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#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <math.h>
#include <limits.h>
#include <time.h>
#include "nmglobal.h"
#include "randnum.h"
/*************************
** FOURIER COEFFICIENTS **
*************************/
static clock_t DoFPUTransIteration(double *abase,
double *bbase,
unsigned long arraysize);
static double TrapezoidIntegrate(double x0,
double x1,
int nsteps,
double omega_n,
int select);
static double thefunction(double x,
double omega_n,
int select);
/**************
** DoFourier **
***************
** Perform the transcendental/trigonometric portion of the
** benchmark. This benchmark calculates the first n
** fourier coefficients of the function (x+1)^x defined
** on the interval 0,2.
*/
void
DoFourier(void)
{
const char* context = "FPU:Transcendental";
FourierStruct* locfourierstruct = &global_fourierstruct;
clock_t total_time = 0;
int iterations = 0;
double* abase = NULL;
double* bbase = NULL;
/*
** See if we need to do self-adjustment code.
*/
if (locfourierstruct->adjust == FALSE) {
locfourierstruct->adjust = TRUE;
locfourierstruct->arraysize = 100L; /* Start at 100 elements */
while (1) {
abase = realloc(abase, locfourierstruct->arraysize * sizeof(double));
if (!abase) {
fprintf(stderr, "Error in %s, could not allocate memory. Exitting...\n", context);
exit(1);
}
bbase = realloc(bbase, locfourierstruct->arraysize * sizeof(double));
if (!bbase) {
fprintf(stderr, "Error in %s, could not allocate memory. Exitting...\n", context);
free(abase);
exit(1);
}
/*
** Do an iteration of the tests. If the elapsed time is
** less than or equal to the permitted minimum, re-allocate
** larger arrays and try again.
*/
if (DoFPUTransIteration(abase,bbase, locfourierstruct->arraysize) > global_min_ticks) {
break;
}
/*
** Make bigger arrays and try again.
*/
locfourierstruct->arraysize += 50L;
}
} else {
/*
** Don't need self-adjustment. Just allocate the
** arrays, and go.
*/
abase = malloc(locfourierstruct->arraysize * sizeof(double));
if (!abase) {
fprintf(stderr, "Error in %s, could not allocate memory. Exitting...\n", context);
exit(1);
}
bbase = malloc(locfourierstruct->arraysize * sizeof(double));
if (!bbase) {
fprintf(stderr, "Error in %s, could not allocate memory. Exitting...\n", context);
free(abase);
exit(1);
}
}
do {
total_time += DoFPUTransIteration(abase,bbase,locfourierstruct->arraysize);
iterations += locfourierstruct->arraysize * 2 - 1;
} while (total_time < locfourierstruct->request_secs * CLOCKS_PER_SEC);
free(abase);
free(bbase);
locfourierstruct->fflops = (double)(iterations * CLOCKS_PER_SEC) / (double)total_time;
}
/************************
** DoFPUTransIteration **
*************************
** Perform an iteration of the FPU Transcendental/trigonometric
** benchmark. Here, an iteration consists of calculating the
** first n fourier coefficients of the function (x+1)^x on
** the interval 0,2. n is given by arraysize.
** NOTE: The # of integration steps is fixed at
** 200.
*/
static clock_t
DoFPUTransIteration(double *abase, double *bbase, unsigned long arraysize)
{
clock_t start, stop;
double omega; /* Fundamental frequency */
unsigned long i; /* Index */
start = clock();
/*
** Calculate the fourier series. Begin by
** calculating A[0].
*/
*abase = TrapezoidIntegrate(0.0, 2.0, 200, 0.0, 0) / 2.0;
/*
** Calculate the fundamental frequency.
** ( 2 * pi ) / period...and since the period
** is 2, omega is simply pi.
*/
omega = M_PI;
for(i = 1; i < arraysize; i++) {
/*
** Calculate A[i] terms. Note, once again, that we
** can ignore the 2/period term outside the integral
** since the period is 2 and the term cancels itself
** out.
*/
*(abase + i) = TrapezoidIntegrate(0.0, 2.0, 200, omega * (double)i, 1);
/*
** Calculate the B[i] terms.
*/
*(bbase + i) = TrapezoidIntegrate(0.0, 2.0, 200, omega * (double)i, 2);
}
stop = clock();
return stop - start;
}
/***********************
** TrapezoidIntegrate **
************************
** Perform a simple trapezoid integration on the
** function (x+1)**x.
** x0,x1 set the lower and upper bounds of the
** integration.
** nsteps indicates # of trapezoidal sections
** omega_n is the fundamental frequency times
** the series member #
** select = 0 for the A[0] term, 1 for cosine terms, and
** 2 for sine terms.
** Returns the value.
** double x0 - lower bound
** double x1 - upper bound
** int nsteps - number of steps
** double omega_n - omega * n
** int select - select functions FIXME: this is dumb
*/
static double
TrapezoidIntegrate( double x0, double x1, int nsteps, double omega_n, int select)
{
double x = x0; /* Independent variable */
double dx = (x1 - x0) / (double)nsteps; /* Stepsize */
double rvalue = thefunction(x0, omega_n, select) / 2.0;
/*
** Compute the other terms of the integral.
*/
if(nsteps!=1)
{ --nsteps; /* Already done 1 step */
while(--nsteps )
{
x+=dx;
rvalue+=thefunction(x,omega_n,select);
}
}
/*
** Finish computation
*/
rvalue=(rvalue+thefunction(x1,omega_n,select)/(double)2.0)*dx;
return(rvalue);
}
/****************
** thefunction **
*****************
** This routine selects the function to be used
** in the Trapezoid integration.
** x is the independent variable
** omega_n is omega * n
** select chooses which of the sine/cosine functions
** are used. note the special case for select=0.
*/
static double thefunction(double x, /* Independent variable */
double omega_n, /* Omega * term */
int select) /* Choose term */
{
/*
** Use select to pick which function we call.
*/
switch(select)
{
case 0: return(pow(x+(double)1.0,x));
case 1: return(pow(x+(double)1.0,x) * cos(omega_n * x));
case 2: return(pow(x+(double)1.0,x) * sin(omega_n * x));
}
/*
** We should never reach this point, but the following
** keeps compilers from issuing a warning message.
*/
return(0.0);
}
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