add desiderata split_array_refactor

C/alt/04-factor-out-paralellization/why.md

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+So that the mixture distribution could be composable with other functions in squiggle.c

C/alt/05-refactor-split-array/desiderata.md

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+Instead of
+
+```C
+#pragma omp parallel private(i, sample_index, split_array_length)
+{
+    #pragma omp for
+    for (i = 0; i < n_threads; i++) {
+        split_array_length = split_array_get_length(i, N, n_threads);
+        for (int j = 0; j < split_array_length; j++) {
+            results[i][j] = sampler(seeds[i]);
+        }
+    }
+}
+
+```
+
+Algo como
+
+```C
+#pragma omp parallel private(i, sample_index, bounds)
+{
+    #pragma omp for
+    for (i = 0; i < n_threads; i++) {
+        int bounds[2] = split_array_get_bounds(i, N, n_threads);
+        for (int j = bound[0]; j < bounds[1] + 1; j++) {
+            // o j < bounds[1], no se si el +1 va a ser más elegante
+            // dentro o fuera, aunque algo me dice que dentro
+            results[j] = sampler(seeds[i]);
+        }
+    }
+}
+
+```
+
+Por qué? Porque esto hace que la estructura subyacente sea un solo array, 
+lo cual implica que no *tengo* que utilizar split_array_functions especializadas 
+si no quiero

