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Naive Use of SSE Intrinsics

The implementation presented here uses SSE intrinsics. In my naive way of thinking I expected a compiler to produce this implementation on assembly level when optimizing the demo-pure-c micro kernel. However, no matter what attributes, optimization flags and tricks I used, the compiler never could optimize the demo-pure-c micro kernel to the performance level of this micro kernel.

Select the demo-naive-sse-with-intrinsics Branch

Again, we do a make clean before switching a branch:

$shell> cd ulmBLAS                                                       
$shell> make clean                                                       
for dir in src refblas test bench; do make -C $dir clean; done
rm -f  auxiliary/xerbla.o  level1/dasum.o level1/daxpy.o level1/dcopy.o level1/ddot.o level1/dnrm2.o level1/drot.o level1/drotg.o level1/drotm.o level1/drotmg.o level1/dscal.o level1/dswap.o level1/idamax.o  level3/dgemm.o level3/dgemm_nn.o level3/dsymm.o level3/stubs.o
rm -f  auxiliary/atl_xerbla.o  level1/atl_dasum.o level1/atl_daxpy.o level1/atl_dcopy.o level1/atl_ddot.o level1/atl_dnrm2.o level1/atl_drot.o level1/atl_drotg.o level1/atl_drotm.o level1/atl_drotmg.o level1/atl_dscal.o level1/atl_dswap.o level1/atl_idamax.o  level3/atl_dgemm.o level3/atl_dgemm_nn.o level3/atl_dsymm.o level3/atl_stubs.o
rm -f ../libulmblas.a
rm -f ../libatlulmblas.a
rm -f caxpy.o ccopy.o cdotc.o cdotu.o cgbmv.o cgemm.o cgemv.o cgerc.o cgeru.o chbmv.o chemm.o chemv.o cher.o cher2.o cher2k.o cherk.o chpmv.o chpr.o chpr2.o crotg.o cscal.o csrot.o csscal.o cswap.o csymm.o csyr2k.o csyrk.o ctbmv.o ctbsv.o ctpmv.o ctpsv.o ctrmm.o ctrmv.o ctrsm.o ctrsv.o dasum.o daxpy.o dcabs1.o dcopy.o ddot.o dgbmv.o dgemm.o dgemv.o dger.o dnrm2.o drot.o drotg.o drotm.o drotmg.o dsbmv.o dscal.o dsdot.o dspmv.o dspr.o dspr2.o dswap.o dsymm.o dsymv.o dsyr.o dsyr2.o dsyr2k.o dsyrk.o dtbmv.o dtbsv.o dtpmv.o dtpsv.o dtrmm.o dtrmv.o dtrsm.o dtrsv.o dzasum.o dznrm2.o icamax.o idamax.o isamax.o izamax.o lsame.o sasum.o saxpy.o scabs1.o scasum.o scnrm2.o scopy.o sdot.o sdsdot.o sgbmv.o sgemm.o sgemv.o sger.o snrm2.o srot.o srotg.o srotm.o srotmg.o ssbmv.o sscal.o sspmv.o sspr.o sspr2.o sswap.o ssymm.o ssymv.o ssyr.o ssyr2.o ssyr2k.o ssyrk.o stbmv.o stbsv.o stpmv.o stpsv.o strmm.o strmv.o strsm.o strsv.o xerbla.o xerbla_array.o zaxpy.o zcopy.o zdotc.o zdotu.o zdrot.o zdscal.o zgbmv.o zgemm.o zgemv.o zgerc.o zgeru.o zhbmv.o zhemm.o zhemv.o zher.o zher2.o zher2k.o zherk.o zhpmv.o zhpr.o zhpr2.o zrotg.o zscal.o zswap.o zsymm.o zsyr2k.o zsyrk.o ztbmv.o ztbsv.o ztpmv.o ztpsv.o ztrmm.o ztrmv.o ztrsm.o ztrsv.o
rm -f ../librefblas.a
rm -f  dblat1_ref  dblat3_ref  dblat1_ulm  dblat3_ulm *.SUMM
rm -f xdl1blastst libtstatlas.a l1blastst.o  ATL_cputime.o  ATL_epsilon.o  ATL_f77amax.o  ATL_f77asum.o  ATL_f77axpy.o  ATL_f77copy.o  ATL_f77dot.o  ATL_f77gemm.o  ATL_f77nrm2.o  ATL_f77rot.o  ATL_f77rotg.o  ATL_f77rotm.o  ATL_f77rotmg.o  ATL_f77scal.o  ATL_f77swap.o  ATL_f77symm.o  ATL_f77syr2k.o  ATL_f77syrk.o  ATL_f77trmm.o  ATL_f77trsm.o  ATL_flushcache.o  ATL_gediffnrm1.o  ATL_gegen.o  ATL_genrm1.o  ATL_infnrm.o  ATL_rand.o  ATL_set.o  ATL_synrm.o  ATL_trnrm1.o  ATL_vdiff.o  ATL_zero.o  ATL_df77wrap.o

Then we are checking out the demo-naive-sse-with-intrinsics branch:

$shell> git branch -a                                                    
* demo-pure-c
  master
  remotes/origin/HEAD -> origin/master
  remotes/origin/bench-atlas
  remotes/origin/bench-blis
  remotes/origin/bench-eigen
  remotes/origin/bench-mkl
  remotes/origin/blis-avx-microkernel
  remotes/origin/demo-naive-avx-with-intrinsics
  remotes/origin/demo-naive-sse-with-intrinsics
  remotes/origin/demo-naive-sse-with-intrinsics-unrolled
  remotes/origin/demo-pure-c
  remotes/origin/demo-sse-all-asm
  remotes/origin/demo-sse-all-asm-try-prefetching
  remotes/origin/demo-sse-all-asm-try-prefetching-v2
  remotes/origin/demo-sse-all-asm-with-prefetching
  remotes/origin/demo-sse-asm
  remotes/origin/demo-sse-asm-for-AB-loop
  remotes/origin/demo-sse-asm-unrolled
  remotes/origin/demo-sse-asm-unrolled-v2
  remotes/origin/demo-sse-asm-unrolled-v3
  remotes/origin/demo-sse-asm-unrolled-with-prefetch
  remotes/origin/demo-sse-intrinsics
  remotes/origin/demo-sse-intrinsics-for-AB-loop
  remotes/origin/demo-sse-intrinsics-v2
  remotes/origin/demo-sse-intrinsics-v3
  remotes/origin/demo-with-sse-intrinsics
  remotes/origin/master
  remotes/origin/trsm-assignment
  remotes/origin/trsm-pure-c
$shell> git checkout -B demo-naive-sse-with-intrinsics remotes/origin/demo-naive-sse-with-intrinsics       
Switched to a new branch 'demo-naive-sse-with-intrinsics'
Branch demo-naive-sse-with-intrinsics set up to track remote branch demo-naive-sse-with-intrinsics from origin.

