Initial folder refactor

CUDA/examples/core/00_example_template/example.c

@@ -0,0 +1,14 @@
+#include "../../../squiggle.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    // ...
+
+    free(seed);
+}

CUDA/examples/core/01_one_sample/example.c

@@ -0,0 +1,34 @@
+#include "../../../squiggle.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+// Estimate functions
+
+double sample_0(uint64_t* seed) { UNUSED(seed); return 0; }
+double sample_1(uint64_t* seed) { UNUSED(seed); return 1; }
+double sample_few(uint64_t* seed) { return sample_to(1, 3, seed); }
+double sample_many(uint64_t* seed) { return sample_to(2, 10, seed); }
+
+double sample_model(uint64_t* seed){
+
+    double p_a = 0.8;
+    double p_b = 0.5;
+    double p_c = p_a * p_b;
+
+    int n_dists = 4;
+    double weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
+    double (*samplers[])(uint64_t*) = { sample_0, sample_1, sample_few, sample_many };
+    double result = sample_mixture(samplers, weights, n_dists, seed);
+
+    return result;
+}
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    printf("result_one: %f\n", sample_model(seed));
+    free(seed);
+}

CUDA/examples/core/02_time_to_botec/example.c

@@ -0,0 +1,38 @@
+#include "../../../squiggle.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+double sample_0(uint64_t* seed) { UNUSED(seed); return 0; }
+double sample_1(uint64_t* seed) { UNUSED(seed); return 1; }
+double sample_few(uint64_t* seed) { return sample_to(1, 3, seed); }
+double sample_many(uint64_t* seed) { return sample_to(2, 10, seed); }
+
+double sample_model(uint64_t* seed){
+
+    double p_a = 0.8;
+    double p_b = 0.5;
+    double p_c = p_a * p_b;
+
+    int n_dists = 4;
+    double weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
+    double (*samplers[])(uint64_t*) = { sample_0, sample_1, sample_few, sample_many };
+    double result = sample_mixture(samplers, weights, n_dists, seed);
+
+    return result;
+}
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    int n_samples = 1000000;
+    double* result_many = (double*)malloc((size_t)n_samples * sizeof(double));
+    for (int i = 0; i < n_samples; i++) {
+        result_many[i] = sample_model(seed);
+    }
+    printf("Mean: %f\n", array_mean(result_many, n_samples));
+
+    free(seed);
+}

CUDA/examples/core/03_gcc_nested_function/example.c

@@ -0,0 +1,44 @@
+#include "../../../squiggle.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+double sample_model(uint64_t* seed){
+
+    double sample_0(uint64_t* seed) { UNUSED(seed); return 0; }
+    // Using a gcc extension, you can define a function inside another function
+    double sample_1(uint64_t* seed) { UNUSED(seed); return 1; }
+    double sample_few(uint64_t* seed) { return sample_to(1, 3, seed); }
+    double sample_many(uint64_t* seed) { return sample_to(2, 10, seed); }
+
+    double p_a = 0.8;
+    double p_b = 0.5;
+    double p_c = p_a * p_b;
+
+    int n_dists = 4;
+    double weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
+    double (*samplers[])(uint64_t*) = { sample_0, sample_1, sample_few, sample_many };
+    double result = sample_mixture(samplers, weights, n_dists, seed);
+
+    return result;
+}
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    int n_samples = 1000000;
+    double* result_many = (double*)malloc((size_t)n_samples * sizeof(double));
+    for (int i = 0; i < n_samples; i++) {
+        result_many[i] = sample_model(seed);
+    }
+
+    printf("result_many: [");
+    for (int i = 0; i < 100; i++) {
+        printf("%.2f, ", result_many[i]);
+    }
+    printf("]\n");
+
+    free(seed);
+}

CUDA/examples/core/04_gamma_beta/example.c

@@ -0,0 +1,29 @@
+#include "../../../squiggle.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    int n = 1000 * 1000;
+    double* gamma_array = malloc(sizeof(double) * (size_t)n);
+    for (int i = 0; i < n; i++) {
+        gamma_array[i] = sample_gamma(1.0, seed);
+    }
+    printf("gamma(1) summary statistics = mean: %f, std: %f\n", array_mean(gamma_array, n), array_std(gamma_array, n));
+    printf("\n");
+
+    double* beta_array = malloc(sizeof(double) * (size_t)n);
+    for (int i = 0; i < n; i++) {
+        beta_array[i] = sample_beta(1, 2.0, seed);
+    }
+    printf("beta(1,2) summary statistics: mean: %f, std: %f\n", array_mean(beta_array, n), array_std(beta_array, n));
+    printf("\n");
+
+    free(gamma_array);
+    free(beta_array);
+    free(seed);
+}

