043122384966e-05, -1.1710592695891665e-05,
-        -4.3957554155084504e-05, -2.6752574970654273e-06, -1.1546591538391639e-05,
-         1.1606603435837950e-05,  2.6515013939545564e-06,
-         1.6794598764719960e-05,  4.7243461185578233e-06, -5.4058549896015648e-06,
-        -1.6645463879424616e-05, -1.3229289098014698e-06, -4.6823942490099374e-06,
-         5.3578513680151396e-06,  1.3111813918058868e-06,
-         5.2735603406759165e-06,  1.5789778675299268e-06, -1.9989826780664712e-06,
-        -5.2267314864994830e-06, -5.1808733150377238e-07, -1.5649566523489707e-06,
-         1.9812318489709252e-06,  5.1348675152926985e-07,
-        // idx[0] = 12;
-         8.5771895799448463e-03,  3.1197886695786712e-04,  1.2589091675382295e-04,
-        -8.5010247246790835e-03,  2.3881143669295742e-04, -3.0920851601408221e-04,
-        -1.2477301404636147e-04, -2.3669080751226941e-04,
-         8.2661626046304885e-03,  1.0720660909669306e-03, -3.0982027320798947e-04,
-        -8.1927596475759902e-03,  1.8255117221452561e-04, -1.0625462175989969e-03,
-         3.0706909042867208e-04, -1.8093013032420406e-04,
-         6.6575398175439011e-03,  1.4760068941306471e-03, -5.9457869281011441e-04,
-        -6.5984213205230440e-03,  4.2899447104076090e-05, -1.4629000541319605e-03,
-         5.8929887479281385e-04, -4.2518502955738542e-05,
-         4.4799350811575711e-03,  1.3955105208072918e-03, -6.3033616055554532e-04,
-        -4.4401535648606475e-03, -8.3328432799330363e-05, -1.3831184830834593e-03,
-         6.2473881867683195e-04,  8.2588482030546096e-05,
-         2.5178444512609479e-03,  1.0028214075435281e-03, -4.8235931958416503e-04,
-        -2.4954861652017948e-03, -1.3193983394577959e-04, -9.9391642221575223e-04,
-         4.7807600190536255e-04,  1.3076821726847499e-04,
-         1.1813969572080783e-03,  5.6871985765870141e-04, -2.8575381884705388e-04,
-        -1.1709062332455860e-03, -1.1130086733193673e-04, -5.6366966432420582e-04,
-         2.8321634453203873e-04,  1.1031252326278932e-04,
-         4.6254048415618595e-04,  2.5918239859045285e-04, -1.3487188316997178e-04,
-        -4.5843315637685304e-04, -6.6255494613212145e-05, -2.5688087666510880e-04,
-         1.3367423009662933e-04,  6.5667150364697886e-05,
-         1.5102266511218463e-04,  9.5873653213552430e-05, -5.1458764419249627e-05,
-        -1.4968159420277919e-04, -3.0014361827430350e-05, -9.5022301747813123e-05,
-         5.1001814120131696e-05,  2.9747836352719439e-05,
-         4.9288640555562537e-05,  1.9197719093399958e-05, -9.3898074536993173e-06,
-        -4.8850960807531967e-05, -1.7734142076995751e-05, -1.9027244664386457e-05,
-         9.3064266074420962e-06,  1.7576664111519137e-05,
-         7.4312889120419612e-05, -3.9559856706301425e-05,  2.5345644730922928e-05,
-        -7.3652995761239122e-05, -1.7079041586904331e-05,  3.9208567891674429e-05,
-        -2.5120577143858990e-05,  1.6927380868854436e-05,
-         2.4668363462348900e-04, -1.2316540125222137e-04,  8.0544516023109083e-05,
-        -2.4449310086503489e-04, -3.4617348824034278e-05,  1.2207170093550459e-04,
-        -7.9829286244383513e-05,  3.4309949140455846e-05,
-         6.9889469196789068e-04, -2.9144378275440763e-04,  1.9257347432050185e-04,
-        -6.9268855503182346e-04, -6.3595836624040557e-05,  2.8885578195009997e-04,
-        -1.9086343507478647e-04,  6.3031109956076864e-05,
-         1.6531830617114835e-03, -5.4719482372872844e-04,  3.7015196128372313e-04,
-        -1.6385029094950184e-03, -8.0981230730739408e-05,  5.4233577121939294e-04,
-        -3.6686503725170299e-04,  8.0262122955358892e-05,
-         3.2662572681362470e-03, -7.8998871116982131e-04,  5.6119422549585842e-04,
-        -3.2372531275876876e-03, -5.0252394101103727e-05,  7.8297366559026060e-04,
-        -5.5621085925887826e-04,  4.9806156287680392e-05,
-         5.3918935380395400e-03, -8.1066940565628718e-04,  6.4417804850085126e-04,
-        -5.3440138931855393e-03,  4.8296611837007029e-05,  8.0347071692792157e-04,
-        -6.3845779160642867e-04, -4.7867741235965884e-05,
-         7.4385809600035612e-03, -4.2620301983017786e-04,  4.9868993294226453e-04,
-        -7.3725268711996870e-03,  1.7454031661297211e-04,  4.2241836624211989e-04,
-        -4.9426160053675874e-04, -1.7299041057102665e-04,
-        // idx[0] = 19;
-         5.9328259833403563e-03, -3.1592831855465119e-03,  7.6447171990714363e-04,
-        -5.8801428954679998e-03, -1.4953722986172529e-04,  3.1312289675153111e-03,
-        -7.5768326346009965e-04,  1.4820934951547608e-04,
-         8.5438428607558271e-03, -3.1770890503348310e-03,  7.1469750720526751e-04,
-        -8.4679741220696214e-03,  1.4653149000110456e-04,  3.1488767174453966e-03,
-        -7.0835104235361418e-04, -1.4523030041869057e-04,
-         1.0538391888353600e-02, -2.0861147480127039e-03,  4.1035235387424735e-04,
-        -1.0444811691083961e-02,  4.6474412137478837e-04,  2.0675901921113540e-03,
-        -4.0670845311287489e-04, -4.6061722544807500e-04,
-         1.1157187397402466e-02, -1.8349902862187543e-04, -6.0616833961144544e-05,
-        -1.1058112338448060e-02,  5.9620026364061495e-04,  1.8186956983165916e-04,
-         6.0078560632534608e-05, -5.9090604618554376e-04,
-         1.0147502273615178e-02,  1.6812950536897154e-03, -5.0484232418428394e-04,
-        -1.0057393149318094e-02,  4.4927500173372542e-04, -1.6663652689123407e-03,
-         5.0035935896646541e-04, -4.4528547052858725e-04,
-         7.9236576295588640e-03,  2.7048082887694922e-03, -7.4744339840912392e-04,
-        -7.8532960931947931e-03,  1.3680114431856099e-04, -2.6807897766548171e-03,
-         7.4080615228921856e-04, -1.3558635953852334e-04,
-         5.3016792692569745e-03,  2.6754726903120800e-03, -7.3909622093528999e-04,
-        -5.2546007209230746e-03, -1.3556652552430490e-04, -2.6517146762999374e-03,
-         7.3253309717892176e-04,  1.3436270407449278e-04,
-         3.0306885085190473e-03,  1.9748354796544207e-03, -5.6082860635105409e-04,
-        -3.0037762024011207e-03, -2.4639127781914962e-04, -1.9572990760248132e-03,
-         5.5584848678700660e-04,  2.4420334016906899e-04,
-         1.4749219675761613e-03,  1.1511708985332411e-03, -3.4089330270885629e-04,
-        -1.4618247616508778e-03, -2.1626062462549767e-04, -1.1409485798989469e-03,
-         3.3786619355848882e-04,  2.1434024510948494e-04,
-         6.0905145791109738e-04,  5.4222206411941179e-04, -1.6846528502594774e-04,
-        -6.0364312273220987e-04, -1.3353062399755835e-04, -5.3740716937438697e-04,
-         1.6696932484788329e-04,  1.3234488121368636e-04,
-         2.2538939529024023e-04,  1.9086017837583353e-04, -6.0622757673701499e-05,
-        -2.2338795291675480e-04, -7.2883062312442410e-05, -1.8916535308061285e-04,
-         6.0084431742929801e-05,  7.2235865717262487e-05,
-         1.3692552150240531e-04, -2.3628334870109403e-05,  6.7351766555291856e-06,
-        -1.3570963226150468e-04, -5.5072031551511001e-05,  2.3418516876840270e-05,
-        -6.6753687487111750e-06,  5.4582995688048192e-05,
-         2.8180957439635708e-04, -2.6245954825184062e-04,  7.9675931947129452e-05,
-        -2.7930712470157682e-04, -8.6112162611900079e-05,  2.6012892546224296e-04,
-        -7.8968415135433089e-05,  8.5347492513282593e-05,
-         7.5858237184660477e-04, -6.8983776721580120e-04,  2.0188206214678025e-04,
-        -7.5184621240646007e-04, -1.6201786760815427e-04,  6.8371205515042964e-04,
-        -2.0008936327952937e-04,  1.6057916005461062e-04,
-         1.7743608964103583e-03, -1.4228383602125521e-03,  3.9110700695123274e-04,
-        -1.7586046933318674e-03, -2.5501449371086789e-04,  1.4102036531488827e-03,
-        -3.8763400355073456e-04,  2.5274998249502926e-04,
-         3.5176447536171261e-03, -2.3790827021664203e-03,  6.1388697056459030e-04,
-        -3.4864083094370800e-03, -2.8116612144444690e-04,  2.3579566109232599e-03,
-        -6.0843569636494840e-04,  2.7866938556775280e-04,
-        // idx[0] = 28;
-         3.9008280658611207e-04, -2.5603798505596852e-04,  1.8683093211897101e-05,
-        -3.8661889801461870e-04,  1.1175426823790703e-05,  2.5376438530717388e-04,
-        -1.8517188625419492e-05, -1.1076189799980769e-05,
-         4.3680260689641130e-04, -1.8748123385802201e-04,  8.0091734113950957e-06,
-        -4.3292382970210014e-04,  2.7606287551937715e-05,  1.8581641335839929e-04,
-        -7.9380525007527933e-06, -2.7361145611652907e-05,
-         4.4457679107663103e-04, -7.5578664486840552e-05, -3.4115616360440883e-06,
-        -4.4062897965993530e-04,  3.5399985354932533e-05,  7.4907531129210281e-05,
-         3.3812672026731489e-06, -3.5085635912631181e-05,
-         4.1504347649095089e-04,  4.2960315696147049e-05, -1.3312487632414327e-05,
-        -4.1135791888244848e-04,  3.1477256709139010e-05, -4.2578831038885959e-05,
-         1.3194273655178598e-05, -3.1197740828200509e-05,
-         3.5577914498131479e-04,  1.3094475217078906e-04, -2.0440326610361184e-05,
-        -3.5261985057240502e-04,  1.8525522986963621e-05, -1.2978197175140562e-04,
-         2.0258817911812268e-05, -1.8361017613277599e-05,
-         2.7796534980573800e-04,  1.6786465218620076e-04, -2.3905953966682069e-05,
-        -2.7549703656169430e-04,  2.9974039875550468e-06, -1.6637402558656323e-04,
-         2.3693670734873877e-05, -2.9707872457006951e-06,
-         1.9535178824326644e-04,  1.5650334125842896e-04, -2.3209649131201253e-05,
-        -1.9361707776044740e-04, -8.6672787668020905e-06, -1.5511360232069719e-04,
-         2.3003549038581116e-05,  8.5903139257351561e-06,
-         1.2172339077131273e-04,  1.1660274450623213e-04, -1.8887207777222881e-05,
-        -1.2064249540877665e-04, -1.3462333943164936e-05, -1.1556732013136769e-04,
-         1.8719490667402875e-05,  1.3342789340965859e-05,
-         6.7058946442705194e-05,  7.0433021024861683e-05, -1.2563048496751787e-05,
-        -6.6463467597043934e-05, -1.2699023524379705e-05, -6.9807580628297237e-05,
-         1.2451489487645912e-05,  1.2586257066353350e-05,
-         3.4938222906600265e-05,  3.1273776945169202e-05, -6.0324138429606134e-06,
-        -3.4627973883173486e-05, -1.0006175581767381e-05, -3.0996067950580566e-05,
-         5.9788464217243402e-06,  9.9173214288020404e-06,
-         2.4837446165027290e-05, -9.6145358765583846e-07,  1.9699547938565060e-07,
-        -2.4616891346377383e-05, -9.0936978967278239e-06,  9.5291594573175467e-07,
-        -1.9524617303820833e-07,  9.0129464830299899e-06,
-         3.6725180241487430e-05, -3.6057780516486035e-05,  6.7954495238266452e-06,
-        -3.6399063159472330e-05, -1.1694827060907848e-05,  3.5737589898260177e-05,
-        -6.7351063980715334e-06,  1.1590977798611619e-05,
-         7.3131479750304169e-05, -8.5125203228748116e-05,  1.4329502961988946e-05,
-        -7.2482077225311949e-05, -1.6767541211874010e-05,  8.4369297261769594e-05,
-        -1.4202257958371192e-05,  1.6618646595792397e-05,
-         1.3604357772040060e-04, -1.5068140809657870e-04,  2.1787568445735812e-05,
-        -1.3483552007980250e-04, -2.0478489031778651e-05,  1.4934336752606917e-04,
-        -2.1594096332079554e-05,  2.0296641453544639e-05,
-         2.2070902006211332e-04, -2.1925837439635583e-04,  2.6427797458379611e-05,
-        -2.1874913909968418e-04, -1.7877051979819007e-05,  2.1731137506795665e-04,
-        -2.6193120429307424e-05,  1.7718304984205783e-05,
-         3.1225316368462653e-04, -2.6354343092504682e-04,  2.5533068602001434e-05,
-        -3.0948037700471862e-04, -6.4354644170033844e-06,  2.6120318333164132e-04,
-        -2.5306336703815414e-05,  6.3783179343098985e-06,
-      };
-  
-      const double f1m[] =
-      {
-        // idx[1] = 2;
-         7.5742778736170694e-07,  1.3311910271755548e-07,  2.8478156167525587e-07,
-        -7.5070188055260917e-07,  5.4750238065324756e-08, -1.3193701421442880e-07,
-        -2.8225272093725106e-07, -5.4264059705951382e-08,
-         1.2925859849765668e-06,  1.7301030138070181e-07,  5.1100320791830013e-07,
-        -1.2811079100725808e-06,  7.3239351158981957e-08, -1.7147398176909403e-07,
-        -5.0646553447542282e-07, -7.2588990743278259e-08,
-         1.8635824605983989e-06,  1.4918689410169481e-07,  7.1992200307670070e-07,
-        -1.8470339761485296e-06,  3.9576065168750808e-08, -1.4786212471296968e-07,
-        -7.1352914505999257e-07, -3.9224632424088840e-08,
-         2.2073750885337050e-06,  5.4194161567241438e-08,  7.7188487204183924e-07,
-        -2.1877737491242868e-06,  2.2856919929920019e-08, -5.3712921129036553e-08,
-        -7.6503058731221621e-07, -2.2653952048417829e-08,
-         2.3371245739281691e-06,  7.7901820168274173e-08,  7.1291202449929149e-07,
-        -2.3163710679863721e-06, -2.4448859078376251e-07, -7.7210057347509384e-08,
-        -7.0658141461162244e-07,  2.4231754886407394e-07,
-         4.4362078536198185e-06,  1.4349007654002696e-06, -1.4918804712085053e-06,
-        -4.3968146321047141e-06, -7.9055943126041467e-07, -1.4221589450057450e-06,
-         1.4786326749339418e-06,  7.8353931772558917e-07,
-         1.8432855790288429e-05,  7.7265468592736174e-06, -7.0218535854514018e-06,
-        -1.8269173294953980e-05, -3.1418179249565271e-06, -7.6579356530322741e-06,
-         6.9595000071553346e-06,  3.1139187972416376e-06,
-         8.2880124644381316e-05,  3.4710110035730186e-05, -2.7056128318655973e-05,
-        -8.2144154821269593e-05, -1.1646701134768506e-05, -3.4401886638953268e-05,
-         2.6815871754634015e-05,  1.1543279227396033e-05,
-         3.6130932397451928e-04,  1.4417479842687968e-04, -9.7273919862532121e-05,
-        -3.5810092195539682e-04, -3.5891598669338311e-05, -1.4289453610402862e-04,
-         9.6410134124976947e-05,  3.5572883734518748e-05,
-         1.3866911075139233e-03,  4.8934908019720340e-04, -2.7681619210264059e-04,
-        -1.3743773855753208e-03, -7.3086254588880316e-05, -4.8500369392349860e-04,
-         2.7435808330019372e-04,  7.2437253660220146e-05,
-         4.1402065573272135e-03,  1.1066127780317765e-03, -5.1267688697286180e-04,
-        -4.1034418070240936e-03, -3.9937840842209967e-05, -1.0967861324518405e-03,
-         5.0812435137475719e-04,  3.9583195554377857e-05,
-         8.2661626046304885e-03,  1.0720660909669306e-03, -3.0982027320798947e-04,
-        -8.1927596475759902e-03,  1.8255117221452561e-04, -1.0625462175989969e-03,
-         3.0706909042867208e-04, -1.8093013032420406e-04,
-         9.2071430199458723e-03, -6.7468017399297192e-04,  5.5519252734112100e-04,
-        -9.1253842213336704e-03,  2.3350197769444222e-04,  6.6868906031594807e-04,
-        -5.5026245577217254e-04, -2.3142849614555009e-04,
-         4.6562742627774770e-03, -1.5981825134639602e-03,  7.7093816367743357e-04,
-        -4.6149268666407072e-03, -1.2283002048105933e-04,  1.5839907623441212e-03,
-        -7.6409228565316330e-04,  1.2173929832259107e-04,
-         8.4265128323255962e-04, -5.4995291705314407e-04,  2.3627440955229246e-04,
-        -8.3516859762456210e-04, -1.3174780227490776e-04,  5.4506937286423181e-04,
-        -2.3417630899862953e-04,  1.3057789082567117e-04,
-         1.1584483866390626e-04,  4.3858963858025070e-05, -1.6873108923339463e-05,
-        -1.1481614444094626e-04, -4.5483891179512000e-05, -4.3469499266713753e-05,
-         1.6723276873219639e-05,  4.5079997345019702e-05,
-         1.9929185999929553e-03,  1.3468353897936511e-03, -4.5601060935752653e-04,
-        -1.9752216194948405e-03, -2.4418116907756006e-04, -1.3348755838951901e-03,
-         4.5196126641860161e-04,  2.4201285704154009e-04,
-         1.0151660891080033e-02,  2.5306058282125788e-03, -7.5599768765257259e-04,
-        -1.0061514838545048e-02,  2.8830814950777197e-04, -2.5081342220012403e-03,
-         7.4928448003081915e-04, -2.8574799291165951e-04,
-         8.5438428607558271e-03, -3.1770890503348310e-03,  7.1469750720526751e-04,
-        -8.4679741220696214e-03,  1.4653149000110456e-04,  3.1488767174453966e-03,
-        -7.0835104235361418e-04, -1.4523030041869057e-04,
-         8.3058989180792564e-04, -7.7938148858281266e-04,  2.0964975534781683e-04,
-        -8.2321431052863629e-04, -1.7368462202414781e-04,  7.7246063441240638e-04,
-        -2.0778807989763133e-04,  1.7214231449146951e-04,
-         4.8784698194571816e-04,  4.6603525819394176e-04, -1.2686455710601843e-04,
-        -4.8351493420147626e-04, -1.1084020143927416e-04, -4.6189689706081717e-04,
-         1.2573800853899969e-04,  1.0985594805166225e-04,
-         4.8781825809830056e-03,  1.3781496758297112e-03, -3.2928825061709555e-04,
-        -4.8348646541985394e-03,  2.0371545823871589e-04, -1.3659118012187134e-03,
-         3.2636419353345472e-04, -2.0190647893989855e-04,
-         2.3680721830718248e-03, -1.7400576716845859e-03,  2.7950593809693524e-04,
-        -2.3470438644831496e-03, -9.5410574014376798e-05,  1.7246060788892229e-03,
-        -2.7702394453451581e-04,  9.4563334660169134e-05,
-         8.9363290665012558e-05,  3.9704854712887114e-05, -9.8017374005486476e-06,
-        -8.8569750772238376e-05, -3.3694653872762494e-05, -3.9352278325905250e-05,
-         9.7146986446126184e-06,  3.3395447657075059e-05,
-         1.5558629382148325e-03,  5.9445795666028924e-04, -1.1056083435060165e-04,
-        -1.5420469820210249e-03,  6.1304104069997447e-05, -5.8917921077172018e-04,
-         1.0957906172357881e-04, -6.0759727829951777e-05,
-         5.8935835734624667e-04, -5.5038435706920711e-04,  7.6629057291856129e-05,
-        -5.8412489554986722e-04, -4.8460576140242794e-05,  5.4549698172253955e-04,
-        -7.5948596518150819e-05,  4.8030249547433478e-05,
-         1.2304561996882203e-04,  1.2696504265504160e-04, -2.3555535292118696e-05,
-        -1.2195298330168754e-04, -2.1706603802157628e-05, -1.2583760178323854e-04,
-         2.3346363754109702e-05,  2.1513850648983980e-05,
-         4.3680260689641130e-04, -1.8748123385802201e-04,  8.0091734113950957e-06,
-        -4.3292382970210014e-04,  2.7606287551937715e-05,  1.8581641335839929e-04,
-        -7.9380525007527933e-06, -2.7361145611652907e-05,
-         1.6405328706551727e-05,  2.9047681450653114e-06, -5.1336046315663870e-07,
-        -1.6259650512677665e-05, -5.7121417723422041e-06, -2.8789740031395213e-06,
-         5.0880185744890011e-07,  5.6614183451294898e-06,
-         1.2525989018365014e-04, -1.7226749700817367e-05, -1.8059029380175158e-06,
-        -1.2414759094885760e-04,  1.0448806188062650e-05,  1.7073777344845405e-05,
-         1.7898666437726345e-06, -1.0356021505668008e-05,
-         6.1342326303602555e-06, -1.4359128614618765e-06,  2.5224463428371958e-07,
-        -6.0797610652743729e-06, -2.0408390187610221e-06,  1.4231620537237336e-06,
-        -2.5000471922964324e-07,  2.0227165082305203e-06,
-         2.9913061136183802e-05, -9.4004861242035489e-06, -2.0777664618398835e-07,
-        -2.9647435204664162e-05,  2.4116686151255107e-06,  9.3170104520845704e-06,
-         2.0593160381472413e-07, -2.3902531632099425e-06,
-        // idx[1] = 7;
-         3.6490020128125056e-05,  7.3675063786135985e-06,  3.2021281911722955e-06,
-        -3.6165991251789855e-05,  6.9414808136517716e-07, -7.3020834272183321e-06,
-        -3.1736935124293500e-06, -6.8798409400575064e-07,
-         7.1180658041772527e-05,  1.2900664940831104e-05,  6.7559365584194971e-06,
-        -7.0548578679769132e-05,  1.4100360605950567e-06, -1.2786107920854779e-05,
-        -6.6959443050874898e-06, -1.3975150370740391e-06,
-         1.2807110995553272e-04,  2.0058649867687919e-05,  1.3810778814974065e-05,
-        -1.2693384728195296e-04,  2.7419450947357848e-06, -1.9880530432439409e-05,
-        -1.3688140046208898e-05, -2.7175968103308825e-06,
-         2.0858381754799334e-04,  2.6012564754977512e-05,  2.6550477975637763e-05,
-        -2.0673160755237084e-04,  4.5938737655600021e-06, -2.5781574963835826e-05,
-        -2.6314711551985457e-05, -4.5530804815592547e-06,
-         2.9871110310366976e-04,  2.5205913165246253e-05,  4.5389429729346178e-05,
-        -2.9605856899303685e-04,  5.9426328345683972e-06, -2.4982086384903072e-05,
-        -4.4986374706053409e-05, -5.8898626625296713e-06,
-         3.6469434674854203e-04,  1.1237385446411157e-05,  6.5265128683803013e-05,
-        -3.6145588595932354e-04,  6.3539671552325690e-06, -1.1137598234281373e-05,
-        -6.4685578816824895e-05, -6.2975443626347055e-06,
-         3.5893595493224776e-04, -1.4493122690417841e-05,  7.7817247724840170e-05,
-        -3.5574862826746054e-04, -1.6084567762455801e-06,  1.4364424754832286e-05,
-        -7.7126235901573401e-05,  1.5941737903768229e-06,
-         2.6694095601170693e-04, -3.6280004828175835e-05,  7.0464806864678920e-05,
-        -2.6457053862852633e-04, -7.8696688227856493e-06,  3.5957840873301803e-05,
-        -6.9839084212036697e-05,  7.7997867033233192e-06,
-         1.3743518008194365e-04, -3.5616161618941028e-05,  4.3245713680199841e-05,
-        -1.3621476510780793e-04, -1.0173131963280475e-05,  3.5299892546240166e-05,
-        -4.2861694708412319e-05,  1.0082795249096795e-05,
-         4.4281012350574053e-05, -1.7888520118666143e-05,  1.6654315330488873e-05,
-        -4.3887799997592024e-05, -6.9220705758281906e-06,  1.7729671286766401e-05,
-        -1.6506426152469179e-05,  6.8606030638146820e-06,
-         5.1438549738468361e-05,  2.9665824357334224e-05, -1.7900189835034524e-05,
-        -5.0981778944329460e-05, -1.3973723052800237e-05, -2.9402393871455844e-05,
-         1.7741237376853713e-05,  1.3849637350377501e-05,
-         4.6254048415618595e-04,  2.5918239859045285e-04, -1.3487188316997178e-04,
-        -4.5843315637685304e-04, -6.6255494613212145e-05, -2.5688087666510880e-04,
-         1.3367423009662933e-04,  6.5667150364697886e-05,
-         2.8294587601195142e-03,  1.2375254640891553e-03, -5.5518378989416852e-04,
-        -2.8043333603674971e-03, -1.6372300936094285e-04, -1.2265363228347245e-03,
-         5.5025379591314930e-04,  1.6226916026556920e-04,
-         9.1957619553724914e-03,  2.1739429633878338e-03, -7.9765225550990928e-04,
-        -9.1141042198332155e-03,  1.2436740398928127e-04, -2.1546384989570115e-03,
-         7.9056915818215777e-04, -1.2326302997069018e-04,
-         1.2500828315738250e-02, -7.8508011247857622e-04,  3.9877045177863924e-04,
-        -1.2389821817572859e-02,  4.5450998846944439e-04,  7.7810865491877395e-04,
-        -3.9522939751361548e-04, -4.5047397094109647e-04,
-         5.4790816862939707e-03, -2.4387569363537088e-03,  8.7033830325430211e-04,
-        -5.4304278166626358e-03, -1.8988685124215858e-04,  2.4171009420032898e-03,
-        -8.6260975880722460e-04,  1.8820066902513577e-04,
-         5.7215777750936180e-04, -4.7524252007978134e-04,  1.6913878684932202e-04,
-        -5.6707705568235720e-04, -1.2685880911775257e-04,  4.7102239909252349e-04,
-        -1.6763684602125322e-04,  1.2573231159247535e-04,
-         3.7427031371474126e-04,  3.3208117201649346e-04, -1.1114484687922794e-04,
-        -3.7094681899556086e-04, -9.6463580458111862e-05, -3.2913231398235817e-04,
-         1.1015788826100110e-04,  9.5606990478896647e-05,
-         5.3016792692569745e-03,  2.6754726903120800e-03, -7.3909622093528999e-04,
-        -5.2546007209230746e-03, -1.3556652552430490e-04, -2.6517146762999374e-03,
-         7.3253309717892176e-04,  1.3436270407449278e-04,
-         9.1961936544017395e-03, -1.7368826364828002e-03,  2.6809009052306064e-04,
-        -9.1145320854046884e-03,  4.6206186478473183e-04,  1.7214592377822928e-03,
-        -2.6570946890422425e-04, -4.5795878711259467e-04,
-         1.4411213884148821e-03, -1.2810931792856962e-03,  2.9718607020727523e-04,
-        -1.4283243293145838e-03, -2.1624336633437261e-04,  1.2697171597080945e-03,
-        -2.9454707828417920e-04,  2.1432314007080162e-04,
-         2.5492665841420081e-04,  2.4888323947485508e-04, -6.6278567407695297e-05,
-        -2.5266292716977288e-04, -7.1894578026316508e-05, -2.4667317337616465e-04,
-         6.5690018274348292e-05,  7.1256159103809388e-05,
-         3.4578494082033308e-03,  1.1303046461231621e-03, -2.4223248931282091e-04,
-        -3.4271439425899294e-03,  1.3900706598020271e-04, -1.1202676183793090e-03,
-         2.4008148141947591e-04, -1.3777269276708681e-04,
-         1.5781234722698919e-03, -1.2618335200808000e-03,  1.9187865723672629e-04,
-        -1.5641098440602522e-03, -8.2967902797388205e-05,  1.2506285249561542e-03,
-        -1.9017478791906594e-04,  8.2231153510297416e-05,
-         9.6977901902638649e-05,  8.6316756686137649e-05, -1.9677860154673218e-05,
-        -9.6116744784267082e-05, -3.0120448337275501e-05, -8.5550269806171524e-05,
-         1.9503122105962595e-05,  2.9852980821632315e-05,
-         1.1828731451272050e-03,  1.7396447751082442e-04, -4.5145997322417246e-05,
-        -1.1723693127172242e-03,  8.1902648560112776e-05, -1.7241968488061619e-04,
-         4.4745103962203978e-05, -8.1175358657596279e-05,
-         1.8720681143410243e-04, -2.0805519933339648e-04,  3.3414378701706986e-05,
-        -1.8554442778678481e-04, -3.2611926466637799e-05,  2.0620768343126807e-04,
-        -3.3117661310317896e-05,  3.2322334796065803e-05,
-         1.9535178824326644e-04,  1.5650334125842896e-04, -2.3209649131201253e-05,
-        -1.9361707776044740e-04, -8.6672787668020905e-06, -1.5511360232069719e-04,
-         2.3003549038581116e-05,  8.5903139257351561e-06,
-         1.6951067600112064e-04, -1.5119863365618911e-04,  1.3863877085521073e-05,
-        -1.6800543282288719e-04, -4.5044095319893205e-06,  1.4985600015818046e-04,
-        -1.3740766807754799e-05,  4.4644106842474151e-06,
-         3.6276567298503912e-05,  3.6027257115504254e-05, -5.2295393006259687e-06,
-        -3.5954433868657644e-05, -3.9956008741888273e-06, -3.5707337542985901e-05,
-         5.1831013502663178e-06,  3.9601202124352467e-06,
-         5.1575023302046870e-05, -4.4579128212970339e-05,  2.9869584382339701e-06,
-        -5.1117040632022451e-05, -3.2845211577127062e-09,  4.4183268611574342e-05,
-        -2.9604344521412661e-06,  3.2553548350773803e-09,
-         1.2401275268881665e-05,  1.1336295347525180e-05, -1.3473909962905102e-06,
-        -1.2291152794945234e-05, -6.9063884391199019e-07, -1.1235629822256499e-05,
-         1.3354262566444594e-06,  6.8450601834049220e-07,
-        // idx[1] = 10;
-         3.9161987831707695e-05,  8.5585033279271904e-06, -3.0940904155168843e-06,
-        -3.8814232065402164e-05, -6.2790787320485707e-07, -8.4825044052978823e-06,
-         3.0666151048127765e-06,  6.2233209435129094e-07,
-         8.2966973231524862e-05,  1.7351396003363992e-05, -5.8734092978937982e-06,
-        -8.2230232198915169e-05, -9.6285893253993122e-07, -1.7197316796773389e-05,
-         5.8212538261135436e-06,  9.5430881124964793e-07,
-         1.6948528988022327e-04,  3.3617119358933897e-05, -9.1922219423833112e-06,
-        -1.6798027212900247e-04, -8.7142547168146892e-07, -3.3318601644412122e-05,
-         9.1105956419166347e-06,  8.6368727325331598e-07,
-         3.3130814623591096e-04,  6.1194737241075030e-05, -1.1197518621951395e-05,
-        -3.2836615261769482e-04, -4.4059942666451672e-07, -6.0651332170970138e-05,
-         1.1098085424488793e-05,  4.3668693397105754e-07,
-         6.0949868976399916e-04,  1.0001588819084044e-04, -9.8223350700817221e-06,
-        -6.0408638319692828e-04,  3.3693722410867784e-06, -9.9127753962567809e-05,
-         9.7351134082527874e-06, -3.3394524466498374e-06,
-         1.0226479509198823e-03,  1.3603218361846981e-04,  2.0902400504249218e-05,
-        -1.0135669072465832e-03,  1.1408417045058132e-05, -1.3482422715671544e-04,
-        -2.0716788621210686e-05, -1.1307111084061294e-05,
-         1.4988806244302360e-03,  1.3106170460485647e-04,  8.5695676969146863e-05,
-        -1.4855706672751183e-03,  3.0453476425095055e-05, -1.2989788565587895e-04,
-        -8.4934705234475415e-05, -3.0183051642870378e-05,
-         1.8030298257953226e-03,  3.5581460837069158e-05,  1.8651702121554774e-04,
-        -1.7870190445899432e-03,  3.0633437103590942e-05, -3.5265499904931722e-05,
-        -1.8486076285806655e-04, -3.0361414282882376e-05,
-         1.6413216149696490e-03, -1.2558118114409131e-04,  2.6036761791834394e-04,
-        -1.6267467915868207e-03,  5.4223079993272169e-06,  1.2446602886760324e-04,
-        -2.5805557132664797e-04, -5.3741582761426463e-06,
-         1.0189032686435122e-03, -2.1096043183989262e-04,  2.2864831174272861e-04,
-        -1.0098554774920258e-03, -2.7657765772399670e-05,  2.0908711767234067e-04,
-        -2.2661793041463409e-04,  2.7412166709047420e-05,
-         3.7915828230823104e-04, -1.4271127978161287e-04,  1.1053775807032913e-04,
-        -3.7579138276314626e-04, -3.4225960821842870e-05,  1.4144401340396710e-04,
-        -1.0955619035909259e-04,  3.3922036636883500e-05,
-         7.4312889120419612e-05, -3.9559856706301425e-05,  2.5345644730922928e-05,
-        -7.3652995761239122e-05, -1.7079041586904331e-05,  3.9208567891674429e-05,
-        -2.5120577143858990e-05,  1.6927380868854436e-05,
-         1.6452199128976365e-04,  1.1354492403363452e-04, -5.6206288820240358e-05,
-        -1.6306104728965439e-04, -3.6099553950468539e-05, -1.1253665289486835e-04,
-         5.5707180830016014e-05,  3.5778992387013618e-05,
-         1.7045525792129491e-03,  9.4638345870692170e-04, -4.0697719285162913e-04,
-        -1.6894162692038758e-03, -1.8078271052518686e-04, -9.3797963849442858e-04,
-         4.0336326328867662e-04,  1.7917737245339021e-04,
-         8.0791678878996270e-03,  2.6080011965470560e-03, -9.4517642723761621e-04,
-        -8.0074254311060314e-03, -2.5821417318396076e-05, -2.5848423247725079e-03,
-         9.3678332538179568e-04,  2.5592124903382838e-05,
-         1.3356481058149027e-02, -4.3293862331198071e-04,  1.8456831679738910e-04,
-        -1.3237876422309745e-02,  5.5117088081251008e-04,  4.2909415802691434e-04,
-        -1.8292936280150354e-04, -5.4627652118893928e-04,
-         5.8131600430988816e-03, -2.8057188210851179e-03,  8.7511944457940491e-04,
-        -5.7615395805694532e-03, -1.9564030185418527e-04,  2.7808042303636956e-03,
-        -8.6734844392524053e-04,  1.9390302939028701e-04,
-         4.7634326079316506e-04, -4.2920915428436507e-04,  1.4088268702260373e-04,
-        -4.7211336530385869e-04, -1.1855725319570570e-04,  4.2539780642850724e-04,
-        -1.3963165842325711e-04,  1.1750447291771449e-04,
-         6.0905145791109738e-04,  5.4222206411941179e-04, -1.6846528502594774e-04,
-        -6.0364312273220987e-04, -1.3353062399755835e-04, -5.3740716937438697e-04,
-         1.6696932484788329e-04,  1.3234488121368636e-04,
-         6.4242974589046806e-03,  2.4764802964899451e-03, -6.3518193397605162e-04,
-        -6.3672501380333101e-03,  8.6162573411439783e-05, -2.4544893212884973e-03,
-         6.2954156196167615e-04, -8.5397455668379408e-05,
-         6.1192473190725665e-03, -2.6624998539887439e-03,  4.5719660344097069e-04,
-        -6.0649088225232604e-03,  1.3024981958765076e-04,  2.6388570378735065e-03,
-        -4.5313672895591774e-04, -1.2909321012194870e-04,
-         3.6469519543160190e-04, -3.8363095857578216e-04,  9.4090664425710294e-05,
-        -3.6145672710613595e-04, -9.7469050278121223e-05,  3.8022434197216746e-04,
-        -9.3255145778133679e-05,  9.6603531795857238e-05,
-         9.1178047998913031e-04,  7.8751323767825392e-04, -1.7362275060952033e-04,
-        -9.0368393185465785e-04, -1.1501287471403601e-04, -7.8052017413353706e-04,
-         1.7208099249076104e-04,  1.1399156827389669e-04,
-         3.0428994134042461e-03, -6.0542157405543088e-04,  2.7297328115299833e-05,
-        -3.0158786752883344e-03,  2.0376965733455402e-04,  6.0004547199625242e-04,
-        -2.7054929713624570e-05, -2.0196019675148278e-04,
-         2.4486683302324581e-04, -2.7365088383468937e-04,  5.4183415554651385e-05,
-        -2.4269243233840965e-04, -5.7765593385112273e-05,  2.7122088275259229e-04,
-        -5.3702270540301433e-05,  5.7252638877285439e-05,
-         4.8684120652023891e-04,  3.9028286351598619e-04, -6.7232236617642468e-05,
-        -4.8251808999280144e-04, -3.0667260128909864e-05, -3.8681717845267502e-04,
-         6.6635218967111602e-05,  3.0394936962056052e-05,
-         6.3412598830576885e-04, -4.3372366375867428e-04,  3.8776407472195745e-05,
-        -6.2849499301653115e-04,  9.5143346917004076e-06,  4.2987222736827919e-04,
-        -3.8432075633040440e-05, -9.4298480521095317e-06,
-         3.4938222906600265e-05,  3.1273776945169202e-05, -6.0324138429606134e-06,
-        -3.4627973883173486e-05, -1.0006175581767381e-05, -3.0996067950580566e-05,
-         5.9788464217243402e-06,  9.9173214288020404e-06,
-         2.4392083227262556e-04, -5.6676719861446003e-05, -1.1626687511546724e-06,
-        -2.4175483200958035e-04,  1.9445449116177598e-05,  5.6173434475836851e-05,
-         1.1523443323775968e-06, -1.9272774861550602e-05,
-         1.0411319188242268e-05, -3.0681569078749403e-06,  5.5818318185156826e-07,
-        -1.0318867387835258e-05, -3.5693133209550033e-06,  3.0409118849402331e-06,
-        -5.5322655347565932e-07,  3.5376180634403095e-06,
-         6.2185931257129870e-05, -1.0179624868692800e-05, -8.9508031605233602e-07,
-        -6.1633724452136231e-05,  5.2188375294746095e-06,  1.0089230497954324e-05,
-         8.8713206422836305e-07, -5.1724946101088791e-06,
-         3.4821562995004312e-06,  1.0893657152118253e-06, -1.5562699790180428e-07,
-        -3.4512349903592222e-06, -1.0573421757721680e-06, -1.0796922223669664e-06,
-         1.5424504083298160e-07,  1.0479530497614316e-06,
-        // idx[1] = 13;
-         7.6939600011633745e-06,  1.8061169092499393e-06, -1.7409386096072833e-06,
-        -7.6256381639873142e-06, -3.8744241924183407e-07, -1.7900787149551884e-06,
-         1.7254791941435799e-06,  3.8400195712888607e-07,
-         1.7708033426125268e-05,  4.1983811964132660e-06, -3.8745042608883230e-06,
-        -1.7550787303677916e-05, -8.9714935127936357e-07, -4.1610998593045459e-06,
-         3.8400989287563202e-06,  8.8918272656446436e-07,
-         4.1224027239434575e-05,  9.9239799414819331e-06, -8.9605036911705433e-06,
-        -4.0857960704598385e-05, -2.1501854097138079e-06, -9.8358556801655410e-06,
-         8.8809350328839017e-06,  2.1310919107303748e-06,
-         9.7120871429426495e-05,  2.3660577068010910e-05, -1.9999449126191993e-05,
-        -9.6258444751461542e-05, -4.1887526472941376e-06, -2.3450472766235517e-05,
-         1.9821855389468108e-05,  4.1515568110413017e-06,
-         2.2966717127649675e-04,  5.5667830351288630e-05, -3.9586034209482710e-05,
-        -2.2762774254561342e-04, -7.9335419238213832e-06, -5.5173503835342345e-05,
-         3.9234512940422678e-05,  7.8630926156020864e-06,
-         5.3200292659768048e-04,  1.2461168529569132e-04, -7.7661558932109947e-05,
-        -5.2727877709304340e-04, -1.3162232392700854e-05, -1.2350514207585148e-04,
-         7.6971929614645792e-05,  1.3045352671689596e-05,
-         1.1666581574647169e-03,  2.4674867349924984e-04, -1.2191453257652898e-04,
-        -1.1562983130331923e-03, -1.1089595832661965e-05, -2.4455756220003919e-04,
-         1.2083193988787077e-04,  1.0991120982167166e-05,
-         2.2887686678893923e-03,  3.9334003412439531e-04, -1.3148940639503572e-04,
-        -2.2684445590770812e-03,  1.6659921237230303e-05, -3.8984720159573514e-04,
-         1.3032178948349212e-04, -1.6511982279143148e-05,
-         3.7173943219990105e-03,  3.9400146321998456e-04, -3.1956132370684377e-06,
-        -3.6843841153501047e-03,  7.3337556977308329e-05, -3.9050275724631495e-04,
-         3.1672364106713046e-06, -7.2686324500672754e-05,
-         4.5199940871419554e-03,  2.1470803254982653e-05,  2.8930333733463666e-04,
-        -4.4798568496190452e-03,  9.9813558392372950e-05, -2.1280143994497898e-05,
-        -2.8673434353886968e-04, -9.8927220838835293e-05,
-         3.6305853350697154e-03, -5.0640172967673838e-04,  5.0404713216872657e-04,
-        -3.5983459862715781e-03,  1.2471040562830394e-05,  5.0190491704508729e-04,
-        -4.9957122820147365e-04, -1.2360298577867939e-05,
-         1.6531830617114835e-03, -5.4719482372872844e-04,  3.7015196128372313e-04,
-        -1.6385029094950184e-03, -8.0981230730739408e-05,  5.4233577121939294e-04,
-        -3.6686503725170299e-04,  8.0262122955358892e-05,
-         3.5645930339666049e-04, -2.0018386894217195e-04,  1.1080594537964248e-04,
-        -3.5329396922766608e-04, -5.1667624794085499e-05,  1.9840624991411976e-04,
-        -1.0982199618349089e-04,  5.1208819829162221e-05,
-         8.1645729682003766e-05,  3.1518177127831518e-05, -1.4204895571968811e-05,
-        -8.0920721201505936e-05, -3.1610417461887078e-05, -3.1238297876381250e-05,
-         1.4078757073429143e-05,  3.1329719122596009e-05,
-         1.1112012333347322e-03,  7.2994071394047412e-04, -2.9209530026815726e-04,
-        -1.1013338425863719e-03, -1.6061672159759519e-04, -7.2345889045835620e-04,
-         2.8950151403300714e-04,  1.5919045612453774e-04,
-         7.2402254655031442e-03,  2.7989480758611107e-03, -9.5793435231419509e-04,
-        -7.1759327598876653e-03, -9.4784436742530046e-05, -2.7740936088929552e-03,
-         9.4942796095860336e-04,  9.3942757444357306e-05,
-         1.3241006243061248e-02, -4.8348417204651978e-04,  1.1607405154285738e-04,
-        -1.3123427015660945e-02,  6.0299863597532274e-04,  4.7919086575499243e-04,
-        -1.1504332192525146e-04, -5.9764404944013681e-04,
-         5.0513947154027959e-03, -2.8225427733082581e-03,  7.8810546751073931e-04,
-        -5.0065386767431759e-03, -2.3600245213967414e-04,  2.7974787870448416e-03,
-        -7.8110714500572343e-04,  2.3390676654918446e-04,
-         2.8180957439635708e-04, -2.6245954825184062e-04,  7.9675931947129452e-05,
-        -2.7930712470157682e-04, -8.6112162611900079e-05,  2.6012892546224296e-04,
-        -7.8968415135433089e-05,  8.5347492513282593e-05,
-         1.1583383425450180e-03,  9.6723264576604258e-04, -2.6977156771818526e-04,
-        -1.1480523774994261e-03, -1.8655819799419011e-04, -9.5864368620225443e-04,
-         2.6737601469716817e-04,  1.8490157398973845e-04,
-         6.9931044556163944e-03,  1.2000797468667162e-03, -3.3704778425109526e-04,
-        -6.9310061676217134e-03,  3.5590508141603505e-04, -1.1894231210132782e-03,
-         3.3405482304091577e-04, -3.5274466870022149e-04,
-         2.8733758677926486e-03, -2.0671103848013202e-03,  3.8129908297979793e-04,
-        -2.8478604871362292e-03, -1.4871125794988407e-04,  2.0487545863420117e-03,
-        -3.7791317327156090e-04,  1.4739071217756880e-04,
-         1.0322441124946509e-04,  1.8476743202895893e-05, -4.8168812615395016e-06,
-        -1.0230778555646509e-04, -4.0962290464150215e-05, -1.8312670990347184e-05,
-         4.7741076862677817e-06,  4.0598548133929244e-05,
-         1.9582591910971407e-03,  9.7865979301640363e-04, -1.8723018386833398e-04,
-        -1.9408699837731578e-03,  2.3128246186372299e-05, -9.6996936116868003e-04,
-         1.8556759267540323e-04, -2.2922868946319787e-05,
-         1.2887036948865910e-03, -9.7941769109876026e-04,  1.2664939140064258e-04,
-        -1.2772600944523653e-03, -3.3426030714678910e-05,  9.7072052916803990e-04,
-        -1.2552475349033199e-04,  3.3129209854213705e-05,
-         6.9313334777440286e-05,  5.9715287673186067e-05, -1.2957096051837794e-05,
-        -6.8697837117967416e-05, -2.1501206316806118e-05, -5.9185020013786713e-05,
-         1.2842037927465642e-05,  2.1310277079216685e-05,
-         7.4156655404620110e-04,  3.4961769651018976e-05, -2.0021392848953567e-05,
-        -7.3498149390121789e-04,  5.6888820265120965e-05, -3.4651311534116488e-05,
-         1.9843604253476427e-05, -5.6383651442472562e-05,
-         7.3131479750304169e-05, -8.5125203228748116e-05,  1.4329502961988946e-05,
-        -7.2482077225311949e-05, -1.6767541211874010e-05,  8.4369297261769594e-05,
-        -1.4202257958371192e-05,  1.6618646595792397e-05,
-         1.6327041844856348e-04,  9.2190327694195275e-05, -1.2311099334812739e-05,
-        -1.6182058832945405e-04,  3.8034733974350099e-06, -9.1371683906473747e-05,
-         1.2201777616986781e-05, -3.7696988144993334e-06,
-         5.1551691384217362e-05, -5.7564660526755267e-05,  7.0153713767535825e-06,
-        -5.1093915900023203e-05, -6.4107510814715360e-06,  5.7053490288931122e-05,
-        -6.9530753600262190e-06,  6.3538240515027896e-06,
-         4.0328806418053032e-05,  2.5609342610977432e-05, -2.9607290538320635e-06,
-        -3.9970689382718498e-05,  7.0182568367559844e-07, -2.5381933404822401e-05,
-         2.9344379828740971e-06, -6.9559351973416766e-07,
-         1.1170036525578136e-05, -1.3138092309676044e-05,  1.5550589860992071e-06,
-        -1.1070847367246694e-05, -1.6709719218995304e-06,  1.3021426950946600e-05,
-        -1.5412501689450531e-06,  1.6561338058245150e-06,
-      };
-  
-      int nvals0 = sizeof(f0m)/sizeof(f0m[0]);
-      int nvals1 = sizeof(f1m)/sizeof(f1m[0]);
-      for (int i=0; i<nvals0; i++)
-        f0[i] = f0m[i];
-      for (int i=0; i<nvals1; i++)
-        f1[i] = f1m[i];
-    }
-    else {
-      // Upper boundary.
-      const double f0m[] =
-      {
-        // idx[0] = 4;
-         5.2735603406759081e-06,  1.5789778675299249e-06,  1.9989826780663522e-06,
-         5.2267314864994754e-06,  5.1808733150371001e-07,  1.5649566523489684e-06,
-         1.9812318489708070e-06,  5.1348675152920770e-07,
-         1.6794598764719933e-05,  4.7243461185578165e-06,  5.4058549896011972e-06,
-         1.6645463879424589e-05,  1.3229289098012843e-06,  4.6823942490099290e-06,
-         5.3578513680147745e-06,  1.3111813918057051e-06,
-         4.4351391469818912e-05,  1.1650043122384951e-05,  1.1710592695890722e-05,
-         4.3957554155084436e-05,  2.6752574970649754e-06,  1.1546591538391625e-05,
-         1.1606603435837015e-05,  2.6515013939541096e-06,
-         9.7120871429426359e-05,  2.3660577068010880e-05,  1.9999449126189980e-05,
-         9.6258444751461434e-05,  4.1887526472932372e-06,  2.3450472766235483e-05,
-         1.9821855389466126e-05,  4.1515568110403996e-06,
-         1.7634549859606911e-04,  3.9539852198925748e-05,  2.6084796724876194e-05,
-         1.7477956266190908e-04,  4.8370620921000345e-06,  3.9188741022952382e-05,
-         2.5853165518795303e-05,  4.7941093124368999e-06,
-         2.6547493073777355e-04,  5.4303954632757974e-05,  2.4003510429954116e-05,
-         2.6311753155848884e-04,  3.5659721755435086e-06,  5.3821739239660735e-05,
-         2.3790360903442251e-05,  3.5343065871709461e-06,
-         3.3130814623591058e-04,  6.1194737241074962e-05,  1.1197518621945012e-05,
-         3.2836615261769449e-04,  4.4059942666224667e-07,  6.0651332170970071e-05,
-         1.1098085424482478e-05,  4.3668693396879427e-07,
-         3.4269905278866620e-04,  5.6458355498447337e-05, -7.3950701740777095e-06,
-         3.3965590870142407e-04, -2.9844920494099456e-06,  5.5957009173406704e-05,
-        -7.3294024580689704e-06, -2.9579899646808611e-06,
-         2.9374366736149800e-04,  4.2514292127503821e-05, -2.2141578694179419e-05,
-         2.9113524373960021e-04, -4.8573878417806414e-06,  4.2136768128945003e-05,
-        -2.1944962993794169e-05, -4.8142545708542361e-06,
-         2.0858381754799318e-04,  2.6012564754977512e-05, -2.6550477975641544e-05,
-         2.0673160755237065e-04, -4.5938737655610049e-06,  2.5781574963835798e-05,
-        -2.6314711551989231e-05, -4.5530804815602338e-06,
-         1.2266163264877528e-04,  1.2843394764617339e-05, -2.1715606284304565e-05,
-         1.2157240576270986e-04, -3.0737503418031502e-06,  1.2729346299878326e-05,
-        -2.1522773189706808e-05, -3.0464556495587460e-06,
-         5.9715709406034303e-05,  5.0593586542458466e-06, -1.3398359967596715e-05,
-         5.9185438001676212e-05, -1.5246943425721614e-06,  5.0144318963554475e-06,
-        -1.3279383449913500e-05, -1.5111551613701918e-06,
-         2.4056337321823497e-05,  1.5575127200312380e-06, -6.4725989939129826e-06,
-         2.3842718696134580e-05, -5.6131534500858648e-07,  1.5436821138880390e-06,
-        -6.4151227587231497e-06, -5.5633090323863634e-07,
-         8.0151330159023820e-06,  3.5840433095651795e-07, -2.4919021860715822e-06,
-         7.9439591843807530e-06, -1.4691992411679513e-07,  3.5522172507617869e-07,
-        -2.4697742655482486e-06, -1.4561528526607401e-07,
-         2.2073750885337045e-06,  5.4194161567241385e-08, -7.7188487204187968e-07,
-         2.1877737491242860e-06, -2.2856919929925578e-08,  5.3712921129036765e-08,
-        -7.6503058731225592e-07, -2.2653952048423441e-08,
-         1.4147068739149328e-06,  3.9678563980892764e-07,  5.3677388121511292e-07,
-         1.4021443738919469e-06,  2.1663045016554326e-07,  3.9326221053808074e-07,
-         5.3200736596065414e-07,  2.1470678662409674e-07,
-        // idx[0] = 12;
-         7.4385809600035673e-03, -4.2620301983017916e-04, -4.9868993294229142e-04,
-         7.3725268711996930e-03, -1.7454031661270062e-04, -4.2241836624211913e-04,
-        -4.9426160053678498e-04, -1.7299041057075798e-04,
-         5.3918935380395478e-03, -8.1066940565628881e-04, -6.4417804850088346e-04,
-         5.3440138931855462e-03, -4.8296611836812415e-05, -8.0347071692792309e-04,
-        -6.3845779160646109e-04, -4.7867741235772842e-05,
-         3.2662572681362526e-03, -7.8998871116982251e-04, -5.6119422549588910e-04,
-         3.2372531275876946e-03,  5.0252394101218381e-05, -7.8297366559026266e-04,
-        -5.5621085925890883e-04,  4.9806156287794315e-05,
-         1.6531830617114878e-03, -5.4719482372873017e-04, -3.7015196128374682e-04,
-         1.6385029094950227e-03,  8.0981230730795285e-05, -5.4233577121939500e-04,
-        -3.6686503725172652e-04,  8.0262122955414322e-05,
-         6.9889469196789285e-04, -2.9144378275440866e-04, -1.9257347432051673e-04,
-         6.9268855503182584e-04,  6.3595836624062553e-05, -2.8885578195010121e-04,
-        -1.9086343507480132e-04,  6.3031109956098697e-05,
-         2.4668363462349003e-04, -1.2316540125222183e-04, -8.0544516023116727e-05,
-         2.4449310086503576e-04,  3.4617348824041223e-05, -1.2207170093550508e-04,
-        -7.9829286244391116e-05,  3.4309949140462771e-05,
-         7.4312889120419911e-05, -3.9559856706301649e-05, -2.5345644730926249e-05,
-         7.3652995761239434e-05,  1.7079041586906184e-05, -3.9208567891674639e-05,
-        -2.5120577143862260e-05,  1.6927380868856262e-05,
-         4.9288640555562483e-05,  1.9197719093399832e-05,  9.3898074536981298e-06,
-         4.8850960807531919e-05,  1.7734142076997052e-05,  1.9027244664386345e-05,
-         9.3064266074409205e-06,  1.7576664111520431e-05,
-         1.5102266511218419e-04,  9.5873653213552322e-05,  5.1458764419249045e-05,
-         1.4968159420277876e-04,  3.0014361827435697e-05,  9.5022301747812988e-05,
-         5.1001814120131087e-05,  2.9747836352724691e-05,
-         4.6254048415618476e-04,  2.5918239859045258e-04,  1.3487188316997143e-04,
-         4.5843315637685180e-04,  6.6255494613228503e-05,  2.5688087666510847e-04,
-         1.3367423009662892e-04,  6.5667150364714081e-05,
-         1.1813969572080760e-03,  5.6871985765870109e-04,  2.8575381884705361e-04,
-         1.1709062332455834e-03,  1.1130086733197859e-04,  5.6366966432420550e-04,
-         2.8321634453203851e-04,  1.1031252326283079e-04,
-         2.5178444512609440e-03,  1.0028214075435281e-03,  4.8235931958416520e-04,
-         2.4954861652017901e-03,  1.3193983394586925e-04,  9.9391642221575180e-04,
-         4.7807600190536245e-04,  1.3076821726856367e-04,
-         4.4799350811575659e-03,  1.3955105208072922e-03,  6.3033616055554575e-04,
-         4.4401535648606405e-03,  8.3328432799491150e-05,  1.3831184830834593e-03,
-         6.2473881867683195e-04,  8.2588482030706125e-05,
-         6.6575398175438951e-03,  1.4760068941306469e-03,  5.9457869281011257e-04,
-         6.5984213205230388e-03, -4.2899447103834747e-05,  1.4629000541319611e-03,
-         5.8929887479281244e-04, -4.2518502955499150e-05,
-         8.2661626046304833e-03,  1.0720660909669321e-03,  3.0982027320798264e-04,
-         8.1927596475759885e-03, -1.8255117221422333e-04,  1.0625462175989991e-03,
-         3.0706909042866552e-04, -1.8093013032390482e-04,
-         8.5771895799448498e-03,  3.1197886695786821e-04, -1.2589091675383921e-04,
-         8.5010247246790852e-03, -2.3881143669264430e-04,  3.0920851601408308e-04,
-        -1.2477301404637767e-04, -2.3669080751195825e-04,
-        // idx[0] = 19;
-         3.5176447536171117e-03, -2.3790827021664082e-03, -6.1388697056457772e-04,
-         3.4864083094370652e-03,  2.8116612144429246e-04, -2.3579566109232482e-03,
-        -6.0843569636493593e-04,  2.7866938556759982e-04,
-         1.7743608964103485e-03, -1.4228383602125439e-03, -3.9110700695119658e-04,
-         1.7586046933318578e-03,  2.5501449371076240e-04, -1.4102036531488738e-03,
-        -3.8763400355069862e-04,  2.5274998249492469e-04,
-         7.5858237184659968e-04, -6.8983776721579621e-04, -2.0188206214675098e-04,
-         7.5184621240645497e-04,  1.6201786760810326e-04, -6.8371205515042432e-04,
-        -2.0008936327950031e-04,  1.6057916005455996e-04,
-         2.8180957439635491e-04, -2.6245954825183818e-04, -7.9675931947110248e-05,
-         2.7930712470157471e-04,  8.6112162611884019e-05, -2.6012892546224052e-04,
-        -7.8968415135414035e-05,  8.5347492513266669e-05,
-         1.3692552150240488e-04, -2.3628334870108142e-05, -6.7351766555160489e-06,
-         1.3570963226150422e-04,  5.5072031551524784e-05, -2.3418516876839040e-05,
-        -6.6753687486981578e-06,  5.4582995688061867e-05,
-         2.2538939529024113e-04,  1.9086017837583466e-04,  6.0622757673717606e-05,
-         2.2338795291675570e-04,  7.2883062312483610e-05,  1.8916535308061394e-04,
-         6.0084431742945773e-05,  7.2235865717303348e-05,
-         6.0905145791110009e-04,  5.4222206411941353e-04,  1.6846528502596943e-04,
-         6.0364312273221280e-04,  1.3353062399761872e-04,  5.3740716937438848e-04,
-         1.6696932484790475e-04,  1.3234488121374621e-04,
-         1.4749219675761675e-03,  1.1511708985332432e-03,  3.4089330270886968e-04,
-         1.4618247616508841e-03,  2.1626062462555974e-04,  1.1409485798989493e-03,
-         3.3786619355850205e-04,  2.1434024510954647e-04,
-         3.0306885085190582e-03,  1.9748354796544224e-03,  5.6082860635101636e-04,
-         3.0037762024011311e-03,  2.4639127781919706e-04,  1.9572990760248154e-03,
-         5.5584848678696909e-04,  2.4420334016911550e-04,
-         5.3016792692569901e-03,  2.6754726903120783e-03,  7.3909622093513787e-04,
-         5.2546007209230902e-03,  1.3556652552434143e-04,  2.6517146762999361e-03,
-         7.3253309717877138e-04,  1.3436270407452921e-04,
-         7.9236576295588831e-03,  2.7048082887694853e-03,  7.4744339840881547e-04,
-         7.8532960931948122e-03, -1.3680114431851166e-04,  2.6807897766548102e-03,
-         7.4080615228891281e-04, -1.3558635953847444e-04,
-         1.0147502273615196e-02,  1.6812950536897039e-03,  5.0484232418384592e-04,
-         1.0057393149318113e-02, -4.4927500173365929e-04,  1.6663652689123294e-03,
-         5.0035935896603140e-04, -4.4528547052852176e-04,
-         1.1157187397402474e-02, -1.8349902862188801e-04,  6.0616833960680126e-05,
-         1.1058112338448070e-02, -5.9620026364057234e-04, -1.8186956983167152e-04,
-         6.0078560632073659e-05, -5.9090604618550191e-04,
-         1.0538391888353600e-02, -2.0861147480127104e-03, -4.1035235387461852e-04,
-         1.0444811691083959e-02, -4.6474412137482361e-04, -2.0675901921113600e-03,
-        -4.0670845311324271e-04, -4.6061722544811013e-04,
-         8.5438428607558167e-03, -3.1770890503348258e-03, -7.1469750720547990e-04,
-         8.4679741220696093e-03, -1.4653149000122957e-04, -3.1488767174453918e-03,
-        -7.0835104235382441e-04, -1.4523030041881422e-04,
-         5.9328259833403407e-03, -3.1592831855465011e-03, -7.6447171990721248e-04,
-         5.8801428954679841e-03,  1.4953722986155545e-04, -3.1312289675153003e-03,
-        -7.5768326346016773e-04,  1.4820934951530792e-04,
-        // idx[0] = 28;
-         3.1225316368462653e-04, -2.6354343092504693e-04, -2.5533068601899983e-05,
-         3.0948037700471851e-04,  6.4354644170239486e-06, -2.6120318333164132e-04,
-        -2.5306336703714858e-05,  6.3783179343302755e-06,
-         2.2070902006211341e-04, -2.1925837439635602e-04, -2.6427797458292739e-05,
-         2.1874913909968421e-04,  1.7877051979852441e-05, -2.1731137506795673e-04,
-        -2.6193120429221325e-05,  1.7718304984238919e-05,
-         1.3604357772040071e-04, -1.5068140809657886e-04, -2.1787568445674219e-05,
-         1.3483552007980261e-04,  2.0478489031820037e-05, -1.4934336752606933e-04,
-        -2.1594096332018494e-05,  2.0296641453585649e-05,
-         7.3131479750304263e-05, -8.5125203228748197e-05, -1.4329502961952065e-05,
-         7.2482077225312057e-05,  1.6767541211912712e-05, -8.4369297261769675e-05,
-        -1.4202257958334635e-05,  1.6618646595830757e-05,
-         3.6725180241487518e-05, -3.6057780516486069e-05, -6.7954495238028766e-06,
-         3.6399063159472418e-05,  1.1694827060935900e-05, -3.5737589898260231e-05,
-        -6.7351063980479749e-06,  1.1590977798639422e-05,
-         2.4837446165027385e-05, -9.6145358765581644e-07, -1.9699547936173084e-07,
-         2.4616891346377475e-05,  9.0936978967432890e-06, -9.5291594573173095e-07,
-        -1.9524617301449969e-07,  9.0129464830453212e-06,
-         3.4938222906600408e-05,  3.1273776945169290e-05,  6.0324138429933910e-06,
-         3.4627973883173628e-05,  1.0006175581772412e-05,  3.0996067950580641e-05,
-         5.9788464217568256e-06,  9.9173214288070243e-06,
-         6.7058946442705397e-05,  7.0433021024861873e-05,  1.2563048496794633e-05,
-         6.6463467597044124e-05,  1.2699023524377309e-05,  6.9807580628297399e-05,
-         1.2451489487688373e-05,  1.2586257066350973e-05,
-         1.2172339077131295e-04,  1.1660274450623232e-04,  1.8887207777269423e-05,
-         1.2064249540877686e-04,  1.3462333943158600e-05,  1.1556732013136789e-04,
-         1.8719490667449008e-05,  1.3342789340959595e-05,
-         1.9535178824326663e-04,  1.5650334125842918e-04,  2.3209649131246132e-05,
-         1.9361707776044762e-04,  8.6672787667954396e-06,  1.5511360232069738e-04,
-         2.3003549038625602e-05,  8.5903139257285476e-06,
-         2.7796534980573806e-04,  1.6786465218620092e-04,  2.3905953966723439e-05,
-         2.7549703656169435e-04, -2.9974039875562224e-06,  1.6637402558656333e-04,
-         2.3693670734914863e-05, -2.9707872457018826e-06,
-         3.5577914498131474e-04,  1.3094475217078909e-04,  2.0440326610403722e-05,
-         3.5261985057240491e-04, -1.8525522986956615e-05,  1.2978197175140562e-04,
-         2.0258817911854427e-05, -1.8361017613270647e-05,
-         4.1504347649095046e-04,  4.2960315696147001e-05,  1.3312487632465493e-05,
-         4.1135791888244821e-04, -3.1477256709126155e-05,  4.2578831038885878e-05,
-         1.3194273655229314e-05, -3.1197740828187762e-05,
-         4.4457679107663076e-04, -7.5578664486840579e-05,  3.4115616361105143e-06,
-         4.4062897965993503e-04, -3.5399985354919482e-05, -7.4907531129210335e-05,
-         3.3812672027389913e-06, -3.5085635912618252e-05,
-         4.3680260689641108e-04, -1.8748123385802206e-04, -8.0091734113102738e-06,
-         4.3292382970209987e-04, -2.7606287551927432e-05, -1.8581641335839935e-04,
-        -7.9380525006687252e-06, -2.7361145611642716e-05,
-         3.9008280658611196e-04, -2.5603798505596852e-04, -1.8683093211797680e-05,
-         3.8661889801461854e-04, -1.1175426823779215e-05, -2.5376438530717394e-04,
-        -1.8517188625320945e-05, -1.1076189799969395e-05,
-      };
-  
-      const double f1m[] =
-      {
-        // idx[1] = 2;
-         1.0064242557051679e-06,  2.4638105513050012e-07,  3.0952299929100151e-07,
-         9.9748727733279151e-07,  7.1551685415696771e-08,  2.4419320825719352e-07,
-         3.0677445628368039e-07,  7.0916311356057116e-08,
-         2.4501722734192372e-06,  6.2869377552759965e-07,  7.5054342119427020e-07,
-         2.4284149116585134e-06,  2.0047632122023783e-07,  6.2311101791530323e-07,
-         7.4387864708462476e-07,  1.9869610523601224e-07,
-         6.2693514816208999e-06,  1.6983388600546720e-06,  2.0605121390263682e-06,
-         6.2136800704019623e-06,  5.9893969448756465e-07,  1.6832577274456009e-06,
-         2.0422149325370482e-06,  5.9362115107443639e-07,
-         1.6794598764719933e-05,  4.7243461185578165e-06,  5.4058549896011972e-06,
-         1.6645463879424589e-05,  1.3229289098012843e-06,  4.6823942490099290e-06,
-         5.3578513680147745e-06,  1.3111813918057051e-06,
-         4.6722524149225004e-05,  1.3757882849431861e-05,  1.2559267568821096e-05,
-         4.6307631338904288e-05,  3.6001849176655706e-06,  1.3635713793213210e-05,
-         1.2447742134095955e-05,  3.5682155224891871e-06,
-         1.3509589455886354e-04,  4.0376357161087206e-05,  3.4643122769977236e-05,
-         1.3389625227974990e-04,  8.2223573880571182e-06,  4.0017817878415452e-05,
-         3.4335494215526362e-05,  8.1493434183217232e-06,
-         3.8840901300543125e-04,  1.1420438032971131e-04,  8.3157991770278211e-05,
-         3.8495996760614943e-04,  2.2616417530061213e-05,  1.1319025326426001e-04,
-         8.2419554506144016e-05,  2.2415585293376721e-05,
-         1.0598521823626484e-03,  2.8756536278117851e-04,  1.7461178578371693e-04,
-         1.0504407676655194e-03,  3.4239520152090462e-05,  2.8501180208026012e-04,
-         1.7306124510043641e-04,  3.3935475561208271e-05,
-         2.5465331961989765e-03,  5.7389435441791746e-04,  2.7509217369229086e-04,
-         2.5239201560521818e-03,  1.6496079388288131e-05,  5.6879821190705530e-04,
-         2.7264937405509861e-04,  1.6349595334583635e-05,
-         4.8835866960519232e-03,  7.1615900951608373e-04,  2.0939718370369375e-04,
-         4.8402207810962460e-03, -6.7344077386474613e-05,  7.0979956662413596e-04,
-         2.0753775107238749e-04, -6.6746066597586618e-05,
-         6.5963664604376145e-03,  1.6275731066703455e-04, -2.2806276733301181e-04,
-         6.5377911786327313e-03, -1.6368482665102420e-04,  1.6131203690983743e-04,
-        -2.2603758559912031e-04, -1.6223131661549542e-04,
-         5.3918935380395478e-03, -8.1066940565628881e-04, -6.4417804850088346e-04,
-         5.3440138931855462e-03, -4.8296611836812415e-05, -8.0347071692792309e-04,
-        -6.3845779160646109e-04, -4.7867741235772842e-05,
-         2.2325143698531066e-03, -8.4647335003058420e-04, -4.7667889076579453e-04,
-         2.2126897953495669e-03,  1.1597626131718698e-04, -8.3895672473152899e-04,
-        -4.7244601490534796e-04,  1.1494640007007816e-04,
-         3.7918019032058645e-04, -2.4429110051544058e-04, -1.1791962244750706e-04,
-         3.7581309623385434e-04,  6.5545377999984785e-05, -2.4212181229579129e-04,
-        -1.1687250428683259e-04,  6.4963339538297809e-05,
-         1.3265773496585429e-04,  9.0192913254221100e-05,  3.6330610507766499e-05,
-         1.3147974337672313e-04,  4.2769662240897072e-05,  8.9392006369748384e-05,
-         3.6007997177928130e-05,  4.2389870573244011e-05,
-         2.0740722732800190e-03,  1.3049423409384143e-03,  4.7737679678530820e-04,
-         2.0556546537284495e-03,  2.3524506169704339e-04,  1.2933545424408577e-03,
-         4.7313772356726925e-04,  2.3315610168174477e-04,
-         1.0158496318663347e-02,  2.7739047335627711e-03,  8.7039930616657365e-04,
-         1.0068289568000181e-02, -2.0057911001830609e-04,  2.7492726497568079e-03,
-         8.6267022001781804e-04, -1.9879798127660263e-04,
-         1.0744903537459927e-02, -2.7332594355407298e-03, -6.8024602402668875e-04,
-         1.0649489530908321e-02, -3.3891226168725110e-04, -2.7089882791938406e-03,
-        -6.7420548598305674e-04, -3.3590274404529956e-04,
-         1.7743608964103485e-03, -1.4228383602125439e-03, -3.9110700695119658e-04,
-         1.7586046933318578e-03,  2.5501449371076240e-04, -1.4102036531488738e-03,
-        -3.8763400355069862e-04,  2.5274998249492469e-04,
-         1.8587668557072320e-04,  1.4266611485212182e-04,  4.2787284932814561e-05,
-         1.8422611334985533e-04,  6.5393262891317997e-05,  1.4139924953595248e-04,
-         4.2407336776865824e-05,  6.4812575201364270e-05,
-         3.7794409682195629e-03,  2.0869073873386228e-03,  4.9681034418490398e-04,
-         3.7458797916072352e-03,  8.9354392597548640e-05,  2.0683757928544161e-03,
-         4.9239870239866507e-04,  8.8560931719003469e-05,
-         5.3589500608310107e-03, -1.9322998876550560e-03, -2.6621995559220085e-04,
-         5.3113629517954333e-03, -2.1708287121334914e-04, -1.9151411971654085e-03,
-        -2.6385594064330117e-04, -2.1515519020402394e-04,
-         3.5447984105491342e-04, -3.8297317940784757e-04, -8.6790399124008177e-05,
-         3.5133208437576662e-04,  9.1077196943933081e-05, -3.7957240383813508e-04,
-        -8.6019706331675079e-05,  9.0268437680937836e-05,
-         7.7591183917630939e-04,  6.6057430431279971e-04,  1.3512321260020200e-04,
-         7.6902179525469223e-04,  8.3115590710258533e-05,  6.5470844979118492e-04,
-         1.3392332773875466e-04,  8.2377529964629514e-05,
-         1.9625514353073274e-03, -6.9400771096554106e-04, -5.0835475579179123e-05,
-         1.9451241131491104e-03, -1.1538337848761807e-04, -6.8784497008563667e-04,
-        -5.0384060042217249e-05, -1.1435878199937753e-04,
-         8.4095026418060529e-05, -8.6935345625212553e-05, -1.7840996781592987e-05,
-         8.3348268350513742e-05,  2.6621237831636578e-05, -8.6163365717888856e-05,
-        -1.7682569953667403e-05,  2.6384843065315550e-05,
-         5.0821419007155365e-04,  2.7840870285490151e-04,  4.2754573047174882e-05,
-         5.0370128291589108e-04, -9.1435198883331253e-06,  2.7593645266618531e-04,
-         4.2374915370527306e-05, -9.0623260587665063e-06,
-         2.2070902006211341e-04, -2.1925837439635602e-04, -2.6427797458292739e-05,
-         2.1874913909968421e-04,  1.7877051979852441e-05, -2.1731137506795673e-04,
-        -2.6193120429221325e-05,  1.7718304984238919e-05,
-         7.8376321342582138e-05,  7.3618252299111100e-05,  1.0968129522333047e-05,
-         7.7680344983929785e-05,  7.1081816882799169e-06,  7.2964527267267229e-05,
-         1.0870733284344096e-05,  7.0450615223509237e-06,
-         1.0129896530548440e-04, -8.5306127837966829e-05, -6.3059363521162601e-06,
-         1.0039943744042426e-04,  1.7577593965507822e-07, -8.4548615272865850e-05,
-        -6.2499400697562340e-06,  1.7421506136525714e-07,
-         1.9919275589572257e-05,  1.9647328326244563e-05,  2.6426654263499524e-06,
-         1.9742393788355451e-05,  1.9320906579101043e-06,  1.9472861398076579e-05,
-         2.6191987385919478e-06,  1.9149338253662459e-06,
-         2.2776817069048982e-05, -2.1810758063425291e-05, -1.5443168402192109e-06,
-         2.2574560495458119e-05,  4.7017697371218268e-07, -2.1617080027554231e-05,
-        -1.5306034125837987e-06,  4.6600183442928546e-07,
-        // idx[1] = 7;
-         3.9161987831707655e-05,  8.5585033279271802e-06,  3.0940904155156180e-06,
-         3.8814232065402117e-05,  6.2790787320463302e-07,  8.4825044052978738e-06,
-         3.0666151048115204e-06,  6.2233209435106859e-07,
-         8.2966973231524767e-05,  1.7351396003363978e-05,  5.8734092978907861e-06,
-         8.2230232198915074e-05,  9.6285893253930273e-07,  1.7197316796773362e-05,
-         5.8212538261105722e-06,  9.5430881124903129e-07,
-         1.6948528988022310e-04,  3.3617119358933856e-05,  9.1922219423802619e-06,
-         1.6798027212900225e-04,  8.7142547168074894e-07,  3.3318601644412088e-05,
-         9.1105956419135583e-06,  8.6368727325260448e-07,
-         3.3130814623591058e-04,  6.1194737241074962e-05,  1.1197518621945012e-05,
-         3.2836615261769449e-04,  4.4059942666224667e-07,  6.0651332170970071e-05,
-         1.1098085424482478e-05,  4.3668693396879427e-07,
-         6.0949868976399829e-04,  1.0001588819084109e-04,  9.8223350700890946e-06,
-         6.0408638319692741e-04, -3.3693722410864667e-06,  9.9127753962568473e-05,
-         9.7351134082600786e-06, -3.3394524466495121e-06,
-         1.0226479509198830e-03,  1.3603218361846954e-04, -2.0902400504305411e-05,
-         1.0135669072465837e-03, -1.1408417045065111e-05,  1.3482422715671509e-04,
-        -2.0716788621266325e-05, -1.1307111084068212e-05,
-         1.4988806244302360e-03,  1.3106170460485647e-04, -8.5695676969186599e-05,
-         1.4855706672751183e-03, -3.0453476425098579e-05,  1.2989788565587884e-04,
-        -8.4934705234514663e-05, -3.0183051642873811e-05,
-         1.8030298257953232e-03,  3.5581460837068996e-05, -1.8651702121551744e-04,
-         1.7870190445899432e-03, -3.0633437103584870e-05,  3.5265499904931559e-05,
-        -1.8486076285803674e-04, -3.0361414282876413e-05,
-         1.6413216149696493e-03, -1.2558118114409342e-04, -2.6036761791839430e-04,
-         1.6267467915868209e-03, -5.4223079993046918e-06, -1.2446602886760557e-04,
-        -2.5805557132669790e-04, -5.3741582761204354e-06,
-         1.0189032686435142e-03, -2.1096043183989230e-04, -2.2864831174279596e-04,
-         1.0098554774920273e-03,  2.7657765772379680e-05, -2.0908711767234027e-04,
-        -2.2661793041470085e-04,  2.7412166709027565e-05,
-         3.7915828230823055e-04, -1.4271127978161298e-04, -1.1053775807032425e-04,
-         3.7579138276314572e-04,  3.4225960821833308e-05, -1.4144401340396707e-04,
-        -1.0955619035908770e-04,  3.3922036636873959e-05,
-         7.4312889120419911e-05, -3.9559856706301649e-05, -2.5345644730926249e-05,
-         7.3652995761239434e-05,  1.7079041586906184e-05, -3.9208567891674639e-05,
-        -2.5120577143862260e-05,  1.6927380868856262e-05,
-         1.6452199128976321e-04,  1.1354492403363433e-04,  5.6206288820234808e-05,
-         1.6306104728965398e-04,  3.6099553950453624e-05,  1.1253665289486821e-04,
-         5.5707180830010552e-05,  3.5778992386998920e-05,
-         1.7045525792129461e-03,  9.4638345870692116e-04,  4.0697719285157964e-04,
-         1.6894162692038725e-03,  1.8078271052515243e-04,  9.3797963849442793e-04,
-         4.0336326328862745e-04,  1.7917737245335601e-04,
-         8.0791678878996687e-03,  2.6080011965470950e-03,  9.4517642723753457e-04,
-         8.0074254311060748e-03,  2.5821417318181404e-05,  2.5848423247725465e-03,
-         9.3678332538171393e-04,  2.5592124903170118e-05,
-         1.3356481058148951e-02, -4.3293862331202017e-04, -1.8456831679660113e-04,
-         1.3237876422309669e-02, -5.5117088081241728e-04, -4.2909415802695381e-04,
-        -1.8292936280072232e-04, -5.4627652118884712e-04,
-         5.8131600430988686e-03, -2.8057188210851105e-03, -8.7511944457968171e-04,
-         5.7615395805694384e-03,  1.9564030185384277e-04, -2.7808042303636878e-03,
-        -8.6734844392551505e-04,  1.9390302938994804e-04,
-         4.7634326079316609e-04, -4.2920915428436561e-04, -1.4088268702256988e-04,
-         4.7211336530385978e-04,  1.1855725319557678e-04, -4.2539780642850768e-04,
-        -1.3963165842322361e-04,  1.1750447291758676e-04,
-         6.0905145791110009e-04,  5.4222206411941353e-04,  1.6846528502596943e-04,
-         6.0364312273221280e-04,  1.3353062399761872e-04,  5.3740716937438848e-04,
-         1.6696932484790475e-04,  1.3234488121374621e-04,
-         6.4242974589046650e-03,  2.4764802964899277e-03,  6.3518193397627161e-04,
-         6.3672501380332945e-03, -8.6162573411864465e-05,  2.4544893212884809e-03,
-         6.2954156196189386e-04, -8.5397455668800133e-05,
-         6.1192473190725622e-03, -2.6624998539887487e-03, -4.5719660344076035e-04,
-         6.0649088225232552e-03, -1.3024981958776287e-04, -2.6388570378735108e-03,
-        -4.5313672895570958e-04, -1.2909321012205950e-04,
-         3.6469519543160179e-04, -3.8363095857578205e-04, -9.4090664425681766e-05,
-         3.6145672710613579e-04,  9.7469050278256532e-05, -3.8022434197216740e-04,
-        -9.3255145778105395e-05,  9.6603531795991395e-05,
-         9.1178047998913487e-04,  7.8751323767826042e-04,  1.7362275060939670e-04,
-         9.0368393185466219e-04,  1.1501287471411306e-04,  7.8052017413354356e-04,
-         1.7208099249063841e-04,  1.1399156827397299e-04,
-         3.0428994134042461e-03, -6.0542157405543478e-04, -2.7297328115239033e-05,
-         3.0158786752883348e-03, -2.0376965733478786e-04, -6.0004547199625686e-04,
-        -2.7054929713564356e-05, -2.0196019675171445e-04,
-         2.4486683302324668e-04, -2.7365088383469040e-04, -5.4183415554647035e-05,
-         2.4269243233841054e-04,  5.7765593385118677e-05, -2.7122088275259332e-04,
-        -5.3702270540297137e-05,  5.7252638877291795e-05,
-         4.8684120652024178e-04,  3.9028286351599020e-04,  6.7232236617606201e-05,
-         4.8251808999280420e-04,  3.0667260129115022e-05,  3.8681717845267898e-04,
-         6.6635218967075661e-05,  3.0394936962259377e-05,
-         6.3412598830576864e-04, -4.3372366375867385e-04, -3.8776407472139081e-05,
-         6.2849499301653093e-04, -9.5143346916887677e-06, -4.2987222736827886e-04,
-        -3.8432075632984299e-05, -9.4298480520979985e-06,
-         3.4938222906600408e-05,  3.1273776945169290e-05,  6.0324138429933910e-06,
-         3.4627973883173628e-05,  1.0006175581772412e-05,  3.0996067950580641e-05,
-         5.9788464217568256e-06,  9.9173214288070243e-06,
-         2.4392083227262588e-04, -5.6676719861445929e-05,  1.1626687511291100e-06,
-         2.4175483200958067e-04, -1.9445449116183467e-05, -5.6173434475836811e-05,
-         1.1523443323522607e-06, -1.9272774861556413e-05,
-         1.0411319188242222e-05, -3.0681569078749064e-06, -5.5818318185091001e-07,
-         1.0318867387835211e-05,  3.5693133209598589e-06, -3.0409118849401984e-06,
-        -5.5322655347500679e-07,  3.5376180634451215e-06,
-         6.2185931257129586e-05, -1.0179624868692354e-05,  8.9508031604239662e-07,
-         6.1633724452135960e-05, -5.2188375294793664e-06, -1.0089230497953875e-05,
-         8.8713206421851195e-07, -5.1724946101135919e-06,
-         3.4821562995004494e-06,  1.0893657152118484e-06,  1.5562699789901857e-07,
-         3.4512349903592412e-06,  1.0573421757814150e-06,  1.0796922223669888e-06,
-         1.5424504083022067e-07,  1.0479530497705965e-06,
-        // idx[1] = 10;
-         3.6490020128125022e-05,  7.3675063786135918e-06, -3.2021281911734263e-06,
-         3.6165991251789828e-05, -6.9414808136536902e-07,  7.3020834272183270e-06,
-        -3.1736935124304748e-06, -6.8798409400593995e-07,
-         7.1180658041772459e-05,  1.2900664940831099e-05, -6.7559365584218519e-06,
-         7.0548578679769091e-05, -1.4100360605954828e-06,  1.2786107920854769e-05,
-        -6.6959443050898310e-06, -1.3975150370744643e-06,
-         1.2807110995553264e-04,  2.0058649867687895e-05, -1.3810778814976504e-05,
-         1.2693384728195280e-04, -2.7419450947362422e-06,  1.9880530432439396e-05,
-        -1.3688140046211276e-05, -2.7175968103313399e-06,
-         2.0858381754799318e-04,  2.6012564754977512e-05, -2.6550477975641544e-05,
-         2.0673160755237065e-04, -4.5938737655610049e-06,  2.5781574963835798e-05,
-        -2.6314711551989231e-05, -4.5530804815602338e-06,
-         2.9871110310366873e-04,  2.5205913165246944e-05, -4.5389429729339090e-05,
-         2.9605856899303593e-04, -5.9426328345682074e-06,  2.4982086384903736e-05,
-        -4.4986374706046403e-05, -5.8898626625294748e-06,
-         3.6469434674854192e-04,  1.1237385446410865e-05, -6.5265128683820238e-05,
-         3.6145588595932343e-04, -6.3539671552322184e-06,  1.1137598234281054e-05,
-        -6.4685578816841917e-05, -6.2975443626344209e-06,
-         3.5893595493224776e-04, -1.4493122690417814e-05, -7.7817247724849183e-05,
-         3.5574862826746054e-04,  1.6084567762459325e-06, -1.4364424754832272e-05,
-        -7.7126235901582319e-05,  1.5941737903771684e-06,
-         2.6694095601170731e-04, -3.6280004828176018e-05, -7.0464806864673933e-05,
-         2.6457053862852676e-04,  7.8696688227861677e-06, -3.5957840873301966e-05,
-        -6.9839084212031750e-05,  7.7997867033238258e-06,
-         1.3743518008194373e-04, -3.5616161618941401e-05, -4.3245713680204564e-05,
-         1.3621476510780801e-04,  1.0173131963281794e-05, -3.5299892546240518e-05,
-        -4.2861694708416988e-05,  1.0082795249098096e-05,
-         4.4281012350574168e-05, -1.7888520118666163e-05, -1.6654315330492159e-05,
-         4.3887799997592119e-05,  6.9220705758272029e-06, -1.7729671286766401e-05,
-        -1.6506426152472439e-05,  6.8606030638137037e-06,
-         5.1438549738468456e-05,  2.9665824357334248e-05,  1.7900189835036316e-05,
-         5.0981778944329555e-05,  1.3973723052796347e-05,  2.9402393871455861e-05,
-         1.7741237376855478e-05,  1.3849637350373645e-05,
-         4.6254048415618476e-04,  2.5918239859045258e-04,  1.3487188316997143e-04,
-         4.5843315637685180e-04,  6.6255494613228503e-05,  2.5688087666510847e-04,
-         1.3367423009662892e-04,  6.5667150364714081e-05,
-         2.8294587601195094e-03,  1.2375254640891551e-03,  5.5518378989409295e-04,
-         2.8043333603674919e-03,  1.6372300936085449e-04,  1.2265363228347241e-03,
-         5.5025379591307449e-04,  1.6226916026548170e-04,
-         9.1957619553724862e-03,  2.1739429633878351e-03,  7.9765225550964614e-04,
-         9.1141042198332120e-03, -1.2436740398918847e-04,  2.1546384989570141e-03,
-         7.9056915818189724e-04, -1.2326302997059803e-04,
-         1.2500828315738304e-02, -7.8508011247854954e-04, -3.9877045177897329e-04,
-         1.2389821817572911e-02, -4.5450998846959987e-04, -7.7810865491874858e-04,
-        -3.9522939751394622e-04, -4.5047397094125129e-04,
-         5.4790816862939342e-03, -2.4387569363537231e-03, -8.7033830325416366e-04,
-         5.4304278166625993e-03,  1.8988685124218666e-04, -2.4171009420033036e-03,
-        -8.6260975880708712e-04,  1.8820066902516417e-04,
-         5.7215777750935844e-04, -4.7524252007977803e-04, -1.6913878684937368e-04,
-         5.6707705568235394e-04,  1.2685880911773336e-04, -4.7102239909252029e-04,
-        -1.6763684602130442e-04,  1.2573231159245635e-04,
-         3.7427031371474034e-04,  3.3208117201649276e-04,  1.1114484687927514e-04,
-         3.7094681899556005e-04,  9.6463580458143968e-05,  3.2913231398235741e-04,
-         1.1015788826104790e-04,  9.5606990478928455e-05,
-         5.3016792692569901e-03,  2.6754726903120783e-03,  7.3909622093513787e-04,
-         5.2546007209230902e-03,  1.3556652552434143e-04,  2.6517146762999361e-03,
-         7.3253309717877138e-04,  1.3436270407452921e-04,
-         9.1961936544017117e-03, -1.7368826364828100e-03, -2.6809009052276823e-04,
-         9.1145320854046606e-03, -4.6206186478537920e-04, -1.7214592377823002e-03,
-        -2.6570946890393444e-04, -4.5795878711323652e-04,
-         1.4411213884148813e-03, -1.2810931792856986e-03, -2.9718607020745780e-04,
-         1.4283243293145833e-03,  2.1624336633407510e-04, -1.2697171597080966e-03,
-        -2.9454707828436010e-04,  2.1432314007050667e-04,
-         2.5492665841420016e-04,  2.4888323947485432e-04,  6.6278567407822636e-05,
-         2.5266292716977223e-04,  7.1894578026384081e-05,  2.4667317337616389e-04,
-         6.5690018274474520e-05,  7.1256159103876392e-05,
-         3.4578494082033386e-03,  1.1303046461231766e-03,  2.4223248931237062e-04,
-         3.4271439425899376e-03, -1.3900706598036629e-04,  1.1202676183793233e-03,
-         2.4008148141902978e-04, -1.3777269276724882e-04,
-         1.5781234722698934e-03, -1.2618335200808048e-03, -1.9187865723666297e-04,
-         1.5641098440602533e-03,  8.2967902797066034e-05, -1.2506285249561588e-03,
-        -1.9017478791900309e-04,  8.2231153509978078e-05,
-         9.6977901902638622e-05,  8.6316756686137351e-05,  1.9677860154709606e-05,
-         9.6116744784267068e-05,  3.0120448337405375e-05,  8.5550269806171266e-05,
-         1.9503122105998658e-05,  2.9852980821761017e-05,
-         1.1828731451272081e-03,  1.7396447751082816e-04,  4.5145997322302639e-05,
-         1.1723693127172275e-03, -8.1902648559895069e-05,  1.7241968488062006e-04,
-         4.4745103962090367e-05, -8.1175358657380482e-05,
-         1.8720681143410254e-04, -2.0805519933339656e-04, -3.3414378701659159e-05,
-         1.8554442778678492e-04,  3.2611926466714527e-05, -2.0620768343126817e-04,
-        -3.3117661310270503e-05,  3.2322334796141819e-05,
-         1.9535178824326663e-04,  1.5650334125842918e-04,  2.3209649131246132e-05,
-         1.9361707776044762e-04,  8.6672787667954396e-06,  1.5511360232069738e-04,
-         2.3003549038625602e-05,  8.5903139257285476e-06,
-         1.6951067600112074e-04, -1.5119863365618903e-04, -1.3863877085534901e-05,
-         1.6800543282288725e-04,  4.5044095319706036e-06, -1.4985600015818035e-04,
-        -1.3740766807768502e-05,  4.4644106842288668e-06,
-         3.6276567298503925e-05,  3.6027257115504003e-05,  5.2295393006317666e-06,
-         3.5954433868657657e-05,  3.9956008741687153e-06,  3.5707337542985657e-05,
-         5.1831013502720623e-06,  3.9601202124153117e-06,
-         5.1575023302046816e-05, -4.4579128212969987e-05, -2.9869584382357371e-06,
-         5.1117040632022390e-05,  3.2845211634800542e-09, -4.4183268611573997e-05,
-        -2.9604344521430178e-06,  3.2553548407936682e-09,
-         1.2401275268881753e-05,  1.1336295347525348e-05,  1.3473909962804335e-06,
-         1.2291152794945326e-05,  6.9063884390899995e-07,  1.1235629822256665e-05,
-         1.3354262566344723e-06,  6.8450601833752906e-07,
-        // idx[1] = 13;
-         6.2657435059192389e-06,  1.1641163689362830e-06, -1.6403632698369783e-06,
-         6.2101041332771099e-06, -3.2689517205055183e-07,  1.1537790954125808e-06,
-        -1.6257969564932065e-06, -3.2399236534047043e-07,
-         1.1267655777296214e-05,  1.7224008808195605e-06, -3.0785713582669099e-06,
-         1.1167599766704021e-05, -4.9786387303821501e-07,  1.7071060791162162e-06,
-        -3.0512338557269196e-06, -4.9344287598800761e-07,
-         1.7792497642738746e-05,  1.9998167603756296e-06, -4.8547004491311306e-06,
-         1.7634501483840234e-05, -4.9857845221345014e-07,  1.9820585246863783e-06,
-        -4.8115910420671554e-06, -4.9415110974917022e-07,
-         2.4056337321823497e-05,  1.5575127200312380e-06, -6.4725989939129826e-06,
-         2.3842718696134580e-05, -5.6131534500858648e-07,  1.5436821138880390e-06,
-        -6.4151227587231497e-06, -5.5633090323863634e-07,
-         2.7164067597516312e-05,  1.1098766716295953e-07, -8.8660114789262803e-06,
-         2.6922852540100311e-05, -3.1627341965558876e-07,  1.1000210428983373e-07,
-        -8.7872819050043051e-06, -3.1346493337835670e-07,
-         2.3994825830339474e-05, -1.6841247767798238e-06, -7.7539596815715105e-06,
-         2.3781753422476620e-05,  2.6317833456926379e-07, -1.6691698642554609e-06,
-        -7.6851050513480680e-06,  2.6084132900645678e-07,
-         1.6016882937583991e-05, -2.8230768932199529e-06, -6.0290454073971664e-06,
-         1.5874654115499630e-05,  1.3614222825750313e-06, -2.7980081640083472e-06,
-        -5.9755078976376938e-06,  1.3493329460690080e-06,
-         9.8455354864211670e-06,  2.9617890833854716e-07, -6.9489101822206762e-07,
-         9.7581078064861676e-06,  3.1357290448382672e-06,  2.9354885994377525e-07,
-        -6.8872043363429996e-07,  3.1078839859612674e-06,
-         3.9011083818695911e-05,  1.9902575296058611e-05,  1.4677088296293310e-05,
-         3.8664668069677257e-05,  7.5064936588684329e-06,  1.9725841792302946e-05,
-         1.4546756758743548e-05,  7.4398365099559416e-06,
-         2.3888049043531946e-04,  1.1483546140429011e-04,  7.1312268443981844e-05,
-         2.3675924806213432e-04,  2.9643345516891777e-05,  1.1381573038217466e-04,
-         7.0679020390632398e-05,  2.9380114641574981e-05,
-         1.2234867187375981e-03,  5.1387522103972256e-04,  2.8134955828176556e-04,
-         1.2126222405791434e-03,  9.3470469345815967e-05,  5.0931204431728318e-04,
-         2.7885119349853603e-04,  9.2640457988017256e-05,
-         4.4799350811575659e-03,  1.3955105208072922e-03,  6.3033616055554575e-04,
-         4.4401535648606405e-03,  8.3328432799491150e-05,  1.3831184830834593e-03,
-         6.2473881867683195e-04,  8.2588482030706125e-05,
-         9.7716297507283792e-03,  1.3456395734362109e-03,  4.2230678771116898e-04,
-         9.6848583486580462e-03, -2.3479472920207153e-04,  1.3336903863049993e-03,
-         4.1855673239713247e-04, -2.3270976810844599e-04,
-         1.0306703041584746e-02, -1.1825534137556507e-03, -6.7086169125845014e-04,
-         1.0215180225385718e-02, -2.6682678254561637e-04, -1.1720524205383232e-03,
-        -6.6490448544624355e-04, -2.6445737901498439e-04,
-         4.1568120046519205e-03, -1.8174644792154824e-03, -7.5296484661487636e-04,
-         4.1198997991153197e-03,  1.9040708381710860e-04, -1.8013255192776273e-03,
-        -7.4627857041355196e-04,  1.8871628197049720e-04,
-         4.8860692316653393e-04, -3.8023488046055041e-04, -1.4753883724741325e-04,
-         4.8426812719636612e-04,  1.0196923908055593e-04, -3.7685842079770358e-04,
-        -1.4622870249053404e-04,  1.0106375923033906e-04,
-         2.9294848655103347e-04,  2.4980931921513331e-04,  9.0157589311276736e-05,
-         2.9034712408020091e-04,  8.0321792535837242e-05,  2.4759102959185763e-04,
-         8.9356996100994944e-05,  7.9608540526404764e-05,
-         4.4254596134883665e-03,  2.4549067862642271e-03,  7.3848760727670605e-04,
-         4.3861618356085411e-03,  2.3344588158139668e-04,  2.4331073823541218e-03,
-         7.3192988796788876e-04,  2.3137289816214148e-04,
-         1.1157187397402474e-02, -1.8349902862188801e-04,  6.0616833960680126e-05,
-         1.1058112338448070e-02, -5.9620026364057234e-04, -1.8186956983167152e-04,
-         6.0078560632073659e-05, -5.9090604618550191e-04,
-         3.4746815254179230e-03, -2.4230957949160658e-03, -5.5706413873520704e-04,
-         3.4438265917579652e-03,  2.4825618773810390e-04, -2.4015788704276086e-03,
-        -5.5211744738542956e-04,  2.4605168981583451e-04,
-         1.2967070437580762e-04, -3.0372989641602543e-05, -8.4366829497824695e-06,
-         1.2851923741347230e-04,  5.2883604796430712e-05, -3.0103279576495651e-05,
-        -8.3617657837569207e-06,  5.2414002012475693e-05,
-         2.3207575119290032e-03,  1.5289575356248154e-03,  3.4582312161757889e-04,
-         2.3001493443753429e-03,  1.1872552071725908e-04,  1.5153804975608961e-03,
-         3.4275223601337767e-04,  1.1767124623521591e-04,
-         4.0562948476909767e-03, -1.4421644508333046e-03, -1.5972876124242848e-04,
-         4.0202752276149523e-03, -1.9704447144722474e-04, -1.4293581294102611e-03,
-        -1.5831038079643057e-04, -1.9529473005363505e-04,
-         2.3072328684209585e-04, -2.5397968959006082e-04, -5.5574896425858917e-05,
-         2.2867447987741607e-04,  6.3533756465527876e-05, -2.5172436736385032e-04,
-        -5.5081395156797248e-05,  6.2969581065114454e-05,
-         7.4703445644323579e-04,  5.8308309956022755e-04,  1.0745158404378290e-04,
-         7.4040084169994325e-04,  4.8758475781811738e-05,  5.7790536162264500e-04,
-         1.0649742134625928e-04,  4.8325503860614624e-05,
-         1.1026100056389333e-03, -6.4967562903913128e-04, -5.9942438906131847e-05,
-         1.0928189044033454e-03, -3.1102503922783453e-05, -6.4390655400654037e-04,
-        -5.9410154159361466e-05, -3.0826315820888077e-05,
-         3.6855264730397853e-05,  9.9690149435174425e-06,  2.1646015699630160e-06,
-         3.6527992507042120e-05,  1.3351157106268053e-05,  9.8804907744713724e-06,
-         2.1453800564651972e-06,  1.3232599746756376e-05,
-         4.1504347649095046e-04,  4.2960315696147001e-05,  1.3312487632465493e-05,
-         4.1135791888244821e-04, -3.1477256709126155e-05,  4.2578831038885878e-05,
-         1.3194273655229314e-05, -3.1197740828187762e-05,
-         4.0208731565052655e-05, -4.6888305906027664e-05, -7.6469715151629098e-06,
-         3.9851680786178314e-05,  9.5815298552671653e-06, -4.6471940965075453e-05,
-        -7.5790669325201704e-06,  9.4964465272319093e-06,
-         9.8837846986583506e-05,  4.0861517241056017e-05,  5.4635998823661205e-06,
-         9.7960173683417302e-05, -5.0402301787694723e-06,  4.0498669770145315e-05,
-         5.4150834900919591e-06, -4.9954732804295155e-06,
-         1.6363308286919829e-05, -1.9376034559952714e-05, -2.6746074969222150e-06,
-         1.6218003231490433e-05,  3.2094122010726464e-06, -1.9203976701824692e-05,
-        -2.6508571657680423e-06,  3.1809128408213089e-06,
-         2.5559272241391462e-05,  6.3438828943389592e-06,  9.7748053065870137e-07,
-         2.5332307656684648e-05, -1.7965596045881944e-06,  6.2875496492862865e-06,
-         9.6880057057984307e-07, -1.7806062785034210e-06,
-      };
-  
-      int nvals0 = sizeof(f0m)/sizeof(f0m[0]);
-      int nvals1 = sizeof(f1m)/sizeof(f1m[0]);
-      for (int i=0; i<nvals0; i++)
-        f0[i] = f0m[i];
-      for (int i=0; i<nvals1; i++)
-        f1[i] = f1m[i];
-    }
-  
-    struct gkyl_range check_ghost_rng = ghost_rng;
-    struct gkyl_range_iter iter;
-    gkyl_range_iter_init(&iter, &check_ghost_rng);
-    while (gkyl_range_iter_next(&iter)) {
-      for (int i=0; i<num_ref0; i++) {
-        if (iter.idx[0]==idx0_ref[i]) {
-          long linidx = gkyl_range_idx(&check_ghost_rng, iter.idx);
-          double *f_c = gkyl_array_fetch(distf_ho, linidx);
-          int refidx = iter.idx[1]-1;
-          for (int k=0; k<basis.num_basis; ++k) {
-            TEST_CHECK( gkyl_compare(f0[i*cells[1]*basis.num_basis+refidx*basis.num_basis+k], f_c[k], 1e-9) );
-            TEST_MSG( "Expected: %.9e | Got: %.9e\n", f0[i*cells[1]*basis.num_basis+refidx*basis.num_basis+k], f_c[k] );
-          }
-        }
-      }
-      for (int i=0; i<num_ref1; i++) {
-        if (iter.idx[1]==idx1_ref[i]) {
-          long linidx = gkyl_range_idx(&check_ghost_rng, iter.idx);
-          double *f_c = gkyl_array_fetch(distf_ho, linidx);
-          int refidx = iter.idx[0]-1;
-          for (int k=0; k<basis.num_basis; ++k) {
-            TEST_CHECK( gkyl_compare(f1[i*cells[0]*basis.num_basis+refidx*basis.num_basis+k], f_c[k], 1e-8) );
-            TEST_MSG( "Expected: %.9e | Got: %.9e\n", f1[i*cells[0]*basis.num_basis+refidx*basis.num_basis+k], f_c[k] );
-          }
-        }
-      }
+      gkyl_array_release(f);
     }
+    gkyl_array_release(f_pre);
   }
-
-
-  gkyl_free(app_ctx.r_lut);
-  gkyl_free(app_ctx.dPsidr_int_lut);
-
-  gkyl_array_release(buff_per);
-  test_bc_twistshift_array_meta_release(mt);
-  gkyl_bc_twistshift_release(tsup);
-  gkyl_proj_on_basis_release(projDistf);
-  gkyl_array_release(distf_ho);
-  gkyl_array_release(distf);
-}
-
-void
-test_bc_twistshift_3x_cbc(bool use_gpu)
-{
-  const int cells0[] = {32, 16, 4};
-
-  test_bc_twistshift_3x_cbc_wcells(cells0, GKYL_LOWER_EDGE, true, use_gpu, false);
-  test_bc_twistshift_3x_cbc_wcells(cells0, GKYL_UPPER_EDGE, true, use_gpu, false);
 }
 