Then we compile the project

$shell> make                                                             
make -C src
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o auxiliary/xerbla.o auxiliary/xerbla.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/dasum.o level1/dasum.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/daxpy.o level1/daxpy.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/dcopy.o level1/dcopy.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/ddot.o level1/ddot.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/dnrm2.o level1/dnrm2.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/drot.o level1/drot.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/drotg.o level1/drotg.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/drotm.o level1/drotm.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/drotmg.o level1/drotmg.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/dscal.o level1/dscal.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/dswap.o level1/dswap.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level1/idamax.o level1/idamax.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level3/dgemm.o level3/dgemm.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level3/dgemm_nn.o level3/dgemm_nn.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level3/dsymm.o level3/dsymm.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -c -o level3/stubs.o level3/stubs.c
ar cru ../libulmblas.a  auxiliary/xerbla.o  level1/dasum.o level1/daxpy.o level1/dcopy.o level1/ddot.o level1/dnrm2.o level1/drot.o level1/drotg.o level1/drotm.o level1/drotmg.o level1/dscal.o level1/dswap.o level1/idamax.o  level3/dgemm.o level3/dgemm_nn.o level3/dsymm.o level3/stubs.o
ranlib ../libulmblas.a
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o auxiliary/atl_xerbla.o auxiliary/xerbla.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_dasum.o level1/dasum.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_daxpy.o level1/daxpy.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_dcopy.o level1/dcopy.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_ddot.o level1/ddot.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_dnrm2.o level1/dnrm2.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_drot.o level1/drot.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_drotg.o level1/drotg.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_drotm.o level1/drotm.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_drotmg.o level1/drotmg.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_dscal.o level1/dscal.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_dswap.o level1/dswap.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_idamax.o level1/idamax.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level3/atl_dgemm.o level3/dgemm.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level3/atl_dgemm_nn.o level3/dgemm_nn.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level3/atl_dsymm.o level3/dsymm.c
gcc-4.8 -Wall -I. -O2  -msse3 -mfpmath=sse -fomit-frame-pointer -DFAKE_ATLAS -c -o level3/atl_stubs.o level3/stubs.c
ar cru ../libatlulmblas.a  auxiliary/atl_xerbla.o  level1/atl_dasum.o level1/atl_daxpy.o level1/atl_dcopy.o level1/atl_ddot.o level1/atl_dnrm2.o level1/atl_drot.o level1/atl_drotg.o level1/atl_drotm.o level1/atl_drotmg.o level1/atl_dscal.o level1/atl_dswap.o level1/atl_idamax.o  level3/atl_dgemm.o level3/atl_dgemm_nn.o level3/atl_dsymm.o level3/atl_stubs.o
ranlib ../libatlulmblas.a
make -C refblas
gfortran -fimplicit-none -O3 -c -o caxpy.o caxpy.f
gfortran -fimplicit-none -O3 -c -o ccopy.o ccopy.f
gfortran -fimplicit-none -O3 -c -o cdotc.o cdotc.f
gfortran -fimplicit-none -O3 -c -o cdotu.o cdotu.f
gfortran -fimplicit-none -O3 -c -o cgbmv.o cgbmv.f
gfortran -fimplicit-none -O3 -c -o cgemm.o cgemm.f
gfortran -fimplicit-none -O3 -c -o cgemv.o cgemv.f
gfortran -fimplicit-none -O3 -c -o cgerc.o cgerc.f
gfortran -fimplicit-none -O3 -c -o cgeru.o cgeru.f
gfortran -fimplicit-none -O3 -c -o chbmv.o chbmv.f
gfortran -fimplicit-none -O3 -c -o chemm.o chemm.f
gfortran -fimplicit-none -O3 -c -o chemv.o chemv.f
gfortran -fimplicit-none -O3 -c -o cher.o cher.f
gfortran -fimplicit-none -O3 -c -o cher2.o cher2.f
gfortran -fimplicit-none -O3 -c -o cher2k.o cher2k.f
gfortran -fimplicit-none -O3 -c -o cherk.o cherk.f
gfortran -fimplicit-none -O3 -c -o chpmv.o chpmv.f
gfortran -fimplicit-none -O3 -c -o chpr.o chpr.f
gfortran -fimplicit-none -O3 -c -o chpr2.o chpr2.f
gfortran -fimplicit-none -O3 -c -o crotg.o crotg.f
gfortran -fimplicit-none -O3 -c -o cscal.o cscal.f
gfortran -fimplicit-none -O3 -c -o csrot.o csrot.f
gfortran -fimplicit-none -O3 -c -o csscal.o csscal.f
gfortran -fimplicit-none -O3 -c -o cswap.o cswap.f
gfortran -fimplicit-none -O3 -c -o csymm.o csymm.f
gfortran -fimplicit-none -O3 -c -o csyr2k.o csyr2k.f
gfortran -fimplicit-none -O3 -c -o csyrk.o csyrk.f
gfortran -fimplicit-none -O3 -c -o ctbmv.o ctbmv.f
gfortran -fimplicit-none -O3 -c -o ctbsv.o ctbsv.f
gfortran -fimplicit-none -O3 -c -o ctpmv.o ctpmv.f
gfortran -fimplicit-none -O3 -c -o ctpsv.o ctpsv.f
gfortran -fimplicit-none -O3 -c -o ctrmm.o ctrmm.f
gfortran -fimplicit-none -O3 -c -o ctrmv.o ctrmv.f
gfortran -fimplicit-none -O3 -c -o ctrsm.o ctrsm.f
gfortran -fimplicit-none -O3 -c -o ctrsv.o ctrsv.f
gfortran -fimplicit-none -O3 -c -o dasum.o dasum.f
gfortran -fimplicit-none -O3 -c -o daxpy.o daxpy.f
gfortran -fimplicit-none -O3 -c -o dcabs1.o dcabs1.f
gfortran -fimplicit-none -O3 -c -o dcopy.o dcopy.f
gfortran -fimplicit-none -O3 -c -o ddot.o ddot.f
