Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 1 | """Random variable generators. |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 2 | |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 3 | bytes |
| 4 | ----- |
| 5 | uniform bytes (values between 0 and 255) |
| 6 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 7 | integers |
| 8 | -------- |
| 9 | uniform within range |
| 10 | |
| 11 | sequences |
| 12 | --------- |
| 13 | pick random element |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 14 | pick random sample |
Raymond Hettinger | e8f1e00 | 2016-09-06 17:15:29 -0700 | [diff] [blame] | 15 | pick weighted random sample |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 16 | generate random permutation |
| 17 | |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 18 | distributions on the real line: |
| 19 | ------------------------------ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 20 | uniform |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 21 | triangular |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 22 | normal (Gaussian) |
| 23 | lognormal |
| 24 | negative exponential |
| 25 | gamma |
| 26 | beta |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 27 | pareto |
| 28 | Weibull |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 29 | |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 30 | distributions on the circle (angles 0 to 2pi) |
| 31 | --------------------------------------------- |
| 32 | circular uniform |
| 33 | von Mises |
| 34 | |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 35 | General notes on the underlying Mersenne Twister core generator: |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 36 | |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 37 | * The period is 2**19937-1. |
Thomas Wouters | 0e3f591 | 2006-08-11 14:57:12 +0000 | [diff] [blame] | 38 | * It is one of the most extensively tested generators in existence. |
Thomas Wouters | 0e3f591 | 2006-08-11 14:57:12 +0000 | [diff] [blame] | 39 | * The random() method is implemented in C, executes in a single Python step, |
| 40 | and is, therefore, threadsafe. |
Tim Peters | e360d95 | 2001-01-26 10:00:39 +0000 | [diff] [blame] | 41 | |
Guido van Rossum | e7b146f | 2000-02-04 15:28:42 +0000 | [diff] [blame] | 42 | """ |
Guido van Rossum | d03e119 | 1998-05-29 17:51:31 +0000 | [diff] [blame] | 43 | |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 44 | # Translated by Guido van Rossum from C source provided by |
| 45 | # Adrian Baddeley. Adapted by Raymond Hettinger for use with |
| 46 | # the Mersenne Twister and os.urandom() core generators. |
| 47 | |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 48 | from warnings import warn as _warn |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 49 | from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil |
Raymond Hettinger | 26a1ad1 | 2020-06-22 19:38:59 -0700 | [diff] [blame] | 50 | from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin |
Ram Rachum | b0dfc75 | 2020-09-29 04:32:10 +0300 | [diff] [blame] | 51 | from math import tau as TWOPI, floor as _floor, isfinite as _isfinite |
Raymond Hettinger | c1c43ca | 2004-09-05 00:00:42 +0000 | [diff] [blame] | 52 | from os import urandom as _urandom |
Christian Heimes | f1dc3ee | 2013-10-13 02:04:20 +0200 | [diff] [blame] | 53 | from _collections_abc import Set as _Set, Sequence as _Sequence |
Raymond Hettinger | a9621bb | 2020-12-28 11:10:34 -0800 | [diff] [blame] | 54 | from operator import index as _index |
Raymond Hettinger | 5382203 | 2019-02-16 13:30:51 -0800 | [diff] [blame] | 55 | from itertools import accumulate as _accumulate, repeat as _repeat |
Raymond Hettinger | cfd31f0 | 2019-02-13 02:04:17 -0800 | [diff] [blame] | 56 | from bisect import bisect as _bisect |
Antoine Pitrou | 346cbd3 | 2017-05-27 17:50:54 +0200 | [diff] [blame] | 57 | import os as _os |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 58 | import _random |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 59 | |
Christian Heimes | d914596 | 2019-04-10 22:18:02 +0200 | [diff] [blame] | 60 | try: |
| 61 | # hashlib is pretty heavy to load, try lean internal module first |
| 62 | from _sha512 import sha512 as _sha512 |
| 63 | except ImportError: |
| 64 | # fallback to official implementation |
| 65 | from hashlib import sha512 as _sha512 |
| 66 | |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 67 | __all__ = [ |
| 68 | "Random", |
| 69 | "SystemRandom", |
| 70 | "betavariate", |
| 71 | "choice", |
| 72 | "choices", |
| 73 | "expovariate", |
| 74 | "gammavariate", |
| 75 | "gauss", |
| 76 | "getrandbits", |
| 77 | "getstate", |
| 78 | "lognormvariate", |
| 79 | "normalvariate", |
| 80 | "paretovariate", |
Setrak Balian | 998ae1f | 2021-01-15 17:50:42 +0000 | [diff] [blame] | 81 | "randbytes", |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 82 | "randint", |
| 83 | "random", |
| 84 | "randrange", |
| 85 | "sample", |
| 86 | "seed", |
| 87 | "setstate", |
| 88 | "shuffle", |
| 89 | "triangular", |
| 90 | "uniform", |
| 91 | "vonmisesvariate", |
| 92 | "weibullvariate", |
| 93 | ] |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 94 | |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 95 | NV_MAGICCONST = 4 * _exp(-0.5) / _sqrt(2.0) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 96 | LOG4 = _log(4.0) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 97 | SG_MAGICCONST = 1.0 + _log(4.5) |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 98 | BPF = 53 # Number of bits in a float |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 99 | RECIP_BPF = 2 ** -BPF |
Raymond Hettinger | 768fa14 | 2021-01-02 10:24:51 -0800 | [diff] [blame] | 100 | _ONE = 1 |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 101 | |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 102 | |
Raymond Hettinger | 145a4a0 | 2003-01-07 10:25:55 +0000 | [diff] [blame] | 103 | class Random(_random.Random): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 104 | """Random number generator base class used by bound module functions. |
| 105 | |
| 106 | Used to instantiate instances of Random to get generators that don't |
Raymond Hettinger | 28de64f | 2008-01-13 23:40:30 +0000 | [diff] [blame] | 107 | share state. |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 108 | |
| 109 | Class Random can also be subclassed if you want to use a different basic |
| 110 | generator of your own devising: in that case, override the following |
Raymond Hettinger | 28de64f | 2008-01-13 23:40:30 +0000 | [diff] [blame] | 111 | methods: random(), seed(), getstate(), and setstate(). |
Benjamin Peterson | d18de0e | 2008-07-31 20:21:46 +0000 | [diff] [blame] | 112 | Optionally, implement a getrandbits() method so that randrange() |
Raymond Hettinger | 2f726e9 | 2003-10-05 09:09:15 +0000 | [diff] [blame] | 113 | can cover arbitrarily large ranges. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 114 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 115 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 116 | |
Christian Heimes | cbf3b5c | 2007-12-03 21:02:03 +0000 | [diff] [blame] | 117 | VERSION = 3 # used by getstate/setstate |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 118 | |
| 119 | def __init__(self, x=None): |
| 120 | """Initialize an instance. |
| 121 | |
| 122 | Optional argument x controls seeding, as for Random.seed(). |
