AArch64 NRM2: recover finite results near overflow

[BenKnill]

Candidate repair for #6094. Adds an exact recovery path for large finite inputs to distinguish avoidable infinity from genuine overflow, retaining the existing ordinary-input arithmetic.

Tested in ARMV8 and NEOVERSEN1 configurations on native AArch64 Ubuntu using the 0.3.32 source tree. The same 12,148-case suite passed through CBLAS and Fortran in each configuration; existing unit tests also passed. Upstream regression-test integration, a full current-upstream build, and recovery-path timing remain outstanding.

The change covers the shared assembly kernels; zero-stride shortcuts, separate C kernels, and repeated-infinity behavior remain outside its scope.

Opened as a draft for discussion.

Opus 5.5 discovered this bug. GPT-6 Astra and GPT-6 Sol investigated and characterized the failure, then wrote and tested the candidate patch.

[martin-frbg]

Thanks - the nrm2_range recovery should live with the other arm64-specific files in kernel/arm64 in my opinion (driver/others is for general setup code), and ultimately I think this would probably be solved by adopting the more thorough NRM2 scaling introduced by the recent Reference BLAS - which unfortunately requires rewriting kernels across all architectures. (But I haven't run your reproducer against said Reference BLAS yet)

[BenKnill]

Thanks. Moved: nrm2_range.c is now in kernel/arm64, built once per library as an arm64-only common kernel object, as x86 builds cpuid.S. Its arm64-guarded build lines are in kernel/Makefile and kernel/CMakeLists.txt (the KERNEL.* files only set variables), and the PR no longer touches driver/others. For ARMV8 and NEOVERSEN1 the 12,148-case suite output is unchanged, with no spurious infinities in the tested cases.

Against Reference BLAS at LAPACK master 6de9594, the reproducer returns finite results in round-to-nearest, but its double-precision case returns inf under FE_UPWARD. A targeted search also found longer vectors whose exact norm is below DBL_MAX but which return inf in round-to-nearest. For example, this eight-element vector, about 0.05 ulp below DBL_MAX, returns inf on both arm64 and x86-64:

0x1.bd2788e9e8b9ap+1023 0x1.cb33a7ccd84f4p+1021 0x1.52c1bd33cfe1fp+1021 0x1.fb2a0fcb66de1p+1021
0x1.6c278b240b52dp+1021 0x1.1f0c45e85aa4dp+1021 0x1.27cf1d741ec94p+1021 0x1.73f734386dff4p+1021

These cases suggest that adopting the current Reference BLAS scaling would still leave some avoidable-overflow cases. The candidate recovery handles them in the tested arm64 builds.