C/alt/05-refactor-split-array/makefile

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+# Interface: 
+#   make
+#   make build
+#   make format
+#   make run
+
+# Compiler
+CC=gcc
+# CC=tcc # <= faster compilation
+
+# Main file
+SRC=samples.c
+OUTPUT=out/samples
+
+SRC_ONE_THREAD=./samples-one-thread.c
+OUTPUT_ONE_THREAD=out/samples-one-thread
+
+## Dependencies
+#  Has no dependencies
+MATH=-lm
+
+## Flags
+DEBUG= #'-g'
+STANDARD=-std=c99
+WARNINGS=-Wall
+OPTIMIZED=-O3 #-O3 actually gives better performance than -Ofast, at least for this version
+OPENMP=-fopenmp
+
+## Formatter
+STYLE_BLUEPRINT=webkit
+FORMATTER=clang-format -i -style=$(STYLE_BLUEPRINT)
+
+## make build
+build: $(SRC)
+	$(CC) $(OPTIMIZED) $(DEBUG) $(SRC) $(OPENMP) $(MATH) -o $(OUTPUT)
+
+static:
+	$(CC) $(OPTIMIZED) $(DEBUG) $(SRC) $(OPENMP) $(MATH) -o $(OUTPUT)
+
+format: $(SRC)
+	$(FORMATTER) $(SRC)
+
+run: $(SRC) $(OUTPUT)
+	OMP_NUM_THREADS=1 ./$(OUTPUT) && echo
+
+multi:
+	OMP_NUM_THREADS=1 ./$(OUTPUT) && echo
+	OMP_NUM_THREADS=2 ./$(OUTPUT) && echo
+	OMP_NUM_THREADS=4 ./$(OUTPUT) && echo
+	OMP_NUM_THREADS=8 ./$(OUTPUT) && echo
+	OMP_NUM_THREADS=16 ./$(OUTPUT) && echo
+
+## Timing
+
+time-linux: 
+	@echo "Requires /bin/time, found on GNU/Linux systems" && echo
+	
+	@echo "Running 100x and taking avg time: OMP_NUM_THREADS=1 $(OUTPUT)"
+	@t=$$(/usr/bin/time -f "%e" -p bash -c 'for i in {1..100}; do OMP_NUM_THREADS=1 $(OUTPUT); done' 2>&1 >/dev/null | grep real | awk '{print $$2}' ); echo "scale=2; 1000 * $$t / 100" | bc | sed "s|^|Time using 1 thread: |" | sed 's|$$|ms|' && echo
+	
+	@echo "Running 100x and taking avg time: OMP_NUM_THREADS=2 $(OUTPUT)"
+	@t=$$(/usr/bin/time -f "%e" -p bash -c 'for i in {1..100}; do OMP_NUM_THREADS=2 $(OUTPUT); done' 2>&1 >/dev/null | grep real | awk '{print $$2}' ); echo "scale=2; 1000 * $$t / 100" | bc | sed "s|^|Time using 2 threads: |" | sed 's|$$|ms|' && echo
+	
+	@echo "Running 100x and taking avg time: OMP_NUM_THREADS=4 $(OUTPUT)"
+	@t=$$(/usr/bin/time -f "%e" -p bash -c 'for i in {1..100}; do OMP_NUM_THREADS=4 $(OUTPUT); done' 2>&1 >/dev/null | grep real | awk '{print $$2}' ); echo "scale=2; 1000 * $$t / 100" | bc | sed "s|^|Time for 4 threads: |" | sed 's|$$|ms|' && echo
+	
+	@echo "Running 100x and taking avg time: OMP_NUM_THREADS=8 $(OUTPUT)"
+	@t=$$(/usr/bin/time -f "%e" -p bash -c 'for i in {1..100}; do OMP_NUM_THREADS=8 $(OUTPUT); done' 2>&1 >/dev/null | grep real | awk '{print $$2}' ); echo "scale=2; 1000 * $$t / 100" | bc | sed "s|^|Time using 8 threads: |" | sed 's|$$|ms|' && echo
+	
+	@echo "Running 100x and taking avg time: OMP_NUM_THREADS=16 $(OUTPUT)"
+	@t=$$(/usr/bin/time -f "%e" -p bash -c 'for i in {1..100}; do OMP_NUM_THREADS=16 $(OUTPUT); done' 2>&1 >/dev/null | grep real | awk '{print $$2}' ); echo "scale=2; 1000 * $$t / 100" | bc | sed "s|^|Time using 16 threads: |" | sed 's|$$|ms|' && echo
+
+time-linux-fastest: 
+	@echo "Running 100x and taking avg time: OMP_NUM_THREADS=16 $(OUTPUT)"
+	@t=$$(/usr/bin/time -f "%e" -p bash -c 'for i in {1..100}; do OMP_NUM_THREADS=16 $(OUTPUT); done' 2>&1 >/dev/null | grep real | awk '{print $$2}' ); echo "scale=2; 1000 * $$t / 100" | bc | sed "s|^|Time using 16 threads: |" | sed 's|$$|ms|' && echo
+
+time-linux-simple:
+	@echo "Requires /bin/time, found on GNU/Linux systems" && echo
+	OMP_NUM_THREADS=1 /bin/time -f "Time: %es" ./$(OUTPUT) && echo
+	OMP_NUM_THREADS=2 /bin/time -f "Time: %es" ./$(OUTPUT) && echo
+	OMP_NUM_THREADS=4 /bin/time -f "Time: %es" ./$(OUTPUT) && echo
+	OMP_NUM_THREADS=8 /bin/time -f "Time: %es" ./$(OUTPUT) && echo
+	OMP_NUM_THREADS=16 /bin/time -f "Time: %es" ./$(OUTPUT) && 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) $(OPENMP) $(MATH) -o $(OUTPUT)
+	# ./$(OUTPUT)
+	# gprof: 
+	# gprof $(OUTPUT) gmon.out > analysis.txt
+	# rm gmon.out
+	# vim analysis.txt
+	# rm analysis.txt
+	# perf: 
+	OMP_NUM_THREADS=16 sudo perf record $(OUTPUT)
+	sudo perf report
+	rm perf.data
+	
+
+## Install
+debian-install-dependencies:
+	sudo apt-get install libomp-dev
+

