Naive Use of AVX Intrinsics

Using AVX intrinsics instead of SSE we follow the straight forward approach of Naive Use of SSE Intrinsics.

Clone the ulmBLAS Repository

If not done already clone the ulmBLAS repository.

$shell> git clone https://github.com/michael-lehn/ulmBLAS.git            
Cloning into 'ulmBLAS'...

Select the demo-naive-avx-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-avx-with-intrinsics branch:

$shell> git branch -a                                                    
* master
  remotes/origin/HEAD -> origin/master
  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-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
$shell> git checkout -B demo-naive-avx-with-intrinsics remotes/origin/demo-naive-avx-with-intrinsics       
Switched to a new branch 'demo-naive-avx-with-intrinsics'
Branch demo-naive-avx-with-intrinsics set up to track remote branch demo-naive-avx-with-intrinsics from origin.

Then we compile the project

$shell> make                                                             
make -C src
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o auxiliary/xerbla.o auxiliary/xerbla.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/dasum.o level1/dasum.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/daxpy.o level1/daxpy.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/dcopy.o level1/dcopy.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/ddot.o level1/ddot.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/dnrm2.o level1/dnrm2.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/drot.o level1/drot.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/drotg.o level1/drotg.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/drotm.o level1/drotm.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/drotmg.o level1/drotmg.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/dscal.o level1/dscal.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/dswap.o level1/dswap.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level1/idamax.o level1/idamax.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level3/dgemm.o level3/dgemm.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level3/dgemm_nn.o level3/dgemm_nn.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -c -o level3/dsymm.o level3/dsymm.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -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 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o auxiliary/atl_xerbla.o auxiliary/xerbla.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_dasum.o level1/dasum.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_daxpy.o level1/daxpy.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_dcopy.o level1/dcopy.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_ddot.o level1/ddot.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_dnrm2.o level1/dnrm2.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_drot.o level1/drot.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_drotg.o level1/drotg.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_drotm.o level1/drotm.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_drotmg.o level1/drotmg.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_dscal.o level1/dscal.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_dswap.o level1/dswap.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level1/atl_idamax.o level1/idamax.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level3/atl_dgemm.o level3/dgemm.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level3/atl_dgemm_nn.o level3/dgemm_nn.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -fomit-frame-pointer -DFAKE_ATLAS -c -o level3/atl_dsymm.o level3/dsymm.c
gcc-4.8 -Wall -I. -O2 -Xassembler -q -mavx -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
gcc-4.8 -c -DL2SIZE=4194304 -DAdd_ -DF77_INTEGER=int -DStringSunStyle -DATL_SSE2 -DDREAL   -c -o l3blastst.o l3blastst.c
gfortran -o xdl3blastst l3blastst.o libtstatlas.a ../libatlulmblas.a ../librefblas.a

The Micro Kernel Algorithm

We use parameters \(m_r = 8\) and \(n_r=4\) in the micor kernel. We merely optimize the update step

\[\mathbf{AB} \leftarrow \mathbf{AB} + \begin{pmatrix} a_{4l } \\ a_{4l+1} \\ a_{4l+2} \\ a_{4l+3} a_{4l+4} \\ a_{4l+5} \\ a_{4l+6} \\ a_{4l+7} \end{pmatrix} \begin{pmatrix} b_{4l}, & b_{4l+1}, & b_{4l+2}, & b_{4l+3}\end{pmatrix}\]

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

\[\mathbf{AB} \leftarrow \mathbf{AB} + \begin{pmatrix} b_{4l} \begin{pmatrix} a_{4l } \\ a_{4l+1} \\ a_{4l+2} \\ a_{4l+3} a_{4l+4} \\ a_{4l+5} \\ a_{4l+6} \\ a_{4l+7} \end{pmatrix}, & b_{4l+1} \begin{pmatrix} a_{4l } \\ a_{4l+1} \\ a_{4l+2} \\ a_{4l+3} a_{4l+4} \\ a_{4l+5} \\ a_{4l+6} \\ a_{4l+7} \end{pmatrix}, & b_{4l+2} \begin{pmatrix} a_{4l } \\ a_{4l+1} \\ a_{4l+2} \\ a_{4l+3} a_{4l+4} \\ a_{4l+5} \\ a_{4l+6} \\ a_{4l+7} \end{pmatrix}, & b_{4l+3} \begin{pmatrix} a_{4l } \\ a_{4l+1} \\ a_{4l+2} \\ a_{4l+3} a_{4l+4} \\ a_{4l+5} \\ a_{4l+6} \\ a_{4l+7} \end{pmatrix} \end{pmatrix}\]

