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Merge pull request #82 from xianyi/develop 

rebase
tags/v0.3.11^2
Martin Kroeker GitHub 5 years ago
parent
0d1f30a297 e72430fe46
commit
c8f029a518
No known key found for this signature in database GPG Key ID: 4AEE18F83AFDEB23
13 changed files with 555 additions and 15 deletions
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  1. +5
    -0
      Makefile.arm64
  2. +1
    -0
      TargetList.txt
  3. +17
    -8
      benchmark/asum.c
  4. +32
    -3
      cpuid_arm64.c
  5. +1
    -0
      kernel/arm64/KERNEL.VORTEX
  6. +2
    -0
      kernel/x86_64/KERNEL.HASWELL
  7. +82
    -0
      kernel/x86_64/dasum.c
  8. +86
    -0
      kernel/x86_64/dasum_microk_haswell-2.c
  9. +80
    -0
      kernel/x86_64/dasum_microk_skylakex-2.c
  10. +90
    -0
      kernel/x86_64/sasum.c
  11. +82
    -0
      kernel/x86_64/sasum_microk_haswell-2.c
  12. +73
    -0
      kernel/x86_64/sasum_microk_skylakex-2.c
  13. +4
    -4
      lapack-netlib/TESTING/EIG/cchkhb2stg.f

+ 5
- 0
Makefile.arm64 View File

@@ -66,6 +66,11 @@ FCOMMON_OPT += -march=armv8.1-a -mtune=thunderx2t99
endif
endif

ifeq ($(CORE), VORTEX)
CCOMMON_OPT += -march=armv8.3-a
FCOMMON_OPT += -march=armv8.3-a
endif

ifeq ($(GCCVERSIONGTEQ9), 1)
ifeq ($(CORE), TSV110)
CCOMMON_OPT += -march=armv8.2-a -mtune=tsv110


+ 1
- 0
TargetList.txt View File

@@ -98,6 +98,7 @@ THUNDERX
THUNDERX2T99
TSV110
THUNDERX3T110
VORTEX

9.System Z:
ZARCH_GENERIC


+ 17
- 8
benchmark/asum.c View File

@@ -128,8 +128,13 @@ int main(int argc, char *argv[]){
int to = 200;
int step = 1;

#if defined(__WIN32__) || defined(__WIN64__) || !defined(_POSIX_TIMERS)
struct timeval start, stop;
double time1,timeg;
#else
struct timespec start = { 0, 0 }, stop = { 0, 0 };
double time1, timeg;
#endif

argc--;argv++;

@@ -160,26 +165,30 @@ int main(int argc, char *argv[]){

fprintf(stderr, " %6d : ", (int)m);


for (l=0; l<loops; l++)
{

for(i = 0; i < m * COMPSIZE * abs(inc_x); i++){
x[i] = ((FLOAT) rand() / (FLOAT) RAND_MAX) - 0.5;
}
#if defined(__WIN32__) || defined(__WIN64__) || !defined(_POSIX_TIMERS)
gettimeofday( &start, (struct timezone *)0);

#else
clock_gettime(CLOCK_REALTIME, &start);
#endif
result = ASUM (&m, x, &inc_x);

gettimeofday( &stop, (struct timezone *)0);

time1 = (double)(stop.tv_sec - start.tv_sec) + (double)((stop.tv_usec - start.tv_usec)) * 1.e-6;
#if defined(__WIN32__) || defined(__WIN64__) || !defined(_POSIX_TIMERS)
clock_gettime(CLOCK_REALTIME, &stop);
time1 = (double)(stop.tv_sec - start.tv_sec) + (double)((stop.tv_usec - start.tv_usec)) * 1.e-6;
#else
gettimeofday( &stop, (struct timezone *)0);
time1 = (double)(stop.tv_sec - start.tv_sec) + (double)((stop.tv_nsec - start.tv_nsec)) / 1.e9;
#endif

timeg += time1;

}
if (loops >1)
timeg /= loops;

#ifdef COMPLEX


+ 32
- 3
cpuid_arm64.c View File

@@ -26,6 +26,11 @@
*****************************************************************************/

#include <string.h>
#ifdef OS_DARWIN
#include <sys/sysctl.h>
int32_t value;
size_t length=sizeof(value);
#endif

