reorganize C code
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# C-Optimized
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An optimized version of the original C implementation.
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The main changes are:
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- an optimization of the mixture function (it passes the functions instead of the whole arrays, reducing in great measure the memory usage and the computation time) and
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- the implementation of multi-threading with OpenMP.
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## Performance
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The mean time of execution is 6 ms. With the following distribution:
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The hardware used has been an AMD 5800x3D and 16GB of DDR4-3200 MHz.
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Also, the time data has been collected by executing the interior of the main() function 1000 times in a for loop, not executing the program itself 1000 times.
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## Multithreading
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Take into account that the multi-threading introduces a bit of dispersion in the execution time due to the creation and destruction of threads.
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In Nuño's machine, multithreading actually introduces a noticeable slowdown factor.
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## To do
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- [ ] Use proper profiling tool to capture timing with 1M samples.
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- [ ] Update above with correct timing
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- [ ] Add Windows/Powershell time-measuring commands
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- [ ] Add CUDA?
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- [ ] See if program can be reworded so as to use multithreading effectively, e.g., so that you see speed gains proportional to the number of threads used
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# Interface:
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# make
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# make build
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# make format
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# make run
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# Compiler
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CC=gcc
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# CC=tcc # <= faster compilation
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# Main file
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SRC=samples.c
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OUTPUT=out/samples
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SRC_ONE_THREAD=./samples-one-thread.c
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OUTPUT_ONE_THREAD=out/samples-one-thread
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## Dependencies
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# Has no dependencies
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MATH=-lm
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## Flags
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DEBUG= #'-g'
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STANDARD=-std=c99
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WARNINGS=-Wall
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OPTIMIZED=-O3 #-O3 actually gives better performance than -Ofast, at least for this version
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OPENMP=-fopenmp
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## Formatter
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STYLE_BLUEPRINT=webkit
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FORMATTER=clang-format -i -style=$(STYLE_BLUEPRINT)
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## make build
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build: $(SRC)
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$(CC) $(OPTIMIZED) $(DEBUG) $(SRC) $(OPENMP) $(MATH) -o $(OUTPUT)
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$(CC) $(OPTIMIZED) $(DEBUG) $(SRC_ONE_THREAD) $(OPENMP) $(MATH) -o $(OUTPUT_ONE_THREAD)
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format: $(SRC)
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$(FORMATTER) $(SRC)
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run: $(SRC) $(OUTPUT)
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OMP_NUM_THREADS=1 ./$(OUTPUT) && echo
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./$(OUTPUT_ONE_THREAD)
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multi:
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OMP_NUM_THREADS=1 ./$(OUTPUT) && echo
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OMP_NUM_THREADS=2 ./$(OUTPUT) && echo
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OMP_NUM_THREADS=4 ./$(OUTPUT) && echo
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OMP_NUM_THREADS=8 ./$(OUTPUT) && echo
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OMP_NUM_THREADS=16 ./$(OUTPUT) && echo
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./$(OUTPUT_ONE_THREAD) && echo
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time-linux-simple:
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@echo "Requires /bin/time, found on GNU/Linux systems" && echo
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OMP_NUM_THREADS=1 /bin/time -f "Time: %es" ./$(OUTPUT) && echo
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OMP_NUM_THREADS=2 /bin/time -f "Time: %es" ./$(OUTPUT) && echo
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OMP_NUM_THREADS=4 /bin/time -f "Time: %es" ./$(OUTPUT) && echo
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OMP_NUM_THREADS=8 /bin/time -f "Time: %es" ./$(OUTPUT) && echo
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OMP_NUM_THREADS=16 /bin/time -f "Time: %es" ./$(OUTPUT) && echo
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/bin/time -f "Time: %es" ./$(OUTPUT_ONE_THREAD) && echo
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time-linux:
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@echo "Requires /bin/time, found on GNU/Linux systems" && echo
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@echo "Running 100x and taking avg time: OMP_NUM_THREADS=1 $(OUTPUT)"
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@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
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@echo "Running 100x and taking avg time: OMP_NUM_THREADS=2 $(OUTPUT)"
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@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
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@echo "Running 100x and taking avg time: OMP_NUM_THREADS=4 $(OUTPUT)"
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@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
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@echo "Running 100x and taking avg time: OMP_NUM_THREADS=8 $(OUTPUT)"
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@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
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@echo "Running 100x and taking avg time: OMP_NUM_THREADS=16 $(OUTPUT)"
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@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
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debian-install-dependencies:
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sudo apt-get install libomp-dev
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#include <math.h>
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#include <omp.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <time.h>
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const float PI = 3.14159265358979323846;
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#define N 1000000
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//Array helpers
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void array_print(float* array, int length)
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{
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for (int i = 0; i < length; i++) {
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printf("item[%d] = %f\n", i, array[i]);
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}
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printf("\n");
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}
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void array_fill(float* array, int length, float item)
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{
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int i;
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#pragma omp private(i)
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{
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#pragma omp for
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for (i = 0; i < length; i++) {
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array[i] = item;
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}
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}
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}
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float array_sum(float* array, int length)
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{
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float output = 0.0;
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for (int i = 0; i < length; i++) {
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output += array[i];
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}
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return output;
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}
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void array_cumsum(float* array_to_sum, float* array_cumsummed, int length)
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{
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array_cumsummed[0] = array_to_sum[0];
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for (int i = 1; i < length; i++) {
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array_cumsummed[i] = array_cumsummed[i - 1] + array_to_sum[i];
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}
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}
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float rand_float(float to, unsigned int* seed)
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{
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return ((float)rand_r(seed) / (float)RAND_MAX) * to;
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// See: <https://stackoverflow.com/questions/43151361/how-to-create-thread-safe-random-number-generator-in-c-using-rand-r>
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// rand() is not thread-safe, as it relies on (shared) hidden state.