gfortran -fimplicit-none -O3 -c -o dgbmv.o dgbmv.f
gfortran -fimplicit-none -O3 -c -o dgemm.o dgemm.f
gfortran -fimplicit-none -O3 -c -o dgemv.o dgemv.f
gfortran -fimplicit-none -O3 -c -o dger.o dger.f
gfortran -fimplicit-none -O3 -c -o dnrm2.o dnrm2.f
gfortran -fimplicit-none -O3 -c -o drot.o drot.f
gfortran -fimplicit-none -O3 -c -o drotg.o drotg.f
gfortran -fimplicit-none -O3 -c -o drotm.o drotm.f
gfortran -fimplicit-none -O3 -c -o drotmg.o drotmg.f
gfortran -fimplicit-none -O3 -c -o dsbmv.o dsbmv.f
gfortran -fimplicit-none -O3 -c -o dscal.o dscal.f
gfortran -fimplicit-none -O3 -c -o dsdot.o dsdot.f
gfortran -fimplicit-none -O3 -c -o dspmv.o dspmv.f
gfortran -fimplicit-none -O3 -c -o dspr.o dspr.f
gfortran -fimplicit-none -O3 -c -o dspr2.o dspr2.f
gfortran -fimplicit-none -O3 -c -o dswap.o dswap.f
gfortran -fimplicit-none -O3 -c -o dsymm.o dsymm.f
gfortran -fimplicit-none -O3 -c -o dsymv.o dsymv.f
gfortran -fimplicit-none -O3 -c -o dsyr.o dsyr.f
gfortran -fimplicit-none -O3 -c -o dsyr2.o dsyr2.f
gfortran -fimplicit-none -O3 -c -o dsyr2k.o dsyr2k.f
gfortran -fimplicit-none -O3 -c -o dsyrk.o dsyrk.f
gfortran -fimplicit-none -O3 -c -o dtbmv.o dtbmv.f
gfortran -fimplicit-none -O3 -c -o dtbsv.o dtbsv.f
gfortran -fimplicit-none -O3 -c -o dtpmv.o dtpmv.f
gfortran -fimplicit-none -O3 -c -o dtpsv.o dtpsv.f
gfortran -fimplicit-none -O3 -c -o dtrmm.o dtrmm.f
gfortran -fimplicit-none -O3 -c -o dtrmv.o dtrmv.f
gfortran -fimplicit-none -O3 -c -o dtrsm.o dtrsm.f
gfortran -fimplicit-none -O3 -c -o dtrsv.o dtrsv.f
gfortran -fimplicit-none -O3 -c -o dzasum.o dzasum.f
gfortran -fimplicit-none -O3 -c -o dznrm2.o dznrm2.f
gfortran -fimplicit-none -O3 -c -o icamax.o icamax.f
gfortran -fimplicit-none -O3 -c -o idamax.o idamax.f
gfortran -fimplicit-none -O3 -c -o isamax.o isamax.f
gfortran -fimplicit-none -O3 -c -o izamax.o izamax.f
gfortran -fimplicit-none -O3 -c -o lsame.o lsame.f
gfortran -fimplicit-none -O3 -c -o sasum.o sasum.f
gfortran -fimplicit-none -O3 -c -o saxpy.o saxpy.f
gfortran -fimplicit-none -O3 -c -o scabs1.o scabs1.f
gfortran -fimplicit-none -O3 -c -o scasum.o scasum.f
gfortran -fimplicit-none -O3 -c -o scnrm2.o scnrm2.f
gfortran -fimplicit-none -O3 -c -o scopy.o scopy.f
gfortran -fimplicit-none -O3 -c -o sdot.o sdot.f
gfortran -fimplicit-none -O3 -c -o sdsdot.o sdsdot.f
gfortran -fimplicit-none -O3 -c -o sgbmv.o sgbmv.f
gfortran -fimplicit-none -O3 -c -o sgemm.o sgemm.f
gfortran -fimplicit-none -O3 -c -o sgemv.o sgemv.f
gfortran -fimplicit-none -O3 -c -o sger.o sger.f
gfortran -fimplicit-none -O3 -c -o snrm2.o snrm2.f
gfortran -fimplicit-none -O3 -c -o srot.o srot.f
gfortran -fimplicit-none -O3 -c -o srotg.o srotg.f
gfortran -fimplicit-none -O3 -c -o srotm.o srotm.f
gfortran -fimplicit-none -O3 -c -o srotmg.o srotmg.f
gfortran -fimplicit-none -O3 -c -o ssbmv.o ssbmv.f
gfortran -fimplicit-none -O3 -c -o sscal.o sscal.f
gfortran -fimplicit-none -O3 -c -o sspmv.o sspmv.f
gfortran -fimplicit-none -O3 -c -o sspr.o sspr.f
gfortran -fimplicit-none -O3 -c -o sspr2.o sspr2.f
gfortran -fimplicit-none -O3 -c -o sswap.o sswap.f
gfortran -fimplicit-none -O3 -c -o ssymm.o ssymm.f
gfortran -fimplicit-none -O3 -c -o ssymv.o ssymv.f
gfortran -fimplicit-none -O3 -c -o ssyr.o ssyr.f
gfortran -fimplicit-none -O3 -c -o ssyr2.o ssyr2.f
gfortran -fimplicit-none -O3 -c -o ssyr2k.o ssyr2k.f
gfortran -fimplicit-none -O3 -c -o ssyrk.o ssyrk.f
gfortran -fimplicit-none -O3 -c -o stbmv.o stbmv.f
gfortran -fimplicit-none -O3 -c -o stbsv.o stbsv.f
gfortran -fimplicit-none -O3 -c -o stpmv.o stpmv.f
gfortran -fimplicit-none -O3 -c -o stpsv.o stpsv.f
gfortran -fimplicit-none -O3 -c -o strmm.o strmm.f
gfortran -fimplicit-none -O3 -c -o strmv.o strmv.f
gfortran -fimplicit-none -O3 -c -o strsm.o strsm.f
gfortran -fimplicit-none -O3 -c -o strsv.o strsv.f
gfortran -fimplicit-none -O3 -c -o xerbla.o xerbla.f
gfortran -fimplicit-none -O3 -c -o xerbla_array.o xerbla_array.f
gfortran -fimplicit-none -O3 -c -o zaxpy.o zaxpy.f
gfortran -fimplicit-none -O3 -c -o zcopy.o zcopy.f
gfortran -fimplicit-none -O3 -c -o zdotc.o zdotc.f
gfortran -fimplicit-none -O3 -c -o zdotu.o zdotu.f
gfortran -fimplicit-none -O3 -c -o zdrot.o zdrot.f
gfortran -fimplicit-none -O3 -c -o zdscal.o zdscal.f
gfortran -fimplicit-none -O3 -c -o zgbmv.o zgbmv.f
gfortran -fimplicit-none -O3 -c -o zgemm.o zgemm.f
gfortran -fimplicit-none -O3 -c -o zgemv.o zgemv.f
gfortran -fimplicit-none -O3 -c -o zgerc.o zgerc.f
gfortran -fimplicit-none -O3 -c -o zgeru.o zgeru.f
gfortran -fimplicit-none -O3 -c -o zhbmv.o zhbmv.f
gfortran -fimplicit-none -O3 -c -o zhemm.o zhemm.f
gfortran -fimplicit-none -O3 -c -o zhemv.o zhemv.f
gfortran -fimplicit-none -O3 -c -o zher.o zher.f
gfortran -fimplicit-none -O3 -c -o zher2.o zher2.f
gfortran -fimplicit-none -O3 -c -o zher2k.o zher2k.f
gfortran -fimplicit-none -O3 -c -o zherk.o zherk.f
gfortran -fimplicit-none -O3 -c -o zhpmv.o zhpmv.f
gfortran -fimplicit-none -O3 -c -o zhpr.o zhpr.f
gfortran -fimplicit-none -O3 -c -o zhpr2.o zhpr2.f
gfortran -fimplicit-none -O3 -c -o zrotg.o zrotg.f
gfortran -fimplicit-none -O3 -c -o zscal.o zscal.f
gfortran -fimplicit-none -O3 -c -o zswap.o zswap.f
gfortran -fimplicit-none -O3 -c -o zsymm.o zsymm.f
gfortran -fimplicit-none -O3 -c -o zsyr2k.o zsyr2k.f
gfortran -fimplicit-none -O3 -c -o zsyrk.o zsyrk.f
gfortran -fimplicit-none -O3 -c -o ztbmv.o ztbmv.f
gfortran -fimplicit-none -O3 -c -o ztbsv.o ztbsv.f
gfortran -fimplicit-none -O3 -c -o ztpmv.o ztpmv.f
gfortran -fimplicit-none -O3 -c -o ztpsv.o ztpsv.f
gfortran -fimplicit-none -O3 -c -o ztrmm.o ztrmm.f
gfortran -fimplicit-none -O3 -c -o ztrmv.o ztrmv.f
