Squashed 'third_party/blasfeo/' content from commit 2a828ca

Change-Id: If1c3caa4799b2d4eb287ef83fa17043587ef07a3
git-subtree-dir: third_party/blasfeo
git-subtree-split: 2a828ca5442108c4c58e4b42b061a0469043f6ea
diff --git a/auxiliary/avx/kernel_dgecp_lib4.c b/auxiliary/avx/kernel_dgecp_lib4.c
new file mode 100644
index 0000000..4bc8c9a
--- /dev/null
+++ b/auxiliary/avx/kernel_dgecp_lib4.c
@@ -0,0 +1,3024 @@
+/**************************************************************************************************
+*                                                                                                 *
+* This file is part of BLASFEO.                                                                   *
+*                                                                                                 *
+* BLASFEO -- BLAS For Embedded Optimization.                                                      *
+* Copyright (C) 2016-2017 by Gianluca Frison.                                                     *
+* Developed at IMTEK (University of Freiburg) under the supervision of Moritz Diehl.              *
+* All rights reserved.                                                                            *
+*                                                                                                 *
+* HPMPC is free software; you can redistribute it and/or                                          *
+* modify it under the terms of the GNU Lesser General Public                                      *
+* License as published by the Free Software Foundation; either                                    *
+* version 2.1 of the License, or (at your option) any later version.                              *
+*                                                                                                 *
+* HPMPC is distributed in the hope that it will be useful,                                        *
+* but WITHOUT ANY WARRANTY; without even the implied warranty of                                  *
+* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                                            *
+* See the GNU Lesser General Public License for more details.                                     *
+*                                                                                                 *
+* You should have received a copy of the GNU Lesser General Public                                *
+* License along with HPMPC; if not, write to the Free Software                                    *
+* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA                  *
+*                                                                                                 *
+* Author: Gianluca Frison, giaf (at) dtu.dk                                                       *
+*                          gianluca.frison (at) imtek.uni-freiburg.de                             *
+*                                                                                                 *
+**************************************************************************************************/
+
+#include <mmintrin.h>
+#include <xmmintrin.h>  // SSE
+#include <emmintrin.h>  // SSE2
+#include <pmmintrin.h>  // SSE3
+#include <smmintrin.h>  // SSE4
+#include <immintrin.h>  // AVX
+
+
+
+// both A and B are aligned to 256-bit boundaries
+void kernel_dgecp_8_0_lib4(int tri, int kmax, double alpha, double *A0, int sda,  double *B0, int sdb)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 8-wide + end 7x7 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+	
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+	double *B1 = B0 + bs*sdb;
+
+	__m256d
+		alpha_0,
+		a_0;
+	
+	__m128d
+		c_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B0[0+bs*0], a_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B0[0+bs*1], a_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B0[0+bs*2], a_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B0[0+bs*3], a_0 );
+
+		A0 += 16;
+		B0 += 16;
+
+		a_0 = _mm256_load_pd( &A1[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B1[0+bs*0], a_0 );
+
+		a_0 = _mm256_load_pd( &A1[0+bs*1] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B1[0+bs*1], a_0 );
+
+		a_0 = _mm256_load_pd( &A1[0+bs*2] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B1[0+bs*2], a_0 );
+
+		a_0 = _mm256_load_pd( &A1[0+bs*3] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B1[0+bs*3], a_0 );
+
+		A1 += 16;
+		B1 += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B0[0+bs*0], a_0 );
+
+		A0 += 4;
+		B0 += 4;
+
+		a_0 = _mm256_load_pd( &A1[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B1[0+bs*0], a_0 );
+
+		A1 += 4;
+		B1 += 4;
+
+		}
+	
+	if(tri==1)
+		{
+		// 7x7 triangle 
+
+		c_0 = _mm_load_sd( &A0[1+0*bs] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[1+0*bs], c_0 );
+		c_0 = _mm_load_pd( &A0[2+0*bs] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B0[2+0*bs], c_0 );
+		a_0 = _mm256_load_pd( &A1[0+0*bs] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B1[0+0*bs], a_0 );
+
+		c_0 = _mm_load_pd( &A0[2+1*bs] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B0[2+1*bs], c_0 );
+		a_0 = _mm256_load_pd( &A1[0+1*bs] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B1[0+1*bs], a_0 );
+
+		c_0 = _mm_load_sd( &A0[3+2*bs] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[3+2*bs], c_0 );
+		a_0 = _mm256_load_pd( &A1[0+2*bs] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B1[0+2*bs], a_0 );
+
+		a_0 = _mm256_load_pd( &A1[0+3*bs] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B1[0+3*bs], a_0 );
+
+		c_0 = _mm_load_sd( &A1[1+4*bs] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[1+4*bs], c_0 );
+		c_0 = _mm_load_pd( &A1[2+4*bs] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[2+4*bs], c_0 );
+
+		c_0 = _mm_load_pd( &A1[2+5*bs] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[2+5*bs], c_0 );
+
+		c_0 = _mm_load_sd( &A1[3+6*bs] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+6*bs], c_0 );
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 1 element of A must be skipped
+void kernel_dgecp_8_1_lib4(int tri, int kmax, double alpha, double *A0, int sda, double *B0, int sdb)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 8-wide + end 7x7 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+	double *A2 = A1 + bs*sda;
+	double *B1 = B0 + bs*sdb;
+
+	__m256d
+		alpha_0,
+		a_0, a_1, a_2,
+		b_0, b_1;
+	
+	__m128d
+		c_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_2 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_shuffle_pd( a_1, a_2, 0x5 );
+		b_0 = _mm256_shuffle_pd( a_0, b_0, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+
+		a_2 = _mm256_load_pd( &A2[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_2 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_shuffle_pd( a_1, a_2, 0x5 );
+		b_0 = _mm256_shuffle_pd( a_0, b_0, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B1[0+bs*1], b_1 );