| 123 | """ |
| 124 | |
| 125 | self.seed(x) |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 126 | self.gauss_next = None |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 127 | |
Raymond Hettinger | f763a72 | 2010-09-07 00:38:15 +0000 | [diff] [blame] | 128 | def seed(self, a=None, version=2): |
Raymond Hettinger | d0cdeaa | 2019-08-22 09:19:36 -0700 | [diff] [blame] | 129 | """Initialize internal state from a seed. |
| 130 | |
| 131 | The only supported seed types are None, int, float, |
| 132 | str, bytes, and bytearray. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 133 | |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 134 | None or no argument seeds from current time or from an operating |
| 135 | system specific randomness source if available. |
Tim Peters | 0de88fc | 2001-02-01 04:59:18 +0000 | [diff] [blame] | 136 | |
Raymond Hettinger | 183cd1f | 2010-09-08 18:48:21 +0000 | [diff] [blame] | 137 | If *a* is an int, all bits are used. |
Raymond Hettinger | f763a72 | 2010-09-07 00:38:15 +0000 | [diff] [blame] | 138 | |
Raymond Hettinger | 16eb827 | 2016-09-04 11:17:28 -0700 | [diff] [blame] | 139 | For version 2 (the default), all of the bits are used if *a* is a str, |
| 140 | bytes, or bytearray. For version 1 (provided for reproducing random |
| 141 | sequences from older versions of Python), the algorithm for str and |
| 142 | bytes generates a narrower range of seeds. |
| 143 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 144 | """ |
| 145 | |
Raymond Hettinger | c7bab7c | 2016-08-31 15:01:08 -0700 | [diff] [blame] | 146 | if version == 1 and isinstance(a, (str, bytes)): |
Raymond Hettinger | 132a7d7 | 2017-09-17 09:04:30 -0700 | [diff] [blame] | 147 | a = a.decode('latin-1') if isinstance(a, bytes) else a |
Raymond Hettinger | c7bab7c | 2016-08-31 15:01:08 -0700 | [diff] [blame] | 148 | x = ord(a[0]) << 7 if a else 0 |
Raymond Hettinger | 132a7d7 | 2017-09-17 09:04:30 -0700 | [diff] [blame] | 149 | for c in map(ord, a): |
| 150 | x = ((1000003 * x) ^ c) & 0xFFFFFFFFFFFFFFFF |
Raymond Hettinger | c7bab7c | 2016-08-31 15:01:08 -0700 | [diff] [blame] | 151 | x ^= len(a) |
| 152 | a = -2 if x == -1 else x |
| 153 | |
Raymond Hettinger | d0cdeaa | 2019-08-22 09:19:36 -0700 | [diff] [blame] | 154 | elif version == 2 and isinstance(a, (str, bytes, bytearray)): |
Raymond Hettinger | 2f9cc7a | 2016-08-31 23:00:32 -0700 | [diff] [blame] | 155 | if isinstance(a, str): |
| 156 | a = a.encode() |
| 157 | a += _sha512(a).digest() |
| 158 | a = int.from_bytes(a, 'big') |
Raymond Hettinger | f763a72 | 2010-09-07 00:38:15 +0000 | [diff] [blame] | 159 | |
Raymond Hettinger | d0cdeaa | 2019-08-22 09:19:36 -0700 | [diff] [blame] | 160 | elif not isinstance(a, (type(None), int, float, str, bytes, bytearray)): |
| 161 | _warn('Seeding based on hashing is deprecated\n' |
| 162 | 'since Python 3.9 and will be removed in a subsequent ' |
| 163 | 'version. The only \n' |
| 164 | 'supported seed types are: None, ' |
| 165 | 'int, float, str, bytes, and bytearray.', |
| 166 | DeprecationWarning, 2) |
| 167 | |
Guido van Rossum | cd16bf6 | 2007-06-13 18:07:49 +0000 | [diff] [blame] | 168 | super().seed(a) |
Tim Peters | 46c04e1 | 2002-05-05 20:40:00 +0000 | [diff] [blame] | 169 | self.gauss_next = None |
| 170 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 171 | def getstate(self): |
| 172 | """Return internal state; can be passed to setstate() later.""" |
Guido van Rossum | cd16bf6 | 2007-06-13 18:07:49 +0000 | [diff] [blame] | 173 | return self.VERSION, super().getstate(), self.gauss_next |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 174 | |
| 175 | def setstate(self, state): |
| 176 | """Restore internal state from object returned by getstate().""" |
| 177 | version = state[0] |
Christian Heimes | cbf3b5c | 2007-12-03 21:02:03 +0000 | [diff] [blame] | 178 | if version == 3: |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 179 | version, internalstate, self.gauss_next = state |
Guido van Rossum | cd16bf6 | 2007-06-13 18:07:49 +0000 | [diff] [blame] | 180 | super().setstate(internalstate) |
Christian Heimes | cbf3b5c | 2007-12-03 21:02:03 +0000 | [diff] [blame] | 181 | elif version == 2: |
| 182 | version, internalstate, self.gauss_next = state |
| 183 | # In version 2, the state was saved as signed ints, which causes |
| 184 | # inconsistencies between 32/64-bit systems. The state is |
| 185 | # really unsigned 32-bit ints, so we convert negative ints from |
| 186 | # version 2 to positive longs for version 3. |
| 187 | try: |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 188 | internalstate = tuple(x % (2 ** 32) for x in internalstate) |
Christian Heimes | cbf3b5c | 2007-12-03 21:02:03 +0000 | [diff] [blame] | 189 | except ValueError as e: |
| 190 | raise TypeError from e |
Raymond Hettinger | 183cd1f | 2010-09-08 18:48:21 +0000 | [diff] [blame] | 191 | super().setstate(internalstate) |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 192 | else: |
| 193 | raise ValueError("state with version %s passed to " |
| 194 | "Random.setstate() of version %s" % |
| 195 | (version, self.VERSION)) |
| 196 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 197 | |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 198 | ## ------------------------------------------------------- |
| 199 | ## ---- Methods below this point do not need to be overridden or extended |
| 200 | ## ---- when subclassing for the purpose of using a different core generator. |
Victor Stinner | 2d87577 | 2020-04-29 18:49:00 +0200 | [diff] [blame] | 201 | |
Victor Stinner | 2d87577 | 2020-04-29 18:49:00 +0200 | [diff] [blame] | 202 | |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 203 | ## -------------------- pickle support ------------------- |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 204 | |
R David Murray | d9ebf4d | 2013-04-02 13:10:52 -0400 | [diff] [blame] | 205 | # Issue 17489: Since __reduce__ was defined to fix #759889 this is no |
| 206 | # longer called; we leave it here because it has been here since random was |
| 207 | # rewritten back in 2001 and why risk breaking something. |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 208 | def __getstate__(self): # for pickle |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 209 | return self.getstate() |
| 210 | |
| 211 | def __setstate__(self, state): # for pickle |
| 212 | self.setstate(state) |
| 213 | |
Raymond Hettinger | 5f078ff | 2003-06-24 20:29:04 +0000 | [diff] [blame] | 214 | def __reduce__(self): |
| 215 | return self.__class__, (), self.getstate() |
| 216 | |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 217 | |
| 218 | ## ---- internal support method for evenly distributed integers ---- |
| 219 | |
| 220 | def __init_subclass__(cls, /, **kwargs): |
| 221 | """Control how subclasses generate random integers. |
| 222 | |
| 223 | The algorithm a subclass can use depends on the random() and/or |
| 224 | getrandbits() implementation available to it and determines |
| 225 | whether it can generate random integers from arbitrarily large |
| 226 | ranges. |
| 227 | """ |
| 228 | |
| 229 | for c in cls.__mro__: |
| 230 | if '_randbelow' in c.__dict__: |
| 231 | # just inherit it |
| 232 | break |
| 233 | if 'getrandbits' in c.__dict__: |
| 234 | cls._randbelow = cls._randbelow_with_getrandbits |
| 235 | break |
| 236 | if 'random' in c.__dict__: |
