random.py revision f2eb2b44fc532c77c03bc95789817a20d7c558c3
1e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum"""Random variable generators. 2e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum 3d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters integers 4d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters -------- 5d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters uniform within range 6d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 7d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters sequences 8d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters --------- 9d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters pick random element 10f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger pick random sample 11d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters generate random permutation 12d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 13e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum distributions on the real line: 14e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum ------------------------------ 15d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters uniform 16bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger triangular 17e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum normal (Gaussian) 18e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum lognormal 19e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum negative exponential 20e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum gamma 21e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum beta 2240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger pareto 2340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Weibull 24e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum 25e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum distributions on the circle (angles 0 to 2pi) 26e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum --------------------------------------------- 27e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum circular uniform 28e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum von Mises 29e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum 3040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond HettingerGeneral notes on the underlying Mersenne Twister core generator: 3140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 3240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger* The period is 2**19937-1. 330e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters* It is one of the most extensively tested generators in existence. 340e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters* Without a direct way to compute N steps forward, the semantics of 350e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters jumpahead(n) are weakened to simply jump to another distant state and rely 360e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters on the large period to avoid overlapping sequences. 370e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters* The random() method is implemented in C, executes in a single Python step, 380e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters and is, therefore, threadsafe. 3940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 40e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum""" 41d03e1197cb5052e3f758794e2a7aecf9f5ca5f46Guido van Rossum 42c4f7bab0a0cd208bcab3c4f6cd8324ed8d08f98eRaymond Hettingerfrom __future__ import division 432f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettingerfrom warnings import warn as _warn 442f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettingerfrom types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType 4591e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettingerfrom math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil 46d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersfrom math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin 47c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettingerfrom os import urandom as _urandom 48c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettingerfrom binascii import hexlify as _hexlify 49d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 50f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger__all__ = ["Random","seed","random","uniform","randint","choice","sample", 510de65807e6bdc5254f5a7e99b2f39adeea6b883bSkip Montanaro "randrange","shuffle","normalvariate","lognormvariate", 52bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger "expovariate","vonmisesvariate","gammavariate","triangular", 53f8a52d38ad784b34a60720cb148180d6eb6de373Raymond Hettinger "gauss","betavariate","paretovariate","weibullvariate", 54356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger "getstate","setstate","jumpahead", "WichmannHill", "getrandbits", 5523f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "SystemRandom"] 56ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 57d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersNV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0) 58d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersTWOPI = 2.0*_pi 59d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersLOG4 = _log(4.0) 60d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersSG_MAGICCONST = 1.0 + _log(4.5) 612f726e9093381572b21edbfc42659ea89fbdf686Raymond HettingerBPF = 53 # Number of bits in a float 627c2a85b2d44851c2442ade579b760f86447bf848Tim PetersRECIP_BPF = 2**-BPF 6333d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 64356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 65d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters# Translated by Guido van Rossum from C source provided by 6640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# Adrian Baddeley. Adapted by Raymond Hettinger for use with 673fa19d7ff89be87139e2864fb9186b424d180a58Raymond Hettinger# the Mersenne Twister and os.urandom() core generators. 6833d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 69145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettingerimport _random 7040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 71145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettingerclass Random(_random.Random): 72c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Random number generator base class used by bound module functions. 73c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 74c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Used to instantiate instances of Random to get generators that don't 75c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger share state. Especially useful for multi-threaded programs, creating 76c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger a different instance of Random for each thread, and using the jumpahead() 77c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger method to ensure that the generated sequences seen by each thread don't 78c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger overlap. 79c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 80c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Class Random can also be subclassed if you want to use a different basic 81c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger generator of your own devising: in that case, override the following 82f2eb2b44fc532c77c03bc95789817a20d7c558c3Benjamin Peterson methods: random(), seed(), getstate(), setstate() and jumpahead(). 83f2eb2b44fc532c77c03bc95789817a20d7c558c3Benjamin Peterson Optionally, implement a getrandbits() method so that randrange() can cover 84f2eb2b44fc532c77c03bc95789817a20d7c558c3Benjamin Peterson arbitrarily large ranges. 85ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 86c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 8733d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 886b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis VERSION = 3 # used by getstate/setstate 8933d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 90d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def __init__(self, x=None): 91d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Initialize an instance. 9233d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 93d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters Optional argument x controls seeding, as for Random.seed(). 94d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 9533d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 96d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.seed(x) 9740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 98ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 990de88fc4b108751b86443852b6741680d704168fTim Peters def seed(self, a=None): 1000de88fc4b108751b86443852b6741680d704168fTim Peters """Initialize internal state from hashable object. 101d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 10223f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger None or no argument seeds from current time or from an operating 10323f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger system specific randomness source if available. 1040de88fc4b108751b86443852b6741680d704168fTim Peters 105bcd725fc456faca13f4598f87c0517f917711cdaTim Peters If a is not None or an int or long, hash(a) is used instead. 