move some functions from scratchpad => squiggle.c, reorg
This commit is contained in:
parent
68e7730f24
commit
ee9ed34287
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@ -9,7 +9,7 @@ CC=gcc # required for nested functions
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# CC=tcc # <= faster compilation
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# Main file
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SRC=scratchpad.c
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SRC=scratchpad.c ../squiggle.c
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OUTPUT=./scratchpad
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## Dependencies
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Binary file not shown.
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@ -1,33 +1,13 @@
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#include <float.h> // FLT_MAX, FLT_MIN
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#include <limits.h> // INT_MAX
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#include <math.h> // erf, sqrt
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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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#include "../squiggle.h"
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#define EXIT_ON_ERROR 0
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#define MAX_ERROR_LENGTH 500
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#define PROCESS_ERROR(...) \
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do { \
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if (EXIT_ON_ERROR) { \
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printf("@, in %s (%d)", __FILE__, __LINE__); \
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exit(1); \
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} else { \
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char error_msg[MAX_ERROR_LENGTH]; \
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snprintf(error_msg, MAX_ERROR_LENGTH, "@, in %s (%d)", __FILE__, __LINE__); \
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struct box error = { .empty = 1, .error_msg = error_msg }; \
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return error; \
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} \
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} while (0)
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#define NUM_SAMPLES 1000000
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struct box {
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int empty;
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float content;
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char* error_msg;
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};
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#define STOP_BETA 1.0e-8
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#define TINY_BETA 1.0e-30
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// Example cdf
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float cdf_uniform_0_1(float x)
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@ -59,16 +39,10 @@ float cdf_normal_0_1(float x)
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return 0.5 * (1 + erf((x - mean) / (std * sqrt(2)))); // erf from math.h
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}
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// [x] to do: add beta.
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// [x] for the cdf, use this incomplete beta function implementation, based on continuous fractions:
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// <https://codeplea.com/incomplete-beta-function-c>
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// <https://github.com/codeplea/incbeta>
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#define STOP_BETA 1.0e-8
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#define TINY_BETA 1.0e-30
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struct box incbeta(float a, float b, float x)
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{
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// Descended from <https://github.com/codeplea/incbeta/blob/master/incbeta.c>,
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// <https://codeplea.com/incomplete-beta-function-c>
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// but modified to return a box struct and floats instead of doubles.
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// [ ] to do: add attribution in README
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// Original code under this license:
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@ -174,200 +148,6 @@ struct box cdf_beta(float x)
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}
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}
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// Inverse cdf at point
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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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// 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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struct box cdf_low = cdf_box(low);
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if (cdf_low.empty) {
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PROCESS_ERROR(cdf_low.error_msg);
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}
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struct box cdf_high = cdf_box(high);
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if (cdf_high.empty) {
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PROCESS_ERROR(cdf_low.error_msg);
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}
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int low_condition = (cdf_low.content < p);
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int high_condition = (p < cdf_high.content);
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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 (mid_not_new) {
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// if ((width < 1e-8) || mid_not_new){
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convergence_condition = 1;
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} else {
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struct box cdf_mid = cdf_box(mid);
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if (cdf_mid.empty) {
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PROCESS_ERROR(cdf_mid.error_msg);
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}
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float mid_sign = cdf_mid.content - 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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// Some randomness functions for:
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// - Sampling from a cdf
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// - Benchmarking against a previous approach, which will be faster, but less general
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// Get random number between 0 and 1
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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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// Sampler based on inverse cdf and randomness function
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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_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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// Comparison point with raw normal sampler
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const float PI = 3.14159265358979323846;
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float sampler_normal_0_1(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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// Some testers
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void test_inverse_cdf_float(char* cdf_name, float cdf_float(float))
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{
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@ -445,12 +225,12 @@ int main()
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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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printf("\nGetting some samples from unit_normal\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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float normal_sample = unit_normal(seed);
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// printf("%f\n", normal_sample);
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}
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@ -460,11 +240,11 @@ int main()
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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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// Ok, this is slower than python!!
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// Partly this is because I am using a more general algorithm,
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// which applies to any cdf
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// But I am also using really anal convergence conditions.
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// This could be optimized.
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// Ok, this is slower than python!!
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// Partly this is because I am using a more general algorithm,
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// which applies to any cdf
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// But I am also using really anal convergence conditions.
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// This could be optimized.
