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use new pattern to reduce nested functions extension

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This commit is contained in:
NunoSempere 2024-01-29 18:29:17 +01:00
parent 279fb12dee
commit fa832cbd17
5 changed files with 130 additions and 147 deletions
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10
examples/core/01_one_sample/example.c
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@ -4,12 +4,12 @@
// Estimate functions
double sample_model(uint64_t* seed){
double sample_0(uint64_t* seed) { UNUSED(seed); return 0; }
double sample_1(uint64_t* seed) { UNUSED(seed); return 1; }
double sample_few(uint64_t* seed) { return sample_to(1, 3, seed); }
double sample_many(uint64_t* seed) { return sample_to(2, 10, seed); }
double sample_0(uint64_t* seed) { UNUSED(seed); return 0; }
double sample_1(uint64_t* seed) { UNUSED(seed); return 1; }
double sample_few(uint64_t* seed) { return sample_to(1, 3, seed); }
double sample_many(uint64_t* seed) { return sample_to(2, 10, seed); }
double sample_model(uint64_t* seed){
double p_a = 0.8;
double p_b = 0.5;

42
examples/core/02_time_to_botec/example.c
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@ -2,37 +2,35 @@
#include <stdio.h>
#include <stdlib.h>
double sample_0(uint64_t* seed) { UNUSED(seed); return 0; }
double sample_1(uint64_t* seed) { UNUSED(seed); return 1; }
double sample_few(uint64_t* seed) { return sample_to(1, 3, seed); }
double sample_many(uint64_t* seed) { return sample_to(2, 10, seed); }
double sample_model(uint64_t* seed){
double p_a = 0.8;
double p_b = 0.5;
double p_c = p_a * p_b;
int n_dists = 4;
double weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
double (*samplers[])(uint64_t*) = { sample_0, sample_1, sample_few, sample_many };
double result = sample_mixture(samplers, weights, n_dists, seed);
return result;
}
int main()
{
// set randomness seed
uint64_t* seed = malloc(sizeof(uint64_t));
*seed = 1000; // xorshift can't start with 0
double p_a = 0.8;
double p_b = 0.5;
double p_c = p_a * p_b;
double sample_0(uint64_t * seed)
{
UNUSED(seed);
return 0;
}
double sample_1(uint64_t * seed)
{
UNUSED(seed);
return 1;
}
double sample_few(uint64_t * seed) { return sample_to(1, 3, seed); }
double sample_many(uint64_t * seed) { return sample_to(2, 10, seed); }
int n_dists = 4;
double weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
double (*samplers[])(uint64_t*) = { sample_0, sample_1, sample_few, sample_many };
int n_samples = 1000000;
double* result_many = (double*)malloc((size_t)n_samples * sizeof(double));
for (int i = 0; i < n_samples; i++) {
result_many[i] = sample_mixture(samplers, weights, n_dists, seed);
result_many[i] = sample_model(seed);
}
printf("Mean: %f\n", array_mean(result_many, n_samples));

46
examples/core/03_gcc_nested_function/example.c
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@ -2,39 +2,36 @@
#include <stdio.h>
#include <stdlib.h>
double sample_model(uint64_t* seed){
double sample_0(uint64_t* seed) { UNUSED(seed); return 0; }
// Using a gcc extension, you can define a function inside another function
double sample_1(uint64_t* seed) { UNUSED(seed); return 1; }
double sample_few(uint64_t* seed) { return sample_to(1, 3, seed); }
double sample_many(uint64_t* seed) { return sample_to(2, 10, seed); }
double p_a = 0.8;
double p_b = 0.5;
double p_c = p_a * p_b;
int n_dists = 4;
double weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
double (*samplers[])(uint64_t*) = { sample_0, sample_1, sample_few, sample_many };
double result = sample_mixture(samplers, weights, n_dists, seed);
return result;
}
int main()
{
// set randomness seed
uint64_t* seed = malloc(sizeof(uint64_t));
*seed = 1000; // xorshift can't start with 0
double p_a = 0.8;
double p_b = 0.5;
double p_c = p_a * p_b;
int n_dists = 4;
// These are nested functions. They will not compile without gcc.
double sample_0(uint64_t * seed)
{
UNUSED(seed);
return 0;
}
double sample_1(uint64_t * seed)
{
UNUSED(seed);
return 1;
}
double sample_few(uint64_t * seed) { return sample_to(1, 3, seed); }
double sample_many(uint64_t * seed) { return sample_to(2, 10, seed); }
double (*samplers[])(uint64_t*) = { sample_0, sample_1, sample_few, sample_many };
double weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
int n_samples = 1000000;
double* result_many = (double*)malloc((size_t)n_samples * sizeof(double));
for (int i = 0; i < n_samples; i++) {
result_many[i] = sample_mixture(samplers, weights, n_dists, seed);
result_many[i] = sample_model(seed);
}
printf("result_many: [");
@ -42,5 +39,6 @@ int main()
printf("%.2f, ", result_many[i]);
}
printf("]\n");
free(seed);
}

