261 lines
7.1 KiB
C
261 lines
7.1 KiB
C
#include <math.h>
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#include <omp.h>
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#include <stdint.h>
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#include <stdio.h>
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#include <stdlib.h>
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const float PI = 3.14159265358979323846;
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#define N 1000000
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//Array helpers
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void array_print(float* array, int length)
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{
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for (int i = 0; i < length; i++) {
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printf("item[%d] = %f\n", i, array[i]);
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}
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printf("\n");
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}
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float array_sum(float* array, int length)
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{
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float output = 0.0;
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for (int i = 0; i < length; i++) {
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output += array[i];
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}
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return output;
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}
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void array_cumsum(float* array_to_sum, float* array_cumsummed, int length)
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{
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array_cumsummed[0] = array_to_sum[0];
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for (int i = 1; i < length; i++) {
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array_cumsummed[i] = array_cumsummed[i - 1] + array_to_sum[i];
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}
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}
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// Split array helpers
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int split_array_get_length(int index, int total_length, int n_threads)
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{
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return (total_length % n_threads > index ? total_length / n_threads + 1 : total_length / n_threads);
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}
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void split_array_allocate(float** meta_array, int length, int divide_into)
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{
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int split_array_length;
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for (int i = 0; i < divide_into; i++) {
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split_array_length = split_array_get_length(i, length, divide_into);
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meta_array[i] = malloc(split_array_length * sizeof(float));
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}
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}
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void split_array_free(float** meta_array, int divided_into)
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{
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for (int i = 0; i < divided_into; i++) {
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free(meta_array[i]);
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}
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free(meta_array);
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}
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float split_array_sum(float** meta_array, int length, int divided_into)
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{
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int i;
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float output = 0;
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#pragma omp parallel for reduction(+ \
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: output)
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for (int i = 0; i < divided_into; i++) {
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float own_partial_sum = 0;
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int split_array_length = split_array_get_length(i, length, divided_into);
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for (int j = 0; j < split_array_length; j++) {
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own_partial_sum += meta_array[i][j];
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}
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output += own_partial_sum;
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}
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return output;
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}
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// Pseudo Random number generator
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uint32_t xorshift32(uint32_t* seed)
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{
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// Algorithm "xor" from p. 4 of Marsaglia, "Xorshift RNGs"
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// See <https://stackoverflow.com/questions/53886131/how-does-xorshift32-works>
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// https://en.wikipedia.org/wiki/Xorshift
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// Also some drama: <https://www.pcg-random.org/posts/on-vignas-pcg-critique.html>, <https://prng.di.unimi.it/>
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uint32_t x = *seed;
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x ^= x << 13;
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x ^= x >> 17;
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x ^= x << 5;
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return *seed = x;
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}
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// Distribution & sampling functions
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float rand_0_to_1(uint32_t* seed)
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{
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return ((float)xorshift32(seed)) / ((float)UINT32_MAX);
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/*
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uint32_t x = *seed;
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x ^= x << 13;
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x ^= x >> 17;
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x ^= x << 5;
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return ((float)(*seed = x))/((float) UINT32_MAX);
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*/
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// previously:
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// ((float)rand_r(seed) / (float)RAND_MAX)
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// and before that: rand, but it wasn't thread-safe.
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// See: <https://stackoverflow.com/questions/43151361/how-to-create-thread-safe-random-number-generator-in-c-using-rand-r> for why to use rand_r:
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// rand() is not thread-safe, as it relies on (shared) hidden seed.
