mirror of https://github.com/ptitSeb/box64.git
889 lines
22 KiB
C
Executable File
889 lines
22 KiB
C
Executable File
/*
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**
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** LINPACK.C Linpack benchmark, calculates FLOPS.
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** (FLoating Point Operations Per Second)
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**
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** Translated to C by Bonnie Toy 5/88
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**
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** Modified by Will Menninger, 10/93, with these features:
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** (modified on 2/25/94 to fix a problem with daxpy for
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** unequal increments or equal increments not equal to 1.
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** Jack Dongarra)
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**
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** - Defaults to double precision.
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** - Averages ROLLed and UNROLLed performance.
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** - User selectable array sizes.
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** - Automatically does enough repetitions to take at least 10 CPU seconds.
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** - Prints machine precision.
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** - ANSI prototyping.
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**
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** To compile: cc -O -o linpack linpack.c -lm
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**
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**
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <math.h>
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#include <time.h>
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#include <float.h>
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#define DP
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#ifdef SP
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#define ZERO 0.0
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#define ONE 1.0
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#define PREC "Single"
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#define BASE10DIG FLT_DIG
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typedef float REAL;
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#endif
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#ifdef DP
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#define ZERO 0.0e0
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#define ONE 1.0e0
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#define PREC "Double"
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#define BASE10DIG DBL_DIG
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typedef double REAL;
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#endif
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static REAL linpack (long nreps,int arsize);
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static void matgen (REAL *a,int lda,int n,REAL *b,REAL *norma);
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static void dgefa (REAL *a,int lda,int n,int *ipvt,int *info,int roll);
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static void dgesl (REAL *a,int lda,int n,int *ipvt,REAL *b,int job,int roll);
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static void daxpy_r (int n,REAL da,REAL *dx,int incx,REAL *dy,int incy);
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static REAL ddot_r (int n,REAL *dx,int incx,REAL *dy,int incy);
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static void dscal_r (int n,REAL da,REAL *dx,int incx);
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static void daxpy_ur (int n,REAL da,REAL *dx,int incx,REAL *dy,int incy);
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static REAL ddot_ur (int n,REAL *dx,int incx,REAL *dy,int incy);
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static void dscal_ur (int n,REAL da,REAL *dx,int incx);
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static int idamax (int n,REAL *dx,int incx);
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static REAL second (void);
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static void *mempool;
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void main(int argc, const char** argv)
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{
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char buf[80];
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int arsize;
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long arsize2d,memreq,nreps;
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size_t malloc_arg;
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if(argc>1)
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strcpy(buf, argv[1]);
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while (1)
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{
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/*printf("Enter array size (q to quit) [200]: ");
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fgets(buf,79,stdin);*/
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if (buf[0]=='q' || buf[0]=='Q')
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break;
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if (buf[0]=='\0' || buf[0]=='\n')
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arsize=200;
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else
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arsize=atoi(buf);
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arsize/=2;
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arsize*=2;
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if (arsize<10)
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{
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printf("Too small.\n");
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continue;
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}
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arsize2d = (long)arsize*(long)arsize;
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memreq=arsize2d*sizeof(REAL)+(long)arsize*sizeof(REAL)+(long)arsize*sizeof(int);
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printf("Memory required: %ldK.\n",(memreq+512L)>>10);
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malloc_arg=(size_t)memreq;
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if (malloc_arg!=memreq || (mempool=malloc(malloc_arg))==NULL)
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{
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printf("Not enough memory available for given array size.\n\n");
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continue;
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}
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printf("\n\nLINPACK benchmark, %s precision.\n",PREC);
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printf("Machine precision: %d digits.\n",BASE10DIG);
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printf("Array size %d X %d.\n",arsize,arsize);
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printf("Average rolled and unrolled performance:\n\n");
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printf(" Reps Time(s) DGEFA DGESL OVERHEAD KFLOPS\n");
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printf("----------------------------------------------------\n");
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nreps=1;
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while (linpack(nreps,arsize)<10.)
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nreps*=2;
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free(mempool);
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printf("\n");
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strcpy(buf, "q");
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}
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}
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static REAL linpack(long nreps,int arsize)
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{
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REAL *a,*b;
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REAL norma,t1,kflops,tdgesl,tdgefa,totalt,toverhead,ops;
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int *ipvt,n,info,lda;
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long i,arsize2d;
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lda = arsize;
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n = arsize/2;
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arsize2d = (long)arsize*(long)arsize;
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ops=((2.0*n*n*n)/3.0+2.0*n*n);
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a=(REAL *)mempool;
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b=a+arsize2d;
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ipvt=(int *)&b[arsize];
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tdgesl=0;
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tdgefa=0;
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totalt=second();
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for (i=0;i<nreps;i++)
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{
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matgen(a,lda,n,b,&norma);
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t1 = second();
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dgefa(a,lda,n,ipvt,&info,1);
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tdgefa += second()-t1;
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t1 = second();
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dgesl(a,lda,n,ipvt,b,0,1);
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tdgesl += second()-t1;
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}
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for (i=0;i<nreps;i++)
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{
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matgen(a,lda,n,b,&norma);
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t1 = second();
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dgefa(a,lda,n,ipvt,&info,0);
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tdgefa += second()-t1;
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t1 = second();
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dgesl(a,lda,n,ipvt,b,0,0);
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tdgesl += second()-t1;
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}
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totalt=second()-totalt;
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if (totalt<0.5 || tdgefa+tdgesl<0.2)
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return(0.);
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kflops=2.*nreps*ops/(1000.*(tdgefa+tdgesl));
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toverhead=totalt-tdgefa-tdgesl;
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if (tdgefa<0.)