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}
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float ur_normal(unsigned int* seed)
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{
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float u1 = rand_float(1.0, seed);
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float u2 = rand_float(1.0, seed);
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float z = sqrtf(-2.0 * log(u1)) * sin(2 * PI * u2);
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return z;
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}
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inline float random_uniform(float from, float to, unsigned int* seed)
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{
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return ((float) rand_r(seed) / (float)RAND_MAX) * (to - from) + from;
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}
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inline float random_normal(float mean, float sigma, unsigned int* seed)
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{
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return (mean + sigma * ur_normal(seed));
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}
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inline float random_lognormal(float logmean, float logsigma, unsigned int* seed)
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{
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return expf(random_normal(logmean, logsigma, seed));
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}
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inline float random_to(float low, float high, unsigned int* seed)
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{
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const float NORMAL95CONFIDENCE = 1.6448536269514722;
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float loglow = logf(low);
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float loghigh = logf(high);
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float logmean = (loglow + loghigh) / 2;
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float logsigma = (loghigh - loglow) / (2.0 * NORMAL95CONFIDENCE);
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return random_lognormal(logmean, logsigma, seed);
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}
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int split_array_get_my_length(int index, int total_length, int n_threads)
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{
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return (total_length % n_threads > index ? total_length / n_threads + 1 : total_length / n_threads);
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}
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//Old version, don't use it!! Optimized version is called mixture_f. This one is just for display
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/*
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void mixture(float* dists[], float* weights, int n_dists, float* results)
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{
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float sum_weights = array_sum(weights, n_dists);
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float* normalized_weights = malloc(n_dists * sizeof(float));
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for (int i = 0; i < n_dists; i++) {
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normalized_weights[i] = weights[i] / sum_weights;
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}
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float* cummulative_weights = malloc(n_dists * sizeof(float));
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array_cumsum(normalized_weights, cummulative_weights, n_dists);
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//create var holders
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float p1, p2;
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int index_found, index_counter, sample_index, i;
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#pragma omp parallel private(i, p1, p2, index_found, index_counter, sample_index)
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{
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#pragma omp for
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for (i = 0; i < N; i++) {
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p1 = random_uniform(0, 1);
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p2 = random_uniform(0, 1);
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index_found = 0;
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index_counter = 0;
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while ((index_found == 0) && (index_counter < n_dists)) {
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if (p1 < cummulative_weights[index_counter]) {
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index_found = 1;
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} else {
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index_counter++;
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}
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}
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if (index_found != 0) {
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sample_index = (int)(p2 * N);
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results[i] = dists[index_counter][sample_index];
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} else
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printf("This shouldn't be able to happen.\n");
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}
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}
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free(normalized_weights);
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free(cummulative_weights);
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}
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*/
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void mixture_f(float (*samplers[])(unsigned int* ), float* weights, int n_dists, float** results, int n_threads)
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{
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float sum_weights = array_sum(weights, n_dists);
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float* normalized_weights = malloc(n_dists * sizeof(float));
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for (int i = 0; i < n_dists; i++) {
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normalized_weights[i] = weights[i] / sum_weights;
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}
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float* cummulative_weights = malloc(n_dists * sizeof(float));
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array_cumsum(normalized_weights, cummulative_weights, n_dists);
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//create var holders
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float p1;
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int sample_index, i, own_length;
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unsigned int* seeds[n_threads];
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for(unsigned int i=0; i<n_threads; i++){
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seeds[i] = malloc(sizeof(unsigned int));
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*seeds[i] = i;
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}
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#pragma omp parallel private(i, p1, sample_index, own_length)
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{
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#pragma omp for
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for (i = 0; i < n_threads; i++) {
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own_length = split_array_get_my_length(i, N, n_threads);
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for (int j = 0; j < own_length; j++) {
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p1 = random_uniform(0, 1, seeds[i]);
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for (int k = 0; k < n_dists; k++) {
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if (p1 < cummulative_weights[k]) {
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results[i][j] = samplers[k](seeds[i]);
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break;