106d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 107d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 1083081d59f920229b26293c7a3ee3f1a9da0da53e9Raymond Hettinger if a is None: 109c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger try: 110c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger a = long(_hexlify(_urandom(16)), 16) 111c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger except NotImplementedError: 112356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger import time 113356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger a = long(time.time() * 256) # use fractional seconds 114356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 115145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger super(Random, self).seed(a) 11646c04e140cf26d1b44935c28c6f15ea467400d22Tim Peters self.gauss_next = None 11746c04e140cf26d1b44935c28c6f15ea467400d22Tim Peters 118d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def getstate(self): 119d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Return internal state; can be passed to setstate() later.""" 120145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger return self.VERSION, super(Random, self).getstate(), self.gauss_next 121d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 122d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def setstate(self, state): 123d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Restore internal state from object returned by getstate().""" 124d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters version = state[0] 1256b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis if version == 3: 12640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version, internalstate, self.gauss_next = state 127145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger super(Random, self).setstate(internalstate) 1286b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis elif version == 2: 1296b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis version, internalstate, self.gauss_next = state 1306b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # In version 2, the state was saved as signed ints, which causes 1316b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # inconsistencies between 32/64-bit systems. The state is 1326b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # really unsigned 32-bit ints, so we convert negative ints from 1336b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # version 2 to positive longs for version 3. 1346b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis try: 1356b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis internalstate = tuple( long(x) % (2**32) for x in internalstate ) 1366b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis except ValueError, e: 1376b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis raise TypeError, e 1386b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis super(Random, self).setstate(internalstate) 139d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 140d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError("state with version %s passed to " 141d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters "Random.setstate() of version %s" % 142d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters (version, self.VERSION)) 143d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 144cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## ---- Methods below this point do not need to be overridden when 145cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## ---- subclassing for the purpose of using a different core generator. 146d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 147cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- pickle support ------------------- 148d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 149cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters def __getstate__(self): # for pickle 150cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters return self.getstate() 151d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 152cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters def __setstate__(self, state): # for pickle 153cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters self.setstate(state) 154cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 1555f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger def __reduce__(self): 1565f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger return self.__class__, (), self.getstate() 1575f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger 158cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- integer methods ------------------- 159d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 1602f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger def randrange(self, start, stop=None, step=1, int=int, default=None, 1612f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger maxwidth=1L<<BPF): 162d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Choose a random item from range(start, stop[, step]). 163d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 164d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters This fixes the problem with randint() which includes the 165d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters endpoint; in Python this is usually not what you want. 1662f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger Do not supply the 'int', 'default', and 'maxwidth' arguments. 167d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 168d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 169d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # This code is a bit messy to make it fast for the 1709146f27b7799dab231083f194a14c6157b57549fTim Peters # common case while still doing adequate error checking. 171d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters istart = int(start) 172d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istart != start: 173d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer arg 1 for randrange()" 174d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if stop is default: 175d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istart > 0: 1762f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if istart >= maxwidth: 1772f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return self._randbelow(istart) 178d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return int(self.random() * istart) 179d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "empty range for randrange()" 1809146f27b7799dab231083f194a14c6157b57549fTim Peters 1819146f27b7799dab231083f194a14c6157b57549fTim Peters # stop argument supplied. 182d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters istop = int(stop) 183d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istop != stop: 184d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer stop for randrange()" 1852f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger width = istop - istart 1862f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if step == 1 and width > 0: 18776ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # Note that 1882f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # int(istart + self.random()*width) 18976ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # instead would be incorrect. For example, consider istart 19076ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # = -2 and istop = 0. Then the guts would be in 19176ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # -2.0 to 0.0 exclusive on both ends (ignoring that random() 19276ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # might return 0.0), and because int() truncates toward 0, the 19376ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # final result would be -1 or 0 (instead of -2 or -1). 1942f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # istart + int(self.random()*width) 19576ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # would also be incorrect, for a subtler reason: the RHS 19676ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # can return a long, and then randrange() would also return 19776ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # a long, but we're supposed to return an int (for backward 19876ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # compatibility). 1992f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2002f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if width >= maxwidth: 20158eb11cf62dd04ccc2c364b62fd51b4265e2e203Tim Peters return int(istart + self._randbelow(width)) 2022f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return int(istart + int(self.random()*width)) 203d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if step == 1: 2042f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger raise ValueError, "empty range for randrange() (%d,%d, %d)" % (istart, istop, width) 2059146f27b7799dab231083f194a14c6157b57549fTim Peters 2069146f27b7799dab231083f194a14c6157b57549fTim Peters # Non-unit step argument supplied. 