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460 lines
15 KiB
460 lines
15 KiB
#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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#include <string.h> // memcpy
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/* Cache optimizations */
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#define CACHE_LINE_SIZE 64
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// getconf LEVEL1_DCACHE_LINESIZE
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// <https://stackoverflow.com/questions/794632/programmatically-get-the-cache-line-size>
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typedef struct seed_cache_box_t {
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uint64_t seed;
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char padding[CACHE_LINE_SIZE - sizeof(uint64_t)];
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// Cache line size is 64 *bytes*, uint64_t is 64 *bits* (8 bytes). Different units!
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} seed_cache_box;
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// This avoids "false sharing", i.e., different threads competing for the same cache line
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// Dealing with this shaves 4ms from a 12ms process, or a third of runtime
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// <http://www.nic.uoregon.edu/~khuck/ts/acumem-report/manual_html/ch06s07.html>
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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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// Terms of the division:
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// a = b * quotient + reminder
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// a = b * (a/b) + (a%b)
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// dividend: a
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// divisor: b
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// quotient = a/b
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// reminder = a%b
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// "divisor's multiple" := b*(a/b)
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// now, we have n_samples and n_threads
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// to make our life easy, each thread will have a number of samples of: a/b (quotient)
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// and we'll compute the remainder of samples separately
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// to possibly do by Jorge: improve so that the remainder is included in the threads
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int quotient = n_samples / n_threads;
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int divisor_multiple = quotient * n_threads;
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// uint64_t** seeds = malloc((size_t)n_threads * sizeof(uint64_t*));
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seed_cache_box* cache_box = (seed_cache_box*)malloc(sizeof(seed_cache_box) * (size_t)n_threads);
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// seed_cache_box cache_box[n_threads]; // we could use the C stack. On normal linux machines, it's 8MB ($ ulimit -s). However, it doesn't quite feel right.
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srand(1);
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for (int i = 0; i < n_threads; i++) {
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// Constraints:
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// - xorshift can't start with 0
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// - the seeds should be reasonably separated and not correlated
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cache_box[i].seed = (uint64_t)rand() * (UINT64_MAX / RAND_MAX);
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// Other initializations tried:
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// *seeds[i] = 1 + i;
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// *seeds[i] = (i + 0.5)*(UINT64_MAX/n_threads);
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// *seeds[i] = (i + 0.5)*(UINT64_MAX/n_threads) + constant * i;
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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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// It's possible I don't need the for, and could instead call omp
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// in some different way and get the thread number with omp_get_thread_num()
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int lower_bound_inclusive = i * quotient;
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int upper_bound_not_inclusive = ((i + 1) * quotient); // note the < in the for loop below,
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for (int j = lower_bound_inclusive; j < upper_bound_not_inclusive; j++) {
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results[j] = sampler(&(cache_box[i].seed));
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/*
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t starts at 0 and ends at T
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at t=0,
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thread i accesses: results[i*quotient +0],
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thread i+1 acccesses: results[(i+1)*quotient +0]
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at t=T
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thread i accesses: results[(i+1)*quotient -1]
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thread i+1 acccesses: results[(i+2)*quotient -1]
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The results[j] that are directly adjacent are
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results[(i+1)*quotient -1] (accessed by thread i at time T)
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results[(i+1)*quotient +0] (accessed by thread i+1 at time 0)
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and these are themselves adjacent to
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results[(i+1)*quotient -2] (accessed by thread i at time T-1)
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results[(i+1)*quotient +1] (accessed by thread i+1 at time 2)
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If T is large enough, which it is, two threads won't access the same
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cache line at the same time.
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Pictorially:
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at t=0 ....i.........I.........
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at t=T .............i.........I
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and the two never overlap
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Note that results[j] is a double, a double has 8 bytes (64 bits)
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8 doubles fill a cache line of 64 bytes.