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}
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}
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}
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}
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}
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free(normalized_weights);
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free(cummulative_weights);
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for(unsigned int i=0; i<n_threads; i++){
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free(seeds[i]);
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}
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}
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float sample_0(unsigned int* seed)
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{
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return 0;
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}
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float sample_1(unsigned int* seed)
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{
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return 1;
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}
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float sample_few(unsigned int* seed)
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{
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return random_to(1, 3, seed);
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}
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float sample_many(unsigned int* seed)
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{
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return random_to(2, 10, seed);
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}
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void split_array_allocate(float** meta_array, int length, int divide_into)
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{
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int own_length;
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for (int i = 0; i < divide_into; i++) {
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own_length = split_array_get_my_length(i, length, divide_into);
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meta_array[i] = malloc(own_length * sizeof(float));
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}
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}
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void split_array_free(float** meta_array, int divided_into)
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{
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for (int i = 0; i < divided_into; i++) {
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free(meta_array[i]);
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}
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free(meta_array);
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}
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float split_array_sum(float** meta_array, int length, int divided_into)
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{
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int i;
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float output;
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float* partial_sum = malloc(divided_into * sizeof(float));
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#pragma omp private(i) shared(partial_sum)
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for (int i = 0; i < divided_into; i++) {
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float own_partial_sum = 0;
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int own_length = split_array_get_my_length(i, length, divided_into);
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for (int j = 0; j < own_length; j++) {
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own_partial_sum += meta_array[i][j];
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}
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partial_sum[i] = own_partial_sum;
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}
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for (int i = 0; i < divided_into; i++) {
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output += partial_sum[i];
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}
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return output;
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}
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int main()
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{
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//initialize randomness
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srand(time(NULL));
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// clock_t start, end;
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// start = clock();
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// Toy example
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// Declare variables in play
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float p_a, p_b, p_c;
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int n_threads = omp_get_max_threads();
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// printf("Max threads: %d\n", n_threads);
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// omp_set_num_threads(n_threads);
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float** dist_mixture = malloc(n_threads * sizeof(float*));
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split_array_allocate(dist_mixture, N, n_threads);
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// Initialize variables
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p_a = 0.8;
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p_b = 0.5;
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p_c = p_a * p_b;
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// Generate mixture
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int n_dists = 4;
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float weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
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float (*samplers[])(unsigned int* ) = { sample_0, sample_1, sample_few, sample_many };
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mixture_f(samplers, weights, n_dists, dist_mixture, n_threads);
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printf("Sum(dist_mixture, N)/N = %f\n", split_array_sum(dist_mixture, N, n_threads) / N);
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// array_print(dist_mixture[0], N);
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split_array_free(dist_mixture, n_threads);
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// end = clock();
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// printf("Time (ms): %f\n", ((double)(end - start)) / (CLOCKS_PER_SEC) * 1000);
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// ^ Will only measure how long it takes the inner main to run, not the whole program,
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// including e.g., loading the program into memory or smth.
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// Also CLOCKS_PER_SEC in POSIX is a constant equal to 1000000.
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// See: https://stackoverflow.com/questions/10455905/why-is-clocks-per-sec-not-the-actual-number-of-clocks-per-second
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return 0;
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}
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53
C/C-01-simple/makefile
Normal file
53
C/C-01-simple/makefile
Normal file
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@ -0,0 +1,53 @@
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# Interface:
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# make
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# make build
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# make format
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# make run
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# Compiler
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CC=gcc
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# CC=tcc # <= faster compilation
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# Main file
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SRC=samples.c
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OUTPUT=samples
