forked from personal/squiggle.c
readd inverse cdf for raw floats. rework examples.
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@ -4,6 +4,7 @@
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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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#include <sys/types.h>
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#include <time.h>
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#define EXIT_ON_ERROR 0
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@ -20,6 +21,7 @@
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return error; \
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} \
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} while (0)
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#define NUM_SAMPLES 10
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struct box {
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int empty;
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@ -41,7 +43,6 @@ float cdf_uniform_0_1(float x)
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float cdf_squared_0_1(float x)
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{
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float result;
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if (x < 0) {
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return 0;
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} else if (x > 1) {
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@ -174,7 +175,76 @@ struct box cdf_beta(float x)
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}
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// Inverse cdf at point
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struct box inverse_cdf(struct box cdf_box(float), float p)
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// Two versions of this function:
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// - raw, dealing with cdfs that return floats
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// - box, dealing with cdfs that return a box.
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// Inverse cdf
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struct box inverse_cdf_float(float cdf(float), float p)
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{
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// given a cdf: [-Inf, Inf] => [0,1]
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// returns a box with either
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// x such that cdf(x) = p
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// or an error
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// if EXIT_ON_ERROR is set to 1, it exits instead of providing an error
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float low = -1.0;
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float high = 1.0;
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// 1. Make sure that cdf(low) < p < cdf(high)
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int interval_found = 0;
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while ((!interval_found) && (low > -FLT_MAX / 4) && (high < FLT_MAX / 4)) {
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// ^ Using FLT_MIN and FLT_MAX is overkill
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// but it's also the *correct* thing to do.
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int low_condition = (cdf(low) < p);
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int high_condition = (p < cdf(high));
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if (low_condition && high_condition) {
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interval_found = 1;
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} else if (!low_condition) {
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low = low * 2;
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} else if (!high_condition) {
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high = high * 2;
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}
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}
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if (!interval_found) {
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PROCESS_ERROR("Interval containing the target value not found, in function inverse_cdf");
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} else {
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int convergence_condition = 0;
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int count = 0;
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while (!convergence_condition && (count < (INT_MAX / 2))) {
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float mid = (high + low) / 2;
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int mid_not_new = (mid == low) || (mid == high);
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// float width = high - low;
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// if ((width < 1e-8) || mid_not_new){
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if (mid_not_new) {
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convergence_condition = 1;
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} else {
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float mid_sign = cdf(mid) - p;
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if (mid_sign < 0) {
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low = mid;
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} else if (mid_sign > 0) {
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high = mid;
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} else if (mid_sign == 0) {
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low = mid;
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high = mid;
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}
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}
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}
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if (convergence_condition) {
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struct box result = {.empty = 0, .content = low};
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return result;
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} else {
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PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
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}
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}
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}
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struct box inverse_cdf_box(struct box cdf_box(float), float p)
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{
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// given a cdf: [-Inf, Inf] => Box([0,1])
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// returns a box with either
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@ -277,10 +347,16 @@ float rand_0_to_1(uint32_t* seed)
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}
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// Sampler based on inverse cdf and randomness function
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struct box sampler(struct box cdf(float), uint32_t* seed)
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struct box sampler_box_cdf(struct box cdf(float), uint32_t* seed)
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{
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float p = rand_0_to_1(seed);
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struct box result = inverse_cdf(cdf, p);
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struct box result = inverse_cdf_box(cdf, p);
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return result;
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}
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struct box sampler_float_cdf(float cdf(float), uint32_t* seed)
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{
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float p = rand_0_to_1(seed);
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struct box result = inverse_cdf_float(cdf, p);
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return result;
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}
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@ -294,83 +370,97 @@ float sampler_normal_0_1(uint32_t* seed)
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return z;
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}
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int main()
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{
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// Get the inverse cdf of a [0,1] uniform distribution at 0.5
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struct box result_1 = inverse_cdf(cdf_uniform_0_1, 0.5);
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char* name_1 = "cdf_uniform_0_1";
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if (result_1.empty) {
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printf("Inverse for %s not calculated\n", name_1);
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// Some testers
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void test_inverse_cdf_float(char* cdf_name, float cdf_float(float)){
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struct box result = inverse_cdf_float(cdf_float, 0.5);
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if (result.empty) {
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printf("Inverse for %s not calculated\n", cdf_name);
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exit(1);
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} else {
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printf("Inverse of %s at %f is: %f\n", name_1, 0.5, result_1.content);
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printf("Inverse of %s at %f is: %f\n", cdf_name, 0.5, result.content);
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}