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tdgefa=0.;
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if (tdgesl<0.)
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tdgesl=0.;
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if (toverhead<0.)
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toverhead=0.;
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printf("%8ld %6.2f %6.2f%% %6.2f%% %6.2f%% %9.3f\n",
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nreps,totalt,100.*tdgefa/totalt,
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100.*tdgesl/totalt,100.*toverhead/totalt,
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kflops);
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return(totalt);
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}
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/*
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** For matgen,
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** We would like to declare a[][lda], but c does not allow it. In this
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** function, references to a[i][j] are written a[lda*i+j].
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*/
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static void matgen(REAL *a,int lda,int n,REAL *b,REAL *norma)
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{
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int init,i,j;
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init = 1325;
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*norma = 0.0;
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for (j = 0; j < n; j++)
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for (i = 0; i < n; i++)
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{
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init = (int)((long)3125*(long)init % 65536L);
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a[lda*j+i] = (init - 32768.0)/16384.0;
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*norma = (a[lda*j+i] > *norma) ? a[lda*j+i] : *norma;
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}
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for (i = 0; i < n; i++)
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b[i] = 0.0;
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for (j = 0; j < n; j++)
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for (i = 0; i < n; i++)
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b[i] = b[i] + a[lda*j+i];
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}
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/*
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**
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** DGEFA benchmark
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**
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** We would like to declare a[][lda], but c does not allow it. In this
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** function, references to a[i][j] are written a[lda*i+j].
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**
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** dgefa factors a double precision matrix by gaussian elimination.
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**
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** dgefa is usually called by dgeco, but it can be called
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** directly with a saving in time if rcond is not needed.
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** (time for dgeco) = (1 + 9/n)*(time for dgefa) .
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**
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** on entry
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**
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** a REAL precision[n][lda]
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** the matrix to be factored.
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**
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** lda integer
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** the leading dimension of the array a .
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**
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** n integer
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** the order of the matrix a .
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**
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** on return
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**
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** a an upper triangular matrix and the multipliers
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** which were used to obtain it.
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** the factorization can be written a = l*u where
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** l is a product of permutation and unit lower
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** triangular matrices and u is upper triangular.
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**
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** ipvt integer[n]
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** an integer vector of pivot indices.
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**
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** info integer
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** = 0 normal value.
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** = k if u[k][k] .eq. 0.0 . this is not an error
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** condition for this subroutine, but it does
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** indicate that dgesl or dgedi will divide by zero
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** if called. use rcond in dgeco for a reliable
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** indication of singularity.
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**
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** linpack. this version dated 08/14/78 .
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** cleve moler, university of New Mexico, argonne national lab.
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**
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** functions
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**
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** blas daxpy,dscal,idamax
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**
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*/
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static void dgefa(REAL *a,int lda,int n,int *ipvt,int *info,int roll)
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{
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REAL t;
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int idamax(),j,k,kp1,l,nm1;
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/* gaussian elimination with partial pivoting */
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if (roll)
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{
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*info = 0;
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nm1 = n - 1;
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if (nm1 >= 0)
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for (k = 0; k < nm1; k++)
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{
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kp1 = k + 1;
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/* find l = pivot index */
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l = idamax(n-k,&a[lda*k+k],1) + k;
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ipvt[k] = l;
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/* zero pivot implies this column already
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triangularized */
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if (a[lda*k+l] != ZERO)
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{
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/* interchange if necessary */
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if (l != k)
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{
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t = a[lda*k+l];
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a[lda*k+l] = a[lda*k+k];
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a[lda*k+k] = t;
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}
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/* compute multipliers */
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t = -ONE/a[lda*k+k];
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dscal_r(n-(k+1),t,&a[lda*k+k+1],1);
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/* row elimination with column indexing */
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for (j = kp1; j < n; j++)
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{
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t = a[lda*j+l];
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if (l != k)
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{
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a[lda*j+l] = a[lda*j+k];
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a[lda*j+k] = t;
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}
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daxpy_r(n-(k+1),t,&a[lda*k+k+1],1,&a[lda*j+k+1],1);
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}
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}
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else
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(*info) = k;
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}
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ipvt[n-1] = n-1;
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if (a[lda*(n-1)+(n-1)] == ZERO)
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(*info) = n-1;
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}
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else
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{
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*info = 0;
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nm1 = n - 1;
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if (nm1 >= 0)
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for (k = 0; k < nm1; k++)
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{
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kp1 = k + 1;
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/* find l = pivot index */
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l = idamax(n-k,&a[lda*k+k],1) + k;
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ipvt[k] = l;
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/* zero pivot implies this column already
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triangularized */
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if (a[lda*k+l] != ZERO)
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{
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/* interchange if necessary */
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if (l != k)
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{
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t = a[lda*k+l];
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a[lda*k+l] = a[lda*k+k];
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a[lda*k+k] = t;
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}
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/* compute multipliers */
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t = -ONE/a[lda*k+k];
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dscal_ur(n-(k+1),t,&a[lda*k+k+1],1);
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/* row elimination with column indexing */
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for (j = kp1; j < n; j++)
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{
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t = a[lda*j+l];
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if (l != k)
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{
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a[lda*j+l] = a[lda*j+k];
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a[lda*j+k] = t;
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}
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daxpy_ur(n-(k+1),t,&a[lda*k+k+1],1,&a[lda*j+k+1],1);
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}
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}
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else
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(*info) = k;
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}
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ipvt[n-1] = n-1;
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if (a[lda*(n-1)+(n-1)] == ZERO)
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(*info) = n-1;
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}
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}
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/*
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**
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** DGESL benchmark
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**
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** We would like to declare a[][lda], but c does not allow it. In this
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** function, references to a[i][j] are written a[lda*i+j].