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## Dependencies
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DEPS='gsl'
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## Flags
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INCS=`pkg-config --cflags ${DEPS}`
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LIBS=`pkg-config --libs ${DEPS}`
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DEBUG= #'-g'
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STANDARD=-std=c99
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WARNINGS=-Wall
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FAST=-Ofast
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## Formatter
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STYLE_BLUEPRINT=webkit
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FORMATTER=clang-format -i -style=$(STYLE_BLUEPRINT)
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## make build
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build: $(SRC)
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$(CC) $(DEBUG) $(INCS) $(PLUGS) $(SRC) -o samples $(LIBS)
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fast: $(SRC)
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$(CC) $(FAST) $(DEBUG) $(INCS) $(PLUGS) $(SRC) -o samples $(LIBS)
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format: $(SRC)
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$(FORMATTER) $(SRC)
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run: $(SRC) $(OUTPUT)
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echo "Increasing stack size limit, because we are dealing with 1M samples"
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# ulimit: increase stack size limit
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# -Ss: the soft limit. If you set the hard limit, you then can't raise it
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# 256000: around 250Mbs, if I'm reading it correctly.
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# Then run the program
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ulimit -Ss 256000 && ./$(OUTPUT)
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# Old:
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# Link libraries, for good measure
|
||||
# LD_LIBRARY_PATH=/usr/local/lib
|
||||
# export LD_LIBRARY_PATH
|
||||
|
||||
157
C/C-01-simple/samples.c
Normal file
157
C/C-01-simple/samples.c
Normal file
|
|
@ -0,0 +1,157 @@
|
|||
#include <gsl/gsl_randist.h>
|
||||
#include <gsl/gsl_rng.h>
|
||||
#include <math.h>
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <time.h>
|
||||
|
||||
#define N 1000000
|
||||
/*
|
||||
* For very high values of N, you will want to increase the maximum stack trace, otherwise you will suffer a segmentation fault
|
||||
* In Ubuntu/bash you can do this with $ ulimit -Ss 256000 ## ~256Mbs
|
||||
* And confirm it with $ ulimit -a
|
||||
*/
|
||||
|
||||
/* Helpers */
|
||||
void print(double* ys)
|
||||
{
|
||||
for (int i = 0; i < N; i++) {
|
||||
printf("%f\n", ys[i]);
|
||||
}
|
||||
printf("\n");
|
||||
}
|
||||
|
||||
void fill(double* ys, float f)
|
||||
{
|
||||
for (int i = 0; i < N; i++) {
|
||||
ys[i] = f;
|
||||
}
|
||||
}
|
||||
|
||||
double sum(double* ps, int n)
|
||||
{
|
||||
double result = 0;
|
||||
for (int i = 0; i < n; i++) {
|
||||
result += ps[i];
|
||||
}
|
||||
return (result);
|
||||
}
|
||||
|
||||
void cumsum(double* ps, double* rs, int n)
|
||||
{
|
||||
double counter = 0;
|
||||
for (int i = 0; i < n; i++) {
|
||||
counter += ps[i];
|
||||
rs[i] = counter;
|
||||
}
|
||||
}
|
||||
|
||||
/* Distributions*/
|
||||
void normal(gsl_rng* r, double* ys, double mean, double std)
|
||||
{
|
||||
for (int i = 0; i < N; i++) {
|
||||
ys[i] = mean + gsl_ran_gaussian(r, std);
|
||||
}
|
||||
}
|
||||
|
||||
void lognormal(gsl_rng* r, double* ys, double zeta, double sigma)
|
||||
{
|
||||
for (int i = 0; i < N; i++) {
|
||||
ys[i] = gsl_ran_lognormal(r, zeta, sigma);
|
||||
}
|
||||
}
|
||||
|
||||
void to(gsl_rng* r, double* ys, double low, double high)
|
||||
{
|
||||
double normal95confidencePoint = 1.6448536269514722;
|
||||
double log_low = log(low);
|
||||
double log_high = log(high);
|
||||
double zeta = (log_low + log_high) / 2;
|
||||
double sigma = (log_high - log_low) / (2.0 * normal95confidencePoint);
|
||||
lognormal(r, ys, zeta, sigma);
|
||||
}
|
||||
|
||||
/* Mixture of distributions */
|
||||
void mixture(gsl_rng* r, double* dists[], double* weights, int n, double* results)
|
||||
{
|
||||
/* Get cummulative, normalized weights */
|
||||
double sum_weights = sum(weights, n);
|
||||
double normalized_weights[n];
|
||||
for (int i = 0; i < n; i++) {
|
||||
normalized_weights[i] = weights[i] / sum_weights;
|
||||
}
|
||||
double cummulative_weights[n];
|
||||
cumsum(normalized_weights, cummulative_weights, n);
|
||||
|
||||
/* Get N samples, drawn from the different distributions in proportion to their weights. */
|
||||
for (int i = 0; i < N; i++) {
|
||||
double p_1 = gsl_rng_uniform(r);
|
||||
double p_2 = gsl_rng_uniform(r);
|
||||
|
||||
int index_found = 0;
|
||||
int index_counter = 0;
|
||||
while ((index_found == 0) && (index_counter < n)) {
|
||||
if (p_1 < cummulative_weights[index_counter]) {
|
||||
index_found = 1;
|
||||
} else {
|
||||
index_counter++;
|
||||
}
|
||||
}
|
||||
if (index_found == 0) {
|
||||
printf("\nThis shouldn't be able to happen");
|
||||
// gsl_rng_free (r);
|
||||
// abort(); // this shouldn't have happened.
|
||||
|
||||
} else {
|
||||
int sample_index = (int)floor(p_2 * N);
|
||||
results[i] = dists[index_counter][sample_index];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* Main */
|
||||
int main(void)
|
||||
{
|
||||
// Start clock
|
||||
clock_t start, end;
|
||||
start = clock();
|
||||
|
||||
/* Initialize GNU Statistical Library (GSL) stuff */
|
||||
const gsl_rng_type* T;
|
||||
gsl_rng* r;
|
||||
// gsl_rng_env_setup();
|
||||
T = gsl_rng_default;
|
||||
r = gsl_rng_alloc(T);
|
||||
|
||||
/* Toy example */
|
||||
/* Declare variables in play */
|
||||
double p_a, p_b, p_c;
|
||||
double dist_none[N], dist_one[N], dist_few[N], dist_many[N], dist_mixture[N];
|
||||
|
||||
/* Initialize variables */
|
||||
p_a = 0.8;
|
||||
p_b = 0.5;
|
||||
p_c = p_a * p_b;
|
||||
|
||||
fill(dist_none, 0);
|
||||
fill(dist_one, 1);
|
||||
to(r, dist_few, 1, 3);
|
||||
to(r, dist_many, 2, 10);
|
||||
|
||||
/* Generate mixture */
|
||||
int n = 4;
|
||||
double weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
|
||||
double* dists[] = { dist_none, dist_one, dist_few, dist_many };
|
||||
|
||||
mixture(r, dists, weights, n, dist_mixture);
|
||||
printf("%f\n", sum(dist_mixture, N) / N);
|
||||
|
||||
/* Clean up GSL */
|
||||
gsl_rng_free(r);
|
||||
|
||||
// End clock
|
||||
end = clock();
|
||||
printf("Total time (ms): %f\n", ((double)(end - start)) / CLOCKS_PER_SEC * 1000);
|
||||
/* Return success*/
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
53
C/C-02-better-algorithm-one-thread/makefile
Normal file
53
C/C-02-better-algorithm-one-thread/makefile
Normal file
|
|
@ -0,0 +1,53 @@
|
|||
# Interface:
|
||||
# make
|
||||
# make build
|
||||
# make format
|
||||
# make run
|
||||
|
||||
# Compiler
|
||||
CC=gcc
|
||||
# CC=tcc # <= faster compilation
|
||||
|
||||
# Main file
|
||||
|
||||
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_ONE_THREAD)
|
||||
mkdir -p out
|
||||
$(CC) $(OPTIMIZED) $(DEBUG) $(SRC_ONE_THREAD) $(OPENMP) $(MATH) -o $(OUTPUT_ONE_THREAD)
|
||||
|
||||
format: $(SRC_ONE_THREAD)
|
||||
$(FORMATTER) $(SRC_ONE_THREAD)
|
||||
|
||||
run: $(SRC_ONE_THREAD) $(OUTPUT_ONE_THREAD)
|
||||
./$(OUTPUT_ONE_THREAD)
|
||||
|
||||
time-linux:
|
||||
@echo "Requires /bin/time, found on GNU/Linux systems" && echo
|
||||
@echo "Running 100x and taking avg time: $(OUTPUT_ONE_THREAD)"
|
||||
@t=$$(/usr/bin/time -f "%e" -p bash -c 'for i in {1..100}; do $(OUTPUT_ONE_THREAD); done' 2>&1 >/dev/null | grep real | awk '{print $$2}' ); echo "scale=2; 1000 * $$t / 100" | bc | sed "s|^|Time: |" | sed 's|$$|ms|' && echo
|
||||
|
||||
time-linux-simple:
|
||||
@echo "Requires /bin/time, found on GNU/Linux systems" && echo
|
||||
/bin/time -f "Time: %es" ./$(OUTPUT_ONE_THREAD) && echo
|
||||
|
||||
debian-install-dependencies:
|
||||
sudo apt-get install libomp-dev
|
||||
|
||||
BIN
C/C-02-better-algorithm-one-thread/out/samples-one-thread
Executable file
BIN
C/C-02-better-algorithm-one-thread/out/samples-one-thread
Executable file
Binary file not shown.