 void
-test_bc_twistshift_3x_fig6(bool use_gpu)
+test_zero_shear_is_cell_translation(void)
 {
-  const int cells0[] = {1, 10, 4};
+  // Check that a uniform shift is equivalent to a cell translation, for any upsampling.
+  int num_cells = 3;
+  double dy = (ts_upper[1]-ts_lower[1])/ts_cells[1];
+  struct ts_ctx tctx = { .offset = num_cells*dy, .shear = 0.0 };
 
-  enum gkyl_edge_loc edgelo = GKYL_LOWER_EDGE; // Lower edge.
-  test_bc_twistshift_3x_fig6_wcells(cells0, edgelo, true, use_gpu, false);
-}
+  for (int e=0; e<2; e++) {
+    enum gkyl_edge_loc edge = e == 0? GKYL_LOWER_EDGE : GKYL_UPPER_EDGE;
+    struct ts_setup s;
+    ts_setup_init(&s, edge);
 
-void
-test_bc_twistshift_3x2v_fig6(bool use_gpu)
-{
-  const int cells0[] = {1, 10, 4, 2, 1};
+    struct gkyl_array *f_pre = ts_donor_new(&s);
+    struct gkyl_array *f = ts_run(&s, edge, 1, 0, 0.0, NULL, &tctx);
 
-  enum gkyl_edge_loc edgelo = GKYL_LOWER_EDGE; // Lower edge.
-  test_bc_twistshift_3x2v_fig6_wcells(cells0, edgelo, true, use_gpu, false);
-}
-
-void
-test_bc_twistshift_3x_fig11(bool use_gpu)
-{
-  const int cells0[] = {10, 5,  4};
-  const int cells1[] = {20, 10, 4};
-  const int cells2[] = {40, 20, 4};
-  const int cells3[] = {80, 40, 4};
-
-  enum gkyl_edge_loc edgelo = GKYL_LOWER_EDGE; // Lower edge.
-  test_bc_twistshift_3x_fig11_wcells(cells0, edgelo, 0, true, use_gpu, false);
-  test_bc_twistshift_3x_fig11_wcells(cells1, edgelo, 0, false, use_gpu, false);
-  test_bc_twistshift_3x_fig11_wcells(cells2, edgelo, 0, false, use_gpu, false);
-  test_bc_twistshift_3x_fig11_wcells(cells3, edgelo, 0, false, use_gpu, false);
-
-  enum gkyl_edge_loc edgeup = GKYL_UPPER_EDGE; // Upper edge.
-  test_bc_twistshift_3x_fig11_wcells(cells0, edgeup, 0, true, use_gpu, false);
-  test_bc_twistshift_3x_fig11_wcells(cells1, edgeup, 0, false, use_gpu, false);
-  test_bc_twistshift_3x_fig11_wcells(cells2, edgeup, 0, false, use_gpu, false);
-  test_bc_twistshift_3x_fig11_wcells(cells3, edgeup, 0, false, use_gpu, false);
-
-  // Apply the TS BC on the lower half of the x domain.
-  test_bc_twistshift_3x_fig11_wcells(cells0, edgelo, -1, true, use_gpu, false);
-  test_bc_twistshift_3x_fig11_wcells(cells1, edgelo, -1, false, use_gpu, false);
-  test_bc_twistshift_3x_fig11_wcells(cells2, edgelo, -1, false, use_gpu, false);
-
-  // Apply the TS BC on the upper half of the x domain.
-  test_bc_twistshift_3x_fig11_wcells(cells0, edgelo, 1, true, use_gpu, false);
-  test_bc_twistshift_3x_fig11_wcells(cells1, edgelo, 1, false, use_gpu, false);
-  test_bc_twistshift_3x_fig11_wcells(cells2, edgelo, 1, false, use_gpu, false);
-}
+    double maxd = 0.0;
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &s.ghost_r);
+    while (gkyl_range_iter_next(&iter)) {
+      int idx_do[GKYL_MAX_DIM];
+      gkyl_copy_int_arr(ts_ndim, iter.idx, idx_do);
+      int ny = ts_cells[1];
+      idx_do[1] = ((iter.idx[1]-1-num_cells) % ny + ny) % ny + 1;
 
-void
-test_bc_twistshift_3x_fig14(bool use_gpu)
-{
-  const int cells0[] = {8 , 8 , 4};
-  const int cells1[] = {16, 16, 4};
-  const int cells2[] = {32, 32, 4};
-  const int cells3[] = {64, 32, 4};
-
-  enum gkyl_edge_loc edgelo = GKYL_LOWER_EDGE; // Lower edge.
-  test_bc_twistshift_3x_fig14_wcells(cells0, edgelo, 0, true, use_gpu, false);
-  test_bc_twistshift_3x_fig14_wcells(cells1, edgelo, 0, false, use_gpu, false);
-  test_bc_twistshift_3x_fig14_wcells(cells2, edgelo, 0, false, use_gpu, false);
-  test_bc_twistshift_3x_fig14_wcells(cells3, edgelo, 0, false, use_gpu, false);
-
-  enum gkyl_edge_loc edgeup = GKYL_UPPER_EDGE; // Upper edge.
-  test_bc_twistshift_3x_fig14_wcells(cells0, edgeup, 0, true, use_gpu, false);
-  test_bc_twistshift_3x_fig14_wcells(cells1, edgeup, 0, false, use_gpu, false);
-  test_bc_twistshift_3x_fig14_wcells(cells2, edgeup, 0, false, use_gpu, false);
-  test_bc_twistshift_3x_fig14_wcells(cells3, edgeup, 0, false, use_gpu, false);
-}
+      const double *tar = gkyl_array_cfetch(f, gkyl_range_idx(&s.ghost_r, iter.idx));
+      const double *don = gkyl_array_cfetch(f_pre, gkyl_range_idx(&s.ghost_r, idx_do));
+      for (int k=0; k<s.basis.num_basis; k++)
+        maxd = GKYL_MAX2(maxd, fabs(tar[k]-don[k]));
+    }
+    TEST_CHECK( maxd < 1.0e-13 );
+    TEST_MSG("edge %d: shift of %d cells is not an exact translation, off by %.3e",
+      e, num_cells, maxd);
 
-void
-test_bc_twistshift_3x2v_fig11(bool use_gpu)
-{
-  const int cells0[] = {10, 5,  4, 2, 1};
-  const int cells1[] = {20, 10, 4, 2, 1};
-  const int cells2[] = {40, 20, 4, 2, 1};
-  const int cells3[] = {80, 40, 4, 2, 1};
-
-  enum gkyl_edge_loc edgelo = GKYL_LOWER_EDGE; // Lower edge.
-  test_bc_twistshift_3x2v_fig11_wcells(cells0, edgelo, 0, true, use_gpu, false);
-  test_bc_twistshift_3x2v_fig11_wcells(cells1, edgelo, 0, false, use_gpu, false);
-  test_bc_twistshift_3x2v_fig11_wcells(cells2, edgelo, 0, false, use_gpu, false);
-  test_bc_twistshift_3x2v_fig11_wcells(cells3, edgelo, 0, false, use_gpu, false);
-
-  enum gkyl_edge_loc edgeup = GKYL_UPPER_EDGE; // Upper edge.
-  test_bc_twistshift_3x2v_fig11_wcells(cells0, edgeup, 0, true, use_gpu, false);
-  test_bc_twistshift_3x2v_fig11_wcells(cells1, edgeup, 0, false, use_gpu, false);
-  test_bc_twistshift_3x2v_fig11_wcells(cells2, edgeup, 0, false, use_gpu, false);
-  test_bc_twistshift_3x2v_fig11_wcells(cells3, edgeup, 0, false, use_gpu, false);
-
-  // Apply the TS BC on the lower half of the x domain.
-  test_bc_twistshift_3x2v_fig11_wcells(cells0, edgelo, -1, true, use_gpu, false);
-  test_bc_twistshift_3x2v_fig11_wcells(cells1, edgelo, -1, false, use_gpu, false);
-  test_bc_twistshift_3x2v_fig11_wcells(cells2, edgelo, -1, false, use_gpu, false);
-
-  // Apply the TS BC on the upper half of the x domain.
-  test_bc_twistshift_3x2v_fig11_wcells(cells0, edgelo, 1, true, use_gpu, false);
-  test_bc_twistshift_3x2v_fig11_wcells(cells1, edgelo, 1, false, use_gpu, false);
-  test_bc_twistshift_3x2v_fig11_wcells(cells2, edgelo, 1, false, use_gpu, false);
+    gkyl_array_release(f);
+    gkyl_array_release(f_pre);
+  }
 }
 
