add fermi paradox to examples

examples/core/06_dissolving_fermi_paradox/makefile

@@ -0,0 +1,56 @@
+# Interface: 
+#   make
+#   make build
+#   make format
+#   make run
+
+# Compiler
+CC=gcc
+# CC=tcc # <= faster compilation
+
+# Main file
+SRC=scratchpad.c ../squiggle.c ../squiggle_more.c
+OUTPUT=scratchpad
+
+## Dependencies
+MATH=-lm
+
+## Flags
+DEBUG= #'-g'
+STANDARD=-std=c99
+WARNINGS=-Wall
+OPTIMIZED=-O3  #-Ofast
+# OPENMP=-fopenmp
+
+## Formatter
+STYLE_BLUEPRINT=webkit
+FORMATTER=clang-format -i -style=$(STYLE_BLUEPRINT)
+
+## make build
+build: $(SRC)
+	$(CC) $(OPTIMIZED) $(DEBUG) $(SRC) $(MATH) -o $(OUTPUT)
+
+format: $(SRC)
+	$(FORMATTER) $(SRC)
+
+run: $(SRC) $(OUTPUT)
+	./$(OUTPUT)
+
+verify: $(SRC) $(OUTPUT)
+	./$(OUTPUT) | grep "NOT passed" -A 2 --group-separator='' || true
+
+time-linux: 
+	@echo "Requires /bin/time, found on GNU/Linux systems" && echo
+	
+	@echo "Running 100x and taking avg time $(OUTPUT)"
+	@t=$$(/usr/bin/time -f "%e" -p bash -c 'for i in {1..100}; do $(OUTPUT); done' 2>&1 >/dev/null | grep real | awk '{print $$2}' ); echo "scale=2; 1000 * $$t / 100" | bc | sed "s|^|Time using 1 thread: |" | sed 's|$$|ms|' && echo
+
+## Profiling
+
+profile-linux: 
+	echo "Requires perf, which depends on the kernel version, and might be in linux-tools package or similar"
+	echo "Must be run as sudo"
+	$(CC) $(SRC) $(MATH) -o $(OUTPUT)
+	sudo perf record ./$(OUTPUT)
+	sudo perf report
+	rm perf.data

