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 49ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettingerimport hashlib as _hashlib 50d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 51f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger__all__ = ["Random","seed","random","uniform","randint","choice","sample", 520de65807e6bdc5254f5a7e99b2f39adeea6b883bSkip Montanaro "randrange","shuffle","normalvariate","lognormvariate", 53bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger "expovariate","vonmisesvariate","gammavariate","triangular", 54f8a52d38ad784b34a60720cb148180d6eb6de373Raymond Hettinger "gauss","betavariate","paretovariate","weibullvariate", 55356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger "getstate","setstate","jumpahead", "WichmannHill", "getrandbits", 5623f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "SystemRandom"] 57ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 58d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersNV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0) 59d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersTWOPI = 2.0*_pi 60d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersLOG4 = _log(4.0) 61d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersSG_MAGICCONST = 1.0 + _log(4.5) 622f726e9093381572b21edbfc42659ea89fbdf686Raymond HettingerBPF = 53 # Number of bits in a float 637c2a85b2d44851c2442ade579b760f86447bf848Tim PetersRECIP_BPF = 2**-BPF 6433d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 65356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 66d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters# Translated by Guido van Rossum from C source provided by 6740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# Adrian Baddeley. Adapted by Raymond Hettinger for use with 683fa19d7ff89be87139e2864fb9186b424d180a58Raymond Hettinger# the Mersenne Twister and os.urandom() core generators. 6933d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 70145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettingerimport _random 7140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 72145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettingerclass Random(_random.Random): 73c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Random number generator base class used by bound module functions. 74c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 75c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Used to instantiate instances of Random to get generators that don't 76c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger share state. Especially useful for multi-threaded programs, creating 77c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger a different instance of Random for each thread, and using the jumpahead() 78c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger method to ensure that the generated sequences seen by each thread don't 79c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger overlap. 80c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 81c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Class Random can also be subclassed if you want to use a different basic 82c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger generator of your own devising: in that case, override the following 83f2eb2b44fc532c77c03bc95789817a20d7c558c3Benjamin Peterson methods: random(), seed(), getstate(), setstate() and jumpahead(). 84f2eb2b44fc532c77c03bc95789817a20d7c558c3Benjamin Peterson Optionally, implement a getrandbits() method so that randrange() can cover 85f2eb2b44fc532c77c03bc95789817a20d7c558c3Benjamin Peterson arbitrarily large ranges. 86ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 87c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 8833d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 896b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis VERSION = 3 # used by getstate/setstate 9033d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 91d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def __init__(self, x=None): 92d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Initialize an instance. 9333d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 94d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters Optional argument x controls seeding, as for Random.seed(). 95d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 9633d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 97d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.seed(x) 9840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 99ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 1000de88fc4b108751b86443852b6741680d704168fTim Peters def seed(self, a=None): 1010de88fc4b108751b86443852b6741680d704168fTim Peters """Initialize internal state from hashable object. 102d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 10323f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger None or no argument seeds from current time or from an operating 10423f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger system specific randomness source if available. 1050de88fc4b108751b86443852b6741680d704168fTim Peters 106bcd725fc456faca13f4598f87c0517f917711cdaTim Peters If a is not None or an int or long, hash(a) is used instead. 107d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 108d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 1093081d59f920229b26293c7a3ee3f1a9da0da53e9Raymond Hettinger if a is None: 110c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger try: 111ddb39e799d65748c5ea42c344170befc90af9e64Raymond Hettinger # Seed with enough bytes to span the 19937 bit 112ddb39e799d65748c5ea42c344170befc90af9e64Raymond Hettinger # state space for the Mersenne Twister 113ddb39e799d65748c5ea42c344170befc90af9e64Raymond Hettinger a = long(_hexlify(_urandom(2500)), 16) 114c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger except NotImplementedError: 115356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger import time 116356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger a = long(time.time() * 256) # use fractional seconds 117356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 118145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger super(Random, self).seed(a) 11946c04e140cf26d1b44935c28c6f15ea467400d22Tim Peters self.gauss_next = None 12046c04e140cf26d1b44935c28c6f15ea467400d22Tim Peters 121d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def getstate(self): 122d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Return internal state; can be passed to setstate() later.""" 123145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger return self.VERSION, super(Random, self).getstate(), self.gauss_next 124d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 125d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def setstate(self, state): 126d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Restore internal state from object returned by getstate().""" 127d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters version = state[0] 1286b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis if version == 3: 12940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version, internalstate, self.gauss_next = state 130145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger super(Random, self).setstate(internalstate) 1316b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis elif version == 2: 1326b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis version, internalstate, self.gauss_next = state 1336b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # In version 2, the state was saved as signed ints, which causes 1346b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # inconsistencies between 32/64-bit systems. The state is 1356b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # really unsigned 32-bit ints, so we convert negative ints from 1366b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # version 2 to positive longs for version 3. 