+		_mm256_store_pd( &B0[0+bs*1], b_0 );
+
+		a_2 = _mm256_load_pd( &A2[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_2 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_shuffle_pd( a_1, a_2, 0x5 );
+		b_0 = _mm256_shuffle_pd( a_0, b_0, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B1[0+bs*2], b_1 );
+		_mm256_store_pd( &B0[0+bs*2], b_0 );
+
+		a_2 = _mm256_load_pd( &A2[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_2 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_shuffle_pd( a_1, a_2, 0x5 );
+		b_0 = _mm256_shuffle_pd( a_0, b_0, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B1[0+bs*3], b_1 );
+		_mm256_store_pd( &B0[0+bs*3], b_0 );
+
+		A0 += 16;
+		A1 += 16;
+		A2 += 16;
+		B0 += 16;
+		B1 += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_2 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_shuffle_pd( a_1, a_2, 0x5 );
+		b_0 = _mm256_shuffle_pd( a_0, b_0, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+
+		A0 += 4;
+		A1 += 4;
+		A2 += 4;
+		B0 += 4;
+		B1 += 4;
+
+		}
+
+	if(tri==1)
+		{
+		// 7x7 triangle
+
+		c_0 = _mm_load_pd( &A0[2+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B0[1+bs*0], c_0 );
+		c_0 = _mm_load_sd( &A1[0+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[3+bs*0], c_0 );
+		c_0 = _mm_load_sd( &A1[1+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[0+bs*0], c_0 );
+		c_0 = _mm_load_pd( &A1[2+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B1[1+bs*0], c_0 );
+		c_0 = _mm_load_sd( &A2[0+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*0], c_0 );
+
+		c_0 = _mm_load_sd( &A0[3+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[2+bs*1], c_0 );
+		c_0 = _mm_load_sd( &A1[0+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[3+bs*1], c_0 );
+		c_0 = _mm_load_sd( &A1[1+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[0+bs*1], c_0 );
+		c_0 = _mm_load_pd( &A1[2+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B1[1+bs*1], c_0 );
+		c_0 = _mm_load_sd( &A2[0+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*1], c_0 );
+
+		c_0 = _mm_load_sd( &A1[0+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[3+bs*2], c_0 );
+		c_0 = _mm_load_sd( &A1[1+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[0+bs*2], c_0 );
+		c_0 = _mm_load_pd( &A1[2+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B1[1+bs*2], c_0 );
+		c_0 = _mm_load_sd( &A2[0+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*2], c_0 );
+
+		c_0 = _mm_load_sd( &A1[1+bs*3] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[0+bs*3], c_0 );
+		c_0 = _mm_load_pd( &A1[2+bs*3] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B1[1+bs*3], c_0 );
+		c_0 = _mm_load_sd( &A2[0+bs*3] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*3], c_0 );
+
+		c_0 = _mm_load_pd( &A1[2+bs*4] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B1[1+bs*4], c_0 );
+		c_0 = _mm_load_sd( &A2[0+bs*4] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*4], c_0 );
+
+		c_0 = _mm_load_sd( &A1[3+bs*5] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[2+bs*5], c_0 );
+		c_0 = _mm_load_sd( &A2[0+bs*5] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*5], c_0 );
+
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		c_0 = _mm_load_sd( &A2[0+bs*6] );
+		_mm_store_sd( &B1[3+bs*6], c_0 );
+
+		}
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 2 elements of A must be skipped
+void kernel_dgecp_8_2_lib4(int tri, int kmax, double alpha, double *A0, int sda, double *B0, int sdb)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 8-wide + end 7x7 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+	double *A2 = A1 + bs*sda;
+	double *B1 = B0 + bs*sdb;
+
+	__m256d
+		alpha_0,
+		a_0, a_1, a_2,
+		b_0, b_1;
+	
+	__m128d
+		c_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		a_2 = _mm256_load_pd( &A2[0+bs*1] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B0[0+bs*1], b_0 );
+		_mm256_store_pd( &B1[0+bs*1], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		a_2 = _mm256_load_pd( &A2[0+bs*2] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B0[0+bs*2], b_0 );
+		_mm256_store_pd( &B1[0+bs*2], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		a_2 = _mm256_load_pd( &A2[0+bs*3] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B0[0+bs*3], b_0 );
+		_mm256_store_pd( &B1[0+bs*3], b_1 );
+
+		A0 += 16;
+		A1 += 16;
+		A2 += 16;
+		B0 += 16;
+		B1 += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+
+		A0 += 4;
+		A1 += 4;
+		A2 += 4;
+		B0 += 4;
+		B1 += 4;
+
+		}
+
+	if(tri==1)
+		{
+		// 7x7 triangle 
+
+		c_0 = _mm_load_sd( &A0[3+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[1+bs*0], c_0 );
+		c_0 = _mm_load_pd( &A1[0+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B0[2+bs*0], c_0 );
+		c_0 = _mm_load_pd( &A1[2+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[0+bs*0], c_0 );
+		c_0 = _mm_load_pd( &A2[0+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[2+bs*0], c_0 );
+
+		c_0 = _mm_load_pd( &A1[0+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B0[2+bs*1], c_0 );
+		c_0 = _mm_load_pd( &A1[2+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[0+bs*1], c_0 );
+		c_0 = _mm_load_pd( &A2[0+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[2+bs*1], c_0 );
+
+		c_0 = _mm_load_sd( &A1[1+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[3+bs*2], c_0 );
+		c_0 = _mm_load_pd( &A1[2+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[0+bs*2], c_0 );
+		c_0 = _mm_load_pd( &A2[0+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[2+bs*2], c_0 );
+
+		c_0 = _mm_load_pd( &A1[2+bs*3] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[0+bs*3], c_0 );
+		c_0 = _mm_load_pd( &A2[0+bs*3] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[2+bs*3], c_0 );
+
+		c_0 = _mm_load_sd( &A1[3+bs*4] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[1+bs*4], c_0 );
+		c_0 = _mm_load_pd( &A2[0+bs*4] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[2+bs*4], c_0 );
+
+		c_0 = _mm_load_pd( &A2[0+bs*5] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B1[2+bs*5], c_0 );
+
+		c_0 = _mm_load_sd( &A2[1+bs*6] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*6], c_0 );
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 3 elements of A must be skipped
+void kernel_dgecp_8_3_lib4(int tri, int kmax, double alpha, double *A0, int sda, double *B0, int sdb)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 8-wide + end 7x7 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+	double *A2 = A1 + bs*sda;
+	double *B1 = B0 + bs*sdb;
+
+	__m256d
+		alpha_0,
+		a_0, a_1, a_2,
+		b_0, b_1;
+	
+	__m128d
+		c_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_1 = _mm256_shuffle_pd( b_1, a_2, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		a_2 = _mm256_load_pd( &A2[0+bs*1] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_1 = _mm256_shuffle_pd( b_1, a_2, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B0[0+bs*1], b_0 );
