flops.c
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C
649 行
#include <stdlib.h>
#include <stdio.h>
#include "report.h"
#include "timer.h"
/*--------------------- Start flops.c source code ----------------------*/
/*****************************/
/* FLOPS.c */
/* Version 2.0, 18 Dec 1992 */
/* Al Aburto */
/* aburto@nosc.mil */
/*****************************/
/*
Flops.c is a 'c' program which attempts to estimate your systems
floating-point 'MFLOPS' rating for the FADD, FSUB, FMUL, and FDIV
operations based on specific 'instruction mixes' (discussed below).
The program provides an estimate of PEAK MFLOPS performance by making
maximal use of register variables with minimal interaction with main
memory. The execution loops are all small so that they will fit in
any cache. Flops.c can be used along with Linpack and the Livermore
kernels (which exersize memory much more extensively) to gain further
insight into the limits of system performance. The flops.c execution
modules also include various percent weightings of FDIV's (from 0% to
25% FDIV's) so that the range of performance can be obtained when
using FDIV's. FDIV's, being computationally more intensive than
FADD's or FMUL's, can impact performance considerably on some systems.
Flops.c consists of 8 independent modules (routines) which, except for
module 2, conduct numerical integration of various functions. Module
2, estimates the value of pi based upon the Maclaurin series expansion
of atan(1). MFLOPS ratings are provided for each module, but the
programs overall results are summerized by the MFLOPS(1), MFLOPS(2),
MFLOPS(3), and MFLOPS(4) outputs.
The MFLOPS(1) result is identical to the result provided by all
previous versions of flops.c. It is based only upon the results from
modules 2 and 3. Two problems surfaced in using MFLOPS(1). First, it
was difficult to completely 'vectorize' the result due to the
recurrence of the 's' variable in module 2. This problem is addressed
in the MFLOPS(2) result which does not use module 2, but maintains
nearly the same weighting of FDIV's (9.2%) as in MFLOPS(1) (9.6%).
The second problem with MFLOPS(1) centers around the percentage of
FDIV's (9.6%) which was viewed as too high for an important class of
problems. This concern is addressed in the MFLOPS(3) result where NO
FDIV's are conducted at all.
The number of floating-point instructions per iteration (loop) is
given below for each module executed:
MODULE FADD FSUB FMUL FDIV TOTAL Comment
1 7 0 6 1 14 7.1% FDIV's
2 3 2 1 1 7 difficult to vectorize.
3 6 2 9 0 17 0.0% FDIV's
4 7 0 8 0 15 0.0% FDIV's
5 13 0 15 1 29 3.4% FDIV's
6 13 0 16 0 29 0.0% FDIV's
7 3 3 3 3 12 25.0% FDIV's
8 13 0 17 0 30 0.0% FDIV's
A*2+3 21 12 14 5 52 A=5, MFLOPS(1), Same as
40.4% 23.1% 26.9% 9.6% previous versions of the
flops.c program. Includes
only Modules 2 and 3, does
9.6% FDIV's, and is not
easily vectorizable.
1+3+4 58 14 66 14 152 A=4, MFLOPS(2), New output
+5+6+ 38.2% 9.2% 43.4% 9.2% does not include Module 2,
A*7 but does 9.2% FDIV's.
1+3+4 62 5 74 5 146 A=0, MFLOPS(3), New output
+5+6+ 42.9% 3.4% 50.7% 3.4% does not include Module 2,
7+8 but does 3.4% FDIV's.
3+4+6 39 2 50 0 91 A=0, MFLOPS(4), New output
+8 42.9% 2.2% 54.9% 0.0% does not include Module 2,
and does NO FDIV's.
NOTE: Various timer routines are included as indicated below. The
timer routines, with some comments, are attached at the end
of the main program.
NOTE: Please do not remove any of the printouts.
EXAMPLE COMPILATION:
UNIX based systems
cc -DUNIX -O flops20.c -o flops
cc -DUNIX -DROPT flops20.c -o flops
cc -DUNIX -fast -O4 flops20.c -o flops
.
.
.
etc.