1376b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis try: 1386b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis internalstate = tuple( long(x) % (2**32) for x in internalstate ) 1396b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis except ValueError, e: 1406b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis raise TypeError, e 1416b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis super(Random, self).setstate(internalstate) 142d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 143d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError("state with version %s passed to " 144d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters "Random.setstate() of version %s" % 145d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters (version, self.VERSION)) 146d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 147ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger def jumpahead(self, n): 148ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger """Change the internal state to one that is likely far away 149ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger from the current state. This method will not be in Py3.x, 150ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger so it is better to simply reseed. 151ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger """ 152ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger # The super.jumpahead() method uses shuffling to change state, 153ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger # so it needs a large and "interesting" n to work with. Here, 154ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger # we use hashing to create a large n for the shuffle. 155ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger s = repr(n) + repr(self.getstate()) 156ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger n = int(_hashlib.new('sha512', s).hexdigest(), 16) 157ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger super(Random, self).jumpahead(n) 158ffd2a4215a0bfe82f48ff71381bbfce8552f5f0cRaymond Hettinger 159cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## ---- Methods below this point do not need to be overridden when 160cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## ---- subclassing for the purpose of using a different core generator. 161d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 162cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- pickle support ------------------- 163d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 164cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters def __getstate__(self): # for pickle 165cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters return self.getstate() 166d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 167cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters def __setstate__(self, state): # for pickle 168cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters self.setstate(state) 169cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 1705f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger def __reduce__(self): 1715f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger return self.__class__, (), self.getstate() 1725f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger 173cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- integer methods ------------------- 174d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 1758dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger def randrange(self, start, stop=None, step=1, _int=int, _maxwidth=1L<<BPF): 176d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Choose a random item from range(start, stop[, step]). 177d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 178d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters This fixes the problem with randint() which includes the 179d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters endpoint; in Python this is usually not what you want. 1808dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger 181d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 182d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 183d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # This code is a bit messy to make it fast for the 1849146f27b7799dab231083f194a14c6157b57549fTim Peters # common case while still doing adequate error checking. 1858dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger istart = _int(start) 186d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istart != start: 187d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer arg 1 for randrange()" 1888dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger if stop is None: 189d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istart > 0: 1908dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger if istart >= _maxwidth: 1912f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return self._randbelow(istart) 1928dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger return _int(self.random() * istart) 193d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "empty range for randrange()" 1949146f27b7799dab231083f194a14c6157b57549fTim Peters 1959146f27b7799dab231083f194a14c6157b57549fTim Peters # stop argument supplied. 1968dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger istop = _int(stop) 197d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istop != stop: 198d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer stop for randrange()" 1992f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger width = istop - istart 2002f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if step == 1 and width > 0: 20176ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # Note that 2022f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # int(istart + self.random()*width) 20376ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # instead would be incorrect. For example, consider istart 20476ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # = -2 and istop = 0. Then the guts would be in 20576ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # -2.0 to 0.0 exclusive on both ends (ignoring that random() 20676ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # might return 0.0), and because int() truncates toward 0, the 20776ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # final result would be -1 or 0 (instead of -2 or -1). 2082f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # istart + int(self.random()*width) 20976ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # would also be incorrect, for a subtler reason: the RHS 21076ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # can return a long, and then randrange() would also return 21176ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # a long, but we're supposed to return an int (for backward 21276ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # compatibility). 2132f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2148dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger if width >= _maxwidth: 2158dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger return _int(istart + self._randbelow(width)) 2168dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger return _int(istart + _int(self.random()*width)) 217d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if step == 1: 2182f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger raise ValueError, "empty range for randrange() (%d,%d, %d)" % (istart, istop, width) 2199146f27b7799dab231083f194a14c6157b57549fTim Peters 2209146f27b7799dab231083f194a14c6157b57549fTim Peters # Non-unit step argument supplied. 