Revert "Revert "Merge branch 'master' into quickselect""

This reverts commit 4d218468cf.

examples/core/02_time_to_botec/example.c

@@ -12,10 +12,10 @@ int main()
     double p_b = 0.5;
     double p_c = p_a * p_b;
 
-    double sample_0(uint64_t* seed){ return 0; }
-    double sample_1(uint64_t* 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_0(uint64_t * seed) { return 0; }
+    double sample_1(uint64_t * 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); }
 
     int n_dists = 4;
     double weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };

examples/more/03_ci_beta/example.c

@@ -15,8 +15,9 @@ int main()
     uint64_t* seed = malloc(sizeof(uint64_t));
     *seed = 1000; // xorshift can't start with 0
 
-    ci beta_1_2_ci_90 = get_90_confidence_interval(beta_1_2_sampler, seed);
+    ci beta_1_2_ci_90 = sampler_get_90_ci(beta_1_2_sampler, 1000000, seed);
     printf("90%% confidence interval of beta(1,2) is [%f, %f]\n", beta_1_2_ci_90.low, beta_1_2_ci_90.high);
+    printf("You can check this in <https://nunosempere.com/blog/2023/03/15/fit-beta/>\n");
 
     free(seed);
 }

examples/more/04_nuclear_war/example.c

@@ -60,7 +60,7 @@ int main()
     }
     printf("... ]\n");
 
-    ci ci_90 = get_90_confidence_interval(mixture, seed);
+    ci ci_90 = sampler_get_90_ci(mixture, 1000000, seed);
     printf("mean: %f\n", array_mean(mixture_result, n));
     printf("90%% confidence interval: [%f, %f]\n", ci_90.low, ci_90.high);
 

examples/more/05_burn_10kg_fat/example.c

@@ -41,7 +41,7 @@ int main()
     }
     printf("... ]\n");
 
-    ci ci_90 = get_90_confidence_interval(sample_minutes_per_day_jumping_rope_needed_to_burn_10kg, seed);
+    ci ci_90 = sampler_get_90_ci(sample_minutes_per_day_jumping_rope_needed_to_burn_10kg, 1000000, seed);
     printf("90%% confidence interval: [%f, %f]\n", ci_90.low, ci_90.high);
 
     free(seed);

examples/more/06_nuclear_recovery/example.c

@@ -50,7 +50,7 @@ int main()
 
     // Before a first nuclear collapse
     printf("## Before the first nuclear collapse\n");
-    ci ci_90_2023 = get_90_confidence_interval(yearly_probability_nuclear_collapse_2023, seed);
+    ci ci_90_2023 = sampler_get_90_ci(yearly_probability_nuclear_collapse_2023, 1000000, seed);
     printf("90%% confidence interval: [%f, %f]\n", ci_90_2023.low, ci_90_2023.high);
 
     double* yearly_probability_nuclear_collapse_2023_samples = malloc(sizeof(double) * num_samples);
@@ -61,7 +61,7 @@ int main()
 
     // After the first nuclear collapse
     printf("\n## After the first nuclear collapse\n");
-    ci ci_90_2070 = get_90_confidence_interval(yearly_probability_nuclear_collapse_after_recovery_example, seed);
+    ci ci_90_2070 = sampler_get_90_ci(yearly_probability_nuclear_collapse_after_recovery_example, 1000000, seed);
     printf("90%% confidence interval: [%f, %f]\n", ci_90_2070.low, ci_90_2070.high);
 
     double* yearly_probability_nuclear_collapse_after_recovery_samples = malloc(sizeof(double) * num_samples);
@@ -72,7 +72,7 @@ int main()
 
