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/* Generate random permutations.
Copyright (C) 2006-2012 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 <http://www.gnu.org/licenses/>. */
/* Written by Paul Eggert. */
#include <config.h>
#include "hash.h"
#include "randperm.h"
#include <limits.h>
#include <stdlib.h>
#include "xalloc.h"
/* Return the ceiling of the log base 2 of N. If N is zero, return
an unspecified value. */
static size_t _GL_ATTRIBUTE_CONST
ceil_lg (size_t n)
{
size_t b = 0;
for (n--; n != 0; n /= 2)
b++;
return b;
}
/* 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. */
size_t lg_n = ceil_lg (n);
/* Upper bound on number of bits needed to generated the first H elements. */
size_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;
}
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