forked from personal/squiggle.c
reorder scratchpad stuff
This commit is contained in:
parent
78e1838569
commit
e05baa6fee
|
|
@ -41,6 +41,7 @@ float cdf_uniform_0_1(float x)
|
|||
|
||||
float cdf_squared_0_1(float x)
|
||||
{
|
||||
float result;
|
||||
if (x < 0) {
|
||||
return 0;
|
||||
} 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
|
||||
}
|
||||
|
||||
// Inverse cdf
|
||||
struct box inverse_cdf(float cdf(float), float p)
|
||||
// [x] to do: add beta.
|
||||
// [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]
|
||||
// returns a box with either
|
||||
// x such that cdf(x) = p
|
||||
// or an error
|
||||
// if EXIT_ON_ERROR is set to 1, it exits instead of providing an error
|
||||
// Descended from <https://github.com/codeplea/incbeta/blob/master/incbeta.c>,
|
||||
// but modified to return a box struct and floats instead of doubles.
|
||||
// [ ] 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");
|
||||
}
|
||||
|
||||
float low = -1.0;
|
||||
float high = 1.0;
|
||||
|
||||
// 1. Make sure that cdf(low) < p < cdf(high)
|
||||
int interval_found = 0;
|
||||
while ((!interval_found) && (low > -FLT_MAX / 4) && (high < FLT_MAX / 4)) {
|
||||
// ^ Using FLT_MIN and FLT_MAX is overkill
|
||||
// but it's also the *correct* thing to do.
|
||||
|
||||
int low_condition = (cdf(low) < p);
|
||||
int high_condition = (p < cdf(high));
|
||||
if (low_condition && high_condition) {
|
||||
interval_found = 1;
|
||||
} else if (!low_condition) {
|
||||
low = low * 2;
|
||||
} else if (!high_condition) {
|
||||
high = high * 2;
|
||||
/*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;
|
||||
}
|
||||
}
|
||||
|
||||
if (!interval_found) {
|
||||
PROCESS_ERROR("Interval containing the target value not found, in function inverse_cdf");
|
||||
} else {
|
||||
/*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;
|
||||
|
||||
int convergence_condition = 0;
|
||||
int count = 0;
|
||||
while (!convergence_condition && (count < (INT_MAX / 2))) {
|
||||
float mid = (high + low) / 2;
|
||||
int mid_not_new = (mid == low) || (mid == high);
|
||||
// float width = high - low;
|
||||
// if ((width < 1e-8) || mid_not_new){
|
||||
if (mid_not_new) {
|
||||
convergence_condition = 1;
|
||||
} else {
|
||||
float mid_sign = cdf(mid) - p;
|
||||
if (mid_sign < 0) {
|
||||
low = mid;
|
||||
} else if (mid_sign > 0) {
|
||||
high = mid;
|
||||
} else if (mid_sign == 0) {
|
||||
low = mid;
|
||||
high = mid;
|
||||
}
|
||||
}
|
||||
}
|
||||
/*Use Lentz's algorithm to evaluate the continued fraction.*/
|
||||
float f = 1.0, c = 1.0, d = 0.0;
|
||||
|
||||
if (convergence_condition) {
|
||||
struct box result = {.empty = 0, .content = low};
|
||||
return result;
|
||||
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 {
|
||||
PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
|
||||
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_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;
|
||||
}
|
||||
}
|
||||
|
||||
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);
|
||||
}
|
||||
}
|
||||
|
||||
// Inverse cdf at point, but this time taking a struct box.
|
||||
struct box inverse_cdf_box(struct box cdf_box(float), float p)
|
||||
// Inverse cdf at point
|
||||
struct box inverse_cdf(struct box cdf_box(float), float p)
|
||||
{
|
||||
// given a cdf: [-Inf, Inf] => Box([0,1])
|
||||
// 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
|
||||
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);
|
||||
}
|
||||
|
||||
// Sampler based on inverse cdf
|
||||
struct box sampler(float cdf(float), uint32_t* seed)
|
||||
// Sampler based on inverse cdf and randomness function
|
||||
struct box sampler(struct box cdf(float), uint32_t* seed)
|
||||
{
|
||||
float p = rand_0_to_1(seed);
|
||||
struct box result = inverse_cdf(cdf, p);
|
||||
return result;
|
||||
}
|
||||
|
||||
// For comparison, raw sampler
|
||||
// Comparison point with raw normal sampler
|
||||
const float PI = 3.14159265358979323846;
|
||||
float sampler_normal_0_1(uint32_t* seed)
|
||||
{
|
||||
|
|
@ -239,155 +294,6 @@ float sampler_normal_0_1(uint32_t* seed)
|
|||
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()
|
||||
{
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user