     // After the first nuclear collapse (antiinductive)
     printf("\n## After the first nuclear collapse (antiinductive)\n");
-    ci ci_90_antiinductive = get_90_confidence_interval(yearly_probability_nuclear_collapse_after_recovery_antiinductive, seed);
+    ci ci_90_antiinductive = sampler_get_90_ci(yearly_probability_nuclear_collapse_after_recovery_antiinductive, 1000000, seed);
     printf("90%% confidence interval: [%f, %f]\n", ci_90_antiinductive.low, ci_90_antiinductive.high);
 
     double* yearly_probability_nuclear_collapse_after_recovery_antiinductive_samples = malloc(sizeof(double) * num_samples);

examples/more/11_billion_lognormals_paralell/example.c

@@ -9,21 +9,22 @@ int main()
     // set randomness seed
     // uint64_t* seed = malloc(sizeof(uint64_t));
     // *seed = 1000; // xorshift can't start with 0
-    // ^ not necessary, because parallel_sampler takes care of the seed.
+    // ^ not necessary, because sampler_parallel takes care of the seed.
 
     int n_samples = 1000 * 1000 * 1000;
     int n_threads = 16;
-    double sampler(uint64_t* seed){
+    double sampler(uint64_t * seed)
+    {
         return sample_lognormal(0, 10, seed);
     }
     double* results = malloc(n_samples * sizeof(double));
 
-    parallel_sampler(sampler, results, n_threads, n_samples);
-    double avg = array_sum(results, n_samples)/n_samples;
+    sampler_parallel(sampler, results, n_threads, n_samples);
+    double avg = array_sum(results, n_samples) / n_samples;
     printf("Average of 1B lognormal(0,10): %f", avg);
 
     free(results);
 
     // free(seed);
-    // ^ not necessary, because parallel_sampler takes care of the seed.
+    // ^ not necessary, because sampler_parallel takes care of the seed.
 }

examples/more/12_time_to_botec_parallel/example.c

@@ -9,21 +9,22 @@ int main()
     double p_b = 0.5;
     double p_c = p_a * p_b;
 
-    double sample_0(uint64_t* seed){ return 0; }
-    double sample_1(uint64_t* 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_0(uint64_t * seed) { return 0; }
+    double sample_1(uint64_t * 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); }
 
     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 sampler_result(uint64_t* seed) { 
+    double sampler_result(uint64_t * seed)
+    {
         return sample_mixture(samplers, weights, n_dists, seed);
     }
 
     int n_samples = 1000 * 1000, n_threads = 16;
     double* results = malloc(n_samples * sizeof(double));
-    parallel_sampler(sampler_result, results, n_threads, n_samples);
-    printf("Avg: %f\n", array_sum(results, n_samples)/n_samples);
+    sampler_parallel(sampler_result, results, n_threads, n_samples);
+    printf("Avg: %f\n", array_sum(results, n_samples) / n_samples);
     free(results);
 }

examples/more/13_parallelize_min/example.c

@@ -13,57 +13,58 @@ int main()
 
     /* Option 1: parallelize taking from n samples */
     // Question being asked: what is the distribution of sampling 1000 times and taking the min?
-    double sample_min_of_n(uint64_t* seed, int n){
+    double sample_min_of_n(uint64_t * seed, int n)
+    {
         double min = sample_normal(5, 2, seed);
-        for(int i=0; i<(n-1); i++){
+        for (int i = 0; i < (n - 2); i++) {
             double sample = sample_normal(5, 2, seed);
-            if(sample < min){
+            if (sample < min) {
                 min = sample;
             }
         }
         return min;
     }
-    double sampler_min_of_1000(uint64_t* seed) { 
+    double sample_min_of_1000(uint64_t * seed)
+    {
         return sample_min_of_n(seed, 1000);
     }
 
-    int n_samples = 10000, n_threads = 16;
+    int n_samples = 1000000, n_threads = 16;
     double* results = malloc(n_samples * sizeof(double));
-    parallel_sampler(sampler_min_of_1000, results, n_threads, n_samples);
+    sampler_parallel(sample_min_of_1000, results, n_threads, n_samples);
     printf("Mean of the distribution of (taking the min of 1000 samples of a normal(5,2)): %f\n", array_mean(results, n_samples));
     free(results);
 