gfortran -fimplicit-none -O3 -c -o ztrsm.o ztrsm.f
gfortran -fimplicit-none -O3 -c -o ztrsv.o ztrsv.f
ar cru ../librefblas.a caxpy.o ccopy.o cdotc.o cdotu.o cgbmv.o cgemm.o cgemv.o cgerc.o cgeru.o chbmv.o chemm.o chemv.o cher.o cher2.o cher2k.o cherk.o chpmv.o chpr.o chpr2.o crotg.o cscal.o csrot.o csscal.o cswap.o csymm.o csyr2k.o csyrk.o ctbmv.o ctbsv.o ctpmv.o ctpsv.o ctrmm.o ctrmv.o ctrsm.o ctrsv.o dasum.o daxpy.o dcabs1.o dcopy.o ddot.o dgbmv.o dgemm.o dgemv.o dger.o dnrm2.o drot.o drotg.o drotm.o drotmg.o dsbmv.o dscal.o dsdot.o dspmv.o dspr.o dspr2.o dswap.o dsymm.o dsymv.o dsyr.o dsyr2.o dsyr2k.o dsyrk.o dtbmv.o dtbsv.o dtpmv.o dtpsv.o dtrmm.o dtrmv.o dtrsm.o dtrsv.o dzasum.o dznrm2.o icamax.o idamax.o isamax.o izamax.o lsame.o sasum.o saxpy.o scabs1.o scasum.o scnrm2.o scopy.o sdot.o sdsdot.o sgbmv.o sgemm.o sgemv.o sger.o snrm2.o srot.o srotg.o srotm.o srotmg.o ssbmv.o sscal.o sspmv.o sspr.o sspr2.o sswap.o ssymm.o ssymv.o ssyr.o ssyr2.o ssyr2k.o ssyrk.o stbmv.o stbsv.o stpmv.o stpsv.o strmm.o strmv.o strsm.o strsv.o xerbla.o xerbla_array.o zaxpy.o zcopy.o zdotc.o zdotu.o zdrot.o zdscal.o zgbmv.o zgemm.o zgemv.o zgerc.o zgeru.o zhbmv.o zhemm.o zhemv.o zher.o zher2.o zher2k.o zherk.o zhpmv.o zhpr.o zhpr2.o zrotg.o zscal.o zswap.o zsymm.o zsyr2k.o zsyrk.o ztbmv.o ztbsv.o ztpmv.o ztpsv.o ztrmm.o ztrmv.o ztrsm.o ztrsv.o
ranlib ../librefblas.a
make -C test
gfortran dblat1.f -L.. -lrefblas -o dblat1_ref
dblat1.f:215.44:
               CALL STEST1(DNRM2(N,SX,INCX),STEMP,STEMP,SFAC)           
                                            1
Warning: Rank mismatch in argument 'strue1' at (1) (scalar and rank-1)
dblat1.f:219.44:
               CALL STEST1(DASUM(N,SX,INCX),STEMP,STEMP,SFAC)           
                                            1
Warning: Rank mismatch in argument 'strue1' at (1) (scalar and rank-1)
gfortran dblat3.f -L.. -lrefblas -o dblat3_ref
gfortran dblat1.f -L.. -lulmblas -o dblat1_ulm
dblat1.f:215.44:
               CALL STEST1(DNRM2(N,SX,INCX),STEMP,STEMP,SFAC)           
                                            1
Warning: Rank mismatch in argument 'strue1' at (1) (scalar and rank-1)
dblat1.f:219.44:
               CALL STEST1(DASUM(N,SX,INCX),STEMP,STEMP,SFAC)           
                                            1
Warning: Rank mismatch in argument 'strue1' at (1) (scalar and rank-1)
gfortran dblat3.f -L.. -lulmblas -o dblat3_ulm
make -C bench
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o l1blastst.o l1blastst.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_cputime.o ATL_cputime.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_epsilon.o ATL_epsilon.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77amax.o ATL_f77amax.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77asum.o ATL_f77asum.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77axpy.o ATL_f77axpy.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77copy.o ATL_f77copy.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77dot.o ATL_f77dot.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77gemm.o ATL_f77gemm.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77nrm2.o ATL_f77nrm2.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77rot.o ATL_f77rot.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77rotg.o ATL_f77rotg.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77rotm.o ATL_f77rotm.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77rotmg.o ATL_f77rotmg.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77scal.o ATL_f77scal.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77swap.o ATL_f77swap.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77symm.o ATL_f77symm.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77syr2k.o ATL_f77syr2k.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77syrk.o ATL_f77syrk.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77trmm.o ATL_f77trmm.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_f77trsm.o ATL_f77trsm.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_flushcache.o ATL_flushcache.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_gediffnrm1.o ATL_gediffnrm1.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_gegen.o ATL_gegen.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_genrm1.o ATL_genrm1.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_infnrm.o ATL_infnrm.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_rand.o ATL_rand.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_set.o ATL_set.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_synrm.o ATL_synrm.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_trnrm1.o ATL_trnrm1.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_vdiff.o ATL_vdiff.c
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o ATL_zero.o ATL_zero.c
gfortran   -c -o ATL_df77wrap.o ATL_df77wrap.f
ar r libtstatlas.a  ATL_cputime.o  ATL_epsilon.o  ATL_f77amax.o  ATL_f77asum.o  ATL_f77axpy.o  ATL_f77copy.o  ATL_f77dot.o  ATL_f77gemm.o  ATL_f77nrm2.o  ATL_f77rot.o  ATL_f77rotg.o  ATL_f77rotm.o  ATL_f77rotmg.o  ATL_f77scal.o  ATL_f77swap.o  ATL_f77symm.o  ATL_f77syr2k.o  ATL_f77syrk.o  ATL_f77trmm.o  ATL_f77trsm.o  ATL_flushcache.o  ATL_gediffnrm1.o  ATL_gegen.o  ATL_genrm1.o  ATL_infnrm.o  ATL_rand.o  ATL_set.o  ATL_synrm.o  ATL_trnrm1.o  ATL_vdiff.o  ATL_zero.o  ATL_df77wrap.o
ar: creating archive libtstatlas.a
ranlib libtstatlas.a
gfortran -o xdl1blastst l1blastst.o libtstatlas.a ../libatlulmblas.a ../librefblas.a
gfortran -o xdl3blastst l3blastst.o libtstatlas.a ../libatlulmblas.a ../librefblas.a

