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Loop Unrolling

We optimize our previous implementation by manual loop unrolling. Again, the performance achieved here I would have expected from a smart compiler for the demo-pure-c branch. At least if we provide enough hints through compiler flags and attributes.

Select the demo-naive-sse-with-intrinsics-unrolled 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-naive-sse-with-intrinsics
  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-unrolled remotes/origin/demo-naive-sse-with-intrinsics-unrolled       
Switched to a new branch 'demo-naive-sse-with-intrinsics-unrolled'
Branch demo-naive-sse-with-intrinsics-unrolled set up to track remote branch demo-naive-sse-with-intrinsics-unrolled 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

Unrolling

TODO:

The dgemm_nn Code

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/4; ++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;

        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;

        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;

        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;
    }

    for (l=0; l<kc%4; ++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 4132.2 2.30 PASS 
   1 N N  200  200  200   1.0 1000 1000   1.0 1000  0.01 1960.8 1.00 -----
   1 N N  200  200  200   1.0 1000 1000   1.0 1000  0.00 4770.4 2.43 PASS 
   2 N N  300  300  300   1.0 1000 1000   1.0 1000  0.03 2000.0 1.00 -----
   2 N N  300  300  300   1.0 1000 1000   1.0 1000  0.01 4873.6 2.44 PASS 
   3 N N  400  400  400   1.0 1000 1000   1.0 1000  0.07 1929.6 1.00 -----
   3 N N  400  400  400   1.0 1000 1000   1.0 1000  0.03 4881.0 2.53 PASS 
   4 N N  500  500  500   1.0 1000 1000   1.0 1000  0.12 2063.5 1.00 -----
   4 N N  500  500  500   1.0 1000 1000   1.0 1000  0.05 4986.1 2.42 PASS 
   5 N N  600  600  600   1.0 1000 1000   1.0 1000  0.32 1339.5 1.00 -----
   5 N N  600  600  600   1.0 1000 1000   1.0 1000  0.09 5059.9 3.78 PASS 
   6 N N  700  700  700   1.0 1000 1000   1.0 1000  0.66 1032.4 1.00 -----
   6 N N  700  700  700   1.0 1000 1000   1.0 1000  0.13 5095.1 4.94 PASS 
   7 N N  800  800  800   1.0 1000 1000   1.0 1000  0.97 1053.7 1.00 -----
   7 N N  800  800  800   1.0 1000 1000   1.0 1000  0.20 5055.0 4.80 PASS 
   8 N N  900  900  900   1.0 1000 1000   1.0 1000  1.38 1053.9 1.00 -----
   8 N N  900  900  900   1.0 1000 1000   1.0 1000  0.29 5099.5 4.84 PASS 
   9 N N 1000 1000 1000   1.0 1000 1000   1.0 1000  1.73 1154.4 1.00 -----
   9 N N 1000 1000 1000   1.0 1000 1000   1.0 1000  0.39 5133.4 4.45 PASS 
10 tests run, 10 passed

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

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

With the gnuplot script

ulmBLAS/bench/bench4.gps
set terminal svg size 1140,480
set output "bench4.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"

we feed gnuplot

$shell> gnuplot bench4.gps

and get

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