/*
**
** LINPACK.C Linpack benchmark, calculates FLOPS.
** (FLoating Point Operations Per Second)
**
** Translated to C by Bonnie Toy 5/88
**
** Modified by Will Menninger, 10/93, with these features:
** (modified on 2/25/94 to fix a problem with daxpy for
** unequal increments or equal increments not equal to 1.
** Jack Dongarra)
**
** - Defaults to double precision.
** - Averages ROLLed and UNROLLed performance.
** - User selectable array sizes.
** - Automatically does enough repetitions to take at least 10 CPU seconds.
** - Prints machine precision.
** - ANSI prototyping.
**
** To compile: cc -O -o linpack linpack.c -lm
**
**
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include <float.h>
#define DP
#ifdef SP
#define ZERO 0.0
#define ONE 1.0
#define PREC "Single"
#define BASE10DIG FLT_DIG
typedef float REAL;
#endif
#ifdef DP
#define ZERO 0.0e0
#define ONE 1.0e0
#define PREC "Double"
#define BASE10DIG DBL_DIG
typedef double REAL;
#endif
static REAL linpack (long nreps,int arsize);
static void matgen (REAL *a,int lda,int n,REAL *b,REAL *norma);
static void dgefa (REAL *a,int lda,int n,int *ipvt,int *info,int roll);
static void dgesl (REAL *a,int lda,int n,int *ipvt,REAL *b,int job,int roll);
static void daxpy_r (int n,REAL da,REAL *dx,int incx,REAL *dy,int incy);
static REAL ddot_r (int n,REAL *dx,int incx,REAL *dy,int incy);
static void dscal_r (int n,REAL da,REAL *dx,int incx);
static void daxpy_ur (int n,REAL da,REAL *dx,int incx,REAL *dy,int incy);
static REAL ddot_ur (int n,REAL *dx,int incx,REAL *dy,int incy);
static void dscal_ur (int n,REAL da,REAL *dx,int incx);
static int idamax (int n,REAL *dx,int incx);
static REAL second (void);
static void *mempool;
int main(int argc, char *argv[]) {
char buf[80];
int arsize;
long arsize2d,memreq,nreps;
size_t malloc_arg;
int count = 1;
while (count > 0)
{
/* printf("Enter array size (q to quit) [200]: ");
* fgets(buf,79,stdin);
*/
if (argc == 2) {
arsize = atoi(argv[1]);
printf("Size: %d\n", arsize);
}
/*if (buf[0]=='q' || buf[0]=='Q')
* break;
*
*if (buf[0]=='\0' || buf[0]=='\n')
* arsize=200;
*/
else
// arsize=atoi(buf);
arsize=200;
arsize/=2;
arsize*=2;
if (arsize<10) {
printf("Too small.\n");
//continue;
break;
}
arsize2d = (long)arsize*(long)arsize;
memreq=arsize2d*sizeof(REAL)+(long)arsize*sizeof(REAL)+(long)arsize*sizeof(int);
printf("Memory required: %ldK.\n",(memreq+512L)>>10);
malloc_arg=(size_t)memreq;
if (malloc_arg!=memreq || (mempool=malloc(malloc_arg))==NULL)
{
printf("Not enough memory available for given array size.\n\n");
continue;
}
printf("\n\nLINPACK benchmark, %s precision.\n",PREC);
printf("Machine precision: %d digits.\n",BASE10DIG);
printf("Array size %d X %d.\n",arsize,arsize);
printf("Average rolled and unrolled performance:\n\n");
printf(" Reps Time(s) DGEFA DGESL OVERHEAD KFLOPS\n");
printf("----------------------------------------------------\n");
nreps=1;
while (linpack(nreps,arsize)<10.)
nreps*=2;
free(mempool);
printf("\n");
count--;
}
return 0;
}
static REAL linpack(long nreps,int arsize)
{
REAL *a,*b;
REAL norma,t1,kflops,tdgesl,tdgefa,totalt,toverhead,ops;
int *ipvt,n,info,lda;
long i,arsize2d;
lda = arsize;
n = arsize/2;
arsize2d = (long)arsize*(long)arsize;
ops=((2.0*n*n*n)/3.0+2.0*n*n);
a=(REAL *)mempool;
b=a+arsize2d;
ipvt=(int *)&b[arsize];
tdgesl=0;
tdgefa=0;
totalt=second();
for (i=0;i<nreps;i++)
{
matgen(a,lda,n,b,&norma);
t1 = second();
dgefa(a,lda,n,ipvt,&info,1);
tdgefa += second()-t1;
t1 = second();
dgesl(a,lda,n,ipvt,b,0,1);
tdgesl += second()-t1;
}
for (i=0;i<nreps;i++)
{
matgen(a,lda,n,b,&norma);
t1 = second();
dgefa(a,lda,n,ipvt,&info,0);
tdgefa += second()-t1;
t1 = second();
dgesl(a,lda,n,ipvt,b,0,0);
tdgesl += second()-t1;
}
totalt=second()-totalt;
if (totalt<0.5 || tdgefa+tdgesl<0.2)
return(0.);
kflops=2.*nreps*ops/(1000.*(tdgefa+tdgesl));
toverhead=totalt-tdgefa-tdgesl;
if (tdgefa<0.)