207d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters istep = int(step) 208d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istep != step: 209d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer step for randrange()" 210d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istep > 0: 211ffdb8bb99c4017152a9dca70669f9d6b9831d454Raymond Hettinger n = (width + istep - 1) // istep 212d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters elif istep < 0: 213ffdb8bb99c4017152a9dca70669f9d6b9831d454Raymond Hettinger n = (width + istep + 1) // istep 214d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 215d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "zero step for randrange()" 216d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 217d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if n <= 0: 218d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "empty range for randrange()" 2192f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2202f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if n >= maxwidth: 22194547f7646895e032f8fc145529d9efc3a70760dRaymond Hettinger return istart + istep*self._randbelow(n) 222d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return istart + istep*int(self.random() * n) 223d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 224d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def randint(self, a, b): 225cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters """Return random integer in range [a, b], including both end points. 226d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 227d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 228d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return self.randrange(a, b+1) 229d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 2302f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger def _randbelow(self, n, _log=_log, int=int, _maxwidth=1L<<BPF, 2312f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger _Method=_MethodType, _BuiltinMethod=_BuiltinMethodType): 2322f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger """Return a random int in the range [0,n) 2332f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2342f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger Handles the case where n has more bits than returned 2352f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger by a single call to the underlying generator. 2362f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger """ 2372f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2382f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger try: 2392f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger getrandbits = self.getrandbits 2402f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger except AttributeError: 2412f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger pass 2422f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger else: 2432f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # Only call self.getrandbits if the original random() builtin method 2442f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # has not been overridden or if a new getrandbits() was supplied. 2452f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # This assures that the two methods correspond. 2462f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method: 2472f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger k = int(1.00001 + _log(n-1, 2.0)) # 2**k > n-1 > 2**(k-2) 2482f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger r = getrandbits(k) 2492f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger while r >= n: 2502f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger r = getrandbits(k) 2512f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return r 2522f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if n >= _maxwidth: 2532f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger _warn("Underlying random() generator does not supply \n" 2542f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger "enough bits to choose from a population range this large") 2552f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return int(self.random() * n) 2562f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 257cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- sequence methods ------------------- 258cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 259d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def choice(self, seq): 260d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Choose a random element from a non-empty sequence.""" 2615dae505bbd59641a948c81bea981e7c44d4c2343Raymond Hettinger return seq[int(self.random() * len(seq))] # raises IndexError if seq is empty 262d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 263d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def shuffle(self, x, random=None, int=int): 264d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """x, random=random.random -> shuffle list x in place; return None. 265d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 266d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters Optional arg random is a 0-argument function returning a random 267d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters float in [0.0, 1.0); by default, the standard random.random. 268d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 269d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 270d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if random is None: 271d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 27285c20a41dfcec04d161ad7da7260e7b94c62d228Raymond Hettinger for i in reversed(xrange(1, len(x))): 273cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters # pick an element in x[:i+1] with which to exchange x[i] 274d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters j = int(random() * (i+1)) 275d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x[i], x[j] = x[j], x[i] 276d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 277fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger def sample(self, population, k): 278f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger """Chooses k unique random elements from a population sequence. 279f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 280c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger Returns a new list containing elements from the population while 281c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger leaving the original population unchanged. The resulting list is 282c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger in selection order so that all sub-slices will also be valid random 283c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger samples. This allows raffle winners (the sample) to be partitioned 284c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger into grand prize and second place winners (the subslices). 285f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 286c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger Members of the population need not be hashable or unique. If the 287c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger population contains repeats, then each occurrence is a possible 288c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger selection in the sample. 289f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 290c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger To choose a sample in a range of integers, use xrange as an argument. 291c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger This is especially fast and space efficient for sampling from a 292c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger large population: sample(xrange(10000000), 60) 293f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger """ 294f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 295c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX Although the documentation says `population` is "a sequence", 296c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX attempts are made to cater to any iterable with a __len__ 297c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX method. This has had mixed success. Examples from both 298c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX sides: sets work fine, and should become officially supported; 299c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX dicts are much harder, and have failed in various subtle 300c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX ways across attempts. Support for mapping types should probably 301c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX be dropped (and users should pass mapping.keys() or .values() 302c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX explicitly). 303c17976e9833f3093adb1019356737e728a24f7c9Tim Peters 304c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger # Sampling without replacement entails tracking either potential 30591e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # selections (the pool) in a list or previous selections in a set. 306c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger 3072b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # When the number of selections is small compared to the 3082b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # population, then tracking selections is efficient, requiring 30991e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # only a small set and an occasional reselection. For 3102b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # a larger number of selections, the pool tracking method is 3112b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # preferred since the list takes less space than the 31291e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # set and it doesn't suffer from frequent reselections. 