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reorder scratchpad stuff

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NunoSempere 2023-07-16 17:10:36 +02:00
parent 78e1838569
commit e05baa6fee
1 changed files with 112 additions and 206 deletions
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scratchpad/scratchpad.c
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@ -41,6 +41,7 @@ float cdf_uniform_0_1(float x)
float cdf_squared_0_1(float x) float cdf_squared_0_1(float x)
{ {
float result;
if (x < 0) { if (x < 0) {
return 0; return 0;
} else if (x > 1) { } else if (x > 1) {
@ -57,73 +58,123 @@ float cdf_normal_0_1(float x)
return 0.5 * (1 + erf((x - mean) / (std * sqrt(2)))); // erf from math.h return 0.5 * (1 + erf((x - mean) / (std * sqrt(2)))); // erf from math.h
} }
// Inverse cdf // [x] to do: add beta.
struct box inverse_cdf(float cdf(float), float p) // [x] for the cdf, use this incomplete beta function implementation, based on continuous fractions:
// <https://codeplea.com/incomplete-beta-function-c>
// <https://github.com/codeplea/incbeta>
#define STOP_BETA 1.0e-8
#define TINY_BETA 1.0e-30
struct box incbeta(float a, float b, float x)
{ {
// given a cdf: [-Inf, Inf] => [0,1] // Descended from <https://github.com/codeplea/incbeta/blob/master/incbeta.c>,
// returns a box with either // but modified to return a box struct and floats instead of doubles.
// x such that cdf(x) = p // [ ] to do: add attribution in README
// or an error // Original code under this license:
// if EXIT_ON_ERROR is set to 1, it exits instead of providing an error /*
* zlib License
float low = -1.0; *
float high = 1.0; * Regularized Incomplete Beta Function
*
// 1. Make sure that cdf(low) < p < cdf(high) * Copyright (c) 2016, 2017 Lewis Van Winkle
int interval_found = 0; * http://CodePlea.com
while ((!interval_found) && (low > -FLT_MAX / 4) && (high < FLT_MAX / 4)) { *
// ^ Using FLT_MIN and FLT_MAX is overkill * This software is provided 'as-is', without any express or implied
// but it's also the *correct* thing to do. * warranty. In no event will the authors be held liable for any damages
* arising from the use of this software.
int low_condition = (cdf(low) < p); *
int high_condition = (p < cdf(high)); * Permission is granted to anyone to use this software for any purpose,
if (low_condition && high_condition) { * including commercial applications, and to alter it and redistribute it
interval_found = 1; * freely, subject to the following restrictions:
} else if (!low_condition) { *
low = low * 2; * 1. The origin of this software must not be misrepresented; you must not
} else if (!high_condition) { * claim that you wrote the original software. If you use this software
high = high * 2; * in a product, an acknowledgement in the product documentation would be
} * appreciated but is not required.
* 2. Altered source versions must be plainly marked as such, and must not be
* misrepresented as being the original software.
* 3. This notice may not be removed or altered from any source distribution.
