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Improving Pipelining

Loading data from memory (even the L1 cache) into registers takes some CPU cycles. We have several loads in the update loop. Instead of waiting for all of them to complete we could try to do some useful work between the load calls.

This is another step to discover the brilliancy of the BLIS micro kernel!

Select the demo-sse-intrinsics-v2 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-v2 branch:

$shell> git branch -a                                                    
  demo-naive-sse-with-intrinsics
  demo-naive-sse-with-intrinsics-unrolled
  demo-pure-c
* demo-sse-intrinsics
  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-sse-intrinsics-v2 remotes/origin/demo-sse-intrinsics-v2            
Switched to a new branch 'demo-sse-intrinsics-v2'
Branch demo-sse-intrinsics-v2 set up to track remote branch demo-sse-intrinsics-v2 from origin.

Then we compile the project

$shell> make                                                             
make -C src
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o auxiliary/xerbla.o auxiliary/xerbla.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/dasum.o level1/dasum.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/daxpy.o level1/daxpy.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/dcopy.o level1/dcopy.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/ddot.o level1/ddot.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/dnrm2.o level1/dnrm2.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/drot.o level1/drot.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/drotg.o level1/drotg.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/drotm.o level1/drotm.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/drotmg.o level1/drotmg.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/dscal.o level1/dscal.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/dswap.o level1/dswap.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level1/idamax.o level1/idamax.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level3/dgemm.o level3/dgemm.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level3/dgemm_nn.o level3/dgemm_nn.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -c -o level3/dsymm.o level3/dsymm.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -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
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o auxiliary/atl_xerbla.o auxiliary/xerbla.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_dasum.o level1/dasum.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_daxpy.o level1/daxpy.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_dcopy.o level1/dcopy.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_ddot.o level1/ddot.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_dnrm2.o level1/dnrm2.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_drot.o level1/drot.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_drotg.o level1/drotg.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_drotm.o level1/drotm.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_drotmg.o level1/drotmg.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_dscal.o level1/dscal.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_dswap.o level1/dswap.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level1/atl_idamax.o level1/idamax.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level3/atl_dgemm.o level3/dgemm.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level3/atl_dgemm_nn.o level3/dgemm_nn.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -DFAKE_ATLAS -c -o level3/atl_dsymm.o level3/dsymm.c
clang -Wall -I. -O2  -mfpmath=sse -fomit-frame-pointer -DULM_BLOCKED -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 make 6 modifications:

The dgemm_nn Code

ulmBLAS/src/level3/dgemm_nn.c
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#include <ulmblas.h>
#include <stdio.h>
#include <emmintrin.h>
#include <immintrin.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(long kc,
                   double alpha, const double *A, const double *B,
                   double beta,
                   double *C, long incRowC, long incColC)
{
    double AB[MR*NR] __attribute__ ((aligned (16)));

    int i, j, l;

//
//  Compute AB = A*B
//
    register __m128d ab_00_11, ab_20_31;
    register __m128d ab_01_10, ab_21_30;
    register __m128d ab_02_13, ab_22_33;
    register __m128d ab_03_12, ab_23_32;

    register __m128d tmp0, tmp1, tmp2, tmp3;
    register __m128d tmp4, tmp5, tmp6, tmp7;

    tmp0     = _mm_load_pd(A);                                      // (1)
    tmp1     = _mm_load_pd(A+2);                                    // (2)
    tmp2     = _mm_load_pd(B);                                      // (3)

    ab_00_11 = _mm_setzero_pd(); ab_20_31 = _mm_setzero_pd();
    ab_01_10 = _mm_setzero_pd(); ab_21_30 = _mm_setzero_pd();
    ab_02_13 = _mm_setzero_pd(); ab_22_33 = _mm_setzero_pd();
    ab_03_12 = _mm_setzero_pd(); ab_23_32 = _mm_setzero_pd();

    for (l=0; l<kc; ++l) {
        tmp3     = _mm_load_pd(B+2);

        tmp4     = _mm_shuffle_pd(tmp2, tmp2, _MM_SHUFFLE2(0, 1));
        tmp5     = _mm_shuffle_pd(tmp3, tmp3, _MM_SHUFFLE2(0, 1));

        tmp6     = tmp2;
        tmp2     = _mm_mul_pd(tmp2, tmp0);
        tmp6     = _mm_mul_pd(tmp6, tmp1);
        ab_00_11 = _mm_add_pd(ab_00_11, tmp2);
        ab_20_31 = _mm_add_pd(ab_20_31, tmp6);

        tmp7     = tmp4;
        tmp4     = _mm_mul_pd(tmp4, tmp0);
        tmp7     = _mm_mul_pd(tmp7, tmp1);
        ab_01_10 = _mm_add_pd(ab_01_10, tmp4);
        ab_21_30 = _mm_add_pd(ab_21_30, tmp7);

        tmp2     = _mm_load_pd(B+4);                                // (6)
        tmp6     = tmp3;
        tmp3     = _mm_mul_pd(tmp3, tmp0);
        tmp6     = _mm_mul_pd(tmp6, tmp1);
        ab_02_13 = _mm_add_pd(ab_02_13, tmp3);
        ab_22_33 = _mm_add_pd(ab_22_33, tmp6);

        tmp7     = tmp5;
        tmp5     = _mm_mul_pd(tmp5, tmp0);
        tmp0     = _mm_load_pd(A+4);                                // (4)
        tmp7     = _mm_mul_pd(tmp7, tmp1);
        tmp1     = _mm_load_pd(A+6);                                // (5)
        ab_03_12 = _mm_add_pd(ab_03_12, tmp5);
        ab_23_32 = _mm_add_pd(ab_23_32, tmp7);

