squiggle.c/scratchpad/scratchpad.c

#include <float.h> // FLT_MAX, FLT_MIN
#include <limits.h> // INT_MAX
#include <math.h> // erf, sqrt
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/types.h>
#include <time.h>

#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)
#define NUM_SAMPLES 10

struct box {
    int empty;
    float content;
    char* error_msg;
};

// 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
}

// [x] to do: add beta.
// [x] for the cdf, use this incomplete beta function implementation, based on continuous fractions:
// <https://codeplea.com/incomplete-beta-function-c>
// <https://github.com/codeplea/incbeta>

#define STOP_BETA 1.0e-8
#define TINY_BETA 1.0e-30
struct box incbeta(float a, float b, float x)
{
    // Descended from <https://github.com/codeplea/incbeta/blob/master/incbeta.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);
    }
}

// Inverse cdf at point
// Two versions of this function:
//   - raw, dealing with cdfs that return floats
//   - box, dealing with cdfs that return a box.

// Inverse cdf
struct box inverse_cdf_float(float cdf(float), float p)
{
    // given a cdf: [-Inf, Inf] => [0,1]
    // returns a box with either
    // x such that cdf(x) = p
    // or an error
    // if EXIT_ON_ERROR is set to 1, it exits instead of providing an error

    float low = -1.0;
    float high = 1.0;

    // 1. Make sure that cdf(low) < p < cdf(high)
    int interval_found = 0;
    while ((!interval_found) && (low > -FLT_MAX / 4) && (high < FLT_MAX / 4)) {
        // ^ Using FLT_MIN and FLT_MAX is overkill
        // but it's also the *correct* thing to do.

        int low_condition = (cdf(low) < p);
        int high_condition = (p < cdf(high));
        if (low_condition && high_condition) {
            interval_found = 1;
        } else if (!low_condition) {
            low = low * 2;
        } else if (!high_condition) {
            high = high * 2;
        }
    }

    if (!interval_found) {
        PROCESS_ERROR("Interval containing the target value not found, in function inverse_cdf");
    } else {

        int convergence_condition = 0;
        int count = 0;
        while (!convergence_condition && (count < (INT_MAX / 2))) {
            float mid = (high + low) / 2;
            int mid_not_new = (mid == low) || (mid == high);
            // float width = high - low;
            // if ((width < 1e-8) || mid_not_new){
            if (mid_not_new) {
                convergence_condition = 1;
            } else {
                float mid_sign = cdf(mid) - p;
                if (mid_sign < 0) {
                    low = mid;
                } else if (mid_sign > 0) {
                    high = mid;
                } else if (mid_sign == 0) {
                    low = mid;
                    high = mid;
                }
            }
        }

        if (convergence_condition) {
            struct box result = { .empty = 0, .content = low };
            return result;
        } else {
            PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
        }
    }
}

struct box inverse_cdf_box(struct box cdf_box(float), float p)
{
    // given a cdf: [-Inf, Inf] => Box([0,1])
    // returns a box with either
    // x such that cdf(x) = p
    // or an error
    // if EXIT_ON_ERROR is set to 1, it exits instead of providing an error

    float low = -1.0;
    float high = 1.0;

    // 1. Make sure that cdf(low) < p < cdf(high)
    int interval_found = 0;
    while ((!interval_found) && (low > -FLT_MAX / 4) && (high < FLT_MAX / 4)) {
        // ^ Using FLT_MIN and FLT_MAX is overkill
        // but it's also the *correct* thing to do.
        struct box cdf_low = cdf_box(low);
        if (cdf_low.empty) {
            PROCESS_ERROR(cdf_low.error_msg);
        }

        struct box cdf_high = cdf_box(high);
        if (cdf_high.empty) {
            PROCESS_ERROR(cdf_low.error_msg);
        }

        int low_condition = (cdf_low.content < p);
        int high_condition = (p < cdf_high.content);
        if (low_condition && high_condition) {
            interval_found = 1;
        } else if (!low_condition) {
            low = low * 2;
        } else if (!high_condition) {
            high = high * 2;
        }
    }

    if (!interval_found) {
        PROCESS_ERROR("Interval containing the target value not found, in function inverse_cdf");
    } else {

        int convergence_condition = 0;
        int count = 0;
        while (!convergence_condition && (count < (INT_MAX / 2))) {
            float mid = (high + low) / 2;
            int mid_not_new = (mid == low) || (mid == high);
            // float width = high - low;
            if (mid_not_new) {
                // if ((width < 1e-8) || mid_not_new){
                convergence_condition = 1;
            } else {
                struct box cdf_mid = cdf_box(mid);
                if (cdf_mid.empty) {
                    PROCESS_ERROR(cdf_mid.error_msg);
                }
                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");
        }
    }
}

// Some randomness functions for:
//   - Sampling from a cdf
//   - Benchmarking against a previous approach, which will be faster, but less general

// Get random number between 0 and 1
uint32_t xorshift32(uint32_t* seed)
{
    // Algorithm "xor" from p. 4 of Marsaglia, "Xorshift RNGs"
    // See <https://stackoverflow.com/questions/53886131/how-does-xorshift32-works>
    // https://en.wikipedia.org/wiki/Xorshift
    // Also some drama: <https://www.pcg-random.org/posts/on-vignas-pcg-critique.html>, <https://prng.di.unimi.it/>

    uint32_t x = *seed;
    x ^= x << 13;
    x ^= x >> 17;
    x ^= x << 5;
    return *seed = x;
}

// Distribution & sampling functions
float rand_0_to_1(uint32_t* seed)
{
    return ((float)xorshift32(seed)) / ((float)UINT32_MAX);
}

// 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;
}

// Comparison point with raw normal sampler
const float PI = 3.14159265358979323846;
float sampler_normal_0_1(uint32_t* seed)
{
    float u1 = rand_0_to_1(seed);
    float u2 = rand_0_to_1(seed);
    float z = sqrtf(-2.0 * log(u1)) * sin(2 * PI * u2);
    return z;
}

// 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 sampler_normal_0_1\n");

    clock_t begin_2 = clock();

    for (int i = 0; i < NUM_SAMPLES; i++) {
        float normal_sample = sampler_normal_0_1(seed);
        printf("%f\n", normal_sample);
    }

    clock_t end_2 = clock();
    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);

    free(seed);
    return 0;
}