CUDA/examples/core/05_hundred_lognormals/example.c

@@ -0,0 +1,17 @@
+#include "../../../squiggle.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+// Estimate functions
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    for (int i = 0; i < 100; i++) {
+        double sample = sample_lognormal(0, 10, seed);
+        printf("%f\n", sample);
+    }
+    free(seed);
+}

CUDA/examples/core/05_hundred_lognormals/run-sorted.sh

@@ -0,0 +1 @@
+./example | sort -h

CUDA/examples/core/06_dissolving_fermi_paradox/example.c

@@ -0,0 +1,99 @@
+#include "../../../squiggle.h"
+#include <math.h>
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+double sample_fermi_logspace(uint64_t * seed)
+{
+    // Replicate <https://arxiv.org/pdf/1806.02404.pdf>, and in particular the red line in page 11.
+    // You can see a simple version of this function in naive.c in this same folder
+    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_rate_of_life_formation_in_habitable_planets = sample_normal(1, 50, seed);
+    double log_fraction_of_habitable_planets_in_which_any_life_appears;
+    /* 
+        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)
+
+        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
+        
+        Empirically, the two numbers as calculated in C do become really close around 11 or so, 
+        and at 38 that calculation results in a -inf (so probably a floating point error or similar.)
+        So we should be using that formula for somewhere between -38 << a < -11
+
+        I chose -16 as a happy medium after playing around with 
+        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));
+        }
+        and <https://www.wolframalpha.com/input?i=log%281-exp%28-exp%28-16%29%29%29>
+    */
+    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);
+    }
+
+    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);
+
+    double log_n = 
+        log_rate_of_star_formation + 
+        log_fraction_of_stars_with_planets + 
+        log_number_of_habitable_planets_per_star_system + 
+        log_fraction_of_habitable_planets_in_which_any_life_appears + 
+        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;
+    return log_n;
+}
+
+double sample_are_we_alone_logspace(uint64_t * seed)
+{
+    double log_n = sample_fermi_logspace(seed);
+    return ((log_n > 0) ? 1 : 0);
+    // log_n > 0 => n > 1
+}
+
+
+int main()
+{
+
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1001; // xorshift can't start with a seed of 0
+
+    double logspace_fermi_proportion = 0;
+    int n_samples = 1000 * 1000;
+    for (int i = 0; i < n_samples; i++) {
+        double result = sample_are_we_alone_logspace(seed);
+        logspace_fermi_proportion += result;
+    }
+    double p_not_alone = logspace_fermi_proportion / n_samples;
+    printf("Probability that we are not alone: %lf (%.lf%%)\n", p_not_alone, p_not_alone * 100);
+
+    free(seed);
+}

CUDA/examples/core/06_dissolving_fermi_paradox/naive.c

@@ -0,0 +1,79 @@
+#include "../../../squiggle.h"
+#include <math.h>
+#include <stdint.h>
+#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));
+}
+
+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
+
+    // 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);
+        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);
+
+        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)
+        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_are_we_alone_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_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);
+
+    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));
+        }
+    */
+}