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So we specifically won't get problems as long as n_samples/n_threads > 8
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n_threads is normally 16, so n_samples > 128
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Note also that this is only a problem in terms of speed, if n_samples<128
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the results are still computed, it'll just be slower
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*/
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}
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}
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}
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for (int j = divisor_multiple; j < n_samples; j++) {
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results[j] = sampler(&(cache_box[0].seed));
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// we can just reuse a seed,
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// this isn't problematic because we;ve now stopped doing multithreading
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}
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free(cache_box);
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}
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/* Get confidence intervals, given a sampler */
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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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inline 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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if (low > high || high >= length) {
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printf("Invariant violated for function partition in %s (%d)", __FILE__, __LINE__);
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exit(1);
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}
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// Note: the scratchpad/ folder in commit 578bfa27 has printfs sprinkled throughout
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int pivot = low + (int)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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double* ys = malloc((size_t)n * sizeof(double));
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memcpy(ys, xs, (size_t)n * sizeof(double));
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// ^: don't rearrange item order in the original array
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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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double result = ys[low];
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free(ys);
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return result;
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}
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int pivot = partition(low, high, ys, n);
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if (pivot == k) {
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double result = ys[pivot];
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free(ys);
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return result;
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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 = (int)floor(interval.low * n);
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int high_k = (int)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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double array_get_median(double xs[], int n)
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{
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int median_k = (int)floor(0.5 * n);
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return quickselect(median_k, xs, n);
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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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void array_print_stats(double xs[], int n)
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{
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ci ci_90 = array_get_ci((ci) { .low = 0.05, .high = 0.95 }, xs, n);
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ci ci_80 = array_get_ci((ci) { .low = 0.1, .high = 0.9 }, xs, n);
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ci ci_50 = array_get_ci((ci) { .low = 0.25, .high = 0.75 }, xs, n);
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double median = array_get_median(xs, n);
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double mean = array_mean(xs, n);
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double std = array_std(xs, n);
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printf("| Statistic | Value |\n"
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"| --- | --- |\n"
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"| Mean | %lf |\n"
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"| Median | %lf |\n"
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"| Std | %lf |\n"
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"| 90%% confidence interval | %lf to %lf |\n"
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"| 80%% confidence interval | %lf to %lf |\n"
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"| 50%% confidence interval | %lf to %lf |\n",
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mean, median, std, ci_90.low, ci_90.high, ci_80.low, ci_80.high, ci_50.low, ci_50.high);
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}
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void array_print_histogram(double* xs, int n_samples, int n_bins)
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{
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// Interface inspired by <https://github.com/red-data-tools/YouPlot>
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if (n_bins <= 1) {
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fprintf(stderr, "Number of bins must be greater than 1.\n");
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return;
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} else if (n_samples <= 1) {
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fprintf(stderr, "Number of samples must be higher than 1.\n");
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return;
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}
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int* bins = (int*)calloc((size_t)n_bins, sizeof(int));
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if (bins == NULL) {
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fprintf(stderr, "Memory allocation for bins failed.\n");
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return;
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}
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// Find the minimum and maximum values from the samples
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double min_value = xs[0], max_value = xs[0];
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for (int i = 0; i < n_samples; i++) {
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if (xs[i] < min_value) {
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min_value = xs[i];
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}
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if (xs[i] > max_value) {
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max_value = xs[i];
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}
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}
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// Avoid division by zero for a single unique value
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if (min_value == max_value) {
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max_value++;
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}
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// Calculate bin width
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double bin_width = (max_value - min_value) / n_bins;
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// Fill the bins with sample counts
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for (int i = 0; i < n_samples; i++) {
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int bin_index = (int)((xs[i] - min_value) / bin_width);
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if (bin_index == n_bins) {
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bin_index--; // Last bin includes max_value
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}
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bins[bin_index]++;
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}
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// Calculate the scaling factor based on the maximum bin count
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int max_bin_count = 0;
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for (int i = 0; i < n_bins; i++) {
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if (bins[i] > max_bin_count) {
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max_bin_count = bins[i];
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}
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}
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const int MAX_WIDTH = 50; // Adjust this to your terminal width
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double scale = max_bin_count > MAX_WIDTH ? (double)MAX_WIDTH / max_bin_count : 1.0;
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// Print the histogram
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for (int i = 0; i < n_bins; i++) {
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double bin_start = min_value + i * bin_width;
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double bin_end = bin_start + bin_width;
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int decimalPlaces = 1;
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if ((0 < bin_width) && (bin_width < 1)) {
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int magnitude = (int)floor(log10(bin_width));
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decimalPlaces = -magnitude;
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decimalPlaces = decimalPlaces > 10 ? 10 : decimalPlaces;
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}
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printf("[%*.*f, %*.*f", 4 + decimalPlaces, decimalPlaces, bin_start, 4 + decimalPlaces, decimalPlaces, bin_end);
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char interval_delimiter = ')';
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if (i == (n_bins - 1)) {
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interval_delimiter = ']'; // last bucket is inclusive
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}
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printf("%c: ", interval_delimiter);
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int marks = (int)(bins[i] * scale);
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for (int j = 0; j < marks; j++) {
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printf("█");
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}
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printf(" %d\n", bins[i]);
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}
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// Free the allocated memory for bins
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free(bins);
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}
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void array_print_90_ci_histogram(double* xs, int n_samples, int n_bins)
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{
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// Code duplicated from previous function
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// I'll consider simplifying it at some future point
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// Possible ideas:
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// - having only one function that takes any confidence interval?
