Merge pull request #3335 from guowangy/small-matrix-latest

Add GEMM optimization for small matrix and single/double kernel for skylakex

Makefile.system

@@ -244,6 +244,14 @@ else
 ONLY_CBLAS = 0
 endif
 
+#For small matrix optimization
+ifeq ($(ARCH), x86_64)
+SMALL_MATRIX_OPT = 1
+endif
+ifeq ($(SMALL_MATRIX_OPT), 1)
+CCOMMON_OPT += -DSMALL_MATRIX_OPT
+endif
+
 # This operation is expensive, so execution should be once.
 ifndef GOTOBLAS_MAKEFILE
 export GOTOBLAS_MAKEFILE = 1

cmake/system.cmake

@@ -258,6 +258,13 @@ if (NEED_PIC)
   endif()
 endif ()
 
+if (X86_64)
+  set(SMALL_MATRIX_OPT TRUE)
+endif ()
+if (SMALL_MATRIX_OPT)
+  set(CCOMMON_OPT "${CCOMMON_OPT} -DSMALL_MATRIX_OPT")
+endif ()
+
 if (DYNAMIC_ARCH)
   if (X86 OR X86_64 OR ARM64 OR PPC)
     set(CCOMMON_OPT "${CCOMMON_OPT} -DDYNAMIC_ARCH")

common_c.h

@@ -232,6 +232,8 @@
 
 #define CGEADD_K                cgeadd_k 
 
+#define CGEMM_SMALL_MATRIX_PERMIT	cgemm_small_matrix_permit
+
 #else
 
 #define	CAMAX_K			gotoblas -> camax_k
@@ -426,8 +428,51 @@
 
 #define CGEADD_K                gotoblas -> cgeadd_k 
 
+#define CGEMM_SMALL_MATRIX_PERMIT	gotoblas -> cgemm_small_matrix_permit
+
 #endif
 
+#define CGEMM_SMALL_KERNEL_NN		FUNC_OFFSET(cgemm_small_kernel_nn)
+#define CGEMM_SMALL_KERNEL_NT		FUNC_OFFSET(cgemm_small_kernel_nt)
+#define CGEMM_SMALL_KERNEL_NR		FUNC_OFFSET(cgemm_small_kernel_nr)
+#define CGEMM_SMALL_KERNEL_NC		FUNC_OFFSET(cgemm_small_kernel_nc)
+
+#define CGEMM_SMALL_KERNEL_TN		FUNC_OFFSET(cgemm_small_kernel_tn)
+#define CGEMM_SMALL_KERNEL_TT		FUNC_OFFSET(cgemm_small_kernel_tt)
+#define CGEMM_SMALL_KERNEL_TR		FUNC_OFFSET(cgemm_small_kernel_tr)
+#define CGEMM_SMALL_KERNEL_TC		FUNC_OFFSET(cgemm_small_kernel_tc)
+
+#define CGEMM_SMALL_KERNEL_RN		FUNC_OFFSET(cgemm_small_kernel_rn)
+#define CGEMM_SMALL_KERNEL_RT		FUNC_OFFSET(cgemm_small_kernel_rt)
+#define CGEMM_SMALL_KERNEL_RR		FUNC_OFFSET(cgemm_small_kernel_rr)
+#define CGEMM_SMALL_KERNEL_RC		FUNC_OFFSET(cgemm_small_kernel_rc)
+
+#define CGEMM_SMALL_KERNEL_CN		FUNC_OFFSET(cgemm_small_kernel_cn)
+#define CGEMM_SMALL_KERNEL_CT		FUNC_OFFSET(cgemm_small_kernel_ct)
+#define CGEMM_SMALL_KERNEL_CR		FUNC_OFFSET(cgemm_small_kernel_cr)
+#define CGEMM_SMALL_KERNEL_CC		FUNC_OFFSET(cgemm_small_kernel_cc)
+
+#define CGEMM_SMALL_KERNEL_B0_NN	FUNC_OFFSET(cgemm_small_kernel_b0_nn)
+#define CGEMM_SMALL_KERNEL_B0_NT	FUNC_OFFSET(cgemm_small_kernel_b0_nt)
+#define CGEMM_SMALL_KERNEL_B0_NR	FUNC_OFFSET(cgemm_small_kernel_b0_nr)
+#define CGEMM_SMALL_KERNEL_B0_NC	FUNC_OFFSET(cgemm_small_kernel_b0_nc)
+
+#define CGEMM_SMALL_KERNEL_B0_TN	FUNC_OFFSET(cgemm_small_kernel_b0_tn)
+#define CGEMM_SMALL_KERNEL_B0_TT	FUNC_OFFSET(cgemm_small_kernel_b0_tt)
+#define CGEMM_SMALL_KERNEL_B0_TR	FUNC_OFFSET(cgemm_small_kernel_b0_tr)
+#define CGEMM_SMALL_KERNEL_B0_TC	FUNC_OFFSET(cgemm_small_kernel_b0_tc)
+
+#define CGEMM_SMALL_KERNEL_B0_RN	FUNC_OFFSET(cgemm_small_kernel_b0_rn)
+#define CGEMM_SMALL_KERNEL_B0_RT	FUNC_OFFSET(cgemm_small_kernel_b0_rt)
+#define CGEMM_SMALL_KERNEL_B0_RR	FUNC_OFFSET(cgemm_small_kernel_b0_rr)
+#define CGEMM_SMALL_KERNEL_B0_RC	FUNC_OFFSET(cgemm_small_kernel_b0_rc)
+
+#define CGEMM_SMALL_KERNEL_B0_CN	FUNC_OFFSET(cgemm_small_kernel_b0_cn)
+#define CGEMM_SMALL_KERNEL_B0_CT	FUNC_OFFSET(cgemm_small_kernel_b0_ct)
+#define CGEMM_SMALL_KERNEL_B0_CR	FUNC_OFFSET(cgemm_small_kernel_b0_cr)
+#define CGEMM_SMALL_KERNEL_B0_CC	FUNC_OFFSET(cgemm_small_kernel_b0_cc)
+
+
 #define	CGEMM_NN		cgemm_nn
 #define	CGEMM_CN		cgemm_cn
 #define	CGEMM_TN		cgemm_tn

common_d.h

@@ -157,6 +157,8 @@
 #define DIMATCOPY_K_RT      dimatcopy_k_rt
 #define DGEADD_K                dgeadd_k 
 
+#define DGEMM_SMALL_MATRIX_PERMIT	dgemm_small_matrix_permit
+
 #else
 
 #define	DAMAX_K			gotoblas -> damax_k
@@ -281,8 +283,21 @@
 
 #define DGEADD_K                gotoblas -> dgeadd_k 
 
+#define DGEMM_SMALL_MATRIX_PERMIT	gotoblas -> dgemm_small_matrix_permit
+
 #endif
 
+#define DGEMM_SMALL_KERNEL_NN		FUNC_OFFSET(dgemm_small_kernel_nn)
+#define DGEMM_SMALL_KERNEL_NT		FUNC_OFFSET(dgemm_small_kernel_nt)
+#define DGEMM_SMALL_KERNEL_TN		FUNC_OFFSET(dgemm_small_kernel_tn)
+#define DGEMM_SMALL_KERNEL_TT		FUNC_OFFSET(dgemm_small_kernel_tt)
+
+#define DGEMM_SMALL_KERNEL_B0_NN	FUNC_OFFSET(dgemm_small_kernel_b0_nn)
+#define DGEMM_SMALL_KERNEL_B0_NT	FUNC_OFFSET(dgemm_small_kernel_b0_nt)
+#define DGEMM_SMALL_KERNEL_B0_TN	FUNC_OFFSET(dgemm_small_kernel_b0_tn)
+#define DGEMM_SMALL_KERNEL_B0_TT	FUNC_OFFSET(dgemm_small_kernel_b0_tt)
+
+
 #define	DGEMM_NN		dgemm_nn
 #define	DGEMM_CN		dgemm_tn
 #define	DGEMM_TN		dgemm_tn

common_level3.h

@@ -515,6 +515,117 @@ int qgemm_kernel(BLASLONG, BLASLONG, BLASLONG, xidouble *, xidouble *, xidouble
 int qgemm_kernel(BLASLONG, BLASLONG, BLASLONG, xdouble, xdouble *, xdouble *, xdouble *, BLASLONG);
 #endif
 
+#ifdef SMALL_MATRIX_OPT
+int sgemm_small_matrix_permit(int transa, int transb, BLASLONG m, BLASLONG n, BLASLONG k, float alpha, float beta);
+
+int sgemm_small_kernel_nn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float beta, float * C, BLASLONG ldc);
+int sgemm_small_kernel_nt(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float beta, float * C, BLASLONG ldc);
+int sgemm_small_kernel_tn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float beta, float * C, BLASLONG ldc);
+int sgemm_small_kernel_tt(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float beta, float * C, BLASLONG ldc);
+
+int dgemm_small_matrix_permit(int transa, int transb, BLASLONG m, BLASLONG n, BLASLONG k, double alpha, double beta);
+
+int dgemm_small_kernel_nn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double beta, double * C, BLASLONG ldc);
+int dgemm_small_kernel_nt(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double beta, double * C, BLASLONG ldc);
+int dgemm_small_kernel_tn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double beta, double * C, BLASLONG ldc);
+int dgemm_small_kernel_tt(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double beta, double * C, BLASLONG ldc);
+
+int sgemm_small_kernel_b0_nn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float * C, BLASLONG ldc);
+int sgemm_small_kernel_b0_nt(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float * C, BLASLONG ldc);
+int sgemm_small_kernel_b0_tn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float * C, BLASLONG ldc);
+int sgemm_small_kernel_b0_tt(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float * C, BLASLONG ldc);
+
+int dgemm_small_kernel_b0_nn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double * C, BLASLONG ldc);
+int dgemm_small_kernel_b0_nt(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double * C, BLASLONG ldc);
+int dgemm_small_kernel_b0_tn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double * C, BLASLONG ldc);
+int dgemm_small_kernel_b0_tt(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double * C, BLASLONG ldc);
+
+int cgemm_small_matrix_permit(int transa, int transb, BLASLONG m, BLASLONG n, BLASLONG k, float alpha0, float alpha1, float beta0, float beta1);
+
+int cgemm_small_kernel_nn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_nt(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_nr(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_nc(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+	
+int cgemm_small_kernel_tn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_tt(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_tr(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_tc(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+
+int cgemm_small_kernel_rn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_rt(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_rr(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_rc(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+
+int cgemm_small_kernel_cn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_ct(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_cr(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+int cgemm_small_kernel_cc(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+
+int zgemm_small_matrix_permit(int transa, int transb, BLASLONG m, BLASLONG n, BLASLONG k, double alpha0, double alpha1, double beta0, double beta1);
+
+int zgemm_small_kernel_nn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_nt(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_nr(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_nc(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+	
+int zgemm_small_kernel_tn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_tt(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_tr(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_tc(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+
+int zgemm_small_kernel_rn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_rt(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_rr(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_rc(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+
+int zgemm_small_kernel_cn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_ct(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_cr(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+int zgemm_small_kernel_cc(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+
+int cgemm_small_kernel_b0_nn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);	
+int cgemm_small_kernel_b0_nt(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+int cgemm_small_kernel_b0_nr(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+int cgemm_small_kernel_b0_nc(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+	
+int cgemm_small_kernel_b0_tn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+int cgemm_small_kernel_b0_tt(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+int cgemm_small_kernel_b0_tr(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+int cgemm_small_kernel_b0_tc(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+
+int cgemm_small_kernel_b0_rn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+int cgemm_small_kernel_b0_rt(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+int cgemm_small_kernel_b0_rr(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+int cgemm_small_kernel_b0_rc(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+
+int cgemm_small_kernel_b0_cn(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+int cgemm_small_kernel_b0_ct(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+int cgemm_small_kernel_b0_cr(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+int cgemm_small_kernel_b0_cc(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+
+int zgemm_small_kernel_b0_nn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);	
+int zgemm_small_kernel_b0_nt(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+int zgemm_small_kernel_b0_nr(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+int zgemm_small_kernel_b0_nc(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+	
+int zgemm_small_kernel_b0_tn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+int zgemm_small_kernel_b0_tt(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+int zgemm_small_kernel_b0_tr(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+int zgemm_small_kernel_b0_tc(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+
+int zgemm_small_kernel_b0_rn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+int zgemm_small_kernel_b0_rt(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+int zgemm_small_kernel_b0_rr(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+int zgemm_small_kernel_b0_rc(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+
+int zgemm_small_kernel_b0_cn(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+int zgemm_small_kernel_b0_ct(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+int zgemm_small_kernel_b0_cr(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+int zgemm_small_kernel_b0_cc(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+
+#endif
+
 int cgemm_kernel_n(BLASLONG, BLASLONG, BLASLONG, float,  float,  float  *, float  *, float  *, BLASLONG);
 int cgemm_kernel_l(BLASLONG, BLASLONG, BLASLONG, float,  float,  float  *, float  *, float  *, BLASLONG);
 int cgemm_kernel_r(BLASLONG, BLASLONG, BLASLONG, float,  float,  float  *, float  *, float  *, BLASLONG);

common_macro.h

@@ -644,6 +644,17 @@
 
 #define GEADD_K                 DGEADD_K
 
+#define GEMM_SMALL_MATRIX_PERMIT	DGEMM_SMALL_MATRIX_PERMIT
+
+#define GEMM_SMALL_KERNEL_NN    DGEMM_SMALL_KERNEL_NN
+#define GEMM_SMALL_KERNEL_NT    DGEMM_SMALL_KERNEL_NT
+#define GEMM_SMALL_KERNEL_TN    DGEMM_SMALL_KERNEL_TN
+#define GEMM_SMALL_KERNEL_TT    DGEMM_SMALL_KERNEL_TT
+#define GEMM_SMALL_KERNEL_B0_NN    DGEMM_SMALL_KERNEL_B0_NN
+#define GEMM_SMALL_KERNEL_B0_NT    DGEMM_SMALL_KERNEL_B0_NT
+#define GEMM_SMALL_KERNEL_B0_TN    DGEMM_SMALL_KERNEL_B0_TN
+#define GEMM_SMALL_KERNEL_B0_TT    DGEMM_SMALL_KERNEL_B0_TT
+
 #elif defined(BFLOAT16)
 
 #define D_TO_BF16_K     SBDTOBF16_K
@@ -931,6 +942,18 @@
 
 #define GEADD_K 		SGEADD_K
 
+#define GEMM_SMALL_MATRIX_PERMIT	SGEMM_SMALL_MATRIX_PERMIT
+
+#define GEMM_SMALL_KERNEL_NN    SGEMM_SMALL_KERNEL_NN
+#define GEMM_SMALL_KERNEL_NT    SGEMM_SMALL_KERNEL_NT
+#define GEMM_SMALL_KERNEL_TN    SGEMM_SMALL_KERNEL_TN
+#define GEMM_SMALL_KERNEL_TT    SGEMM_SMALL_KERNEL_TT
+
+#define GEMM_SMALL_KERNEL_B0_NN    SGEMM_SMALL_KERNEL_B0_NN
+#define GEMM_SMALL_KERNEL_B0_NT    SGEMM_SMALL_KERNEL_B0_NT
+#define GEMM_SMALL_KERNEL_B0_TN    SGEMM_SMALL_KERNEL_B0_TN
+#define GEMM_SMALL_KERNEL_B0_TT    SGEMM_SMALL_KERNEL_B0_TT
+
 #endif
 
 #else
@@ -1236,6 +1259,19 @@
 #define IMATCOPY_K_RT		SIMATCOPY_K_RT
 
 #define GEADD_K 		SGEADD_K
+
+#define GEMM_SMALL_MATRIX_PERMIT	SGEMM_SMALL_MATRIX_PERMIT
+
+#define GEMM_SMALL_KERNEL_NN    SGEMM_SMALL_KERNEL_NN
+#define GEMM_SMALL_KERNEL_NT    SGEMM_SMALL_KERNEL_NT
+#define GEMM_SMALL_KERNEL_TN    SGEMM_SMALL_KERNEL_TN
+#define GEMM_SMALL_KERNEL_TT    SGEMM_SMALL_KERNEL_TT
+
+#define GEMM_SMALL_KERNEL_B0_NN    SGEMM_SMALL_KERNEL_B0_NN
+#define GEMM_SMALL_KERNEL_B0_NT    SGEMM_SMALL_KERNEL_B0_NT
+#define GEMM_SMALL_KERNEL_B0_TN    SGEMM_SMALL_KERNEL_B0_TN
+#define GEMM_SMALL_KERNEL_B0_TT    SGEMM_SMALL_KERNEL_B0_TT
+
 #endif
 #else
 #ifdef XDOUBLE
@@ -2063,6 +2099,48 @@
 
 #define GEADD_K                 ZGEADD_K
 
+#define GEMM_SMALL_MATRIX_PERMIT	ZGEMM_SMALL_MATRIX_PERMIT
+
+#define GEMM_SMALL_KERNEL_NN    ZGEMM_SMALL_KERNEL_NN
+#define GEMM_SMALL_KERNEL_NT    ZGEMM_SMALL_KERNEL_NT
+#define GEMM_SMALL_KERNEL_NR    ZGEMM_SMALL_KERNEL_NR
+#define GEMM_SMALL_KERNEL_NC    ZGEMM_SMALL_KERNEL_NC
+
+#define GEMM_SMALL_KERNEL_TN    ZGEMM_SMALL_KERNEL_TN
+#define GEMM_SMALL_KERNEL_TT    ZGEMM_SMALL_KERNEL_TT
+#define GEMM_SMALL_KERNEL_TR    ZGEMM_SMALL_KERNEL_TR
+#define GEMM_SMALL_KERNEL_TC    ZGEMM_SMALL_KERNEL_TC
+
+#define GEMM_SMALL_KERNEL_RN    ZGEMM_SMALL_KERNEL_RN
+#define GEMM_SMALL_KERNEL_RT    ZGEMM_SMALL_KERNEL_RT
+#define GEMM_SMALL_KERNEL_RR    ZGEMM_SMALL_KERNEL_RR
+#define GEMM_SMALL_KERNEL_RC    ZGEMM_SMALL_KERNEL_RC
+
+#define GEMM_SMALL_KERNEL_CN    ZGEMM_SMALL_KERNEL_CN
+#define GEMM_SMALL_KERNEL_CT    ZGEMM_SMALL_KERNEL_CT
+#define GEMM_SMALL_KERNEL_CR    ZGEMM_SMALL_KERNEL_CR
+#define GEMM_SMALL_KERNEL_CC    ZGEMM_SMALL_KERNEL_CC
+
+#define GEMM_SMALL_KERNEL_B0_NN    ZGEMM_SMALL_KERNEL_B0_NN
+#define GEMM_SMALL_KERNEL_B0_NT    ZGEMM_SMALL_KERNEL_B0_NT
+#define GEMM_SMALL_KERNEL_B0_NR    ZGEMM_SMALL_KERNEL_B0_NR
+#define GEMM_SMALL_KERNEL_B0_NC    ZGEMM_SMALL_KERNEL_B0_NC
+
+#define GEMM_SMALL_KERNEL_B0_TN    ZGEMM_SMALL_KERNEL_B0_TN
+#define GEMM_SMALL_KERNEL_B0_TT    ZGEMM_SMALL_KERNEL_B0_TT
+#define GEMM_SMALL_KERNEL_B0_TR    ZGEMM_SMALL_KERNEL_B0_TR
+#define GEMM_SMALL_KERNEL_B0_TC    ZGEMM_SMALL_KERNEL_B0_TC
+
+#define GEMM_SMALL_KERNEL_B0_RN    ZGEMM_SMALL_KERNEL_B0_RN
+#define GEMM_SMALL_KERNEL_B0_RT    ZGEMM_SMALL_KERNEL_B0_RT
+#define GEMM_SMALL_KERNEL_B0_RR    ZGEMM_SMALL_KERNEL_B0_RR
+#define GEMM_SMALL_KERNEL_B0_RC    ZGEMM_SMALL_KERNEL_B0_RC
+
+#define GEMM_SMALL_KERNEL_B0_CN    ZGEMM_SMALL_KERNEL_B0_CN
+#define GEMM_SMALL_KERNEL_B0_CT    ZGEMM_SMALL_KERNEL_B0_CT
+#define GEMM_SMALL_KERNEL_B0_CR    ZGEMM_SMALL_KERNEL_B0_CR
+#define GEMM_SMALL_KERNEL_B0_CC    ZGEMM_SMALL_KERNEL_B0_CC
+
 #else
 
 #define	AMAX_K			CAMAX_K
@@ -2486,6 +2564,48 @@
 
 #define GEADD_K                 CGEADD_K
 
+#define GEMM_SMALL_MATRIX_PERMIT	CGEMM_SMALL_MATRIX_PERMIT
+
+#define GEMM_SMALL_KERNEL_NN    CGEMM_SMALL_KERNEL_NN
+#define GEMM_SMALL_KERNEL_NT    CGEMM_SMALL_KERNEL_NT
+#define GEMM_SMALL_KERNEL_NR    CGEMM_SMALL_KERNEL_NR
+#define GEMM_SMALL_KERNEL_NC    CGEMM_SMALL_KERNEL_NC
+
+#define GEMM_SMALL_KERNEL_TN    CGEMM_SMALL_KERNEL_TN
+#define GEMM_SMALL_KERNEL_TT    CGEMM_SMALL_KERNEL_TT
+#define GEMM_SMALL_KERNEL_TR    CGEMM_SMALL_KERNEL_TR
+#define GEMM_SMALL_KERNEL_TC    CGEMM_SMALL_KERNEL_TC
+
+#define GEMM_SMALL_KERNEL_RN    CGEMM_SMALL_KERNEL_RN
+#define GEMM_SMALL_KERNEL_RT    CGEMM_SMALL_KERNEL_RT
+#define GEMM_SMALL_KERNEL_RR    CGEMM_SMALL_KERNEL_RR
+#define GEMM_SMALL_KERNEL_RC    CGEMM_SMALL_KERNEL_RC
+
+#define GEMM_SMALL_KERNEL_CN    CGEMM_SMALL_KERNEL_CN
+#define GEMM_SMALL_KERNEL_CT    CGEMM_SMALL_KERNEL_CT
+#define GEMM_SMALL_KERNEL_CR    CGEMM_SMALL_KERNEL_CR
+#define GEMM_SMALL_KERNEL_CC    CGEMM_SMALL_KERNEL_CC
+
+#define GEMM_SMALL_KERNEL_B0_NN    CGEMM_SMALL_KERNEL_B0_NN
+#define GEMM_SMALL_KERNEL_B0_NT    CGEMM_SMALL_KERNEL_B0_NT
+#define GEMM_SMALL_KERNEL_B0_NR    CGEMM_SMALL_KERNEL_B0_NR
+#define GEMM_SMALL_KERNEL_B0_NC    CGEMM_SMALL_KERNEL_B0_NC
+
+#define GEMM_SMALL_KERNEL_B0_TN    CGEMM_SMALL_KERNEL_B0_TN
+#define GEMM_SMALL_KERNEL_B0_TT    CGEMM_SMALL_KERNEL_B0_TT
+#define GEMM_SMALL_KERNEL_B0_TR    CGEMM_SMALL_KERNEL_B0_TR
+#define GEMM_SMALL_KERNEL_B0_TC    CGEMM_SMALL_KERNEL_B0_TC
+
+#define GEMM_SMALL_KERNEL_B0_RN    CGEMM_SMALL_KERNEL_B0_RN
+#define GEMM_SMALL_KERNEL_B0_RT    CGEMM_SMALL_KERNEL_B0_RT
+#define GEMM_SMALL_KERNEL_B0_RR    CGEMM_SMALL_KERNEL_B0_RR
+#define GEMM_SMALL_KERNEL_B0_RC    CGEMM_SMALL_KERNEL_B0_RC
+
+#define GEMM_SMALL_KERNEL_B0_CN    CGEMM_SMALL_KERNEL_B0_CN
+#define GEMM_SMALL_KERNEL_B0_CT    CGEMM_SMALL_KERNEL_B0_CT
+#define GEMM_SMALL_KERNEL_B0_CR    CGEMM_SMALL_KERNEL_B0_CR
+#define GEMM_SMALL_KERNEL_B0_CC    CGEMM_SMALL_KERNEL_B0_CC
+
 #endif
 #endif
 

common_param.h

@@ -207,6 +207,20 @@ BLASLONG (*ismin_k) (BLASLONG, float *, BLASLONG);
   int    (*sgemm_otcopy   )(BLASLONG, BLASLONG, float *, BLASLONG, float *);
 #endif
 #ifdef BUILD_SINGLE  
+#ifdef SMALL_MATRIX_OPT
+  int    (*sgemm_small_matrix_permit)(int transa, int transb, BLASLONG m, BLASLONG n, BLASLONG k, float alpha, float beta);
+
+  int    (*sgemm_small_kernel_nn    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float beta, float * C, BLASLONG ldc);
+  int    (*sgemm_small_kernel_nt    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float beta, float * C, BLASLONG ldc);
+  int    (*sgemm_small_kernel_tn    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float beta, float * C, BLASLONG ldc);
+  int    (*sgemm_small_kernel_tt    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float beta, float * C, BLASLONG ldc);
+
+  int    (*sgemm_small_kernel_b0_nn )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float * C, BLASLONG ldc);
+  int    (*sgemm_small_kernel_b0_nt )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float * C, BLASLONG ldc);
+  int    (*sgemm_small_kernel_b0_tn )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float * C, BLASLONG ldc);
+  int    (*sgemm_small_kernel_b0_tt )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha, float * B, BLASLONG ldb, float * C, BLASLONG ldc);
+#endif
+
   int    (*strsm_kernel_LN)(BLASLONG, BLASLONG, BLASLONG, float, float *, float *, float *, BLASLONG, BLASLONG);
   int    (*strsm_kernel_LT)(BLASLONG, BLASLONG, BLASLONG, float, float *, float *, float *, BLASLONG, BLASLONG);
   int    (*strsm_kernel_RN)(BLASLONG, BLASLONG, BLASLONG, float, float *, float *, float *, BLASLONG, BLASLONG);
@@ -314,6 +328,19 @@ BLASLONG (*idmin_k) (BLASLONG, double *, BLASLONG);
   int    (*dgemm_otcopy   )(BLASLONG, BLASLONG, double *, BLASLONG, double *);
 #endif
 #ifdef BUILD_DOUBLE
+#ifdef SMALL_MATRIX_OPT
+  int    (*dgemm_small_matrix_permit)(int transa, int transb, BLASLONG m, BLASLONG n, BLASLONG k, double alpha, double beta);
+
+  int    (*dgemm_small_kernel_nn    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double beta, double * C, BLASLONG ldc);
+  int    (*dgemm_small_kernel_nt    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double beta, double * C, BLASLONG ldc);
+  int    (*dgemm_small_kernel_tn    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double beta, double * C, BLASLONG ldc);
+  int    (*dgemm_small_kernel_tt    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double beta, double * C, BLASLONG ldc);
+
+  int    (*dgemm_small_kernel_b0_nn )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double * C, BLASLONG ldc);
+  int    (*dgemm_small_kernel_b0_nt )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double * C, BLASLONG ldc);
+  int    (*dgemm_small_kernel_b0_tn )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double * C, BLASLONG ldc);
+  int    (*dgemm_small_kernel_b0_tt )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha, double * B, BLASLONG ldb, double * C, BLASLONG ldc);
+#endif
   int    (*dtrsm_kernel_LN)(BLASLONG, BLASLONG, BLASLONG, double, double *, double *, double *, BLASLONG, BLASLONG);
   int    (*dtrsm_kernel_LT)(BLASLONG, BLASLONG, BLASLONG, double, double *, double *, double *, BLASLONG, BLASLONG);
   int    (*dtrsm_kernel_RN)(BLASLONG, BLASLONG, BLASLONG, double, double *, double *, double *, BLASLONG, BLASLONG);
@@ -513,6 +540,50 @@ BLASLONG (*icamin_k)(BLASLONG, float *, BLASLONG);
   int    (*cgemm_oncopy   )(BLASLONG, BLASLONG, float *, BLASLONG, float *);
   int    (*cgemm_otcopy   )(BLASLONG, BLASLONG, float *, BLASLONG, float *);
 
