144 lines
3.6 KiB
C
144 lines
3.6 KiB
C
#include <stdio.h>
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#include <stdlib.h>
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#include <time.h>
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#include <math.h>
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#include <complex.h>
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#define STRRED "\x1b[31m"
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#define STRGREEN "\x1b[32m"
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#define STRNORM "\x1b[m"
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#define NUM_LOOPS 100000
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double complex complex_turn(double turn)
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{
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return cexp(I*M_PI*turn);
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}
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double complex approx_turn(double turn)
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{
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const static double a = 8*M_SQRT2/3 - 3;
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const static double b = 4 - 8*M_SQRT2/3;
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double p = turn*(b * turn * turn + a);
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double q = p*p;
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double r = 1 + q;
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double c = (1 - q) / r, s = 2*p / r;
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return (c*c - s*s) + I*(2*c*s);
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}
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void print_errors(const double *inputs,
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const double complex *ideals,
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const double complex *approxs,
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int n)
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{
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double c_error, s_error;
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double largest_c_error, largest_s_error;
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size_t largest_c_index, largest_s_index;
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double total_c_error = 0, total_s_error = 0;
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size_t i;
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double complex ideal, approx;
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for (i = 0; i < n; i++) {
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ideal = ideals[i];
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approx = approxs[i];
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//squared error in c components
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c_error = creal(ideal) - creal(approx);
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c_error *= c_error;
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//squared error in s components
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s_error = cimag(ideal) - cimag(approx);
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s_error *= s_error;
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if (largest_c_error < c_error) {
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largest_c_error = c_error;
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largest_c_index = i;
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}
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if (largest_s_error < s_error) {
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largest_s_error = s_error;
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largest_s_index = i;
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}
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total_c_error += c_error;
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total_s_error += s_error;
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}
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//these now contain the *average* squared error
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total_c_error /= (double) n;
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total_s_error /= (double) n;
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printf("Squared error in cosines: \n"\
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"\tAverage: %f (%f%% error)\n""\tLargest: %f (%f%% error)" \
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"\n\t\tInput:\t\t%f\n\t\tValue:\t\t%f\n\t\tApproximation:\t%f\n"
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, total_c_error, sqrt(total_c_error) * 100
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, largest_c_error, sqrt(largest_c_error) * 100
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, inputs[largest_c_index]
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, creal(ideals[largest_c_index]), creal(approxs[largest_c_index]));
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printf("Squared error in sines: \n"\
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"\tAverage: %f (%f%% error)\n\tLargest: %f (%f%% error)" \
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"\n\t\tInput:\t\t%f\n\t\tValue:\t\t%f\n\t\tApproximation:\t%f\n"
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, total_s_error, sqrt(total_s_error) * 100
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, largest_s_error, sqrt(largest_s_error) * 100
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, inputs[largest_c_index]
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, cimag(ideals[largest_s_index]), cimag(approxs[largest_s_index]));
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}
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//time the length of the computation `f` in nanoseconds
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long time_computation( double complex (*f)(double),
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const double *inputs,
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double complex *results,
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int n)
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{
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size_t i;
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long tick;
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struct timespec tp;
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clock_gettime(CLOCK_MONOTONIC, &tp);
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tick = tp.tv_nsec;
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for (i = 0; i < n; i++) {
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results[i] = f(inputs[i]);
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}
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//this isn't quite proper, since the clock may have ticked over a second
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clock_gettime(CLOCK_MONOTONIC, &tp);
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return tp.tv_nsec - tick;
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}
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int main(int argn, char **args)
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{
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long trig_time, rat_time;
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double rands[NUM_LOOPS];
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double complex trigs[NUM_LOOPS];
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double complex rats[NUM_LOOPS];
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size_t i;
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for (i = 0; i < NUM_LOOPS; i++) {
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rands[i] = rand() / (double) RAND_MAX;
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}
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trig_time = time_computation(&complex_turn, rands, trigs, NUM_LOOPS);
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printf("Timing for %d math.h sin and cos:\t%ldns\n", NUM_LOOPS, trig_time);
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rat_time = time_computation(&approx_turn, rands, rats, NUM_LOOPS);
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printf("Timing for %d approximations:\t%ldns\n", NUM_LOOPS, rat_time);
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long diff = rat_time - trig_time;
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double frac_speed;
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if (diff > 0) {
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frac_speed = rat_time / (double) trig_time;
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printf(STRRED "math.h" STRNORM " faster, speedup: %ldns (%2.2fx)\n",
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diff, frac_speed);
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} else {
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frac_speed = trig_time / (double) rat_time;
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printf(STRGREEN "Approximation" STRNORM " faster, speedup: %ldns (%2.2fx)\n",
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-diff, frac_speed);
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print_errors(rands, trigs, rats, NUM_LOOPS);
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}
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return 0;
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}
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