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// - having a utility function that is called by both functions?
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ci ci_90 = array_get_90_ci(xs, n_samples);
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if (n_bins <= 1) {
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fprintf(stderr, "Number of bins must be greater than 1.\n");
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return;
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} else if (n_samples <= 10) {
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fprintf(stderr, "Number of samples must be higher than 10.\n");
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return;
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}
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int* bins = (int*)calloc((size_t)n_bins, sizeof(int));
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if (bins == NULL) {
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fprintf(stderr, "Memory allocation for bins failed.\n");
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return;
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}
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double min_value = ci_90.low, max_value = ci_90.high;
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// Avoid division by zero for a single unique value
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if (min_value == max_value) {
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max_value++;
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}
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double bin_width = (max_value - min_value) / n_bins;
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// Fill the bins with sample counts
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int below_min = 0, above_max = 0;
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for (int i = 0; i < n_samples; i++) {
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if (xs[i] < min_value) {
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below_min++;
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} else if (xs[i] > max_value) {
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above_max++;
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} else {
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int bin_index = (int)((xs[i] - min_value) / bin_width);
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if (bin_index == n_bins) {
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bin_index--; // Last bin includes max_value
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}
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bins[bin_index]++;
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}
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}
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// Calculate the scaling factor based on the maximum bin count
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int max_bin_count = 0;
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for (int i = 0; i < n_bins; i++) {
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if (bins[i] > max_bin_count) {
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max_bin_count = bins[i];
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}
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}
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const int MAX_WIDTH = 40; // Adjust this to your terminal width
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double scale = max_bin_count > MAX_WIDTH ? (double)MAX_WIDTH / max_bin_count : 1.0;
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// Print the histogram
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int decimalPlaces = 1;
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if ((0 < bin_width) && (bin_width < 1)) {
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int magnitude = (int)floor(log10(bin_width));
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decimalPlaces = -magnitude;
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decimalPlaces = decimalPlaces > 10 ? 10 : decimalPlaces;
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}
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printf("(%*s, %*.*f): ", 6 + decimalPlaces, "-∞", 4 + decimalPlaces, decimalPlaces, min_value);
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int marks_below_min = (int)(below_min * scale);
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for (int j = 0; j < marks_below_min; j++) {
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printf("█");
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}
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printf(" %d\n", below_min);
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for (int i = 0; i < n_bins; i++) {
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double bin_start = min_value + i * bin_width;
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double bin_end = bin_start + bin_width;
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printf("[%*.*f, %*.*f", 4 + decimalPlaces, decimalPlaces, bin_start, 4 + decimalPlaces, decimalPlaces, bin_end);
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char interval_delimiter = ')';
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if (i == (n_bins - 1)) {
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interval_delimiter = ']'; // last bucket is inclusive
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}
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printf("%c: ", interval_delimiter);
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int marks = (int)(bins[i] * scale);
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for (int j = 0; j < marks; j++) {
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printf("█");
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}
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printf(" %d\n", bins[i]);
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}
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printf("(%*.*f, %*s): ", 4 + decimalPlaces, decimalPlaces, max_value, 6 + decimalPlaces, "+∞");
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int marks_above_max = (int)(above_max * scale);
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for (int j = 0; j < marks_above_max; j++) {
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printf("█");
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}
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printf(" %d\n", above_max);
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// Free the allocated memory for bins
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free(bins);
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}
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/* Algebra manipulations */
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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 = log(x.high);
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double loglow = log(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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