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linpack.c
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linpack.c
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/* gcc linpack.c cpuidc64.o cpuida64.o -m64 -lrt -lc -lm -o linpack
*
* Linpack 100x100 Benchmark In C/C++ For PCs
*
* Different compilers can produce different floating point numeric
* results, probably due to compiling instructions in a different
* sequence. As the program checks these, they may need to be changed.
* The log file indicates non-standard results and these values can
* be copied and pasted into this program. See // Values near the
* end of main().
*
* Different compilers do not optimise the code in the same way.
* This can lead to wide variations in benchmark speeds. See results
* with MS6 compiler ID and compare with those from same CPUs from
* the Watcom compiler generated code.
*
***************************************************************************
*/
#define _CRT_SECURE_NO_WARNINGS 1
#ifdef WIN32
#include <Windows.h>
#else
#include <sys/time.h>
#endif
#define UNROLL
#define DP
#ifdef SP
#define REAL float
#define ZERO 0.0
#define ONE 1.0
#define PREC "Single"
#endif
#ifdef DP
#define REAL double
#define ZERO 0.0e0
#define ONE 1.0e0
#define PREC "Double"
#endif
#ifdef ROLL
#define ROLLING "Rolled"
#endif
#ifdef UNROLL
#define ROLLING "Unrolled"
#endif
// VERSION
#ifdef CNNT
#define options "Non-optimised"
#define opt "0"
#else
// #define options "Optimised"
#define options "Opt 3 64 Bit"
#define opt "1"
#endif
#define NTIMES 10
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <time.h>
/* this is truly rank, but it's minimally invasive, and lifted in part from the STREAM scores */
static double secs;
#ifndef WIN32
double mysecond()
{
struct timeval tp;
struct timezone tzp;
int i;
i = gettimeofday(&tp,&tzp);
return ( (double) tp.tv_sec + (double) tp.tv_usec * 1.e-6 );
}
#else
double mysecond()
{
static LARGE_INTEGER freq = {0};
LARGE_INTEGER count = {0};
if(freq.QuadPart == 0LL) {
QueryPerformanceFrequency(&freq);
}
QueryPerformanceCounter(&count);
return (double)count.QuadPart / (double)freq.QuadPart;
}
#endif
void start_time()
{
secs = mysecond();
}
void end_time()
{
secs = mysecond() - secs;
}
void print_time (int row);
void matgen (REAL a[], int lda, int n, REAL b[], REAL *norma);
void dgefa (REAL a[], int lda, int n, int ipvt[], int *info);
void dgesl (REAL a[],int lda,int n,int ipvt[],REAL b[],int job);
void dmxpy (int n1, REAL y[], int n2, int ldm, REAL x[], REAL m[]);
void daxpy (int n, REAL da, REAL dx[], int incx, REAL dy[], int incy);
REAL epslon (REAL x);
int idamax (int n, REAL dx[], int incx);
void dscal (int n, REAL da, REAL dx[], int incx);
REAL ddot (int n, REAL dx[], int incx, REAL dy[], int incy);
static REAL atime[9][15];
double runSecs = 1;
int main (int argc, char *argv[])
{
static REAL aa[200*200],a[200*201],b[200],x[200];
REAL cray,ops,total,norma,normx;
REAL resid,residn,eps,tm2,epsn,x1,x2;
REAL mflops;
static int ipvt[200],n,i,j,ntimes,info,lda,ldaa;
int endit, pass, loop;
REAL overhead1, overhead2, time2;
REAL max1, max2;
char was[5][20];
char expect[5][20];
char title[5][20];
int errors;
printf("\n");
printf("##########################################\n");
lda = 201;
ldaa = 200;
cray = .056;
n = 100;
fprintf(stdout, "%s ", ROLLING);
fprintf(stdout, "%s ", PREC);
fprintf(stdout,"Precision Linpack Benchmark - PC Version in 'C/C++'\n\n");