2218dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger istep = _int(step) 222d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istep != step: 223d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer step for randrange()" 224d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istep > 0: 225ffdb8bb99c4017152a9dca70669f9d6b9831d454Raymond Hettinger n = (width + istep - 1) // istep 226d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters elif istep < 0: 227ffdb8bb99c4017152a9dca70669f9d6b9831d454Raymond Hettinger n = (width + istep + 1) // istep 228d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 229d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "zero step for randrange()" 230d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 231d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if n <= 0: 232d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "empty range for randrange()" 2332f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2348dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger if n >= _maxwidth: 23594547f7646895e032f8fc145529d9efc3a70760dRaymond Hettinger return istart + istep*self._randbelow(n) 2368dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger return istart + istep*_int(self.random() * n) 237d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 238d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def randint(self, a, b): 239cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters """Return random integer in range [a, b], including both end points. 240d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 241d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 242d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return self.randrange(a, b+1) 243d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 2448dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger def _randbelow(self, n, _log=_log, _int=int, _maxwidth=1L<<BPF, 2452f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger _Method=_MethodType, _BuiltinMethod=_BuiltinMethodType): 2462f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger """Return a random int in the range [0,n) 2472f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2482f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger Handles the case where n has more bits than returned 2492f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger by a single call to the underlying generator. 2502f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger """ 2512f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2522f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger try: 2532f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger getrandbits = self.getrandbits 2542f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger except AttributeError: 2552f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger pass 2562f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger else: 2572f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # Only call self.getrandbits if the original random() builtin method 2582f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # has not been overridden or if a new getrandbits() was supplied. 2592f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # This assures that the two methods correspond. 2602f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method: 2618dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger k = _int(1.00001 + _log(n-1, 2.0)) # 2**k > n-1 > 2**(k-2) 2622f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger r = getrandbits(k) 2632f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger while r >= n: 2642f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger r = getrandbits(k) 2652f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return r 2662f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if n >= _maxwidth: 2672f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger _warn("Underlying random() generator does not supply \n" 2682f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger "enough bits to choose from a population range this large") 2698dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger return _int(self.random() * n) 2702f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 271cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- sequence methods ------------------- 272cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 273d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def choice(self, seq): 274d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Choose a random element from a non-empty sequence.""" 2755dae505bbd59641a948c81bea981e7c44d4c2343Raymond Hettinger return seq[int(self.random() * len(seq))] # raises IndexError if seq is empty 276d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 2778dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger def shuffle(self, x, random=None): 278d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """x, random=random.random -> shuffle list x in place; return None. 279d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 280d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters Optional arg random is a 0-argument function returning a random 281d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters float in [0.0, 1.0); by default, the standard random.random. 28237851d0e55b4f759dadf2ed6dc8ce7a28197e49fSenthil Kumaran 283d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 284d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 285d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if random is None: 286d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 2878dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger _int = int 28885c20a41dfcec04d161ad7da7260e7b94c62d228Raymond Hettinger for i in reversed(xrange(1, len(x))): 289cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters # pick an element in x[:i+1] with which to exchange x[i] 2908dc1692337c4551a6ccf27091478f67027b573c4Raymond Hettinger j = _int(random() * (i+1)) 291d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x[i], x[j] = x[j], x[i] 292d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 293fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger def sample(self, population, k): 294f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger """Chooses k unique random elements from a population sequence. 295f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 296c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger Returns a new list containing elements from the population while 297c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger leaving the original population unchanged. The resulting list is 298c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger in selection order so that all sub-slices will also be valid random 299c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger samples. This allows raffle winners (the sample) to be partitioned 300c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger into grand prize and second place winners (the subslices). 301f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 302c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger Members of the population need not be hashable or unique. If the 303c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger population contains repeats, then each occurrence is a possible 304c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger selection in the sample. 305f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 306c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger To choose a sample in a range of integers, use xrange as an argument. 