Enforce bit-for-bit symmetry in gen_spd matrix generation - #33
Merged
Conversation
…under icpx mkl_potrf_suites failed on Icelake with icpx (default -fp-model=fast) for the row-major cases at n=30 and n=43: row uplo=L V=8 nm=8 n=30 | ... untouched 1e-15 FAIL row uplo=U V=8 nm=11 n=43 | ... untouched 2e-15 FAIL This is not a factorization or tolerance problem: the reconstruction residual, the elementwise-vs-LAPACK factor and every column-major case pass with wide margin. The input is at fault. A = M^T M is symmetric in exact arithmetic, but under a value-unsafe FP model the dot products for A(i,j) and A(j,i) can round a ULP apart. suite1's row-major "opposite triangle untouched" gate unpacks the factor row-major, which reads the transpose partner, so it effectively compares A(j,i) against A(i,j); a sub-ULP asymmetry there masquerades as the kernel having written the wrong triangle. gcc and clang keep the product bit-symmetric, so it only surfaced on icpx. Mirror the lower triangle onto the upper at the end of gen_spd so A(j,i) equals A(i,j) bit-for-bit on every compiler and FP model. The cond>0 congruence scales A(i,j) and A(j,i) by the same si*sj, so mirroring last preserves it. Verified with icpx 2025.2 -O3 -xHOST: gen_spd asymmetry drops from 1.3e-15 (n=30) / 1.8e-15 (n=43) to 0, a faithful MKL-free model of the suite1 pack/factor/unpack path goes from the reported 4 failures to all checks passing, and portable_potrf still passes under gcc, icpx, and icpx -xHOST. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01K4dGBpSViJAgHSxYxzin9L
Comment-only: same explanation, clearer phrasing. No behavior change. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01K4dGBpSViJAgHSxYxzin9L
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Summary
This change ensures that the symmetric positive-definite (SPD) matrix generated by
gen_spd()is exactly symmetric bit-for-bit by explicitly mirroring the lower triangle onto the upper triangle after the congruence transformation.Key Changes
-fp-model=fast)Implementation Details
The change addresses a subtle but critical issue: while
A = M^T Mis mathematically symmetric, the computed dot products forA(i,j)andA(j,i)may differ by one ULP depending on the floating-point model used. Some compilers with aggressive FP optimizations can produce asymmetric results.The fix mirrors the lower triangle onto the upper triangle after the congruence scaling (
D A D), which preserves the symmetry properties while enforcing exact bit-for-bit equality. This is essential for row-major unpacking tests that read the transpose partner and compareA(j,i)againstA(i,j)— even sub-ULP asymmetries would otherwise be misinterpreted as kernel errors.https://claude.ai/code/session_01K4dGBpSViJAgHSxYxzin9L