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The CGEMM micro-kernel built every complex product into a temporary and
then added it to the accumulator:
tmp = vfmul(Ai, Bi); tmp = VFMACC(tmp, Br, Ar); ACC = vfadd(ACC, tmp)
Three vector instructions per accumulator and k-step. The two FMAs
write the same destination, so applying them straight to ACC yields the
same per-k-step sum for two instructions instead:
ACCr = VFMACC_RR( ACCr, Bi, Ai);
ACCr = VFMACC_RR( ACCr, Br, Ar);
ACCi = FOLD_OPA( ACCi, Br, Ai);
ACCi = FOLD_OPB( ACCi, Bi, Ar);
VFMACC_RR/VFMACC_RI already encode the +/- conjugation of the variant
being compiled, but the imaginary fold needs an op sequence that has no
existing macro, so it is spelled out per variant as FOLD_OPA/FOLD_OPB
next to them.
Two FMAs compose to a plain accumulation because vfmsac(x,u,v)=u*v-x and
vfmsac(vfmsac(a,u,v),w,y)=a+w*y-u*v, and likewise for vfmacc/vfnmsac.
The value added per k-step is therefore unchanged and the per-column
accumulation order is preserved. Only the FP rounding order differs, by
a few ULP; measured against an exact double reference the patched kernel
has the same error as the unpatched one.
A packed A element has its real and imaginary halves adjacent, so one
strided segment-2 load replaces the two separate strided loads.
Measured on a SpaceMiT X100 (2.2 GHz, single thread, ZVL256B), median of
three runs: cblas_cgemm +44.3% at 256, +45.0% at 512, +42.3% at 1024.
Tests: make tests returns 0; 125/125 utest and 1473/1473 extension tests
pass; the CBLAS L1/L2/L3 suites show no new failures.
Co-authored-by: Yuansheng <yuansheng@isrc.iscas.ac.cn>
Co-authored-by: Ning Tian <tianning24@iscas.ac.cn>
Signed-off-by: jiakai xu <xujiakai2025@iscas.ac.cn>
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The CGEMM micro-kernel for ZVL256B built every complex product into a temporary and then added it to the accumulator:
That is three vector instructions per accumulator and k-step. The two FMAs write the same destination, so applying them straight to ACC yields the same per-k-step sum for two instructions instead:
VFMACC_RR/VFMACC_RIalready encode the +/- conjugation of the variant being compiled, but the imaginary fold needs an op sequence that has no existing macro, so it is spelled out per variant asFOLD_OPA/FOLD_OPBnext to them.Two FMAs compose to a plain accumulation because
vfmsac(x,u,v)=u*v-xandvfmsac(vfmsac(a,u,v),w,y)=a+w*y-u*v, and likewise forvfmacc/vfnmsac. The value added per k-step is therefore unchanged and the per-column accumulation order is preserved. Only the FP rounding order differs, by a few ULP; measured against an exact double reference the patched kernel has the same error as the unpatched one.A packed A element has its real and imaginary halves adjacent, so one strided segment-2 load replaces the two separate strided loads.
Performance
Measured on a SpaceMiT X100 (2.2 GHz, single thread, ZVL256B), median of three runs:
cblas_cgemm+44.3% at 256, +45.0% at 512, +42.3% at 1024.Testing
make testsreturns 0; 125/125 utest and 1473/1473 extension tests pass; the CBLAS L1/L2/L3 suites show no new failures.