-void test_bc_twistshift_3x_fig6_ho(){ test_bc_twistshift_3x_fig6(false); }
-void test_bc_twistshift_3x_fig11_ho(){ test_bc_twistshift_3x_fig11(false); }
-void test_bc_twistshift_3x_fig14_ho(){ test_bc_twistshift_3x_fig14(false); }
-void test_bc_twistshift_3x_cbc_ho(){ test_bc_twistshift_3x_cbc(false); }
-
-void test_bc_twistshift_3x2v_fig6_ho(){ test_bc_twistshift_3x2v_fig6(false); }
-void test_bc_twistshift_3x2v_fig11_ho(){ test_bc_twistshift_3x2v_fig11(false); }
-
-#ifdef GKYL_HAVE_CUDA
-void test_bc_twistshift_3x_fig6_dev(){ test_bc_twistshift_3x_fig6(true); }
-void test_bc_twistshift_3x_fig11_dev(){ test_bc_twistshift_3x_fig11(true); }
-void test_bc_twistshift_3x_fig14_dev(){ test_bc_twistshift_3x_fig14(true); }
-void test_bc_twistshift_3x_cbc_dev(){ test_bc_twistshift_3x_cbc(true); }
-
-void test_bc_twistshift_3x2v_fig6_dev(){ test_bc_twistshift_3x2v_fig6(true); }
-void test_bc_twistshift_3x2v_fig11_dev(){ test_bc_twistshift_3x2v_fig11(true); }
-#endif
-
 TEST_LIST = {
-  { "test_bc_twistshift_3x_fig6_ho", test_bc_twistshift_3x_fig6_ho },
-  { "test_bc_twistshift_3x_fig11_ho", test_bc_twistshift_3x_fig11_ho },
-  { "test_bc_twistshift_3x_fig14_ho", test_bc_twistshift_3x_fig14_ho },
-  { "test_bc_twistshift_3x_cbc_ho", test_bc_twistshift_3x_cbc_ho },
-  { "test_bc_twistshift_3x2v_fig6_ho", test_bc_twistshift_3x2v_fig6_ho },
-  { "test_bc_twistshift_3x2v_fig11_ho", test_bc_twistshift_3x2v_fig11_ho },
-#ifdef GKYL_HAVE_CUDA
-  { "test_bc_twistshift_3x_fig6_dev", test_bc_twistshift_3x_fig6_dev },
-  { "test_bc_twistshift_3x_fig11_dev", test_bc_twistshift_3x_fig11_dev },
-  { "test_bc_twistshift_3x_fig14_dev", test_bc_twistshift_3x_fig14_dev },
-  { "test_bc_twistshift_3x_cbc_dev", test_bc_twistshift_3x_cbc_dev },
-  { "test_bc_twistshift_3x2v_fig6_dev", test_bc_twistshift_3x2v_fig6_dev },
-  { "test_bc_twistshift_3x2v_fig11_dev", test_bc_twistshift_3x2v_fig11_dev },
-#endif
+  { "test_zero_shift_is_identity", test_zero_shift_is_identity },
+  { "test_zero_shear_is_cell_translation", test_zero_shear_is_cell_translation },
+  { "test_plain_matches_twistshift_dg", test_plain_matches_twistshift_dg },
+  { "test_conserves_particles", test_conserves_particles },
+  { "test_only_ghost_plane_written", test_only_ghost_plane_written },
+  { "test_identity_filter_matches_plain", test_identity_filter_matches_plain },
+  { "test_upsample_no_shear_matches_plain", test_upsample_no_shear_matches_plain },
+  { "test_shift_dg_matches_shift_func", test_shift_dg_matches_shift_func },
+  { "test_dealiasing_smooths_shear_direction", test_dealiasing_smooths_shear_direction },
   { NULL, NULL },
 };
diff --git a/gyrokinetic/unit/ctest_twistshift_dg.c b/gyrokinetic/unit/ctest_twistshift_dg.c
new file mode 100644
index 0000000000..ae00cdb2cd
--- /dev/null
+++ b/gyrokinetic/unit/ctest_twistshift_dg.c
@@ -0,0 +1,3835 @@
+// Test creation and deallocation of updater that applies the
+// twist shift BCs.
+//
+#include <acutest.h>
+
+#include <gkyl_array_ops.h>
+#include <gkyl_array_reduce.h>
+#include <gkyl_range.h>
+#include <gkyl_rect_grid.h>
+#include <gkyl_rect_decomp.h>
+#include <gkyl_basis.h>
+#include <gkyl_proj_on_basis.h>
+#include <mpack.h>
+#include <gkyl_array_rio.h>
+#include <gkyl_twistshift_dg.h>
+#include <gkyl_velocity_map.h>
+#include <gkyl_position_map.h>
+#include <gkyl_gk_geometry.h>
+#include <gkyl_gk_geometry_mapc2p.h>
+#include <gkyl_dg_updater_moment_gyrokinetic.h>
+#include <gkyl_math.h>
+#include <gkyl_const.h>
+
+// Compare two DG coefficients with a mixed relative/absolute tolerance.
+// Needed to pass the CBC 3x test on stellar nvcc installation.
+static bool
+ts_compare_coeff(double ref, double val)
+{
+  return gkyl_compare(ref, val, 1e-13) || fabs(ref-val) < 1e-14;
+}
+
+// Meta-data for IO
+struct test_bc_twistshift_output_meta {
+  int poly_order; // polynomial order
+  const char *basis_type; // name of basis functions
+};
+
+// returned gkyl_array_meta must be freed using gyrokinetic_array_meta_release
+static struct gkyl_msgpack_data*
+test_bc_twistshift_array_meta_new(struct test_bc_twistshift_output_meta meta)
+{
+  struct gkyl_msgpack_data *mt = gkyl_malloc(sizeof(*mt));
+
+  mt->meta_sz = 0;
+  mpack_writer_t writer;
+  mpack_writer_init_growable(&writer, &mt->meta, &mt->meta_sz);
+
+  // add some data to mpack
+  mpack_build_map(&writer);
+
+  mpack_write_cstr(&writer, "polyOrder");
+  mpack_write_i64(&writer, meta.poly_order);
+
+  mpack_write_cstr(&writer, "basisType");
+  mpack_write_cstr(&writer, meta.basis_type);
+
+  mpack_complete_map(&writer);
+
+  int status = mpack_writer_destroy(&writer);
+
+  if (status != mpack_ok) {
+    free(mt->meta); // we need to use free here as mpack does its own malloc
+    gkyl_free(mt);
+    mt = 0;
+  }
+
+  return mt;
+}
+
+static void
+test_bc_twistshift_array_meta_release(struct gkyl_msgpack_data *mt)
+{
+  if (!mt) return;
+  MPACK_FREE(mt->meta);
+  gkyl_free(mt);
+}
+
+struct skin_ghost_ranges {
+  struct gkyl_range lower_skin[GKYL_MAX_DIM];
+  struct gkyl_range lower_ghost[GKYL_MAX_DIM];
+
+  struct gkyl_range upper_skin[GKYL_MAX_DIM];
+  struct gkyl_range upper_ghost[GKYL_MAX_DIM];
+};
+
+// Create ghost and skin sub-ranges given a parent range
+static void
+skin_ghost_ranges_init(struct skin_ghost_ranges *sgr,
+  const struct gkyl_range *parent, const int *ghost)
+{
+  int ndim = parent->ndim;
+
+  for (int d=0; d<ndim; ++d) {
+    gkyl_skin_ghost_ranges(&sgr->lower_skin[d], &sgr->lower_ghost[d],
+      d, GKYL_LOWER_EDGE, parent, ghost);
+    gkyl_skin_ghost_ranges(&sgr->upper_skin[d], &sgr->upper_ghost[d],
+      d, GKYL_UPPER_EDGE, parent, ghost);
+  }
+}
+// Apply periodic BCs along parallel direction
+void
+apply_periodic_bc(struct gkyl_array *buff, struct gkyl_array *fld, const int dir, const struct skin_ghost_ranges sgr)
+{
+  gkyl_array_copy_to_buffer(buff->data, fld, &(sgr.lower_skin[dir]));
+  gkyl_array_copy_from_buffer(fld, buff->data, &(sgr.upper_ghost[dir]));
+
+  gkyl_array_copy_to_buffer(buff->data, fld, &(sgr.upper_skin[dir]));
+  gkyl_array_copy_from_buffer(fld, buff->data, &(sgr.lower_ghost[dir]));
+}
+
+static struct gkyl_array*
+mkarr(bool on_gpu, long nc, long size)
+{
+  struct gkyl_array* a;
+  if (on_gpu)
+    a = gkyl_array_cu_dev_new(GKYL_DOUBLE, nc, size);
+  else
+    a = gkyl_array_new(GKYL_DOUBLE, nc, size);
+  return a;
+}
+
+struct test_bc_twistshift_ctx {
+  double lower[GKYL_MAX_DIM], upper[GKYL_MAX_DIM];
+  int cells[GKYL_MAX_DIM];
+  double B0;
+  double vt;
+  double mass;
+  enum gkyl_edge_loc edge;
+};
+
+void
+mapc2p(double t, const double *xc, double* GKYL_RESTRICT xp, void *ctx)
+{
+  xp[0] = xc[0]; xp[1] = xc[1]; xp[2] = xc[2];
+}
+
+void eval_bfield_3x(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+
+  struct test_bc_twistshift_ctx *pars = ctx;
+  double B0 = pars->B0;
+
+  fout[0] = 0.0;
+  fout[1] = 0.0;
+  fout[2] = B0;
+}
+
+void
+shift1_fig6(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct test_bc_twistshift_ctx *pars = ctx;
+  double Lx[2] = {pars->upper[0]-pars->lower[0], pars->upper[1]-pars->lower[1]};
+  double dx[2] = {Lx[0]/pars->cells[0], Lx[1]/pars->cells[1]};
+
+  fout[0] = 4.0*dx[1];
+}
+
+void
+shift1m_fig6(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  shift1_fig6(t, xn, fout, ctx);
+  fout[0] *= -1.0;
+}
+
+void
+shift2_fig6(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  fout[0] = 1.1;
+}
+
+void
+shift2m_fig6(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  shift2_fig6(t, xn, fout, ctx);
+  fout[0] *= -1.0;
+}
+
+void
+init_donor_fig6(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  double y = xn[1];
+
+  double mu = 0.0;
+  double sigma = 0.3;
+
+  fout[0] = ( 1.0/sqrt(2.0*M_PI*pow(sigma,2)) ) * exp( -pow(y-mu,2)/(2.0*pow(sigma,2)) );
+}
+
+void
+shift_fig9(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct test_bc_twistshift_ctx *pars = ctx;
+  double Lx[2] = {pars->upper[0]-pars->lower[0], pars->upper[1]-pars->lower[1]};
+  double dx[2] = {Lx[0]/pars->cells[0], Lx[1]/pars->cells[1]};
+
+  fout[0] = dx[1]/2.0;
+}
+
+void
+shiftm_fig9(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  shift_fig9(t, xn, fout, ctx);
+  fout[0] *= -1.0;
+}
+
+void
+init_donor_fig9(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  double y = xn[1];
+
+  struct test_bc_twistshift_ctx *pars = ctx;
+  double ymid = 0.5*(pars->upper[1]+pars->lower[1]);
+  double dy = (pars->upper[1]-pars->lower[1])/pars->cells[1];
+
+  fout[0] = 0.;
+  if (ymid < y && y < ymid+dy)
+    fout[0] = 1.;
+}
+
+void
+test_bc_twistshift_3x_fig6_wcells(const int *cells, enum gkyl_edge_loc edge,
+  bool check_distf, bool use_gpu, bool write_f)
+{
+  double vt = 1.0; // Thermal speed.
+  double mass = 1.0;
+  double B0 = 1.0; // Magnetic field magnitude.
+  int bc_dir = 2; // Direction in which to apply TS.
+
+  int poly_order = 1;
+  const double lower[] = {-2.0, -1.50, -3.0};
+  const double upper[] = { 2.0,  1.50,  3.0};
+  int vdim = 0;
+  int ndim = sizeof(lower)/sizeof(lower[0]);
+  int cdim = ndim - vdim;
+
+  double lower_conf[cdim], upper_conf[cdim];
+  int cells_conf[cdim];
+  for (int d=0; d<cdim; d++) {
+    lower_conf[d] = lower[d];
+    upper_conf[d] = upper[d];
+    cells_conf[d] = cells[d];
+  }
+
+  // Grid.
+  struct gkyl_rect_grid grid;
+  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
+  struct gkyl_rect_grid grid_conf;
+  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
+
+  // Basis functions.
+  struct gkyl_basis basis;
+  gkyl_cart_modal_serendip(&basis, ndim, poly_order);
+  struct gkyl_basis basis_conf;
+  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
+
+  // Ranges.
+  int ghost_conf[cdim];
+  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
+  struct gkyl_range local_conf, local_ext_conf; // local, local-ext position-space ranges
+  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
+
+  int ghost[ndim];
+  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
+  struct gkyl_range local, local_ext; // local, local-ext phase-space ranges
+  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
+
+  struct skin_ghost_ranges skin_ghost; // skin/ghost.
+  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
+  struct skin_ghost_ranges skin_ghost_conf; // skin/ghost.
+  skin_ghost_ranges_init(&skin_ghost_conf, &local_ext_conf, ghost_conf);
+
+  // Pick skin and ghost ranges based on 'edge'.
+  struct gkyl_range skin_rng, ghost_rng;
+  struct gkyl_range skin_rng_conf, ghost_rng_conf;
+  if (edge == GKYL_LOWER_EDGE) {
+    skin_rng = skin_ghost.upper_skin[bc_dir];
+    ghost_rng = skin_ghost.lower_ghost[bc_dir];
+    skin_rng_conf = skin_ghost_conf.upper_skin[bc_dir];
+    ghost_rng_conf = skin_ghost_conf.lower_ghost[bc_dir];
+  }
+  else {
+    skin_rng = skin_ghost.lower_skin[bc_dir];
+    ghost_rng = skin_ghost.upper_ghost[bc_dir];
+    skin_rng_conf = skin_ghost_conf.lower_skin[bc_dir];
+    ghost_rng_conf = skin_ghost_conf.upper_ghost[bc_dir];
+  }
+
+  struct test_bc_twistshift_ctx proj_ctx = {
+    .lower = {lower[0], lower[1], lower[2]},
+    .upper = {upper[0], upper[1], upper[2]},
+    .cells = {cells[0], cells[1], cells[2]},
+    .B0 = B0,
+    .vt = vt,
+    .mass = mass,
+  };
+
+  // Initialize the distribution
+  struct gkyl_array *distf = mkarr(use_gpu, basis.num_basis, local_ext.volume);
+  struct gkyl_array *distf_ho = use_gpu? mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
+  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew( &(struct gkyl_proj_on_basis_inp) {
+      .grid = &grid,
+      .basis = &basis,
+      .num_ret_vals = 1,
+      .eval = init_donor_fig6,
+//      .eval = init_donor_fig9,
+      .ctx = &proj_ctx,
+    }
+  );
+  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
+  gkyl_array_copy(distf, distf_ho);
+  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new( (struct test_bc_twistshift_output_meta) {
+      .poly_order = poly_order,
+      .basis_type = basis.id
+    }
+  );
+  if (write_f)
+    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho, "ctest_bc_twistshift_3x_fig6_do.gkyl");
+
+  // Create a range only extended in bc_dir.
+  struct gkyl_range update_rng;
+  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
+  for (int d=0; d<ndim; d++) {
+    lower_bcdir_ext[d] = local.lower[d];
+    upper_bcdir_ext[d] = local.upper[d];
+  }
+  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
+  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
+  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
+
+  // Create the twist-shift updater and shift the donor field.
+  struct gkyl_twistshift_dg_inp tsinp = {
+    .bc_dir = bc_dir,
+    .shift_dir = 1, // y shift.
+    .shear_dir = 0, // shift varies with x.
+    .edge = edge,
+    .cdim = cdim,
+    .bcdir_ext_update_r = &update_rng,
+    .num_ghost = ghost,
+    .basis = &basis,
+    .grid = &grid,
+    .shift_func = shift1_fig6,
+//    .shift_func = shift_fig9,
+    .shift_func_ctx = &proj_ctx,
+    .use_gpu = use_gpu,
+  };
+
+  struct gkyl_twistshift_dg *tsup = gkyl_twistshift_dg_inew(&tsinp);
+
+  // First apply periodicity in z.
+  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
+  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
+
+  gkyl_twistshift_dg_advance(tsup, distf, distf);
+  gkyl_array_copy(distf_ho, distf);
+
+  // Write out the target in the extended range.
+  if (write_f) {
+    double lower_ext[ndim], upper_ext[ndim];
+    int cells_ext[ndim];
+    for (int d=0; d<ndim; d++) {
+      double dx = (upper[d]-lower[d])/cells[d];
+      lower_ext[d] = lower[d]-dx*ghost[d];
+      upper_ext[d] = upper[d]+dx*ghost[d];
+      cells_ext[d] = cells[d]+2*ghost[d];
+    }
+    struct gkyl_rect_grid grid_ext;
+    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
+    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x_fig6_tar.gkyl");
+  }
+
+  if (check_distf) {
+    // Check 0th and 2nd DG coeffs.
+    const double f0[] =
+    {
+      2.5656054446469541e+00, 4.0323377043325592e-01, 2.4549376970832818e-02,
+      5.6930416832388616e-04, 5.6930416832388561e-04, 2.4549376970832790e-02,
+      4.0323377043325587e-01, 2.5656054446469554e+00, 6.4341275514494081e+00,
+      6.4341275514494081e+00,
+    };
+    const double f2[] =
+    {
+      -1.0463462350335195e+00, -2.4917980000416121e-01, -1.8802664978950782e-02,
+      -4.9044149652606374e-04,  4.9044149652607144e-04,  1.8802664978951094e-02,
+       2.4917980000416726e-01,  1.0463462350335588e+00,  9.2229040193425293e-01,
+      -9.2229040193415335e-01,
+    };
+
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &ghost_rng);
+    while (gkyl_range_iter_next(&iter)) {
+      long linidx = gkyl_range_idx(&ghost_rng, iter.idx);
+      double *f_c = gkyl_array_fetch(distf_ho, linidx);
+      int refidx = (iter.idx[1]-1)*cells[0] + iter.idx[0]-1;
+      TEST_CHECK( gkyl_compare(f0[refidx]/pow(sqrt(2.0),2), f_c[0], 1e-13) );
+      TEST_CHECK( gkyl_compare(f2[refidx]/pow(sqrt(2.0),2), f_c[2], 1e-13) );
+    }
+  }
+
+  // Copy the ghost cell back to the skin cell, and apply the negated shift to
+  // see if we recover the donor field approximately.
+  gkyl_array_copy_range_to_range(distf, distf, &skin_rng, &ghost_rng);
+  tsinp.shift_func = shift1m_fig6;
+//  tsinp.shift_func = shiftm_fig9;
+  struct gkyl_twistshift_dg *tsup_m = gkyl_twistshift_dg_inew(&tsinp);
+  gkyl_twistshift_dg_advance(tsup_m, distf, distf);
+  gkyl_array_copy(distf_ho, distf);
+
+  if (write_f) {
+    double lower_ext[ndim], upper_ext[ndim];
+    int cells_ext[ndim];
+    for (int d=0; d<ndim; d++) {
+      double dx = (upper[d]-lower[d])/cells[d];
+      lower_ext[d] = lower[d]-dx*ghost[d];
+      upper_ext[d] = upper[d]+dx*ghost[d];
+      cells_ext[d] = cells[d]+2*ghost[d];
+    }
+    struct gkyl_rect_grid grid_ext;
+    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
+    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x_fig6_tar_shifted.gkyl");
+  }
+
+  if (check_distf) {
+    // Check 0th and 2nd DG coeffs.
+    const double f0[] =
+    {
+      5.6930416832388551e-04, 2.4549376970832783e-02, 4.0323377043325570e-01,
+      2.5656054446469541e+00, 6.4341275514494018e+00, 6.4341275514494001e+00,
+      2.5656054446469501e+00, 4.0323377043325520e-01, 2.4549376970832770e-02,
+      5.6930416832388496e-04,
+    };
+    const double f2[] =
+    {
+      4.9044149652607047e-04,  1.8802664978951059e-02,  2.4917980000416681e-01,
+      1.0463462350335573e+00,  9.2229040193425282e-01, -9.2229040193414913e-01,
+     -1.0463462350335162e+00, -2.4917980000416048e-01, -1.8802664978950730e-02,
+     -4.9044149652606244e-04,
+    };
+
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &ghost_rng);
+    while (gkyl_range_iter_next(&iter)) {
+      long linidx = gkyl_range_idx(&ghost_rng, iter.idx);
+      double *f_c = gkyl_array_fetch(distf_ho, linidx);
+      int refidx = (iter.idx[1]-1)*cells[0] + iter.idx[0]-1;
+      TEST_CHECK( gkyl_compare(f0[refidx]/pow(sqrt(2.0),2), f_c[0], 1e-13) );
+      TEST_CHECK( gkyl_compare(f2[refidx]/pow(sqrt(2.0),2), f_c[2], 1e-13) );
+    }
+  }
+
+  gkyl_array_release(buff_per);
+  test_bc_twistshift_array_meta_release(mt);
+  gkyl_twistshift_dg_release(tsup);
+  gkyl_twistshift_dg_release(tsup_m);
+  gkyl_proj_on_basis_release(projDistf);
+  gkyl_array_release(distf_ho);
+  gkyl_array_release(distf);
+
+}
+void
+test_bc_twistshift_3x2v_fig6_wcells(const int *cells, enum gkyl_edge_loc edge,
+  bool check_distf, bool use_gpu, bool write_f)
+{
+  double vt = 1.0; // Thermal speed.
+  double mass = 1.0;
+  double B0 = 1.0; // Magnetic field magnitude.
+  int bc_dir = 2; // Direction in which to apply TS.
+
+  int poly_order = 1;
+  const double lower[] = {-2.0, -1.50, -3.0, -5.0*vt, 0.};
+  const double upper[] = { 2.0,  1.50,  3.0,  5.0*vt, mass*(pow(5.0*vt,2))/(2.0*B0)};
+  int vdim = 2;
+  int ndim = sizeof(lower)/sizeof(lower[0]);
+  int cdim = ndim - vdim;
+
+  double lower_conf[cdim], upper_conf[cdim];
+  int cells_conf[cdim];
+  for (int d=0; d<cdim; d++) {
+    lower_conf[d] = lower[d];
+    upper_conf[d] = upper[d];
+    cells_conf[d] = cells[d];
+  }
+  double lower_vel[vdim], upper_vel[vdim];
+  int cells_vel[vdim];
+  for (int d=0; d<vdim; d++) {
+    lower_vel[d] = lower[cdim+d];
+    upper_vel[d] = upper[cdim+d];
+    cells_vel[d] = cells[cdim+d];
+  }
+
+  // Grid.
+  struct gkyl_rect_grid grid;
+  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
+  struct gkyl_rect_grid grid_conf;
+  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
+  struct gkyl_rect_grid grid_vel;
+  gkyl_rect_grid_init(&grid_vel, vdim, lower_vel, upper_vel, cells_vel);
+
+  // Basis functions.
+  struct gkyl_basis basis;
+  if (poly_order == 1) 
+    gkyl_cart_modal_gkhybrid(&basis, cdim, vdim);
+  else
+    gkyl_cart_modal_serendip(&basis, ndim, poly_order);
+  struct gkyl_basis basis_conf;
+  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
+
+  // Ranges.
+  int ghost_conf[cdim];
+  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
+  struct gkyl_range local_conf, local_ext_conf; // local, local-ext position-space ranges
+  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
+
+  int ghost_vel[vdim];
+  for (int d=0; d<vdim; d++) ghost_vel[d] = 0;
+  struct gkyl_range local_vel, local_ext_vel; // local, local-ext position-space ranges
+  gkyl_create_grid_ranges(&grid_vel, ghost_vel, &local_ext_vel, &local_vel);
+
+  int ghost[ndim];
+  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
+  for (int d=cdim; d<ndim; d++) ghost[d] = ghost_vel[d-cdim];
+  struct gkyl_range local, local_ext; // local, local-ext phase-space ranges
+  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
+
+  struct skin_ghost_ranges skin_ghost; // skin/ghost.
+  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
+  struct skin_ghost_ranges skin_ghost_conf; // skin/ghost.
+  skin_ghost_ranges_init(&skin_ghost_conf, &local_ext_conf, ghost_conf);
+
+  // Pick skin and ghost ranges based on 'edge'.
+  struct gkyl_range skin_rng, ghost_rng;
+  struct gkyl_range skin_rng_conf, ghost_rng_conf;
+  if (edge == GKYL_LOWER_EDGE) {
+    skin_rng = skin_ghost.upper_skin[bc_dir];
+    ghost_rng = skin_ghost.lower_ghost[bc_dir];
+    skin_rng_conf = skin_ghost_conf.upper_skin[bc_dir];
+    ghost_rng_conf = skin_ghost_conf.lower_ghost[bc_dir];
+  }
+  else {
+    skin_rng = skin_ghost.lower_skin[bc_dir];
+    ghost_rng = skin_ghost.upper_ghost[bc_dir];
+    skin_rng_conf = skin_ghost_conf.lower_skin[bc_dir];
+    ghost_rng_conf = skin_ghost_conf.upper_ghost[bc_dir];
+  }
+
+  struct test_bc_twistshift_ctx proj_ctx = {
+    .lower = {lower[0], lower[1], lower[2], lower[3], lower[4]},
+    .upper = {upper[0], upper[1], upper[2], upper[3], upper[4]},
+    .cells = {cells[0], cells[1], cells[2], cells[3], cells[4]},
+    .B0 = B0,
+    .vt = vt,
+    .mass = mass,
+  };
+
+  // Initialize the distribution
+  struct gkyl_array *distf = mkarr(use_gpu, basis.num_basis, local_ext.volume);
+  struct gkyl_array *distf_ho = use_gpu? mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
+  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew( &(struct gkyl_proj_on_basis_inp) {
+      .grid = &grid,
+      .basis = &basis,
+      .num_ret_vals = 1,
+      .eval = init_donor_fig6,
+//      .eval = init_donor_fig9,
+      .ctx = &proj_ctx,
+    }
+  );
+  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
+  gkyl_array_copy(distf, distf_ho);
+  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new( (struct test_bc_twistshift_output_meta) {
+      .poly_order = poly_order,
+      .basis_type = basis.id
+    }
+  );
+  if (write_f)
+    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho, "ctest_bc_twistshift_3x2v_fig6_do.gkyl");
+
+  // Create a range only extended in bc_dir.
+  struct gkyl_range update_rng;
+  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
+  for (int d=0; d<ndim; d++) {
+    lower_bcdir_ext[d] = local.lower[d];
+    upper_bcdir_ext[d] = local.upper[d];
+  }
+  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
+  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
+  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
+
+  // Create the twist-shift updater and shift the donor field.
+  struct gkyl_twistshift_dg_inp tsinp = {
+    .bc_dir = bc_dir,
+    .shift_dir = 1, // y shift.
+    .shear_dir = 0, // shift varies with x.
+    .edge = edge,
+    .cdim = cdim,
+    .bcdir_ext_update_r = &update_rng,
+    .num_ghost = ghost,
+    .basis = &basis,
+    .grid = &grid,
+    .shift_func = shift1_fig6,
+//    .shift_func = shift_fig9,
+    .shift_func_ctx = &proj_ctx,
+    .use_gpu = use_gpu,
+  };
+
+  struct gkyl_twistshift_dg *tsup = gkyl_twistshift_dg_inew(&tsinp);
+
+  // First apply periodicity in z.
+  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
+  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
+
+  gkyl_twistshift_dg_advance(tsup, distf, distf);
+  gkyl_array_copy(distf_ho, distf);
+
+  // Write out the target in the extended range.
+  if (write_f) {
+    double lower_ext[ndim], upper_ext[ndim];
+    int cells_ext[ndim];
+    for (int d=0; d<ndim; d++) {
+      double dx = (upper[d]-lower[d])/cells[d];
+      lower_ext[d] = lower[d]-dx*ghost[d];
+      upper_ext[d] = upper[d]+dx*ghost[d];
+      cells_ext[d] = cells[d]+2*ghost[d];
+    }
+    struct gkyl_rect_grid grid_ext;
+    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
+    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x2v_fig6_tar.gkyl");
+  }
+
+  // Compute the integrated moments of the skin cell and the ghost cell.
+  // Velocity space mapping.
+  struct gkyl_mapc2p_inp c2p_in = { };
+  struct gkyl_velocity_map *gvm = gkyl_velocity_map_new(c2p_in, grid, grid_vel,
+    local, local_ext, local_vel, local_ext_vel, use_gpu);
+  struct gkyl_position_map *pmap = gkyl_position_map_null_new();
+
+  // Initialize geometry
+  struct gkyl_gk_geometry_inp geometry_inp = {
+    .geometry_id = GKYL_GEOMETRY_MAPC2P,
+    .c2p_ctx = 0,
+    .mapc2p = mapc2p,
+    .bfield_ctx = &proj_ctx,
+    .bfield_func = eval_bfield_3x,
+    .position_map = pmap,
+    .grid = grid_conf,
+    .local = local_conf,
+    .local_ext = local_ext_conf,
+    .global = local_conf,
+    .global_ext = local_ext_conf,
+    .basis = basis_conf,
+    .geo_grid = grid_conf,
+    .geo_local = local_conf,
+    .geo_local_ext = local_ext_conf,
+    .geo_global = local_conf,
+    .geo_global_ext = local_ext_conf,
+    .geo_basis = basis_conf,
+  };
+  struct gk_geometry* gk_geom_3d = gkyl_gk_geometry_mapc2p_new(&geometry_inp);
+  struct gk_geometry* gk_geom = gkyl_gk_geometry_acquire(gk_geom_3d);
+  gkyl_gk_geometry_release(gk_geom_3d); // release temporary 3d geometry
+  if (use_gpu) {  // If we are on the gpu, copy from host
+    struct gk_geometry* gk_geom_dev = gkyl_gk_geometry_new(gk_geom, &geometry_inp, use_gpu);
+    gkyl_gk_geometry_release(gk_geom);
+    gk_geom = gkyl_gk_geometry_acquire(gk_geom_dev);
+    gkyl_gk_geometry_release(gk_geom_dev);
+  }
+  // Need the magnetic field to be initialized in the ghost cell in order to
+  // compute integrated moments in the ghost cell (for checking moment
+  // conservation).
+  gkyl_array_clear(gk_geom->geo_corn.bmag, 0.0);
+  gkyl_array_shiftc(gk_geom->geo_corn.bmag, B0*pow(sqrt(2.0),cdim), 0);
+
+  struct gkyl_dg_updater_moment *mcalc = gkyl_dg_updater_moment_gyrokinetic_new(&grid, &basis_conf,
+    &basis, &local_conf, mass, 0, gvm, gk_geom, NULL, GKYL_F_MOMENT_M0M1M2, true, use_gpu);
+  int num_mom = gkyl_dg_updater_moment_gyrokinetic_num_mom(mcalc);
+
+  struct gkyl_array *marr = mkarr(use_gpu, num_mom, local_ext_conf.volume);
+  double *red_integ_mom_skin, *red_integ_mom_ghost;
+  if (use_gpu) {
+    red_integ_mom_skin = gkyl_cu_malloc(sizeof(double[num_mom]));
+    red_integ_mom_ghost = gkyl_cu_malloc(sizeof(double[num_mom]));
+  }
+  else {
+    red_integ_mom_skin = gkyl_malloc(sizeof(double[num_mom]));
+    red_integ_mom_ghost = gkyl_malloc(sizeof(double[num_mom]));
+  }
+  double *red_integ_mom_skin_ho = gkyl_malloc(sizeof(double[num_mom]));
+  double *red_integ_mom_ghost_ho = gkyl_malloc(sizeof(double[num_mom]));
+
+  gkyl_dg_updater_moment_gyrokinetic_advance(mcalc,
+      &skin_rng, &skin_rng_conf, distf, marr);
+  gkyl_array_reduce_range(red_integ_mom_skin, marr, GKYL_SUM, &skin_rng_conf);
+
+  gkyl_dg_updater_moment_gyrokinetic_advance(mcalc,
+      &ghost_rng, &ghost_rng_conf, distf, marr);
+  gkyl_array_reduce_range(red_integ_mom_ghost, marr, GKYL_SUM, &ghost_rng_conf);
+
+  if (use_gpu) {
+    gkyl_cu_memcpy(red_integ_mom_skin_ho, red_integ_mom_skin, sizeof(double[num_mom]), GKYL_CU_MEMCPY_D2H);
+    gkyl_cu_memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]), GKYL_CU_MEMCPY_D2H);
+  }
+  else {
+    memcpy(red_integ_mom_skin_ho, red_integ_mom_skin, sizeof(double[num_mom]));
+    memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]));
+  }
+
+  for (int k=0; k<num_mom; k++) {
+    TEST_CHECK( gkyl_compare(red_integ_mom_skin_ho[k], red_integ_mom_ghost_ho[k], 1e-12));
+    TEST_MSG( "integ_mom %d | Expected: %.14e | Got: %.14e\n",k,red_integ_mom_skin_ho[k],red_integ_mom_ghost_ho[k]);
+  }
+
+  if (check_distf) {
+    // Check 0th and 2nd DG coeffs.
+    const double f0[] =
+    {
+      2.5656054446469541e+00, 4.0323377043325592e-01, 2.4549376970832818e-02,
+      5.6930416832388616e-04, 5.6930416832388561e-04, 2.4549376970832790e-02,
+      4.0323377043325587e-01, 2.5656054446469554e+00, 6.4341275514494081e+00,
+      6.4341275514494081e+00,
+    };
+    const double f2[] =
+    {
+      -1.0463462350335195e+00, -2.4917980000416121e-01, -1.8802664978950782e-02,
+      -4.9044149652606374e-04,  4.9044149652607144e-04,  1.8802664978951094e-02,
+       2.4917980000416726e-01,  1.0463462350335588e+00,  9.2229040193425293e-01,
+      -9.2229040193415335e-01,
+    };
+
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &ghost_rng);
+    while (gkyl_range_iter_next(&iter)) {
+      if (iter.idx[3]==1 && iter.idx[4]==1) {
+        long linidx = gkyl_range_idx(&ghost_rng, iter.idx);
+        double *f_c = gkyl_array_fetch(distf_ho, linidx);
+        int refidx = (iter.idx[1]-1)*cells[0] + iter.idx[0]-1;
+        TEST_CHECK( gkyl_compare(f0[refidx], f_c[0], 1e-13) );
+        TEST_CHECK( gkyl_compare(f2[refidx], f_c[2], 1e-13) );
+      }
+    }
+  }
+
+  // Copy the ghost cell back to the skin cell, and apply the negated shift to
+  // see if we recover the donor field approximately.
+  gkyl_array_copy_range_to_range(distf, distf, &skin_rng, &ghost_rng);
+  tsinp.shift_func = shift1m_fig6;
+//  tsinp.shift_func = shiftm_fig9;
+  struct gkyl_twistshift_dg *tsup_m = gkyl_twistshift_dg_inew(&tsinp);
+  gkyl_twistshift_dg_advance(tsup_m, distf, distf);
+  gkyl_array_copy(distf_ho, distf);
+
+  if (write_f) {
+    double lower_ext[ndim], upper_ext[ndim];
+    int cells_ext[ndim];
+    for (int d=0; d<ndim; d++) {
+      double dx = (upper[d]-lower[d])/cells[d];
+      lower_ext[d] = lower[d]-dx*ghost[d];
+      upper_ext[d] = upper[d]+dx*ghost[d];
+      cells_ext[d] = cells[d]+2*ghost[d];
+    }
+    struct gkyl_rect_grid grid_ext;
+    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
+    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x2v_fig6_tar_shifted.gkyl");
+  }
+
+  gkyl_dg_updater_moment_gyrokinetic_advance(mcalc,
+      &ghost_rng, &ghost_rng_conf, distf, marr);
+  gkyl_array_reduce_range(red_integ_mom_ghost, marr, GKYL_SUM, &ghost_rng_conf);
+
+  if (use_gpu)
+    gkyl_cu_memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]), GKYL_CU_MEMCPY_D2H);
+  else
+    memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]));
+
+  for (int k=0; k<num_mom; k++) {
+    TEST_CHECK( gkyl_compare(red_integ_mom_skin_ho[k], red_integ_mom_ghost_ho[k], 1e-12));
+    TEST_MSG( "integ_mom %d | Expected: %.14e | Got: %.14e\n",k,red_integ_mom_skin_ho[k],red_integ_mom_ghost_ho[k]);
+  }
+
+  if (check_distf) {
+    // Check 0th and 2nd DG coeffs.
+    const double f0[] =
+    {
+      5.6930416832388551e-04, 2.4549376970832783e-02, 4.0323377043325570e-01,
+      2.5656054446469541e+00, 6.4341275514494018e+00, 6.4341275514494001e+00,
+      2.5656054446469501e+00, 4.0323377043325520e-01, 2.4549376970832770e-02,
+      5.6930416832388496e-04,
+    };
+    const double f2[] =
+    {
+      4.9044149652607047e-04,  1.8802664978951059e-02,  2.4917980000416681e-01,
+      1.0463462350335573e+00,  9.2229040193425282e-01, -9.2229040193414913e-01,
+     -1.0463462350335162e+00, -2.4917980000416048e-01, -1.8802664978950730e-02,
+     -4.9044149652606244e-04,
+    };
+
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &ghost_rng);
+    while (gkyl_range_iter_next(&iter)) {
+      if (iter.idx[3]==1 && iter.idx[4]==1) {
+        long linidx = gkyl_range_idx(&ghost_rng, iter.idx);
+        double *f_c = gkyl_array_fetch(distf_ho, linidx);
+        int refidx = (iter.idx[1]-1)*cells[0] + iter.idx[0]-1;
+        TEST_CHECK( gkyl_compare(f0[refidx], f_c[0], 1e-13) );
+        TEST_CHECK( gkyl_compare(f2[refidx], f_c[2], 1e-13) );
+      }
+    }
+  }
+
+  gkyl_free(red_integ_mom_skin_ho);
+  gkyl_free(red_integ_mom_ghost_ho);
+  if (use_gpu) {
+    gkyl_cu_free(red_integ_mom_skin);
+    gkyl_cu_free(red_integ_mom_ghost);
+  }
+  else {
+    gkyl_free(red_integ_mom_skin);
+    gkyl_free(red_integ_mom_ghost);
+  }
+  gkyl_dg_updater_moment_gyrokinetic_release(mcalc);
+  gkyl_array_release(marr);
+  gkyl_gk_geometry_release(gk_geom);
+  gkyl_position_map_release(pmap);
+  gkyl_velocity_map_release(gvm);
+  gkyl_array_release(buff_per);
+  test_bc_twistshift_array_meta_release(mt);
+  gkyl_twistshift_dg_release(tsup);
+  gkyl_twistshift_dg_release(tsup_m);
+  gkyl_proj_on_basis_release(projDistf);
+  gkyl_array_release(distf_ho);
+  gkyl_array_release(distf);
+
+}
+
+void
+shift_fig11(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  double x = xn[0];
+
+  struct test_bc_twistshift_ctx *pars = ctx;
+  double Lx[2] = {pars->upper[0]-pars->lower[0], pars->upper[1]-pars->lower[1]};
+  double dx[2] = {Lx[0]/pars->cells[0], Lx[1]/pars->cells[1]};
+
+  fout[0] = 0.6*x+1.8;
+}
+
+void
+init_donor_3x_fig11(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+
+  struct test_bc_twistshift_ctx *pars = ctx;
+  double Lx[2] = {pars->upper[0]-pars->lower[0], pars->upper[1]-pars->lower[1]};
+  double B0 = pars->B0;
+  double vt = pars->vt;
+  double mass = pars->mass;
+  double vtsq = vt*vt;
+
+  double beta[2] = {0.0, 0.0};
+  double sigma[2] = {0.6, 0.2};
+
+  fout[0] = ( 1.0/pow(sqrt(2.0*M_PI*vtsq),3) )
+    * exp( -pow(x-beta[0],2)/(2.0*pow(sigma[0],2)) -pow(y-beta[1],2)/(2.0*pow(sigma[1],2)) );  
+}
+
+void
+init_donor_3x2v_fig11(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2], vpar = xn[3], mu = xn[4];
+
+  struct test_bc_twistshift_ctx *pars = ctx;
+  double B0 = pars->B0;
+  double vt = pars->vt;
+  double mass = pars->mass;
+  double vtsq = vt*vt;
+
+  init_donor_3x_fig11(t, xn, fout, ctx);
+  fout[0] *= exp( -(pow(vpar,2)+2.0*mu*B0/mass)/(2.0*vtsq) );  
+}
+
+void
+test_bc_twistshift_3x_fig11_wcells(const int *cells, enum gkyl_edge_loc edge,
+  int apply_in_half_x, bool check_distf, bool use_gpu, bool write_f)
+{
+  double vt = 1.0; // Thermal speed.
+  double mass = 1.0;
+  double B0 = 1.0; // Magnetic field magnitude.
+  int bc_dir = 2; // Direction in which to apply TS.
+
+  int poly_order = 1;
+  const double lower[] = {-2.0, -1.50, -3.0};
+  const double upper[] = { 2.0,  1.50,  3.0};
+  int vdim = 0;
+  int ndim = sizeof(lower)/sizeof(lower[0]);
+  int cdim = ndim - vdim;
+
+  double lower_conf[cdim], upper_conf[cdim];
+  int cells_conf[cdim];
+  for (int d=0; d<cdim; d++) {
+    lower_conf[d] = lower[d];
+    upper_conf[d] = upper[d];
+    cells_conf[d] = cells[d];
+  }
+
+  // Grid.
+  struct gkyl_rect_grid grid;
+  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
+  struct gkyl_rect_grid grid_conf;
+  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
+
+  // Basis functions.
+  struct gkyl_basis basis;
+  gkyl_cart_modal_serendip(&basis, ndim, poly_order);
+  struct gkyl_basis basis_conf;
+  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
+
+  // Ranges.
+  int ghost_conf[cdim];
+  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
+  struct gkyl_range local_conf, local_ext_conf; // local, local-ext position-space ranges
+  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
+
+  int ghost[ndim];
+  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
+  struct gkyl_range local, local_ext; // local, local-ext phase-space ranges
+  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
+
+  struct skin_ghost_ranges skin_ghost; // skin/ghost.
+  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
+  struct skin_ghost_ranges skin_ghost_conf; // skin/ghost.
+  skin_ghost_ranges_init(&skin_ghost_conf, &local_ext_conf, ghost_conf);
+
+  // Pick skin and ghost ranges based on 'edge'.
+  struct gkyl_range skin_rng, ghost_rng;
+  struct gkyl_range skin_rng_conf, ghost_rng_conf;
+  if (edge == GKYL_LOWER_EDGE) {
+    skin_rng = skin_ghost.upper_skin[bc_dir];
+    ghost_rng = skin_ghost.lower_ghost[bc_dir];
+    skin_rng_conf = skin_ghost_conf.upper_skin[bc_dir];
+    ghost_rng_conf = skin_ghost_conf.lower_ghost[bc_dir];
+  }
+  else {
+    skin_rng = skin_ghost.lower_skin[bc_dir];
+    ghost_rng = skin_ghost.upper_ghost[bc_dir];
+    skin_rng_conf = skin_ghost_conf.lower_skin[bc_dir];
+    ghost_rng_conf = skin_ghost_conf.upper_ghost[bc_dir];
+  }
+
+  struct test_bc_twistshift_ctx proj_ctx = {
+    .lower = {lower[0], lower[1], lower[2]},
+    .upper = {upper[0], upper[1], upper[2]},
+    .cells = {cells[0], cells[1], cells[2]},
+    .B0 = B0,
+    .vt = vt,
+    .mass = mass,
+  };
+
+  // Initialize the distribution
+  struct gkyl_array *distf = mkarr(use_gpu, basis.num_basis, local_ext.volume);
+  struct gkyl_array *distf_ho = use_gpu? mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
+  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew( &(struct gkyl_proj_on_basis_inp) {
+      .grid = &grid,
+      .basis = &basis,
+      .num_ret_vals = 1,
+      .eval = init_donor_3x_fig11,
+      .ctx = &proj_ctx,
+    }
+  );
+  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
+  gkyl_array_copy(distf, distf_ho);
+  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new( (struct test_bc_twistshift_output_meta) {
+      .poly_order = poly_order,
+      .basis_type = basis.id
+    }
+  );
+  if (write_f)
+    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho, "ctest_bc_twistshift_3x_fig11_do.gkyl");
+
+  // Create a range only extended in bc_dir.
+  struct gkyl_range update_rng;
+  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
+  for (int d=0; d<ndim; d++) {
+    lower_bcdir_ext[d] = local.lower[d];
+    upper_bcdir_ext[d] = local.upper[d];
+  }
+  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
+  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
+  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
+
+  if (apply_in_half_x < 0) {
+    // Apply the BC only on the lower half of the domain.
+    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
+    gkyl_range_shorten_from_above(&update_rng, &update_rng, 0, x_half_len);
+  }
+  else if (apply_in_half_x > 0) {
+    // Apply the BC only on the upper half of the domain.
+    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
+    gkyl_range_shorten_from_below(&update_rng, &update_rng, 0, x_half_len);
+  }
+
+  // Create the twist-shift updater and shift the donor field.
+  struct gkyl_twistshift_dg_inp tsinp = {
+    .bc_dir = bc_dir,
+    .shift_dir = 1, // y shift.
+    .shear_dir = 0, // shift varies with x.
+    .edge = edge,
+    .cdim = cdim,
+    .bcdir_ext_update_r = &update_rng,
+    .num_ghost = ghost,
+    .basis = &basis,
+    .grid = &grid,
+    .shift_func = shift_fig11,
+    .shift_func_ctx = &proj_ctx,
+    .use_gpu = use_gpu,
+  };
+
+  struct gkyl_twistshift_dg *tsup = gkyl_twistshift_dg_inew(&tsinp);
+
+  // First apply periodicity in z.
+  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
+  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
+
+  gkyl_twistshift_dg_advance(tsup, distf, distf);
+  gkyl_array_copy(distf_ho, distf);
+
+  // Write out the target in the extended range.
+  if (write_f) {
+    double lower_ext[ndim], upper_ext[ndim];
+    int cells_ext[ndim];
+    for (int d=0; d<ndim; d++) {
+      double dx = (upper[d]-lower[d])/cells[d];
+      lower_ext[d] = lower[d]-dx*ghost[d];
+      upper_ext[d] = upper[d]+dx*ghost[d];
+      cells_ext[d] = cells[d]+2*ghost[d];
+    }
+    struct gkyl_rect_grid grid_ext;
+    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
+    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x_fig11_tar.gkyl");
+  }
+
+  if (check_distf) {
+    // Check 0th, 1st, 2nd and 6th DG coeffs.
+    const double f0[] =
+    {
+     -6.2583195868812408e-06,  7.9567311608137231e-10,  5.0509906078140035e-05,
+      1.2343352957621956e-03,  5.3472486075120380e-04,
+      1.8256130045163409e-04,  3.0009163112130789e-09, -1.3326694681034118e-05,
+      3.7575576376431747e-03,  6.1716772244852208e-03,
+      4.4292093668301044e-03, -7.7229340458416127e-05, -3.8275760062292437e-05,
+      3.0421687066165188e-03,  2.9194555762249566e-02,
+      3.7056203209553537e-02,  1.4705657602094287e-04,  2.0550274812940050e-08,
+      1.0240094716951157e-03,  4.7863752496844179e-02,
+      9.6491415121706434e-02,  4.8597593964605536e-03,  8.0126693914598593e-08,
+     -4.3972043519208224e-04,  3.1180735654073199e-02,
+      9.6491415121706420e-02,  3.1180735654073172e-02, -4.3972043519208387e-04,
+      8.0126693914598646e-08,  4.8597593964605458e-03,
+      3.7056203209553502e-02,  4.7863752496844159e-02,  1.0240094716951155e-03,
+      2.0550274812939984e-08,  1.4705657602094392e-04,
+      4.4292093668300931e-03,  2.9194555762249559e-02,  3.0421687066165266e-03,
+     -3.8275760062292789e-05, -7.7229340458415897e-05,
+      1.8256130045163365e-04,  6.1716772244852129e-03,  3.7575576376431765e-03,
+     -1.3326694681033820e-05,  3.0009163112130839e-09,
+     -6.2583195868812094e-06,  5.3472486075120294e-04,  1.2343352957621958e-03,
+      5.0509906078140123e-05,  7.9567311608137107e-10,
+    };
+    const double f1[] =
+    {
+     -2.4097311206019044e-06,  7.6833036063548360e-11,  7.2344842311530572e-06,
+      5.2914450025189400e-04,  4.1028939039880680e-04,
+      1.6599629313756654e-04,  2.2461980415131899e-09, -4.1694729744125476e-05,
+      7.8438224724348157e-04,  3.3439621031217184e-03,
+      3.6040320392418893e-03, -8.7133864207591700e-05,  3.8447881347591303e-05,
+     -8.6762333862857460e-04,  8.6496739552592294e-03,
+      1.4945209682648789e-02,  4.5852653062261286e-04, -3.3068454717620671e-09,
+     -6.2529388927217496e-04,  1.5882293198893030e-03,
+      1.7368783554643934e-02,  2.3314728455433925e-03,  4.3253655108451250e-08,
+      9.4609992614394520e-06, -1.1247642251296977e-02,
+     -1.7368783554643944e-02,  1.1247642251296978e-02, -9.4609992614413358e-06,
+     -4.3253655108451283e-08, -2.3314728455433894e-03,
+     -1.4945209682648786e-02, -1.5882293198893067e-03,  6.2529388927217593e-04,
+      3.3068454717620489e-09, -4.5852653062261221e-04,
+     -3.6040320392418802e-03, -8.6496739552592190e-03,  8.6762333862857905e-04,
+     -3.8447881347591479e-05,  8.7133864207591442e-05,
+     -1.6599629313756624e-04, -3.3439621031217180e-03, -7.8438224724348212e-04,
+      4.1694729744125585e-05, -2.2461980415131949e-09,
+      2.4097311206018891e-06, -4.1028939039880621e-04, -5.2914450025189443e-04,
+     -7.2344842311531317e-06, -7.6833036063549213e-11,
+    };
+    const double f2[] =
+    {
+      5.3070807682913396e-06,  1.3751826183769400e-09,  6.8926303153258719e-05,
+      4.1882549426144460e-04, -4.9306025336561313e-04,
+     -2.8467596971097078e-04, -5.0150358149508259e-09,  1.3960594126194340e-05,
+      3.0887163471536865e-03, -2.8179959565330977e-03,
+     -4.7580701893096058e-03,  1.1300292822992238e-04, -5.7287804480022883e-05,
+      3.3338137165750199e-03,  1.3685413489847044e-03,
+     -2.7243387375233196e-02, -5.6694093500983371e-04,  2.2529555439069578e-08,
+      1.7831031494975383e-03,  2.6027202631190245e-02,
+     -2.3565987663701497e-02, -5.9773227818891196e-03, -1.1962791428901063e-07,
+     -4.8028129954664068e-04,  3.0023711373051848e-02,
+      2.3565987663701948e-02, -3.0023711373051674e-02,  4.8028129954667072e-04,
+      1.1962791428901214e-07,  5.9773227818891586e-03,
+      2.7243387375233262e-02, -2.6027202631190141e-02, -1.7831031494975104e-03,
+     -2.2529555439068645e-08,  5.6694093500985290e-04,
+      4.7580701893096223e-03, -1.3685413489846329e-03, -3.3338137165750282e-03,
+      5.7287804480022280e-05, -1.1300292822991837e-04,
+      2.8467596971097305e-04,  2.8179959565330925e-03, -3.0887163471536604e-03,
+     -1.3960594126190875e-05,  5.0150358149509500e-09,
+     -5.3070807682908602e-06,  4.9306025336561432e-04, -4.1882549426144140e-04,
+     -6.8926303153258244e-05, -1.3751826183769166e-09,
+    };
+    const double f6[] =
+    {
+      2.0154146681198872e-24, -3.5688851136225351e-27,  8.0173640710989959e-24,
+     -3.7540344263165092e-21, -8.5473941658947867e-21,
+      2.1098399411304440e-21, -3.2987430986791354e-26, -1.2786887990890647e-22,
+      5.5774262155530719e-21, -5.2422242910241063e-20,
+     -1.3146241530559257e-19, -2.7562828879312281e-22, -1.0734417010552807e-22,
+     -4.3870259352886555e-20,  2.4194632944932309e-19,
+      2.1137135832652420e-19,  1.9015676044847855e-21, -8.5272613545944742e-25,
+     -4.3773733626837943e-20, -9.3076782806108862e-19,
+     -2.2823024255915727e-19,  1.2271105194682399e-19, -1.3400884207613767e-24,
+     -1.0649198357855089e-21,  3.4926449572105291e-20,
+     -3.0499841362447923e-19, -1.8965105476591979e-20, -2.6902054933988774e-21,
+      7.0876511626018948e-26,  2.9290027937202072e-20,
+      8.7582274320145349e-19, -6.0508072579716399e-19, -2.2396479411516622e-20,
+     -2.8336961187045548e-26,  1.0484792769983417e-20,
+     -1.2817391312059265e-19, -1.2999883788145454e-19,  5.2404683918956681e-22,
+      7.0852375629219591e-22, -1.6110515602546699e-24,
+     -4.7728594396620859e-21, -5.5496727075010419e-20,  7.7181639308670794e-21,
+     -3.5828835842015954e-22, -2.4162654496516419e-26,
+     -1.2872700269810765e-22,  3.0405747283361938e-21, -1.5767712674352063e-20,
+     -9.1281108005001305e-22,  6.4377759843551990e-27,
+    };
+
+    struct gkyl_range check_ghost_rng, check_other_ghost_rng;
+    if (apply_in_half_x < 0) {
+      // Applied the BC only on the lower half of the domain.
+      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
+      gkyl_range_shorten_from_above(&check_ghost_rng, &ghost_rng, 0, x_half_len);
+      gkyl_range_shorten_from_below(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
+    }
+    else if (apply_in_half_x > 0) {
+      // Applied the BC only on the upper half of the domain.
+      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
+      gkyl_range_shorten_from_below(&check_ghost_rng, &ghost_rng, 0, x_half_len);
+      gkyl_range_shorten_from_above(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
+    }
+    else
+      check_ghost_rng = ghost_rng;
+
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &check_ghost_rng);
+    while (gkyl_range_iter_next(&iter)) {
+      long linidx = gkyl_range_idx(&check_ghost_rng, iter.idx);
+      double *f_c = gkyl_array_fetch(distf_ho, linidx);
+      int refidx = (iter.idx[0]-1)*cells[1] + iter.idx[1]-1;
+      TEST_CHECK( gkyl_compare(f0[refidx], f_c[0], 1e-13) );
+      TEST_CHECK( gkyl_compare(f1[refidx], f_c[1], 1e-13) );
+      TEST_CHECK( gkyl_compare(f2[refidx], f_c[2], 1e-12) );
+      TEST_CHECK( gkyl_compare(f6[refidx], f_c[6], 1e-12) );
+    }
+
+    if (apply_in_half_x != 0) {
+      // Check that the other half is untouched. 
+      int skin_idx[GKYL_MAX_DIM];
+      gkyl_range_iter_init(&iter, &check_other_ghost_rng);
+      while (gkyl_range_iter_next(&iter)) {
+        long linidx = gkyl_range_idx(&check_other_ghost_rng, iter.idx);
+        double *f_c = gkyl_array_fetch(distf_ho, linidx);
+  
+        for (int d=0; d<check_other_ghost_rng.ndim; d++)
+          skin_idx[d] = iter.idx[d];
+        if (edge == GKYL_LOWER_EDGE)
+          skin_idx[bc_dir] = local.upper[bc_dir];
+        else
+          skin_idx[bc_dir] = local.lower[bc_dir];
+  
+        linidx = gkyl_range_idx(&local_ext, skin_idx);
+        double *fskin_c = gkyl_array_fetch(distf_ho, linidx);
+  
+        for (int k=0; k<distf_ho->ncomp; k++)
+          TEST_CHECK( gkyl_compare(fskin_c[k], f_c[k], 1e-15) );
+      }
+    }
+  }
+
+  gkyl_array_release(buff_per);
+  test_bc_twistshift_array_meta_release(mt);
+  gkyl_twistshift_dg_release(tsup);
+  gkyl_proj_on_basis_release(projDistf);
+  gkyl_array_release(distf_ho);
+  gkyl_array_release(distf);
+
+}
+
+void
+init_donor_3x_fig14(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  double x = xn[0], y = xn[1], z = xn[2];
+
+  struct test_bc_twistshift_ctx *pars = ctx;
+  double Lx[3] = {
+    pars->upper[0]-pars->lower[0],
+    pars->upper[1]-pars->lower[1],
+    pars->upper[2]-pars->lower[2],
+  };
+
+  double f_amplitude = 1.0;
+  double f_floor = 1.0e-10;
+
+  // Cube
+  double rx2 = pow(x-Lx[0]/2,2);
+  double ry2 = pow(y-Lx[1]/2,2);
+  double rz2 = pow(z-Lx[2]/2,2);
+
+  if (rx2 < pow(Lx[0]/4,2) && ry2 < pow(Lx[1]/4,2))
+    fout[0] = f_amplitude;
+  else
+    fout[0] = f_floor;
+}
+
+void
+shift_fig14(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  double x = xn[0];
+
+  struct test_bc_twistshift_ctx *pars = ctx;
+  double Lx[3] = {
+    pars->upper[0]-pars->lower[0],
+    pars->upper[1]-pars->lower[1],
+    pars->upper[2]-pars->lower[2],
+  };
+  double dx[3] = {
+    Lx[0]/pars->cells[0],
+    Lx[1]/pars->cells[1],
+    Lx[2]/pars->cells[2],
+  };
+  enum gkyl_edge_loc edge = pars->edge;
+
+  fout[0] = -(x-0.5);
+
+  if (edge == GKYL_UPPER_EDGE)
+    fout[0] *= -1.0;
+}
+
+void
+test_bc_twistshift_3x_fig14_wcells(const int *cells, enum gkyl_edge_loc edge,
+  int apply_in_half_x, bool check_distf, bool use_gpu, bool write_f)
+{
+  double vt = 1.0; // Thermal speed.
+  double mass = 1.0;
+  double B0 = 1.0; // Magnetic field magnitude.
+  int bc_dir = 2; // Direction in which to apply TS.
+
+  int poly_order = 1;
+  const double lower[] = {0.0, 0.0, 0.0};
+  const double upper[] = {1.0, 1.0, 1.0};
+  int vdim = 0;
+  int ndim = sizeof(lower)/sizeof(lower[0]);
+  int cdim = ndim - vdim;
+
+  double lower_conf[cdim], upper_conf[cdim];
+  int cells_conf[cdim];
+  for (int d=0; d<cdim; d++) {
+    lower_conf[d] = lower[d];
+    upper_conf[d] = upper[d];
+    cells_conf[d] = cells[d];
+  }
+
+  // Grid.
+  struct gkyl_rect_grid grid;
+  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
+  struct gkyl_rect_grid grid_conf;
+  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
+
+  // Basis functions.
+  struct gkyl_basis basis;
+  gkyl_cart_modal_serendip(&basis, ndim, poly_order);
+  struct gkyl_basis basis_conf;
+  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
+
+  // Ranges.
+  int ghost_conf[cdim];
+  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
+  struct gkyl_range local_conf, local_ext_conf; // local, local-ext position-space ranges
+  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
+
+  int ghost[ndim];
+  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
+  struct gkyl_range local, local_ext; // local, local-ext phase-space ranges
+  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
+
+  struct skin_ghost_ranges skin_ghost; // skin/ghost.
+  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
+  struct skin_ghost_ranges skin_ghost_conf; // skin/ghost.
+  skin_ghost_ranges_init(&skin_ghost_conf, &local_ext_conf, ghost_conf);
+
+  // Pick skin and ghost ranges based on 'edge'.
+  struct gkyl_range skin_rng, ghost_rng;
+  struct gkyl_range skin_rng_conf, ghost_rng_conf;
+  if (edge == GKYL_LOWER_EDGE) {
+    skin_rng = skin_ghost.upper_skin[bc_dir];
+    ghost_rng = skin_ghost.lower_ghost[bc_dir];
+    skin_rng_conf = skin_ghost_conf.upper_skin[bc_dir];
+    ghost_rng_conf = skin_ghost_conf.lower_ghost[bc_dir];
+  }
+  else {
+    skin_rng = skin_ghost.lower_skin[bc_dir];
+    ghost_rng = skin_ghost.upper_ghost[bc_dir];
+    skin_rng_conf = skin_ghost_conf.lower_skin[bc_dir];
+    ghost_rng_conf = skin_ghost_conf.upper_ghost[bc_dir];
+  }
+
+  struct test_bc_twistshift_ctx proj_ctx = {
+    .lower = {lower[0], lower[1], lower[2]},
+    .upper = {upper[0], upper[1], upper[2]},
+    .cells = {cells[0], cells[1], cells[2]},
+    .B0 = B0,
+    .vt = vt,
+    .mass = mass,
+    .edge = edge,
+  };
+
+  // Initialize the distribution
+  struct gkyl_array *distf = mkarr(use_gpu, basis.num_basis, local_ext.volume);
+  struct gkyl_array *distf_ho = use_gpu? mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
+  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew( &(struct gkyl_proj_on_basis_inp) {
+      .grid = &grid,
+      .basis = &basis,
+      .num_ret_vals = 1,
+      .eval = init_donor_3x_fig14,
+      .ctx = &proj_ctx,
+    }
+  );
+  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
+  gkyl_array_copy(distf, distf_ho);
+  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new( (struct test_bc_twistshift_output_meta) {
+      .poly_order = poly_order,
+      .basis_type = basis.id
+    }
+  );
+  if (write_f)
+    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho, "ctest_bc_twistshift_3x_fig14_do.gkyl");
+
+  // Create a range only extended in bc_dir.
+  struct gkyl_range update_rng;
+  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
+  for (int d=0; d<ndim; d++) {
+    lower_bcdir_ext[d] = local.lower[d];
+    upper_bcdir_ext[d] = local.upper[d];
+  }
+  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
+  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
+  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
+
+  if (apply_in_half_x < 0) {
+    // Apply the BC only on the lower half of the domain.
+    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
+    gkyl_range_shorten_from_above(&update_rng, &update_rng, 0, x_half_len);
+  }
+  else if (apply_in_half_x > 0) {
+    // Apply the BC only on the upper half of the domain.
+    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
+    gkyl_range_shorten_from_below(&update_rng, &update_rng, 0, x_half_len);
+  }
+
+  // Create the twist-shift updater and shift the donor field.
+  struct gkyl_twistshift_dg_inp tsinp = {
+    .bc_dir = bc_dir,
+    .shift_dir = 1, // y shift.
+    .shear_dir = 0, // shift varies with x.
+    .edge = edge,
+    .cdim = cdim,
+    .bcdir_ext_update_r = &update_rng,
+    .num_ghost = ghost,
+    .basis = &basis,
+    .grid = &grid,
+    .shift_func = shift_fig14,
+    .shift_func_ctx = &proj_ctx,
+    .use_gpu = use_gpu,
+  };
+
+  struct gkyl_twistshift_dg *tsup = gkyl_twistshift_dg_inew(&tsinp);
+
+  // First apply periodicity in z.
+  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
+  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
+
+  gkyl_twistshift_dg_advance(tsup, distf, distf);
+  gkyl_array_copy(distf_ho, distf);
+
+  // Write out the target in the extended range.
+  if (write_f) {
+    double lower_ext[ndim], upper_ext[ndim];
+    int cells_ext[ndim];
+    for (int d=0; d<ndim; d++) {
+      double dx = (upper[d]-lower[d])/cells[d];
+      lower_ext[d] = lower[d]-dx*ghost[d];
+      upper_ext[d] = upper[d]+dx*ghost[d];
+      cells_ext[d] = cells[d]+2*ghost[d];
+    }
+    struct gkyl_rect_grid grid_ext;
+    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
+    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x_fig14_tar.gkyl");
+  }
+
+  if (check_distf) {
+    // Check 0th, 1st, 2nd and 6th DG coeffs.
+    double f0[64], f1[64], f2[64], f6[64];
+
+    if (edge == GKYL_UPPER_EDGE) {
+      const double f0m[] =
+      {
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        1.4142135625145160e+00, 2.8284271247461894e+00,
+        2.8284271247461894e+00, 2.8284271247461894e+00, 1.4142135625145160e+00,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 1.4142135625145160e+00,
+        2.8284271247461894e+00, 2.8284271247461894e+00, 2.8284271247461894e+00,
+        1.4142135625145160e+00, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+        1.4142135625145160e+00, 2.8284271247461894e+00, 2.8284271247461894e+00,
+        2.8284271247461894e+00, 1.4142135625145160e+00, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 1.4142135625145160e+00, 2.8284271247461894e+00,
+        2.8284271247461894e+00, 2.8284271247461894e+00, 1.4142135625145160e+00,
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+      };
+      const double f1m[] =
+      {
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -8.1649658084607613e-01,  0.0000000000000000e+00,  0.0000000000000000e+00,
+         0.0000000000000000e+00,  8.1649658084607613e-01, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -8.1649658084607613e-01,  0.0000000000000000e+00,
+         0.0000000000000000e+00,  0.0000000000000000e+00,  8.1649658084607613e-01,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -8.1649658084607613e-01,
+         0.0000000000000000e+00,  0.0000000000000000e+00,  0.0000000000000000e+00,
+         8.1649658084607613e-01, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -8.1649658084607613e-01,  0.0000000000000000e+00,  0.0000000000000000e+00,
+         0.0000000000000000e+00,  8.1649658084607613e-01,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+      };
+      const double f2m[] =
+      {
+        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
+        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
+        -5.2991257991678335e-25, -5.2991257991678335e-25,
+        -3.4896682092080855e-25, -3.4896682092080855e-25, -3.4896682092080855e-25,
+        -3.4896682092080855e-25, -3.4896682092080855e-25, -3.4896682092080855e-25,
+        -3.4896682092080855e-25, -3.4896682092080855e-25,
+         8.1649658084607457e-01, -2.5535129566378600e-15, -2.5535129566378600e-15,
+        -2.5535129566378600e-15, -8.1649658084607712e-01, -2.5849394142282115e-25,
+        -2.5849394142282115e-25, -2.5849394142282115e-25,
+        -6.4623485355705287e-26,  8.1649658084607535e-01, -6.6613381477509392e-16,
+        -6.6613381477509392e-16, -6.6613381477509392e-16, -8.1649658084607601e-01,
+        -6.4623485355705287e-26, -6.4623485355705287e-26,
+         6.4623485355705287e-26,  6.4623485355705287e-26,  8.1649658084607601e-01,
+         6.6613381477509392e-16,  6.6613381477509392e-16,  6.6613381477509392e-16,
+        -8.1649658084607535e-01,  6.4623485355705287e-26,
+         2.5849394142282115e-25,  2.5849394142282115e-25,  2.5849394142282115e-25,
+         8.1649658084607712e-01,  2.5535129566378600e-15,  2.5535129566378600e-15,
+         2.5535129566378600e-15, -8.1649658084607457e-01,
+         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
+         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
+         5.2991257991678335e-25,  5.2991257991678335e-25,
+         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
+         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
+         5.2991257991678335e-25,  5.2991257991678335e-25,
+      };
+      const double f6m[] =
+      {
+         1.2712579668354740e-41,  1.2712579668354740e-41,  1.2712579668354740e-41,
+         1.2712579668354740e-41,  1.2712579668354740e-41,  1.2712579668354740e-41,
+         1.2712579668354740e-41,  1.2712579668354740e-41,
+        -3.1389085600875902e-43, -3.1389085600875902e-43, -3.1389085600875902e-43,
+        -3.1389085600875902e-43, -3.1389085600875902e-43, -3.1389085600875902e-43,
+        -3.1389085600875902e-43, -3.1389085600875902e-43,
+        -1.1538233466087235e-28,  0.0000000000000000e+00,  0.0000000000000000e+00,
+         0.0000000000000000e+00,  1.1538233466087551e-28,  3.1613293355167873e-42,
+         3.1613293355167873e-42,  3.1613293355167873e-42,
+         3.2061708863751815e-42, -1.1538233466087102e-28,  0.0000000000000000e+00,
+         0.0000000000000000e+00,  0.0000000000000000e+00,  1.1538233466087423e-28,
+         3.2061708863751815e-42,  3.2061708863751815e-42,
+         1.9730282377693424e-42,  1.9730282377693424e-42, -1.1538233466087044e-28,
+         0.0000000000000000e+00,  0.0000000000000000e+00,  0.0000000000000000e+00,
+         1.1538233466087241e-28,  1.9730282377693424e-42,
+         9.8651411888467122e-43,  9.8651411888467122e-43,  9.8651411888467122e-43,
+        -1.1538233466086849e-28,  0.0000000000000000e+00,  0.0000000000000000e+00,
+         0.0000000000000000e+00,  1.1538233466086948e-28,
+         1.9057659114817512e-42,  1.9057659114817512e-42,  1.9057659114817512e-42,
+         1.9057659114817512e-42,  1.9057659114817512e-42,  1.9057659114817512e-42,
+         1.9057659114817512e-42,  1.9057659114817512e-42,
+        -1.5470335046145980e-42, -1.5470335046145980e-42, -1.5470335046145980e-42,
+        -1.5470335046145980e-42, -1.5470335046145980e-42, -1.5470335046145980e-42,
+        -1.5470335046145980e-42, -1.5470335046145980e-42,
+      };
+      int nvals = sizeof(f0m)/sizeof(f0m[0]);
+      for (int i=0; i<nvals; i++) {
+        f0[i] = f0m[i];  f1[i] = f1m[i];  f2[i] = f2m[i]; f6[i] = f6m[i];
+      }
+    }
+    else {
+      const double f0m[] =
+      {
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        1.4142135625145160e+00, 2.8284271247461894e+00, 2.8284271247461894e+00,
+        2.8284271247461894e+00, 1.4142135625145160e+00,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 1.4142135625145160e+00,
+        2.8284271247461894e+00, 2.8284271247461894e+00, 2.8284271247461894e+00,
+        1.4142135625145160e+00, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 1.4142135625145160e+00, 2.8284271247461894e+00,
+        2.8284271247461894e+00, 2.8284271247461894e+00, 1.4142135625145160e+00,
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+        1.4142135625145160e+00, 2.8284271247461894e+00, 2.8284271247461894e+00,
+        2.8284271247461894e+00, 1.4142135625145160e+00, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10, 2.8284271247461891e-10,
+        2.8284271247461891e-10, 2.8284271247461891e-10,
+      };
+      const double f1m[] =
+      {
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+         8.1649658084607613e-01,  0.0000000000000000e+00,  0.0000000000000000e+00,
+         0.0000000000000000e+00, -8.1649658084607613e-01,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,  8.1649658084607613e-01,
+         0.0000000000000000e+00,  0.0000000000000000e+00,  0.0000000000000000e+00,
+        -8.1649658084607613e-01, -2.5849394142282115e-26,
+        -2.5849394142282115e-26,  8.1649658084607613e-01,  0.0000000000000000e+00,
+         0.0000000000000000e+00,  0.0000000000000000e+00, -8.1649658084607613e-01,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+         8.1649658084607613e-01,  0.0000000000000000e+00,  0.0000000000000000e+00,
+         0.0000000000000000e+00, -8.1649658084607613e-01, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26, -2.5849394142282115e-26,
+        -2.5849394142282115e-26, -2.5849394142282115e-26,
+      };
+      const double f2m[] =
+      {
+         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
+         5.2991257991678335e-25,  5.2991257991678335e-25,  5.2991257991678335e-25,
+         5.2991257991678335e-25,  5.2991257991678335e-25,
+         3.4896682092080855e-25,  3.4896682092080855e-25,  3.4896682092080855e-25,
+         3.4896682092080855e-25,  3.4896682092080855e-25,  3.4896682092080855e-25,
+         3.4896682092080855e-25,  3.4896682092080855e-25,
+         2.5849394142282115e-25,  2.5849394142282115e-25,  2.5849394142282115e-25,
+         8.1649658084607712e-01,  2.5535129566378600e-15,  2.5535129566378600e-15,
+         2.5535129566378600e-15, -8.1649658084607457e-01,
+         6.4623485355705287e-26,  6.4623485355705287e-26,  8.1649658084607601e-01,
+         6.6613381477509392e-16,  6.6613381477509392e-16,  6.6613381477509392e-16,
+        -8.1649658084607535e-01,  6.4623485355705287e-26,
+        -6.4623485355705287e-26,  8.1649658084607535e-01, -6.6613381477509392e-16,
+        -6.6613381477509392e-16, -6.6613381477509392e-16, -8.1649658084607601e-01,
+        -6.4623485355705287e-26, -6.4623485355705287e-26,
+         8.1649658084607457e-01, -2.5535129566378600e-15, -2.5535129566378600e-15,
+        -2.5535129566378600e-15, -8.1649658084607712e-01, -2.5849394142282115e-25,
+        -2.5849394142282115e-25, -2.5849394142282115e-25,
+        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
+        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
+        -5.2991257991678335e-25, -5.2991257991678335e-25,
+        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
+        -5.2991257991678335e-25, -5.2991257991678335e-25, -5.2991257991678335e-25,
+        -5.2991257991678335e-25, -5.2991257991678335e-25,
+      };
+      const double f6m[] =
+      {
+        -5.3809861030072976e-43, -5.3809861030072976e-43, -5.3809861030072976e-43,
+        -5.3809861030072976e-43, -5.3809861030072976e-43, -5.3809861030072976e-43,
+        -5.3809861030072976e-43, -5.3809861030072976e-43,
+        -1.0941338409448172e-41, -1.0941338409448172e-41, -1.0941338409448172e-41,
+        -1.0941338409448172e-41, -1.0941338409448172e-41, -1.0941338409448172e-41,
+        -1.0941338409448172e-41, -1.0941338409448172e-41,
+        -6.0984509167416039e-42, -6.0984509167416039e-42, -6.0984509167416039e-42,
+         1.2692056812695856e-27,  0.0000000000000000e+00,  0.0000000000000000e+00,
+         0.0000000000000000e+00, -1.2692056812695917e-27,
+        -1.7936620343357659e-42, -1.7936620343357659e-42,  1.2692056812695897e-27,
+         0.0000000000000000e+00,  0.0000000000000000e+00,  0.0000000000000000e+00,
+        -1.2692056812695915e-27, -1.7936620343357659e-42,
+        -1.2555634240350361e-42,  1.2692056812695930e-27,  0.0000000000000000e+00,
+         0.0000000000000000e+00,  0.0000000000000000e+00, -1.2692056812695942e-27,
+        -1.2555634240350361e-42, -1.2555634240350361e-42,
+         1.2692056812695946e-27,  0.0000000000000000e+00,  0.0000000000000000e+00,
+         0.0000000000000000e+00, -1.2692056812695955e-27, -8.9683101716788293e-43,
+        -8.9683101716788293e-43, -8.9683101716788293e-43,
+         3.7666902721051083e-42,  3.7666902721051083e-42,  3.7666902721051083e-42,
+         3.7666902721051083e-42,  3.7666902721051083e-42,  3.7666902721051083e-42,
+         3.7666902721051083e-42,  3.7666902721051083e-42,
+         5.3809861030072976e-43,  5.3809861030072976e-43,  5.3809861030072976e-43,
+         5.3809861030072976e-43,  5.3809861030072976e-43,  5.3809861030072976e-43,
+         5.3809861030072976e-43,  5.3809861030072976e-43,
+      };
+      int nvals = sizeof(f0m)/sizeof(f0m[0]);
+      for (int i=0; i<nvals; i++) {
+        f0[i] = f0m[i];  f1[i] = f1m[i];  f2[i] = f2m[i]; f6[i] = f6m[i];
+      }
+    }
+
+    struct gkyl_range check_ghost_rng, check_other_ghost_rng;
+    if (apply_in_half_x < 0) {
+      // Applied the BC only on the lower half of the domain.
+      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
+      gkyl_range_shorten_from_above(&check_ghost_rng, &ghost_rng, 0, x_half_len);
+      gkyl_range_shorten_from_below(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
+    }
+    else if (apply_in_half_x > 0) {
+      // Applied the BC only on the upper half of the domain.
+      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
+      gkyl_range_shorten_from_below(&check_ghost_rng, &ghost_rng, 0, x_half_len);
+      gkyl_range_shorten_from_above(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
+    }
+    else
+      check_ghost_rng = ghost_rng;
+
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &check_ghost_rng);
+    while (gkyl_range_iter_next(&iter)) {
+      long linidx = gkyl_range_idx(&check_ghost_rng, iter.idx);
+      double *f_c = gkyl_array_fetch(distf_ho, linidx);
+      int refidx = (iter.idx[0]-1)*cells[1] + iter.idx[1]-1;
+      TEST_CHECK( gkyl_compare(f0[refidx], f_c[0], 1e-13) );
+      TEST_CHECK( gkyl_compare(f1[refidx], f_c[1], 1e-13) );
+      TEST_CHECK( gkyl_compare(f2[refidx], f_c[2], 1e-12) );
+      TEST_CHECK( gkyl_compare(f6[refidx], f_c[6], 1e-12) );
+    }
+
+  }
+
+  gkyl_array_release(buff_per);
+  test_bc_twistshift_array_meta_release(mt);
+  gkyl_twistshift_dg_release(tsup);
+  gkyl_proj_on_basis_release(projDistf);
+  gkyl_array_release(distf_ho);
+  gkyl_array_release(distf);
+
+}
+
+void
+test_bc_twistshift_3x2v_fig11_wcells(const int *cells, enum gkyl_edge_loc edge,
+  int apply_in_half_x, bool check_distf, bool use_gpu, bool write_f)
+{
+  double vt = 1.0; // Thermal speed.
+  double mass = 1.0;
+  double B0 = 1.0; // Magnetic field magnitude.
+  int bc_dir = 2; // Direction in which to apply TS.
+
+  int poly_order = 1;
+  const double lower[] = {-2.0, -1.50, -3.0, -5.0*vt, 0.};
+  const double upper[] = { 2.0,  1.50,  3.0,  5.0*vt, mass*(pow(5.0*vt,2))/(2.0*B0)};
+  int vdim = 2;
+  int ndim = sizeof(lower)/sizeof(lower[0]);
+  int cdim = ndim - vdim;
+
+  double lower_conf[cdim], upper_conf[cdim];
+  int cells_conf[cdim];
+  for (int d=0; d<cdim; d++) {
+    lower_conf[d] = lower[d];
+    upper_conf[d] = upper[d];
+    cells_conf[d] = cells[d];
+  }
+  double lower_vel[vdim], upper_vel[vdim];
+  int cells_vel[vdim];
+  for (int d=0; d<vdim; d++) {
+    lower_vel[d] = lower[cdim+d];
+    upper_vel[d] = upper[cdim+d];
+    cells_vel[d] = cells[cdim+d];
+  }
+
+  // Grid.
+  struct gkyl_rect_grid grid;
+  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
+  struct gkyl_rect_grid grid_conf;
+  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
+  struct gkyl_rect_grid grid_vel;
+  gkyl_rect_grid_init(&grid_vel, vdim, lower_vel, upper_vel, cells_vel);
+
+  // Basis functions.
+  struct gkyl_basis basis;
+  if (poly_order == 1) 
+    gkyl_cart_modal_gkhybrid(&basis, cdim, vdim);
+  else
+    gkyl_cart_modal_serendip(&basis, ndim, poly_order);
+  struct gkyl_basis basis_conf;
+  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
+
+  // Ranges.
+  int ghost_conf[cdim];
+  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
+  struct gkyl_range local_conf, local_ext_conf; // local, local-ext position-space ranges
+  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
+
+  int ghost_vel[vdim];
+  for (int d=0; d<vdim; d++) ghost_vel[d] = 0;
+  struct gkyl_range local_vel, local_ext_vel; // local, local-ext position-space ranges
+  gkyl_create_grid_ranges(&grid_vel, ghost_vel, &local_ext_vel, &local_vel);
+
+  int ghost[ndim];
+  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
+  for (int d=cdim; d<ndim; d++) ghost[d] = ghost_vel[d-cdim];
+  struct gkyl_range local, local_ext; // local, local-ext phase-space ranges
+  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
+
+  struct skin_ghost_ranges skin_ghost; // skin/ghost.
+  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
+  struct skin_ghost_ranges skin_ghost_conf; // skin/ghost.
+  skin_ghost_ranges_init(&skin_ghost_conf, &local_ext_conf, ghost_conf);
+
+  // Pick skin and ghost ranges based on 'edge'.
+  struct gkyl_range skin_rng, ghost_rng;
+  struct gkyl_range skin_rng_conf, ghost_rng_conf;
+  if (edge == GKYL_LOWER_EDGE) {
+    skin_rng = skin_ghost.upper_skin[bc_dir];
+    ghost_rng = skin_ghost.lower_ghost[bc_dir];
+    skin_rng_conf = skin_ghost_conf.upper_skin[bc_dir];
+    ghost_rng_conf = skin_ghost_conf.lower_ghost[bc_dir];
+  }
+  else {
+    skin_rng = skin_ghost.lower_skin[bc_dir];
+    ghost_rng = skin_ghost.upper_ghost[bc_dir];
+    skin_rng_conf = skin_ghost_conf.lower_skin[bc_dir];
+    ghost_rng_conf = skin_ghost_conf.upper_ghost[bc_dir];
+  }
+
+  struct test_bc_twistshift_ctx proj_ctx = {
+    .lower = {lower[0], lower[1], lower[2], lower[3], lower[4]},
+    .upper = {upper[0], upper[1], upper[2], upper[3], upper[4]},
+    .cells = {cells[0], cells[1], cells[2], cells[3], cells[4]},
+    .B0 = B0,
+    .vt = vt,
+    .mass = mass,
+  };
+
+  // Initialize the distribution
+  struct gkyl_array *distf = mkarr(use_gpu, basis.num_basis, local_ext.volume);
+  struct gkyl_array *distf_ho = use_gpu? mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
+  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew( &(struct gkyl_proj_on_basis_inp) {
+      .grid = &grid,
+      .basis = &basis,
+      .num_ret_vals = 1,
+      .eval = init_donor_3x2v_fig11,
+      .ctx = &proj_ctx,
+    }
+  );
+  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
+  gkyl_array_copy(distf, distf_ho);
+  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new( (struct test_bc_twistshift_output_meta) {
+      .poly_order = poly_order,
+      .basis_type = basis.id
+    }
+  );
+  if (write_f)
+    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho, "ctest_bc_twistshift_3x2v_fig11_do.gkyl");
+
+  // Create a range only extended in bc_dir.
+  struct gkyl_range update_rng;
+  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
+  for (int d=0; d<ndim; d++) {
+    lower_bcdir_ext[d] = local.lower[d];
+    upper_bcdir_ext[d] = local.upper[d];
+  }
+  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
+  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
+  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
+
+  if (apply_in_half_x < 0) {
+    // Apply the BC only on the lower half of the domain.
+    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
+    gkyl_range_shorten_from_above(&update_rng, &update_rng, 0, x_half_len);
+  }
+  else if (apply_in_half_x > 0) {
+    // Apply the BC only on the upper half of the domain.
+    int x_half_len = (update_rng.upper[0] - update_rng.lower[0] + 1)/2;
+    gkyl_range_shorten_from_below(&update_rng, &update_rng, 0, x_half_len);
+  }
+
+  // Create the twist-shift updater and shift the donor field.
+  struct gkyl_twistshift_dg_inp tsinp = {
+    .bc_dir = bc_dir,
+    .shift_dir = 1, // y shift.
+    .shear_dir = 0, // shift varies with x.
+    .edge = edge,
+    .cdim = cdim,
+    .bcdir_ext_update_r = &update_rng,
+    .num_ghost = ghost,
+    .basis = &basis,
+    .grid = &grid,
+    .shift_func = shift_fig11,
+    .shift_func_ctx = &proj_ctx,
+    .use_gpu = use_gpu,
+  };
+
+  struct gkyl_twistshift_dg *tsup = gkyl_twistshift_dg_inew(&tsinp);
+
+  // First apply periodicity in z.
+  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
+  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
+
+  gkyl_twistshift_dg_advance(tsup, distf, distf);
+  gkyl_array_copy(distf_ho, distf);
+
+  // Write out the target in the extended range.
+  if (write_f) {
+    double lower_ext[ndim], upper_ext[ndim];
+    int cells_ext[ndim];
+    for (int d=0; d<ndim; d++) {
+      double dx = (upper[d]-lower[d])/cells[d];
+      lower_ext[d] = lower[d]-dx*ghost[d];
+      upper_ext[d] = upper[d]+dx*ghost[d];
+      cells_ext[d] = cells[d]+2*ghost[d];
+    }
+    struct gkyl_rect_grid grid_ext;
+    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
+    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho, "ctest_bc_twistshift_3x2v_fig11_tar.gkyl");
+  }
+
+  // Compute the integrated moments of the skin cell and the ghost cell.
+  // Velocity space mapping.
+  struct gkyl_mapc2p_inp c2p_in = { };
+  struct gkyl_velocity_map *gvm = gkyl_velocity_map_new(c2p_in, grid, grid_vel,
+    local, local_ext, local_vel, local_ext_vel, use_gpu);
+  struct gkyl_position_map *pmap = gkyl_position_map_null_new();
+
+  // Initialize geometry
+  struct gkyl_gk_geometry_inp geometry_inp = {
+    .geometry_id = GKYL_GEOMETRY_MAPC2P,
+    .c2p_ctx = 0,
+    .mapc2p = mapc2p,
+    .bfield_ctx = &proj_ctx,
+    .bfield_func = eval_bfield_3x,
+    .position_map = pmap,
+    .grid = grid_conf,
+    .local = local_conf,
+    .local_ext = local_ext_conf,
+    .global = local_conf,
+    .global_ext = local_ext_conf,
+    .basis = basis_conf,
+    .geo_grid = grid_conf,
+    .geo_local = local_conf,
+    .geo_local_ext = local_ext_conf,
+    .geo_global = local_conf,
+    .geo_global_ext = local_ext_conf,
+    .geo_basis = basis_conf,
+  };
+  struct gk_geometry* gk_geom_3d = gkyl_gk_geometry_mapc2p_new(&geometry_inp);
+  struct gk_geometry* gk_geom = gkyl_gk_geometry_acquire(gk_geom_3d);
+  gkyl_gk_geometry_release(gk_geom_3d); // release temporary 3d geometry
+  if (use_gpu) {  // If we are on the gpu, copy from host
+    struct gk_geometry* gk_geom_dev = gkyl_gk_geometry_new(gk_geom, &geometry_inp, use_gpu);
+    gkyl_gk_geometry_release(gk_geom);
+    gk_geom = gkyl_gk_geometry_acquire(gk_geom_dev);
+    gkyl_gk_geometry_release(gk_geom_dev);
+  }
+  // Need the magnetic field to be initialized in the ghost cell in order to
+  // compute integrated moments in the ghost cell (for checking moment
+  // conservation).
+  gkyl_array_clear(gk_geom->geo_corn.bmag, 0.0);
+  gkyl_array_shiftc(gk_geom->geo_corn.bmag, B0*pow(sqrt(2.0),cdim), 0);
+
+  struct gkyl_dg_updater_moment *mcalc = gkyl_dg_updater_moment_gyrokinetic_new(&grid, &basis_conf,
+    &basis, &local_conf, mass, 0, gvm, gk_geom, NULL, GKYL_F_MOMENT_M0M1M2, true, use_gpu);
+  int num_mom = gkyl_dg_updater_moment_gyrokinetic_num_mom(mcalc);
+
+  struct gkyl_array *marr = mkarr(use_gpu, num_mom, local_ext_conf.volume);
+  double *red_integ_mom_skin, *red_integ_mom_ghost;
+  if (use_gpu) {
+    red_integ_mom_skin = gkyl_cu_malloc(sizeof(double[num_mom]));
+    red_integ_mom_ghost = gkyl_cu_malloc(sizeof(double[num_mom]));
+  }
+  else {
+    red_integ_mom_skin = gkyl_malloc(sizeof(double[num_mom]));
+    red_integ_mom_ghost = gkyl_malloc(sizeof(double[num_mom]));
+  }
+  double *red_integ_mom_skin_ho = gkyl_malloc(sizeof(double[num_mom]));
+  double *red_integ_mom_ghost_ho = gkyl_malloc(sizeof(double[num_mom]));
+
+  gkyl_dg_updater_moment_gyrokinetic_advance(mcalc,
+      &skin_rng, &skin_rng_conf, distf, marr);
+  gkyl_array_reduce_range(red_integ_mom_skin, marr, GKYL_SUM, &skin_rng_conf);
+
+  gkyl_dg_updater_moment_gyrokinetic_advance(mcalc,
+      &ghost_rng, &ghost_rng_conf, distf, marr);
+  gkyl_array_reduce_range(red_integ_mom_ghost, marr, GKYL_SUM, &ghost_rng_conf);
+
+  if (use_gpu) {
+    gkyl_cu_memcpy(red_integ_mom_skin_ho, red_integ_mom_skin, sizeof(double[num_mom]), GKYL_CU_MEMCPY_D2H);
+    gkyl_cu_memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]), GKYL_CU_MEMCPY_D2H);
+  }
+  else {
+    memcpy(red_integ_mom_skin_ho, red_integ_mom_skin, sizeof(double[num_mom]));
+    memcpy(red_integ_mom_ghost_ho, red_integ_mom_ghost, sizeof(double[num_mom]));
+  }
+
+  for (int k=0; k<num_mom; k++) {
+    TEST_CHECK( gkyl_compare(red_integ_mom_skin_ho[k], red_integ_mom_ghost_ho[k], 1e-12));
+    TEST_MSG( "integ_mom %d | Expected: %.14e | Got: %.14e\n",k,red_integ_mom_skin_ho[k],red_integ_mom_ghost_ho[k]);
+  }
+
+  if (check_distf) {
+    // Check 0th, 1st, 2nd and 6th DG coeffs.
+    const double f0[] =
+    {
+      -1.2776583204321330e-07,  1.6243951159613727e-11,  1.0311777925221165e-06,
+       2.5199396402501986e-05,  1.0916599224379850e-05,
+       3.7270542239467049e-06,  6.1264779478169708e-11, -2.7206923690464824e-07,
+       7.6711882696143613e-05,  1.2599699723571620e-04,
+       9.0423892898165817e-05, -1.5766645989926764e-06, -7.8141332726062177e-07,
+       6.2106961880222910e-05,  5.9601729446907966e-04,
+       7.5651563805650783e-04,  3.0022125798956283e-06,  4.1954120810574047e-10,
+       2.0905519501674566e-05,  9.7715562102146359e-04,
+       1.9699067404442962e-03,  9.9213725697257197e-05,  1.6358151057562534e-09,
+      -8.9770499075323632e-06,  6.3656586712399692e-04,
+       1.9699067404442966e-03,  6.3656586712399627e-04, -8.9770499075323903e-06,
+       1.6358151057562547e-09,  9.9213725697256980e-05,
+       7.5651563805650697e-04,  9.7715562102146315e-04,  2.0905519501674579e-05,
+       4.1954120810574011e-10,  3.0022125798956054e-06,
+       9.0423892898165560e-05,  5.9601729446907923e-04,  6.2106961880223127e-05,
+      -7.8141332726062940e-07, -1.5766645989926737e-06,
+       3.7270542239466922e-06,  1.2599699723571601e-04,  7.6711882696143640e-05,
+      -2.7206923690464432e-07,  6.1264779478169876e-11,
+      -1.2776583204321266e-07,  1.0916599224379833e-05,  2.5199396402501990e-05,
+       1.0311777925221199e-06,  1.6243951159613701e-11,
+    };
+    const double f1[] =
+    {
+      -4.9195522432173540e-08,  1.5685739030718726e-12,  1.4769458228600922e-07,
+       1.0802674169515287e-05,  8.3762046049376821e-06,
+       3.3888736767723010e-06,  4.5856936150936589e-11, -8.5121281577597483e-07,
+       1.6013444035211209e-05,  6.8268181976822328e-05,
+       7.3577602711338998e-05, -1.7788689927180866e-06,  7.8492724484237293e-07,
+      -1.7712840678887841e-05,  1.7658618650808429e-04,
+       3.0511179936649428e-04,  9.3609830699107460e-06, -6.7510432676475386e-11,
+      -1.2765598324806747e-05,  3.2424269440705722e-05,
+       3.5458992651786952e-04,  4.7597851765421919e-05,  8.8303883448615030e-10,
+       1.9314968272504524e-07, -2.2962463818142971e-04,
+      -3.5458992651786996e-04,  2.2962463818142974e-04, -1.9314968272508097e-07,
+      -8.8303883448615154e-10, -4.7597851765421851e-05,
+      -3.0511179936649438e-04, -3.2424269440705817e-05,  1.2765598324806735e-05,
+       6.7510432676475619e-11, -9.3609830699107308e-06,
+      -7.3577602711338781e-05, -1.7658618650808405e-04,  1.7712840678887892e-05,
+      -7.8492724484237631e-07,  1.7788689927180847e-06,
+      -3.3888736767722963e-06, -6.8268181976822274e-05, -1.6013444035211209e-05,
+       8.5121281577597260e-07, -4.5856936150936738e-11,
+       4.9195522432173143e-08, -8.3762046049376720e-06, -1.0802674169515287e-05,
+      -1.4769458228601091e-07, -1.5685739030718849e-12,
+    };
+    const double f2[] =
+    {
+       1.0834595144400169e-07,  2.8074844853976726e-11,  1.4071551236371810e-06,
+       8.5504722173976439e-06, -1.0066001367323685e-05,
+      -5.8117617082185942e-06, -1.0238374930018830e-10,  2.8501052072984633e-07,
+       6.3057248605008680e-05, -5.7530395033770669e-05,
+      -9.7137704174052986e-05,  2.3069951842792511e-06, -1.1695510118502272e-06,
+       6.8060999036891783e-05,  2.7939260964732569e-05,
+      -5.5618349420324920e-04, -1.1574301899303677e-05,  4.5994892978466414e-10,
+       3.6402688349758515e-05,  5.3135464780386854e-04,
+      -4.8110806422932840e-04, -1.2202918179822416e-04, -2.4422466434550431e-09,
+      -9.8051144559640598e-06,  6.1294480273016622e-04,
+       4.8110806422933762e-04, -6.1294480273016254e-04,  9.8051144559646528e-06,
+       2.4422466434550737e-09,  1.2202918179822499e-04,
+       5.5618349420325061e-04, -5.3135464780386637e-04, -3.6402688349757959e-05,
+      -4.5994892978464471e-10,  1.1574301899304035e-05,
+       9.7137704174053312e-05, -2.7939260964731105e-05, -6.8060999036891905e-05,
+       1.1695510118502157e-06, -2.3069951842791736e-06,
+       5.8117617082186383e-06,  5.7530395033770560e-05, -6.3057248605008110e-05,
+      -2.8501052072977417e-07,  1.0238374930019089e-10,
+      -1.0834595144399179e-07,  1.0066001367323711e-05, -8.5504722173975829e-06,
+      -1.4071551236371706e-06, -2.8074844853976218e-11,
+    };
+    const double f6[] =
+    {
+      -1.6760873656052127e-08,  6.9405324157913410e-12,  3.9141599258817577e-07,
+       6.6551168467387512e-06, -7.0297789062032620e-06,
+      -4.5612495563369940e-06, -1.0697208933100729e-10, -1.2131836499023975e-06,
+       2.2469828589386375e-05, -1.6695288411057533e-05,
+      -7.7165270659134859e-05,  2.5304169488836587e-06,  1.1365688119276509e-06,
+      -1.6574594816272132e-05,  9.0072879714596268e-05,
+      -1.3067050406710185e-04, -1.7045882735192163e-05, -5.6876686935148544e-10,
+      -1.3656577294632045e-05,  1.6137353286379611e-04,
+       2.1258539335022546e-04, -4.1000351637691106e-05, -8.2479310847183273e-10,
+      -3.5225958304071601e-06, -1.6806162108901716e-04,
+       2.1258539335022143e-04, -1.6806162108901589e-04, -3.5225958304067087e-06,
+      -8.2479310847182528e-10, -4.1000351637691127e-05,
+      -1.3067050406710394e-04,  1.6137353286379722e-04, -1.3656577294632221e-05,
+      -5.6876686935149423e-10, -1.7045882735192441e-05,
+      -7.7165270659135103e-05,  9.0072879714595211e-05, -1.6574594816271881e-05,
+       1.1365688119277396e-06,  2.5304169488835875e-06,
+      -4.5612495563370270e-06, -1.6695288411057713e-05,  2.2469828589386263e-05,
+      -1.2131836499024202e-06, -1.0697208933100851e-10,
+      -1.6760873656069723e-08, -7.0297789062032917e-06,  6.6551168467386817e-06,
+       3.9141599258816127e-07,  6.9405324157907182e-12,
+    };
+
+    struct gkyl_range check_ghost_rng, check_other_ghost_rng;
+    if (apply_in_half_x < 0) {
+      // Applied the BC only on the lower half of the domain.
+      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
+      gkyl_range_shorten_from_above(&check_ghost_rng, &ghost_rng, 0, x_half_len);
+      gkyl_range_shorten_from_below(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
+    }
+    else if (apply_in_half_x > 0) {
+      // Applied the BC only on the upper half of the domain.
+      int x_half_len = (ghost_rng.upper[0] - ghost_rng.lower[0] + 1)/2;
+      gkyl_range_shorten_from_below(&check_ghost_rng, &ghost_rng, 0, x_half_len);
+      gkyl_range_shorten_from_above(&check_other_ghost_rng, &ghost_rng, 0, x_half_len);
+    }
+    else
+      check_ghost_rng = ghost_rng;
+
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &check_ghost_rng);
+    while (gkyl_range_iter_next(&iter)) {
+      if (iter.idx[3]==1 && iter.idx[4]==1) {
+        long linidx = gkyl_range_idx(&check_ghost_rng, iter.idx);
+        double *f_c = gkyl_array_fetch(distf_ho, linidx);
+        int refidx = (iter.idx[0]-1)*cells[1] + iter.idx[1]-1;
+        TEST_CHECK( gkyl_compare(f0[refidx], f_c[0], 1e-13) );
+        TEST_CHECK( gkyl_compare(f1[refidx], f_c[1], 1e-13) );
+        TEST_CHECK( gkyl_compare(f2[refidx], f_c[2], 1e-12) );
+        TEST_CHECK( gkyl_compare(f6[refidx], f_c[6], 1e-12) );
+      }
+    }
+
+    if (apply_in_half_x != 0) {
+      // Check that the other half is untouched. 
+      int skin_idx[GKYL_MAX_DIM];
+      gkyl_range_iter_init(&iter, &check_other_ghost_rng);
+      while (gkyl_range_iter_next(&iter)) {
+        long linidx = gkyl_range_idx(&check_other_ghost_rng, iter.idx);
+        double *f_c = gkyl_array_fetch(distf_ho, linidx);
+  
+        for (int d=0; d<check_other_ghost_rng.ndim; d++)
+          skin_idx[d] = iter.idx[d];
+        if (edge == GKYL_LOWER_EDGE)
+          skin_idx[bc_dir] = local.upper[bc_dir];
+        else
+          skin_idx[bc_dir] = local.lower[bc_dir];
+  
+        linidx = gkyl_range_idx(&local_ext, skin_idx);
+        double *fskin_c = gkyl_array_fetch(distf_ho, linidx);
+  
+        for (int k=0; k<distf_ho->ncomp; k++)
+          TEST_CHECK( gkyl_compare(fskin_c[k], f_c[k], 1e-15) );
+      }
+    }
+  }
+
+  gkyl_free(red_integ_mom_skin_ho);
+  gkyl_free(red_integ_mom_ghost_ho);
+  if (use_gpu) {
+    gkyl_cu_free(red_integ_mom_skin);
+    gkyl_cu_free(red_integ_mom_ghost);
+  }
+  else {
+    gkyl_free(red_integ_mom_skin);
+    gkyl_free(red_integ_mom_ghost);
+  }
+  gkyl_dg_updater_moment_gyrokinetic_release(mcalc);
+  gkyl_array_release(marr);
+  gkyl_gk_geometry_release(gk_geom);
+  gkyl_position_map_release(pmap);
+  gkyl_velocity_map_release(gvm);
+  gkyl_array_release(buff_per);
+  test_bc_twistshift_array_meta_release(mt);
+  gkyl_twistshift_dg_release(tsup);
+  gkyl_proj_on_basis_release(projDistf);
+  gkyl_array_release(distf_ho);
+  gkyl_array_release(distf);
+
+}
+
+// CBC geometry (see rt_gk_cbc_passive_3x2v_p1.c)
+
+static double
+interp_1x_lut_cbc(double x, double *lut_grid, double *lut_val, int N)
+{
+  double x_min = lut_grid[0];
+  double x_max = lut_grid[N-1];
+  if (x <= x_min) return lut_val[0];
+  if (x >= x_max) return lut_val[N-1];
+  double dx = (x_max - x_min)/(N-1);
+  int idx = (int)((x - x_min)/dx);
+  if (idx < 0) idx = 0;
+  if (idx >= N-1) idx = N-2;
+  return lut_val[idx] + (lut_val[idx+1] - lut_val[idx])*(x - lut_grid[idx])/(lut_grid[idx+1] - lut_grid[idx]);
+}
+
+struct gk_cbc_app_ctx {
+  double a_shift, Z_axis, R_axis, R0, a_mid, r0, B0, kappa, delta, q0, Cy, qaxis, qlcfs;
+  double Lx, Ly, Lz;
+  double x_min, y_min, z_min, x_max, y_max, z_max;
+  int psi_lut_size;
+  double *r_lut;
+  double *dPsidr_int_lut;
+};
+
+struct integrand_cbc_ctx {
+  struct gk_cbc_app_ctx *app_ctx;
+  double r;
+  double theta;
+};
+
+static double r_x_cbc(double x, double r0) { return x + r0; }
+
+static double qprofile_cbc(double r, double a_mid, double qaxis, double qlcfs)
+{
+  return 1.0 + 2.78*pow(r/a_mid, 2.8);
+}
+
+static double R_rtheta_cbc(double r, double theta, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  return app->R_axis - app->a_shift*r*r/(2.*app->R_axis)
+    + r*cos(theta + asin(app->delta)*sin(theta));
+}
+
+static double dRdr_cbc(double r, double theta, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  return -app->a_shift*r/app->R_axis + cos(theta + asin(app->delta)*sin(theta));
+}
+
+static double dRdtheta_cbc(double r, double theta, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  return -r*sin(theta + asin(app->delta)*sin(theta))*(1. + asin(app->delta)*cos(theta));
+}
+
+static double dZdr_cbc(double r, double theta, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  return app->kappa*sin(theta);
+}
+
+static double dZdtheta_cbc(double r, double theta, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  return app->kappa*r*cos(theta);
+}
+
+static double Jr_cbc(double r, double theta, void *ctx)
+{
+  return R_rtheta_cbc(r, theta, ctx)
+    *(dRdr_cbc(r, theta, ctx)*dZdtheta_cbc(r, theta, ctx)
+      - dRdtheta_cbc(r, theta, ctx)*dZdr_cbc(r, theta, ctx));
+}
+
+static double Bphi_cbc(double R, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  return app->B0*app->R0/R;
+}
+
+static double integrand_JoRsq_cbc(double t, void *int_ctx)
+{
+  struct integrand_cbc_ctx *inctx = int_ctx;
+  return Jr_cbc(inctx->r, t, inctx->app_ctx)
+    / pow(R_rtheta_cbc(inctx->r, t, inctx->app_ctx), 2);
+}
+
+static double intdPsidr_cbc(double r, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  struct integrand_cbc_ctx tmp_ctx = {.app_ctx = app, .r = r};
+  struct gkyl_qr_res integral = gkyl_dbl_exp(integrand_JoRsq_cbc, &tmp_ctx, 0., 2.*M_PI, 7, 1e-10);
+  return integral.res;
+}
+
+static double dPsidr_cbc(double r, double theta, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  double integral_val = interp_1x_lut_cbc(r, app->r_lut, app->dPsidr_int_lut, app->psi_lut_size);
+  double R = R_rtheta_cbc(r, theta, ctx);
+  double Bt = Bphi_cbc(R, ctx);
+  return (R*Bt/(2.*M_PI*qprofile_cbc(r, app->a_mid, app->qaxis, app->qlcfs)))*integral_val;
+}
+
+static double compute_alpha_integral_cbc(double r, double twrap, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  struct integrand_cbc_ctx tmp_ctx = {.app_ctx = app, .r = r};
+  struct gkyl_qr_res integral;
+  if (twrap == 0.0) return 0.0;
+  if (0. < twrap) {
+    integral = gkyl_dbl_exp(integrand_JoRsq_cbc, &tmp_ctx, 0., twrap, 7, 1e-10);
+    return integral.res;
+  } else {
+    integral = gkyl_dbl_exp(integrand_JoRsq_cbc, &tmp_ctx, twrap, 0., 7, 1e-10);
+    return -integral.res;
+  }
+}
+
+static double alpha_cbc(double r, double theta, double phi, void *ctx)
+{
+  double twrap = theta;
+  while (twrap < -M_PI) twrap += 2.*M_PI;
+  while (twrap >  M_PI) twrap -= 2.*M_PI;
+  double integral_val = compute_alpha_integral_cbc(r, twrap, ctx);
+  double R  = R_rtheta_cbc(r, theta, ctx);
+  double Bt = Bphi_cbc(R, ctx);
+  return phi - R*Bt*integral_val/dPsidr_cbc(r, theta, ctx);
+}
+
+void bc_shift_func_lo_cbc(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  double r = r_x_cbc(xc[0], app->r0);
+  fout[0] = app->Cy*(alpha_cbc(r, app->z_min, 0.0, ctx) - alpha_cbc(r, app->z_max, 0.0, ctx));
+}
+
+void bc_shift_func_up_cbc(double t, const double *xc, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  double r = r_x_cbc(xc[0], app->r0);
+  fout[0] = -app->Cy*(alpha_cbc(r, app->z_min, 0.0, ctx) - alpha_cbc(r, app->z_max, 0.0, ctx));
+}
+
+void init_donor_3x_cbc(double t, const double *xn, double* GKYL_RESTRICT fout, void *ctx)
+{
+  struct gk_cbc_app_ctx *app = ctx;
+  double x = xn[0], y = xn[1], z = xn[2];
+  double sigx = app->Lx/7.0, sigy = app->Ly/7.0, sigz = app->Lz/10.0;
+  double mux = 0.*app->Lx;
+  fout[0] = exp(-pow(x-mux,2)/(2.*pow(sigx,2)) - pow(y,2)/(2.*pow(sigy,2)) - pow(z,2)/(2.*pow(sigz,2)));
+}
+
+void
+test_bc_twistshift_3x_cbc_wcells(const int *cells, enum gkyl_edge_loc edge,
+  bool check_distf, bool use_gpu, bool write_f)
+{
+  int bc_dir = 2;
+  int poly_order = 1;
+
+  // Physical parameters matching rt_gk_cbc_passive_3x2v_p1.c create_ctx().
+  double eV  = GKYL_ELEMENTARY_CHARGE;
+  double mp  = GKYL_PROTON_MASS;
+  double qi  = eV;
+  double mi  = mp; // AMU = 1 (hydrogen)
+  double Te0 = 2000.*eV;
+
+  double R_axis = 1.6714;
+  double B_axis = 1.54;
+  double a_mid  = 0.604;
+  double R0     = R_axis + 0.5*a_mid;
+  double r0     = 0.5*a_mid;
+  double B0     = B_axis*(R_axis/R0);
+  double qaxis  = 1.2;
+  double qlcfs  = 2.0;
+
+  double c_s      = sqrt(Te0/mi);
+  double omega_ci = fabs(qi*B0/mi);
+  double rho_s    = c_s/omega_ci;
+  double q0       = qprofile_cbc(r0, a_mid, qaxis, qlcfs);
+  double Cy       = r0/q0;
+
+  double Lx = 150.*rho_s;
+  double Ly = 150.*rho_s;
+  Ly = 2.*M_PI*Cy/round(2.*M_PI*Cy/Ly); // adjust to integer toroidal mode number
+  double Lz = 2.*M_PI - 1e-10;
+
+  // Use a fixed LUT size sufficient for accurate geometry evaluation.
+  int psi_lut_size = 200;
+
+  struct gk_cbc_app_ctx app_ctx = {
+    .a_shift = 0.0, .Z_axis = 0.0,
+    .R_axis  = R_axis, .R0 = R0, .a_mid = a_mid, .r0 = r0,
+    .B0      = B0, .kappa = 1.0, .delta = 0.0,
+    .q0 = q0, .Cy = Cy, .qaxis = qaxis, .qlcfs = qlcfs,
+    .Lx = Lx, .Ly = Ly, .Lz = Lz,
+    .x_min = -Lx/2., .x_max = Lx/2.,
+    .y_min = -Ly/2., .y_max = Ly/2.,
+    .z_min = -Lz/2., .z_max = Lz/2.,
+    .psi_lut_size = psi_lut_size,
+  };
+
+  // Populate lookup tables (avoids redundant integration in geometry evaluations).
+  app_ctx.r_lut        = gkyl_malloc(psi_lut_size*sizeof(double));
+  app_ctx.dPsidr_int_lut = gkyl_malloc(psi_lut_size*sizeof(double));
+  double r_lut_min = 0.0, r_lut_max = 2.0*a_mid;
+  for (int i=0; i<psi_lut_size; i++)
+    app_ctx.r_lut[i] = i*(r_lut_max - r_lut_min)/(psi_lut_size - 1);
+  for (int i=0; i<psi_lut_size; i++)
+    app_ctx.dPsidr_int_lut[i] = intdPsidr_cbc(app_ctx.r_lut[i], &app_ctx);
+
+  const double lower[] = {app_ctx.x_min, app_ctx.y_min, app_ctx.z_min};
+  const double upper[] = {app_ctx.x_max, app_ctx.y_max, app_ctx.z_max};
+  int ndim = 3, cdim = 3, vdim = 0;
+
+  double lower_conf[cdim], upper_conf[cdim];
+  int cells_conf[cdim];
+  for (int d=0; d<cdim; d++) {
+    lower_conf[d] = lower[d];
+    upper_conf[d] = upper[d];
+    cells_conf[d] = cells[d];
+  }
+
+  struct gkyl_rect_grid grid;
+  gkyl_rect_grid_init(&grid, ndim, lower, upper, cells);
+  struct gkyl_rect_grid grid_conf;
+  gkyl_rect_grid_init(&grid_conf, cdim, lower_conf, upper_conf, cells_conf);
+
+  struct gkyl_basis basis;
+  gkyl_cart_modal_serendip(&basis, ndim, poly_order);
+  struct gkyl_basis basis_conf;
+  gkyl_cart_modal_serendip(&basis_conf, cdim, poly_order);
+
+  int ghost_conf[cdim];
+  for (int d=0; d<cdim; d++) ghost_conf[d] = 1;
+  struct gkyl_range local_conf, local_ext_conf;
+  gkyl_create_grid_ranges(&grid_conf, ghost_conf, &local_ext_conf, &local_conf);
+
+  int ghost[ndim];
+  for (int d=0; d<cdim; d++) ghost[d] = ghost_conf[d];
+  struct gkyl_range local, local_ext;
+  gkyl_create_grid_ranges(&grid, ghost, &local_ext, &local);
+
+  struct skin_ghost_ranges skin_ghost;
+  skin_ghost_ranges_init(&skin_ghost, &local_ext, ghost);
+
+  struct gkyl_range skin_rng, ghost_rng;
+  if (edge == GKYL_LOWER_EDGE) {
+    skin_rng  = skin_ghost.upper_skin[bc_dir];
+    ghost_rng = skin_ghost.lower_ghost[bc_dir];
+  } else {
+    skin_rng  = skin_ghost.lower_skin[bc_dir];
+    ghost_rng = skin_ghost.upper_ghost[bc_dir];
+  }
+
+  struct gkyl_array *distf    = mkarr(use_gpu, basis.num_basis, local_ext.volume);
+  struct gkyl_array *distf_ho = use_gpu?
+    mkarr(false, basis.num_basis, local_ext.volume) : gkyl_array_acquire(distf);
+
+  gkyl_proj_on_basis *projDistf = gkyl_proj_on_basis_inew(
+    &(struct gkyl_proj_on_basis_inp){
+      .grid = &grid, .basis = &basis,
+      .num_ret_vals = 1,
+      .eval = init_donor_3x_cbc,
+      .ctx  = &app_ctx,
+    }
+  );
+  gkyl_proj_on_basis_advance(projDistf, 0.0, &local, distf_ho);
+  gkyl_array_copy(distf, distf_ho);
+
+  struct gkyl_msgpack_data *mt = test_bc_twistshift_array_meta_new(
+    (struct test_bc_twistshift_output_meta){
+      .poly_order = poly_order, .basis_type = basis.id
+    }
+  );
+  if (write_f)
+    gkyl_grid_sub_array_write(&grid, &local, mt, distf_ho,
+      "ctest_bc_twistshift_3x_cbc_do.gkyl");
+
+  // Range extended only in bc_dir.
+  struct gkyl_range update_rng;
+  int lower_bcdir_ext[ndim], upper_bcdir_ext[ndim];
+  for (int d=0; d<ndim; d++) {
+    lower_bcdir_ext[d] = local.lower[d];
+    upper_bcdir_ext[d] = local.upper[d];
+  }
+  lower_bcdir_ext[bc_dir] = local.lower[bc_dir] - ghost[bc_dir];
+  upper_bcdir_ext[bc_dir] = local.upper[bc_dir] + ghost[bc_dir];
+  gkyl_sub_range_init(&update_rng, &local_ext, lower_bcdir_ext, upper_bcdir_ext);
+
+  // Choose shift function based on edge.
+  struct gkyl_twistshift_dg_inp tsinp = {
+    .bc_dir   = bc_dir,
+    .shift_dir = 1,
+    .shear_dir = 0,
+    .edge      = edge,
+    .cdim      = cdim,
+    .bcdir_ext_update_r = &update_rng,
+    .num_ghost = ghost,
+    .basis = &basis,
+    .grid = &grid,
+    .shift_func = (edge == GKYL_LOWER_EDGE) ? bc_shift_func_lo_cbc : bc_shift_func_up_cbc,
+    .shift_func_ctx = &app_ctx,
+    .use_gpu   = use_gpu,
+  };
+
+  struct gkyl_twistshift_dg *tsup = gkyl_twistshift_dg_inew(&tsinp);
+
+  struct gkyl_array *buff_per = mkarr(use_gpu, basis.num_basis, skin_rng.volume);
+  apply_periodic_bc(buff_per, distf, bc_dir, skin_ghost);
+
+  gkyl_twistshift_dg_advance(tsup, distf, distf);
+  gkyl_array_copy(distf_ho, distf);
+
+  if (write_f) {
+    double lower_ext[ndim], upper_ext[ndim];
+    int cells_ext[ndim];
+    for (int d=0; d<ndim; d++) {
+      double dx = (upper[d] - lower[d])/cells[d];
+      lower_ext[d] = lower[d] - dx*ghost[d];
+      upper_ext[d] = upper[d] + dx*ghost[d];
+      cells_ext[d] = cells[d] + 2*ghost[d];
+    }
+    struct gkyl_rect_grid grid_ext;
+    gkyl_rect_grid_init(&grid_ext, ndim, lower_ext, upper_ext, cells_ext);
+    gkyl_grid_sub_array_write(&grid_ext, &local_ext, mt, distf_ho,
+      "ctest_bc_twistshift_3x_cbc_tar.gkyl");
+  }
+
+  if (check_distf) {
+    // Check 4 x=const lines, and 4 y=const lines.
+    int idx0_ref[] = {4,12,19,28};
+    int idx1_ref[] = {2,7,10,13};
+    int num_ref0 = sizeof(idx0_ref)/sizeof(idx0_ref[0]);
+    int num_ref1 = sizeof(idx1_ref)/sizeof(idx1_ref[0]);
+    double f0[num_ref0*cells[1]*basis.num_basis];
+    double f1[num_ref1*cells[0]*basis.num_basis];
+    if (edge == GKYL_LOWER_EDGE) {
+      const double f0m[] =
+      {
+        // idx[0] = 4;
+         1.4147068739149354e-06,  3.9678563980892827e-07, -5.3677388121514690e-07,
+        -1.4021443738919494e-06, -2.1663045016556100e-07, -3.9326221053808132e-07,
+         5.3200736596068834e-07,  2.1470678662411421e-07,
+         2.2073750885337050e-06,  5.4194161567241438e-08,  7.7188487204183924e-07,
+        -2.1877737491242868e-06,  2.2856919929920019e-08, -5.3712921129036553e-08,
+        -7.6503058731221621e-07, -2.2653952048417829e-08,
+         8.0151330159023854e-06,  3.5840433095651838e-07,  2.4919021860714378e-06,
+        -7.9439591843807564e-06,  1.4691992411677311e-07, -3.5522172507617932e-07,
+        -2.4697742655481038e-06, -1.4561528526605157e-07,
+         2.4056337321823511e-05,  1.5575127200312389e-06,  6.4725989939125481e-06,
+        -2.3842718696134587e-05,  5.6131534500851025e-07, -1.5436821138880369e-06,
+        -6.4151227587227262e-06, -5.5633090323856011e-07,
+         5.9715709406034343e-05,  5.0593586542458534e-06,  1.3398359967595644e-05,
+        -5.9185438001676253e-05,  1.5246943425719446e-06, -5.0144318963554509e-06,
+        -1.3279383449912431e-05, -1.5111551613699758e-06,
+         1.2266163264877539e-04,  1.2843394764617348e-05,  2.1715606284302345e-05,
+        -1.2157240576270994e-04,  3.0737503418026385e-06, -1.2729346299878336e-05,
+        -2.1522773189704626e-05, -3.0464556495582395e-06,
+         2.0858381754799334e-04,  2.6012564754977512e-05,  2.6550477975637763e-05,
+        -2.0673160755237084e-04,  4.5938737655600021e-06, -2.5781574963835826e-05,
+        -2.6314711551985457e-05, -4.5530804815592547e-06,
+         2.9374366736149827e-04,  4.2514292127503834e-05,  2.2141578694173991e-05,
+        -2.9113524373960048e-04,  4.8573878417790354e-06, -4.2136768128945044e-05,
+        -2.1944962993788802e-05, -4.8142545708526606e-06,
+         3.4269905278866652e-04,  5.6458355498447365e-05,  7.3950701740712856e-06,
+        -3.3965590870142440e-04,  2.9844920494078483e-06, -5.5957009173406751e-05,
+        -7.3294024580625872e-06, -2.9579899646787672e-06,
+         3.3130814623591096e-04,  6.1194737241075030e-05, -1.1197518621951395e-05,
+        -3.2836615261769482e-04, -4.4059942666451672e-07, -6.0651332170970138e-05,
+         1.1098085424488793e-05,  4.3668693397105754e-07,
+         2.6547493073777388e-04,  5.4303954632758055e-05, -2.4003510429959307e-05,
+        -2.6311753155848911e-04, -3.5659721755455483e-06, -5.3821739239660803e-05,
+         2.3790360903447407e-05,  3.5343065871729570e-06,
+         1.7634549859606930e-04,  3.9539852198925795e-05, -2.6084796724879738e-05,
+        -1.7477956266190929e-04, -4.8370620921015304e-06, -3.9188741022952437e-05,
+         2.5853165518798813e-05,  4.7941093124383771e-06,
+         9.7120871429426495e-05,  2.3660577068010910e-05, -1.9999449126191993e-05,
+        -9.6258444751461542e-05, -4.1887526472941376e-06, -2.3450472766235517e-05,
+         1.9821855389468108e-05,  4.1515568110413017e-06,
+         4.4351391469818973e-05,  1.1650043122384966e-05, -1.1710592695891665e-05,
+        -4.3957554155084504e-05, -2.6752574970654273e-06, -1.1546591538391639e-05,
+         1.1606603435837950e-05,  2.6515013939545564e-06,
+         1.6794598764719960e-05,  4.7243461185578233e-06, -5.4058549896015648e-06,
+        -1.6645463879424616e-05, -1.3229289098014698e-06, -4.6823942490099374e-06,
+         5.3578513680151396e-06,  1.3111813918058868e-06,
+         5.2735603406759165e-06,  1.5789778675299268e-06, -1.9989826780664712e-06,
+        -5.2267314864994830e-06, -5.1808733150377238e-07, -1.5649566523489707e-06,
+         1.9812318489709252e-06,  5.1348675152926985e-07,
+        // idx[0] = 12;
+         8.5771895799448463e-03,  3.1197886695786712e-04,  1.2589091675382295e-04,
+        -8.5010247246790835e-03,  2.3881143669295742e-04, -3.0920851601408221e-04,
+        -1.2477301404636147e-04, -2.3669080751226941e-04,