CUDA/examples/core/makefile

@@ -0,0 +1,91 @@
+# Interface: 
+# make all 
+# make format-all
+# make run-all
+# make one             DIR=01_one_sample
+# make format-one      DIR=01_one_sample
+# make run-one         DIR=01_one_sample
+# make time-linux-one  DIR=01_one_sample
+# make profile-one     DIR=01_one_sample
+
+# Compiler
+CC=gcc
+# CC=tcc # <= faster compilation
+
+# Main file
+SRC=example.c
+OUTPUT=example
+
+## Dependencies
+SQUIGGLE=../../squiggle.c
+MATH=-lm
+DEPS=$(SQUIGGLE) $(MATH)
+
+## Flags
+# DEBUG=-fsanitize=address,undefined -fanalyzer
+# DEBUG=-g
+# DEBUG=
+WARN=-Wall -Wextra -Wdouble-promotion -Wconversion
+STANDARD=-std=c99
+OPTIMIZED=-O3  #-Ofast
+
+## Formatter
+STYLE_BLUEPRINT=webkit
+FORMATTER=clang-format -i -style=$(STYLE_BLUEPRINT)
+
+## make all
+all:
+	$(CC) $(OPTIMIZED) $(DEBUG) $(WARN) 00_example_template/$(SRC) $(DEPS) -o 00_example_template/$(OUTPUT)
+	$(CC) $(OPTIMIZED) $(DEBUG) $(WARN) 01_one_sample/$(SRC) $(DEPS) -o 01_one_sample/$(OUTPUT)
+	$(CC) $(OPTIMIZED) $(DEBUG) $(WARN) 02_time_to_botec/$(SRC) $(DEPS) -o 02_time_to_botec/$(OUTPUT)
+	$(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)
+	$(FORMATTER) 01_one_sample/$(SRC)
+	$(FORMATTER) 02_time_to_botec/$(SRC)
+	$(FORMATTER) 03_gcc_nested_function/$(SRC)
+	$(FORMATTER) 04_gamma_beta/$(SRC)
+	$(FORMATTER) 05_hundred_lognormals/$(SRC)
+	$(FORMATTER) 06_dissolving_fermi_paradox/$(SRC)
+
+run-all:
+	00_example_template/$(OUTPUT)
+	01_one_sample/$(OUTPUT)
+	02_time_to_botec/$(OUTPUT)
+	03_gcc_nested_function/$(OUTPUT)
+	04_gamma_beta/$(OUTPUT)
+	05_hundred_lognormals/$(OUTPUT)
+	06_dissolving_fermi_paradox/$(OUTPUT)
+	
+## make one DIR=01_one_sample
+one: $(DIR)/$(SRC)
+	$(CC) $(OPTIMIZED) $(DEBUG) $(WARN) $(DIR)/$(SRC) $(DEPS) -o $(DIR)/$(OUTPUT)
+
+## make format-one DIR=01_one_sample
+format-one: $(DIR)/$(SRC)
+	$(FORMATTER) $(DIR)/$(SRC)
+
+## make run-one DIR=01_one_sample
+run-one: $(DIR)/$(OUTPUT)
+	$(DIR)/$(OUTPUT) && echo
+
+## make time-linux-one DIR=01_one_sample
+time-linux-one: $(DIR)/$(OUTPUT)
+	@echo "Requires /bin/time, found on GNU/Linux systems" && echo
+	@echo "Running 100x and taking avg time $(DIR)/$(OUTPUT)"
+	@t=$$(/usr/bin/time -f "%e" -p bash -c 'for i in {1..100}; do $(DIR)/$(OUTPUT); done' 2>&1 >/dev/null | grep real | awk '{print $$2}' ); echo "scale=2; 1000 * $$t / 100" | bc | sed "s|^|Time using 1 thread: |" | sed 's|$$|ms|' && echo
+
+## e.g., make profile-linux-one DIR=01_one_sample
+profile-linux-one: 
+	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) $(OPTIMIZED) $(DEBUG) $(WARN) $(DIR)/$(SRC) $(DEPS) -o $(DIR)/$(OUTPUT)
+	# $(CC) $(SRC) $(DEPS) -o $(OUTPUT)
+	sudo perf record $(DIR)/$(OUTPUT)
+	sudo perf report
+	rm perf.data

CUDA/examples/more/00_example_template/example.c

@@ -0,0 +1,19 @@
+#include "../../../squiggle.h"
+#include "../../../squiggle_more.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+double sample_model(uint64_t* seed){
+    return sample_to(1, 10, seed);
+}
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    // ...
+
+    free(seed);
+}

CUDA/examples/more/02_ci_beta/example.c

@@ -0,0 +1,30 @@
+#include "../../../squiggle.h"
+#include "../../../squiggle_more.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+// Estimate functions
+double sample_beta_3_2(uint64_t* seed)
+{
+    return sample_beta(3.0, 2.0, seed);
+}
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    int n_samples = 1 * MILLION;
+    double* xs = malloc(sizeof(double) * (size_t)n_samples);
+    for (int i = 0; i < n_samples; i++) {
+        xs[i] = sample_beta_3_2(seed);
+    }
+
+    printf("\n# Stats\n");
+    array_print_stats(xs, n_samples);
+    printf("\n# Histogram\n");
+    array_print_histogram(xs, n_samples, 23);
+
+    free(seed);
+}

