squiggle.c/scratchpad/scratchpad.c

252 lines
7.6 KiB
C

#include <math.h> // erf, sqrt
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include "../squiggle.h"
#define NUM_SAMPLES 1000000
#define STOP_BETA 1.0e-8
#define TINY_BETA 1.0e-30
// Example cdf
float cdf_uniform_0_1(float x)
{
if (x < 0) {
return 0;
} else if (x > 1) {
return 1;
} else {
return x;
}
}
float cdf_squared_0_1(float x)
{
if (x < 0) {
return 0;
} else if (x > 1) {
return 1;
} else {
return x * x;
}
}
float cdf_normal_0_1(float x)
{
float mean = 0;
float std = 1;
return 0.5 * (1 + erf((x - mean) / (std * sqrt(2)))); // erf from math.h
}
struct box incbeta(float a, float b, float x)
{
// Descended from <https://github.com/codeplea/incbeta/blob/master/incbeta.c>,
// <https://codeplea.com/incomplete-beta-function-c>
// but modified to return a box struct and floats instead of doubles.
// [ ] to do: add attribution in README
// Original code under this license:
/*
* zlib License
*
* Regularized Incomplete Beta Function
*
* Copyright (c) 2016, 2017 Lewis Van Winkle
* http://CodePlea.com
*
* This software is provided 'as-is', without any express or implied
* warranty. In no event will the authors be held liable for any damages
* arising from the use of this software.
*
* Permission is granted to anyone to use this software for any purpose,
* including commercial applications, and to alter it and redistribute it
* freely, subject to the following restrictions:
*
* 1. The origin of this software must not be misrepresented; you must not
* claim that you wrote the original software. If you use this software
* in a product, an acknowledgement in the product documentation would be
* appreciated but is not required.
* 2. Altered source versions must be plainly marked as such, and must not be
* misrepresented as being the original software.
* 3. This notice may not be removed or altered from any source distribution.
*/
if (x < 0.0 || x > 1.0) {
PROCESS_ERROR("x out of bounds [0, 1], in function incbeta");
}
/*The continued fraction converges nicely for x < (a+1)/(a+b+2)*/
if (x > (a + 1.0) / (a + b + 2.0)) {
struct box symmetric_incbeta = incbeta(b, a, 1.0 - x);
if (symmetric_incbeta.empty) {
return symmetric_incbeta; // propagate error
} else {
struct box result = {
.empty = 0,
.content = 1 - symmetric_incbeta.content
};
return result;
}
}
/*Find the first part before the continued fraction.*/
const float lbeta_ab = lgamma(a) + lgamma(b) - lgamma(a + b);
const float front = exp(log(x) * a + log(1.0 - x) * b - lbeta_ab) / a;
/*Use Lentz's algorithm to evaluate the continued fraction.*/
float f = 1.0, c = 1.0, d = 0.0;
int i, m;
for (i = 0; i <= 200; ++i) {
m = i / 2;
float numerator;
if (i == 0) {
numerator = 1.0; /*First numerator is 1.0.*/
} else if (i % 2 == 0) {
numerator = (m * (b - m) * x) / ((a + 2.0 * m - 1.0) * (a + 2.0 * m)); /*Even term.*/
} else {
numerator = -((a + m) * (a + b + m) * x) / ((a + 2.0 * m) * (a + 2.0 * m + 1)); /*Odd term.*/
}
/*Do an iteration of Lentz's algorithm.*/
d = 1.0 + numerator * d;
if (fabs(d) < TINY_BETA)
d = TINY_BETA;
d = 1.0 / d;
c = 1.0 + numerator / c;
if (fabs(c) < TINY_BETA)
c = TINY_BETA;
const float cd = c * d;
f *= cd;
/*Check for stop.*/
if (fabs(1.0 - cd) < STOP_BETA) {
struct box result = {
.empty = 0,
.content = front * (f - 1.0)
};
return result;
}
}