C/alt/05-refactor-split-array/samples.c

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+#include <math.h>
+#include <omp.h>
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+const float PI = 3.14159265358979323846;
+
+#define N 1000000
+
+//Array helpers
+
+void array_print(float* array, int length)
+{
+    for (int i = 0; i < length; i++) {
+        printf("item[%d] = %f\n", i, array[i]);
+    }
+    printf("\n");
+}
+
+float array_sum(float* array, int length)
+{
+    float output = 0.0;
+    for (int i = 0; i < length; i++) {
+        output += array[i];
+    }
+    return output;
+}
+
+void array_cumsum(float* array_to_sum, float* array_cumsummed, int length)
+{
+    array_cumsummed[0] = array_to_sum[0];
+    for (int i = 1; i < length; i++) {
+        array_cumsummed[i] = array_cumsummed[i - 1] + array_to_sum[i];
+    }
+}
+
+// Split array helpers
+int split_array_get_length(int index, int total_length, int n_threads)
+{
+    return (total_length % n_threads > index ? total_length / n_threads + 1 : total_length / n_threads);
+}
+
+void split_array_allocate(float** meta_array, int length, int divide_into)
+{
+    int split_array_length;
+
+    for (int i = 0; i < divide_into; i++) {
+        split_array_length = split_array_get_length(i, length, divide_into);
+        meta_array[i] = malloc(split_array_length * sizeof(float));
+    }
+}
+
+void split_array_free(float** meta_array, int divided_into)
+{
+    for (int i = 0; i < divided_into; i++) {
+        free(meta_array[i]);
+    }
+    free(meta_array);
+}
+
+float split_array_sum(float** meta_array, int length, int divided_into)
+{
+    int i;
+    float output = 0;
+
+#pragma omp parallel for reduction(+ \
+                                   : output)
+    for (int i = 0; i < divided_into; i++) {
+        float own_partial_sum = 0;
+        int split_array_length = split_array_get_length(i, length, divided_into);
+        for (int j = 0; j < split_array_length; j++) {
+            own_partial_sum += meta_array[i][j];
+        }
+        output += own_partial_sum;
+    }
+    return output;
+}
+
+// Pseudo Random number generator
+
+uint32_t xorshift32(uint32_t* seed)
+{
+    // Algorithm "xor" from p. 4 of Marsaglia, "Xorshift RNGs"
+    // See <https://stackoverflow.com/questions/53886131/how-does-xorshift32-works>
+    // https://en.wikipedia.org/wiki/Xorshift
+    // Also some drama: <https://www.pcg-random.org/posts/on-vignas-pcg-critique.html>, <https://prng.di.unimi.it/>
+
+    uint32_t x = *seed;
+    x ^= x << 13;
+    x ^= x >> 17;
+    x ^= x << 5;
+    return *seed = x;
+}
+
+// Distribution & sampling functions
+
+float rand_0_to_1(uint32_t* seed)
+{
+    return ((float)xorshift32(seed)) / ((float)UINT32_MAX);
+    /* 
+	uint32_t x = *seed;
+	x ^= x << 13;
+	x ^= x >> 17;
+	x ^= x << 5;
+	return ((float)(*seed = x))/((float) UINT32_MAX);
+	*/
+    // previously:
+    // ((float)rand_r(seed) / (float)RAND_MAX)
+    // and before that: rand, but it wasn't thread-safe.
+    // See: <https://stackoverflow.com/questions/43151361/how-to-create-thread-safe-random-number-generator-in-c-using-rand-r> for why to use rand_r:
+    // rand() is not thread-safe, as it relies on (shared) hidden seed.
+}
+
+float rand_float(float max, uint32_t* seed)
+{
+    return rand_0_to_1(seed) * max;
+}
+
+float ur_normal(uint32_t* seed)
+{
+    float u1 = rand_0_to_1(seed);
+    float u2 = rand_0_to_1(seed);
+    float z = sqrtf(-2.0 * log(u1)) * sin(2 * PI * u2);
+    return z;
+}
+
+float random_uniform(float from, float to, uint32_t* seed)
+{
+    return rand_0_to_1(seed) * (to - from) + from;
+}
+
+float random_normal(float mean, float sigma, uint32_t* seed)
+{