|
|
@ -5,7 +5,7 @@
|
|||
|
||||
const float PI = 3.14159265358979323846;
|
||||
|
||||
#define N 10000000
|
||||
#define N 1000000
|
||||
|
||||
//Array helpers
|
||||
|
||||
15
C/README.md
Normal file
15
C/README.md
Normal file
|
|
@ -0,0 +1,15 @@
|
|||
# Time to BOTEC in C
|
||||
|
||||
This repository contains a few implementations of a simple botec (back-of-the-envelope) calculation in C:
|
||||
|
||||
- In the folder C-01-simple/, you can see a simple implementation, which passes large arrays
|
||||
- In the folder C-02-better-algorithm-one-thread/ you can see a better implementations, that passes around pointers to functions, which makes the implementation more efficient
|
||||
- In the top level, you can see an implementation that uses the better implementation in C-02..., and that also implements multithreading using OpenMP
|
||||
|
||||
## To do
|
||||
|
||||
- [ ] Update repository with correct timing
|
||||
- [ ] Add Windows/Powershell time-measuring commands
|
||||
- [ ] Add CUDA?
|
||||
- [x] Use better profiling approach to capture timing with 1M samples.
|
||||
- [x] See if program can be reworded so as to use multithreading effectively, e.g., so that you see speed gains proportional to the number of threads used
|
||||
67
C/makefile
67
C/makefile
|
|
@ -10,44 +10,73 @@ CC=gcc
|
|||
|
||||
# Main file
|
||||
SRC=samples.c
|
||||
OUTPUT=samples
|
||||
OUTPUT=out/samples
|
||||
|
||||
SRC_ONE_THREAD=./samples-one-thread.c
|
||||
OUTPUT_ONE_THREAD=out/samples-one-thread
|
||||
|
||||
## Dependencies
|
||||
DEPS='gsl'
|
||||
# Has no dependencies
|
||||
MATH=-lm
|
||||
|
||||
## Flags
|
||||
INCS=`pkg-config --cflags ${DEPS}`
|
||||
LIBS=`pkg-config --libs ${DEPS}`
|
||||
DEBUG= #'-g'
|
||||
STANDARD=-std=c99
|
||||
WARNINGS=-Wall
|
||||
FAST=-Ofast
|
||||
OPTIMIZED=-O3 #-O3 actually gives better performance than -Ofast, at least for this version
|
||||
OPENMP=-fopenmp
|
||||
|
||||
## Formatter
|
||||
STYLE_BLUEPRINT=webkit
|
||||
FORMATTER=clang-format -i -style=$(STYLE_BLUEPRINT)
|
||||
|
||||
## make build
|
||||
build: $(SRC)
|
||||
$(CC) $(DEBUG) $(INCS) $(PLUGS) $(SRC) -o samples $(LIBS)
|
||||
|
||||
fast: $(SRC)
|
||||
$(CC) $(FAST) $(DEBUG) $(INCS) $(PLUGS) $(SRC) -o samples $(LIBS)
|
||||
$(CC) $(OPTIMIZED) $(DEBUG) $(SRC) $(OPENMP) $(MATH) -o $(OUTPUT)
|
||||
$(CC) $(OPTIMIZED) $(DEBUG) $(SRC_ONE_THREAD) $(OPENMP) $(MATH) -o $(OUTPUT_ONE_THREAD)
|
||||
|
||||
format: $(SRC)
|
||||
$(FORMATTER) $(SRC)
|
||||
|
||||
run: $(SRC) $(OUTPUT)
|
||||
echo "Increasing stack size limit, because we are dealing with 1M samples"