+		_mm256_store_pd( &B1[0+bs*1], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		a_2 = _mm256_load_pd( &A2[0+bs*2] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_1 = _mm256_shuffle_pd( b_1, a_2, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B0[0+bs*2], b_0 );
+		_mm256_store_pd( &B1[0+bs*2], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		a_2 = _mm256_load_pd( &A2[0+bs*3] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_1 = _mm256_shuffle_pd( b_1, a_2, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B0[0+bs*3], b_0 );
+		_mm256_store_pd( &B1[0+bs*3], b_1 );
+
+		A0 += 16;
+		A1 += 16;
+		A2 += 16;
+		B0 += 16;
+		B1 += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_1 = _mm256_shuffle_pd( b_1, a_2, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+
+		A0 += 4;
+		A1 += 4;
+		A2 += 4;
+		B0 += 4;
+		B1 += 4;
+
+		}
+
+	if(tri==1)
+		{
+		// 7x7 triangle 
+
+		c_0 = _mm_load_pd( &A1[0+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B0[1+bs*0], c_0 );
+		c_0 = _mm_load_sd( &A1[2+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[3+bs*0], c_0 );
+		c_0 = _mm_load_sd( &A1[3+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[0+bs*0], c_0 );
+		c_0 = _mm_load_pd( &A2[0+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B1[1+bs*0], c_0 );
+		c_0 = _mm_load_sd( &A2[2+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*0], c_0 );
+
+		c_0 = _mm_load_sd( &A1[1+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[2+bs*1], c_0 );
+		c_0 = _mm_load_sd( &A1[2+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[3+bs*1], c_0 );
+		c_0 = _mm_load_sd( &A1[3+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[0+bs*1], c_0 );
+		c_0 = _mm_load_pd( &A2[0+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B1[1+bs*1], c_0 );
+		c_0 = _mm_load_sd( &A2[2+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*1], c_0 );
+
+		c_0 = _mm_load_sd( &A1[2+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B0[3+bs*2], c_0 );
+		c_0 = _mm_load_sd( &A1[3+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[0+bs*2], c_0 );
+		c_0 = _mm_load_pd( &A2[0+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B1[1+bs*2], c_0 );
+		c_0 = _mm_load_sd( &A2[2+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*2], c_0 );
+
+		c_0 = _mm_load_sd( &A1[3+bs*3] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[0+bs*3], c_0 );
+		c_0 = _mm_load_pd( &A2[0+bs*3] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B1[1+bs*3], c_0 );
+		c_0 = _mm_load_sd( &A2[2+bs*3] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*3], c_0 );
+
+		c_0 = _mm_load_pd( &A2[0+bs*4] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B1[1+bs*4], c_0 );
+		c_0 = _mm_load_sd( &A2[2+bs*4] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*4], c_0 );
+
+		c_0 = _mm_load_sd( &A2[1+bs*5] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[2+bs*5], c_0 );
+		c_0 = _mm_load_sd( &A2[2+bs*5] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*5], c_0 );
+
+		c_0 = _mm_load_sd( &A2[2+bs*6] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B1[3+bs*6], c_0 );
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries
+void kernel_dgecp_4_0_lib4(int tri, int kmax, double alpha, double *A, double *B)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 4-wide + end 3x3 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	__m256d
+		alpha_0,
+		a_0;
+	
+	__m128d
+		c_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B[0+bs*0], a_0 );
+
+		a_0 = _mm256_load_pd( &A[0+bs*1] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B[0+bs*1], a_0 );
+
+		a_0 = _mm256_load_pd( &A[0+bs*2] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B[0+bs*2], a_0 );
+
+		a_0 = _mm256_load_pd( &A[0+bs*3] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B[0+bs*3], a_0 );
+
+		A += 16;
+		B += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		_mm256_store_pd( &B[0+bs*0], a_0 );
+
+		A += 4;
+		B += 4;
+
+		}
+	
+	if(tri==1)
+		{
+		// 3x3 triangle
+
+		c_0 = _mm_load_sd( &A[1+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[1+bs*0], c_0 );
+		c_0 = _mm_load_pd( &A[2+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B[2+bs*0], c_0 );
+
+		c_0 = _mm_load_pd( &A[2+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B[2+bs*1], c_0 );
+
+		c_0 = _mm_load_sd( &A[3+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[3+bs*2], c_0 );
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 1 element of A must be skipped
+void kernel_dgecp_4_1_lib4(int tri, int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 4-wide + end 3x3 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m256d
+		alpha_0,
+		a_0, a_1,
+		b_0;
+	
+	__m128d
+		c_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_1 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		a_1 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*1], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		a_1 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*2], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		a_1 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*3], b_0 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_1 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+	
+	if(tri==1)
+		{
+		// 3x3 triangle
+
+		c_0 = _mm_load_pd( &A0[2+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B[1+bs*0], c_0 );
+		c_0 = _mm_load_sd( &A1[0+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[3+bs*0], c_0 );
+
+		c_0 = _mm_load_sd( &A0[3+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[2+bs*1], c_0 );
+		c_0 = _mm_load_sd( &A1[0+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[3+bs*1], c_0 );
+
+		c_0 = _mm_load_sd( &A1[0+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[3+bs*2], c_0 );
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 2 elements of A must be skipped
+void kernel_dgecp_4_2_lib4(int tri, int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 4-wide + end 3x3 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m256d
+		alpha_0,
+		a_0, a_1,
+		b_0;
+	
+	__m128d
+		c_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*1], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*2], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*3], b_0 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+	
+	if(tri==1)
+		{
+		// 3x3 triangle
+
+		c_0 = _mm_load_sd( &A0[3+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[1+bs*0], c_0 );
+		c_0 = _mm_load_pd( &A1[0+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B[2+bs*0], c_0 );
+
+		c_0 = _mm_load_pd( &A1[0+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_pd( &B[2+bs*1], c_0 );
+
+		c_0 = _mm_load_sd( &A1[1+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[3+bs*2], c_0 );
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 3 elements of A must be skipped
+void kernel_dgecp_4_3_lib4(int tri, int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 4-wide + end 3x3 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m256d