30
examples/core/04_gamma_beta/example.c
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@ -2,8 +2,6 @@
#include <stdio.h>
#include <stdlib.h>
// Estimate functions
int main()
{
// set randomness seed
@ -11,33 +9,21 @@ int main()
*seed = 1000; // xorshift can't start with 0
int n = 1000 * 1000;
/*
for (int i = 0; i < n; i++) {
double gamma_0 = sample_gamma(0.0, seed);
// printf("sample_gamma(0.0): %f\n", gamma_0);
}
printf("\n");
*/
double* gamma_1_array = malloc(sizeof(double) * (size_t)n);
double* gamma_array = malloc(sizeof(double) * (size_t)n);
for (int i = 0; i < n; i++) {
double gamma_1 = sample_gamma(1.0, seed);
// printf("sample_gamma(1.0): %f\n", gamma_1);
gamma_1_array[i] = gamma_1;
gamma_array[i] = sample_gamma(1.0, seed);
}
printf("gamma(1) summary statistics = mean: %f, std: %f\n", array_mean(gamma_1_array, n), array_std(gamma_1_array, n));
free(gamma_1_array);
printf("gamma(1) summary statistics = mean: %f, std: %f\n", array_mean(gamma_array, n), array_std(gamma_array, n));
printf("\n");
double* beta_1_2_array = malloc(sizeof(double) * (size_t)n);
double* beta_array = malloc(sizeof(double) * (size_t)n);
for (int i = 0; i < n; i++) {
double beta_1_2 = sample_beta(1, 2.0, seed);
// printf("sample_beta(1.0, 2.0): %f\n", beta_1_2);
beta_1_2_array[i] = beta_1_2;
beta_array[i] = sample_beta(1, 2.0, seed);
}
printf("beta(1,2) summary statistics: mean: %f, std: %f\n", array_mean(beta_1_2_array, n), array_std(beta_1_2_array, n));
free(beta_1_2_array);
printf("beta(1,2) summary statistics: mean: %f, std: %f\n", array_mean(beta_array, n), array_std(beta_array, n));
printf("\n");
free(gamma_array);
free(beta_array);
free(seed);
}

