feat: log_approx_f32 polynomial natural log intrinsic - #31
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Eigen/Cephes-family approach — bit-level decomposition of x = m·2^e (frexp convention, m in [0.5, 1)), √2/2 rebalance to center the polynomial range, degree-8 Eigen-coefficient Horner in (m - 1), Cody-Waite recombine with e·ln(2). Avoids @llvm.log which LLVM scalarizes to per-lane libm logf. Verbatim Eigen MathFunctionsImpl.h coefficients (MPL2) kept at upstream's published double precision for diff-friendliness; the compiler truncates each to f32 at compile time. LN2_HI is exact in f32 (binary 0.10110001 1, 9 mantissa bits); LN2_LO carries the residual so e·ln(2) preserves precision for large e. Cody-Waite recombine order matters: small-magnitude terms first (-u²/2, then e·LN2_LO), dominant terms last (+u, then e·LN2_HI). Same discipline exp_poly_f32 uses for ldexp. Max abs error ~3e-6 across (0, +∞). Same f32-vector-only typeck shape as exp_poly_f32 and tanh_approx_f32. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
13 tests mirroring phase14_exp_poly.rs / phase14_tanh_approx.rs:
- at_one: smoke that log(1) = 0 in all 4 lanes.
- boundary_points (x4 + x8): powers of 2 across the f32 exponent
range (1/1024 to 1e9), transcendental constants (e, π), and the
rebalance boundary [√2/2, √2]. Absolute (not relative) error
≤ 3e-6 because log(x) → 0 as x → 1 makes relative error explode
near 1.
- random (x4 + x8): 256 log-uniform samples over [exp(-4.6),
exp(4.6)] ≈ [0.01, 100] — covers the dense middle of the input
distribution.
- then_exp_poly_roundtrip: exp_poly_f32(log_approx_f32(x)) ≈ x to
1e-4 relative. Pins composition of the two intrinsics — they
share the Cody-Waite ln(2) discipline, so an order-of-operations
regression in either would surface here.
- does_not_emit_llvm_log: IR guard against future simplification
that delegates to @llvm.log (which LLVM scalarizes).
- emits_expected_pattern (x4 + x8): IR has ≥8 FMAs + lshr + float
↔ int bitcasts + sitofp.
- Four typeck rejections: scalar f32, f64x2, i32x4, wrong arity.
Boundary point constants use std::f32::consts::{FRAC_1_SQRT_2,
SQRT_2} per clippy's approx_constant lint.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
CHANGELOG entry under v1.14.0 Added. ROADMAP gets a Shipped entry; the Future API consistency line is rewritten from a three-item bullet (tanh/log/sin_cos) to just sin_cos_approx_f32 — the remaining transcendental in the original trio, kept as speculative until a real consumer asks (angle range, periodicity strategy, and sin-vs-cos-vs-pair API shape are all open design questions). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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Summary
log_approx_f32(v: f32xN) -> f32xNintrinsic — Eigen/Cephes-family polynomial natural log. Bit-level decomposition ofx = m · 2^e(frexp convention,m ∈ [0.5, 1)), √2/2 rebalance, degree-8 Horner in(m - 1), Cody-Waite recombine withe · ln(2).(0, +∞). Composes cleanly withexp_poly_f32— pin-tested via a roundtrip kernel at ~1e-4 relative.@llvm.log.v*f32, which LLVM scalarizes to per-lane libmlogf.Family progress
exp_poly_f32tanh_approx_f32log_approx_f32sin_cos_approx_f32ROADMAP "Future API consistency" line trimmed accordingly — only
sin_cos_approx_f32remains, with open design questions on angle range, periodicity strategy, and API shape.Cody-Waite ln(2) discipline
The recombine order matters: small-magnitude terms first (
-u²/2, thene · LN2_LO), dominant terms last (+u, thene · LN2_HI). Same disciplineexp_poly_f32uses for ldexp; thethen_exp_poly_roundtriptest pins that both intrinsics keep this contract.Test plan
cargo test --features llvm --release— 937 tests pass (924 baseline + 13 new)cargo clippy --features llvm --all-targets— cleancargo fmt --check— cleanlog_approx_f32(splat(1.0))returns 0 (smoke)logf: powers of 2 from 1/1024 to 1e9,e,π, the √2/2 rebalance boundary; abs error ≤ 3e-6[0.01, 100]for f32x4 and f32x8exp_poly_f32(log_approx_f32(x)) ≈ xto 1e-4 relative (composition guard)@llvm.log; ≥8 FMAs;lshr <N x i32>; float↔int bitcasts;sitofp🤖 Generated with Claude Code