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}
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float rand_float(float max, uint32_t* seed)
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{
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return rand_0_to_1(seed) * max;
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}
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float ur_normal(uint32_t* seed)
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{
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float u1 = rand_0_to_1(seed);
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float u2 = rand_0_to_1(seed);
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float z = sqrtf(-2.0 * log(u1)) * sin(2 * PI * u2);
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return z;
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}
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float random_uniform(float from, float to, uint32_t* seed)
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{
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return rand_0_to_1(seed) * (to - from) + from;
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}
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float random_normal(float mean, float sigma, uint32_t* seed)
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{
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return (mean + sigma * ur_normal(seed));
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}
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float random_lognormal(float logmean, float logsigma, uint32_t* seed)
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{
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return expf(random_normal(logmean, logsigma, seed));
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}
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float random_to(float low, float high, uint32_t* seed)
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{
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const float NORMAL95CONFIDENCE = 1.6448536269514722;
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float loglow = logf(low);
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float loghigh = logf(high);
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float logmean = (loglow + loghigh) / 2;
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float logsigma = (loghigh - loglow) / (2.0 * NORMAL95CONFIDENCE);
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return random_lognormal(logmean, logsigma, seed);
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}
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// Mixture function
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float mixture(float (*samplers[])(uint32_t*), float* weights, int n_dists, uint32_t* seed)
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{
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// You can see a slightly simpler version of this function in the git history
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// or in alt/C-02-better-algorithm-one-thread/
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float sum_weights = array_sum(weights, n_dists);
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float* cumsummed_normalized_weights = malloc(n_dists * sizeof(float));
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cumsummed_normalized_weights[0] = weights[0] / sum_weights;
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for (int i = 1; i < n_dists; i++) {
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cumsummed_normalized_weights[i] = cumsummed_normalized_weights[i - 1] + weights[i] / sum_weights;
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}
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//create var holders
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float p1, result;
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int sample_index, i, own_length;
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p1 = random_uniform(0, 1, seed);
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for (int i = 0; i < n_dists; i++) {
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if (p1 < cumsummed_normalized_weights[i]) {
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result = samplers[i](seed);
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break;
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}
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}
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free(cumsummed_normalized_weights);
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return result;
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}
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// Parallization function
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void paralellize(float (*sampler)(uint32_t* seed), float** results, int n_threads){
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int sample_index, i, split_array_length;
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uint32_t** seeds = malloc(n_threads * sizeof(uint32_t*));
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for (uint32_t i = 0; i < n_threads; i++) {
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seeds[i] = malloc(sizeof(uint32_t));
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*seeds[i] = i + 1; // xorshift can't start with 0
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}
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#pragma omp parallel private(i, sample_index, split_array_length)
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{
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#pragma omp for
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for (i = 0; i < n_threads; i++) {
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split_array_length = split_array_get_length(i, N, n_threads);
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for (int j = 0; j < split_array_length; j++) {
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results[i][j] = sampler(seeds[i]);
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}
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}
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}
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for (uint32_t i = 0; i < n_threads; i++) {
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free(seeds[i]);
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}
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free(seeds);
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}
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// Functions used for the BOTEC.
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// Their type has to be the same, as we will be passing them around.
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float sample_0(uint32_t* seed)
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{
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return 0;
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}
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float sample_1(uint32_t* seed)
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{
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return 1;
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}
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float sample_few(uint32_t* seed)
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{
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return random_to(1, 3, seed);
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}
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float sample_many(uint32_t* seed)
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{
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return random_to(2, 10, seed);
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}
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float sample_mixture(uint32_t* seed){
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float p_a, p_b, p_c;
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// Initialize variables
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p_a = 0.8;
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p_b = 0.5;
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p_c = p_a * p_b;
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// Generate mixture
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int n_dists = 4;
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float weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
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float (*samplers[])(uint32_t*) = { sample_0, sample_1, sample_few, sample_many };
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return mixture(samplers, weights, n_dists, seed);
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}
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int main()
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{
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int n_threads = omp_get_max_threads();
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// printf("Max threads: %d\n", n_threads);
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// omp_set_num_threads(n_threads);
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float** split_array_results = malloc(n_threads * sizeof(float*));
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split_array_allocate(split_array_results, N, n_threads);
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paralellize(sample_mixture, split_array_results, n_threads);
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printf("Sum(split_array_results, N)/N = %f\n", split_array_sum(split_array_results, N, n_threads) / N);
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split_array_free(split_array_results, n_threads);
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return 0;
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}
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