|
||||
# ulimit: increase stack size limit
|
||||
# -Ss: the soft limit. If you set the hard limit, you then can't raise it
|
||||
# 256000: around 250Mbs, if I'm reading it correctly.
|
||||
# Then run the program
|
||||
ulimit -Ss 256000 && ./$(OUTPUT)
|
||||
OMP_NUM_THREADS=1 ./$(OUTPUT) && echo
|
||||
./$(OUTPUT_ONE_THREAD)
|
||||
|
||||
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 ./$(OUTPUT) && echo
|
||||
./$(OUTPUT_ONE_THREAD) && echo
|
||||
|
||||
time-linux:
|
||||
@echo "Requires /bin/time, found on GNU/Linux systems" && echo
|
||||
|
||||
# Old:
|
||||
# Link libraries, for good measure
|
||||
# LD_LIBRARY_PATH=/usr/local/lib
|
||||
# export LD_LIBRARY_PATH
|
||||
@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-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" ./$(OUTPUT) && echo
|
||||
/bin/time -f "Time: %es" ./$(OUTPUT_ONE_THREAD) && echo
|
||||
|
||||
debian-install-dependencies:
|
||||
sudo apt-get install libomp-dev
|
||||
|
||||
|
|
|
|||
322
C/samples.c
322
C/samples.c
|
|
@ -1,157 +1,281 @@
|
|||
#include <gsl/gsl_randist.h>
|
||||
#include <gsl/gsl_rng.h>
|
||||
#include <math.h>
|
||||
#include <omp.h>
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <time.h>
|
||||
|
||||
#define N 1000000
|
||||
/*
|
||||
* For very high values of N, you will want to increase the maximum stack trace, otherwise you will suffer a segmentation fault
|
||||
* In Ubuntu/bash you can do this with $ ulimit -Ss 256000 ## ~256Mbs
|
||||
* And confirm it with $ ulimit -a
|
||||
*/
|
||||
const float PI = 3.14159265358979323846;
|
||||
|
||||
/* Helpers */
|
||||
void print(double* ys)
|
||||
#define N 1000000
|
||||
|
||||
//Array helpers
|
||||
|
||||
void array_print(float* array, int length)
|
||||
{
|
||||
for (int i = 0; i < N; i++) {
|
||||
printf("%f\n", ys[i]);
|
||||
for (int i = 0; i < length; i++) {
|
||||
printf("item[%d] = %f\n", i, array[i]);
|
||||
}
|
||||
printf("\n");
|
||||
}
|
||||
|
||||
void fill(double* ys, float f)
|
||||
void array_fill(float* array, int length, float item)
|
||||
{
|
||||
for (int i = 0; i < N; i++) {
|
||||
ys[i] = f;
|
||||
int i;
|
||||
#pragma omp private(i)
|
||||
{
|
||||
#pragma omp for
|
||||
for (i = 0; i < length; i++) {
|
||||
array[i] = item;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
double sum(double* ps, int n)
|
||||
float array_sum(float* array, int length)
|
||||
{
|
||||
double result = 0;
|
||||
for (int i = 0; i < n; i++) {
|
||||
result += ps[i];
|
||||
float output = 0.0;
|
||||
for (int i = 0; i < length; i++) {
|
||||
output += array[i];
|
||||
}
|
||||
return (result);
|
||||
return output;
|
||||
}
|
||||
|
||||
void cumsum(double* ps, double* rs, int n)
|
||||
void array_cumsum(float* array_to_sum, float* array_cumsummed, int length)
|
||||
{
|
||||
double counter = 0;
|
||||
for (int i = 0; i < n; i++) {
|
||||
counter += ps[i];
|
||||
rs[i] = counter;
|
||||
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];
|
||||
}
|
||||
}
|
||||
|
||||
/* Distributions*/
|
||||
void normal(gsl_rng* r, double* ys, double mean, double std)
|
||||
float rand_float(float to, unsigned int* seed)
|
||||
{
|
||||
for (int i = 0; i < N; i++) {
|
||||
ys[i] = mean + gsl_ran_gaussian(r, std);
|
||||
}
|
||||
return ((float)rand_r(seed) / (float)RAND_MAX) * to;
|
||||
// See: <https://stackoverflow.com/questions/43151361/how-to-create-thread-safe-random-number-generator-in-c-using-rand-r>
|
||||
// rand() is not thread-safe, as it relies on (shared) hidden state.
|
||||
}
|
||||
|
||||
void lognormal(gsl_rng* r, double* ys, double zeta, double sigma)
|
||||
float ur_normal(unsigned int* seed)
|
||||
{
|
||||
for (int i = 0; i < N; i++) {
|
||||
ys[i] = gsl_ran_lognormal(r, zeta, sigma);
|
||||
}
|
||||
float u1 = rand_float(1.0, seed);
|
||||
float u2 = rand_float(1.0, seed);
|
||||
float z = sqrtf(-2.0 * log(u1)) * sin(2 * PI * u2);
|
||||
return z;
|
||||
}
|
||||
|
||||
void to(gsl_rng* r, double* ys, double low, double high)
|
||||
inline float random_uniform(float from, float to, unsigned int* seed)
|
||||
{
|
||||
double normal95confidencePoint = 1.6448536269514722;
|
||||
double log_low = log(low);
|
||||
double log_high = log(high);
|
||||
double zeta = (log_low + log_high) / 2;
|
||||
double sigma = (log_high - log_low) / (2.0 * normal95confidencePoint);
|
||||
lognormal(r, ys, zeta, sigma);
|
||||
return ((float) rand_r(seed) / (float)RAND_MAX) * (to - from) + from;
|
||||
}
|
||||
|
||||
/* Mixture of distributions */
|
||||
void mixture(gsl_rng* r, double* dists[], double* weights, int n, double* results)
|
||||