*/
if (x < 0.0 || x > 1.0) {
PROCESS_ERROR("x out of bounds [0, 1], in function incbeta");
} }
if (!interval_found) { /*The continued fraction converges nicely for x < (a+1)/(a+b+2)*/
PROCESS_ERROR("Interval containing the target value not found, in function inverse_cdf"); if (x > (a + 1.0) / (a + b + 2.0)) {
struct box symmetric_incbeta = incbeta(b, a, 1.0 - x);
if (symmetric_incbeta.empty) {
return symmetric_incbeta; // propagate error
} else { } else {
struct box result = {
.empty = 0,
.content = 1 - symmetric_incbeta.content
};
return result;
}
}
int convergence_condition = 0; /*Find the first part before the continued fraction.*/
int count = 0; const float lbeta_ab = lgamma(a) + lgamma(b) - lgamma(a + b);
while (!convergence_condition && (count < (INT_MAX / 2))) { const float front = exp(log(x) * a + log(1.0 - x) * b - lbeta_ab) / a;
float mid = (high + low) / 2;
int mid_not_new = (mid == low) || (mid == high); /*Use Lentz's algorithm to evaluate the continued fraction.*/
// float width = high - low; float f = 1.0, c = 1.0, d = 0.0;
// if ((width < 1e-8) || mid_not_new){
if (mid_not_new) { int i, m;
convergence_condition = 1; for (i = 0; i <= 200; ++i) {
m = i / 2;
float numerator;
if (i == 0) {
numerator = 1.0; /*First numerator is 1.0.*/
} else if (i % 2 == 0) {
numerator = (m * (b - m) * x) / ((a + 2.0 * m - 1.0) * (a + 2.0 * m)); /*Even term.*/
} else { } else {
float mid_sign = cdf(mid) - p; numerator = -((a + m) * (a + b + m) * x) / ((a + 2.0 * m) * (a + 2.0 * m + 1)); /*Odd term.*/
if (mid_sign < 0) {
low = mid;
} else if (mid_sign > 0) {
high = mid;
} else if (mid_sign == 0) {
low = mid;
high = mid;
} }
/*Do an iteration of Lentz's algorithm.*/
d = 1.0 + numerator * d;
if (fabs(d) < TINY_BETA)
d = TINY_BETA;
d = 1.0 / d;
c = 1.0 + numerator / c;
if (fabs(c) < TINY_BETA)
c = TINY_BETA;
const float cd = c * d;
f *= cd;
/*Check for stop.*/
if (fabs(1.0 - cd) < STOP_BETA) {
struct box result = {
.empty = 0,
.content = front * (f - 1.0)
};
return result;
} }
} }
if (convergence_condition) { PROCESS_ERROR("More loops needed, did not converge, in function incbeta");
struct box result = {.empty = 0, .content = low}; }
struct box cdf_beta(float x)
{
if (x < 0) {
struct box result = { .empty = 0, .content = 0 };
return result;
} else if (x > 1) {
struct box result = { .empty = 0, .content = 1 };
return result; return result;
} else { } else {
PROCESS_ERROR("Search process did not converge, in function inverse_cdf"); float successes = 1, failures = (2023 - 1945);
} return incbeta(successes, failures, x);
} }
} }
// Inverse cdf at point, but this time taking a struct box. // Inverse cdf at point
struct box inverse_cdf_box(struct box cdf_box(float), float p) struct box inverse_cdf(struct box cdf_box(float), float p)
{ {
// given a cdf: [-Inf, Inf] => Box([0,1]) // given a cdf: [-Inf, Inf] => Box([0,1])
// returns a box with either // returns a box with either
@ -200,6 +251,10 @@ struct box inverse_cdf_box(struct box cdf_box(float), float p)
} }
} }
// Some randomness functions for:
// - Sampling from a cdf
// - Benchmarking against a previous approach, which will be faster, but less general
// Get random number between 0 and 1 // Get random number between 0 and 1
uint32_t xorshift32(uint32_t* seed) uint32_t xorshift32(uint32_t* seed)
{ {
@ -221,15 +276,15 @@ float rand_0_to_1(uint32_t* seed)
return ((float)xorshift32(seed)) / ((float)UINT32_MAX); return ((float)xorshift32(seed)) / ((float)UINT32_MAX);
} }
// Sampler based on inverse cdf // Sampler based on inverse cdf and randomness function
struct box sampler(float cdf(float), uint32_t* seed) struct box sampler(struct box cdf(float), uint32_t* seed)
{ {
float p = rand_0_to_1(seed); float p = rand_0_to_1(seed);
struct box result = inverse_cdf(cdf, p); struct box result = inverse_cdf(cdf, p);
return result; return result;
} }
// For comparison, raw sampler // Comparison point with raw normal sampler
const float PI = 3.14159265358979323846; const float PI = 3.14159265358979323846;
float sampler_normal_0_1(uint32_t* seed) float sampler_normal_0_1(uint32_t* seed)
{ {
@ -239,155 +294,6 @@ float sampler_normal_0_1(uint32_t* seed)
return z; return z;
} }
// to do: add beta.
