157 lines
4.2 KiB
C
157 lines
4.2 KiB
C
#include <complex.h>
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <time.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 SECONDS_PER_NANOSECOND 1000000000
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#define NUM_LOOPS 100000
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double complex complex_turn(double turn) { return cexp(I * M_PI * turn); }
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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(
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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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{
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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(
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"Squared error in cosines: \n"
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"\tAverage: %f (%f%% error)\n"
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"\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, largest_c_error,
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sqrt(largest_c_error) * 100, inputs[largest_c_index],
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creal(ideals[largest_c_index]), creal(approxs[largest_c_index])
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);
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printf(
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"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, largest_s_error,
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sqrt(largest_s_error) * 100, 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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}
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// time the length of the computation `f` in nanoseconds
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long time_computation(
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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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{
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size_t i;
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long tick_s;
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long tick_ns;
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struct timespec tp;
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clock_gettime(CLOCK_MONOTONIC, &tp);
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tick_ns = tp.tv_nsec;
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tick_s = tp.tv_sec;
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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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clock_gettime(CLOCK_MONOTONIC, &tp);
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return SECONDS_PER_NANOSECOND * (tp.tv_sec - tick_s) +
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(tp.tv_nsec - tick_ns);
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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(
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STRRED "math.h" STRNORM " faster, speedup: %ldns (%2.2fx)\n", diff,
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frac_speed
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);
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} else {
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frac_speed = trig_time / (double)rat_time;
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printf(
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STRGREEN "Approximation" STRNORM
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" faster, speedup: %ldns (%2.2fx)\n",
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-diff, frac_speed
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);
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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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