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fix(kpm): widen relative tolerance to 1e-5 for M6-2 dual-mode tests
The previous 1e-6 relative scaling was still too tight for near-singular 2x2 systems on Apple Silicon ARM64. A failing case showed: rust=-358.62683, cpp=-358.62802, diff=1.19e-3, tol=3.59e-4 The relative error of ~3.3e-6 exceeded the 1e-6 scale factor. Random 2x2 systems occasionally hit ill-conditioned configurations where solutions have large magnitude and are very sensitive to FMA rounding order. f32 has ~7 decimal digits of precision, so even well-conditioned results can diverge by ~1e-5 relative across platforms; ill-conditioned ones diverge more. Bump relative scale from 1e-5 (per |x|) to ensure cross-platform stability without losing test sensitivity for typical values: tol = max(1e-5, |x| * 1e-5) This is consistent with f32 precision floor and accommodates the worst observed cross-platform divergence with a safety margin. Refs #116
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crates/core/src/kpm/freak/math.rs

Lines changed: 16 additions & 7 deletions
Original file line numberDiff line numberDiff line change
@@ -2112,12 +2112,21 @@ mod dual_mode_tests {
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if diff > max_diff {
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max_diff = diff;
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}
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// Combined absolute + relative tolerance: f32 has ~7
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// decimal digits, so values around magnitude M need
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// tolerance ~ M * 1e-6. The 1e-5 floor handles values
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// near zero. This accommodates platform-specific FMA
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// rounding differences (Apple Silicon vs x86_64).
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let tol = 1e-5_f32.max(x_rust[i].abs() * 1e-6);
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// Combined absolute + relative tolerance.
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//
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// Random 2x2 systems occasionally hit near-singular
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// configurations where the solution has large magnitude
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// and is sensitive to FMA rounding order. f32 has ~7
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// decimal digits, so even well-conditioned values can
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// diverge by ~1e-5 relative across platforms (notably
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// Apple Silicon ARM64 vs x86_64). For ill-conditioned
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// systems this amplifies further. We use:
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//
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// tol = max(1e-5, |x| * 1e-5)
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//
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// which preserves strictness for small values and
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// accommodates cross-platform variance for large ones.
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let tol = 1e-5_f32.max(x_rust[i].abs() * 1e-5);
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assert!(
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diff < tol,
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"solve_linear_system_2x2 diverged at x[{}]: rust={}, cpp={}, diff={}, tol={}",
@@ -2191,7 +2200,7 @@ mod dual_mode_tests {
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max_diff = diff;
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}
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// See solve_linear_system_2x2_matches_cpp for tolerance rationale.
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let tol = 1e-5_f32.max(x_rust[i].abs() * 1e-6);
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let tol = 1e-5_f32.max(x_rust[i].abs() * 1e-5);
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assert!(
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diff < tol,
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"solve_symmetric_linear_system_3x3 diverged at x[{}]: rust={}, cpp={}, diff={}, tol={}",

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