The Micro Kernel Algorithm

We merely optimize the update step

\[\mathbf{AB} \leftarrow \mathbf{AB} + \begin{pmatrix} a_{4l} \\ a_{4l+1} \\ a_{4l+2} \\ a_{4l+3}\end{pmatrix} \begin{pmatrix} b_{4l}, & b_{4l+1}, & b_{4l+2}, & b_{4l+3}\end{pmatrix}\]

by using SSE intrinsics. Looking at the original C code

for (l=0; l<kc; ++l) {
        for (j=0; j<NR; ++j) {
            for (i=0; i<MR; ++i) {
                AB[i+j*MR] += A[i]*B[j];
            }
        }
        A += MR;
        B += NR;
    }

we notice that in the most inner loop the value B[j] does not change. The natural idea is to compute this step as

\[\mathbf{AB} \leftarrow \mathbf{AB} + \begin{pmatrix} b_{4l} \begin{pmatrix} a_{4l} \\ a_{4l+1} \\ a_{4l+2} \\ a_{4l+3}\end{pmatrix}, & b_{4l+1} \begin{pmatrix} a_{4l} \\ a_{4l+1} \\ a_{4l+2} \\ a_{4l+3}\end{pmatrix}, & b_{4l+2} \begin{pmatrix} a_{4l} \\ a_{4l+1} \\ a_{4l+2} \\ a_{4l+3}\end{pmatrix}, & b_{4l+3} \begin{pmatrix} a_{4l} \\ a_{4l+1} \\ a_{4l+2} \\ a_{4l+3}\end{pmatrix} \end{pmatrix}\]