| 237 | cls._randbelow = cls._randbelow_without_getrandbits |
| 238 | break |
| 239 | |
| 240 | def _randbelow_with_getrandbits(self, n): |
| 241 | "Return a random int in the range [0,n). Returns 0 if n==0." |
| 242 | |
| 243 | if not n: |
| 244 | return 0 |
| 245 | getrandbits = self.getrandbits |
| 246 | k = n.bit_length() # don't use (n-1) here because n can be 1 |
| 247 | r = getrandbits(k) # 0 <= r < 2**k |
| 248 | while r >= n: |
| 249 | r = getrandbits(k) |
| 250 | return r |
| 251 | |
| 252 | def _randbelow_without_getrandbits(self, n, maxsize=1<<BPF): |
| 253 | """Return a random int in the range [0,n). Returns 0 if n==0. |
| 254 | |
| 255 | The implementation does not use getrandbits, but only random. |
| 256 | """ |
| 257 | |
| 258 | random = self.random |
| 259 | if n >= maxsize: |
| 260 | _warn("Underlying random() generator does not supply \n" |
| 261 | "enough bits to choose from a population range this large.\n" |
| 262 | "To remove the range limitation, add a getrandbits() method.") |
| 263 | return _floor(random() * n) |
| 264 | if n == 0: |
| 265 | return 0 |
| 266 | rem = maxsize % n |
| 267 | limit = (maxsize - rem) / maxsize # int(limit * maxsize) % n == 0 |
| 268 | r = random() |
| 269 | while r >= limit: |
| 270 | r = random() |
| 271 | return _floor(r * maxsize) % n |
| 272 | |
| 273 | _randbelow = _randbelow_with_getrandbits |
| 274 | |
| 275 | |
| 276 | ## -------------------------------------------------------- |
| 277 | ## ---- Methods below this point generate custom distributions |
| 278 | ## ---- based on the methods defined above. They do not |
| 279 | ## ---- directly touch the underlying generator and only |
| 280 | ## ---- access randomness through the methods: random(), |
| 281 | ## ---- getrandbits(), or _randbelow(). |
| 282 | |
| 283 | |
| 284 | ## -------------------- bytes methods --------------------- |
| 285 | |
| 286 | def randbytes(self, n): |
| 287 | """Generate n random bytes.""" |
| 288 | return self.getrandbits(n * 8).to_bytes(n, 'little') |
| 289 | |
| 290 | |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 291 | ## -------------------- integer methods ------------------- |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 292 | |
Raymond Hettinger | 768fa14 | 2021-01-02 10:24:51 -0800 | [diff] [blame] | 293 | def randrange(self, start, stop=None, step=_ONE): |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 294 | """Choose a random item from range(start, stop[, step]). |
| 295 | |
| 296 | This fixes the problem with randint() which includes the |
| 297 | endpoint; in Python this is usually not what you want. |
Raymond Hettinger | 3051cc3 | 2010-09-07 00:48:40 +0000 | [diff] [blame] | 298 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 299 | """ |
| 300 | |
| 301 | # This code is a bit messy to make it fast for the |
Tim Peters | 9146f27 | 2002-08-16 03:41:39 +0000 | [diff] [blame] | 302 | # common case while still doing adequate error checking. |
Raymond Hettinger | a9621bb | 2020-12-28 11:10:34 -0800 | [diff] [blame] | 303 | try: |
| 304 | istart = _index(start) |
| 305 | except TypeError: |
Serhiy Storchaka | f066bd9 | 2021-01-25 23:02:04 +0200 | [diff] [blame] | 306 | istart = int(start) |
| 307 | if istart != start: |
Raymond Hettinger | a9621bb | 2020-12-28 11:10:34 -0800 | [diff] [blame] | 308 | _warn('randrange() will raise TypeError in the future', |
| 309 | DeprecationWarning, 2) |
| 310 | raise ValueError("non-integer arg 1 for randrange()") |
Serhiy Storchaka | f066bd9 | 2021-01-25 23:02:04 +0200 | [diff] [blame] | 311 | _warn('non-integer arguments to randrange() have been deprecated ' |
| 312 | 'since Python 3.10 and will be removed in a subsequent ' |
| 313 | 'version', |
| 314 | DeprecationWarning, 2) |
Raymond Hettinger | 3051cc3 | 2010-09-07 00:48:40 +0000 | [diff] [blame] | 315 | if stop is None: |
Raymond Hettinger | 768fa14 | 2021-01-02 10:24:51 -0800 | [diff] [blame] | 316 | # We don't check for "step != 1" because it hasn't been |
| 317 | # type checked and converted to an integer yet. |
| 318 | if step is not _ONE: |
| 319 | raise TypeError('Missing a non-None stop argument') |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 320 | if istart > 0: |
Raymond Hettinger | 0515661 | 2010-09-07 04:44:52 +0000 | [diff] [blame] | 321 | return self._randbelow(istart) |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 322 | raise ValueError("empty range for randrange()") |
Tim Peters | 9146f27 | 2002-08-16 03:41:39 +0000 | [diff] [blame] | 323 | |
| 324 | # stop argument supplied. |
Raymond Hettinger | a9621bb | 2020-12-28 11:10:34 -0800 | [diff] [blame] | 325 | try: |
| 326 | istop = _index(stop) |
| 327 | except TypeError: |
Serhiy Storchaka | f066bd9 | 2021-01-25 23:02:04 +0200 | [diff] [blame] | 328 | istop = int(stop) |
| 329 | if istop != stop: |
Raymond Hettinger | a9621bb | 2020-12-28 11:10:34 -0800 | [diff] [blame] | 330 | _warn('randrange() will raise TypeError in the future', |
| 331 | DeprecationWarning, 2) |
| 332 | raise ValueError("non-integer stop for randrange()") |
Serhiy Storchaka | f066bd9 | 2021-01-25 23:02:04 +0200 | [diff] [blame] | 333 | _warn('non-integer arguments to randrange() have been deprecated ' |
| 334 | 'since Python 3.10 and will be removed in a subsequent ' |
| 335 | 'version', |
| 336 | DeprecationWarning, 2) |
| 337 | width = istop - istart |
Raymond Hettinger | a9621bb | 2020-12-28 11:10:34 -0800 | [diff] [blame] | 338 | try: |
| 339 | istep = _index(step) |
| 340 | except TypeError: |
Serhiy Storchaka | f066bd9 | 2021-01-25 23:02:04 +0200 | [diff] [blame] | 341 | istep = int(step) |
| 342 | if istep != step: |
Raymond Hettinger | a9621bb | 2020-12-28 11:10:34 -0800 | [diff] [blame] | 343 | _warn('randrange() will raise TypeError in the future', |
| 344 | DeprecationWarning, 2) |
| 345 | raise ValueError("non-integer step for randrange()") |
Serhiy Storchaka | f066bd9 | 2021-01-25 23:02:04 +0200 | [diff] [blame] | 346 | _warn('non-integer arguments to randrange() have been deprecated ' |
| 347 | 'since Python 3.10 and will be removed in a subsequent ' |
| 348 | 'version', |
| 349 | DeprecationWarning, 2) |
| 350 | # Fast path. |
Raymond Hettinger | a9621bb | 2020-12-28 11:10:34 -0800 | [diff] [blame] | 351 | if istep == 1: |
Raymond Hettinger | 8f8de73 | 2021-01-02 12:09:56 -0800 | [diff] [blame] | 352 | if width > 0: |
| 353 | return istart + self._randbelow(width) |
Kumar Akshay | 2433a2a | 2019-01-22 00:49:59 +0530 | [diff] [blame] | 354 | raise ValueError("empty range for randrange() (%d, %d, %d)" % (istart, istop, width)) |
Tim Peters | 9146f27 | 2002-08-16 03:41:39 +0000 | [diff] [blame] | 355 | |
| 356 | # Non-unit step argument supplied. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 357 | if istep > 0: |
Raymond Hettinger | ffdb8bb | 2004-09-27 15:29:05 +0000 | [diff] [blame] | 358 | n = (width + istep - 1) // istep |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 359 | elif istep < 0: |
Raymond Hettinger | ffdb8bb | 2004-09-27 15:29:05 +0000 | [diff] [blame] | 360 | n = (width + istep + 1) // istep |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 361 | else: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 362 | raise ValueError("zero step for randrange()") |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 363 | if n <= 0: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 364 | raise ValueError("empty range for randrange()") |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 365 | return istart + istep * self._randbelow(n) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 366 | |