313c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger 314f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger n = len(population) 315f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger if not 0 <= k <= n: 316f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger raise ValueError, "sample larger than population" 3178b9aa8dbba644da23ce8417f2d30b218392b3282Raymond Hettinger random = self.random 318fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger _int = int 319c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger result = [None] * k 32091e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger setsize = 21 # size of a small set minus size of an empty list 32191e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger if k > 5: 3229e34c047325651853a95f95e538582a4f6d5b7f6Tim Peters setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets 323c17976e9833f3093adb1019356737e728a24f7c9Tim Peters if n <= setsize or hasattr(population, "keys"): 324c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # An n-length list is smaller than a k-length set, or this is a 325c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # mapping type so the other algorithm wouldn't work. 326311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger pool = list(population) 327311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger for i in xrange(k): # invariant: non-selected at [0,n-i) 328fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger j = _int(random() * (n-i)) 329311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger result[i] = pool[j] 3308b9aa8dbba644da23ce8417f2d30b218392b3282Raymond Hettinger pool[j] = pool[n-i-1] # move non-selected item into vacancy 331c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger else: 33266d09f1b3029d9cf975ccf26c437c9fb2605db91Raymond Hettinger try: 3333c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger selected = set() 3343c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger selected_add = selected.add 3353c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger for i in xrange(k): 336fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger j = _int(random() * n) 3373c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger while j in selected: 3383c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger j = _int(random() * n) 3393c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger selected_add(j) 3403c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger result[i] = population[j] 341c17976e9833f3093adb1019356737e728a24f7c9Tim Peters except (TypeError, KeyError): # handle (at least) sets 3423c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger if isinstance(population, list): 3433c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger raise 344c17976e9833f3093adb1019356737e728a24f7c9Tim Peters return self.sample(tuple(population), k) 345311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger return result 346f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 347cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- real-valued distributions ------------------- 348cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 349cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- uniform distribution ------------------- 350d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 351d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def uniform(self, a, b): 352d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Get a random number in the range [a, b).""" 353d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return a + (b-a) * self.random() 354ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 355bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger## -------------------- triangular -------------------- 356bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger 357c4f7bab0a0cd208bcab3c4f6cd8324ed8d08f98eRaymond Hettinger def triangular(self, low=0.0, high=1.0, mode=None): 358bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger """Triangular distribution. 359bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger 360bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger Continuous distribution bounded by given lower and upper limits, 361bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger and having a given mode value in-between. 362bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger 363bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger http://en.wikipedia.org/wiki/Triangular_distribution 364bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger 365bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger """ 366bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger u = self.random() 367c4f7bab0a0cd208bcab3c4f6cd8324ed8d08f98eRaymond Hettinger c = 0.5 if mode is None else (mode - low) / (high - low) 368bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger if u > c: 369c4f7bab0a0cd208bcab3c4f6cd8324ed8d08f98eRaymond Hettinger u = 1.0 - u 370c4f7bab0a0cd208bcab3c4f6cd8324ed8d08f98eRaymond Hettinger c = 1.0 - c 371bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger low, high = high, low 372bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger return low + (high - low) * (u * c) ** 0.5 373bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger 374cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- normal distribution -------------------- 375ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 376d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def normalvariate(self, mu, sigma): 377c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Normal distribution. 378c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 379c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean, and sigma is the standard deviation. 380ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 381c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 382d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # mu = mean, sigma = standard deviation 383d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 384d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses Kinderman and Monahan method. Reference: Kinderman, 385d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # A.J. and Monahan, J.F., "Computer generation of random 386d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # variables using the ratio of uniform deviates", ACM Trans 387d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Math Software, 3, (1977), pp257-260. 388d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 389d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 39042406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 391d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 39273ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u2 = 1.0 - random() 393d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = NV_MAGICCONST*(u1-0.5)/u2 394d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters zz = z*z/4.0 395d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if zz <= -_log(u2): 396d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 397d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return mu + z*sigma 398ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 399cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- lognormal distribution -------------------- 400ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 401d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def lognormvariate(self, mu, sigma): 402c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Log normal distribution. 403c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 404c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger If you take the natural logarithm of this distribution, you'll get a 405c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger normal distribution with mean mu and standard deviation sigma. 406c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu can have any value, and sigma must be greater than zero. 407ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 408c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 409d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return _exp(self.normalvariate(mu, sigma)) 410ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 411cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- exponential distribution -------------------- 412ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 413d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def expovariate(self, lambd): 414c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Exponential distribution. 415c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 416c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger lambd is 1.0 divided by the desired mean. (The parameter would be 417c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger called "lambda", but that is a reserved word in Python.) Returned 418c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger values range from 0 to positive infinity. 419ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 420c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 421d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # lambd: rate lambd = 1/mean 422d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # ('lambda' is a Python reserved word) 423ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 424d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 4250c9886d589ddebf32de0ca3f027a173222ed383aTim Peters u = random() 426d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters while u <= 1e-7: 427d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u = random() 428d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return -_log(u)/lambd 429ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 430cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- von Mises distribution -------------------- 431ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 432d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def vonmisesvariate(self, mu, kappa): 433c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Circular data distribution. 434ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 435c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean angle, expressed in radians between 0 and 2*pi, and 436c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger kappa is the concentration parameter, which must be greater than or 437c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger equal to zero. If kappa is equal to zero, this distribution reduces 438c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger to a uniform random angle over the range 0 to 2*pi. 439ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 440c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 441d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # mu: mean angle (in radians between 0 and 2*pi) 442d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # kappa: concentration parameter kappa (>= 0) 443d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # if kappa = 0 generate uniform random angle 4445810297052003f28788f6790ac799fe8e5373494Guido van Rossum 445d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Based upon an algorithm published in: Fisher, N.I., 446d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # "Statistical Analysis of Circular Data", Cambridge 447d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # University Press, 1993. 4485810297052003f28788f6790ac799fe8e5373494Guido van Rossum 449d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Thanks to Magnus Kessler for a correction to the 450d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # implementation of step 4. 4515810297052003f28788f6790ac799fe8e5373494Guido van Rossum 452d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 453d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if kappa <= 1e-6: 454d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return TWOPI * random() 455ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 456d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa) 457d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters b = (a - _sqrt(2.0 * a))/(2.0 * kappa) 458d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters r = (1.0 + b * b)/(2.0 * b) 459ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 46042406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 461d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 462ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 463d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = _cos(_pi * u1) 464d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters f = (1.0 + r * z)/(r + z) 465d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters c = kappa * (r - f) 466ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 467d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u2 = random() 468ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 46942406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger if u2 < c * (2.0 - c) or u2 <= c * _exp(1.0 - c): 470d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 471ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 472d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u3 = random() 473d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if u3 > 0.5: 474d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters theta = (mu % TWOPI) + _acos(f) 475d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 476d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters theta = (mu % TWOPI) - _acos(f) 477ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 478d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return theta 479ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 480cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- gamma distribution -------------------- 481ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 482d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def gammavariate(self, alpha, beta): 483c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Gamma distribution. Not the gamma function! 484c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 485c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Conditions on the parameters are alpha > 0 and beta > 0. 486c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 487c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 4888ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 489b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 4908ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 491570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum # Warning: a few older sources define the gamma distribution in terms 492570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum # of alpha > -1.0 493570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum if alpha <= 0.0 or beta <= 0.0: 494570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum raise ValueError, 'gammavariate: alpha and beta must be > 0.0' 4958ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 496d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 497d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if alpha > 1.0: 498d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 499d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses R.C.H. Cheng, "The generation of Gamma 500d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # variables with non-integral shape parameters", 501d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Applied Statistics, (1977), 26, No. 1, p71-74 502d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 503ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger ainv = _sqrt(2.0 * alpha - 1.0) 504ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger bbb = alpha - LOG4 505ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger ccc = alpha + ainv 5068ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 50742406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 508d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 50973ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger if not 1e-7 < u1 < .9999999: 51073ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger continue 51173ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u2 = 1.0 - random() 512d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters v = _log(u1/(1.0-u1))/ainv 513d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x = alpha*_exp(v) 514d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = u1*u1*u2 515d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters r = bbb+ccc*v-x 516d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z): 517b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return x * beta 518d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 519d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters elif alpha == 1.0: 520d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # expovariate(1) 5210c9886d589ddebf32de0ca3f027a173222ed383aTim Peters u = random() 522d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters while u <= 1e-7: 523d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u = random() 524b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return -_log(u) * beta 525d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 526d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: # alpha is between 0 and 1 (exclusive) 527d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 528d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle 529d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 53042406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 531d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u = random() 532d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters b = (_e + alpha)/_e 533d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters p = b*u 534d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if p <= 1.0: 53542406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger x = p ** (1.0/alpha) 536d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 537d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x = -_log((b-p)/alpha) 538d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 53942406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger if p > 1.0: 54042406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger if u1 <= x ** (alpha - 1.0): 54142406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger break 54242406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger elif u1 <= _exp(-x): 543d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 544b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return x * beta 545b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger 546cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Gauss (faster alternative) -------------------- 54795bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 548d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def gauss(self, mu, sigma): 549c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Gaussian distribution. 550c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 551c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean, and sigma is the standard deviation. This is 552c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger slightly faster than the normalvariate() function. 553c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 554c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Not thread-safe without a lock around calls. 555ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 556c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 557d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 558d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # When x and y are two variables from [0, 1), uniformly 559d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # distributed, then 560d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # 561d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # cos(2*pi*x)*sqrt(-2*log(1-y)) 562d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # sin(2*pi*x)*sqrt(-2*log(1-y)) 563d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # 564d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # are two *independent* variables with normal distribution 565d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (mu = 0, sigma = 1). 566d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (Lambert Meertens) 567d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (corrected version; bug discovered by Mike Miller, fixed by LM) 568d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 569d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Multithreading note: When two threads call this function 570d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # simultaneously, it is possible that they will receive the 571d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # same return value. The window is very small though. To 572d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # avoid this, you have to use a lock around all calls. (I 573d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # didn't want to slow this down in the serial case by using a 574d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # lock here.) 575d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 576d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 577d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = self.gauss_next 578d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.gauss_next = None 579d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if z is None: 580d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x2pi = random() * TWOPI 581d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters g2rad = _sqrt(-2.0 * _log(1.0 - random())) 582d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = _cos(x2pi) * g2rad 583d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.gauss_next = _sin(x2pi) * g2rad 584d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 585d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return mu + z*sigma 58695bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 587cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- beta -------------------- 58885e2e4742d0a1accecd02058a7907df36308297eTim Peters## See 58985e2e4742d0a1accecd02058a7907df36308297eTim Peters## http://sourceforge.net/bugs/?func=detailbug&bug_id=130030&group_id=5470 59085e2e4742d0a1accecd02058a7907df36308297eTim Peters## for Ivan Frohne's insightful analysis of why the original implementation: 59185e2e4742d0a1accecd02058a7907df36308297eTim Peters## 59285e2e4742d0a1accecd02058a7907df36308297eTim Peters## def betavariate(self, alpha, beta): 59385e2e4742d0a1accecd02058a7907df36308297eTim Peters## # Discrete Event Simulation in C, pp 87-88. 59485e2e4742d0a1accecd02058a7907df36308297eTim Peters## 59585e2e4742d0a1accecd02058a7907df36308297eTim Peters## y = self.expovariate(alpha) 59685e2e4742d0a1accecd02058a7907df36308297eTim Peters## z = self.expovariate(1.0/beta) 59785e2e4742d0a1accecd02058a7907df36308297eTim Peters## return z/(y+z) 59885e2e4742d0a1accecd02058a7907df36308297eTim Peters## 59985e2e4742d0a1accecd02058a7907df36308297eTim Peters## was dead wrong, and how it probably got that way. 60095bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 601d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def betavariate(self, alpha, beta): 602c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Beta distribution. 603c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 6041b0ce8527112b997194a4e2fb9a1a850c6d73ee8Raymond Hettinger Conditions on the parameters are alpha > 0 and beta > 0. 605c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Returned values range between 0 and 1. 606ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 607c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 608ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 60985e2e4742d0a1accecd02058a7907df36308297eTim Peters # This version due to Janne Sinkkonen, and matches all the std 61085e2e4742d0a1accecd02058a7907df36308297eTim Peters # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). 61185e2e4742d0a1accecd02058a7907df36308297eTim Peters y = self.gammavariate(alpha, 1.) 61285e2e4742d0a1accecd02058a7907df36308297eTim Peters if y == 0: 61385e2e4742d0a1accecd02058a7907df36308297eTim Peters return 0.0 61485e2e4742d0a1accecd02058a7907df36308297eTim Peters else: 61585e2e4742d0a1accecd02058a7907df36308297eTim Peters return y / (y + self.gammavariate(beta, 1.)) 61695bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 617cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Pareto -------------------- 618cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 619d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def paretovariate(self, alpha): 620c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Pareto distribution. alpha is the shape parameter.""" 621d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Jain, pg. 495 622cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 62373ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u = 1.0 - self.random() 624d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return 1.0 / pow(u, 1.0/alpha) 625cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 626cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Weibull -------------------- 627cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 628d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def weibullvariate(self, alpha, beta): 629c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Weibull distribution. 630c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 631c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger alpha is the scale parameter and beta is the shape parameter. 632ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 633c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 634d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Jain, pg. 499; bug fix courtesy Bill Arms 635cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 63673ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u = 1.0 - self.random() 637d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return alpha * pow(-_log(u), 1.0/beta) 6386c395ba31609eeffce2428280cc5d95e4fb8058aGuido van Rossum 63940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger## -------------------- Wichmann-Hill ------------------- 64040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 64140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettingerclass WichmannHill(Random): 64240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 64340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger VERSION = 1 # used by getstate/setstate 64440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 64540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def seed(self, a=None): 64640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Initialize internal state from hashable object. 64740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 64823f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger None or no argument seeds from current time or from an operating 64923f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger system specific randomness source if available. 65040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 65140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger If a is not None or an int or long, hash(a) is used instead. 65240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 65340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger If a is an int or long, a is used directly. Distinct values between 65440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 0 and 27814431486575L inclusive are guaranteed to yield distinct 65540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger internal states (this guarantee is specific to the default 65640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Wichmann-Hill generator). 65740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 65840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 65940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if a is None: 660c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger try: 661c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger a = long(_hexlify(_urandom(16)), 16) 662c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger except NotImplementedError: 663356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger import time 664356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger a = long(time.time() * 256) # use fractional seconds 66540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 66640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not isinstance(a, (int, long)): 66740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a = hash(a) 66840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 66940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, x = divmod(a, 30268) 67040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, y = divmod(a, 30306) 67140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, z = divmod(a, 30322) 67240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = int(x)+1, int(y)+1, int(z)+1 67340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 67440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 67540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 67640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def random(self): 67740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Get the next random number in the range [0.0, 1.0).""" 