        A += 4;
        B += 4;
    }

    _mm_storel_pd(&AB[0+0*4], ab_00_11);
    _mm_storeh_pd(&AB[1+0*4], ab_01_10);
    _mm_storel_pd(&AB[2+0*4], ab_20_31);
    _mm_storeh_pd(&AB[3+0*4], ab_21_30);

    _mm_storel_pd(&AB[0+1*4], ab_01_10);
    _mm_storeh_pd(&AB[1+1*4], ab_00_11);
    _mm_storel_pd(&AB[2+1*4], ab_21_30);
    _mm_storeh_pd(&AB[3+1*4], ab_20_31);

    _mm_storel_pd(&AB[0+2*4], ab_02_13);
    _mm_storeh_pd(&AB[1+2*4], ab_03_12);
    _mm_storel_pd(&AB[2+2*4], ab_22_33);
    _mm_storeh_pd(&AB[3+2*4], ab_23_32);

    _mm_storel_pd(&AB[0+3*4], ab_03_12);
    _mm_storeh_pd(&AB[1+3*4], ab_02_13);
    _mm_storel_pd(&AB[2+3*4], ab_23_32);
    _mm_storeh_pd(&AB[3+3*4], ab_22_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
ULMBLAS(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 1806.7 1.00 -----
   0 N N  100  100  100   1.0 1000 1000   1.0 1000  0.00 4890.0 2.71 PASS 
   1 N N  200  200  200   1.0 1000 1000   1.0 1000  0.01 1960.5 1.00 -----
   1 N N  200  200  200   1.0 1000 1000   1.0 1000  0.00 5856.5 2.99 PASS 
   2 N N  300  300  300   1.0 1000 1000   1.0 1000  0.03 2018.6 1.00 -----
   2 N N  300  300  300   1.0 1000 1000   1.0 1000  0.01 6157.4 3.05 PASS 
   3 N N  400  400  400   1.0 1000 1000   1.0 1000  0.07 1888.4 1.00 -----
   3 N N  400  400  400   1.0 1000 1000   1.0 1000  0.02 6066.6 3.21 PASS 
   4 N N  500  500  500   1.0 1000 1000   1.0 1000  0.12 2030.9 1.00 -----
   4 N N  500  500  500   1.0 1000 1000   1.0 1000  0.04 6218.3 3.06 PASS 
   5 N N  600  600  600   1.0 1000 1000   1.0 1000  0.32 1367.3 1.00 -----
   5 N N  600  600  600   1.0 1000 1000   1.0 1000  0.07 6320.1 4.62 PASS 
   6 N N  700  700  700   1.0 1000 1000   1.0 1000  0.67 1020.3 1.00 -----
   6 N N  700  700  700   1.0 1000 1000   1.0 1000  0.11 6394.8 6.27 PASS 
   7 N N  800  800  800   1.0 1000 1000   1.0 1000  0.97 1053.3 1.00 -----
   7 N N  800  800  800   1.0 1000 1000   1.0 1000  0.16 6343.0 6.02 PASS 
   8 N N  900  900  900   1.0 1000 1000   1.0 1000  1.38 1058.7 1.00 -----
   8 N N  900  900  900   1.0 1000 1000   1.0 1000  0.23 6394.9 6.04 PASS 
   9 N N 1000 1000 1000   1.0 1000 1000   1.0 1000  1.72 1163.6 1.00 -----
   9 N N 1000 1000 1000   1.0 1000 1000   1.0 1000  0.31 6450.5 5.54 PASS 
10 tests run, 10 passed

and filter out the results for the demo-sse-intrinsics-v2 branch:

$shell> grep PASS report > demo-sse-intrinsics-v2

With the gnuplot script

ulmBLAS/bench/bench7.gps
set terminal svg size 1140,480
set output "bench7.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", "demo-naive-sse-with-intrinsics-unrolled" using 4:13 with linespoints lt 6 title "demo-naive-sse-with-intrinsics-unrolled", "demo-sse-intrinsics" using 4:13 with linespoints lt 7 title "demo-sse-intrinsics", "demo-sse-intrinsics-v2" using 4:13 with linespoints lt 8 title "demo-sse-intrinsics-v2"

we feed gnuplot

$shell> gnuplot bench7.gps

and get

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