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// Get the inverse cdf of a [0,1] squared distribution at 0.5
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struct box result_2 = inverse_cdf(cdf_squared_0_1, 0.5);
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char* name_2 = "cdf_squared_0_1";
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if (result_2.empty) {
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printf("Inverse for %s not calculated\n", name_2);
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}
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void test_inverse_cdf_box(char* cdf_name, struct box cdf_box(float)){
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struct box result = inverse_cdf_box(cdf_box, 0.5);
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if (result.empty) {
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printf("Inverse for %s not calculated\n", cdf_name);
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exit(1);
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} else {
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printf("Inverse of %s at %f is: %f\n", name_2, 0.5, result_2.content);
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printf("Inverse of %s at %f is: %f\n", cdf_name, 0.5, result.content);
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}
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// Get the inverse of a normal(0,1) cdf distribution
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struct box result_3 = inverse_cdf(cdf_normal_0_1, 0.5);
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char* name_3 = "cdf_normal_0_1";
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if (result_3.empty) {
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printf("Inverse for %s not calculated\n", name_3);
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exit(1);
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} else {
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printf("Inverse of %s at %f is: %f\n", name_3, 0.5, result_3.content);
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}
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// Use the sampler on a normal(0,1)
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// set randomness seed
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uint32_t* seed = malloc(sizeof(uint32_t));
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*seed = 1000; // xorshift can't start with 0
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int n = 100;
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printf("\n\nGetting some samples from %s:\n", name_3);
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void test_and_time_sampler_float(char* cdf_name, float cdf_float(float), uint32_t* seed){
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printf("\nGetting some samples from %s:\n", cdf_name);
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clock_t begin = clock();
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for (int i = 0; i < n; i++) {
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struct box sample = sampler(cdf_normal_0_1, seed);
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for (int i = 0; i < NUM_SAMPLES; i++) {
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struct box sample = sampler_float_cdf(cdf_float, seed);
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if (sample.empty) {
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printf("Error in sampler function");
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printf("Error in sampler function for %s", cdf_name);
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} else {
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printf("%f\n", sample.content);
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}
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}
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clock_t end = clock();
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float time_spent = (float)(end - begin) / CLOCKS_PER_SEC;
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printf("Time spent: %f", time_spent);
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// Get some normal samples using the previous method.
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clock_t begin_2 = clock();
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printf("\n\nGetting some samples from sampler_normal_0_1\n");
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for (int i = 0; i < n; i++) {
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float normal_sample = sampler_normal_0_1(seed);
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printf("%f\n", normal_sample);
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printf("Time spent: %f\n", time_spent);
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}
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clock_t end_2 = clock();
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float time_spent_2 = (float)(end_2 - begin_2) / CLOCKS_PER_SEC;
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printf("Time spent: %f", time_spent_2);
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// Get some beta samples
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clock_t begin_3 = clock();
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printf("\n\nGetting some samples from box sampler_dangerous_beta\n");
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for (int i = 0; i < n; i++) {
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struct box sample = sampler(cdf_dangerous_beta, seed);
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void test_and_time_sampler_box(char* cdf_name, struct box cdf_box(float), uint32_t* seed){
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printf("\nGetting some samples from %s:\n", cdf_name);
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clock_t begin = clock();
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for (int i = 0; i < NUM_SAMPLES; i++) {
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struct box sample = sampler_box_cdf(cdf_box, seed);
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if (sample.empty) {
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printf("Error in sampler function");
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printf("Error in sampler function for %s", cdf_name);
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} else {
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printf("%f\n", sample.content);
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}
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}
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clock_t end_3 = clock();
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float time_spent_3 = (float)(end_3 - begin_3) / CLOCKS_PER_SEC;
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printf("Time spent: %f\n", time_spent_3);
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clock_t end = clock();
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float time_spent = (float)(end - begin) / CLOCKS_PER_SEC;
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printf("Time spent: %f\n", time_spent);
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}
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int main()
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{
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// Test inverse cdf float
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test_inverse_cdf_float("cdf_uniform_0_1", cdf_uniform_0_1);
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test_inverse_cdf_float("cdf_squared_0_1", cdf_squared_0_1);
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test_inverse_cdf_float("cdf_normal_0_1", cdf_normal_0_1);
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// Test inverse cdf box
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test_inverse_cdf_box("cdf_beta", cdf_beta);
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// Testing samplers
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// set randomness seed
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uint32_t* seed = malloc(sizeof(uint32_t));
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*seed = 1000; // xorshift can't start with 0
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// Test float sampler
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test_and_time_sampler_float("cdf_uniform_0_1", cdf_uniform_0_1, seed);
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test_and_time_sampler_float("cdf_squared_0_1", cdf_squared_0_1, seed);
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test_and_time_sampler_float("cdf_normal_0_1", cdf_normal_0_1, seed);
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// Get some normal samples using a previous approach
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printf("\nGetting some samples from sampler_normal_0_1\n");
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clock_t begin_2 = clock();
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for (int i = 0; i < NUM_SAMPLES; i++) {
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float normal_sample = sampler_normal_0_1(seed);
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printf("%f\n", normal_sample);
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}
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clock_t end_2 = clock();
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float time_spent_2 = (float)(end_2 - begin_2) / CLOCKS_PER_SEC;
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printf("Time spent: %f\n", time_spent_2);
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// Test box sampler
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test_and_time_sampler_box("cdf_beta", cdf_beta, seed);
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free(seed);
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return 0;
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}
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