| 367 | def randint(self, a, b): |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 368 | """Return random integer in range [a, b], including both end points. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 369 | """ |
| 370 | |
| 371 | return self.randrange(a, b+1) |
| 372 | |
Wolfgang Maier | ba3a87a | 2018-04-17 17:16:17 +0200 | [diff] [blame] | 373 | |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 374 | ## -------------------- sequence methods ------------------- |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 375 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 376 | def choice(self, seq): |
| 377 | """Choose a random element from a non-empty sequence.""" |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 378 | # raises IndexError if seq is empty |
| 379 | return seq[self._randbelow(len(seq))] |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 380 | |
Raymond Hettinger | 8fe47c3 | 2013-10-05 21:48:21 -0700 | [diff] [blame] | 381 | def shuffle(self, x, random=None): |
Antoine Pitrou | 5e39433 | 2012-11-04 02:10:33 +0100 | [diff] [blame] | 382 | """Shuffle list x in place, and return None. |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 383 | |
Antoine Pitrou | 5e39433 | 2012-11-04 02:10:33 +0100 | [diff] [blame] | 384 | Optional argument random is a 0-argument function returning a |
| 385 | random float in [0.0, 1.0); if it is the default None, the |
| 386 | standard random.random will be used. |
Senthil Kumaran | f8ce51a | 2013-09-11 22:54:31 -0700 | [diff] [blame] | 387 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 388 | """ |
| 389 | |
Raymond Hettinger | 8fe47c3 | 2013-10-05 21:48:21 -0700 | [diff] [blame] | 390 | if random is None: |
| 391 | randbelow = self._randbelow |
| 392 | for i in reversed(range(1, len(x))): |
| 393 | # pick an element in x[:i+1] with which to exchange x[i] |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 394 | j = randbelow(i + 1) |
Raymond Hettinger | 8fe47c3 | 2013-10-05 21:48:21 -0700 | [diff] [blame] | 395 | x[i], x[j] = x[j], x[i] |
| 396 | else: |
Raymond Hettinger | 190fac9 | 2020-05-02 16:45:32 -0700 | [diff] [blame] | 397 | _warn('The *random* parameter to shuffle() has been deprecated\n' |
| 398 | 'since Python 3.9 and will be removed in a subsequent ' |
| 399 | 'version.', |
| 400 | DeprecationWarning, 2) |
Raymond Hettinger | 26a1ad1 | 2020-06-22 19:38:59 -0700 | [diff] [blame] | 401 | floor = _floor |
Raymond Hettinger | 8fe47c3 | 2013-10-05 21:48:21 -0700 | [diff] [blame] | 402 | for i in reversed(range(1, len(x))): |
| 403 | # pick an element in x[:i+1] with which to exchange x[i] |
Raymond Hettinger | 26a1ad1 | 2020-06-22 19:38:59 -0700 | [diff] [blame] | 404 | j = floor(random() * (i + 1)) |
Raymond Hettinger | 8fe47c3 | 2013-10-05 21:48:21 -0700 | [diff] [blame] | 405 | x[i], x[j] = x[j], x[i] |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 406 | |
Raymond Hettinger | 81a5fc3 | 2020-05-08 07:53:15 -0700 | [diff] [blame] | 407 | def sample(self, population, k, *, counts=None): |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 408 | """Chooses k unique random elements from a population sequence or set. |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 409 | |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 410 | Returns a new list containing elements from the population while |
| 411 | leaving the original population unchanged. The resulting list is |
| 412 | in selection order so that all sub-slices will also be valid random |
| 413 | samples. This allows raffle winners (the sample) to be partitioned |
| 414 | into grand prize and second place winners (the subslices). |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 415 | |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 416 | Members of the population need not be hashable or unique. If the |
| 417 | population contains repeats, then each occurrence is a possible |
| 418 | selection in the sample. |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 419 | |
Raymond Hettinger | 81a5fc3 | 2020-05-08 07:53:15 -0700 | [diff] [blame] | 420 | Repeated elements can be specified one at a time or with the optional |
| 421 | counts parameter. For example: |
| 422 | |
| 423 | sample(['red', 'blue'], counts=[4, 2], k=5) |
| 424 | |
| 425 | is equivalent to: |
| 426 | |
| 427 | sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5) |
| 428 | |
| 429 | To choose a sample from a range of integers, use range() for the |
| 430 | population argument. This is especially fast and space efficient |
| 431 | for sampling from a large population: |
| 432 | |
| 433 | sample(range(10000000), 60) |
| 434 | |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 435 | """ |
| 436 | |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 437 | # Sampling without replacement entails tracking either potential |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 438 | # selections (the pool) in a list or previous selections in a set. |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 439 | |
Jeremy Hylton | 2b55d35 | 2004-02-23 17:27:57 +0000 | [diff] [blame] | 440 | # When the number of selections is small compared to the |
| 441 | # population, then tracking selections is efficient, requiring |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 442 | # only a small set and an occasional reselection. For |
Jeremy Hylton | 2b55d35 | 2004-02-23 17:27:57 +0000 | [diff] [blame] | 443 | # a larger number of selections, the pool tracking method is |
| 444 | # preferred since the list takes less space than the |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 445 | # set and it doesn't suffer from frequent reselections. |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 446 | |
Raymond Hettinger | 7fc633f | 2018-12-04 00:13:38 -0800 | [diff] [blame] | 447 | # The number of calls to _randbelow() is kept at or near k, the |
| 448 | # theoretical minimum. This is important because running time |
| 449 | # is dominated by _randbelow() and because it extracts the |
| 450 | # least entropy from the underlying random number generators. |
| 451 | |
| 452 | # Memory requirements are kept to the smaller of a k-length |
| 453 | # set or an n-length list. |
| 454 | |
| 455 | # There are other sampling algorithms that do not require |
| 456 | # auxiliary memory, but they were rejected because they made |
| 457 | # too many calls to _randbelow(), making them slower and |
| 458 | # causing them to eat more entropy than necessary. |
| 459 | |
Raymond Hettinger | 57d1a88 | 2011-02-23 00:46:28 +0000 | [diff] [blame] | 460 | if not isinstance(population, _Sequence): |
masklinn | 1e27b57 | 2020-12-19 05:33:36 +0100 | [diff] [blame] | 461 | if isinstance(population, _Set): |
| 462 | _warn('Sampling from a set deprecated\n' |
| 463 | 'since Python 3.9 and will be removed in a subsequent version.', |
| 464 | DeprecationWarning, 2) |
| 465 | population = tuple(population) |
| 466 | else: |
| 467 | raise TypeError("Population must be a sequence. For dicts or sets, use sorted(d).") |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 468 | n = len(population) |
Raymond Hettinger | 81a5fc3 | 2020-05-08 07:53:15 -0700 | [diff] [blame] | 469 | if counts is not None: |