Let \(\mathbb{b}_{0000}, \mathbb{b}_{1111}, \mathbb{b}_{2222}, \mathbb{b}_{3333}\) and \(\mathbb{a}_{0123}, \mathbb{a}_{4567}\) denote AVX registers. We use this 6 registers to store the operands:

\[\begin{array}{llllll}\mathbb{b}_{0000} \leftarrow \begin{pmatrix} b_{4l } \\ b_{4l } \\ b_{4l } \\ b_{4l } \end{pmatrix}, &\mathbb{b}_{1111} \leftarrow \begin{pmatrix} b_{4l+1} \\ b_{4l+1} \\ b_{4l+1} \\ b_{4l+1} \end{pmatrix}, &\mathbb{b}_{2222} \leftarrow \begin{pmatrix} b_{4l+2} \\ b_{4l+2} \\ b_{4l+2} \\ b_{4l+2} \end{pmatrix}, &\mathbb{b}_{3333} \leftarrow \begin{pmatrix} b_{4l+3} \\ b_{4l+3} \\ b_{4l+2} \\ b_{4l+2} \end{pmatrix}, &\mathbb{a}_{0123} \leftarrow \begin{pmatrix} a_{4l } \\ a_{4l+1} \\ a_{4l+2} \\ a_{4l+3} \end{pmatrix}, &\mathbb{a}_{4567} \leftarrow \begin{pmatrix} a_{4l+4} \\ a_{4l+5} \\ a_{4l+6} \\ a_{4l+7} \end{pmatrix}\end{array}\]

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

\[\begin{array}{llll}\mathbb{ab}_{00,10,20,30} \leftarrow \begin{pmatrix} ab_{0,0} \\ ab_{1,0} \\ ab_{2,0} \\ ab_{3,0} \end{pmatrix}, &\mathbb{ab}_{00,10,20,30} \leftarrow \begin{pmatrix} ab_{0,1} \\ ab_{1,1} \\ ab_{2,1} \\ ab_{3,1} \end{pmatrix}, &\mathbb{ab}_{00,10,20,30} \leftarrow \begin{pmatrix} ab_{0,2} \\ ab_{1,2} \\ ab_{2,2} \\ ab_{3,2} \end{pmatrix}, &\mathbb{ab}_{00,10,20,30} \leftarrow \begin{pmatrix} ab_{0,3} \\ ab_{1,3} \\ ab_{2,3} \\ ab_{3,3} \end{pmatrix} \\[0.5cm]\mathbb{ab}_{00,10,20,30} \leftarrow \begin{pmatrix} ab_{4,0} \\ ab_{5,0} \\ ab_{6,0} \\ ab_{7,0} \end{pmatrix}, &\mathbb{ab}_{00,10,20,30} \leftarrow \begin{pmatrix} ab_{4,1} \\ ab_{5,1} \\ ab_{6,1} \\ ab_{7,1} \end{pmatrix}, &\mathbb{ab}_{00,10,20,30} \leftarrow \begin{pmatrix} ab_{4,2} \\ ab_{5,2} \\ ab_{6,2} \\ ab_{7,2} \end{pmatrix}, &\mathbb{ab}_{00,10,20,30} \leftarrow \begin{pmatrix} ab_{4,3} \\ ab_{5,3} \\ ab_{6,3} \\ ab_{7,3} \end{pmatrix}\end{array}\]

As our architecture has a total of 16 AVX 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

