squiggle.c/squiggle_more.c

#include <float.h>
#include <math.h>
#include <limits.h>
#include <omp.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include "squiggle.h"

/* Math constants */
#define PI 3.14159265358979323846 // M_PI in gcc gnu99
#define NORMAL90CONFIDENCE 1.6448536269514727

/* Some error niceties */
// These won't be used until later 
#define MAX_ERROR_LENGTH 500
#define EXIT_ON_ERROR 0
#define PROCESS_ERROR(error_msg) process_error(error_msg, EXIT_ON_ERROR, __FILE__, __LINE__)

/* Get confidence intervals, given a sampler */
// Not in core yet because I'm not sure how much I like the struct
// and the built-in 100k samples
// to do: add n to function parameters and document
typedef struct ci_t {
    float low;
    float high;
} ci;
int compare_doubles(const void* p, const void* q)
{
    // https://wikiless.esmailelbob.xyz/wiki/Qsort?lang=en
    double x = *(const double*)p;
    double y = *(const double*)q;

    /* Avoid returning x - y, which can cause undefined behaviour
       because of signed integer overflow. */
    if (x < y)
        return -1; // Return -1 if you want ascending, 1 if you want descending order.
    else if (x > y)
        return 1; // Return 1 if you want ascending, -1 if you want descending order.

    return 0;
}
ci get_90_confidence_interval(double (*sampler)(uint64_t*), uint64_t* seed)
{
    int n = 100 * 1000;
    double* samples_array = malloc(n * sizeof(double));
    for (int i = 0; i < n; i++) {
        samples_array[i] = sampler(seed);
    }
    qsort(samples_array, n, sizeof(double), compare_doubles);

    ci result = {
        .low = samples_array[5000],
        .high = samples_array[94999],
    };
    free(samples_array);

    return result;
}

/* Scaffolding to handle errors */
// We are building towards sample from an arbitrary cdf
// and that operation might fail
// so we build some scaffolding here
struct box {
    int empty;
    double content;
    char* error_msg;
};

struct box process_error(const char* error_msg, int should_exit, char* file, int line)
{
    if (should_exit) {
        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); // NOLINT: We are being carefull here by considering MAX_ERROR_LENGTH explicitly.
        struct box error = { .empty = 1, .error_msg = error_msg };
        return error;
    }
}

/* Invert an arbitrary cdf at a point */
// Version #1:
// - input: (cdf: double => double, p)
// - output: Box(number|error)
struct box inverse_cdf_double(double cdf(double), double 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

    double low = -1.0;
    double 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) {
        return 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))) {
            double mid = (high + low) / 2;
            int mid_not_new = (mid == low) || (mid == high);
            // double width = high - low;
            // if ((width < 1e-8) || mid_not_new){
            if (mid_not_new) {
                convergence_condition = 1;
            } else {
                double 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 {
            return PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
        }
    }
}

// Version #2: 
// - input: (cdf: double => Box(number|error), p)
// - output: Box(number|error)
struct box inverse_cdf_box(struct box cdf_box(double), double 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

    double low = -1.0;
    double 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) {
            return PROCESS_ERROR(cdf_low.error_msg);
        }

        struct box cdf_high = cdf_box(high);
        if (cdf_high.empty) {
            return 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) {
        return 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))) {
            double mid = (high + low) / 2;
            int mid_not_new = (mid == low) || (mid == high);
            // double 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) {
                    return PROCESS_ERROR(cdf_mid.error_msg);
                }
                double 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 {
            return PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
        }
    }
}

/* Sample from an arbitrary cdf */
// Before: invert an arbitrary cdf at a point
// Now: from an arbitrary cdf, get a sample
struct box sampler_cdf_box(struct box cdf(double), uint64_t* seed)
{
    double p = sample_unit_uniform(seed);
    struct box result = inverse_cdf_box(cdf, p);
    return result;
}
struct box sampler_cdf_double(double cdf(double), uint64_t* seed)
{
    double p = sample_unit_uniform(seed);
    struct box result = inverse_cdf_double(cdf, p);
    return result;
}
double sampler_cdf_danger(struct box cdf(double), uint64_t* seed)
{
    double p = sample_unit_uniform(seed);
    struct box result = inverse_cdf_box(cdf, p);
	if(result.empty){
	    exit(1);
	}else{
		return result.content;
	}
}

