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NunoSempere 2023-07-16 16:30:38 +02:00
parent 607554f22b
commit c487bdfaf5
1 changed files with 149 additions and 144 deletions
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289
scratchpad/scratchpad.c
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@ -1,9 +1,9 @@
#include <limits.h> // INT_MAX
#include <stdint.h>
#include <stdlib.h>
#include <float.h> // FLT_MAX, FLT_MIN #include <float.h> // FLT_MAX, FLT_MIN
#include <stdio.h> #include <limits.h> // INT_MAX
#include <math.h> // erf, sqrt #include <math.h> // erf, sqrt
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h> #include <time.h>
#define EXIT_ON_ERROR 0 #define EXIT_ON_ERROR 0
@ -12,7 +12,7 @@
struct box { struct box {
int empty; int empty;
float content; float content;
char * error_msg; char* error_msg;
}; };
// Example cdf // Example cdf
@ -50,9 +50,9 @@ struct box inverse_cdf(float cdf(float), float p)
{ {
// given a cdf: [-Inf, Inf] => [0,1] // given a cdf: [-Inf, Inf] => [0,1]
// returns a box with either // returns a box with either
// x such that cdf(x) = p // x such that cdf(x) = p
// or an error // or an error
// if EXIT_ON_ERROR is set to 1, it exits instead of providing an error // if EXIT_ON_ERROR is set to 1, it exits instead of providing an error
struct box result; struct box result;
float low = -1.0; float low = -1.0;
@ -75,17 +75,17 @@ struct box inverse_cdf(float cdf(float), float p)
} }
} }
if (!interval_found) { if (!interval_found) {
if(EXIT_ON_ERROR){ if (EXIT_ON_ERROR) {
printf("Interval containing the target value not found, in function inverse_cdf, in %s (%d)", __FILE__, __LINE__); printf("Interval containing the target value not found, in function inverse_cdf, in %s (%d)", __FILE__, __LINE__);
exit(1); exit(1);
}else{ } else {
char error_msg[200]; char error_msg[200];
snprintf(error_msg, 200, "Interval containing the target value not found in function inverse_cdf, in %s (%d)", __FILE__, __LINE__); snprintf(error_msg, 200, "Interval containing the target value not found in function inverse_cdf, in %s (%d)", __FILE__, __LINE__);
result.empty = 1; result.empty = 1;
result.error_msg = error_msg; result.error_msg = error_msg;
return result; return result;
} }
} else { } else {
int convergence_condition = 0; int convergence_condition = 0;
@ -93,9 +93,9 @@ struct box inverse_cdf(float cdf(float), float p)
while (!convergence_condition && (count < (INT_MAX / 2))) { while (!convergence_condition && (count < (INT_MAX / 2))) {
float mid = (high + low) / 2; float mid = (high + low) / 2;
int mid_not_new = (mid == low) || (mid == high); int mid_not_new = (mid == low) || (mid == high);
// float width = high - low; // float width = high - low;
if (mid_not_new) { if (mid_not_new) {
// if ((width < 1e-8) || mid_not_new){ // if ((width < 1e-8) || mid_not_new){
convergence_condition = 1; convergence_condition = 1;
} else { } else {
float mid_sign = cdf(mid) - p; float mid_sign = cdf(mid) - p;
@ -114,17 +114,17 @@ struct box inverse_cdf(float cdf(float), float p)
result.content = low; result.content = low;
result.empty = 0; result.empty = 0;
} else { } else {
if(EXIT_ON_ERROR){ if (EXIT_ON_ERROR) {
printf("Search process did not converge, in function inverse_cdf, in %s (%d)", __FILE__, __LINE__); printf("Search process did not converge, in function inverse_cdf, in %s (%d)", __FILE__, __LINE__);
exit(1); exit(1);
}else{ } else {
char error_msg[200]; char error_msg[200];
snprintf(error_msg, 200, "Search process did not converge, in function inverse_cdf, in %s (%d)", __FILE__, __LINE__); snprintf(error_msg, 200, "Search process did not converge, in function inverse_cdf, in %s (%d)", __FILE__, __LINE__);
result.empty = 1; result.empty = 1;
result.error_msg = error_msg; result.error_msg = error_msg;
return result; return result;
} }
} }
return result; return result;
} }
@ -178,12 +178,13 @@ float sampler_normal_0_1(uint32_t* seed)
#define STOP 1.0e-8 #define STOP 1.0e-8
#define TINY 1.0e-30 #define TINY 1.0e-30
struct box incbeta(float a, float b, float x) { struct box incbeta(float a, float b, float x)
// Descended from <https://github.com/codeplea/incbeta/blob/master/incbeta.c>, {
// but modified to return a box struct and floats instead of doubles. // Descended from <https://github.com/codeplea/incbeta/blob/master/incbeta.c>,
// [x] to do: add attribution in README // but modified to return a box struct and floats instead of doubles.
