fixes for stereographic approximation reporting
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@ -3,166 +3,172 @@
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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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#include <unistd.h>
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#define STR_RED "\x1b[31m"
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#define STR_GREEN "\x1b[32m"
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#define STR_NORM "\x1b[m"
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#define SECONDS_PER_NANOSECOND 1000000000
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#define NUM_LOOPS 100000
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#define SQRT_NUM_LOOPS 100
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#define NUM_STATS 100000
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#define SQRT_NUM_STATS 100
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#define NUM_LOOPS 10000000
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struct circle {
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double c;
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double s;
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double c;
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double s;
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};
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void turn_update(double turn, void* result);
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void approx_turn_update(double turn, void* result);
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#ifdef USE_COMPLEX
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#define EXTRACT_REAL(a) creal(a)
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#define EXTRACT_IMAG(a) cimag(a)
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#define EXTRACT_COSINE(a) creal(a)
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#define EXTRACT_SINE(a) cimag(a)
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#define CIRCLE_TYPE double complex
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#else
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#define EXTRACT_REAL(a) (a.c)
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#define EXTRACT_IMAG(a) (a.s)
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#define EXTRACT_COSINE(a) (a.c)
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#define EXTRACT_SINE(a) (a.s)
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#define CIRCLE_TYPE struct circle
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#endif
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void print_errors(
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const double* inputs,
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const CIRCLE_TYPE* ideals,
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const CIRCLE_TYPE* 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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void turn_update(double turn, CIRCLE_TYPE *result);
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void approx_turn_update(double turn, CIRCLE_TYPE *result);
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double total_c_error = 0, total_s_error = 0;
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void print_errors(const double *inputs, const CIRCLE_TYPE *ideals,
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const CIRCLE_TYPE *approxs, int n) {
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double c_error, s_error;
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double largest_c_error = 0, largest_s_error = 0;
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size_t largest_c_index, largest_s_index;
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size_t i;
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CIRCLE_TYPE ideal, approx;
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double total_c_error = 0, total_s_error = 0;
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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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size_t i;
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CIRCLE_TYPE ideal, approx;
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// squared error in c components
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c_error = EXTRACT_REAL(ideal) - EXTRACT_REAL(approx);
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c_error *= c_error;
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// squared error in s components
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s_error = EXTRACT_IMAG(ideal) - EXTRACT_IMAG(approx);
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s_error *= s_error;
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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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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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// squared error in c components
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c_error = EXTRACT_COSINE(ideal) - EXTRACT_COSINE(approx);
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c_error *= c_error;
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// squared error in s components
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s_error = EXTRACT_SINE(ideal) - EXTRACT_SINE(approx);
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s_error *= s_error;
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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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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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// 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)\n"
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"\t\tInput:\t\t%f\n"
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"\t\tValue:\t\t%f\n"
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"\t\tApproximation:\t%f\n",
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total_c_error, sqrt(total_c_error) * SQRT_NUM_LOOPS, largest_c_error,
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sqrt(largest_c_error) * SQRT_NUM_LOOPS, inputs[largest_c_index],
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EXTRACT_REAL(ideals[largest_c_index]),
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EXTRACT_REAL(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"
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"\tLargest: %f (%f%% error)\n"
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"\t\tInput:\t\t%f\n"
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"\t\tValue:\t\t%f\n"
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"\t\tApproximation:\t%f\n",
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total_s_error, sqrt(total_s_error) * SQRT_NUM_LOOPS, largest_s_error,
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sqrt(largest_s_error) * SQRT_NUM_LOOPS, inputs[largest_c_index],
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EXTRACT_IMAG(ideals[largest_s_index]),
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EXTRACT_IMAG(approxs[largest_s_index])
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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 (%d runs): \n"
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"\tAverage: %f (%f%% error)\n"
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"\tLargest: %f (%f%% error)\n"
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"\t\tInput:\t\t%f\n"
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"\t\tValue:\t\t%f\n"
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"\t\tApproximation:\t%f\n",
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NUM_STATS, total_c_error, sqrt(total_c_error) * SQRT_NUM_STATS,
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largest_c_error, sqrt(largest_c_error) * SQRT_NUM_STATS,
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inputs[largest_c_index], EXTRACT_COSINE(ideals[largest_c_index]),
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EXTRACT_COSINE(approxs[largest_c_index]));
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printf("Squared error in sines (%d runs): \n"
