squiggle.c/squiggle_more.c

449 lines
15 KiB
C

#include "squiggle.h"
#include <float.h>
#include <limits.h>
#include <math.h>
#include <omp.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h> // memcpy
/* Cache optimizations */
#define CACHE_LINE_SIZE 64
// getconf LEVEL1_DCACHE_LINESIZE
// <https://stackoverflow.com/questions/794632/programmatically-get-the-cache-line-size>
typedef struct seed_cache_box_t {
uint64_t seed;
char padding[CACHE_LINE_SIZE - sizeof(uint64_t)];
// Cache line size is 64 *bytes*, uint64_t is 64 *bits* (8 bytes). Different units!
} seed_cache_box;
// This avoids "false sharing", i.e., different threads competing for the same cache line
// Dealing with this shaves 4ms from a 12ms process, or a third of runtime
// <http://www.nic.uoregon.edu/~khuck/ts/acumem-report/manual_html/ch06s07.html>
/* Parallel sampler */
void sampler_parallel(double (*sampler)(uint64_t* seed), double* results, int n_threads, int n_samples)
{
// Terms of the division:
// a = b * quotient + reminder
// a = b * (a/b) + (a%b)
// dividend: a
// divisor: b
// quotient = a/b
// reminder = a%b
// "divisor's multiple" := b*(a/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 divisor_multiple = quotient * n_threads;
// uint64_t** seeds = malloc((size_t)n_threads * sizeof(uint64_t*));
seed_cache_box* cache_box = (seed_cache_box*)malloc(sizeof(seed_cache_box) * (size_t)n_threads);
// 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.
srand(1);
for (int i = 0; i < n_threads; i++) {
// Constraints:
// - xorshift can't start with 0
// - the seeds should be reasonably separated and not correlated
cache_box[i].seed = (uint64_t)rand() * (UINT64_MAX / RAND_MAX);
// 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++) {
// It's possible I don't need the for, and could instead call omp
// in some different way and get the thread number with omp_get_thread_num()
int lower_bound_inclusive = i * quotient;
int upper_bound_not_inclusive = ((i + 1) * quotient); // note the < in the for loop below,
for (int j = lower_bound_inclusive; j < upper_bound_not_inclusive; j++) {
results[j] = sampler(&(cache_box[i].seed));
/*
t starts at 0 and ends at T
at t=0,
thread i accesses: results[i*quotient +0],
thread i+1 acccesses: results[(i+1)*quotient +0]
at t=T
thread i accesses: results[(i+1)*quotient -1]
thread i+1 acccesses: results[(i+2)*quotient -1]
The results[j] that are directly adjacent are
results[(i+1)*quotient -1] (accessed by thread i at time T)
results[(i+1)*quotient +0] (accessed by thread i+1 at time 0)
and these are themselves adjacent to
results[(i+1)*quotient -2] (accessed by thread i at time T-1)
results[(i+1)*quotient +1] (accessed by thread i+1 at time 2)
If T is large enough, which it is, two threads won't access the same
cache line at the same time.
Pictorially:
at t=0 ....i.........I.........
at t=T .............i.........I
and the two never overlap
Note that results[j] is a double, a double has 8 bytes (64 bits)
8 doubles fill a cache line of 64 bytes.