+		alpha_0,
+		a_0, a_1,
+		b_0;
+	
+	__m128d
+		c_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*1], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*2], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*3], b_0 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+	
+	if(tri==1)
+		{
+		// 3x3 triangle
+
+		c_0 = _mm_load_pd( &A1[0+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_storeu_pd( &B[1+bs*0], c_0 );
+		c_0 = _mm_load_sd( &A1[2+bs*0] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[3+bs*0], c_0 );
+
+		c_0 = _mm_load_sd( &A1[1+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[2+bs*1], c_0 );
+		c_0 = _mm_load_sd( &A1[2+bs*1] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[3+bs*1], c_0 );
+
+		c_0 = _mm_load_sd( &A1[2+bs*2] );
+		c_0 = _mm_mul_pd( _mm256_castpd256_pd128( alpha_0 ), c_0 );
+		_mm_store_sd( &B[3+bs*2], c_0 );
+		}
+
+
+	}
+
+
+
+// both A and B are aligned to 64-bit boundaries
+void kernel_dgecp_3_0_lib4(int tri, int kmax, double alpha, double *A, double *B)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 3-wide + end 2x2 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	__m128d
+		alpha_0,
+		a_0, a_1;
+	
+	int k;
+
+	alpha_0 = _mm_loaddup_pd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_loadu_pd( &A[0+bs*0] );
+		a_1 = _mm_load_sd( &A[2+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+		_mm_store_sd( &B[2+bs*0], a_1 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*1] );
+		a_1 = _mm_load_sd( &A[2+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_storeu_pd( &B[0+bs*1], a_0 );
+		_mm_store_sd( &B[2+bs*1], a_1 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*2] );
+		a_1 = _mm_load_sd( &A[2+bs*2] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_storeu_pd( &B[0+bs*2], a_0 );
+		_mm_store_sd( &B[2+bs*2], a_1 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*3] );
+		a_1 = _mm_load_sd( &A[2+bs*3] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_storeu_pd( &B[0+bs*3], a_0 );
+		_mm_store_sd( &B[2+bs*3], a_1 );
+
+		A += 16;
+		B += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_loadu_pd( &A[0+bs*0] );
+		a_1 = _mm_load_sd( &A[2+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+		_mm_store_sd( &B[2+bs*0], a_1 );
+
+		A += 4;
+		B += 4;
+
+		}
+	
+	if(tri==1)
+		{
+		// 2x2 triangle
+
+		a_0 = _mm_loadu_pd( &A[1+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[1+bs*0], a_0 );
+
+		a_0 = _mm_load_sd( &A[2+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[2+bs*1], a_0 );
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 2 elements of A must be skipped
+void kernel_dgecp_3_2_lib4(int tri, int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 3-wide + end 2x2 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m128d
+		alpha_0,
+		a_0, a_1;
+	
+	int k;
+
+	alpha_0 = _mm_loaddup_pd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_loadu_pd( &A0[2+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+		a_1 = _mm_load_sd( &A1[0+bs*0] );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_store_sd( &B[2+bs*0], a_1 );
+
+		a_0 = _mm_loadu_pd( &A0[2+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*1], a_0 );
+		a_1 = _mm_load_sd( &A1[0+bs*1] );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_store_sd( &B[2+bs*1], a_1 );
+
+		a_0 = _mm_loadu_pd( &A0[2+bs*2] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*2], a_0 );
+		a_1 = _mm_load_sd( &A1[0+bs*2] );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_store_sd( &B[2+bs*2], a_1 );
+
+		a_0 = _mm_loadu_pd( &A0[2+bs*3] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*3], a_0 );
+		a_1 = _mm_load_sd( &A1[0+bs*3] );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_store_sd( &B[2+bs*3], a_1 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_loadu_pd( &A0[2+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+		a_1 = _mm_load_sd( &A1[0+bs*0] );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_store_sd( &B[2+bs*0], a_1 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+	
+	if(tri==1)
+		{
+		// 2x2 triangle
+
+		a_0 = _mm_load_sd( &A0[3+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[1+bs*0], a_0 );
+		a_0 = _mm_load_sd( &A1[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[2+bs*0], a_0 );
+
+		a_0 = _mm_load_sd( &A1[0+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[2+bs*1], a_0 );
+
+		}
+
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 3 elements of A must be skipped
+void kernel_dgecp_3_3_lib4(int tri, int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 3-wide + end 2x2 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m128d
+		alpha_0,
+		a_0, a_1;
+	
+	int k;
+
+	alpha_0 = _mm_loaddup_pd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_load_sd( &A0[3+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[0+bs*0], a_0 );
+		a_1 = _mm_loadu_pd( &A1[0+bs*0] );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_storeu_pd( &B[1+bs*0], a_1 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[0+bs*1], a_0 );
+		a_1 = _mm_loadu_pd( &A1[0+bs*1] );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_storeu_pd( &B[1+bs*1], a_1 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*2] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[0+bs*2], a_0 );
+		a_1 = _mm_loadu_pd( &A1[0+bs*2] );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_storeu_pd( &B[1+bs*2], a_1 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*3] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[0+bs*3], a_0 );
+		a_1 = _mm_loadu_pd( &A1[0+bs*3] );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_storeu_pd( &B[1+bs*3], a_1 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_load_sd( &A0[3+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[0+bs*0], a_0 );
+		a_1 = _mm_loadu_pd( &A1[0+bs*0] );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		_mm_storeu_pd( &B[1+bs*0], a_1 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+	
+	if(tri==1)
+		{
+		// 2x2 triangle
+
+		a_0 = _mm_loadu_pd( &A1[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[1+bs*0], a_0 );
+
+		a_0 = _mm_load_sd( &A1[1+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[2+bs*1], a_0 );
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 64-bit boundaries
+void kernel_dgecp_2_0_lib4(int tri, int kmax, double alpha, double *A, double *B)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 2-wide + end 1x1 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	__m128d
+		alpha_0,
+		a_0;
+	
+	int k;
+
+	alpha_0 = _mm_loaddup_pd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_loadu_pd( &A[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*1], a_0 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*2] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*2], a_0 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*3] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*3], a_0 );