     /* Option 2: take the min from n samples cleverly using parallelism */
     // Question being asked: can we take the min of n samples cleverly?
-    double sample_n_parallel(int n){
+    double sample_n_parallel(int n)
+    {
 
         int n_threads = 16;
         int quotient = n / 16;
         int remainder = n % 16;
 
-        uint64_t seed = 100;
+        uint64_t seed = 1000;
         double result_remainder = sample_min_of_n(&seed, remainder);
 
-        double sample_min_of_quotient(uint64_t* seed) { 
-            double result = sample_min_of_n(seed, quotient);
-            // printf("Result: %f\n", result);
-            return result;
+        double sample_min_of_quotient(uint64_t * seed)
+        {
+            return sample_min_of_n(seed, quotient);
         }
-        double* results = malloc(n_threads * sizeof(double));
-        parallel_sampler(sample_min_of_quotient, results, n_threads, n_threads);
+        double* results_quotient = malloc(quotient * sizeof(double));
+        sampler_parallel(sample_min_of_quotient, results_quotient, n_threads, quotient);
 
-        double min = results[0];
-        for(int i=1; i<n_threads; i++){
-            if(min > results[i]){
-                min = results[i];
+        double min = results_quotient[0];
+        for (int i = 1; i < quotient; i++) {
+            if (min > results_quotient[i]) {
+                min = results_quotient[i];
             }
         }
-        if(min > result_remainder){
+        if (min > result_remainder) {
             min = result_remainder;
         }
-        free(results);
+        free(results_quotient);
         return min;
     }
-    printf("Minimum of 10M samples of normal(5,2): %f\n", sample_n_parallel(1000 * 1000));
-
+    printf("Minimum of 1M samples of normal(5,2): %f\n", sample_n_parallel(1000000));
 }

examples/more/14_check_confidence_interval/example.c

@@ -0,0 +1,21 @@
+#include "../../../squiggle.h"
+#include "../../../squiggle_more.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 a seed of 0
+
+    int n = 1000000;
+    double* xs = malloc(sizeof(double) * n);
+    for (int i = 0; i < n; i++) {
+        xs[i] = sample_to(10, 100, seed);
+    }
+    ci ci_90 = array_get_90_ci(xs, n);
+    printf("Recovering confidence interval of sample_to(10, 100):\n  low: %f, high: %f\n", ci_90.low, ci_90.high);
+
+    free(seed);
+}

examples/more/makefile

@@ -49,6 +49,7 @@ all:
 	$(CC) $(OPTIMIZED) $(DEBUG) 11_billion_lognormals_paralell/$(SRC)  $(DEPS) -o 11_billion_lognormals_paralell/$(OUTPUT)
 	$(CC) $(OPTIMIZED) $(DEBUG) 12_time_to_botec_parallel/$(SRC)       $(DEPS) -o 12_time_to_botec_parallel/$(OUTPUT)
 	$(CC) $(OPTIMIZED) $(DEBUG) 13_parallelize_min/$(SRC)              $(DEPS) -o 13_parallelize_min/$(OUTPUT)
+	$(CC) $(OPTIMIZED) $(DEBUG) 14_check_confidence_interval/$(SRC)    $(DEPS) -o 14_check_confidence_interval/$(OUTPUT)
 
 format-all:
 	$(FORMATTER) 00_example_template/$(SRC)
@@ -65,6 +66,7 @@ format-all:
 	$(FORMATTER) 11_billion_lognormals_paralell/$(SRC)
 	$(FORMATTER) 12_time_to_botec_parallel/$(SRC)
 	$(FORMATTER) 13_parallelize_min/$(SRC)
+	$(FORMATTER) 14_check_confidence_interval/$(SRC)
 
 run-all:
 	00_example_template/$(OUTPUT)
@@ -81,6 +83,7 @@ run-all:
 	11_billion_lognormals_paralell/$(OUTPUT)
 	12_time_to_botec_parallel/$(OUTPUT)
 	13_parallelize_min/$(OUTPUT)
+	14_check_confidence_interval/$(OUTPUT)
 