Let \(\mathbb{b}_{00}, \mathbb{b}_{11}, \mathbb{b}_{22}, \mathbb{b}_{33}\) and \(\mathbb{a}_{01}, \mathbb{a}_{23}\) denote SSE registers. We use this 6 registers to store the operands:

\[\begin{array}{llllll}\mathbb{b}_{00} \leftarrow \begin{pmatrix} b_{4l } \\ b_{4l } \end{pmatrix}, &\mathbb{b}_{11} \leftarrow \begin{pmatrix} b_{4l+1} \\ b_{4l+1} \end{pmatrix}, &\mathbb{b}_{22} \leftarrow \begin{pmatrix} b_{4l+2} \\ b_{4l+2} \end{pmatrix}, &\mathbb{b}_{33} \leftarrow \begin{pmatrix} b_{4l+3} \\ b_{4l+3} \end{pmatrix}, &\mathbb{a}_{01} \leftarrow \begin{pmatrix} a_{4l } \\ a_{4l+1} \end{pmatrix}, &\mathbb{a}_{23} \leftarrow \begin{pmatrix} a_{4l+2} \\ a_{4l+3} \end{pmatrix}\end{array}\]

Another 8 SSE registers denoted as \(\mathbb{ab}_{\cdot,\cdot}\) are used to represent \(\mathbf{AB}\):

\[\begin{array}{llll}\mathbb{ab}_{00,10} \leftarrow \begin{pmatrix} ab_{0,0} \\ ab_{1,0} \end{pmatrix}, &\mathbb{ab}_{01,11} \leftarrow \begin{pmatrix} ab_{0,1} \\ ab_{1,1} \end{pmatrix}, &\mathbb{ab}_{02,12} \leftarrow \begin{pmatrix} ab_{0,2} \\ ab_{1,2} \end{pmatrix}, &\mathbb{ab}_{03,13} \leftarrow \begin{pmatrix} ab_{0,3} \\ ab_{1,3} \end{pmatrix} \\[0.5cm]\mathbb{ab}_{20,30} \leftarrow \begin{pmatrix} ab_{2,0} \\ ab_{3,0} \end{pmatrix}, &\mathbb{ab}_{21,31} \leftarrow \begin{pmatrix} ab_{2,1} \\ ab_{3,1} \end{pmatrix}, &\mathbb{ab}_{22,32} \leftarrow \begin{pmatrix} ab_{2,2} \\ ab_{3,2} \end{pmatrix}, &\mathbb{ab}_{23,33} \leftarrow \begin{pmatrix} ab_{2,3} \\ ab_{3,3} \end{pmatrix}\end{array}\]

As our architecture has a total of 16 SSE registers we have two registers left. We use them for temporary results and denote them as \(\mathbb{tmp}_1\) and \(\mathbb{tmp}_2\).

A single update can now be computed as

Hereby \(\odot\) denotes the usual component wise multiplication of SSE registers. We also assume that previous to the first update step all the \(\mathbb{ab}\) registers are zero initialized.

Once we have completed the total of \(k_c\) updates we write the result back to memory into \(\mathbf{AB}\).

The dgemm_nn Code

Note that we also added an attribute for 16 byte alignment to the definition of local buffers _A, _B, _C and AB. Having a 16-byte alignment is required for the load and store intrinsics used in the micro kernel.

ulmBLAS/src/level3/dgemm_nn.c
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#include <ulmblas.h>
#include <stdio.h>
#include <emmintrin.h>

#define MC  384
#define KC  384
#define NC  4096

#define MR  4
#define NR  4

//
//  Local buffers for storing panels from A, B and C
//
static double _A[MC*KC] __attribute__ ((aligned (16)));
static double _B[KC*NC] __attribute__ ((aligned (16)));
static double _C[MR*NR] __attribute__ ((aligned (16)));

//
//  Packing complete panels from A (i.e. without padding)
//
static void
pack_MRxk(int k, const double *A, int incRowA, int incColA,
          double *buffer)
{
    int i, j;

    for (j=0; j<k; ++j) {
        for (i=0; i<MR; ++i) {
            buffer[i] = A[i*incRowA];
        }
        buffer += MR;
        A      += incColA;
    }
}

//
//  Packing panels from A with padding if required
//
static void
pack_A(int mc, int kc, const double *A, int incRowA, int incColA,
       double *buffer)
{
    int mp  = mc / MR;
    int _mr = mc % MR;

    int i, j;

    for (i=0; i<mp; ++i) {
        pack_MRxk(kc, A, incRowA, incColA, buffer);
        buffer += kc*MR;
        A      += MR*incRowA;
    }
    if (_mr>0) {
        for (j=0; j<kc; ++j) {
            for (i=0; i<_mr; ++i) {
                buffer[i] = A[i*incRowA];
            }
            for (i=_mr; i<MR; ++i) {
                buffer[i] = 0.0;
            }
            buffer += MR;
            A      += incColA;
        }
    }
}

//
//  Packing complete panels from B (i.e. without padding)
//
static void
pack_kxNR(int k, const double *B, int incRowB, int incColB,
          double *buffer)
{
    int i, j;

    for (i=0; i<k; ++i) {
        for (j=0; j<NR; ++j) {
            buffer[j] = B[j*incColB];
        }
        buffer += NR;
        B      += incRowB;
    }
}

//
//  Packing panels from B with padding if required
//
static void
pack_B(int kc, int nc, const double *B, int incRowB, int incColB,
       double *buffer)
{
    int np  = nc / NR;
    int _nr = nc % NR;

    int i, j;

    for (j=0; j<np; ++j) {
        pack_kxNR(kc, B, incRowB, incColB, buffer);
        buffer += kc*NR;
        B      += NR*incColB;
    }
    if (_nr>0) {
        for (i=0; i<kc; ++i) {
            for (j=0; j<_nr; ++j) {
                buffer[j] = B[j*incColB];
            }
            for (j=_nr; j<NR; ++j) {
                buffer[j] = 0.0;
            }
            buffer += NR;
            B      += incRowB;
        }
    }
}

//
//  Micro kernel for multiplying panels from A and B.
//
static void
dgemm_micro_kernel(int kc,
                   double alpha, const double *A, const double *B,
                   double beta,
                   double *C, int incRowC, int incColC)
{
    double AB[MR*NR] __attribute__ ((aligned (16)));

    // Cols of AB in SSE registers
    __m128d   ab_00_10, ab_20_30;
    __m128d   ab_01_11, ab_21_31;
    __m128d   ab_02_12, ab_22_32;
    __m128d   ab_03_13, ab_23_33;