67840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 67940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Wichman-Hill random number generator. 68040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 68140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Wichmann, B. A. & Hill, I. D. (1982) 68240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Algorithm AS 183: 68340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # An efficient and portable pseudo-random number generator 68440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 31 (1982) 188-190 68540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 68640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # see also: 68740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Correction to Algorithm AS 183 68840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 33 (1984) 123 68940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 69040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # McLeod, A. I. (1985) 69140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # A remark on Algorithm AS 183 69240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 34 (1985),198-200 69340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 69440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # This part is thread-unsafe: 69540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # BEGIN CRITICAL SECTION 69640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x, y, z = self._seed 69740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = (171 * x) % 30269 69840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = (172 * y) % 30307 69940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = (170 * z) % 30323 70040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = x, y, z 70140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # END CRITICAL SECTION 70240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 70340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Note: on a platform using IEEE-754 double arithmetic, this can 70440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # never return 0.0 (asserted by Tim; proof too long for a comment). 70540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0 70640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 70740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def getstate(self): 70840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Return internal state; can be passed to setstate() later.""" 70940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return self.VERSION, self._seed, self.gauss_next 71040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 71140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def setstate(self, state): 71240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Restore internal state from object returned by getstate().""" 71340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version = state[0] 71440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if version == 1: 71540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version, self._seed, self.gauss_next = state 71640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger else: 71740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError("state with version %s passed to " 71840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger "Random.setstate() of version %s" % 71940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger (version, self.VERSION)) 72040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 72140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def jumpahead(self, n): 72240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Act as if n calls to random() were made, but quickly. 72340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 72440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger n is an int, greater than or equal to 0. 72540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 72640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Example use: If you have 2 threads and know that each will 72740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger consume no more than a million random numbers, create two Random 72840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger objects r1 and r2, then do 72940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger r2.setstate(r1.getstate()) 73040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger r2.jumpahead(1000000) 73140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Then r1 and r2 will use guaranteed-disjoint segments of the full 73240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger period. 73340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 73440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 73540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not n >= 0: 73640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError("n must be >= 0") 73740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x, y, z = self._seed 73840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = int(x * pow(171, n, 30269)) % 30269 73940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = int(y * pow(172, n, 30307)) % 30307 74040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = int(z * pow(170, n, 30323)) % 30323 74140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = x, y, z 74240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 74340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def __whseed(self, x=0, y=0, z=0): 74440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Set the Wichmann-Hill seed from (x, y, z). 74540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 74640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger These must be integers in the range [0, 256). 74740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 74840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 74940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not type(x) == type(y) == type(z) == int: 75040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise TypeError('seeds must be integers') 75140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256): 75240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError('seeds must be in range(0, 256)') 75340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if 0 == x == y == z: 75440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Initialize from current time 75540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger import time 75640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t = long(time.time() * 256) 75740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t = int((t&0xffffff) ^ (t>>24)) 75840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, x = divmod(t, 256) 75940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, y = divmod(t, 256) 76040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, z = divmod(t, 256) 76140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Zero is a poor seed, so substitute 1 76240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = (x or 1, y or 1, z or 1) 76340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 76440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 76540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 76640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def whseed(self, a=None): 76740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Seed from hashable object's hash code. 76840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 76940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger None or no argument seeds from current time. It is not guaranteed 77040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger that objects with distinct hash codes lead to distinct internal 77140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger states. 77240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 77340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger This is obsolete, provided for compatibility with the seed routine 77440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger used prior to Python 2.1. Use the .seed() method instead. 77540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 77640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 77740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if a is None: 77840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.__whseed() 77940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return 78040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a = hash(a) 78140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, x = divmod(a, 256) 78240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, y = divmod(a, 256) 78340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, z = divmod(a, 256) 78440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = (x + a) % 256 or 1 78540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = (y + a) % 256 or 1 78640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = (z + a) % 256 or 1 78740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.