307c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger This is especially fast and space efficient for sampling from a 308c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger large population: sample(xrange(10000000), 60) 309f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger """ 310f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 311c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger # Sampling without replacement entails tracking either potential 31291e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # selections (the pool) in a list or previous selections in a set. 313c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger 3142b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # When the number of selections is small compared to the 3152b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # population, then tracking selections is efficient, requiring 31691e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # only a small set and an occasional reselection. For 3172b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # a larger number of selections, the pool tracking method is 3182b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # preferred since the list takes less space than the 31991e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # set and it doesn't suffer from frequent reselections. 320c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger 321f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger n = len(population) 322f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger if not 0 <= k <= n: 32322d8f7b9b80cf4f89ad2c383e566f8fd1c6d5e52Raymond Hettinger raise ValueError("sample larger than population") 3248b9aa8dbba644da23ce8417f2d30b218392b3282Raymond Hettinger random = self.random 325fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger _int = int 326c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger result = [None] * k 32791e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger setsize = 21 # size of a small set minus size of an empty list 32891e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger if k > 5: 3299e34c047325651853a95f95e538582a4f6d5b7f6Tim Peters setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets 330c17976e9833f3093adb1019356737e728a24f7c9Tim Peters if n <= setsize or hasattr(population, "keys"): 331c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # An n-length list is smaller than a k-length set, or this is a 332c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # mapping type so the other algorithm wouldn't work. 333311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger pool = list(population) 334311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger for i in xrange(k): # invariant: non-selected at [0,n-i) 335fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger j = _int(random() * (n-i)) 336311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger result[i] = pool[j] 3378b9aa8dbba644da23ce8417f2d30b218392b3282Raymond Hettinger pool[j] = pool[n-i-1] # move non-selected item into vacancy 338c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger else: 33966d09f1b3029d9cf975ccf26c437c9fb2605db91Raymond Hettinger try: 3403c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger selected = set() 3413c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger selected_add = selected.add 3423c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger for i in xrange(k): 343fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger j = _int(random() * n) 3443c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger while j in selected: 3453c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger j = _int(random() * n) 3463c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger selected_add(j) 3473c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger result[i] = population[j] 348c17976e9833f3093adb1019356737e728a24f7c9Tim Peters except (TypeError, KeyError): # handle (at least) sets 3493c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger if isinstance(population, list): 3503c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger raise 351c17976e9833f3093adb1019356737e728a24f7c9Tim Peters return self.sample(tuple(population), k) 352311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger return result 353f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 354cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- real-valued distributions ------------------- 355cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 356cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- uniform distribution ------------------- 357d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 358d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def uniform(self, a, b): 3592c0cdca56447d33e714a010459ee4318fff89c66Raymond Hettinger "Get a random number in the range [a, b) or [a, b] depending on rounding." 360d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return a + (b-a) * self.random() 361ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 362bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger## -------------------- triangular -------------------- 363bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger 364c4f7bab0a0cd208bcab3c4f6cd8324ed8d08f98eRaymond Hettinger def triangular(self, low=0.0, high=1.0, mode=None): 365bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger """Triangular distribution. 366bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger 367bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger Continuous distribution bounded by given lower and upper limits, 368bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger and having a given mode value in-between. 369bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger 370bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger http://en.wikipedia.org/wiki/Triangular_distribution 371bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger 372bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger """ 373bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger u = self.random() 37492df7529cb6c863d0fcd3247829b24833f62e285Raymond Hettinger try: 37592df7529cb6c863d0fcd3247829b24833f62e285Raymond Hettinger c = 0.5 if mode is None else (mode - low) / (high - low) 37692df7529cb6c863d0fcd3247829b24833f62e285Raymond Hettinger except ZeroDivisionError: 37792df7529cb6c863d0fcd3247829b24833f62e285Raymond Hettinger return low 378bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger if u > c: 379c4f7bab0a0cd208bcab3c4f6cd8324ed8d08f98eRaymond Hettinger u = 1.0 - u 380c4f7bab0a0cd208bcab3c4f6cd8324ed8d08f98eRaymond Hettinger c = 1.0 - c 381bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger low, high = high, low 382bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger return low + (high - low) * (u * c) ** 0.5 383bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger 384cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- normal distribution -------------------- 385ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 386d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def normalvariate(self, mu, sigma): 387c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Normal distribution. 388c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 389c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean, and sigma is the standard deviation. 390ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 391c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 392d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # mu = mean, sigma = standard deviation 393d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 394d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses Kinderman and Monahan method. Reference: Kinderman, 395d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # A.J. and Monahan, J.F., "Computer generation of random 396d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # variables using the ratio of uniform deviates", ACM Trans 397d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Math Software, 3, (1977), pp257-260. 