Update the first column:
- \(\mathbb{tmp}_1 \leftarrow \mathbb{ab}_{00,10,20,30}\)
- \(\mathbb{tmp}_2 \leftarrow \mathbb{ab}_{40,50,60,70}\)
- \(\mathbb{tmp}_1 \leftarrow \mathbb{tmp}_1 \odot \mathbb{b}_{0000}\)
- \(\mathbb{tmp}_2 \leftarrow \mathbb{tmp}_2 \odot \mathbb{b}_{0000}\)
- \(\mathbb{ab}_{00,10,20,30} \leftarrow \mathbb{ab}_{00,10,20,30} + \mathbb{tmp}_1\)
- \(\mathbb{ab}_{40,50,60,70} \leftarrow \mathbb{ab}_{40,50,60,70} + \mathbb{tmp}_2\)
Update the second column:
- \(\mathbb{tmp}_1 \leftarrow \mathbb{ab}_{01,11,21,31}\)
- \(\mathbb{tmp}_2 \leftarrow \mathbb{ab}_{41,51,61,71}\)
- \(\mathbb{tmp}_1 \leftarrow \mathbb{tmp}_1 \odot \mathbb{b}_{1111}\)
- \(\mathbb{tmp}_2 \leftarrow \mathbb{tmp}_2 \odot \mathbb{b}_{1111}\)
- \(\mathbb{ab}_{01,11,21,31} \leftarrow \mathbb{ab}_{01,11,21,31} + \mathbb{tmp}_1\)
- \(\mathbb{ab}_{41,51,61,71} \leftarrow \mathbb{ab}_{41,51,61,71} + \mathbb{tmp}_2\)
Update the third column:
- \(\mathbb{tmp}_1 \leftarrow \mathbb{ab}_{02,12,22,32}\)
- \(\mathbb{tmp}_2 \leftarrow \mathbb{ab}_{42,52,62,72}\)
- \(\mathbb{tmp}_1 \leftarrow \mathbb{tmp}_1 \odot \mathbb{b}_{2222}\)
- \(\mathbb{tmp}_2 \leftarrow \mathbb{tmp}_2 \odot \mathbb{b}_{2222}\)
- \(\mathbb{ab}_{02,12,22,32} \leftarrow \mathbb{ab}_{02,12,22,32} + \mathbb{tmp}_1\)
- \(\mathbb{ab}_{42,52,62,72} \leftarrow \mathbb{ab}_{42,52,62,72} + \mathbb{tmp}_2\)
Update the forth column:
- \(\mathbb{tmp}_1 \leftarrow \mathbb{ab}_{03,13,23,33}\)
- \(\mathbb{tmp}_2 \leftarrow \mathbb{ab}_{43,53,63,73}\)
- \(\mathbb{tmp}_1 \leftarrow \mathbb{tmp}_1 \odot \mathbb{b}_{3333}\)
- \(\mathbb{tmp}_2 \leftarrow \mathbb{tmp}_2 \odot \mathbb{b}_{3333}\)
- \(\mathbb{ab}_{03,13,23,33} \leftarrow \mathbb{ab}_{03,13,23,33} + \mathbb{tmp}_1\)
- \(\mathbb{ab}_{43,53,63,73} \leftarrow \mathbb{ab}_{43,53,63,73} + \mathbb{tmp}_2\)

Hereby \(\odot\) denotes the usual component wise multiplication of AVX 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 32 byte alignment to the definition of local buffers _A, _B, _C and AB. Having a 32-byte alignment is required for the load and store intrinsics used in the micro kernel.

