commit 487de4a731f4af5726d61e6996fdaa12d8bc9e0b
parent e05baa6fee6c6f760297d9cc256bb880ac4ed3b1
Author: NunoSempere <nuno.sempere@protonmail.com>
Date: Sun, 16 Jul 2023 17:33:37 +0200
readd inverse cdf for raw floats. rework examples.
Diffstat:
2 files changed, 147 insertions(+), 57 deletions(-)
diff --git a/scratchpad/scratchpad b/scratchpad/scratchpad
Binary files differ.
diff --git a/scratchpad/scratchpad.c b/scratchpad/scratchpad.c
@@ -4,6 +4,7 @@
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
+#include <sys/types.h>
#include <time.h>
#define EXIT_ON_ERROR 0
@@ -20,6 +21,7 @@
return error; \
} \
} while (0)
+#define NUM_SAMPLES 10
struct box {
int empty;
@@ -41,7 +43,6 @@ float cdf_uniform_0_1(float x)
float cdf_squared_0_1(float x)
{
- float result;
if (x < 0) {
return 0;
} else if (x > 1) {
@@ -174,7 +175,76 @@ struct box cdf_beta(float x)
}
// Inverse cdf at point
-struct box inverse_cdf(struct box cdf_box(float), float p)
+// Two versions of this function:
+// - raw, dealing with cdfs that return floats
+// - box, dealing with cdfs that return a box.
+
+// Inverse cdf
+struct box inverse_cdf_float(float cdf(float), float p)
+{
+ // given a cdf: [-Inf, Inf] => [0,1]
+ // returns a box with either
+ // x such that cdf(x) = p
+ // or an error
+ // if EXIT_ON_ERROR is set to 1, it exits instead of providing an error
+
+ float low = -1.0;
+ float high = 1.0;
+
+ // 1. Make sure that cdf(low) < p < cdf(high)
+ int interval_found = 0;
+ while ((!interval_found) && (low > -FLT_MAX / 4) && (high < FLT_MAX / 4)) {
+ // ^ Using FLT_MIN and FLT_MAX is overkill
+ // but it's also the *correct* thing to do.
+
+ int low_condition = (cdf(low) < p);
+ int high_condition = (p < cdf(high));
+ if (low_condition && high_condition) {
+ interval_found = 1;
+ } else if (!low_condition) {
+ low = low * 2;
+ } else if (!high_condition) {
+ high = high * 2;
+ }
+ }
+
+ if (!interval_found) {
+ PROCESS_ERROR("Interval containing the target value not found, in function inverse_cdf");
+ } else {
+
+ int convergence_condition = 0;
+ int count = 0;
+ while (!convergence_condition && (count < (INT_MAX / 2))) {
+ float mid = (high + low) / 2;
+ int mid_not_new = (mid == low) || (mid == high);
+ // float width = high - low;
+ // if ((width < 1e-8) || mid_not_new){
+ if (mid_not_new) {
+ convergence_condition = 1;
+ } else {
+ float mid_sign = cdf(mid) - p;
+ if (mid_sign < 0) {
+ low = mid;
+ } else if (mid_sign > 0) {
+ high = mid;
+ } else if (mid_sign == 0) {
+ low = mid;
+ high = mid;
+ }
+ }
+ }
+
+ if (convergence_condition) {
+ struct box result = {.empty = 0, .content = low};
+ return result;
+ } else {
+ PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
+ }
+
+ }
+}
+
+struct box inverse_cdf_box(struct box cdf_box(float), float p)
{
// given a cdf: [-Inf, Inf] => Box([0,1])
// returns a box with either
@@ -277,10 +347,16 @@ float rand_0_to_1(uint32_t* seed)
}
// Sampler based on inverse cdf and randomness function
-struct box sampler(struct box cdf(float), uint32_t* seed)
+struct box sampler_box_cdf(struct box cdf(float), uint32_t* seed)
+{
+ float p = rand_0_to_1(seed);
+ struct box result = inverse_cdf_box(cdf, p);
+ return result;
+}
+struct box sampler_float_cdf(float cdf(float), uint32_t* seed)
{
float p = rand_0_to_1(seed);
- struct box result = inverse_cdf(cdf, p);
+ struct box result = inverse_cdf_float(cdf, p);
return result;
}
@@ -294,83 +370,97 @@ float sampler_normal_0_1(uint32_t* seed)
return z;
}
-int main()
-{
-
- // Get the inverse cdf of a [0,1] uniform distribution at 0.5
- struct box result_1 = inverse_cdf(cdf_uniform_0_1, 0.5);
- char* name_1 = "cdf_uniform_0_1";
- if (result_1.empty) {
- printf("Inverse for %s not calculated\n", name_1);
+// Some testers
+void test_inverse_cdf_float(char* cdf_name, float cdf_float(float)){
+ struct box result = inverse_cdf_float(cdf_float, 0.5);
+ if (result.empty) {
+ printf("Inverse for %s not calculated\n", cdf_name);
exit(1);
} else {
- printf("Inverse of %s at %f is: %f\n", name_1, 0.5, result_1.content);
+ printf("Inverse of %s at %f is: %f\n", cdf_name, 0.5, result.content);
}
- // Get the inverse cdf of a [0,1] squared distribution at 0.5