+#ifdef SMALL_MATRIX_OPT
+  int    (*cgemm_small_matrix_permit)(int transa, int transb, BLASLONG m, BLASLONG n, BLASLONG k, float alpha0, float alpha1, float beta0, float beta1);
+
+  int    (*cgemm_small_kernel_nn    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_nt    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_nr    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_nc    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+
+  int    (*cgemm_small_kernel_tn    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_tt    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_tr    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_tc    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+
+  int    (*cgemm_small_kernel_rn    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_rt    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_rr    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_rc    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+
+  int    (*cgemm_small_kernel_cn    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_ct    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_cr    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_cc    )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb, float beta0, float beta1, float * C, BLASLONG ldc);
+
+  int    (*cgemm_small_kernel_b0_nn )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_nt )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_nr )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_nc )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+
+  int    (*cgemm_small_kernel_b0_tn )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_tt )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_tr )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_tc )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+
+  int    (*cgemm_small_kernel_b0_rn )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_rt )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_rr )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_rc )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+
+  int    (*cgemm_small_kernel_b0_cn )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_ct )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_cr )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+  int    (*cgemm_small_kernel_b0_cc )(BLASLONG m, BLASLONG n, BLASLONG k, float * A, BLASLONG lda, float alpha0, float alpha1, float * B, BLASLONG ldb,  float * C, BLASLONG ldc);
+#endif
+
   int    (*ctrsm_kernel_LN)(BLASLONG, BLASLONG, BLASLONG, float, float, float *, float *, float *, BLASLONG, BLASLONG);
   int    (*ctrsm_kernel_LT)(BLASLONG, BLASLONG, BLASLONG, float, float, float *, float *, float *, BLASLONG, BLASLONG);
   int    (*ctrsm_kernel_LR)(BLASLONG, BLASLONG, BLASLONG, float, float, float *, float *, float *, BLASLONG, BLASLONG);
@@ -679,6 +750,50 @@ BLASLONG (*izamin_k)(BLASLONG, double *, BLASLONG);
   int    (*zgemm_oncopy   )(BLASLONG, BLASLONG, double *, BLASLONG, double *);
   int    (*zgemm_otcopy   )(BLASLONG, BLASLONG, double *, BLASLONG, double *);
 
+#ifdef SMALL_MATRIX_OPT
+  int    (*zgemm_small_matrix_permit)(int transa, int transb, BLASLONG m, BLASLONG n, BLASLONG k, double alpha0, double alpha1, double beta0, double beta1);
+
+  int    (*zgemm_small_kernel_nn    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_nt    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_nr    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_nc    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+
+  int    (*zgemm_small_kernel_tn    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_tt    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_tr    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_tc    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+
+  int    (*zgemm_small_kernel_rn    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_rt    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_rr    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_rc    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+
+  int    (*zgemm_small_kernel_cn    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_ct    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_cr    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_cc    )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb, double beta0, double beta1, double * C, BLASLONG ldc);
+
+  int    (*zgemm_small_kernel_b0_nn )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_nt )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_nr )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_nc )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+
+  int    (*zgemm_small_kernel_b0_tn )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_tt )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_tr )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_tc )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+
+  int    (*zgemm_small_kernel_b0_rn )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_rt )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_rr )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_rc )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+
+  int    (*zgemm_small_kernel_b0_cn )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_ct )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_cr )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+  int    (*zgemm_small_kernel_b0_cc )(BLASLONG m, BLASLONG n, BLASLONG k, double * A, BLASLONG lda, double alpha0, double alpha1, double * B, BLASLONG ldb,  double * C, BLASLONG ldc);
+#endif
+
   int    (*ztrsm_kernel_LN)(BLASLONG, BLASLONG, BLASLONG, double, double, double *, double *, double *, BLASLONG, BLASLONG);
   int    (*ztrsm_kernel_LT)(BLASLONG, BLASLONG, BLASLONG, double, double, double *, double *, double *, BLASLONG, BLASLONG);
   int    (*ztrsm_kernel_LR)(BLASLONG, BLASLONG, BLASLONG, double, double, double *, double *, double *, BLASLONG, BLASLONG);
@@ -1069,6 +1184,8 @@ BLASLONG (*ixamin_k)(BLASLONG, xdouble *, BLASLONG);
 
 extern gotoblas_t *gotoblas;
 
+#define FUNC_OFFSET(func)	(size_t)(&((gotoblas_t *)NULL)->func)
+
 #define DTB_ENTRIES  gotoblas -> dtb_entries
 #define GEMM_OFFSET_A	gotoblas -> offsetA
 #define GEMM_OFFSET_B	gotoblas -> offsetB
@@ -1174,6 +1291,8 @@ extern gotoblas_t *gotoblas;
 
 #else
 
+#define FUNC_OFFSET(func)	(size_t)(func)
+
 #define DTB_ENTRIES  DTB_DEFAULT_ENTRIES
 
 #define GEMM_OFFSET_A	GEMM_DEFAULT_OFFSET_A

common_s.h

@@ -164,6 +164,8 @@
 
 #define SGEADD_K                sgeadd_k 
 
+#define SGEMM_SMALL_MATRIX_PERMIT	sgemm_small_matrix_permit
+
 #else
 
 #define	SAMAX_K			gotoblas -> samax_k
@@ -299,8 +301,21 @@
 
 #define SGEADD_K                gotoblas -> sgeadd_k 
 
+#define SGEMM_SMALL_MATRIX_PERMIT	gotoblas -> sgemm_small_matrix_permit
+
 #endif
 
+#define SGEMM_SMALL_KERNEL_NN		FUNC_OFFSET(sgemm_small_kernel_nn)
+#define SGEMM_SMALL_KERNEL_NT		FUNC_OFFSET(sgemm_small_kernel_nt)
+#define SGEMM_SMALL_KERNEL_TN		FUNC_OFFSET(sgemm_small_kernel_tn)
+#define SGEMM_SMALL_KERNEL_TT		FUNC_OFFSET(sgemm_small_kernel_tt)
+
+#define SGEMM_SMALL_KERNEL_B0_NN	FUNC_OFFSET(sgemm_small_kernel_b0_nn)
+#define SGEMM_SMALL_KERNEL_B0_NT	FUNC_OFFSET(sgemm_small_kernel_b0_nt)
+#define SGEMM_SMALL_KERNEL_B0_TN	FUNC_OFFSET(sgemm_small_kernel_b0_tn)
+#define SGEMM_SMALL_KERNEL_B0_TT	FUNC_OFFSET(sgemm_small_kernel_b0_tt)
+
+
 #define	SGEMM_NN		sgemm_nn
 #define	SGEMM_CN		sgemm_tn
 #define	SGEMM_TN		sgemm_tn

common_z.h

@@ -232,6 +232,8 @@
 
 #define ZGEADD_K                zgeadd_k 
 
+#define ZGEMM_SMALL_MATRIX_PERMIT	zgemm_small_matrix_permit
+
 #else
 
 #define	ZAMAX_K			gotoblas -> zamax_k
@@ -426,8 +428,51 @@
 
 #define ZGEADD_K                gotoblas -> zgeadd_k
 
+#define ZGEMM_SMALL_MATRIX_PERMIT	gotoblas -> zgemm_small_matrix_permit
+
 #endif
 
+#define ZGEMM_SMALL_KERNEL_NN		FUNC_OFFSET(zgemm_small_kernel_nn)
+#define ZGEMM_SMALL_KERNEL_NT		FUNC_OFFSET(zgemm_small_kernel_nt)
+#define ZGEMM_SMALL_KERNEL_NR		FUNC_OFFSET(zgemm_small_kernel_nr)
+#define ZGEMM_SMALL_KERNEL_NC		FUNC_OFFSET(zgemm_small_kernel_nc)
+
+#define ZGEMM_SMALL_KERNEL_TN		FUNC_OFFSET(zgemm_small_kernel_tn)
+#define ZGEMM_SMALL_KERNEL_TT		FUNC_OFFSET(zgemm_small_kernel_tt)
+#define ZGEMM_SMALL_KERNEL_TR		FUNC_OFFSET(zgemm_small_kernel_tr)
+#define ZGEMM_SMALL_KERNEL_TC		FUNC_OFFSET(zgemm_small_kernel_tc)
+
+#define ZGEMM_SMALL_KERNEL_RN		FUNC_OFFSET(zgemm_small_kernel_rn)
+#define ZGEMM_SMALL_KERNEL_RT		FUNC_OFFSET(zgemm_small_kernel_rt)
+#define ZGEMM_SMALL_KERNEL_RR		FUNC_OFFSET(zgemm_small_kernel_rr)
+#define ZGEMM_SMALL_KERNEL_RC		FUNC_OFFSET(zgemm_small_kernel_rc)
+
+#define ZGEMM_SMALL_KERNEL_CN		FUNC_OFFSET(zgemm_small_kernel_cn)
+#define ZGEMM_SMALL_KERNEL_CT		FUNC_OFFSET(zgemm_small_kernel_ct)
+#define ZGEMM_SMALL_KERNEL_CR		FUNC_OFFSET(zgemm_small_kernel_cr)
+#define ZGEMM_SMALL_KERNEL_CC		FUNC_OFFSET(zgemm_small_kernel_cc)
+
+#define ZGEMM_SMALL_KERNEL_B0_NN	FUNC_OFFSET(zgemm_small_kernel_b0_nn)
+#define ZGEMM_SMALL_KERNEL_B0_NT	FUNC_OFFSET(zgemm_small_kernel_b0_nt)
+#define ZGEMM_SMALL_KERNEL_B0_NR	FUNC_OFFSET(zgemm_small_kernel_b0_nr)
+#define ZGEMM_SMALL_KERNEL_B0_NC	FUNC_OFFSET(zgemm_small_kernel_b0_nc)
+
+#define ZGEMM_SMALL_KERNEL_B0_TN	FUNC_OFFSET(zgemm_small_kernel_b0_tn)
+#define ZGEMM_SMALL_KERNEL_B0_TT	FUNC_OFFSET(zgemm_small_kernel_b0_tt)
+#define ZGEMM_SMALL_KERNEL_B0_TR	FUNC_OFFSET(zgemm_small_kernel_b0_tr)
+#define ZGEMM_SMALL_KERNEL_B0_TC	FUNC_OFFSET(zgemm_small_kernel_b0_tc)
+
+#define ZGEMM_SMALL_KERNEL_B0_RN	FUNC_OFFSET(zgemm_small_kernel_b0_rn)
+#define ZGEMM_SMALL_KERNEL_B0_RT	FUNC_OFFSET(zgemm_small_kernel_b0_rt)
+#define ZGEMM_SMALL_KERNEL_B0_RR	FUNC_OFFSET(zgemm_small_kernel_b0_rr)
+#define ZGEMM_SMALL_KERNEL_B0_RC	FUNC_OFFSET(zgemm_small_kernel_b0_rc)
+
+#define ZGEMM_SMALL_KERNEL_B0_CN	FUNC_OFFSET(zgemm_small_kernel_b0_cn)
+#define ZGEMM_SMALL_KERNEL_B0_CT	FUNC_OFFSET(zgemm_small_kernel_b0_ct)
+#define ZGEMM_SMALL_KERNEL_B0_CR	FUNC_OFFSET(zgemm_small_kernel_b0_cr)
+#define ZGEMM_SMALL_KERNEL_B0_CC	FUNC_OFFSET(zgemm_small_kernel_b0_cc)
+
+
 #define	ZGEMM_NN		zgemm_nn
 #define	ZGEMM_CN		zgemm_cn
 #define	ZGEMM_TN		zgemm_tn

interface/gemm.c

@@ -105,6 +105,55 @@ static int (*gemm[])(blas_arg_t *, BLASLONG *, BLASLONG *, IFLOAT *, IFLOAT *, B
 #endif
 };
 
+#if defined(SMALL_MATRIX_OPT) && !defined(GEMM3M) && !defined(XDOUBLE) && !defined(BFLOAT16)
+#define USE_SMALL_MATRIX_OPT 1
+#else
+#define USE_SMALL_MATRIX_OPT 0
+#endif
+
+#if USE_SMALL_MATRIX_OPT
+#ifndef DYNAMIC_ARCH
+#define SMALL_KERNEL_ADDR(table, idx) ((void *)(table[idx]))
+#else
+#define SMALL_KERNEL_ADDR(table, idx) ((void *)(*(uintptr_t *)((char *)gotoblas + (size_t)(table[idx]))))
+#endif
+
+
+#ifndef COMPLEX
+static size_t gemm_small_kernel[] = {
+	GEMM_SMALL_KERNEL_NN, GEMM_SMALL_KERNEL_TN, 0, 0,
+	GEMM_SMALL_KERNEL_NT, GEMM_SMALL_KERNEL_TT, 0, 0,
+};
+
+
+static size_t gemm_small_kernel_b0[] = {
+	GEMM_SMALL_KERNEL_B0_NN, GEMM_SMALL_KERNEL_B0_TN, 0, 0,
+	GEMM_SMALL_KERNEL_B0_NT, GEMM_SMALL_KERNEL_B0_TT, 0, 0,
+};
+
+#define GEMM_SMALL_KERNEL_B0(idx) (int (*)(BLASLONG, BLASLONG, BLASLONG, FLOAT *, BLASLONG, FLOAT, FLOAT *, BLASLONG, FLOAT *, BLASLONG)) SMALL_KERNEL_ADDR(gemm_small_kernel_b0, (idx))
+#define GEMM_SMALL_KERNEL(idx) (int (*)(BLASLONG, BLASLONG, BLASLONG, FLOAT *, BLASLONG, FLOAT ,FLOAT *, BLASLONG, FLOAT, FLOAT *, BLASLONG)) SMALL_KERNEL_ADDR(gemm_small_kernel, (idx))
+#else
+
+static size_t zgemm_small_kernel[] = {
+	GEMM_SMALL_KERNEL_NN, GEMM_SMALL_KERNEL_TN, GEMM_SMALL_KERNEL_RN, GEMM_SMALL_KERNEL_CN,
+	GEMM_SMALL_KERNEL_NT, GEMM_SMALL_KERNEL_TT, GEMM_SMALL_KERNEL_RT, GEMM_SMALL_KERNEL_CT,
+	GEMM_SMALL_KERNEL_NR, GEMM_SMALL_KERNEL_TR, GEMM_SMALL_KERNEL_RR, GEMM_SMALL_KERNEL_CR,
+	GEMM_SMALL_KERNEL_NC, GEMM_SMALL_KERNEL_TC, GEMM_SMALL_KERNEL_RC, GEMM_SMALL_KERNEL_CC,
+};
+
+static size_t zgemm_small_kernel_b0[] = {
+	GEMM_SMALL_KERNEL_B0_NN, GEMM_SMALL_KERNEL_B0_TN, GEMM_SMALL_KERNEL_B0_RN, GEMM_SMALL_KERNEL_B0_CN,
+	GEMM_SMALL_KERNEL_B0_NT, GEMM_SMALL_KERNEL_B0_TT, GEMM_SMALL_KERNEL_B0_RT, GEMM_SMALL_KERNEL_B0_CT,
+	GEMM_SMALL_KERNEL_B0_NR, GEMM_SMALL_KERNEL_B0_TR, GEMM_SMALL_KERNEL_B0_RR, GEMM_SMALL_KERNEL_B0_CR,
+	GEMM_SMALL_KERNEL_B0_NC, GEMM_SMALL_KERNEL_B0_TC, GEMM_SMALL_KERNEL_B0_RC, GEMM_SMALL_KERNEL_B0_CC,
+};
+
+#define ZGEMM_SMALL_KERNEL(idx) (int (*)(BLASLONG, BLASLONG, BLASLONG, FLOAT *, BLASLONG, FLOAT , FLOAT, FLOAT *, BLASLONG, FLOAT , FLOAT, FLOAT *, BLASLONG)) SMALL_KERNEL_ADDR(zgemm_small_kernel, (idx))
+#define ZGEMM_SMALL_KERNEL_B0(idx) (int (*)(BLASLONG, BLASLONG, BLASLONG, FLOAT *, BLASLONG, FLOAT , FLOAT, FLOAT *, BLASLONG, FLOAT *, BLASLONG)) SMALL_KERNEL_ADDR(zgemm_small_kernel_b0, (idx))
+#endif
+#endif
+
 #ifndef CBLAS
 
 void NAME(char *TRANSA, char *TRANSB,
@@ -417,6 +466,28 @@ void CNAME(enum CBLAS_ORDER order, enum CBLAS_TRANSPOSE TransA, enum CBLAS_TRANS
 
   FUNCTION_PROFILE_START();
 
+#if USE_SMALL_MATRIX_OPT
+#if !defined(COMPLEX)
+  if(GEMM_SMALL_MATRIX_PERMIT(transa, transb, args.m, args.n, args.k, *(FLOAT *)(args.alpha), *(FLOAT *)(args.beta))){
+	  if(*(FLOAT *)(args.beta) == 0.0){
+		(GEMM_SMALL_KERNEL_B0((transb << 2) | transa))(args.m, args.n, args.k, args.a, args.lda, *(FLOAT *)(args.alpha), args.b, args.ldb, args.c, args.ldc);
+	  }else{
+		(GEMM_SMALL_KERNEL((transb << 2) | transa))(args.m, args.n, args.k, args.a, args.lda, *(FLOAT *)(args.alpha), args.b, args.ldb, *(FLOAT *)(args.beta), args.c, args.ldc);
+	  }
+	  return;
+  }
+#else
+  if(GEMM_SMALL_MATRIX_PERMIT(transa, transb, args.m, args.n, args.k, alpha[0], alpha[1], beta[0], beta[1])){
+	  if(beta[0] == 0.0 && beta[1] == 0.0){
+		(ZGEMM_SMALL_KERNEL_B0((transb << 2) | transa))(args.m, args.n, args.k, args.a, args.lda, alpha[0], alpha[1], args.b, args.ldb, args.c, args.ldc);
+	  }else{
+		(ZGEMM_SMALL_KERNEL((transb << 2) | transa))(args.m, args.n, args.k, args.a, args.lda, alpha[0], alpha[1], args.b, args.ldb, beta[0], beta[1], args.c, args.ldc);
+	  }
+	  return;
+  }
+#endif
+#endif
+
   buffer = (XFLOAT *)blas_memory_alloc(0);
 
   sa = (XFLOAT *)((BLASLONG)buffer +GEMM_OFFSET_A);

kernel/CMakeLists.txt

@@ -458,7 +458,117 @@ function (build_core TARGET_CORE KDIR TSUFFIX KERNEL_DEFINITIONS)
       GenerateNamedObjects("${KERNELDIR}/${${float_char}TRSMKERNEL_RN}" "UPPER;RN;TRSMKERNEL" "trsm_kernel_RN" false "" "" false ${float_type})
       GenerateNamedObjects("${KERNELDIR}/${${float_char}TRSMKERNEL_RT}" "RT;TRSMKERNEL" "trsm_kernel_RT" false "" "" false ${float_type})
 
+      if (NOT DEFINED ${float_char}GEMM_SMALL_M_PERMIT)
+        if (${float_char} STREQUAL "Z" OR ${float_char} STREQUAL "C")
+          set(${float_char}GEMM_SMALL_M_PERMIT ../generic/zgemm_small_matrix_permit.c)
+        else ()
+          set(${float_char}GEMM_SMALL_M_PERMIT ../generic/gemm_small_matrix_permit.c)
+        endif ()
+      endif ()
+      if (NOT DEFINED ${float_char}GEMM_SMALL_K_NN)
+        if (${float_char} STREQUAL "Z" OR ${float_char} STREQUAL "C")
+          set(${float_char}GEMM_SMALL_K_NN ../generic/zgemm_small_matrix_kernel_nn.c)
+        else ()
+          set(${float_char}GEMM_SMALL_K_NN ../generic/gemm_small_matrix_kernel_nn.c)
+        endif ()
+      endif ()
+      if (NOT DEFINED ${float_char}GEMM_SMALL_K_NT)
+        if (${float_char} STREQUAL "Z" OR ${float_char} STREQUAL "C")
+          set(${float_char}GEMM_SMALL_K_NT ../generic/zgemm_small_matrix_kernel_nt.c)
+        else ()
+          set(${float_char}GEMM_SMALL_K_NT ../generic/gemm_small_matrix_kernel_nt.c)
+        endif ()
+      endif ()
+      if (NOT DEFINED ${float_char}GEMM_SMALL_K_TN)
+        if (${float_char} STREQUAL "Z" OR ${float_char} STREQUAL "C")
+          set(${float_char}GEMM_SMALL_K_TN ../generic/zgemm_small_matrix_kernel_tn.c)
+        else ()
+          set(${float_char}GEMM_SMALL_K_TN ../generic/gemm_small_matrix_kernel_tn.c)
+        endif ()
+      endif ()
+      if (NOT DEFINED ${float_char}GEMM_SMALL_K_TT)
+        if (${float_char} STREQUAL "Z" OR ${float_char} STREQUAL "C")
+          set(${float_char}GEMM_SMALL_K_TT ../generic/zgemm_small_matrix_kernel_tt.c)
+        else ()
+          set(${float_char}GEMM_SMALL_K_TT ../generic/gemm_small_matrix_kernel_tt.c)
+        endif ()
+      endif ()
+      if (NOT DEFINED ${float_char}GEMM_SMALL_K_B0_NN)
+        if (${float_char} STREQUAL "Z" OR ${float_char} STREQUAL "C")
+          set(${float_char}GEMM_SMALL_K_B0_NN ../generic/zgemm_small_matrix_kernel_nn.c)
+        else ()
+          set(${float_char}GEMM_SMALL_K_B0_NN ../generic/gemm_small_matrix_kernel_nn.c)
+        endif ()
+      endif ()
+      if (NOT DEFINED ${float_char}GEMM_SMALL_K_B0_NT)
+        if (${float_char} STREQUAL "Z" OR ${float_char} STREQUAL "C")
+          set(${float_char}GEMM_SMALL_K_B0_NT ../generic/zgemm_small_matrix_kernel_nt.c)
+        else ()
+          set(${float_char}GEMM_SMALL_K_B0_NT ../generic/gemm_small_matrix_kernel_nt.c)
+        endif ()
+      endif ()
+      if (NOT DEFINED ${float_char}GEMM_SMALL_K_B0_TN)
+        if (${float_char} STREQUAL "Z" OR ${float_char} STREQUAL "C")
+          set(${float_char}GEMM_SMALL_K_B0_TN ../generic/zgemm_small_matrix_kernel_tn.c)
+        else ()
+          set(${float_char}GEMM_SMALL_K_B0_TN ../generic/gemm_small_matrix_kernel_tn.c)
+        endif ()
+      endif ()
+      if (NOT DEFINED ${float_char}GEMM_SMALL_K_B0_TT)
+        if (${float_char} STREQUAL "Z" OR ${float_char} STREQUAL "C")
+          set(${float_char}GEMM_SMALL_K_B0_TT ../generic/zgemm_small_matrix_kernel_tt.c)
+        else ()
+          set(${float_char}GEMM_SMALL_K_B0_TT ../generic/gemm_small_matrix_kernel_tt.c)
+        endif ()
+      endif ()
 