#define CPU_UNKNOWN 0
#define CPU_ARMV8 1
@@ -45,6 +50,8 @@
#define CPU_TSV110 9
// Ampere
#define CPU_EMAG8180 10
// Apple
#define CPU_VORTEX 13

static char *cpuname[] = {
"UNKNOWN",
@@ -59,7 +66,8 @@ static char *cpuname[] = {
"TSV110",
"EMAG8180",
"NEOVERSEN1",
"THUNDERX3T110"
"THUNDERX3T110",
"VORTEX"
};

static char *cpuname_lower[] = {
@@ -75,7 +83,8 @@ static char *cpuname_lower[] = {
"tsv110",
"emag8180",
"neoversen1",
"thunderx3t110"
"thunderx3t110",
"vortex"
};

int get_feature(char *search)
@@ -198,6 +207,10 @@ int detect(void)

}
#else
#ifdef DARWIN
sysctlbyname("hw.cpufamily",&value,&length,NULL,0);
if (value ==131287967) return CPU_VORTEX;
#endif
return CPU_ARMV8;
#endif

@@ -247,7 +260,10 @@ int n=0;

printf("#define NUM_CORES %d\n",n);
#endif

#ifdef DARWIN
sysctlbyname("hw.physicalcpu_max",&value,&length,NULL,0);
printf("#define NUM_CORES %d\n",value);
#endif
}


@@ -398,6 +414,19 @@ void get_cpuconfig(void)
printf("#define DTB_DEFAULT_ENTRIES 64 \n");
printf("#define DTB_SIZE 4096 \n");
break;
#ifdef DARWIN
case CPU_VORTEX:
printf("#define VORTEX \n");
sysctlbyname("hw.l1icachesize",&value,&length,NULL,0);
printf("#define L1_CODE_SIZE %d \n",value);
sysctlbyname("hw.cachelinesize",&value,&length,NULL,0);
printf("#define L1_CODE_LINESIZE %d \n",value);
sysctlbyname("hw.l1dcachesize",&value,&length,NULL,0);
printf("#define L1_DATA_SIZE %d \n",value);
sysctlbyname("hw.l2dcachesize",&value,&length,NULL,0);
printf("#define L2_DATA_SIZE %d \n",value);
break;
#endif
}
get_cpucount();
}


+ 1
- 0
kernel/arm64/KERNEL.VORTEX View File

@@ -0,0 +1 @@
include $(KERNELDIR)/KERNEL.ARMV8

+ 2
- 0
kernel/x86_64/KERNEL.HASWELL View File

@@ -100,3 +100,5 @@ ZTRSMKERNEL_RT = ../generic/trsm_kernel_RT.c
CGEMM3MKERNEL = cgemm3m_kernel_8x4_haswell.c
ZGEMM3MKERNEL = zgemm3m_kernel_4x4_haswell.c

SASUMKERNEL = sasum.c
DASUMKERNEL = dasum.c

+ 82
- 0
kernel/x86_64/dasum.c View File

@@ -0,0 +1,82 @@
#include "common.h"

#ifndef ABS_K
#define ABS_K(a) ((a) > 0 ? (a) : (-(a)))
#endif

#if defined(SKYLAKEX)
#include "dasum_microk_skylakex-2.c"
#elif defined(HASWELL)
#include "dasum_microk_haswell-2.c"
#endif

#ifndef HAVE_DASUM_KERNEL
static FLOAT dasum_kernel(BLASLONG n, FLOAT *x1)
{

BLASLONG i=0;
BLASLONG n_8 = n & -8;
FLOAT *x = x1;
FLOAT temp0, temp1, temp2, temp3;
FLOAT temp4, temp5, temp6, temp7;
FLOAT sum0 = 0.0;
FLOAT sum1 = 0.0;
FLOAT sum2 = 0.0;
FLOAT sum3 = 0.0;
FLOAT sum4 = 0.0;
while (i < n_8) {
temp0 = ABS_K(x[0]);
temp1 = ABS_K(x[1]);
temp2 = ABS_K(x[2]);
temp3 = ABS_K(x[3]);
temp4 = ABS_K(x[4]);
temp5 = ABS_K(x[5]);
temp6 = ABS_K(x[6]);
temp7 = ABS_K(x[7]);
sum0 += temp0;
sum1 += temp1;
sum2 += temp2;
sum3 += temp3;
sum0 += temp4;
sum1 += temp5;
sum2 += temp6;
sum3 += temp7;
x+=8;
i+=8;
}

