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1 | /* Random pseudo generator number which returns a single 32 bit value |
2 | uniformly distributed but with an upper_bound. | |
3 | Copyright (C) 2022 Free Software Foundation, Inc. | |
4 | This file is part of the GNU C Library. | |
5 | ||
6 | The GNU C Library is free software; you can redistribute it and/or | |
7 | modify it under the terms of the GNU Lesser General Public | |
8 | License as published by the Free Software Foundation; either | |
9 | version 2.1 of the License, or (at your option) any later version. | |
10 | ||
11 | The GNU C Library is distributed in the hope that it will be useful, | |
12 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 | Lesser General Public License for more details. | |
15 | ||
16 | You should have received a copy of the GNU Lesser General Public | |
17 | License along with the GNU C Library; if not, see | |
18 | <https://www.gnu.org/licenses/>. */ | |
19 | ||
20 | #include <endian.h> | |
21 | #include <libc-lock.h> | |
22 | #include <stdlib.h> | |
23 | #include <sys/param.h> | |
24 | ||
25 | /* Return the number of bytes which cover values up to the limit. */ | |
26 | __attribute__ ((const)) | |
27 | static uint32_t | |
28 | byte_count (uint32_t n) | |
29 | { | |
30 | if (n < (1U << 8)) | |
31 | return 1; | |
32 | else if (n < (1U << 16)) | |
33 | return 2; | |
34 | else if (n < (1U << 24)) | |
35 | return 3; | |
36 | else | |
37 | return 4; | |
38 | } | |
39 | ||
40 | /* Fill the lower bits of the result with randomness, according to the | |
41 | number of bytes requested. */ | |
42 | static void | |
43 | random_bytes (uint32_t *result, uint32_t byte_count) | |
44 | { | |
45 | *result = 0; | |
46 | unsigned char *ptr = (unsigned char *) result; | |
47 | if (__BYTE_ORDER == __BIG_ENDIAN) | |
48 | ptr += 4 - byte_count; | |
49 | __arc4random_buf (ptr, byte_count); | |
50 | } | |
51 | ||
52 | uint32_t | |
53 | __arc4random_uniform (uint32_t n) | |
54 | { | |
55 | if (n <= 1) | |
56 | /* There is no valid return value for a zero limit, and 0 is the | |
57 | only possible result for limit 1. */ | |
58 | return 0; | |
59 | ||
60 | /* The bits variable serves as a source for bits. Prefetch the | |
61 | minimum number of bytes needed. */ | |
62 | uint32_t count = byte_count (n); | |
63 | uint32_t bits_length = count * CHAR_BIT; | |
64 | uint32_t bits; | |
65 | random_bytes (&bits, count); | |
66 | ||
67 | /* Powers of two are easy. */ | |
68 | if (powerof2 (n)) | |
69 | return bits & (n - 1); | |
70 | ||
71 | /* The general case. This algorithm follows Jérémie Lumbroso, | |
72 | Optimal Discrete Uniform Generation from Coin Flips, and | |
73 | Applications (2013), who credits Donald E. Knuth and Andrew | |
74 | C. Yao, The complexity of nonuniform random number generation | |
75 | (1976), for solving the general case. | |
76 | ||
77 | The implementation below unrolls the initialization stage of the | |
78 | loop, where v is less than n. */ | |
79 | ||
80 | /* Use 64-bit variables even though the intermediate results are | |
81 | never larger than 33 bits. This ensures the code is easier to | |
82 | compile on 64-bit architectures. */ | |
83 | uint64_t v; | |
84 | uint64_t c; | |
85 | ||
86 | /* Initialize v and c. v is the smallest power of 2 which is larger | |
87 | than n.*/ | |
88 | { | |
89 | uint32_t log2p1 = 32 - __builtin_clz (n); | |
90 | v = 1ULL << log2p1; | |
91 | c = bits & (v - 1); | |
92 | bits >>= log2p1; | |
93 | bits_length -= log2p1; | |
94 | } | |
95 | ||
96 | /* At the start of the loop, c is uniformly distributed within the | |
97 | half-open interval [0, v), and v < 2n < 2**33. */ | |
98 | while (true) | |
99 | { | |
100 | if (v >= n) | |
101 | { | |
102 | /* If the candidate is less than n, accept it. */ | |
103 | if (c < n) | |
104 | /* c is uniformly distributed on [0, n). */ | |
105 | return c; | |
106 | else | |
107 | { | |
108 | /* c is uniformly distributed on [n, v). */ | |
109 | v -= n; | |
110 | c -= n; | |
111 | /* The distribution was shifted, so c is uniformly | |
112 | distributed on [0, v) again. */ | |
113 | } | |
114 | } | |
115 | /* v < n here. */ | |
116 | ||
117 | /* Replenish the bit source if necessary. */ | |
118 | if (bits_length == 0) | |
119 | { | |
120 | /* Overwrite the least significant byte. */ | |
121 | random_bytes (&bits, 1); | |
122 | bits_length = CHAR_BIT; | |
123 | } | |
124 | ||
125 | /* Double the range. No overflow because v < n < 2**32. */ | |
126 | v *= 2; | |
127 | /* v < 2n here. */ | |
128 | ||
129 | /* Extract a bit and append it to c. c remains less than v and | |
130 | thus 2**33. */ | |
131 | c = (c << 1) | (bits & 1); | |
132 | bits >>= 1; | |
133 | --bits_length; | |
134 | ||
135 | /* At this point, c is uniformly distributed on [0, v) again, | |
136 | and v < 2n < 2**33. */ | |
137 | } | |
138 | } | |
139 | libc_hidden_def (__arc4random_uniform) | |
140 | weak_alias (__arc4random_uniform, arc4random_uniform) |