tdgefa=0.;
if (tdgesl<0.)
tdgesl=0.;
if (toverhead<0.)
toverhead=0.;
printf("%8ld %6.2f %6.2f%% %6.2f%% %6.2f%% %9.3f\n",
nreps,totalt,100.*tdgefa/totalt,
100.*tdgesl/totalt,100.*toverhead/totalt,
kflops);
return(totalt);
}
/*
** For matgen,
** 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].
*/
static void matgen(REAL *a,int lda,int n,REAL *b,REAL *norma)
{
int init,i,j;
init = 1325;
*norma = 0.0;
for (j = 0; j < n; j++)
for (i = 0; i < n; i++)
{
init = (int)((long)3125*(long)init % 65536L);
a[lda*j+i] = (init - 32768.0)/16384.0;
*norma = (a[lda*j+i] > *norma) ? a[lda*j+i] : *norma;
}
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];
}
/*
**
** DGEFA benchmark
**
** 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
**
*/
static void dgefa(REAL *a,int lda,int n,int *ipvt,int *info,int roll)
{
REAL t;
int idamax(),j,k,kp1,l,nm1;
/* gaussian elimination with partial pivoting */
if (roll)
{
*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_r(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_r(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;
}
else
{
*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_ur(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_ur(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;
}
}
/*
**
** DGESL benchmark
**
** 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
*/
static void dgesl(REAL *a,int lda,int n,int *ipvt,REAL *b,int job,int roll)
{
REAL t;
int k,kb,l,nm1;
if (roll)
{
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_r(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_r(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_r(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_r(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;
}
}
}
}
else
{
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_ur(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_ur(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_ur(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_ur(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;
}
}
}
}
}
/*
** Constant times a vector plus a vector.
** Jack Dongarra, linpack, 3/11/78.
** ROLLED version
*/
static void daxpy_r(int n,REAL da,REAL *dx,int incx,REAL *dy,int incy)
{
int i,ix,iy;
if (n <= 0)
return;
if (da == ZERO)
return;
if (incx != 1 || incy != 1)
{
/* code for unequal increments or equal increments != 1 */
ix = 1;
iy = 1;
if(incx < 0) ix = (-n+1)*incx + 1;
if(incy < 0)iy = (-n+1)*incy + 1;
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 */
for (i = 0;i < n; i++)
dy[i] = dy[i] + da*dx[i];
}
/*
** Forms the dot product of two vectors.
** Jack Dongarra, linpack, 3/11/78.
** ROLLED version
*/
static REAL ddot_r(int n,REAL *dx,int incx,REAL *dy,int incy)
{
REAL dtemp;
int i,ix,iy;
dtemp = ZERO;
if (n <= 0)
return(ZERO);
if (incx != 1 || incy != 1)
{
/* code for unequal increments or equal increments != 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 */
for (i=0;i < n; i++)
dtemp = dtemp + dx[i]*dy[i];
return(dtemp);
}
/*
** Scales a vector by a constant.
** Jack Dongarra, linpack, 3/11/78.
** ROLLED version
*/
static void dscal_r(int n,REAL da,REAL *dx,int incx)
{
int i,nincx;
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 */
for (i = 0; i < n; i++)
dx[i] = da*dx[i];
}
/*
** constant times a vector plus a vector.
** Jack Dongarra, linpack, 3/11/78.
** UNROLLED version
*/
static void daxpy_ur(int n,REAL da,REAL *dx,int incx,REAL *dy,int incy)
{
int i,ix,iy,m;
if (n <= 0)
return;
if (da == ZERO)
return;
if (incx != 1 || incy != 1)
{
/* code for unequal increments or equal increments != 1 */
ix = 1;
iy = 1;
if(incx < 0) ix = (-n+1)*incx + 1;
if(incy < 0)iy = (-n+1)*incy + 1;
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 */
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];
}
}
/*
** Forms the dot product of two vectors.
** Jack Dongarra, linpack, 3/11/78.
** UNROLLED version
*/
static REAL ddot_ur(int n,REAL *dx,int incx,REAL *dy,int incy)
{
REAL dtemp;
int i,ix,iy,m;
dtemp = ZERO;
if (n <= 0)
return(ZERO);
if (incx != 1 || incy != 1)
{
/* code for unequal increments or equal increments != 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 */
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);
}
/*
** Scales a vector by a constant.
** Jack Dongarra, linpack, 3/11/78.
** UNROLLED version
*/
static void dscal_ur(int n,REAL da,REAL *dx,int incx)
{
int i,m,nincx;
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 */
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];
}
}
/*
** Finds the index of element having max. absolute value.
** Jack Dongarra, linpack, 3/11/78.
*/
static int idamax(int n,REAL *dx,int incx)
{
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);
}
static REAL second(void)
{
return ((REAL)((REAL)clock()/(REAL)CLOCKS_PER_SEC));
}