 ## make one DIR=06_nuclear_recovery
 one: $(DIR)/$(SRC)

makefile

@@ -13,8 +13,8 @@ format-examples:
 	cd examples/more && make format-all
 
 format: squiggle.c squiggle.h
-	$(FORMATTER) squiggle.c
-	$(FORMATTER) squiggle.h
+	$(FORMATTER) squiggle.c squiggle.h
+	$(FORMATTER) squiggle_more.c squiggle_more.h
 
 lint:
 	clang-tidy squiggle.c -- -lm

scratchpad/core.c

@@ -1,27 +0,0 @@
-
-uint64_t xorshift64(uint64_t* seed)
-{
-    // Algorithm "xor" from p. 4 of Marsaglia, "Xorshift RNGs"
-    // <https://en.wikipedia.org/wiki/Xorshift>
-    uint64_t x = *seed;
-    x ^= x << 13;
-    x ^= x >> 7;
-    x ^= x << 17;
-    return *seed = x;
-}
-
-double sample_unit_uniform(uint64_t* seed)
-{
-    // samples uniform from [0,1] interval.
-    return ((double)xorshift64(seed)) / ((double)UINT64_MAX);
-}
-
-double sample_unit_normal(uint64_t* seed)
-{
-    // // See: <https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform>
-    double u1 = sample_unit_uniform(seed);
-    double u2 = sample_unit_uniform(seed);
-    double z = sqrtf(-2.0 * log(u1)) * sin(2 * PI * u2);
-    return z;
-}
-

scratchpad/scratchpad.c

@@ -10,25 +10,14 @@ int main()
     // set randomness seed
     uint64_t* seed = malloc(sizeof(uint64_t));
     *seed = 1000; // xorshift can't start with a seed of 0
-    /*
-    for (int i = 0; i < 100; i++) {
-        double draw = sample_unit_uniform(seed);
-        printf("%f\n", draw);
     
-    }*/
-    // Test division
-    // printf("\n%d\n", 10 % 3);
-    //
-    
-    int n_samples = 100, n_threads = 16;
-    double* results = malloc(n_samples * sizeof(double));
-    double sampler_scratchpad(uint64_t* seed){
-        return 1;
-    }
-    parallel_sampler(sampler_scratchpad, results, n_threads, n_samples);
-    for(int i=0; i<n_samples; i++){
-        printf("Sample %d: %f\n", i, results[i]);
+    int n = 1000000;
+    double* xs = malloc(sizeof(double) * n);
+    for (int i = 0; i < n; i++) {
+        xs[i] = sample_to(10, 100, seed);
     }
+    ci ci_90 = array_get_90_ci(xs, n);
+    printf("Recovering confidence interval of sample_to(10, 100):\n  low: %f, high: %f\n", ci_90.low, ci_90.high);
 
     free(seed);
 }

squiggle.c

@@ -8,7 +8,7 @@
 #define NORMAL90CONFIDENCE 1.6448536269514727
 
 // Pseudo Random number generator
-uint64_t xorshift32(uint32_t* seed)
+static uint64_t xorshift32(uint32_t* seed)
 {
     // Algorithm "xor" from p. 4 of Marsaglia, "Xorshift RNGs"
     // See:
@@ -24,7 +24,7 @@ uint64_t xorshift32(uint32_t* seed)
     return *seed = x;
 }
 
-uint64_t xorshift64(uint64_t* seed)
+static uint64_t xorshift64(uint64_t* seed)
 {
     // same as above, but for generating doubles instead of floats
     uint64_t x = *seed;

squiggle_more.c

@@ -1,67 +1,195 @@
+#include "squiggle.h"
 #include <float.h>
-#include <math.h>
 #include <limits.h>
+#include <math.h>
 #include <omp.h>
 #include <stdint.h>
 #include <stdio.h>
 #include <stdlib.h>
-#include "squiggle.h"
 