So we specifically won't get problems as long as n_samples/n_threads > 8
n_threads is normally 16, so n_samples > 128
Note also that this is only a problem in terms of speed, if n_samples<128
the results are still computed, it'll just be slower
*/
}
}
}
for (int j = divisor_multiple; j < n_samples; j++) {
results[j] = sampler(&(cache_box[0].seed));
// we can just reuse a seed,
// this isn't problematic because we;ve now stopped doing multithreading
}
free(cache_box);
}
/* Get confidence intervals, given a sampler */
typedef struct ci_t {
double low;
double high;
} ci;
inline static void swp(int i, int j, double xs[])
{
double tmp = xs[i];
xs[i] = xs[j];
xs[j] = tmp;
}
static int partition(int low, int high, double xs[], int length)
{
if (low > high || high >= length) {
printf("Invariant violated for function partition in %s (%d)", __FILE__, __LINE__);
exit(1);
}
// Note: the scratchpad/ folder in commit 578bfa27 has printfs sprinkled throughout
int pivot = low + (int)floor((high - low) / 2);
double pivot_value = xs[pivot];
swp(pivot, high, xs);
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. */
for (int i = low; i < high; i++) {
if (xs[i] < pivot_value) {
swp(gt, i, xs);
gt++;
}
}
swp(high, gt, xs);
return gt;
}
static double quickselect(int k, double xs[], int n)
{
// https://en.wikipedia.org/wiki/Quickselect
double* ys = malloc((size_t)n * sizeof(double));
memcpy(ys, xs, (size_t)n * sizeof(double));
// ^: don't rearrange item order in the original array
int low = 0;
int high = n - 1;
for (;;) {
if (low == high) {
double result = ys[low];
free(ys);
return result;
}
int pivot = partition(low, high, ys, n);
if (pivot == k) {
double result = ys[pivot];
free(ys);
return result;
} else if (k < pivot) {
high = pivot - 1;
} else {
low = pivot + 1;
}
}
}
ci array_get_ci(ci interval, double* xs, int n)
{
int low_k = (int)floor(interval.low * n);
int high_k = (int)ceil(interval.high * n);
ci result = {
.low = quickselect(low_k, xs, n),
.high = quickselect(high_k, xs, n),
};
return result;
}
ci array_get_90_ci(double xs[], int n)
{
return array_get_ci((ci) { .low = 0.05, .high = 0.95 }, xs, n);
}
double array_get_median(double xs[], int n){
int median_k = (int)floor(0.5 * n);
return quickselect(median_k, xs, n);
}
/* array print: potentially useful for debugging */
void array_print(double xs[], int n)
{
printf("[");
for (int i = 0; i < n - 1; i++) {
printf("%f, ", xs[i]);
}
printf("%f", xs[n - 1]);
printf("]\n");
}
void array_print_stats(double xs[], int n){
ci ci_90 = array_get_ci((ci) { .low = 0.05, .high = 0.95 }, xs, n);
ci ci_80 = array_get_ci((ci) { .low = 0.1, .high = 0.9 }, xs, n);
ci ci_50 = array_get_ci((ci) { .low = 0.25, .high = 0.75 }, xs, n);
double median = array_get_median(xs, n);
double mean = array_mean(xs, n);
double std = array_std(xs, n);
printf("Avg: %lf\n"
"Std: %lf\n"
" 5%%: %lf\n"
"10%%: %lf\n"
"25%%: %lf\n"
"50%%: %lf\n"
"75%%: %lf\n"
"90%%: %lf\n"
"95%%: %lf\n",
mean, std, ci_90.low, ci_80.low, ci_50.low, median, ci_50.high, ci_80.high, ci_90.high);
}
void array_print_histogram(double* xs, int n_samples, int n_bins) {
// Interface inspired by <https://github.com/red-data-tools/YouPlot>
// Generated with the help of an llm; there might be subtle off-by-one errors
if (n_bins <= 1) {
fprintf(stderr, "Number of bins must be greater than 1.\n");
return;
} else if (n_samples <= 1) {
fprintf(stderr, "Number of samples must be higher than 1.\n");
return;
}
int *bins = (int*) calloc((size_t)n_bins, sizeof(int));
if (bins == NULL) {
fprintf(stderr, "Memory allocation for bins failed.\n");
return;
}
// Find the minimum and maximum values from the samples
double min_value = xs[0], max_value = xs[0];
for (int i = 0; i < n_samples; i++) {
if (xs[i] < min_value) {
min_value = xs[i];
}
if (xs[i] > max_value) {
max_value = xs[i];
}
}
// Avoid division by zero for a single unique value
if (min_value == max_value) {
max_value++;
}
// Calculate bin width
double bin_width = (max_value - min_value) / n_bins;
// Fill the bins with sample counts