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**
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** dgesl solves the double precision system
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** a * x = b or trans(a) * x = b
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** using the factors computed by dgeco or dgefa.
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**
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** on entry
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**
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** a double precision[n][lda]
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** the output from dgeco or dgefa.
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**
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** lda integer
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** the leading dimension of the array a .
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**
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** n integer
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** the order of the matrix a .
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**
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** ipvt integer[n]
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** the pivot vector from dgeco or dgefa.
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**
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** b double precision[n]
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** the right hand side vector.
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**
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** job integer
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** = 0 to solve a*x = b ,
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** = nonzero to solve trans(a)*x = b where
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** trans(a) is the transpose.
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**
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** on return
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**
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** b the solution vector x .
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**
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** error condition
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**
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** a division by zero will occur if the input factor contains a
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** zero on the diagonal. technically this indicates singularity
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** but it is often caused by improper arguments or improper
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** setting of lda . it will not occur if the subroutines are
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** called correctly and if dgeco has set rcond .gt. 0.0
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** or dgefa has set info .eq. 0 .
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**
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** to compute inverse(a) * c where c is a matrix
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** with p columns
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** dgeco(a,lda,n,ipvt,rcond,z)
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** if (!rcond is too small){
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** for (j=0,j<p,j++)
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** dgesl(a,lda,n,ipvt,c[j][0],0);
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** }
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**
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** linpack. this version dated 08/14/78 .
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** cleve moler, university of new mexico, argonne national lab.
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**
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** functions
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**
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** blas daxpy,ddot
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*/
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static void dgesl(REAL *a,int lda,int n,int *ipvt,REAL *b,int job,int roll)
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{
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REAL t;
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int k,kb,l,nm1;
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if (roll)
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{
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nm1 = n - 1;
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if (job == 0)
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{
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/* job = 0 , solve a * x = b */
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/* first solve l*y = b */
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if (nm1 >= 1)
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for (k = 0; k < nm1; k++)
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{
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l = ipvt[k];
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t = b[l];
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if (l != k)
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{
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b[l] = b[k];
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b[k] = t;
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}
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daxpy_r(n-(k+1),t,&a[lda*k+k+1],1,&b[k+1],1);
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}
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/* now solve u*x = y */
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for (kb = 0; kb < n; kb++)
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{
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k = n - (kb + 1);
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b[k] = b[k]/a[lda*k+k];
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t = -b[k];
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daxpy_r(k,t,&a[lda*k+0],1,&b[0],1);
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}
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}
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else
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{
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/* job = nonzero, solve trans(a) * x = b */
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/* first solve trans(u)*y = b */
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for (k = 0; k < n; k++)
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{
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t = ddot_r(k,&a[lda*k+0],1,&b[0],1);
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b[k] = (b[k] - t)/a[lda*k+k];
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}
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/* now solve trans(l)*x = y */
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if (nm1 >= 1)
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for (kb = 1; kb < nm1; kb++)
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{
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k = n - (kb+1);
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b[k] = b[k] + ddot_r(n-(k+1),&a[lda*k+k+1],1,&b[k+1],1);
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l = ipvt[k];
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if (l != k)
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{
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t = b[l];
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b[l] = b[k];
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b[k] = t;
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}
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}
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}
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}
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else
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{
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nm1 = n - 1;
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if (job == 0)
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{
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/* job = 0 , solve a * x = b */
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/* first solve l*y = b */
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if (nm1 >= 1)
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for (k = 0; k < nm1; k++)
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{
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l = ipvt[k];
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t = b[l];
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if (l != k)
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{
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b[l] = b[k];
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b[k] = t;
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}
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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));
|
|
}
|
|
|
|
|