forked from personal/squiggle.c
396 lines
12 KiB
C
396 lines
12 KiB
C
#include "squiggle.h"
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#include <float.h>
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#include <limits.h>
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#include <math.h>
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#include <omp.h>
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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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/* Parallel sampler */
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void sampler_parallel(double (*sampler)(uint64_t* seed), double* results, int n_threads, int n_samples)
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{
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if ((n_samples % n_threads) != 0) {
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fprintf(stderr, "Number of samples isn't divisible by number of threads, aborting\n");
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exit(1);
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}
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uint64_t** seeds = malloc(n_threads * sizeof(uint64_t*));
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for (uint64_t i = 0; i < n_threads; i++) {
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seeds[i] = malloc(sizeof(uint64_t));
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*seeds[i] = i + 1; // xorshift can't start with 0
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}
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int i;
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#pragma omp parallel private(i)
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{
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#pragma omp for
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for (i = 0; i < n_threads; i++) {
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int lower_bound = i * (n_samples / n_threads);
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int upper_bound = ((i + 1) * (n_samples / n_threads)) - 1;
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// printf("Lower bound: %d, upper bound: %d\n", lower_bound, upper_bound);
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for (int j = lower_bound; j < upper_bound; j++) {
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results[j] = sampler(seeds[i]);
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}
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}
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}
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for (uint64_t i = 0; i < n_threads; i++) {
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free(seeds[i]);
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}
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free(seeds);
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}
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/* Get confidence intervals, given a sampler */
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// Not in core yet because I'm not sure how much I like the struct
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// and the built-in 100k samples
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// to do: add n to function parameters and document
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typedef struct ci_t {
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double low;
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double high;
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} ci;
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static void swp(int i, int j, double xs[])
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{
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double tmp = xs[i];
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xs[i] = xs[j];
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xs[j] = tmp;
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}
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static int partition(int low, int high, double xs[], int length)
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{
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// To understand this function:
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// - see the note after gt variable definition
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// - go to commit 578bfa27 and the scratchpad/ folder in it, which has printfs sprinkled throughout
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int pivot = low + floor((high - low) / 2);
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double pivot_value = xs[pivot];
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swp(pivot, high, xs);
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int gt = low; /* This pointer will iterate until finding an element which is greater than the pivot. Then it will move elements that are smaller before it--more specifically, it will move elements to its position and then increment. As a result all elements between gt and i will be greater than the pivot. */
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for (int i = low; i < high; i++) {
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if (xs[i] < pivot_value) {
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swp(gt, i, xs);
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gt++;
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}
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}
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swp(high, gt, xs);
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return gt;
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}
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static double quickselect(int k, double xs[], int n)
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{
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// https://en.wikipedia.org/wiki/Quickselect
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int low = 0;
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int high = n - 1;
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for (;;) {
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if (low == high) {
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return xs[low];
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}
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int pivot = partition(low, high, xs, n);
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if (pivot == k) {
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return xs[pivot];
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} else if (k < pivot) {
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high = pivot - 1;
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} else {
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low = pivot + 1;
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}
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}
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}
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ci array_get_ci(ci interval, double* xs, int n)
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{
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int low_k = floor(interval.low * n);
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int high_k = ceil(interval.high * n);
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ci result = {
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.low = quickselect(low_k, xs, n),
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.high = quickselect(high_k, xs, n),
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};
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return result;
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}
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ci array_get_90_ci(double xs[], int n)
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{
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return array_get_ci((ci) { .low = 0.05, .high = 0.95 }, xs, n);
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}
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ci sampler_get_ci(ci interval, double (*sampler)(uint64_t*), int n, uint64_t* seed)
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{
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double* xs = malloc(n * sizeof(double));
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/*for (int i = 0; i < n; i++) {
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xs[i] = sampler(seed);
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}*/
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sampler_parallel(sampler, xs, 16, n);
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ci result = array_get_ci(interval, xs, n);
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free(xs);
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return result;
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}
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ci sampler_get_90_ci(double (*sampler)(uint64_t*), int n, uint64_t* seed)
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{
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return sampler_get_ci((ci) { .low = 0.05, .high = 0.95 }, sampler, n, seed);
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}
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/* Algebra manipulations */
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// here I discover named structs,
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// which mean that I don't have to be typing
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// struct blah all the time.