-/* Math constants */
-#define PI 3.14159265358979323846 // M_PI in gcc gnu99
-#define NORMAL90CONFIDENCE 1.6448536269514727
+/* Parallel sampler */
+void sampler_parallel(double (*sampler)(uint64_t* seed), double* results, int n_threads, int n_samples)
+{
+    if ((n_samples % n_threads) != 0) {
+        fprintf(stderr, "Number of samples isn't divisible by number of threads, aborting\n");
+        exit(1);
+    }
+    uint64_t** seeds = malloc(n_threads * sizeof(uint64_t*));
+    for (uint64_t i = 0; i < n_threads; i++) {
+        seeds[i] = malloc(sizeof(uint64_t));
+        *seeds[i] = i + 1; // xorshift can't start with 0
+    }
 
-/* Some error niceties */
-// These won't be used until later 
-#define MAX_ERROR_LENGTH 500
-#define EXIT_ON_ERROR 0
-#define PROCESS_ERROR(error_msg) process_error(error_msg, EXIT_ON_ERROR, __FILE__, __LINE__)
+    int i;
+#pragma omp parallel private(i)
+    {
+#pragma omp for
+        for (i = 0; i < n_threads; i++) {
+            int lower_bound = i * (n_samples / n_threads);
+            int upper_bound = ((i + 1) * (n_samples / n_threads)) - 1;
+            // printf("Lower bound: %d, upper bound: %d\n", lower_bound, upper_bound);
+            for (int j = lower_bound; j < upper_bound; j++) {
+                results[j] = sampler(seeds[i]);
+            }
+        }
+    }
+
+    for (uint64_t i = 0; i < n_threads; i++) {
+        free(seeds[i]);
+    }
+    free(seeds);
+}
 
 /* Get confidence intervals, given a sampler */
 // Not in core yet because I'm not sure how much I like the struct
 // and the built-in 100k samples
 // to do: add n to function parameters and document
+
 typedef struct ci_t {
-    float low;
-    float high;
+    double low;
+    double high;
 } ci;
-int compare_doubles(const void* p, const void* q)
+
+static void swp(int i, int j, double xs[])
 {
-    // https://wikiless.esmailelbob.xyz/wiki/Qsort?lang=en
-    double x = *(const double*)p;
-    double y = *(const double*)q;
-
-    /* Avoid returning x - y, which can cause undefined behaviour
-       because of signed integer overflow. */
-    if (x < y)
-        return -1; // Return -1 if you want ascending, 1 if you want descending order.
-    else if (x > y)
-        return 1; // Return 1 if you want ascending, -1 if you want descending order.
-
-    return 0;
+    double tmp = xs[i];
+    xs[i] = xs[j];
+    xs[j] = tmp;
 }
-ci get_90_confidence_interval(double (*sampler)(uint64_t*), uint64_t* seed)
+
+static int partition(int low, int high, double xs[], int length)
 {
-    int n = 100 * 1000;
-    double* samples_array = malloc(n * sizeof(double));
-    for (int i = 0; i < n; i++) {
-        samples_array[i] = sampler(seed);
+    // To understand this function:
+    // - see the note after gt variable definition
+    // - go to commit 578bfa27 and the scratchpad/ folder in it, which has printfs sprinkled throughout
+    int pivot = low + floor((high - low) / 2);
+    double pivot_value = xs[pivot];
+    swp(pivot, high, xs);
+    int gt = low; /* This pointer will iterate until finding an element which is greater than the pivot. Then it will move elements that are smaller before it--more specifically, it will move elements to its position and then increment. As a result all elements between gt and i will be greater than the pivot. */
+    for (int i = low; i < high; i++) {
+        if (xs[i] < pivot_value) {
+            swp(gt, i, xs);
+            gt++;
         }
-    qsort(samples_array, n, sizeof(double), compare_doubles);
+    }
+    swp(high, gt, xs);
+    return gt;
+}
 