for (int i = 0; i < n_samples; i++) {
int bin_index = (int)((xs[i] - min_value) / bin_width);
if (bin_index == n_bins) {
bin_index--; // Last bin includes max_value
}
bins[bin_index]++;
}
// Calculate the scaling factor based on the maximum bin count
int max_bin_count = 0;
for (int i = 0; i < n_bins; i++) {
if (bins[i] > max_bin_count) {
max_bin_count = bins[i];
}
}
const int MAX_WIDTH = 50; // Adjust this to your terminal width
double scale = max_bin_count > MAX_WIDTH ? (double)MAX_WIDTH / max_bin_count : 1.0;
// Print the histogram
for (int i = 0; i < n_bins; i++) {
double bin_start = min_value + i * bin_width;
double bin_end = bin_start + bin_width;
int decimalPlaces = 1;
if((0 < bin_width) && (bin_width < 1)){
int magnitude = (int) floor(log10(bin_width));
decimalPlaces = -magnitude;
decimalPlaces = decimalPlaces > 10 ? 10 : decimalPlaces;
}
printf("[%*.*f, %*.*f", 4+decimalPlaces, decimalPlaces, bin_start, 4+decimalPlaces, decimalPlaces, bin_end);
char interval_delimiter = ')';
if(i == (n_bins-1)){
interval_delimiter = ']'; // last bucket is inclusive
}
printf("%c: ", interval_delimiter);
int marks = (int)(bins[i] * scale);
for (int j = 0; j < marks; j++) {
printf("");
}
printf(" %d\n", bins[i]);
}
// Free the allocated memory for bins
free(bins);
}
void array_print_90_ci_histogram(double* xs, int n_samples, int n_bins){
// Code duplicated from previous function
// I'll consider simplifying it at some future point
// Possible ideas:
// - having only one function that takes any confidence interval?
// - having a utility function that is called by both functions?
ci ci_90 = array_get_90_ci(xs, n_samples);
if (n_bins <= 1) {
fprintf(stderr, "Number of bins must be greater than 1.\n");
return;
} else if (n_samples <= 10) {
fprintf(stderr, "Number of samples must be higher than 10.\n");
return;
}
int *bins = (int*) calloc((size_t)n_bins, sizeof(int));
if (bins == NULL) {
fprintf(stderr, "Memory allocation for bins failed.\n");
return;
}
double min_value = ci_90.low, max_value = ci_90.high;
// Avoid division by zero for a single unique value
if (min_value == max_value) {
max_value++;
}
double bin_width = (max_value - min_value) / n_bins;
// Fill the bins with sample counts
int below_min = 0, above_max = 0;
for (int i = 0; i < n_samples; i++) {
if(xs[i] < min_value){
below_min++;
}else if (xs[i] > max_value){
above_max++;
}else{
int bin_index = (int)((xs[i] - min_value) / bin_width);
if (bin_index == n_bins) {
bin_index--; // Last bin includes max_value
}
bins[bin_index]++;
}
}
// Calculate the scaling factor based on the maximum bin count
int max_bin_count = 0;
for (int i = 0; i < n_bins; i++) {
if (bins[i] > max_bin_count) {
max_bin_count = bins[i];
}
}
const int MAX_WIDTH = 50; // Adjust this to your terminal width
double scale = max_bin_count > MAX_WIDTH ? (double)MAX_WIDTH / max_bin_count : 1.0;
// Print the histogram
int decimalPlaces = 1;
if((0 < bin_width) && (bin_width < 1)){
int magnitude = (int) floor(log10(bin_width));
decimalPlaces = -magnitude;
decimalPlaces = decimalPlaces > 10 ? 10 : decimalPlaces;
}
printf( "(-∞, %*.*f): %d\n", 4+decimalPlaces, decimalPlaces, min_value, below_min);
for (int i = 0; i < n_bins; i++) {
double bin_start = min_value + i * bin_width;
double bin_end = bin_start + bin_width;
printf("[%*.*f, %*.*f", 4+decimalPlaces, decimalPlaces, bin_start, 4+decimalPlaces, decimalPlaces, bin_end);
char interval_delimiter = ')';
if(i == (n_bins-1)){
interval_delimiter = ']'; // last bucket is inclusive
}
printf("%c: ", interval_delimiter);
int marks = (int)(bins[i] * scale);
for (int j = 0; j < marks; j++) {
printf("");
}
printf(" %d\n", bins[i]);
}
printf( "(%*.*f, +∞): %d\n", 4+decimalPlaces, decimalPlaces, max_value, above_max);
// Free the allocated memory for bins
free(bins);
}
/* Algebra manipulations */
#define NORMAL90CONFIDENCE 1.6448536269514727
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 = log(x.high);
double loglow = log(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;
}