| 470 | cum_counts = list(_accumulate(counts)) |
| 471 | if len(cum_counts) != n: |
| 472 | raise ValueError('The number of counts does not match the population') |
| 473 | total = cum_counts.pop() |
| 474 | if not isinstance(total, int): |
| 475 | raise TypeError('Counts must be integers') |
| 476 | if total <= 0: |
| 477 | raise ValueError('Total of counts must be greater than zero') |
jonanifranco | f7b5bacd | 2021-01-18 19:04:29 +0100 | [diff] [blame] | 478 | selections = self.sample(range(total), k=k) |
Raymond Hettinger | 81a5fc3 | 2020-05-08 07:53:15 -0700 | [diff] [blame] | 479 | bisect = _bisect |
| 480 | return [population[bisect(cum_counts, s)] for s in selections] |
| 481 | randbelow = self._randbelow |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 482 | if not 0 <= k <= n: |
Raymond Hettinger | bf87126 | 2016-11-21 14:34:33 -0800 | [diff] [blame] | 483 | raise ValueError("Sample larger than population or is negative") |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 484 | result = [None] * k |
Raymond Hettinger | 91e27c2 | 2005-08-19 01:36:35 +0000 | [diff] [blame] | 485 | setsize = 21 # size of a small set minus size of an empty list |
| 486 | if k > 5: |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 487 | setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 488 | if n <= setsize: |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 489 | # An n-length list is smaller than a k-length set. |
| 490 | # Invariant: non-selected at pool[0 : n-i] |
Raymond Hettinger | 311f419 | 2002-11-18 09:01:24 +0000 | [diff] [blame] | 491 | pool = list(population) |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 492 | for i in range(k): |
| 493 | j = randbelow(n - i) |
Raymond Hettinger | 311f419 | 2002-11-18 09:01:24 +0000 | [diff] [blame] | 494 | result[i] = pool[j] |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 495 | pool[j] = pool[n - i - 1] # move non-selected item into vacancy |
Raymond Hettinger | c0b4034 | 2002-11-13 15:26:37 +0000 | [diff] [blame] | 496 | else: |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 497 | selected = set() |
| 498 | selected_add = selected.add |
| 499 | for i in range(k): |
Raymond Hettinger | 05a505f | 2010-09-07 19:19:33 +0000 | [diff] [blame] | 500 | j = randbelow(n) |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 501 | while j in selected: |
Raymond Hettinger | 05a505f | 2010-09-07 19:19:33 +0000 | [diff] [blame] | 502 | j = randbelow(n) |
Raymond Hettinger | 1acde19 | 2008-01-14 01:00:53 +0000 | [diff] [blame] | 503 | selected_add(j) |
| 504 | result[i] = population[j] |
Raymond Hettinger | 311f419 | 2002-11-18 09:01:24 +0000 | [diff] [blame] | 505 | return result |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 506 | |
Raymond Hettinger | 9016f28 | 2016-09-26 21:45:57 -0700 | [diff] [blame] | 507 | def choices(self, population, weights=None, *, cum_weights=None, k=1): |
Raymond Hettinger | e8f1e00 | 2016-09-06 17:15:29 -0700 | [diff] [blame] | 508 | """Return a k sized list of population elements chosen with replacement. |
| 509 | |
| 510 | If the relative weights or cumulative weights are not specified, |
| 511 | the selections are made with equal probability. |
| 512 | |
| 513 | """ |
Raymond Hettinger | 30d00e5 | 2016-10-29 16:55:36 -0700 | [diff] [blame] | 514 | random = self.random |
Raymond Hettinger | e69cd16 | 2018-07-04 15:28:20 -0700 | [diff] [blame] | 515 | n = len(population) |
Raymond Hettinger | e8f1e00 | 2016-09-06 17:15:29 -0700 | [diff] [blame] | 516 | if cum_weights is None: |
| 517 | if weights is None: |
Raymond Hettinger | 26a1ad1 | 2020-06-22 19:38:59 -0700 | [diff] [blame] | 518 | floor = _floor |
Raymond Hettinger | 0a18e05 | 2018-11-09 02:39:50 -0800 | [diff] [blame] | 519 | n += 0.0 # convert to float for a small speed improvement |
Raymond Hettinger | 26a1ad1 | 2020-06-22 19:38:59 -0700 | [diff] [blame] | 520 | return [population[floor(random() * n)] for i in _repeat(None, k)] |
Raymond Hettinger | cfd31f0 | 2019-02-13 02:04:17 -0800 | [diff] [blame] | 521 | cum_weights = list(_accumulate(weights)) |
Raymond Hettinger | e8f1e00 | 2016-09-06 17:15:29 -0700 | [diff] [blame] | 522 | elif weights is not None: |
Raymond Hettinger | 24e4239 | 2016-11-13 00:42:56 -0500 | [diff] [blame] | 523 | raise TypeError('Cannot specify both weights and cumulative weights') |
Raymond Hettinger | e69cd16 | 2018-07-04 15:28:20 -0700 | [diff] [blame] | 524 | if len(cum_weights) != n: |
Raymond Hettinger | e8f1e00 | 2016-09-06 17:15:29 -0700 | [diff] [blame] | 525 | raise ValueError('The number of weights does not match the population') |
Raymond Hettinger | 0a18e05 | 2018-11-09 02:39:50 -0800 | [diff] [blame] | 526 | total = cum_weights[-1] + 0.0 # convert to float |
Raymond Hettinger | 041d8b4 | 2019-11-23 02:22:13 -0800 | [diff] [blame] | 527 | if total <= 0.0: |
| 528 | raise ValueError('Total of weights must be greater than zero') |
Ram Rachum | b0dfc75 | 2020-09-29 04:32:10 +0300 | [diff] [blame] | 529 | if not _isfinite(total): |
| 530 | raise ValueError('Total of weights must be finite') |
Raymond Hettinger | 041d8b4 | 2019-11-23 02:22:13 -0800 | [diff] [blame] | 531 | bisect = _bisect |
Raymond Hettinger | e69cd16 | 2018-07-04 15:28:20 -0700 | [diff] [blame] | 532 | hi = n - 1 |
Raymond Hettinger | ddf7171 | 2018-06-27 01:08:31 -0700 | [diff] [blame] | 533 | return [population[bisect(cum_weights, random() * total, 0, hi)] |
Raymond Hettinger | 5382203 | 2019-02-16 13:30:51 -0800 | [diff] [blame] | 534 | for i in _repeat(None, k)] |
Raymond Hettinger | e8f1e00 | 2016-09-06 17:15:29 -0700 | [diff] [blame] | 535 | |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 536 | |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 537 | ## -------------------- real-valued distributions ------------------- |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 538 | |
| 539 | def uniform(self, a, b): |
Raymond Hettinger | be40db0 | 2009-06-11 23:12:14 +0000 | [diff] [blame] | 540 | "Get a random number in the range [a, b) or [a, b] depending on rounding." |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 541 | return a + (b - a) * self.random() |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 542 | |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 543 | def triangular(self, low=0.0, high=1.0, mode=None): |
| 544 | """Triangular distribution. |
| 545 | |
| 546 | Continuous distribution bounded by given lower and upper limits, |
| 547 | and having a given mode value in-between. |
| 548 | |
| 549 | http://en.wikipedia.org/wiki/Triangular_distribution |
| 550 | |
| 551 | """ |
| 552 | u = self.random() |
Raymond Hettinger | 978c6ab | 2014-05-25 17:25:27 -0700 | [diff] [blame] | 553 | try: |
| 554 | c = 0.5 if mode is None else (mode - low) / (high - low) |
| 555 | except ZeroDivisionError: |
| 556 | return low |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 557 | if u > c: |
| 558 | u = 1.0 - u |
| 559 | c = 1.0 - c |
| 560 | low, high = high, low |
Raymond Hettinger | f5ea83f | 2017-09-04 16:51:06 -0700 | [diff] [blame] | 561 | return low + (high - low) * _sqrt(u * c) |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 562 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 563 | def normalvariate(self, mu, sigma): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 564 | """Normal distribution. |