__whseed(x, y, z) 78840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 78923f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger## --------------- Operating System Random Source ------------------ 790356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 79123f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettingerclass SystemRandom(Random): 79223f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger """Alternate random number generator using sources provided 79323f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger by the operating system (such as /dev/urandom on Unix or 79423f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger CryptGenRandom on Windows). 795356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 796356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger Not available on all systems (see os.urandom() for details). 797356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """ 798356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 799356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def random(self): 800356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """Get the next random number in the range [0.0, 1.0).""" 8017c2a85b2d44851c2442ade579b760f86447bf848Tim Peters return (long(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF 802356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 803356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def getrandbits(self, k): 804356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """getrandbits(k) -> x. Generates a long int with k random bits.""" 805356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger if k <= 0: 806356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger raise ValueError('number of bits must be greater than zero') 807356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger if k != int(k): 808356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger raise TypeError('number of bits should be an integer') 809356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger bytes = (k + 7) // 8 # bits / 8 and rounded up 810356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger x = long(_hexlify(_urandom(bytes)), 16) 811356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger return x >> (bytes * 8 - k) # trim excess bits 812356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 813356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def _stub(self, *args, **kwds): 81423f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "Stub method. Not used for a system random number generator." 815356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger return None 816356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger seed = jumpahead = _stub 817356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 818356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def _notimplemented(self, *args, **kwds): 81923f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "Method should not be called for a system random number generator." 82023f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger raise NotImplementedError('System entropy source does not have state.') 821356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger getstate = setstate = _notimplemented 822356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 823cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- test program -------------------- 824ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 82562297132215490e9cb406e1a21f03aff40d421cbRaymond Hettingerdef _test_generator(n, func, args): 8260c9886d589ddebf32de0ca3f027a173222ed383aTim Peters import time 82762297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger print n, 'times', func.__name__ 828b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger total = 0.0 8290c9886d589ddebf32de0ca3f027a173222ed383aTim Peters sqsum = 0.0 8300c9886d589ddebf32de0ca3f027a173222ed383aTim Peters smallest = 1e10 8310c9886d589ddebf32de0ca3f027a173222ed383aTim Peters largest = -1e10 8320c9886d589ddebf32de0ca3f027a173222ed383aTim Peters t0 = time.time() 8330c9886d589ddebf32de0ca3f027a173222ed383aTim Peters for i in range(n): 83462297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger x = func(*args) 835b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger total += x 8360c9886d589ddebf32de0ca3f027a173222ed383aTim Peters sqsum = sqsum + x*x 8370c9886d589ddebf32de0ca3f027a173222ed383aTim Peters smallest = min(x, smallest) 8380c9886d589ddebf32de0ca3f027a173222ed383aTim Peters largest = max(x, largest) 8390c9886d589ddebf32de0ca3f027a173222ed383aTim Peters t1 = time.time() 8400c9886d589ddebf32de0ca3f027a173222ed383aTim Peters print round(t1-t0, 3), 'sec,', 841b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger avg = total/n 842d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters stddev = _sqrt(sqsum/n - avg*avg) 8430c9886d589ddebf32de0ca3f027a173222ed383aTim Peters print 'avg %g, stddev %g, min %g, max %g' % \ 8440c9886d589ddebf32de0ca3f027a173222ed383aTim Peters (avg, stddev, smallest, largest) 845ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 846f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 847f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettingerdef _test(N=2000): 84862297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, random, ()) 84962297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, normalvariate, (0.0, 1.0)) 85062297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, lognormvariate, (0.0, 1.0)) 85162297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, vonmisesvariate, (0.0, 1.0)) 85262297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.01, 1.0)) 85362297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.1, 1.0)) 85462297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.1, 2.0)) 85562297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.5, 1.0)) 85662297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.9, 1.0)) 85762297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (1.0, 1.0)) 85862297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (2.0, 1.0)) 85962297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (20.0, 1.0)) 86062297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (200.0, 1.0)) 86162297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gauss, (0.0, 1.0)) 86262297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, betavariate, (3.0, 3.0)) 863bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger _test_generator(N, triangular, (0.0, 1.0, 1.0/3.0)) 864cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 865715c4c412b21f68ad59773698d06eea8eb0c5a44Tim Peters# Create one instance, seeded from current time, and export its methods 86640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# as module-level functions. The functions share state across all uses 86740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger#(both in the user's code and in the Python libraries), but that's fine 86840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# for most programs and is easier for the casual user than making them 86940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# instantiate their own Random() instance. 87040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 871d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters_inst = Random() 872d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersseed = _inst.seed 873d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandom = _inst.random 874d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersuniform = _inst.uniform 875bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettingertriangular = _inst.triangular 876d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandint = _inst.randint 877d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterschoice = _inst.choice 878d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandrange = _inst.randrange 879f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettingersample = _inst.sample 880d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersshuffle = _inst.shuffle 881d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersnormalvariate = _inst.normalvariate 882d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterslognormvariate = _inst.lognormvariate 883d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersexpovariate = _inst.expovariate 884d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersvonmisesvariate = _inst.vonmisesvariate 885d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgammavariate = _inst.gammavariate 886d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgauss = _inst.gauss 887d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersbetavariate = _inst.betavariate 888d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersparetovariate = _inst.paretovariate 889d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersweibullvariate = _inst.weibullvariate 890d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgetstate = _inst.getstate 891d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterssetstate = _inst.setstate 892d52269bfd029c4a517ea74c17edd5c3a250c366cTim Petersjumpahead = _inst.jumpahead 8932f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettingergetrandbits = _inst.getrandbits 894d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 895ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossumif __name__ == '__main__': 896d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters _test() 897