+      if (SMALL_MATRIX_OPT)
+        GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_M_PERMIT}" "" "gemm_small_matrix_permit" false "" "" false ${float_type})
+        if (${float_char} STREQUAL "Z" OR ${float_char} STREQUAL "C")
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_NN}" "NN" "gemm_small_kernel_nn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_NN}" "NR" "gemm_small_kernel_nr" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_NN}" "RN" "gemm_small_kernel_rn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_NN}" "RR" "gemm_small_kernel_rr" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_NT}" "NT" "gemm_small_kernel_nt" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_NT}" "NC" "gemm_small_kernel_nc" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_NT}" "RT" "gemm_small_kernel_rt" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_NT}" "RC" "gemm_small_kernel_rc" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_TN}" "TN" "gemm_small_kernel_tn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_TN}" "TR" "gemm_small_kernel_tr" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_TN}" "CN" "gemm_small_kernel_cn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_TN}" "CR" "gemm_small_kernel_cr" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_TT}" "TT" "gemm_small_kernel_tt" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_TT}" "TC" "gemm_small_kernel_tc" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_TT}" "CT" "gemm_small_kernel_ct" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_TT}" "CC" "gemm_small_kernel_cc" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_NN}" "NN;B0" "gemm_small_kernel_b0_nn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_NN}" "NR;B0" "gemm_small_kernel_b0_nr" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_NN}" "RN;B0" "gemm_small_kernel_b0_rn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_NN}" "RR;B0" "gemm_small_kernel_b0_rr" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_NT}" "NT;B0" "gemm_small_kernel_b0_nt" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_NT}" "NC;B0" "gemm_small_kernel_b0_nc" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_NT}" "RT;B0" "gemm_small_kernel_b0_rt" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_NT}" "RC;B0" "gemm_small_kernel_b0_rc" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_TN}" "TN;B0" "gemm_small_kernel_b0_tn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_TN}" "TR;B0" "gemm_small_kernel_b0_tr" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_TN}" "CN;B0" "gemm_small_kernel_b0_cn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_TN}" "CR;B0" "gemm_small_kernel_b0_cr" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_TT}" "TT;B0" "gemm_small_kernel_b0_tt" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_TT}" "TC;B0" "gemm_small_kernel_b0_tc" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_TT}" "CT;B0" "gemm_small_kernel_b0_ct" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_TT}" "CC;B0" "gemm_small_kernel_b0_cc" false "" "" false ${float_type})
+
+        else ()
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_NN}" "" "gemm_small_kernel_nn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_NT}" "" "gemm_small_kernel_nt" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_TN}" "" "gemm_small_kernel_tn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_NT}" "" "gemm_small_kernel_tt" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_NN}" "B0" "gemm_small_kernel_b0_nn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_NT}" "B0" "gemm_small_kernel_b0_nt" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_TN}" "B0" "gemm_small_kernel_b0_tn" false "" "" false ${float_type})
+            GenerateNamedObjects("${KERNELDIR}/${${float_char}GEMM_SMALL_K_B0_NT}" "B0" "gemm_small_kernel_b0_tt" false "" "" false ${float_type})
+        endif ()
+      endif ()
 
       if (NOT DEFINED ${float_char}OMATCOPY_CN)
         if (${float_char} STREQUAL "Z" OR ${float_char} STREQUAL "C")

kernel/Makefile.L3

@@ -447,6 +447,63 @@ XBLASOBJS += \
 
 endif
 
+######  BLAS small matrix optimization #####
+ifeq ($(SMALL_MATRIX_OPT), 1)
+
+SBLASOBJS += \
+	sgemm_small_matrix_permit$(TSUFFIX).$(SUFFIX) \
+	sgemm_small_kernel_nn$(TSUFFIX).$(SUFFIX) sgemm_small_kernel_nt$(TSUFFIX).$(SUFFIX) \
+	sgemm_small_kernel_tn$(TSUFFIX).$(SUFFIX) sgemm_small_kernel_tt$(TSUFFIX).$(SUFFIX) \
+	sgemm_small_kernel_b0_nn$(TSUFFIX).$(SUFFIX) sgemm_small_kernel_b0_nt$(TSUFFIX).$(SUFFIX) \
+	sgemm_small_kernel_b0_tn$(TSUFFIX).$(SUFFIX) sgemm_small_kernel_b0_tt$(TSUFFIX).$(SUFFIX)
+
+DBLASOBJS += \
+	dgemm_small_matrix_permit$(TSUFFIX).$(SUFFIX) \
+	dgemm_small_kernel_nn$(TSUFFIX).$(SUFFIX) dgemm_small_kernel_nt$(TSUFFIX).$(SUFFIX) \
+	dgemm_small_kernel_tn$(TSUFFIX).$(SUFFIX) dgemm_small_kernel_tt$(TSUFFIX).$(SUFFIX) \
+	dgemm_small_kernel_b0_nn$(TSUFFIX).$(SUFFIX) dgemm_small_kernel_b0_nt$(TSUFFIX).$(SUFFIX) \
+	dgemm_small_kernel_b0_tn$(TSUFFIX).$(SUFFIX) dgemm_small_kernel_b0_tt$(TSUFFIX).$(SUFFIX)
+
+CBLASOBJS += \
+	cgemm_small_matrix_permit$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_nn$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_nt$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_nr$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_nc$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_tn$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_tt$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_tr$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_tc$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_rn$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_rt$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_rr$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_rc$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_cn$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_ct$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_cr$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_cc$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_b0_nn$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_b0_nt$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_b0_nr$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_b0_nc$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_b0_tn$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_b0_tt$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_b0_tr$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_b0_tc$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_b0_rn$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_b0_rt$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_b0_rr$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_b0_rc$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_b0_cn$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_b0_ct$(TSUFFIX).$(SUFFIX) \
+	cgemm_small_kernel_b0_cr$(TSUFFIX).$(SUFFIX) cgemm_small_kernel_b0_cc$(TSUFFIX).$(SUFFIX)
+
+ZBLASOBJS += \
+	zgemm_small_matrix_permit$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_nn$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_nt$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_nr$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_nc$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_tn$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_tt$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_tr$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_tc$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_rn$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_rt$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_rr$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_rc$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_cn$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_ct$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_cr$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_cc$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_b0_nn$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_b0_nt$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_b0_nr$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_b0_nc$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_b0_tn$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_b0_tt$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_b0_tr$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_b0_tc$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_b0_rn$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_b0_rt$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_b0_rr$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_b0_rc$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_b0_cn$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_b0_ct$(TSUFFIX).$(SUFFIX) \
+	zgemm_small_kernel_b0_cr$(TSUFFIX).$(SUFFIX) zgemm_small_kernel_b0_cc$(TSUFFIX).$(SUFFIX)
+
+endif
+
 ######  BLAS extensions #####
 
 ifeq ($(BUILD_SINGLE),1)
@@ -4237,3 +4294,403 @@ endif
 $(KDIR)zgeadd_k$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEADD_K)
 	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -UROWM $< -o $@
 
+
+
+######  BLAS small matrix optimization #####
+
+ifndef DGEMM_SMALL_M_PERMIT
+DGEMM_SMALL_M_PERMIT = ../generic/gemm_small_matrix_permit.c
+endif
+
+ifndef DGEMM_SMALL_K_NN
+DGEMM_SMALL_K_NN = ../generic/gemm_small_matrix_kernel_nn.c
+endif
+
+ifndef DGEMM_SMALL_K_NT
+DGEMM_SMALL_K_NT = ../generic/gemm_small_matrix_kernel_nt.c
+endif
+
+ifndef DGEMM_SMALL_K_TN
+DGEMM_SMALL_K_TN = ../generic/gemm_small_matrix_kernel_tn.c
+endif
+
+ifndef DGEMM_SMALL_K_TT
+DGEMM_SMALL_K_TT = ../generic/gemm_small_matrix_kernel_tt.c
+endif
+
+$(KDIR)dgemm_small_matrix_permit$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(DGEMM_SMALL_M_PERMIT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -UCOMPLEX $< -o $@
+
+$(KDIR)dgemm_small_kernel_nn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(DGEMM_SMALL_K_NN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -UCOMPLEX $< -o $@
+
+$(KDIR)dgemm_small_kernel_nt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(DGEMM_SMALL_K_NT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -UCOMPLEX $< -o $@
+
+$(KDIR)dgemm_small_kernel_tn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(DGEMM_SMALL_K_TN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -UCOMPLEX $< -o $@
+
+$(KDIR)dgemm_small_kernel_tt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(DGEMM_SMALL_K_TT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -UCOMPLEX $< -o $@
+
+ifndef DGEMM_SMALL_K_B0_NN
+DGEMM_SMALL_K_B0_NN = ../generic/gemm_small_matrix_kernel_nn.c
+endif
+
+ifndef DGEMM_SMALL_K_B0_NT
+DGEMM_SMALL_K_B0_NT = ../generic/gemm_small_matrix_kernel_nt.c
+endif
+
+ifndef DGEMM_SMALL_K_B0_TN
+DGEMM_SMALL_K_B0_TN = ../generic/gemm_small_matrix_kernel_tn.c
+endif
+
+ifndef DGEMM_SMALL_K_B0_TT
+DGEMM_SMALL_K_B0_TT = ../generic/gemm_small_matrix_kernel_tt.c
+endif
+
+$(KDIR)dgemm_small_kernel_b0_nn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(DGEMM_SMALL_K_B0_NN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -UCOMPLEX -DB0 $< -o $@
+
+$(KDIR)dgemm_small_kernel_b0_nt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(DGEMM_SMALL_K_B0_NT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -UCOMPLEX -DB0 $< -o $@
+
+$(KDIR)dgemm_small_kernel_b0_tn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(DGEMM_SMALL_K_B0_TN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -UCOMPLEX -DB0 $< -o $@
+
+$(KDIR)dgemm_small_kernel_b0_tt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(DGEMM_SMALL_K_B0_TT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -UCOMPLEX -DB0 $< -o $@
+
+ifndef SGEMM_SMALL_M_PERMIT
+SGEMM_SMALL_M_PERMIT = ../generic/gemm_small_matrix_permit.c
+endif
+
+ifndef SGEMM_SMALL_K_NN
+SGEMM_SMALL_K_NN = ../generic/gemm_small_matrix_kernel_nn.c
+endif
+
+ifndef SGEMM_SMALL_K_NT
+SGEMM_SMALL_K_NT = ../generic/gemm_small_matrix_kernel_nt.c
+endif
+
+ifndef SGEMM_SMALL_K_TN
+SGEMM_SMALL_K_TN = ../generic/gemm_small_matrix_kernel_tn.c
+endif
+
+ifndef SGEMM_SMALL_K_TT
+SGEMM_SMALL_K_TT = ../generic/gemm_small_matrix_kernel_tt.c
+endif
+
+$(KDIR)sgemm_small_matrix_permit$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(SGEMM_SMALL_M_PERMIT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -UCOMPLEX $< -o $@
+
+$(KDIR)sgemm_small_kernel_nn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(SGEMM_SMALL_K_NN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -UCOMPLEX $< -o $@
+
+$(KDIR)sgemm_small_kernel_nt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(SGEMM_SMALL_K_NT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -UCOMPLEX $< -o $@
+
+$(KDIR)sgemm_small_kernel_tn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(SGEMM_SMALL_K_TN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -UCOMPLEX $< -o $@
+
+$(KDIR)sgemm_small_kernel_tt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(SGEMM_SMALL_K_TT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -UCOMPLEX $< -o $@
+
+ifndef SGEMM_SMALL_K_B0_NN
+SGEMM_SMALL_K_B0_NN = ../generic/gemm_small_matrix_kernel_nn.c
+endif
+
+ifndef SGEMM_SMALL_K_B0_NT
+SGEMM_SMALL_K_B0_NT = ../generic/gemm_small_matrix_kernel_nt.c
+endif
+
+ifndef SGEMM_SMALL_K_B0_TN
+SGEMM_SMALL_K_B0_TN = ../generic/gemm_small_matrix_kernel_tn.c
+endif
+
+ifndef SGEMM_SMALL_K_B0_TT
+SGEMM_SMALL_K_B0_TT = ../generic/gemm_small_matrix_kernel_tt.c
+endif
+
+$(KDIR)sgemm_small_kernel_b0_nn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(SGEMM_SMALL_K_B0_NN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -UCOMPLEX -DB0 $< -o $@
+
+$(KDIR)sgemm_small_kernel_b0_nt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(SGEMM_SMALL_K_B0_NT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -UCOMPLEX -DB0 $< -o $@
+
+$(KDIR)sgemm_small_kernel_b0_tn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(SGEMM_SMALL_K_B0_TN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -UCOMPLEX -DB0 $< -o $@
+
+$(KDIR)sgemm_small_kernel_b0_tt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(SGEMM_SMALL_K_B0_TT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -UCOMPLEX -DB0 $< -o $@
+
+ifndef CGEMM_SMALL_M_PERMIT
+CGEMM_SMALL_M_PERMIT = ../generic/zgemm_small_matrix_permit.c
+endif
+
+ifndef CGEMM_SMALL_K_NN
+CGEMM_SMALL_K_NN = ../generic/zgemm_small_matrix_kernel_nn.c
+endif
+
+ifndef CGEMM_SMALL_K_NT
+CGEMM_SMALL_K_NT = ../generic/zgemm_small_matrix_kernel_nt.c
+endif
+
+ifndef CGEMM_SMALL_K_TN
+CGEMM_SMALL_K_TN = ../generic/zgemm_small_matrix_kernel_tn.c
+endif
+
+ifndef CGEMM_SMALL_K_TT
+CGEMM_SMALL_K_TT = ../generic/zgemm_small_matrix_kernel_tt.c
+endif
+
+$(KDIR)cgemm_small_matrix_permit$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_M_PERMIT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX $< -o $@
+
+$(KDIR)cgemm_small_kernel_nn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_NN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DNN $< -o $@
+	
+$(KDIR)cgemm_small_kernel_nr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_NN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DNR $< -o $@
+
+$(KDIR)cgemm_small_kernel_rn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_NN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DRN $< -o $@
+
+$(KDIR)cgemm_small_kernel_rr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_NN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DRR $< -o $@
+
+$(KDIR)cgemm_small_kernel_nt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_NT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DNT $< -o $@
+
+$(KDIR)cgemm_small_kernel_nc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_NT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DNC $< -o $@
+
+$(KDIR)cgemm_small_kernel_rt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_NT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DRT $< -o $@
+
+$(KDIR)cgemm_small_kernel_rc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_NT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DRC $< -o $@
+
+$(KDIR)cgemm_small_kernel_tn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_TN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DTN $< -o $@
+
+$(KDIR)cgemm_small_kernel_tr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_TN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DTR $< -o $@
+
+$(KDIR)cgemm_small_kernel_cn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_TN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DCN $< -o $@
+
+$(KDIR)cgemm_small_kernel_cr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_TN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DCR $< -o $@
+
+$(KDIR)cgemm_small_kernel_tt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_TT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DTT $< -o $@
+
+$(KDIR)cgemm_small_kernel_tc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_TT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DTC $< -o $@
+
+$(KDIR)cgemm_small_kernel_ct$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_TT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DCT $< -o $@
+
+$(KDIR)cgemm_small_kernel_cc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_TT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DCC $< -o $@
+
+ifndef CGEMM_SMALL_K_B0_NN
+CGEMM_SMALL_K_B0_NN = ../generic/zgemm_small_matrix_kernel_nn.c
+endif
+
+ifndef CGEMM_SMALL_K_B0_NT
+CGEMM_SMALL_K_B0_NT = ../generic/zgemm_small_matrix_kernel_nt.c
+endif
+
+ifndef CGEMM_SMALL_K_B0_TN
+CGEMM_SMALL_K_B0_TN = ../generic/zgemm_small_matrix_kernel_tn.c
+endif
+
+ifndef CGEMM_SMALL_K_B0_TT
+CGEMM_SMALL_K_B0_TT = ../generic/zgemm_small_matrix_kernel_tt.c
+endif
+
+$(KDIR)cgemm_small_kernel_b0_nn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_NN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DNN -DB0 $< -o $@
+	
+$(KDIR)cgemm_small_kernel_b0_nr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_NN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DNR -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_rn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_NN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DRN -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_rr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_NN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DRR -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_nt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_NT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DNT -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_nc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_NT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DNC -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_rt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_NT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DRT -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_rc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_NT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DRC -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_tn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_TN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DTN -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_tr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_TN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DTR -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_cn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_TN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DCN -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_cr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_TN)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DCR -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_tt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_TT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DTT -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_tc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_TT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DTC -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_ct$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_TT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DCT -DB0 $< -o $@
+
+$(KDIR)cgemm_small_kernel_b0_cc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(CGEMM_SMALL_K_B0_TT)
+	$(CC) $(CFLAGS) -c -UDOUBLE -DCOMPLEX -DCC -DB0 $< -o $@
+
+ifndef ZGEMM_SMALL_M_PERMIT
+ZGEMM_SMALL_M_PERMIT = ../generic/zgemm_small_matrix_permit.c
+endif
+
+ifndef ZGEMM_SMALL_K_NN
+ZGEMM_SMALL_K_NN = ../generic/zgemm_small_matrix_kernel_nn.c
+endif
+
+ifndef ZGEMM_SMALL_K_NT
+ZGEMM_SMALL_K_NT = ../generic/zgemm_small_matrix_kernel_nt.c
+endif
+
+ifndef ZGEMM_SMALL_K_TN
+ZGEMM_SMALL_K_TN = ../generic/zgemm_small_matrix_kernel_tn.c
+endif
+
+ifndef ZGEMM_SMALL_K_TT
+ZGEMM_SMALL_K_TT = ../generic/zgemm_small_matrix_kernel_tt.c
+endif
+
+$(KDIR)zgemm_small_matrix_permit$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_M_PERMIT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX $< -o $@
+
+
+$(KDIR)zgemm_small_kernel_nn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_NN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DNN $< -o $@
+	
+$(KDIR)zgemm_small_kernel_nr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_NN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DNR $< -o $@
+
+$(KDIR)zgemm_small_kernel_rn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_NN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DRN $< -o $@
+
+$(KDIR)zgemm_small_kernel_rr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_NN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DRR $< -o $@
+
+$(KDIR)zgemm_small_kernel_nt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_NT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DNT $< -o $@
+
+$(KDIR)zgemm_small_kernel_nc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_NT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DNC $< -o $@
+
+$(KDIR)zgemm_small_kernel_rt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_NT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DRT $< -o $@
+
+$(KDIR)zgemm_small_kernel_rc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_NT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DRC $< -o $@
+
+$(KDIR)zgemm_small_kernel_tn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_TN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DTN $< -o $@
+
+$(KDIR)zgemm_small_kernel_tr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_TN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DTR $< -o $@
+
+$(KDIR)zgemm_small_kernel_cn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_TN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DCN $< -o $@
+
+$(KDIR)zgemm_small_kernel_cr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_TN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DCR $< -o $@
+
+$(KDIR)zgemm_small_kernel_tt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_TT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DTT $< -o $@
+
+$(KDIR)zgemm_small_kernel_tc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_TT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DTC $< -o $@
+
+$(KDIR)zgemm_small_kernel_ct$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_TT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DCT $< -o $@
+
+$(KDIR)zgemm_small_kernel_cc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_TT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DCC $< -o $@
+
+ifndef ZGEMM_SMALL_K_B0_NN
+ZGEMM_SMALL_K_B0_NN = ../generic/zgemm_small_matrix_kernel_nn.c
+endif
+
+ifndef ZGEMM_SMALL_K_B0_NT
+ZGEMM_SMALL_K_B0_NT = ../generic/zgemm_small_matrix_kernel_nt.c
+endif
+
+ifndef ZGEMM_SMALL_K_B0_TN
+ZGEMM_SMALL_K_B0_TN = ../generic/zgemm_small_matrix_kernel_tn.c
+endif
+
+ifndef ZGEMM_SMALL_K_B0_TT
+ZGEMM_SMALL_K_B0_TT = ../generic/zgemm_small_matrix_kernel_tt.c
+endif
+
+$(KDIR)zgemm_small_kernel_b0_nn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_NN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DNN -DB0 $< -o $@
+	
+$(KDIR)zgemm_small_kernel_b0_nr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_NN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DNR -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_rn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_NN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DRN -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_rr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_NN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DRR -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_nt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_NT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DNT -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_nc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_NT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DNC -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_rt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_NT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DRT -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_rc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_NT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DRC -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_tn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_TN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DTN -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_tr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_TN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DTR -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_cn$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_TN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DCN -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_cr$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_TN)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DCR -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_tt$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_TT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DTT -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_tc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_TT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DTC -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_ct$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_TT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DCT -DB0 $< -o $@
+
+$(KDIR)zgemm_small_kernel_b0_cc$(TSUFFIX).$(SUFFIX) : $(KERNELDIR)/$(ZGEMM_SMALL_K_B0_TT)
+	$(CC) $(CFLAGS) -c -DDOUBLE -DCOMPLEX -DCC -DB0 $< -o $@

kernel/generic/gemm_small_matrix_kernel_nn.c

@@ -0,0 +1,56 @@
+/***************************************************************************
+Copyright (c) 2020, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+#ifdef B0
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb,FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	//naive implemtation
+	//Column major
+
+	BLASLONG i,j,k;
+	FLOAT result=0.0;
+
+	for(i=0; i<M; i++){
+		for(j=0; j<N; j++){
+			result=0.0;
+			for(k=0; k<K; k++){
+				result += A[i+k*lda] * B[k+j*ldb];
+			}
+#ifdef B0
+			C[i+j*ldc]=alpha * result;
+#else
+			C[i+j*ldc]=C[i+j*ldc] * beta + alpha * result;
+#endif
+		}
+	}
+	return 0;
+}

kernel/generic/gemm_small_matrix_kernel_nt.c

@@ -0,0 +1,56 @@
+/***************************************************************************
+Copyright (c) 2020, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+#ifdef B0
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	//naive implemtation
+	//Column major
+
+	BLASLONG i,j,k;
+	FLOAT result=0.0;
+
+	for(i=0; i<M; i++){
+		for(j=0; j<N; j++){
+			result=0.0;
+			for(k=0; k<K; k++){
+				result += A[i+k*lda] * B[k*ldb+j];
+			}
+#ifdef B0
+			C[i+j*ldc]=alpha * result;
+#else
+			C[i+j*ldc]=C[i+j*ldc] * beta + alpha * result;
+#endif
+		}
+	}
+	return 0;
+}

kernel/generic/gemm_small_matrix_kernel_tn.c

@@ -0,0 +1,57 @@
+/***************************************************************************
+Copyright (c) 2020, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+#ifdef B0
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb,FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	//naive implemtation
+	//Column major
+
+	BLASLONG i,j,k;
+	FLOAT result=0.0;
+
+	for(i=0; i<M; i++){
+		for(j=0; j<N; j++){
+			result=0.0;
+			for(k=0; k<K; k++){
+				result += A[i*lda+k] * B[k+j*ldb];
+			}
+#ifdef B0
+			C[i+j*ldc]=alpha * result;
+#else
+			C[i+j*ldc]=C[i+j*ldc] * beta + alpha * result;
+#endif
+		}
+	}
+
+	return 0;
+}

kernel/generic/gemm_small_matrix_kernel_tt.c

@@ -0,0 +1,57 @@
+/***************************************************************************
+Copyright (c) 2020, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+#ifdef B0
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	//naive implemtation
+	//Column major
+
+	BLASLONG i,j,k;
+	FLOAT result=0.0;
+
+	for(i=0; i<M; i++){
+		for(j=0; j<N; j++){
+			result=0.0;
+			for(k=0; k<K; k++){
+				result += A[i*lda+k] * B[k*ldb+j];
+			}
+#ifdef B0
+			C[i+j*ldc]=alpha * result;
+#else
+			C[i+j*ldc]=C[i+j*ldc] * beta + alpha * result;
+#endif
+		}
+	}
+
+	return 0;
+}

kernel/generic/gemm_small_matrix_permit.c

@@ -0,0 +1,40 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+int CNAME(int transa, int transb, BLASLONG M, BLASLONG N, BLASLONG K, FLOAT alpha, FLOAT beta)
+{
+	return 0;
+/*
+	double MNK = (double) M * (double) N * (double) K;
+	if (MNK <= 100.0*100.0*100.0)
+		return 1;
+	else
+		return 0;
+*/
+}

kernel/generic/zgemm_small_matrix_kernel_nn.c

@@ -0,0 +1,89 @@
+/***************************************************************************
+Copyright (c) 2020, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+#ifndef B0
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha0, FLOAT alpha1, FLOAT * B, BLASLONG ldb, FLOAT beta0, FLOAT beta1, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha0, FLOAT alpha1, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	FLOAT real, imag;
+#ifndef B0
+	FLOAT tmp0, tmp1;
+#endif
+	int i, j, l;
+	for(i = 0; i < M; i++){
+		for(j = 0; j < N; j++){
+			real=0;
+			imag=0;
+
+			for(l = 0; l < K; l++){
+#if defined(NN)
+				real += (A[l*2*lda + 2*i]*B[j*2*ldb + 2*l]      
+					 -A[l*2*lda + 2*i + 1] * B[j*2*ldb + 2*l + 1]);
+
+				imag+=(A[l*2*lda + 2*i] * B[j*2*ldb + 2*l + 1]        
+				       + A[l*2*lda + 2*i + 1] * B[j*2*ldb + 2*l]);
+#elif defined(NR)
+				real += (A[l*2*lda + 2*i]*B[j*2*ldb + 2*l]      
+					 +A[l*2*lda + 2*i + 1] * B[j*2*ldb + 2*l + 1]);
+
+				imag+=(-A[l*2*lda + 2*i] * B[j*2*ldb + 2*l + 1]      
+				       + A[l*2*lda + 2*i + 1] * B[j*2*ldb + 2*l]);
+#elif defined(RN)
+				real += (A[l*2*lda + 2*i]*B[j*2*ldb + 2*l]
+					 +A[l*2*lda + 2*i + 1] * B[j*2*ldb + 2*l + 1]);
+
+				imag+=(A[l*2*lda + 2*i] * B[j*2*ldb + 2*l + 1]
+				       - A[l*2*lda + 2*i + 1] * B[j*2*ldb + 2*l]);
+#elif defined(RR)
+				real += (A[l*2*lda + 2*i]*B[j*2*ldb + 2*l]
+					 -A[l*2*lda + 2*i + 1] * B[j*2*ldb + 2*l + 1]);
+
+				imag+=(-A[l*2*lda + 2*i] * B[j*2*ldb + 2*l + 1]
+				       - A[l*2*lda + 2*i + 1] * B[j*2*ldb + 2*l]);
+#endif
+			}
+
+#ifndef B0
+			tmp0 = beta0*C[j*2*ldc + 2*i] - beta1*C[j*2*ldc+ 2*i + 1];
+			tmp1 = beta0*C[j*2*ldc+ 2*i + 1] + beta1*C[j*2*ldc + 2*i];
+
+
+			C[j*2*ldc + 2*i] =tmp0+ alpha0*real - alpha1*imag;
+			C[j*2*ldc+ 2*i + 1] = tmp1+ alpha0*imag + real*alpha1;
+#else
+			C[j*2*ldc + 2*i] = alpha0*real - alpha1*imag;
+			C[j*2*ldc+ 2*i + 1] = alpha0*imag + real*alpha1;
+#endif
+		}
+	}
+	
+	return 0;
+}

