feat: sin_approx_f32 + cos_approx_f32 — closes the transcendental family - #32
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Two intrinsics sharing a common range-reduction + polynomial core: reduce mod π/2 via 2-piece Cody-Waite (PI_2_HI exact f32, PI_2_LO negative residual; sum reproduces π/2 to ~2e-15 in f64), then compute both sin and cos polynomials over d' ∈ [-π/4, π/4]: - sin: degree-3 in s=d², covers d through d^7 — truncation ≤3.4e-7 - cos: degree-4 in s, covers d^0 through d^8 — truncation ≤2.6e-8 The cos variant reuses the same core with q += 1 — a precision-free integer shift expressing the mathematical identity cos(x) = sin(x + π/2). Adding π/2 to v before reduction would lose bits for large |v|; shifting the integer quadrant index after reduction is exact. Final blend: swap = (k & 1), negate = (k & 2). Both polynomials are always computed (~4 wasted FMAs) for branchless SIMD execution; LLVM CSE eliminates redundant range reduction at the caller level when both intrinsics see the same input. Max abs error ~3e-6 across the documented [-1e7, 1e7] range. Avoids @llvm.sin / @llvm.cos which LLVM scalarizes to per-lane libm sinf/cosf on every supported architecture. Pair-return form deferred — Eä has no precedent for multi-return intrinsics, and the established single-return pattern composes cleanly with the rest of the transcendental family. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
19 tests covering:
- at_zero (sin + cos): smoke that sin(0)=0 and cos(0)=1.
- boundary_points (sin × {x4, x8} + cos × {x4, x8}): vs libm
sinf/cosf across {-2π … 2π} plus moderate (10, 100) and edge
(1e6) inputs within the documented [-1e7, 1e7] range. Abs error
≤ 3e-6.
- random (sin × {x4, x8} + cos × x4): 256 LCG samples over [-10π,
10π] exercising range reduction over multiple quadrants.
- pythagorean_identity: pins sin²(x) + cos²(x) ≈ 1 to 6e-6 across
4 inputs. A regression in either intrinsic's q-handling would
surface here even if individual tolerance still passes.
- does_not_emit_llvm_sin_cos: IR guard against @llvm.sin/@llvm.cos
delegation (LLVM scalarizes both to libm).
- emits_expected_pattern (sin × {x4, x8}): IR has ≥6 FMAs +
@llvm.nearbyint + fptosi <N x float> → <N x i32>.
- Six typeck rejections (3 per intrinsic): scalar f32, f64x2,
integer vector; arity for sin.
An earlier draft of the Cody-Waite constants had a transcription
error (3-piece Sleef-derived values that didn't sum to π/2,
off by 6e-8). The boundary_points test caught it loudly — cos(1e6)
showed 0.014 error vs the 3e-6 tolerance. Fix was the 2-piece
Eigen-style split now in the source; lesson is to verify constants
against their claimed identity, not transcribe by eye.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
CHANGELOG entry under v1.14.0 Added. ROADMAP Shipped entry + collapses the Future API consistency section: the v1.11.0-era trio (tanh, log, sin/cos plus u16x32 and wider wmul_u64) is fully closed out by v1.14.0. The f32 transcendental approximation family is feature-complete; new entries land here as real consumers surface them. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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Summary
sin_approx_f32(v: f32xN) -> f32xNandcos_approx_f32(v: f32xN) -> f32xNintrinsics with a shared range-reduction + polynomial core.d' ∈ [-π/4, π/4](degree 3 ins = d'²for sin, degree 4 for cos), quadrant blend.cosreuses the same core viaq += 1— a precision-free integer shift expressingcos(x) = sin(x + π/2).[-1e7, 1e7]. Avoids@llvm.sin/@llvm.cos(LLVM scalarizes to per-lane libm).Closes the transcendental approximation family
The original "Future API consistency" trio (
tanh_approx_f32,log_approx_f32,sin_cos_approx_f32) is fully closed by v1.14.0:exp_poly_f32tanh_approx_f32log_approx_f32sin_approx_f32cos_approx_f32The f32 transcendental approximation family is feature-complete for typical SIMD workloads.
API shape: two intrinsics, not a pair-return
The roadmap line was
sin_cos_approx_f32(singular, pair-return). Shipping as two separate intrinsics because:If a real consumer benchmarks the pair form as significantly better, that's a follow-up with a different name.
Cody-Waite constants — verify-first reminder
An earlier draft used 3-piece values transcribed from Sleef. They didn't actually sum to π/2 (off by 6e-8). The
boundary_pointstest caught it:cos(1e6)showed 0.014 error vs the 3e-6 tolerance. Fix was a 2-piece Eigen-style split (PI_2_HI = closest f32 to π/2, PI_2_LO = -4.37e-8 residual; sum reproduces π/2 to ~2e-15 in f64). Documented in the post-mortem.Test plan
cargo test --features llvm --release— 943 tests pass (924 baseline + 19 new)cargo clippy --features llvm --all-targets— cleancargo fmt --check— cleansin(0) = 0,cos(0) = 1(smoke)sinf/cosf; abs error ≤ 3e-6[-10π, 10π]for f32x4 and f32x8sin²(x) + cos²(x) ≈ 1within 6e-6 (composition guard)@llvm.sin/@llvm.cos; ≥6 FMAs;@llvm.nearbyint;fptosi <N x float>🤖 Generated with Claude Code