fprintf(stdout,"Optimisation %s\n\n",options);
ops = (2.0e0*(n*n*n))/3.0 + 2.0*(n*n);
matgen(a,lda,n,b,&norma);
start_time();
dgefa(a,lda,n,ipvt,&info);
end_time();
atime[0][0] = secs;
start_time();
dgesl(a,lda,n,ipvt,b,0);
end_time();
atime[1][0] = secs;
total = atime[0][0] + atime[1][0];
/* compute a residual to verify results. */
for (i = 0; i < n; i++) {
x[i] = b[i];
}
matgen(a,lda,n,b,&norma);
for (i = 0; i < n; i++) {
b[i] = -b[i];
}
dmxpy(n,b,n,lda,x,a);
resid = 0.0;
normx = 0.0;
for (i = 0; i < n; i++) {
resid = (resid > fabs((double)b[i]))
? resid : fabs((double)b[i]);
normx = (normx > fabs((double)x[i]))
? normx : fabs((double)x[i]);
}
eps = epslon(ONE);
residn = resid/( n*norma*normx*eps );
epsn = eps;
x1 = x[0] - 1;
x2 = x[n-1] - 1;
printf("norm resid resid machep");
printf(" x[0]-1 x[n-1]-1\n");
printf("%6.1f %17.8e%17.8e%17.8e%17.8e\n\n",
(double)residn, (double)resid, (double)epsn,
(double)x1, (double)x2);
printf("Times are reported for matrices of order %5d\n",n);
printf("1 pass times for array with leading dimension of%5d\n\n",lda);
printf(" dgefa dgesl total Mflops unit");
printf(" ratio\n");
atime[2][0] = total;
if (total > 0.0)
{
atime[3][0] = ops/(1.0e6*total);
atime[4][0] = 2.0/atime[3][0];
}
else
{
atime[3][0] = 0.0;
atime[4][0] = 0.0;
}
atime[5][0] = total/cray;
print_time(0);
/************************************************************************
* Calculate overhead of executing matgen procedure *
************************************************************************/
printf("\nCalculating matgen overhead\n");
pass = -20;
loop = NTIMES;
do
{
start_time();
pass = pass + 1;
for ( i = 0 ; i < loop ; i++)
{
matgen(a,lda,n,b,&norma);
}
end_time();
overhead1 = secs;
printf("%10d times %6.2f seconds\n", loop, overhead1);
if (overhead1 > runSecs)
{
pass = 0;
}
if (pass < 0)
{
if (overhead1 < 0.1)
{
loop = loop * 10;
}
else
{
loop = loop * 2;
}
}
}
while (pass < 0);
overhead1 = overhead1 / (double)loop;
printf("Overhead for 1 matgen %12.5f seconds\n\n", overhead1);
/************************************************************************
* Calculate matgen/dgefa passes for runSecs seconds *
************************************************************************/
printf("Calculating matgen/dgefa passes for %d seconds\n", (int)runSecs);
pass = -20;
ntimes = NTIMES;
do
{
start_time();
pass = pass + 1;
for ( i = 0 ; i < ntimes ; i++)
{
matgen(a,lda,n,b,&norma);
dgefa(a,lda,n,ipvt,&info );
}
end_time();
time2 = secs;
printf("%10d times %6.2f seconds\n", ntimes, time2);
if (time2 > runSecs)
{
pass = 0;
}
if (pass < 0)
{
if (time2 < 0.1)
{
ntimes = ntimes * 10;
}
else
{
ntimes = ntimes * 2;
}
}
}
while (pass < 0);
ntimes = (int)(runSecs * (double)ntimes / time2);
if (ntimes == 0) ntimes = 1;
printf("Passes used %10d \n\n", ntimes);
printf("Times for array with leading dimension of%4d\n\n",lda);
printf(" dgefa dgesl total Mflops unit");
printf(" ratio\n");
/************************************************************************
* Execute 5 passes *
************************************************************************/
tm2 = ntimes * overhead1;
atime[3][6] = 0;
for (j=1 ; j<6 ; j++)
{
start_time();
for (i = 0; i < ntimes; i++)
{
matgen(a,lda,n,b,&norma);
dgefa(a,lda,n,ipvt,&info );
}
end_time();
atime[0][j] = (secs - tm2)/ntimes;
start_time();
for (i = 0; i < ntimes; i++)
{
dgesl(a,lda,n,ipvt,b,0);
}
end_time();
atime[1][j] = secs/ntimes;
total = atime[0][j] + atime[1][j];