kernel/generic/zgemm_small_matrix_kernel_nt.c

@@ -0,0 +1,93 @@
+/***************************************************************************
+Copyright (c) 2020, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+#ifndef B0
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha0, FLOAT alpha1, FLOAT * B, BLASLONG ldb, FLOAT beta0, FLOAT beta1, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha0, FLOAT alpha1, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	FLOAT real, imag;
+#ifndef B0
+	FLOAT tmp0, tmp1;
+#endif
+	int i, j, l;
+	for(i = 0; i < M; i++){
+		for(j = 0; j < N; j++){
+			real=0;
+			imag=0;
+
+			for(l = 0; l < K; l++){
+#if defined(NT)
+				real += (A[l*2*lda + 2*i]*B[l*2*ldb + 2*j]
+					 -A[l*2*lda + 2*i + 1] * B[l*2*ldb + 2*j + 1]);
+
+				imag+=(A[l*2*lda + 2*i] * B[l*2*ldb + 2*j + 1]    
+				       + A[l*2*lda + 2*i + 1] * B[l*2*ldb + 2*j]);
+
+#elif defined(NC)
+		                real += (A[l*2*lda + 2*i]*B[l*2*ldb + 2*j]          
+					 +A[l*2*lda + 2*i + 1] * B[l*2*ldb + 2*j + 1]);
+
+				imag+=(-A[l*2*lda + 2*i] * B[l*2*ldb + 2*j + 1]
+				       + A[l*2*lda + 2*i + 1] * B[l*2*ldb + 2*j]);
+
+#elif defined(RT)
+		                real += (A[l*2*lda + 2*i]*B[l*2*ldb + 2*j]
+					 +A[l*2*lda + 2*i + 1] * B[l*2*ldb + 2*j + 1]);
+
+				imag+=(A[l*2*lda + 2*i] * B[l*2*ldb + 2*j + 1]    
+				       - A[l*2*lda + 2*i + 1] * B[l*2*ldb + 2*j]);
+
+#elif defined(RC)
+		                real += (A[l*2*lda + 2*i]*B[l*2*ldb + 2*j]
+					 -A[l*2*lda + 2*i + 1] * B[l*2*ldb + 2*j + 1]);
+
+				imag+=(-A[l*2*lda + 2*i] * B[l*2*ldb + 2*j + 1]
+				       - A[l*2*lda + 2*i + 1] * B[l*2*ldb + 2*j]);
+
+#endif
+			}
+
+#ifndef B0
+			tmp0 = beta0*C[j*2*ldc + 2*i] - beta1*C[j*2*ldc+ 2*i + 1];
+			tmp1 = beta0*C[j*2*ldc+ 2*i + 1] + beta1*C[j*2*ldc + 2*i];
+
+
+			C[j*2*ldc + 2*i] =tmp0+ alpha0*real - alpha1*imag;
+			C[j*2*ldc+ 2*i + 1] = tmp1+ alpha0*imag + real*alpha1;
+#else
+			C[j*2*ldc + 2*i] = alpha0*real - alpha1*imag;
+			C[j*2*ldc+ 2*i + 1] = alpha0*imag + real*alpha1;
+#endif
+		}
+	}
+	
+	return 0;
+}

kernel/generic/zgemm_small_matrix_kernel_tn.c

@@ -0,0 +1,93 @@
+/***************************************************************************
+Copyright (c) 2020, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+#ifndef B0
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha0, FLOAT alpha1, FLOAT * B, BLASLONG ldb, FLOAT beta0, FLOAT beta1, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha0, FLOAT alpha1, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	FLOAT real, imag;
+#ifndef B0
+	FLOAT tmp0, tmp1;
+#endif
+	int i, j, l;
+	for(i = 0; i < M; i++){
+		for(j = 0; j < N; j++){
+			real=0;
+			imag=0;
+
+			for(l = 0; l < K; l++){
+#if defined(TN)
+				real += (A[i*2*lda + 2*l]*B[j*2*ldb + 2*l]
+					 -A[i*2*lda + 2*l + 1] * B[j*2*ldb + 2*l + 1]);
+
+				imag+=(A[i*2*lda + 2*l] * B[j*2*ldb + 2*l + 1]
+				       + A[i*2*lda + 2*l + 1] * B[j*2*ldb + 2*l]);
+
+#elif defined(TR)
+				real += (A[i*2*lda + 2*l]*B[j*2*ldb + 2*l]
+					 +A[i*2*lda + 2*l + 1] * B[j*2*ldb + 2*l + 1]);
+
+				imag+=(-A[i*2*lda + 2*l] * B[j*2*ldb + 2*l + 1]
+				       + A[i*2*lda + 2*l + 1] * B[j*2*ldb + 2*l]);
+
+#elif defined(CN)
+				real += (A[i*2*lda + 2*l]*B[j*2*ldb + 2*l]
+					 +A[i*2*lda + 2*l + 1] * B[j*2*ldb + 2*l + 1]);
+
+				imag+=(A[i*2*lda + 2*l] * B[j*2*ldb + 2*l + 1]
+				       - A[i*2*lda + 2*l + 1] * B[j*2*ldb + 2*l]);
+
+#elif defined(CR)
+				real += (A[i*2*lda + 2*l]*B[j*2*ldb + 2*l]
+					 -A[i*2*lda + 2*l + 1] * B[j*2*ldb + 2*l + 1]);
+
+				imag+=(-A[i*2*lda + 2*l] * B[j*2*ldb + 2*l + 1]
+				       - A[i*2*lda + 2*l + 1] * B[j*2*ldb + 2*l]);
+
+#endif
+			}
+
+#ifndef B0
+			tmp0 = beta0*C[j*2*ldc + 2*i] - beta1*C[j*2*ldc+ 2*i + 1];
+			tmp1 = beta0*C[j*2*ldc+ 2*i + 1] + beta1*C[j*2*ldc + 2*i];
+
+
+			C[j*2*ldc + 2*i] =tmp0+ alpha0*real - alpha1*imag;
+			C[j*2*ldc+ 2*i + 1] = tmp1+ alpha0*imag + real*alpha1;
+#else
+			C[j*2*ldc + 2*i] = alpha0*real - alpha1*imag;
+			C[j*2*ldc+ 2*i + 1] = alpha0*imag + real*alpha1;
+#endif
+		}
+	}
+	
+	return 0;
+}

kernel/generic/zgemm_small_matrix_kernel_tt.c

@@ -0,0 +1,93 @@
+/***************************************************************************
+Copyright (c) 2020, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+#ifndef B0
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha0, FLOAT alpha1, FLOAT * B, BLASLONG ldb, FLOAT beta0, FLOAT beta1, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha0, FLOAT alpha1, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	FLOAT real, imag;
+#ifndef B0
+	FLOAT tmp0, tmp1;
+#endif
+	int i, j, l;
+	for(i = 0; i < M; i++){
+		for(j = 0; j < N; j++){
+			real=0;
+			imag=0;
+
+			for(l = 0; l < K; l++){
+#if defined(TT)
+				real += (A[i*2*lda + 2*l]*B[l*2*ldb + 2*j]
+					 -A[i*2*lda + 2*l + 1] * B[l*2*ldb + 2*j + 1]);
+
+				imag+=(A[i*2*lda + 2*l] * B[l*2*ldb + 2*j + 1]
+				       + A[i*2*lda + 2*l + 1] * B[l*2*ldb + 2*j]);
+
+#elif defined(TC)
+				real += (A[i*2*lda + 2*l]*B[l*2*ldb + 2*j]
+					 +A[i*2*lda + 2*l + 1] * B[l*2*ldb + 2*j + 1]);
+
+				imag+=(-A[i*2*lda + 2*l] * B[l*2*ldb + 2*j + 1]
+				       + A[i*2*lda + 2*l + 1] * B[l*2*ldb + 2*j]);
+
+#elif defined(CT)
+				real += (A[i*2*lda + 2*l]*B[l*2*ldb + 2*j]
+					 +A[i*2*lda + 2*l + 1] * B[l*2*ldb + 2*j + 1]);
+
+				imag+=(A[i*2*lda + 2*l] * B[l*2*ldb + 2*j + 1]
+				       - A[i*2*lda + 2*l + 1] * B[l*2*ldb + 2*j]);
+
+#elif defined(CC)
+				real += (A[i*2*lda + 2*l]*B[l*2*ldb + 2*j]
+					 -A[i*2*lda + 2*l + 1] * B[l*2*ldb + 2*j + 1]);
+
+				imag+=(-A[i*2*lda + 2*l] * B[l*2*ldb + 2*j + 1]
+				       - A[i*2*lda + 2*l + 1] * B[l*2*ldb + 2*j]);
+
+#endif
+			}
+
+#ifndef B0
+			tmp0 = beta0*C[j*2*ldc + 2*i] - beta1*C[j*2*ldc+ 2*i + 1];
+			tmp1 = beta0*C[j*2*ldc+ 2*i + 1] + beta1*C[j*2*ldc + 2*i];
+
+
+			C[j*2*ldc + 2*i] =tmp0+ alpha0*real - alpha1*imag;
+			C[j*2*ldc+ 2*i + 1] = tmp1+ alpha0*imag + real*alpha1;
+#else
+			C[j*2*ldc + 2*i] = alpha0*real - alpha1*imag;
+			C[j*2*ldc+ 2*i + 1] = alpha0*imag + real*alpha1;
+#endif
+		}
+	}
+	
+	return 0;
+}

kernel/generic/zgemm_small_matrix_permit.c

@@ -0,0 +1,40 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+int CNAME(int transa, int transb, BLASLONG M, BLASLONG N, BLASLONG K, FLOAT alpha0, FLOAT alpha1, FLOAT beta0, FLOAT beta1)
+{
+	return 0;
+/*
+	double MNK = (double) M * (double) N * (double) K;
+	if (MNK <= 100.0*100.0*100.0)
+		return 1;
+	else
+		return 0;
+*/
+}

kernel/setparam-ref.c

@@ -171,6 +171,14 @@ gotoblas_t TABLE_NAME = {
   sgemm_oncopyTS, sgemm_otcopyTS,
 #endif
 
+#if BUILD_SINGLE == 1
+#ifdef SMALL_MATRIX_OPT
+  sgemm_small_matrix_permitTS,
+  sgemm_small_kernel_nnTS, sgemm_small_kernel_ntTS, sgemm_small_kernel_tnTS, sgemm_small_kernel_ttTS,
+  sgemm_small_kernel_b0_nnTS, sgemm_small_kernel_b0_ntTS, sgemm_small_kernel_b0_tnTS, sgemm_small_kernel_b0_ttTS,
+#endif
+#endif
+
 #if (BUILD_SINGLE==1) || (BUILD_DOUBLE==1) 
   strsm_kernel_LNTS, strsm_kernel_LTTS, strsm_kernel_RNTS, strsm_kernel_RTTS,
 #if SGEMM_DEFAULT_UNROLL_M != SGEMM_DEFAULT_UNROLL_N
@@ -257,6 +265,11 @@ gotoblas_t TABLE_NAME = {
 #endif
 
 #if  (BUILD_DOUBLE==1)  
+#ifdef SMALL_MATRIX_OPT
+  dgemm_small_matrix_permitTS,
+  dgemm_small_kernel_nnTS, dgemm_small_kernel_ntTS, dgemm_small_kernel_tnTS, dgemm_small_kernel_ttTS,
+  dgemm_small_kernel_b0_nnTS, dgemm_small_kernel_b0_ntTS, dgemm_small_kernel_b0_tnTS, dgemm_small_kernel_b0_ttTS,
+#endif
   dtrsm_kernel_LNTS, dtrsm_kernel_LTTS, dtrsm_kernel_RNTS, dtrsm_kernel_RTTS,
 #if DGEMM_DEFAULT_UNROLL_M != DGEMM_DEFAULT_UNROLL_N
   dtrsm_iunucopyTS, dtrsm_iunncopyTS, dtrsm_iutucopyTS, dtrsm_iutncopyTS,
@@ -389,6 +402,18 @@ gotoblas_t TABLE_NAME = {
 #endif
   cgemm_oncopyTS, cgemm_otcopyTS,
 
+#ifdef SMALL_MATRIX_OPT
+  cgemm_small_matrix_permitTS,
+  cgemm_small_kernel_nnTS, cgemm_small_kernel_ntTS, cgemm_small_kernel_nrTS, cgemm_small_kernel_ncTS,
+  cgemm_small_kernel_tnTS, cgemm_small_kernel_ttTS, cgemm_small_kernel_trTS, cgemm_small_kernel_tcTS,
+  cgemm_small_kernel_rnTS, cgemm_small_kernel_rtTS, cgemm_small_kernel_rrTS, cgemm_small_kernel_rcTS,
+  cgemm_small_kernel_cnTS, cgemm_small_kernel_ctTS, cgemm_small_kernel_crTS, cgemm_small_kernel_ccTS,
+  cgemm_small_kernel_b0_nnTS, cgemm_small_kernel_b0_ntTS, cgemm_small_kernel_b0_nrTS, cgemm_small_kernel_b0_ncTS,
+  cgemm_small_kernel_b0_tnTS, cgemm_small_kernel_b0_ttTS, cgemm_small_kernel_b0_trTS, cgemm_small_kernel_b0_tcTS,
+  cgemm_small_kernel_b0_rnTS, cgemm_small_kernel_b0_rtTS, cgemm_small_kernel_b0_rrTS, cgemm_small_kernel_b0_rcTS,
+  cgemm_small_kernel_b0_cnTS, cgemm_small_kernel_b0_ctTS, cgemm_small_kernel_b0_crTS, cgemm_small_kernel_b0_ccTS,
+#endif
+
   ctrsm_kernel_LNTS, ctrsm_kernel_LTTS, ctrsm_kernel_LRTS, ctrsm_kernel_LCTS,
   ctrsm_kernel_RNTS, ctrsm_kernel_RTTS, ctrsm_kernel_RRTS, ctrsm_kernel_RCTS,
 
@@ -533,6 +558,18 @@ gotoblas_t TABLE_NAME = {
 #endif
   zgemm_oncopyTS, zgemm_otcopyTS,
 
+#ifdef SMALL_MATRIX_OPT
+  zgemm_small_matrix_permitTS,
+  zgemm_small_kernel_nnTS, zgemm_small_kernel_ntTS, zgemm_small_kernel_nrTS, zgemm_small_kernel_ncTS,
+  zgemm_small_kernel_tnTS, zgemm_small_kernel_ttTS, zgemm_small_kernel_trTS, zgemm_small_kernel_tcTS,
+  zgemm_small_kernel_rnTS, zgemm_small_kernel_rtTS, zgemm_small_kernel_rrTS, zgemm_small_kernel_rcTS,
+  zgemm_small_kernel_cnTS, zgemm_small_kernel_ctTS, zgemm_small_kernel_crTS, zgemm_small_kernel_ccTS,
+  zgemm_small_kernel_b0_nnTS, zgemm_small_kernel_b0_ntTS, zgemm_small_kernel_b0_nrTS, zgemm_small_kernel_b0_ncTS,
+  zgemm_small_kernel_b0_tnTS, zgemm_small_kernel_b0_ttTS, zgemm_small_kernel_b0_trTS, zgemm_small_kernel_b0_tcTS,
+  zgemm_small_kernel_b0_rnTS, zgemm_small_kernel_b0_rtTS, zgemm_small_kernel_b0_rrTS, zgemm_small_kernel_b0_rcTS,
+  zgemm_small_kernel_b0_cnTS, zgemm_small_kernel_b0_ctTS, zgemm_small_kernel_b0_crTS, zgemm_small_kernel_b0_ccTS,
+#endif
+
   ztrsm_kernel_LNTS, ztrsm_kernel_LTTS, ztrsm_kernel_LRTS, ztrsm_kernel_LCTS,
   ztrsm_kernel_RNTS, ztrsm_kernel_RTTS, ztrsm_kernel_RRTS, ztrsm_kernel_RCTS,
 

kernel/x86_64/KERNEL.SKYLAKEX

@@ -10,6 +10,15 @@ STRSMKERNEL_LN =  ../generic/trsm_kernel_LN.c
 STRSMKERNEL_LT =  ../generic/trsm_kernel_LT.c
 STRSMKERNEL_RN =  ../generic/trsm_kernel_RN.c
 STRSMKERNEL_RT =  ../generic/trsm_kernel_RT.c
+SGEMM_SMALL_M_PERMIT = sgemm_small_kernel_permit_skylakex.c
+SGEMM_SMALL_K_NN = sgemm_small_kernel_nn_skylakex.c
+SGEMM_SMALL_K_B0_NN = sgemm_small_kernel_nn_skylakex.c
+SGEMM_SMALL_K_NT = sgemm_small_kernel_nt_skylakex.c
+SGEMM_SMALL_K_B0_NT = sgemm_small_kernel_nt_skylakex.c
+SGEMM_SMALL_K_TN = sgemm_small_kernel_tn_skylakex.c
+SGEMM_SMALL_K_B0_TN = sgemm_small_kernel_tn_skylakex.c
+SGEMM_SMALL_K_TT = sgemm_small_kernel_tt_skylakex.c
+SGEMM_SMALL_K_B0_TT = sgemm_small_kernel_tt_skylakex.c
 
 DGEMMKERNEL    =  dgemm_kernel_16x2_skylakex.c
 DTRMMKERNEL    =  dgemm_kernel_16x2_skylakex.c
@@ -18,6 +27,15 @@ DGEMMITCOPY    =  dgemm_tcopy_16_skylakex.c
 DGEMMONCOPY    =  ../generic/gemm_ncopy_2.c
 DGEMMOTCOPY    =  ../generic/gemm_tcopy_2.c
 DTRSMKERNEL_RN =  ../generic/trsm_kernel_RN.c
+DGEMM_SMALL_M_PERMIT = dgemm_small_kernel_permit_skylakex.c
+DGEMM_SMALL_K_NN = dgemm_small_kernel_nn_skylakex.c
+DGEMM_SMALL_K_B0_NN = dgemm_small_kernel_nn_skylakex.c
+DGEMM_SMALL_K_NT = dgemm_small_kernel_nt_skylakex.c
+DGEMM_SMALL_K_B0_NT = dgemm_small_kernel_nt_skylakex.c
+DGEMM_SMALL_K_TN = dgemm_small_kernel_tn_skylakex.c
+DGEMM_SMALL_K_B0_TN = dgemm_small_kernel_tn_skylakex.c
+DGEMM_SMALL_K_TT = dgemm_small_kernel_tt_skylakex.c
+DGEMM_SMALL_K_B0_TT = dgemm_small_kernel_tt_skylakex.c
 
 SGEMM_BETA = sgemm_beta_skylakex.c
 DGEMM_BETA = dgemm_beta_skylakex.c

kernel/x86_64/dgemm_small_kernel_nn_skylakex.c

@@ -0,0 +1,590 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include <immintrin.h>
+#include "common.h"
+#include <stdio.h>
+#include <memory.h>
+
+#define DECLARE_RESULT_512(M, N) __m512d result##M##N = _mm512_setzero_pd()
+#define LOAD_A_512(M, N) __m512d Aval##M = _mm512_loadu_pd(&A[lda * k + i + (M*8)])
+#define MASK_LOAD_A_512(M, N) __m512d Aval##M = _mm512_maskz_loadu_pd(mask, &A[lda * k + i + (M*8)])
+#define BROADCAST_LOAD_B_512(M, N) __m512d Bval##N = _mm512_broadcastsd_pd(_mm_load_pd1(&B[k + ldb * (j+N)]))
+#define MATMUL_512(M, N) result##M##N = _mm512_fmadd_pd(Aval##M, Bval##N, result##M##N)
+#if defined(B0)
+#define STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+			_mm512_storeu_pd(&C[(j+N)*ldc + i + (M*8)], result##M##N)
+#define MASK_STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+			_mm512_mask_storeu_pd(&C[(j+N)*ldc + i + (M*8)], mask, result##M##N)
+#else
+#define STORE_512(M, N) \
+	result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+	asm("vfmadd231pd (%1), %2, %0": "+v"(result##M##N):"r"(&C[(j+N)*ldc + i + (M*8)]), "v"(beta_512)); \
+	_mm512_storeu_pd(&C[(j+N)*ldc + i + (M*8)], result##M##N)
+#define MASK_STORE_512(M, N) \
+	result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+	asm("vfmadd231pd (%1), %2, %0 %{%3%}": "+v"(result##M##N):"r"(&C[(j+N)*ldc + i + (M*8)]), "v"(beta_512), "k"(mask)); \
+	_mm512_mask_storeu_pd(&C[(j+N)*ldc + i + (M*8)], mask, result##M##N)
+#endif
+
+#define LOAD_KA_512(M, N) __m512d Aval##M = _mm512_loadu_pd(&mbuf[(mi + M)*K + k]);
+#define LOAD_KB_512(M, N) __m512d Bval##N = _mm512_loadu_pd(&B[(j + N)*ldb + k])
+#define MASK_LOAD_KA_512(M, N) __m512d Aval##M = _mm512_maskz_loadu_pd(mask, &mbuf[(mi + M)*K + k])
+#define MASK_LOAD_KB_512(M, N) __m512d Bval##N = _mm512_maskz_loadu_pd(mask, &B[(j + N)*ldb + k])
+#define REDUCE_4(rr0, rr1, rr2, rr3) \
+	__m512d r0, r1, r2, r3, t0, t1, t2, t3;\
+	r0 = _mm512_unpacklo_pd(rr0, rr1); r1 = _mm512_unpackhi_pd(rr0, rr1); \
+	r2 = _mm512_unpacklo_pd(rr2, rr3); r3 = _mm512_unpackhi_pd(rr2, rr3); \
+	t0 = _mm512_permutex2var_pd(r0, idx_lo, r2); t1 = _mm512_permutex2var_pd(r1, idx_lo, r3); \
+	t2 = _mm512_permutex2var_pd(r0, idx_hi, r2); t3 = _mm512_permutex2var_pd(r1, idx_hi, r3); \
+	r0 = _mm512_add_pd(t0, t1); r1 = _mm512_add_pd(t2, t3); t0 = _mm512_add_pd(r0, r1); \
+	__m256d s0, s1; \
+	s0 = _mm512_extractf64x4_pd(t0, 0); s1 = _mm512_extractf64x4_pd(t0, 1); \
+	s0 = _mm256_add_pd(s0, s1); s0 = _mm256_mul_pd(alpha_256, s0);
+#define REDUCE_M4(N) REDUCE_4(result0##N, result1##N, result2##N, result3##N)
+#define REDUCE_N4(M) REDUCE_4(result##M##0, result##M##1, result##M##2, result##M##3)
+#if defined(B0)
+#define STORE_REDUCE(M, N) C[(j+N)*ldc + i + M] = alpha * _mm512_reduce_add_pd(result##M##N);
+#define STORE_REDUCE_M4(N) {\
+	REDUCE_M4(N) \
+	_mm256_storeu_pd(&C[(j + N)*ldc + i], s0); \
+}
+#define STORE_REDUCE_N4(M) {\
+	REDUCE_N4(M) \
+	_mm256_i64scatter_pd(&C[j*ldc + i + M], vindex_n, s0, 8); \
+}
+#else
+#define STORE_REDUCE(M, N) C[(j+N)*ldc + i + M] = alpha * _mm512_reduce_add_pd(result##M##N) + beta * C[(j+N)*ldc + i + M];
+#define STORE_REDUCE_M4(N) {\
+	REDUCE_M4(N) \
+	asm("vfmadd231pd (%1), %2, %0": "+v"(s0):"r"(&C[(j + N)*ldc + i]), "v"(beta_256)); \
+	_mm256_storeu_pd(&C[(j + N)*ldc + i], s0); \
+}
+#define STORE_REDUCE_N4(M) {\
+	REDUCE_N4(M) \
+	s1 = _mm256_i64gather_pd(&C[j*ldc + i + M], vindex_n, 8); \
+	s0 = _mm256_fmadd_pd(s1, beta_256, s0); \
+	_mm256_i64scatter_pd(&C[j*ldc + i + M], vindex_n, s0, 8); \
+}
+#endif
+
+#if defined(B0)
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	// column major
+	BLASLONG i, j, k;
+
+	BLASLONG m32 = M & ~31;
+	BLASLONG m16 = M & ~15;
+	BLASLONG m8 = M & ~7;
+	BLASLONG m4 = M & ~3;
+	BLASLONG m2 = M & ~1;
+
+	BLASLONG n6 = N - (N % 6);
+	BLASLONG n4 = N & ~3;
+	BLASLONG n2 = N & ~1;
+
+
+	__m512d alpha_512 = _mm512_broadcastsd_pd(_mm_load_pd1(&alpha));
+#if !defined(B0)
+	__m512d beta_512 = _mm512_broadcastsd_pd(_mm_load_pd1(&beta));
+#endif
+
+	for (i = 0; i < m32; i += 32) {
+		for (j = 0; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+			STORE_512(0, 1); STORE_512(1, 1); STORE_512(2, 1); STORE_512(3, 1);
+			STORE_512(0, 2); STORE_512(1, 2); STORE_512(2, 2); STORE_512(3, 2);
+			STORE_512(0, 3); STORE_512(1, 3); STORE_512(2, 3); STORE_512(3, 3);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+			STORE_512(0, 1); STORE_512(1, 1); STORE_512(2, 1); STORE_512(3, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+		}
+	}
+	for (; i < m16; i += 16) {
+		for (j = 0; j < n6; j += 6) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+			DECLARE_RESULT_512(0, 4); DECLARE_RESULT_512(1, 4);
+			DECLARE_RESULT_512(0, 5); DECLARE_RESULT_512(1, 5);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3);
+				MATMUL_512(0, 4); MATMUL_512(1, 4);
+				MATMUL_512(0, 5); MATMUL_512(1, 5);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+			STORE_512(0, 1); STORE_512(1, 1);
+			STORE_512(0, 2); STORE_512(1, 2);
+			STORE_512(0, 3); STORE_512(1, 3);
+			STORE_512(0, 4); STORE_512(1, 4);
+			STORE_512(0, 5); STORE_512(1, 5);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+			STORE_512(0, 1); STORE_512(1, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+		}
+	}
+	for (; i < m8; i += 8) {
+		for (j = 0; j < n6; j += 6) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			DECLARE_RESULT_512(0, 4);
+			DECLARE_RESULT_512(0, 5);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+				MATMUL_512(0, 4);
+				MATMUL_512(0, 5);
+			}
+			STORE_512(0, 0);
+			STORE_512(0, 1);
+			STORE_512(0, 2);
+			STORE_512(0, 3);
+			STORE_512(0, 4);
+			STORE_512(0, 5);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			STORE_512(0, 0);
+			STORE_512(0, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0);
+			}
+			STORE_512(0, 0);
+		}
+	}
+	int mm = M - i;
+	if (!mm) return 0;
+	if (mm > 4 || K < 16) {
+		register __mmask8 mask asm("k1") = (1UL << mm) - 1;
+		for (j = 0; j < n6; j += 6) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			DECLARE_RESULT_512(0, 4);
+			DECLARE_RESULT_512(0, 5);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+				MATMUL_512(0, 4);
+				MATMUL_512(0, 5);
+			}
+			MASK_STORE_512(0, 0);
+			MASK_STORE_512(0, 1);
+			MASK_STORE_512(0, 2);
+			MASK_STORE_512(0, 3);
+			MASK_STORE_512(0, 4);
+			MASK_STORE_512(0, 5);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			MASK_STORE_512(0, 0);
+			MASK_STORE_512(0, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0);
+			}
+			MASK_STORE_512(0, 0);
+		}
+	} else {
+		/* M => [1, 4]
+		 *
+		 * This kernel use dot-like style to calc a value - C(x, y):
+		 * C(x, y) = A(x, 0)*B(0, y) + A(x, 1)*B(1, y) +....+ A(x, K)*B(K, y)
+		 *
+		 * Alloc a buf to copy rest of A as row major,
+		 * so memory access from 0 to K is continuous for both A & B.
+		 *
+		 * Loading to zmm and FMA 8 of k at one loop,
+		 * finally reduce_add zmm to a single float result in C(x, y).
+		 *
+		 * Note: performance is bad when K is small.
+		 */
+		FLOAT *mbuf = (FLOAT *) malloc(sizeof(FLOAT)*mm*K);
+		__mmask8 mask = (1UL << mm) - 1;
+		BLASLONG k8 = K & ~7;
+		BLASLONG k4 = K & ~3;
+		for (k = 0; k < k4; k += 4) {
+			__m256d  r0, r1, r2, r3;
+			__m256d  t0, t1, t2, t3;
+			r0 = _mm256_maskz_loadu_pd(mask, &A[i + lda*(0 + k)]);
+			r1 = _mm256_maskz_loadu_pd(mask, &A[i + lda*(1 + k)]);
+			r2 = _mm256_maskz_loadu_pd(mask, &A[i + lda*(2 + k)]);
+			r3 = _mm256_maskz_loadu_pd(mask, &A[i + lda*(3 + k)]);
+
+			t0 = _mm256_unpacklo_pd(r0, r1);
+			t1 = _mm256_unpackhi_pd(r0, r1);
+			t2 = _mm256_unpacklo_pd(r2, r3);
+			t3 = _mm256_unpackhi_pd(r2, r3);
+
+			r0 = _mm256_permute2f128_pd(t0, t2, 0x20);
+			r1 = _mm256_permute2f128_pd(t1, t3, 0x20);
+			r2 = _mm256_permute2f128_pd(t0, t2, 0x31);
+			r3 = _mm256_permute2f128_pd(t1, t3, 0x31);
+
+			switch (mm) {
+				case 4: _mm256_storeu_pd(&mbuf[k + 3*K], r3);
+				case 3: _mm256_storeu_pd(&mbuf[k + 2*K], r2);
+				case 2: _mm256_storeu_pd(&mbuf[k + 1*K], r1);
+				case 1: _mm256_storeu_pd(&mbuf[k + 0*K], r0);
+			}
+		}
+		for (; k < K; k++) {
+			for (int ii = 0; ii < mm; ii++) {
+				mbuf[k + ii*K] = A[i + lda*k + ii];
+			}
+		}
+		int mi = 0;
+		__m256d alpha_256 = _mm256_broadcast_sd(&alpha);
+#if !defined(B0)
+		__m256d beta_256 = _mm256_broadcast_sd(&beta);
+#endif
+		__m256i vindex_n = _mm256_set_epi64x(ldc*3, ldc*2, ldc*1, 0);
+		long long permute_table[] = {
+			0, 1, 0|8, 1|8, 4, 5, 4|8, 5|8,
+			2, 3, 2|8, 3|8, 6, 7, 6|8, 7|8,
+		};
+		__m512i idx_lo = _mm512_loadu_si512(permute_table);
+		__m512i idx_hi = _mm512_loadu_si512(permute_table + 8);
+		for (; i < m4; i += 4, mi += 4) {
+			for (j = 0; j < n4; j += 4) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+				DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+				DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+				for (k = 0; k < k8; k += 8) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+				}
+				STORE_REDUCE_M4(0); STORE_REDUCE_M4(1); STORE_REDUCE_M4(2); STORE_REDUCE_M4(3);
+			}
+			for (; j < n2; j += 2) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+				for (k = 0; k < k8; k += 8) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				}
+				STORE_REDUCE_M4(0); STORE_REDUCE_M4(1);
+			}
+			for (; j < N; j += 1) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				for (k = 0; k < k8; k += 8) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+					LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+					MASK_LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				}
+				STORE_REDUCE_M4(0);
+			}
+
+		}
+		for (; i < m2; i += 2, mi += 2) {
+			for (j = 0; j < n4; j += 4) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+				DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+				for (k = 0; k < k8; k += 8) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3);
+				}
+				STORE_REDUCE_N4(0); STORE_REDUCE_N4(1);
+			}
+			for (; j < n2; j += 2) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				for (k = 0; k < k8; k += 8) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+				}
+				STORE_REDUCE(0, 0); STORE_REDUCE(1, 0);
+				STORE_REDUCE(0, 1); STORE_REDUCE(1, 1);
+
+			}
+			for (; j < N; j += 1) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				for (k = 0; k < k8; k += 8) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+					LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+					MASK_LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+				}
+				STORE_REDUCE(0, 0); STORE_REDUCE(1, 0);
+			}
+		}
+		for (; i < M; i += 1, mi += 1) {
+			for (j = 0; j < n4; j += 4) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				DECLARE_RESULT_512(0, 2);
+				DECLARE_RESULT_512(0, 3);
+				for (k = 0; k < k8; k += 8) {
+					LOAD_KA_512(0, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+					MATMUL_512(0, 2);
+					MATMUL_512(0, 3);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+					MATMUL_512(0, 2);
+					MATMUL_512(0, 3);
+				}
+				STORE_REDUCE_N4(0);
+			}
+			for (; j < n2; j += 2) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				for (k = 0; k < k8; k += 8) {
+					LOAD_KA_512(0, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+				}
+				STORE_REDUCE(0, 0);
+				STORE_REDUCE(0, 1);
+
+			}
+			for (; j < N; j += 1) {
+				DECLARE_RESULT_512(0, 0);
+				for (k = 0; k < k8; k += 8) {
+					LOAD_KA_512(0, x);
+					LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x);
+					MASK_LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0);
+				}
+				STORE_REDUCE(0, 0);
+			}
+		}
+		free(mbuf);
+	}
+	return 0;
+}

