472 lines
15 KiB
C
472 lines
15 KiB
C
#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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#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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// Example cdf
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float cdf_uniform_0_1(float x)
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{
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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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return 1;
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} else {
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return x;
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}
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}
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float cdf_squared_0_1(float x)
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{
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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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return 1;
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} else {
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return x * x;
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}
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}
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float cdf_normal_0_1(float x)
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{
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float mean = 0;
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float std = 1;
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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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// 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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/*
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* zlib License
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*
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* Regularized Incomplete Beta Function
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*
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* Copyright (c) 2016, 2017 Lewis Van Winkle
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* http://CodePlea.com
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*
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* This software is provided 'as-is', without any express or implied
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* warranty. In no event will the authors be held liable for any damages
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* arising from the use of this software.
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*
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* Permission is granted to anyone to use this software for any purpose,
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* including commercial applications, and to alter it and redistribute it
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* freely, subject to the following restrictions:
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*
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* 1. The origin of this software must not be misrepresented; you must not
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* claim that you wrote the original software. If you use this software
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* in a product, an acknowledgement in the product documentation would be
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* appreciated but is not required.
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* 2. Altered source versions must be plainly marked as such, and must not be
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* misrepresented as being the original software.
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* 3. This notice may not be removed or altered from any source distribution.
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*/
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if (x < 0.0 || x > 1.0) {
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PROCESS_ERROR("x out of bounds [0, 1], in function incbeta");
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}
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/*The continued fraction converges nicely for x < (a+1)/(a+b+2)*/
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if (x > (a + 1.0) / (a + b + 2.0)) {
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struct box symmetric_incbeta = incbeta(b, a, 1.0 - x);
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if (symmetric_incbeta.empty) {
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return symmetric_incbeta; // propagate error
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} else {
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struct box result = {
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.empty = 0,
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.content = 1 - symmetric_incbeta.content
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};
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return result;
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}
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}
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/*Find the first part before the continued fraction.*/
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const float lbeta_ab = lgamma(a) + lgamma(b) - lgamma(a + b);
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const float front = exp(log(x) * a + log(1.0 - x) * b - lbeta_ab) / a;
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/*Use Lentz's algorithm to evaluate the continued fraction.*/
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float f = 1.0, c = 1.0, d = 0.0;
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int i, m;
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for (i = 0; i <= 200; ++i) {
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m = i / 2;
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float numerator;
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if (i == 0) {
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numerator = 1.0; /*First numerator is 1.0.*/
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} else if (i % 2 == 0) {
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numerator = (m * (b - m) * x) / ((a + 2.0 * m - 1.0) * (a + 2.0 * m)); /*Even term.*/
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} else {
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numerator = -((a + m) * (a + b + m) * x) / ((a + 2.0 * m) * (a + 2.0 * m + 1)); /*Odd term.*/
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}
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/*Do an iteration of Lentz's algorithm.*/
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d = 1.0 + numerator * d;
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if (fabs(d) < TINY_BETA)
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d = TINY_BETA;
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d = 1.0 / d;
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c = 1.0 + numerator / c;
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if (fabs(c) < TINY_BETA)
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c = TINY_BETA;
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const float cd = c * d;
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f *= cd;
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/*Check for stop.*/
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if (fabs(1.0 - cd) < STOP_BETA) {
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struct box result = {
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.empty = 0,
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.content = front * (f - 1.0)
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};
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return result;
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}
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}
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PROCESS_ERROR("More loops needed, did not converge, in function incbeta");
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}
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struct box cdf_beta(float x)
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{
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if (x < 0) {
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struct box result = { .empty = 0, .content = 0 };
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return result;
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} else if (x > 1) {
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struct box result = { .empty = 0, .content = 1 };
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return result;
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} else {
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float successes = 1, failures = (2023 - 1945);
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return incbeta(successes, failures, 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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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", cdf_name, 0.5, result.content);
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}
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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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{
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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", cdf_name, 0.5, result.content);
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}
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}
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void test_and_time_sampler_float(char* cdf_name, float cdf_float(float), uint32_t* seed)
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{
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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_float_cdf(cdf_float, seed);
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if (sample.empty) {
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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\n", time_spent);
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}
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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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{
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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 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\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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// 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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}
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