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free(seed);
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return 0;
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187
squiggle.c
187
squiggle.c
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@ -1,6 +1,25 @@
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#include <math.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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#include <float.h>
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#include <limits.h>
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#include <time.h>
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// #include <sys/types.h>
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#define EXIT_ON_ERROR 0
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#define MAX_ERROR_LENGTH 500
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#define PROCESS_ERROR(...) \
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do { \
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if (EXIT_ON_ERROR) { \
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printf("@, in %s (%d)", __FILE__, __LINE__); \
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exit(1); \
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} else { \
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char error_msg[MAX_ERROR_LENGTH]; \
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snprintf(error_msg, MAX_ERROR_LENGTH, "@, in %s (%d)", __FILE__, __LINE__); \
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struct box error = { .empty = 1, .error_msg = error_msg }; \
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return error; \
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} \
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} while (0)
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// PI constant
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const float PI = M_PI; // 3.14159265358979323846;
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@ -112,3 +131,171 @@ float mixture(float (*samplers[])(uint32_t*), float* weights, int n_dists, uint3
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free(cumsummed_normalized_weights);
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return result;
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}
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// Sample from an arbitrary cdf
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struct box {
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int empty;
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float content;
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char* error_msg;
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};
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// Inverse cdf at point
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// Two versions of this function:
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// - raw, dealing with cdfs that return floats
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// - input: cdf: float => float, p
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// - output: Box(number|error)
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// - box, dealing with cdfs that return a box.
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// - input: cdf: float => Box(number|error), p
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// - output: Box(number|error)
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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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// 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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struct box cdf_low = cdf_box(low);
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if (cdf_low.empty) {
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PROCESS_ERROR(cdf_low.error_msg);
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}
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struct box cdf_high = cdf_box(high);
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if (cdf_high.empty) {
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PROCESS_ERROR(cdf_low.error_msg);
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}
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int low_condition = (cdf_low.content < p);
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int high_condition = (p < cdf_high.content);
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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 (mid_not_new) {
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// if ((width < 1e-8) || mid_not_new){
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convergence_condition = 1;
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} else {
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struct box cdf_mid = cdf_box(mid);
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if (cdf_mid.empty) {
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PROCESS_ERROR(cdf_mid.error_msg);
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}
|
||||
float mid_sign = cdf_mid.content - 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");
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Sampler based on inverse cdf and randomness function
|
||||
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_float(cdf, p);
|
||||
return result;
|
||||
}
|
||||
|
|
|
|||
34
squiggle.h
34
squiggle.h
|
|
@ -4,13 +4,29 @@
|
|||
// uint32_t header
|
||||
#include <stdint.h>
|
||||
|
||||
// Macros
|
||||
#define EXIT_ON_ERROR 0
|
||||
#define MAX_ERROR_LENGTH 500
|
||||
#define PROCESS_ERROR(...) \
|
||||
do { \
|
||||
if (EXIT_ON_ERROR) { \
|
||||
printf("@, in %s (%d)", __FILE__, __LINE__); \
|
||||
exit(1); \
|
||||
} else { \
|
||||
char error_msg[MAX_ERROR_LENGTH]; \
|
||||
snprintf(error_msg, MAX_ERROR_LENGTH, "@, in %s (%d)", __FILE__, __LINE__); \
|
||||
struct box error = { .empty = 1, .error_msg = error_msg }; \
|
||||
return error; \
|
||||
} \
|
||||
} while (0)
|
||||
|
||||
// Pseudo Random number generator
|
||||
uint32_t xorshift32(uint32_t* seed);
|
||||
|
||||
// Distribution & sampling functions
|
||||
float rand_0_to_1(uint32_t* seed);
|
||||
float rand_float(float max, uint32_t* seed);
|
||||
float ur_normal(uint32_t* seed);
|
||||
float unit_normal(uint32_t* seed);
|
||||
float random_uniform(float from, float to, uint32_t* seed);
|
||||
float random_normal(float mean, float sigma, uint32_t* seed);
|
||||
float random_lognormal(float logmean, float logsigma, uint32_t* seed);
|
||||
|
|
@ -23,4 +39,20 @@ void array_cumsum(float* array_to_sum, float* array_cumsummed, int length);
|
|||
// Mixture function
|
||||
float mixture(float (*samplers[])(uint32_t*), float* weights, int n_dists, uint32_t* seed);
|
||||
|
||||
// Box
|
||||
struct box {
|
||||
int empty;
|
||||
float content;
|
||||
char* error_msg;
|
||||
};
|
||||
|
||||
// Inverse cdf
|
||||
struct box inverse_cdf_float(float cdf(float), float p);
|
||||
struct box inverse_cdf_box(struct box cdf_box(float), float p);
|
||||
|
||||
// Samplers from cdf
|
||||
struct box sampler_box_cdf(struct box cdf(float), uint32_t* seed);
|
||||
struct box sampler_float_cdf(float cdf(float), uint32_t* seed);
|
||||
|
||||
#endif
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user