naive.c (3956B)
1 #include "../../../squiggle.h" 2 #include <math.h> 3 #include <stdint.h> 4 #include <stdio.h> 5 #include <stdlib.h> 6 7 #define VERBOSE 0 8 9 double sample_loguniform(double a, double b, uint64_t* seed) 10 { 11 return exp(sample_uniform(log(a), log(b), seed)); 12 } 13 14 int main() 15 { 16 // Replicate <https://arxiv.org/pdf/1806.02404.pdf>, and in particular the red line in page 11. 17 // Could also be interesting to just produce and save many samples. 18 19 // set randomness seed 20 uint64_t* seed = malloc(sizeof(uint64_t)); 21 *seed = UINT64_MAX / 64; // xorshift can't start with a seed of 0 22 23 // Do this naïvely, without worrying that much about numerical precision 24 double sample_fermi_naive(uint64_t * seed) 25 { 26 double rate_of_star_formation = sample_loguniform(1, 100, seed); 27 double fraction_of_stars_with_planets = sample_loguniform(0.1, 1, seed); 28 double number_of_habitable_planets_per_star_system = sample_loguniform(0.1, 1, seed); 29 double rate_of_life_formation_in_habitable_planets = sample_lognormal(1, 50, seed); 30 double fraction_of_habitable_planets_in_which_any_life_appears = -expm1(-rate_of_life_formation_in_habitable_planets); 31 // double fraction_of_habitable_planets_in_which_any_life_appears = 1-exp(-rate_of_life_formation_in_habitable_planets); 32 // but with more precision 33 double fraction_of_planets_with_life_in_which_intelligent_life_appears = sample_loguniform(0.001, 1, seed); 34 double fraction_of_intelligent_planets_which_are_detectable_as_such = sample_loguniform(0.01, 1, seed); 35 double longevity_of_detectable_civilizations = sample_loguniform(100, 10000000000, seed); 36 37 if(VERBOSE) printf(" rate_of_star_formation = %lf\n", rate_of_star_formation); 38 if(VERBOSE) printf(" fraction_of_stars_with_planets = %lf\n", fraction_of_stars_with_planets); 39 if(VERBOSE) printf(" number_of_habitable_planets_per_star_system = %lf\n", number_of_habitable_planets_per_star_system); 40 if(VERBOSE) printf(" rate_of_life_formation_in_habitable_planets = %.16lf\n", rate_of_life_formation_in_habitable_planets); 41 if(VERBOSE) printf(" fraction_of_habitable_planets_in_which_any_life_appears = %lf\n", fraction_of_habitable_planets_in_which_any_life_appears); 42 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); 43 if(VERBOSE) printf(" fraction_of_intelligent_planets_which_are_detectable_as_such = %lf\n", fraction_of_intelligent_planets_which_are_detectable_as_such); 44 if(VERBOSE) printf(" longevity_of_detectable_civilizations = %lf\n", longevity_of_detectable_civilizations); 45 46 // Expected number of civilizations in the Milky way; 47 // see footnote 3 (p. 5) 48 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; 49 50 return n; 51 } 52 53 double sample_are_we_alone_naive(uint64_t * seed) 54 { 55 double n = sample_fermi_naive(seed); 56 return ((n > 1) ? 1 : 0); 57 } 58 59 double n = 1000000; 60 double naive_fermi_proportion = 0; 61 for (int i = 0; i < n; i++) { 62 double result = sample_are_we_alone_naive(seed); 63 if(VERBOSE) printf("result: %lf\n", result); 64 naive_fermi_proportion += result; 65 } 66 printf("Naïve %% that we are not alone: %lf\n", naive_fermi_proportion / n); 67 68 free(seed); 69 70 /* 71 double invert(double x){ 72 return log(1-exp(-exp(-x))); 73 } 74 for(int i=0; i<64; i++){ 75 double j = i; 76 printf("for %lf, log(1-exp(-exp(-x))) is calculated as... %lf\n", j, invert(j)); 77 } 78 */ 79 }