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"\tAverage: %f (%f%% error)\n"
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"\tLargest: %f (%f%% error)\n"
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"\t\tInput:\t\t%f\n"
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"\t\tValue:\t\t%f\n"
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"\t\tApproximation:\t%f\n",
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NUM_STATS, total_s_error, sqrt(total_s_error) * SQRT_NUM_STATS,
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largest_s_error, sqrt(largest_s_error) * SQRT_NUM_STATS,
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inputs[largest_s_index], EXTRACT_SINE(ideals[largest_s_index]),
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EXTRACT_SINE(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(
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void (*f)(double, void*), const double* inputs, CIRCLE_TYPE* results, int n
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)
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{
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size_t i;
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struct timespec tp1;
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struct timespec tp2;
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// using a macro rather than a function taking a function pointer for
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// more accurate time
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#define TIME_COMPUTATION(f, inputs, results, n_stats, n_loop, time) \
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do { \
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size_t i; \
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struct timespec tp1; \
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struct timespec tp2; \
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\
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for (i = 0; i < n_stats; i++) { \
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f(inputs[i], results + i); \
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} \
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CIRCLE_TYPE temp; \
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clock_gettime(CLOCK_MONOTONIC, &tp1); \
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for (i = 0; i < n_stats; i++) { \
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f(rand() / (double)RAND_MAX, &temp); \
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} \
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clock_gettime(CLOCK_MONOTONIC, &tp2); \
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\
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time = SECONDS_PER_NANOSECOND * (tp2.tv_sec - tp1.tv_sec) + \
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(tp2.tv_nsec - tp1.tv_nsec); \
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} while (0)
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clock_gettime(CLOCK_MONOTONIC, &tp1);
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for (i = 0; i < n; i++) {
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f(inputs[i], results + i);
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}
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clock_gettime(CLOCK_MONOTONIC, &tp2);
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int main(int argn, char **args) {
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long trig_time, rat_time;
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return SECONDS_PER_NANOSECOND * (tp2.tv_sec - tp1.tv_sec) +
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(tp2.tv_nsec - tp1.tv_sec);
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}
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double rands[NUM_STATS];
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CIRCLE_TYPE trigs[NUM_STATS];
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CIRCLE_TYPE rats[NUM_STATS];
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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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size_t i;
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for (i = 0; i < NUM_STATS; i++) {
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rands[i] = rand() / (double)RAND_MAX;
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}
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double rands[NUM_LOOPS];
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CIRCLE_TYPE trigs[NUM_LOOPS];
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CIRCLE_TYPE 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(&turn_update, rands, trigs, NUM_LOOPS);
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printf(
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TIME_COMPUTATION(turn_update, rands, trigs, NUM_STATS, NUM_LOOPS, trig_time);
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printf(
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#ifdef USE_COMPLEX
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"Timing for %d complex.h cexp:\t%ldns\n",
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#else
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"Timing for %d math.h sin and cos:\t%ldns\n",
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#endif
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NUM_LOOPS,
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trig_time
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);
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NUM_LOOPS, trig_time);
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rat_time = time_computation(&approx_turn_update, rands, rats, NUM_LOOPS);
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printf("Timing for %d approximations:\t%ldns\n", NUM_LOOPS, rat_time);
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TIME_COMPUTATION(approx_turn_update, rands, rats, NUM_STATS, NUM_LOOPS,
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rat_time);
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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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STR_RED "stdlib" STR_NORM " faster, speedup: %ldns (%2.2fx)\n",
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diff, frac_speed
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);
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// Report results
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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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// Disable colors for non-terminal output
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if (isatty(STDOUT_FILENO)) {
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printf(STR_RED "stdlib" STR_NORM " 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(
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STR_GREEN "Approximation" STR_NORM
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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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printf("stdlib faster, speedup: %ldns (%2.2fx)\n", diff, 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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// Disable colors for non-terminal output
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if (isatty(STDOUT_FILENO)) {
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printf(STR_GREEN "Approximation" STR_NORM
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" faster, speedup: %ldns (%2.2fx)\n",
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-diff, frac_speed);
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} else {
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printf("Approximation faster, speedup: %ldns (%2.2fx)\n", -diff,
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frac_speed);
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}
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return 0;
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print_errors(rands, trigs, rats, NUM_STATS);
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}
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return 0;
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}
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