diff --git a/examples/core/01_one_sample/example.c b/examples/core/01_one_sample/example.c index 611011a..a74718b 100644 --- a/examples/core/01_one_sample/example.c +++ b/examples/core/01_one_sample/example.c @@ -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; diff --git a/examples/core/02_time_to_botec/example.c b/examples/core/02_time_to_botec/example.c index 9d0aa21..de3b3e9 100644 --- a/examples/core/02_time_to_botec/example.c +++ b/examples/core/02_time_to_botec/example.c @@ -2,37 +2,35 @@ #include #include +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)); diff --git a/examples/core/03_gcc_nested_function/example.c b/examples/core/03_gcc_nested_function/example.c index d00e983..828aaea 100644 --- a/examples/core/03_gcc_nested_function/example.c +++ b/examples/core/03_gcc_nested_function/example.c @@ -2,39 +2,36 @@ #include #include +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); } diff --git a/examples/core/04_gamma_beta/example.c b/examples/core/04_gamma_beta/example.c index d606be4..1243235 100644 --- a/examples/core/04_gamma_beta/example.c +++ b/examples/core/04_gamma_beta/example.c @@ -2,8 +2,6 @@ #include #include -// 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); } diff --git a/examples/core/06_dissolving_fermi_paradox/example.c b/examples/core/06_dissolving_fermi_paradox/example.c index 12cd535..1fd185c 100644 --- a/examples/core/06_dissolving_fermi_paradox/example.c +++ b/examples/core/06_dissolving_fermi_paradox/example.c @@ -4,87 +4,88 @@ #include #include -int main() +double sample_fermi_logspace(uint64_t * seed) { // Replicate , 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. + + 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 + */ + 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. - - 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 - */ - 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++) {