// Original code under this license: // [x] to do: add attribution in README
/* // Original code under this license:
/*
* zlib License * zlib License
* *
* Regularized Incomplete Beta Function * Regularized Incomplete Beta Function
@ -207,127 +208,131 @@ struct box incbeta(float a, float b, float x) {
* misrepresented as being the original software. * misrepresented as being the original software.
* 3. This notice may not be removed or altered from any source distribution. * 3. This notice may not be removed or altered from any source distribution.
*/ */
struct box result; struct box result;
if (x < 0.0 || x > 1.0){ if (x < 0.0 || x > 1.0) {
if(EXIT_ON_ERROR){ if (EXIT_ON_ERROR) {
printf("x = %f, x out of bounds [0, 1], in function incbeta, in %s (%d)", __FILE__, __LINE__); printf("x = %f, x out of bounds [0, 1], in function incbeta, in %s (%d)", __FILE__, __LINE__);
exit(1); exit(1);
}else{ } else {
char error_msg[200]; char error_msg[200];
snprintf(error_msg, 200, "x = %f, x out of bounds [0, 1], in function incbeta, in %s (%d)", x, __FILE__, __LINE__); snprintf(error_msg, 200, "x = %f, x out of bounds [0, 1], in function incbeta, in %s (%d)", x, __FILE__, __LINE__);
result.empty = 1; result.empty = 1;
result.error_msg = error_msg; result.error_msg = error_msg;
return result; return result;
} }
} }
/*The continued fraction converges nicely for x < (a+1)/(a+b+2)*/ /*The continued fraction converges nicely for x < (a+1)/(a+b+2)*/
if (x > (a+1.0)/(a+b+2.0)) { if (x > (a + 1.0) / (a + b + 2.0)) {
struct box symmetric_incbeta = incbeta(b,a,1.0-x); struct box symmetric_incbeta = incbeta(b, a, 1.0 - x);
if(symmetric_incbeta.empty){ if (symmetric_incbeta.empty) {
return symmetric_incbeta; // propagate error return symmetric_incbeta; // propagate error
}else{ } else {
result.empty = 0; result.empty = 0;
result.content = 1-symmetric_incbeta.content; result.content = 1 - symmetric_incbeta.content;
return result; return result;
} }
} }
/*Find the first part before the continued fraction.*/ /*Find the first part before the continued fraction.*/
const float lbeta_ab = lgamma(a)+lgamma(b)-lgamma(a+b); const float lbeta_ab = lgamma(a) + lgamma(b) - lgamma(a + b);
const float front = exp(log(x)*a+log(1.0-x)*b-lbeta_ab) / a; const float front = exp(log(x) * a + log(1.0 - x) * b - lbeta_ab) / a;
/*Use Lentz's algorithm to evaluate the continued fraction.*/ /*Use Lentz's algorithm to evaluate the continued fraction.*/
float f = 1.0, c = 1.0, d = 0.0; float f = 1.0, c = 1.0, d = 0.0;
int i, m; int i, m;
for (i = 0; i <= 200; ++i) { for (i = 0; i <= 200; ++i) {
m = i/2; m = i / 2;
float numerator; float numerator;
if (i == 0) { if (i == 0) {
numerator = 1.0; /*First numerator is 1.0.*/ numerator = 1.0; /*First numerator is 1.0.*/
} else if (i % 2 == 0) { } else if (i % 2 == 0) {
numerator = (m*(b-m)*x)/((a+2.0*m-1.0)*(a+2.0*m)); /*Even term.*/ numerator = (m * (b - m) * x) / ((a + 2.0 * m - 1.0) * (a + 2.0 * m)); /*Even term.*/
} else { } else {
numerator = -((a+m)*(a+b+m)*x)/((a+2.0*m)*(a+2.0*m+1)); /*Odd term.*/ numerator = -((a + m) * (a + b + m) * x) / ((a + 2.0 * m) * (a + 2.0 * m + 1)); /*Odd term.*/
} }
/*Do an iteration of Lentz's algorithm.*/ /*Do an iteration of Lentz's algorithm.*/
d = 1.0 + numerator * d; d = 1.0 + numerator * d;
if (fabs(d) < TINY) d = TINY; if (fabs(d) < TINY)
d = TINY;