// for the cdf, use this incomplete beta function implementation, based on continuous fractions:
// <https://codeplea.com/incomplete-beta-function-c>
// <https://github.com/codeplea/incbeta>
#define STOP 1.0e-8
#define TINY 1.0e-30
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.
// [x] to do: add attribution in README
// Original code under this license:
/*
* zlib License
*
* Regularized Incomplete Beta Function
*
* Copyright (c) 2016, 2017 Lewis Van Winkle
* http://CodePlea.com
*
* This software is provided 'as-is', without any express or implied
* warranty. In no event will the authors be held liable for any damages
* arising from the use of this software.
*
* Permission is granted to anyone to use this software for any purpose,
* including commercial applications, and to alter it and redistribute it
* freely, subject to the following restrictions:
*
* 1. The origin of this software must not be misrepresented; you must not
* claim that you wrote the original software. If you use this software
* in a product, an acknowledgement in the product documentation would be
* appreciated but is not required.
* 2. Altered source versions must be plainly marked as such, and must not be
* misrepresented as being the original software.
* 3. This notice may not be removed or altered from any source distribution.
*/
if (x < 0.0 || x > 1.0) {
PROCESS_ERROR("x out of bounds [0, 1], in function incbeta");
}
/*The continued fraction converges nicely for x < (a+1)/(a+b+2)*/
if (x > (a + 1.0) / (a + b + 2.0)) {
struct box symmetric_incbeta = incbeta(b, a, 1.0 - x);
if (symmetric_incbeta.empty) {
return symmetric_incbeta; // propagate error
} else {
struct box result = {
.empty = 0,
.content = 1 - symmetric_incbeta.content
};
return result;
}
}
/*Find the first part before the continued fraction.*/
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;
/*Use Lentz's algorithm to evaluate the continued fraction.*/
float f = 1.0, c = 1.0, d = 0.0;
int i, m;
for (i = 0; i <= 200; ++i) {
m = i / 2;
float numerator;
if (i == 0) {
numerator = 1.0; /*First numerator is 1.0.*/
} else if (i % 2 == 0) {
numerator = (m * (b - m) * x) / ((a + 2.0 * m - 1.0) * (a + 2.0 * m)); /*Even term.*/
} else {
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.*/
d = 1.0 + numerator * d;
if (fabs(d) < TINY)
d = TINY;
d = 1.0 / d;
c = 1.0 + numerator / c;
if (fabs(c) < TINY)
c = TINY;
const float cd = c * d;
f *= cd;
/*Check for stop.*/
if (fabs(1.0 - cd) < STOP) {
struct box result = {
.empty = 0,
.content = front * (f - 1.0)
};
return result;
}
}
PROCESS_ERROR("More loops needed, did not converge, in function incbeta");
}
struct box cdf_beta(float x)
{
if (x < 0) {
struct box result = { .empty = 0, .content = 0 };
return result;
} else if (x > 1) {
struct box result = { .empty = 0, .content = 1 };
return result;
} else {
float successes = 1, failures = (2023 - 1945);
return incbeta(successes, failures, x);
}
}
float cdf_dangerous_beta(float x)
{
// So the thing is, this works
// But it will propagate through the code
// So it doesn't feel like a great architectural choice;
// I prefer my choice of setting a variable which will determine whether to exit on failure or not.
// Ok, so the proper thing to do would be to refactor inverse_cdf
// but, I could also use a GOTO? <https://stackoverflow.com/questions/245742/examples-of-good-gotos-in-c-or-c>
// Ok, alternatives are:
// - Refactor inverse_cdf to take a box, take the small complexity + penalty. Add a helper
// - Duplicate the code, have a refactored inverse_cdf as well as a normal cdf
// - Do something hacky
// a. dangerous beta, which exits
// b. clever & hacky go-to statements
// i. They actually look fun to implement
// ii. But they would be hard for others to use.
if (x < 0) {
return 0;
} else if (x > 1) {
return 1;
} else {
float successes = 100, failures = 100;
struct box result = incbeta(successes, failures, x);
if (result.empty) {
printf("%s\n", result.error_msg);
exit(1);
return 1;
} else {
return result.content;
}
}
}
int main() int main()
{ {