kernel/x86_64/dgemm_small_kernel_nt_skylakex.c

@@ -0,0 +1,535 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include <immintrin.h>
+#include "common.h"
+#include <stdio.h>
+#include <memory.h>
+
+#define DECLARE_RESULT_512(M, N) __m512d result##M##N = _mm512_setzero_pd()
+#define LOAD_A_512(M, N) __m512d Aval##M = _mm512_loadu_pd(&A[lda * k + i + (M*8)])
+#define MASK_LOAD_A_512(M, N) __m512d Aval##M = _mm512_maskz_loadu_pd(mask, &A[lda * k + i + (M*8)])
+#define BROADCAST_LOAD_B_512(M, N) __m512d Bval##N = _mm512_broadcastsd_pd(_mm_load_sd(&B[ldb * k + j + N]))
+#define MATMUL_512(M, N) result##M##N = _mm512_fmadd_pd(Aval##M, Bval##N, result##M##N)
+
+#define BROADCAST_LOAD_A_512(M, N) __m512d Aval##M = _mm512_broadcastsd_pd(_mm_load_sd(&A[lda * k + i + M]))
+#define LOAD_B_512(M, N) __m512d Bval##N = _mm512_loadu_pd(&B[ldb * k + j + (N*8)])
+#define MASK_LOAD_B_512(M, N) __m512d Bval##N = _mm512_maskz_loadu_pd(mask, &B[ldb * k + j + (N*8)])
+#if defined(B0)
+#define STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+			_mm512_storeu_pd(&C[(j+N)*ldc + i + (M*8)], result##M##N)
+#define MASK_STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+			_mm512_mask_storeu_pd(&C[(j+N)*ldc + i + (M*8)], mask, result##M##N)
+#define SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+				_mm512_i64scatter_pd(&C[(j + N*8)*ldc + i + M], vindex_n, result##M##N, 8);
+#define MASK_SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+				_mm512_mask_i64scatter_pd(&C[(j + N*8)*ldc + i + M], mask, vindex_n, result##M##N, 8)
+#else
+#define STORE_512(M, N) \
+	result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+	asm("vfmadd231pd (%1), %2, %0": "+v"(result##M##N):"r"(&C[(j+N)*ldc + i + (M*8)]), "v"(beta_512)); \
+	_mm512_storeu_pd(&C[(j+N)*ldc + i + (M*8)], result##M##N)
+#define MASK_STORE_512(M, N) \
+	result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+	asm("vfmadd231pd (%1), %2, %0 %{%3%}": "+v"(result##M##N):"r"(&C[(j+N)*ldc + i + (M*8)]), "v"(beta_512), "k"(mask)); \
+	_mm512_mask_storeu_pd(&C[(j+N)*ldc + i + (M*8)], mask, result##M##N)
+#define SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+				__m512d tmp##M##N = _mm512_i64gather_pd(vindex_n, &C[(j + N*8)*ldc + i + M], 8); \
+				result##M##N = _mm512_fmadd_pd(tmp##M##N, beta_512, result##M##N); \
+				_mm512_i64scatter_pd(&C[(j + N*8)*ldc + i + M], vindex_n, result##M##N, 8);
+#define MASK_SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+				__m512d tmp##M##N = _mm512_mask_i64gather_pd(_mm512_setzero_pd(), mask, vindex_n, &C[(j + N*8)*ldc + i + M], 8); \
+				result##M##N = _mm512_fmadd_pd(tmp##M##N, beta_512, result##M##N); \
+				_mm512_mask_i64scatter_pd(&C[(j + N*8)*ldc + i + M], mask, vindex_n, result##M##N, 8);
+#endif
+
+#if defined(B0)
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	// column major
+	BLASLONG i, j, k;
+
+	BLASLONG m32 = M & ~31;
+	BLASLONG m16 = M & ~15;
+	BLASLONG m8 = M & ~7;
+	BLASLONG m4 = M & ~3;
+	BLASLONG m2 = M & ~1;
+
+	BLASLONG n32 = N & ~31;
+	BLASLONG n16 = N & ~15;
+	BLASLONG n8 = N & ~7;
+	BLASLONG n6 = N - (N % 6);
+	BLASLONG n4 = N & ~3;
+	BLASLONG n2 = N & ~1;
+
+
+	__m512d alpha_512 = _mm512_broadcastsd_pd(_mm_load_sd(&alpha));
+#if !defined(B0)
+	__m512d beta_512 = _mm512_broadcastsd_pd(_mm_load_sd(&beta));
+#endif
+
+	for (i = 0; i < m32; i += 32) {
+		for (j = 0; j < n6; j += 6) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+			DECLARE_RESULT_512(0, 4); DECLARE_RESULT_512(1, 4); DECLARE_RESULT_512(2, 4); DECLARE_RESULT_512(3, 4);
+			DECLARE_RESULT_512(0, 5); DECLARE_RESULT_512(1, 5); DECLARE_RESULT_512(2, 5); DECLARE_RESULT_512(3, 5);
+
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+				MATMUL_512(0, 4); MATMUL_512(1, 4); MATMUL_512(2, 4); MATMUL_512(3, 4);
+				MATMUL_512(0, 5); MATMUL_512(1, 5); MATMUL_512(2, 5); MATMUL_512(3, 5);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+			STORE_512(0, 1); STORE_512(1, 1); STORE_512(2, 1); STORE_512(3, 1);
+			STORE_512(0, 2); STORE_512(1, 2); STORE_512(2, 2); STORE_512(3, 2);
+			STORE_512(0, 3); STORE_512(1, 3); STORE_512(2, 3); STORE_512(3, 3);
+			STORE_512(0, 4); STORE_512(1, 4); STORE_512(2, 4); STORE_512(3, 4);
+			STORE_512(0, 5); STORE_512(1, 5); STORE_512(2, 5); STORE_512(3, 5);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+			STORE_512(0, 1); STORE_512(1, 1); STORE_512(2, 1); STORE_512(3, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+		}
+	}
+	for (; i < m16; i += 16) {
+		for (j = 0; j < n8; j += 8) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+			DECLARE_RESULT_512(0, 4); DECLARE_RESULT_512(1, 4);
+			DECLARE_RESULT_512(0, 5); DECLARE_RESULT_512(1, 5);
+			DECLARE_RESULT_512(0, 6); DECLARE_RESULT_512(1, 6);
+			DECLARE_RESULT_512(0, 7); DECLARE_RESULT_512(1, 7);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+				BROADCAST_LOAD_B_512(x, 6); BROADCAST_LOAD_B_512(x, 7);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3);
+				MATMUL_512(0, 4); MATMUL_512(1, 4);
+				MATMUL_512(0, 5); MATMUL_512(1, 5);
+				MATMUL_512(0, 6); MATMUL_512(1, 6);
+				MATMUL_512(0, 7); MATMUL_512(1, 7);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+			STORE_512(0, 1); STORE_512(1, 1);
+			STORE_512(0, 2); STORE_512(1, 2);
+			STORE_512(0, 3); STORE_512(1, 3);
+			STORE_512(0, 4); STORE_512(1, 4);
+			STORE_512(0, 5); STORE_512(1, 5);
+			STORE_512(0, 6); STORE_512(1, 6);
+			STORE_512(0, 7); STORE_512(1, 7);
+		}
+		for (;j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+			STORE_512(0, 1); STORE_512(1, 1);
+			STORE_512(0, 2); STORE_512(1, 2);
+			STORE_512(0, 3); STORE_512(1, 3);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+			STORE_512(0, 1); STORE_512(1, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+		}
+	}
+	for (; i < m8; i += 8) {
+		for (j = 0; j < n8; j += 8) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			DECLARE_RESULT_512(0, 4);
+			DECLARE_RESULT_512(0, 5);
+			DECLARE_RESULT_512(0, 6);
+			DECLARE_RESULT_512(0, 7);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+				BROADCAST_LOAD_B_512(x, 6); BROADCAST_LOAD_B_512(x, 7);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+				MATMUL_512(0, 4);
+				MATMUL_512(0, 5);
+				MATMUL_512(0, 6);
+				MATMUL_512(0, 7);
+			}
+			STORE_512(0, 0);
+			STORE_512(0, 1);
+			STORE_512(0, 2);
+			STORE_512(0, 3);
+			STORE_512(0, 4);
+			STORE_512(0, 5);
+			STORE_512(0, 6);
+			STORE_512(0, 7);
+		}
+		for (; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+			}
+			STORE_512(0, 0);
+			STORE_512(0, 1);
+			STORE_512(0, 2);
+			STORE_512(0, 3);
+		}
+
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			STORE_512(0, 0);
+			STORE_512(0, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0);
+			}
+			STORE_512(0, 0);
+		}
+	}
+	int mm = M - i;
+	if (mm >= 6) {
+		register __mmask16 mask asm("k1") = (1UL << mm) - 1;
+		for (j = 0; j < n8; j += 8) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			DECLARE_RESULT_512(0, 4);
+			DECLARE_RESULT_512(0, 5);
+			DECLARE_RESULT_512(0, 6);
+			DECLARE_RESULT_512(0, 7);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+				BROADCAST_LOAD_B_512(x, 6); BROADCAST_LOAD_B_512(x, 7);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+				MATMUL_512(0, 4);
+				MATMUL_512(0, 5);
+				MATMUL_512(0, 6);
+				MATMUL_512(0, 7);
+			}
+			MASK_STORE_512(0, 0);
+			MASK_STORE_512(0, 1);
+			MASK_STORE_512(0, 2);
+			MASK_STORE_512(0, 3);
+			MASK_STORE_512(0, 4);
+			MASK_STORE_512(0, 5);
+			MASK_STORE_512(0, 6);
+			MASK_STORE_512(0, 7);
+		}
+		for (; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+			}
+			MASK_STORE_512(0, 0);
+			MASK_STORE_512(0, 1);
+			MASK_STORE_512(0, 2);
+			MASK_STORE_512(0, 3);
+		}
+
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			MASK_STORE_512(0, 0);
+			MASK_STORE_512(0, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0);
+			}
+			MASK_STORE_512(0, 0);
+		}
+	} else if (mm > 0) {
+		long long index_n[8];
+		for (int ii = 0; ii < 8; ii++) {
+			index_n[ii] = ii * ldc;
+		}
+		__m512i vindex_n = _mm512_loadu_si512(index_n);
+		for (; i < m4; i += 4) {
+			for (j = 0; j < n32; j += 32) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+				DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+				DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					LOAD_B_512(x, 2);
+					LOAD_B_512(x, 3);
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0); SCATTER_STORE_512(2, 0); SCATTER_STORE_512(3, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1); SCATTER_STORE_512(2, 1); SCATTER_STORE_512(3, 1);
+				SCATTER_STORE_512(0, 2); SCATTER_STORE_512(1, 2); SCATTER_STORE_512(2, 2); SCATTER_STORE_512(3, 2);
+				SCATTER_STORE_512(0, 3); SCATTER_STORE_512(1, 3); SCATTER_STORE_512(2, 3); SCATTER_STORE_512(3, 3);
+			}
+			for (; j < n16; j += 16) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0); SCATTER_STORE_512(2, 0); SCATTER_STORE_512(3, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1); SCATTER_STORE_512(2, 1); SCATTER_STORE_512(3, 1);
+			}
+			__mmask8 mask = 0xff;
+			for (; j < N; j += 8) {
+				int remains = N - j;
+				if (remains < 8) mask = (1UL << remains) - 1;
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+					MASK_LOAD_B_512(x, 0);
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				}
+				MASK_SCATTER_STORE_512(0, 0); MASK_SCATTER_STORE_512(1, 0); MASK_SCATTER_STORE_512(2, 0); MASK_SCATTER_STORE_512(3, 0);
+			}
+		}
+		for (; i < m2; i += 2) {
+			for (j = 0; j < n32; j += 32) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+				DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					LOAD_B_512(x, 2);
+					LOAD_B_512(x, 3);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1);
+				SCATTER_STORE_512(0, 2); SCATTER_STORE_512(1, 2);
+				SCATTER_STORE_512(0, 3); SCATTER_STORE_512(1, 3);
+			}
+			for (; j < n16; j += 16) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1);
+			}
+			__mmask8 mask = 0xff;
+			for (; j < N; j += 8) {
+				int remains = N - j;
+				if (remains < 8) mask = (1UL << remains) - 1;
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					MASK_LOAD_B_512(x, 0);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+				}
+				MASK_SCATTER_STORE_512(0, 0); MASK_SCATTER_STORE_512(1, 0);
+			}
+		}
+		for (; i < M; i += 1) {
+			for (j = 0; j < n32; j += 32) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				DECLARE_RESULT_512(0, 2);
+				DECLARE_RESULT_512(0, 3);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					LOAD_B_512(x, 2);
+					LOAD_B_512(x, 3);
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+					MATMUL_512(0, 2);
+					MATMUL_512(0, 3);
+				}
+				SCATTER_STORE_512(0, 0);
+				SCATTER_STORE_512(0, 1);
+				SCATTER_STORE_512(0, 2);
+				SCATTER_STORE_512(0, 3);
+			}
+			for (; j < n16; j += 16) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+				}
+				SCATTER_STORE_512(0, 0);
+				SCATTER_STORE_512(0, 1);
+			}
+			__mmask8 mask = 0xff;
+			for (; j < N; j += 8) {
+				int remains = N - j;
+				if (remains < 8) mask = (1UL << remains) - 1;
+				DECLARE_RESULT_512(0, 0);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					MASK_LOAD_B_512(x, 0);
+					MATMUL_512(0, 0);
+				}
+				MASK_SCATTER_STORE_512(0, 0);
+			}
+		}
+	}
+	return 0;
+}

kernel/x86_64/dgemm_small_kernel_permit_skylakex.c

@@ -0,0 +1,44 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+int CNAME(int transa, int transb, BLASLONG M, BLASLONG N, BLASLONG K, FLOAT alpha, FLOAT beta)
+{
+	double MNK = (double) M * (double) N * (double) K;
+	if (MNK > 100.0*100.0*100.0)  // disable for big size matrix
+		return 0;
+	if (transa && !transb) {
+		/* TN kernel perform not good when:
+		 * 1. C matrix is too big
+		 * 2. K is too small
+		 */
+		if (M * N > 1200 || K < 32)
+			return 0;
+	}
+	return 1;
+}

kernel/x86_64/dgemm_small_kernel_tn_skylakex.c

@@ -0,0 +1,322 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include <immintrin.h>
+#include "common.h"
+#include <stdio.h>
+#include <memory.h>
+
+#define DECLARE_RESULT_512(M, N) __m512d result##M##N = _mm512_setzero_pd()
+#define MATMUL_512(M, N) result##M##N = _mm512_fmadd_pd(Aval##M, Bval##N, result##M##N)
+
+#define LOAD_KA_512(M, N) __m512d Aval##M = _mm512_loadu_pd(&A[(i + M)*lda + k]);
+#define LOAD_KB_512(M, N) __m512d Bval##N = _mm512_loadu_pd(&B[(j + N)*ldb + k])
+#define MASK_LOAD_KA_512(M, N) __m512d Aval##M = _mm512_maskz_loadu_pd(mask, &A[(i + M)*lda + k])
+#define MASK_LOAD_KB_512(M, N) __m512d Bval##N = _mm512_maskz_loadu_pd(mask, &B[(j + N)*ldb + k])
+
+#define REDUCE_4(rr0, rr1, rr2, rr3) \
+	__m512d r0, r1, r2, r3, t0, t1, t2, t3;\
+	r0 = _mm512_unpacklo_pd(rr0, rr1); r1 = _mm512_unpackhi_pd(rr0, rr1); \
+	r2 = _mm512_unpacklo_pd(rr2, rr3); r3 = _mm512_unpackhi_pd(rr2, rr3); \
+	t0 = _mm512_permutex2var_pd(r0, idx_lo, r2); t1 = _mm512_permutex2var_pd(r1, idx_lo, r3); \
+	t2 = _mm512_permutex2var_pd(r0, idx_hi, r2); t3 = _mm512_permutex2var_pd(r1, idx_hi, r3); \
+	r0 = _mm512_add_pd(t0, t1); r1 = _mm512_add_pd(t2, t3); t0 = _mm512_add_pd(r0, r1); \
+	__m256d s0, s1; \
+	s0 = _mm512_extractf64x4_pd(t0, 0); s1 = _mm512_extractf64x4_pd(t0, 1); \
+	s0 = _mm256_add_pd(s0, s1); s0 = _mm256_mul_pd(alpha_256, s0);
+
+#define REDUCE_M4(N) REDUCE_4(result0##N, result1##N, result2##N, result3##N)
+#define REDUCE_N4(M) REDUCE_4(result##M##0, result##M##1, result##M##2, result##M##3)
+
+#if defined(B0)
+#define STORE_REDUCE(M, N) C[(j+N)*ldc + i + M] = alpha * _mm512_reduce_add_pd(result##M##N)
+#define STORE_M4(N, s0) _mm256_storeu_pd(&C[(j + N)*ldc + i], s0);
+#define STORE_N4(M, s0) _mm256_i64scatter_pd(&C[j*ldc + i + M], vindex_n, s0, 8);
+#else
+#define STORE_REDUCE(M, N) C[(j+N)*ldc + i + M] = alpha * _mm512_reduce_add_pd(result##M##N) + beta * C[(j+N)*ldc + i + M]
+#define STORE_M4(N, s0) \
+	asm("vfmadd231pd (%1), %2, %0": "+v"(s0):"r"(&C[(j + N)*ldc + i]), "v"(beta_256)); \
+	_mm256_storeu_pd(&C[(j + N)*ldc + i], s0);
+
+#define STORE_N4(M, s0) \
+	s0 = _mm256_fmadd_pd(_mm256_i64gather_pd(&C[j*ldc + i + M], vindex_n, 8), beta_256, s0); \
+	_mm256_i64scatter_pd(&C[j*ldc + i + M], vindex_n, s0, 8);
+#endif
+#define STORE_REDUCE_M4(N) {\
+	REDUCE_M4(N) \
+	STORE_M4(N, s0) \
+}
+#define STORE_REDUCE_N4(M) {\
+	REDUCE_N4(M) \
+	STORE_N4(M, s0) \
+}
+
+
+#if defined(B0)
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	// column major
+	BLASLONG i, j, k;
+
+	BLASLONG m4 = M & ~3;
+	BLASLONG m2 = M & ~1;
+
+	BLASLONG n4 = N & ~3;
+	BLASLONG n2 = N & ~1;
+
+	BLASLONG k8 = K & ~7;
+
+	__mmask8 mask;
+
+	__m256i vindex_n = _mm256_set_epi64x(ldc*3, ldc*2, ldc, 0);
+	__m256d alpha_256 = _mm256_broadcast_sd(&alpha);
+#if !defined(B0)
+	__m256d beta_256 = _mm256_broadcast_sd(&beta);
+#endif
+
+	long long permute_table[] = {
+		0, 1, 0|8, 1|8, 4, 5, 4|8, 5|8,
+		2, 3, 2|8, 3|8, 6, 7, 6|8, 7|8,
+	};
+	__m512i idx_lo = _mm512_loadu_si512(permute_table);
+	__m512i idx_hi = _mm512_loadu_si512(permute_table + 8);
+
+	for (i = 0; i < m4; i += 4) {
+		for (j = 0; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+			for (k = 0; k < k8; k += 8) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+			}
+			STORE_REDUCE_M4(0); STORE_REDUCE_M4(1); STORE_REDUCE_M4(2); STORE_REDUCE_M4(3);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			for (k = 0; k < k8; k += 8) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+			}
+			STORE_REDUCE_M4(0); STORE_REDUCE_M4(1);
+		}
+		for (; j < N; j += 1) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			for (k = 0; k < k8; k += 8) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+				LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+				MASK_LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+			}
+			STORE_REDUCE_M4(0);
+		}
+
+	}
+	for (; i < m2; i += 2) {
+		for (j = 0; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+			for (k = 0; k < k8; k += 8) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3);
+			}
+			STORE_REDUCE_N4(0); STORE_REDUCE_N4(1);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			for (k = 0; k < k8; k += 8) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+			}
+			STORE_REDUCE(0, 0); STORE_REDUCE(1, 0);
+			STORE_REDUCE(0, 1); STORE_REDUCE(1, 1);
+
+		}
+		for (; j < N; j += 1) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			for (k = 0; k < k8; k += 8) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+				LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+				MASK_LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+			}
+			STORE_REDUCE(0, 0); STORE_REDUCE(1, 0);
+		}
+	}
+	for (; i < M; i += 1) {
+		for (j = 0; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			for (k = 0; k < k8; k += 8) {
+				LOAD_KA_512(0, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+			}
+			STORE_REDUCE_N4(0);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			for (k = 0; k < k8; k += 8) {
+				LOAD_KA_512(0, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			STORE_REDUCE(0, 0);
+			STORE_REDUCE(0, 1);
+
+		}
+		for (; j < N; j += 1) {
+			DECLARE_RESULT_512(0, 0);
+			for (k = 0; k < k8; k += 8) {
+				LOAD_KA_512(0, x);
+				LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x);
+				MASK_LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0);
+			}
+			STORE_REDUCE(0, 0);
+		}
+	}
+	return 0;
+}