+         8.2661626046304885e-03,  1.0720660909669306e-03, -3.0982027320798947e-04,
+        -8.1927596475759902e-03,  1.8255117221452561e-04, -1.0625462175989969e-03,
+         3.0706909042867208e-04, -1.8093013032420406e-04,
+         6.6575398175439011e-03,  1.4760068941306471e-03, -5.9457869281011441e-04,
+        -6.5984213205230440e-03,  4.2899447104076090e-05, -1.4629000541319605e-03,
+         5.8929887479281385e-04, -4.2518502955738542e-05,
+         4.4799350811575711e-03,  1.3955105208072918e-03, -6.3033616055554532e-04,
+        -4.4401535648606475e-03, -8.3328432799330363e-05, -1.3831184830834593e-03,
+         6.2473881867683195e-04,  8.2588482030546096e-05,
+         2.5178444512609479e-03,  1.0028214075435281e-03, -4.8235931958416503e-04,
+        -2.4954861652017948e-03, -1.3193983394577959e-04, -9.9391642221575223e-04,
+         4.7807600190536255e-04,  1.3076821726847499e-04,
+         1.1813969572080783e-03,  5.6871985765870141e-04, -2.8575381884705388e-04,
+        -1.1709062332455860e-03, -1.1130086733193673e-04, -5.6366966432420582e-04,
+         2.8321634453203873e-04,  1.1031252326278932e-04,
+         4.6254048415618595e-04,  2.5918239859045285e-04, -1.3487188316997178e-04,
+        -4.5843315637685304e-04, -6.6255494613212145e-05, -2.5688087666510880e-04,
+         1.3367423009662933e-04,  6.5667150364697886e-05,
+         1.5102266511218463e-04,  9.5873653213552430e-05, -5.1458764419249627e-05,
+        -1.4968159420277919e-04, -3.0014361827430350e-05, -9.5022301747813123e-05,
+         5.1001814120131696e-05,  2.9747836352719439e-05,
+         4.9288640555562537e-05,  1.9197719093399958e-05, -9.3898074536993173e-06,
+        -4.8850960807531967e-05, -1.7734142076995751e-05, -1.9027244664386457e-05,
+         9.3064266074420962e-06,  1.7576664111519137e-05,
+         7.4312889120419612e-05, -3.9559856706301425e-05,  2.5345644730922928e-05,
+        -7.3652995761239122e-05, -1.7079041586904331e-05,  3.9208567891674429e-05,
+        -2.5120577143858990e-05,  1.6927380868854436e-05,
+         2.4668363462348900e-04, -1.2316540125222137e-04,  8.0544516023109083e-05,
+        -2.4449310086503489e-04, -3.4617348824034278e-05,  1.2207170093550459e-04,
+        -7.9829286244383513e-05,  3.4309949140455846e-05,
+         6.9889469196789068e-04, -2.9144378275440763e-04,  1.9257347432050185e-04,
+        -6.9268855503182346e-04, -6.3595836624040557e-05,  2.8885578195009997e-04,
+        -1.9086343507478647e-04,  6.3031109956076864e-05,
+         1.6531830617114835e-03, -5.4719482372872844e-04,  3.7015196128372313e-04,
+        -1.6385029094950184e-03, -8.0981230730739408e-05,  5.4233577121939294e-04,
+        -3.6686503725170299e-04,  8.0262122955358892e-05,
+         3.2662572681362470e-03, -7.8998871116982131e-04,  5.6119422549585842e-04,
+        -3.2372531275876876e-03, -5.0252394101103727e-05,  7.8297366559026060e-04,
+        -5.5621085925887826e-04,  4.9806156287680392e-05,
+         5.3918935380395400e-03, -8.1066940565628718e-04,  6.4417804850085126e-04,
+        -5.3440138931855393e-03,  4.8296611837007029e-05,  8.0347071692792157e-04,
+        -6.3845779160642867e-04, -4.7867741235965884e-05,
+         7.4385809600035612e-03, -4.2620301983017786e-04,  4.9868993294226453e-04,
+        -7.3725268711996870e-03,  1.7454031661297211e-04,  4.2241836624211989e-04,
+        -4.9426160053675874e-04, -1.7299041057102665e-04,
+        // idx[0] = 19;
+         5.9328259833403563e-03, -3.1592831855465119e-03,  7.6447171990714363e-04,
+        -5.8801428954679998e-03, -1.4953722986172529e-04,  3.1312289675153111e-03,
+        -7.5768326346009965e-04,  1.4820934951547608e-04,
+         8.5438428607558271e-03, -3.1770890503348310e-03,  7.1469750720526751e-04,
+        -8.4679741220696214e-03,  1.4653149000110456e-04,  3.1488767174453966e-03,
+        -7.0835104235361418e-04, -1.4523030041869057e-04,
+         1.0538391888353600e-02, -2.0861147480127039e-03,  4.1035235387424735e-04,
+        -1.0444811691083961e-02,  4.6474412137478837e-04,  2.0675901921113540e-03,
+        -4.0670845311287489e-04, -4.6061722544807500e-04,
+         1.1157187397402466e-02, -1.8349902862187543e-04, -6.0616833961144544e-05,
+        -1.1058112338448060e-02,  5.9620026364061495e-04,  1.8186956983165916e-04,
+         6.0078560632534608e-05, -5.9090604618554376e-04,
+         1.0147502273615178e-02,  1.6812950536897154e-03, -5.0484232418428394e-04,
+        -1.0057393149318094e-02,  4.4927500173372542e-04, -1.6663652689123407e-03,
+         5.0035935896646541e-04, -4.4528547052858725e-04,
+         7.9236576295588640e-03,  2.7048082887694922e-03, -7.4744339840912392e-04,
+        -7.8532960931947931e-03,  1.3680114431856099e-04, -2.6807897766548171e-03,
+         7.4080615228921856e-04, -1.3558635953852334e-04,
+         5.3016792692569745e-03,  2.6754726903120800e-03, -7.3909622093528999e-04,
+        -5.2546007209230746e-03, -1.3556652552430490e-04, -2.6517146762999374e-03,
+         7.3253309717892176e-04,  1.3436270407449278e-04,
+         3.0306885085190473e-03,  1.9748354796544207e-03, -5.6082860635105409e-04,
+        -3.0037762024011207e-03, -2.4639127781914962e-04, -1.9572990760248132e-03,
+         5.5584848678700660e-04,  2.4420334016906899e-04,
+         1.4749219675761613e-03,  1.1511708985332411e-03, -3.4089330270885629e-04,
+        -1.4618247616508778e-03, -2.1626062462549767e-04, -1.1409485798989469e-03,
+         3.3786619355848882e-04,  2.1434024510948494e-04,
+         6.0905145791109738e-04,  5.4222206411941179e-04, -1.6846528502594774e-04,
+        -6.0364312273220987e-04, -1.3353062399755835e-04, -5.3740716937438697e-04,
+         1.6696932484788329e-04,  1.3234488121368636e-04,
+         2.2538939529024023e-04,  1.9086017837583353e-04, -6.0622757673701499e-05,
+        -2.2338795291675480e-04, -7.2883062312442410e-05, -1.8916535308061285e-04,
+         6.0084431742929801e-05,  7.2235865717262487e-05,
+         1.3692552150240531e-04, -2.3628334870109403e-05,  6.7351766555291856e-06,
+        -1.3570963226150468e-04, -5.5072031551511001e-05,  2.3418516876840270e-05,
+        -6.6753687487111750e-06,  5.4582995688048192e-05,
+         2.8180957439635708e-04, -2.6245954825184062e-04,  7.9675931947129452e-05,
+        -2.7930712470157682e-04, -8.6112162611900079e-05,  2.6012892546224296e-04,
+        -7.8968415135433089e-05,  8.5347492513282593e-05,
+         7.5858237184660477e-04, -6.8983776721580120e-04,  2.0188206214678025e-04,
+        -7.5184621240646007e-04, -1.6201786760815427e-04,  6.8371205515042964e-04,
+        -2.0008936327952937e-04,  1.6057916005461062e-04,
+         1.7743608964103583e-03, -1.4228383602125521e-03,  3.9110700695123274e-04,
+        -1.7586046933318674e-03, -2.5501449371086789e-04,  1.4102036531488827e-03,
+        -3.8763400355073456e-04,  2.5274998249502926e-04,
+         3.5176447536171261e-03, -2.3790827021664203e-03,  6.1388697056459030e-04,
+        -3.4864083094370800e-03, -2.8116612144444690e-04,  2.3579566109232599e-03,
+        -6.0843569636494840e-04,  2.7866938556775280e-04,
+        // idx[0] = 28;
+         3.9008280658611207e-04, -2.5603798505596852e-04,  1.8683093211897101e-05,
+        -3.8661889801461870e-04,  1.1175426823790703e-05,  2.5376438530717388e-04,
+        -1.8517188625419492e-05, -1.1076189799980769e-05,
+         4.3680260689641130e-04, -1.8748123385802201e-04,  8.0091734113950957e-06,
+        -4.3292382970210014e-04,  2.7606287551937715e-05,  1.8581641335839929e-04,
+        -7.9380525007527933e-06, -2.7361145611652907e-05,
+         4.4457679107663103e-04, -7.5578664486840552e-05, -3.4115616360440883e-06,
+        -4.4062897965993530e-04,  3.5399985354932533e-05,  7.4907531129210281e-05,
+         3.3812672026731489e-06, -3.5085635912631181e-05,
+         4.1504347649095089e-04,  4.2960315696147049e-05, -1.3312487632414327e-05,
+        -4.1135791888244848e-04,  3.1477256709139010e-05, -4.2578831038885959e-05,
+         1.3194273655178598e-05, -3.1197740828200509e-05,
+         3.5577914498131479e-04,  1.3094475217078906e-04, -2.0440326610361184e-05,
+        -3.5261985057240502e-04,  1.8525522986963621e-05, -1.2978197175140562e-04,
+         2.0258817911812268e-05, -1.8361017613277599e-05,
+         2.7796534980573800e-04,  1.6786465218620076e-04, -2.3905953966682069e-05,
+        -2.7549703656169430e-04,  2.9974039875550468e-06, -1.6637402558656323e-04,
+         2.3693670734873877e-05, -2.9707872457006951e-06,
+         1.9535178824326644e-04,  1.5650334125842896e-04, -2.3209649131201253e-05,
+        -1.9361707776044740e-04, -8.6672787668020905e-06, -1.5511360232069719e-04,
+         2.3003549038581116e-05,  8.5903139257351561e-06,
+         1.2172339077131273e-04,  1.1660274450623213e-04, -1.8887207777222881e-05,
+        -1.2064249540877665e-04, -1.3462333943164936e-05, -1.1556732013136769e-04,
+         1.8719490667402875e-05,  1.3342789340965859e-05,
+         6.7058946442705194e-05,  7.0433021024861683e-05, -1.2563048496751787e-05,
+        -6.6463467597043934e-05, -1.2699023524379705e-05, -6.9807580628297237e-05,
+         1.2451489487645912e-05,  1.2586257066353350e-05,
+         3.4938222906600265e-05,  3.1273776945169202e-05, -6.0324138429606134e-06,
+        -3.4627973883173486e-05, -1.0006175581767381e-05, -3.0996067950580566e-05,
+         5.9788464217243402e-06,  9.9173214288020404e-06,
+         2.4837446165027290e-05, -9.6145358765583846e-07,  1.9699547938565060e-07,
+        -2.4616891346377383e-05, -9.0936978967278239e-06,  9.5291594573175467e-07,
+        -1.9524617303820833e-07,  9.0129464830299899e-06,
+         3.6725180241487430e-05, -3.6057780516486035e-05,  6.7954495238266452e-06,
+        -3.6399063159472330e-05, -1.1694827060907848e-05,  3.5737589898260177e-05,
+        -6.7351063980715334e-06,  1.1590977798611619e-05,
+         7.3131479750304169e-05, -8.5125203228748116e-05,  1.4329502961988946e-05,
+        -7.2482077225311949e-05, -1.6767541211874010e-05,  8.4369297261769594e-05,
+        -1.4202257958371192e-05,  1.6618646595792397e-05,
+         1.3604357772040060e-04, -1.5068140809657870e-04,  2.1787568445735812e-05,
+        -1.3483552007980250e-04, -2.0478489031778651e-05,  1.4934336752606917e-04,
+        -2.1594096332079554e-05,  2.0296641453544639e-05,
+         2.2070902006211332e-04, -2.1925837439635583e-04,  2.6427797458379611e-05,
+        -2.1874913909968418e-04, -1.7877051979819007e-05,  2.1731137506795665e-04,
+        -2.6193120429307424e-05,  1.7718304984205783e-05,
+         3.1225316368462653e-04, -2.6354343092504682e-04,  2.5533068602001434e-05,
+        -3.0948037700471862e-04, -6.4354644170033844e-06,  2.6120318333164132e-04,
+        -2.5306336703815414e-05,  6.3783179343098985e-06,
+      };
+  
+      const double f1m[] =
+      {
+        // idx[1] = 2;
+         7.5742778736170694e-07,  1.3311910271755548e-07,  2.8478156167525587e-07,
+        -7.5070188055260917e-07,  5.4750238065324756e-08, -1.3193701421442880e-07,
+        -2.8225272093725106e-07, -5.4264059705951382e-08,
+         1.2925859849765668e-06,  1.7301030138070181e-07,  5.1100320791830013e-07,
+        -1.2811079100725808e-06,  7.3239351158981957e-08, -1.7147398176909403e-07,
+        -5.0646553447542282e-07, -7.2588990743278259e-08,
+         1.8635824605983989e-06,  1.4918689410169481e-07,  7.1992200307670070e-07,
+        -1.8470339761485296e-06,  3.9576065168750808e-08, -1.4786212471296968e-07,
+        -7.1352914505999257e-07, -3.9224632424088840e-08,
+         2.2073750885337050e-06,  5.4194161567241438e-08,  7.7188487204183924e-07,
+        -2.1877737491242868e-06,  2.2856919929920019e-08, -5.3712921129036553e-08,
+        -7.6503058731221621e-07, -2.2653952048417829e-08,
+         2.3371245739281691e-06,  7.7901820168274173e-08,  7.1291202449929149e-07,
+        -2.3163710679863721e-06, -2.4448859078376251e-07, -7.7210057347509384e-08,
+        -7.0658141461162244e-07,  2.4231754886407394e-07,
+         4.4362078536198185e-06,  1.4349007654002696e-06, -1.4918804712085053e-06,
+        -4.3968146321047141e-06, -7.9055943126041467e-07, -1.4221589450057450e-06,
+         1.4786326749339418e-06,  7.8353931772558917e-07,
+         1.8432855790288429e-05,  7.7265468592736174e-06, -7.0218535854514018e-06,
+        -1.8269173294953980e-05, -3.1418179249565271e-06, -7.6579356530322741e-06,
+         6.9595000071553346e-06,  3.1139187972416376e-06,
+         8.2880124644381316e-05,  3.4710110035730186e-05, -2.7056128318655973e-05,
+        -8.2144154821269593e-05, -1.1646701134768506e-05, -3.4401886638953268e-05,
+         2.6815871754634015e-05,  1.1543279227396033e-05,
+         3.6130932397451928e-04,  1.4417479842687968e-04, -9.7273919862532121e-05,
+        -3.5810092195539682e-04, -3.5891598669338311e-05, -1.4289453610402862e-04,
+         9.6410134124976947e-05,  3.5572883734518748e-05,
+         1.3866911075139233e-03,  4.8934908019720340e-04, -2.7681619210264059e-04,
+        -1.3743773855753208e-03, -7.3086254588880316e-05, -4.8500369392349860e-04,
+         2.7435808330019372e-04,  7.2437253660220146e-05,
+         4.1402065573272135e-03,  1.1066127780317765e-03, -5.1267688697286180e-04,
+        -4.1034418070240936e-03, -3.9937840842209967e-05, -1.0967861324518405e-03,
+         5.0812435137475719e-04,  3.9583195554377857e-05,
+         8.2661626046304885e-03,  1.0720660909669306e-03, -3.0982027320798947e-04,
+        -8.1927596475759902e-03,  1.8255117221452561e-04, -1.0625462175989969e-03,
+         3.0706909042867208e-04, -1.8093013032420406e-04,
+         9.2071430199458723e-03, -6.7468017399297192e-04,  5.5519252734112100e-04,
+        -9.1253842213336704e-03,  2.3350197769444222e-04,  6.6868906031594807e-04,
+        -5.5026245577217254e-04, -2.3142849614555009e-04,
+         4.6562742627774770e-03, -1.5981825134639602e-03,  7.7093816367743357e-04,
+        -4.6149268666407072e-03, -1.2283002048105933e-04,  1.5839907623441212e-03,
+        -7.6409228565316330e-04,  1.2173929832259107e-04,
+         8.4265128323255962e-04, -5.4995291705314407e-04,  2.3627440955229246e-04,
+        -8.3516859762456210e-04, -1.3174780227490776e-04,  5.4506937286423181e-04,
+        -2.3417630899862953e-04,  1.3057789082567117e-04,
+         1.1584483866390626e-04,  4.3858963858025070e-05, -1.6873108923339463e-05,
+        -1.1481614444094626e-04, -4.5483891179512000e-05, -4.3469499266713753e-05,
+         1.6723276873219639e-05,  4.5079997345019702e-05,
+         1.9929185999929553e-03,  1.3468353897936511e-03, -4.5601060935752653e-04,
+        -1.9752216194948405e-03, -2.4418116907756006e-04, -1.3348755838951901e-03,
+         4.5196126641860161e-04,  2.4201285704154009e-04,
+         1.0151660891080033e-02,  2.5306058282125788e-03, -7.5599768765257259e-04,
+        -1.0061514838545048e-02,  2.8830814950777197e-04, -2.5081342220012403e-03,
+         7.4928448003081915e-04, -2.8574799291165951e-04,
+         8.5438428607558271e-03, -3.1770890503348310e-03,  7.1469750720526751e-04,
+        -8.4679741220696214e-03,  1.4653149000110456e-04,  3.1488767174453966e-03,
+        -7.0835104235361418e-04, -1.4523030041869057e-04,
+         8.3058989180792564e-04, -7.7938148858281266e-04,  2.0964975534781683e-04,
+        -8.2321431052863629e-04, -1.7368462202414781e-04,  7.7246063441240638e-04,
+        -2.0778807989763133e-04,  1.7214231449146951e-04,
+         4.8784698194571816e-04,  4.6603525819394176e-04, -1.2686455710601843e-04,
+        -4.8351493420147626e-04, -1.1084020143927416e-04, -4.6189689706081717e-04,
+         1.2573800853899969e-04,  1.0985594805166225e-04,
+         4.8781825809830056e-03,  1.3781496758297112e-03, -3.2928825061709555e-04,
+        -4.8348646541985394e-03,  2.0371545823871589e-04, -1.3659118012187134e-03,
+         3.2636419353345472e-04, -2.0190647893989855e-04,
+         2.3680721830718248e-03, -1.7400576716845859e-03,  2.7950593809693524e-04,
+        -2.3470438644831496e-03, -9.5410574014376798e-05,  1.7246060788892229e-03,
+        -2.7702394453451581e-04,  9.4563334660169134e-05,
+         8.9363290665012558e-05,  3.9704854712887114e-05, -9.8017374005486476e-06,
+        -8.8569750772238376e-05, -3.3694653872762494e-05, -3.9352278325905250e-05,
+         9.7146986446126184e-06,  3.3395447657075059e-05,
+         1.5558629382148325e-03,  5.9445795666028924e-04, -1.1056083435060165e-04,
+        -1.5420469820210249e-03,  6.1304104069997447e-05, -5.8917921077172018e-04,
+         1.0957906172357881e-04, -6.0759727829951777e-05,
+         5.8935835734624667e-04, -5.5038435706920711e-04,  7.6629057291856129e-05,
+        -5.8412489554986722e-04, -4.8460576140242794e-05,  5.4549698172253955e-04,
+        -7.5948596518150819e-05,  4.8030249547433478e-05,
+         1.2304561996882203e-04,  1.2696504265504160e-04, -2.3555535292118696e-05,
+        -1.2195298330168754e-04, -2.1706603802157628e-05, -1.2583760178323854e-04,
+         2.3346363754109702e-05,  2.1513850648983980e-05,
+         4.3680260689641130e-04, -1.8748123385802201e-04,  8.0091734113950957e-06,
+        -4.3292382970210014e-04,  2.7606287551937715e-05,  1.8581641335839929e-04,
+        -7.9380525007527933e-06, -2.7361145611652907e-05,
+         1.6405328706551727e-05,  2.9047681450653114e-06, -5.1336046315663870e-07,
+        -1.6259650512677665e-05, -5.7121417723422041e-06, -2.8789740031395213e-06,
+         5.0880185744890011e-07,  5.6614183451294898e-06,
+         1.2525989018365014e-04, -1.7226749700817367e-05, -1.8059029380175158e-06,
+        -1.2414759094885760e-04,  1.0448806188062650e-05,  1.7073777344845405e-05,
+         1.7898666437726345e-06, -1.0356021505668008e-05,
+         6.1342326303602555e-06, -1.4359128614618765e-06,  2.5224463428371958e-07,
+        -6.0797610652743729e-06, -2.0408390187610221e-06,  1.4231620537237336e-06,
+        -2.5000471922964324e-07,  2.0227165082305203e-06,
+         2.9913061136183802e-05, -9.4004861242035489e-06, -2.0777664618398835e-07,
+        -2.9647435204664162e-05,  2.4116686151255107e-06,  9.3170104520845704e-06,
+         2.0593160381472413e-07, -2.3902531632099425e-06,
+        // idx[1] = 7;
+         3.6490020128125056e-05,  7.3675063786135985e-06,  3.2021281911722955e-06,
+        -3.6165991251789855e-05,  6.9414808136517716e-07, -7.3020834272183321e-06,
+        -3.1736935124293500e-06, -6.8798409400575064e-07,
+         7.1180658041772527e-05,  1.2900664940831104e-05,  6.7559365584194971e-06,
+        -7.0548578679769132e-05,  1.4100360605950567e-06, -1.2786107920854779e-05,
+        -6.6959443050874898e-06, -1.3975150370740391e-06,
+         1.2807110995553272e-04,  2.0058649867687919e-05,  1.3810778814974065e-05,
+        -1.2693384728195296e-04,  2.7419450947357848e-06, -1.9880530432439409e-05,
+        -1.3688140046208898e-05, -2.7175968103308825e-06,
+         2.0858381754799334e-04,  2.6012564754977512e-05,  2.6550477975637763e-05,
+        -2.0673160755237084e-04,  4.5938737655600021e-06, -2.5781574963835826e-05,
+        -2.6314711551985457e-05, -4.5530804815592547e-06,
+         2.9871110310366976e-04,  2.5205913165246253e-05,  4.5389429729346178e-05,
+        -2.9605856899303685e-04,  5.9426328345683972e-06, -2.4982086384903072e-05,
+        -4.4986374706053409e-05, -5.8898626625296713e-06,
+         3.6469434674854203e-04,  1.1237385446411157e-05,  6.5265128683803013e-05,
+        -3.6145588595932354e-04,  6.3539671552325690e-06, -1.1137598234281373e-05,
+        -6.4685578816824895e-05, -6.2975443626347055e-06,
+         3.5893595493224776e-04, -1.4493122690417841e-05,  7.7817247724840170e-05,
+        -3.5574862826746054e-04, -1.6084567762455801e-06,  1.4364424754832286e-05,
+        -7.7126235901573401e-05,  1.5941737903768229e-06,
+         2.6694095601170693e-04, -3.6280004828175835e-05,  7.0464806864678920e-05,
+        -2.6457053862852633e-04, -7.8696688227856493e-06,  3.5957840873301803e-05,
+        -6.9839084212036697e-05,  7.7997867033233192e-06,
+         1.3743518008194365e-04, -3.5616161618941028e-05,  4.3245713680199841e-05,
+        -1.3621476510780793e-04, -1.0173131963280475e-05,  3.5299892546240166e-05,
+        -4.2861694708412319e-05,  1.0082795249096795e-05,
+         4.4281012350574053e-05, -1.7888520118666143e-05,  1.6654315330488873e-05,
+        -4.3887799997592024e-05, -6.9220705758281906e-06,  1.7729671286766401e-05,
+        -1.6506426152469179e-05,  6.8606030638146820e-06,
+         5.1438549738468361e-05,  2.9665824357334224e-05, -1.7900189835034524e-05,
+        -5.0981778944329460e-05, -1.3973723052800237e-05, -2.9402393871455844e-05,
+         1.7741237376853713e-05,  1.3849637350377501e-05,
+         4.6254048415618595e-04,  2.5918239859045285e-04, -1.3487188316997178e-04,
+        -4.5843315637685304e-04, -6.6255494613212145e-05, -2.5688087666510880e-04,
+         1.3367423009662933e-04,  6.5667150364697886e-05,
+         2.8294587601195142e-03,  1.2375254640891553e-03, -5.5518378989416852e-04,
+        -2.8043333603674971e-03, -1.6372300936094285e-04, -1.2265363228347245e-03,
+         5.5025379591314930e-04,  1.6226916026556920e-04,
+         9.1957619553724914e-03,  2.1739429633878338e-03, -7.9765225550990928e-04,
+        -9.1141042198332155e-03,  1.2436740398928127e-04, -2.1546384989570115e-03,
+         7.9056915818215777e-04, -1.2326302997069018e-04,
+         1.2500828315738250e-02, -7.8508011247857622e-04,  3.9877045177863924e-04,
+        -1.2389821817572859e-02,  4.5450998846944439e-04,  7.7810865491877395e-04,
+        -3.9522939751361548e-04, -4.5047397094109647e-04,
+         5.4790816862939707e-03, -2.4387569363537088e-03,  8.7033830325430211e-04,
+        -5.4304278166626358e-03, -1.8988685124215858e-04,  2.4171009420032898e-03,
+        -8.6260975880722460e-04,  1.8820066902513577e-04,
+         5.7215777750936180e-04, -4.7524252007978134e-04,  1.6913878684932202e-04,
+        -5.6707705568235720e-04, -1.2685880911775257e-04,  4.7102239909252349e-04,
+        -1.6763684602125322e-04,  1.2573231159247535e-04,
+         3.7427031371474126e-04,  3.3208117201649346e-04, -1.1114484687922794e-04,
+        -3.7094681899556086e-04, -9.6463580458111862e-05, -3.2913231398235817e-04,
+         1.1015788826100110e-04,  9.5606990478896647e-05,
+         5.3016792692569745e-03,  2.6754726903120800e-03, -7.3909622093528999e-04,
+        -5.2546007209230746e-03, -1.3556652552430490e-04, -2.6517146762999374e-03,
+         7.3253309717892176e-04,  1.3436270407449278e-04,
+         9.1961936544017395e-03, -1.7368826364828002e-03,  2.6809009052306064e-04,
+        -9.1145320854046884e-03,  4.6206186478473183e-04,  1.7214592377822928e-03,
+        -2.6570946890422425e-04, -4.5795878711259467e-04,
+         1.4411213884148821e-03, -1.2810931792856962e-03,  2.9718607020727523e-04,
+        -1.4283243293145838e-03, -2.1624336633437261e-04,  1.2697171597080945e-03,
+        -2.9454707828417920e-04,  2.1432314007080162e-04,
+         2.5492665841420081e-04,  2.4888323947485508e-04, -6.6278567407695297e-05,
+        -2.5266292716977288e-04, -7.1894578026316508e-05, -2.4667317337616465e-04,
+         6.5690018274348292e-05,  7.1256159103809388e-05,
+         3.4578494082033308e-03,  1.1303046461231621e-03, -2.4223248931282091e-04,
+        -3.4271439425899294e-03,  1.3900706598020271e-04, -1.1202676183793090e-03,
+         2.4008148141947591e-04, -1.3777269276708681e-04,
+         1.5781234722698919e-03, -1.2618335200808000e-03,  1.9187865723672629e-04,
+        -1.5641098440602522e-03, -8.2967902797388205e-05,  1.2506285249561542e-03,
+        -1.9017478791906594e-04,  8.2231153510297416e-05,
+         9.6977901902638649e-05,  8.6316756686137649e-05, -1.9677860154673218e-05,
+        -9.6116744784267082e-05, -3.0120448337275501e-05, -8.5550269806171524e-05,
+         1.9503122105962595e-05,  2.9852980821632315e-05,
+         1.1828731451272050e-03,  1.7396447751082442e-04, -4.5145997322417246e-05,
+        -1.1723693127172242e-03,  8.1902648560112776e-05, -1.7241968488061619e-04,
+         4.4745103962203978e-05, -8.1175358657596279e-05,
+         1.8720681143410243e-04, -2.0805519933339648e-04,  3.3414378701706986e-05,
+        -1.8554442778678481e-04, -3.2611926466637799e-05,  2.0620768343126807e-04,
+        -3.3117661310317896e-05,  3.2322334796065803e-05,
+         1.9535178824326644e-04,  1.5650334125842896e-04, -2.3209649131201253e-05,
+        -1.9361707776044740e-04, -8.6672787668020905e-06, -1.5511360232069719e-04,
+         2.3003549038581116e-05,  8.5903139257351561e-06,
+         1.6951067600112064e-04, -1.5119863365618911e-04,  1.3863877085521073e-05,
+        -1.6800543282288719e-04, -4.5044095319893205e-06,  1.4985600015818046e-04,
+        -1.3740766807754799e-05,  4.4644106842474151e-06,
+         3.6276567298503912e-05,  3.6027257115504254e-05, -5.2295393006259687e-06,
+        -3.5954433868657644e-05, -3.9956008741888273e-06, -3.5707337542985901e-05,
+         5.1831013502663178e-06,  3.9601202124352467e-06,
+         5.1575023302046870e-05, -4.4579128212970339e-05,  2.9869584382339701e-06,
+        -5.1117040632022451e-05, -3.2845211577127062e-09,  4.4183268611574342e-05,
+        -2.9604344521412661e-06,  3.2553548350773803e-09,
+         1.2401275268881665e-05,  1.1336295347525180e-05, -1.3473909962905102e-06,
+        -1.2291152794945234e-05, -6.9063884391199019e-07, -1.1235629822256499e-05,
+         1.3354262566444594e-06,  6.8450601834049220e-07,
+        // idx[1] = 10;
+         3.9161987831707695e-05,  8.5585033279271904e-06, -3.0940904155168843e-06,
+        -3.8814232065402164e-05, -6.2790787320485707e-07, -8.4825044052978823e-06,
+         3.0666151048127765e-06,  6.2233209435129094e-07,
+         8.2966973231524862e-05,  1.7351396003363992e-05, -5.8734092978937982e-06,
+        -8.2230232198915169e-05, -9.6285893253993122e-07, -1.7197316796773389e-05,
+         5.8212538261135436e-06,  9.5430881124964793e-07,
+         1.6948528988022327e-04,  3.3617119358933897e-05, -9.1922219423833112e-06,
+        -1.6798027212900247e-04, -8.7142547168146892e-07, -3.3318601644412122e-05,
+         9.1105956419166347e-06,  8.6368727325331598e-07,
+         3.3130814623591096e-04,  6.1194737241075030e-05, -1.1197518621951395e-05,
+        -3.2836615261769482e-04, -4.4059942666451672e-07, -6.0651332170970138e-05,
+         1.1098085424488793e-05,  4.3668693397105754e-07,
+         6.0949868976399916e-04,  1.0001588819084044e-04, -9.8223350700817221e-06,
+        -6.0408638319692828e-04,  3.3693722410867784e-06, -9.9127753962567809e-05,
+         9.7351134082527874e-06, -3.3394524466498374e-06,
+         1.0226479509198823e-03,  1.3603218361846981e-04,  2.0902400504249218e-05,
+        -1.0135669072465832e-03,  1.1408417045058132e-05, -1.3482422715671544e-04,
+        -2.0716788621210686e-05, -1.1307111084061294e-05,
+         1.4988806244302360e-03,  1.3106170460485647e-04,  8.5695676969146863e-05,
+        -1.4855706672751183e-03,  3.0453476425095055e-05, -1.2989788565587895e-04,
+        -8.4934705234475415e-05, -3.0183051642870378e-05,
+         1.8030298257953226e-03,  3.5581460837069158e-05,  1.8651702121554774e-04,
+        -1.7870190445899432e-03,  3.0633437103590942e-05, -3.5265499904931722e-05,
+        -1.8486076285806655e-04, -3.0361414282882376e-05,
+         1.6413216149696490e-03, -1.2558118114409131e-04,  2.6036761791834394e-04,
+        -1.6267467915868207e-03,  5.4223079993272169e-06,  1.2446602886760324e-04,
+        -2.5805557132664797e-04, -5.3741582761426463e-06,
+         1.0189032686435122e-03, -2.1096043183989262e-04,  2.2864831174272861e-04,
+        -1.0098554774920258e-03, -2.7657765772399670e-05,  2.0908711767234067e-04,
+        -2.2661793041463409e-04,  2.7412166709047420e-05,
+         3.7915828230823104e-04, -1.4271127978161287e-04,  1.1053775807032913e-04,
+        -3.7579138276314626e-04, -3.4225960821842870e-05,  1.4144401340396710e-04,
+        -1.0955619035909259e-04,  3.3922036636883500e-05,
+         7.4312889120419612e-05, -3.9559856706301425e-05,  2.5345644730922928e-05,
+        -7.3652995761239122e-05, -1.7079041586904331e-05,  3.9208567891674429e-05,
+        -2.5120577143858990e-05,  1.6927380868854436e-05,
+         1.6452199128976365e-04,  1.1354492403363452e-04, -5.6206288820240358e-05,
+        -1.6306104728965439e-04, -3.6099553950468539e-05, -1.1253665289486835e-04,
+         5.5707180830016014e-05,  3.5778992387013618e-05,
+         1.7045525792129491e-03,  9.4638345870692170e-04, -4.0697719285162913e-04,
+        -1.6894162692038758e-03, -1.8078271052518686e-04, -9.3797963849442858e-04,
+         4.0336326328867662e-04,  1.7917737245339021e-04,
+         8.0791678878996270e-03,  2.6080011965470560e-03, -9.4517642723761621e-04,
+        -8.0074254311060314e-03, -2.5821417318396076e-05, -2.5848423247725079e-03,
+         9.3678332538179568e-04,  2.5592124903382838e-05,
+         1.3356481058149027e-02, -4.3293862331198071e-04,  1.8456831679738910e-04,
+        -1.3237876422309745e-02,  5.5117088081251008e-04,  4.2909415802691434e-04,
+        -1.8292936280150354e-04, -5.4627652118893928e-04,
+         5.8131600430988816e-03, -2.8057188210851179e-03,  8.7511944457940491e-04,
+        -5.7615395805694532e-03, -1.9564030185418527e-04,  2.7808042303636956e-03,
+        -8.6734844392524053e-04,  1.9390302939028701e-04,
+         4.7634326079316506e-04, -4.2920915428436507e-04,  1.4088268702260373e-04,
+        -4.7211336530385869e-04, -1.1855725319570570e-04,  4.2539780642850724e-04,
+        -1.3963165842325711e-04,  1.1750447291771449e-04,
+         6.0905145791109738e-04,  5.4222206411941179e-04, -1.6846528502594774e-04,
+        -6.0364312273220987e-04, -1.3353062399755835e-04, -5.3740716937438697e-04,
+         1.6696932484788329e-04,  1.3234488121368636e-04,
+         6.4242974589046806e-03,  2.4764802964899451e-03, -6.3518193397605162e-04,
+        -6.3672501380333101e-03,  8.6162573411439783e-05, -2.4544893212884973e-03,
+         6.2954156196167615e-04, -8.5397455668379408e-05,
+         6.1192473190725665e-03, -2.6624998539887439e-03,  4.5719660344097069e-04,
+        -6.0649088225232604e-03,  1.3024981958765076e-04,  2.6388570378735065e-03,
+        -4.5313672895591774e-04, -1.2909321012194870e-04,
+         3.6469519543160190e-04, -3.8363095857578216e-04,  9.4090664425710294e-05,
+        -3.6145672710613595e-04, -9.7469050278121223e-05,  3.8022434197216746e-04,
+        -9.3255145778133679e-05,  9.6603531795857238e-05,
+         9.1178047998913031e-04,  7.8751323767825392e-04, -1.7362275060952033e-04,
+        -9.0368393185465785e-04, -1.1501287471403601e-04, -7.8052017413353706e-04,
+         1.7208099249076104e-04,  1.1399156827389669e-04,
+         3.0428994134042461e-03, -6.0542157405543088e-04,  2.7297328115299833e-05,
+        -3.0158786752883344e-03,  2.0376965733455402e-04,  6.0004547199625242e-04,
+        -2.7054929713624570e-05, -2.0196019675148278e-04,
+         2.4486683302324581e-04, -2.7365088383468937e-04,  5.4183415554651385e-05,
+        -2.4269243233840965e-04, -5.7765593385112273e-05,  2.7122088275259229e-04,
+        -5.3702270540301433e-05,  5.7252638877285439e-05,
+         4.8684120652023891e-04,  3.9028286351598619e-04, -6.7232236617642468e-05,
+        -4.8251808999280144e-04, -3.0667260128909864e-05, -3.8681717845267502e-04,
+         6.6635218967111602e-05,  3.0394936962056052e-05,
+         6.3412598830576885e-04, -4.3372366375867428e-04,  3.8776407472195745e-05,
+        -6.2849499301653115e-04,  9.5143346917004076e-06,  4.2987222736827919e-04,
+        -3.8432075633040440e-05, -9.4298480521095317e-06,
+         3.4938222906600265e-05,  3.1273776945169202e-05, -6.0324138429606134e-06,
+        -3.4627973883173486e-05, -1.0006175581767381e-05, -3.0996067950580566e-05,
+         5.9788464217243402e-06,  9.9173214288020404e-06,
+         2.4392083227262556e-04, -5.6676719861446003e-05, -1.1626687511546724e-06,
+        -2.4175483200958035e-04,  1.9445449116177598e-05,  5.6173434475836851e-05,
+         1.1523443323775968e-06, -1.9272774861550602e-05,
+         1.0411319188242268e-05, -3.0681569078749403e-06,  5.5818318185156826e-07,
+        -1.0318867387835258e-05, -3.5693133209550033e-06,  3.0409118849402331e-06,
+        -5.5322655347565932e-07,  3.5376180634403095e-06,
+         6.2185931257129870e-05, -1.0179624868692800e-05, -8.9508031605233602e-07,
+        -6.1633724452136231e-05,  5.2188375294746095e-06,  1.0089230497954324e-05,
+         8.8713206422836305e-07, -5.1724946101088791e-06,
+         3.4821562995004312e-06,  1.0893657152118253e-06, -1.5562699790180428e-07,
+        -3.4512349903592222e-06, -1.0573421757721680e-06, -1.0796922223669664e-06,
+         1.5424504083298160e-07,  1.0479530497614316e-06,
+        // idx[1] = 13;
+         7.6939600011633745e-06,  1.8061169092499393e-06, -1.7409386096072833e-06,
+        -7.6256381639873142e-06, -3.8744241924183407e-07, -1.7900787149551884e-06,
+         1.7254791941435799e-06,  3.8400195712888607e-07,
+         1.7708033426125268e-05,  4.1983811964132660e-06, -3.8745042608883230e-06,
+        -1.7550787303677916e-05, -8.9714935127936357e-07, -4.1610998593045459e-06,
+         3.8400989287563202e-06,  8.8918272656446436e-07,
+         4.1224027239434575e-05,  9.9239799414819331e-06, -8.9605036911705433e-06,
+        -4.0857960704598385e-05, -2.1501854097138079e-06, -9.8358556801655410e-06,
+         8.8809350328839017e-06,  2.1310919107303748e-06,
+         9.7120871429426495e-05,  2.3660577068010910e-05, -1.9999449126191993e-05,
+        -9.6258444751461542e-05, -4.1887526472941376e-06, -2.3450472766235517e-05,
+         1.9821855389468108e-05,  4.1515568110413017e-06,
+         2.2966717127649675e-04,  5.5667830351288630e-05, -3.9586034209482710e-05,
+        -2.2762774254561342e-04, -7.9335419238213832e-06, -5.5173503835342345e-05,
+         3.9234512940422678e-05,  7.8630926156020864e-06,
+         5.3200292659768048e-04,  1.2461168529569132e-04, -7.7661558932109947e-05,
+        -5.2727877709304340e-04, -1.3162232392700854e-05, -1.2350514207585148e-04,
+         7.6971929614645792e-05,  1.3045352671689596e-05,
+         1.1666581574647169e-03,  2.4674867349924984e-04, -1.2191453257652898e-04,
+        -1.1562983130331923e-03, -1.1089595832661965e-05, -2.4455756220003919e-04,
+         1.2083193988787077e-04,  1.0991120982167166e-05,
+         2.2887686678893923e-03,  3.9334003412439531e-04, -1.3148940639503572e-04,
+        -2.2684445590770812e-03,  1.6659921237230303e-05, -3.8984720159573514e-04,
+         1.3032178948349212e-04, -1.6511982279143148e-05,
+         3.7173943219990105e-03,  3.9400146321998456e-04, -3.1956132370684377e-06,
+        -3.6843841153501047e-03,  7.3337556977308329e-05, -3.9050275724631495e-04,
+         3.1672364106713046e-06, -7.2686324500672754e-05,
+         4.5199940871419554e-03,  2.1470803254982653e-05,  2.8930333733463666e-04,
+        -4.4798568496190452e-03,  9.9813558392372950e-05, -2.1280143994497898e-05,
+        -2.8673434353886968e-04, -9.8927220838835293e-05,
+         3.6305853350697154e-03, -5.0640172967673838e-04,  5.0404713216872657e-04,
+        -3.5983459862715781e-03,  1.2471040562830394e-05,  5.0190491704508729e-04,
+        -4.9957122820147365e-04, -1.2360298577867939e-05,
+         1.6531830617114835e-03, -5.4719482372872844e-04,  3.7015196128372313e-04,
+        -1.6385029094950184e-03, -8.0981230730739408e-05,  5.4233577121939294e-04,
+        -3.6686503725170299e-04,  8.0262122955358892e-05,
+         3.5645930339666049e-04, -2.0018386894217195e-04,  1.1080594537964248e-04,
+        -3.5329396922766608e-04, -5.1667624794085499e-05,  1.9840624991411976e-04,
+        -1.0982199618349089e-04,  5.1208819829162221e-05,
+         8.1645729682003766e-05,  3.1518177127831518e-05, -1.4204895571968811e-05,
+        -8.0920721201505936e-05, -3.1610417461887078e-05, -3.1238297876381250e-05,
+         1.4078757073429143e-05,  3.1329719122596009e-05,
+         1.1112012333347322e-03,  7.2994071394047412e-04, -2.9209530026815726e-04,
+        -1.1013338425863719e-03, -1.6061672159759519e-04, -7.2345889045835620e-04,
+         2.8950151403300714e-04,  1.5919045612453774e-04,
+         7.2402254655031442e-03,  2.7989480758611107e-03, -9.5793435231419509e-04,
+        -7.1759327598876653e-03, -9.4784436742530046e-05, -2.7740936088929552e-03,
+         9.4942796095860336e-04,  9.3942757444357306e-05,
+         1.3241006243061248e-02, -4.8348417204651978e-04,  1.1607405154285738e-04,
+        -1.3123427015660945e-02,  6.0299863597532274e-04,  4.7919086575499243e-04,
+        -1.1504332192525146e-04, -5.9764404944013681e-04,
+         5.0513947154027959e-03, -2.8225427733082581e-03,  7.8810546751073931e-04,
+        -5.0065386767431759e-03, -2.3600245213967414e-04,  2.7974787870448416e-03,
+        -7.8110714500572343e-04,  2.3390676654918446e-04,
+         2.8180957439635708e-04, -2.6245954825184062e-04,  7.9675931947129452e-05,
+        -2.7930712470157682e-04, -8.6112162611900079e-05,  2.6012892546224296e-04,
+        -7.8968415135433089e-05,  8.5347492513282593e-05,
+         1.1583383425450180e-03,  9.6723264576604258e-04, -2.6977156771818526e-04,
+        -1.1480523774994261e-03, -1.8655819799419011e-04, -9.5864368620225443e-04,
+         2.6737601469716817e-04,  1.8490157398973845e-04,
+         6.9931044556163944e-03,  1.2000797468667162e-03, -3.3704778425109526e-04,
+        -6.9310061676217134e-03,  3.5590508141603505e-04, -1.1894231210132782e-03,
+         3.3405482304091577e-04, -3.5274466870022149e-04,
+         2.8733758677926486e-03, -2.0671103848013202e-03,  3.8129908297979793e-04,
+        -2.8478604871362292e-03, -1.4871125794988407e-04,  2.0487545863420117e-03,
+        -3.7791317327156090e-04,  1.4739071217756880e-04,
+         1.0322441124946509e-04,  1.8476743202895893e-05, -4.8168812615395016e-06,
+        -1.0230778555646509e-04, -4.0962290464150215e-05, -1.8312670990347184e-05,
+         4.7741076862677817e-06,  4.0598548133929244e-05,
+         1.9582591910971407e-03,  9.7865979301640363e-04, -1.8723018386833398e-04,
+        -1.9408699837731578e-03,  2.3128246186372299e-05, -9.6996936116868003e-04,
+         1.8556759267540323e-04, -2.2922868946319787e-05,
+         1.2887036948865910e-03, -9.7941769109876026e-04,  1.2664939140064258e-04,
+        -1.2772600944523653e-03, -3.3426030714678910e-05,  9.7072052916803990e-04,
+        -1.2552475349033199e-04,  3.3129209854213705e-05,
+         6.9313334777440286e-05,  5.9715287673186067e-05, -1.2957096051837794e-05,
+        -6.8697837117967416e-05, -2.1501206316806118e-05, -5.9185020013786713e-05,
+         1.2842037927465642e-05,  2.1310277079216685e-05,
+         7.4156655404620110e-04,  3.4961769651018976e-05, -2.0021392848953567e-05,
+        -7.3498149390121789e-04,  5.6888820265120965e-05, -3.4651311534116488e-05,
+         1.9843604253476427e-05, -5.6383651442472562e-05,
+         7.3131479750304169e-05, -8.5125203228748116e-05,  1.4329502961988946e-05,
+        -7.2482077225311949e-05, -1.6767541211874010e-05,  8.4369297261769594e-05,
+        -1.4202257958371192e-05,  1.6618646595792397e-05,
+         1.6327041844856348e-04,  9.2190327694195275e-05, -1.2311099334812739e-05,
+        -1.6182058832945405e-04,  3.8034733974350099e-06, -9.1371683906473747e-05,
+         1.2201777616986781e-05, -3.7696988144993334e-06,
+         5.1551691384217362e-05, -5.7564660526755267e-05,  7.0153713767535825e-06,
+        -5.1093915900023203e-05, -6.4107510814715360e-06,  5.7053490288931122e-05,
+        -6.9530753600262190e-06,  6.3538240515027896e-06,
+         4.0328806418053032e-05,  2.5609342610977432e-05, -2.9607290538320635e-06,
+        -3.9970689382718498e-05,  7.0182568367559844e-07, -2.5381933404822401e-05,
+         2.9344379828740971e-06, -6.9559351973416766e-07,
+         1.1170036525578136e-05, -1.3138092309676044e-05,  1.5550589860992071e-06,
+        -1.1070847367246694e-05, -1.6709719218995304e-06,  1.3021426950946600e-05,
+        -1.5412501689450531e-06,  1.6561338058245150e-06,
+      };
+  
+      int nvals0 = sizeof(f0m)/sizeof(f0m[0]);
+      int nvals1 = sizeof(f1m)/sizeof(f1m[0]);
+      for (int i=0; i<nvals0; i++)
+        f0[i] = f0m[i];
+      for (int i=0; i<nvals1; i++)
+        f1[i] = f1m[i];
+    }
+    else {
+      // Upper boundary.
+      const double f0m[] =
+      {
+        // idx[0] = 4;
+         5.2735603406759081e-06,  1.5789778675299249e-06,  1.9989826780663522e-06,
+         5.2267314864994754e-06,  5.1808733150371001e-07,  1.5649566523489684e-06,
+         1.9812318489708070e-06,  5.1348675152920770e-07,
+         1.6794598764719933e-05,  4.7243461185578165e-06,  5.4058549896011972e-06,
+         1.6645463879424589e-05,  1.3229289098012843e-06,  4.6823942490099290e-06,
+         5.3578513680147745e-06,  1.3111813918057051e-06,
+         4.4351391469818912e-05,  1.1650043122384951e-05,  1.1710592695890722e-05,
+         4.3957554155084436e-05,  2.6752574970649754e-06,  1.1546591538391625e-05,
+         1.1606603435837015e-05,  2.6515013939541096e-06,
+         9.7120871429426359e-05,  2.3660577068010880e-05,  1.9999449126189980e-05,
+         9.6258444751461434e-05,  4.1887526472932372e-06,  2.3450472766235483e-05,
+         1.9821855389466126e-05,  4.1515568110403996e-06,
+         1.7634549859606911e-04,  3.9539852198925748e-05,  2.6084796724876194e-05,
+         1.7477956266190908e-04,  4.8370620921000345e-06,  3.9188741022952382e-05,
+         2.5853165518795303e-05,  4.7941093124368999e-06,
+         2.6547493073777355e-04,  5.4303954632757974e-05,  2.4003510429954116e-05,
+         2.6311753155848884e-04,  3.5659721755435086e-06,  5.3821739239660735e-05,
+         2.3790360903442251e-05,  3.5343065871709461e-06,
+         3.3130814623591058e-04,  6.1194737241074962e-05,  1.1197518621945012e-05,
+         3.2836615261769449e-04,  4.4059942666224667e-07,  6.0651332170970071e-05,
+         1.1098085424482478e-05,  4.3668693396879427e-07,
+         3.4269905278866620e-04,  5.6458355498447337e-05, -7.3950701740777095e-06,
+         3.3965590870142407e-04, -2.9844920494099456e-06,  5.5957009173406704e-05,
+        -7.3294024580689704e-06, -2.9579899646808611e-06,
+         2.9374366736149800e-04,  4.2514292127503821e-05, -2.2141578694179419e-05,
+         2.9113524373960021e-04, -4.8573878417806414e-06,  4.2136768128945003e-05,
+        -2.1944962993794169e-05, -4.8142545708542361e-06,
+         2.0858381754799318e-04,  2.6012564754977512e-05, -2.6550477975641544e-05,
+         2.0673160755237065e-04, -4.5938737655610049e-06,  2.5781574963835798e-05,
+        -2.6314711551989231e-05, -4.5530804815602338e-06,
+         1.2266163264877528e-04,  1.2843394764617339e-05, -2.1715606284304565e-05,
+         1.2157240576270986e-04, -3.0737503418031502e-06,  1.2729346299878326e-05,
+        -2.1522773189706808e-05, -3.0464556495587460e-06,
+         5.9715709406034303e-05,  5.0593586542458466e-06, -1.3398359967596715e-05,
+         5.9185438001676212e-05, -1.5246943425721614e-06,  5.0144318963554475e-06,
+        -1.3279383449913500e-05, -1.5111551613701918e-06,
+         2.4056337321823497e-05,  1.5575127200312380e-06, -6.4725989939129826e-06,
+         2.3842718696134580e-05, -5.6131534500858648e-07,  1.5436821138880390e-06,
+        -6.4151227587231497e-06, -5.5633090323863634e-07,
+         8.0151330159023820e-06,  3.5840433095651795e-07, -2.4919021860715822e-06,
+         7.9439591843807530e-06, -1.4691992411679513e-07,  3.5522172507617869e-07,
+        -2.4697742655482486e-06, -1.4561528526607401e-07,
+         2.2073750885337045e-06,  5.4194161567241385e-08, -7.7188487204187968e-07,
+         2.1877737491242860e-06, -2.2856919929925578e-08,  5.3712921129036765e-08,
+        -7.6503058731225592e-07, -2.2653952048423441e-08,
+         1.4147068739149328e-06,  3.9678563980892764e-07,  5.3677388121511292e-07,
+         1.4021443738919469e-06,  2.1663045016554326e-07,  3.9326221053808074e-07,
+         5.3200736596065414e-07,  2.1470678662409674e-07,
+        // idx[0] = 12;
+         7.4385809600035673e-03, -4.2620301983017916e-04, -4.9868993294229142e-04,
+         7.3725268711996930e-03, -1.7454031661270062e-04, -4.2241836624211913e-04,
+        -4.9426160053678498e-04, -1.7299041057075798e-04,
+         5.3918935380395478e-03, -8.1066940565628881e-04, -6.4417804850088346e-04,
+         5.3440138931855462e-03, -4.8296611836812415e-05, -8.0347071692792309e-04,
+        -6.3845779160646109e-04, -4.7867741235772842e-05,
+         3.2662572681362526e-03, -7.8998871116982251e-04, -5.6119422549588910e-04,
+         3.2372531275876946e-03,  5.0252394101218381e-05, -7.8297366559026266e-04,
+        -5.5621085925890883e-04,  4.9806156287794315e-05,
+         1.6531830617114878e-03, -5.4719482372873017e-04, -3.7015196128374682e-04,
+         1.6385029094950227e-03,  8.0981230730795285e-05, -5.4233577121939500e-04,
+        -3.6686503725172652e-04,  8.0262122955414322e-05,
+         6.9889469196789285e-04, -2.9144378275440866e-04, -1.9257347432051673e-04,
+         6.9268855503182584e-04,  6.3595836624062553e-05, -2.8885578195010121e-04,
+        -1.9086343507480132e-04,  6.3031109956098697e-05,
+         2.4668363462349003e-04, -1.2316540125222183e-04, -8.0544516023116727e-05,
+         2.4449310086503576e-04,  3.4617348824041223e-05, -1.2207170093550508e-04,
+        -7.9829286244391116e-05,  3.4309949140462771e-05,
+         7.4312889120419911e-05, -3.9559856706301649e-05, -2.5345644730926249e-05,
+         7.3652995761239434e-05,  1.7079041586906184e-05, -3.9208567891674639e-05,
+        -2.5120577143862260e-05,  1.6927380868856262e-05,
+         4.9288640555562483e-05,  1.9197719093399832e-05,  9.3898074536981298e-06,
+         4.8850960807531919e-05,  1.7734142076997052e-05,  1.9027244664386345e-05,
+         9.3064266074409205e-06,  1.7576664111520431e-05,
+         1.5102266511218419e-04,  9.5873653213552322e-05,  5.1458764419249045e-05,
+         1.4968159420277876e-04,  3.0014361827435697e-05,  9.5022301747812988e-05,
+         5.1001814120131087e-05,  2.9747836352724691e-05,
+         4.6254048415618476e-04,  2.5918239859045258e-04,  1.3487188316997143e-04,
+         4.5843315637685180e-04,  6.6255494613228503e-05,  2.5688087666510847e-04,
+         1.3367423009662892e-04,  6.5667150364714081e-05,
+         1.1813969572080760e-03,  5.6871985765870109e-04,  2.8575381884705361e-04,
+         1.1709062332455834e-03,  1.1130086733197859e-04,  5.6366966432420550e-04,
+         2.8321634453203851e-04,  1.1031252326283079e-04,
+         2.5178444512609440e-03,  1.0028214075435281e-03,  4.8235931958416520e-04,
+         2.4954861652017901e-03,  1.3193983394586925e-04,  9.9391642221575180e-04,
+         4.7807600190536245e-04,  1.3076821726856367e-04,
+         4.4799350811575659e-03,  1.3955105208072922e-03,  6.3033616055554575e-04,
+         4.4401535648606405e-03,  8.3328432799491150e-05,  1.3831184830834593e-03,
+         6.2473881867683195e-04,  8.2588482030706125e-05,
+         6.6575398175438951e-03,  1.4760068941306469e-03,  5.9457869281011257e-04,
+         6.5984213205230388e-03, -4.2899447103834747e-05,  1.4629000541319611e-03,
+         5.8929887479281244e-04, -4.2518502955499150e-05,
+         8.2661626046304833e-03,  1.0720660909669321e-03,  3.0982027320798264e-04,
+         8.1927596475759885e-03, -1.8255117221422333e-04,  1.0625462175989991e-03,
+         3.0706909042866552e-04, -1.8093013032390482e-04,
+         8.5771895799448498e-03,  3.1197886695786821e-04, -1.2589091675383921e-04,
+         8.5010247246790852e-03, -2.3881143669264430e-04,  3.0920851601408308e-04,
+        -1.2477301404637767e-04, -2.3669080751195825e-04,
+        // idx[0] = 19;
+         3.5176447536171117e-03, -2.3790827021664082e-03, -6.1388697056457772e-04,
+         3.4864083094370652e-03,  2.8116612144429246e-04, -2.3579566109232482e-03,
+        -6.0843569636493593e-04,  2.7866938556759982e-04,
+         1.7743608964103485e-03, -1.4228383602125439e-03, -3.9110700695119658e-04,
+         1.7586046933318578e-03,  2.5501449371076240e-04, -1.4102036531488738e-03,
+        -3.8763400355069862e-04,  2.5274998249492469e-04,
+         7.5858237184659968e-04, -6.8983776721579621e-04, -2.0188206214675098e-04,
+         7.5184621240645497e-04,  1.6201786760810326e-04, -6.8371205515042432e-04,
+        -2.0008936327950031e-04,  1.6057916005455996e-04,
+         2.8180957439635491e-04, -2.6245954825183818e-04, -7.9675931947110248e-05,
+         2.7930712470157471e-04,  8.6112162611884019e-05, -2.6012892546224052e-04,
+        -7.8968415135414035e-05,  8.5347492513266669e-05,
+         1.3692552150240488e-04, -2.3628334870108142e-05, -6.7351766555160489e-06,
+         1.3570963226150422e-04,  5.5072031551524784e-05, -2.3418516876839040e-05,
+        -6.6753687486981578e-06,  5.4582995688061867e-05,
+         2.2538939529024113e-04,  1.9086017837583466e-04,  6.0622757673717606e-05,
+         2.2338795291675570e-04,  7.2883062312483610e-05,  1.8916535308061394e-04,
+         6.0084431742945773e-05,  7.2235865717303348e-05,
+         6.0905145791110009e-04,  5.4222206411941353e-04,  1.6846528502596943e-04,
+         6.0364312273221280e-04,  1.3353062399761872e-04,  5.3740716937438848e-04,
+         1.6696932484790475e-04,  1.3234488121374621e-04,
+         1.4749219675761675e-03,  1.1511708985332432e-03,  3.4089330270886968e-04,
+         1.4618247616508841e-03,  2.1626062462555974e-04,  1.1409485798989493e-03,
+         3.3786619355850205e-04,  2.1434024510954647e-04,
+         3.0306885085190582e-03,  1.9748354796544224e-03,  5.6082860635101636e-04,
+         3.0037762024011311e-03,  2.4639127781919706e-04,  1.9572990760248154e-03,
+         5.5584848678696909e-04,  2.4420334016911550e-04,
+         5.3016792692569901e-03,  2.6754726903120783e-03,  7.3909622093513787e-04,
+         5.2546007209230902e-03,  1.3556652552434143e-04,  2.6517146762999361e-03,
+         7.3253309717877138e-04,  1.3436270407452921e-04,
+         7.9236576295588831e-03,  2.7048082887694853e-03,  7.4744339840881547e-04,
+         7.8532960931948122e-03, -1.3680114431851166e-04,  2.6807897766548102e-03,
+         7.4080615228891281e-04, -1.3558635953847444e-04,
+         1.0147502273615196e-02,  1.6812950536897039e-03,  5.0484232418384592e-04,
+         1.0057393149318113e-02, -4.4927500173365929e-04,  1.6663652689123294e-03,
+         5.0035935896603140e-04, -4.4528547052852176e-04,
+         1.1157187397402474e-02, -1.8349902862188801e-04,  6.0616833960680126e-05,
+         1.1058112338448070e-02, -5.9620026364057234e-04, -1.8186956983167152e-04,
+         6.0078560632073659e-05, -5.9090604618550191e-04,
+         1.0538391888353600e-02, -2.0861147480127104e-03, -4.1035235387461852e-04,
+         1.0444811691083959e-02, -4.6474412137482361e-04, -2.0675901921113600e-03,
+        -4.0670845311324271e-04, -4.6061722544811013e-04,
+         8.5438428607558167e-03, -3.1770890503348258e-03, -7.1469750720547990e-04,
+         8.4679741220696093e-03, -1.4653149000122957e-04, -3.1488767174453918e-03,
+        -7.0835104235382441e-04, -1.4523030041881422e-04,
+         5.9328259833403407e-03, -3.1592831855465011e-03, -7.6447171990721248e-04,
+         5.8801428954679841e-03,  1.4953722986155545e-04, -3.1312289675153003e-03,
+        -7.5768326346016773e-04,  1.4820934951530792e-04,
+        // idx[0] = 28;
+         3.1225316368462653e-04, -2.6354343092504693e-04, -2.5533068601899983e-05,
+         3.0948037700471851e-04,  6.4354644170239486e-06, -2.6120318333164132e-04,
+        -2.5306336703714858e-05,  6.3783179343302755e-06,
+         2.2070902006211341e-04, -2.1925837439635602e-04, -2.6427797458292739e-05,
+         2.1874913909968421e-04,  1.7877051979852441e-05, -2.1731137506795673e-04,
+        -2.6193120429221325e-05,  1.7718304984238919e-05,
+         1.3604357772040071e-04, -1.5068140809657886e-04, -2.1787568445674219e-05,
+         1.3483552007980261e-04,  2.0478489031820037e-05, -1.4934336752606933e-04,
+        -2.1594096332018494e-05,  2.0296641453585649e-05,
+         7.3131479750304263e-05, -8.5125203228748197e-05, -1.4329502961952065e-05,
+         7.2482077225312057e-05,  1.6767541211912712e-05, -8.4369297261769675e-05,
+        -1.4202257958334635e-05,  1.6618646595830757e-05,
+         3.6725180241487518e-05, -3.6057780516486069e-05, -6.7954495238028766e-06,
+         3.6399063159472418e-05,  1.1694827060935900e-05, -3.5737589898260231e-05,
+        -6.7351063980479749e-06,  1.1590977798639422e-05,
+         2.4837446165027385e-05, -9.6145358765581644e-07, -1.9699547936173084e-07,
+         2.4616891346377475e-05,  9.0936978967432890e-06, -9.5291594573173095e-07,
+        -1.9524617301449969e-07,  9.0129464830453212e-06,
+         3.4938222906600408e-05,  3.1273776945169290e-05,  6.0324138429933910e-06,
+         3.4627973883173628e-05,  1.0006175581772412e-05,  3.0996067950580641e-05,
+         5.9788464217568256e-06,  9.9173214288070243e-06,
+         6.7058946442705397e-05,  7.0433021024861873e-05,  1.2563048496794633e-05,
+         6.6463467597044124e-05,  1.2699023524377309e-05,  6.9807580628297399e-05,
+         1.2451489487688373e-05,  1.2586257066350973e-05,
+         1.2172339077131295e-04,  1.1660274450623232e-04,  1.8887207777269423e-05,
+         1.2064249540877686e-04,  1.3462333943158600e-05,  1.1556732013136789e-04,
+         1.8719490667449008e-05,  1.3342789340959595e-05,
+         1.9535178824326663e-04,  1.5650334125842918e-04,  2.3209649131246132e-05,
+         1.9361707776044762e-04,  8.6672787667954396e-06,  1.5511360232069738e-04,
+         2.3003549038625602e-05,  8.5903139257285476e-06,
+         2.7796534980573806e-04,  1.6786465218620092e-04,  2.3905953966723439e-05,
+         2.7549703656169435e-04, -2.9974039875562224e-06,  1.6637402558656333e-04,
+         2.3693670734914863e-05, -2.9707872457018826e-06,
+         3.5577914498131474e-04,  1.3094475217078909e-04,  2.0440326610403722e-05,
+         3.5261985057240491e-04, -1.8525522986956615e-05,  1.2978197175140562e-04,
+         2.0258817911854427e-05, -1.8361017613270647e-05,
+         4.1504347649095046e-04,  4.2960315696147001e-05,  1.3312487632465493e-05,
+         4.1135791888244821e-04, -3.1477256709126155e-05,  4.2578831038885878e-05,
+         1.3194273655229314e-05, -3.1197740828187762e-05,
+         4.4457679107663076e-04, -7.5578664486840579e-05,  3.4115616361105143e-06,
+         4.4062897965993503e-04, -3.5399985354919482e-05, -7.4907531129210335e-05,
+         3.3812672027389913e-06, -3.5085635912618252e-05,
+         4.3680260689641108e-04, -1.8748123385802206e-04, -8.0091734113102738e-06,
+         4.3292382970209987e-04, -2.7606287551927432e-05, -1.8581641335839935e-04,
+        -7.9380525006687252e-06, -2.7361145611642716e-05,
+         3.9008280658611196e-04, -2.5603798505596852e-04, -1.8683093211797680e-05,
+         3.8661889801461854e-04, -1.1175426823779215e-05, -2.5376438530717394e-04,
+        -1.8517188625320945e-05, -1.1076189799969395e-05,
+      };
+  
+      const double f1m[] =
+      {
+        // idx[1] = 2;
+         1.0064242557051679e-06,  2.4638105513050012e-07,  3.0952299929100151e-07,
+         9.9748727733279151e-07,  7.1551685415696771e-08,  2.4419320825719352e-07,
+         3.0677445628368039e-07,  7.0916311356057116e-08,
+         2.4501722734192372e-06,  6.2869377552759965e-07,  7.5054342119427020e-07,
+         2.4284149116585134e-06,  2.0047632122023783e-07,  6.2311101791530323e-07,
+         7.4387864708462476e-07,  1.9869610523601224e-07,
+         6.2693514816208999e-06,  1.6983388600546720e-06,  2.0605121390263682e-06,
+         6.2136800704019623e-06,  5.9893969448756465e-07,  1.6832577274456009e-06,
+         2.0422149325370482e-06,  5.9362115107443639e-07,
+         1.6794598764719933e-05,  4.7243461185578165e-06,  5.4058549896011972e-06,
+         1.6645463879424589e-05,  1.3229289098012843e-06,  4.6823942490099290e-06,
+         5.3578513680147745e-06,  1.3111813918057051e-06,
+         4.6722524149225004e-05,  1.3757882849431861e-05,  1.2559267568821096e-05,
+         4.6307631338904288e-05,  3.6001849176655706e-06,  1.3635713793213210e-05,
+         1.2447742134095955e-05,  3.5682155224891871e-06,
+         1.3509589455886354e-04,  4.0376357161087206e-05,  3.4643122769977236e-05,
+         1.3389625227974990e-04,  8.2223573880571182e-06,  4.0017817878415452e-05,
+         3.4335494215526362e-05,  8.1493434183217232e-06,
+         3.8840901300543125e-04,  1.1420438032971131e-04,  8.3157991770278211e-05,
+         3.8495996760614943e-04,  2.2616417530061213e-05,  1.1319025326426001e-04,
+         8.2419554506144016e-05,  2.2415585293376721e-05,
+         1.0598521823626484e-03,  2.8756536278117851e-04,  1.7461178578371693e-04,
+         1.0504407676655194e-03,  3.4239520152090462e-05,  2.8501180208026012e-04,
+         1.7306124510043641e-04,  3.3935475561208271e-05,
+         2.5465331961989765e-03,  5.7389435441791746e-04,  2.7509217369229086e-04,
+         2.5239201560521818e-03,  1.6496079388288131e-05,  5.6879821190705530e-04,
+         2.7264937405509861e-04,  1.6349595334583635e-05,
+         4.8835866960519232e-03,  7.1615900951608373e-04,  2.0939718370369375e-04,
+         4.8402207810962460e-03, -6.7344077386474613e-05,  7.0979956662413596e-04,
+         2.0753775107238749e-04, -6.6746066597586618e-05,
+         6.5963664604376145e-03,  1.6275731066703455e-04, -2.2806276733301181e-04,
+         6.5377911786327313e-03, -1.6368482665102420e-04,  1.6131203690983743e-04,
+        -2.2603758559912031e-04, -1.6223131661549542e-04,
+         5.3918935380395478e-03, -8.1066940565628881e-04, -6.4417804850088346e-04,
+         5.3440138931855462e-03, -4.8296611836812415e-05, -8.0347071692792309e-04,
+        -6.3845779160646109e-04, -4.7867741235772842e-05,
+         2.2325143698531066e-03, -8.4647335003058420e-04, -4.7667889076579453e-04,
+         2.2126897953495669e-03,  1.1597626131718698e-04, -8.3895672473152899e-04,
+        -4.7244601490534796e-04,  1.1494640007007816e-04,
+         3.7918019032058645e-04, -2.4429110051544058e-04, -1.1791962244750706e-04,
+         3.7581309623385434e-04,  6.5545377999984785e-05, -2.4212181229579129e-04,
+        -1.1687250428683259e-04,  6.4963339538297809e-05,
+         1.3265773496585429e-04,  9.0192913254221100e-05,  3.6330610507766499e-05,
+         1.3147974337672313e-04,  4.2769662240897072e-05,  8.9392006369748384e-05,
+         3.6007997177928130e-05,  4.2389870573244011e-05,
+         2.0740722732800190e-03,  1.3049423409384143e-03,  4.7737679678530820e-04,
+         2.0556546537284495e-03,  2.3524506169704339e-04,  1.2933545424408577e-03,
+         4.7313772356726925e-04,  2.3315610168174477e-04,
+         1.0158496318663347e-02,  2.7739047335627711e-03,  8.7039930616657365e-04,
+         1.0068289568000181e-02, -2.0057911001830609e-04,  2.7492726497568079e-03,
+         8.6267022001781804e-04, -1.9879798127660263e-04,
+         1.0744903537459927e-02, -2.7332594355407298e-03, -6.8024602402668875e-04,
+         1.0649489530908321e-02, -3.3891226168725110e-04, -2.7089882791938406e-03,
+        -6.7420548598305674e-04, -3.3590274404529956e-04,
+         1.7743608964103485e-03, -1.4228383602125439e-03, -3.9110700695119658e-04,
+         1.7586046933318578e-03,  2.5501449371076240e-04, -1.4102036531488738e-03,
+        -3.8763400355069862e-04,  2.5274998249492469e-04,
+         1.8587668557072320e-04,  1.4266611485212182e-04,  4.2787284932814561e-05,
+         1.8422611334985533e-04,  6.5393262891317997e-05,  1.4139924953595248e-04,
+         4.2407336776865824e-05,  6.4812575201364270e-05,
+         3.7794409682195629e-03,  2.0869073873386228e-03,  4.9681034418490398e-04,
+         3.7458797916072352e-03,  8.9354392597548640e-05,  2.0683757928544161e-03,
+         4.9239870239866507e-04,  8.8560931719003469e-05,
+         5.3589500608310107e-03, -1.9322998876550560e-03, -2.6621995559220085e-04,
+         5.3113629517954333e-03, -2.1708287121334914e-04, -1.9151411971654085e-03,
+        -2.6385594064330117e-04, -2.1515519020402394e-04,
+         3.5447984105491342e-04, -3.8297317940784757e-04, -8.6790399124008177e-05,
+         3.5133208437576662e-04,  9.1077196943933081e-05, -3.7957240383813508e-04,
+        -8.6019706331675079e-05,  9.0268437680937836e-05,
+         7.7591183917630939e-04,  6.6057430431279971e-04,  1.3512321260020200e-04,
+         7.6902179525469223e-04,  8.3115590710258533e-05,  6.5470844979118492e-04,
+         1.3392332773875466e-04,  8.2377529964629514e-05,
+         1.9625514353073274e-03, -6.9400771096554106e-04, -5.0835475579179123e-05,
+         1.9451241131491104e-03, -1.1538337848761807e-04, -6.8784497008563667e-04,
+        -5.0384060042217249e-05, -1.1435878199937753e-04,
+         8.4095026418060529e-05, -8.6935345625212553e-05, -1.7840996781592987e-05,
+         8.3348268350513742e-05,  2.6621237831636578e-05, -8.6163365717888856e-05,
+        -1.7682569953667403e-05,  2.6384843065315550e-05,
+         5.0821419007155365e-04,  2.7840870285490151e-04,  4.2754573047174882e-05,
+         5.0370128291589108e-04, -9.1435198883331253e-06,  2.7593645266618531e-04,
+         4.2374915370527306e-05, -9.0623260587665063e-06,
+         2.2070902006211341e-04, -2.1925837439635602e-04, -2.6427797458292739e-05,
+         2.1874913909968421e-04,  1.7877051979852441e-05, -2.1731137506795673e-04,
+        -2.6193120429221325e-05,  1.7718304984238919e-05,
+         7.8376321342582138e-05,  7.3618252299111100e-05,  1.0968129522333047e-05,
+         7.7680344983929785e-05,  7.1081816882799169e-06,  7.2964527267267229e-05,
+         1.0870733284344096e-05,  7.0450615223509237e-06,
+         1.0129896530548440e-04, -8.5306127837966829e-05, -6.3059363521162601e-06,
+         1.0039943744042426e-04,  1.7577593965507822e-07, -8.4548615272865850e-05,
+        -6.2499400697562340e-06,  1.7421506136525714e-07,
+         1.9919275589572257e-05,  1.9647328326244563e-05,  2.6426654263499524e-06,
+         1.9742393788355451e-05,  1.9320906579101043e-06,  1.9472861398076579e-05,
+         2.6191987385919478e-06,  1.9149338253662459e-06,
+         2.2776817069048982e-05, -2.1810758063425291e-05, -1.5443168402192109e-06,
+         2.2574560495458119e-05,  4.7017697371218268e-07, -2.1617080027554231e-05,
+        -1.5306034125837987e-06,  4.6600183442928546e-07,
+        // idx[1] = 7;
+         3.9161987831707655e-05,  8.5585033279271802e-06,  3.0940904155156180e-06,
+         3.8814232065402117e-05,  6.2790787320463302e-07,  8.4825044052978738e-06,
+         3.0666151048115204e-06,  6.2233209435106859e-07,
+         8.2966973231524767e-05,  1.7351396003363978e-05,  5.8734092978907861e-06,
+         8.2230232198915074e-05,  9.6285893253930273e-07,  1.7197316796773362e-05,
+         5.8212538261105722e-06,  9.5430881124903129e-07,
+         1.6948528988022310e-04,  3.3617119358933856e-05,  9.1922219423802619e-06,
+         1.6798027212900225e-04,  8.7142547168074894e-07,  3.3318601644412088e-05,
+         9.1105956419135583e-06,  8.6368727325260448e-07,
+         3.3130814623591058e-04,  6.1194737241074962e-05,  1.1197518621945012e-05,
+         3.2836615261769449e-04,  4.4059942666224667e-07,  6.0651332170970071e-05,
+         1.1098085424482478e-05,  4.3668693396879427e-07,
+         6.0949868976399829e-04,  1.0001588819084109e-04,  9.8223350700890946e-06,
+         6.0408638319692741e-04, -3.3693722410864667e-06,  9.9127753962568473e-05,
+         9.7351134082600786e-06, -3.3394524466495121e-06,
+         1.0226479509198830e-03,  1.3603218361846954e-04, -2.0902400504305411e-05,
+         1.0135669072465837e-03, -1.1408417045065111e-05,  1.3482422715671509e-04,
+        -2.0716788621266325e-05, -1.1307111084068212e-05,
+         1.4988806244302360e-03,  1.3106170460485647e-04, -8.5695676969186599e-05,
+         1.4855706672751183e-03, -3.0453476425098579e-05,  1.2989788565587884e-04,
+        -8.4934705234514663e-05, -3.0183051642873811e-05,
+         1.8030298257953232e-03,  3.5581460837068996e-05, -1.8651702121551744e-04,
+         1.7870190445899432e-03, -3.0633437103584870e-05,  3.5265499904931559e-05,
+        -1.8486076285803674e-04, -3.0361414282876413e-05,
+         1.6413216149696493e-03, -1.2558118114409342e-04, -2.6036761791839430e-04,
+         1.6267467915868209e-03, -5.4223079993046918e-06, -1.2446602886760557e-04,
+        -2.5805557132669790e-04, -5.3741582761204354e-06,
+         1.0189032686435142e-03, -2.1096043183989230e-04, -2.2864831174279596e-04,
+         1.0098554774920273e-03,  2.7657765772379680e-05, -2.0908711767234027e-04,
+        -2.2661793041470085e-04,  2.7412166709027565e-05,
+         3.7915828230823055e-04, -1.4271127978161298e-04, -1.1053775807032425e-04,
+         3.7579138276314572e-04,  3.4225960821833308e-05, -1.4144401340396707e-04,
+        -1.0955619035908770e-04,  3.3922036636873959e-05,
+         7.4312889120419911e-05, -3.9559856706301649e-05, -2.5345644730926249e-05,
+         7.3652995761239434e-05,  1.7079041586906184e-05, -3.9208567891674639e-05,
+        -2.5120577143862260e-05,  1.6927380868856262e-05,
+         1.6452199128976321e-04,  1.1354492403363433e-04,  5.6206288820234808e-05,
+         1.6306104728965398e-04,  3.6099553950453624e-05,  1.1253665289486821e-04,
+         5.5707180830010552e-05,  3.5778992386998920e-05,
+         1.7045525792129461e-03,  9.4638345870692116e-04,  4.0697719285157964e-04,
+         1.6894162692038725e-03,  1.8078271052515243e-04,  9.3797963849442793e-04,
+         4.0336326328862745e-04,  1.7917737245335601e-04,
+         8.0791678878996687e-03,  2.6080011965470950e-03,  9.4517642723753457e-04,
+         8.0074254311060748e-03,  2.5821417318181404e-05,  2.5848423247725465e-03,
+         9.3678332538171393e-04,  2.5592124903170118e-05,
+         1.3356481058148951e-02, -4.3293862331202017e-04, -1.8456831679660113e-04,
+         1.3237876422309669e-02, -5.5117088081241728e-04, -4.2909415802695381e-04,
+        -1.8292936280072232e-04, -5.4627652118884712e-04,
+         5.8131600430988686e-03, -2.8057188210851105e-03, -8.7511944457968171e-04,
+         5.7615395805694384e-03,  1.9564030185384277e-04, -2.7808042303636878e-03,
+        -8.6734844392551505e-04,  1.9390302938994804e-04,
+         4.7634326079316609e-04, -4.2920915428436561e-04, -1.4088268702256988e-04,
+         4.7211336530385978e-04,  1.1855725319557678e-04, -4.2539780642850768e-04,
+        -1.3963165842322361e-04,  1.1750447291758676e-04,
+         6.0905145791110009e-04,  5.4222206411941353e-04,  1.6846528502596943e-04,
+         6.0364312273221280e-04,  1.3353062399761872e-04,  5.3740716937438848e-04,
+         1.6696932484790475e-04,  1.3234488121374621e-04,
+         6.4242974589046650e-03,  2.4764802964899277e-03,  6.3518193397627161e-04,
+         6.3672501380332945e-03, -8.6162573411864465e-05,  2.4544893212884809e-03,
+         6.2954156196189386e-04, -8.5397455668800133e-05,
+         6.1192473190725622e-03, -2.6624998539887487e-03, -4.5719660344076035e-04,
+         6.0649088225232552e-03, -1.3024981958776287e-04, -2.6388570378735108e-03,
+        -4.5313672895570958e-04, -1.2909321012205950e-04,
+         3.6469519543160179e-04, -3.8363095857578205e-04, -9.4090664425681766e-05,
+         3.6145672710613579e-04,  9.7469050278256532e-05, -3.8022434197216740e-04,
+        -9.3255145778105395e-05,  9.6603531795991395e-05,
+         9.1178047998913487e-04,  7.8751323767826042e-04,  1.7362275060939670e-04,
+         9.0368393185466219e-04,  1.1501287471411306e-04,  7.8052017413354356e-04,
+         1.7208099249063841e-04,  1.1399156827397299e-04,
+         3.0428994134042461e-03, -6.0542157405543478e-04, -2.7297328115239033e-05,
+         3.0158786752883348e-03, -2.0376965733478786e-04, -6.0004547199625686e-04,
+        -2.7054929713564356e-05, -2.0196019675171445e-04,
+         2.4486683302324668e-04, -2.7365088383469040e-04, -5.4183415554647035e-05,
+         2.4269243233841054e-04,  5.7765593385118677e-05, -2.7122088275259332e-04,
+        -5.3702270540297137e-05,  5.7252638877291795e-05,
+         4.8684120652024178e-04,  3.9028286351599020e-04,  6.7232236617606201e-05,
+         4.8251808999280420e-04,  3.0667260129115022e-05,  3.8681717845267898e-04,
+         6.6635218967075661e-05,  3.0394936962259377e-05,
+         6.3412598830576864e-04, -4.3372366375867385e-04, -3.8776407472139081e-05,
+         6.2849499301653093e-04, -9.5143346916887677e-06, -4.2987222736827886e-04,
+        -3.8432075632984299e-05, -9.4298480520979985e-06,
+         3.4938222906600408e-05,  3.1273776945169290e-05,  6.0324138429933910e-06,
+         3.4627973883173628e-05,  1.0006175581772412e-05,  3.0996067950580641e-05,
+         5.9788464217568256e-06,  9.9173214288070243e-06,
+         2.4392083227262588e-04, -5.6676719861445929e-05,  1.1626687511291100e-06,
+         2.4175483200958067e-04, -1.9445449116183467e-05, -5.6173434475836811e-05,
+         1.1523443323522607e-06, -1.9272774861556413e-05,
+         1.0411319188242222e-05, -3.0681569078749064e-06, -5.5818318185091001e-07,
+         1.0318867387835211e-05,  3.5693133209598589e-06, -3.0409118849401984e-06,
+        -5.5322655347500679e-07,  3.5376180634451215e-06,
+         6.2185931257129586e-05, -1.0179624868692354e-05,  8.9508031604239662e-07,
+         6.1633724452135960e-05, -5.2188375294793664e-06, -1.0089230497953875e-05,
+         8.8713206421851195e-07, -5.1724946101135919e-06,
+         3.4821562995004494e-06,  1.0893657152118484e-06,  1.5562699789901857e-07,
+         3.4512349903592412e-06,  1.0573421757814150e-06,  1.0796922223669888e-06,
+         1.5424504083022067e-07,  1.0479530497705965e-06,
+        // idx[1] = 10;
+         3.6490020128125022e-05,  7.3675063786135918e-06, -3.2021281911734263e-06,
+         3.6165991251789828e-05, -6.9414808136536902e-07,  7.3020834272183270e-06,
+        -3.1736935124304748e-06, -6.8798409400593995e-07,
+         7.1180658041772459e-05,  1.2900664940831099e-05, -6.7559365584218519e-06,
+         7.0548578679769091e-05, -1.4100360605954828e-06,  1.2786107920854769e-05,
+        -6.6959443050898310e-06, -1.3975150370744643e-06,
+         1.2807110995553264e-04,  2.0058649867687895e-05, -1.3810778814976504e-05,
+         1.2693384728195280e-04, -2.7419450947362422e-06,  1.9880530432439396e-05,
+        -1.3688140046211276e-05, -2.7175968103313399e-06,
+         2.0858381754799318e-04,  2.6012564754977512e-05, -2.6550477975641544e-05,
+         2.0673160755237065e-04, -4.5938737655610049e-06,  2.5781574963835798e-05,
+        -2.6314711551989231e-05, -4.5530804815602338e-06,
+         2.9871110310366873e-04,  2.5205913165246944e-05, -4.5389429729339090e-05,
+         2.9605856899303593e-04, -5.9426328345682074e-06,  2.4982086384903736e-05,
+        -4.4986374706046403e-05, -5.8898626625294748e-06,
+         3.6469434674854192e-04,  1.1237385446410865e-05, -6.5265128683820238e-05,
+         3.6145588595932343e-04, -6.3539671552322184e-06,  1.1137598234281054e-05,
+        -6.4685578816841917e-05, -6.2975443626344209e-06,
+         3.5893595493224776e-04, -1.4493122690417814e-05, -7.7817247724849183e-05,
+         3.5574862826746054e-04,  1.6084567762459325e-06, -1.4364424754832272e-05,
+        -7.7126235901582319e-05,  1.5941737903771684e-06,
+         2.6694095601170731e-04, -3.6280004828176018e-05, -7.0464806864673933e-05,
+         2.6457053862852676e-04,  7.8696688227861677e-06, -3.5957840873301966e-05,
+        -6.9839084212031750e-05,  7.7997867033238258e-06,
+         1.3743518008194373e-04, -3.5616161618941401e-05, -4.3245713680204564e-05,
+         1.3621476510780801e-04,  1.0173131963281794e-05, -3.5299892546240518e-05,
+        -4.2861694708416988e-05,  1.0082795249098096e-05,
+         4.4281012350574168e-05, -1.7888520118666163e-05, -1.6654315330492159e-05,
+         4.3887799997592119e-05,  6.9220705758272029e-06, -1.7729671286766401e-05,
+        -1.6506426152472439e-05,  6.8606030638137037e-06,
+         5.1438549738468456e-05,  2.9665824357334248e-05,  1.7900189835036316e-05,
+         5.0981778944329555e-05,  1.3973723052796347e-05,  2.9402393871455861e-05,
+         1.7741237376855478e-05,  1.3849637350373645e-05,
+         4.6254048415618476e-04,  2.5918239859045258e-04,  1.3487188316997143e-04,
+         4.5843315637685180e-04,  6.6255494613228503e-05,  2.5688087666510847e-04,
+         1.3367423009662892e-04,  6.5667150364714081e-05,
+         2.8294587601195094e-03,  1.2375254640891551e-03,  5.5518378989409295e-04,
+         2.8043333603674919e-03,  1.6372300936085449e-04,  1.2265363228347241e-03,
+         5.5025379591307449e-04,  1.6226916026548170e-04,
+         9.1957619553724862e-03,  2.1739429633878351e-03,  7.9765225550964614e-04,
+         9.1141042198332120e-03, -1.2436740398918847e-04,  2.1546384989570141e-03,
+         7.9056915818189724e-04, -1.2326302997059803e-04,
+         1.2500828315738304e-02, -7.8508011247854954e-04, -3.9877045177897329e-04,
+         1.2389821817572911e-02, -4.5450998846959987e-04, -7.7810865491874858e-04,
+        -3.9522939751394622e-04, -4.5047397094125129e-04,
+         5.4790816862939342e-03, -2.4387569363537231e-03, -8.7033830325416366e-04,
+         5.4304278166625993e-03,  1.8988685124218666e-04, -2.4171009420033036e-03,
+        -8.6260975880708712e-04,  1.8820066902516417e-04,
+         5.7215777750935844e-04, -4.7524252007977803e-04, -1.6913878684937368e-04,
+         5.6707705568235394e-04,  1.2685880911773336e-04, -4.7102239909252029e-04,
+        -1.6763684602130442e-04,  1.2573231159245635e-04,
+         3.7427031371474034e-04,  3.3208117201649276e-04,  1.1114484687927514e-04,
+         3.7094681899556005e-04,  9.6463580458143968e-05,  3.2913231398235741e-04,
+         1.1015788826104790e-04,  9.5606990478928455e-05,
+         5.3016792692569901e-03,  2.6754726903120783e-03,  7.3909622093513787e-04,
+         5.2546007209230902e-03,  1.3556652552434143e-04,  2.6517146762999361e-03,
+         7.3253309717877138e-04,  1.3436270407452921e-04,
+         9.1961936544017117e-03, -1.7368826364828100e-03, -2.6809009052276823e-04,
+         9.1145320854046606e-03, -4.6206186478537920e-04, -1.7214592377823002e-03,
+        -2.6570946890393444e-04, -4.5795878711323652e-04,
+         1.4411213884148813e-03, -1.2810931792856986e-03, -2.9718607020745780e-04,
+         1.4283243293145833e-03,  2.1624336633407510e-04, -1.2697171597080966e-03,
+        -2.9454707828436010e-04,  2.1432314007050667e-04,
+         2.5492665841420016e-04,  2.4888323947485432e-04,  6.6278567407822636e-05,
+         2.5266292716977223e-04,  7.1894578026384081e-05,  2.4667317337616389e-04,
+         6.5690018274474520e-05,  7.1256159103876392e-05,
+         3.4578494082033386e-03,  1.1303046461231766e-03,  2.4223248931237062e-04,
+         3.4271439425899376e-03, -1.3900706598036629e-04,  1.1202676183793233e-03,
+         2.4008148141902978e-04, -1.3777269276724882e-04,
+         1.5781234722698934e-03, -1.2618335200808048e-03, -1.9187865723666297e-04,
+         1.5641098440602533e-03,  8.2967902797066034e-05, -1.2506285249561588e-03,
+        -1.9017478791900309e-04,  8.2231153509978078e-05,
+         9.6977901902638622e-05,  8.6316756686137351e-05,  1.9677860154709606e-05,
+         9.6116744784267068e-05,  3.0120448337405375e-05,  8.5550269806171266e-05,
+         1.9503122105998658e-05,  2.9852980821761017e-05,
+         1.1828731451272081e-03,  1.7396447751082816e-04,  4.5145997322302639e-05,
+         1.1723693127172275e-03, -8.1902648559895069e-05,  1.7241968488062006e-04,
+         4.4745103962090367e-05, -8.1175358657380482e-05,
+         1.8720681143410254e-04, -2.0805519933339656e-04, -3.3414378701659159e-05,
+         1.8554442778678492e-04,  3.2611926466714527e-05, -2.0620768343126817e-04,
+        -3.3117661310270503e-05,  3.2322334796141819e-05,
+         1.9535178824326663e-04,  1.5650334125842918e-04,  2.3209649131246132e-05,
+         1.9361707776044762e-04,  8.6672787667954396e-06,  1.5511360232069738e-04,
+         2.3003549038625602e-05,  8.5903139257285476e-06,
+         1.6951067600112074e-04, -1.5119863365618903e-04, -1.3863877085534901e-05,
+         1.6800543282288725e-04,  4.5044095319706036e-06, -1.4985600015818035e-04,
+        -1.3740766807768502e-05,  4.4644106842288668e-06,
+         3.6276567298503925e-05,  3.6027257115504003e-05,  5.2295393006317666e-06,
+         3.5954433868657657e-05,  3.9956008741687153e-06,  3.5707337542985657e-05,
+         5.1831013502720623e-06,  3.9601202124153117e-06,
+         5.1575023302046816e-05, -4.4579128212969987e-05, -2.9869584382357371e-06,
+         5.1117040632022390e-05,  3.2845211634800542e-09, -4.4183268611573997e-05,
+        -2.9604344521430178e-06,  3.2553548407936682e-09,
+         1.2401275268881753e-05,  1.1336295347525348e-05,  1.3473909962804335e-06,
+         1.2291152794945326e-05,  6.9063884390899995e-07,  1.1235629822256665e-05,
+         1.3354262566344723e-06,  6.8450601833752906e-07,
+        // idx[1] = 13;
+         6.2657435059192389e-06,  1.1641163689362830e-06, -1.6403632698369783e-06,
+         6.2101041332771099e-06, -3.2689517205055183e-07,  1.1537790954125808e-06,
+        -1.6257969564932065e-06, -3.2399236534047043e-07,
+         1.1267655777296214e-05,  1.7224008808195605e-06, -3.0785713582669099e-06,
+         1.1167599766704021e-05, -4.9786387303821501e-07,  1.7071060791162162e-06,
+        -3.0512338557269196e-06, -4.9344287598800761e-07,
+         1.7792497642738746e-05,  1.9998167603756296e-06, -4.8547004491311306e-06,
+         1.7634501483840234e-05, -4.9857845221345014e-07,  1.9820585246863783e-06,
+        -4.8115910420671554e-06, -4.9415110974917022e-07,
+         2.4056337321823497e-05,  1.5575127200312380e-06, -6.4725989939129826e-06,
+         2.3842718696134580e-05, -5.6131534500858648e-07,  1.5436821138880390e-06,
+        -6.4151227587231497e-06, -5.5633090323863634e-07,
+         2.7164067597516312e-05,  1.1098766716295953e-07, -8.8660114789262803e-06,
+         2.6922852540100311e-05, -3.1627341965558876e-07,  1.1000210428983373e-07,
+        -8.7872819050043051e-06, -3.1346493337835670e-07,
+         2.3994825830339474e-05, -1.6841247767798238e-06, -7.7539596815715105e-06,
+         2.3781753422476620e-05,  2.6317833456926379e-07, -1.6691698642554609e-06,
+        -7.6851050513480680e-06,  2.6084132900645678e-07,
+         1.6016882937583991e-05, -2.8230768932199529e-06, -6.0290454073971664e-06,
+         1.5874654115499630e-05,  1.3614222825750313e-06, -2.7980081640083472e-06,
+        -5.9755078976376938e-06,  1.3493329460690080e-06,
+         9.8455354864211670e-06,  2.9617890833854716e-07, -6.9489101822206762e-07,
+         9.7581078064861676e-06,  3.1357290448382672e-06,  2.9354885994377525e-07,
+        -6.8872043363429996e-07,  3.1078839859612674e-06,
+         3.9011083818695911e-05,  1.9902575296058611e-05,  1.4677088296293310e-05,
+         3.8664668069677257e-05,  7.5064936588684329e-06,  1.9725841792302946e-05,
+         1.4546756758743548e-05,  7.4398365099559416e-06,
+         2.3888049043531946e-04,  1.1483546140429011e-04,  7.1312268443981844e-05,
+         2.3675924806213432e-04,  2.9643345516891777e-05,  1.1381573038217466e-04,
+         7.0679020390632398e-05,  2.9380114641574981e-05,
+         1.2234867187375981e-03,  5.1387522103972256e-04,  2.8134955828176556e-04,
+         1.2126222405791434e-03,  9.3470469345815967e-05,  5.0931204431728318e-04,
+         2.7885119349853603e-04,  9.2640457988017256e-05,
+         4.4799350811575659e-03,  1.3955105208072922e-03,  6.3033616055554575e-04,
+         4.4401535648606405e-03,  8.3328432799491150e-05,  1.3831184830834593e-03,
+         6.2473881867683195e-04,  8.2588482030706125e-05,
+         9.7716297507283792e-03,  1.3456395734362109e-03,  4.2230678771116898e-04,
+         9.6848583486580462e-03, -2.3479472920207153e-04,  1.3336903863049993e-03,
+         4.1855673239713247e-04, -2.3270976810844599e-04,
+         1.0306703041584746e-02, -1.1825534137556507e-03, -6.7086169125845014e-04,
+         1.0215180225385718e-02, -2.6682678254561637e-04, -1.1720524205383232e-03,
+        -6.6490448544624355e-04, -2.6445737901498439e-04,
+         4.1568120046519205e-03, -1.8174644792154824e-03, -7.5296484661487636e-04,
+         4.1198997991153197e-03,  1.9040708381710860e-04, -1.8013255192776273e-03,
+        -7.4627857041355196e-04,  1.8871628197049720e-04,
+         4.8860692316653393e-04, -3.8023488046055041e-04, -1.4753883724741325e-04,
+         4.8426812719636612e-04,  1.0196923908055593e-04, -3.7685842079770358e-04,
+        -1.4622870249053404e-04,  1.0106375923033906e-04,
+         2.9294848655103347e-04,  2.4980931921513331e-04,  9.0157589311276736e-05,
+         2.9034712408020091e-04,  8.0321792535837242e-05,  2.4759102959185763e-04,
+         8.9356996100994944e-05,  7.9608540526404764e-05,
+         4.4254596134883665e-03,  2.4549067862642271e-03,  7.3848760727670605e-04,
+         4.3861618356085411e-03,  2.3344588158139668e-04,  2.4331073823541218e-03,
+         7.3192988796788876e-04,  2.3137289816214148e-04,
+         1.1157187397402474e-02, -1.8349902862188801e-04,  6.0616833960680126e-05,
+         1.1058112338448070e-02, -5.9620026364057234e-04, -1.8186956983167152e-04,
+         6.0078560632073659e-05, -5.9090604618550191e-04,
+         3.4746815254179230e-03, -2.4230957949160658e-03, -5.5706413873520704e-04,
+         3.4438265917579652e-03,  2.4825618773810390e-04, -2.4015788704276086e-03,
+        -5.5211744738542956e-04,  2.4605168981583451e-04,
+         1.2967070437580762e-04, -3.0372989641602543e-05, -8.4366829497824695e-06,
+         1.2851923741347230e-04,  5.2883604796430712e-05, -3.0103279576495651e-05,
+        -8.3617657837569207e-06,  5.2414002012475693e-05,
+         2.3207575119290032e-03,  1.5289575356248154e-03,  3.4582312161757889e-04,
+         2.3001493443753429e-03,  1.1872552071725908e-04,  1.5153804975608961e-03,
+         3.4275223601337767e-04,  1.1767124623521591e-04,
+         4.0562948476909767e-03, -1.4421644508333046e-03, -1.5972876124242848e-04,
+         4.0202752276149523e-03, -1.9704447144722474e-04, -1.4293581294102611e-03,
+        -1.5831038079643057e-04, -1.9529473005363505e-04,
+         2.3072328684209585e-04, -2.5397968959006082e-04, -5.5574896425858917e-05,
+         2.2867447987741607e-04,  6.3533756465527876e-05, -2.5172436736385032e-04,
+        -5.5081395156797248e-05,  6.2969581065114454e-05,
+         7.4703445644323579e-04,  5.8308309956022755e-04,  1.0745158404378290e-04,
+         7.4040084169994325e-04,  4.8758475781811738e-05,  5.7790536162264500e-04,
+         1.0649742134625928e-04,  4.8325503860614624e-05,
+         1.1026100056389333e-03, -6.4967562903913128e-04, -5.9942438906131847e-05,
+         1.0928189044033454e-03, -3.1102503922783453e-05, -6.4390655400654037e-04,
+        -5.9410154159361466e-05, -3.0826315820888077e-05,
+         3.6855264730397853e-05,  9.9690149435174425e-06,  2.1646015699630160e-06,
+         3.6527992507042120e-05,  1.3351157106268053e-05,  9.8804907744713724e-06,
+         2.1453800564651972e-06,  1.3232599746756376e-05,
+         4.1504347649095046e-04,  4.2960315696147001e-05,  1.3312487632465493e-05,
+         4.1135791888244821e-04, -3.1477256709126155e-05,  4.2578831038885878e-05,
+         1.3194273655229314e-05, -3.1197740828187762e-05,
+         4.0208731565052655e-05, -4.6888305906027664e-05, -7.6469715151629098e-06,
+         3.9851680786178314e-05,  9.5815298552671653e-06, -4.6471940965075453e-05,
+        -7.5790669325201704e-06,  9.4964465272319093e-06,
+         9.8837846986583506e-05,  4.0861517241056017e-05,  5.4635998823661205e-06,
+         9.7960173683417302e-05, -5.0402301787694723e-06,  4.0498669770145315e-05,
+         5.4150834900919591e-06, -4.9954732804295155e-06,
+         1.6363308286919829e-05, -1.9376034559952714e-05, -2.6746074969222150e-06,
+         1.6218003231490433e-05,  3.2094122010726464e-06, -1.9203976701824692e-05,
+        -2.6508571657680423e-06,  3.1809128408213089e-06,
+         2.5559272241391462e-05,  6.3438828943389592e-06,  9.7748053065870137e-07,
+         2.5332307656684648e-05, -1.7965596045881944e-06,  6.2875496492862865e-06,
+         9.6880057057984307e-07, -1.7806062785034210e-06,
+      };
+  
+      int nvals0 = sizeof(f0m)/sizeof(f0m[0]);
+      int nvals1 = sizeof(f1m)/sizeof(f1m[0]);
+      for (int i=0; i<nvals0; i++)
+        f0[i] = f0m[i];
+      for (int i=0; i<nvals1; i++)
+        f1[i] = f1m[i];
+    }
+  
+    struct gkyl_range check_ghost_rng = ghost_rng;
+    struct gkyl_range_iter iter;
+    gkyl_range_iter_init(&iter, &check_ghost_rng);
+    while (gkyl_range_iter_next(&iter)) {
+      for (int i=0; i<num_ref0; i++) {
+        if (iter.idx[0]==idx0_ref[i]) {
+          long linidx = gkyl_range_idx(&check_ghost_rng, iter.idx);
+          double *f_c = gkyl_array_fetch(distf_ho, linidx);
+          int refidx = iter.idx[1]-1;
+          for (int k=0; k<basis.num_basis; ++k) {
+            TEST_CHECK( ts_compare_coeff(f0[i*cells[1]*basis.num_basis+refidx*basis.num_basis+k], f_c[k]) );
+          }
+        }
+      }
+      for (int i=0; i<num_ref1; i++) {
+        if (iter.idx[1]==idx1_ref[i]) {
+          long linidx = gkyl_range_idx(&check_ghost_rng, iter.idx);
+          double *f_c = gkyl_array_fetch(distf_ho, linidx);
+          int refidx = iter.idx[0]-1;
+          for (int k=0; k<basis.num_basis; ++k) {
+            TEST_CHECK( ts_compare_coeff(f1[i*cells[0]*basis.num_basis+refidx*basis.num_basis+k], f_c[k]) );
+          }
+        }
+      }
+    }
+  }
+
+
+  gkyl_free(app_ctx.r_lut);
+  gkyl_free(app_ctx.dPsidr_int_lut);
+
+  gkyl_array_release(buff_per);
+  test_bc_twistshift_array_meta_release(mt);
+  gkyl_twistshift_dg_release(tsup);
+  gkyl_proj_on_basis_release(projDistf);
+  gkyl_array_release(distf_ho);
+  gkyl_array_release(distf);
+}
+
+void
+test_bc_twistshift_3x_cbc(bool use_gpu)
+{
+  const int cells0[] = {32, 16, 4};
+
+  test_bc_twistshift_3x_cbc_wcells(cells0, GKYL_LOWER_EDGE, true, use_gpu, false);
+  test_bc_twistshift_3x_cbc_wcells(cells0, GKYL_UPPER_EDGE, true, use_gpu, false);
+}
+
+void
+test_bc_twistshift_3x_fig6(bool use_gpu)
+{
+  const int cells0[] = {1, 10, 4};
+
+  enum gkyl_edge_loc edgelo = GKYL_LOWER_EDGE; // Lower edge.
+  test_bc_twistshift_3x_fig6_wcells(cells0, edgelo, true, use_gpu, false);
+}
+
+void
+test_bc_twistshift_3x2v_fig6(bool use_gpu)
+{
+  const int cells0[] = {1, 10, 4, 2, 1};
+
+  enum gkyl_edge_loc edgelo = GKYL_LOWER_EDGE; // Lower edge.
+  test_bc_twistshift_3x2v_fig6_wcells(cells0, edgelo, true, use_gpu, false);
+}
+
+void
+test_bc_twistshift_3x_fig11(bool use_gpu)
+{
+  const int cells0[] = {10, 5,  4};
+  const int cells1[] = {20, 10, 4};
+  const int cells2[] = {40, 20, 4};
+  const int cells3[] = {80, 40, 4};
+
+  enum gkyl_edge_loc edgelo = GKYL_LOWER_EDGE; // Lower edge.
+  test_bc_twistshift_3x_fig11_wcells(cells0, edgelo, 0, true, use_gpu, false);
+  test_bc_twistshift_3x_fig11_wcells(cells1, edgelo, 0, false, use_gpu, false);
+  test_bc_twistshift_3x_fig11_wcells(cells2, edgelo, 0, false, use_gpu, false);
+  test_bc_twistshift_3x_fig11_wcells(cells3, edgelo, 0, false, use_gpu, false);
+
+  enum gkyl_edge_loc edgeup = GKYL_UPPER_EDGE; // Upper edge.
+  test_bc_twistshift_3x_fig11_wcells(cells0, edgeup, 0, true, use_gpu, false);
+  test_bc_twistshift_3x_fig11_wcells(cells1, edgeup, 0, false, use_gpu, false);
+  test_bc_twistshift_3x_fig11_wcells(cells2, edgeup, 0, false, use_gpu, false);
+  test_bc_twistshift_3x_fig11_wcells(cells3, edgeup, 0, false, use_gpu, false);
+
+  // Apply the TS BC on the lower half of the x domain.
+  test_bc_twistshift_3x_fig11_wcells(cells0, edgelo, -1, true, use_gpu, false);
+  test_bc_twistshift_3x_fig11_wcells(cells1, edgelo, -1, false, use_gpu, false);
+  test_bc_twistshift_3x_fig11_wcells(cells2, edgelo, -1, false, use_gpu, false);
+
+  // Apply the TS BC on the upper half of the x domain.
+  test_bc_twistshift_3x_fig11_wcells(cells0, edgelo, 1, true, use_gpu, false);
+  test_bc_twistshift_3x_fig11_wcells(cells1, edgelo, 1, false, use_gpu, false);
+  test_bc_twistshift_3x_fig11_wcells(cells2, edgelo, 1, false, use_gpu, false);
+}
+
+void
+test_bc_twistshift_3x_fig14(bool use_gpu)
+{
+  const int cells0[] = {8 , 8 , 4};
+  const int cells1[] = {16, 16, 4};
+  const int cells2[] = {32, 32, 4};
+  const int cells3[] = {64, 32, 4};
+
+  enum gkyl_edge_loc edgelo = GKYL_LOWER_EDGE; // Lower edge.
+  test_bc_twistshift_3x_fig14_wcells(cells0, edgelo, 0, true, use_gpu, false);
+  test_bc_twistshift_3x_fig14_wcells(cells1, edgelo, 0, false, use_gpu, false);
+  test_bc_twistshift_3x_fig14_wcells(cells2, edgelo, 0, false, use_gpu, false);
+  test_bc_twistshift_3x_fig14_wcells(cells3, edgelo, 0, false, use_gpu, false);
+
+  enum gkyl_edge_loc edgeup = GKYL_UPPER_EDGE; // Upper edge.
+  test_bc_twistshift_3x_fig14_wcells(cells0, edgeup, 0, true, use_gpu, false);
+  test_bc_twistshift_3x_fig14_wcells(cells1, edgeup, 0, false, use_gpu, false);
+  test_bc_twistshift_3x_fig14_wcells(cells2, edgeup, 0, false, use_gpu, false);
+  test_bc_twistshift_3x_fig14_wcells(cells3, edgeup, 0, false, use_gpu, false);
+}
+
+void
+test_bc_twistshift_3x2v_fig11(bool use_gpu)
+{
+  const int cells0[] = {10, 5,  4, 2, 1};
+  const int cells1[] = {20, 10, 4, 2, 1};
+  const int cells2[] = {40, 20, 4, 2, 1};
+  const int cells3[] = {80, 40, 4, 2, 1};
+
+  enum gkyl_edge_loc edgelo = GKYL_LOWER_EDGE; // Lower edge.
+  test_bc_twistshift_3x2v_fig11_wcells(cells0, edgelo, 0, true, use_gpu, false);
+  test_bc_twistshift_3x2v_fig11_wcells(cells1, edgelo, 0, false, use_gpu, false);
+  test_bc_twistshift_3x2v_fig11_wcells(cells2, edgelo, 0, false, use_gpu, false);
+  test_bc_twistshift_3x2v_fig11_wcells(cells3, edgelo, 0, false, use_gpu, false);
+
+  enum gkyl_edge_loc edgeup = GKYL_UPPER_EDGE; // Upper edge.
+  test_bc_twistshift_3x2v_fig11_wcells(cells0, edgeup, 0, true, use_gpu, false);
+  test_bc_twistshift_3x2v_fig11_wcells(cells1, edgeup, 0, false, use_gpu, false);
+  test_bc_twistshift_3x2v_fig11_wcells(cells2, edgeup, 0, false, use_gpu, false);
+  test_bc_twistshift_3x2v_fig11_wcells(cells3, edgeup, 0, false, use_gpu, false);
+
+  // Apply the TS BC on the lower half of the x domain.
+  test_bc_twistshift_3x2v_fig11_wcells(cells0, edgelo, -1, true, use_gpu, false);
+  test_bc_twistshift_3x2v_fig11_wcells(cells1, edgelo, -1, false, use_gpu, false);
+  test_bc_twistshift_3x2v_fig11_wcells(cells2, edgelo, -1, false, use_gpu, false);
+
+  // Apply the TS BC on the upper half of the x domain.
+  test_bc_twistshift_3x2v_fig11_wcells(cells0, edgelo, 1, true, use_gpu, false);
+  test_bc_twistshift_3x2v_fig11_wcells(cells1, edgelo, 1, false, use_gpu, false);
+  test_bc_twistshift_3x2v_fig11_wcells(cells2, edgelo, 1, false, use_gpu, false);
+}
+
+void test_bc_twistshift_3x_fig6_ho(){ test_bc_twistshift_3x_fig6(false); }
+void test_bc_twistshift_3x_fig11_ho(){ test_bc_twistshift_3x_fig11(false); }
+void test_bc_twistshift_3x_fig14_ho(){ test_bc_twistshift_3x_fig14(false); }
+void test_bc_twistshift_3x_cbc_ho(){ test_bc_twistshift_3x_cbc(false); }
+
+void test_bc_twistshift_3x2v_fig6_ho(){ test_bc_twistshift_3x2v_fig6(false); }
+void test_bc_twistshift_3x2v_fig11_ho(){ test_bc_twistshift_3x2v_fig11(false); }
+
+#ifdef GKYL_HAVE_CUDA
+void test_bc_twistshift_3x_fig6_dev(){ test_bc_twistshift_3x_fig6(true); }
+void test_bc_twistshift_3x_fig11_dev(){ test_bc_twistshift_3x_fig11(true); }
+void test_bc_twistshift_3x_fig14_dev(){ test_bc_twistshift_3x_fig14(true); }
+void test_bc_twistshift_3x_cbc_dev(){ test_bc_twistshift_3x_cbc(true); }
+
+void test_bc_twistshift_3x2v_fig6_dev(){ test_bc_twistshift_3x2v_fig6(true); }
+void test_bc_twistshift_3x2v_fig11_dev(){ test_bc_twistshift_3x2v_fig11(true); }
+#endif
+
+TEST_LIST = {
+  { "test_bc_twistshift_3x_fig6_ho", test_bc_twistshift_3x_fig6_ho },
+  { "test_bc_twistshift_3x_fig11_ho", test_bc_twistshift_3x_fig11_ho },
+  { "test_bc_twistshift_3x_fig14_ho", test_bc_twistshift_3x_fig14_ho },
+  { "test_bc_twistshift_3x_cbc_ho", test_bc_twistshift_3x_cbc_ho },
+  { "test_bc_twistshift_3x2v_fig6_ho", test_bc_twistshift_3x2v_fig6_ho },
+  { "test_bc_twistshift_3x2v_fig11_ho", test_bc_twistshift_3x2v_fig11_ho },
+#ifdef GKYL_HAVE_CUDA
+  { "test_bc_twistshift_3x_fig6_dev", test_bc_twistshift_3x_fig6_dev },
+  { "test_bc_twistshift_3x_fig11_dev", test_bc_twistshift_3x_fig11_dev },
+  { "test_bc_twistshift_3x_fig14_dev", test_bc_twistshift_3x_fig14_dev },
+  { "test_bc_twistshift_3x_cbc_dev", test_bc_twistshift_3x_cbc_dev },
+  { "test_bc_twistshift_3x2v_fig6_dev", test_bc_twistshift_3x2v_fig6_dev },
+  { "test_bc_twistshift_3x2v_fig11_dev", test_bc_twistshift_3x2v_fig11_dev },
+#endif
+  { NULL, NULL },
+};
diff --git a/gyrokinetic/zero/bc_twistshift.c b/gyrokinetic/zero/bc_twistshift.c
index bf65db7ccb..e6d61c980a 100644
--- a/gyrokinetic/zero/bc_twistshift.c
+++ b/gyrokinetic/zero/bc_twistshift.c
@@ -1,1899 +1,223 @@
 #include <gkyl_alloc.h>
 #include <gkyl_array.h>
-#include <gkyl_mat.h>
+#include <gkyl_array_ops.h>
+#include <gkyl_basis.h>
 #include <gkyl_bc_twistshift.h>
 #include <gkyl_bc_twistshift_priv.h>
-#include <gkyl_util.h>
-#include <gkyl_eval_on_nodes.h>
-#include <gkyl_array_ops.h>
-#include <gkyl_array_rio.h>
-
-// Notes:
-//   a) Hard-coded parameters:
-//     - wrap_to_range: eps.
-//     - find_donors: delta_frac, num_test_pt.
-//     - find_intersect: tol, max_iter, num_steps.
-//     - calc_mats: shift_dir_idx_tar.
-//     - tol_xi: Minimum allowed spacing between the lower and
-//               upper xi (logical x) limits of subcell integral.
-//   b) Unlike the procedures described in M. Francisquez, et al. CPC 298
-//   (2024) 109109, all subcell integrals are now done with variable y limits.
-//   This is possible once we realize that figure 4 is not drawn accurately;
-//   the blue lines should be separated by Delta y at all points.
-//   c) This updater only works on 5D distributions. Likely only minor changes
-//   are needed to make it work in other dimensions.
-//   d) 99% of the code is written to support a BC, a shift and shear in any
-//   direction. Maybe the only thing that needs to change is the permutted
-//   range and its use.
-//
-// List of functions used in computing sub-cell integrals (scimat).
-//   - ts_grid_cell_boundary_in_dir: cell boundary coordinate in given dir.
-//   - ts_grid_cell_boundaries: get all cell boundary coords.
-//   - ts_p2l: physical to logical transform.
-//   - ts_interval_dx_and_xc: compute length and center of an interval.
-//   - ts_grid_length_in_dir: length of the grid in given dir.
-//   - ts_wrap_to_range: wrap a number to a range assuming periodicity.
-//   - ts_shift_dir_idx_do_linidx: linear index to first donor of a given target
-//                                cell in shift_dir_idx_do.
-//   - ts_check_shifted_test_point: evaluate a shifted point's cell as a
-//                                  potential donor cell.
-//   - ts_find_donors: find and record the donor cells for each target.
-//   - ts_root_find: Finds the root of a given function.
-//   - ts_shifted_coord_loss_func: Loss function used to find where yTar-S
-//                                intersects yDo.
-//   - ts_sign: return the sign of a double.
-//   - ts_ts_donor_target_offset: offset between donor and target cells.
-//   - ts_find_intersect: finds the intersection of yTar-S and yDo.
-//   - ts_comp_to_phys: transform a computational to a physical coord.
-//   - ts_nod2mod_proj_1d: evaluate a 1D function at nodes and do a n2m transform
-//                         to get the coefficients of the DG representation.
-//   - ts_integral_xlimdg: subcell integral with variable x limits.
-//   - ts_integral_ylimdg: subcell integral with variable y limits.
-//   - ts_integral_fullcelllimdg: integral over the whole cell.
-//   - ts_one: return 1 (for projections).
-//   - ts_minus_one: return -1 (for projections).
-//   - ts_shift_coord_shifted_log: coordinate in shift_dir shifted and transformed
-//                                 to logical space.
-//   - ts_subcellint_sNi_sNii: subcell integral sNi or sNii.
-//   - ts_subcellint_si_sii: subcell integral si or sii.
-//   - ts_subcellint_siii_siv: subcell integral siii or siv.
-//   - ts_subcellint_sv_svi: subcell integral sv or svi.
-//   - ts_subcellint_svii_sviii: subcell integral svii or sviii.
-//   - ts_subcellint_six_sx: subcell integral six or sx.
-//   - ts_subcellint_sxi_sxii: subcell integral sxi or sxii.
-//   - ts_subcellint_sxiii_sxiv: subcell integral sxiii or sxiv.
-//   - ts_subcellint_sxv_sxvi: subcell integral sxv or sxvi.
-//   - ts_calc_mats: create scimat with the result of the subcell integrals.
-//
-//  Two additional helper functions:
-//   - ts_calc_num_numcol_fidx_do: index map to populate fmat with donors.
-//   - ts_calc_num_numcol_fidx_tar: index map to get mat-mat mult results.
-
-// Option to use the user-provided function describing the shift
-// or a DG representation of it:
-//   = 0 DG representation (default and preferred).
-//   = 1 user-provided shift function.
-// Note: the kernels that ultimately perform the integrals
-// always use the DG representation.
-#define shift_func_op 0
-
-// Minimum allowed spacing between the lower and
-// upper xi (logical x) limits of subcell integral.
-#define tol_xi 1.0e-15
-
-// Indices in 4-element cell boundary array.
-#define cellb_lo(dir) (2*dir)
-#define cellb_up(dir) (2*dir+1)
-
-double
-ts_grid_cell_boundary_in_dir(struct gkyl_rect_grid *grid, const int *idx, enum gkyl_edge_loc edge, int dir)
-{
-  // Get the coordinate of the cell boundary in specified direction.
-  double xc[grid->ndim];
-  gkyl_rect_grid_cell_center(grid, idx, xc);
-  return edge == GKYL_LOWER_EDGE? xc[dir]-0.5*grid->dx[dir] : xc[dir]+0.5*grid->dx[dir];
-}
-
-void
-ts_grid_cell_boundaries(struct gkyl_rect_grid *grid, const int *idx, double *cell_bounds)
-{
-  // Get the cell boundaries in every dimension. The array cell_bounds
-  // must be a 2*grid->ndim array.
-  for (int d=0; d<grid->ndim; d++) {
-    cell_bounds[d*2] = ts_grid_cell_boundary_in_dir(grid, idx, GKYL_LOWER_EDGE, d);
-    cell_bounds[d*2+1] = ts_grid_cell_boundary_in_dir(grid, idx, GKYL_UPPER_EDGE, d);
-  }
-}
-
-static inline double
-ts_p2l(double coord, double cell_center, double dx)
-{
-  // Transform a physical coordinate (coord) to the [-1,1] logical
-  // space in a cell centered at cell_center and with length dx. 
-  return 2.0*(coord - cell_center)/dx;
-}
-
-// Evaluation of the shift through the DG representation.
-static inline void
-ts_shift_dg_eval(double t, const double *coord, double *fout, void *ctx)
-{
-  struct ts_shift_dg_eval_ctx *tsectx = ctx;
-
-  int cell_idx[GKYL_MAX_DIM];
-  gkyl_rect_grid_coord_idx(tsectx->shear_grid, coord, cell_idx);
-  // Ensure that we do not go outside of the range 
-  // (it does sometimes if x=x_max,x_min).
-  cell_idx[0] = fmin(cell_idx[0], tsectx->shear_r->upper[0]);
-  cell_idx[0] = fmax(cell_idx[0], tsectx->shear_r->lower[0]);
-
-  double xc[GKYL_MAX_DIM];
-  gkyl_rect_grid_cell_center(tsectx->shear_grid, cell_idx, xc);
-
-  long shift_loc = gkyl_range_idx(tsectx->shear_r, cell_idx);
-  double *shift_c = (double *) gkyl_array_fetch(tsectx->shift_dg, shift_loc);
-  double xp = ts_p2l(coord[0], xc[0], tsectx->shear_grid->dx[0]);
-
-  fout[0] = tsectx->shift_b->eval_expand(&(double) {xp}, shift_c);
-}
-
-void
-ts_interval_dx_and_xc(const double *interval, double *dx, double *xc)
-{
-  // Compute the lenth (dx) and center (xc) of [interval[0], interval[1]].
-  double lo = interval[0], up = interval[1];
-  dx[0] = up - lo;
-  xc[0] = 0.5*(up + lo);
-}
-
-static inline double
-ts_grid_length_in_dir(struct gkyl_rect_grid *grid, int dir)
-{
-  return grid->upper[dir] - grid->lower[dir];
-}
-
-double
-ts_wrap_to_range(double val, double lower, double upper, bool pick_upper)
-{
-  // Wrap a number to range [lower,upper]. If pickUpper=true, output upper when
-  // val is a multiple of upper. Otherwise multiples of upper wrap to lower.
-  double L        = upper - lower;
-  double disp     = fmod(val - lower, L);
-  double vwrapped = lower + fmod(L + disp, L);
-  double eps      = 1.e-12;
-  if ( (lower-eps < vwrapped && vwrapped < lower + eps) ||
-       (upper-eps < vwrapped && vwrapped < upper + eps) ) {
-    if (pick_upper) 
-      return upper;
-    else
-      return lower;
-  }
-  else
-    return vwrapped;
-}
-
-long
-ts_shift_dir_idx_do_linidx(const int *num_do, int shear_dir_idx, int shift_dir_idx,
-  int shift_dir_num_cells, int shear_r_lower)
-{
-  // Return the linear index to the first donor for the idx=(i,j) target cell,
-  // in the shift_dir_idx_do array. We assume shift_dir_idx_do (whose dimensions
-  // are Nx,Ny,num_do(i)) is in row-major order, and that it has num_do donors
-  // at each cell in the shear_dir_in_ts_grid direction.
-  long linc = 0;
-  // Count the number of donors in cells with an idx in the shear dir lower
-  // than this one. NOTE: the -1 here is because the idx is often 1-index
-  // (since ghost cells are the 0th index) but num_do is only defined on the
-  // local range. 
-  for (int i=0; i<shear_dir_idx-shear_r_lower; i++)
-    linc += num_do[i] * shift_dir_num_cells;
-
-  // Count the number of donors in cells with the same idx in the shear dir.
-  // NOTE: the -1 here is because the idx is often 1-index
-  // (since ghost cells are the 0th index) but num_do is only defined on the
-  // local range.
-  linc += num_do[shear_dir_idx-shear_r_lower] * (shift_dir_idx-1);
 