PROCESS_ERROR("More loops needed, did not converge, in function incbeta");
}
struct box cdf_beta(float x)
{
if (x < 0) {
struct box result = { .empty = 0, .content = 0 };
return result;
} else if (x > 1) {
struct box result = { .empty = 0, .content = 1 };
return result;
} else {
float successes = 1, failures = (2023 - 1945);
return incbeta(successes, failures, x);
}
}
// Some testers
void test_inverse_cdf_float(char* cdf_name, float cdf_float(float))
{
struct box result = inverse_cdf_float(cdf_float, 0.5);
if (result.empty) {
printf("Inverse for %s not calculated\n", cdf_name);
exit(1);
} else {
printf("Inverse of %s at %f is: %f\n", cdf_name, 0.5, result.content);
}
}
void test_inverse_cdf_box(char* cdf_name, struct box cdf_box(float))
{
struct box result = inverse_cdf_box(cdf_box, 0.5);
if (result.empty) {
printf("Inverse for %s not calculated\n", cdf_name);
exit(1);
} else {
printf("Inverse of %s at %f is: %f\n", cdf_name, 0.5, result.content);
}
}
void test_and_time_sampler_float(char* cdf_name, float cdf_float(float), uint32_t* seed)
{
printf("\nGetting some samples from %s:\n", cdf_name);
clock_t begin = clock();
for (int i = 0; i < NUM_SAMPLES; i++) {
struct box sample = sampler_float_cdf(cdf_float, seed);
if (sample.empty) {
printf("Error in sampler function for %s", cdf_name);
} else {
// printf("%f\n", sample.content);
}
}
clock_t end = clock();
float time_spent = (float)(end - begin) / CLOCKS_PER_SEC;
printf("Time spent: %f\n", time_spent);
}
void test_and_time_sampler_box(char* cdf_name, struct box cdf_box(float), uint32_t* seed)
{
printf("\nGetting some samples from %s:\n", cdf_name);
clock_t begin = clock();
for (int i = 0; i < NUM_SAMPLES; i++) {
struct box sample = sampler_box_cdf(cdf_box, seed);
if (sample.empty) {
printf("Error in sampler function for %s", cdf_name);
} else {
// printf("%f\n", sample.content);
}
}
clock_t end = clock();
float time_spent = (float)(end - begin) / CLOCKS_PER_SEC;
printf("Time spent: %f\n", time_spent);
}
int main()
{
// Test inverse cdf float
test_inverse_cdf_float("cdf_uniform_0_1", cdf_uniform_0_1);
test_inverse_cdf_float("cdf_squared_0_1", cdf_squared_0_1);
test_inverse_cdf_float("cdf_normal_0_1", cdf_normal_0_1);
// Test inverse cdf box
test_inverse_cdf_box("cdf_beta", cdf_beta);
// Testing samplers
// set randomness seed
uint32_t* seed = malloc(sizeof(uint32_t));
*seed = 1000; // xorshift can't start with 0
// Test float sampler
test_and_time_sampler_float("cdf_uniform_0_1", cdf_uniform_0_1, seed);
test_and_time_sampler_float("cdf_squared_0_1", cdf_squared_0_1, seed);
test_and_time_sampler_float("cdf_normal_0_1", cdf_normal_0_1, seed);
// Get some normal samples using a previous approach
printf("\nGetting some samples from unit_normal\n");
clock_t begin_2 = clock();
for (int i = 0; i < NUM_SAMPLES; i++) {
float normal_sample = unit_normal(seed);
// printf("%f\n", normal_sample);
}
clock_t end_2 = clock();
float time_spent_2 = (float)(end_2 - begin_2) / CLOCKS_PER_SEC;
printf("Time spent: %f\n", time_spent_2);
// Test box sampler
test_and_time_sampler_box("cdf_beta", cdf_beta, seed);
// Ok, this is slower than python!!
// Partly this is because I am using a more general algorithm,
// which applies to any cdf
// But I am also using really anal convergence conditions.
// This could be optimized.
free(seed);
return 0;
}