reorder scratchpad stuff
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78e1838569
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e05baa6fee
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@ -41,6 +41,7 @@ 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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@ -57,73 +58,123 @@ 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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// Inverse cdf
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struct box inverse_cdf(float cdf(float), float p)
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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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// 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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// 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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if (!interval_found) {
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PROCESS_ERROR("Interval containing the target value not found, in function inverse_cdf");
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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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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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/*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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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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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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if (convergence_condition) {
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struct box result = {.empty = 0, .content = low};
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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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PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
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}
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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, but this time taking a struct box.
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struct box inverse_cdf_box(struct box cdf_box(float), float p)
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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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{
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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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@ -200,6 +251,10 @@ struct box inverse_cdf_box(struct box cdf_box(float), float p)
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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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@ -221,15 +276,15 @@ float rand_0_to_1(uint32_t* seed)
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return ((float)xorshift32(seed)) / ((float)UINT32_MAX);
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}
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// Sampler based on inverse cdf
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struct box sampler(float cdf(float), uint32_t* seed)
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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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{
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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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return result;
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}
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// For comparison, raw sampler
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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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@ -239,155 +294,6 @@ float sampler_normal_0_1(uint32_t* seed)
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return z;
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}
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// to do: add beta.
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// 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 1.0e-8
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#define TINY 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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// [x] 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)
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d = TINY;
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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)
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c = TINY;
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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) {
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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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float cdf_dangerous_beta(float x)
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{
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// So the thing is, this works
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// But it will propagate through the code
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// So it doesn't feel like a great architectural choice;
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// I prefer my choice of setting a variable which will determine whether to exit on failure or not.
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// Ok, so the proper thing to do would be to refactor inverse_cdf
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// but, I could also use a GOTO? <https://stackoverflow.com/questions/245742/examples-of-good-gotos-in-c-or-c>
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// Ok, alternatives are:
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// - Refactor inverse_cdf to take a box, take the small complexity + penalty. Add a helper
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// - Duplicate the code, have a refactored inverse_cdf as well as a normal cdf
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// - Do something hacky
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// a. dangerous beta, which exits
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// b. clever & hacky go-to statements
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// i. They actually look fun to implement
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// ii. But they would be hard for others to use.
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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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float successes = 100, failures = 100;
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struct box result = incbeta(successes, failures, x);
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if (result.empty) {
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printf("%s\n", result.error_msg);
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exit(1);
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return 1;
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} else {
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return result.content;
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}
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}
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}
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int main()
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{
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