inline float random_normal(float mean, float sigma, unsigned int* seed)
|
||||
{
|
||||
/* Get cummulative, normalized weights */
|
||||
double sum_weights = sum(weights, n);
|
||||
double normalized_weights[n];
|
||||
for (int i = 0; i < n; i++) {
|
||||
return (mean + sigma * ur_normal(seed));
|
||||
}
|
||||
|
||||
inline float random_lognormal(float logmean, float logsigma, unsigned int* seed)
|
||||
{
|
||||
return expf(random_normal(logmean, logsigma, seed));
|
||||
}
|
||||
|
||||
inline float random_to(float low, float high, unsigned int* 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);
|
||||
}
|
||||
|
||||
int split_array_get_my_length(int index, int total_length, int n_threads)
|
||||
{
|
||||
return (total_length % n_threads > index ? total_length / n_threads + 1 : total_length / n_threads);
|
||||
}
|
||||
|
||||
//Old version, don't use it!! Optimized version is called mixture_f. This one is just for display
|
||||
/*
|
||||
void mixture(float* dists[], float* weights, int n_dists, float* results)
|
||||
{
|
||||
float sum_weights = array_sum(weights, n_dists);
|
||||
float* normalized_weights = malloc(n_dists * sizeof(float));
|
||||
for (int i = 0; i < n_dists; i++) {
|
||||
normalized_weights[i] = weights[i] / sum_weights;
|
||||
}
|
||||
double cummulative_weights[n];
|
||||
cumsum(normalized_weights, cummulative_weights, n);
|
||||
|
||||
/* Get N samples, drawn from the different distributions in proportion to their weights. */
|
||||
for (int i = 0; i < N; i++) {
|
||||
double p_1 = gsl_rng_uniform(r);
|
||||
double p_2 = gsl_rng_uniform(r);
|
||||
float* cummulative_weights = malloc(n_dists * sizeof(float));
|
||||
array_cumsum(normalized_weights, cummulative_weights, n_dists);
|
||||
|
||||
int index_found = 0;
|
||||
int index_counter = 0;
|
||||
while ((index_found == 0) && (index_counter < n)) {
|
||||
if (p_1 < cummulative_weights[index_counter]) {
|
||||
//create var holders
|
||||
float p1, p2;
|
||||
int index_found, index_counter, sample_index, i;
|
||||
|
||||
#pragma omp parallel private(i, p1, p2, index_found, index_counter, sample_index)
|
||||
{
|
||||
#pragma omp for
|
||||
for (i = 0; i < N; i++) {
|
||||
p1 = random_uniform(0, 1);
|
||||
p2 = random_uniform(0, 1);
|
||||
|
||||
index_found = 0;
|
||||
index_counter = 0;
|
||||
|
||||
while ((index_found == 0) && (index_counter < n_dists)) {
|
||||
if (p1 < cummulative_weights[index_counter]) {
|
||||
index_found = 1;
|
||||
} else {
|
||||
index_counter++;
|
||||
}
|
||||
}
|
||||
if (index_found == 0) {
|
||||
printf("\nThis shouldn't be able to happen");
|
||||
// gsl_rng_free (r);
|
||||
// abort(); // this shouldn't have happened.
|
||||
|
||||
} else {
|
||||
int sample_index = (int)floor(p_2 * N);
|
||||
if (index_found != 0) {
|
||||
sample_index = (int)(p2 * N);
|
||||
results[i] = dists[index_counter][sample_index];
|
||||
} else
|
||||
printf("This shouldn't be able to happen.\n");
|
||||
}
|
||||
}
|
||||
free(normalized_weights);
|
||||
free(cummulative_weights);
|
||||
}
|
||||
*/
|
||||
void mixture_f(float (*samplers[])(unsigned int* ), float* weights, int n_dists, float** results, int n_threads)
|
||||
{
|
||||
float sum_weights = array_sum(weights, n_dists);
|
||||
float* normalized_weights = malloc(n_dists * sizeof(float));
|
||||
for (int i = 0; i < n_dists; i++) {
|
||||
normalized_weights[i] = weights[i] / sum_weights;
|
||||
}
|
||||
|
||||
float* cummulative_weights = malloc(n_dists * sizeof(float));
|
||||
array_cumsum(normalized_weights, cummulative_weights, n_dists);
|
||||
|
||||
//create var holders
|
||||
float p1;
|
||||
int sample_index, i, own_length;
|
||||
unsigned int* seeds[n_threads];
|
||||
for(unsigned int i=0; i<n_threads; i++){
|
||||
seeds[i] = malloc(sizeof(unsigned int));
|
||||
*seeds[i] = i;
|
||||
}
|
||||
|
||||
#pragma omp parallel private(i, p1, sample_index, own_length)
|
||||
{
|
||||
#pragma omp for
|
||||
for (i = 0; i < n_threads; i++) {
|
||||
own_length = split_array_get_my_length(i, N, n_threads);
|
||||
for (int j = 0; j < own_length; j++) {
|
||||
p1 = random_uniform(0, 1, seeds[i]);
|
||||
for (int k = 0; k < n_dists; k++) {
|
||||
if (p1 < cummulative_weights[k]) {
|
||||
results[i][j] = samplers[k](seeds[i]);
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
free(normalized_weights);
|
||||
free(cummulative_weights);
|
||||
for(unsigned int i=0; i<n_threads; i++){
|
||||
free(seeds[i]);
|
||||
}
|
||||
}
|
||||
|
||||
/* Main */
|
||||
int main(void)
|
||||
float sample_0(unsigned int* seed)
|
||||
{
|
||||
// Start clock
|
||||
clock_t start, end;
|
||||
start = clock();