ulmBLAS/src/level3/dgemm_nn.c

       1
       2
       3
       4
       5
       6
       7
       8
       9
      10
      11
      12
      13
      14
      15
      16
      17
      18
      19
      20
      21
      22
      23
      24
      25
      26
      27
      28
      29
      30
      31
      32
      33
      34
      35
      36
      37
      38
      39
      40
      41
      42
      43
      44
      45
      46
      47
      48
      49
      50
      51
      52
      53
      54
      55
      56
      57
      58
      59
      60
      61
      62
      63
      64
      65
      66
      67
      68
      69
      70
      71
      72
      73
      74
      75
      76
      77
      78
      79
      80
      81
      82
      83
      84
      85
      86
      87
      88
      89
      90
      91
      92
      93
      94
      95
      96
      97
      98
      99
     100
     101
     102
     103
     104
     105
     106
     107
     108
     109
     110
     111
     112
     113
     114
     115
     116
     117
     118
     119
     120
     121
     122
     123
     124
     125
     126
     127
     128
     129
     130
     131
     132
     133
     134
     135
     136
     137
     138
     139
     140
     141
     142
     143
     144
     145
     146
     147
     148
     149
     150
     151
     152
     153
     154
     155
     156
     157
     158
     159
     160
     161
     162
     163
     164
     165
     166
     167
     168
     169
     170
     171
     172
     173
     174
     175
     176
     177
     178
     179
     180
     181
     182
     183
     184
     185
     186
     187
     188
     189
     190
     191
     192
     193
     194
     195
     196
     197
     198
     199
     200
     201
     202
     203
     204
     205
     206
     207
     208
     209
     210
     211
     212
     213
     214
     215
     216
     217
     218
     219
     220
     221
     222
     223
     224
     225
     226
     227
     228
     229
     230
     231
     232
     233
     234
     235
     236
     237
     238
     239
     240
     241
     242
     243
     244
     245
     246
     247
     248
     249
     250
     251
     252
     253
     254
     255
     256
     257
     258
     259
     260
     261
     262
     263
     264
     265
     266
     267
     268
     269
     270
     271
     272
     273
     274
     275
     276
     277
     278
     279
     280
     281
     282
     283
     284
     285
     286
     287
     288
     289
     290
     291
     292
     293
     294
     295
     296
     297
     298
     299
     300
     301
     302
     303
     304
     305
     306
     307
     308
     309
     310
     311
     312
     313
     314
     315
     316
     317
     318
     319
     320
     321
     322
     323
     324
     325
     326
     327
     328
     329
     330
     331
     332
     333
     334
     335
     336
     337
     338
     339
     340
     341
     342
     343
     344
     345
     346
     347
     348
     349
     350
     351
     352
     353
     354
     355
     356
     357
     358
     359
     360
     361
     362
     363
     364
     365
     366
     367
     368
     369
     370
     371
     372
     373
     374
     375
     376
     377
     378
     379
     380
     381
     382
     383
     384
     385
     386
     387
     388
     389
     390
     391
     392
     393
     394
     395
     396
     397
     398
     399
     400
     401
     402
     403
     404
     405
     406
     407
     408
     409

#include <ulmblas.h>

#include <stdio.h>

#include <immintrin.h>

#define MC  384

#define KC  384

#define NC  4096

#define MR  8

#define NR  4

//

//  Local buffers for storing panels from A, B and C

//

static double _A[MC*KC] __attribute__ ((aligned (32)));

static double _B[KC*NC] __attribute__ ((aligned (32)));

static double _C[MR*NR] __attribute__ ((aligned (32)));

//

//  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 (32)));

    // Cols of AB in SSE registers

    __m256d   ab_00_10_20_30,  ab_40_50_60_70;

    __m256d   ab_01_11_21_31,  ab_41_51_61_71;

    __m256d   ab_02_12_22_32,  ab_42_52_62_72;

    __m256d   ab_03_13_23_33,  ab_43_53_63_73;

    __m256d   a_0123, a_4567;

    __m256d   b_0000, b_1111, b_2222, b_3333;

    __m256d   tmp1, tmp2;

    int i, j, l;

    ab_00_10_20_30 = _mm256_setzero_pd(); ab_40_50_60_70 = _mm256_setzero_pd();

    ab_01_11_21_31 = _mm256_setzero_pd(); ab_41_51_61_71 = _mm256_setzero_pd();

    ab_02_12_22_32 = _mm256_setzero_pd(); ab_42_52_62_72 = _mm256_setzero_pd();

    ab_03_13_23_33 = _mm256_setzero_pd(); ab_43_53_63_73 = _mm256_setzero_pd();

//

//  Compute AB = A*B

//

    for (l=0; l<kc; ++l) {

        a_0123 = _mm256_load_pd(A);

        a_4567 = _mm256_load_pd(A+4);

        b_0000 = _mm256_broadcast_sd(B);

        b_1111 = _mm256_broadcast_sd(B+1);

        b_2222 = _mm256_broadcast_sd(B+2);

        b_3333 = _mm256_broadcast_sd(B+3);

        // col 0 of AB

        tmp1 = a_0123;

        tmp2 = a_4567;

        tmp1 = _mm256_mul_pd(tmp1, b_0000);

        tmp2 = _mm256_mul_pd(tmp2, b_0000);

        ab_00_10_20_30 = _mm256_add_pd(tmp1, ab_00_10_20_30);

        ab_40_50_60_70 = _mm256_add_pd(tmp2, ab_40_50_60_70);

        // col 1 of AB

        tmp1 = a_0123;

        tmp2 = a_4567;

        tmp1 = _mm256_mul_pd(tmp1, b_1111);

        tmp2 = _mm256_mul_pd(tmp2, b_1111);

        ab_01_11_21_31 = _mm256_add_pd(tmp1, ab_01_11_21_31);

        ab_41_51_61_71 = _mm256_add_pd(tmp2, ab_41_51_61_71);