kernel/x86_64/dgemm_small_kernel_tt_skylakex.c

@@ -0,0 +1,392 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include <immintrin.h>
+#include "common.h"
+#include <stdio.h>
+
+#define DECLARE_RESULT_512(M, N) __m512d result##M##N = _mm512_setzero_pd()
+#define BROADCAST_LOAD_A_512(M, N) __m512d Aval##M = _mm512_broadcastsd_pd(_mm_load_sd(&A[k  + lda * (i+M)]))
+#define LOAD_B_512(M,N)  __m512d Bval##N = _mm512_loadu_pd(&B[ldb * k + j + (N*8)])
+#define MASK_LOAD_B_512(M, N) __m512d Bval##N = _mm512_maskz_loadu_pd(mask, &B[ldb * k + j + (N*8)])
+#define MATMUL_512(M, N) result##M##N = _mm512_fmadd_pd(Aval##M, Bval##N, result##M##N)
+
+#if defined(B0)
+#define STORE_8xy(v, N, x, y) _mm512_storeu_pd(&C[(j + N*8 + x + y*8)*ldc + i], v)
+#define STORE_4xy(v, N, x, y) _mm256_storeu_pd(&C[(j + N*8 + x + y*4)*ldc + i], v)
+#define SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+				_mm512_i64scatter_pd(&C[(j + N*8)*ldc + i + M], vindex_n, result##M##N, 8);
+#define MASK_SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+				    _mm512_mask_i64scatter_pd(&C[(j + N*8)*ldc + i + M], mask, vindex_n, result##M##N, 8);
+#else
+#define STORE_8xy(v, N, x, y) \
+	asm("vfmadd231pd (%1), %2, %0": "+v"(v): "r"(&C[(j + N*8 + x + y*8)*ldc + i]), "v"(beta_512)); \
+	_mm512_storeu_pd(&C[(j + N*8 + x + y*8)*ldc + i], v)
+#define STORE_4xy(v, N, x, y) \
+	asm("vfmadd231pd (%1), %2, %0": "+v"(v): "r"(&C[(j + N*8 + x + y*4)*ldc + i]), "v"(beta_256)); \
+	_mm256_storeu_pd(&C[(j + N*8 + x + y*4)*ldc + i], v)
+#define SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+				__m512d tmp##M##N = _mm512_i64gather_pd(vindex_n, &C[(j + N*8)*ldc + i + M], 8); \
+				result##M##N = _mm512_fmadd_pd(tmp##M##N, beta_512, result##M##N); \
+				_mm512_i64scatter_pd(&C[(j + N*8)*ldc + i + M], vindex_n, result##M##N, 8);
+#define MASK_SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_pd(result##M##N, alpha_512); \
+				__m512d tmp##M##N = _mm512_mask_i64gather_pd(_mm512_setzero_pd(), mask, vindex_n, &C[(j + N*8)*ldc + i + M], 8); \
+				result##M##N = _mm512_fmadd_pd(tmp##M##N, beta_512, result##M##N); \
+				_mm512_mask_i64scatter_pd(&C[(j + N*8)*ldc + i + M], mask, vindex_n, result##M##N, 8);
+#endif
+
+#define REORDER_8x8(r0, r1, r2, r3, r4, r5, r6, r7) \
+	__m512d t0, t1, t2, t3, t4, t5, t6, t7; \
+	t0 = _mm512_unpacklo_pd(r0, r1); \
+	t1 = _mm512_unpackhi_pd(r0, r1); \
+	t2 = _mm512_unpacklo_pd(r2, r3); \
+	t3 = _mm512_unpackhi_pd(r2, r3); \
+	t4 = _mm512_unpacklo_pd(r4, r5); \
+	t5 = _mm512_unpackhi_pd(r4, r5); \
+	t6 = _mm512_unpacklo_pd(r6, r7); \
+	t7 = _mm512_unpackhi_pd(r6, r7); \
+	r0 = _mm512_shuffle_f64x2(t0, t2, 0x88); \
+	r1 = _mm512_shuffle_f64x2(t1, t3, 0x88); \
+	r2 = _mm512_shuffle_f64x2(t0, t2, 0xdd); \
+	r3 = _mm512_shuffle_f64x2(t1, t3, 0xdd); \
+	r4 = _mm512_shuffle_f64x2(t4, t6, 0x88); \
+	r5 = _mm512_shuffle_f64x2(t5, t7, 0x88); \
+	r6 = _mm512_shuffle_f64x2(t4, t6, 0xdd); \
+	r7 = _mm512_shuffle_f64x2(t5, t7, 0xdd); \
+	t0 = _mm512_permutex2var_pd(r0, idx_lo, r4); \
+	t1 = _mm512_permutex2var_pd(r1, idx_lo, r5); \
+	t2 = _mm512_permutex2var_pd(r2, idx_lo, r6); \
+	t3 = _mm512_permutex2var_pd(r3, idx_lo, r7); \
+	t4 = _mm512_permutex2var_pd(r0, idx_hi, r4); \
+	t5 = _mm512_permutex2var_pd(r1, idx_hi, r5); \
+	t6 = _mm512_permutex2var_pd(r2, idx_hi, r6); \
+	t7 = _mm512_permutex2var_pd(r3, idx_hi, r7); \
+	t0 = _mm512_mul_pd(t0, alpha_512); \
+	t1 = _mm512_mul_pd(t1, alpha_512); \
+	t2 = _mm512_mul_pd(t2, alpha_512); \
+	t3 = _mm512_mul_pd(t3, alpha_512); \
+	t4 = _mm512_mul_pd(t4, alpha_512); \
+	t5 = _mm512_mul_pd(t5, alpha_512); \
+	t6 = _mm512_mul_pd(t6, alpha_512); \
+	t7 = _mm512_mul_pd(t7, alpha_512);
+
+#define SAVE_8(N, x) {\
+	STORE_8xy(t##x, N, x, 0); \
+}
+
+#define REORDER_STORE_8x8(N) {\
+	REORDER_8x8(result0##N, result1##N, result2##N, result3##N, result4##N, result5##N, result6##N, result7##N); \
+	SAVE_8(N, 0); SAVE_8(N, 1); SAVE_8(N, 2); SAVE_8(N, 3); SAVE_8(N, 4); SAVE_8(N, 5); SAVE_8(N, 6); SAVE_8(N, 7); \
+}
+
+#define MASK_SAVE_8() \
+	switch (nn) { \
+		case 8: SAVE_8(0, 7); \
+		case 7: SAVE_8(0, 6); \
+		case 6: SAVE_8(0, 5); \
+		case 5: SAVE_8(0, 4); \
+		case 4: SAVE_8(0, 3); \
+		case 3: SAVE_8(0, 2); \
+		case 2: SAVE_8(0, 1); \
+		case 1: SAVE_8(0, 0); \
+	}
+
+#define MASK_REORDER_STORE_8x8(N) {\
+	REORDER_8x8(result0##N, result1##N, result2##N, result3##N, result4##N, result5##N, result6##N, result7##N); \
+	MASK_SAVE_8(); \
+}
+
+#define REORDER_4x8(r0, r1, r2, r3) \
+	__m512d t0, t1, t2, t3; \
+	t0 = _mm512_unpacklo_pd(r0, r1); \
+	t1 = _mm512_unpackhi_pd(r0, r1); \
+	t2 = _mm512_unpacklo_pd(r2, r3); \
+	t3 = _mm512_unpackhi_pd(r2, r3); \
+	r0 = _mm512_permutex2var_pd(t0, idx_lo, t2); \
+	r1 = _mm512_permutex2var_pd(t1, idx_lo, t3); \
+	r2 = _mm512_permutex2var_pd(t0, idx_hi, t2); \
+	r3 = _mm512_permutex2var_pd(t1, idx_hi, t3); \
+	t0 = _mm512_mul_pd(r0, alpha_512); \
+	t1 = _mm512_mul_pd(r1, alpha_512); \
+	t2 = _mm512_mul_pd(r2, alpha_512); \
+	t3 = _mm512_mul_pd(r3, alpha_512);
+
+#define SAVE_4(N, x, y) {\
+	__m256d v4 = _mm512_extractf64x4_pd(t##x, y); \
+	STORE_4xy(v4, N, x, y); \
+}
+
+#define REORDER_STORE_4x8(N) {\
+	REORDER_4x8(result0##N, result1##N, result2##N, result3##N); \
+	SAVE_4(N, 0, 0); SAVE_4(N, 1, 0); SAVE_4(N, 2, 0); SAVE_4(N, 3, 0); \
+	SAVE_4(N, 0, 1); SAVE_4(N, 1, 1); SAVE_4(N, 2, 1); SAVE_4(N, 3, 1); \
+}
+
+#define MASK_SAVE_4() \
+	switch (nn) { \
+		case 8: SAVE_4(0, 3, 1); \
+		case 7: SAVE_4(0, 2, 1); \
+		case 6: SAVE_4(0, 1, 1); \
+		case 5: SAVE_4(0, 0, 1); \
+		case 4: SAVE_4(0, 3, 0); \
+		case 3: SAVE_4(0, 2, 0); \
+		case 2: SAVE_4(0, 1, 0); \
+		case 1: SAVE_4(0, 0, 0); \
+	}
+
+#define MASK_REORDER_STORE_4x8(N) {\
+	REORDER_4x8(result0##N, result1##N, result2##N, result3##N); \
+	MASK_SAVE_4(); \
+}
+
+
+#if defined(B0)
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	// column major
+	BLASLONG i, j, k;
+
+	BLASLONG m8 = M & ~7;
+	BLASLONG m4 = M & ~3;
+	BLASLONG m2 = M & ~1;
+
+	BLASLONG n32 = N & ~31;
+	BLASLONG n16 = N & ~15;
+
+	__m512d alpha_512 = _mm512_broadcastsd_pd(_mm_load_sd(&alpha));
+#if !defined(B0)
+	__m512d beta_512 = _mm512_broadcastsd_pd(_mm_load_sd(&beta));
+	__m256d beta_256 = _mm256_broadcastsd_pd(_mm_load_sd(&beta));
+#endif
+	long long permute_table[] = {
+		0, 1, 4, 5, 0|8, 1|8, 4|8, 5|8,
+		2, 3, 6, 7, 2|8, 3|8, 6|8, 7|8,
+	};
+	__m512i idx_lo = _mm512_loadu_si512(permute_table);
+	__m512i idx_hi = _mm512_loadu_si512(permute_table + 8);
+
+	for (i = 0; i < m8; i += 8) {
+		for (j = 0; j < n16; j += 16) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(4, 0); DECLARE_RESULT_512(5, 0); DECLARE_RESULT_512(6, 0); DECLARE_RESULT_512(7, 0);
+
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			DECLARE_RESULT_512(4, 1); DECLARE_RESULT_512(5, 1); DECLARE_RESULT_512(6, 1); DECLARE_RESULT_512(7, 1);
+			for (k = 0; k < K; k++) {
+				BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+				BROADCAST_LOAD_A_512(4, x); BROADCAST_LOAD_A_512(5, x); BROADCAST_LOAD_A_512(6, x); BROADCAST_LOAD_A_512(7, x);
+				LOAD_B_512(x, 0); LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(4, 0); MATMUL_512(5, 0); MATMUL_512(6, 0); MATMUL_512(7, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				MATMUL_512(4, 1); MATMUL_512(5, 1); MATMUL_512(6, 1); MATMUL_512(7, 1);
+			}
+			REORDER_STORE_8x8(0);
+			REORDER_STORE_8x8(1);
+		}
+		__mmask8 mask = 0xff;
+		int nn = 8;
+		for (; j < N; j += 8) {
+			if (N - j < 8) {
+				nn = N - j;
+				mask = (1UL << nn) - 1;
+			}
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(4, 0); DECLARE_RESULT_512(5, 0); DECLARE_RESULT_512(6, 0); DECLARE_RESULT_512(7, 0);
+			for (k = 0; k < K; k++) {
+				BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+				BROADCAST_LOAD_A_512(4, x); BROADCAST_LOAD_A_512(5, x); BROADCAST_LOAD_A_512(6, x); BROADCAST_LOAD_A_512(7, x);
+				MASK_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(4, 0); MATMUL_512(5, 0); MATMUL_512(6, 0); MATMUL_512(7, 0);
+			}
+			MASK_REORDER_STORE_8x8(0);
+		}
+	}
+	for (; i < m4; i += 4) {
+		long long permute_table2[] = {
+			0, 1, 0|8, 1|8, 4, 5, 4|8, 5|8,
+			2, 3, 2|8, 3|8, 6, 7, 6|8, 7|8,
+		};
+		idx_lo = _mm512_loadu_si512(permute_table2);
+		idx_hi = _mm512_loadu_si512(permute_table2 + 8);
+
+		for (j = 0; j < n32; j += 32) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+			for (k = 0; k < K; k++) {
+				BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+				LOAD_B_512(x, 0); LOAD_B_512(x, 1); LOAD_B_512(x, 2); LOAD_B_512(x, 3);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+			}
+			REORDER_STORE_4x8(0);
+			REORDER_STORE_4x8(1);
+			REORDER_STORE_4x8(2);
+			REORDER_STORE_4x8(3);
+		}
+		for (; j < n16; j += 16) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			for (k = 0; k < K; k++) {
+				BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+				LOAD_B_512(x, 0); LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+			}
+			REORDER_STORE_4x8(0);
+			REORDER_STORE_4x8(1);
+		}
+		__mmask8 mask = 0xff;
+		int nn = 8;
+		for (; j < N; j += 8) {
+			if (N - j < 8) {
+				nn = N - j;
+				mask = (1UL << nn) - 1;
+			}
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			for (k = 0; k < K; k++) {
+				BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+				MASK_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+			}
+			MASK_REORDER_STORE_4x8(0);
+		}
+	}
+	if (i < M) {
+		long long index_n[8];
+		for (int ii = 0; ii < 8; ii++) {
+			index_n[ii] = ii * ldc;
+		}
+		__m512i vindex_n = _mm512_loadu_si512(index_n);
+#if !defined(B0)
+		__m512d beta_512 = _mm512_broadcastsd_pd(_mm_load_sd(&beta));
+#endif
+		for (; i < m2; i += 2) {
+			for (j = 0; j < n32; j += 32) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+				DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					LOAD_B_512(x, 0); LOAD_B_512(x, 1); LOAD_B_512(x, 2); LOAD_B_512(x, 3);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1);
+				SCATTER_STORE_512(0, 2); SCATTER_STORE_512(1, 2);
+				SCATTER_STORE_512(0, 3); SCATTER_STORE_512(1, 3);
+			}
+			for (; j < n16; j += 16) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					LOAD_B_512(x, 0); LOAD_B_512(x, 1);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1);
+			}
+			__mmask8 mask = 0xff;
+			int nn = 8;
+			for (; j < N; j += 8) {
+				if (N - j < 8) {
+					nn = N - j;
+					mask = (1UL << nn) - 1;
+				}
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					MASK_LOAD_B_512(x, 0);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+				}
+				MASK_SCATTER_STORE_512(0, 0); MASK_SCATTER_STORE_512(1, 0);
+			}
+		}
+		for (; i < M; i += 1) {
+			for (j = 0; j < n32; j += 32) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				DECLARE_RESULT_512(0, 2);
+				DECLARE_RESULT_512(0, 3);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					LOAD_B_512(x, 0); LOAD_B_512(x, 1); LOAD_B_512(x, 2); LOAD_B_512(x, 3);
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+					MATMUL_512(0, 2);
+					MATMUL_512(0, 3);
+				}
+				SCATTER_STORE_512(0, 0);
+				SCATTER_STORE_512(0, 1);
+				SCATTER_STORE_512(0, 2);
+				SCATTER_STORE_512(0, 3);
+			}
+			for (; j < n16; j += 16) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					LOAD_B_512(x, 0); LOAD_B_512(x, 1);
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+				}
+				SCATTER_STORE_512(0, 0);
+				SCATTER_STORE_512(0, 1);
+			}
+			__mmask8 mask = 0xff;
+			int nn = 8;
+			for (; j < N; j += 8) {
+				if (N - j < 8) {
+					nn = N - j;
+					mask = (1UL << nn) - 1;
+				}
+				DECLARE_RESULT_512(0, 0);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					MASK_LOAD_B_512(x, 0);
+					MATMUL_512(0, 0);
+				}
+				MASK_SCATTER_STORE_512(0, 0);
+			}
+		}
+	}
+	return 0;
+}

kernel/x86_64/sgemm_small_kernel_nn_skylakex.c

@@ -0,0 +1,612 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include <immintrin.h>
+#include "common.h"
+#include <stdio.h>
+#include <memory.h>
+
+#define DECLARE_RESULT_512(M, N) __m512 result##M##N = _mm512_setzero_ps()
+#define LOAD_A_512(M, N) __m512 Aval##M = _mm512_loadu_ps(&A[lda * k + i + (M*16)])
+#define MASK_LOAD_A_512(M, N) __m512 Aval##M = _mm512_maskz_loadu_ps(mask, &A[lda * k + i + (M*16)])
+#define BROADCAST_LOAD_B_512(M, N) __m512 Bval##N = _mm512_broadcastss_ps(_mm_load_ss(&B[k + ldb * (j+N)]))
+#define MATMUL_512(M, N) result##M##N = _mm512_fmadd_ps(Aval##M, Bval##N, result##M##N)
+#if defined(B0)
+#define STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+			_mm512_storeu_ps(&C[(j+N)*ldc + i + (M*16)], result##M##N)
+#define MASK_STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+			_mm512_mask_storeu_ps(&C[(j+N)*ldc + i + (M*16)], mask, result##M##N)
+#else
+#define STORE_512(M, N) \
+	result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+	asm("vfmadd231ps (%1), %2, %0": "+v"(result##M##N):"r"(&C[(j+N)*ldc + i + (M*16)]), "v"(beta_512)); \
+	_mm512_storeu_ps(&C[(j+N)*ldc + i + (M*16)], result##M##N)
+#define MASK_STORE_512(M, N) \
+	result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+	asm("vfmadd231ps (%1), %2, %0 %{%3%}": "+v"(result##M##N):"r"(&C[(j+N)*ldc + i + (M*16)]), "v"(beta_512), "k"(mask)); \
+	_mm512_mask_storeu_ps(&C[(j+N)*ldc + i + (M*16)], mask, result##M##N)
+#endif
+
+#define LOAD_KA_512(M, N) __m512 Aval##M = _mm512_loadu_ps(&mbuf[(mi + M)*K + k]);
+#define LOAD_KB_512(M, N) __m512 Bval##N = _mm512_loadu_ps(&B[(j + N)*ldb + k])
+#define MASK_LOAD_KA_512(M, N) __m512 Aval##M = _mm512_maskz_loadu_ps(mask, &mbuf[(mi + M)*K + k])
+#define MASK_LOAD_KB_512(M, N) __m512 Bval##N = _mm512_maskz_loadu_ps(mask, &B[(j + N)*ldb + k])
+#define REDUCE_4(rr0, rr1, rr2, rr3) \
+	__m512 r0, r1, r2, r3, t0, t1, t2, t3;\
+	r0 = _mm512_unpacklo_ps(rr0, rr1); r1 = _mm512_unpackhi_ps(rr0, rr1); \
+	r2 = _mm512_unpacklo_ps(rr2, rr3); r3 = _mm512_unpackhi_ps(rr2, rr3); \
+	t0 = _mm512_shuffle_ps(r0, r2, _MM_SHUFFLE(1, 0, 1, 0)); t1 = _mm512_shuffle_ps(r0, r2, _MM_SHUFFLE(3, 2, 3, 2)); \
+	t2 = _mm512_shuffle_ps(r1, r3, _MM_SHUFFLE(1, 0, 1, 0)); t3 = _mm512_shuffle_ps(r1, r3, _MM_SHUFFLE(3, 2, 3, 2)); \
+	r0 = _mm512_add_ps(t0, t1); r1 = _mm512_add_ps(t2, t3); t0 = _mm512_add_ps(r0, r1); \
+	__m128 s0, s1, s2, s3; \
+	s0 = _mm512_extractf32x4_ps(t0, 0); s1 = _mm512_extractf32x4_ps(t0, 1); s2 = _mm512_extractf32x4_ps(t0, 2); s3 = _mm512_extractf32x4_ps(t0, 3); \
+	s0 = _mm_maskz_add_ps(mask8, s0, s1); s2 = _mm_maskz_add_ps(mask8, s2, s3); s0 = _mm_maskz_add_ps(mask8, s0, s2); \
+	s0 = _mm_maskz_mul_ps(mask8, alpha_128, s0);
+#define REDUCE_M4(N) REDUCE_4(result0##N, result1##N, result2##N, result3##N)
+#define REDUCE_N4(M) REDUCE_4(result##M##0, result##M##1, result##M##2, result##M##3)
+#if defined(B0)
+#define STORE_REDUCE(M, N) C[(j+N)*ldc + i + M] = alpha * _mm512_reduce_add_ps(result##M##N);
+#define STORE_REDUCE_M4(N) {\
+	REDUCE_M4(N) \
+	_mm_mask_storeu_ps(&C[(j + N)*ldc + i], mask8, s0); \
+}
+#define STORE_REDUCE_N4(M) {\
+	REDUCE_N4(M) \
+	_mm_i32scatter_ps(&C[j*ldc + i + M], vindex_n, s0, 4); \
+}
+#else
+#define STORE_REDUCE(M, N) C[(j+N)*ldc + i + M] = alpha * _mm512_reduce_add_ps(result##M##N) + beta * C[(j+N)*ldc + i + M];
+#define STORE_REDUCE_M4(N) {\
+	REDUCE_M4(N) \
+	asm("vfmadd231ps (%1), %2, %0": "+v"(s0):"r"(&C[(j + N)*ldc + i]), "v"(beta_128)); \
+	_mm_mask_storeu_ps(&C[(j + N)*ldc + i], mask8, s0); \
+}
+#define STORE_REDUCE_N4(M) {\
+	REDUCE_N4(M) \
+	s1 = _mm_i32gather_ps(&C[j*ldc + i + M], vindex_n, 4); \
+	s0 = _mm_fmadd_ps(s1, beta_128, s0); \
+	_mm_i32scatter_ps(&C[j*ldc + i + M], vindex_n, s0, 4); \
+}
+#endif
+
+#if defined(B0)
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	// column major
+	BLASLONG i, j, k;
+
+	BLASLONG m64 = M & ~63;
+	BLASLONG m32 = M & ~31;
+	BLASLONG m16 = M & ~15;
+	BLASLONG m4 = M & ~3;
+	BLASLONG m2 = M & ~1;
+
+	BLASLONG n6 = N - (N % 6);
+	BLASLONG n4 = N & ~3;
+	BLASLONG n2 = N & ~1;
+
+
+	__m512 alpha_512 = _mm512_broadcastss_ps(_mm_load_ss(&alpha));
+#if !defined(B0)
+	__m512 beta_512 = _mm512_broadcastss_ps(_mm_load_ss(&beta));
+#endif
+
+	for (i = 0; i < m64; i += 64) {
+		for (j = 0; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+			STORE_512(0, 1); STORE_512(1, 1); STORE_512(2, 1); STORE_512(3, 1);
+			STORE_512(0, 2); STORE_512(1, 2); STORE_512(2, 2); STORE_512(3, 2);
+			STORE_512(0, 3); STORE_512(1, 3); STORE_512(2, 3); STORE_512(3, 3);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+			STORE_512(0, 1); STORE_512(1, 1); STORE_512(2, 1); STORE_512(3, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+		}
+	}
+	for (; i < m32; i += 32) {
+		for (j = 0; j < n6; j += 6) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+			DECLARE_RESULT_512(0, 4); DECLARE_RESULT_512(1, 4);
+			DECLARE_RESULT_512(0, 5); DECLARE_RESULT_512(1, 5);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3);
+				MATMUL_512(0, 4); MATMUL_512(1, 4);
+				MATMUL_512(0, 5); MATMUL_512(1, 5);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+			STORE_512(0, 1); STORE_512(1, 1);
+			STORE_512(0, 2); STORE_512(1, 2);
+			STORE_512(0, 3); STORE_512(1, 3);
+			STORE_512(0, 4); STORE_512(1, 4);
+			STORE_512(0, 5); STORE_512(1, 5);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+			STORE_512(0, 1); STORE_512(1, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+		}
+	}
+	for (; i < m16; i += 16) {
+		for (j = 0; j < n6; j += 6) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			DECLARE_RESULT_512(0, 4);
+			DECLARE_RESULT_512(0, 5);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+				MATMUL_512(0, 4);
+				MATMUL_512(0, 5);
+			}
+			STORE_512(0, 0);
+			STORE_512(0, 1);
+			STORE_512(0, 2);
+			STORE_512(0, 3);
+			STORE_512(0, 4);
+			STORE_512(0, 5);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			STORE_512(0, 0);
+			STORE_512(0, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0);
+			}
+			STORE_512(0, 0);
+		}
+	}
+	int mm = M - i;
+	if (!mm) return 0;
+	if (mm > 8 || K < 32) {
+		register __mmask16 mask asm("k1") = (1UL << mm) - 1;
+		for (j = 0; j < n6; j += 6) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			DECLARE_RESULT_512(0, 4);
+			DECLARE_RESULT_512(0, 5);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+				MATMUL_512(0, 4);
+				MATMUL_512(0, 5);
+			}
+			MASK_STORE_512(0, 0);
+			MASK_STORE_512(0, 1);
+			MASK_STORE_512(0, 2);
+			MASK_STORE_512(0, 3);
+			MASK_STORE_512(0, 4);
+			MASK_STORE_512(0, 5);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			MASK_STORE_512(0, 0);
+			MASK_STORE_512(0, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0);
+			}
+			MASK_STORE_512(0, 0);
+		}
+	} else {
+		/* M => [1, 8]
+		 *
+		 * This kernel use dot-like style to calc a value - C(x, y):
+		 * C(x, y) = A(x, 0)*B(0, y) + A(x, 1)*B(1, y) +....+ A(x, K)*B(K, y)
+		 *
+		 * Alloc a buf to copy rest of A as row major,
+		 * so memory access from 0 to K is continuous for both A & B.
+		 *
+		 * Loading to zmm and FMA 16 of k at one loop,
+		 * finally reduce_add zmm to a single float result in C(x, y).
+		 *
+		 * Note: performance is bad when K is small.
+		 */
+		FLOAT *mbuf = (FLOAT *) malloc(sizeof(FLOAT)*mm*K);
+		__mmask8 mask8 = (1UL << mm) - 1;
+		__mmask16 mask;
+		BLASLONG k16 = K & ~15;
+		BLASLONG k8 = K & ~7;
+		for (k = 0; k < k8; k += 8) {
+			__m256  r0, r1, r2, r3, r4, r5, r6, r7;
+			__m256  t0, t1, t2, t3, t4, t5, t6, t7;
+			r0 = _mm256_maskz_loadu_ps(mask8, &A[i + lda*(0 + k)]);
+			r1 = _mm256_maskz_loadu_ps(mask8, &A[i + lda*(1 + k)]);
+			r2 = _mm256_maskz_loadu_ps(mask8, &A[i + lda*(2 + k)]);
+			r3 = _mm256_maskz_loadu_ps(mask8, &A[i + lda*(3 + k)]);
+			r4 = _mm256_maskz_loadu_ps(mask8, &A[i + lda*(4 + k)]);
+			r5 = _mm256_maskz_loadu_ps(mask8, &A[i + lda*(5 + k)]);
+			r6 = _mm256_maskz_loadu_ps(mask8, &A[i + lda*(6 + k)]);
+			r7 = _mm256_maskz_loadu_ps(mask8, &A[i + lda*(7 + k)]);
+
+			t0 = _mm256_unpacklo_ps(r0, r1);
+			t1 = _mm256_unpackhi_ps(r0, r1);
+			t2 = _mm256_unpacklo_ps(r2, r3);
+			t3 = _mm256_unpackhi_ps(r2, r3);
+			t4 = _mm256_unpacklo_ps(r4, r5);
+			t5 = _mm256_unpackhi_ps(r4, r5);
+			t6 = _mm256_unpacklo_ps(r6, r7);
+			t7 = _mm256_unpackhi_ps(r6, r7);
+
+			r0 = _mm256_shuffle_ps(t0,t2,_MM_SHUFFLE(1,0,1,0));
+			r1 = _mm256_shuffle_ps(t0,t2,_MM_SHUFFLE(3,2,3,2));
+			r2 = _mm256_shuffle_ps(t1,t3,_MM_SHUFFLE(1,0,1,0));
+			r3 = _mm256_shuffle_ps(t1,t3,_MM_SHUFFLE(3,2,3,2));
+			r4 = _mm256_shuffle_ps(t4,t6,_MM_SHUFFLE(1,0,1,0));
+			r5 = _mm256_shuffle_ps(t4,t6,_MM_SHUFFLE(3,2,3,2));
+			r6 = _mm256_shuffle_ps(t5,t7,_MM_SHUFFLE(1,0,1,0));
+			r7 = _mm256_shuffle_ps(t5,t7,_MM_SHUFFLE(3,2,3,2));
+
+			t0 = _mm256_permute2f128_ps(r0, r4, 0x20);
+			t1 = _mm256_permute2f128_ps(r1, r5, 0x20);
+			t2 = _mm256_permute2f128_ps(r2, r6, 0x20);
+			t3 = _mm256_permute2f128_ps(r3, r7, 0x20);
+			t4 = _mm256_permute2f128_ps(r0, r4, 0x31);
+			t5 = _mm256_permute2f128_ps(r1, r5, 0x31);
+			t6 = _mm256_permute2f128_ps(r2, r6, 0x31);
+			t7 = _mm256_permute2f128_ps(r3, r7, 0x31);
+
+			switch (mm) {
+				case 8: _mm256_storeu_ps(&mbuf[k + 7*K], t7);
+				case 7: _mm256_storeu_ps(&mbuf[k + 6*K], t6);
+				case 6: _mm256_storeu_ps(&mbuf[k + 5*K], t5);
+				case 5: _mm256_storeu_ps(&mbuf[k + 4*K], t4);
+				case 4: _mm256_storeu_ps(&mbuf[k + 3*K], t3);
+				case 3: _mm256_storeu_ps(&mbuf[k + 2*K], t2);
+				case 2: _mm256_storeu_ps(&mbuf[k + 1*K], t1);
+				case 1: _mm256_storeu_ps(&mbuf[k + 0*K], t0);
+			}
+		}
+		for (; k < K; k++) {
+			for (int ii = 0; ii < mm; ii++) {
+				mbuf[k + ii*K] = A[i + lda*k + ii];
+			}
+		}
+		int mi = 0;
+		mask8 = 0xff;  // just use to avoid SSE instruction
+		__m128 alpha_128 = _mm_broadcast_ss(&alpha);
+#if !defined(B0)
+		__m128 beta_128 = _mm_broadcast_ss(&beta);
+#endif
+		__m128i vindex_n = _mm_set_epi32(ldc*3, ldc*2, ldc, 0);
+		for (; i < m4; i += 4, mi += 4) {
+			for (j = 0; j < n4; j += 4) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+				DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+				DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+				for (k = 0; k < k16; k += 16) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+				}
+				STORE_REDUCE_M4(0); STORE_REDUCE_M4(1); STORE_REDUCE_M4(2); STORE_REDUCE_M4(3);
+			}
+			for (; j < n2; j += 2) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+				for (k = 0; k < k16; k += 16) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				}
+				STORE_REDUCE_M4(0); STORE_REDUCE_M4(1);
+			}
+			for (; j < N; j += 1) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				for (k = 0; k < k16; k += 16) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+					LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+					MASK_LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				}
+				STORE_REDUCE_M4(0);
+			}
+
+		}
+		for (; i < m2; i += 2, mi += 2) {
+			for (j = 0; j < n4; j += 4) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+				DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+				for (k = 0; k < k16; k += 16) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3);
+				}
+				STORE_REDUCE_N4(0); STORE_REDUCE_N4(1);
+			}
+			for (; j < n2; j += 2) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				for (k = 0; k < k16; k += 16) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+				}
+				STORE_REDUCE(0, 0); STORE_REDUCE(1, 0);
+				STORE_REDUCE(0, 1); STORE_REDUCE(1, 1);
+
+			}
+			for (; j < N; j += 1) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				for (k = 0; k < k16; k += 16) {
+					LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+					LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+					MASK_LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+				}
+				STORE_REDUCE(0, 0); STORE_REDUCE(1, 0);
+			}
+		}
+		for (; i < M; i += 1, mi += 1) {
+			for (j = 0; j < n4; j += 4) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				DECLARE_RESULT_512(0, 2);
+				DECLARE_RESULT_512(0, 3);
+				for (k = 0; k < k16; k += 16) {
+					LOAD_KA_512(0, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+					MATMUL_512(0, 2);
+					MATMUL_512(0, 3);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+					MATMUL_512(0, 2);
+					MATMUL_512(0, 3);
+				}
+				STORE_REDUCE_N4(0);
+			}
+			for (; j < n2; j += 2) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				for (k = 0; k < k16; k += 16) {
+					LOAD_KA_512(0, x);
+					LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x);
+					MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+				}
+				STORE_REDUCE(0, 0);
+				STORE_REDUCE(0, 1);
+
+			}
+			for (; j < N; j += 1) {
+				DECLARE_RESULT_512(0, 0);
+				for (k = 0; k < k16; k += 16) {
+					LOAD_KA_512(0, x);
+					LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0);
+				}
+				int remains = K - k;
+				if (remains) {
+					mask = (1UL << remains) - 1;
+					MASK_LOAD_KA_512(0, x);
+					MASK_LOAD_KB_512(x, 0);
+
+					MATMUL_512(0, 0);
+				}
+				STORE_REDUCE(0, 0);
+			}
+		}
+		free(mbuf);
+	}
+	return 0;
+}

