277 lines
8.1 KiB
C
277 lines
8.1 KiB
C
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#include "test/jemalloc_test.h"
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/******************************************************************************/
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/*
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* General purpose tool for examining random number distributions.
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*
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* Input -
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* (a) a random number generator, and
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* (b) the buckets:
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* (1) number of buckets,
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* (2) width of each bucket, in log scale,
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* (3) expected mean and stddev of the count of random numbers in each
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* bucket, and
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* (c) number of iterations to invoke the generator.
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*
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* The program generates the specified amount of random numbers, and assess how
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* well they conform to the expectations: for each bucket, output -
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* (a) the (given) expected mean and stddev,
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* (b) the actual count and any interesting level of deviation:
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* (1) ~68% buckets should show no interesting deviation, meaning a
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* deviation less than stddev from the expectation;
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* (2) ~27% buckets should show '+' / '-', meaning a deviation in the range
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* of [stddev, 2 * stddev) from the expectation;
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* (3) ~4% buckets should show '++' / '--', meaning a deviation in the
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* range of [2 * stddev, 3 * stddev) from the expectation; and
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* (4) less than 0.3% buckets should show more than two '+'s / '-'s.
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*
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* Technical remarks:
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* (a) The generator is expected to output uint64_t numbers, so you might need
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* to define a wrapper.
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* (b) The buckets must be of equal width and the lowest bucket starts at
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* [0, 2^lg_bucket_width - 1).
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* (c) Any generated number >= n_bucket * 2^lg_bucket_width will be counted
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* towards the last bucket; the expected mean and stddev provided should
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* also reflect that.
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* (d) The number of iterations is adviced to be determined so that the bucket
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* with the minimal expected proportion gets a sufficient count.
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*/
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static void
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fill(size_t a[], const size_t n, const size_t k) {
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for (size_t i = 0; i < n; ++i) {
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a[i] = k;
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}
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}
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static void
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collect_buckets(uint64_t (*gen)(void *), void *opaque, size_t buckets[],
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const size_t n_bucket, const size_t lg_bucket_width, const size_t n_iter) {
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for (size_t i = 0; i < n_iter; ++i) {
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uint64_t num = gen(opaque);
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uint64_t bucket_id = num >> lg_bucket_width;
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if (bucket_id >= n_bucket) {
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bucket_id = n_bucket - 1;
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}
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++buckets[bucket_id];
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}
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}
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static void
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print_buckets(const size_t buckets[], const size_t means[],
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const size_t stddevs[], const size_t n_bucket) {
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for (size_t i = 0; i < n_bucket; ++i) {
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malloc_printf("%zu:\tmean = %zu,\tstddev = %zu,\tbucket = %zu",
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i, means[i], stddevs[i], buckets[i]);
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/* Make sure there's no overflow. */
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assert(buckets[i] + stddevs[i] >= stddevs[i]);
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assert(means[i] + stddevs[i] >= stddevs[i]);
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if (buckets[i] + stddevs[i] <= means[i]) {
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malloc_write(" ");
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for (size_t t = means[i] - buckets[i]; t >= stddevs[i];
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t -= stddevs[i]) {
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malloc_write("-");
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}
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} else if (buckets[i] >= means[i] + stddevs[i]) {
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malloc_write(" ");
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for (size_t t = buckets[i] - means[i]; t >= stddevs[i];
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t -= stddevs[i]) {
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malloc_write("+");
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}
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}
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malloc_write("\n");
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}
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}
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static void
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bucket_analysis(uint64_t (*gen)(void *), void *opaque, size_t buckets[],
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const size_t means[], const size_t stddevs[], const size_t n_bucket,
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const size_t lg_bucket_width, const size_t n_iter) {
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for (size_t i = 1; i <= 3; ++i) {
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malloc_printf("round %zu\n", i);
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fill(buckets, n_bucket, 0);
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collect_buckets(gen, opaque, buckets, n_bucket,
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lg_bucket_width, n_iter);
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print_buckets(buckets, means, stddevs, n_bucket);
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}
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}
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/* (Recommended) minimal bucket mean. */
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#define MIN_BUCKET_MEAN 10000
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/******************************************************************************/
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/* Uniform random number generator. */
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typedef struct uniform_gen_arg_s uniform_gen_arg_t;
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struct uniform_gen_arg_s {
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uint64_t state;
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const unsigned lg_range;
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};
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static uint64_t
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uniform_gen(void *opaque) {
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uniform_gen_arg_t *arg = (uniform_gen_arg_t *)opaque;
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return prng_lg_range_u64(&arg->state, arg->lg_range);
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}
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TEST_BEGIN(test_uniform) {
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#define LG_N_BUCKET 5
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#define N_BUCKET (1 << LG_N_BUCKET)
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#define QUOTIENT_CEIL(n, d) (((n) - 1) / (d) + 1)
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const unsigned lg_range_test = 25;
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/*
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* Mathematical tricks to guarantee that both mean and stddev are
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* integers, and that the minimal bucket mean is at least
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* MIN_BUCKET_MEAN.