| 565 | |
| 566 | mu is the mean, and sigma is the standard deviation. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 567 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 568 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 569 | # Uses Kinderman and Monahan method. Reference: Kinderman, |
| 570 | # A.J. and Monahan, J.F., "Computer generation of random |
| 571 | # variables using the ratio of uniform deviates", ACM Trans |
| 572 | # Math Software, 3, (1977), pp257-260. |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 573 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 574 | random = self.random |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 575 | while True: |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 576 | u1 = random() |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 577 | u2 = 1.0 - random() |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 578 | z = NV_MAGICCONST * (u1 - 0.5) / u2 |
| 579 | zz = z * z / 4.0 |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 580 | if zz <= -_log(u2): |
| 581 | break |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 582 | return mu + z * sigma |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 583 | |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 584 | def gauss(self, mu, sigma): |
| 585 | """Gaussian distribution. |
| 586 | |
| 587 | mu is the mean, and sigma is the standard deviation. This is |
| 588 | slightly faster than the normalvariate() function. |
| 589 | |
| 590 | Not thread-safe without a lock around calls. |
| 591 | |
| 592 | """ |
| 593 | # When x and y are two variables from [0, 1), uniformly |
| 594 | # distributed, then |
| 595 | # |
| 596 | # cos(2*pi*x)*sqrt(-2*log(1-y)) |
| 597 | # sin(2*pi*x)*sqrt(-2*log(1-y)) |
| 598 | # |
| 599 | # are two *independent* variables with normal distribution |
| 600 | # (mu = 0, sigma = 1). |
| 601 | # (Lambert Meertens) |
| 602 | # (corrected version; bug discovered by Mike Miller, fixed by LM) |
| 603 | |
| 604 | # Multithreading note: When two threads call this function |
| 605 | # simultaneously, it is possible that they will receive the |
| 606 | # same return value. The window is very small though. To |
| 607 | # avoid this, you have to use a lock around all calls. (I |
| 608 | # didn't want to slow this down in the serial case by using a |
| 609 | # lock here.) |
| 610 | |
| 611 | random = self.random |
| 612 | z = self.gauss_next |
| 613 | self.gauss_next = None |
| 614 | if z is None: |
| 615 | x2pi = random() * TWOPI |
| 616 | g2rad = _sqrt(-2.0 * _log(1.0 - random())) |
| 617 | z = _cos(x2pi) * g2rad |
| 618 | self.gauss_next = _sin(x2pi) * g2rad |
| 619 | |
| 620 | return mu + z * sigma |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 621 | |
| 622 | def lognormvariate(self, mu, sigma): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 623 | """Log normal distribution. |
| 624 | |
| 625 | If you take the natural logarithm of this distribution, you'll get a |
| 626 | normal distribution with mean mu and standard deviation sigma. |
| 627 | mu can have any value, and sigma must be greater than zero. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 628 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 629 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 630 | return _exp(self.normalvariate(mu, sigma)) |
| 631 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 632 | def expovariate(self, lambd): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 633 | """Exponential distribution. |
| 634 | |
Mark Dickinson | 2f94736 | 2009-01-07 17:54:07 +0000 | [diff] [blame] | 635 | lambd is 1.0 divided by the desired mean. It should be |
| 636 | nonzero. (The parameter would be called "lambda", but that is |
| 637 | a reserved word in Python.) Returned values range from 0 to |
| 638 | positive infinity if lambd is positive, and from negative |
| 639 | infinity to 0 if lambd is negative. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 640 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 641 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 642 | # lambd: rate lambd = 1/mean |
| 643 | # ('lambda' is a Python reserved word) |
| 644 | |
Raymond Hettinger | 5279fb9 | 2011-06-25 11:30:53 +0200 | [diff] [blame] | 645 | # we use 1-random() instead of random() to preclude the |
| 646 | # possibility of taking the log of zero. |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 647 | return -_log(1.0 - self.random()) / lambd |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 648 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 649 | def vonmisesvariate(self, mu, kappa): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 650 | """Circular data distribution. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 651 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 652 | mu is the mean angle, expressed in radians between 0 and 2*pi, and |
| 653 | kappa is the concentration parameter, which must be greater than or |
| 654 | equal to zero. If kappa is equal to zero, this distribution reduces |
| 655 | to a uniform random angle over the range 0 to 2*pi. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 656 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 657 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 658 | # Based upon an algorithm published in: Fisher, N.I., |
| 659 | # "Statistical Analysis of Circular Data", Cambridge |
| 660 | # University Press, 1993. |
| 661 | |
| 662 | # Thanks to Magnus Kessler for a correction to the |
| 663 | # implementation of step 4. |
| 664 | |
| 665 | random = self.random |
| 666 | if kappa <= 1e-6: |
| 667 | return TWOPI * random() |
| 668 | |
Serhiy Storchaka | 6c22b1d | 2013-02-10 19:28:56 +0200 | [diff] [blame] | 669 | s = 0.5 / kappa |
| 670 | r = s + _sqrt(1.0 + s * s) |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 671 | |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 672 | while True: |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 673 | u1 = random() |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 674 | z = _cos(_pi * u1) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 675 | |
Serhiy Storchaka | 6c22b1d | 2013-02-10 19:28:56 +0200 | [diff] [blame] | 676 | d = z / (r + z) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 677 | u2 = random() |
Serhiy Storchaka | 6c22b1d | 2013-02-10 19:28:56 +0200 | [diff] [blame] | 678 | if u2 < 1.0 - d * d or u2 <= (1.0 - d) * _exp(d): |
Tim Peters | 0c9886d | 2001-01-15 01:18:21 +0000 | [diff] [blame] | 679 | break |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 680 | |
Serhiy Storchaka | 6c22b1d | 2013-02-10 19:28:56 +0200 | [diff] [blame] | 681 | q = 1.0 / r |
| 682 | f = (q + z) / (1.0 + q * z) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 683 | u3 = random() |
| 684 | if u3 > 0.5: |
Mark Dickinson | be5f919 | 2013-02-10 14:16:10 +0000 | [diff] [blame] | 685 | theta = (mu + _acos(f)) % TWOPI |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 686 | else: |
Mark Dickinson | be5f919 | 2013-02-10 14:16:10 +0000 | [diff] [blame] | 687 | theta = (mu - _acos(f)) % TWOPI |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 688 | |
| 689 | return theta |
| 690 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 691 | def gammavariate(self, alpha, beta): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 692 | """Gamma distribution. Not the gamma function! |
