1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
|
/* Generate random permutations.
Copyright (C) 2006-2016 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;
}
|
