From f57fc932ac39c394e8f89bf7b6df3f1bddd315fd Mon Sep 17 00:00:00 2001
From: Wangyang Guo <wangyang.guo@intel.com>
Date: Tue, 1 Jun 2021 14:23:56 +0000
Subject: [PATCH] Small Matrix: skylakex: add dgemm nt kernel

---
 kernel/x86_64/KERNEL.SKYLAKEX                 |   2 +
 .../dgemm_small_kernel_b0_nt_skylakex.c       |   2 +
 .../x86_64/dgemm_small_kernel_nt_skylakex.c   | 535 ++++++++++++++++++
 3 files changed, 539 insertions(+)
 create mode 100644 kernel/x86_64/dgemm_small_kernel_b0_nt_skylakex.c
 create mode 100644 kernel/x86_64/dgemm_small_kernel_nt_skylakex.c

diff --git a/kernel/x86_64/KERNEL.SKYLAKEX b/kernel/x86_64/KERNEL.SKYLAKEX
index a3c6f0556..db1e6cbff 100644
--- a/kernel/x86_64/KERNEL.SKYLAKEX
+++ b/kernel/x86_64/KERNEL.SKYLAKEX
@@ -29,6 +29,8 @@ DGEMMOTCOPY    =  ../generic/gemm_tcopy_2.c
 DTRSMKERNEL_RN =  ../generic/trsm_kernel_RN.c
 DGEMM_SMALL_K_NN = dgemm_small_kernel_nn_skylakex.c
 DGEMM_SMALL_K_B0_NN = dgemm_small_kernel_b0_nn_skylakex.c
+DGEMM_SMALL_K_NT = dgemm_small_kernel_nt_skylakex.c
+DGEMM_SMALL_K_B0_NT = dgemm_small_kernel_b0_nt_skylakex.c
 
 SGEMM_BETA = sgemm_beta_skylakex.c
 DGEMM_BETA = dgemm_beta_skylakex.c
diff --git a/kernel/x86_64/dgemm_small_kernel_b0_nt_skylakex.c b/kernel/x86_64/dgemm_small_kernel_b0_nt_skylakex.c
new file mode 100644
index 000000000..eafe2ce49
--- /dev/null
+++ b/kernel/x86_64/dgemm_small_kernel_b0_nt_skylakex.c
@@ -0,0 +1,2 @@
+#define B0 1
+#include "./dgemm_small_kernel_nt_skylakex.c"
diff --git a/kernel/x86_64/dgemm_small_kernel_nt_skylakex.c b/kernel/x86_64/dgemm_small_kernel_nt_skylakex.c
new file mode 100644
index 000000000..0a95a68e2
--- /dev/null
+++ b/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_epi64(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;
+}