d = 1.0 / d; d = 1.0 / d;
c = 1.0 + numerator / c; c = 1.0 + numerator / c;
if (fabs(c) < TINY) c = TINY; if (fabs(c) < TINY)
c = TINY;
const float cd = c*d; const float cd = c * d;
f *= cd; f *= cd;
/*Check for stop.*/ /*Check for stop.*/
if (fabs(1.0-cd) < STOP) { if (fabs(1.0 - cd) < STOP) {
result.content = front * (f-1.0); result.content = front * (f - 1.0);
result.empty = 0; result.empty = 0;
return result; return result;
} }
} }
if(EXIT_ON_ERROR){ if (EXIT_ON_ERROR) {
printf("More loops needed, did not converge, in function incbeta, in %s (%d)", __FILE__, __LINE__); printf("More loops needed, did not converge, in function incbeta, in %s (%d)", __FILE__, __LINE__);
exit(1); exit(1);
}else{ } else {
char error_msg[200]; char error_msg[200];
snprintf(error_msg, 200, "More loops needed, did not converge, in function incbeta, in %s (%d)", __FILE__, __LINE__); snprintf(error_msg, 200, "More loops needed, did not converge, in function incbeta, in %s (%d)", __FILE__, __LINE__);
result.empty = 1; result.empty = 1;
result.error_msg = error_msg; result.error_msg = error_msg;
return result; return result;
} }
} }
struct box cdf_beta(float x){ struct box cdf_beta(float x)
if(x < 0){ {
struct box result = { .empty = 0, .content = 0}; if (x < 0) {
return result; struct box result = { .empty = 0, .content = 0 };
} else if(x > 1){ return result;
struct box result = { .empty = 0, .content = 1}; } else if (x > 1) {
return result; struct box result = { .empty = 0, .content = 1 };
} else { return result;
float successes = 1, failures = (2023-1945); } else {
return incbeta(successes, failures, x); float successes = 1, failures = (2023 - 1945);
} return incbeta(successes, failures, x);
}
} }
float cdf_dangerous_beta(float x){ float cdf_dangerous_beta(float x)
// So the thing is, this works {
// But it will propagate through the code // So the thing is, this works
// So it doesn't feel like a great architectural choice; // But it will propagate through the code
// I prefer my choice of setting a variable which will determine whether to exit on failure or not. // So it doesn't feel like a great architectural choice;
// Ok, so the proper thing to do would be to refactor inverse_cdf // I prefer my choice of setting a variable which will determine whether to exit on failure or not.
// but, I could also use a GOTO? <https://stackoverflow.com/questions/245742/examples-of-good-gotos-in-c-or-c> // Ok, so the proper thing to do would be to refactor inverse_cdf
// Ok, alternatives are: // but, I could also use a GOTO? <https://stackoverflow.com/questions/245742/examples-of-good-gotos-in-c-or-c>
// - Refactor inverse_cdf to take a box, take the small complexity + penalty. Add a helper // Ok, alternatives are:
// - Duplicate the code, have a refactored inverse_cdf as well as a normal cdf // - Refactor inverse_cdf to take a box, take the small complexity + penalty. Add a helper
// - Do something hacky // - Duplicate the code, have a refactored inverse_cdf as well as a normal cdf
// a. dangerous beta, which exits // - Do something hacky
// b. clever & hacky go-to statements // a. dangerous beta, which exits
// i. They actually look fun to implement // b. clever & hacky go-to statements
// ii. But they would be hard for others to use. // i. They actually look fun to implement
if(x < 0){ // ii. But they would be hard for others to use.