| 693 | |
| 694 | Conditions on the parameters are alpha > 0 and beta > 0. |
| 695 | |
Raymond Hettinger | a8e4d6e | 2011-03-22 15:55:51 -0700 | [diff] [blame] | 696 | The probability distribution function is: |
| 697 | |
| 698 | x ** (alpha - 1) * math.exp(-x / beta) |
| 699 | pdf(x) = -------------------------------------- |
| 700 | math.gamma(alpha) * beta ** alpha |
| 701 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 702 | """ |
Raymond Hettinger | b760efb | 2002-05-14 06:40:34 +0000 | [diff] [blame] | 703 | # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 |
Tim Peters | 8ac1495 | 2002-05-23 15:15:30 +0000 | [diff] [blame] | 704 | |
Guido van Rossum | 570764d | 2002-05-14 14:08:12 +0000 | [diff] [blame] | 705 | # Warning: a few older sources define the gamma distribution in terms |
| 706 | # of alpha > -1.0 |
| 707 | if alpha <= 0.0 or beta <= 0.0: |
Collin Winter | ce36ad8 | 2007-08-30 01:19:48 +0000 | [diff] [blame] | 708 | raise ValueError('gammavariate: alpha and beta must be > 0.0') |
Tim Peters | 8ac1495 | 2002-05-23 15:15:30 +0000 | [diff] [blame] | 709 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 710 | random = self.random |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 711 | if alpha > 1.0: |
| 712 | |
| 713 | # Uses R.C.H. Cheng, "The generation of Gamma |
| 714 | # variables with non-integral shape parameters", |
| 715 | # Applied Statistics, (1977), 26, No. 1, p71-74 |
| 716 | |
Raymond Hettinger | ca6cdc2 | 2002-05-13 23:40:14 +0000 | [diff] [blame] | 717 | ainv = _sqrt(2.0 * alpha - 1.0) |
| 718 | bbb = alpha - LOG4 |
| 719 | ccc = alpha + ainv |
Tim Peters | 8ac1495 | 2002-05-23 15:15:30 +0000 | [diff] [blame] | 720 | |
Raymond Hettinger | 6a613f9 | 2020-08-02 12:03:32 -0700 | [diff] [blame] | 721 | while True: |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 722 | u1 = random() |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 723 | if not 1e-7 < u1 < 0.9999999: |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 724 | continue |
| 725 | u2 = 1.0 - random() |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 726 | v = _log(u1 / (1.0 - u1)) / ainv |
| 727 | x = alpha * _exp(v) |
| 728 | z = u1 * u1 * u2 |
| 729 | r = bbb + ccc * v - x |
| 730 | if r + SG_MAGICCONST - 4.5 * z >= 0.0 or r >= _log(z): |
Raymond Hettinger | b760efb | 2002-05-14 06:40:34 +0000 | [diff] [blame] | 731 | return x * beta |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 732 | |
| 733 | elif alpha == 1.0: |
leodema | 9f396b6 | 2017-06-04 07:41:41 +0100 | [diff] [blame] | 734 | # expovariate(1/beta) |
leodema | 63d1522 | 2018-12-24 07:54:25 +0100 | [diff] [blame] | 735 | return -_log(1.0 - random()) * beta |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 736 | |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 737 | else: |
| 738 | # alpha is between 0 and 1 (exclusive) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 739 | # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 740 | while True: |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 741 | u = random() |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 742 | b = (_e + alpha) / _e |
| 743 | p = b * u |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 744 | if p <= 1.0: |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 745 | x = p ** (1.0 / alpha) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 746 | else: |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 747 | x = -_log((b - p) / alpha) |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 748 | u1 = random() |
Raymond Hettinger | 42406e6 | 2005-04-30 09:02:51 +0000 | [diff] [blame] | 749 | if p > 1.0: |
| 750 | if u1 <= x ** (alpha - 1.0): |
| 751 | break |
| 752 | elif u1 <= _exp(-x): |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 753 | break |
Raymond Hettinger | b760efb | 2002-05-14 06:40:34 +0000 | [diff] [blame] | 754 | return x * beta |
| 755 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 756 | def betavariate(self, alpha, beta): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 757 | """Beta distribution. |
| 758 | |
Thomas Wouters | b213704 | 2007-02-01 18:02:27 +0000 | [diff] [blame] | 759 | Conditions on the parameters are alpha > 0 and beta > 0. |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 760 | Returned values range between 0 and 1. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 761 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 762 | """ |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 763 | ## See |
| 764 | ## http://mail.python.org/pipermail/python-bugs-list/2001-January/003752.html |
| 765 | ## for Ivan Frohne's insightful analysis of why the original implementation: |
| 766 | ## |
| 767 | ## def betavariate(self, alpha, beta): |
| 768 | ## # Discrete Event Simulation in C, pp 87-88. |
| 769 | ## |
| 770 | ## y = self.expovariate(alpha) |
| 771 | ## z = self.expovariate(1.0/beta) |
| 772 | ## return z/(y+z) |
| 773 | ## |
| 774 | ## was dead wrong, and how it probably got that way. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 775 | |
Tim Peters | 85e2e47 | 2001-01-26 06:49:56 +0000 | [diff] [blame] | 776 | # This version due to Janne Sinkkonen, and matches all the std |
| 777 | # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). |
Raymond Hettinger | 650c1c9 | 2016-06-25 05:36:42 +0300 | [diff] [blame] | 778 | y = self.gammavariate(alpha, 1.0) |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 779 | if y: |
Raymond Hettinger | 650c1c9 | 2016-06-25 05:36:42 +0300 | [diff] [blame] | 780 | return y / (y + self.gammavariate(beta, 1.0)) |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 781 | return 0.0 |
Guido van Rossum | 95bfcda | 1994-03-09 14:21:05 +0000 | [diff] [blame] | 782 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 783 | def paretovariate(self, alpha): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 784 | """Pareto distribution. alpha is the shape parameter.""" |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 785 | # Jain, pg. 495 |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 786 | |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 787 | u = 1.0 - self.random() |
Raymond Hettinger | 5c32709 | 2020-08-01 01:18:26 -0700 | [diff] [blame] | 788 | return u ** (-1.0 / alpha) |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 789 | |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 790 | def weibullvariate(self, alpha, beta): |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 791 | """Weibull distribution. |
| 792 | |
| 793 | alpha is the scale parameter and beta is the shape parameter. |
Raymond Hettinger | ef4d4bd | 2002-05-23 23:58:17 +0000 | [diff] [blame] | 794 | |
Raymond Hettinger | c32f033 | 2002-05-23 19:44:49 +0000 | [diff] [blame] | 795 | """ |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 796 | # Jain, pg. 499; bug fix courtesy Bill Arms |
Guido van Rossum | cf4559a | 1997-12-02 02:47:39 +0000 | [diff] [blame] | 797 | |
Raymond Hettinger | 73ced7e | 2003-01-04 09:26:32 +0000 | [diff] [blame] | 798 | u = 1.0 - self.random() |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 799 | return alpha * (-_log(u)) ** (1.0 / beta) |
| 800 | |
