commit 4b158c95df603db845c8084359320804269c3e19
parent 1d89eb6231aa02415e2d8e906d6ee929d54e7366
Author: NunoSempere <nuno.sempere@protonmail.com>
Date: Sat, 20 Jan 2024 19:48:55 +0100
update fermi example
Diffstat:
3 files changed, 66 insertions(+), 109 deletions(-)
diff --git a/examples/core/06_dissolving_fermi_paradox/example b/examples/core/06_dissolving_fermi_paradox/example
Binary files differ.
diff --git a/examples/core/06_dissolving_fermi_paradox/example.c b/examples/core/06_dissolving_fermi_paradox/example.c
@@ -4,6 +4,8 @@
#include <stdio.h>
#include <stdlib.h>
+#define VERBOSE 0
+
double sample_loguniform(double a, double b, uint64_t* seed)
{
return exp(sample_uniform(log(a), log(b), seed));
@@ -18,6 +20,7 @@ int main()
uint64_t* seed = malloc(sizeof(uint64_t));
*seed = UINT64_MAX / 64; // xorshift can't start with a seed of 0
+ // Do this naïvely, without worrying that much about numerical precision
double sample_fermi_naive(uint64_t * seed)
{
double rate_of_star_formation = sample_loguniform(1, 100, seed);
@@ -31,14 +34,14 @@ int main()
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);
+ if(VERBOSE) printf(" rate_of_star_formation = %lf\n", rate_of_star_formation);
+ if(VERBOSE) printf(" fraction_of_stars_with_planets = %lf\n", fraction_of_stars_with_planets);
+ if(VERBOSE) printf(" number_of_habitable_planets_per_star_system = %lf\n", number_of_habitable_planets_per_star_system);
+ if(VERBOSE) printf(" rate_of_life_formation_in_habitable_planets = %.16lf\n", rate_of_life_formation_in_habitable_planets);
+ if(VERBOSE) printf(" fraction_of_habitable_planets_in_which_any_life_appears = %lf\n", fraction_of_habitable_planets_in_which_any_life_appears);
+ 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);
+ if(VERBOSE) printf(" fraction_of_intelligent_planets_which_are_detectable_as_such = %lf\n", fraction_of_intelligent_planets_which_are_detectable_as_such);
+ if(VERBOSE) printf(" longevity_of_detectable_civilizations = %lf\n", longevity_of_detectable_civilizations);
// Expected number of civilizations in the Milky way;
// see footnote 3 (p. 5)
@@ -47,7 +50,7 @@ int main()
return n;
}
- double sample_fermi_paradox_naive(uint64_t * seed)
+ double sample_are_we_alone_naive(uint64_t * seed)
{
double n = sample_fermi_naive(seed);
return ((n > 1) ? 1 : 0);
@@ -56,13 +59,14 @@ int main()
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);
+ double result = sample_are_we_alone_naive(seed);
+ if(VERBOSE) 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
+ // Taking care of numerical precision
double sample_fermi_logspace(uint64_t * seed)
{
double log_rate_of_star_formation = sample_uniform(log(1), log(100), seed);
@@ -72,64 +76,63 @@ int main()
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);
+ if(VERBOSE) printf(" log_rate_of_star_formation = %lf\n", log_rate_of_star_formation);
+ if(VERBOSE) printf(" log_fraction_of_stars_with_planets = %lf\n", log_fraction_of_stars_with_planets);
+ if(VERBOSE) printf(" log_number_of_habitable_planets_per_star_system = %lf\n", log_number_of_habitable_planets_per_star_system);
+ if(VERBOSE) 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);
+ if(VERBOSE) printf(" log_fraction_of_intelligent_planets_which_are_detectable_as_such = %lf\n", log_fraction_of_intelligent_planets_which_are_detectable_as_such);
+ if(VERBOSE) 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
+ if(VERBOSE) printf("first part of calculation: %lf\n", log_n1);
+
+ /*
+ Consider:
+ a = underlying normal
+ b = rate_of_life_formation_in_habitable_planets = exp(underlying normal) = exp(a)
+ c = 1 - exp(-b) = fraction_of_habitable_planets_in_which_any_life_appears
+ d = log(c)
+
+ Now, is there some way we can get 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
+
+ Now, we could play around with estimating errors,
+ and indeed if we want b^2/2 = exp(a)^2/2 < 10^(-n), i.e., to have n decimal digits of precision,
+ we could compute this as e.g., a < (nlog(10) + log(2))/2
+ so for example if we want ten digits of precision, that's a < -11
+
+ But more empirically, the two numbers do become really close around 11 or so, and at 38 that calculation results in a -inf (so probably an overflow.)
+ So we should be using that formula for somewhere between -38 << a < -11
+ I chose -16 for the sake of it after playing with:
+ <https://www.wolframalpha.com/input?i=log%281-exp%28-exp%28-16%29%29%29>
*/
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);
+ if(VERBOSE) 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) {
+ if (log_rate_of_life_formation_in_habitable_planets < -16) {
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);
+ if(VERBOSE) 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 sample_are_we_alone_logspace(uint64_t * seed)
{
double n = sample_fermi_logspace(seed);
return ((n > 0) ? 1 : 0);
@@ -137,11 +140,21 @@ int main()
double logspace_fermi_proportion = 0;
for (int i = 0; i < n; i++) {
- double result = sample_fermi_paradox_logspace(seed);
- // printf("result: %lf\n", result);
+ double result = sample_are_we_alone_logspace(seed);
+ if(VERBOSE) 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);
free(seed);
+
+ /*
+ double invert(double x){
+ return log(1-exp(-exp(-x)));
+ }
+ for(int i=0; i<64; i++){
+ double j = i;
+ printf("for %lf, log(1-exp(-exp(-x))) is calculated as... %lf\n", j, invert(j));
+ }
+ */
}
diff --git a/examples/core/06_dissolving_fermi_paradox/makefile b/examples/core/06_dissolving_fermi_paradox/makefile
@@ -1,56 +0,0 @@
-# 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