examples/core/06_dissolving_fermi_paradox/scratchpad.c

@@ -0,0 +1,157 @@
+#include "../squiggle.h"
+// #include "../squiggle_more.h"
+#include <math.h>
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+double sample_loguniform(double a, double b, uint64_t* seed){
+    return exp(sample_uniform(log(a), log(b), seed));
+}
+
+int main()
+{
+    // Replicate <https://arxiv.org/pdf/1806.02404.pdf>, and in particular the red line in page 11.
+    // Could also be interesting to just produce and save many samples.
+
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = UINT64_MAX/64; // xorshift can't start with a seed of 0
+    
+    double sample_fermi_naive(uint64_t* seed){
+        double rate_of_star_formation = sample_loguniform(1,100, seed);
+        double fraction_of_stars_with_planets = sample_loguniform(0.1, 1, seed);
+        double number_of_habitable_planets_per_star_system = sample_loguniform(0.1, 1, seed);
+        double rate_of_life_formation_in_habitable_planets = sample_lognormal(1, 50, seed);
+        double fraction_of_habitable_planets_in_which_any_life_appears = -expm1(-rate_of_life_formation_in_habitable_planets);
+        // double fraction_of_habitable_planets_in_which_any_life_appears = 1-exp(-rate_of_life_formation_in_habitable_planets);
+        // but with more precision
+        double fraction_of_planets_with_life_in_which_intelligent_life_appears = sample_loguniform(0.001, 1, seed);
+        double fraction_of_intelligent_planets_which_are_detectable_as_such = sample_loguniform(0.01, 1, seed);
+        double longevity_of_detectable_civilizations = sample_loguniform(100, 10000000000, seed);
+
+        // printf(" rate_of_star_formation = %lf\n", rate_of_star_formation);
+        // printf(" fraction_of_stars_with_planets = %lf\n", fraction_of_stars_with_planets);
+        // printf(" number_of_habitable_planets_per_star_system = %lf\n", number_of_habitable_planets_per_star_system);
+        // printf(" rate_of_life_formation_in_habitable_planets = %.16lf\n", rate_of_life_formation_in_habitable_planets);
+        // printf(" fraction_of_habitable_planets_in_which_any_life_appears = %lf\n", fraction_of_habitable_planets_in_which_any_life_appears);
+        // printf(" fraction_of_planets_with_life_in_which_intelligent_life_appears = %lf\n", fraction_of_planets_with_life_in_which_intelligent_life_appears);
+        // printf(" fraction_of_intelligent_planets_which_are_detectable_as_such = %lf\n", fraction_of_intelligent_planets_which_are_detectable_as_such);
+        // printf(" longevity_of_detectable_civilizations = %lf\n", longevity_of_detectable_civilizations);
+
+        // Expected number of civilizations in the Milky way;
+        // see footnote 3 (p. 5)
+        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;
+
+        return n;
+    }
+
+    double sample_fermi_paradox_naive(uint64_t* seed){
+        double n = sample_fermi_naive(seed);
+        return ((n > 1) ? 1 : 0);
+    }
+
+    double n = 1000000;
+    double naive_fermi_proportion = 0;
+    for(int i=0; i<n; i++){
+        double result = sample_fermi_paradox_naive(seed);
+        // printf("result: %lf\n", result);
+        naive_fermi_proportion+=result;
+    }
+    printf("Naïve %% that we are not alone: %lf\n", naive_fermi_proportion/n);
+
+
+    // Thinking in log space
+    double sample_fermi_logspace(uint64_t* seed){
+        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_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);
+
+        // printf(" log_rate_of_star_formation = %lf\n", log_rate_of_star_formation);
+        // printf(" log_fraction_of_stars_with_planets = %lf\n", log_fraction_of_stars_with_planets);
+        // printf(" log_number_of_habitable_planets_per_star_system = %lf\n", log_number_of_habitable_planets_per_star_system);
+        // printf(" log_fraction_of_planets_with_life_in_which_intelligent_life_appears = %lf\n", log_fraction_of_planets_with_life_in_which_intelligent_life_appears);
+        // printf(" log_fraction_of_intelligent_planets_which_are_detectable_as_such = %lf\n", log_fraction_of_intelligent_planets_which_are_detectable_as_such);
+        // printf(" log_longevity_of_detectable_civilizations = %lf\n", log_longevity_of_detectable_civilizations);
+
+        double log_n1 = 
+            log_rate_of_star_formation +
+            log_fraction_of_stars_with_planets +
+            log_number_of_habitable_planets_per_star_system + 
+            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;
+        // printf("first part of calculation: %lf\n", log_n1);
+
+        /* Consider fraction_of_habitable_planets_in_which_any_life_appears separately.
+        Imprecisely, we could do:
+
+        double rate_of_life_formation_in_habitable_planets = sample_lognormal(1, 50, seed);
+        double fraction_of_habitable_planets_in_which_any_life_appears = 1- exp(-rate_of_life_formation_in_habitable_planets);
+        double log_fraction_of_habitable_planets_in_which_any_life_appears = log(1-fraction_of_habitable_planets_in_which_any_life_appears);
+        double n = exp(log_n1) * fraction_of_habitable_planets_in_which_any_life_appears;
+        // or: 
+        double n2 = exp(log_n1 + log(fraction_of_habitable_planets_in_which_any_life_appears))
+
+        However, we lose all precision here.
+
+        Now, say
+        a = underlying normal 
+        b = rate_of_life_formation_in_habitable_planets = exp(underlying normal)
+        c = 1 - exp(-b) = fraction_of_habitable_planets_in_which_any_life_appears
+        d = log(c)
+
+        Now, is there some way we can d more efficiently/precisely?
+        Turns out there is!
+
+        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
+        */
+        double log_rate_of_life_formation_in_habitable_planets = sample_normal(1, 50, seed);
+        // printf("log_rate_of_life_formation_in_habitable_planets: %lf\n", log_rate_of_life_formation_in_habitable_planets);
+
+        double log_fraction_of_habitable_planets_in_which_any_life_appears;
+        if(log_rate_of_life_formation_in_habitable_planets < -32){
+            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);
+        }
+        // printf(" log_fraction_of_habitable_planets_in_which_any_life_appears: %lf\n", log_fraction_of_habitable_planets_in_which_any_life_appears);
+
+        double log_n = log_n1 + log_fraction_of_habitable_planets_in_which_any_life_appears;
+
+        return log_n;
+    }
+
+    double sample_fermi_paradox_logspace(uint64_t* seed){
+        double n = sample_fermi_logspace(seed);
+        return ((n > 0) ? 1 : 0);
+    }
+
+    double logspace_fermi_proportion = 0;
+    for(int i=0; i<n; i++){
+        double result = sample_fermi_paradox_logspace(seed);
+        // printf("result: %lf\n", result);
+        logspace_fermi_proportion+=result;
+    }
+    printf("Using more accurate logspace computations, %% that we are not alone: %lf\n", logspace_fermi_proportion/n);
+    double result2;
+
+    free(seed);
+}

examples/core/makefile

@@ -41,6 +41,8 @@ all:
 	$(CC) $(OPTIMIZED) $(DEBUG) $(WARN)  03_gcc_nested_function/$(SRC) $(DEPS) -o 03_gcc_nested_function/$(OUTPUT)
 	$(CC) $(OPTIMIZED) $(DEBUG) $(WARN) 04_gamma_beta/$(SRC)          $(DEPS) -o 04_gamma_beta/$(OUTPUT)
 	$(CC) $(OPTIMIZED) $(DEBUG) $(WARN) 05_hundred_lognormals/$(SRC)  $(DEPS) -o 05_hundred_lognormals/$(OUTPUT)
+	$(CC) $(OPTIMIZED) $(DEBUG) $(WARN) 06_dissolving_fermi_paradox/$(SRC)  $(DEPS) -o 06_dissolving_fermi_paradox/$(OUTPUT)
+
 
 format-all:
 	$(FORMATTER) 00_example_template/$(SRC)
@@ -49,6 +51,7 @@ format-all:
 	$(FORMATTER) 03_gcc_nested_function/$(SRC)
 	$(FORMATTER) 04_gamma_beta/$(SRC)
 	$(FORMATTER) 05_hundred_lognormals/$(SRC)
+	$(FORMATTER) 06_dissolving_fermi_paradox/$(SRC)
 
 run-all:
 	00_example_template/$(OUTPUT)
@@ -57,6 +60,7 @@ run-all:
 	03_gcc_nested_function/$(OUTPUT)
 	04_gamma_beta/$(OUTPUT)
 	05_hundred_lognormals/$(OUTPUT)
+	06_dissolving_fermi_paradox/$(OUTPUT)
 	
 ## make one DIR=01_one_sample
 one: $(DIR)/$(SRC)