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*/
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const size_t q = 1 << QUOTIENT_CEIL(LG_CEIL(QUOTIENT_CEIL(
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MIN_BUCKET_MEAN, N_BUCKET * (N_BUCKET - 1))), 2);
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const size_t stddev = (N_BUCKET - 1) * q;
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const size_t mean = N_BUCKET * stddev * q;
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const size_t n_iter = N_BUCKET * mean;
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size_t means[N_BUCKET];
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fill(means, N_BUCKET, mean);
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size_t stddevs[N_BUCKET];
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fill(stddevs, N_BUCKET, stddev);
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uniform_gen_arg_t arg = {(uint64_t)(uintptr_t)&lg_range_test,
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lg_range_test};
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size_t buckets[N_BUCKET];
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assert_zu_ge(lg_range_test, LG_N_BUCKET, "");
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const size_t lg_bucket_width = lg_range_test - LG_N_BUCKET;
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bucket_analysis(uniform_gen, &arg, buckets, means, stddevs,
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N_BUCKET, lg_bucket_width, n_iter);
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#undef LG_N_BUCKET
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#undef N_BUCKET
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#undef QUOTIENT_CEIL
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}
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TEST_END
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/******************************************************************************/
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/* Geometric random number generator; compiled only when prof is on. */
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#ifdef JEMALLOC_PROF
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/*
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* Fills geometric proportions and returns the minimal proportion. See
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* comments in test_prof_sample for explanations for n_divide.
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*/
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static double
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fill_geometric_proportions(double proportions[], const size_t n_bucket,
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const size_t n_divide) {
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assert(n_bucket > 0);
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assert(n_divide > 0);
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double x = 1.;
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for (size_t i = 0; i < n_bucket; ++i) {
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if (i == n_bucket - 1) {
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proportions[i] = x;
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} else {
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double y = x * exp(-1. / n_divide);
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proportions[i] = x - y;
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x = y;
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}
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}
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/*
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* The minimal proportion is the smaller one of the last two
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* proportions for geometric distribution.
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*/
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double min_proportion = proportions[n_bucket - 1];
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if (n_bucket >= 2 && proportions[n_bucket - 2] < min_proportion) {
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min_proportion = proportions[n_bucket - 2];
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}
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return min_proportion;
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}
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static size_t
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round_to_nearest(const double x) {
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return (size_t)(x + .5);
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}
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static void
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fill_references(size_t means[], size_t stddevs[], const double proportions[],
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const size_t n_bucket, const size_t n_iter) {
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for (size_t i = 0; i < n_bucket; ++i) {
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double x = n_iter * proportions[i];
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means[i] = round_to_nearest(x);
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stddevs[i] = round_to_nearest(sqrt(x * (1. - proportions[i])));
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}
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}
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static uint64_t
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prof_sample_gen(void *opaque) {
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return prof_sample_new_event_wait((tsd_t *)opaque) - 1;
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}
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#endif /* JEMALLOC_PROF */
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TEST_BEGIN(test_prof_sample) {
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test_skip_if(!config_prof);
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#ifdef JEMALLOC_PROF
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/* Number of divisions within [0, mean). */
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#define LG_N_DIVIDE 3
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#define N_DIVIDE (1 << LG_N_DIVIDE)
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/* Coverage of buckets in terms of multiples of mean. */
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#define LG_N_MULTIPLY 2
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#define N_GEO_BUCKET (N_DIVIDE << LG_N_MULTIPLY)
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test_skip_if(!opt_prof);
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size_t lg_prof_sample_test = 25;
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size_t lg_prof_sample_orig = lg_prof_sample;
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assert_d_eq(mallctl("prof.reset", NULL, NULL, &lg_prof_sample_test,
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sizeof(size_t)), 0, "");
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malloc_printf("lg_prof_sample = %zu\n", lg_prof_sample_test);
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double proportions[N_GEO_BUCKET + 1];
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const double min_proportion = fill_geometric_proportions(proportions,
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N_GEO_BUCKET + 1, N_DIVIDE);
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const size_t n_iter = round_to_nearest(MIN_BUCKET_MEAN /
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min_proportion);
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size_t means[N_GEO_BUCKET + 1];
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size_t stddevs[N_GEO_BUCKET + 1];
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fill_references(means, stddevs, proportions, N_GEO_BUCKET + 1, n_iter);
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tsd_t *tsd = tsd_fetch();
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assert_ptr_not_null(tsd, "");
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size_t buckets[N_GEO_BUCKET + 1];
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assert_zu_ge(lg_prof_sample, LG_N_DIVIDE, "");
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const size_t lg_bucket_width = lg_prof_sample - LG_N_DIVIDE;
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bucket_analysis(prof_sample_gen, tsd, buckets, means, stddevs,
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N_GEO_BUCKET + 1, lg_bucket_width, n_iter);
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assert_d_eq(mallctl("prof.reset", NULL, NULL, &lg_prof_sample_orig,
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sizeof(size_t)), 0, "");
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#undef LG_N_DIVIDE
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#undef N_DIVIDE
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#undef LG_N_MULTIPLY
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#undef N_GEO_BUCKET
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#endif /* JEMALLOC_PROF */
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}
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TEST_END
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/******************************************************************************/
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int
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main(void) {
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return test_no_reentrancy(
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test_uniform,
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test_prof_sample);
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}
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