-  return linc;
-}
+#include <assert.h>
 
-void
-ts_check_shifted_test_point(struct gkyl_bc_twistshift *up, const double *test_pt, const double *xc,
-  const double *dx, double *shift_c, const int *idx, bool pick_lower, int *num_do_curr,
-  gkyl_mem_buff shift_dir_idx_do_buff)
+// allocate array (filled with zeros)
+static inline struct gkyl_array*
+mkarr(bool use_gpu, long nc, long size)
 {
-  // Shift the test point, find the cell that contains it, and if we
-  // haven't included it yet, add it to our list of donors.
-
-  int shear_idx[] = {idx[up->shear_dir_in_ts_grid]};
-  int shift_idx[] = {idx[up->shift_dir_in_ts_grid]};
-
-  int *shift_dir_idx_do_buff_ptr = (int *) gkyl_mem_buff_data(shift_dir_idx_do_buff);
-
-  // Evaluate the shift at this test point.
-  double test_pt_in_shear_dir = test_pt[up->shear_dir_in_ts_grid];
-  double xc_in_shear_dir = xc[up->shear_dir_in_ts_grid];
-  double dx_in_shear_dir = dx[up->shear_dir_in_ts_grid];
-  double shift_at_pt = up->shift_b.eval_expand(
-    &(double) {ts_p2l(test_pt_in_shear_dir, xc_in_shear_dir, dx_in_shear_dir)}, shift_c);
-
-  // Find the index of the cell that owns the shifted point.
-  double shifted_test_pt[] = { ts_wrap_to_range(test_pt[up->shift_dir_in_ts_grid] - shift_at_pt,
-    up->ts_grid.lower[up->shift_dir_in_ts_grid], up->ts_grid.upper[up->shift_dir_in_ts_grid],
-    false) }; // Shifted test point.
-  int shift_dir_idx_test_pt[1];
-  gkyl_rect_grid_find_cell(&up->shift_grid, shifted_test_pt, (bool[]) {pick_lower}, (int[]) {-1}, shift_dir_idx_test_pt);
-
-  // Get the linear index to the list of donors for this target.
-  long linidx = ts_shift_dir_idx_do_linidx(up->num_do,
-    shear_idx[0], shift_idx[0], up->ts_grid.cells[up->shift_dir_in_ts_grid], up->shear_r.lower[0]);
-  // If this donor is not in our list of donors, include it.
-  bool donor_not_found = true;
-  for (int k=0; k<num_do_curr[0]; k++) {
-    if (shift_dir_idx_do_buff_ptr[linidx+k] == shift_dir_idx_test_pt[0]) {
-      donor_not_found = false;
-      break;
-    }
-  }
-  if (donor_not_found) {
-    if (num_do_curr[0] > 0) {
-      // Insert one more int. Only if num_do_curr>0 because we already
-      // allocated space for the first donor.
-      size_t new_buff_sz = gkyl_mem_buff_size(shift_dir_idx_do_buff) + sizeof(int);
-      shift_dir_idx_do_buff = gkyl_mem_buff_resize(shift_dir_idx_do_buff, new_buff_sz);
-    }
-
-    // Get the pointer again in case it changed.
-    shift_dir_idx_do_buff_ptr = (int *) gkyl_mem_buff_data(shift_dir_idx_do_buff);
-    shift_dir_idx_do_buff_ptr[linidx+num_do_curr[0]] = shift_dir_idx_test_pt[0];
-
-    num_do_curr[0] += 1;
-  }
+  return use_gpu? gkyl_array_cu_dev_new(GKYL_DOUBLE, nc, size)
+                : gkyl_array_new(GKYL_DOUBLE, nc, size);
 }
 