atime[2][j] = total;
atime[3][j] = ops/(1.0e6*total);
atime[4][j] = 2.0/atime[3][j];
atime[5][j] = total/cray;
atime[3][6] = atime[3][6] + atime[3][j];
print_time(j);
}
atime[3][6] = atime[3][6] / 5.0;
printf("Average %11.2f\n",
(double)atime[3][6]);
printf("\nCalculating matgen2 overhead\n");
/************************************************************************
* Calculate overhead of executing matgen procedure *
************************************************************************/
start_time();
for ( i = 0 ; i < loop ; i++)
{
matgen(aa,ldaa,n,b,&norma);
}
end_time();
overhead2 = secs;
overhead2 = overhead2 / (double)loop;
printf("Overhead for 1 matgen %12.5f seconds\n\n", overhead2);
printf("Times for array with leading dimension of%4d\n\n",ldaa);
printf(" dgefa dgesl total Mflops unit");
printf(" ratio\n");
/************************************************************************
* Execute 5 passes *
************************************************************************/
tm2 = ntimes * overhead2;
atime[3][12] = 0;
for (j=7 ; j<12 ; j++)
{
start_time();
for (i = 0; i < ntimes; i++)
{
matgen(aa,ldaa,n,b,&norma);
dgefa(aa,ldaa,n,ipvt,&info );
}
end_time();
atime[0][j] = (secs - tm2)/ntimes;
start_time();
for (i = 0; i < ntimes; i++)
{
dgesl(aa,ldaa,n,ipvt,b,0);
}
end_time();
atime[1][j] = secs/ntimes;
total = atime[0][j] + atime[1][j];
atime[2][j] = total;
atime[3][j] = ops/(1.0e6*total);
atime[4][j] = 2.0/atime[3][j];
atime[5][j] = total/cray;
atime[3][12] = atime[3][12] + atime[3][j];
print_time(j);
}
atime[3][12] = atime[3][12] / 5.0;
printf("Average %11.2f\n",
(double)atime[3][12]);
/************************************************************************
* Use minimum average as overall Mflops rating *
************************************************************************/
mflops = atime[3][6];
if (atime[3][12] < mflops) mflops = atime[3][12];
printf("\n");
printf( "%s ", ROLLING);
printf( "%s ", PREC);
printf(" Precision %11.2f Mflops \n\n",mflops);
max1 = 0;
for (i=1 ; i<6 ; i++)
{
if (atime[3][i] > max1) max1 = atime[3][i];
}
max2 = 0;
for (i=7 ; i<12 ; i++)
{
if (atime[3][i] > max2) max2 = atime[3][i];
}
if (max1 < max2) max2 = max1;
sprintf(was[0], "%16.1f",(double)residn);
sprintf(was[1], "%16.8e",(double)resid);
sprintf(was[2], "%16.8e",(double)epsn);
sprintf(was[3], "%16.8e",(double)x1);
sprintf(was[4], "%16.8e",(double)x2);
/*
// Values for Watcom
sprintf(expect[0], " 0.4");
sprintf(expect[1], " 7.41628980e-014");
sprintf(expect[2], " 1.00000000e-015");
sprintf(expect[3], "-1.49880108e-014");
sprintf(expect[4], "-1.89848137e-014");
// Values for Visual C++
sprintf(expect[0], " 1.7");
sprintf(expect[1], " 7.41628980e-014");
sprintf(expect[2], " 2.22044605e-016");
sprintf(expect[3], "-1.49880108e-014");
sprintf(expect[4], "-1.89848137e-014");
// Values for Ubuntu GCC 32 Bit
sprintf(expect[0], " 1.9");
sprintf(expect[1], " 8.39915160e-14");
sprintf(expect[2], " 2.22044605e-16");
sprintf(expect[3], " -6.22835117e-14");
sprintf(expect[4], " -4.16333634e-14");
*/
// Values for Ubuntu GCC 32 Bit
sprintf(expect[0], " 1.7");
sprintf(expect[1], " 7.41628980e-14");
sprintf(expect[2], " 2.22044605e-16");
sprintf(expect[3], " -1.49880108e-14");
sprintf(expect[4], " -1.89848137e-14");
sprintf(title[0], "norm. resid");
sprintf(title[1], "resid ");
sprintf(title[2], "machep ");
sprintf(title[3], "x[0]-1 ");
sprintf(title[4], "x[n-1]-1 ");