+    return (mean + sigma * ur_normal(seed));
+}
+
+float random_lognormal(float logmean, float logsigma, uint32_t* seed)
+{
+    return expf(random_normal(logmean, logsigma, seed));
+}
+
+float random_to(float low, float high, uint32_t* seed)
+{
+    const float NORMAL95CONFIDENCE = 1.6448536269514722;
+    float loglow = logf(low);
+    float loghigh = logf(high);
+    float logmean = (loglow + loghigh) / 2;
+    float logsigma = (loghigh - loglow) / (2.0 * NORMAL95CONFIDENCE);
+    return random_lognormal(logmean, logsigma, seed);
+}
+
+// Mixture function
+
+float mixture(float (*samplers[])(uint32_t*), float* weights, int n_dists, uint32_t* seed)
+{
+
+    // You can see a slightly simpler version of this function in the git history
+    // or in alt/C-02-better-algorithm-one-thread/
+    float sum_weights = array_sum(weights, n_dists);
+    float* cumsummed_normalized_weights = malloc(n_dists * sizeof(float));
+    cumsummed_normalized_weights[0] = weights[0] / sum_weights;
+    for (int i = 1; i < n_dists; i++) {
+        cumsummed_normalized_weights[i] = cumsummed_normalized_weights[i - 1] + weights[i] / sum_weights;
+    }
+
+    //create var holders
+    float p1, result;
+    int sample_index, i, own_length;
+    p1 = random_uniform(0, 1, seed);
+    for (int i = 0; i < n_dists; i++) {
+        if (p1 < cumsummed_normalized_weights[i]) {
+            result = samplers[i](seed);
+            break;
+        }
+    }
+    free(cumsummed_normalized_weights);
+    return result;
+}
+
+// Parallization function
+void paralellize(float (*sampler)(uint32_t* seed), float** results, int n_threads){
+
+    int sample_index, i, split_array_length;
+    uint32_t** seeds = malloc(n_threads * sizeof(uint32_t*));
+    for (uint32_t i = 0; i < n_threads; i++) {
+        seeds[i] = malloc(sizeof(uint32_t));
+        *seeds[i] = i + 1; // xorshift can't start with 0
+    }
+
+    #pragma omp parallel private(i, sample_index, split_array_length)
+    {
+        #pragma omp for
+        for (i = 0; i < n_threads; i++) {
+            split_array_length = split_array_get_length(i, N, n_threads);
+            for (int j = 0; j < split_array_length; j++) {
+                results[i][j] = sampler(seeds[i]);
+            }
+        }
+    }
+
+    for (uint32_t i = 0; i < n_threads; i++) {
+        free(seeds[i]);
+    }
+    free(seeds);
+}
+
+// Functions used for the BOTEC.
+// Their type has to be the same, as we will be passing them around.
+
+float sample_0(uint32_t* seed)
+{
+    return 0;
+}
+
+float sample_1(uint32_t* seed)
+{
+    return 1;
+}
+
+float sample_few(uint32_t* seed)
+{
+    return random_to(1, 3, seed);
+}
+
+float sample_many(uint32_t* seed)
+{
+    return random_to(2, 10, seed);
+}
+
+float sample_mixture(uint32_t* seed){
+    float p_a, p_b, p_c;
+
+    // Initialize variables
+    p_a = 0.8;
+    p_b = 0.5;
+    p_c = p_a * p_b;
+
+    // Generate mixture
+    int n_dists = 4;
+    float weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
+    float (*samplers[])(uint32_t*) = { sample_0, sample_1, sample_few, sample_many };
+
+    return mixture(samplers, weights, n_dists, seed);
+}
+
+int main()
+{
+    int n_threads = omp_get_max_threads();
+    // printf("Max threads: %d\n", n_threads);
+    // omp_set_num_threads(n_threads);
+    float** split_array_results = malloc(n_threads * sizeof(float*));
+    split_array_allocate(split_array_results, N, n_threads);
+
+    paralellize(sample_mixture, split_array_results, n_threads);
+    printf("Sum(split_array_results, N)/N = %f\n", split_array_sum(split_array_results, N, n_threads) / N);
+
+    split_array_free(split_array_results, n_threads);
+    return 0;
+}