80 lines
3.9 KiB
C
80 lines
3.9 KiB
C
#include "../../../squiggle.h"
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#include <math.h>
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#include <stdint.h>
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#include <stdio.h>
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#include <stdlib.h>
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#define VERBOSE 0
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double sample_loguniform(double a, double b, uint64_t* seed)
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{
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return exp(sample_uniform(log(a), log(b), seed));
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}
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int main()
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{
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// Replicate <https://arxiv.org/pdf/1806.02404.pdf>, and in particular the red line in page 11.
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// Could also be interesting to just produce and save many samples.
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// set randomness seed
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uint64_t* seed = malloc(sizeof(uint64_t));
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*seed = UINT64_MAX / 64; // xorshift can't start with a seed of 0
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// Do this naïvely, without worrying that much about numerical precision
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double sample_fermi_naive(uint64_t * seed)
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{
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double rate_of_star_formation = sample_loguniform(1, 100, seed);
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double fraction_of_stars_with_planets = sample_loguniform(0.1, 1, seed);
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double number_of_habitable_planets_per_star_system = sample_loguniform(0.1, 1, seed);
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double rate_of_life_formation_in_habitable_planets = sample_lognormal(1, 50, seed);
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double fraction_of_habitable_planets_in_which_any_life_appears = -expm1(-rate_of_life_formation_in_habitable_planets);
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// double fraction_of_habitable_planets_in_which_any_life_appears = 1-exp(-rate_of_life_formation_in_habitable_planets);
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// but with more precision
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double fraction_of_planets_with_life_in_which_intelligent_life_appears = sample_loguniform(0.001, 1, seed);
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double fraction_of_intelligent_planets_which_are_detectable_as_such = sample_loguniform(0.01, 1, seed);
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double longevity_of_detectable_civilizations = sample_loguniform(100, 10000000000, seed);
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if(VERBOSE) printf(" rate_of_star_formation = %lf\n", rate_of_star_formation);
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if(VERBOSE) printf(" fraction_of_stars_with_planets = %lf\n", fraction_of_stars_with_planets);
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if(VERBOSE) printf(" number_of_habitable_planets_per_star_system = %lf\n", number_of_habitable_planets_per_star_system);
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if(VERBOSE) printf(" rate_of_life_formation_in_habitable_planets = %.16lf\n", rate_of_life_formation_in_habitable_planets);
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if(VERBOSE) printf(" fraction_of_habitable_planets_in_which_any_life_appears = %lf\n", fraction_of_habitable_planets_in_which_any_life_appears);
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if(VERBOSE) printf(" fraction_of_planets_with_life_in_which_intelligent_life_appears = %lf\n", fraction_of_planets_with_life_in_which_intelligent_life_appears);
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if(VERBOSE) printf(" fraction_of_intelligent_planets_which_are_detectable_as_such = %lf\n", fraction_of_intelligent_planets_which_are_detectable_as_such);
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if(VERBOSE) printf(" longevity_of_detectable_civilizations = %lf\n", longevity_of_detectable_civilizations);
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// Expected number of civilizations in the Milky way;
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// see footnote 3 (p. 5)
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double n = rate_of_star_formation * fraction_of_stars_with_planets * number_of_habitable_planets_per_star_system * fraction_of_habitable_planets_in_which_any_life_appears * fraction_of_planets_with_life_in_which_intelligent_life_appears * fraction_of_intelligent_planets_which_are_detectable_as_such * longevity_of_detectable_civilizations;
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return n;
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}
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double sample_are_we_alone_naive(uint64_t * seed)
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{
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double n = sample_fermi_naive(seed);
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return ((n > 1) ? 1 : 0);
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}
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double n = 1000000;
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double naive_fermi_proportion = 0;
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for (int i = 0; i < n; i++) {
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double result = sample_are_we_alone_naive(seed);
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if(VERBOSE) printf("result: %lf\n", result);
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naive_fermi_proportion += result;
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}
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printf("Naïve %% that we are not alone: %lf\n", naive_fermi_proportion / n);
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free(seed);
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/*
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double invert(double x){
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return log(1-exp(-exp(-x)));
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}
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for(int i=0; i<64; i++){
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double j = i;
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printf("for %lf, log(1-exp(-exp(-x))) is calculated as... %lf\n", j, invert(j));
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}
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*/
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}
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