The skylakex/cooperlake d/s/c/z asum and c/z sum microkernels peel leading
elements until the input pointer reaches a 64-byte boundary (a scalar loop in
dasum/sasum, a masked header load in the complex variants) before entering an
aligned-load accumulator loop. The peel count depends on the buffer address
mod 64, so the grouping of the sum into accumulators - and therefore the
rounding of the result - depends on where the caller's buffer happens to sit
in memory. The same data at a different address can give a bitwise-different
sum.
That address dependence surfaced as non-reproducibility in OrcaFlex: LAPACK's
dstein scales each inverse-iteration eigenvector by 1/dasum(...) over a heap
array whose alignment varies with allocation history, so eigenvectors from
identical inputs differed run to run in the last bits, which zero-tolerance
regression comparison flags.
Fix by dropping the alignment peel and using unaligned loads throughout, so
the summation order is a function of the length alone. On AVX-512 hardware
unaligned load instructions on addresses that happen to be aligned cost the
same as aligned loads; only genuinely split cache lines pay a small penalty,
negligible for these level-1 reductions.
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Commit def4996 fixed issues with inf and nan values in zscal,
but used FLT_MAX, where DBL_MAX or isinf() is more appropriate,
as FLT_MAX is for single precision only.
Using FLT_MAX caused test case failures in the LAPACK tests.
isinf() is consistent with the later fix 969601a1
for skylake kernels. This is the same method as used in [sd]asum.
_mm_set1_epi64x was commented out for zasum, but has the advantage
of avoiding possible undefined behaviour (using an uninitialized
variable), optimized out by NVHPC and icx. The new code works
fine with those compilers.
For GCC 12.3 the generated code is identical; no matter what method
you use, the compiler optimizes the code into a compile-time
constant, there is no performance benefit using mm_cmpeq_epi8
since the corresponding instruction (VPCMPEQB) isn't actually
generated!
This kernel is only used on Skylake+ if the kernel with AVX512
intrinsics can't be used, but used the variable x1 incorrectly
in the tail end of the loop, as it is still at the initial
value instead of where x points to.
This caused 55 "other error"s in the LAPACK tests
(https://github.com/OpenMathLib/OpenBLAS/issues/4282)
This change makes casum.c as similar as possible as zasum.c,
because zasum.c does this correctly.
David Heffernan