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Initialize GNU Statistical Library (GSL) stuff */
|
||||
const gsl_rng_type* T;
|
||||
gsl_rng* r;
|
||||
// gsl_rng_env_setup();
|
||||
T = gsl_rng_default;
|
||||
r = gsl_rng_alloc(T);
|
||||
float sample_1(unsigned int* seed)
|
||||
{
|
||||
return 1;
|
||||
}
|
||||
|
||||
/* Toy example */
|
||||
/* Declare variables in play */
|
||||
double p_a, p_b, p_c;
|
||||
double dist_none[N], dist_one[N], dist_few[N], dist_many[N], dist_mixture[N];
|
||||
float sample_few(unsigned int* seed)
|
||||
{
|
||||
return random_to(1, 3, seed);
|
||||
}
|
||||
|
||||
/* Initialize variables */
|
||||
float sample_many(unsigned int* seed)
|
||||
{
|
||||
return random_to(2, 10, seed);
|
||||
}
|
||||
|
||||
void split_array_allocate(float** meta_array, int length, int divide_into)
|
||||
{
|
||||
int own_length;
|
||||
|
||||
for (int i = 0; i < divide_into; i++) {
|
||||
own_length = split_array_get_my_length(i, length, divide_into);
|
||||
meta_array[i] = malloc(own_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;
|
||||
float* partial_sum = malloc(divided_into * sizeof(float));
|
||||
|
||||
#pragma omp private(i) shared(partial_sum)
|
||||
for (int i = 0; i < divided_into; i++) {
|
||||
float own_partial_sum = 0;
|
||||
int own_length = split_array_get_my_length(i, length, divided_into);
|
||||
for (int j = 0; j < own_length; j++) {
|
||||
own_partial_sum += meta_array[i][j];
|
||||
}
|
||||
partial_sum[i] = own_partial_sum;
|
||||
}
|
||||
for (int i = 0; i < divided_into; i++) {
|
||||
output += partial_sum[i];
|
||||
}
|
||||
return output;
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
//initialize randomness
|
||||
srand(time(NULL));
|
||||
|
||||
// clock_t start, end;
|
||||
// start = clock();
|
||||
|
||||
// Toy example
|
||||
// Declare variables in play
|
||||
float p_a, p_b, p_c;
|
||||
int n_threads = omp_get_max_threads();
|
||||
// printf("Max threads: %d\n", n_threads);
|
||||
// omp_set_num_threads(n_threads);
|
||||
float** dist_mixture = malloc(n_threads * sizeof(float*));
|
||||
split_array_allocate(dist_mixture, N, n_threads);
|
||||
|
||||
// Initialize variables
|
||||
p_a = 0.8;
|
||||
p_b = 0.5;
|
||||
p_c = p_a * p_b;
|
||||
|
||||
fill(dist_none, 0);
|
||||
fill(dist_one, 1);
|
||||
to(r, dist_few, 1, 3);
|
||||
to(r, dist_many, 2, 10);
|
||||
// Generate mixture
|
||||
int n_dists = 4;
|
||||
float weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
|
||||
float (*samplers[])(unsigned int* ) = { sample_0, sample_1, sample_few, sample_many };
|
||||
|
||||
/* Generate mixture */
|
||||
int n = 4;
|
||||
double weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
|
||||
double* dists[] = { dist_none, dist_one, dist_few, dist_many };
|
||||
mixture_f(samplers, weights, n_dists, dist_mixture, n_threads);
|
||||
printf("Sum(dist_mixture, N)/N = %f\n", split_array_sum(dist_mixture, N, n_threads) / N);
|
||||
// array_print(dist_mixture[0], N);
|
||||
split_array_free(dist_mixture, n_threads);
|
||||
|
||||
mixture(r, dists, weights, n, dist_mixture);
|
||||
printf("%f\n", sum(dist_mixture, N) / N);
|
||||
|
||||
/* Clean up GSL */
|
||||
gsl_rng_free(r);
|
||||
|
||||
// End clock
|
||||
end = clock();
|
||||
printf("Total time (ms): %f\n", ((double)(end - start)) / CLOCKS_PER_SEC * 1000);
|
||||
/* Return success*/
|
||||
return EXIT_SUCCESS;
|
||||
// end = clock();
|
||||
// printf("Time (ms): %f\n", ((double)(end - start)) / (CLOCKS_PER_SEC) * 1000);
|
||||
// ^ Will only measure how long it takes the inner main to run, not the whole program,
|
||||
// including e.g., loading the program into memory or smth.
|
||||
// Also CLOCKS_PER_SEC in POSIX is a constant equal to 1000000.
|
||||
// See: https://stackoverflow.com/questions/10455905/why-is-clocks-per-sec-not-the-actual-number-of-clocks-per-second
|
||||
return 0;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -30,10 +30,10 @@ As of now, it may be useful for checking the validity of simple estimations. The
|
|||
## Comparison table
|
||||
|
||||
| Language | Time | Lines of code |
|
||||
|--------------------------|-----------|---------------|
|
||||
| C (optimized, 1 thread) | 30ms | 183 |
|
||||
|-----------------------------|-----------|---------------|
|
||||
| C (optimized, 16 threads) | 6ms | 183 |
|
||||
| Nim | 68ms | 84 |
|
||||
| C | 292ms | 149 |
|
||||
| C (naïve implementation) | 292ms | 149 |
|
||||
| Javascript (NodeJS) | 732ms | 69 |
|
||||
| Squiggle | 1,536s | 14 |
|
||||
| R | 7,000s | 49 |
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user