kernel/x86_64/sgemm_small_kernel_nt_skylakex.c

@@ -0,0 +1,535 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include <immintrin.h>
+#include "common.h"
+#include <stdio.h>
+#include <memory.h>
+
+#define DECLARE_RESULT_512(M, N) __m512 result##M##N = _mm512_setzero_ps()
+#define LOAD_A_512(M, N) __m512 Aval##M = _mm512_loadu_ps(&A[lda * k + i + (M*16)])
+#define MASK_LOAD_A_512(M, N) __m512 Aval##M = _mm512_maskz_loadu_ps(mask, &A[lda * k + i + (M*16)])
+#define BROADCAST_LOAD_B_512(M, N) __m512 Bval##N = _mm512_broadcastss_ps(_mm_load_ss(&B[ldb * k + j + N]))
+#define MATMUL_512(M, N) result##M##N = _mm512_fmadd_ps(Aval##M, Bval##N, result##M##N)
+
+#define BROADCAST_LOAD_A_512(M, N) __m512 Aval##M = _mm512_broadcastss_ps(_mm_load_ss(&A[lda * k + i + M]))
+#define LOAD_B_512(M, N) __m512 Bval##N = _mm512_loadu_ps(&B[ldb * k + j + (N*16)])
+#define MASK_LOAD_B_512(M, N) __m512 Bval##N = _mm512_maskz_loadu_ps(mask, &B[ldb * k + j + (N*16)])
+#if defined(B0)
+#define STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+			_mm512_storeu_ps(&C[(j+N)*ldc + i + (M*16)], result##M##N)
+#define MASK_STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+			_mm512_mask_storeu_ps(&C[(j+N)*ldc + i + (M*16)], mask, result##M##N)
+#define SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+				_mm512_i32scatter_ps(&C[(j + N*16)*ldc + i + M], vindex_n, result##M##N, 4);
+#define MASK_SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+				_mm512_mask_i32scatter_ps(&C[(j + N*16)*ldc + i + M], mask, vindex_n, result##M##N, 4)
+#else
+#define STORE_512(M, N) \
+	result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+	asm("vfmadd231ps (%1), %2, %0": "+v"(result##M##N):"r"(&C[(j+N)*ldc + i + (M*16)]), "v"(beta_512)); \
+	_mm512_storeu_ps(&C[(j+N)*ldc + i + (M*16)], result##M##N)
+#define MASK_STORE_512(M, N) \
+	result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+	asm("vfmadd231ps (%1), %2, %0 %{%3%}": "+v"(result##M##N):"r"(&C[(j+N)*ldc + i + (M*16)]), "v"(beta_512), "k"(mask)); \
+	_mm512_mask_storeu_ps(&C[(j+N)*ldc + i + (M*16)], mask, result##M##N)
+#define SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+				__m512 tmp##M##N = _mm512_i32gather_ps(vindex_n, &C[(j + N*16)*ldc + i + M], 4); \
+				result##M##N = _mm512_fmadd_ps(tmp##M##N, beta_512, result##M##N); \
+				_mm512_i32scatter_ps(&C[(j + N*16)*ldc + i + M], vindex_n, result##M##N, 4);
+#define MASK_SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+				__m512 tmp##M##N = _mm512_mask_i32gather_ps(_mm512_setzero_ps(), mask, vindex_n, &C[(j + N*16)*ldc + i + M], 4); \
+				result##M##N = _mm512_fmadd_ps(tmp##M##N, beta_512, result##M##N); \
+				_mm512_mask_i32scatter_ps(&C[(j + N*16)*ldc + i + M], mask, vindex_n, result##M##N, 4);
+#endif
+
+#if defined(B0)
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	// column major
+	BLASLONG i, j, k;
+
+	BLASLONG m64 = M & ~63;
+	BLASLONG m32 = M & ~31;
+	BLASLONG m16 = M & ~15;
+	BLASLONG m4 = M & ~3;
+	BLASLONG m2 = M & ~1;
+
+	BLASLONG n64 = N & ~63;
+	BLASLONG n32 = N & ~31;
+	BLASLONG n8 = N & ~7;
+	BLASLONG n6 = N - (N % 6);
+	BLASLONG n4 = N & ~3;
+	BLASLONG n2 = N & ~1;
+
+
+	__m512 alpha_512 = _mm512_broadcastss_ps(_mm_load_ss(&alpha));
+#if !defined(B0)
+	__m512 beta_512 = _mm512_broadcastss_ps(_mm_load_ss(&beta));
+#endif
+
+	for (i = 0; i < m64; i += 64) {
+		for (j = 0; j < n6; j += 6) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+			DECLARE_RESULT_512(0, 4); DECLARE_RESULT_512(1, 4); DECLARE_RESULT_512(2, 4); DECLARE_RESULT_512(3, 4);
+			DECLARE_RESULT_512(0, 5); DECLARE_RESULT_512(1, 5); DECLARE_RESULT_512(2, 5); DECLARE_RESULT_512(3, 5);
+
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+				MATMUL_512(0, 4); MATMUL_512(1, 4); MATMUL_512(2, 4); MATMUL_512(3, 4);
+				MATMUL_512(0, 5); MATMUL_512(1, 5); MATMUL_512(2, 5); MATMUL_512(3, 5);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+			STORE_512(0, 1); STORE_512(1, 1); STORE_512(2, 1); STORE_512(3, 1);
+			STORE_512(0, 2); STORE_512(1, 2); STORE_512(2, 2); STORE_512(3, 2);
+			STORE_512(0, 3); STORE_512(1, 3); STORE_512(2, 3); STORE_512(3, 3);
+			STORE_512(0, 4); STORE_512(1, 4); STORE_512(2, 4); STORE_512(3, 4);
+			STORE_512(0, 5); STORE_512(1, 5); STORE_512(2, 5); STORE_512(3, 5);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+			STORE_512(0, 1); STORE_512(1, 1); STORE_512(2, 1); STORE_512(3, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x); LOAD_A_512(2, x); LOAD_A_512(3, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+			}
+			STORE_512(0, 0); STORE_512(1, 0); STORE_512(2, 0); STORE_512(3, 0);
+		}
+	}
+	for (; i < m32; i += 32) {
+		for (j = 0; j < n8; j += 8) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+			DECLARE_RESULT_512(0, 4); DECLARE_RESULT_512(1, 4);
+			DECLARE_RESULT_512(0, 5); DECLARE_RESULT_512(1, 5);
+			DECLARE_RESULT_512(0, 6); DECLARE_RESULT_512(1, 6);
+			DECLARE_RESULT_512(0, 7); DECLARE_RESULT_512(1, 7);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+				BROADCAST_LOAD_B_512(x, 6); BROADCAST_LOAD_B_512(x, 7);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3);
+				MATMUL_512(0, 4); MATMUL_512(1, 4);
+				MATMUL_512(0, 5); MATMUL_512(1, 5);
+				MATMUL_512(0, 6); MATMUL_512(1, 6);
+				MATMUL_512(0, 7); MATMUL_512(1, 7);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+			STORE_512(0, 1); STORE_512(1, 1);
+			STORE_512(0, 2); STORE_512(1, 2);
+			STORE_512(0, 3); STORE_512(1, 3);
+			STORE_512(0, 4); STORE_512(1, 4);
+			STORE_512(0, 5); STORE_512(1, 5);
+			STORE_512(0, 6); STORE_512(1, 6);
+			STORE_512(0, 7); STORE_512(1, 7);
+		}
+		for (;j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+			STORE_512(0, 1); STORE_512(1, 1);
+			STORE_512(0, 2); STORE_512(1, 2);
+			STORE_512(0, 3); STORE_512(1, 3);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+			STORE_512(0, 1); STORE_512(1, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x); LOAD_A_512(1, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+			}
+			STORE_512(0, 0); STORE_512(1, 0);
+		}
+	}
+	for (; i < m16; i += 16) {
+		for (j = 0; j < n8; j += 8) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			DECLARE_RESULT_512(0, 4);
+			DECLARE_RESULT_512(0, 5);
+			DECLARE_RESULT_512(0, 6);
+			DECLARE_RESULT_512(0, 7);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+				BROADCAST_LOAD_B_512(x, 6); BROADCAST_LOAD_B_512(x, 7);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+				MATMUL_512(0, 4);
+				MATMUL_512(0, 5);
+				MATMUL_512(0, 6);
+				MATMUL_512(0, 7);
+			}
+			STORE_512(0, 0);
+			STORE_512(0, 1);
+			STORE_512(0, 2);
+			STORE_512(0, 3);
+			STORE_512(0, 4);
+			STORE_512(0, 5);
+			STORE_512(0, 6);
+			STORE_512(0, 7);
+		}
+		for (; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+			}
+			STORE_512(0, 0);
+			STORE_512(0, 1);
+			STORE_512(0, 2);
+			STORE_512(0, 3);
+		}
+
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			STORE_512(0, 0);
+			STORE_512(0, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0);
+			for (k = 0; k < K; k++) {
+				LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0);
+			}
+			STORE_512(0, 0);
+		}
+	}
+	int mm = M - i;
+	if (mm >= 12) {
+		register __mmask16 mask asm("k1") = (1UL << mm) - 1;
+		for (j = 0; j < n8; j += 8) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			DECLARE_RESULT_512(0, 4);
+			DECLARE_RESULT_512(0, 5);
+			DECLARE_RESULT_512(0, 6);
+			DECLARE_RESULT_512(0, 7);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+				BROADCAST_LOAD_B_512(x, 4); BROADCAST_LOAD_B_512(x, 5);
+				BROADCAST_LOAD_B_512(x, 6); BROADCAST_LOAD_B_512(x, 7);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+				MATMUL_512(0, 4);
+				MATMUL_512(0, 5);
+				MATMUL_512(0, 6);
+				MATMUL_512(0, 7);
+			}
+			MASK_STORE_512(0, 0);
+			MASK_STORE_512(0, 1);
+			MASK_STORE_512(0, 2);
+			MASK_STORE_512(0, 3);
+			MASK_STORE_512(0, 4);
+			MASK_STORE_512(0, 5);
+			MASK_STORE_512(0, 6);
+			MASK_STORE_512(0, 7);
+		}
+		for (; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				BROADCAST_LOAD_B_512(x, 2); BROADCAST_LOAD_B_512(x, 3);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+			}
+			MASK_STORE_512(0, 0);
+			MASK_STORE_512(0, 1);
+			MASK_STORE_512(0, 2);
+			MASK_STORE_512(0, 3);
+		}
+
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0); BROADCAST_LOAD_B_512(x, 1);
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			MASK_STORE_512(0, 0);
+			MASK_STORE_512(0, 1);
+		}
+		for (; j < N; j++) {
+			DECLARE_RESULT_512(0, 0);
+			for (k = 0; k < K; k++) {
+				MASK_LOAD_A_512(0, x);
+				BROADCAST_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0);
+			}
+			MASK_STORE_512(0, 0);
+		}
+	} else if (mm > 0) {
+		int index_n[16];
+		for (int ii = 0; ii < 16; ii++) {
+			index_n[ii] = ii * ldc;
+		}
+		__m512i vindex_n = _mm512_loadu_si512(index_n);
+		for (; i < m4; i += 4) {
+			for (j = 0; j < n64; j += 64) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+				DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+				DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					LOAD_B_512(x, 2);
+					LOAD_B_512(x, 3);
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0); SCATTER_STORE_512(2, 0); SCATTER_STORE_512(3, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1); SCATTER_STORE_512(2, 1); SCATTER_STORE_512(3, 1);
+				SCATTER_STORE_512(0, 2); SCATTER_STORE_512(1, 2); SCATTER_STORE_512(2, 2); SCATTER_STORE_512(3, 2);
+				SCATTER_STORE_512(0, 3); SCATTER_STORE_512(1, 3); SCATTER_STORE_512(2, 3); SCATTER_STORE_512(3, 3);
+			}
+			for (; j < n32; j += 32) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0); SCATTER_STORE_512(2, 0); SCATTER_STORE_512(3, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1); SCATTER_STORE_512(2, 1); SCATTER_STORE_512(3, 1);
+			}
+			__mmask16 mask = 0xffff;
+			for (; j < N; j += 16) {
+				int remains = N - j;
+				if (remains < 16) mask = (1UL << remains) - 1;
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+					MASK_LOAD_B_512(x, 0);
+					MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				}
+				MASK_SCATTER_STORE_512(0, 0); MASK_SCATTER_STORE_512(1, 0); MASK_SCATTER_STORE_512(2, 0); MASK_SCATTER_STORE_512(3, 0);
+			}
+		}
+		for (; i < m2; i += 2) {
+			for (j = 0; j < n64; j += 64) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+				DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					LOAD_B_512(x, 2);
+					LOAD_B_512(x, 3);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1);
+				SCATTER_STORE_512(0, 2); SCATTER_STORE_512(1, 2);
+				SCATTER_STORE_512(0, 3); SCATTER_STORE_512(1, 3);
+			}
+			for (; j < n32; j += 32) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1);
+			}
+			__mmask16 mask = 0xffff;
+			for (; j < N; j += 16) {
+				int remains = N - j;
+				if (remains < 16) mask = (1UL << remains) - 1;
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					MASK_LOAD_B_512(x, 0);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+				}
+				MASK_SCATTER_STORE_512(0, 0); MASK_SCATTER_STORE_512(1, 0);
+			}
+		}
+		for (; i < M; i += 1) {
+			for (j = 0; j < n64; j += 64) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				DECLARE_RESULT_512(0, 2);
+				DECLARE_RESULT_512(0, 3);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					LOAD_B_512(x, 2);
+					LOAD_B_512(x, 3);
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+					MATMUL_512(0, 2);
+					MATMUL_512(0, 3);
+				}
+				SCATTER_STORE_512(0, 0);
+				SCATTER_STORE_512(0, 1);
+				SCATTER_STORE_512(0, 2);
+				SCATTER_STORE_512(0, 3);
+			}
+			for (; j < n32; j += 32) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					LOAD_B_512(x, 0);
+					LOAD_B_512(x, 1);
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+				}
+				SCATTER_STORE_512(0, 0);
+				SCATTER_STORE_512(0, 1);
+			}
+			__mmask16 mask = 0xffff;
+			for (; j < N; j += 16) {
+				int remains = N - j;
+				if (remains < 16) mask = (1UL << remains) - 1;
+				DECLARE_RESULT_512(0, 0);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					MASK_LOAD_B_512(x, 0);
+					MATMUL_512(0, 0);
+				}
+				MASK_SCATTER_STORE_512(0, 0);
+			}
+		}
+	}
+	return 0;
+}

kernel/x86_64/sgemm_small_kernel_permit_skylakex.c

@@ -0,0 +1,53 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include "common.h"
+
+int CNAME(int transa, int transb, BLASLONG M, BLASLONG N, BLASLONG K, FLOAT alpha, FLOAT beta)
+{
+	double MNK = (double) M * (double) N * (double) K;
+	if (MNK > 100.0*100.0*100.0)  // disable for big size matrix
+		return 0;
+	// tuning for A transpose
+	if (transa) {
+		if (transb) {
+			/* TT kernel perform not good when:
+			 * 1. K is too small.
+			 */
+			if (K < 4) return 0;
+		} else {
+			/* TN kernel perform not good when:
+			 * 1. C matrix is too big
+			 * 2. K is too small
+			 */
+			if (M * N > 1200 || K < 32)
+				return 0;
+		}
+	}
+
+	return 1;
+}

