Approximate Random Gaussian Generator
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// Approximate Random Gaussian Generator | |
// $ cc -O3 -fopenmp -o randn randn.c -lm | |
// $ ./randn | |
// Ref: https://old.reddit.com/r/algorithms/comments/yyz59u | |
// This is free and unencumbered software released into the public domain. | |
#include <math.h> | |
#include <stdint.h> | |
#include <stdio.h> | |
struct kahan { double sum, err; }; | |
static struct kahan kahan(struct kahan k, double x) | |
{ | |
double y = x - k.err; | |
double t = k.sum + y; | |
k.err = t - k.sum - y; | |
k.sum = t; | |
return k; | |
} | |
static uint64_t sfc64(uint64_t s[4]) | |
{ | |
uint64_t r = s[0] + s[1] + s[3]++; | |
s[0] = (s[1] >> 11) ^ s[1]; | |
s[1] = (s[2] << 3) + s[2]; | |
s[2] = r + (s[2]<<24 | s[2] >>40); | |
return r; | |
} | |
static double randn(uint64_t s[4]) | |
{ | |
uint64_t u = sfc64(s); | |
double x = __builtin_popcount(u>>32); | |
x += (uint32_t)u * (1 / 4294967296.); | |
x -= 16.5; | |
x *= 0.3517262290563295; | |
return x; | |
} | |
int main(void) | |
{ | |
#pragma omp parallel for | |
for (int i = 0; i < 20; i++) { | |
long n = 100000000; | |
struct kahan sum1={0}, sum2={0}; | |
uint64_t s[4] = {i+1, i+2, i+3, i+4}; | |
sfc64(s); sfc64(s); sfc64(s); sfc64(s); // mix | |
for (long i = 0; i < n; i++) { | |
double x = randn(s); | |
sum1 = kahan(sum1, x); | |
sum2 = kahan(sum2, x*x); | |
} | |
double mean = sum1.sum/n; | |
double stddev = sqrt(sum2.sum/n - mean*mean); | |
printf("%-+23.17g %-+.17g\n", mean, stddev); | |
} | |
} |
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