    __m128d   a_01, a_23;
    __m128d   b_00, b_11, b_22, b_33;
    __m128d   tmp1, tmp2;

    int i, j, l;

    ab_00_10 = _mm_setzero_pd();
    ab_20_30 = _mm_setzero_pd();
    ab_01_11 = _mm_setzero_pd();
    ab_21_31 = _mm_setzero_pd();
    ab_02_12 = _mm_setzero_pd();
    ab_22_32 = _mm_setzero_pd();
    ab_03_13 = _mm_setzero_pd();
    ab_23_33 = _mm_setzero_pd();

//
//  Compute AB = A*B
//
    for (l=0; l<kc; ++l) {
        a_01 = _mm_load_pd(A);
        a_23 = _mm_load_pd(A+2);

        b_00 = _mm_load_pd1(B);
        b_11 = _mm_load_pd1(B+1);
        b_22 = _mm_load_pd1(B+2);
        b_33 = _mm_load_pd1(B+3);

        tmp1 = a_01;
        tmp2 = a_23;

        // col 0 of AB
        tmp1 = _mm_mul_pd(tmp1, b_00);
        tmp2 = _mm_mul_pd(tmp2, b_00);
        ab_00_10 = _mm_add_pd(tmp1, ab_00_10);
        ab_20_30 = _mm_add_pd(tmp2, ab_20_30);

        // col 1 of AB
        tmp1 = a_01;
        tmp2 = a_23;
        tmp1 = _mm_mul_pd(tmp1, b_11);
        tmp2 = _mm_mul_pd(tmp2, b_11);
        ab_01_11 = _mm_add_pd(tmp1, ab_01_11);
        ab_21_31 = _mm_add_pd(tmp2, ab_21_31);

        // col 2 of AB
        tmp1 = a_01;
        tmp2 = a_23;
        tmp1 = _mm_mul_pd(tmp1, b_22);
        tmp2 = _mm_mul_pd(tmp2, b_22);
        ab_02_12 = _mm_add_pd(tmp1, ab_02_12);
        ab_22_32 = _mm_add_pd(tmp2, ab_22_32);

        // col 3 of AB
        tmp1 = a_01;
        tmp2 = a_23;
        tmp1 = _mm_mul_pd(tmp1, b_33);
        tmp2 = _mm_mul_pd(tmp2, b_33);
        ab_03_13 = _mm_add_pd(tmp1, ab_03_13);
        ab_23_33 = _mm_add_pd(tmp2, ab_23_33);

        A += 4;
        B += 4;
    }

    _mm_store_pd(AB+ 0, ab_00_10);
    _mm_store_pd(AB+ 2, ab_20_30);

    _mm_store_pd(AB+ 4, ab_01_11);
    _mm_store_pd(AB+ 6, ab_21_31);

    _mm_store_pd(AB+ 8, ab_02_12);
    _mm_store_pd(AB+10, ab_22_32);

    _mm_store_pd(AB+12, ab_03_13);
    _mm_store_pd(AB+14, ab_23_33);

//
//  Update C <- beta*C
//
    if (beta==0.0) {
        for (j=0; j<NR; ++j) {
            for (i=0; i<MR; ++i) {
                C[i*incRowC+j*incColC] = 0.0;
            }
        }
    } else if (beta!=1.0) {
        for (j=0; j<NR; ++j) {
            for (i=0; i<MR; ++i) {
                C[i*incRowC+j*incColC] *= beta;
            }
        }
    }

//
//  Update C <- C + alpha*AB (note: the case alpha==0.0 was already treated in
//                                  the above layer dgemm_nn)
//
    if (alpha==1.0) {
        for (j=0; j<NR; ++j) {
            for (i=0; i<MR; ++i) {
                C[i*incRowC+j*incColC] += AB[i+j*MR];
            }
        }
    } else {
        for (j=0; j<NR; ++j) {
            for (i=0; i<MR; ++i) {
                C[i*incRowC+j*incColC] += alpha*AB[i+j*MR];
            }
        }
    }
}

//
//  Compute Y += alpha*X
//
static void
dgeaxpy(int           m,
        int           n,
        double        alpha,
        const double  *X,
        int           incRowX,
        int           incColX,
        double        *Y,
        int           incRowY,
        int           incColY)
{
    int i, j;


    if (alpha!=1.0) {
        for (j=0; j<n; ++j) {
            for (i=0; i<m; ++i) {
                Y[i*incRowY+j*incColY] += alpha*X[i*incRowX+j*incColX];
            }
        }
    } else {
        for (j=0; j<n; ++j) {
            for (i=0; i<m; ++i) {
                Y[i*incRowY+j*incColY] += X[i*incRowX+j*incColX];
            }
        }
    }
}

//
//  Compute X *= alpha
//
static void
dgescal(int     m,
        int     n,
        double  alpha,
        double  *X,
        int     incRowX,
        int     incColX)
{
    int i, j;

    if (alpha!=0.0) {
        for (j=0; j<n; ++j) {
            for (i=0; i<m; ++i) {
                X[i*incRowX+j*incColX] *= alpha;
            }
        }
    } else {
        for (j=0; j<n; ++j) {
            for (i=0; i<m; ++i) {
                X[i*incRowX+j*incColX] = 0.0;
            }
        }
    }
}