        // col 2 of AB

        tmp1 = a_0123;

        tmp2 = a_4567;

        tmp1 = _mm256_mul_pd(tmp1, b_2222);

        tmp2 = _mm256_mul_pd(tmp2, b_2222);

        ab_02_12_22_32 = _mm256_add_pd(tmp1, ab_02_12_22_32);

        ab_42_52_62_72 = _mm256_add_pd(tmp2, ab_42_52_62_72);

        // col 3 of AB

        tmp1 = a_0123;

        tmp2 = a_4567;

        tmp1 = _mm256_mul_pd(tmp1, b_3333);

        tmp2 = _mm256_mul_pd(tmp2, b_3333);

        ab_03_13_23_33 = _mm256_add_pd(tmp1, ab_03_13_23_33);

        ab_43_53_63_73 = _mm256_add_pd(tmp2, ab_43_53_63_73);

        A += 8;

        B += 4;

    }

    _mm256_store_pd(AB+ 0, ab_00_10_20_30);

    _mm256_store_pd(AB+ 4, ab_40_50_60_70);

    _mm256_store_pd(AB+ 8, ab_01_11_21_31);

    _mm256_store_pd(AB+12, ab_41_51_61_71);

    _mm256_store_pd(AB+16, ab_02_12_22_32);

    _mm256_store_pd(AB+20, ab_42_52_62_72);

    _mm256_store_pd(AB+24, ab_03_13_23_33);

    _mm256_store_pd(AB+28, ab_43_53_63_73);