while (i < n) {
sum4 += ABS_K(x1[i]);
i++;
}

return sum0+sum1+sum2+sum3+sum4;
}

#endif

FLOAT CNAME(BLASLONG n, FLOAT *x, BLASLONG inc_x)
{
BLASLONG i=0;
FLOAT sumf = 0.0;

if (n <= 0 || inc_x <= 0) return(sumf);

if ( inc_x == 1 ) {
sumf = dasum_kernel(n, x);
}
else {
n *= inc_x;
while(i < n) {
sumf += ABS_K(x[i]);
i += inc_x;
}
}
return(sumf);
}


+ 86
- 0
kernel/x86_64/dasum_microk_haswell-2.c View File

@@ -0,0 +1,86 @@
#if (( defined(__GNUC__) && __GNUC__ > 6 ) || (defined(__clang__) && __clang_major__ >= 6)) && defined(__AVX2__)

#define HAVE_DASUM_KERNEL

#include <immintrin.h>
#include <stdint.h>

#ifndef ABS_K
#define ABS_K(a) ((a) > 0 ? (a) : (-(a)))
#endif

static FLOAT dasum_kernel(BLASLONG n, FLOAT *x1)
{
BLASLONG i = 0;
FLOAT sumf = 0.0;

if (n >= 256) {
BLASLONG align_256 = ((32 - ((uintptr_t)x1 & (uintptr_t)0x1f)) >> 3) & 0x3;

for (i = 0; i < align_256; i++) {
sumf += ABS_K(x1[i]);
}

n -= align_256;
x1 += align_256;
}

BLASLONG tail_index_SSE = n&(~7);
BLASLONG tail_index_AVX2 = n&(~255);

if (n >= 256) {
__m256d accum_0, accum_1, accum_2, accum_3;

accum_0 = _mm256_setzero_pd();
accum_1 = _mm256_setzero_pd();
accum_2 = _mm256_setzero_pd();
accum_3 = _mm256_setzero_pd();

__m256i abs_mask = _mm256_set1_epi64x(0x7fffffffffffffff);
for (i = 0; i < tail_index_AVX2; i += 16) {
accum_0 += (__m256d)_mm256_and_si256(_mm256_load_si256(&x1[i+ 0]), abs_mask);
accum_1 += (__m256d)_mm256_and_si256(_mm256_load_si256(&x1[i+ 4]), abs_mask);
accum_2 += (__m256d)_mm256_and_si256(_mm256_load_si256(&x1[i+ 8]), abs_mask);
accum_3 += (__m256d)_mm256_and_si256(_mm256_load_si256(&x1[i+12]), abs_mask);
}

accum_0 = accum_0 + accum_1 + accum_2 + accum_3;

__m128d half_accum0;
half_accum0 = _mm_add_pd(_mm256_extractf128_pd(accum_0, 0), _mm256_extractf128_pd(accum_0, 1));

half_accum0 = _mm_hadd_pd(half_accum0, half_accum0);

sumf += half_accum0[0];
}
if (n >= 8) {
__m128d accum_20, accum_21, accum_22, accum_23;
accum_20 = _mm_setzero_pd();
accum_21 = _mm_setzero_pd();
accum_22 = _mm_setzero_pd();
accum_23 = _mm_setzero_pd();

__m128i abs_mask2 = _mm_set1_epi64x(0x7fffffffffffffff);
for (i = tail_index_AVX2; i < tail_index_SSE; i += 8) {
accum_20 += (__m128d)_mm_and_si128(_mm_loadu_si128(&x1[i + 0]), abs_mask2);
accum_21 += (__m128d)_mm_and_si128(_mm_loadu_si128(&x1[i + 2]), abs_mask2);
accum_22 += (__m128d)_mm_and_si128(_mm_loadu_si128(&x1[i + 4]), abs_mask2);
accum_23 += (__m128d)_mm_and_si128(_mm_loadu_si128(&x1[i + 6]), abs_mask2);
}

accum_20 = accum_20 + accum_21 + accum_22 + accum_23;
__m128d half_accum20;
half_accum20 = _mm_hadd_pd(accum_20, accum_20);

sumf += half_accum20[0];
}
for (i = tail_index_SSE; i < n; ++i) {
sumf += ABS_K(x1[i]);
}

return sumf;