398d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 399d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 40042406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 401d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 40273ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u2 = 1.0 - random() 403d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = NV_MAGICCONST*(u1-0.5)/u2 404d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters zz = z*z/4.0 405d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if zz <= -_log(u2): 406d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 407d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return mu + z*sigma 408ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 409cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- lognormal distribution -------------------- 410ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 411d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def lognormvariate(self, mu, sigma): 412c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Log normal distribution. 413c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 414c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger If you take the natural logarithm of this distribution, you'll get a 415c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger normal distribution with mean mu and standard deviation sigma. 416c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu can have any value, and sigma must be greater than zero. 417ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 418c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 419d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return _exp(self.normalvariate(mu, sigma)) 420ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 421cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- exponential distribution -------------------- 422ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 423d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def expovariate(self, lambd): 424c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Exponential distribution. 425c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 426e6dc53120d52f58057fd1a6d666d21cb9d71c08dMark Dickinson lambd is 1.0 divided by the desired mean. It should be 427e6dc53120d52f58057fd1a6d666d21cb9d71c08dMark Dickinson nonzero. (The parameter would be called "lambda", but that is 428e6dc53120d52f58057fd1a6d666d21cb9d71c08dMark Dickinson a reserved word in Python.) Returned values range from 0 to 429e6dc53120d52f58057fd1a6d666d21cb9d71c08dMark Dickinson positive infinity if lambd is positive, and from negative 430e6dc53120d52f58057fd1a6d666d21cb9d71c08dMark Dickinson infinity to 0 if lambd is negative. 431ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 432c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 433d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # lambd: rate lambd = 1/mean 434d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # ('lambda' is a Python reserved word) 435ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 436cba87311d2dc395cbc56d00d7161d191ff7375d2Raymond Hettinger # we use 1-random() instead of random() to preclude the 437cba87311d2dc395cbc56d00d7161d191ff7375d2Raymond Hettinger # possibility of taking the log of zero. 438cba87311d2dc395cbc56d00d7161d191ff7375d2Raymond Hettinger return -_log(1.0 - self.random())/lambd 439ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 440cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- von Mises distribution -------------------- 441ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 442d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def vonmisesvariate(self, mu, kappa): 443c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Circular data distribution. 444ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 445c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean angle, expressed in radians between 0 and 2*pi, and 446c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger kappa is the concentration parameter, which must be greater than or 447c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger equal to zero. If kappa is equal to zero, this distribution reduces 448c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger to a uniform random angle over the range 0 to 2*pi. 449ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 450c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 451d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # mu: mean angle (in radians between 0 and 2*pi) 452d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # kappa: concentration parameter kappa (>= 0) 453d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # if kappa = 0 generate uniform random angle 4545810297052003f28788f6790ac799fe8e5373494Guido van Rossum 455d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Based upon an algorithm published in: Fisher, N.I., 456d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # "Statistical Analysis of Circular Data", Cambridge 457d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # University Press, 1993. 4585810297052003f28788f6790ac799fe8e5373494Guido van Rossum 459d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Thanks to Magnus Kessler for a correction to the 460d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # implementation of step 4. 4615810297052003f28788f6790ac799fe8e5373494Guido van Rossum 462d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 463d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if kappa <= 1e-6: 464d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return TWOPI * random() 465ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 46665d56390bbf74553221dd94123c9f04776c6f8cbSerhiy Storchaka s = 0.5 / kappa 46765d56390bbf74553221dd94123c9f04776c6f8cbSerhiy Storchaka r = s + _sqrt(1.0 + s * s) 468ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 46942406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 470d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 471d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = _cos(_pi * u1) 472ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 47365d56390bbf74553221dd94123c9f04776c6f8cbSerhiy Storchaka d = z / (r + z) 474d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u2 = random() 47565d56390bbf74553221dd94123c9f04776c6f8cbSerhiy Storchaka if u2 < 1.0 - d * d or u2 <= (1.0 - d) * _exp(d): 476d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 477ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 47865d56390bbf74553221dd94123c9f04776c6f8cbSerhiy Storchaka q = 1.0 / r 47965d56390bbf74553221dd94123c9f04776c6f8cbSerhiy Storchaka f = (q + z) / (1.0 + q * z) 480d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u3 = random() 481d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if u3 > 0.5: 4829aaeb5e0c8b5946b305590eb85312c282a457098Mark Dickinson theta = (mu + _acos(f)) % TWOPI 483d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 4849aaeb5e0c8b5946b305590eb85312c282a457098Mark Dickinson theta = (mu - _acos(f)) % TWOPI 485ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 486d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return theta 487ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 488cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- gamma distribution -------------------- 489ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 490d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def gammavariate(self, alpha, beta): 491c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Gamma distribution. Not the gamma function! 492c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 493c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Conditions on the parameters are alpha > 0 and beta > 0. 