+
+		A += 16;
+		B += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_loadu_pd( &A[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+
+		A += 4;
+		B += 4;
+
+		}
+	
+	if(tri==1)
+		{
+		// 1x1 triangle
+
+		a_0 = _mm_load_sd( &A[1+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[1+bs*0], a_0 );
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 128-bit boundaries, 3 elements of A must be skipped
+void kernel_dgecp_2_3_lib4(int tri, int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 2-wide + end 1x1 triangle
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m128d
+		alpha_0,
+		a_0;
+	
+	int k;
+
+	alpha_0 = _mm_loaddup_pd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_load_sd( &A0[3+bs*0] );
+		a_0 = _mm_loadh_pd( a_0, &A1[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*1] );
+		a_0 = _mm_loadh_pd( a_0, &A1[0+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*1], a_0 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*2] );
+		a_0 = _mm_loadh_pd( a_0, &A1[0+bs*2] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*2], a_0 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*3] );
+		a_0 = _mm_loadh_pd( a_0, &A1[0+bs*3] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*3], a_0 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_load_sd( &A0[3+bs*0] );
+		a_0 = _mm_loadh_pd( a_0, &A1[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+	
+	if(tri==1)
+		{
+		// 1x1 triangle
+
+		a_0 = _mm_load_sd( &A1[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[1+bs*0], a_0 );
+
+		}
+
+	}
+
+
+
+// both A and B are aligned 64-bit boundaries
+void kernel_dgecp_1_0_lib4(int tri, int kmax, double alpha, double *A, double *B)
+	{
+
+	if(tri==1)
+		{
+		// A and C are lower triangular
+		// kmax+1 1-wide
+
+		kmax += 1;
+		}
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	__m128d
+		alpha_0,
+		a_0;
+	
+	int k;
+
+	alpha_0 = _mm_loaddup_pd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_load_sd( &A[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[0+bs*0], a_0 );
+
+		a_0 = _mm_load_sd( &A[0+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[0+bs*1], a_0 );
+
+		a_0 = _mm_load_sd( &A[0+bs*2] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[0+bs*2], a_0 );
+
+		a_0 = _mm_load_sd( &A[0+bs*3] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[0+bs*3], a_0 );
+
+		A += 16;
+		B += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_load_sd( &A[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		_mm_store_sd( &B[0+bs*0], a_0 );
+
+		A += 4;
+		B += 4;
+
+		}
+
+	}
+
+
+
+
+// both A and B are aligned to 256-bit boundaries
+void kernel_dgead_8_0_lib4(int kmax, double alpha, double *A0, int sda,  double *B0, int sdb)
+	{
+
+	if(kmax<=0)
+		return;
+	
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+	double *B1 = B0 + bs*sdb;
+
+	__m256d
+		a_0, c_0, alpha_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		c_0 = _mm256_load_pd( &B0[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( a_0, c_0 );
+		_mm256_store_pd( &B0[0+bs*0], a_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		c_0 = _mm256_load_pd( &B0[0+bs*1] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( a_0, c_0 );
+		_mm256_store_pd( &B0[0+bs*1], a_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		c_0 = _mm256_load_pd( &B0[0+bs*2] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( a_0, c_0 );
+		_mm256_store_pd( &B0[0+bs*2], a_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		c_0 = _mm256_load_pd( &B0[0+bs*3] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( a_0, c_0 );
+		_mm256_store_pd( &B0[0+bs*3], a_0 );
+
+		A0 += 16;
+		B0 += 16;
+
+		a_0 = _mm256_load_pd( &A1[0+bs*0] );
+		c_0 = _mm256_load_pd( &B1[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( a_0, c_0 );
+		_mm256_store_pd( &B1[0+bs*0], a_0 );
+
+		a_0 = _mm256_load_pd( &A1[0+bs*1] );
+		c_0 = _mm256_load_pd( &B1[0+bs*1] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( a_0, c_0 );
+		_mm256_store_pd( &B1[0+bs*1], a_0 );
+
+		a_0 = _mm256_load_pd( &A1[0+bs*2] );
+		c_0 = _mm256_load_pd( &B1[0+bs*2] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( a_0, c_0 );
+		_mm256_store_pd( &B1[0+bs*2], a_0 );
+
+		a_0 = _mm256_load_pd( &A1[0+bs*3] );
+		c_0 = _mm256_load_pd( &B1[0+bs*3] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( a_0, c_0 );
+		_mm256_store_pd( &B1[0+bs*3], a_0 );
+
+		A1 += 16;
+		B1 += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		c_0 = _mm256_load_pd( &B0[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( a_0, c_0 );
+		_mm256_store_pd( &B0[0+bs*0], a_0 );
+
+		A0 += 4;
+		B0 += 4;
+
+		a_0 = _mm256_load_pd( &A1[0+bs*0] );
+		c_0 = _mm256_load_pd( &B1[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( a_0, c_0 );
+		_mm256_store_pd( &B1[0+bs*0], a_0 );
+
+		A1 += 4;
+		B1 += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 1 element of A must be skipped
+void kernel_dgead_8_1_lib4(int kmax, double alpha, double *A0, int sda, double *B0, int sdb)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+	double *A2 = A1 + bs*sda;
+	double *B1 = B0 + bs*sdb;
+
+	__m256d
+		a_0, a_1, a_2,
+		b_0, b_1,
+		alpha_0, c_0, c_1;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_2 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_shuffle_pd( a_1, a_2, 0x5 );
+		b_0 = _mm256_shuffle_pd( a_0, b_0, 0x5 );
+		c_1 = _mm256_load_pd( &B1[0+bs*0] );
+		c_0 = _mm256_load_pd( &B0[0+bs*0] );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+
+		a_2 = _mm256_load_pd( &A2[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_2 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_shuffle_pd( a_1, a_2, 0x5 );
+		b_0 = _mm256_shuffle_pd( a_0, b_0, 0x5 );
+		c_1 = _mm256_load_pd( &B1[0+bs*1] );
+		c_0 = _mm256_load_pd( &B0[0+bs*1] );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		_mm256_store_pd( &B1[0+bs*1], b_1 );
+		_mm256_store_pd( &B0[0+bs*1], b_0 );
+
+		a_2 = _mm256_load_pd( &A2[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_2 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_shuffle_pd( a_1, a_2, 0x5 );
+		b_0 = _mm256_shuffle_pd( a_0, b_0, 0x5 );
+		c_1 = _mm256_load_pd( &B1[0+bs*2] );
+		c_0 = _mm256_load_pd( &B0[0+bs*2] );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		_mm256_store_pd( &B1[0+bs*2], b_1 );
+		_mm256_store_pd( &B0[0+bs*2], b_0 );
+
+		a_2 = _mm256_load_pd( &A2[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_2 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_shuffle_pd( a_1, a_2, 0x5 );
+		b_0 = _mm256_shuffle_pd( a_0, b_0, 0x5 );
+		c_1 = _mm256_load_pd( &B1[0+bs*3] );
+		c_0 = _mm256_load_pd( &B0[0+bs*3] );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		_mm256_store_pd( &B1[0+bs*3], b_1 );
+		_mm256_store_pd( &B0[0+bs*3], b_0 );
+
+		A0 += 16;
+		A1 += 16;
+		A2 += 16;
+		B0 += 16;
+		B1 += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_2 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_shuffle_pd( a_1, a_2, 0x5 );