}
#endif

+ 80
- 0
kernel/x86_64/dasum_microk_skylakex-2.c View File

@@ -0,0 +1,80 @@
/* need a new enough GCC for avx512 support */
#if (( defined(__GNUC__) && __GNUC__ > 6 && defined(__AVX512CD__)) || (defined(__clang__) && __clang_major__ >= 9))

#define HAVE_DASUM_KERNEL 1

#include <immintrin.h>

#include <stdint.h>

#ifndef ABS_K
#define ABS_K(a) ((a) > 0 ? (a) : (-(a)))
#endif

static FLOAT dasum_kernel(BLASLONG n, FLOAT *x1)
{
BLASLONG i = 0;
FLOAT sumf = 0.0;

if (n >= 256) {
BLASLONG align_512 = ((64 - ((uintptr_t)x1 & (uintptr_t)0x3f)) >> 3) & 0x7;

for (i = 0; i < align_512; i++) {
sumf += ABS_K(x1[i]);
}
n -= align_512;
x1 += align_512;
}

BLASLONG tail_index_SSE = n&(~7);
BLASLONG tail_index_AVX512 = n&(~255);

//
if ( n >= 256 ) {

__m512d accum_0, accum_1, accum_2, accum_3;
accum_0 = _mm512_setzero_pd();
accum_1 = _mm512_setzero_pd();
accum_2 = _mm512_setzero_pd();
accum_3 = _mm512_setzero_pd();
for (i = 0; i < tail_index_AVX512; i += 32) {
accum_0 += _mm512_abs_pd(_mm512_load_pd(&x1[i + 0]));
accum_1 += _mm512_abs_pd(_mm512_load_pd(&x1[i + 8]));
accum_2 += _mm512_abs_pd(_mm512_load_pd(&x1[i +16]));
accum_3 += _mm512_abs_pd(_mm512_load_pd(&x1[i +24]));
}

accum_0 = accum_0 + accum_1 + accum_2 + accum_3;
sumf += _mm512_reduce_add_pd(accum_0);
}

if (n >= 8) {
__m128d accum_20, accum_21, accum_22, accum_23;
accum_20 = _mm_setzero_pd();
accum_21 = _mm_setzero_pd();
accum_22 = _mm_setzero_pd();
accum_23 = _mm_setzero_pd();

__m128i abs_mask2 = _mm_set1_epi64x(0x7fffffffffffffff);
for (i = tail_index_AVX512; i < tail_index_SSE; i += 8) {
accum_20 += (__m128d)_mm_and_si128(_mm_loadu_si128(&x1[i + 0]), abs_mask2);
accum_21 += (__m128d)_mm_and_si128(_mm_loadu_si128(&x1[i + 2]), abs_mask2);
accum_22 += (__m128d)_mm_and_si128(_mm_loadu_si128(&x1[i + 4]), abs_mask2);
accum_23 += (__m128d)_mm_and_si128(_mm_loadu_si128(&x1[i + 6]), abs_mask2);
}

accum_20 = accum_20 + accum_21 + accum_22 + accum_23;
__m128d half_accum20;
half_accum20 = _mm_hadd_pd(accum_20, accum_20);

sumf += half_accum20[0];
}

for (i = tail_index_SSE; i < n; ++i) {
sumf += ABS_K(x1[i]);
}

return sumf;
}
#endif

+ 90
- 0
kernel/x86_64/sasum.c View File

@@ -0,0 +1,90 @@
#include "common.h"

#if defined(DOUBLE)
#error supports float only
#else
#ifndef ABS_K
#define ABS_K(a) ((a) > 0 ? (a) : (-(a)))
#endif

#endif

#if defined(SKYLAKEX)
#include "sasum_microk_skylakex-2.c"
#elif defined(HASWELL)
#include "sasum_microk_haswell-2.c"
#endif