-void
-ts_find_donors(struct gkyl_bc_twistshift *up)
+static void
+bc_twistshift_refine_enabled(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo)
 {
-  // Find the donor cells for each target cell in the TS grid.
-
-  double delta_frac = 1.e-4; // Distance away from the boundary, as fraction of cell length.
-  // Must be larger than the eps=1e-6 tolerance in is_in_cell (used by
-  // gkyl_rect_grid_find_cell) so that shifted test points are never
-  // ambiguously on a cell boundary.
-  int num_test_pt[2] = {10, 10}; // Number of test points taken along each side of the cell.
-
-  double step_sz[2] = {0.0}; // Size of the step between test points.
-  double delta[2] = {0.0}; // Space between cell boundary and test points.
-  for (int d=0; d<2; d++) {
-    delta[d] = delta_frac*up->ts_grid.dx[d];
-    step_sz[d] = (up->ts_grid.dx[d] - 2.0*delta[d])/(num_test_pt[d]-1);
-  }
-
-  // Number of donors at each cell of the shear direction.
-  up->num_do = (int*) gkyl_malloc(up->shear_r.volume * sizeof(int));
-  for (int i=0; i<up->shear_r.volume; i++)
-    up->num_do[i] = -1;
-
-  // Temporary buffer to store donors at (resized below).
-  size_t curr_buff_sz = up->ts_r.volume * sizeof(int);
-  gkyl_mem_buff shift_dir_idx_do_buff = gkyl_mem_buff_new(curr_buff_sz);
-
-  int idx[] = {up->shear_r.lower[0]};
-  long linidx = gkyl_range_idx(&up->shear_r, idx);
-  struct gkyl_range_iter iter;
-  gkyl_range_iter_init(&iter, &up->ts_r);
-  while (gkyl_range_iter_next(&iter)) {
-
-    // Get the cell boundaries and cell center.
-    double cell_b[4] = {0.0}; // Cell boundaries, x lo and up, y lo and up;
-    double xc[2] = {0.0}; // Cell center.
-    ts_grid_cell_boundaries(&up->ts_grid, iter.idx, cell_b);
-    gkyl_rect_grid_cell_center(&up->ts_grid, iter.idx, xc);
-
-    int shear_idx[] = {iter.idx[up->shear_dir_in_ts_grid]};
-    int shift_idx[] = {iter.idx[up->shift_dir_in_ts_grid]};
-    long shift_loc = gkyl_range_idx(&up->shear_r, shear_idx);
-    double *shift_c = (double *) gkyl_array_fetch(up->shift_dg, shift_loc);
-
-    int num_do_curr = 0;
-
-    for (int dC=0; dC<2; dC++) { // dC=0: x=const, dC=1: y=const (boundaries).
-      for (int xS=0; xS<2; xS++) { // xS=0: lower, xS=1 upper (boundary).
-
-        double test_pt[2] = {0.0}; // Test point to shift.
-        for (int d=0; d<2; d++)
-          test_pt[d] = cell_b[2*d]+delta[d];
-
-        // Search first shifted point. Use pick_lower=false in find_cell unless
-        // searching for points along a x=const line near the upper y-boundary. 
-        bool pick_lower = dC==0 && xS==1;
-        test_pt[dC] += xS*(up->ts_grid.dx[dC]-2.0*delta[dC]);
-
-        // Shift the test point, find the cell that contains it, and if we
-        // haven't included it yet, add it to our list of donors.
-        ts_check_shifted_test_point(up, test_pt, xc, up->ts_grid.dx,
-          shift_c, iter.idx, pick_lower, &num_do_curr, shift_dir_idx_do_buff);
-
-        // Search for other shifted points along this line. 
-        int step_dim = (dC+1) % 2;
-        for (int sI=1; sI<num_test_pt[step_dim]; sI++) {
-          test_pt[step_dim] += step_sz[step_dim];
-
-          // Shift the test point, find the cell that contains it, and if we
-          // haven't included it yet, add it to our list of donors.
-          ts_check_shifted_test_point(up, test_pt, xc, up->ts_grid.dx,
-            shift_c, iter.idx, pick_lower, &num_do_curr, shift_dir_idx_do_buff);
-        }
-      }
-    }
-
-    up->num_do[shear_idx[0]-up->shear_r.lower[0]] = num_do_curr;
-
-  }
-
-  // Copy the donor list to the persistent object and release the buffer.
-  size_t buff_sz = gkyl_mem_buff_size(shift_dir_idx_do_buff);
-  up->shift_dir_idx_do = (int *) gkyl_malloc(buff_sz);
-  int *shift_dir_idx_do_buff_ptr = (int *) gkyl_mem_buff_data(shift_dir_idx_do_buff);
-  memcpy(up->shift_dir_idx_do, shift_dir_idx_do_buff_ptr, buff_sz);
-  gkyl_mem_buff_release(shift_dir_idx_do_buff);
+  gkyl_dg_interpolate_advance(up->refine, fdo, up->ffine);
 }
 
-struct gkyl_qr_res
-ts_root_find(double (*func)(double,void*), void *ctx, const double *lims, int max_iter, double tol)
+static void
+bc_twistshift_refine_disabled(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo)
 {
-  // Use a Ridder's root finder to find the root of func in the interval
-  // [lims[0],lims[1]] down to a tolerance 'tol'. Return the interval limit
-  // if the function is smaller than the tolerance there. Return nil if the
-  // function does not change sign in the interval (interval doesn't contain the root).
-  double funcLo = func(lims[0], ctx), funcUp = func(lims[1], ctx);
-//  if (fabs(funcLo) < tol)
-//    return (struct gkyl_qr_res) {.res=lims[0], .status=0, .nevals=2};
-//  else if (fabs(funcUp) < tol)                                     
-//    return (struct gkyl_qr_res) {.res=lims[1], .status=0, .nevals=2};
-//  else {
-//    if (funcLo*funcUp < 0)
-//      return gkyl_ridders(func, ctx, lims[0], lims[1], funcLo, funcUp, max_iter, tol);
-//    else
-//      return (struct gkyl_qr_res) {.status=1, .nevals=2};
-//  }
-  if (fabs(funcLo) > tol && fabs(funcUp) > tol) {
-    if (funcLo*funcUp < 0)
-      return gkyl_ridders(func, ctx, lims[0], lims[1], funcLo, funcUp, max_iter, tol);
-    else
-      return (struct gkyl_qr_res) {.status=1, .nevals=2};
-  }
-  else if (fabs(funcLo) < tol && fabs(funcUp) < tol)
-    return (struct gkyl_qr_res) {.status=1, .nevals=2};
-  else if (fabs(funcLo) < tol)
-    return (struct gkyl_qr_res) {.res=lims[0], .status=0, .nevals=2};
-  else if (fabs(funcUp) < tol)                                     
-    return (struct gkyl_qr_res) {.res=lims[1], .status=0, .nevals=2};
-  return (struct gkyl_qr_res) {.status=1, .nevals=2};
+  gkyl_array_copy_range_to_range(up->ffine, fdo, &up->ghost_r, &up->coarse_ghost_r);
 }
 
-struct ts_shifted_coord_loss_func_ctx {
-  double shiftCoordTar; // Target coordinate in shift_dir.
-  double shiftCoordDo; // Donor coordinate in shift_dir.
-  double shiftDirL; // Length of the domain in shift_dir.
-  int periodicCopyIdx; // Used to search a periodic copy of the domain (signed).
-  evalf_t shift_func; // Function defining the shift.
-  void *shift_func_ctx; // Context for shift_func.
-};
-
-double ts_shifted_coord_loss_func(double shearCoord, void *ctx)
+static void
+bc_twistshift_coarsen_enabled(struct gkyl_bc_twistshift *up, struct gkyl_array *ftar)
 {
-  // Loss function used to find the shear coord.
-  struct ts_shifted_coord_loss_func_ctx *tsctx = ctx;
-
-  double shift;
-  tsctx->shift_func(0.0, (double[]){shearCoord}, &shift, tsctx->shift_func_ctx);
-
-  return tsctx->shiftCoordTar - shift
-    - (tsctx->shiftCoordDo - tsctx->periodicCopyIdx * tsctx->shiftDirL);
+  gkyl_dg_interpolate_advance(up->coarsen, up->ffine, ftar);
 }
 
-int static inline
-ts_sign(double a)
+static void
+bc_twistshift_coarsen_disabled(struct gkyl_bc_twistshift *up, struct gkyl_array *ftar)
 {
-  if (a < 0.0)
-    return -1;
-  else if (a > 0.0)
-    return 1;
-  else
-    return 0;
-}
-
-double
-ts_donor_target_offset(struct gkyl_bc_twistshift *up, const double *xc_do, const double *xc_tar) {
-  // y-offset between the donor and the target cell (yDo-yTar), in the direction of the shift.
-  //   xc_do:  cell center coordinates of donor cell.
-  //   xc_tar: cell center coordinates of target cell.
-  int shear_dir = up->shear_dir_in_ts_grid;
-  int shift_dir = up->shift_dir_in_ts_grid;
-  double x_eval = xc_do[up->shear_dir];
-  double shift;
-  up->shift_func(0.0, (double[]){x_eval}, &shift, up->shift_func_ctx);
-
-  int shift_sign = ts_sign(shift);
-  double shift_dir_L = up->ts_grid.upper[up->shift_dir] - up->ts_grid.lower[up->shift_dir];
-                             
-  // The idea here is that we keep shifting the donor cell center until it is in a
-  // periodic copy of our domain which overlaps with the shifted target cell center.
-  double xs_shifted_do = xc_do[shift_dir];
-  double xs_shifted_tar = xc_tar[shift_dir] - shift;
-  bool keep_shifting = true;
-  while (keep_shifting) {
-    double xs_shifted_dolo = xs_shifted_do - shift_dir_L/2.0;
-    double xs_shifted_doup = xs_shifted_do + shift_dir_L/2.0;
-    if (xs_shifted_dolo <= xs_shifted_tar && xs_shifted_tar <= xs_shifted_doup) {
-      keep_shifting = false;
-      break;
-    }
-    else
-      xs_shifted_do = xs_shifted_do - shift_sign*shift_dir_L;
-  }
-  return xc_tar[shift_dir] - xs_shifted_do;
+  gkyl_array_copy_range_to_range(ftar, up->ffine, &up->coarse_ghost_r, &up->ghost_r);
 }
 
-struct gkyl_qr_res
-ts_find_intersect(struct gkyl_bc_twistshift *up, double shiftCoordTar, double shiftCoordDo,
-  const double *shearDirBounds, const double *shiftDirLimits, int nP_primary)
+static void
+bc_twistshift_advance_ts(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo,
+  struct gkyl_array *ftar)
 {
-  // Given a y-coordinate of the target cell (yTar), and a y-coordinate
-  // of the donor cell (yDo), find the x-coordinate where yTar-yShift(x)=yDo
-  // for the periodic copy identified by nP_primary, i.e. the root of
-  // yTar - yShift(x) - (yDo - nP_primary*Ly) = 0 in [shearDirBounds[0], shearDirBounds[1]].
-  // Returns status=1 (not found) if no root exists for that specific nP_primary.
-  //
-  // nP_primary must be the same for all 4 inter_pts of a donor-target pair: all four
-  // intersection conditions describe corners of a single physical overlap diamond and
-  // therefore belong to the same periodic copy of the domain.
-  double tol = 1.e-13;
-  int max_iter = 100;
-
-  double shiftDirL = shiftDirLimits[1] - shiftDirLimits[0];
-
-  struct ts_shifted_coord_loss_func_ctx func_ctx = {
-    .shiftCoordTar = shiftCoordTar,
-    .shiftCoordDo = shiftCoordDo,
-    .shiftDirL = shiftDirL,
-    .periodicCopyIdx = nP_primary,
-    .shift_func = up->shift_func,
-    .shift_func_ctx = up->shift_func_ctx,
-  };
-  return ts_root_find(ts_shifted_coord_loss_func, &func_ctx, shearDirBounds, max_iter, tol);
+  gkyl_twistshift_dg_advance(up->ts, fdo, ftar);
 }
 
-struct ts_val_found {
-  bool status; // =0 not found, =1 found.
-  double value; // value found.
-};
-
-static inline void
-ts_comp_to_phys(int ndim, const double *eta,
-  const double * GKYL_RESTRICT dx, const double * GKYL_RESTRICT xc,
-  double* GKYL_RESTRICT xout)
+static void
+bc_twistshift_advance_ts_filtered(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo,
+  struct gkyl_array *ftar)
 {
-  for (int d=0; d<ndim; ++d) xout[d] = 0.5*dx[d]*eta[d]+xc[d];
+  up->refine_func(up, fdo);
+  gkyl_twistshift_dg_advance(up->ts, up->ffine, up->ffine);
+  gkyl_dg_lowpass_filter_advance(up->filter, up->ffine, up->filt_buff);
+  gkyl_array_copy_range(up->ffine, up->filt_buff, &up->ghost_r);
+  up->coarsen_func(up, ftar);
 }
 
-void
-ts_nod2mod_proj_1d(struct gkyl_bc_twistshift *up, evalf_t func, void *func_ctx, const double *interval, double *out)
+static void
+bc_twistshift_refine_shift(const struct gkyl_bc_twistshift_inp *inp,
+  const struct gkyl_rect_grid *ts_grid, const struct gkyl_range *shear_r_fine,
+  struct gkyl_array *shift_dg_fine)
 {
-  // Project 'func' onto 1D DG basis in [interval[0], interval[1]]
-  // evaluating at nodes and transforming to modal representation.
-  //   func: 1D scalar function to be projected.
-  //   interval: limits of the interval in which to project the function.
-  //   out: DG field output.
-  double dx[] = {0.0}, xc[] = {0.0}, xmu[] = {0.0};
-  ts_interval_dx_and_xc(interval, dx, xc);
+  // Refine the DG shift to match the supersampled shear grid.
+  int shear_dir = inp->shear_dir;
+  int shift_poly_order = inp->shift_poly_order? inp->shift_poly_order : inp->basis->poly_order;
 
-  for (int i=0; i<up->shift_b.num_basis; ++i) {
-    ts_comp_to_phys(1, gkyl_eval_on_nodes_fetch_node(up->ev_on_nod1d, i),
-      dx, xc, xmu);
-    func(0.0, xmu, (double *)gkyl_array_fetch(up->func_nod1d,i), func_ctx);
-  }
-  gkyl_eval_on_nodes_nod2mod(up->ev_on_nod1d, up->func_nod1d, out); 
-}
-
-void
-ts_integral_xlimdg(struct gkyl_bc_twistshift *up, double sFac, const double *xLimLo,
-  const double *xLimUp, double yLimLo, double yLimUp, double dyDo, double yOff,
-  const double *ySh, struct gkyl_mat *mat_do) {
-  // Populate a matrix (mat_do) with a sub-cell integral that has variably x limits
-  // represented by a DG polynomial, and a y-integral that goes from yLimLo to yLimUp.
-  //   up: BC updater.
-  //   sFac: +/-1 factor to add or subtract this subcell integral.
-  //   xLimLo: DG representation of the lower x-limit.
-  //   xLimUp: DG representation of the upper x-limit.
-  //   yLimLo: lower y-limit.
-  //   yLimUp: upper y-limit.
-  //   dyDo: Cell length along y.
-  //   yOff: Offset along y.
-  //   ySh: DG representation of the y shift.
-  //   mat_do: donor matrix.
-  up->kernels->xlimdg(sFac, xLimLo, xLimUp, yLimLo, yLimUp, dyDo, yOff, ySh, mat_do);
-}
-
-void
-ts_integral_ylimdg(struct gkyl_bc_twistshift *up, double sFac, double xLimLo, double xLimUp,
-  const double *yLimLo, const double *yLimUp, double dyDo, double yOff,
-  const double *ySh, struct gkyl_mat *mat_do) {
-  // Populate a matrix (mat_do) with a sub-cell integral that has variable y limits
-  // represented by a DG polynomial, and a x-integral that goes from xLimLo to xLimUp.
-  //   up: BC updater.
-  //   sFac: +/-1 factor to add or subtract this subcell integral.
-  //   xLimLo: lower x-limit.
-  //   xLimUp: upper x-limit.
-  //   yLimLo: DG representation of the lower y-limit.
-  //   yLimUp: DG representation of the upper y-limit.
-  //   dyDo: Cell length along y.
-  //   yOff: Offset along y.
-  //   ySh: DG representation of the y shift.
-  //   mat_do: donor matrix.
-  up->kernels->ylimdg(sFac, xLimLo, xLimUp, yLimLo, yLimUp, dyDo, yOff, ySh, mat_do);
-}
+  struct gkyl_basis shift_b;
+  gkyl_cart_modal_serendip(&shift_b, 1, shift_poly_order);
+  assert(inp->shift_dg->ncomp == shift_b.num_basis);
+  assert(shift_dg_fine->ncomp == shift_b.num_basis);
+  assert(shift_dg_fine->size == shear_r_fine->volume);
 
-void
-ts_integral_fullcelllimdg(struct gkyl_bc_twistshift *up, double dyDo, double yOff,
-  const double *ySh, struct gkyl_mat *mat_do) {
-  // Populate a matrix (mat_do) with the full-cell integral.
-  //   up: BC updater.
-  //   sFac: +/-1 factor to add or subtract this subcell integral.
-  //   dyDo: Cell length along y.
-  //   yOff: Offset along y.
-  //   ySh: DG representation of the y shift.
-  //   mat_do: donor matrix.
-  up->kernels->fullcell(dyDo, yOff, ySh, mat_do);
-}
+  struct gkyl_rect_grid grid_do, grid_tar;
+  gkyl_rect_grid_init(&grid_do, 1, &inp->grid->lower[shear_dir],
+    &inp->grid->upper[shear_dir], &inp->grid->cells[shear_dir]);
+  gkyl_rect_grid_init(&grid_tar, 1, &ts_grid->lower[shear_dir],
+    &ts_grid->upper[shear_dir], &ts_grid->cells[shear_dir]);
 
-static inline void
-ts_one(double t, const double *xn, double *fout, void *ctx)
-{
-  fout[0] = 1.0;
-}
+  struct gkyl_range shear_r_do;
+  gkyl_range_init(&shear_r_do, 1, (int[]) {inp->bcdir_ext_update_r->lower[shear_dir]},
+                                 (int[]) {inp->bcdir_ext_update_r->upper[shear_dir]});
+  assert(inp->shift_dg->size == shear_r_do.volume);
 
-static inline void
-ts_minus_one(double t, const double *xn, double *fout, void *ctx)
-{
-  fout[0] = -1.0;
-}
-
-struct ts_shift_coord_shifted_log_ctx {
-  double shift_coord_tar; // Target coordinate in shift_dir.
-  int shift_sign_fac;
-  const double *xc_do, *xc_tar; // Cell centers (donor and target).
-  double *dx; // Cell lengths.
-  bool pick_upper;
-  int shear_dir, shift_dir; // Shear and shift directions.
-  double shift_dir_bounds[2]; // Domain boundaries in shift_dir.
-  evalf_t shift_func; // Function defining the shift.
-  void *shift_func_ctx; // Context for shift_func.
-};
-
-void
-ts_shift_coord_shifted_log(double t, const double *xn, double *fout, void *ctx)
-{
-  // Given a logical space x coordinate (xi) and a (physical) y-coordinate in the target cell,
-  // compute the shifted y-coordinate in the logical space of the donor cell (eta \in [-1,1]).
-  //   xi:    logical space x coordinate.
-  //   yTar:  physical y-coordinate in target cell.
-  //   pmSh:  factor multiplying the y-shift (+/- 1).
-  //   xcDo:  cell center coordinates of donor cell.
-  //   xcTar: cell center coordinates of target cell.
-  //   dx:    cell lengths.
-  //   pickUpper: boolean indicating if wrapping function should return upper/lower boundary.
-
-  double xi = xn[0];
-
-  struct ts_shift_coord_shifted_log_ctx *tsctx = ctx;
-  double shift_coord_tar = tsctx->shift_coord_tar;
-  int shift_sign_fac = tsctx->shift_sign_fac;
-  const double *xc_do = tsctx->xc_do, *xc_tar = tsctx->xc_tar;
-  double *dx = tsctx->dx;
-  bool pick_upper = tsctx->pick_upper;
-  int shear_dir = tsctx->shear_dir, shift_dir = tsctx->shift_dir;
-  double *shift_dir_bounds = tsctx->shift_dir_bounds;
-
-  double shear_coord_phys = xc_tar[shear_dir] + 0.5*dx[shear_dir]*xi;
-  double shift;
-  tsctx->shift_func(0.0, (double[]){shear_coord_phys}, &shift, tsctx->shift_func_ctx);
-
-  double shift_coord_shifted = shift_coord_tar - shift_sign_fac * shift;
-  shift_coord_shifted = ts_wrap_to_range(shift_coord_shifted, shift_dir_bounds[0], shift_dir_bounds[1], pick_upper);
-
-  fout[0] = ts_p2l(shift_coord_shifted, xc_do[shift_dir], dx[shift_dir]);
-}
-
-void
-ts_subcellint_sNi_sNii(struct gkyl_bc_twistshift *up, struct ts_val_found *inter_pts,
-  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
-  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
-{
-  // Perform sNi or sNii subcell integrals.
-  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
-  //   xc_do: cell center of donor cell.
-  //   xc_tar: cell center of target cell.
-  //   cellb_do: boundaries of target cell.
-  //   cellb_tar: boundaries of target cell.
-  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
-  //   shift_c: DG coefficients of the shift.
-  //   mat_do: current donor matrix.
-
-  bool is_sNi = inter_pts[2].value < inter_pts[0].value;
-
-  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
-    .shift_sign_fac = 1,
-    .xc_do = xc_do,
-    .xc_tar = xc_tar,
-    .dx = up->ts_grid.dx,
-    .pick_upper = is_upper_shift_dir_cell,
-    .shear_dir = up->shear_dir_in_ts_grid,
-    .shift_dir = up->shift_dir_in_ts_grid,
-    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
-                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
-    .shift_func = up->shift_func,
-    .shift_func_ctx = up->shift_func_ctx,
-  };
-
-  double xi_b[2]; // Limits of xi integral.
-  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
-  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
-
-  // Offset between cell centers in direction of the shift.
-  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
-
-  if (is_sNi) {
-    // sNi
-    // 1) Add the contribution of the left portion.
-    xi_b[0] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_minus_one;
-    eta_lims[1] = ts_shift_coord_shifted_log;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-
-    // 2) Add the contribution of the right portion.
-    xi_b[0] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_shift_coord_shifted_log;
-    eta_lims[1] = ts_one;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-  }
-  else {
-    // sNii
-    // 1) Add the contribution of the left portion.
-    xi_b[0] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_shift_coord_shifted_log;
-    eta_lims[1] = ts_one;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-
-    // 2) Add the contribution of the right portion.
-    xi_b[0] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_minus_one;
-    eta_lims[1] = ts_shift_coord_shifted_log;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-  }
-}
-
-void
-ts_subcellint_si_sii(struct gkyl_bc_twistshift *up, struct ts_val_found *inter_pts,
-  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
-  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
-{
-  // Perform subcell integral si or sii, using fixed x-limits and variable y limits.
-  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
-  //   xc_do: cell center of donor cell.
-  //   xc_tar: cell center of target cell.
-  //   cellb_do: boundaries of target cell.
-  //   cellb_tar: boundaries of target cell.
-  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
-  //   shift_c: DG coefficients of the shift.
-  //   mat_do: current donor matrix.
-
-  double x_up = cellb_tar[cellb_up(up->shear_dir_in_ts_grid)];
-  double x_lo = cellb_tar[cellb_lo(up->shear_dir_in_ts_grid)];
-  double shift_lo, shift_up;
-
-  up->shift_func(0.0, (double[]){x_lo}, &shift_lo, up->shift_func_ctx);
-  up->shift_func(0.0, (double[]){x_up}, &shift_up, up->shift_func_ctx);
-
-  bool is_si = -shift_lo < -shift_up;
-
-  double xi_b[2];  // Limits of xi integral.
-  if (is_si) {
-    // si integral.
-    xi_b[0] = -1.0;
-    xi_b[1] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);;
-  }
-  else {
-    // sii integral.
-    xi_b[0] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);;
-    xi_b[1] = 1.0;
-  }
-
-  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
-  eta_lims[0] = ts_shift_coord_shifted_log;
-  eta_lims[1] = ts_one;
-
-  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
-    .shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)],
-    .shift_sign_fac = 1,
-    .xc_do = xc_do,
-    .xc_tar = xc_tar,
-    .dx = up->ts_grid.dx,
-    .pick_upper = is_upper_shift_dir_cell,
-    .shear_dir = up->shear_dir_in_ts_grid,
-    .shift_dir = up->shift_dir_in_ts_grid,
-    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
-                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
-    .shift_func = up->shift_func,
-    .shift_func_ctx = up->shift_func_ctx,
-  };
-
-  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
-  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-  // Offset between cell centers in direction of the shift.
-  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
-
-  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-}
-
-void
-ts_subcellint_siii_siv(struct gkyl_bc_twistshift *up, struct ts_val_found *inter_pts,
-  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
-  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
-{
-  // Perform subcell integral siii or siv, using fixed x-limits and variable y limits.
-  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
-  //   xc_do: cell center of donor cell.
-  //   xc_tar: cell center of target cell.
-  //   cellb_do: boundaries of target cell.
-  //   cellb_tar: boundaries of target cell.
-  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
-  //   shift_c: DG coefficients of the shift.
-  //   mat_do: current donor matrix.
-  
-  double x_lo = cellb_tar[cellb_lo(up->shear_dir_in_ts_grid)];
-  double x_up = cellb_tar[cellb_up(up->shear_dir_in_ts_grid)];
-  double shift_lo, shift_up;
-
-  up->shift_func(0.0, (double[]){x_lo}, &shift_lo, up->shift_func_ctx);
-  up->shift_func(0.0, (double[]){x_up}, &shift_up, up->shift_func_ctx);
-
-  bool is_siii = -shift_lo > -shift_up;
-
-  double xi_b[2];  // Limits of xi integral.
-  if (is_siii) {
-    // siii integral.
-    xi_b[0] = -1.0;
-    xi_b[1] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);;
-  }
-  else {
-    // siv integral.
-    xi_b[0] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);;
-    xi_b[1] = 1.0;
-  }
-
-  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
-  eta_lims[0] = ts_minus_one;
-  eta_lims[1] = ts_shift_coord_shifted_log;
-
-  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
-    .shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)],
-    .shift_sign_fac = 1,
-    .xc_do = xc_do,
-    .xc_tar = xc_tar,
-    .dx = up->ts_grid.dx,
-    .pick_upper = is_upper_shift_dir_cell,
-    .shear_dir = up->shear_dir_in_ts_grid,
-    .shift_dir = up->shift_dir_in_ts_grid,
-    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
-                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
-    .shift_func = up->shift_func,
-    .shift_func_ctx = up->shift_func_ctx,
-  };
-
-  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
-  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-  // Offset between cell centers in direction of the shift.
-  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
-
-  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-}
-
-void
-ts_subcellint_sv_svi(struct gkyl_bc_twistshift *up, struct ts_val_found *inter_pts,
-  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
-  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
-{
-  // Perform sv or svi subcell integrals.
-  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
-  //   xc_do: cell center of donor cell.
-  //   xc_tar: cell center of target cell.
-  //   cellb_do: boundaries of target cell.
-  //   cellb_tar: boundaries of target cell.
-  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
-  //   shift_c: DG coefficients of the shift.
-  //   mat_do: current donor matrix.
-
-  bool is_sv = inter_pts[3].value < inter_pts[1].value;
-
-  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
-    .shift_sign_fac = 1,
-    .xc_do = xc_do,
-    .xc_tar = xc_tar,
-    .dx = up->ts_grid.dx,
-    .pick_upper = is_upper_shift_dir_cell,
-    .shear_dir = up->shear_dir_in_ts_grid,
-    .shift_dir = up->shift_dir_in_ts_grid,
-    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
-                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
-    .shift_func = up->shift_func,
-    .shift_func_ctx = up->shift_func_ctx,
-  };
-
-  double xi_b[2]; // Limits of xi integral.
-  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
-  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
-
-  // Offset between cell centers in direction of the shift.
-  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
-
-  if (is_sv) {
-    // sv
-    // 1) Add the contribution of the left portion.
-    xi_b[0] = -1.0;
-    xi_b[1] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_minus_one;
-    eta_lims[1] = ts_shift_coord_shifted_log;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-
-    // 2) Add the contribution of the right portion.
-    xi_b[0] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_shift_coord_shifted_log;
-    eta_lims[1] = ts_one;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-  }
-  else {
-    // svi
-    // 1) Add the contribution of the left portion.
-    xi_b[0] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_shift_coord_shifted_log;
-    eta_lims[1] = ts_one;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-
-    // 2) Add the contribution of the right portion.
-    xi_b[0] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = 1.0;
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_minus_one;
-    eta_lims[1] = ts_shift_coord_shifted_log;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-  }
-}
-
-void
-ts_subcellint_svii_sviii(struct gkyl_bc_twistshift *up, struct ts_val_found *inter_pts,
-  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
-  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
-{
-  // Perform svii or sviii subcell integrals.
-  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
-  //   xc_do: cell center of donor cell.
-  //   xc_tar: cell center of target cell.
-  //   cellb_do: boundaries of target cell.
-  //   cellb_tar: boundaries of target cell.
-  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
-  //   shift_c: DG coefficients of the shift.
-  //   mat_do: current donor matrix.
-
-  bool is_svii = inter_pts[0].value < inter_pts[2].value;
-
-  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
-    .shift_sign_fac = 1,
-    .xc_do = xc_do,
-    .xc_tar = xc_tar,
-    .dx = up->ts_grid.dx,
-    .pick_upper = is_upper_shift_dir_cell,
-    .shear_dir = up->shear_dir_in_ts_grid,
-    .shift_dir = up->shift_dir_in_ts_grid,
-    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
-                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
-    .shift_func = up->shift_func,
-    .shift_func_ctx = up->shift_func_ctx,
-  };
-
-  double xi_b[2]; // Limits of xi integral.
-  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
-  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
-
-  // Offset between cell centers in direction of the shift.
-  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
-
-  if (is_svii) {
-    // svii
-    // 1) Add the contribution of the left portion.
-    xi_b[0] = -1.0;
-    xi_b[1] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_shift_coord_shifted_log;
-    eta_lims[1] = ts_one;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-
-    // 2) Add the contribution of the right portion.
-    xi_b[0] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_minus_one;
-    eta_lims[1] = ts_shift_coord_shifted_log;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-  }
-  else {
-    // sviii
-    // 1) Add the contribution of the left portion.
-    xi_b[0] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_minus_one;
-    eta_lims[1] = ts_shift_coord_shifted_log;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-
-    // 2) Add the contribution of the right portion.
-    xi_b[0] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = 1.0;
-
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_shift_coord_shifted_log;
-    eta_lims[1] = ts_one;
-
-    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-  }
-}
-
-void
-ts_subcellint_six_sx(struct gkyl_bc_twistshift *up, struct ts_val_found *inter_pts,
-  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
-  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
-{
-  // Perform six or sx subcell integrals.
-  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
-  //   xc_do: cell center of donor cell.
-  //   xc_tar: cell center of target cell.
-  //   cellb_do: boundaries of target cell.
-  //   cellb_tar: boundaries of target cell.
-  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
-  //   shift_c: DG coefficients of the shift.
-  //   mat_do: current donor matrix.
-
-  bool is_six = inter_pts[0].value < inter_pts[1].value;
-
-  // Limits of xi integral.
-  double xi_b[2];
-  if (is_six) {
-    // six
-    xi_b[0] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-  }
-  else {
-    // sx
-    xi_b[0] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-  }
-
-  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
-    .shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)],
-    .shift_sign_fac = 1,
-    .xc_do = xc_do,
-    .xc_tar = xc_tar,
-    .dx = up->ts_grid.dx,
-    .pick_upper = is_upper_shift_dir_cell,
-    .shear_dir = up->shear_dir_in_ts_grid,
-    .shift_dir = up->shift_dir_in_ts_grid,
-    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
-                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
-    .shift_func = up->shift_func,
-    .shift_func_ctx = up->shift_func_ctx,
-  };
-
-  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
-  eta_lims[0] = ts_shift_coord_shifted_log;
-  eta_lims[1] = ts_one;
-
-  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
-  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-  // Offset between cell centers in direction of the shift.
-  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
-
-  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-}
-
-void
-ts_subcellint_sxi_sxii(struct gkyl_bc_twistshift *up, struct ts_val_found *inter_pts,
-  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
-  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
-{
-  // Perform sxi or sxii subcell integrals.
-  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
-  //   xc_do: cell center of donor cell.
-  //   xc_tar: cell center of target cell.
-  //   cellb_do: boundaries of target cell.
-  //   cellb_tar: boundaries of target cell.
-  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
-  //   shift_c: DG coefficients of the shift.
-  //   mat_do: current donor matrix.
-
-  bool is_sxi = inter_pts[3].value < inter_pts[2].value;
-
-  // Limits of xi integral.
-  double xi_b[2];
-  if (is_sxi) {
-    // six
-    xi_b[0] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-  }
-  else {
-    // sx
-    xi_b[0] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-    xi_b[1] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-  }
-
-  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
-    .shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)],
-    .shift_sign_fac = 1,
-    .xc_do = xc_do,
-    .xc_tar = xc_tar,
-    .dx = up->ts_grid.dx,
-    .pick_upper = is_upper_shift_dir_cell,
-    .shear_dir = up->shear_dir_in_ts_grid,
-    .shift_dir = up->shift_dir_in_ts_grid,
-    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
-                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
-    .shift_func = up->shift_func,
-    .shift_func_ctx = up->shift_func_ctx,
-  };
-
-  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
-  eta_lims[0] = ts_minus_one;
-  eta_lims[1] = ts_shift_coord_shifted_log;
-
-  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
-  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-  // Offset between cell centers in direction of the shift.
-  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
-
-  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-}
-
-void
-ts_subcellint_sxiii_sxiv(struct gkyl_bc_twistshift *up, struct ts_val_found *inter_pts,
-  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
-  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
-{
-  // Perform sxiii or sxiv subcell integrals.
-  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
-  //   xc_do: cell center of donor cell.
-  //   xc_tar: cell center of target cell.
-  //   cellb_do: boundaries of target cell.
-  //   cellb_tar: boundaries of target cell.
-  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
-  //   shift_c: DG coefficients of the shift.
-  //   mat_do: current donor matrix.
-
-  double x_lo = cellb_tar[cellb_lo(up->shear_dir_in_ts_grid)];
-  double x_up = cellb_tar[cellb_up(up->shear_dir_in_ts_grid)];
-  double shift_lo, shift_up;
-
-  up->shift_func(0.0, (double[]){x_lo}, &shift_lo, up->shift_func_ctx);
-  up->shift_func(0.0, (double[]){x_up}, &shift_up, up->shift_func_ctx);
-
-  bool is_sxiii = -shift_lo < -shift_up;
-
-  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
-    .shift_sign_fac = 1,
-    .xc_do = xc_do,
-    .xc_tar = xc_tar,
-    .dx = up->ts_grid.dx,
-    .pick_upper = is_upper_shift_dir_cell,
-    .shear_dir = up->shear_dir_in_ts_grid,
-    .shift_dir = up->shift_dir_in_ts_grid,
-    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
-                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
-    .shift_func = up->shift_func,
-    .shift_func_ctx = up->shift_func_ctx,
-  };
-
-  double xi_b[2]; // Limits of xi integral.
-  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
-  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
-
-  // Offset between cell centers in direction of the shift.
-  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
-
-  // 1) Add the contribution of the left portion.
-  xi_b[0] = -1.0;
-  xi_b[1] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-
-  if (is_sxiii) {
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_minus_one;
-    eta_lims[1] = ts_shift_coord_shifted_log;
-  }
-  else {
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_shift_coord_shifted_log;
-    eta_lims[1] = ts_one;
-  }
-
-  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-
-  // 2) Add the contribution of the right portion.
-  xi_b[0] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
-  xi_b[1] = 1.0;
-
-  if (is_sxiii) {
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_shift_coord_shifted_log;
-    eta_lims[1] = ts_one;
-  }
-  else {
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_minus_one;
-    eta_lims[1] = ts_shift_coord_shifted_log;
-  }
-
-  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-
-  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-}
-
-void
-ts_subcellint_sxv_sxvi(struct gkyl_bc_twistshift *up, struct ts_val_found *inter_pts,
-  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
-  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
-{
-  // Perform subcell integral sxv or sxvi, using fixed x-limits and variable y limits.
-  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
-  //   xc_do: cell center of donor cell.
-  //   xc_tar: cell center of target cell.
-  //   cellb_do: boundaries of target cell.
-  //   cellb_tar: boundaries of target cell.
-  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
-  //   shift_c: DG coefficients of the shift.
-  //   mat_do: current donor matrix.
-
-  double xi_b[] = {-1.0, 1.0};  // Limits of xi integral.
-
-  double shift_dir_bounds[] = {up->ts_grid.lower[up->shift_dir_in_ts_grid],
-                               up->ts_grid.upper[up->shift_dir_in_ts_grid]};
-
-  double x_eval = xc_do[up->shear_dir_in_ts_grid];
-  double shift;
-
-  up->shift_func(0.0, (double[]){x_eval}, &shift, up->shift_func_ctx);
-
-  double shifted_coord = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)] - shift;
-  shifted_coord = ts_wrap_to_range(shifted_coord, shift_dir_bounds[0], shift_dir_bounds[1],
-    is_upper_shift_dir_cell);
-
-  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
-    .shift_sign_fac = 1,
-    .xc_do = xc_do,
-    .xc_tar = xc_tar,
-    .dx = up->ts_grid.dx,
-    .pick_upper = is_upper_shift_dir_cell,
-    .shear_dir = up->shear_dir_in_ts_grid,
-    .shift_dir = up->shift_dir_in_ts_grid,
-    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
-                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
-    .shift_func = up->shift_func,
-    .shift_func_ctx = up->shift_func_ctx,
-  };
-
-  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
-  if ( cellb_do[cellb_lo(up->shift_dir_in_ts_grid)] <= shifted_coord &&
-       shifted_coord <= cellb_do[cellb_up(up->shift_dir_in_ts_grid)] ) {
-    // sxv integral.
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_shift_coord_shifted_log;
-    eta_lims[1] = ts_one;
-  }
-  else {
-    // sxvi integral.
-    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
-    eta_lims[0] = ts_minus_one;
-    eta_lims[1] = ts_shift_coord_shifted_log;
-  }
-
-  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
-  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
-  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
-  // Offset between cell centers in direction of the shift.
-  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
-
-  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
-    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
-      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
-}
-
-struct gkyl_nmat *
-ts_calc_mats(struct gkyl_bc_twistshift *up)
-{
-
-  // Allocate matrices containing the discrete subcell integrals.
-  int num_do_tot = 0;
-  for (int i=0; i<up->shear_r.volume; i++)
-    num_do_tot += up->num_do[i];
-
-  struct gkyl_nmat *matsdo = gkyl_nmat_new(num_do_tot, up->basis.num_basis, up->basis.num_basis);
-  for (int n=0; n<matsdo->num; ++n) {
-    struct gkyl_mat mat = gkyl_nmat_get(matsdo, n);
-    for (int j=0; j<matsdo->nc; ++j)
-      for (int i=0; i<matsdo->nr; ++i)
-        gkyl_mat_set(&mat, i, j, 0.0);
-  }
-
-  // y-index of the reference target used to precalc matrices. For positive(negative)
-  // yShift idx=1(last) might be better, but ideally it shouldn't matter.
-  int shift_dir_idx_tar = 1;
-
-  double shift_dir_lims[] = {up->ts_grid.lower[up->shift_dir_in_ts_grid],
-                             up->ts_grid.upper[up->shift_dir_in_ts_grid]};
-
-  // Create an eval_on_nodes updater to use its nodes and functions (but not
-  // the whole advance method).
-  up->ev_on_nod1d = gkyl_eval_on_nodes_new(&up->shear_grid, &up->shift_b, 1, ts_one, NULL);
-  // Create an array to store evaluations of a function at 1D nodes.
-  up->func_nod1d = gkyl_array_new(GKYL_DOUBLE, 1, up->shift_b.num_basis);
-
-  struct gkyl_range_iter iter;
-  gkyl_range_iter_init(&iter, &up->shear_r);
-  while (gkyl_range_iter_next(&iter)) {
-
-    // Get the cell boundaries and cell center.
-    int idx_tar[2]; // Target index.
-    idx_tar[up->shift_dir_in_ts_grid] = shift_dir_idx_tar;
-    idx_tar[up->shear_dir_in_ts_grid] = iter.idx[0];
-    double cellb_tar[4] = {0.0}; // Cell boundaries, x lo and up, y lo and up;
-    double xc_tar[2] = {0.0}; // Cell center.
-    ts_grid_cell_boundaries(&up->ts_grid, idx_tar, cellb_tar);
-    gkyl_rect_grid_cell_center(&up->ts_grid, idx_tar, xc_tar);
-
-    long shift_loc = gkyl_range_idx(&up->shear_r, iter.idx);
-    double *shift_c = (double *) gkyl_array_fetch(up->shift_dg, shift_loc);
-
-    long linidx_do = ts_shift_dir_idx_do_linidx(up->num_do, iter.idx[0], shift_dir_idx_tar,
-      up->ts_grid.cells[up->shift_dir_in_ts_grid], up->shear_r.lower[0]);
-    int *shift_dir_idx_do_ptr = &up->shift_dir_idx_do[linidx_do];
-
-    long linidx_mats_do = 0;
-    for (int i=0; i<iter.idx[0]-up->shear_r.lower[0]; i++)
-      linidx_mats_do += up->num_do[i];
-
-    // Check that the shift variation within this x-cell < Ly.
-    // The algorithm assumes at most one x-intersection per (y-boundary, y-boundary) pair,
-    // which breaks when |S(x_up) - S(x_lo)| >= Ly.
-    double x_lo = cellb_tar[cellb_lo(up->shear_dir_in_ts_grid)];
-    double x_up = cellb_tar[cellb_up(up->shear_dir_in_ts_grid)];
-    double Ly = shift_dir_lims[1] - shift_dir_lims[0];
-    double S_lo, S_up, S_c;
-    up->shift_func(0.0, (double[]){x_lo}, &S_lo, up->shift_func_ctx);
-    up->shift_func(0.0, (double[]){x_up}, &S_up, up->shift_func_ctx);
-    up->shift_func(0.0, (double[]){xc_tar[up->shear_dir_in_ts_grid]}, &S_c, up->shift_func_ctx);
-
-    if (fabs(S_up - S_lo) >= Ly) {
-      fprintf(stderr, "bc_twistshift: shift variation |S(x_up)-S(x_lo)| = %g across a single x-cell"
-        " exceeds Ly = %g (cell ix=%d). Increase Nx, reduce the shear, or increase Ly.\n",
-        fabs(S_up - S_lo), Ly, iter.idx[0]);
-      assert(false);
-    }
-
-    for (int iC=0; iC<up->num_do[iter.idx[0]-up->shear_r.lower[0]]; iC++){
-      int idx_do[2]; // Target index.
-      idx_do[up->shift_dir_in_ts_grid] = shift_dir_idx_do_ptr[iC];
-      idx_do[up->shear_dir_in_ts_grid] = iter.idx[0];
-
-      double cellb_do[4] = {0.0}; // Cell boundaries, x lo and up, y lo and up;
-      double xc_do[2] = {0.0}; // Cell center.
-      ts_grid_cell_boundaries(&up->ts_grid, idx_do, cellb_do);
-      gkyl_rect_grid_cell_center(&up->ts_grid, idx_do, xc_do);
-
-      // Get the matrix we are presently assigning.
-      struct gkyl_mat mat_do = gkyl_nmat_get(matsdo, linidx_mats_do+iC);
-
-      // Periodic copy in which to find the target for this donor-target pair: the integer nP such that
-      // S_c \approx y_tar_c - y_do_c + nP*Ly. All 4 inter_pts must use this same nP so that only
-      // roots from the physical intersection are accepted (not roots from other periodic copies).
-      int nP_primary = (int)round((S_c - (xc_tar[up->shift_dir_in_ts_grid] - xc_do[up->shift_dir_in_ts_grid])) / Ly);
-
-      // Find the points where y_{j_tar-/+1/2}-yShift intersect the y=y_{j_do-/+1/2} lines.
-      // Also record the number and indices of points found/not found.
-      struct ts_val_found inter_pts[4] = {};
-      int num_inter_pts_found = 0, num_inter_pts_not_found = 4;
-      int inter_pts_found_idxs[4], inter_pts_not_found_idxs[4];
-      for (int i=0; i<2; i++) { // Loop over j_tar-/+1/2
-        for (int j=0; j<2; j++) { // Loop over j_do-/+1/2
-          double shift_dir_coord_tar = cellb_tar[2*up->shift_dir_in_ts_grid+i];
-          double shift_dir_coord_do = cellb_do[2*up->shift_dir_in_ts_grid+j];
-          struct gkyl_qr_res inter_res = ts_find_intersect(up, shift_dir_coord_tar, shift_dir_coord_do,
-            (double[]) {cellb_tar[cellb_lo(up->shear_dir_in_ts_grid)],cellb_tar[cellb_up(up->shear_dir_in_ts_grid)]},
-            shift_dir_lims, nP_primary);
-          int ip_linc = i*2+j;
-          inter_pts[ip_linc].status = inter_res.status == 0;
-          if (inter_res.status == 0) {
-            inter_pts[ip_linc].value = inter_res.res;
-            inter_pts_found_idxs[num_inter_pts_found] = ip_linc;
-            num_inter_pts_found++;
-          }
-          else {
-            inter_pts_not_found_idxs[num_inter_pts_not_found] = ip_linc;
-            num_inter_pts_not_found--;
-          }
-        }
-      }
-
-      bool is_upper_shift_dir_cell = idx_do[up->shift_dir_in_ts_grid] == up->ts_grid.cells[up->shift_dir_in_ts_grid];
-
-      if (num_inter_pts_found == 4) {
-        // sN: all intersections are found at this cell.
-        ts_subcellint_sNi_sNii(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
-      }
-      else if (num_inter_pts_found == 1) {
-        if (inter_pts[1].status) {
-          // si:   y_{j_tar-1/2}-yShift intersects x_{i-1/2}.
-          // sii:  y_{j_tar-1/2}-yShift intersects x_{i+1/2}.
-          ts_subcellint_si_sii(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
-        }
-        else {
-          // siii: y_{j_tar+1/2}-yShift intersects x_{i-1/2}.
-          // siv:  y_{j_tar+1/2}-yShift intersects x_{i+1/2}.
-          ts_subcellint_siii_siv(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
-        }
-      }
-      else if (num_inter_pts_found == 3) {
-        if (!inter_pts[2].status) {
-          // sv:    y_{j_tar+1/2}-yShift doesn't intersect y_{j_do-1/2} & intersects x_{i-1/2}.
-          // svi:   y_{j_tar+1/2}-yShift doesn't intersect y_{j_do-1/2} & intersects x_{i+1/2}.
-          ts_subcellint_sv_svi(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
-        }
-        else {
-          // svii:  y_{j_tar-1/2}-yShift doesn't intersect y_{j_do+1/2} & intersects x_{i-1/2}.
-          // sviii: y_{j_tar-1/2}-yShift doesn't intersect y_{j_do+1/2} & intersects x_{i+1/2}.
-          ts_subcellint_svii_sviii(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
-        }
-      }
-      else if (num_inter_pts_found == 2) {
-        if (inter_pts[0].status && inter_pts[1].status) {
-          // six:   y_{j_tar-1/2}-yShift crosses y_{j_do-/+1/2} (increasing yShift).
-          // sx:    y_{j_tar-1/2}-yShift crosses y_{j_do-/+1/2} (decreasing yShift).
-          ts_subcellint_six_sx(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
-        }
-        else if (inter_pts[2].status && inter_pts[3].status) {
-          // sxi:   y_{j_tar+1/2}-yShift crosses y_{j_do-/+1/2} (decreasing yShift).
-          // sxii:  y_{j_tar+1/2}-yShift crosses y_{j_do-/+1/2} (increasing yShift).
-          ts_subcellint_sxi_sxii(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
-        }
-        else {
-          // sxiii: y_{j_tar-1/2}-yShift crosses y_{j_do-1/2} & y_{j_tar+1/2}-yShift crosses y_{j_do+1/2} (increasing yShift).
-          // sxiv:  y_{j_tar-1/2}-yShift crosses y_{j_do-1/2} & y_{j_tar+1/2}-yShift crosses y_{j_do+1/2} (decreasing yShift).
-          ts_subcellint_sxiii_sxiv(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
-        }
-      }
-      else if (num_inter_pts_found == 0) {
-        // sxv:  y_{j_tar-1/2}-yShift crosses x_{i-/+1/2}.
-        // sxvi: y_{j_tar+1/2}-yShift crosses x_{i-/+1/2}.
-        ts_subcellint_sxv_sxvi(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
-      }
-      else {
-        // An error occurred. This shouldn't happen.
-        assert(false);
-      }
-    }
-
-  }
-
-  gkyl_array_release(up->func_nod1d);
-  gkyl_eval_on_nodes_release(up->ev_on_nod1d);
-
-  struct gkyl_nmat *matsdo_out = up->use_gpu? gkyl_nmat_cu_dev_new(matsdo->num, matsdo->nr, matsdo->nc)
-                                            : gkyl_nmat_acquire(matsdo); 
-  gkyl_nmat_copy(matsdo_out, matsdo);
-  gkyl_nmat_release(matsdo);
-
-  return matsdo_out;
-}
-
-long *
-ts_calc_num_numcol_fidx_do(struct gkyl_bc_twistshift *up)
-{
-  // Calculate the linear indices into the donor distribution function gkyl_array
-  // for each num-numcol plane (in the num-numcol-num_basis) space.
-
-  long *num_numcol_fidx_do_ho = (long*) gkyl_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
-
-  // Location in the direction of the BC from which to take donor
-  // distributions. We assume that the user filled the ghost cell with the skin
-  // on the other side (i.e. applied periodicity first).
-  int bc_dir_loc_do = up->edge == GKYL_LOWER_EDGE? up->local_bcdir_ext_r.lower[up->bc_dir]
-                                                 : up->local_bcdir_ext_r.upper[up->bc_dir];
-
-  // Range over directions other than shear and bc dirs.
-  struct gkyl_range shearbc_perp_r;
-  int remove[GKYL_MAX_DIM] = {0}, loc_in_dir[GKYL_MAX_DIM] = {0};;
-  remove[up->shear_dir] = remove[up->bc_dir] = 1;
-  loc_in_dir[up->shear_dir] = up->local_bcdir_ext_r.lower[up->shear_dir];
-  loc_in_dir[up->bc_dir] = bc_dir_loc_do;
-  gkyl_range_deflate(&shearbc_perp_r, &up->local_bcdir_ext_r, remove, loc_in_dir);
-
-  int shift_dir_in_shearbc_perp_r;
-  if (up->shift_dir < up->shear_dir && up->shift_dir < up->bc_dir)
-    shift_dir_in_shearbc_perp_r = up->shift_dir;
-  else if (up->shift_dir > up->shear_dir && up->shift_dir > up->bc_dir)
-    shift_dir_in_shearbc_perp_r = up->shift_dir-2;
-  else
-    shift_dir_in_shearbc_perp_r = up->shift_dir-1;
-
-  int prev_shift_dir_idx = 0;
-  int donor_count = 0;
-  int do_idx[up->local_bcdir_ext_r.ndim];
-
-  // Loop over directions perpendicular to shear and BC dirs.
-  struct gkyl_range_iter iter;
-  gkyl_range_iter_init(&iter, &shearbc_perp_r);
-  while (gkyl_range_iter_next(&iter)) {
-    int ic = 0;
-    for (int d=0; d<up->local_bcdir_ext_r.ndim; d++) {
-      if (d != up->bc_dir && d != up->shear_dir) {
-        do_idx[d] = iter.idx[ic];
-        ic++;
-      }
-    }
-    do_idx[up->bc_dir] = bc_dir_loc_do;
-
-    struct gkyl_range_iter shear_dir_iter;
-    gkyl_range_iter_init(&shear_dir_iter, &up->shear_r);
-    while (gkyl_range_iter_next(&shear_dir_iter)) {
-
-      int shear_dir_idx = shear_dir_iter.idx[0];
-
-      long linidx_do = ts_shift_dir_idx_do_linidx(up->num_do, shear_dir_idx,
-        iter.idx[shift_dir_in_shearbc_perp_r], up->ts_grid.cells[up->shift_dir_in_ts_grid], up->shear_r.lower[0]);
-
-      for (int i = 0; i < up->num_do[shear_dir_idx-up->shear_r.lower[0]]; i++) {
-        do_idx[up->shear_dir] = shear_dir_idx;
-        do_idx[up->shift_dir] = up->shift_dir_idx_do[linidx_do+i];
-
-        long loc = gkyl_range_idx(&up->local_bcdir_ext_r, do_idx);
-        num_numcol_fidx_do_ho[donor_count] = loc;
-
-        donor_count += 1;
-      }
-    }
-    prev_shift_dir_idx = iter.idx[shift_dir_in_shearbc_perp_r];
-  }
-
-  long *num_numcol_fidx_do;
-  if (!up->use_gpu) {
-    num_numcol_fidx_do = (long*) gkyl_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
-    memcpy(num_numcol_fidx_do, num_numcol_fidx_do_ho, up->fmat->num * up->fmat->nc * sizeof(long));
-  }
-#ifdef GKYL_HAVE_CUDA
-  if (up->use_gpu) {
-    num_numcol_fidx_do = (long*) gkyl_cu_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
-    gkyl_cu_memcpy(num_numcol_fidx_do, num_numcol_fidx_do_ho, up->fmat->num * up->fmat->nc * sizeof(long), GKYL_CU_MEMCPY_H2D);
-  }
-#endif
-
-  gkyl_free(num_numcol_fidx_do_ho);
-
-  return num_numcol_fidx_do;
-}
-
-long *
-ts_calc_num_numcol_fidx_tar(struct gkyl_bc_twistshift *up)
-{
-
-  long *num_numcol_fidx_tar_ho = (long*) gkyl_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
-
-  // Location in the direction of the BC in which to place the target
-  // distributions. We assume that the local_bcdir_ext_r is a range extended in z (it
-  // includes the z ghose cell).
-  int bc_dir_loc_tar = up->edge == GKYL_LOWER_EDGE? up->local_bcdir_ext_r.lower[up->bc_dir]
-                                                  : up->local_bcdir_ext_r.upper[up->bc_dir];
-
-  // Range over directions other than shear and bc dirs.
-  struct gkyl_range shearbc_perp_r;
-  int remove[GKYL_MAX_DIM] = {0}, loc_in_dir[GKYL_MAX_DIM] = {0};;
-  remove[up->shear_dir] = remove[up->bc_dir] = 1;
-  loc_in_dir[up->shear_dir] = up->local_bcdir_ext_r.lower[up->shear_dir];
-  loc_in_dir[up->bc_dir] = bc_dir_loc_tar;
-  gkyl_range_deflate(&shearbc_perp_r, &up->local_bcdir_ext_r, remove, loc_in_dir);
-
-  int tar_idx[up->local_bcdir_ext_r.ndim];
-  int tar_count = 0;
-
-  // Loop over directions perpendicular to shear and BC dirs.
-  struct gkyl_range_iter iter;
-  gkyl_range_iter_init(&iter, &shearbc_perp_r);
-  while (gkyl_range_iter_next(&iter)) {
-
-    int ic = 0;
-    for (int d=0; d<up->local_bcdir_ext_r.ndim; d++) {
-      if (d != up->bc_dir && d != up->shear_dir) {
-        tar_idx[d] = iter.idx[ic];
-        ic++;
-      }
-    }
-    tar_idx[up->bc_dir] = bc_dir_loc_tar;
-
-
-    struct gkyl_range_iter shear_dir_iter;
-    gkyl_range_iter_init(&shear_dir_iter, &up->shear_r);
-    while (gkyl_range_iter_next(&shear_dir_iter)) {
-      int shear_dir_idx = shear_dir_iter.idx[0];
-      tar_idx[up->shear_dir] = shear_dir_idx;
-
-      long loc = gkyl_range_idx(&up->local_bcdir_ext_r, tar_idx);
-      num_numcol_fidx_tar_ho[tar_count] = loc;
-      tar_count += 1;
-    }
-  }
-
-  long *num_numcol_fidx_tar;
-  if (!up->use_gpu) {
-    num_numcol_fidx_tar = (long*) gkyl_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
-    memcpy(num_numcol_fidx_tar, num_numcol_fidx_tar_ho, up->fmat->num * up->fmat->nc * sizeof(long));
-  }
-#ifdef GKYL_HAVE_CUDA
-  if (up->use_gpu) {
-    num_numcol_fidx_tar = (long*) gkyl_cu_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
-    gkyl_cu_memcpy(num_numcol_fidx_tar, num_numcol_fidx_tar_ho, up->fmat->num * up->fmat->nc * sizeof(long), GKYL_CU_MEMCPY_H2D);
-  }
-#endif
-
-  gkyl_free(num_numcol_fidx_tar_ho);
-
-  return num_numcol_fidx_tar;
-}
-
-void
-gkyl_bc_twistshift_choose_kernels(struct gkyl_basis basis, int cdim, int shift_poly_order,
-  struct gkyl_bc_twistshift_kernels *kers)
-{
-  int dim = basis.ndim;
-  int vdim = dim - cdim;
-  enum gkyl_basis_type basis_type = basis.b_type;
-  int poly_order = basis.poly_order;
-  switch (basis_type) {
-    case GKYL_BASIS_MODAL_GKHYBRID:
-    case GKYL_BASIS_MODAL_SERENDIPITY:
-      if (shift_poly_order == 1) {
-        kers->xlimdg   = vdim==0? ser_twistshift_xlimdg_list_0v_yShp1[cdim-2].kernels[poly_order]
-                                : ser_twistshift_xlimdg_list_2v_yShp1[cdim-2].kernels[poly_order];
-        kers->ylimdg   = vdim==0? ser_twistshift_ylimdg_list_0v_yShp1[cdim-2].kernels[poly_order]
-                                : ser_twistshift_ylimdg_list_2v_yShp1[cdim-2].kernels[poly_order];
-        kers->fullcell = vdim==0? ser_twistshift_fullcell_list_0v_yShp1[cdim-2].kernels[poly_order]
-                                : ser_twistshift_fullcell_list_2v_yShp1[cdim-2].kernels[poly_order];
-      }
-      else if (shift_poly_order == 2) {
-        assert(false); // MF 2025/09/20: removed 3x2v kernel because it's 8.5 MB.
-        kers->xlimdg   = vdim==0? ser_twistshift_xlimdg_list_0v_yShp2[cdim-2].kernels[poly_order]
-                                : ser_twistshift_xlimdg_list_2v_yShp2[cdim-2].kernels[poly_order];
-        kers->ylimdg   = vdim==0? ser_twistshift_ylimdg_list_0v_yShp2[cdim-2].kernels[poly_order]
-                                : ser_twistshift_ylimdg_list_2v_yShp2[cdim-2].kernels[poly_order];
-        kers->fullcell = vdim==0? ser_twistshift_fullcell_list_0v_yShp2[cdim-2].kernels[poly_order]
-                                : ser_twistshift_fullcell_list_2v_yShp2[cdim-2].kernels[poly_order];
-      }
-      return;
-    default:
-      assert(false);
-      break;
-  }
+  struct gkyl_dg_interpolate *interp = gkyl_dg_interpolate_new(1, &shift_b,
+    &grid_do, &grid_tar, &shear_r_do, shear_r_fine, (int[]) {0}, false);
+  gkyl_dg_interpolate_advance(interp, inp->shift_dg, shift_dg_fine);
+  gkyl_dg_interpolate_release(interp);
 }
 
 struct gkyl_bc_twistshift*
 gkyl_bc_twistshift_inew(const struct gkyl_bc_twistshift_inp *inp)
 {
+  struct gkyl_bc_twistshift *up = gkyl_malloc(sizeof(*up));
 
-  // Allocate space for new updater.
-  struct gkyl_bc_twistshift *up = gkyl_malloc(sizeof(struct gkyl_bc_twistshift));
-
-  up->bc_dir = inp->bc_dir;
-  up->shift_dir = inp->shift_dir;
-  up->shear_dir = inp->shear_dir;
-  up->edge = inp->edge;
-  up->basis = *inp->basis;
-  up->grid = *inp->grid;
   up->use_gpu = inp->use_gpu;
-  up->local_bcdir_ext_r = *inp->bcdir_ext_update_r;
-
-  // Assume the poly order of the DG shift is the same as that of the field,
-  // unless requested otherwise.
-  up->shift_poly_order = inp->basis->poly_order;
-  if (inp->shift_poly_order)
-    up->shift_poly_order = inp->shift_poly_order;
-
+  up->filter_half_width = inp->filter_half_width;
+  up->filter_cutoff_wavelength = inp->filter_cutoff_wavelength;
+  up->upsample_factor = inp->upsample_factor > 1 ? inp->upsample_factor : 1;
+
+  up->filter = NULL;
+  up->filt_buff = NULL;
+  up->ffine = NULL;
+  up->shift_dg_fine = NULL;
+  up->refine = NULL;
+  up->coarsen = NULL;
+  up->refine_func = bc_twistshift_refine_disabled;
+  up->coarsen_func = bc_twistshift_coarsen_disabled;
+
+  // The half-width counts cells of the original grid.
+  up->half_width_fine = up->filter_half_width * up->upsample_factor;
+
+  // A stencil one fine cell wide is the identity kernel.
+  assert(up->half_width_fine != 1);
+  // Supersampling is only useful if there is filtering.
+  if (up->upsample_factor > 1)
+    assert(up->filter_half_width > 0 && up->filter_cutoff_wavelength > 0.0);
+
+  if (up->filter_half_width == 0) {
+    // Plain twist-shift.
+    struct gkyl_twistshift_dg_inp tsinp = {
+      .bc_dir = inp->bc_dir,
+      .shift_dir = inp->shift_dir,
+      .shear_dir = inp->shear_dir,
+      .edge = inp->edge,
+      .cdim = inp->cdim,
+      .bcdir_ext_update_r = inp->bcdir_ext_update_r,
+      .num_ghost = inp->num_ghost,
+      .basis = inp->basis,
+      .grid = inp->grid,
+      .shift_func = inp->shift_func,
+      .shift_func_ctx = inp->shift_func_ctx,
+      .shift_dg = inp->shift_dg,
+      .use_gpu = inp->use_gpu,
+      .shift_poly_order = inp->shift_poly_order,
+    };
+    up->ts = gkyl_twistshift_dg_inew(&tsinp);
+    up->advance_func = bc_twistshift_advance_ts;
+    return up;
+  }
+
+  // Upsampling and filtering attributes.
   const int ndim = inp->bcdir_ext_update_r->ndim;
-  // Check that it is being used for 3D or 5D. Likely only small changes are
-  // needed to make it work in other dimensions.
-  assert(ndim == 3 || ndim == 5); 
-
-  double lo1d[1], up1d[1];  int cells1d[1];
-
-  // Create 1D grid and range in the direction of the shear.
-  gkyl_range_init(&up->shear_r, 1, (int[]) {up->local_bcdir_ext_r.lower[inp->shear_dir]},
-                                   (int[]) {up->local_bcdir_ext_r.upper[inp->shear_dir]});
-  lo1d[0] = inp->grid->lower[up->shear_dir];
-  up1d[0] = inp->grid->upper[up->shear_dir];
-  cells1d[0] = inp->grid->cells[up->shear_dir];
-  gkyl_rect_grid_init(&up->shear_grid, 1, lo1d, up1d, cells1d);
-  int idx[] = {up->shear_r.lower[0]};
-  long linidx = gkyl_range_idx(&up->shear_r, idx);
-
-  // Create 1D grid and range in the diretion of the shift.
-  gkyl_range_init(&up->shift_r, 1, (int[]) {up->local_bcdir_ext_r.lower[inp->shift_dir]},
-                                   (int[]) {up->local_bcdir_ext_r.upper[inp->shift_dir]});
-  lo1d[0] = inp->grid->lower[up->shift_dir];
-  up1d[0] = inp->grid->upper[up->shift_dir];
-  cells1d[0] = inp->grid->cells[up->shift_dir];
-  gkyl_rect_grid_init(&up->shift_grid, 1, lo1d, up1d, cells1d);
-
-  // Create 2D grid (and range) the twist-shift takes place in.
-  int dimlo, dimup;
-  if (up->shift_dir < up->shear_dir) {
-    dimlo = up->shift_dir;
-    dimup = up->shear_dir;
-    up->shift_dir_in_ts_grid = 0;
-    up->shear_dir_in_ts_grid = 1;
-  }
-  else {
-    dimlo = up->shear_dir;
-    dimup = up->shift_dir;
-    up->shift_dir_in_ts_grid = 1;
-    up->shear_dir_in_ts_grid = 0;
-  }
-  gkyl_range_init(&up->ts_r, 2, (int[]) {up->local_bcdir_ext_r.lower[dimlo], up->local_bcdir_ext_r.lower[dimup]},
-                                (int[]) {up->local_bcdir_ext_r.upper[dimlo], up->local_bcdir_ext_r.upper[dimup]});
-  double lo2d[] = {inp->grid->lower[dimlo], inp->grid->lower[dimup]};
-  double up2d[] = {inp->grid->upper[dimlo], inp->grid->upper[dimup]};
-  int cells2d[] = {inp->grid->cells[dimlo], inp->grid->cells[dimup]};
-  gkyl_rect_grid_init(&up->ts_grid, 2, lo2d, up2d, cells2d);
-
-  // Project the shift onto the shift basis.
-  gkyl_cart_modal_serendip(&up->shift_b, 1, up->shift_poly_order);
-  if (inp->shift_func) {
-    up->shift_dg = gkyl_array_new(GKYL_DOUBLE, up->shift_b.num_basis, up->shear_r.volume);
-    gkyl_eval_on_nodes *evup = gkyl_eval_on_nodes_new(&up->shear_grid, &up->shift_b, 1,
-      inp->shift_func, inp->shift_func_ctx);
-    gkyl_eval_on_nodes_advance(evup, 0.0, &up->shear_r, up->shift_dg);
-    gkyl_eval_on_nodes_release(evup);
-  }
-  else {
-    up->shift_dg = gkyl_array_acquire(inp->shift_dg);
-  }
-
-  // Function defining the shift (and its context).
-  if (shift_func_op == 0) {
-    up->shift_func = ts_shift_dg_eval;
-    up->shift_dg_eval_ctx.shift_dg = up->shift_dg;
-    up->shift_dg_eval_ctx.shift_b = &up->shift_b;
-    up->shift_dg_eval_ctx.shear_grid = &up->shear_grid;
-    up->shift_dg_eval_ctx.shear_r = &up->shear_r;
-    up->shift_func_ctx = &up->shift_dg_eval_ctx;
-  }
-  else if (shift_func_op == 1) {
-    up->shift_func     = inp->shift_func;
-    up->shift_func_ctx = inp->shift_func_ctx;
-  }
-  else {
-    fprintf(stderr, "Twist-shift function option not recognized. Exiting...\n");
-    assert(false);
-  }
-
-  // Find the donor cells for each target. Store the number of donors for each
-  // shear_dir idx (num_do) & the shift_dir idx of each donor (shift_dir_idx_do).
-  // i.e. allocates and assigns num_do and up->shift_dir_idx_do.
-  ts_find_donors(up);
-
-  // Array of cummulative number of donors at given shear_dir cell.
-  const int num_do_cum_sz = up->grid.cells[up->shear_dir]+1;
-  int num_do_cum_ho[num_do_cum_sz];
-  for (int i=0; i<num_do_cum_sz; i++)
-    num_do_cum_ho[i] = 0;
-  for (int i=up->shear_r.lower[0]; i<up->shear_r.upper[0]+1; i++)
-    num_do_cum_ho[i] = num_do_cum_ho[i-1] + up->num_do[i-up->shear_r.lower[0]];
-
-  if (!up->use_gpu) {
-    up->num_do_cum = gkyl_malloc(num_do_cum_sz * sizeof(int));
-    memcpy(up->num_do_cum, num_do_cum_ho, num_do_cum_sz * sizeof(int));
-  }
-#ifdef GKYL_HAVE_CUDA
-  if (up->use_gpu) {
-    up->num_do_cum = gkyl_cu_malloc(num_do_cum_sz * sizeof(int));
-    gkyl_cu_memcpy(up->num_do_cum, num_do_cum_ho, num_do_cum_sz * sizeof(int), GKYL_CU_MEMCPY_H2D);
-  }
-#endif
-
-  // Choose the kernels that do the subcell and full cell integrals
-  up->kernels = gkyl_malloc(sizeof(struct gkyl_bc_twistshift_kernels));
-  gkyl_bc_twistshift_choose_kernels(*inp->basis, inp->cdim, up->shift_poly_order, up->kernels);
-
-  // The BC is applied as a set of matrix-matrix multiplications
-  //   f_i = sum_{q}^{N_do(i)} A_q,i B_q,i
-  // where i indicates the shear_dir cell index, A_q is a
-  // num_basis x num_basis matrix containing the discretization
-  // of subcell integrals, B_q is a num_basis x (Ny * Nvpar * Nmu) matrix with
-  // the DG coefficients of f common to a given A_q matrix, and thus where f_i
-  // is a num_basis x (Ny*Nvpar*Nmu) matrix.
-  //
-  // Naming scheme:
-  //   A_q: scimat (subscell integral matrices).
-  //   B_q: fmat (distribution function matrices).
-  //   A_q . B_q: mm_contr (contributions from mat-mat multiplication).
-
-  // Calculate the entries in the matrices used to apply the BC.
-  up->scimat = ts_calc_mats(up);
-
-  // Number of colums in fmat.
-  int fmat_num_col = 1;
+  // Ghost plane this BC fills, on the field's own grid.
+  if (inp->edge == GKYL_LOWER_EDGE)
+    gkyl_range_shorten_from_above(&up->coarse_ghost_r, inp->bcdir_ext_update_r,
+      inp->bc_dir, inp->num_ghost[inp->bc_dir]);
+  else
+    gkyl_range_shorten_from_below(&up->coarse_ghost_r, inp->bcdir_ext_update_r,
+      inp->bc_dir, inp->num_ghost[inp->bc_dir]);
+
+  // Grid supersampled along shear_dir.
+  int fine_cells[GKYL_MAX_DIM];
+  for (int d=0; d<ndim; d++) fine_cells[d] = inp->grid->cells[d];
+  fine_cells[inp->shear_dir] *= up->upsample_factor;
+  gkyl_rect_grid_init(&up->ts_grid, ndim, inp->grid->lower, inp->grid->upper, fine_cells);
+  // Range for supersampled cells.
+  int flo[GKYL_MAX_DIM], fup[GKYL_MAX_DIM];
   for (int d=0; d<ndim; d++) {
-    if (d != up->bc_dir && d != up->shear_dir)
-      fmat_num_col *= up->local_bcdir_ext_r.upper[d] - up->local_bcdir_ext_r.lower[d] + 1;
-  }
-
-  if (!up->use_gpu) {
-    up->fmat = gkyl_nmat_new(up->scimat->num, up->scimat->nr, fmat_num_col);
-    up->mm_contr = gkyl_nmat_new(up->scimat->num, up->scimat->nr, fmat_num_col);
-  }
-#ifdef GKYL_HAVE_CUDA
-  if (up->use_gpu) {
-    up->fmat = gkyl_nmat_cu_dev_new(up->scimat->num, up->scimat->nr, fmat_num_col);
-    up->mm_contr = gkyl_nmat_cu_dev_new(up->scimat->num, up->scimat->nr, fmat_num_col);
+    flo[d] = up->coarse_ghost_r.lower[d];
+    fup[d] = up->coarse_ghost_r.upper[d];
   }
-#endif
+  flo[inp->shear_dir] = (flo[inp->shear_dir]-1)*up->upsample_factor + 1;
+  fup[inp->shear_dir] = fup[inp->shear_dir]*up->upsample_factor;
+  gkyl_range_init(&up->ts_ext_r, ndim, flo, fup);
+  gkyl_sub_range_init(&up->ts_update_r, &up->ts_ext_r, flo, fup);
 