+		b_0 = _mm256_shuffle_pd( a_0, b_0, 0x5 );
+		c_1 = _mm256_load_pd( &B1[0+bs*0] );
+		c_0 = _mm256_load_pd( &B0[0+bs*0] );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+
+		A0 += 4;
+		A1 += 4;
+		A2 += 4;
+		B0 += 4;
+		B1 += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 2 elements of A must be skipped
+void kernel_dgead_8_2_lib4(int kmax, double alpha, double *A0, int sda, double *B0, int sdb)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+	double *A2 = A1 + bs*sda;
+	double *B1 = B0 + bs*sdb;
+
+	__m256d
+		a_0, a_1, a_2,
+		b_0, b_1,
+		alpha_0, c_0, c_1;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		c_0 = _mm256_load_pd( &B0[0+bs*0] );
+		c_1 = _mm256_load_pd( &B1[0+bs*0] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		a_2 = _mm256_load_pd( &A2[0+bs*1] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		c_0 = _mm256_load_pd( &B0[0+bs*1] );
+		c_1 = _mm256_load_pd( &B1[0+bs*1] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		_mm256_store_pd( &B0[0+bs*1], b_0 );
+		_mm256_store_pd( &B1[0+bs*1], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		a_2 = _mm256_load_pd( &A2[0+bs*2] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		c_0 = _mm256_load_pd( &B0[0+bs*2] );
+		c_1 = _mm256_load_pd( &B1[0+bs*2] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		_mm256_store_pd( &B0[0+bs*2], b_0 );
+		_mm256_store_pd( &B1[0+bs*2], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		a_2 = _mm256_load_pd( &A2[0+bs*3] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		c_0 = _mm256_load_pd( &B0[0+bs*3] );
+		c_1 = _mm256_load_pd( &B1[0+bs*3] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		_mm256_store_pd( &B0[0+bs*3], b_0 );
+		_mm256_store_pd( &B1[0+bs*3], b_1 );
+
+		A0 += 16;
+		A1 += 16;
+		A2 += 16;
+		B0 += 16;
+		B1 += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		c_0 = _mm256_load_pd( &B0[0+bs*0] );
+		c_1 = _mm256_load_pd( &B1[0+bs*0] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+
+		A0 += 4;
+		A1 += 4;
+		A2 += 4;
+		B0 += 4;
+		B1 += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 3 elements of A must be skipped
+void kernel_dgead_8_3_lib4(int kmax, double alpha, double *A0, int sda, double *B0, int sdb)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+	double *A2 = A1 + bs*sda;
+	double *B1 = B0 + bs*sdb;
+
+	__m256d
+		a_0, a_1, a_2,
+		b_0, b_1,
+		alpha_0, c_0, c_1;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_1 = _mm256_shuffle_pd( b_1, a_2, 0x5 );
+		c_0 = _mm256_load_pd( &B0[0+bs*0] );
+		c_1 = _mm256_load_pd( &B1[0+bs*0] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		a_2 = _mm256_load_pd( &A2[0+bs*1] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_1 = _mm256_shuffle_pd( b_1, a_2, 0x5 );
+		c_0 = _mm256_load_pd( &B0[0+bs*1] );
+		c_1 = _mm256_load_pd( &B1[0+bs*1] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		_mm256_store_pd( &B0[0+bs*1], b_0 );
+		_mm256_store_pd( &B1[0+bs*1], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		a_2 = _mm256_load_pd( &A2[0+bs*2] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_1 = _mm256_shuffle_pd( b_1, a_2, 0x5 );
+		c_0 = _mm256_load_pd( &B0[0+bs*2] );
+		c_1 = _mm256_load_pd( &B1[0+bs*2] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		_mm256_store_pd( &B0[0+bs*2], b_0 );
+		_mm256_store_pd( &B1[0+bs*2], b_1 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		a_2 = _mm256_load_pd( &A2[0+bs*3] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_1 = _mm256_shuffle_pd( b_1, a_2, 0x5 );
+		c_0 = _mm256_load_pd( &B0[0+bs*3] );
+		c_1 = _mm256_load_pd( &B1[0+bs*3] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		_mm256_store_pd( &B0[0+bs*3], b_0 );
+		_mm256_store_pd( &B1[0+bs*3], b_1 );
+
+		A0 += 16;
+		A1 += 16;
+		A2 += 16;
+		B0 += 16;
+		B1 += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_2 = _mm256_load_pd( &A2[0+bs*0] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_1 = _mm256_permute2f128_pd( a_1, a_2, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		b_1 = _mm256_shuffle_pd( b_1, a_2, 0x5 );
+		c_0 = _mm256_load_pd( &B0[0+bs*0] );
+		c_1 = _mm256_load_pd( &B1[0+bs*0] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_1 = _mm256_mul_pd( alpha_0, b_1 );
+		b_0 = _mm256_add_pd ( c_0, b_0 );
+		b_1 = _mm256_add_pd ( c_1, b_1 );
+		_mm256_store_pd( &B0[0+bs*0], b_0 );
+		_mm256_store_pd( &B1[0+bs*0], b_1 );
+
+		A0 += 4;
+		A1 += 4;
+		A2 += 4;
+		B0 += 4;
+		B1 += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries
+void kernel_dgead_4_0_lib4(int kmax, double alpha, double *A, double *B)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	__m256d
+		a_0, c_0, alpha_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A[0+bs*0] );
+		c_0 = _mm256_load_pd( &B[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( c_0, a_0 );
+		_mm256_store_pd( &B[0+bs*0], a_0 );
+
+		a_0 = _mm256_load_pd( &A[0+bs*1] );
+		c_0 = _mm256_load_pd( &B[0+bs*1] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( c_0, a_0 );
+		_mm256_store_pd( &B[0+bs*1], a_0 );
+
+		a_0 = _mm256_load_pd( &A[0+bs*2] );
+		c_0 = _mm256_load_pd( &B[0+bs*2] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( c_0, a_0 );
+		_mm256_store_pd( &B[0+bs*2], a_0 );
+
+		a_0 = _mm256_load_pd( &A[0+bs*3] );
+		c_0 = _mm256_load_pd( &B[0+bs*3] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( c_0, a_0 );
+		_mm256_store_pd( &B[0+bs*3], a_0 );
+
+		A += 16;
+		B += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A[0+bs*0] );
+		c_0 = _mm256_load_pd( &B[0+bs*0] );
+		a_0 = _mm256_mul_pd( alpha_0, a_0 );
+		a_0 = _mm256_add_pd( c_0, a_0 );
+		_mm256_store_pd( &B[0+bs*0], a_0 );
+
+		A += 4;
+		B += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 1 element of A must be skipped
+void kernel_dgead_4_1_lib4(int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m256d
+		a_0, a_1,
+		b_0,
+		alpha_0, c_0;
+	
+	int k;
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_1 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		c_0 = _mm256_load_pd( &B[0+bs*0] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		a_1 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		c_0 = _mm256_load_pd( &B[0+bs*1] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*1], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		a_1 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		c_0 = _mm256_load_pd( &B[0+bs*2] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*2], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		a_1 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		c_0 = _mm256_load_pd( &B[0+bs*3] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*3], b_0 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_1 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		c_0 = _mm256_load_pd( &B[0+bs*0] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 2 elements of A must be skipped