return 0; if (x < 0) {
} else if(x > 1){ return 0;
return 1; } else if (x > 1) {
} else { return 1;
float successes = 100, failures = 100; } else {
struct box result = incbeta(successes, failures, x); float successes = 100, failures = 100;
if(result.empty){ struct box result = incbeta(successes, failures, x);
printf("%s\n", result.error_msg); if (result.empty) {
exit(1); printf("%s\n", result.error_msg);
return 1; exit(1);
}else{ return 1;
return result.content; } else {
} return result.content;
} }
}
} }
int main() int main()
@ -353,7 +358,7 @@ int main()
printf("Inverse of %s at %f is: %f\n", name_2, 0.5, result_2.content); printf("Inverse of %s at %f is: %f\n", name_2, 0.5, result_2.content);
} }
// Get the inverse of a normal(0,1) cdf distribution // Get the inverse of a normal(0,1) cdf distribution
struct box result_3 = inverse_cdf(cdf_normal_0_1, 0.5); struct box result_3 = inverse_cdf(cdf_normal_0_1, 0.5);
char* name_3 = "cdf_normal_0_1"; char* name_3 = "cdf_normal_0_1";
if (result_3.empty) { if (result_3.empty) {
@ -363,15 +368,15 @@ int main()
printf("Inverse of %s at %f is: %f\n", name_3, 0.5, result_3.content); printf("Inverse of %s at %f is: %f\n", name_3, 0.5, result_3.content);
} }
// Use the sampler on a normal(0,1) // Use the sampler on a normal(0,1)
// set randomness seed // set randomness seed
uint32_t* seed = malloc(sizeof(uint32_t)); uint32_t* seed = malloc(sizeof(uint32_t));
*seed = 1000; // xorshift can't start with 0 *seed = 1000; // xorshift can't start with 0
int n = 100; int n = 100;
printf("\n\nGetting some samples from %s:\n", name_3); printf("\n\nGetting some samples from %s:\n", name_3);
clock_t begin = clock(); clock_t begin = clock();
for (int i = 0; i < n; i++) { for (int i = 0; i < n; i++) {
struct box sample = sampler(cdf_normal_0_1, seed); struct box sample = sampler(cdf_normal_0_1, seed);
if (sample.empty) { if (sample.empty) {
printf("Error in sampler function"); printf("Error in sampler function");
@ -379,23 +384,23 @@ int main()
printf("%f\n", sample.content); printf("%f\n", sample.content);
} }
} }
clock_t end = clock(); clock_t end = clock();
float time_spent = (float)(end - begin) / CLOCKS_PER_SEC; float time_spent = (float)(end - begin) / CLOCKS_PER_SEC;
printf("Time spent: %f", time_spent); printf("Time spent: %f", time_spent);
// Get some normal samples using the previous method. // Get some normal samples using the previous method.
clock_t begin_2 = clock(); clock_t begin_2 = clock();
printf("\n\nGetting some samples from sampler_normal_0_1\n"); printf("\n\nGetting some samples from sampler_normal_0_1\n");
for (int i = 0; i < n; i++) { for (int i = 0; i < n; i++) {
float normal_sample = sampler_normal_0_1(seed); float normal_sample = sampler_normal_0_1(seed);
printf("%f\n", normal_sample); printf("%f\n", normal_sample);
} }
clock_t end_2 = clock(); clock_t end_2 = clock();
float time_spent_2 = (float)(end_2 - begin_2) / CLOCKS_PER_SEC; float time_spent_2 = (float)(end_2 - begin_2) / CLOCKS_PER_SEC;
printf("Time spent: %f", time_spent_2); printf("Time spent: %f", time_spent_2);
// Get some beta samples // Get some beta samples
clock_t begin_3 = clock(); clock_t begin_3 = clock();
printf("\n\nGetting some samples from box sampler_dangerous_beta\n"); printf("\n\nGetting some samples from box sampler_dangerous_beta\n");
for (int i = 0; i < n; i++) { for (int i = 0; i < n; i++) {
struct box sample = sampler(cdf_dangerous_beta, seed); struct box sample = sampler(cdf_dangerous_beta, seed);
@ -405,8 +410,8 @@ int main()
printf("%f\n", sample.content); printf("%f\n", sample.content);
} }
} }
clock_t end_3 = clock(); clock_t end_3 = clock();
float time_spent_3 = (float)(end_3 - begin_3) / CLOCKS_PER_SEC; float time_spent_3 = (float)(end_3 - begin_3) / CLOCKS_PER_SEC;
printf("Time spent: %f", time_spent_3); printf("Time spent: %f", time_spent_3);
return 0; return 0;
} }