CUDA/examples/more/03_ci_beta_parallel/example.c

@@ -0,0 +1,28 @@
+#include "../../../squiggle.h"
+#include "../../../squiggle_more.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+// Estimate functions
+double sample_beta_3_2(uint64_t* seed)
+{
+    return sample_beta(3.0, 2.0, seed);
+}
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    int n_samples = 1 * MILLION;
+    double* xs = malloc(sizeof(double) * (size_t)n_samples);
+    sampler_parallel(sample_beta_3_2, xs, 16, n_samples);
+
+    printf("\n# Stats\n");
+    array_print_stats(xs, n_samples);
+    printf("\n# Histogram\n");
+    array_print_histogram(xs, n_samples, 23);
+
+    free(seed);
+}

CUDA/examples/more/04_nuclear_war/example.c

@@ -0,0 +1,63 @@
+#include "../../../squiggle.h"
+#include "../../../squiggle_more.h"
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+double probability_of_dying_nuno(uint64_t* seed)
+{
+    double first_year_russian_nuclear_weapons = 1953;
+    double current_year = 2022;
+    double laplace_probability_nuclear_exchange_year = sample_beta(1, current_year - first_year_russian_nuclear_weapons + 1, seed);
+    double laplace_probability_nuclear_exchange_month = 1 - pow(1 - laplace_probability_nuclear_exchange_year, (1.0 / 12.0));
+
+    double london_hit_conditional_on_russia_nuclear_weapon_usage = sample_beta(7.67, 69.65, seed);
+    // I.e., a beta distribution with a range of 0.05 to 0.16 into: https://nunosempere.com/blog/2023/03/15/fit-beta/
+    // 0.05 were my estimate and Samotsvety's estimate in March 2022, respectively:
+    // https://forum.effectivealtruism.org/posts/KRFXjCqqfGQAYirm5/samotsvety-nuclear-risk-forecasts-march-2022#Nu_o_Sempere
+    double informed_actor_not_able_to_escape = sample_beta(3.26212166586967, 3.26228162008564, seed);
+    // 0.2 to 0.8, i.e., 20% to 80%, again using the previous tool
+    double proportion_which_die_if_bomb_drops_in_london = sample_beta(10.00, 2.45, seed); // 60% to 95%
+
+    double probability_of_dying = laplace_probability_nuclear_exchange_month * london_hit_conditional_on_russia_nuclear_weapon_usage * informed_actor_not_able_to_escape * proportion_which_die_if_bomb_drops_in_london;
+    return probability_of_dying;
+}
+
+double probability_of_dying_eli(uint64_t* seed)
+{
+    double russia_nato_nuclear_exchange_in_next_month = sample_beta(1.30, 1182.99, seed); // .0001 to .003
+    double london_hit_conditional = sample_beta(3.47, 8.97, seed); // 0.1 to 0.5
+    double informed_actors_not_able_to_escape = sample_beta(2.73, 5.67, seed); // .1 to .6
+    double proportion_which_die_if_bomb_drops_in_london = sample_beta(3.00, 1.46, seed); // 0.3 to 0.95;
+
+    double probability_of_dying = russia_nato_nuclear_exchange_in_next_month * london_hit_conditional * informed_actors_not_able_to_escape * proportion_which_die_if_bomb_drops_in_london;
+    return probability_of_dying;
+}
+
+double sample_nuclear_model(uint64_t* seed)
+{
+    double (*samplers[])(uint64_t*) = { probability_of_dying_nuno, probability_of_dying_eli };
+    double weights[] = { 0.5, 0.5 };
+    return sample_mixture(samplers, weights, 2, seed);
+}
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    int n = 1 * MILLION;
+    double* xs = malloc(sizeof(double) * (size_t)n);
+    for (int i = 0; i < n; i++) {
+        xs[i] = sample_nuclear_model(seed);
+    }
+
+    printf("\n# Stats\n");
+    array_print_stats(xs, n);
+    printf("\n# Histogram\n");
+    array_print_90_ci_histogram(xs, n, 20);
+
+    free(xs);
+    free(seed);
+}

CUDA/examples/more/04_nuclear_war/scratchpad/example.c

@@ -0,0 +1,20 @@
+#include "../../../squiggle.h"
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+		double firstYearRussianNuclearWeapons = 1953;
+		double	currentYear = 2023;
+
+		for(int i=0; i<10; i++){
+			double laplace_beta = sample_beta(currentYear-firstYearRussianNuclearWeapons + 1, 1, seed);
+			printf("%f\n", laplace_beta);
+		}
+		
+    free(seed);
+}