+void kernel_dgead_4_2_lib4(int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m256d
+		a_0, a_1,
+		b_0,
+		alpha_0, c_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		c_0 = _mm256_load_pd( &B[0+bs*0] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		c_0 = _mm256_load_pd( &B[0+bs*1] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*1], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		c_0 = _mm256_load_pd( &B[0+bs*2] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*2], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		c_0 = _mm256_load_pd( &B[0+bs*3] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*3], b_0 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		b_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		c_0 = _mm256_load_pd( &B[0+bs*0] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 3 elements of A must be skipped
+void kernel_dgead_4_3_lib4(int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m256d
+		a_0, a_1,
+		b_0,
+		alpha_0, c_0;
+	
+	int k;
+
+	alpha_0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		c_0 = _mm256_load_pd( &B[0+bs*0] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*1] );
+		a_1 = _mm256_load_pd( &A1[0+bs*1] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		c_0 = _mm256_load_pd( &B[0+bs*1] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*1], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*2] );
+		a_1 = _mm256_load_pd( &A1[0+bs*2] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		c_0 = _mm256_load_pd( &B[0+bs*2] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*2], b_0 );
+
+		a_0 = _mm256_load_pd( &A0[0+bs*3] );
+		a_1 = _mm256_load_pd( &A1[0+bs*3] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		c_0 = _mm256_load_pd( &B[0+bs*3] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*3], b_0 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm256_load_pd( &A0[0+bs*0] );
+		a_1 = _mm256_load_pd( &A1[0+bs*0] );
+		a_0 = _mm256_permute2f128_pd( a_0, a_1, 0x21 );
+		b_0 = _mm256_shuffle_pd( a_0, a_1, 0x5 );
+		c_0 = _mm256_load_pd( &B[0+bs*0] );
+		b_0 = _mm256_mul_pd( alpha_0, b_0 );
+		b_0 = _mm256_add_pd( c_0, b_0 );
+		_mm256_store_pd( &B[0+bs*0], b_0 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 64-bit boundaries
+void kernel_dgead_3_0_lib4(int kmax, double alpha, double *A, double *B)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	__m128d
+		a_0, a_1,
+		alpha_0, c_0, c_1;
+	
+	int k;
+
+	alpha_0 = _mm_loaddup_pd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_loadu_pd( &A[0+bs*0] );
+		a_1 = _mm_load_sd( &A[2+bs*0] );
+		c_0 = _mm_loadu_pd( &B[0+bs*0] );
+		c_1 = _mm_load_sd( &B[2+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_sd( alpha_0, a_1 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		a_1 = _mm_add_sd( c_1, a_1 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+		_mm_store_sd( &B[2+bs*0], a_1 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*1] );
+		a_1 = _mm_load_sd( &A[2+bs*1] );
+		c_0 = _mm_loadu_pd( &B[0+bs*1] );
+		c_1 = _mm_load_sd( &B[2+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_sd( alpha_0, a_1 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		a_1 = _mm_add_sd( c_1, a_1 );
+		_mm_storeu_pd( &B[0+bs*1], a_0 );
+		_mm_store_sd( &B[2+bs*1], a_1 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*2] );
+		a_1 = _mm_load_sd( &A[2+bs*2] );
+		c_0 = _mm_loadu_pd( &B[0+bs*2] );
+		c_1 = _mm_load_sd( &B[2+bs*2] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_sd( alpha_0, a_1 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		a_1 = _mm_add_sd( c_1, a_1 );
+		_mm_storeu_pd( &B[0+bs*2], a_0 );
+		_mm_store_sd( &B[2+bs*2], a_1 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*3] );
+		a_1 = _mm_load_sd( &A[2+bs*3] );
+		c_0 = _mm_loadu_pd( &B[0+bs*3] );
+		c_1 = _mm_load_sd( &B[2+bs*3] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_sd( alpha_0, a_1 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		a_1 = _mm_add_sd( c_1, a_1 );
+		_mm_storeu_pd( &B[0+bs*3], a_0 );
+		_mm_store_sd( &B[2+bs*3], a_1 );
+
+		A += 16;
+		B += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_loadu_pd( &A[0+bs*0] );
+		a_1 = _mm_load_sd( &A[2+bs*0] );
+		c_0 = _mm_loadu_pd( &B[0+bs*0] );
+		c_1 = _mm_load_sd( &B[2+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_sd( alpha_0, a_1 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		a_1 = _mm_add_sd( c_1, a_1 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+		_mm_store_sd( &B[2+bs*0], a_1 );
+
+		A += 4;
+		B += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 2 elements of A must be skipped
+void kernel_dgead_3_2_lib4(int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m128d
+		a_0, a_1,
+		alpha_0, c_0, c_1;
+	
+	int k;
+
+	alpha_0 = _mm_loaddup_pd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_loadu_pd( &A0[2+bs*0] );
+		a_1 = _mm_load_sd( &A1[0+bs*0] );
+		c_0 = _mm_loadu_pd( &B[0+bs*0] );
+		c_1 = _mm_load_sd( &B[2+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_sd( alpha_0, a_1 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		a_1 = _mm_add_sd( c_1, a_1 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+		_mm_store_sd( &B[2+bs*0], a_1 );
+
+		a_0 = _mm_loadu_pd( &A0[2+bs*1] );
+		a_1 = _mm_load_sd( &A1[0+bs*1] );
+		c_0 = _mm_loadu_pd( &B[0+bs*1] );
+		c_1 = _mm_load_sd( &B[2+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_sd( alpha_0, a_1 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		a_1 = _mm_add_sd( c_1, a_1 );
+		_mm_storeu_pd( &B[0+bs*1], a_0 );
+		_mm_store_sd( &B[2+bs*1], a_1 );
+
+		a_0 = _mm_loadu_pd( &A0[2+bs*2] );
+		a_1 = _mm_load_sd( &A1[0+bs*2] );
+		c_0 = _mm_loadu_pd( &B[0+bs*2] );
+		c_1 = _mm_load_sd( &B[2+bs*2] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_sd( alpha_0, a_1 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		a_1 = _mm_add_sd( c_1, a_1 );
+		_mm_storeu_pd( &B[0+bs*2], a_0 );
+		_mm_store_sd( &B[2+bs*2], a_1 );
+
+		a_0 = _mm_loadu_pd( &A0[2+bs*3] );
+		a_1 = _mm_load_sd( &A1[0+bs*3] );
+		c_0 = _mm_loadu_pd( &B[0+bs*3] );
+		c_1 = _mm_load_sd( &B[2+bs*3] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_sd( alpha_0, a_1 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		a_1 = _mm_add_sd( c_1, a_1 );
+		_mm_storeu_pd( &B[0+bs*3], a_0 );
+		_mm_store_sd( &B[2+bs*3], a_1 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_loadu_pd( &A0[2+bs*0] );
+		a_1 = _mm_load_sd( &A1[0+bs*0] );
+		c_0 = _mm_loadu_pd( &B[0+bs*0] );
+		c_1 = _mm_load_sd( &B[2+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_1 = _mm_mul_sd( alpha_0, a_1 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		a_1 = _mm_add_sd( c_1, a_1 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+		_mm_store_sd( &B[2+bs*0], a_1 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 256-bit boundaries, 3 elements of A must be skipped
+void kernel_dgead_3_3_lib4(int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m128d
+		a_0, a_1,