#ifndef HAVE_SASUM_KERNEL

static FLOAT sasum_kernel(BLASLONG n, FLOAT *x1)
{

BLASLONG i=0;
BLASLONG n_8 = n & -8;
FLOAT *x = x1;
FLOAT temp0, temp1, temp2, temp3;
FLOAT temp4, temp5, temp6, temp7;
FLOAT sum0 = 0.0;
FLOAT sum1 = 0.0;
FLOAT sum2 = 0.0;
FLOAT sum3 = 0.0;
FLOAT sum4 = 0.0;

while (i < n_8) {

temp0 = ABS_K(x[0]);
temp1 = ABS_K(x[1]);
temp2 = ABS_K(x[2]);
temp3 = ABS_K(x[3]);
temp4 = ABS_K(x[4]);
temp5 = ABS_K(x[5]);
temp6 = ABS_K(x[6]);
temp7 = ABS_K(x[7]);

sum0 += temp0;
sum1 += temp1;
sum2 += temp2;
sum3 += temp3;

sum0 += temp4;
sum1 += temp5;
sum2 += temp6;
sum3 += temp7;

x+=8;
i+=8;

}

while (i < n) {
sum4 += ABS_K(x1[i]);
i++;
}

return sum0+sum1+sum2+sum3+sum4;
}

#endif

FLOAT CNAME(BLASLONG n, FLOAT *x, BLASLONG inc_x)
{
BLASLONG i=0;
FLOAT sumf = 0.0;

if (n <= 0 || inc_x <= 0) return(sumf);

if ( inc_x == 1 ) {
sumf = sasum_kernel(n, x);
}
else {

n *= inc_x;
while(i < n) {
sumf += ABS_K(x[i]);
i += inc_x;
}

}
return(sumf);
}

+ 82
- 0
kernel/x86_64/sasum_microk_haswell-2.c View File

@@ -0,0 +1,82 @@
#if (( defined(__GNUC__) && __GNUC__ > 6 ) || (defined(__clang__) && __clang_major__ >= 6)) && defined(__AVX2__)

#define HAVE_SASUM_KERNEL 1

#include <immintrin.h>
#include <stdint.h>

#ifndef ABS_K
#define ABS_K(a) ((a) > 0 ? (a) : (-(a)))
#endif

static FLOAT sasum_kernel(BLASLONG n, FLOAT *x1)
{
BLASLONG i = 0;
FLOAT sumf = 0.0;

if (n >= 256) {
BLASLONG align_256 = ((32 - ((uintptr_t)x1 & (uintptr_t)0x1f)) >> 2) & 0x7;

for (i = 0; i < align_256; i++) {
sumf += ABS_K(x1[i]);
}

n -= align_256;
x1 += align_256;
}

BLASLONG tail_index_SSE = n&(~7);
BLASLONG tail_index_AVX2 = n&(~255);

if (n >= 256) {
__m256 accum_0, accum_1, accum_2, accum_3;
accum_0 = _mm256_setzero_ps();
accum_1 = _mm256_setzero_ps();
accum_2 = _mm256_setzero_ps();
accum_3 = _mm256_setzero_ps();

__m256i abs_mask = _mm256_set1_epi32(0x7fffffff);
for (i = 0; i < tail_index_AVX2; i += 32) {
accum_0 += (__m256)_mm256_and_si256(_mm256_load_si256(&x1[i+ 0]), abs_mask);
accum_1 += (__m256)_mm256_and_si256(_mm256_load_si256(&x1[i+ 8]), abs_mask);
accum_2 += (__m256)_mm256_and_si256(_mm256_load_si256(&x1[i+16]), abs_mask);
accum_3 += (__m256)_mm256_and_si256(_mm256_load_si256(&x1[i+24]), abs_mask);
}

accum_0 = accum_0 + accum_1 + accum_2 + accum_3;
__m128 half_accum0;
half_accum0 = _mm_add_ps(_mm256_extractf128_ps(accum_0, 0), _mm256_extractf128_ps(accum_0, 1));

half_accum0 = _mm_hadd_ps(half_accum0, half_accum0);
half_accum0 = _mm_hadd_ps(half_accum0, half_accum0);

sumf += half_accum0[0];
}
if (n >= 8) {
__m128 accum_20, accum_21;
accum_20 = _mm_setzero_ps();
accum_21 = _mm_setzero_ps();