if (strtol(opt, NULL, 10) == 0)
{
sprintf(expect[2], " 8.88178420e-016");
}
errors = 0;
printf ("\n");
}
/*----------------------*/
void print_time (int row)
{
printf("%11.5f%11.5f%11.5f%11.2f%11.4f%11.4f\n", (double)atime[0][row],
(double)atime[1][row], (double)atime[2][row], (double)atime[3][row],
(double)atime[4][row], (double)atime[5][row]);
return;
}
/*----------------------*/
void matgen (REAL a[], int lda, int n, REAL b[], REAL *norma)
/* We would like to declare a[][lda], but c does not allow it. In this
function, references to a[i][j] are written a[lda*i+j]. */
{
int init, i, j;
init = 1325;
*norma = 0.0;
for (j = 0; j < n; j++) {
for (i = 0; i < n; i++) {
init = 3125*init % 65536;
a[lda*j+i] = (init - 32768.0)/16384.0;
*norma = (a[lda*j+i] > *norma) ? a[lda*j+i] : *norma;
/* alternative for some compilers
if (fabs(a[lda*j+i]) > *norma) *norma = fabs(a[lda*j+i]);
*/
}
}
for (i = 0; i < n; i++) {
b[i] = 0.0;
}
for (j = 0; j < n; j++) {
for (i = 0; i < n; i++) {
b[i] = b[i] + a[lda*j+i];
}
}
return;
}
/*----------------------*/
void dgefa(REAL a[], int lda, int n, int ipvt[], int *info)
/* We would like to declare a[][lda], but c does not allow it. In this
function, references to a[i][j] are written a[lda*i+j]. */
/*
dgefa factors a double precision matrix by gaussian elimination.
dgefa is usually called by dgeco, but it can be called
directly with a saving in time if rcond is not needed.
(time for dgeco) = (1 + 9/n)*(time for dgefa) .
on entry
a REAL precision[n][lda]
the matrix to be factored.
lda integer
the leading dimension of the array a .
n integer
the order of the matrix a .
on return
a an upper triangular matrix and the multipliers
which were used to obtain it.
the factorization can be written a = l*u where
l is a product of permutation and unit lower
triangular matrices and u is upper triangular.
ipvt integer[n]
an integer vector of pivot indices.
info integer
= 0 normal value.
= k if u[k][k] .eq. 0.0 . this is not an error
condition for this subroutine, but it does
indicate that dgesl or dgedi will divide by zero
if called. use rcond in dgeco for a reliable
indication of singularity.
linpack. this version dated 08/14/78 .
cleve moler, university of new mexico, argonne national lab.
functions
blas daxpy,dscal,idamax
*/
{
/* internal variables */
REAL t;
int j,k,kp1,l,nm1;
/* gaussian elimination with partial pivoting */
*info = 0;
nm1 = n - 1;
if (nm1 >= 0) {
for (k = 0; k < nm1; k++) {
kp1 = k + 1;
/* find l = pivot index */
l = idamax(n-k,&a[lda*k+k],1) + k;
ipvt[k] = l;
/* zero pivot implies this column already
triangularized */
if (a[lda*k+l] != ZERO) {
/* interchange if necessary */
if (l != k) {
t = a[lda*k+l];
a[lda*k+l] = a[lda*k+k];
a[lda*k+k] = t;
}
/* compute multipliers */
t = -ONE/a[lda*k+k];
dscal(n-(k+1),t,&a[lda*k+k+1],1);
/* row elimination with column indexing */
for (j = kp1; j < n; j++) {
t = a[lda*j+l];
if (l != k) {
a[lda*j+l] = a[lda*j+k];
a[lda*j+k] = t;
}
daxpy(n-(k+1),t,&a[lda*k+k+1],1,
&a[lda*j+k+1],1);
}
}
else {
*info = k;
}
}
}
ipvt[n-1] = n-1;
if (a[lda*(n-1)+(n-1)] == ZERO) *info = n-1;
return;
}
/*----------------------*/
void dgesl(REAL a[],int lda,int n,int ipvt[],REAL b[],int job )
/* We would like to declare a[][lda], but c does not allow it. In this
function, references to a[i][j] are written a[lda*i+j]. */
/*
dgesl solves the double precision system
a * x = b or trans(a) * x = b
using the factors computed by dgeco or dgefa.