CUDA/examples/more/04_nuclear_war/scratchpad/makefile

@@ -0,0 +1,53 @@
+# Interface: 
+#   make
+#   make build
+#   make format
+#   make run
+
+# Compiler
+CC=gcc
+# CC=tcc # <= faster compilation
+
+# Main file
+SRC=example.c ../../../squiggle.c
+OUTPUT=example
+
+## 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) $(OUTPUT)
+	OMP_NUM_THREADS=1 ./$(OUTPUT) && echo
+
+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

CUDA/examples/more/05_burn_10kg_fat/example.c

@@ -0,0 +1,43 @@
+#include "../../../squiggle.h"
+#include "../../../squiggle_more.h"
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+double sample_minutes_per_day_jumping_rope_needed_to_burn_10kg(uint64_t* seed)
+{
+    double kcal_jumping_rope_minute = sample_to(15, 20, seed);
+    double kcal_jumping_rope_hour = kcal_jumping_rope_minute * 60;
+
+    double kcal_in_kg_of_fat = 7700;
+    double num_kg_of_fat_to_lose = 10;
+
+    double hours_jumping_rope_needed = kcal_in_kg_of_fat * num_kg_of_fat_to_lose / kcal_jumping_rope_hour;
+
+    double days_until_end_of_year = 152; // as of 2023-08-01
+    double hours_per_day = hours_jumping_rope_needed / days_until_end_of_year;
+    double minutes_per_day = hours_per_day * 60;
+    return minutes_per_day;
+}
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    int n = 1000 * 1000;
+    double* xs = malloc(sizeof(double) * (size_t)n);
+    for (int i = 0; i < n; i++) {
+        xs[i] = sample_minutes_per_day_jumping_rope_needed_to_burn_10kg(seed);
+    }
+
+    printf("## How many minutes per day do I have to jump rope to lose 10kg of fat by the end of the year?\n");
+
+    printf("\n# Stats\n");
+    array_print_stats(xs, n);
+    printf("\n# Histogram\n");
+    array_print_histogram(xs, n, 23);
+
+    free(seed);
+}

CUDA/examples/more/06_nuclear_recovery/example.c

@@ -0,0 +1,84 @@
+#include "../../../squiggle.h"
+#include "../../../squiggle_more.h"
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+double yearly_probability_nuclear_collapse(double year, uint64_t* seed)
+{
+    double successes = 0;
+    double failures = (year - 1960);
+    return sample_laplace(successes, failures, seed);
+    // ^ can change to (successes + 1)/(trials + 2)
+    // to get a probability,
+    // rather than sampling from a distribution over probabilities.
+}
+double yearly_probability_nuclear_collapse_2023(uint64_t* seed)
+{
+    return yearly_probability_nuclear_collapse(2023, seed);
+}
+
+double yearly_probability_nuclear_collapse_after_recovery(double year, double rebuilding_period_length_years, uint64_t* seed)
+{
+    // assumption: nuclear
+    double successes = 1.0;
+    double failures = (year - rebuilding_period_length_years - 1960 - 1);
+    return sample_laplace(successes, failures, seed);
+}
+double yearly_probability_nuclear_collapse_after_recovery_example(uint64_t* seed)
+{
+    double year = 2070;
+    double rebuilding_period_length_years = 30;
+    // So, there was a nuclear collapse in 2040,
+    // then a recovery period of 30 years
+    // and it's now 2070
+    return yearly_probability_nuclear_collapse_after_recovery(year, rebuilding_period_length_years, seed);
+}
+
+double yearly_probability_nuclear_collapse_after_recovery_antiinductive(uint64_t* seed)
+{
+    return yearly_probability_nuclear_collapse(2023, seed) / 2;
+}
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    int n_samples = 1000000;
+
+    // Before a first nuclear collapse
+    printf("## Before the first nuclear collapse\n");
+    double* yearly_probability_nuclear_collapse_2023_samples = malloc(sizeof(double) * (size_t)n_samples);
+    for (int i = 0; i < n_samples; i++) {
+        yearly_probability_nuclear_collapse_2023_samples[i] = yearly_probability_nuclear_collapse_2023(seed);
+    }
+    ci ci_90_2023 = array_get_90_ci(yearly_probability_nuclear_collapse_2023_samples, n_samples);
+    printf("90%% confidence interval: [%f, %f]\n", ci_90_2023.low, ci_90_2023.high);
+
+    // After the first nuclear collapse
+    printf("\n## After the first nuclear collapse\n");
+
+    double* yearly_probability_nuclear_collapse_after_recovery_samples = malloc(sizeof(double) * (size_t)n_samples);
+    for (int i = 0; i < n_samples; i++) {
+        yearly_probability_nuclear_collapse_after_recovery_samples[i] = yearly_probability_nuclear_collapse_after_recovery_example(seed);
+    }
+    ci ci_90_2070 = array_get_90_ci(yearly_probability_nuclear_collapse_after_recovery_samples, 1000000);
+    printf("90%% confidence interval: [%f, %f]\n", ci_90_2070.low, ci_90_2070.high);
+
+    // After the first nuclear collapse (antiinductive)
+    printf("\n## After the first nuclear collapse (antiinductive)\n");
+    double* yearly_probability_nuclear_collapse_after_recovery_antiinductive_samples = malloc(sizeof(double) * (size_t)n_samples);
+    for (int i = 0; i < n_samples; i++) {
+        yearly_probability_nuclear_collapse_after_recovery_antiinductive_samples[i] = yearly_probability_nuclear_collapse_after_recovery_antiinductive(seed);
+    }
+    ci ci_90_antiinductive = array_get_90_ci(yearly_probability_nuclear_collapse_after_recovery_antiinductive_samples, 1000000);
+    printf("90%% confidence interval: [%f, %f]\n", ci_90_antiinductive.low, ci_90_antiinductive.high);
+
+    // free seeds
+    free(yearly_probability_nuclear_collapse_2023_samples);
+    free(yearly_probability_nuclear_collapse_after_recovery_samples);
+    free(yearly_probability_nuclear_collapse_after_recovery_antiinductive_samples);
+    free(seed);
+}