+static double quickselect(int k, double xs[], int n)
+{
+    // https://en.wikipedia.org/wiki/Quickselect
+    int low = 0;
+    int high = n - 1;
+    for (;;) {
+        if (low == high) {
+            return xs[low];
+        }
+        int pivot = partition(low, high, xs, n);
+        if (pivot == k) {
+            return xs[pivot];
+        } else if (k < pivot) {
+            high = pivot - 1;
+        } else {
+            low = pivot + 1;
+        }
+    }
+}
+
+ci array_get_ci(ci interval, double* xs, int n)
+{
+
+    int low_k = floor(interval.low * n);
+    int high_k = ceil(interval.high * n);
     ci result = {
-        .low = samples_array[5000],
-        .high = samples_array[94999],
+        .low = quickselect(low_k, xs, n),
+        .high = quickselect(high_k, xs, n),
     };
-    free(samples_array);
+    return result;
+}
+ci array_get_90_ci(double xs[], int n)
+{
+    return array_get_ci((ci) { .low = 0.05, .high = 0.95 }, xs, n);
+}
 
+ci sampler_get_ci(ci interval, double (*sampler)(uint64_t*), int n, uint64_t* seed)
+{
+    double* xs = malloc(n * sizeof(double));
+    for (int i = 0; i < n; i++) {
+        xs[i] = sampler(seed);
+    }
+    ci result = array_get_ci(interval, xs, n);
+    free(xs);
+    return result;
+}
+ci sampler_get_90_ci(double (*sampler)(uint64_t*), int n, uint64_t* seed)
+{
+    return sampler_get_ci((ci) { .low = 0.05, .high = 0.95 }, sampler, n, seed);
+}
+
+/* Algebra manipulations */
+// here I discover named structs,
+// which mean that I don't have to be typing
+// struct blah all the time.
+
+#define NORMAL90CONFIDENCE 1.6448536269514727
+
+typedef struct normal_params_t {
+    double mean;
+    double std;
+} normal_params;
+
+normal_params algebra_sum_normals(normal_params a, normal_params b)
+{
+    normal_params result = {
+        .mean = a.mean + b.mean,
+        .std = sqrt((a.std * a.std) + (b.std * b.std)),
+    };
+    return result;
+}
+
+typedef struct lognormal_params_t {
+    double logmean;
+    double logstd;
+} lognormal_params;
+
+lognormal_params algebra_product_lognormals(lognormal_params a, lognormal_params b)
+{
+    lognormal_params result = {
+        .logmean = a.logmean + b.logmean,
+        .logstd = sqrt((a.logstd * a.logstd) + (b.logstd * b.logstd)),
+    };
+    return result;
+}
+
+lognormal_params convert_ci_to_lognormal_params(ci x)
+{
+    double loghigh = logf(x.high);
+    double loglow = logf(x.low);
+    double logmean = (loghigh + loglow) / 2.0;
+    double logstd = (loghigh - loglow) / (2.0 * NORMAL90CONFIDENCE);
+    lognormal_params result = { .logmean = logmean, .logstd = logstd };
+    return result;
+}
+
+ci convert_lognormal_params_to_ci(lognormal_params y)
+{
+    double h = y.logstd * NORMAL90CONFIDENCE;
+    double loghigh = y.logmean + h;
+    double loglow = y.logmean - h;
+    ci result = { .low = exp(loglow), .high = exp(loghigh) };
     return result;
 }
 
 /* Scaffolding to handle errors */
-// We are building towards sample from an arbitrary cdf
+// We will sample from an arbitrary cdf
 // and that operation might fail
 // so we build some scaffolding here
+
+#define MAX_ERROR_LENGTH 500
+#define EXIT_ON_ERROR 0
+#define PROCESS_ERROR(error_msg) process_error(error_msg, EXIT_ON_ERROR, __FILE__, __LINE__)
+
 struct box {
     int empty;
     double content;
@@ -246,122 +374,21 @@ double sampler_cdf_danger(struct box cdf(double), uint64_t* seed)
 {
     double p = sample_unit_uniform(seed);
     struct box result = inverse_cdf_box(cdf, p);
-	if(result.empty){
+    if (result.empty) {
         exit(1);
-	}else{
+    } else {
         return result.content;
     }
 }
 
