diff options
Diffstat (limited to 'lib/randperm.c')
| -rw-r--r-- | lib/randperm.c | 242 |
1 files changed, 242 insertions, 0 deletions
diff --git a/lib/randperm.c b/lib/randperm.c new file mode 100644 index 0000000..e9f46cd --- /dev/null +++ b/lib/randperm.c @@ -0,0 +1,242 @@ +/* Generate random permutations. + + Copyright (C) 2006-2020 Free Software Foundation, Inc. + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see <https://www.gnu.org/licenses/>. */ + +/* Written by Paul Eggert. */ + +#include <config.h> + +#include "randperm.h" + +#include <limits.h> +#include <stdint.h> +#include <stdlib.h> + +#include "count-leading-zeros.h" +#include "hash.h" +#include "verify.h" +#include "xalloc.h" + +/* Return the floor of the log base 2 of N. If N is zero, return -1. */ + +static int _GL_ATTRIBUTE_CONST +floor_lg (size_t n) +{ + verify (SIZE_WIDTH <= ULLONG_WIDTH); + return (n == 0 ? -1 + : SIZE_WIDTH <= UINT_WIDTH + ? UINT_WIDTH - 1 - count_leading_zeros (n) + : SIZE_WIDTH <= ULONG_WIDTH + ? ULONG_WIDTH - 1 - count_leading_zeros_l (n) + : ULLONG_WIDTH - 1 - count_leading_zeros_ll (n)); +} + +/* Return an upper bound on the number of random bytes needed to + generate the first H elements of a random permutation of N + elements. H must not exceed N. */ + +size_t +randperm_bound (size_t h, size_t n) +{ + /* Upper bound on number of bits needed to generate the first number + of the permutation. */ + uintmax_t lg_n = floor_lg (n) + 1; + + /* Upper bound on number of bits needed to generated the first H elements. */ + uintmax_t ar = lg_n * h; + + /* Convert the bit count to a byte count. */ + size_t bound = (ar + CHAR_BIT - 1) / CHAR_BIT; + + return bound; +} + +/* Swap elements I and J in array V. */ + +static void +swap (size_t *v, size_t i, size_t j) +{ + size_t t = v[i]; + v[i] = v[j]; + v[j] = t; +} + +/* Structures and functions for a sparse_map abstract data type that's + used to effectively swap elements I and J in array V like swap(), + but in a more memory efficient manner (when the number of permutations + performed is significantly less than the size of the input). */ + +struct sparse_ent_ +{ + size_t index; + size_t val; +}; + +static size_t +sparse_hash_ (void const *x, size_t table_size) +{ + struct sparse_ent_ const *ent = x; + return ent->index % table_size; +} + +static bool +sparse_cmp_ (void const *x, void const *y) +{ + struct sparse_ent_ const *ent1 = x; + struct sparse_ent_ const *ent2 = y; + return ent1->index == ent2->index; +} + +typedef Hash_table sparse_map; + +/* Initialize the structure for the sparse map, + when a best guess as to the number of entries + specified with SIZE_HINT. */ + +static sparse_map * +sparse_new (size_t size_hint) +{ + return hash_initialize (size_hint, NULL, sparse_hash_, sparse_cmp_, free); +} + +/* Swap the values for I and J. If a value is not already present + then assume it's equal to the index. Update the value for + index I in array V. */ + +static void +sparse_swap (sparse_map *sv, size_t* v, size_t i, size_t j) +{ + struct sparse_ent_ *v1 = hash_delete (sv, &(struct sparse_ent_) {i,0}); + struct sparse_ent_ *v2 = hash_delete (sv, &(struct sparse_ent_) {j,0}); + + /* FIXME: reduce the frequency of these mallocs. */ + if (!v1) + { + v1 = xmalloc (sizeof *v1); + v1->index = v1->val = i; + } + if (!v2) + { + v2 = xmalloc (sizeof *v2); + v2->index = v2->val = j; + } + + size_t t = v1->val; + v1->val = v2->val; + v2->val = t; + if (!hash_insert (sv, v1)) + xalloc_die (); + if (!hash_insert (sv, v2)) + xalloc_die (); + + v[i] = v1->val; +} + +static void +sparse_free (sparse_map *sv) +{ + hash_free (sv); +} + + +/* From R, allocate and return a malloc'd array of the first H elements + of a random permutation of N elements. H must not exceed N. + Return NULL if H is zero. */ + +size_t * +randperm_new (struct randint_source *r, size_t h, size_t n) +{ + size_t *v; + + switch (h) + { + case 0: + v = NULL; + break; + + case 1: + v = xmalloc (sizeof *v); + v[0] = randint_choose (r, n); + break; + + default: + { + /* The algorithm is essentially the same in both + the sparse and non sparse case. In the sparse case we use + a hash to implement sparse storage for the set of n numbers + we're shuffling. When to use the sparse method was + determined with the help of this script: + + #!/bin/sh + for n in $(seq 2 32); do + for h in $(seq 2 32); do + test $h -gt $n && continue + for s in o n; do + test $s = o && shuf=shuf || shuf=./shuf + num=$(env time -f "$s:${h},${n} = %e,%M" \ + $shuf -i0-$((2**$n-2)) -n$((2**$h-2)) | wc -l) + test $num = $((2**$h-2)) || echo "$s:${h},${n} = failed" >&2 + done + done + done + + This showed that if sparseness = n/h, then: + + sparseness = 128 => .125 mem used, and about same speed + sparseness = 64 => .25 mem used, but 1.5 times slower + sparseness = 32 => .5 mem used, but 2 times slower + + Also the memory usage was only significant when n > 128Ki + */ + bool sparse = (n >= (128 * 1024)) && (n / h >= 32); + + size_t i; + sparse_map *sv; + + if (sparse) + { + sv = sparse_new (h * 2); + if (sv == NULL) + xalloc_die (); + v = xnmalloc (h, sizeof *v); + } + else + { + sv = NULL; /* To placate GCC's -Wuninitialized. */ + v = xnmalloc (n, sizeof *v); + for (i = 0; i < n; i++) + v[i] = i; + } + + for (i = 0; i < h; i++) + { + size_t j = i + randint_choose (r, n - i); + if (sparse) + sparse_swap (sv, v, i, j); + else + swap (v, i, j); + } + + if (sparse) + sparse_free (sv); + else + v = xnrealloc (v, h, sizeof *v); + } + break; + } + + return v; +} |