kernel/x86_64/sgemm_small_kernel_tn_skylakex.c

@@ -0,0 +1,316 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include <immintrin.h>
+#include "common.h"
+#include <stdio.h>
+#include <memory.h>
+
+#define DECLARE_RESULT_512(M, N) __m512 result##M##N = _mm512_setzero_ps()
+#define MATMUL_512(M, N) result##M##N = _mm512_fmadd_ps(Aval##M, Bval##N, result##M##N)
+
+#define LOAD_KA_512(M, N) __m512 Aval##M = _mm512_loadu_ps(&A[(i + M)*lda + k]);
+#define LOAD_KB_512(M, N) __m512 Bval##N = _mm512_loadu_ps(&B[(j + N)*ldb + k])
+#define MASK_LOAD_KA_512(M, N) __m512 Aval##M = _mm512_maskz_loadu_ps(mask, &A[(i + M)*lda + k])
+#define MASK_LOAD_KB_512(M, N) __m512 Bval##N = _mm512_maskz_loadu_ps(mask, &B[(j + N)*ldb + k])
+
+#define REDUCE_4(rr0, rr1, rr2, rr3) \
+	__m512 r0, r1, r2, r3, t0, t1, t2, t3;\
+	r0 = _mm512_unpacklo_ps(rr0, rr1); r1 = _mm512_unpackhi_ps(rr0, rr1); \
+	r2 = _mm512_unpacklo_ps(rr2, rr3); r3 = _mm512_unpackhi_ps(rr2, rr3); \
+	t0 = _mm512_shuffle_ps(r0, r2, _MM_SHUFFLE(1, 0, 1, 0)); t1 = _mm512_shuffle_ps(r0, r2, _MM_SHUFFLE(3, 2, 3, 2)); \
+	t2 = _mm512_shuffle_ps(r1, r3, _MM_SHUFFLE(1, 0, 1, 0)); t3 = _mm512_shuffle_ps(r1, r3, _MM_SHUFFLE(3, 2, 3, 2)); \
+	r0 = _mm512_add_ps(t0, t1); r1 = _mm512_add_ps(t2, t3); t0 = _mm512_add_ps(r0, r1); \
+	__m128 s0, s1, s2, s3; \
+	s0 = _mm512_extractf32x4_ps(t0, 0); s1 = _mm512_extractf32x4_ps(t0, 1); s2 = _mm512_extractf32x4_ps(t0, 2); s3 = _mm512_extractf32x4_ps(t0, 3); \
+	s0 = _mm_maskz_add_ps(mask8, s0, s1); s2 = _mm_maskz_add_ps(mask8, s2, s3); s0 = _mm_maskz_add_ps(mask8, s0, s2); \
+	s0 = _mm_maskz_mul_ps(mask8, alpha_128, s0);
+
+#define REDUCE_M4(N) REDUCE_4(result0##N, result1##N, result2##N, result3##N)
+#define REDUCE_N4(M) REDUCE_4(result##M##0, result##M##1, result##M##2, result##M##3)
+
+#if defined(B0)
+#define STORE_REDUCE(M, N) C[(j+N)*ldc + i + M] = alpha * _mm512_reduce_add_ps(result##M##N)
+#define STORE_M4(N, s0) _mm_mask_storeu_ps(&C[(j + N)*ldc + i], mask8, s0);
+#define STORE_N4(M, s0) _mm_i32scatter_ps(&C[j*ldc + i + M], vindex_n, s0, 4);
+#else
+#define STORE_REDUCE(M, N) C[(j+N)*ldc + i + M] = alpha * _mm512_reduce_add_ps(result##M##N) + beta * C[(j+N)*ldc + i + M]
+#define STORE_M4(N, s0) \
+	asm("vfmadd231ps (%1), %2, %0": "+v"(s0):"r"(&C[(j + N)*ldc + i]), "v"(beta_128)); \
+	_mm_mask_storeu_ps(&C[(j + N)*ldc + i], mask8, s0);
+
+#define STORE_N4(M, s0) \
+	s0 = _mm_fmadd_ps(_mm_i32gather_ps(&C[j*ldc + i + M], vindex_n, 4), beta_128, s0); \
+	_mm_i32scatter_ps(&C[j*ldc + i + M], vindex_n, s0, 4);
+#endif
+#define STORE_REDUCE_M4(N) {\
+	REDUCE_M4(N) \
+	STORE_M4(N, s0) \
+}
+#define STORE_REDUCE_N4(M) {\
+	REDUCE_N4(M) \
+	STORE_N4(M, s0) \
+}
+
+
+#if defined(B0)
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	// column major
+	BLASLONG i, j, k;
+
+	BLASLONG m4 = M & ~3;
+	BLASLONG m2 = M & ~1;
+
+	BLASLONG n4 = N & ~3;
+	BLASLONG n2 = N & ~1;
+
+	BLASLONG k16 = K & ~15;
+
+	__mmask16 mask;
+	__mmask8 mask8 = 0xff;  // just use to avoid SSE instruction
+
+	__m128i vindex_n = _mm_set_epi32(ldc*3, ldc*2, ldc, 0);
+	__m128 alpha_128 = _mm_broadcast_ss(&alpha);
+#if !defined(B0)
+	__m128 beta_128 = _mm_broadcast_ss(&beta);
+#endif
+	for (i = 0; i < m4; i += 4) {
+		for (j = 0; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+			for (k = 0; k < k16; k += 16) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+			}
+			STORE_REDUCE_M4(0); STORE_REDUCE_M4(1); STORE_REDUCE_M4(2); STORE_REDUCE_M4(3);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			for (k = 0; k < k16; k += 16) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+			}
+			STORE_REDUCE_M4(0); STORE_REDUCE_M4(1);
+		}
+		for (; j < N; j += 1) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			for (k = 0; k < k16; k += 16) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x); LOAD_KA_512(2, x); LOAD_KA_512(3, x);
+				LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x); MASK_LOAD_KA_512(2, x); MASK_LOAD_KA_512(3, x);
+				MASK_LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+			}
+			STORE_REDUCE_M4(0);
+		}
+
+	}
+	for (; i < m2; i += 2) {
+		for (j = 0; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+			for (k = 0; k < k16; k += 16) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3);
+			}
+			STORE_REDUCE_N4(0); STORE_REDUCE_N4(1);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+			for (k = 0; k < k16; k += 16) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1);
+			}
+			STORE_REDUCE(0, 0); STORE_REDUCE(1, 0);
+			STORE_REDUCE(0, 1); STORE_REDUCE(1, 1);
+
+		}
+		for (; j < N; j += 1) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+			for (k = 0; k < k16; k += 16) {
+				LOAD_KA_512(0, x); LOAD_KA_512(1, x);
+				LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x); MASK_LOAD_KA_512(1, x);
+				MASK_LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0); MATMUL_512(1, 0);
+			}
+			STORE_REDUCE(0, 0); STORE_REDUCE(1, 0);
+		}
+	}
+	for (; i < M; i += 1) {
+		for (j = 0; j < n4; j += 4) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			DECLARE_RESULT_512(0, 2);
+			DECLARE_RESULT_512(0, 3);
+			for (k = 0; k < k16; k += 16) {
+				LOAD_KA_512(0, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1); LOAD_KB_512(x, 2); LOAD_KB_512(x, 3);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1); MASK_LOAD_KB_512(x, 2); MASK_LOAD_KB_512(x, 3);
+
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+				MATMUL_512(0, 2);
+				MATMUL_512(0, 3);
+			}
+			STORE_REDUCE_N4(0);
+		}
+		for (; j < n2; j += 2) {
+			DECLARE_RESULT_512(0, 0);
+			DECLARE_RESULT_512(0, 1);
+			for (k = 0; k < k16; k += 16) {
+				LOAD_KA_512(0, x);
+				LOAD_KB_512(x, 0); LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x);
+				MASK_LOAD_KB_512(x, 0); MASK_LOAD_KB_512(x, 1);
+
+				MATMUL_512(0, 0);
+				MATMUL_512(0, 1);
+			}
+			STORE_REDUCE(0, 0);
+			STORE_REDUCE(0, 1);
+
+		}
+		for (; j < N; j += 1) {
+			DECLARE_RESULT_512(0, 0);
+			for (k = 0; k < k16; k += 16) {
+				LOAD_KA_512(0, x);
+				LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0);
+			}
+			int remains = K - k;
+			if (remains) {
+				mask = (1UL << remains) - 1;
+				MASK_LOAD_KA_512(0, x);
+				MASK_LOAD_KB_512(x, 0);
+
+				MATMUL_512(0, 0);
+			}
+			STORE_REDUCE(0, 0);
+		}
+	}
+	return 0;
+}

kernel/x86_64/sgemm_small_kernel_tt_skylakex.c

@@ -0,0 +1,414 @@
+/***************************************************************************
+Copyright (c) 2021, The OpenBLAS Project
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in
+the documentation and/or other materials provided with the
+distribution.
+3. Neither the name of the OpenBLAS project nor the names of
+its contributors may be used to endorse or promote products
+derived from this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE OPENBLAS PROJECT OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*****************************************************************************/
+
+#include <immintrin.h>
+#include "common.h"
+#include <stdio.h>
+
+#define DECLARE_RESULT_512(M, N) __m512 result##M##N = _mm512_setzero_ps()
+#define BROADCAST_LOAD_A_512(M, N) __m512 Aval##M = _mm512_broadcastss_ps(_mm_load_ss(&A[k  + lda * (i+M)]))
+#define LOAD_B_512(M,N)  __m512 Bval##N = _mm512_loadu_ps(&B[ldb * k + j + (N*16)])
+#define MASK_LOAD_B_512(M, N) __m512 Bval##N = _mm512_maskz_loadu_ps(mask, &B[ldb * k + j + (N*16)])
+#define MATMUL_512(M, N) result##M##N = _mm512_fmadd_ps(Aval##M, Bval##N, result##M##N)
+
+#if defined(B0)
+#define STORE_8xy(v, N, x, y) _mm256_storeu_ps(&C[(j + N*16 + x + y*8)*ldc + i], v)
+#define STORE_4xy(v, N, x, y) _mm_mask_storeu_ps(&C[(j + N*16 + x + y*4)*ldc + i], mask8, v)
+#define SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+				_mm512_i32scatter_ps(&C[(j + N*16)*ldc + i + M], vindex_n, result##M##N, 4);
+#define MASK_SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+				    _mm512_mask_i32scatter_ps(&C[(j + N*16)*ldc + i + M], mask, vindex_n, result##M##N, 4);
+#else
+#define STORE_8xy(v, N, x, y) \
+	asm("vfmadd231ps (%1), %2, %0": "+v"(v): "r"(&C[(j + N*16 + x + y*8)*ldc + i]), "v"(beta_256)); \
+	_mm256_storeu_ps(&C[(j + N*16 + x + y*8)*ldc + i], v)
+#define STORE_4xy(v, N, x, y) \
+	asm("vfmadd231ps (%1), %2, %0": "+v"(v): "r"(&C[(j + N*16 + x + y*4)*ldc + i]), "v"(beta_128)); \
+	_mm_mask_storeu_ps(&C[(j + N*16 + x + y*4)*ldc + i], mask8, v)
+#define SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+				__m512 tmp##M##N = _mm512_i32gather_ps(vindex_n, &C[(j + N*16)*ldc + i + M], 4); \
+				result##M##N = _mm512_fmadd_ps(tmp##M##N, beta_512, result##M##N); \
+				_mm512_i32scatter_ps(&C[(j + N*16)*ldc + i + M], vindex_n, result##M##N, 4);
+#define MASK_SCATTER_STORE_512(M, N) result##M##N = _mm512_mul_ps(result##M##N, alpha_512); \
+				__m512 tmp##M##N = _mm512_mask_i32gather_ps(_mm512_setzero_ps(), mask, vindex_n, &C[(j + N*16)*ldc + i + M], 4); \
+				result##M##N = _mm512_fmadd_ps(tmp##M##N, beta_512, result##M##N); \
+				_mm512_mask_i32scatter_ps(&C[(j + N*16)*ldc + i + M], mask, vindex_n, result##M##N, 4);
+#endif
+
+#define REORDER_8x16(r0, r1, r2, r3, r4, r5, r6, r7) \
+	__m512 t0, t1, t2, t3, t4, t5, t6, t7, v; \
+	t0 = _mm512_unpacklo_ps(r0, r1); \
+	t1 = _mm512_unpackhi_ps(r0, r1); \
+	t2 = _mm512_unpacklo_ps(r2, r3); \
+	t3 = _mm512_unpackhi_ps(r2, r3); \
+	t4 = _mm512_unpacklo_ps(r4, r5); \
+	t5 = _mm512_unpackhi_ps(r4, r5); \
+	t6 = _mm512_unpacklo_ps(r6, r7); \
+	t7 = _mm512_unpackhi_ps(r6, r7); \
+	v = _mm512_shuffle_ps(t0, t2, 0x4E);  \
+	r0 = _mm512_mask_blend_ps(kc, t0, v); \
+	r1 = _mm512_mask_blend_ps(k3, t2, v); \
+	v = _mm512_shuffle_ps(t1, t3, 0x4E);  \
+	r2 = _mm512_mask_blend_ps(kc, t1, v); \
+	r3 = _mm512_mask_blend_ps(k3, t3, v); \
+	v = _mm512_shuffle_ps(t4, t6, 0x4E);  \
+	r4 = _mm512_mask_blend_ps(kc, t4, v); \
+	r5 = _mm512_mask_blend_ps(k3, t6, v); \
+	v = _mm512_shuffle_ps(t5, t7, 0x4E);  \
+	r6 = _mm512_mask_blend_ps(kc, t5, v); \
+	r7 = _mm512_mask_blend_ps(k3, t7, v); \
+	t0 = _mm512_permutex2var_ps(r0, idx_lo, r4); \
+	t1 = _mm512_permutex2var_ps(r1, idx_lo, r5); \
+	t2 = _mm512_permutex2var_ps(r2, idx_lo, r6); \
+	t3 = _mm512_permutex2var_ps(r3, idx_lo, r7); \
+	t4 = _mm512_permutex2var_ps(r0, idx_hi, r4); \
+	t5 = _mm512_permutex2var_ps(r1, idx_hi, r5); \
+	t6 = _mm512_permutex2var_ps(r2, idx_hi, r6); \
+	t7 = _mm512_permutex2var_ps(r3, idx_hi, r7); \
+	t0 = _mm512_mul_ps(t0, alpha_512); \
+	t1 = _mm512_mul_ps(t1, alpha_512); \
+	t2 = _mm512_mul_ps(t2, alpha_512); \
+	t3 = _mm512_mul_ps(t3, alpha_512); \
+	t4 = _mm512_mul_ps(t4, alpha_512); \
+	t5 = _mm512_mul_ps(t5, alpha_512); \
+	t6 = _mm512_mul_ps(t6, alpha_512); \
+	t7 = _mm512_mul_ps(t7, alpha_512);
+
+#define SAVE_8(N, x, y) {\
+	__m256 v8 = _mm512_extractf32x8_ps(t##x, y); \
+	STORE_8xy(v8, N, x, y); \
+}
+
+#define REORDER_STORE_8x16(N) {\
+	REORDER_8x16(result0##N, result1##N, result2##N, result3##N, result4##N, result5##N, result6##N, result7##N); \
+	SAVE_8(N, 0, 0); SAVE_8(N, 1, 0); SAVE_8(N, 2, 0); SAVE_8(N, 3, 0); SAVE_8(N, 4, 0); SAVE_8(N, 5, 0); SAVE_8(N, 6, 0); SAVE_8(N, 7, 0); \
+	SAVE_8(N, 0, 1); SAVE_8(N, 1, 1); SAVE_8(N, 2, 1); SAVE_8(N, 3, 1); SAVE_8(N, 4, 1); SAVE_8(N, 5, 1); SAVE_8(N, 6, 1); SAVE_8(N, 7, 1); \
+}
+
+#define MASK_SAVE_8() \
+	switch (nn) { \
+		case 16: SAVE_8(0, 7, 1); \
+		case 15: SAVE_8(0, 6, 1); \
+		case 14: SAVE_8(0, 5, 1); \
+		case 13: SAVE_8(0, 4, 1); \
+		case 12: SAVE_8(0, 3, 1); \
+		case 11: SAVE_8(0, 2, 1); \
+		case 10: SAVE_8(0, 1, 1); \
+		case 9: SAVE_8(0, 0, 1); \
+		case 8: SAVE_8(0, 7, 0); \
+		case 7: SAVE_8(0, 6, 0); \
+		case 6: SAVE_8(0, 5, 0); \
+		case 5: SAVE_8(0, 4, 0); \
+		case 4: SAVE_8(0, 3, 0); \
+		case 3: SAVE_8(0, 2, 0); \
+		case 2: SAVE_8(0, 1, 0); \
+		case 1: SAVE_8(0, 0, 0); \
+	}
+
+#define MASK_REORDER_STORE_8x16(N) {\
+	REORDER_8x16(result0##N, result1##N, result2##N, result3##N, result4##N, result5##N, result6##N, result7##N); \
+	MASK_SAVE_8(); \
+}
+
+#define REORDER_4x16(r0, r1, r2, r3) \
+	__m512 t0, t1, t2, t3, v; \
+	t0 = _mm512_unpacklo_ps(r0, r1); \
+	t1 = _mm512_unpackhi_ps(r0, r1); \
+	t2 = _mm512_unpacklo_ps(r2, r3); \
+	t3 = _mm512_unpackhi_ps(r2, r3); \
+	v = _mm512_shuffle_ps(t0, t2, 0x4E);  \
+	r0 = _mm512_mask_blend_ps(kc, t0, v); \
+	r1 = _mm512_mask_blend_ps(k3, t2, v); \
+	v = _mm512_shuffle_ps(t1, t3, 0x4E);  \
+	r2 = _mm512_mask_blend_ps(kc, t1, v); \
+	r3 = _mm512_mask_blend_ps(k3, t3, v); \
+	t0 = _mm512_mul_ps(r0, alpha_512); \
+	t1 = _mm512_mul_ps(r1, alpha_512); \
+	t2 = _mm512_mul_ps(r2, alpha_512); \
+	t3 = _mm512_mul_ps(r3, alpha_512);
+
+#define SAVE_4(N, x, y) {\
+	__m128 v4 = _mm512_extractf32x4_ps(t##x, y); \
+	STORE_4xy(v4, N, x, y); \
+}
+
+#define REORDER_STORE_4x16(N) {\
+	REORDER_4x16(result0##N, result1##N, result2##N, result3##N); \
+	SAVE_4(N, 0, 0); SAVE_4(N, 1, 0); SAVE_4(N, 2, 0); SAVE_4(N, 3, 0); \
+	SAVE_4(N, 0, 1); SAVE_4(N, 1, 1); SAVE_4(N, 2, 1); SAVE_4(N, 3, 1); \
+	SAVE_4(N, 0, 2); SAVE_4(N, 1, 2); SAVE_4(N, 2, 2); SAVE_4(N, 3, 2); \
+	SAVE_4(N, 0, 3); SAVE_4(N, 1, 3); SAVE_4(N, 2, 3); SAVE_4(N, 3, 3); \
+}
+
+#define MASK_SAVE_4() \
+	switch (nn) { \
+		case 16: SAVE_4(0, 3, 3); \
+		case 15: SAVE_4(0, 2, 3); \
+		case 14: SAVE_4(0, 1, 3); \
+		case 13: SAVE_4(0, 0, 3); \
+		case 12: SAVE_4(0, 3, 2); \
+		case 11: SAVE_4(0, 2, 2); \
+		case 10: SAVE_4(0, 1, 2); \
+		case 9: SAVE_4(0, 0, 2); \
+		case 8: SAVE_4(0, 3, 1); \
+		case 7: SAVE_4(0, 2, 1); \
+		case 6: SAVE_4(0, 1, 1); \
+		case 5: SAVE_4(0, 0, 1); \
+		case 4: SAVE_4(0, 3, 0); \
+		case 3: SAVE_4(0, 2, 0); \
+		case 2: SAVE_4(0, 1, 0); \
+		case 1: SAVE_4(0, 0, 0); \
+	}
+
+#define MASK_REORDER_STORE_4x16(N) {\
+	REORDER_4x16(result0##N, result1##N, result2##N, result3##N); \
+	MASK_SAVE_4(); \
+}
+
+
+#if defined(B0)
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT * C, BLASLONG ldc)
+#else
+int CNAME(BLASLONG M, BLASLONG N, BLASLONG K, FLOAT * A, BLASLONG lda, FLOAT alpha, FLOAT * B, BLASLONG ldb, FLOAT beta, FLOAT * C, BLASLONG ldc)
+#endif
+{
+	// column major
+	BLASLONG i, j, k;
+
+	BLASLONG m8 = M & ~7;
+	BLASLONG m4 = M & ~3;
+	BLASLONG m2 = M & ~1;
+
+	BLASLONG n64 = N & ~63;
+	BLASLONG n32 = N & ~31;
+
+	__m512 alpha_512 = _mm512_broadcastss_ps(_mm_load_ss(&alpha));
+#if !defined(B0)
+	__m256 beta_256 = _mm256_broadcastss_ps(_mm_load_ss(&beta));
+	__m128 beta_128 = _mm_broadcastss_ps(_mm_load_ss(&beta));
+#endif
+	int permute_table[] = {
+		0x0, 0x1, 0x2, 0x3, 0x10, 0x11, 0x12, 0x13, 0x8, 0x9, 0xa, 0xb, 0x18, 0x19, 0x1a, 0x1b,
+		0x4, 0x5, 0x6, 0x7, 0x14, 0x15, 0x16, 0x17, 0xc, 0xd, 0xe, 0xf, 0x1c, 0x1d, 0x1e, 0x1f,
+	};
+	__m512i idx_lo = _mm512_loadu_si512(permute_table);
+	__m512i idx_hi = _mm512_loadu_si512(permute_table + 16);
+	__mmask16 kc = 0xcccc;
+	__mmask16 k3 = 0x3333;
+	__mmask8 mask8 = 0xff;  // force use AVX128 instead of SSE
+
+	for (i = 0; i < m8; i += 8) {
+		for (j = 0; j < n32; j += 32) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(4, 0); DECLARE_RESULT_512(5, 0); DECLARE_RESULT_512(6, 0); DECLARE_RESULT_512(7, 0);
+
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			DECLARE_RESULT_512(4, 1); DECLARE_RESULT_512(5, 1); DECLARE_RESULT_512(6, 1); DECLARE_RESULT_512(7, 1);
+			for (k = 0; k < K; k++) {
+				BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+				BROADCAST_LOAD_A_512(4, x); BROADCAST_LOAD_A_512(5, x); BROADCAST_LOAD_A_512(6, x); BROADCAST_LOAD_A_512(7, x);
+				LOAD_B_512(x, 0); LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(4, 0); MATMUL_512(5, 0); MATMUL_512(6, 0); MATMUL_512(7, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				MATMUL_512(4, 1); MATMUL_512(5, 1); MATMUL_512(6, 1); MATMUL_512(7, 1);
+			}
+			REORDER_STORE_8x16(0);
+			REORDER_STORE_8x16(1);
+		}
+		__mmask16 mask = 0xffff;
+		int nn = 16;
+		for (; j < N; j += 16) {
+			if (N - j < 16) {
+				nn = N - j;
+				mask = (1UL << nn) - 1;
+			}
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(4, 0); DECLARE_RESULT_512(5, 0); DECLARE_RESULT_512(6, 0); DECLARE_RESULT_512(7, 0);
+			for (k = 0; k < K; k++) {
+				BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+				BROADCAST_LOAD_A_512(4, x); BROADCAST_LOAD_A_512(5, x); BROADCAST_LOAD_A_512(6, x); BROADCAST_LOAD_A_512(7, x);
+				MASK_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(4, 0); MATMUL_512(5, 0); MATMUL_512(6, 0); MATMUL_512(7, 0);
+			}
+			MASK_REORDER_STORE_8x16(0);
+		}
+	}
+	for (; i < m4; i += 4) {
+		for (j = 0; j < n64; j += 64) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2); DECLARE_RESULT_512(2, 2); DECLARE_RESULT_512(3, 2);
+			DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3); DECLARE_RESULT_512(2, 3); DECLARE_RESULT_512(3, 3);
+			for (k = 0; k < K; k++) {
+				BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+				LOAD_B_512(x, 0); LOAD_B_512(x, 1); LOAD_B_512(x, 2); LOAD_B_512(x, 3);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+				MATMUL_512(0, 2); MATMUL_512(1, 2); MATMUL_512(2, 2); MATMUL_512(3, 2);
+				MATMUL_512(0, 3); MATMUL_512(1, 3); MATMUL_512(2, 3); MATMUL_512(3, 3);
+			}
+			REORDER_STORE_4x16(0);
+			REORDER_STORE_4x16(1);
+			REORDER_STORE_4x16(2);
+			REORDER_STORE_4x16(3);
+		}
+		for (; j < n32; j += 32) {
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1); DECLARE_RESULT_512(2, 1); DECLARE_RESULT_512(3, 1);
+			for (k = 0; k < K; k++) {
+				BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+				LOAD_B_512(x, 0); LOAD_B_512(x, 1);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+				MATMUL_512(0, 1); MATMUL_512(1, 1); MATMUL_512(2, 1); MATMUL_512(3, 1);
+			}
+			REORDER_STORE_4x16(0);
+			REORDER_STORE_4x16(1);
+		}
+		__mmask16 mask = 0xffff;
+		int nn = 16;
+		for (; j < N; j += 16) {
+			if (N - j < 16) {
+				nn = N - j;
+				mask = (1UL << nn) - 1;
+			}
+			DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0); DECLARE_RESULT_512(2, 0); DECLARE_RESULT_512(3, 0);
+			for (k = 0; k < K; k++) {
+				BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x); BROADCAST_LOAD_A_512(2, x); BROADCAST_LOAD_A_512(3, x);
+				MASK_LOAD_B_512(x, 0);
+				MATMUL_512(0, 0); MATMUL_512(1, 0); MATMUL_512(2, 0); MATMUL_512(3, 0);
+			}
+			MASK_REORDER_STORE_4x16(0);
+		}
+	}
+	if (i < M) {
+		int index_n[16];
+		for (int ii = 0; ii < 16; ii++) {
+			index_n[ii] = ii * ldc;
+		}
+		__m512i vindex_n = _mm512_loadu_si512(index_n);
+#if !defined(B0)
+		__m512 beta_512 = _mm512_broadcastss_ps(_mm_load_ss(&beta));
+#endif
+		for (; i < m2; i += 2) {
+			for (j = 0; j < n64; j += 64) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				DECLARE_RESULT_512(0, 2); DECLARE_RESULT_512(1, 2);
+				DECLARE_RESULT_512(0, 3); DECLARE_RESULT_512(1, 3);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					LOAD_B_512(x, 0); LOAD_B_512(x, 1); LOAD_B_512(x, 2); LOAD_B_512(x, 3);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+					MATMUL_512(0, 2); MATMUL_512(1, 2);
+					MATMUL_512(0, 3); MATMUL_512(1, 3);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1);
+				SCATTER_STORE_512(0, 2); SCATTER_STORE_512(1, 2);
+				SCATTER_STORE_512(0, 3); SCATTER_STORE_512(1, 3);
+			}
+			for (; j < n32; j += 32) {
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				DECLARE_RESULT_512(0, 1); DECLARE_RESULT_512(1, 1);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					LOAD_B_512(x, 0); LOAD_B_512(x, 1);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+					MATMUL_512(0, 1); MATMUL_512(1, 1);
+				}
+				SCATTER_STORE_512(0, 0); SCATTER_STORE_512(1, 0);
+				SCATTER_STORE_512(0, 1); SCATTER_STORE_512(1, 1);
+			}
+			__mmask16 mask = 0xffff;
+			int nn = 16;
+			for (; j < N; j += 16) {
+				if (N - j < 16) {
+					nn = N - j;
+					mask = (1UL << nn) - 1;
+				}
+				DECLARE_RESULT_512(0, 0); DECLARE_RESULT_512(1, 0);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x); BROADCAST_LOAD_A_512(1, x);
+					MASK_LOAD_B_512(x, 0);
+					MATMUL_512(0, 0); MATMUL_512(1, 0);
+				}
+				MASK_SCATTER_STORE_512(0, 0); MASK_SCATTER_STORE_512(1, 0);
+			}
+		}
+		for (; i < M; i += 1) {
+			for (j = 0; j < n64; j += 64) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				DECLARE_RESULT_512(0, 2);
+				DECLARE_RESULT_512(0, 3);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					LOAD_B_512(x, 0); LOAD_B_512(x, 1); LOAD_B_512(x, 2); LOAD_B_512(x, 3);
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+					MATMUL_512(0, 2);
+					MATMUL_512(0, 3);
+				}
+				SCATTER_STORE_512(0, 0);
+				SCATTER_STORE_512(0, 1);
+				SCATTER_STORE_512(0, 2);
+				SCATTER_STORE_512(0, 3);
+			}
+			for (; j < n32; j += 32) {
+				DECLARE_RESULT_512(0, 0);
+				DECLARE_RESULT_512(0, 1);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					LOAD_B_512(x, 0); LOAD_B_512(x, 1);
+					MATMUL_512(0, 0);
+					MATMUL_512(0, 1);
+				}
+				SCATTER_STORE_512(0, 0);
+				SCATTER_STORE_512(0, 1);
+			}
+			__mmask16 mask = 0xffff;
+			int nn = 16;
+			for (; j < N; j += 16) {
+				if (N - j < 16) {
+					nn = N - j;
+					mask = (1UL << nn) - 1;
+				}
+				DECLARE_RESULT_512(0, 0);
+				for (k = 0; k < K; k++) {
+					BROADCAST_LOAD_A_512(0, x);
+					MASK_LOAD_B_512(x, 0);
+					MATMUL_512(0, 0);
+				}
+				MASK_SCATTER_STORE_512(0, 0);
+			}
+		}
+	}
+	return 0;
+}