/* Algebra manipulations */
// here I discover named structs,
// which mean that I don't have to be typing
// struct blah all the time.
typedef struct normal_params_t {
    double mean;
    double std;
} normal_params;

normal_params algebra_sum_normals(normal_params a, normal_params b)
{
    normal_params result = {
        .mean = a.mean + b.mean,
        .std = sqrt((a.std * a.std) + (b.std * b.std)),
    };
    return result;
}

typedef struct lognormal_params_t {
    double logmean;
    double logstd;
} lognormal_params;

lognormal_params algebra_product_lognormals(lognormal_params a, lognormal_params b)
{
    lognormal_params result = {
        .logmean = a.logmean + b.logmean,
        .logstd = sqrt((a.logstd * a.logstd) + (b.logstd * b.logstd)),
    };
    return result;
}

lognormal_params convert_ci_to_lognormal_params(ci x)
{
    double loghigh = logf(x.high);
    double loglow = logf(x.low);
    double logmean = (loghigh + loglow) / 2.0;
    double logstd = (loghigh - loglow) / (2.0 * NORMAL90CONFIDENCE);
    lognormal_params result = { .logmean = logmean, .logstd = logstd };
    return result;
}

ci convert_lognormal_params_to_ci(lognormal_params y)
{
    double h = y.logstd * NORMAL90CONFIDENCE;
    double loghigh = y.logmean + h;
    double loglow = y.logmean - h;
    ci result = { .low = exp(loglow), .high = exp(loghigh) };
    return result;
}

/* Parallel sampler */
void parallel_sampler(double (*sampler)(uint64_t* seed), double* results, int n_threads, int n_samples){
    
    // Division terminology:
    // a =  b * quotient + reminder
    // a = (a/b)*b + (a%b)
    // dividend: a
    // divisor: b
    // quotient = a / b
    // reminder = a % b
    // "divisor's multiple" := (a/b)*b

    // now, we have n_samples and n_threads
    // to make our life easy, each thread will have a number of samples of: a/b (quotient)
    // and we'll compute the remainder of samples separately
    // to possibly do by Jorge: improve so that the remainder is included in the threads

    int quotient = n_samples / n_threads;
    int remainder = n_samples % n_threads;
    int divisor_multiple = quotient * n_threads; 

    uint64_t** seeds = malloc(n_threads * sizeof(uint64_t*));
    // printf("UINT64_MAX: %lu\n", UINT64_MAX);
    srand(1);
    for (uint64_t i = 0; i < n_threads; i++) {
        seeds[i] = malloc(sizeof(uint64_t));
        // Constraints: 
        // - xorshift can't start with 0
        // - the seeds should be reasonably separated and not correlated
        *seeds[i] = (uint64_t) rand() * (UINT64_MAX / RAND_MAX);
        // printf("#%ld: %lu\n",i, *seeds[i]);

        // Other initializations tried:
        // *seeds[i] = 1 + i;
        // *seeds[i] = (i + 0.5)*(UINT64_MAX/n_threads);
        // *seeds[i] = (i + 0.5)*(UINT64_MAX/n_threads) + constant * i;
    }

    int i;
    #pragma omp parallel private(i)
        {
        #pragma omp for
        for (i = 0; i < n_threads; i++) {
            int lower_bound_inclusive = i * quotient;
            int upper_bound_not_inclusive = ((i+1) * quotient); // note the < in the for loop below, 
            // printf("Lower bound: %d, upper bound: %d\n", lower_bound, upper_bound);
            for (int j = lower_bound_inclusive; j < upper_bound_not_inclusive; j++) {
                results[j] = sampler(seeds[i]);
            }
        }
    }
    for(int j=divisor_multiple; j<n_samples; j++){
        results[j] = sampler(seeds[0]);
        // we can just reuse a seed, this isn't problematic because we are not doing multithreading
    }

    for (uint64_t i = 0; i < n_threads; i++) {
        free(seeds[i]);
    }
    free(seeds);
}