-/* Algebra manipulations */
-// here I discover named structs,
-// which mean that I don't have to be typing
-// struct blah all the time.
-typedef struct normal_params_t {
-    double mean;
-    double std;
-} normal_params;
+/* array print: potentially useful for debugging */
 
-normal_params algebra_sum_normals(normal_params a, normal_params b)
+void array_print(double xs[], int n)
 {
-    normal_params result = {
-        .mean = a.mean + b.mean,
-        .std = sqrt((a.std * a.std) + (b.std * b.std)),
-    };
-    return result;
-}
-
-typedef struct lognormal_params_t {
-    double logmean;
-    double logstd;
-} lognormal_params;
-
-lognormal_params algebra_product_lognormals(lognormal_params a, lognormal_params b)
-{
-    lognormal_params result = {
-        .logmean = a.logmean + b.logmean,
-        .logstd = sqrt((a.logstd * a.logstd) + (b.logstd * b.logstd)),
-    };
-    return result;
-}
-
-lognormal_params convert_ci_to_lognormal_params(ci x)
-{
-    double loghigh = logf(x.high);
-    double loglow = logf(x.low);
-    double logmean = (loghigh + loglow) / 2.0;
-    double logstd = (loghigh - loglow) / (2.0 * NORMAL90CONFIDENCE);
-    lognormal_params result = { .logmean = logmean, .logstd = logstd };
-    return result;
-}
-
-ci convert_lognormal_params_to_ci(lognormal_params y)
-{
-    double h = y.logstd * NORMAL90CONFIDENCE;
-    double loghigh = y.logmean + h;
-    double loglow = y.logmean - h;
-    ci result = { .low = exp(loglow), .high = exp(loghigh) };
-    return result;
-}
-
-/* Parallel sampler */
-void parallel_sampler(double (*sampler)(uint64_t* seed), double* results, int n_threads, int n_samples){
-    
-    // Division terminology:
-    // a =  b * quotient + reminder
-    // a = (a/b)*b + (a%b)
-    // dividend: a
-    // divisor: b
-    // quotient = a / b
-    // reminder = a % b
-    // "divisor's multiple" := (a/b)*b
-
-    // now, we have n_samples and n_threads
-    // to make our life easy, each thread will have a number of samples of: a/b (quotient)
-    // and we'll compute the remainder of samples separately
-    // to possibly do by Jorge: improve so that the remainder is included in the threads
-
-    int quotient = n_samples / n_threads;
-    int remainder = n_samples % n_threads;
-    int divisor_multiple = quotient * n_threads; 
-
-    uint64_t** seeds = malloc(n_threads * sizeof(uint64_t*));
-    // printf("UINT64_MAX: %lu\n", UINT64_MAX);
-    srand(1);
-    for (uint64_t i = 0; i < n_threads; i++) {
-        seeds[i] = malloc(sizeof(uint64_t));
-        // Constraints: 
-        // - xorshift can't start with 0
-        // - the seeds should be reasonably separated and not correlated
-        *seeds[i] = (uint64_t) rand() * (UINT64_MAX / RAND_MAX);
-        // printf("#%ld: %lu\n",i, *seeds[i]);
-
-        // Other initializations tried:
-        // *seeds[i] = 1 + i;
-        // *seeds[i] = (i + 0.5)*(UINT64_MAX/n_threads);
-        // *seeds[i] = (i + 0.5)*(UINT64_MAX/n_threads) + constant * i;
-    }
-
-    int i;
-    #pragma omp parallel private(i)
-        {
-        #pragma omp for
-        for (i = 0; i < n_threads; i++) {
-            int lower_bound_inclusive = i * quotient;
-            int upper_bound_not_inclusive = ((i+1) * quotient); // note the < in the for loop below, 
-            // printf("Lower bound: %d, upper bound: %d\n", lower_bound, upper_bound);
-            for (int j = lower_bound_inclusive; j < upper_bound_not_inclusive; j++) {
-                results[j] = sampler(seeds[i]);
-            }
-        }
-    }
-    for(int j=divisor_multiple; j<n_samples; j++){
-        results[j] = sampler(seeds[0]);
-        // we can just reuse a seed, this isn't problematic because we are not doing multithreading
-    }
-
-    for (uint64_t i = 0; i < n_threads; i++) {
-        free(seeds[i]);
-    }
-    free(seeds);
+    printf("[");
+    for (int i = 0; i < n - 1; i++) {
+        printf("%f, ", xs[i]);
+    }
+    printf("%f", xs[n - 1]);
+    printf("]\n");
 }