- struct box result_2 = inverse_cdf(cdf_squared_0_1, 0.5);
- char* name_2 = "cdf_squared_0_1";
- if (result_2.empty) {
- printf("Inverse for %s not calculated\n", name_2);
+}
+void test_inverse_cdf_box(char* cdf_name, struct box cdf_box(float)){
+ struct box result = inverse_cdf_box(cdf_box, 0.5);
+ if (result.empty) {
+ printf("Inverse for %s not calculated\n", cdf_name);
exit(1);
} else {
- printf("Inverse of %s at %f is: %f\n", name_2, 0.5, result_2.content);
+ printf("Inverse of %s at %f is: %f\n", cdf_name, 0.5, result.content);
}
- // Get the inverse of a normal(0,1) cdf distribution
- struct box result_3 = inverse_cdf(cdf_normal_0_1, 0.5);
- char* name_3 = "cdf_normal_0_1";
- if (result_3.empty) {
- printf("Inverse for %s not calculated\n", name_3);
- exit(1);
- } else {
- printf("Inverse of %s at %f is: %f\n", name_3, 0.5, result_3.content);
- }
+}
- // Use the sampler on a normal(0,1)
- // set randomness seed
- uint32_t* seed = malloc(sizeof(uint32_t));
- *seed = 1000; // xorshift can't start with 0
- int n = 100;
+void test_and_time_sampler_float(char* cdf_name, float cdf_float(float), uint32_t* seed){
+ printf("\nGetting some samples from %s:\n", cdf_name);
+ clock_t begin = clock();
+ for (int i = 0; i < NUM_SAMPLES; i++) {
+ struct box sample = sampler_float_cdf(cdf_float, seed);
+ if (sample.empty) {
+ printf("Error in sampler function for %s", cdf_name);
+ } else {
+ printf("%f\n", sample.content);
+ }
+ }
+ clock_t end = clock();
+ float time_spent = (float)(end - begin) / CLOCKS_PER_SEC;
+ printf("Time spent: %f\n", time_spent);
+}
- printf("\n\nGetting some samples from %s:\n", name_3);
+void test_and_time_sampler_box(char* cdf_name, struct box cdf_box(float), uint32_t* seed){
+ printf("\nGetting some samples from %s:\n", cdf_name);
clock_t begin = clock();
- for (int i = 0; i < n; i++) {
- struct box sample = sampler(cdf_normal_0_1, seed);
+ for (int i = 0; i < NUM_SAMPLES; i++) {
+ struct box sample = sampler_box_cdf(cdf_box, seed);
if (sample.empty) {
- printf("Error in sampler function");
+ printf("Error in sampler function for %s", cdf_name);
} else {
printf("%f\n", sample.content);
}
}
clock_t end = clock();
float time_spent = (float)(end - begin) / CLOCKS_PER_SEC;
- printf("Time spent: %f", time_spent);
+ printf("Time spent: %f\n", time_spent);
+}
- // Get some normal samples using the previous method.
+int main()
+{
+ // Test inverse cdf float
+ test_inverse_cdf_float("cdf_uniform_0_1", cdf_uniform_0_1);
+ test_inverse_cdf_float("cdf_squared_0_1", cdf_squared_0_1);
+ test_inverse_cdf_float("cdf_normal_0_1", cdf_normal_0_1);
+
+ // Test inverse cdf box
+ test_inverse_cdf_box("cdf_beta", cdf_beta);
+
+ // Testing samplers
+ // set randomness seed
+ uint32_t* seed = malloc(sizeof(uint32_t));
+ *seed = 1000; // xorshift can't start with 0
+
+ // Test float sampler
+ test_and_time_sampler_float("cdf_uniform_0_1", cdf_uniform_0_1, seed);
+ test_and_time_sampler_float("cdf_squared_0_1", cdf_squared_0_1, seed);
+ test_and_time_sampler_float("cdf_normal_0_1", cdf_normal_0_1, seed);
+
+ // Get some normal samples using a previous approach
+ printf("\nGetting some samples from sampler_normal_0_1\n");
+
clock_t begin_2 = clock();
- printf("\n\nGetting some samples from sampler_normal_0_1\n");
- for (int i = 0; i < n; i++) {
+
+ for (int i = 0; i < NUM_SAMPLES; i++) {
float normal_sample = sampler_normal_0_1(seed);
printf("%f\n", normal_sample);
}
- clock_t end_2 = clock();
+
+ clock_t end_2 = clock();
float time_spent_2 = (float)(end_2 - begin_2) / CLOCKS_PER_SEC;
- printf("Time spent: %f", time_spent_2);
+ printf("Time spent: %f\n", time_spent_2);
- // Get some beta samples
- clock_t begin_3 = clock();
- printf("\n\nGetting some samples from box sampler_dangerous_beta\n");
- for (int i = 0; i < n; i++) {
- struct box sample = sampler(cdf_dangerous_beta, seed);
- if (sample.empty) {
- printf("Error in sampler function");
- } else {
- printf("%f\n", sample.content);
- }
- }
- clock_t end_3 = clock();
- float time_spent_3 = (float)(end_3 - begin_3) / CLOCKS_PER_SEC;
- printf("Time spent: %f\n", time_spent_3);
+ // Test box sampler
+ test_and_time_sampler_box("cdf_beta", cdf_beta, seed);
+
+ free(seed);
return 0;
}