-  // Index translation from num-numcol plane index to linear index into the
-  // donor distribution function gkyl_array.
-  up->num_numcol_fidx_do = ts_calc_num_numcol_fidx_do(up);
+  up->ffine = mkarr(inp->use_gpu, inp->basis->num_basis, up->ts_ext_r.volume);
+  up->filt_buff = mkarr(inp->use_gpu, inp->basis->num_basis, up->ts_ext_r.volume);
 
-  // Index translation from num-numcol plane index to linear index into the
-  // tar distribution function gkyl_array.
-  up->num_numcol_fidx_tar = ts_calc_num_numcol_fidx_tar(up);
-
-  // Permutted ghost range, for indexing into the target field.
-  // Order: Shift direction, redundant directions, shear direction.
-  int lo4D[ndim-1], up4D[ndim-1];
-  lo4D[0] = up->local_bcdir_ext_r.lower[up->shift_dir];
-  up4D[0] = up->local_bcdir_ext_r.upper[up->shift_dir];
-  int ic = 1;
-  for (int d=0; d<ndim; d++) {
-    if (d != up->bc_dir && d != up->shear_dir && d != up->shift_dir) {
-      lo4D[ic] = up->local_bcdir_ext_r.lower[d];
-      up4D[ic] = up->local_bcdir_ext_r.upper[d];
-      ic++;
-    }
-  }
-  lo4D[ndim-2] = up->local_bcdir_ext_r.lower[up->shear_dir];
-  up4D[ndim-2] = up->local_bcdir_ext_r.upper[up->shear_dir];
-  gkyl_range_init(&up->permutted_ghost_r, ndim-1, lo4D, up4D);
-
-  // Create a ghost range, to clear it before adding contributions from TS BC.
+  // Ghost plane on the supersampled grid.
   if (inp->edge == GKYL_LOWER_EDGE)
-    gkyl_range_shorten_from_above(&up->ghost_r, &up->local_bcdir_ext_r, inp->bc_dir, inp->num_ghost[inp->bc_dir]);
+    gkyl_range_shorten_from_above(&up->ghost_r, &up->ts_update_r, inp->bc_dir,
+      inp->num_ghost[inp->bc_dir]);
   else
-    gkyl_range_shorten_from_below(&up->ghost_r, &up->local_bcdir_ext_r, inp->bc_dir, inp->num_ghost[inp->bc_dir]);
+    gkyl_range_shorten_from_below(&up->ghost_r, &up->ts_update_r, inp->bc_dir,
+      inp->num_ghost[inp->bc_dir]);
+
+  up->filter = gkyl_dg_lowpass_filter_new(inp->shear_dir, up->half_width_fine,
+    up->filter_cutoff_wavelength, inp->basis, &up->ts_grid, &up->ghost_r, inp->use_gpu);
+
+  if (up->upsample_factor > 1) {
+    up->refine = gkyl_dg_interpolate_new(inp->cdim, inp->basis, inp->grid, &up->ts_grid,
+      &up->coarse_ghost_r, &up->ghost_r, inp->num_ghost, inp->use_gpu);
+    up->coarsen = gkyl_dg_interpolate_new(inp->cdim, inp->basis, &up->ts_grid, inp->grid,
+      &up->ghost_r, &up->coarse_ghost_r, inp->num_ghost, inp->use_gpu);
+    up->refine_func = bc_twistshift_refine_enabled;
+    up->coarsen_func = bc_twistshift_coarsen_enabled;
+  }
+
+  // Need to upsample the DG shift too.
+  struct gkyl_array *shift_dg = inp->shift_dg;
+  if (inp->shift_dg && up->upsample_factor > 1) {
+    struct gkyl_range shear_r_fine;
+    gkyl_range_init(&shear_r_fine, 1, (int[]) {flo[inp->shear_dir]},
+                                      (int[]) {fup[inp->shear_dir]});
+    up->shift_dg_fine = gkyl_array_new(GKYL_DOUBLE, inp->shift_dg->ncomp, shear_r_fine.volume);
+    bc_twistshift_refine_shift(inp, &up->ts_grid, &shear_r_fine, up->shift_dg_fine);
+    shift_dg = up->shift_dg_fine;
+  }
+
+  struct gkyl_twistshift_dg_inp tsinp = {
+    .bc_dir = inp->bc_dir,
+    .shift_dir = inp->shift_dir,
+    .shear_dir = inp->shear_dir,
+    .edge = inp->edge,
+    .cdim = inp->cdim,
+    .bcdir_ext_update_r = &up->ts_update_r,
+    .num_ghost = inp->num_ghost,
+    .basis = inp->basis,
+    .grid = &up->ts_grid,
+    .shift_func = inp->shift_func,
+    .shift_func_ctx = inp->shift_func_ctx,
+    .shift_dg = shift_dg,
+    .use_gpu = inp->use_gpu,
+    .shift_poly_order = inp->shift_poly_order,
+  };
+  up->ts = gkyl_twistshift_dg_inew(&tsinp);
+  up->advance_func = bc_twistshift_advance_ts_filtered;
 
   return up;
 }
@@ -1902,23 +226,27 @@ struct gkyl_bc_twistshift*
 gkyl_bc_twistshift_new(int bc_dir, int shift_dir, int shear_dir,
   enum gkyl_edge_loc edge, int cdim, const struct gkyl_range *bcdir_ext_update_r, const int *num_ghost,
   const struct gkyl_basis *basis, const struct gkyl_rect_grid *grid, evalf_t shift_func, void *shift_func_ctx,
-  struct gkyl_array *shift_dg, int shift_poly_order, bool use_gpu)
+  struct gkyl_array *shift_dg, int shift_poly_order, int filter_half_width,
+  double filter_cutoff_wavelength, int upsample_factor, bool use_gpu)
 {
   struct gkyl_bc_twistshift_inp inp = {
-    .bc_dir              = bc_dir            ,
-    .shift_dir           = shift_dir         ,
-    .shear_dir           = shear_dir         ,
-    .edge                = edge              ,
-    .cdim                = cdim              ,
-    .bcdir_ext_update_r  = bcdir_ext_update_r,
-    .num_ghost           = num_ghost         ,
-    .basis               = basis             ,
-    .grid                = grid              ,
-    .shift_func          = shift_func        ,
-    .shift_func_ctx      = shift_func_ctx    ,
-    .shift_dg            = shift_dg          ,
-    .use_gpu             = use_gpu           ,
-    .shift_poly_order    = shift_poly_order  ,
+    .bc_dir                   = bc_dir                  ,
+    .shift_dir                = shift_dir               ,
+    .shear_dir                = shear_dir               ,
+    .edge                     = edge                    ,
+    .cdim                     = cdim                    ,
+    .bcdir_ext_update_r       = bcdir_ext_update_r      ,
+    .num_ghost                = num_ghost               ,
+    .basis                    = basis                   ,
+    .grid                     = grid                    ,
+    .shift_func               = shift_func              ,
+    .shift_func_ctx           = shift_func_ctx          ,
+    .shift_dg                 = shift_dg                ,
+    .use_gpu                  = use_gpu                 ,
+    .shift_poly_order         = shift_poly_order        ,
+    .filter_half_width        = filter_half_width       ,
+    .filter_cutoff_wavelength = filter_cutoff_wavelength,
+    .upsample_factor          = upsample_factor         ,
   };
   return gkyl_bc_twistshift_inew(&inp);
 }
@@ -1926,113 +254,23 @@ gkyl_bc_twistshift_new(int bc_dir, int shift_dir, int shear_dir,
 void
 gkyl_bc_twistshift_advance(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar)
 {
-
-#ifdef GKYL_HAVE_CUDA
-  if (up->use_gpu) {
-    gkyl_bc_twistshift_advance_cu(up, fdo, ftar);
-    return;
-  }
-#endif
-
-  // Assign the distribution matrices.
-  // This assumes that fdo->ncomp = fmat->nr.
-  // Recall:
-  //   fmat->num = sum_i^Nx num_do(i)
-  //   fmat->nr = num_basis = ncomp
-  //   fmat->nc = Ny*Nvpar*Nmu
-  for (size_t i=0; i<up->fmat->num * up->fmat->nr * up->fmat->nc; i++) {
-
-    long nc_idx = i / up->fmat->nr; // num-num_col index: current num-num_col plane.
-    int row_idx = i % up->fmat->nr; // row index: current DG coeff.
-
-    // This if-statement may only be needed in GPU kernel, not for CPUs.
-    if ((nc_idx < up->fmat->num * up->fmat->nc) && (row_idx < fdo->ncomp)) {
-      const double *fdo_c = (const double*) gkyl_array_cfetch(fdo, up->num_numcol_fidx_do[nc_idx]);
-      struct gkyl_mat mcurr = gkyl_nmat_get(up->fmat, nc_idx % up->fmat->num);
-
-      gkyl_mat_set(&mcurr, row_idx, nc_idx/up->fmat->num, fdo_c[row_idx]);
-    }
-  }
-
-  // Perform the mat-mat multiplications.
-  gkyl_nmat_mm(1.0, 0.0, GKYL_NO_TRANS, up->scimat, GKYL_NO_TRANS, up->fmat, up->mm_contr);
-
-  // Clear the ghost range.
-  gkyl_array_clear_range(ftar, 0.0, &up->ghost_r);
-
-  // Perform reduction over num_do contributions from mat-mat mults (mm_contr).
-  int num_cells_skin = (up->shear_r.upper[0]-up->shear_r.lower[0]+1) * up->fmat->nc;
-  for (size_t i=0; i<ftar->ncomp * num_cells_skin; i++) {
-
-    long linidx_tar = i / ftar->ncomp;
-    int row_idx = i % ftar->ncomp;
-
-    // This if-statement may only be needed in GPU kernel, not for CPUs.
-    if ((linidx_tar < num_cells_skin) && (row_idx < ftar->ncomp)) {
-      double *ftar_c = (double*) gkyl_array_fetch(ftar, up->num_numcol_fidx_tar[linidx_tar]);
-
-      int idx[GKYL_MAX_DIM] = {1};
-      gkyl_sub_range_inv_idx(&up->permutted_ghost_r, linidx_tar, idx);
-
-      int ac[GKYL_MAX_DIM] = {1};
-      for (int d=2; d<up->grid.ndim-1; d++)
-        ac[d-2] = up->grid.cells[d+1];
-      ac[up->permutted_ghost_r.ndim-2] = up->mm_contr->num;
-  
-      int start = 0;
-      for (int d=0; d<up->permutted_ghost_r.ndim-1; d++)
-        start = (start + (idx[d]-1)) * ac[d];
-
-      int shear_idx = idx[up->permutted_ghost_r.ndim-1];
-
-      int do_start = up->num_do_cum[shear_idx-1];
-      int do_end   = up->num_do_cum[shear_idx-1+1];
-      for (int j=do_start; j<do_end; j++) { // Only loop over num_do[i] elements.
-        long linidx_mm_contr = start + j;
-        struct gkyl_mat mat = gkyl_nmat_get(up->mm_contr, linidx_mm_contr % up->mm_contr->num);
-        ftar_c[row_idx] += gkyl_mat_get(&mat, row_idx, linidx_mm_contr / up->mm_contr->num);
-      }
-    }
-  }
+  up->advance_func(up, fdo, ftar);
 }
 
-struct gkyl_array*
-gkyl_bc_twistshift_get_shift_objects(struct gkyl_bc_twistshift *up, struct gkyl_rect_grid *shear_grid,
-  struct gkyl_range *shear_r, struct gkyl_basis *shift_b)
-{
-  *shear_grid = up->shear_grid;
-  *shear_r    = up->shear_r   ;
-  *shift_b    = up->shift_b   ;
-  return gkyl_array_acquire(up->shift_dg);
-};
-
 void
-gkyl_bc_twistshift_release(struct gkyl_bc_twistshift *up) {
-  // Release memory associated with this updater.
-  if (!up->use_gpu) {
-    gkyl_free(up->num_do_cum);
-    gkyl_free(up->num_numcol_fidx_do);
-    gkyl_free(up->num_numcol_fidx_tar);
+gkyl_bc_twistshift_release(struct gkyl_bc_twistshift *up)
+{
+  gkyl_twistshift_dg_release(up->ts);
+  if (up->filter) {
+    gkyl_dg_lowpass_filter_release(up->filter);
+    gkyl_array_release(up->ffine);
+    gkyl_array_release(up->filt_buff);
   }
-#ifdef GKYL_HAVE_CUDA
-  if (up->use_gpu) {
-    gkyl_cu_free(up->num_do_cum);
-    gkyl_cu_free(up->num_numcol_fidx_do);
-    gkyl_cu_free(up->num_numcol_fidx_tar);
+  if (up->shift_dg_fine)
+    gkyl_array_release(up->shift_dg_fine);
+  if (up->refine) {
+    gkyl_dg_interpolate_release(up->refine);
+    gkyl_dg_interpolate_release(up->coarsen);
   }
-#endif
-
-  gkyl_nmat_release(up->fmat);
-  gkyl_nmat_release(up->mm_contr);
-
-  gkyl_nmat_release(up->scimat);
-
-  gkyl_free(up->kernels);
-
-  gkyl_array_release(up->shift_dg);
-
-  gkyl_free(up->num_do);
-  gkyl_free(up->shift_dir_idx_do);
-
   gkyl_free(up);
 }
diff --git a/gyrokinetic/zero/gkyl_bc_twistshift.h b/gyrokinetic/zero/gkyl_bc_twistshift.h
index cb6ccec89d..73c7952d99 100644
--- a/gyrokinetic/zero/gkyl_bc_twistshift.h
+++ b/gyrokinetic/zero/gkyl_bc_twistshift.h
@@ -7,14 +7,14 @@
 #include <gkyl_evalf_def.h>
 #include <assert.h>
 
-// Object type
+// Object type.
 typedef struct gkyl_bc_twistshift gkyl_bc_twistshift;
 
 struct gkyl_bc_twistshift_inp {
   int bc_dir; // Direction in which to apply this BC.
   int shift_dir; // Direction of the shift.
   int shear_dir; // Direction in which the shift varies (shear).
-  enum gkyl_edge_loc edge; // Edge of to apply this BC at (lower/upper).
+  enum gkyl_edge_loc edge; // Edge to apply this BC at (lower/upper).
   int cdim; // Configuration space dimensions.
   const struct gkyl_range *bcdir_ext_update_r; // Local range where to apply BC, extended in bc_dir.
   const int *num_ghost; // Number of ghost cells in each direction.
@@ -26,23 +26,29 @@ struct gkyl_bc_twistshift_inp {
   bool use_gpu; // Whether to apply the BC using the GPU.
   // Optional inputs:
   int shift_poly_order; // Basis order for the DG representation of the shift.
+  int filter_half_width; // Filter stencil half-width M in cells of grid (0 = no filter).
+  double filter_cutoff_wavelength; // Filter cutoff wavelength (physical units).
+  int upsample_factor; // Supersampling factor along shear_dir (0/1 = none).
 };
 
 /**
- * Create a new updater to apply twist-shift BCs.
+ * Create a new updater to apply the twist-shift BC, optionally with
+ * supersampling and low-pass filtering to de-alias the shifted field. It
+ * combines a gkyl_twistshift_dg updater with, when requested, a
+ * gkyl_dg_lowpass_filter and gkyl_dg_interpolate operators.
  *
  * @param inp bc_twistshift_inp struct containing the inputs to the updater.
  * @return New updater pointer.
  */
 struct gkyl_bc_twistshift* gkyl_bc_twistshift_inew(const struct gkyl_bc_twistshift_inp *inp);
- 
+
 /**
  * Create a new updater to apply twist-shift BCs, passing each argument separately.
  *
  * @param bc_dir Direction in which to apply this BC.
  * @param shift_dir Direction of the shift.
  * @param shear_dir Direction in which the shift varies (shear).
- * @param edge Edge of to apply this BC at (lower/upper).
+ * @param edge Edge to apply this BC at (lower/upper).
  * @param cdim Configuration space dimensions.
  * @param bcdir_ext_update_r Local range where to apply BC, extended in bc_dir.
  * @param num_ghost Number of ghost cells in each direction.
@@ -52,17 +58,21 @@ struct gkyl_bc_twistshift* gkyl_bc_twistshift_inew(const struct gkyl_bc_twistshi
  * @param shift_func_ctx Context for shift_func.
  * @param shift_dg Discretized shift.
  * @param shift_poly_order Basis order for the DG representation of the shift (optional).
+ * @param filter_half_width Filter stencil half-width M in cells of grid (0 = no filter).
+ * @param filter_cutoff_wavelength Filter cutoff wavelength (physical units).
+ * @param upsample_factor Supersampling factor along shear_dir (0/1 = none).
  * @param use_gpu Whether to apply the BC using the GPU.
  * @return New updater pointer.
  */
 struct gkyl_bc_twistshift* gkyl_bc_twistshift_new(int bc_dir, int shift_dir, int shear_dir,
   enum gkyl_edge_loc edge, int cdim, const struct gkyl_range *bcdir_ext_update_r, const int *num_ghost,
   const struct gkyl_basis *basis, const struct gkyl_rect_grid *grid, evalf_t shift_func, void *shift_func_ctx,
-  struct gkyl_array *shift_dg, int shift_poly_order, bool use_gpu);
+  struct gkyl_array *shift_dg, int shift_poly_order, int filter_half_width,
+  double filter_cutoff_wavelength, int upsample_factor, bool use_gpu);
 
 /**
- * Apply the twist-shift. It assumes that periodicity along bc_dir has been
- * applied to the donor field. Can be used in-place.
+ * Apply the twist-shift periodic BC. Expects periodicity along bc_dir to have
+ * been applied to the donor field beforehand. Can be used in-place.
  *
  * @param up Twist-shift BC updater object.
  * @param fdo Donor field.
@@ -71,21 +81,7 @@ struct gkyl_bc_twistshift* gkyl_bc_twistshift_new(int bc_dir, int shift_dir, int
 void gkyl_bc_twistshift_advance(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar);
 
 /**
- * Return pointers to the discretized shift, its range, and grid and basis.
- *
- * Pointer to shift_dg needs to be released with gkyl_array_release.
- *
- * @param up Twist-shift BC updater object.
- * @param shear_grid Grid on which shift is defined.
- * @param shear_r Range for the shift.
- * @param shift_b Basis shift_dg coefficients are expanded on.
- * @return Discretized shift.
- */
-struct gkyl_array* gkyl_bc_twistshift_get_shift_objects(struct gkyl_bc_twistshift *up,
-  struct gkyl_rect_grid *shear_grid, struct gkyl_range *shear_r, struct gkyl_basis *shift_b);
-
-/**
- * Free memory associated with bc_twistshift updater.
+ * Free memory associated with the bc_twistshift updater.
  *
  * @param up BC updater.
  */
diff --git a/gyrokinetic/zero/gkyl_bc_twistshift_priv.h b/gyrokinetic/zero/gkyl_bc_twistshift_priv.h
index f66ffe186d..3b39317cfc 100644
--- a/gyrokinetic/zero/gkyl_bc_twistshift_priv.h
+++ b/gyrokinetic/zero/gkyl_bc_twistshift_priv.h
@@ -1,165 +1,41 @@
 #pragma once
 
-// Private header for bc_twistshift updater, not for direct use in user code.
+// Private header for the bc_twistshift orchestrator, not for direct use in
+// user code.
 
 #include <gkyl_bc_twistshift.h>
-#include <gkyl_bc_twistshift_gyrokinetic_kernels.h>
-#include <assert.h>
-#include <gkyl_mat.h>
-#include <gkyl_math.h>
-#include <gkyl_eval_on_nodes.h>
-#include <string.h> // memcpy
-
-// Function pointer type for twistshift kernels.
-typedef void (*twistshift_xlimdg_t)(double sFac, const double *xLimLo,
-  const double *xLimUp, double yLimLo, double yLimUp,
-  double dyDo, double yOff, const double *ySh, struct gkyl_mat *tsmat);
-
-typedef void (*twistshift_ylimdg_t)(double sFac, double xLimLo,
-  double xLimUp, const double *yLimLo, const double *yLimUp,
-  double dyDo, double yOff, const double *ySh, struct gkyl_mat *tsmat);
-
-typedef void (*twistshift_fullcell_t)(double dyDo, double yOff,
-  const double *ySh, struct gkyl_mat *tsmat);
-
-typedef struct { twistshift_xlimdg_t kernels[3]; }   twistshift_xlimdg_kern_list;  // For use in kernel tables.
-typedef struct { twistshift_ylimdg_t kernels[3]; }   twistshift_ylimdg_kern_list;  // For use in kernel tables.
-typedef struct { twistshift_fullcell_t kernels[3]; } twistshift_fullcell_kern_list;  // For use in kernel tables.
-
-// Serendipity  kernels.
-// p=1 representation of the shift:
-static const twistshift_xlimdg_kern_list ser_twistshift_xlimdg_list_0v_yShp1[] = {
-  {NULL, twistshift_xlimdg_2x_ser_p1_yshift_p1, NULL,},
-  {NULL, twistshift_xlimdg_3x_ser_p1_yshift_p1, NULL,},
-};
-static const twistshift_ylimdg_kern_list ser_twistshift_ylimdg_list_0v_yShp1[] = {
-  {NULL, twistshift_ylimdg_2x_ser_p1_yshift_p1, NULL,},
-  {NULL, twistshift_ylimdg_3x_ser_p1_yshift_p1, NULL,},
-};
-static const twistshift_fullcell_kern_list ser_twistshift_fullcell_list_0v_yShp1[] = {
-  {NULL, twistshift_fullcell_2x_ser_p1_yshift_p1, NULL,},
-  {NULL, twistshift_fullcell_3x_ser_p1_yshift_p1, NULL,},
-};
-
-static const twistshift_xlimdg_kern_list ser_twistshift_xlimdg_list_2v_yShp1[] = {
-  {NULL, NULL, NULL,},
-  {NULL, twistshift_xlimdg_3x2v_ser_p1_yshift_p1, NULL,},
-};
-static const twistshift_ylimdg_kern_list ser_twistshift_ylimdg_list_2v_yShp1[] = {
-  {NULL, NULL, NULL,},
-  {NULL, twistshift_ylimdg_3x2v_ser_p1_yshift_p1, NULL,},
-};
-static const twistshift_fullcell_kern_list ser_twistshift_fullcell_list_2v_yShp1[] = {
-  {NULL, NULL, NULL,},
-  {NULL, twistshift_fullcell_3x2v_ser_p1_yshift_p1, NULL,},
-};
-// p=2 representation of the shift:
-static const twistshift_xlimdg_kern_list ser_twistshift_xlimdg_list_0v_yShp2[] = {
-  {NULL, twistshift_xlimdg_2x_ser_p1_yshift_p2, NULL,},
-  {NULL, twistshift_xlimdg_3x_ser_p1_yshift_p2, NULL,},
-};
-static const twistshift_ylimdg_kern_list ser_twistshift_ylimdg_list_0v_yShp2[] = {
-  {NULL, twistshift_ylimdg_2x_ser_p1_yshift_p2, NULL,},
-  {NULL, twistshift_ylimdg_3x_ser_p1_yshift_p2, NULL,},
-};
-static const twistshift_fullcell_kern_list ser_twistshift_fullcell_list_0v_yShp2[] = {
-  {NULL, twistshift_fullcell_2x_ser_p1_yshift_p2, NULL,},
-  {NULL, twistshift_fullcell_3x_ser_p1_yshift_p2, NULL,},
-};
-
-static const twistshift_xlimdg_kern_list ser_twistshift_xlimdg_list_2v_yShp2[] = {
-  {NULL, NULL, NULL,},
-  {NULL, NULL, NULL,},
-};
-static const twistshift_ylimdg_kern_list ser_twistshift_ylimdg_list_2v_yShp2[] = {
-  {NULL, NULL, NULL,},
-  {NULL, NULL, NULL,},
-};
-static const twistshift_fullcell_kern_list ser_twistshift_fullcell_list_2v_yShp2[] = {
-  {NULL, NULL, NULL,},
-  {NULL, NULL, NULL,},
-};
-
-
-struct gkyl_bc_twistshift_kernels {
-  twistshift_xlimdg_t xlimdg;
-  twistshift_ylimdg_t ylimdg;
-  twistshift_fullcell_t fullcell;
-};
-
-struct ts_shift_dg_eval_ctx {
-  struct gkyl_array *shift_dg; // DG representation of the shift function.
-  struct gkyl_basis *shift_b; // Basis for the shift.
-  struct gkyl_rect_grid *shear_grid; // shear grid along x.
-  struct gkyl_range *shear_r; // Shear grid range.
-};
+#include <gkyl_twistshift_dg.h>
+#include <gkyl_dg_lowpass_filter.h>
+#include <gkyl_dg_interpolate.h>
+#include <gkyl_rect_grid.h>
+#include <gkyl_range.h>
 
 // Primary struct in this updater.
 struct gkyl_bc_twistshift {
-  int bc_dir; // Direction of the BC is applied in.
-  int shift_dir; // Direction of the shift.
-  int shear_dir; // Direction the shift varies in (shear).
-  enum gkyl_edge_loc edge; // Indicates if BC is for lowe/upper edge.
-  struct gkyl_basis basis; // Basis the shifted field is defined with.
-  struct gkyl_range local_bcdir_ext_r; // Local range.
-  struct gkyl_rect_grid grid; // Grid the shifted field is defined in.
-  evalf_t shift_func; // Function defining the shift.
-  void *shift_func_ctx; // Context for shift_func.
-  struct ts_shift_dg_eval_ctx shift_dg_eval_ctx; // Context for DG shift_func.
   bool use_gpu; // Whether to apply the BC on the GPU.
 
-  struct gkyl_rect_grid shift_grid; // 1D grid in the direction of the shift.
-  struct gkyl_range shift_r; // 1D range in the direction of the shift.
+  struct gkyl_twistshift_dg *ts; // Pure twist-shift updater.
 
-  struct gkyl_rect_grid shear_grid; // 1D grid in the direction of the shear.
-  struct gkyl_range shear_r; // 1D range in the direction of the shear.
+  void (*advance_func)(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar);
 
-  struct gkyl_rect_grid ts_grid; // Grid the shift twistshift takes place in.
-  struct gkyl_range ts_r; // Range the twistshift takes place in.
-  int shift_dir_in_ts_grid; // Dimension the shift is in, in the TS grid.
-  int shear_dir_in_ts_grid; // Dimension the shear is in, in the TS grid.
+  int filter_half_width; // Filter stencil half-width M in cells of the field's
+                         // own grid (0 = no filter).
+  int half_width_fine; // The same stencil measured in supersampled cells.
+  double filter_cutoff_wavelength; // Filter cutoff wavelength.
+  int upsample_factor; // Supersampling factor along shear_dir.
 
-  int shift_poly_order; // Poly order of the DG representation of the shift.
-  struct gkyl_basis shift_b; // 1D Basis for the DG shift.
-  struct gkyl_array *shift_dg; // DG shift.
+  struct gkyl_dg_lowpass_filter *filter; // Post-shift filter along shear_dir.
+  struct gkyl_rect_grid ts_grid; // Grid refined along shear_dir.
+  struct gkyl_range ts_ext_r; // ffine and filt_buff range.
+  struct gkyl_range ts_update_r; // Update range on ts_grid.
+  struct gkyl_range ghost_r; // Ghost plane the twist-shift fills, on ts_grid.
+  struct gkyl_range coarse_ghost_r; // Same plane on the field's own grid.
+  struct gkyl_array *ffine; // Ghost plane on the refined grid.
+  struct gkyl_array *filt_buff; // Buffer for the filter (shaped like ffine).
+  struct gkyl_array *shift_dg_fine; // Input shift refined onto the fine shear grid.
 