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#define NORMAL90CONFIDENCE 1.6448536269514727
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typedef struct normal_params_t {
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double mean;
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double std;
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} normal_params;
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normal_params algebra_sum_normals(normal_params a, normal_params b)
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{
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normal_params result = {
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.mean = a.mean + b.mean,
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.std = sqrt((a.std * a.std) + (b.std * b.std)),
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};
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return result;
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}
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typedef struct lognormal_params_t {
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double logmean;
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double logstd;
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} lognormal_params;
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lognormal_params algebra_product_lognormals(lognormal_params a, lognormal_params b)
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{
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lognormal_params result = {
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.logmean = a.logmean + b.logmean,
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.logstd = sqrt((a.logstd * a.logstd) + (b.logstd * b.logstd)),
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};
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return result;
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}
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lognormal_params convert_ci_to_lognormal_params(ci x)
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{
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double loghigh = logf(x.high);
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double loglow = logf(x.low);
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double logmean = (loghigh + loglow) / 2.0;
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double logstd = (loghigh - loglow) / (2.0 * NORMAL90CONFIDENCE);
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lognormal_params result = { .logmean = logmean, .logstd = logstd };
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return result;
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}
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ci convert_lognormal_params_to_ci(lognormal_params y)
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{
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double h = y.logstd * NORMAL90CONFIDENCE;
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double loghigh = y.logmean + h;
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double loglow = y.logmean - h;
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ci result = { .low = exp(loglow), .high = exp(loghigh) };
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return result;
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}
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/* Scaffolding to handle errors */
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// We will sample from an arbitrary cdf
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// and that operation might fail
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// so we build some scaffolding here
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#define MAX_ERROR_LENGTH 500
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#define EXIT_ON_ERROR 0
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#define PROCESS_ERROR(error_msg) process_error(error_msg, EXIT_ON_ERROR, __FILE__, __LINE__)
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struct box {
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int empty;
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double content;
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char* error_msg;
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};
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struct box process_error(const char* error_msg, int should_exit, char* file, int line)
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{
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if (should_exit) {
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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); // NOLINT: We are being carefull here by considering MAX_ERROR_LENGTH explicitly.
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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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}
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/* Invert an arbitrary cdf at a point */
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// Version #1:
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// - input: (cdf: double => double, p)
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// - output: Box(number|error)
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struct box inverse_cdf_double(double cdf(double), double 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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double low = -1.0;
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double 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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return 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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double mid = (high + low) / 2;
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int mid_not_new = (mid == low) || (mid == high);
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// double 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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double 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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return 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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// Version #2:
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// - input: (cdf: double => Box(number|error), p)
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// - output: Box(number|error)
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struct box inverse_cdf_box(struct box cdf_box(double), double 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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double low = -1.0;
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double 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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return 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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return 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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return 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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double mid = (high + low) / 2;
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int mid_not_new = (mid == low) || (mid == high);
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// double 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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return PROCESS_ERROR(cdf_mid.error_msg);
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}
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double 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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return 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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/* Sample from an arbitrary cdf */
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// Before: invert an arbitrary cdf at a point
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// Now: from an arbitrary cdf, get a sample
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struct box sampler_cdf_box(struct box cdf(double), uint64_t* seed)
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{
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double p = sample_unit_uniform(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_cdf_double(double cdf(double), uint64_t* seed)
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{
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double p = sample_unit_uniform(seed);
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struct box result = inverse_cdf_double(cdf, p);
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return result;
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}
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double sampler_cdf_danger(struct box cdf(double), uint64_t* seed)
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{
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double p = sample_unit_uniform(seed);
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struct box result = inverse_cdf_box(cdf, p);
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if (result.empty) {
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exit(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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/* array print: potentially useful for debugging */
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void array_print(double xs[], int n)
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{
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printf("[");
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for (int i = 0; i < n - 1; i++) {
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printf("%f, ", xs[i]);
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}
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printf("%f", xs[n - 1]);
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printf("]\n");
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}
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