__m128i abs_mask2 = _mm_set1_epi32(0x7fffffff);
for (i = tail_index_AVX2; i < tail_index_SSE; i += 8) {
accum_20 += (__m128)_mm_and_si128(_mm_loadu_si128(&x1[i + 0]), abs_mask2);
accum_21 += (__m128)_mm_and_si128(_mm_loadu_si128(&x1[i + 4]), abs_mask2);
}
accum_20 += accum_21;
accum_20 = _mm_hadd_ps(accum_20, accum_20);
accum_20 = _mm_hadd_ps(accum_20, accum_20);
sumf += accum_20[0];
}

for (i = tail_index_SSE; i < n; ++i) {
sumf += ABS_K(x1[i]);
}

return sumf;
}
#endif

+ 73
- 0
kernel/x86_64/sasum_microk_skylakex-2.c View File

@@ -0,0 +1,73 @@
/* need a new enough GCC for avx512 support */
#if (( defined(__GNUC__) && __GNUC__ > 6 && defined(__AVX512CD__)) || (defined(__clang__) && __clang_major__ >= 9))

#define HAVE_SASUM_KERNEL 1

#ifndef ABS_K
#define ABS_K(a) ((a) > 0 ? (a) : (-(a)))
#endif

#include <immintrin.h>
#include <stdint.h>

static FLOAT sasum_kernel(BLASLONG n, FLOAT *x1)
{
BLASLONG i = 0;
FLOAT sumf = 0.0;

if (n >= 256) {
BLASLONG align_512 = ((64 - ((uintptr_t)x1 & (uintptr_t)0x3f)) >> 2) & 0xf;

for (i = 0; i < align_512; i++) {
sumf += ABS_K(x1[i]);
}
n -= align_512;
x1 += align_512;
}

BLASLONG tail_index_SSE = n&(~7);
BLASLONG tail_index_AVX512 = n&(~255);

if (n >= 256) {
__m512 accum_0, accum_1, accum_2, accum_3;
accum_0 = _mm512_setzero_ps();
accum_1 = _mm512_setzero_ps();
accum_2 = _mm512_setzero_ps();
accum_3 = _mm512_setzero_ps();

for (i = 0; i < tail_index_AVX512; i += 64) {
accum_0 += _mm512_abs_ps(_mm512_load_ps(&x1[i + 0]));
accum_1 += _mm512_abs_ps(_mm512_load_ps(&x1[i +16]));
accum_2 += _mm512_abs_ps(_mm512_load_ps(&x1[i +32]));
accum_3 += _mm512_abs_ps(_mm512_load_ps(&x1[i +48]));
}

accum_0 = accum_0 + accum_1 + accum_2 + accum_3;
sumf += _mm512_reduce_add_ps(accum_0);
}

if (n >= 8) {
__m128 accum_20, accum_21;
accum_20 = _mm_setzero_ps();
accum_21 = _mm_setzero_ps();

__m128i abs_mask2 = _mm_set1_epi32(0x7fffffff);
for (i = tail_index_AVX512; i < tail_index_SSE; i += 8) {
accum_20 += (__m128)_mm_and_si128(_mm_loadu_si128(&x1[i + 0]), abs_mask2);
accum_21 += (__m128)_mm_and_si128(_mm_loadu_si128(&x1[i + 4]), abs_mask2);
}
accum_20 += accum_21;
accum_20 = _mm_hadd_ps(accum_20, accum_20);
accum_20 = _mm_hadd_ps(accum_20, accum_20);
sumf += accum_20[0];
}

for (i = tail_index_SSE; i < n; i++) {
sumf += ABS_K(x1[i]);
}

return sumf;
}
#endif

+ 4
- 4
lapack-netlib/TESTING/EIG/cchkhb2stg.f View File

@@ -680,8 +680,8 @@
* the one from above. Compare it with D1 computed
* using the DSBTRD.
*
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SD, 1 )
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SE, 1 )
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SD, N )
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SE, N )
CALL CLACPY( ' ', K+1, N, A, LDA, U, LDU )
LH = MAX(1, 4*N)
LW = LWORK - LH
@@ -753,8 +753,8 @@
* the one from above. Compare it with D1 computed
* using the DSBTRD.
*
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SD, 1 )
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SE, 1 )
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SD, N )
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SE, N )
CALL CLACPY( ' ', K+1, N, A, LDA, U, LDU )
LH = MAX(1, 4*N)
LW = LWORK - LH


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