+		alpha_0, c_0, c_1;
+	
+	int k;
+
+	alpha_0 = _mm_loaddup_pd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_load_sd( &A0[3+bs*0] );
+		a_1 = _mm_loadu_pd( &A1[0+bs*0] );
+		c_0 = _mm_load_sd( &B[0+bs*0] );
+		c_1 = _mm_loadu_pd( &B[1+bs*0] );
+		a_0 = _mm_mul_sd( alpha_0, a_0 );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		a_0 = _mm_add_sd( c_0, a_0 );
+		a_1 = _mm_add_pd( c_1, a_1 );
+		_mm_store_sd( &B[0+bs*0], a_0 );
+		_mm_storeu_pd( &B[1+bs*0], a_1 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*1] );
+		a_1 = _mm_loadu_pd( &A1[0+bs*1] );
+		c_0 = _mm_load_sd( &B[0+bs*1] );
+		c_1 = _mm_loadu_pd( &B[1+bs*1] );
+		a_0 = _mm_mul_sd( alpha_0, a_0 );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		a_0 = _mm_add_sd( c_0, a_0 );
+		a_1 = _mm_add_pd( c_1, a_1 );
+		_mm_store_sd( &B[0+bs*1], a_0 );
+		_mm_storeu_pd( &B[1+bs*1], a_1 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*2] );
+		a_1 = _mm_loadu_pd( &A1[0+bs*2] );
+		c_0 = _mm_load_sd( &B[0+bs*2] );
+		c_1 = _mm_loadu_pd( &B[1+bs*2] );
+		a_0 = _mm_mul_sd( alpha_0, a_0 );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		a_0 = _mm_add_sd( c_0, a_0 );
+		a_1 = _mm_add_pd( c_1, a_1 );
+		_mm_store_sd( &B[0+bs*2], a_0 );
+		_mm_storeu_pd( &B[1+bs*2], a_1 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*3] );
+		a_1 = _mm_loadu_pd( &A1[0+bs*3] );
+		c_0 = _mm_load_sd( &B[0+bs*3] );
+		c_1 = _mm_loadu_pd( &B[1+bs*3] );
+		a_0 = _mm_mul_sd( alpha_0, a_0 );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		a_0 = _mm_add_sd( c_0, a_0 );
+		a_1 = _mm_add_pd( c_1, a_1 );
+		_mm_store_sd( &B[0+bs*3], a_0 );
+		_mm_storeu_pd( &B[1+bs*3], a_1 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_load_sd( &A0[3+bs*0] );
+		a_1 = _mm_loadu_pd( &A1[0+bs*0] );
+		c_0 = _mm_load_sd( &B[0+bs*0] );
+		c_1 = _mm_loadu_pd( &B[1+bs*0] );
+		a_0 = _mm_mul_sd( alpha_0, a_0 );
+		a_1 = _mm_mul_pd( alpha_0, a_1 );
+		a_0 = _mm_add_sd( c_0, a_0 );
+		a_1 = _mm_add_pd( c_1, a_1 );
+		_mm_store_sd( &B[0+bs*0], a_0 );
+		_mm_storeu_pd( &B[1+bs*0], a_1 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 64-bit boundaries
+void kernel_dgead_2_0_lib4(int kmax, double alpha, double *A, double *B)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	__m128d
+		a_0, c_0, alpha_0;
+	
+	int k;
+
+	alpha_0 = _mm_loaddup_pd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_loadu_pd( &A[0+bs*0] );
+		c_0 = _mm_loadu_pd( &B[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*1] );
+		c_0 = _mm_loadu_pd( &B[0+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*1], a_0 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*2] );
+		c_0 = _mm_loadu_pd( &B[0+bs*2] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*2], a_0 );
+
+		a_0 = _mm_loadu_pd( &A[0+bs*3] );
+		c_0 = _mm_loadu_pd( &B[0+bs*3] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*3], a_0 );
+
+		A += 16;
+		B += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_loadu_pd( &A[0+bs*0] );
+		c_0 = _mm_loadu_pd( &B[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+
+		A += 4;
+		B += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned to 128-bit boundaries, 3 elements of A must be skipped
+void kernel_dgead_2_3_lib4(int kmax, double alpha, double *A0, int sda, double *B)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	double *A1 = A0 + bs*sda;
+
+	__m128d
+		a_0, c_0, alpha_0;
+	
+	int k;
+
+	alpha_0 = _mm_loaddup_pd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_load_sd( &A0[3+bs*0] );
+		a_0 = _mm_loadh_pd( a_0, &A1[0+bs*0] );
+		c_0 = _mm_loadu_pd( &B[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*1] );
+		a_0 = _mm_loadh_pd( a_0, &A1[0+bs*1] );
+		c_0 = _mm_loadu_pd( &B[0+bs*1] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*1], a_0 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*2] );
+		a_0 = _mm_loadh_pd( a_0, &A1[0+bs*2] );
+		c_0 = _mm_loadu_pd( &B[0+bs*2] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*2], a_0 );
+
+		a_0 = _mm_load_sd( &A0[3+bs*3] );
+		a_0 = _mm_loadh_pd( a_0, &A1[0+bs*3] );
+		c_0 = _mm_loadu_pd( &B[0+bs*3] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*3], a_0 );
+
+		A0 += 16;
+		A1 += 16;
+		B  += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_load_sd( &A0[3+bs*0] );
+		a_0 = _mm_loadh_pd( a_0, &A1[0+bs*0] );
+		c_0 = _mm_loadu_pd( &B[0+bs*0] );
+		a_0 = _mm_mul_pd( alpha_0, a_0 );
+		a_0 = _mm_add_pd( c_0, a_0 );
+		_mm_storeu_pd( &B[0+bs*0], a_0 );
+
+		A0 += 4;
+		A1 += 4;
+		B  += 4;
+
+		}
+
+	}
+
+
+
+// both A and B are aligned 64-bit boundaries
+void kernel_dgead_1_0_lib4(int kmax, double alpha, double *A, double *B)
+	{
+
+	if(kmax<=0)
+		return;
+
+	const int bs = 4;
+
+	__m128d
+		a_0, c_0, alpha_0;
+	
+	int k;
+
+	alpha_0 = _mm_load_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		a_0 = _mm_load_sd( &A[0+bs*0] );
+		c_0 = _mm_load_sd( &B[0+bs*0] );
+		a_0 = _mm_mul_sd( alpha_0, a_0 );
+		a_0 = _mm_add_sd( c_0, a_0 );
+		_mm_store_sd( &B[0+bs*0], a_0 );
+
+		a_0 = _mm_load_sd( &A[0+bs*1] );
+		c_0 = _mm_load_sd( &B[0+bs*1] );
+		a_0 = _mm_mul_sd( alpha_0, a_0 );
+		a_0 = _mm_add_sd( c_0, a_0 );
+		_mm_store_sd( &B[0+bs*1], a_0 );
+
+		a_0 = _mm_load_sd( &A[0+bs*2] );
+		c_0 = _mm_load_sd( &B[0+bs*2] );
+		a_0 = _mm_mul_sd( alpha_0, a_0 );
+		a_0 = _mm_add_sd( c_0, a_0 );
+		_mm_store_sd( &B[0+bs*2], a_0 );
+
+		a_0 = _mm_load_sd( &A[0+bs*3] );
+		c_0 = _mm_load_sd( &B[0+bs*3] );
+		a_0 = _mm_mul_sd( alpha_0, a_0 );
+		a_0 = _mm_add_sd( c_0, a_0 );
+		_mm_store_sd( &B[0+bs*3], a_0 );
+
+		A += 16;
+		B += 16;
+
+		}
+	for(; k<kmax; k++)
+		{
+
+		a_0 = _mm_load_sd( &A[0+bs*0] );
+		c_0 = _mm_load_sd( &B[0+bs*0] );
+		a_0 = _mm_mul_sd( alpha_0, a_0 );
+		a_0 = _mm_add_sd( c_0, a_0 );
+		_mm_store_sd( &B[0+bs*0], a_0 );
+
+		A += 4;
+		B += 4;
+
+		}
+
+	}
+
+
+
+void kernel_dgeset_4_lib4(int kmax, double alpha, double *A)
+	{
+
+	int k;
+
+	__m256d 
+		a0;
+
+	a0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		_mm256_store_pd( &A[0], a0 );
+		_mm256_store_pd( &A[4], a0 );
+		_mm256_store_pd( &A[8], a0 );
+		_mm256_store_pd( &A[12], a0 );
+
+		A += 16;
+
+		}	
+	for(; k<kmax; k++)
+		{
+
+		_mm256_store_pd( &A[0], a0 );
+
+		A += 4;
+
+		}
+	
+	}
+
+
+// A lower triangular
+void kernel_dtrset_4_lib4(int kmax, double alpha, double *A)
+	{
+
+	int k;
+
+	__m256d 
+		a0;
+
+	a0 = _mm256_broadcast_sd( &alpha );
+
+	for(k=0; k<kmax-3; k+=4)
+		{
+
+		_mm256_store_pd( &A[0], a0 );
+		_mm256_store_pd( &A[4], a0 );
+		_mm256_store_pd( &A[8], a0 );
+		_mm256_store_pd( &A[12], a0 );
+
+		A += 16;
+
+		}	
+	for(; k<kmax; k++)
+		{
+
+		_mm256_store_pd( &A[0], a0 );
+
+		A += 4;
+
+		}
+	
+	// final 4x4 triangle
+	_mm256_store_pd( &A[0], a0 );
+
+	_mm_store_sd( &A[5], _mm256_castpd256_pd128( a0 ) );
+	_mm_store_pd( &A[6], _mm256_castpd256_pd128( a0 ) );
+	
+	_mm_store_pd( &A[10], _mm256_castpd256_pd128( a0 ) );
+
+	_mm_store_sd( &A[15], _mm256_castpd256_pd128( a0 ) );
+
+	}
+
+
+