Al Aburto
aburto@marlin.nosc.mil
*/
#include <stdio.h>
#include <math.h>
/* 'Uncomment' the line below to run */
/* with 'register double' variables */
/* defined, or compile with the */
/* '-DROPT' option. Don't need this if */
/* registers used automatically, but */
/* you might want to try it anyway. */
/* #define ROPT */
/***************************************************************/
/* Timer options. You MUST uncomment one of the options below */
/* or compile, for example, with the '-DUNIX' option. */
/***************************************************************/
/* #define Amiga */
/* #define UNIX */
/* #define UNIX_Old */
/* #define VMS */
/* #define BORLAND_C */
/* #define MSC */
/* #define MAC */
/* #define IPSC */
/* #define FORTRAN_SEC */
/* #define GTODay */
/* #define CTimer */
/* #define UXPM */
/* #define MAC_TMgr */
/* #define PARIX */
/* #define POSIX */
double nulltime, TimeArray[3]; /* Variables needed for 'dtime()'. */
double TLimit; /* Threshold to determine Number of */
/* Loops to run. Fixed at 15.0 seconds.*/
double T[36]; /* Global Array used to hold timing */
/* results and other information. */
double sa,sb,sc,sd,one,two,three;
double four,five,piref,piprg;
double scale,pierr;
double A0 = 1.0;
double A1 = -0.1666666666671334;
double A2 = 0.833333333809067E-2;
double A3 = 0.198412715551283E-3;
double A4 = 0.27557589750762E-5;
double A5 = 0.2507059876207E-7;
double A6 = 0.164105986683E-9;
double B0 = 1.0;
double B1 = -0.4999999999982;
double B2 = 0.4166666664651E-1;
double B3 = -0.1388888805755E-2;
double B4 = 0.24801428034E-4;
double B5 = -0.2754213324E-6;
double B6 = 0.20189405E-8;
double C0 = 1.0;
double C1 = 0.99999999668;
double C2 = 0.49999995173;
double C3 = 0.16666704243;
double C4 = 0.4166685027E-1;
double C5 = 0.832672635E-2;
double C6 = 0.140836136E-2;
double C7 = 0.17358267E-3;
double C8 = 0.3931683E-4;
double D1 = 0.3999999946405E-1;
double D2 = 0.96E-3;
double D3 = 0.1233153E-5;
double E2 = 0.48E-3;
double E3 = 0.411051E-6;
void main()
{
#ifdef ROPT
register double s,u,v,w,x;
#else
double s,u,v,w,x;
#endif
long loops, NLimit;
register long i, m, n;
printf("\n");
printf(" FLOPS C Program (Double Precision), V2.0 18 Dec 1992\n\n");
/****************************/
loops = 15625; /* Initial number of loops. */
/* DO NOT CHANGE! */
/****************************/
/****************************************************/
/* Set Variable Values. */
/* T[1] references all timing results relative to */
/* one million loops. */
/* */
/* The program will execute from 31250 to 128000000 */
/* loops based on a runtime of Module 1 of at least */
/* TLimit = 3.0 seconds. That is, a runtime of 3 */
/* seconds for Module 1 is used to determine the */
/* number of loops to execute. */
/* */
/* No more than NLimit = 128000000 loops are allowed*/
/****************************************************/
T[1] = 1.0E+06/(double)loops;
TLimit = 3.0;
NLimit = 128000000;
piref = 3.14159265358979324;
one = 1.0;
two = 2.0;
three = 3.0;
four = 4.0;
five = 5.0;
scale = one;
printf(" Module Error RunTime MFLOPS\n");
printf(" (usec)\n");
/*************************/
/* Initialize the timer. */
/*************************/
/*******************************************************/
/* Module 1. Calculate integral of df(x)/f(x) defined */
/* below. Result is ln(f(1)). There are 14 */
/* double precision operations per loop */
/* ( 7 +, 0 -, 6 *, 1 / ) that are included */
/* in the timing. */
/* 50.0% +, 00.0% -, 42.9% *, and 07.1% / */
/*******************************************************/
n = loops;
sa = 0.0;
while ( sa < TLimit )
{
n = 2 * n;
x = one / (double)n; /*********************/
s = 0.0; /* Loop 1. */
v = 0.0; /*********************/
w = one;
TimerOn();
for( i = 1 ; i <= n-1 ; i++ )
{
v = v + w;
u = v * x;
s = s + (D1+u*(D2+u*D3))/(w+u*(D1+u*(E2+u*E3)));
}
TimerOff();
sa = TimerElapsed();
if ( n == NLimit ) break;
/* printf(" %10ld %12.5lf\n",n,sa); */
}
scale = 1.0E+06 / (double)n;
T[1] = scale;
/****************************************/
/* Estimate nulltime ('for' loop time). */
/****************************************/
TimerOn();
for( i = 1 ; i <= n-1 ; i++ )
{
}
TimerOff();
nulltime = T[1] * TimerElapsed();
if ( nulltime < 0.0 ) nulltime = 0.0;
T[2] = T[1] * sa - nulltime;
sa = (D1+D2+D3)/(one+D1+E2+E3);
sb = D1;
T[3] = T[2] / 14.0; /*********************/
sa = x * ( sa + sb + two * s ) / two; /* Module 1 Results. */
sb = one / sa; /*********************/
n = (long)( (double)( 40000 * (long)sb ) / scale );
sc = sb - 25.2;
T[4] = one / T[3];
/********************/
/* DO NOT REMOVE */
/* THIS PRINTOUT! */
/********************/
printf(" 1 %13.4le %10.4lf %10.4lf\n",sc,T[2],T[4]);
m = n;
/*******************************************************/
/* Module 2. Calculate value of PI from Taylor Series */
/* expansion of atan(1.0). There are 7 */
/* double precision operations per loop */
/* ( 3 +, 2 -, 1 *, 1 / ) that are included */
/* in the timing. */
/* 42.9% +, 28.6% -, 14.3% *, and 14.3% / */
/*******************************************************/
s = -five; /********************/
sa = -one; /* Loop 2. */
/********************/
TimerOn();
for ( i = 1 ; i <= m ; i++ )
{
s = -s;
sa = sa + s;
}
TimerOff();
T[5] = T[1] * TimerElapsed();
Report( "flops(1)", TimerElapsed() );
if ( T[5] < 0.0 ) T[5] = 0.0;
sc = (double)m;
u = sa; /*********************/
v = 0.0; /* Loop 3. */
w = 0.0; /*********************/
x = 0.0;
TimerOn();
for ( i = 1 ; i <= m ; i++)
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