on entry
a double precision[n][lda]
the output from dgeco or dgefa.
lda integer
the leading dimension of the array a .
n integer
the order of the matrix a .
ipvt integer[n]
the pivot vector from dgeco or dgefa.
b double precision[n]
the right hand side vector.
job integer
= 0 to solve a*x = b ,
= nonzero to solve trans(a)*x = b where
trans(a) is the transpose.
on return
b the solution vector x .
error condition
a division by zero will occur if the input factor contains a
zero on the diagonal. technically this indicates singularity
but it is often caused by improper arguments or improper
setting of lda . it will not occur if the subroutines are
called correctly and if dgeco has set rcond .gt. 0.0
or dgefa has set info .eq. 0 .
to compute inverse(a) * c where c is a matrix
with p columns
dgeco(a,lda,n,ipvt,rcond,z)
if (!rcond is too small){
for (j=0,j<p,j++)
dgesl(a,lda,n,ipvt,c[j][0],0);
}
linpack. this version dated 08/14/78 .
cleve moler, university of new mexico, argonne national lab.
functions
blas daxpy,ddot
*/
{
/* internal variables */
REAL t;
int k,kb,l,nm1;
nm1 = n - 1;
if (job == 0) {
/* job = 0 , solve a * x = b
first solve l*y = b */
if (nm1 >= 1) {
for (k = 0; k < nm1; k++) {
l = ipvt[k];
t = b[l];
if (l != k){
b[l] = b[k];
b[k] = t;
}
daxpy(n-(k+1),t,&a[lda*k+k+1],1,&b[k+1],1 );
}
}
/* now solve u*x = y */
for (kb = 0; kb < n; kb++) {
k = n - (kb + 1);
b[k] = b[k]/a[lda*k+k];
t = -b[k];
daxpy(k,t,&a[lda*k+0],1,&b[0],1 );
}
}
else {
/* job = nonzero, solve trans(a) * x = b
first solve trans(u)*y = b */
for (k = 0; k < n; k++) {
t = ddot(k,&a[lda*k+0],1,&b[0],1);
b[k] = (b[k] - t)/a[lda*k+k];
}
/* now solve trans(l)*x = y */
if (nm1 >= 1) {
for (kb = 1; kb < nm1; kb++) {
k = n - (kb+1);
b[k] = b[k] + ddot(n-(k+1),&a[lda*k+k+1],1,&b[k+1],1);
l = ipvt[k];
if (l != k) {
t = b[l];
b[l] = b[k];
b[k] = t;
}
}
}
}
return;
}
/*----------------------*/
void daxpy(int n, REAL da, REAL dx[], int incx, REAL dy[], int incy)
/*
constant times a vector plus a vector.
jack dongarra, linpack, 3/11/78.