149
examples/core/06_dissolving_fermi_paradox/example.c
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@ -4,87 +4,88 @@
#include <stdio.h>
#include <stdlib.h>
int main()
double sample_fermi_logspace(uint64_t * seed)
{
// Replicate <https://arxiv.org/pdf/1806.02404.pdf>, and in particular the red line in page 11.
// You can see a simple version of this function in naive.c in this same folder
double log_rate_of_star_formation = sample_uniform(log(1), log(100), seed);
double log_fraction_of_stars_with_planets = sample_uniform(log(0.1), log(1), seed);
double log_number_of_habitable_planets_per_star_system = sample_uniform(log(0.1), log(1), seed);
double log_rate_of_life_formation_in_habitable_planets = sample_normal(1, 50, seed);
double log_fraction_of_habitable_planets_in_which_any_life_appears;
/*
Consider:
a = underlying normal
b = rate_of_life_formation_in_habitable_planets = exp(underlying normal) = exp(a)
c = 1 - exp(-b) = fraction_of_habitable_planets_in_which_any_life_appears
d = log(c)
Looking at the Taylor expansion for c = 1 - exp(-b), it's
b - b^2/2 + b^3/6 - x^b/24, etc.
<https://www.wolframalpha.com/input?i=1-exp%28-x%29>
When b ~ 0 (as is often the case), this is close to b.
But now, if b ~ 0, c ~ b
and d = log(c) ~ log(b) = log(exp(a)) = a
Now, we could play around with estimating errors,
and indeed if we want b^2/2 = exp(a)^2/2 < 10^(-n), i.e., to have n decimal digits of precision,
we could compute this as e.g., a < (nlog(10) + log(2))/2
so for example if we want ten digits of precision, that's a < -11
Empirically, the two numbers as calculated in C do become really close around 11 or so,
and at 38 that calculation results in a -inf (so probably a floating point error or similar.)
So we should be using that formula for somewhere between -38 << a < -11
I chose -16 as a happy medium after playing around with
double invert(double x){
return log(1-exp(-exp(-x)));
}
for(int i=0; i<64; i++){
double j = i;
printf("for %lf, log(1-exp(-exp(-x))) is calculated as... %lf\n", j, invert(j));
}
and <https://www.wolframalpha.com/input?i=log%281-exp%28-exp%28-16%29%29%29>
*/
if (log_rate_of_life_formation_in_habitable_planets < -16) {
log_fraction_of_habitable_planets_in_which_any_life_appears = log_rate_of_life_formation_in_habitable_planets;
} else {
double rate_of_life_formation_in_habitable_planets = exp(log_rate_of_life_formation_in_habitable_planets);
double fraction_of_habitable_planets_in_which_any_life_appears = -expm1(-rate_of_life_formation_in_habitable_planets);
log_fraction_of_habitable_planets_in_which_any_life_appears = log(fraction_of_habitable_planets_in_which_any_life_appears);
}
double log_fraction_of_planets_with_life_in_which_intelligent_life_appears = sample_uniform(log(0.001), log(1), seed);
double log_fraction_of_intelligent_planets_which_are_detectable_as_such = sample_uniform(log(0.01), log(1), seed);
double log_longevity_of_detectable_civilizations = sample_uniform(log(100), log(10000000000), seed);
double log_n =
log_rate_of_star_formation +
log_fraction_of_stars_with_planets +
log_number_of_habitable_planets_per_star_system +
log_fraction_of_habitable_planets_in_which_any_life_appears +
log_fraction_of_planets_with_life_in_which_intelligent_life_appears +
log_fraction_of_intelligent_planets_which_are_detectable_as_such +
log_longevity_of_detectable_civilizations;
return log_n;
}
double sample_are_we_alone_logspace(uint64_t * seed)
{
double log_n = sample_fermi_logspace(seed);
return ((log_n > 0) ? 1 : 0);
// log_n > 0 => n > 1
}
int main()
{
// set randomness seed
uint64_t* seed = malloc(sizeof(uint64_t));
*seed = 1001; // xorshift can't start with a seed of 0
double sample_fermi_logspace(uint64_t * seed)
{
// You can see a simple version of this function in naive.c in this same folder
double log_rate_of_star_formation = sample_uniform(log(1), log(100), seed);
double log_fraction_of_stars_with_planets = sample_uniform(log(0.1), log(1), seed);
double log_number_of_habitable_planets_per_star_system = sample_uniform(log(0.1), log(1), seed);
double log_rate_of_life_formation_in_habitable_planets = sample_normal(1, 50, seed);
double log_fraction_of_habitable_planets_in_which_any_life_appears;
/*
Consider:
a = underlying normal
b = rate_of_life_formation_in_habitable_planets = exp(underlying normal) = exp(a)
c = 1 - exp(-b) = fraction_of_habitable_planets_in_which_any_life_appears
d = log(c)
Looking at the Taylor expansion for c = 1 - exp(-b), it's
b - b^2/2 + b^3/6 - x^b/24, etc.
<https://www.wolframalpha.com/input?i=1-exp%28-x%29>
When b ~ 0 (as is often the case), this is close to b.
But now, if b ~ 0, c ~ b
and d = log(c) ~ log(b) = log(exp(a)) = a
Now, we could play around with estimating errors,
and indeed if we want b^2/2 = exp(a)^2/2 < 10^(-n), i.e., to have n decimal digits of precision,
we could compute this as e.g., a < (nlog(10) + log(2))/2
so for example if we want ten digits of precision, that's a < -11
Empirically, the two numbers as calculated in C do become really close around 11 or so,
and at 38 that calculation results in a -inf (so probably a floating point error or similar.)
So we should be using that formula for somewhere between -38 << a < -11
I chose -16 as a happy medium after playing around with
double invert(double x){
return log(1-exp(-exp(-x)));
}
for(int i=0; i<64; i++){
double j = i;
printf("for %lf, log(1-exp(-exp(-x))) is calculated as... %lf\n", j, invert(j));
}
and <https://www.wolframalpha.com/input?i=log%281-exp%28-exp%28-16%29%29%29>
*/
if (log_rate_of_life_formation_in_habitable_planets < -16) {
log_fraction_of_habitable_planets_in_which_any_life_appears = log_rate_of_life_formation_in_habitable_planets;
} else {
double rate_of_life_formation_in_habitable_planets = exp(log_rate_of_life_formation_in_habitable_planets);
double fraction_of_habitable_planets_in_which_any_life_appears = -expm1(-rate_of_life_formation_in_habitable_planets);
log_fraction_of_habitable_planets_in_which_any_life_appears = log(fraction_of_habitable_planets_in_which_any_life_appears);
}
double log_fraction_of_planets_with_life_in_which_intelligent_life_appears = sample_uniform(log(0.001), log(1), seed);
double log_fraction_of_intelligent_planets_which_are_detectable_as_such = sample_uniform(log(0.01), log(1), seed);
double log_longevity_of_detectable_civilizations = sample_uniform(log(100), log(10000000000), seed);
double log_n =
log_rate_of_star_formation +
log_fraction_of_stars_with_planets +
log_number_of_habitable_planets_per_star_system +
log_fraction_of_habitable_planets_in_which_any_life_appears +
log_fraction_of_planets_with_life_in_which_intelligent_life_appears +
log_fraction_of_intelligent_planets_which_are_detectable_as_such +
log_longevity_of_detectable_civilizations;
return log_n;
}
double sample_are_we_alone_logspace(uint64_t * seed)
{
double log_n = sample_fermi_logspace(seed);
return ((log_n > 0) ? 1 : 0);
// log_n > 0 => n > 1
}
double logspace_fermi_proportion = 0;
int n_samples = 1000 * 1000;
for (int i = 0; i < n_samples; i++) {