//
//  Macro Kernel for the multiplication of blocks of A and B.  We assume that
//  these blocks were previously packed to buffers _A and _B.
//
static void
dgemm_macro_kernel(int     mc,
                   int     nc,
                   int     kc,
                   double  alpha,
                   double  beta,
                   double  *C,
                   int     incRowC,
                   int     incColC)
{
    int mp = (mc+MR-1) / MR;
    int np = (nc+NR-1) / NR;

    int _mr = mc % MR;
    int _nr = nc % NR;

    int mr, nr;
    int i, j;

    for (j=0; j<np; ++j) {
        nr    = (j!=np-1 || _nr==0) ? NR : _nr;

        for (i=0; i<mp; ++i) {
            mr    = (i!=mp-1 || _mr==0) ? MR : _mr;

            if (mr==MR && nr==NR) {
                dgemm_micro_kernel(kc, alpha, &_A[i*kc*MR], &_B[j*kc*NR],
                                   beta,
                                   &C[i*MR*incRowC+j*NR*incColC],
                                   incRowC, incColC);
            } else {
                dgemm_micro_kernel(kc, alpha, &_A[i*kc*MR], &_B[j*kc*NR],
                                   0.0,
                                   _C, 1, MR);
                dgescal(mr, nr, beta,
                        &C[i*MR*incRowC+j*NR*incColC], incRowC, incColC);
                dgeaxpy(mr, nr, 1.0, _C, 1, MR,
                        &C[i*MR*incRowC+j*NR*incColC], incRowC, incColC);
            }
        }
    }
}

//
//  Compute C <- beta*C + alpha*A*B
//
void
dgemm_nn(int            m,
         int            n,
         int            k,
         double         alpha,
         const double   *A,
         int            incRowA,
         int            incColA,
         const double   *B,
         int            incRowB,
         int            incColB,
         double         beta,
         double         *C,
         int            incRowC,
         int            incColC)
{
    int mb = (m+MC-1) / MC;
    int nb = (n+NC-1) / NC;
    int kb = (k+KC-1) / KC;

    int _mc = m % MC;
    int _nc = n % NC;
    int _kc = k % KC;

    int mc, nc, kc;
    int i, j, l;

    double _beta;

    if (alpha==0.0 || k==0) {
        dgescal(m, n, beta, C, incRowC, incColC);
        return;
    }

    for (j=0; j<nb; ++j) {
        nc = (j!=nb-1 || _nc==0) ? NC : _nc;

        for (l=0; l<kb; ++l) {
            kc    = (l!=kb-1 || _kc==0) ? KC   : _kc;
            _beta = (l==0) ? beta : 1.0;

            pack_B(kc, nc,
                   &B[l*KC*incRowB+j*NC*incColB], incRowB, incColB,
                   _B);

            for (i=0; i<mb; ++i) {
                mc = (i!=mb-1 || _mc==0) ? MC : _mc;

                pack_A(mc, kc,
                       &A[i*MC*incRowA+l*KC*incColA], incRowA, incColA,
                       _A);

                dgemm_macro_kernel(mc, nc, kc, alpha, _beta,
                                   &C[i*MC*incRowC+j*NC*incColC],
                                   incRowC, incColC);
            }
        }
    }
}

Benchmark Results

We run the benchmarks

$shell> cd bench                                                         
$shell> ./xdl3blastst > report                                           
$shell> cat report                                                       
./xdl3blastst 
--------------------------------- GEMM ----------------------------------
TST# A B    M    N    K ALPHA  LDA  LDB  BETA  LDC  TIME MFLOP SpUp  TEST
==== = = ==== ==== ==== ===== ==== ==== ===== ==== ===== ===== ==== =====
   0 N N  100  100  100   1.0 1000 1000   1.0 1000  0.00 1798.6 1.00 -----
   0 N N  100  100  100   1.0 1000 1000   1.0 1000  0.00 3898.6 2.17 PASS 
   1 N N  200  200  200   1.0 1000 1000   1.0 1000  0.01 1949.6 1.00 -----
   1 N N  200  200  200   1.0 1000 1000   1.0 1000  0.00 4461.8 2.29 PASS 
   2 N N  300  300  300   1.0 1000 1000   1.0 1000  0.03 2018.2 1.00 -----
   2 N N  300  300  300   1.0 1000 1000   1.0 1000  0.01 4634.0 2.30 PASS 
   3 N N  400  400  400   1.0 1000 1000   1.0 1000  0.06 2017.5 1.00 -----
   3 N N  400  400  400   1.0 1000 1000   1.0 1000  0.03 4601.2 2.28 PASS 
   4 N N  500  500  500   1.0 1000 1000   1.0 1000  0.14 1837.7 1.00 -----
   4 N N  500  500  500   1.0 1000 1000   1.0 1000  0.05 4680.6 2.55 PASS 
   5 N N  600  600  600   1.0 1000 1000   1.0 1000  0.32 1337.4 1.00 -----
   5 N N  600  600  600   1.0 1000 1000   1.0 1000  0.09 4740.0 3.54 PASS 
   6 N N  700  700  700   1.0 1000 1000   1.0 1000  0.70 983.0 1.00 -----
   6 N N  700  700  700   1.0 1000 1000   1.0 1000  0.14 4770.6 4.85 PASS 
   7 N N  800  800  800   1.0 1000 1000   1.0 1000  0.98 1045.5 1.00 -----
   7 N N  800  800  800   1.0 1000 1000   1.0 1000  0.22 4752.8 4.55 PASS 
   8 N N  900  900  900   1.0 1000 1000   1.0 1000  1.38 1056.5 1.00 -----
   8 N N  900  900  900   1.0 1000 1000   1.0 1000  0.30 4783.0 4.53 PASS 
   9 N N 1000 1000 1000   1.0 1000 1000   1.0 1000  1.72 1160.3 1.00 -----
   9 N N 1000 1000 1000   1.0 1000 1000   1.0 1000  0.42 4805.7 4.14 PASS 
10 tests run, 10 passed

and filter out the results for the demo-naive-sse-with-intrinsics branch:

$shell> grep PASS report > demo-naive-sse-with-intrinsics

With the gnuplot script

ulmBLAS/bench/bench3.gps
set terminal svg size 940,480
set output "bench3.svg"
set xlabel "Matrix dimensions N=M=K"
set ylabel "MFLOPS"
set yrange [0:9600]
set title "Compute C + A*B"
set key outside
plot "refBLAS" using 4:13 with linespoints lt 2 title "Netlib RefBLAS", "demo-pure-c" using 4:13 with linespoints lt 4 title "demo-pure-c", "demo-naive-sse-with-intrinsics" using 4:13 with linespoints lt 5 title "demo-naive-sse-with-intrinsics"

we feed gnuplot

$shell> gnuplot bench3.gps

and get

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