*/
{
int i,ix,iy,m,mp1;
mp1 = 0;
m = 0;
if(n <= 0) return;
if (da == ZERO) return;
if(incx != 1 || incy != 1) {
/* code for unequal increments or equal increments
not equal to 1 */
ix = 0;
iy = 0;
if(incx < 0) ix = (-n+1)*incx;
if(incy < 0)iy = (-n+1)*incy;
for (i = 0;i < n; i++) {
dy[iy] = dy[iy] + da*dx[ix];
ix = ix + incx;
iy = iy + incy;
}
return;
}
/* code for both increments equal to 1 */
#ifdef ROLL
for (i = 0;i < n; i++) {
dy[i] = dy[i] + da*dx[i];
}
#endif
#ifdef UNROLL
m = n % 4;
if ( m != 0) {
for (i = 0; i < m; i++)
dy[i] = dy[i] + da*dx[i];
if (n < 4) return;
}
for (i = m; i < n; i = i + 4) {
dy[i] = dy[i] + da*dx[i];
dy[i+1] = dy[i+1] + da*dx[i+1];
dy[i+2] = dy[i+2] + da*dx[i+2];
dy[i+3] = dy[i+3] + da*dx[i+3];
}
#endif
return;
}
/*----------------------*/
REAL ddot(int n, REAL dx[], int incx, REAL dy[], int incy)
/*
forms the dot product of two vectors.
jack dongarra, linpack, 3/11/78.
*/
{
REAL dtemp;
int i,ix,iy,m,mp1;
mp1 = 0;
m = 0;
dtemp = ZERO;
if(n <= 0) return(ZERO);
if(incx != 1 || incy != 1) {
/* code for unequal increments or equal increments
not equal to 1 */
ix = 0;
iy = 0;
if (incx < 0) ix = (-n+1)*incx;
if (incy < 0) iy = (-n+1)*incy;
for (i = 0;i < n; i++) {
dtemp = dtemp + dx[ix]*dy[iy];
ix = ix + incx;
iy = iy + incy;
}
return(dtemp);
}
/* code for both increments equal to 1 */
#ifdef ROLL
for (i=0;i < n; i++)
dtemp = dtemp + dx[i]*dy[i];
return(dtemp);
#endif
#ifdef UNROLL
m = n % 5;
if (m != 0) {
for (i = 0; i < m; i++)
dtemp = dtemp + dx[i]*dy[i];
if (n < 5) return(dtemp);
}
for (i = m; i < n; i = i + 5) {
dtemp = dtemp + dx[i]*dy[i] +
dx[i+1]*dy[i+1] + dx[i+2]*dy[i+2] +
dx[i+3]*dy[i+3] + dx[i+4]*dy[i+4];
}
return(dtemp);
#endif
}
/*----------------------*/
void dscal(int n, REAL da, REAL dx[], int incx)
/* scales a vector by a constant.
jack dongarra, linpack, 3/11/78.
*/
{
int i,m,mp1,nincx;
mp1 = 0;
m = 0;
if(n <= 0)return;
if(incx != 1) {
/* code for increment not equal to 1 */
nincx = n*incx;
for (i = 0; i < nincx; i = i + incx)
dx[i] = da*dx[i];
return;
}
/* code for increment equal to 1 */
#ifdef ROLL
for (i = 0; i < n; i++)
dx[i] = da*dx[i];
#endif
#ifdef UNROLL
m = n % 5;
if (m != 0) {
for (i = 0; i < m; i++)
dx[i] = da*dx[i];
if (n < 5) return;
}
for (i = m; i < n; i = i + 5){
dx[i] = da*dx[i];
dx[i+1] = da*dx[i+1];
dx[i+2] = da*dx[i+2];
dx[i+3] = da*dx[i+3];
dx[i+4] = da*dx[i+4];
}
#endif
}
/*----------------------*/
int idamax(int n, REAL dx[], int incx)
/*
finds the index of element having max. absolute value.
jack dongarra, linpack, 3/11/78.
*/
{
REAL dmax;
int i, ix, itemp;
if( n < 1 ) return(-1);
if(n ==1 ) return(0);
if(incx != 1) {
/* code for increment not equal to 1 */
ix = 1;
dmax = fabs((double)dx[0]);
ix = ix + incx;
for (i = 1; i < n; i++) {
if(fabs((double)dx[ix]) > dmax) {
itemp = i;
dmax = fabs((double)dx[ix]);
}
ix = ix + incx;
}
}
else {
/* code for increment equal to 1 */
itemp = 0;
dmax = fabs((double)dx[0]);
for (i = 1; i < n; i++) {
if(fabs((double)dx[i]) > dmax) {
itemp = i;
dmax = fabs((double)dx[i]);
}
}
}
return (itemp);