commit 199e76bdfb061bed4ec0ed1705c2ec0f6780fa41
parent bb91d78859dc446063287f7dee48f7771ce86499
Author: NunoSempere <nuno.sempere@protonmail.com>
Date: Sat, 20 Jan 2024 14:28:20 +0100
add fermi paradox to examples
Diffstat:
5 files changed, 217 insertions(+), 0 deletions(-)
diff --git a/examples/core/06_dissolving_fermi_paradox/fermi.pdf b/examples/core/06_dissolving_fermi_paradox/fermi.pdf
Binary files differ.
diff --git a/examples/core/06_dissolving_fermi_paradox/makefile b/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
diff --git a/examples/core/06_dissolving_fermi_paradox/scratchpad b/examples/core/06_dissolving_fermi_paradox/scratchpad
Binary files differ.
diff --git a/examples/core/06_dissolving_fermi_paradox/scratchpad.c b/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);
+}
diff --git a/examples/core/makefile b/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)