-  int *num_do; // Number of donors at each cell in shear_dir;
-  int *shift_dir_idx_do; // Indices of donor cells, in the direction of the
-                         // shift, for each cell in the TS grid.
-
-  struct gkyl_bc_twistshift_kernels *kernels;  // kernels for sub-cell integrals.
-
-  // Projection object used in constructing the matrices.
-  struct gkyl_eval_on_nodes *ev_on_nod1d;
-  // Evaluations of a function at 1D nodes.
-  struct gkyl_array *func_nod1d;
-
-  struct gkyl_nmat *scimat; // Subcell integral matrices.
-  struct gkyl_nmat *fmat; // Distribution function matrices.
-  struct gkyl_nmat *mm_contr; // Contribution resulting from a mat-mat mult.
-
-  long *num_numcol_fidx_do; // 1D indexer, from a index identitying the num-numcol
-                            // plane (in the num-numcol-num_basis space), to a
-                            // linear index into the donor distribution function f.
-
-  long *num_numcol_fidx_tar; // 1D indexer, from a index identitying the num-numcol
-                             // plane (in the num-numcol-num_basis space), to a
-                             // linear index into the target distribution function f.
-
-  int *num_do_cum; // Cumulative number of donors up to a give cell in shear_dir;
-  struct gkyl_range permutted_ghost_r; // Ghost range to populate in the target
-                                       // field, with some dimensions permutted.
-  struct gkyl_range ghost_r; // Ghost range this BC fills.
+  struct gkyl_dg_interpolate *refine; // Coarse ghost plane -> fine ghost plane.
+  struct gkyl_dg_interpolate *coarsen; // Fine ghost plane -> coarse ghost plane.
+  void (*refine_func)(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo);
+  void (*coarsen_func)(struct gkyl_bc_twistshift *up, struct gkyl_array *ftar);
 };
-
-#ifdef GKYL_HAVE_CUDA
-/**
- * Apply the twist-shift on the NVIDIA GPU. It assumes that periodicity along bc_dir has been
- * applied to the donor field. Can be used in-place.
- *
- * @param up Twist-shift BC updater object.
- * @param fdo Donor field.
- * @param ftar Target field.
- */
-void gkyl_bc_twistshift_advance_cu(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar);
-#endif
diff --git a/gyrokinetic/zero/gkyl_twistshift_dg.h b/gyrokinetic/zero/gkyl_twistshift_dg.h
new file mode 100644
index 0000000000..084bad037d
--- /dev/null
+++ b/gyrokinetic/zero/gkyl_twistshift_dg.h
@@ -0,0 +1,92 @@
+#pragma once
+
+#include <gkyl_range.h>
+#include <gkyl_basis.h>
+#include <gkyl_array.h>
+#include <gkyl_rect_grid.h>
+#include <gkyl_evalf_def.h>
+#include <assert.h>
+
+// Object type
+typedef struct gkyl_twistshift_dg gkyl_twistshift_dg;
+
+struct gkyl_twistshift_dg_inp {
+  int bc_dir; // Direction in which to apply this BC.
+  int shift_dir; // Direction of the shift.
+  int shear_dir; // Direction in which the shift varies (shear).
+  enum gkyl_edge_loc edge; // Edge of to apply this BC at (lower/upper).
+  int cdim; // Configuration space dimensions.
+  const struct gkyl_range *bcdir_ext_update_r; // Local range where to apply BC, extended in bc_dir.
+  const int *num_ghost; // Number of ghost cells in each direction.
+  const struct gkyl_basis *basis; // Basis of the field shifted.
+  const struct gkyl_rect_grid *grid; // Grid the field shifted is defined on.
+  evalf_t shift_func; // Function defining the shift.
+  void *shift_func_ctx; // Context for shift_func.
+  struct gkyl_array *shift_dg; // Discretized shift.
+  bool use_gpu; // Whether to apply the BC using the GPU.
+  // Optional inputs:
+  int shift_poly_order; // Basis order for the DG representation of the shift.
+};
+
+/**
+ * Create a new updater to apply twist-shift BCs.
+ *
+ * @param inp twistshift_dg_inp struct containing the inputs to the updater.
+ * @return New updater pointer.
+ */
+struct gkyl_twistshift_dg* gkyl_twistshift_dg_inew(const struct gkyl_twistshift_dg_inp *inp);
+
+/**
+ * Create a new updater to apply twist-shift BCs, passing each argument separately.
+ *
+ * @param bc_dir Direction in which to apply this BC.
+ * @param shift_dir Direction of the shift.
+ * @param shear_dir Direction in which the shift varies (shear).
+ * @param edge Edge to apply this BC at (lower/upper).
+ * @param cdim Configuration space dimensions.
+ * @param bcdir_ext_update_r Local range where to apply BC, extended in bc_dir.
+ * @param num_ghost Number of ghost cells in each direction.
+ * @param basis Basis of the field shifted.
+ * @param grid Grid the field shifted is defined on.
+ * @param shift_func Function defining the shift.
+ * @param shift_func_ctx Context for shift_func.
+ * @param shift_dg Discretized shift.
+ * @param shift_poly_order Basis order for the DG representation of the shift (optional).
+ * @param use_gpu Whether to apply the BC using the GPU.
+ * @return New updater pointer.
+ */
+struct gkyl_twistshift_dg* gkyl_twistshift_dg_new(int bc_dir, int shift_dir, int shear_dir,
+  enum gkyl_edge_loc edge, int cdim, const struct gkyl_range *bcdir_ext_update_r, const int *num_ghost,
+  const struct gkyl_basis *basis, const struct gkyl_rect_grid *grid, evalf_t shift_func, void *shift_func_ctx,
+  struct gkyl_array *shift_dg, int shift_poly_order, bool use_gpu);
+
+/**
+ * Apply the twist-shift. It assumes that periodicity along bc_dir has been
+ * applied to the donor field. Can be used in-place.
+ *
+ * @param up Twist-shift BC updater object.
+ * @param fdo Donor field.
+ * @param ftar Target field.
+ */
+void gkyl_twistshift_dg_advance(struct gkyl_twistshift_dg *up, struct gkyl_array *fdo, struct gkyl_array *ftar);
+
+/**
+ * Return pointers to the discretized shift, its range, and grid and basis.
+ *
+ * Pointer to shift_dg needs to be released with gkyl_array_release.
+ *
+ * @param up Twist-shift BC updater object.
+ * @param shear_grid Grid on which shift is defined.
+ * @param shear_r Range for the shift.
+ * @param shift_b Basis shift_dg coefficients are expanded on.
+ * @return Discretized shift.
+ */
+struct gkyl_array* gkyl_twistshift_dg_get_shift_objects(struct gkyl_twistshift_dg *up,
+  struct gkyl_rect_grid *shear_grid, struct gkyl_range *shear_r, struct gkyl_basis *shift_b);
+
+/**
+ * Free memory associated with twistshift_dg updater.
+ *
+ * @param up BC updater.
+ */
+void gkyl_twistshift_dg_release(struct gkyl_twistshift_dg *up);
diff --git a/gyrokinetic/zero/gkyl_twistshift_dg_priv.h b/gyrokinetic/zero/gkyl_twistshift_dg_priv.h
new file mode 100644
index 0000000000..d927f0edea
--- /dev/null
+++ b/gyrokinetic/zero/gkyl_twistshift_dg_priv.h
@@ -0,0 +1,165 @@
+#pragma once
+
+// Private header for twistshift_dg updater, not for direct use in user code.
+
+#include <gkyl_twistshift_dg.h>
+#include <gkyl_twistshift_dg_gyrokinetic_kernels.h>
+#include <assert.h>
+#include <gkyl_mat.h>
+#include <gkyl_math.h>
+#include <gkyl_eval_on_nodes.h>
+#include <string.h> // memcpy
+
+// Function pointer type for twistshift kernels.
+typedef void (*twistshift_xlimdg_t)(double sFac, const double *xLimLo,
+  const double *xLimUp, double yLimLo, double yLimUp,
+  double dyDo, double yOff, const double *ySh, struct gkyl_mat *tsmat);
+
+typedef void (*twistshift_ylimdg_t)(double sFac, double xLimLo,
+  double xLimUp, const double *yLimLo, const double *yLimUp,
+  double dyDo, double yOff, const double *ySh, struct gkyl_mat *tsmat);
+
+typedef void (*twistshift_fullcell_t)(double dyDo, double yOff,
+  const double *ySh, struct gkyl_mat *tsmat);
+
+typedef struct { twistshift_xlimdg_t kernels[3]; }   twistshift_xlimdg_kern_list;  // For use in kernel tables.
+typedef struct { twistshift_ylimdg_t kernels[3]; }   twistshift_ylimdg_kern_list;  // For use in kernel tables.
+typedef struct { twistshift_fullcell_t kernels[3]; } twistshift_fullcell_kern_list;  // For use in kernel tables.
+
+// Serendipity  kernels.
+// p=1 representation of the shift:
+static const twistshift_xlimdg_kern_list ser_twistshift_xlimdg_list_0v_yShp1[] = {
+  {NULL, twistshift_xlimdg_2x_ser_p1_yshift_p1, NULL,},
+  {NULL, twistshift_xlimdg_3x_ser_p1_yshift_p1, NULL,},
+};
+static const twistshift_ylimdg_kern_list ser_twistshift_ylimdg_list_0v_yShp1[] = {
+  {NULL, twistshift_ylimdg_2x_ser_p1_yshift_p1, NULL,},
+  {NULL, twistshift_ylimdg_3x_ser_p1_yshift_p1, NULL,},
+};
+static const twistshift_fullcell_kern_list ser_twistshift_fullcell_list_0v_yShp1[] = {
+  {NULL, twistshift_fullcell_2x_ser_p1_yshift_p1, NULL,},
+  {NULL, twistshift_fullcell_3x_ser_p1_yshift_p1, NULL,},
+};
+
+static const twistshift_xlimdg_kern_list ser_twistshift_xlimdg_list_2v_yShp1[] = {
+  {NULL, NULL, NULL,},
+  {NULL, twistshift_xlimdg_3x2v_ser_p1_yshift_p1, NULL,},
+};
+static const twistshift_ylimdg_kern_list ser_twistshift_ylimdg_list_2v_yShp1[] = {
+  {NULL, NULL, NULL,},
+  {NULL, twistshift_ylimdg_3x2v_ser_p1_yshift_p1, NULL,},
+};
+static const twistshift_fullcell_kern_list ser_twistshift_fullcell_list_2v_yShp1[] = {
+  {NULL, NULL, NULL,},
+  {NULL, twistshift_fullcell_3x2v_ser_p1_yshift_p1, NULL,},
+};
+// p=2 representation of the shift:
+static const twistshift_xlimdg_kern_list ser_twistshift_xlimdg_list_0v_yShp2[] = {
+  {NULL, twistshift_xlimdg_2x_ser_p1_yshift_p2, NULL,},
+  {NULL, twistshift_xlimdg_3x_ser_p1_yshift_p2, NULL,},
+};
+static const twistshift_ylimdg_kern_list ser_twistshift_ylimdg_list_0v_yShp2[] = {
+  {NULL, twistshift_ylimdg_2x_ser_p1_yshift_p2, NULL,},
+  {NULL, twistshift_ylimdg_3x_ser_p1_yshift_p2, NULL,},
+};
+static const twistshift_fullcell_kern_list ser_twistshift_fullcell_list_0v_yShp2[] = {
+  {NULL, twistshift_fullcell_2x_ser_p1_yshift_p2, NULL,},
+  {NULL, twistshift_fullcell_3x_ser_p1_yshift_p2, NULL,},
+};
+
+static const twistshift_xlimdg_kern_list ser_twistshift_xlimdg_list_2v_yShp2[] = {
+  {NULL, NULL, NULL,},
+  {NULL, NULL, NULL,},
+};
+static const twistshift_ylimdg_kern_list ser_twistshift_ylimdg_list_2v_yShp2[] = {
+  {NULL, NULL, NULL,},
+  {NULL, NULL, NULL,},
+};
+static const twistshift_fullcell_kern_list ser_twistshift_fullcell_list_2v_yShp2[] = {
+  {NULL, NULL, NULL,},
+  {NULL, NULL, NULL,},
+};
+
+
+struct gkyl_twistshift_dg_kernels {
+  twistshift_xlimdg_t xlimdg;
+  twistshift_ylimdg_t ylimdg;
+  twistshift_fullcell_t fullcell;
+};
+
+struct ts_shift_dg_eval_ctx {
+  struct gkyl_array *shift_dg; // DG representation of the shift function.
+  struct gkyl_basis *shift_b; // Basis for the shift.
+  struct gkyl_rect_grid *shear_grid; // shear grid along x.
+  struct gkyl_range *shear_r; // Shear grid range.
+};
+
+// Primary struct in this updater.
+struct gkyl_twistshift_dg {
+  int bc_dir; // Direction of the BC is applied in.
+  int shift_dir; // Direction of the shift.
+  int shear_dir; // Direction the shift varies in (shear).
+  enum gkyl_edge_loc edge; // Indicates if BC is for lowe/upper edge.
+  struct gkyl_basis basis; // Basis the shifted field is defined with.
+  struct gkyl_range local_bcdir_ext_r; // Local range.
+  struct gkyl_rect_grid grid; // Grid the shifted field is defined in.
+  evalf_t shift_func; // Function defining the shift.
+  void *shift_func_ctx; // Context for shift_func.
+  struct ts_shift_dg_eval_ctx shift_dg_eval_ctx; // Context for DG shift_func.
+  bool use_gpu; // Whether to apply the BC on the GPU.
+
+  struct gkyl_rect_grid shift_grid; // 1D grid in the direction of the shift.
+  struct gkyl_range shift_r; // 1D range in the direction of the shift.
+
+  struct gkyl_rect_grid shear_grid; // 1D grid in the direction of the shear.
+  struct gkyl_range shear_r; // 1D range in the direction of the shear.
+
+  struct gkyl_rect_grid ts_grid; // Grid the shift twistshift takes place in.
+  struct gkyl_range ts_r; // Range the twistshift takes place in.
+  int shift_dir_in_ts_grid; // Dimension the shift is in, in the TS grid.
+  int shear_dir_in_ts_grid; // Dimension the shear is in, in the TS grid.
+
+  int shift_poly_order; // Poly order of the DG representation of the shift.
+  struct gkyl_basis shift_b; // 1D Basis for the DG shift.
+  struct gkyl_array *shift_dg; // DG shift.
+
+  int *num_do; // Number of donors at each cell in shear_dir;
+  int *shift_dir_idx_do; // Indices of donor cells, in the direction of the
+                         // shift, for each cell in the TS grid.
+
+  struct gkyl_twistshift_dg_kernels *kernels;  // kernels for sub-cell integrals.
+
+  // Projection object used in constructing the matrices.
+  struct gkyl_eval_on_nodes *ev_on_nod1d;
+  // Evaluations of a function at 1D nodes.
+  struct gkyl_array *func_nod1d;
+
+  struct gkyl_nmat *scimat; // Subcell integral matrices.
+  struct gkyl_nmat *fmat; // Distribution function matrices.
+  struct gkyl_nmat *mm_contr; // Contribution resulting from a mat-mat mult.
+
+  long *num_numcol_fidx_do; // 1D indexer, from a index identitying the num-numcol
+                            // plane (in the num-numcol-num_basis space), to a
+                            // linear index into the donor distribution function f.
+
+  long *num_numcol_fidx_tar; // 1D indexer, from a index identitying the num-numcol
+                             // plane (in the num-numcol-num_basis space), to a
+                             // linear index into the target distribution function f.
+
+  int *num_do_cum; // Cumulative number of donors up to a give cell in shear_dir;
+  struct gkyl_range permutted_ghost_r; // Ghost range to populate in the target
+                                       // field, with some dimensions permutted.
+  struct gkyl_range ghost_r; // Ghost range this BC fills.
+};
+
+#ifdef GKYL_HAVE_CUDA
+/**
+ * Apply the twist-shift on the NVIDIA GPU. It assumes that periodicity along bc_dir has been
+ * applied to the donor field. Can be used in-place.
+ *
+ * @param up Twist-shift BC updater object.
+ * @param fdo Donor field.
+ * @param ftar Target field.
+ */
+void gkyl_twistshift_dg_advance_cu(struct gkyl_twistshift_dg *up, struct gkyl_array *fdo, struct gkyl_array *ftar);
+#endif
diff --git a/gyrokinetic/zero/twistshift_dg.c b/gyrokinetic/zero/twistshift_dg.c
new file mode 100644
index 0000000000..fc16383692
--- /dev/null
+++ b/gyrokinetic/zero/twistshift_dg.c
@@ -0,0 +1,2040 @@
+#include <gkyl_alloc.h>
+#include <gkyl_array.h>
+#include <gkyl_mat.h>
+#include <gkyl_twistshift_dg.h>
+#include <gkyl_twistshift_dg_priv.h>
+#include <gkyl_util.h>
+#include <gkyl_eval_on_nodes.h>
+#include <gkyl_array_ops.h>
+#include <gkyl_array_rio.h>
+
+// Notes:
+//   a) Hard-coded parameters:
+//     - wrap_to_range: eps.
+//     - find_donors: delta_frac, num_test_pt.
+//     - find_intersect: tol, max_iter, num_steps.
+//     - calc_mats: shift_dir_idx_tar.
+//     - tol_xi: Minimum allowed spacing between the lower and
+//               upper xi (logical x) limits of subcell integral.
+//   b) Unlike the procedures described in M. Francisquez, et al. CPC 298
+//   (2024) 109109, all subcell integrals are now done with variable y limits.
+//   This is possible once we realize that figure 4 is not drawn accurately;
+//   the blue lines should be separated by Delta y at all points.
+//   c) This updater only works on 5D distributions. Likely only minor changes
+//   are needed to make it work in other dimensions.
+//   d) 99% of the code is written to support a BC, a shift and shear in any
+//   direction. Maybe the only thing that needs to change is the permutted
+//   range and its use.
+//
+// List of functions used in computing sub-cell integrals (scimat).
+//   - ts_grid_cell_boundary_in_dir: cell boundary coordinate in given dir.
+//   - ts_grid_cell_boundaries: get all cell boundary coords.
+//   - ts_p2l: physical to logical transform.
+//   - ts_interval_dx_and_xc: compute length and center of an interval.
+//   - ts_grid_length_in_dir: length of the grid in given dir.
+//   - ts_wrap_to_range: wrap a number to a range assuming periodicity.
+//   - ts_shift_dir_idx_do_linidx: linear index to first donor of a given target
+//                                cell in shift_dir_idx_do.
+//   - ts_check_shifted_test_point: evaluate a shifted point's cell as a
+//                                  potential donor cell.
+//   - ts_find_donors: find and record the donor cells for each target.
+//   - ts_root_find: Finds the root of a given function.
+//   - ts_shifted_coord_loss_func: Loss function used to find where yTar-S
+//                                intersects yDo.
+//   - ts_sign: return the sign of a double.
+//   - ts_ts_donor_target_offset: offset between donor and target cells.
+//   - ts_find_intersect: finds the intersection of yTar-S and yDo.
+//   - ts_comp_to_phys: transform a computational to a physical coord.
+//   - ts_nod2mod_proj_1d: evaluate a 1D function at nodes and do a n2m transform
+//                         to get the coefficients of the DG representation.
+//   - ts_integral_xlimdg: subcell integral with variable x limits.
+//   - ts_integral_ylimdg: subcell integral with variable y limits.
+//   - ts_integral_fullcelllimdg: integral over the whole cell.
+//   - ts_one: return 1 (for projections).
+//   - ts_minus_one: return -1 (for projections).
+//   - ts_shift_coord_shifted_log: coordinate in shift_dir shifted and transformed
+//                                 to logical space.
+//   - ts_subcellint_sNi_sNii: subcell integral sNi or sNii.
+//   - ts_subcellint_si_sii: subcell integral si or sii.
+//   - ts_subcellint_siii_siv: subcell integral siii or siv.
+//   - ts_subcellint_sv_svi: subcell integral sv or svi.
+//   - ts_subcellint_svii_sviii: subcell integral svii or sviii.
+//   - ts_subcellint_six_sx: subcell integral six or sx.
+//   - ts_subcellint_sxi_sxii: subcell integral sxi or sxii.
+//   - ts_subcellint_sxiii_sxiv: subcell integral sxiii or sxiv.
+//   - ts_subcellint_sxv_sxvi: subcell integral sxv or sxvi.
+//   - ts_calc_mats: create scimat with the result of the subcell integrals.
+//
+//  Two additional helper functions:
+//   - ts_calc_num_numcol_fidx_do: index map to populate fmat with donors.
+//   - ts_calc_num_numcol_fidx_tar: index map to get mat-mat mult results.
+
+// Option to use the user-provided function describing the shift
+// or a DG representation of it:
+//   = 0 DG representation (default and preferred).
+//   = 1 user-provided shift function.
+// Note: the kernels that ultimately perform the integrals
+// always use the DG representation.
+#define shift_func_op 0
+
+// Minimum allowed spacing between the lower and
+// upper xi (logical x) limits of subcell integral.
+#define tol_xi 1.0e-15
+
+// Indices in 4-element cell boundary array.
+#define cellb_lo(dir) (2*dir)
+#define cellb_up(dir) (2*dir+1)
+
+double
+ts_grid_cell_boundary_in_dir(struct gkyl_rect_grid *grid, const int *idx, enum gkyl_edge_loc edge, int dir)
+{
+  // Get the coordinate of the cell boundary in specified direction.
+  double xc[grid->ndim];
+  gkyl_rect_grid_cell_center(grid, idx, xc);
+  return edge == GKYL_LOWER_EDGE? xc[dir]-0.5*grid->dx[dir] : xc[dir]+0.5*grid->dx[dir];
+}
+
+void
+ts_grid_cell_boundaries(struct gkyl_rect_grid *grid, const int *idx, double *cell_bounds)
+{
+  // Get the cell boundaries in every dimension. The array cell_bounds
+  // must be a 2*grid->ndim array.
+  for (int d=0; d<grid->ndim; d++) {
+    cell_bounds[d*2] = ts_grid_cell_boundary_in_dir(grid, idx, GKYL_LOWER_EDGE, d);
+    cell_bounds[d*2+1] = ts_grid_cell_boundary_in_dir(grid, idx, GKYL_UPPER_EDGE, d);
+  }
+}
+
+static inline double
+ts_p2l(double coord, double cell_center, double dx)
+{
+  // Transform a physical coordinate (coord) to the [-1,1] logical
+  // space in a cell centered at cell_center and with length dx. 
+  return 2.0*(coord - cell_center)/dx;
+}
+
+// Evaluation of the shift through the DG representation.
+static inline void
+ts_shift_dg_eval(double t, const double *coord, double *fout, void *ctx)
+{
+  struct ts_shift_dg_eval_ctx *tsectx = ctx;
+
+  int cell_idx[GKYL_MAX_DIM];
+  gkyl_rect_grid_coord_idx(tsectx->shear_grid, coord, cell_idx);
+  // Ensure that we do not go outside of the range 
+  // (it does sometimes if x=x_max,x_min).
+  cell_idx[0] = fmin(cell_idx[0], tsectx->shear_r->upper[0]);
+  cell_idx[0] = fmax(cell_idx[0], tsectx->shear_r->lower[0]);
+
+  double xc[GKYL_MAX_DIM];
+  gkyl_rect_grid_cell_center(tsectx->shear_grid, cell_idx, xc);
+
+  long shift_loc = gkyl_range_idx(tsectx->shear_r, cell_idx);
+  double *shift_c = (double *) gkyl_array_fetch(tsectx->shift_dg, shift_loc);
+  double xp = ts_p2l(coord[0], xc[0], tsectx->shear_grid->dx[0]);
+
+  fout[0] = tsectx->shift_b->eval_expand(&(double) {xp}, shift_c);
+}
+
+void
+ts_interval_dx_and_xc(const double *interval, double *dx, double *xc)
+{
+  // Compute the lenth (dx) and center (xc) of [interval[0], interval[1]].
+  double lo = interval[0], up = interval[1];
+  dx[0] = up - lo;
+  xc[0] = 0.5*(up + lo);
+}
+
+static inline double
+ts_grid_length_in_dir(struct gkyl_rect_grid *grid, int dir)
+{
+  return grid->upper[dir] - grid->lower[dir];
+}
+
+double
+ts_wrap_to_range(double val, double lower, double upper, bool pick_upper)
+{
+  // Wrap a number to range [lower,upper]. If pickUpper=true, output upper when
+  // val is a multiple of upper. Otherwise multiples of upper wrap to lower.
+  double L        = upper - lower;
+  double disp     = fmod(val - lower, L);
+  double vwrapped = lower + fmod(L + disp, L);
+  double eps      = 1.e-12;
+  if ( (lower-eps < vwrapped && vwrapped < lower + eps) ||
+       (upper-eps < vwrapped && vwrapped < upper + eps) ) {
+    if (pick_upper) 
+      return upper;
+    else
+      return lower;
+  }
+  else
+    return vwrapped;
+}
+
+long
+ts_shift_dir_idx_do_linidx(const int *num_do, int shear_dir_idx, int shift_dir_idx,
+  int shift_dir_num_cells, int shear_r_lower)
+{
+  // Return the linear index to the first donor for the idx=(i,j) target cell,
+  // in the shift_dir_idx_do array. We assume shift_dir_idx_do (whose dimensions
+  // are Nx,Ny,num_do(i)) is in row-major order, and that it has num_do donors
+  // at each cell in the shear_dir_in_ts_grid direction.
+  long linc = 0;
+  // Count the number of donors in cells with an idx in the shear dir lower
+  // than this one. NOTE: the -1 here is because the idx is often 1-index
+  // (since ghost cells are the 0th index) but num_do is only defined on the
+  // local range. 
+  for (int i=0; i<shear_dir_idx-shear_r_lower; i++)
+    linc += num_do[i] * shift_dir_num_cells;
+
+  // Count the number of donors in cells with the same idx in the shear dir.
+  // NOTE: the -1 here is because the idx is often 1-index
+  // (since ghost cells are the 0th index) but num_do is only defined on the
+  // local range.
+  linc += num_do[shear_dir_idx-shear_r_lower] * (shift_dir_idx-1);
+
+  return linc;
+}
+
+void
+ts_check_shifted_test_point(struct gkyl_twistshift_dg *up, const double *test_pt, const double *xc,
+  const double *dx, double *shift_c, const int *idx, bool pick_lower, int *num_do_curr,
+  gkyl_mem_buff shift_dir_idx_do_buff)
+{
+  // Shift the test point, find the cell that contains it, and if we
+  // haven't included it yet, add it to our list of donors.
+
+  int shear_idx[] = {idx[up->shear_dir_in_ts_grid]};
+  int shift_idx[] = {idx[up->shift_dir_in_ts_grid]};
+
+  int *shift_dir_idx_do_buff_ptr = (int *) gkyl_mem_buff_data(shift_dir_idx_do_buff);
+
+  // Evaluate the shift at this test point.
+  double test_pt_in_shear_dir = test_pt[up->shear_dir_in_ts_grid];
+  double xc_in_shear_dir = xc[up->shear_dir_in_ts_grid];
+  double dx_in_shear_dir = dx[up->shear_dir_in_ts_grid];
+  double shift_at_pt = up->shift_b.eval_expand(
+    &(double) {ts_p2l(test_pt_in_shear_dir, xc_in_shear_dir, dx_in_shear_dir)}, shift_c);
+
+  // Find the index of the cell that owns the shifted point.
+  double shifted_test_pt[] = { ts_wrap_to_range(test_pt[up->shift_dir_in_ts_grid] - shift_at_pt,
+    up->ts_grid.lower[up->shift_dir_in_ts_grid], up->ts_grid.upper[up->shift_dir_in_ts_grid],
+    false) }; // Shifted test point.
+  int shift_dir_idx_test_pt[1];
+  gkyl_rect_grid_find_cell(&up->shift_grid, shifted_test_pt, (bool[]) {pick_lower}, (int[]) {-1}, shift_dir_idx_test_pt);
+
+  // Get the linear index to the list of donors for this target.
+  long linidx = ts_shift_dir_idx_do_linidx(up->num_do,
+    shear_idx[0], shift_idx[0], up->ts_grid.cells[up->shift_dir_in_ts_grid], up->shear_r.lower[0]);
+  // If this donor is not in our list of donors, include it.
+  bool donor_not_found = true;
+  for (int k=0; k<num_do_curr[0]; k++) {
+    if (shift_dir_idx_do_buff_ptr[linidx+k] == shift_dir_idx_test_pt[0]) {
+      donor_not_found = false;
+      break;
+    }
+  }
+  if (donor_not_found) {
+    if (num_do_curr[0] > 0) {
+      // Insert one more int. Only if num_do_curr>0 because we already
+      // allocated space for the first donor.
+      size_t new_buff_sz = gkyl_mem_buff_size(shift_dir_idx_do_buff) + sizeof(int);
+      shift_dir_idx_do_buff = gkyl_mem_buff_resize(shift_dir_idx_do_buff, new_buff_sz);
+    }
+
+    // Get the pointer again in case it changed.
+    shift_dir_idx_do_buff_ptr = (int *) gkyl_mem_buff_data(shift_dir_idx_do_buff);
+    shift_dir_idx_do_buff_ptr[linidx+num_do_curr[0]] = shift_dir_idx_test_pt[0];
+
+    num_do_curr[0] += 1;
+  }
+}
+
+void
+ts_find_donors(struct gkyl_twistshift_dg *up)
+{
+  // Find the donor cells for each target cell in the TS grid.
+
+  double delta_frac = 1.e-4; // Distance away from the boundary, as fraction of cell length.
+  // Must be larger than the eps=1e-6 tolerance in is_in_cell (used by
+  // gkyl_rect_grid_find_cell) so that shifted test points are never
+  // ambiguously on a cell boundary.
+  int num_test_pt[2] = {10, 10}; // Number of test points taken along each side of the cell.
+
+  double step_sz[2] = {0.0}; // Size of the step between test points.
+  double delta[2] = {0.0}; // Space between cell boundary and test points.
+  for (int d=0; d<2; d++) {
+    delta[d] = delta_frac*up->ts_grid.dx[d];
+    step_sz[d] = (up->ts_grid.dx[d] - 2.0*delta[d])/(num_test_pt[d]-1);
+  }
+
+  // Number of donors at each cell of the shear direction.
+  up->num_do = (int*) gkyl_malloc(up->shear_r.volume * sizeof(int));
+  for (int i=0; i<up->shear_r.volume; i++)
+    up->num_do[i] = -1;
+
+  // Temporary buffer to store donors at (resized below).
+  size_t curr_buff_sz = up->ts_r.volume * sizeof(int);
+  gkyl_mem_buff shift_dir_idx_do_buff = gkyl_mem_buff_new(curr_buff_sz);
+
+  int idx[] = {up->shear_r.lower[0]};
+  long linidx = gkyl_range_idx(&up->shear_r, idx);
+  struct gkyl_range_iter iter;
+  gkyl_range_iter_init(&iter, &up->ts_r);
+  while (gkyl_range_iter_next(&iter)) {
+
+    // Get the cell boundaries and cell center.
+    double cell_b[4] = {0.0}; // Cell boundaries, x lo and up, y lo and up;
+    double xc[2] = {0.0}; // Cell center.
+    ts_grid_cell_boundaries(&up->ts_grid, iter.idx, cell_b);
+    gkyl_rect_grid_cell_center(&up->ts_grid, iter.idx, xc);
+
+    int shear_idx[] = {iter.idx[up->shear_dir_in_ts_grid]};
+    int shift_idx[] = {iter.idx[up->shift_dir_in_ts_grid]};
+    long shift_loc = gkyl_range_idx(&up->shear_r, shear_idx);
+    double *shift_c = (double *) gkyl_array_fetch(up->shift_dg, shift_loc);
+
+    int num_do_curr = 0;
+
+    for (int dC=0; dC<2; dC++) { // dC=0: x=const, dC=1: y=const (boundaries).
+      for (int xS=0; xS<2; xS++) { // xS=0: lower, xS=1 upper (boundary).
+
+        double test_pt[2] = {0.0}; // Test point to shift.
+        for (int d=0; d<2; d++)
+          test_pt[d] = cell_b[2*d]+delta[d];
+
+        // Search first shifted point. Use pick_lower=false in find_cell unless
+        // searching for points along a x=const line near the upper y-boundary. 
+        bool pick_lower = dC==0 && xS==1;
+        test_pt[dC] += xS*(up->ts_grid.dx[dC]-2.0*delta[dC]);
+
+        // Shift the test point, find the cell that contains it, and if we
+        // haven't included it yet, add it to our list of donors.
+        ts_check_shifted_test_point(up, test_pt, xc, up->ts_grid.dx,
+          shift_c, iter.idx, pick_lower, &num_do_curr, shift_dir_idx_do_buff);
+
+        // Search for other shifted points along this line. 
+        int step_dim = (dC+1) % 2;
+        for (int sI=1; sI<num_test_pt[step_dim]; sI++) {
+          test_pt[step_dim] += step_sz[step_dim];
+
+          // Shift the test point, find the cell that contains it, and if we
+          // haven't included it yet, add it to our list of donors.
+          ts_check_shifted_test_point(up, test_pt, xc, up->ts_grid.dx,
+            shift_c, iter.idx, pick_lower, &num_do_curr, shift_dir_idx_do_buff);
+        }
+      }
+    }
+
+    up->num_do[shear_idx[0]-up->shear_r.lower[0]] = num_do_curr;
+  }
+
+  // Copy the donor list to the persistent object and release the buffer.
+  size_t buff_sz = gkyl_mem_buff_size(shift_dir_idx_do_buff);
+  up->shift_dir_idx_do = (int *) gkyl_malloc(buff_sz);
+  int *shift_dir_idx_do_buff_ptr = (int *) gkyl_mem_buff_data(shift_dir_idx_do_buff);
+  memcpy(up->shift_dir_idx_do, shift_dir_idx_do_buff_ptr, buff_sz);
+  gkyl_mem_buff_release(shift_dir_idx_do_buff);
+}
+
+struct gkyl_qr_res
+ts_root_find(double (*func)(double,void*), void *ctx, const double *lims, int max_iter, double tol)
+{
+  // Use a Ridder's root finder to find the root of func in the interval
+  // [lims[0],lims[1]] down to a tolerance 'tol'. Return the interval limit
+  // if the function is smaller than the tolerance there. Return nil if the
+  // function does not change sign in the interval (interval doesn't contain the root).
+  double funcLo = func(lims[0], ctx), funcUp = func(lims[1], ctx);
+//  if (fabs(funcLo) < tol)
+//    return (struct gkyl_qr_res) {.res=lims[0], .status=0, .nevals=2};
+//  else if (fabs(funcUp) < tol)                                     
+//    return (struct gkyl_qr_res) {.res=lims[1], .status=0, .nevals=2};
+//  else {
+//    if (funcLo*funcUp < 0)
+//      return gkyl_ridders(func, ctx, lims[0], lims[1], funcLo, funcUp, max_iter, tol);
+//    else
+//      return (struct gkyl_qr_res) {.status=1, .nevals=2};
+//  }
+  if (fabs(funcLo) > tol && fabs(funcUp) > tol) {
+    if (funcLo*funcUp < 0)
+      return gkyl_ridders(func, ctx, lims[0], lims[1], funcLo, funcUp, max_iter, tol);
+    else
+      return (struct gkyl_qr_res) {.status=1, .nevals=2};
+  }
+  else if (fabs(funcLo) < tol && fabs(funcUp) < tol)
+    return (struct gkyl_qr_res) {.status=1, .nevals=2};
+  else if (fabs(funcLo) < tol)
+    return (struct gkyl_qr_res) {.res=lims[0], .status=0, .nevals=2};
+  else if (fabs(funcUp) < tol)                                     
+    return (struct gkyl_qr_res) {.res=lims[1], .status=0, .nevals=2};
+  return (struct gkyl_qr_res) {.status=1, .nevals=2};
+}
+
+struct ts_shifted_coord_loss_func_ctx {
+  double shiftCoordTar; // Target coordinate in shift_dir.
+  double shiftCoordDo; // Donor coordinate in shift_dir.
+  double shiftDirL; // Length of the domain in shift_dir.
+  int periodicCopyIdx; // Used to search a periodic copy of the domain (signed).
+  evalf_t shift_func; // Function defining the shift.
+  void *shift_func_ctx; // Context for shift_func.
+};
+
+double ts_shifted_coord_loss_func(double shearCoord, void *ctx)
+{
+  // Loss function used to find the shear coord.
+  struct ts_shifted_coord_loss_func_ctx *tsctx = ctx;
+
+  double shift;
+  tsctx->shift_func(0.0, (double[]){shearCoord}, &shift, tsctx->shift_func_ctx);
+
+  return tsctx->shiftCoordTar - shift
+    - (tsctx->shiftCoordDo - tsctx->periodicCopyIdx * tsctx->shiftDirL);
+}
+
+int static inline
+ts_sign(double a)
+{
+  if (a < 0.0)
+    return -1;
+  else if (a > 0.0)
+    return 1;
+  else
+    return 0;
+}
+
+double
+ts_donor_target_offset(struct gkyl_twistshift_dg *up, const double *xc_do, const double *xc_tar) {
+  // y-offset between the donor and the target cell (yDo-yTar), in the direction of the shift.
+  //   xc_do:  cell center coordinates of donor cell.
+  //   xc_tar: cell center coordinates of target cell.
+  int shift_dir = up->shift_dir_in_ts_grid;
+  double x_eval = xc_do[up->shear_dir];
+  double shift;
+  up->shift_func(0.0, (double[]){x_eval}, &shift, up->shift_func_ctx);
+
+  double shift_dir_L = up->ts_grid.upper[up->shift_dir] - up->ts_grid.lower[up->shift_dir];
+
+  // The idea here is that we keep shifting the donor cell center until it is in a
+  // periodic copy of our domain which overlaps with the shifted target cell center.
+  double xs_shifted_do = xc_do[shift_dir];
+  double xs_shifted_tar = xc_tar[shift_dir] - shift;
+  // Step toward the target.
+  int shift_sign = xs_shifted_tar < xs_shifted_do? 1 : -1;
+  bool keep_shifting = true;
+  while (keep_shifting) {
+    double xs_shifted_dolo = xs_shifted_do - shift_dir_L/2.0;
+    double xs_shifted_doup = xs_shifted_do + shift_dir_L/2.0;
+    if (xs_shifted_dolo <= xs_shifted_tar && xs_shifted_tar <= xs_shifted_doup) {
+      keep_shifting = false;
+      break;
+    }
+    else
+      xs_shifted_do = xs_shifted_do - shift_sign*shift_dir_L;
+  }
+  return xc_tar[shift_dir] - xs_shifted_do;
+}
+
+struct gkyl_qr_res
+ts_find_intersect(struct gkyl_twistshift_dg *up, double shiftCoordTar, double shiftCoordDo,
+  const double *shearDirBounds, const double *shiftDirLimits, int nP_primary)
+{
+  // Given a y-coordinate of the target cell (yTar), and a y-coordinate
+  // of the donor cell (yDo), find the x-coordinate where yTar-yShift(x)=yDo
+  // for the periodic copy identified by nP_primary, i.e. the root of
+  // yTar - yShift(x) - (yDo - nP_primary*Ly) = 0 in [shearDirBounds[0], shearDirBounds[1]].
+  // Returns status=1 (not found) if no root exists for that specific nP_primary.
+  //
+  // nP_primary must be the same for all 4 inter_pts of a donor-target pair: all four
+  // intersection conditions describe corners of a single physical overlap diamond and
+  // therefore belong to the same periodic copy of the domain.
+  double tol = 1.e-13;
+  int max_iter = 100;
+
+  double shiftDirL = shiftDirLimits[1] - shiftDirLimits[0];
+
+  struct ts_shifted_coord_loss_func_ctx func_ctx = {
+    .shiftCoordTar = shiftCoordTar,
+    .shiftCoordDo = shiftCoordDo,
+    .shiftDirL = shiftDirL,
+    .periodicCopyIdx = nP_primary,
+    .shift_func = up->shift_func,
+    .shift_func_ctx = up->shift_func_ctx,
+  };
+  return ts_root_find(ts_shifted_coord_loss_func, &func_ctx, shearDirBounds, max_iter, tol);
+}
+
+struct ts_val_found {
+  bool status; // =0 not found, =1 found.
+  double value; // value found.
+};
+
+static inline void
+ts_comp_to_phys(int ndim, const double *eta,
+  const double * GKYL_RESTRICT dx, const double * GKYL_RESTRICT xc,
+  double* GKYL_RESTRICT xout)
+{
+  for (int d=0; d<ndim; ++d) xout[d] = 0.5*dx[d]*eta[d]+xc[d];
+}
+
+void
+ts_nod2mod_proj_1d(struct gkyl_twistshift_dg *up, evalf_t func, void *func_ctx, const double *interval, double *out)
+{
+  // Project 'func' onto 1D DG basis in [interval[0], interval[1]]
+  // evaluating at nodes and transforming to modal representation.
+  //   func: 1D scalar function to be projected.
+  //   interval: limits of the interval in which to project the function.
+  //   out: DG field output.
+  double dx[] = {0.0}, xc[] = {0.0}, xmu[] = {0.0};
+  ts_interval_dx_and_xc(interval, dx, xc);
+
+  for (int i=0; i<up->shift_b.num_basis; ++i) {
+    ts_comp_to_phys(1, gkyl_eval_on_nodes_fetch_node(up->ev_on_nod1d, i),
+      dx, xc, xmu);
+    func(0.0, xmu, (double *)gkyl_array_fetch(up->func_nod1d,i), func_ctx);
+  }
+  gkyl_eval_on_nodes_nod2mod(up->ev_on_nod1d, up->func_nod1d, out); 
+}
+
+void
+ts_integral_xlimdg(struct gkyl_twistshift_dg *up, double sFac, const double *xLimLo,
+  const double *xLimUp, double yLimLo, double yLimUp, double dyDo, double yOff,
+  const double *ySh, struct gkyl_mat *mat_do) {
+  // Populate a matrix (mat_do) with a sub-cell integral that has variably x limits
+  // represented by a DG polynomial, and a y-integral that goes from yLimLo to yLimUp.
+  //   up: BC updater.
+  //   sFac: +/-1 factor to add or subtract this subcell integral.
+  //   xLimLo: DG representation of the lower x-limit.
+  //   xLimUp: DG representation of the upper x-limit.
+  //   yLimLo: lower y-limit.
+  //   yLimUp: upper y-limit.
+  //   dyDo: Cell length along y.
+  //   yOff: Offset along y.
+  //   ySh: DG representation of the y shift.
+  //   mat_do: donor matrix.
+  up->kernels->xlimdg(sFac, xLimLo, xLimUp, yLimLo, yLimUp, dyDo, yOff, ySh, mat_do);
+}
+
+void
+ts_integral_ylimdg(struct gkyl_twistshift_dg *up, double sFac, double xLimLo, double xLimUp,
+  const double *yLimLo, const double *yLimUp, double dyDo, double yOff,
+  const double *ySh, struct gkyl_mat *mat_do) {
+  // Populate a matrix (mat_do) with a sub-cell integral that has variable y limits
+  // represented by a DG polynomial, and a x-integral that goes from xLimLo to xLimUp.
+  //   up: BC updater.
+  //   sFac: +/-1 factor to add or subtract this subcell integral.
+  //   xLimLo: lower x-limit.
+  //   xLimUp: upper x-limit.
+  //   yLimLo: DG representation of the lower y-limit.
+  //   yLimUp: DG representation of the upper y-limit.
+  //   dyDo: Cell length along y.
+  //   yOff: Offset along y.
+  //   ySh: DG representation of the y shift.
+  //   mat_do: donor matrix.
+  up->kernels->ylimdg(sFac, xLimLo, xLimUp, yLimLo, yLimUp, dyDo, yOff, ySh, mat_do);
+}
+
+void
+ts_integral_fullcelllimdg(struct gkyl_twistshift_dg *up, double dyDo, double yOff,
+  const double *ySh, struct gkyl_mat *mat_do) {
+  // Populate a matrix (mat_do) with the full-cell integral.
+  //   up: BC updater.
+  //   sFac: +/-1 factor to add or subtract this subcell integral.
+  //   dyDo: Cell length along y.
+  //   yOff: Offset along y.
+  //   ySh: DG representation of the y shift.
+  //   mat_do: donor matrix.
+  up->kernels->fullcell(dyDo, yOff, ySh, mat_do);
+}
+
+static inline void
+ts_one(double t, const double *xn, double *fout, void *ctx)
+{
+  fout[0] = 1.0;
+}
+
+static inline void
+ts_minus_one(double t, const double *xn, double *fout, void *ctx)
+{
+  fout[0] = -1.0;
+}
+
+struct ts_shift_coord_shifted_log_ctx {
+  double shift_coord_tar; // Target coordinate in shift_dir.
+  int shift_sign_fac;
+  const double *xc_do, *xc_tar; // Cell centers (donor and target).
+  double *dx; // Cell lengths.
+  bool pick_upper;
+  int shear_dir, shift_dir; // Shear and shift directions.
+  double shift_dir_bounds[2]; // Domain boundaries in shift_dir.
+  evalf_t shift_func; // Function defining the shift.
+  void *shift_func_ctx; // Context for shift_func.
+};
+
+void
+ts_shift_coord_shifted_log(double t, const double *xn, double *fout, void *ctx)
+{
+  // Given a logical space x coordinate (xi) and a (physical) y-coordinate in the target cell,
+  // compute the shifted y-coordinate in the logical space of the donor cell (eta \in [-1,1]).
+  //   xi:    logical space x coordinate.
+  //   yTar:  physical y-coordinate in target cell.
+  //   pmSh:  factor multiplying the y-shift (+/- 1).
+  //   xcDo:  cell center coordinates of donor cell.
+  //   xcTar: cell center coordinates of target cell.
+  //   dx:    cell lengths.
+  //   pickUpper: boolean indicating if wrapping function should return upper/lower boundary.
+
+  double xi = xn[0];
+
+  struct ts_shift_coord_shifted_log_ctx *tsctx = ctx;
+  double shift_coord_tar = tsctx->shift_coord_tar;
+  int shift_sign_fac = tsctx->shift_sign_fac;
+  const double *xc_do = tsctx->xc_do, *xc_tar = tsctx->xc_tar;
+  double *dx = tsctx->dx;
+  bool pick_upper = tsctx->pick_upper;
+  int shear_dir = tsctx->shear_dir, shift_dir = tsctx->shift_dir;
+  double *shift_dir_bounds = tsctx->shift_dir_bounds;
+
+  double shear_coord_phys = xc_tar[shear_dir] + 0.5*dx[shear_dir]*xi;
+  double shift;
+  tsctx->shift_func(0.0, (double[]){shear_coord_phys}, &shift, tsctx->shift_func_ctx);
+
+  double shift_coord_shifted = shift_coord_tar - shift_sign_fac * shift;
+  shift_coord_shifted = ts_wrap_to_range(shift_coord_shifted, shift_dir_bounds[0], shift_dir_bounds[1], pick_upper);
+
+  fout[0] = ts_p2l(shift_coord_shifted, xc_do[shift_dir], dx[shift_dir]);
+}
+
+void
+ts_subcellint_sNi_sNii(struct gkyl_twistshift_dg *up, struct ts_val_found *inter_pts,
+  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
+  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
+{
+  // Perform sNi or sNii subcell integrals.
+  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
+  //   xc_do: cell center of donor cell.
+  //   xc_tar: cell center of target cell.
+  //   cellb_do: boundaries of target cell.
+  //   cellb_tar: boundaries of target cell.
+  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
+  //   shift_c: DG coefficients of the shift.
+  //   mat_do: current donor matrix.
+
+  bool is_sNi = inter_pts[2].value < inter_pts[0].value;
+
+  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
+    .shift_sign_fac = 1,
+    .xc_do = xc_do,
+    .xc_tar = xc_tar,
+    .dx = up->ts_grid.dx,
+    .pick_upper = is_upper_shift_dir_cell,
+    .shear_dir = up->shear_dir_in_ts_grid,
+    .shift_dir = up->shift_dir_in_ts_grid,
+    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
+                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
+    .shift_func = up->shift_func,
+    .shift_func_ctx = up->shift_func_ctx,
+  };
+
+  double xi_b[2]; // Limits of xi integral.
+  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
+  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
+
+  // Offset between cell centers in direction of the shift.
+  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
+
+  if (is_sNi) {
+    // sNi
+    // 1) Add the contribution of the left portion.
+    xi_b[0] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_minus_one;
+    eta_lims[1] = ts_shift_coord_shifted_log;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+
+    // 2) Add the contribution of the right portion.
+    xi_b[0] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_shift_coord_shifted_log;
+    eta_lims[1] = ts_one;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+  }
+  else {
+    // sNii
+    // 1) Add the contribution of the left portion.
+    xi_b[0] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_shift_coord_shifted_log;
+    eta_lims[1] = ts_one;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+
+    // 2) Add the contribution of the right portion.
+    xi_b[0] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_minus_one;
+    eta_lims[1] = ts_shift_coord_shifted_log;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+  }
+}
+
+void
+ts_subcellint_si_sii(struct gkyl_twistshift_dg *up, struct ts_val_found *inter_pts,
+  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
+  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
+{
+  // Perform subcell integral si or sii, using fixed x-limits and variable y limits.
+  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
+  //   xc_do: cell center of donor cell.
+  //   xc_tar: cell center of target cell.
+  //   cellb_do: boundaries of target cell.
+  //   cellb_tar: boundaries of target cell.
+  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
+  //   shift_c: DG coefficients of the shift.
+  //   mat_do: current donor matrix.
+
+  double x_up = cellb_tar[cellb_up(up->shear_dir_in_ts_grid)];
+  double x_lo = cellb_tar[cellb_lo(up->shear_dir_in_ts_grid)];
+  double shift_lo, shift_up;
+
+  up->shift_func(0.0, (double[]){x_lo}, &shift_lo, up->shift_func_ctx);
+  up->shift_func(0.0, (double[]){x_up}, &shift_up, up->shift_func_ctx);
+
+  bool is_si = -shift_lo < -shift_up;
+
+  double xi_b[2];  // Limits of xi integral.
+  if (is_si) {
+    // si integral.
+    xi_b[0] = -1.0;
+    xi_b[1] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);;
+  }
+  else {
+    // sii integral.
+    xi_b[0] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);;
+    xi_b[1] = 1.0;
+  }
+
+  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
+  eta_lims[0] = ts_shift_coord_shifted_log;
+  eta_lims[1] = ts_one;
+
+  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
+    .shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)],
+    .shift_sign_fac = 1,
+    .xc_do = xc_do,
+    .xc_tar = xc_tar,
+    .dx = up->ts_grid.dx,
+    .pick_upper = is_upper_shift_dir_cell,
+    .shear_dir = up->shear_dir_in_ts_grid,
+    .shift_dir = up->shift_dir_in_ts_grid,
+    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
+                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
+    .shift_func = up->shift_func,
+    .shift_func_ctx = up->shift_func_ctx,
+  };
+
+  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
+  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+  // Offset between cell centers in direction of the shift.
+  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
+
+  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+}
+
+void
+ts_subcellint_siii_siv(struct gkyl_twistshift_dg *up, struct ts_val_found *inter_pts,
+  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
+  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
+{
+  // Perform subcell integral siii or siv, using fixed x-limits and variable y limits.
+  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
+  //   xc_do: cell center of donor cell.
+  //   xc_tar: cell center of target cell.
+  //   cellb_do: boundaries of target cell.
+  //   cellb_tar: boundaries of target cell.
+  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
+  //   shift_c: DG coefficients of the shift.
+  //   mat_do: current donor matrix.
+  
+  double x_lo = cellb_tar[cellb_lo(up->shear_dir_in_ts_grid)];
+  double x_up = cellb_tar[cellb_up(up->shear_dir_in_ts_grid)];
+  double shift_lo, shift_up;
+
+  up->shift_func(0.0, (double[]){x_lo}, &shift_lo, up->shift_func_ctx);
+  up->shift_func(0.0, (double[]){x_up}, &shift_up, up->shift_func_ctx);
+
+  bool is_siii = -shift_lo > -shift_up;
+
+  double xi_b[2];  // Limits of xi integral.
+  if (is_siii) {
+    // siii integral.
+    xi_b[0] = -1.0;
+    xi_b[1] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);;
+  }
+  else {
+    // siv integral.
+    xi_b[0] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);;
+    xi_b[1] = 1.0;
+  }
+
+  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
+  eta_lims[0] = ts_minus_one;
+  eta_lims[1] = ts_shift_coord_shifted_log;
+
+  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
+    .shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)],
+    .shift_sign_fac = 1,
+    .xc_do = xc_do,
+    .xc_tar = xc_tar,
+    .dx = up->ts_grid.dx,
+    .pick_upper = is_upper_shift_dir_cell,
+    .shear_dir = up->shear_dir_in_ts_grid,
+    .shift_dir = up->shift_dir_in_ts_grid,
+    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
+                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
+    .shift_func = up->shift_func,
+    .shift_func_ctx = up->shift_func_ctx,
+  };
+
+  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
+  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+  // Offset between cell centers in direction of the shift.
+  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
+
+  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+}
+
+void
+ts_subcellint_sv_svi(struct gkyl_twistshift_dg *up, struct ts_val_found *inter_pts,
+  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
+  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
+{
+  // Perform sv or svi subcell integrals.
+  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
+  //   xc_do: cell center of donor cell.
+  //   xc_tar: cell center of target cell.
+  //   cellb_do: boundaries of target cell.
+  //   cellb_tar: boundaries of target cell.
+  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
+  //   shift_c: DG coefficients of the shift.
+  //   mat_do: current donor matrix.
+
+  bool is_sv = inter_pts[3].value < inter_pts[1].value;
+
+  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
+    .shift_sign_fac = 1,
+    .xc_do = xc_do,
+    .xc_tar = xc_tar,
+    .dx = up->ts_grid.dx,
+    .pick_upper = is_upper_shift_dir_cell,
+    .shear_dir = up->shear_dir_in_ts_grid,
+    .shift_dir = up->shift_dir_in_ts_grid,
+    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
+                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
+    .shift_func = up->shift_func,
+    .shift_func_ctx = up->shift_func_ctx,
+  };
+
+  double xi_b[2]; // Limits of xi integral.
+  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
+  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
+
+  // Offset between cell centers in direction of the shift.
+  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
+
+  if (is_sv) {
+    // sv
+    // 1) Add the contribution of the left portion.
+    xi_b[0] = -1.0;
+    xi_b[1] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_minus_one;
+    eta_lims[1] = ts_shift_coord_shifted_log;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+
+    // 2) Add the contribution of the right portion.
+    xi_b[0] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_shift_coord_shifted_log;
+    eta_lims[1] = ts_one;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+  }
+  else {
+    // svi
+    // 1) Add the contribution of the left portion.
+    xi_b[0] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_shift_coord_shifted_log;
+    eta_lims[1] = ts_one;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+
+    // 2) Add the contribution of the right portion.
+    xi_b[0] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = 1.0;
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_minus_one;
+    eta_lims[1] = ts_shift_coord_shifted_log;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+  }
+}
+
+void
+ts_subcellint_svii_sviii(struct gkyl_twistshift_dg *up, struct ts_val_found *inter_pts,
+  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
+  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
+{
+  // Perform svii or sviii subcell integrals.
+  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
+  //   xc_do: cell center of donor cell.
+  //   xc_tar: cell center of target cell.
+  //   cellb_do: boundaries of target cell.
+  //   cellb_tar: boundaries of target cell.
+  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
+  //   shift_c: DG coefficients of the shift.
+  //   mat_do: current donor matrix.
+
+  bool is_svii = inter_pts[0].value < inter_pts[2].value;
+
+  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
+    .shift_sign_fac = 1,
+    .xc_do = xc_do,
+    .xc_tar = xc_tar,
+    .dx = up->ts_grid.dx,
+    .pick_upper = is_upper_shift_dir_cell,
+    .shear_dir = up->shear_dir_in_ts_grid,
+    .shift_dir = up->shift_dir_in_ts_grid,
+    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
+                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
+    .shift_func = up->shift_func,
+    .shift_func_ctx = up->shift_func_ctx,
+  };
+
+  double xi_b[2]; // Limits of xi integral.
+  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
+  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
+
+  // Offset between cell centers in direction of the shift.
+  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
+
+  if (is_svii) {
+    // svii
+    // 1) Add the contribution of the left portion.
+    xi_b[0] = -1.0;
+    xi_b[1] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_shift_coord_shifted_log;
+    eta_lims[1] = ts_one;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+
+    // 2) Add the contribution of the right portion.
+    xi_b[0] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_minus_one;
+    eta_lims[1] = ts_shift_coord_shifted_log;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+  }
+  else {
+    // sviii
+    // 1) Add the contribution of the left portion.
+    xi_b[0] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_minus_one;
+    eta_lims[1] = ts_shift_coord_shifted_log;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+
+    // 2) Add the contribution of the right portion.
+    xi_b[0] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = 1.0;
+
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_shift_coord_shifted_log;
+    eta_lims[1] = ts_one;
+
+    ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+    ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+    if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+      up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+        up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+  }
+}
+
+void
+ts_subcellint_six_sx(struct gkyl_twistshift_dg *up, struct ts_val_found *inter_pts,
+  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
+  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
+{
+  // Perform six or sx subcell integrals.
+  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
+  //   xc_do: cell center of donor cell.
+  //   xc_tar: cell center of target cell.
+  //   cellb_do: boundaries of target cell.
+  //   cellb_tar: boundaries of target cell.
+  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
+  //   shift_c: DG coefficients of the shift.
+  //   mat_do: current donor matrix.
+
+  bool is_six = inter_pts[0].value < inter_pts[1].value;
+
+  // Limits of xi integral.
+  double xi_b[2];
+  if (is_six) {
+    // six
+    xi_b[0] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+  }
+  else {
+    // sx
+    xi_b[0] = ts_p2l(inter_pts[1].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+  }
+
+  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
+    .shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)],
+    .shift_sign_fac = 1,
+    .xc_do = xc_do,
+    .xc_tar = xc_tar,
+    .dx = up->ts_grid.dx,
+    .pick_upper = is_upper_shift_dir_cell,
+    .shear_dir = up->shear_dir_in_ts_grid,
+    .shift_dir = up->shift_dir_in_ts_grid,
+    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
+                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
+    .shift_func = up->shift_func,
+    .shift_func_ctx = up->shift_func_ctx,
+  };
+
+  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
+  eta_lims[0] = ts_shift_coord_shifted_log;
+  eta_lims[1] = ts_one;
+
+  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
+  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+  // Offset between cell centers in direction of the shift.
+  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
+
+  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+}
+
+void
+ts_subcellint_sxi_sxii(struct gkyl_twistshift_dg *up, struct ts_val_found *inter_pts,
+  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
+  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
+{
+  // Perform sxi or sxii subcell integrals.
+  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
+  //   xc_do: cell center of donor cell.
+  //   xc_tar: cell center of target cell.
+  //   cellb_do: boundaries of target cell.
+  //   cellb_tar: boundaries of target cell.
+  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
+  //   shift_c: DG coefficients of the shift.
+  //   mat_do: current donor matrix.
+
+  bool is_sxi = inter_pts[3].value < inter_pts[2].value;
+
+  // Limits of xi integral.
+  double xi_b[2];
+  if (is_sxi) {
+    // six
+    xi_b[0] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+  }
+  else {
+    // sx
+    xi_b[0] = ts_p2l(inter_pts[2].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+    xi_b[1] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+  }
+
+  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
+    .shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)],
+    .shift_sign_fac = 1,
+    .xc_do = xc_do,
+    .xc_tar = xc_tar,
+    .dx = up->ts_grid.dx,
+    .pick_upper = is_upper_shift_dir_cell,
+    .shear_dir = up->shear_dir_in_ts_grid,
+    .shift_dir = up->shift_dir_in_ts_grid,
+    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
+                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
+    .shift_func = up->shift_func,
+    .shift_func_ctx = up->shift_func_ctx,
+  };
+
+  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
+  eta_lims[0] = ts_minus_one;
+  eta_lims[1] = ts_shift_coord_shifted_log;
+
+  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
+  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+  // Offset between cell centers in direction of the shift.
+  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
+
+  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+}
+
+void
+ts_subcellint_sxiii_sxiv(struct gkyl_twistshift_dg *up, struct ts_val_found *inter_pts,
+  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
+  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
+{
+  // Perform sxiii or sxiv subcell integrals.
+  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
+  //   xc_do: cell center of donor cell.
+  //   xc_tar: cell center of target cell.
+  //   cellb_do: boundaries of target cell.
+  //   cellb_tar: boundaries of target cell.
+  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
+  //   shift_c: DG coefficients of the shift.
+  //   mat_do: current donor matrix.
+
+  double x_lo = cellb_tar[cellb_lo(up->shear_dir_in_ts_grid)];
+  double x_up = cellb_tar[cellb_up(up->shear_dir_in_ts_grid)];
+  double shift_lo, shift_up;
+
+  up->shift_func(0.0, (double[]){x_lo}, &shift_lo, up->shift_func_ctx);
+  up->shift_func(0.0, (double[]){x_up}, &shift_up, up->shift_func_ctx);
+
+  bool is_sxiii = -shift_lo < -shift_up;
+
+  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
+    .shift_sign_fac = 1,
+    .xc_do = xc_do,
+    .xc_tar = xc_tar,
+    .dx = up->ts_grid.dx,
+    .pick_upper = is_upper_shift_dir_cell,
+    .shear_dir = up->shear_dir_in_ts_grid,
+    .shift_dir = up->shift_dir_in_ts_grid,
+    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
+                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
+    .shift_func = up->shift_func,
+    .shift_func_ctx = up->shift_func_ctx,
+  };
+
+  double xi_b[2]; // Limits of xi integral.
+  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
+  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
+
+  // Offset between cell centers in direction of the shift.
+  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
+
+  // 1) Add the contribution of the left portion.
+  xi_b[0] = -1.0;
+  xi_b[1] = ts_p2l(inter_pts[3].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+
+  if (is_sxiii) {
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_minus_one;
+    eta_lims[1] = ts_shift_coord_shifted_log;
+  }
+  else {
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_shift_coord_shifted_log;
+    eta_lims[1] = ts_one;
+  }
+
+  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+
+  // 2) Add the contribution of the right portion.
+  xi_b[0] = ts_p2l(inter_pts[0].value, xc_do[up->shear_dir_in_ts_grid], up->ts_grid.dx[up->shear_dir_in_ts_grid]);
+  xi_b[1] = 1.0;
+
+  if (is_sxiii) {
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_shift_coord_shifted_log;
+    eta_lims[1] = ts_one;
+  }
+  else {
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_minus_one;
+    eta_lims[1] = ts_shift_coord_shifted_log;
+  }
+
+  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+
+  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+}
+
+void
+ts_subcellint_sxv_sxvi(struct gkyl_twistshift_dg *up, struct ts_val_found *inter_pts,
+  const double *xc_do, const double *xc_tar, const double *cellb_do, const double *cellb_tar,
+  bool is_upper_shift_dir_cell, const double *shift_c, struct gkyl_mat *mat_do)
+{
+  // Perform subcell integral sxv or sxvi, using fixed x-limits and variable y limits.
+  //   inter_pts: intersections y_{j_tar-/+1/2}-yShift and y_{j_do-/+1/2} (lower/upper y-boundaries of donor cell).
+  //   xc_do: cell center of donor cell.
+  //   xc_tar: cell center of target cell.
+  //   cellb_do: boundaries of target cell.
+  //   cellb_tar: boundaries of target cell.
+  //   is_upper_shift_dir_cell: is the donor the upper cell in the shift dir?
+  //   shift_c: DG coefficients of the shift.
+  //   mat_do: current donor matrix.
+
+  double xi_b[] = {-1.0, 1.0};  // Limits of xi integral.
+
+  double shift_dir_bounds[] = {up->ts_grid.lower[up->shift_dir_in_ts_grid],
+                               up->ts_grid.upper[up->shift_dir_in_ts_grid]};
+
+  double x_eval = xc_do[up->shear_dir_in_ts_grid];
+  double shift;
+
+  up->shift_func(0.0, (double[]){x_eval}, &shift, up->shift_func_ctx);
+
+  double shifted_coord = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)] - shift;
+  shifted_coord = ts_wrap_to_range(shifted_coord, shift_dir_bounds[0], shift_dir_bounds[1],
+    is_upper_shift_dir_cell);
+
+  struct ts_shift_coord_shifted_log_ctx eta_lims_ctx = {
+    .shift_sign_fac = 1,
+    .xc_do = xc_do,
+    .xc_tar = xc_tar,
+    .dx = up->ts_grid.dx,
+    .pick_upper = is_upper_shift_dir_cell,
+    .shear_dir = up->shear_dir_in_ts_grid,
+    .shift_dir = up->shift_dir_in_ts_grid,
+    .shift_dir_bounds = {up->ts_grid.lower[up->shift_dir_in_ts_grid], 
+                         up->ts_grid.upper[up->shift_dir_in_ts_grid]},
+    .shift_func = up->shift_func,
+    .shift_func_ctx = up->shift_func_ctx,
+  };
+
+  evalf_t eta_lims[2]; // Table of functions definting the limits of eta integral.
+  if ( cellb_do[cellb_lo(up->shift_dir_in_ts_grid)] <= shifted_coord &&
+       shifted_coord <= cellb_do[cellb_up(up->shift_dir_in_ts_grid)] ) {
+    // sxv integral.
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_lo(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_shift_coord_shifted_log;
+    eta_lims[1] = ts_one;
+  }
+  else {
+    // sxvi integral.
+    eta_lims_ctx.shift_coord_tar = cellb_tar[cellb_up(up->shift_dir_in_ts_grid)];
+    eta_lims[0] = ts_minus_one;
+    eta_lims[1] = ts_shift_coord_shifted_log;
+  }
+
+  double etalo_xi[up->shift_b.num_basis], etaup_xi[up->shift_b.num_basis];
+  ts_nod2mod_proj_1d(up, eta_lims[0], &eta_lims_ctx, xi_b, etalo_xi);
+  ts_nod2mod_proj_1d(up, eta_lims[1], &eta_lims_ctx, xi_b, etaup_xi);
+  // Offset between cell centers in direction of the shift.
+  double xs_off = ts_donor_target_offset(up, xc_do, xc_tar);
+
+  if (fabs(xi_b[1] - xi_b[0]) > tol_xi)
+    up->kernels->ylimdg(1.0, xi_b[0], xi_b[1], etalo_xi, etaup_xi,
+      up->ts_grid.dx[up->shift_dir_in_ts_grid], xs_off, shift_c, mat_do);
+}
+
+struct gkyl_nmat *
+ts_calc_mats(struct gkyl_twistshift_dg *up)
+{
+
+  // Allocate matrices containing the discrete subcell integrals.
+  int num_do_tot = 0;
+  for (int i=0; i<up->shear_r.volume; i++)
+    num_do_tot += up->num_do[i];
+
+  struct gkyl_nmat *matsdo = gkyl_nmat_new(num_do_tot, up->basis.num_basis, up->basis.num_basis);
+  for (int n=0; n<matsdo->num; ++n) {
+    struct gkyl_mat mat = gkyl_nmat_get(matsdo, n);
+    for (int j=0; j<matsdo->nc; ++j)
+      for (int i=0; i<matsdo->nr; ++i)
+        gkyl_mat_set(&mat, i, j, 0.0);
+  }
+
+  // y-index of the reference target used to precalc matrices. For positive(negative)
+  // yShift idx=1(last) might be better, but ideally it shouldn't matter.
+  int shift_dir_idx_tar = 1;
+
+  double shift_dir_lims[] = {up->ts_grid.lower[up->shift_dir_in_ts_grid],
+                             up->ts_grid.upper[up->shift_dir_in_ts_grid]};
+
+  // Create an eval_on_nodes updater to use its nodes and functions (but not
+  // the whole advance method).
+  up->ev_on_nod1d = gkyl_eval_on_nodes_new(&up->shear_grid, &up->shift_b, 1, ts_one, NULL);
+  // Create an array to store evaluations of a function at 1D nodes.
+  up->func_nod1d = gkyl_array_new(GKYL_DOUBLE, 1, up->shift_b.num_basis);
+
+  struct gkyl_range_iter iter;
+  gkyl_range_iter_init(&iter, &up->shear_r);
+  while (gkyl_range_iter_next(&iter)) {
+
+    // Get the cell boundaries and cell center.
+    int idx_tar[2]; // Target index.
+    idx_tar[up->shift_dir_in_ts_grid] = shift_dir_idx_tar;
+    idx_tar[up->shear_dir_in_ts_grid] = iter.idx[0];
+    double cellb_tar[4] = {0.0}; // Cell boundaries, x lo and up, y lo and up;
+    double xc_tar[2] = {0.0}; // Cell center.
+    ts_grid_cell_boundaries(&up->ts_grid, idx_tar, cellb_tar);
+    gkyl_rect_grid_cell_center(&up->ts_grid, idx_tar, xc_tar);
+
+    long shift_loc = gkyl_range_idx(&up->shear_r, iter.idx);
+    double *shift_c = (double *) gkyl_array_fetch(up->shift_dg, shift_loc);
+
+    long linidx_do = ts_shift_dir_idx_do_linidx(up->num_do, iter.idx[0], shift_dir_idx_tar,
+      up->ts_grid.cells[up->shift_dir_in_ts_grid], up->shear_r.lower[0]);
+    int *shift_dir_idx_do_ptr = &up->shift_dir_idx_do[linidx_do];
+
+    long linidx_mats_do = 0;
+    for (int i=0; i<iter.idx[0]-up->shear_r.lower[0]; i++)
+      linidx_mats_do += up->num_do[i];
+
+    // Check that the shift variation within this x-cell < Ly.
+    // The algorithm assumes at most one x-intersection per (y-boundary, y-boundary) pair,
+    // which breaks when |S(x_up) - S(x_lo)| >= Ly.
+    double x_lo = cellb_tar[cellb_lo(up->shear_dir_in_ts_grid)];
+    double x_up = cellb_tar[cellb_up(up->shear_dir_in_ts_grid)];
+    double Ly = shift_dir_lims[1] - shift_dir_lims[0];
+    double S_lo, S_up, S_c;
+    up->shift_func(0.0, (double[]){x_lo}, &S_lo, up->shift_func_ctx);
+    up->shift_func(0.0, (double[]){x_up}, &S_up, up->shift_func_ctx);
+    up->shift_func(0.0, (double[]){xc_tar[up->shear_dir_in_ts_grid]}, &S_c, up->shift_func_ctx);
+
+    if (fabs(S_up - S_lo) >= Ly) {
+      fprintf(stderr, "bc_twistshift: shift variation |S(x_up)-S(x_lo)| = %g across a single x-cell"
+        " exceeds Ly = %g (cell ix=%d). Increase Nx, reduce the shear, or increase Ly.\n",
+        fabs(S_up - S_lo), Ly, iter.idx[0]);
+      assert(false);
+    }
+
+    for (int iC=0; iC<up->num_do[iter.idx[0]-up->shear_r.lower[0]]; iC++){
+      int idx_do[2]; // Target index.
+      idx_do[up->shift_dir_in_ts_grid] = shift_dir_idx_do_ptr[iC];
+      idx_do[up->shear_dir_in_ts_grid] = iter.idx[0];
+
+      double cellb_do[4] = {0.0}; // Cell boundaries, x lo and up, y lo and up;
+      double xc_do[2] = {0.0}; // Cell center.
+      ts_grid_cell_boundaries(&up->ts_grid, idx_do, cellb_do);
+      gkyl_rect_grid_cell_center(&up->ts_grid, idx_do, xc_do);
+
+      // Get the matrix we are presently assigning.
+      struct gkyl_mat mat_do = gkyl_nmat_get(matsdo, linidx_mats_do+iC);
+
+      // Periodic copy in which to find the target for this donor-target pair: the integer nP such that
+      // S_c \approx y_tar_c - y_do_c + nP*Ly. All 4 inter_pts must use this same nP so that only
+      // roots from the physical intersection are accepted (not roots from other periodic copies).
+      int nP_primary = (int)round((S_c - (xc_tar[up->shift_dir_in_ts_grid] - xc_do[up->shift_dir_in_ts_grid])) / Ly);
+
+      // Find the points where y_{j_tar-/+1/2}-yShift intersect the y=y_{j_do-/+1/2} lines.
+      // Also record the number and indices of points found/not found.
+      struct ts_val_found inter_pts[4] = {};
+      int num_inter_pts_found = 0, num_inter_pts_not_found = 4;
+      int inter_pts_found_idxs[4], inter_pts_not_found_idxs[4];
+      for (int i=0; i<2; i++) { // Loop over j_tar-/+1/2
+        for (int j=0; j<2; j++) { // Loop over j_do-/+1/2
+          double shift_dir_coord_tar = cellb_tar[2*up->shift_dir_in_ts_grid+i];
+          double shift_dir_coord_do = cellb_do[2*up->shift_dir_in_ts_grid+j];
+          struct gkyl_qr_res inter_res = ts_find_intersect(up, shift_dir_coord_tar, shift_dir_coord_do,
+            (double[]) {cellb_tar[cellb_lo(up->shear_dir_in_ts_grid)],cellb_tar[cellb_up(up->shear_dir_in_ts_grid)]},
+            shift_dir_lims, nP_primary);
+          int ip_linc = i*2+j;
+          inter_pts[ip_linc].status = inter_res.status == 0;
+          if (inter_res.status == 0) {
+            inter_pts[ip_linc].value = inter_res.res;
+            inter_pts_found_idxs[num_inter_pts_found] = ip_linc;
+            num_inter_pts_found++;
+          }
+          else {
+            inter_pts_not_found_idxs[num_inter_pts_not_found] = ip_linc;
+            num_inter_pts_not_found--;
+          }
+        }
+      }
+
+      bool is_upper_shift_dir_cell = idx_do[up->shift_dir_in_ts_grid] == up->ts_grid.cells[up->shift_dir_in_ts_grid];
+
+      if (num_inter_pts_found == 4) {
+        // sN: all intersections are found at this cell.
+        ts_subcellint_sNi_sNii(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
+      }
+      else if (num_inter_pts_found == 1) {
+        if (inter_pts[1].status) {
+          // si:   y_{j_tar-1/2}-yShift intersects x_{i-1/2}.
+          // sii:  y_{j_tar-1/2}-yShift intersects x_{i+1/2}.
+          ts_subcellint_si_sii(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
+        }
+        else {
+          // siii: y_{j_tar+1/2}-yShift intersects x_{i-1/2}.
+          // siv:  y_{j_tar+1/2}-yShift intersects x_{i+1/2}.
+          ts_subcellint_siii_siv(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
+        }
+      }
+      else if (num_inter_pts_found == 3) {
+        if (!inter_pts[2].status) {
+          // sv:    y_{j_tar+1/2}-yShift doesn't intersect y_{j_do-1/2} & intersects x_{i-1/2}.
+          // svi:   y_{j_tar+1/2}-yShift doesn't intersect y_{j_do-1/2} & intersects x_{i+1/2}.
+          ts_subcellint_sv_svi(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
+        }
+        else {
+          // svii:  y_{j_tar-1/2}-yShift doesn't intersect y_{j_do+1/2} & intersects x_{i-1/2}.
+          // sviii: y_{j_tar-1/2}-yShift doesn't intersect y_{j_do+1/2} & intersects x_{i+1/2}.
+          ts_subcellint_svii_sviii(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
+        }
+      }
+      else if (num_inter_pts_found == 2) {
+        if (inter_pts[0].status && inter_pts[1].status) {
+          // six:   y_{j_tar-1/2}-yShift crosses y_{j_do-/+1/2} (increasing yShift).
+          // sx:    y_{j_tar-1/2}-yShift crosses y_{j_do-/+1/2} (decreasing yShift).
+          ts_subcellint_six_sx(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
+        }
+        else if (inter_pts[2].status && inter_pts[3].status) {
+          // sxi:   y_{j_tar+1/2}-yShift crosses y_{j_do-/+1/2} (decreasing yShift).
+          // sxii:  y_{j_tar+1/2}-yShift crosses y_{j_do-/+1/2} (increasing yShift).
+          ts_subcellint_sxi_sxii(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
+        }
+        else {
+          // sxiii: y_{j_tar-1/2}-yShift crosses y_{j_do-1/2} & y_{j_tar+1/2}-yShift crosses y_{j_do+1/2} (increasing yShift).
+          // sxiv:  y_{j_tar-1/2}-yShift crosses y_{j_do-1/2} & y_{j_tar+1/2}-yShift crosses y_{j_do+1/2} (decreasing yShift).
+          ts_subcellint_sxiii_sxiv(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
+        }
+      }
+      else if (num_inter_pts_found == 0) {
+        // sxv:  y_{j_tar-1/2}-yShift crosses x_{i-/+1/2}.
+        // sxvi: y_{j_tar+1/2}-yShift crosses x_{i-/+1/2}.
+        ts_subcellint_sxv_sxvi(up, inter_pts, xc_do, xc_tar, cellb_do, cellb_tar, is_upper_shift_dir_cell, shift_c, &mat_do);
+      }
+      else {
+        // An error occurred. This shouldn't happen.
+        assert(false);
+      }
+    }
+
+  }
+
+  gkyl_array_release(up->func_nod1d);
+  gkyl_eval_on_nodes_release(up->ev_on_nod1d);
+
+  struct gkyl_nmat *matsdo_out = up->use_gpu? gkyl_nmat_cu_dev_new(matsdo->num, matsdo->nr, matsdo->nc)
+                                            : gkyl_nmat_acquire(matsdo); 
+  gkyl_nmat_copy(matsdo_out, matsdo);
+  gkyl_nmat_release(matsdo);
+
+  return matsdo_out;
+}
+
+long *
+ts_calc_num_numcol_fidx_do(struct gkyl_twistshift_dg *up)
+{
+  // Calculate the linear indices into the donor distribution function gkyl_array
+  // for each num-numcol plane (in the num-numcol-num_basis) space.
+
+  long *num_numcol_fidx_do_ho = (long*) gkyl_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
+
+  // Location in the direction of the BC from which to take donor
+  // distributions. We assume that the user filled the ghost cell with the skin
+  // on the other side (i.e. applied periodicity first).
+  int bc_dir_loc_do = up->edge == GKYL_LOWER_EDGE? up->local_bcdir_ext_r.lower[up->bc_dir]
+                                                 : up->local_bcdir_ext_r.upper[up->bc_dir];
+
+  // Range over directions other than shear and bc dirs.
+  struct gkyl_range shearbc_perp_r;
+  int remove[GKYL_MAX_DIM] = {0}, loc_in_dir[GKYL_MAX_DIM] = {0};;
+  remove[up->shear_dir] = remove[up->bc_dir] = 1;
+  loc_in_dir[up->shear_dir] = up->local_bcdir_ext_r.lower[up->shear_dir];
+  loc_in_dir[up->bc_dir] = bc_dir_loc_do;
+  gkyl_range_deflate(&shearbc_perp_r, &up->local_bcdir_ext_r, remove, loc_in_dir);
+
+  int shift_dir_in_shearbc_perp_r;
+  if (up->shift_dir < up->shear_dir && up->shift_dir < up->bc_dir)
+    shift_dir_in_shearbc_perp_r = up->shift_dir;
+  else if (up->shift_dir > up->shear_dir && up->shift_dir > up->bc_dir)
+    shift_dir_in_shearbc_perp_r = up->shift_dir-2;
+  else
+    shift_dir_in_shearbc_perp_r = up->shift_dir-1;
+
+  int prev_shift_dir_idx = 0;
+  int donor_count = 0;
+  int do_idx[up->local_bcdir_ext_r.ndim];
+
+  // Loop over directions perpendicular to shear and BC dirs.
+  struct gkyl_range_iter iter;
+  gkyl_range_iter_init(&iter, &shearbc_perp_r);
+  while (gkyl_range_iter_next(&iter)) {
+    int ic = 0;
+    for (int d=0; d<up->local_bcdir_ext_r.ndim; d++) {
+      if (d != up->bc_dir && d != up->shear_dir) {
+        do_idx[d] = iter.idx[ic];
+        ic++;
+      }
+    }
+    do_idx[up->bc_dir] = bc_dir_loc_do;
+
+    struct gkyl_range_iter shear_dir_iter;
+    gkyl_range_iter_init(&shear_dir_iter, &up->shear_r);
+    while (gkyl_range_iter_next(&shear_dir_iter)) {
+
+      int shear_dir_idx = shear_dir_iter.idx[0];
+
+      long linidx_do = ts_shift_dir_idx_do_linidx(up->num_do, shear_dir_idx,
+        iter.idx[shift_dir_in_shearbc_perp_r], up->ts_grid.cells[up->shift_dir_in_ts_grid], up->shear_r.lower[0]);
+
+      for (int i = 0; i < up->num_do[shear_dir_idx-up->shear_r.lower[0]]; i++) {
+        do_idx[up->shear_dir] = shear_dir_idx;
+        do_idx[up->shift_dir] = up->shift_dir_idx_do[linidx_do+i];
+
+        long loc = gkyl_range_idx(&up->local_bcdir_ext_r, do_idx);
+        num_numcol_fidx_do_ho[donor_count] = loc;
+
+        donor_count += 1;
+      }
+    }
+    prev_shift_dir_idx = iter.idx[shift_dir_in_shearbc_perp_r];
+  }
+
+  long *num_numcol_fidx_do;
+  if (!up->use_gpu) {
+    num_numcol_fidx_do = (long*) gkyl_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
+    memcpy(num_numcol_fidx_do, num_numcol_fidx_do_ho, up->fmat->num * up->fmat->nc * sizeof(long));
+  }
+#ifdef GKYL_HAVE_CUDA
+  if (up->use_gpu) {
+    num_numcol_fidx_do = (long*) gkyl_cu_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
+    gkyl_cu_memcpy(num_numcol_fidx_do, num_numcol_fidx_do_ho, up->fmat->num * up->fmat->nc * sizeof(long), GKYL_CU_MEMCPY_H2D);
+  }
+#endif
+
+  gkyl_free(num_numcol_fidx_do_ho);
+
+  return num_numcol_fidx_do;
+}
+
+long *
+ts_calc_num_numcol_fidx_tar(struct gkyl_twistshift_dg *up)
+{
+
+  long *num_numcol_fidx_tar_ho = (long*) gkyl_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
+
+  // Location in the direction of the BC in which to place the target
+  // distributions. We assume that the local_bcdir_ext_r is a range extended in z (it
+  // includes the z ghose cell).
+  int bc_dir_loc_tar = up->edge == GKYL_LOWER_EDGE? up->local_bcdir_ext_r.lower[up->bc_dir]
+                                                  : up->local_bcdir_ext_r.upper[up->bc_dir];
+
+  // Range over directions other than shear and bc dirs.
+  struct gkyl_range shearbc_perp_r;
+  int remove[GKYL_MAX_DIM] = {0}, loc_in_dir[GKYL_MAX_DIM] = {0};;
+  remove[up->shear_dir] = remove[up->bc_dir] = 1;
+  loc_in_dir[up->shear_dir] = up->local_bcdir_ext_r.lower[up->shear_dir];
+  loc_in_dir[up->bc_dir] = bc_dir_loc_tar;
+  gkyl_range_deflate(&shearbc_perp_r, &up->local_bcdir_ext_r, remove, loc_in_dir);
+
+  int tar_idx[up->local_bcdir_ext_r.ndim];
+  int tar_count = 0;
+
+  // Loop over directions perpendicular to shear and BC dirs.
+  struct gkyl_range_iter iter;
+  gkyl_range_iter_init(&iter, &shearbc_perp_r);
+  while (gkyl_range_iter_next(&iter)) {
+
+    int ic = 0;
+    for (int d=0; d<up->local_bcdir_ext_r.ndim; d++) {
+      if (d != up->bc_dir && d != up->shear_dir) {
+        tar_idx[d] = iter.idx[ic];
+        ic++;
+      }
+    }
+    tar_idx[up->bc_dir] = bc_dir_loc_tar;
+
+
+    struct gkyl_range_iter shear_dir_iter;
+    gkyl_range_iter_init(&shear_dir_iter, &up->shear_r);
+    while (gkyl_range_iter_next(&shear_dir_iter)) {
+      int shear_dir_idx = shear_dir_iter.idx[0];
+      tar_idx[up->shear_dir] = shear_dir_idx;
+
+      long loc = gkyl_range_idx(&up->local_bcdir_ext_r, tar_idx);
+      num_numcol_fidx_tar_ho[tar_count] = loc;
+      tar_count += 1;
+    }
+  }
+
+  long *num_numcol_fidx_tar;
+  if (!up->use_gpu) {
+    num_numcol_fidx_tar = (long*) gkyl_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
+    memcpy(num_numcol_fidx_tar, num_numcol_fidx_tar_ho, up->fmat->num * up->fmat->nc * sizeof(long));
+  }
+#ifdef GKYL_HAVE_CUDA
+  if (up->use_gpu) {
+    num_numcol_fidx_tar = (long*) gkyl_cu_malloc(up->fmat->num * up->fmat->nc * sizeof(long));
+    gkyl_cu_memcpy(num_numcol_fidx_tar, num_numcol_fidx_tar_ho, up->fmat->num * up->fmat->nc * sizeof(long), GKYL_CU_MEMCPY_H2D);
+  }
+#endif
+
+  gkyl_free(num_numcol_fidx_tar_ho);
+
+  return num_numcol_fidx_tar;
+}
+
+void
+gkyl_twistshift_dg_choose_kernels(struct gkyl_basis basis, int cdim, int shift_poly_order,
+  struct gkyl_twistshift_dg_kernels *kers)
+{
+  int dim = basis.ndim;
+  int vdim = dim - cdim;
+  enum gkyl_basis_type basis_type = basis.b_type;
+  int poly_order = basis.poly_order;
+  switch (basis_type) {
+    case GKYL_BASIS_MODAL_GKHYBRID:
+    case GKYL_BASIS_MODAL_SERENDIPITY:
+      if (shift_poly_order == 1) {
+        kers->xlimdg   = vdim==0? ser_twistshift_xlimdg_list_0v_yShp1[cdim-2].kernels[poly_order]
+                                : ser_twistshift_xlimdg_list_2v_yShp1[cdim-2].kernels[poly_order];
+        kers->ylimdg   = vdim==0? ser_twistshift_ylimdg_list_0v_yShp1[cdim-2].kernels[poly_order]
+                                : ser_twistshift_ylimdg_list_2v_yShp1[cdim-2].kernels[poly_order];
+        kers->fullcell = vdim==0? ser_twistshift_fullcell_list_0v_yShp1[cdim-2].kernels[poly_order]
+                                : ser_twistshift_fullcell_list_2v_yShp1[cdim-2].kernels[poly_order];
+      }
+      else if (shift_poly_order == 2) {
+        assert(false); // MF 2025/09/20: removed 3x2v kernel because it's 8.5 MB.
+        kers->xlimdg   = vdim==0? ser_twistshift_xlimdg_list_0v_yShp2[cdim-2].kernels[poly_order]
+                                : ser_twistshift_xlimdg_list_2v_yShp2[cdim-2].kernels[poly_order];
+        kers->ylimdg   = vdim==0? ser_twistshift_ylimdg_list_0v_yShp2[cdim-2].kernels[poly_order]
+                                : ser_twistshift_ylimdg_list_2v_yShp2[cdim-2].kernels[poly_order];
+        kers->fullcell = vdim==0? ser_twistshift_fullcell_list_0v_yShp2[cdim-2].kernels[poly_order]
+                                : ser_twistshift_fullcell_list_2v_yShp2[cdim-2].kernels[poly_order];
+      }
+      return;
+    default:
+      assert(false);
+      break;
+  }
+}
+
+struct gkyl_twistshift_dg*
+gkyl_twistshift_dg_inew(const struct gkyl_twistshift_dg_inp *inp)
+{
+
+  // Allocate space for new updater.
+  struct gkyl_twistshift_dg *up = gkyl_malloc(sizeof(struct gkyl_twistshift_dg));
+
+  up->bc_dir = inp->bc_dir;
+  up->shift_dir = inp->shift_dir;
+  up->shear_dir = inp->shear_dir;
+  up->edge = inp->edge;
+  up->basis = *inp->basis;
+  up->grid = *inp->grid;
+  up->use_gpu = inp->use_gpu;
+  up->local_bcdir_ext_r = *inp->bcdir_ext_update_r;
+
+  // Assume the poly order of the DG shift is the same as that of the field,
+  // unless requested otherwise.
+  up->shift_poly_order = inp->basis->poly_order;
+  if (inp->shift_poly_order)
+    up->shift_poly_order = inp->shift_poly_order;
+
+  const int ndim = inp->bcdir_ext_update_r->ndim;
+  // Check that it is being used for 3D or 5D. Likely only small changes are
+  // needed to make it work in other dimensions.
+  assert(ndim == 3 || ndim == 5); 
+
+  double lo1d[1], up1d[1];  int cells1d[1];
+
+  // Create 1D grid and range in the direction of the shear.
+  gkyl_range_init(&up->shear_r, 1, (int[]) {up->local_bcdir_ext_r.lower[inp->shear_dir]},
+                                   (int[]) {up->local_bcdir_ext_r.upper[inp->shear_dir]});
+  lo1d[0] = inp->grid->lower[up->shear_dir];
+  up1d[0] = inp->grid->upper[up->shear_dir];
+  cells1d[0] = inp->grid->cells[up->shear_dir];
+  gkyl_rect_grid_init(&up->shear_grid, 1, lo1d, up1d, cells1d);
+  int idx[] = {up->shear_r.lower[0]};
+  long linidx = gkyl_range_idx(&up->shear_r, idx);
+
+  // Create 1D grid and range in the diretion of the shift.
+  gkyl_range_init(&up->shift_r, 1, (int[]) {up->local_bcdir_ext_r.lower[inp->shift_dir]},
+                                   (int[]) {up->local_bcdir_ext_r.upper[inp->shift_dir]});
+  lo1d[0] = inp->grid->lower[up->shift_dir];
+  up1d[0] = inp->grid->upper[up->shift_dir];
+  cells1d[0] = inp->grid->cells[up->shift_dir];
+  gkyl_rect_grid_init(&up->shift_grid, 1, lo1d, up1d, cells1d);
+
+  // Create 2D grid (and range) the twist-shift takes place in.
+  int dimlo, dimup;
+  if (up->shift_dir < up->shear_dir) {
+    dimlo = up->shift_dir;
+    dimup = up->shear_dir;
+    up->shift_dir_in_ts_grid = 0;
+    up->shear_dir_in_ts_grid = 1;
+  }
+  else {
+    dimlo = up->shear_dir;
+    dimup = up->shift_dir;
+    up->shift_dir_in_ts_grid = 1;
+    up->shear_dir_in_ts_grid = 0;
+  }
+  gkyl_range_init(&up->ts_r, 2, (int[]) {up->local_bcdir_ext_r.lower[dimlo], up->local_bcdir_ext_r.lower[dimup]},
+                                (int[]) {up->local_bcdir_ext_r.upper[dimlo], up->local_bcdir_ext_r.upper[dimup]});
+  double lo2d[] = {inp->grid->lower[dimlo], inp->grid->lower[dimup]};
+  double up2d[] = {inp->grid->upper[dimlo], inp->grid->upper[dimup]};
+  int cells2d[] = {inp->grid->cells[dimlo], inp->grid->cells[dimup]};
+  gkyl_rect_grid_init(&up->ts_grid, 2, lo2d, up2d, cells2d);
+
+  // Project the shift onto the shift basis.
+  gkyl_cart_modal_serendip(&up->shift_b, 1, up->shift_poly_order);
+  if (inp->shift_func) {
+    up->shift_dg = gkyl_array_new(GKYL_DOUBLE, up->shift_b.num_basis, up->shear_r.volume);
+    gkyl_eval_on_nodes *evup = gkyl_eval_on_nodes_new(&up->shear_grid, &up->shift_b, 1,
+      inp->shift_func, inp->shift_func_ctx);
+    gkyl_eval_on_nodes_advance(evup, 0.0, &up->shear_r, up->shift_dg);
+    gkyl_eval_on_nodes_release(evup);
+  }
+  else {
+    // The shift must be discretized on the shear cells this updater indexes.
+    assert(inp->shift_dg->size == up->shear_r.volume);
+    assert(inp->shift_dg->ncomp == up->shift_b.num_basis);
+    up->shift_dg = gkyl_array_acquire(inp->shift_dg);
+  }
+
+  // Function defining the shift (and its context).
+  if (shift_func_op == 0) {
+    up->shift_func = ts_shift_dg_eval;
+    up->shift_dg_eval_ctx.shift_dg = up->shift_dg;
+    up->shift_dg_eval_ctx.shift_b = &up->shift_b;
+    up->shift_dg_eval_ctx.shear_grid = &up->shear_grid;
+    up->shift_dg_eval_ctx.shear_r = &up->shear_r;
+    up->shift_func_ctx = &up->shift_dg_eval_ctx;
+  }
+  else if (shift_func_op == 1) {
+    up->shift_func     = inp->shift_func;
+    up->shift_func_ctx = inp->shift_func_ctx;
+  }
+  else {
+    fprintf(stderr, "Twist-shift function option not recognized. Exiting...\n");
+    assert(false);
+  }
+
+  // Find the donor cells for each target. Store the number of donors for each
+  // shear_dir idx (num_do) & the shift_dir idx of each donor (shift_dir_idx_do).
+  // i.e. allocates and assigns num_do and up->shift_dir_idx_do.
+  ts_find_donors(up);
+
+  // Array of cummulative number of donors at given shear_dir cell.
+  const int num_do_cum_sz = up->grid.cells[up->shear_dir]+1;
+  int num_do_cum_ho[num_do_cum_sz];
+  for (int i=0; i<num_do_cum_sz; i++)
+    num_do_cum_ho[i] = 0;
+  for (int i=up->shear_r.lower[0]; i<up->shear_r.upper[0]+1; i++)
+    num_do_cum_ho[i] = num_do_cum_ho[i-1] + up->num_do[i-up->shear_r.lower[0]];
+
+  if (!up->use_gpu) {
+    up->num_do_cum = gkyl_malloc(num_do_cum_sz * sizeof(int));
+    memcpy(up->num_do_cum, num_do_cum_ho, num_do_cum_sz * sizeof(int));
+  }
+#ifdef GKYL_HAVE_CUDA
+  if (up->use_gpu) {
+    up->num_do_cum = gkyl_cu_malloc(num_do_cum_sz * sizeof(int));
+    gkyl_cu_memcpy(up->num_do_cum, num_do_cum_ho, num_do_cum_sz * sizeof(int), GKYL_CU_MEMCPY_H2D);
+  }
+#endif
+
+  // Choose the kernels that do the subcell and full cell integrals
+  up->kernels = gkyl_malloc(sizeof(struct gkyl_twistshift_dg_kernels));
+  gkyl_twistshift_dg_choose_kernels(*inp->basis, inp->cdim, up->shift_poly_order, up->kernels);
+
+  // The BC is applied as a set of matrix-matrix multiplications
+  //   f_i = sum_{q}^{N_do(i)} A_q,i B_q,i
+  // where i indicates the shear_dir cell index, A_q is a
+  // num_basis x num_basis matrix containing the discretization
+  // of subcell integrals, B_q is a num_basis x (Ny * Nvpar * Nmu) matrix with
+  // the DG coefficients of f common to a given A_q matrix, and thus where f_i
+  // is a num_basis x (Ny*Nvpar*Nmu) matrix.
+  //
+  // Naming scheme:
+  //   A_q: scimat (subscell integral matrices).
+  //   B_q: fmat (distribution function matrices).
+  //   A_q . B_q: mm_contr (contributions from mat-mat multiplication).
+
+  // Calculate the entries in the matrices used to apply the BC.
+  up->scimat = ts_calc_mats(up);
+
+  // Number of colums in fmat.
+  int fmat_num_col = 1;
+  for (int d=0; d<ndim; d++) {
+    if (d != up->bc_dir && d != up->shear_dir)
+      fmat_num_col *= up->local_bcdir_ext_r.upper[d] - up->local_bcdir_ext_r.lower[d] + 1;
+  }
+
+  if (!up->use_gpu) {
+    up->fmat = gkyl_nmat_new(up->scimat->num, up->scimat->nr, fmat_num_col);
+    up->mm_contr = gkyl_nmat_new(up->scimat->num, up->scimat->nr, fmat_num_col);
+  }
+#ifdef GKYL_HAVE_CUDA
+  if (up->use_gpu) {
+    up->fmat = gkyl_nmat_cu_dev_new(up->scimat->num, up->scimat->nr, fmat_num_col);
+    up->mm_contr = gkyl_nmat_cu_dev_new(up->scimat->num, up->scimat->nr, fmat_num_col);
+  }
+#endif
+
+  // Index translation from num-numcol plane index to linear index into the
+  // donor distribution function gkyl_array.
+  up->num_numcol_fidx_do = ts_calc_num_numcol_fidx_do(up);
+
+  // Index translation from num-numcol plane index to linear index into the
+  // tar distribution function gkyl_array.
+  up->num_numcol_fidx_tar = ts_calc_num_numcol_fidx_tar(up);
+
+  // Permutted ghost range, for indexing into the target field.
+  // Order: Shift direction, redundant directions, shear direction.
+  int lo4D[ndim-1], up4D[ndim-1];
+  lo4D[0] = up->local_bcdir_ext_r.lower[up->shift_dir];
+  up4D[0] = up->local_bcdir_ext_r.upper[up->shift_dir];
+  int ic = 1;
+  for (int d=0; d<ndim; d++) {
+    if (d != up->bc_dir && d != up->shear_dir && d != up->shift_dir) {
+      lo4D[ic] = up->local_bcdir_ext_r.lower[d];
+      up4D[ic] = up->local_bcdir_ext_r.upper[d];
+      ic++;
+    }
+  }
+  lo4D[ndim-2] = up->local_bcdir_ext_r.lower[up->shear_dir];
+  up4D[ndim-2] = up->local_bcdir_ext_r.upper[up->shear_dir];
+  gkyl_range_init(&up->permutted_ghost_r, ndim-1, lo4D, up4D);
+
+  // Create a ghost range, to clear it before adding contributions from TS BC.
+  if (inp->edge == GKYL_LOWER_EDGE)
+    gkyl_range_shorten_from_above(&up->ghost_r, &up->local_bcdir_ext_r, inp->bc_dir, inp->num_ghost[inp->bc_dir]);
+  else
+    gkyl_range_shorten_from_below(&up->ghost_r, &up->local_bcdir_ext_r, inp->bc_dir, inp->num_ghost[inp->bc_dir]);
+
+  return up;
+}
+
+struct gkyl_twistshift_dg*
+gkyl_twistshift_dg_new(int bc_dir, int shift_dir, int shear_dir,
+  enum gkyl_edge_loc edge, int cdim, const struct gkyl_range *bcdir_ext_update_r, const int *num_ghost,
+  const struct gkyl_basis *basis, const struct gkyl_rect_grid *grid, evalf_t shift_func, void *shift_func_ctx,
+  struct gkyl_array *shift_dg, int shift_poly_order, bool use_gpu)
+{
+  struct gkyl_twistshift_dg_inp inp = {
+    .bc_dir              = bc_dir            ,
+    .shift_dir           = shift_dir         ,
+    .shear_dir           = shear_dir         ,
+    .edge                = edge              ,
+    .cdim                = cdim              ,
+    .bcdir_ext_update_r  = bcdir_ext_update_r,
+    .num_ghost           = num_ghost         ,
+    .basis               = basis             ,
+    .grid                = grid              ,
+    .shift_func          = shift_func        ,
+    .shift_func_ctx      = shift_func_ctx    ,
+    .shift_dg            = shift_dg          ,
+    .use_gpu             = use_gpu           ,
+    .shift_poly_order    = shift_poly_order  ,
+  };
+  return gkyl_twistshift_dg_inew(&inp);
+}
+
+void
+gkyl_twistshift_dg_advance(struct gkyl_twistshift_dg *up, struct gkyl_array *fdo, struct gkyl_array *ftar)
+{
+
+#ifdef GKYL_HAVE_CUDA
+  if (up->use_gpu) {
+    gkyl_twistshift_dg_advance_cu(up, fdo, ftar);
+    return;
+  }
+#endif
+
+  // Assign the distribution matrices.
+  // This assumes that fdo->ncomp = fmat->nr.
+  // Recall:
+  //   fmat->num = sum_i^Nx num_do(i)
+  //   fmat->nr = num_basis = ncomp
+  //   fmat->nc = Ny*Nvpar*Nmu
+  for (size_t i=0; i<up->fmat->num * up->fmat->nr * up->fmat->nc; i++) {
+
+    long nc_idx = i / up->fmat->nr; // num-num_col index: current num-num_col plane.
+    int row_idx = i % up->fmat->nr; // row index: current DG coeff.
+
+    // This if-statement may only be needed in GPU kernel, not for CPUs.
+    if ((nc_idx < up->fmat->num * up->fmat->nc) && (row_idx < fdo->ncomp)) {
+      const double *fdo_c = (const double*) gkyl_array_cfetch(fdo, up->num_numcol_fidx_do[nc_idx]);
+      struct gkyl_mat mcurr = gkyl_nmat_get(up->fmat, nc_idx % up->fmat->num);
+
+      gkyl_mat_set(&mcurr, row_idx, nc_idx/up->fmat->num, fdo_c[row_idx]);
+    }
+  }
+
+  // Perform the mat-mat multiplications.
+  gkyl_nmat_mm(1.0, 0.0, GKYL_NO_TRANS, up->scimat, GKYL_NO_TRANS, up->fmat, up->mm_contr);
+
+  // Clear the ghost range.
+  gkyl_array_clear_range(ftar, 0.0, &up->ghost_r);
+
+  // Perform reduction over num_do contributions from mat-mat mults (mm_contr).
+  int num_cells_skin = (up->shear_r.upper[0]-up->shear_r.lower[0]+1) * up->fmat->nc;
+  for (size_t i=0; i<ftar->ncomp * num_cells_skin; i++) {
+
+    long linidx_tar = i / ftar->ncomp;
+    int row_idx = i % ftar->ncomp;
+
+    // This if-statement may only be needed in GPU kernel, not for CPUs.
+    if ((linidx_tar < num_cells_skin) && (row_idx < ftar->ncomp)) {
+      double *ftar_c = (double*) gkyl_array_fetch(ftar, up->num_numcol_fidx_tar[linidx_tar]);
+
+      int idx[GKYL_MAX_DIM] = {1};
+      gkyl_sub_range_inv_idx(&up->permutted_ghost_r, linidx_tar, idx);
+
+      int ac[GKYL_MAX_DIM] = {1};
+      for (int d=2; d<up->grid.ndim-1; d++)
+        ac[d-2] = up->grid.cells[d+1];
+      ac[up->permutted_ghost_r.ndim-2] = up->mm_contr->num;
+  
+      int start = 0;
+      for (int d=0; d<up->permutted_ghost_r.ndim-1; d++)
+        start = (start + (idx[d]-1)) * ac[d];
+
+      int shear_idx = idx[up->permutted_ghost_r.ndim-1];
+
+      int do_start = up->num_do_cum[shear_idx-1];
+      int do_end   = up->num_do_cum[shear_idx-1+1];
+      for (int j=do_start; j<do_end; j++) { // Only loop over num_do[i] elements.
+        long linidx_mm_contr = start + j;
+        struct gkyl_mat mat = gkyl_nmat_get(up->mm_contr, linidx_mm_contr % up->mm_contr->num);
+        ftar_c[row_idx] += gkyl_mat_get(&mat, row_idx, linidx_mm_contr / up->mm_contr->num);
+      }
+    }
+  }
+}
+
+struct gkyl_array*
+gkyl_twistshift_dg_get_shift_objects(struct gkyl_twistshift_dg *up, struct gkyl_rect_grid *shear_grid,
+  struct gkyl_range *shear_r, struct gkyl_basis *shift_b)
+{
+  *shear_grid = up->shear_grid;
+  *shear_r    = up->shear_r   ;
+  *shift_b    = up->shift_b   ;
+  return gkyl_array_acquire(up->shift_dg);
+};
+
+void
+gkyl_twistshift_dg_release(struct gkyl_twistshift_dg *up) {
+  // Release memory associated with this updater.
+  if (!up->use_gpu) {
+    gkyl_free(up->num_do_cum);
+    gkyl_free(up->num_numcol_fidx_do);
+    gkyl_free(up->num_numcol_fidx_tar);
+  }
+#ifdef GKYL_HAVE_CUDA
+  if (up->use_gpu) {
+    gkyl_cu_free(up->num_do_cum);
+    gkyl_cu_free(up->num_numcol_fidx_do);
+    gkyl_cu_free(up->num_numcol_fidx_tar);
+  }
+#endif
+
+  gkyl_nmat_release(up->fmat);
+  gkyl_nmat_release(up->mm_contr);
+
+  gkyl_nmat_release(up->scimat);
+
+  gkyl_free(up->kernels);
+
+  gkyl_array_release(up->shift_dg);
+
+  gkyl_free(up->num_do);
+  gkyl_free(up->shift_dir_idx_do);
+
+  gkyl_free(up);
+}
diff --git a/gyrokinetic/zero/bc_twistshift_cu.cu b/gyrokinetic/zero/twistshift_dg_cu.cu
similarity index 89%
rename from gyrokinetic/zero/bc_twistshift_cu.cu
rename to gyrokinetic/zero/twistshift_dg_cu.cu
index f4cbbecab7..a9987ffc92 100644
--- a/gyrokinetic/zero/bc_twistshift_cu.cu
+++ b/gyrokinetic/zero/twistshift_dg_cu.cu
@@ -8,8 +8,8 @@ extern "C" {
 #include <gkyl_array_ops.h>
 #include <gkyl_mat.h>
 #include <gkyl_util.h>
-#include <gkyl_bc_twistshift.h>
-#include <gkyl_bc_twistshift_priv.h>
+#include <gkyl_twistshift_dg.h>
+#include <gkyl_twistshift_dg_priv.h>
 }
 
 #include <cstdio>
@@ -19,7 +19,7 @@ extern "C" {
 #define START_ID (threadIdx.x + blockIdx.x*blockDim.x)
 
 __global__ void
-gkyl_bc_twistshift_set_distf_mats_cu_ker(const struct gkyl_array *fdo, const long *num_numcol_fidx_do, struct gkyl_nmat *fmat)
+gkyl_twistshift_dg_set_distf_mats_cu_ker(const struct gkyl_array *fdo, const long *num_numcol_fidx_do, struct gkyl_nmat *fmat)
 {
   // Assign the distribution matrices.
   // This assumes that fdo->ncomp = fmat->nr.
@@ -40,7 +40,7 @@ gkyl_bc_twistshift_set_distf_mats_cu_ker(const struct gkyl_array *fdo, const lon
 }
 
 __global__ void
-gkyl_bc_twistshift_add_contr_cu_ker(struct gkyl_array *ftar, long *num_numcol_fidx_tar, int num_cells_skin,
+gkyl_twistshift_dg_add_contr_cu_ker(struct gkyl_array *ftar, long *num_numcol_fidx_tar, int num_cells_skin,
   struct gkyl_nmat *mm_contr, int *num_do_cum, struct gkyl_range permutted_ghost_r, struct gkyl_rect_grid grid)
 {
   long linidx_tar = START_ID / ftar->ncomp;
@@ -75,11 +75,11 @@ gkyl_bc_twistshift_add_contr_cu_ker(struct gkyl_array *ftar, long *num_numcol_fi
 }
 
 void
-gkyl_bc_twistshift_advance_cu(struct gkyl_bc_twistshift *up, struct gkyl_array *fdo, struct gkyl_array *ftar)
+gkyl_twistshift_dg_advance_cu(struct gkyl_twistshift_dg *up, struct gkyl_array *fdo, struct gkyl_array *ftar)
 {
   // Set the columns of the donor matrix with the donor distributions.
   int num_blocks_set = (up->fmat->num * up->fmat->nr * up->fmat->nc+GKYL_DEFAULT_NUM_THREADS-1)/GKYL_DEFAULT_NUM_THREADS;
-  gkyl_bc_twistshift_set_distf_mats_cu_ker<<<num_blocks_set, GKYL_DEFAULT_NUM_THREADS>>>
+  gkyl_twistshift_dg_set_distf_mats_cu_ker<<<num_blocks_set, GKYL_DEFAULT_NUM_THREADS>>>
     (fdo->on_dev, up->num_numcol_fidx_do, up->fmat->on_dev);
 
   // Perform the mat-mat multiplications.
@@ -91,7 +91,7 @@ gkyl_bc_twistshift_advance_cu(struct gkyl_bc_twistshift *up, struct gkyl_array *
   // Add the contributions of mat-vec multiplications.
   int num_cells_skin = (up->shear_r.upper[0]-up->shear_r.lower[0]+1) * up->fmat->nc;
   int num_blocks_add = (ftar->ncomp * num_cells_skin+GKYL_DEFAULT_NUM_THREADS-1)/GKYL_DEFAULT_NUM_THREADS;
-  gkyl_bc_twistshift_add_contr_cu_ker<<<num_blocks_add,GKYL_DEFAULT_NUM_THREADS>>>
+  gkyl_twistshift_dg_add_contr_cu_ker<<<num_blocks_add,GKYL_DEFAULT_NUM_THREADS>>>
     (ftar->on_dev, up->num_numcol_fidx_tar, num_cells_skin, up->mm_contr->on_dev,
      up->num_do_cum, up->permutted_ghost_r, up->grid);
 }