Guido van Rossum | 6c395ba | 1999-08-18 13:53:28 +0000 | [diff] [blame] | 801 | |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 802 | ## ------------------------------------------------------------------ |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 803 | ## --------------- Operating System Random Source ------------------ |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 804 | |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 805 | |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 806 | class SystemRandom(Random): |
| 807 | """Alternate random number generator using sources provided |
| 808 | by the operating system (such as /dev/urandom on Unix or |
| 809 | CryptGenRandom on Windows). |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 810 | |
| 811 | Not available on all systems (see os.urandom() for details). |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 812 | |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 813 | """ |
| 814 | |
| 815 | def random(self): |
| 816 | """Get the next random number in the range [0.0, 1.0).""" |
Raymond Hettinger | 183cd1f | 2010-09-08 18:48:21 +0000 | [diff] [blame] | 817 | return (int.from_bytes(_urandom(7), 'big') >> 3) * RECIP_BPF |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 818 | |
| 819 | def getrandbits(self, k): |
Serhiy Storchaka | 9594942 | 2013-08-27 19:40:23 +0300 | [diff] [blame] | 820 | """getrandbits(k) -> x. Generates an int with k random bits.""" |
Antoine Pitrou | 75a3378 | 2020-04-17 19:32:14 +0200 | [diff] [blame] | 821 | if k < 0: |
| 822 | raise ValueError('number of bits must be non-negative') |
Raymond Hettinger | 63b1767 | 2010-09-08 19:27:59 +0000 | [diff] [blame] | 823 | numbytes = (k + 7) // 8 # bits / 8 and rounded up |
| 824 | x = int.from_bytes(_urandom(numbytes), 'big') |
| 825 | return x >> (numbytes * 8 - k) # trim excess bits |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 826 | |
Victor Stinner | 9f5fe79 | 2020-04-17 19:05:35 +0200 | [diff] [blame] | 827 | def randbytes(self, n): |
| 828 | """Generate n random bytes.""" |
| 829 | # os.urandom(n) fails with ValueError for n < 0 |
| 830 | # and returns an empty bytes string for n == 0. |
| 831 | return _urandom(n) |
| 832 | |
Raymond Hettinger | 28de64f | 2008-01-13 23:40:30 +0000 | [diff] [blame] | 833 | def seed(self, *args, **kwds): |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 834 | "Stub method. Not used for a system random number generator." |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 835 | return None |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 836 | |
| 837 | def _notimplemented(self, *args, **kwds): |
Raymond Hettinger | 23f1241 | 2004-09-13 22:23:21 +0000 | [diff] [blame] | 838 | "Method should not be called for a system random number generator." |
| 839 | raise NotImplementedError('System entropy source does not have state.') |
Raymond Hettinger | 356a459 | 2004-08-30 06:14:31 +0000 | [diff] [blame] | 840 | getstate = setstate = _notimplemented |
| 841 | |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 842 | |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 843 | # ---------------------------------------------------------------------- |
| 844 | # Create one instance, seeded from current time, and export its methods |
| 845 | # as module-level functions. The functions share state across all uses |
| 846 | # (both in the user's code and in the Python libraries), but that's fine |
| 847 | # for most programs and is easier for the casual user than making them |
| 848 | # instantiate their own Random() instance. |
| 849 | |
| 850 | _inst = Random() |
| 851 | seed = _inst.seed |
| 852 | random = _inst.random |
| 853 | uniform = _inst.uniform |
| 854 | triangular = _inst.triangular |
| 855 | randint = _inst.randint |
| 856 | choice = _inst.choice |
| 857 | randrange = _inst.randrange |
| 858 | sample = _inst.sample |
| 859 | shuffle = _inst.shuffle |
| 860 | choices = _inst.choices |
| 861 | normalvariate = _inst.normalvariate |
| 862 | lognormvariate = _inst.lognormvariate |
| 863 | expovariate = _inst.expovariate |
| 864 | vonmisesvariate = _inst.vonmisesvariate |
| 865 | gammavariate = _inst.gammavariate |
| 866 | gauss = _inst.gauss |
| 867 | betavariate = _inst.betavariate |
| 868 | paretovariate = _inst.paretovariate |
| 869 | weibullvariate = _inst.weibullvariate |
| 870 | getstate = _inst.getstate |
| 871 | setstate = _inst.setstate |
| 872 | getrandbits = _inst.getrandbits |
| 873 | randbytes = _inst.randbytes |
| 874 | |
| 875 | |
| 876 | ## ------------------------------------------------------ |
| 877 | ## ----------------- test program ----------------------- |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 878 | |
Raymond Hettinger | 6229713 | 2003-08-30 01:24:19 +0000 | [diff] [blame] | 879 | def _test_generator(n, func, args): |
Raymond Hettinger | 26a1ad1 | 2020-06-22 19:38:59 -0700 | [diff] [blame] | 880 | from statistics import stdev, fmean as mean |
| 881 | from time import perf_counter |
| 882 | |
| 883 | t0 = perf_counter() |
| 884 | data = [func(*args) for i in range(n)] |
| 885 | t1 = perf_counter() |
| 886 | |
| 887 | xbar = mean(data) |
| 888 | sigma = stdev(data, xbar) |
| 889 | low = min(data) |
| 890 | high = max(data) |
| 891 | |
| 892 | print(f'{t1 - t0:.3f} sec, {n} times {func.__name__}') |
| 893 | print('avg %g, stddev %g, min %g, max %g\n' % (xbar, sigma, low, high)) |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 894 | |
Raymond Hettinger | f24eb35 | 2002-11-12 17:41:57 +0000 | [diff] [blame] | 895 | |
| 896 | def _test(N=2000): |
Raymond Hettinger | 6229713 | 2003-08-30 01:24:19 +0000 | [diff] [blame] | 897 | _test_generator(N, random, ()) |
| 898 | _test_generator(N, normalvariate, (0.0, 1.0)) |
| 899 | _test_generator(N, lognormvariate, (0.0, 1.0)) |
| 900 | _test_generator(N, vonmisesvariate, (0.0, 1.0)) |
| 901 | _test_generator(N, gammavariate, (0.01, 1.0)) |
| 902 | _test_generator(N, gammavariate, (0.1, 1.0)) |
| 903 | _test_generator(N, gammavariate, (0.1, 2.0)) |
| 904 | _test_generator(N, gammavariate, (0.5, 1.0)) |
| 905 | _test_generator(N, gammavariate, (0.9, 1.0)) |
| 906 | _test_generator(N, gammavariate, (1.0, 1.0)) |
| 907 | _test_generator(N, gammavariate, (2.0, 1.0)) |
| 908 | _test_generator(N, gammavariate, (20.0, 1.0)) |
| 909 | _test_generator(N, gammavariate, (200.0, 1.0)) |
| 910 | _test_generator(N, gauss, (0.0, 1.0)) |
| 911 | _test_generator(N, betavariate, (3.0, 3.0)) |
Raymond Hettinger | 9db5b8d | 2020-06-13 09:46:47 -0700 | [diff] [blame] | 912 | _test_generator(N, triangular, (0.0, 1.0, 1.0 / 3.0)) |
Tim Peters | cd80410 | 2001-01-25 20:25:57 +0000 | [diff] [blame] | 913 | |
Raymond Hettinger | 40f6217 | 2002-12-29 23:03:38 +0000 | [diff] [blame] | 914 | |
Raymond Hettinger | ef19bad | 2020-06-25 17:03:50 -0700 | [diff] [blame] | 915 | ## ------------------------------------------------------ |
| 916 | ## ------------------ fork support --------------------- |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 917 | |
Antoine Pitrou | 346cbd3 | 2017-05-27 17:50:54 +0200 | [diff] [blame] | 918 | if hasattr(_os, "fork"): |
Gregory P. Smith | 163468a | 2017-05-29 10:03:41 -0700 | [diff] [blame] | 919 | _os.register_at_fork(after_in_child=_inst.seed) |
Antoine Pitrou | 346cbd3 | 2017-05-27 17:50:54 +0200 | [diff] [blame] | 920 | |
| 921 | |
Guido van Rossum | ff03b1a | 1994-03-09 12:55:02 +0000 | [diff] [blame] | 922 | if __name__ == '__main__': |
Tim Peters | d7b5e88 | 2001-01-25 03:36:26 +0000 | [diff] [blame] | 923 | _test() |