CUDA/examples/more/07_algebra/example.c

@@ -0,0 +1,26 @@
+#include "../../../squiggle.h"
+#include "../../../squiggle_more.h"
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    normal_params n1 = { .mean = 1.0, .std = 3.0 };
+    normal_params n2 = { .mean = 2.0, .std = 4.0 };
+    normal_params sn = algebra_sum_normals(n1, n2);
+    printf("The sum of Normal(%f, %f) and Normal(%f, %f) is Normal(%f, %f)\n",
+        n1.mean, n1.std, n2.mean, n2.std, sn.mean, sn.std);
+
+    lognormal_params ln1 = { .logmean = 1.0, .logstd = 3.0 };
+    lognormal_params ln2 = { .logmean = 2.0, .logstd = 4.0 };
+    lognormal_params sln = algebra_product_lognormals(ln1, ln2);
+    printf("The product of Lognormal(%f, %f) and Lognormal(%f, %f) is Lognormal(%f, %f)\n",
+        ln1.logmean, ln1.logstd, ln2.logmean, ln2.logstd, sln.logmean, sln.logstd);
+
+    free(seed);
+}

CUDA/examples/more/08_algebra_and_conversion/example.c

@@ -0,0 +1,33 @@
+#include "../../../squiggle.h"
+#include "../../../squiggle_more.h"
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+int main()
+{
+    // set randomness seed
+    uint64_t* seed = malloc(sizeof(uint64_t));
+    *seed = 1000; // xorshift can't start with 0
+
+    // Convert to 90% confidence interval form and back
+    lognormal_params ln1 = { .logmean = 1.0, .logstd = 3.0 };
+    ci ln1_ci = convert_lognormal_params_to_ci(ln1);
+    printf("The 90%% confidence interval of Lognormal(%f, %f) is [%f, %f]\n",
+        ln1.logmean, ln1.logstd,
+        ln1_ci.low, ln1_ci.high);
+    lognormal_params ln1_params2 = convert_ci_to_lognormal_params(ln1_ci);
+    printf("The lognormal which has 90%% confidence interval [%f, %f] is Lognormal(%f, %f)\n",
+        ln1_ci.low, ln1_ci.high,
+        ln1_params2.logmean, ln1_params2.logstd);
+
+    lognormal_params ln2 = convert_ci_to_lognormal_params((ci) { .low = 1, .high = 10 });
+    lognormal_params ln3 = convert_ci_to_lognormal_params((ci) { .low = 5, .high = 50 });
+
+    lognormal_params sln = algebra_product_lognormals(ln2, ln3);
+    ci sln_ci = convert_lognormal_params_to_ci(sln);
+
+    printf("Result of some lognormal products: to(%f, %f)\n", sln_ci.low, sln_ci.high);
+
+    free(seed);
+}