221 lines
6.1 KiB
C
221 lines
6.1 KiB
C
#include <math.h>
|
|
#include <omp.h>
|
|
#include <stdint.h>
|
|
#include <stdio.h>
|
|
#include <stdlib.h>
|
|
|
|
const float PI = 3.14159265358979323846;
|
|
|
|
#define N_SAMPLES (1024 * 1000)
|
|
|
|
//Array helpers
|
|
void array_print(float* array, int length)
|
|
{
|
|
for (int i = 0; i < length; i++) {
|
|
printf("item[%d] = %f\n", i, array[i]);
|
|
}
|
|
printf("\n");
|
|
}
|
|
|
|
float array_sum(float* array, int length)
|
|
{
|
|
float output = 0.0;
|
|
for (int i = 0; i < length; i++) {
|
|
output += array[i];
|
|
}
|
|
return output;
|
|
}
|
|
|
|
void array_cumsum(float* array_to_sum, float* array_cumsummed, int length)
|
|
{
|
|
array_cumsummed[0] = array_to_sum[0];
|
|
for (int i = 1; i < length; i++) {
|
|
array_cumsummed[i] = array_cumsummed[i - 1] + array_to_sum[i];
|
|
}
|
|
}
|
|
|
|
// Pseudo Random number generator
|
|
|
|
uint32_t xorshift32(uint32_t* seed)
|
|
{
|
|
// Algorithm "xor" from p. 4 of Marsaglia, "Xorshift RN_SAMPLESGs"
|
|
// See <https://stackoverflow.com/questions/53886131/how-does-xorshift32-works>
|
|
// https://en.wikipedia.org/wiki/Xorshift
|
|
// Also some drama: <https://www.pcg-random.org/posts/on-vignas-pcg-critique.html>, <https://prng.di.unimi.it/>
|
|
|
|
uint32_t x = *seed;
|
|
x ^= x << 13;
|
|
x ^= x >> 17;
|
|
x ^= x << 5;
|
|
return *seed = x;
|
|
}
|
|
|
|
// Distribution & sampling functions
|
|
|
|
float rand_0_to_1(uint32_t* seed)
|
|
{
|
|
return ((float)xorshift32(seed)) / ((float)UINT32_MAX);
|
|
/*
|
|
uint32_t x = *seed;
|
|
x ^= x << 13;
|
|
x ^= x >> 17;
|
|
x ^= x << 5;
|
|
return ((float)(*seed = x))/((float) UIN_SAMPLEST32_MAX);
|
|
*/
|
|
// previously:
|
|
// ((float)rand_r(seed) / (float)RAN_SAMPLESD_MAX)
|
|
// and before that: rand, but it wasn't thread-safe.
|
|
// 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:
|
|
// rand() is not thread-safe, as it relies on (shared) hidden seed.
|
|
}
|
|
|
|
float rand_float(float max, uint32_t* seed)
|
|
{
|
|
return rand_0_to_1(seed) * max;
|
|
}
|
|
|
|
float ur_normal(uint32_t* seed)
|
|
{
|
|
float u1 = rand_0_to_1(seed);
|
|
float u2 = rand_0_to_1(seed);
|
|
float z = sqrtf(-2.0 * log(u1)) * sin(2 * PI * u2);
|
|
return z;
|
|
}
|
|
|
|
float random_uniform(float from, float to, uint32_t* seed)
|
|
{
|
|
return rand_0_to_1(seed) * (to - from) + from;
|
|
}
|
|
|
|
float random_normal(float mean, float sigma, uint32_t* seed)
|
|
{
|
|
return (mean + sigma * ur_normal(seed));
|
|
}
|
|
|
|
float random_lognormal(float logmean, float logsigma, uint32_t* seed)
|
|
{
|
|
return expf(random_normal(logmean, logsigma, seed));
|
|
}
|
|
|
|
float random_to(float low, float high, uint32_t* seed)
|
|
{
|
|
const float N_SAMPLESORMAL95CON_SAMPLESFIDEN_SAMPLESCE = 1.6448536269514722;
|
|
float loglow = logf(low);
|
|
float loghigh = logf(high);
|
|
float logmean = (loglow + loghigh) / 2;
|
|
float logsigma = (loghigh - loglow) / (2.0 * N_SAMPLESORMAL95CON_SAMPLESFIDEN_SAMPLESCE);
|
|
return random_lognormal(logmean, logsigma, seed);
|
|
}
|
|
|
|
// Mixture function
|
|
|
|
float mixture(float (*samplers[])(uint32_t*), float* weights, int n_dists, uint32_t* seed)