squiggle_more.h

@@ -1,35 +1,20 @@
 #ifndef SQUIGGLE_C_EXTRA
 #define SQUIGGLE_C_EXTRA
 
-// Box
-struct box {
-    int empty;
-    double content;
-    char* error_msg;
-};
+/* Parallel sampling */
+void sampler_parallel(double (*sampler)(uint64_t* seed), double* results, int n_threads, int n_samples);
 
-// Macros to handle errors
-#define MAX_ERROR_LENGTH 500
-#define EXIT_ON_ERROR 0
-#define PROCESS_ERROR(error_msg) process_error(error_msg, EXIT_ON_ERROR, __FILE__, __LINE__)
-struct box process_error(const char* error_msg, int should_exit, char* file, int line);
-
-// Inverse cdf
-struct box inverse_cdf_double(double cdf(double), double p);
-struct box inverse_cdf_box(struct box cdf_box(double), double p);
-
-// Samplers from cdf
-struct box sampler_cdf_double(double cdf(double), uint64_t* seed);
-struct box sampler_cdf_box(struct box cdf(double), uint64_t* seed);
-
-// Get 90% confidence interval
+/* Get 90% confidence interval */
 typedef struct ci_t {
-    float low;
-    float high;
+    double low;
+    double high;
 } ci;
-ci get_90_confidence_interval(double (*sampler)(uint64_t*), uint64_t* seed);
+ci array_get_ci(ci interval, double* xs, int n);
+ci array_get_90_ci(double xs[], int n);
+ci sampler_get_ci(ci interval, double (*sampler)(uint64_t*), int n, uint64_t* seed);
+ci sampler_get_90_ci(double (*sampler)(uint64_t*), int n, uint64_t* seed);
 
-// small algebra manipulations
+/* Algebra manipulations */
 
 typedef struct normal_params_t {
     double mean;
@@ -46,6 +31,24 @@ lognormal_params algebra_product_lognormals(lognormal_params a, lognormal_params
 lognormal_params convert_ci_to_lognormal_params(ci x);
 ci convert_lognormal_params_to_ci(lognormal_params y);
 
-void parallel_sampler(double (*sampler)(uint64_t* seed), double* results, int n_threads, int n_samples);
+/* Error handling */
+struct box {
+    int empty;
+    double content;
+    char* error_msg;
+};
+#define MAX_ERROR_LENGTH 500
+#define EXIT_ON_ERROR 0
+#define PROCESS_ERROR(error_msg) process_error(error_msg, EXIT_ON_ERROR, __FILE__, __LINE__)
+struct box process_error(const char* error_msg, int should_exit, char* file, int line);
+void array_print(double* array, int length);
+
+/* Inverse cdf */
+struct box inverse_cdf_double(double cdf(double), double p);
+struct box inverse_cdf_box(struct box cdf_box(double), double p);
+
+/* Samplers from cdf */
+struct box sampler_cdf_double(double cdf(double), uint64_t* seed);
+struct box sampler_cdf_box(struct box cdf(double), uint64_t* seed);
 
 #endif