JJSierraM/squiggle.c
1
0
Fork 0
forked from personal/squiggle.c
Code Issues Pull Requests Packages Projects Releases Wiki Activity

add fermi paradox to examples

Browse Source
This commit is contained in:
NunoSempere 2024-01-20 14:28:20 +01:00
parent bb91d78859
commit 199e76bdfb
5 changed files with 217 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

BIN
examples/core/06_dissolving_fermi_paradox/fermi.pdf Normal file
View File

Binary file not shown.

56
examples/core/06_dissolving_fermi_paradox/makefile Normal file
View File

@ -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

BIN
examples/core/06_dissolving_fermi_paradox/scratchpad Executable file
View File

Binary file not shown.

157
examples/core/06_dissolving_fermi_paradox/scratchpad.c Normal file
View File

@ -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);
}

4
examples/core/makefile
View File

@ -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)