|
|
{
|
|
|
|
// You can see a slightly simpler version of this function in the git history
|
|
// or in alt/C-02-better-algorithm-one-thread/
|
|
float sum_weights = array_sum(weights, n_dists);
|
|
float* cumsummed_normalized_weights = malloc(n_dists * sizeof(float));
|
|
cumsummed_normalized_weights[0] = weights[0] / sum_weights;
|
|
for (int i = 1; i < n_dists; i++) {
|
|
cumsummed_normalized_weights[i] = cumsummed_normalized_weights[i - 1] + weights[i] / sum_weights;
|
|
}
|
|
|
|
//create var holders
|
|
float p1, result;
|
|
int sample_index, i, own_length;
|
|
p1 = random_uniform(0, 1, seed);
|
|
for (int i = 0; i < n_dists; i++) {
|
|
if (p1 < cumsummed_normalized_weights[i]) {
|
|
result = samplers[i](seed);
|
|
break;
|
|
}
|
|
}
|
|
free(cumsummed_normalized_weights);
|
|
return result;
|
|
}
|
|
|
|
// Parallization function
|
|
void paralellize(float (*sampler)(uint32_t* seed), float* results, int n_threads, int n_samples){
|
|
if((N_SAMPLES % n_threads) != 0){
|
|
fprintf(stderr, "Number of samples isn't divisible by number of threads, aborting\n");
|
|
exit(1);
|
|
}
|
|
// int n_samples_per_thread = N_SAMPLES / n_thread;
|
|
uint32_t** seeds = malloc(n_threads * sizeof(uint32_t*));
|
|
for (uint32_t i = 0; i < n_threads; i++) {
|
|
seeds[i] = malloc(sizeof(uint32_t));
|
|
*seeds[i] = i + 1; // xorshift can't start with 0
|
|
}
|
|
|
|
int i;
|
|
#pragma omp parallel private(i)
|
|
{
|
|
#pragma omp for
|
|
for (i = 0; i < n_threads; i++) {
|
|
int lower_bound = i * (n_samples / n_threads);
|
|
int upper_bound = ((i+1) * (n_samples / n_threads)) - 1;
|
|
// printf("Lower bound: %d, upper bound: %d\n", lower_bound, upper_bound);
|
|
for (int j = lower_bound; j < upper_bound; j++) {
|
|
results[j] = sampler(seeds[i]);
|
|
}
|
|
}
|
|
}
|
|
|
|
for (uint32_t i = 0; i < n_threads; i++) {
|
|
free(seeds[i]);
|
|
}
|
|
free(seeds);
|
|
}
|
|
|
|
// Functions used for the BOTEC.
|
|
// Their type has to be the same, as we will be passing them around.
|
|
|
|
float sample_0(uint32_t* seed)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
float sample_1(uint32_t* seed)
|
|
{
|
|
return 1;
|
|
}
|
|
|
|
float sample_few(uint32_t* seed)
|
|
{
|
|
return random_to(1, 3, seed);
|
|
}
|
|
|
|
float sample_many(uint32_t* seed)
|
|
{
|
|
return random_to(2, 10, seed);
|
|
}
|
|
|
|
float sample_mixture(uint32_t* seed){
|
|
float p_a, p_b, p_c;
|
|
|
|
// Initialize variables
|
|
p_a = 0.8;
|
|
p_b = 0.5;
|
|
p_c = p_a * p_b;
|
|
|
|
// Generate mixture
|
|
int n_dists = 4;
|
|
float weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
|
|
float (*samplers[])(uint32_t*) = { sample_0, sample_1, sample_few, sample_many };
|
|
|
|
return mixture(samplers, weights, n_dists, seed);
|
|
}
|
|
|
|
int main()
|
|
{
|
|
int n_threads = omp_get_max_threads();
|
|
float* split_array_results = malloc(N_SAMPLES * sizeof(float));
|
|
|
|
paralellize(sample_mixture, split_array_results, n_threads, N_SAMPLES);
|
|
printf("Sum(split_array_results, N_SAMPLES)/N_SAMPLES = %f\n", array_sum(split_array_results, N_SAMPLES) / N_SAMPLES);
|
|
|
|
free(split_array_results);
|
|
return 0;
|
|
}
|