tests: pin exact golden values for deterministic math#3
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…margins) The library advertises bit-exact determinism, but several transcendental tests asserted only accuracy-vs-std within a tolerance (`fabs(lib - ref) < tol`), which does not verify reproducibility. Replace the fixed-input margins with exact `==` against the library's own output, turning them into determinism/regression locks that the multi-arch CI matrix (x64 + ARM, GCC/Clang/MSVC/AppleClang) now verifies. - test_cmath_double.cpp: sin_core, real-arith compose, sqrt(9), sin/cos(47°), sin(180°) → exact hex-float / exact constants (drop the unused std oracle + sv). - test_coverage_corners.cpp: d_cbrt / d_atan2 axis cases → exact golden doubles. - test_storage_flags.cpp: atan/atan2 on a real grid → exact grid values (verified bit-identical on BOTH the double and CORDIC engines). Kept margins only where they remain meaningful: range sweeps vs std (accuracy of the approximation) and the random-input fuzz harness (no fixed golden). Local: double 352/352, CORDIC 395/395. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
…grids New tests/test_determinism.cpp pins the exact (==) output of asin, acos, sinh, cosh, tanh, log10, hypot, pow — plus added corner cases for sqrt, cbrt, atan, atan2, sin, cos, tan — across a VARIETY of grids (notch 1/256…1/65536, different intervals, real storage) and domain corners (0, ±1, edges, axes, quadrants), and the sqrt error path. ~110 exact assertions; values captured from the library and verified bit-identical on BOTH engines except one coarse-grid sinh (per-engine #ifdef). Locks bit-exact determinism, now checked across the x64+ARM × GCC/Clang/ MSVC/AppleClang matrix. Local: double 361/361, CORDIC 404/404. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
…ue-identical State explicitly that the double and integer/CORDIC engines, while each bit-reproducible per engine, can differ by up to one output notch on some transcendental inputs (table-maker's dilemma — worked sinh(4) example), so switching engines is NOT value-preserving: golden/record-replay data is valid within one engine only. Corrects math.md's "interchangeable" / "value does not depend on the engine" claims; adds a per-engine caveat to determinism.md's TL;DR and a new subsection. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Per the determinism guarantee, fixed-input transcendental tests now assert the library's exact output (
==) instead of accuracy-within-a-margin (fabs(lib - std) < tol). A tolerance verifies accuracy, not the bit-exact reproducibility the library advertises; exact golden pins turn these into determinism/regression locks that the multi-arch matrix (x64 + ARM64 Linux, macOS ARM, MSVC x64 + ARM) verifies.test_cmath_double.cpp:sin_core, real-arithmetic compose,sqrt(9),sin/cos(47°),sin(180°)→ exact.test_coverage_corners.cpp:d_cbrt/d_atan2axis cases → exact golden doubles.test_storage_flags.cpp:atan/atan2on a real grid → exact grid values (bit-identical on both the double and CORDIC engines — confirmed locally).Kept margins only where they stay meaningful: range sweeps vs std (approximation accuracy) and the random-input fuzz harness (no fixed golden).
Local: double 352/352, CORDIC 395/395. This PR's cross-platform run is the real determinism check — if any golden pin fails on another compiler/arch, that's a genuine determinism finding to fix in the library.
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