//

//  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 -N 100 2500 100                                    
./xdl3blastst -N 100 2500 100 
--------------------------------- GEMM ----------------------------------
TST# A B    M    N    K ALPHA  LDA  LDB  BETA  LDC  TIME MFLOP SpUp  TEST
==== = = ==== ==== ==== ===== ==== ==== ===== ==== ===== ===== ==== =====
   0 N N  100  100  100   1.0 2500 2500   1.0 2500  0.00 3546.1 1.00 -----
   0 N N  100  100  100   1.0 2500 2500   1.0 2500  0.00 11173.2 3.15 PASS 
   1 N N  200  200  200   1.0 2500 2500   1.0 2500  0.00 3821.4 1.00 -----
   1 N N  200  200  200   1.0 2500 2500   1.0 2500  0.00 14705.9 3.85 PASS 
   2 N N  300  300  300   1.0 2500 2500   1.0 2500  0.01 4033.5 1.00 -----
   2 N N  300  300  300   1.0 2500 2500   1.0 2500  0.00 15826.5 3.92 PASS 
   3 N N  400  400  400   1.0 2500 2500   1.0 2500  0.03 4106.6 1.00 -----
   3 N N  400  400  400   1.0 2500 2500   1.0 2500  0.01 16522.5 4.02 PASS 
   4 N N  500  500  500   1.0 2500 2500   1.0 2500  0.07 3816.7 1.00 -----
   4 N N  500  500  500   1.0 2500 2500   1.0 2500  0.02 16081.3 4.21 PASS 
   5 N N  600  600  600   1.0 2500 2500   1.0 2500  0.12 3576.8 1.00 -----
   5 N N  600  600  600   1.0 2500 2500   1.0 2500  0.03 16313.0 4.56 PASS 
   6 N N  700  700  700   1.0 2500 2500   1.0 2500  0.20 3362.1 1.00 -----
   6 N N  700  700  700   1.0 2500 2500   1.0 2500  0.04 17555.1 5.22 PASS 
   7 N N  800  800  800   1.0 2500 2500   1.0 2500  0.34 2977.9 1.00 -----
   7 N N  800  800  800   1.0 2500 2500   1.0 2500  0.06 17501.6 5.88 PASS 
   8 N N  900  900  900   1.0 2500 2500   1.0 2500  0.52 2795.5 1.00 -----
   8 N N  900  900  900   1.0 2500 2500   1.0 2500  0.08 17201.7 6.15 PASS 
   9 N N 1000 1000 1000   1.0 2500 2500   1.0 2500  0.73 2731.6 1.00 -----
   9 N N 1000 1000 1000   1.0 2500 2500   1.0 2500  0.11 17764.5 6.50 PASS 
  10 N N 1100 1100 1100   1.0 2500 2500   1.0 2500  0.99 2701.9 1.00 -----
  10 N N 1100 1100 1100   1.0 2500 2500   1.0 2500  0.15 17865.4 6.61 PASS 
  11 N N 1200 1200 1200   1.0 2500 2500   1.0 2500  1.26 2743.8 1.00 -----
  11 N N 1200 1200 1200   1.0 2500 2500   1.0 2500  0.19 17934.4 6.54 PASS 
  12 N N 1300 1300 1300   1.0 2500 2500   1.0 2500  1.60 2754.2 1.00 -----
  12 N N 1300 1300 1300   1.0 2500 2500   1.0 2500  0.25 17904.4 6.50 PASS 
  13 N N 1400 1400 1400   1.0 2500 2500   1.0 2500  1.99 2755.0 1.00 -----
  13 N N 1400 1400 1400   1.0 2500 2500   1.0 2500  0.30 18081.2 6.56 PASS 
  14 N N 1500 1500 1500   1.0 2500 2500   1.0 2500  2.43 2781.7 1.00 -----
  14 N N 1500 1500 1500   1.0 2500 2500   1.0 2500  0.39 17398.6 6.25 PASS 
  15 N N 1600 1600 1600   1.0 2500 2500   1.0 2500  2.93 2795.8 1.00 -----
  15 N N 1600 1600 1600   1.0 2500 2500   1.0 2500  0.45 18008.9 6.44 PASS 
  16 N N 1700 1700 1700   1.0 2500 2500   1.0 2500  3.54 2773.3 1.00 -----
  16 N N 1700 1700 1700   1.0 2500 2500   1.0 2500  0.56 17671.4 6.37 PASS 
  17 N N 1800 1800 1800   1.0 2500 2500   1.0 2500  4.15 2812.9 1.00 -----
  17 N N 1800 1800 1800   1.0 2500 2500   1.0 2500  0.65 17813.5 6.33 PASS 
  18 N N 1900 1900 1900   1.0 2500 2500   1.0 2500  4.91 2796.5 1.00 -----
  18 N N 1900 1900 1900   1.0 2500 2500   1.0 2500  0.76 18052.0 6.46 PASS 
  19 N N 2000 2000 2000   1.0 2500 2500   1.0 2500  5.65 2833.3 1.00 -----
  19 N N 2000 2000 2000   1.0 2500 2500   1.0 2500  0.88 18141.8 6.40 PASS 
  20 N N 2100 2100 2100   1.0 2500 2500   1.0 2500  6.64 2790.1 1.00 -----
  20 N N 2100 2100 2100   1.0 2500 2500   1.0 2500  1.04 17817.2 6.39 PASS 
  21 N N 2200 2200 2200   1.0 2500 2500   1.0 2500  7.62 2793.3 1.00 -----
  21 N N 2200 2200 2200   1.0 2500 2500   1.0 2500  1.18 18084.7 6.47 PASS 
  22 N N 2300 2300 2300   1.0 2500 2500   1.0 2500  8.62 2824.5 1.00 -----
  22 N N 2300 2300 2300   1.0 2500 2500   1.0 2500  1.34 18142.4 6.42 PASS 
  23 N N 2400 2400 2400   1.0 2500 2500   1.0 2500  9.87 2799.9 1.00 -----
  23 N N 2400 2400 2400   1.0 2500 2500   1.0 2500  1.69 16380.7 5.85 PASS 
  24 N N 2500 2500 2500   1.0 2500 2500   1.0 2500 10.86 2878.1 1.00 -----
  24 N N 2500 2500 2500   1.0 2500 2500   1.0 2500  1.81 17251.7 5.99 PASS 
25 tests run, 25 passed

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

$shell> ./xdl3blastst -N 100 2500 100 > report                           
$shell> grep PASS report > demo-naive-avx-with-intrinsics                
$shell> grep "\ \-\-\-\-\-$" report > refBLAS

With the gnuplot script

ulmBLAS/bench/bench.gps

set terminal png size 1140,480

set output "bench.png"

set xlabel "Matrix dimensions N=M=K"

set ylabel "MFLOPS"

set yrange [0:21600]

set title "Compute C + A*B"

set key outside

plot "refBLAS" using 4:13 with linespoints lt 2 title "Netlib RefBLAS", "demo-naive-avx-with-intrinsics" using 4:13 with linespoints lt 3 title "demo-naive-avx-with-intrinsics"

we feed gnuplot

$shell> gnuplot bench.gps

and get