494c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 495405a4717e1108b95d5af0e61dd304fe6407bd256Raymond Hettinger The probability distribution function is: 496405a4717e1108b95d5af0e61dd304fe6407bd256Raymond Hettinger 497405a4717e1108b95d5af0e61dd304fe6407bd256Raymond Hettinger x ** (alpha - 1) * math.exp(-x / beta) 498405a4717e1108b95d5af0e61dd304fe6407bd256Raymond Hettinger pdf(x) = -------------------------------------- 499405a4717e1108b95d5af0e61dd304fe6407bd256Raymond Hettinger math.gamma(alpha) * beta ** alpha 500405a4717e1108b95d5af0e61dd304fe6407bd256Raymond Hettinger 501c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 5028ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 503b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 5048ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 505570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum # Warning: a few older sources define the gamma distribution in terms 506570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum # of alpha > -1.0 507570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum if alpha <= 0.0 or beta <= 0.0: 508570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum raise ValueError, 'gammavariate: alpha and beta must be > 0.0' 5098ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 510d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 511d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if alpha > 1.0: 512d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 513d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses R.C.H. Cheng, "The generation of Gamma 514d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # variables with non-integral shape parameters", 515d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Applied Statistics, (1977), 26, No. 1, p71-74 516d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 517ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger ainv = _sqrt(2.0 * alpha - 1.0) 518ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger bbb = alpha - LOG4 519ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger ccc = alpha + ainv 5208ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 52142406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 522d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 52373ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger if not 1e-7 < u1 < .9999999: 52473ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger continue 52573ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u2 = 1.0 - random() 526d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters v = _log(u1/(1.0-u1))/ainv 527d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x = alpha*_exp(v) 528d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = u1*u1*u2 529d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters r = bbb+ccc*v-x 530d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z): 531b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return x * beta 532d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 533d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters elif alpha == 1.0: 534d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # expovariate(1) 5350c9886d589ddebf32de0ca3f027a173222ed383aTim Peters u = random() 536d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters while u <= 1e-7: 537d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u = random() 538b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return -_log(u) * beta 539d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 540d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: # alpha is between 0 and 1 (exclusive) 541d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 542d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle 543d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 54442406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 545d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u = random() 546d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters b = (_e + alpha)/_e 547d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters p = b*u 548d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if p <= 1.0: 54942406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger x = p ** (1.0/alpha) 550d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 551d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x = -_log((b-p)/alpha) 552d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 55342406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger if p > 1.0: 55442406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger if u1 <= x ** (alpha - 1.0): 55542406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger break 55642406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger elif u1 <= _exp(-x): 557d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 558b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return x * beta 559b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger 560cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Gauss (faster alternative) -------------------- 56195bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 562d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def gauss(self, mu, sigma): 563c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Gaussian distribution. 564c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 565c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean, and sigma is the standard deviation. This is 566c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger slightly faster than the normalvariate() function. 567c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 568c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Not thread-safe without a lock around calls. 569ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 570c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 571d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 572d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # When x and y are two variables from [0, 1), uniformly 573d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # distributed, then 574d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # 575d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # cos(2*pi*x)*sqrt(-2*log(1-y)) 576d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # sin(2*pi*x)*sqrt(-2*log(1-y)) 577d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # 578d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # are two *independent* variables with normal distribution 579d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (mu = 0, sigma = 1). 580d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (Lambert Meertens) 581d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (corrected version; bug discovered by Mike Miller, fixed by LM) 582d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 583d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Multithreading note: When two threads call this function 584d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # simultaneously, it is possible that they will receive the 585d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # same return value. The window is very small though. To 586d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # avoid this, you have to use a lock around all calls. (I 587d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # didn't want to slow this down in the serial case by using a 588d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # lock here.) 589d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 590d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 591d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = self.gauss_next 592d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.gauss_next = None 593d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if z is None: 594d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x2pi = random() * TWOPI 595d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters g2rad = _sqrt(-2.0 * _log(1.0 - random())) 596d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = _cos(x2pi) * g2rad 597d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.gauss_next = _sin(x2pi) * g2rad 598d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 599d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return mu + z*sigma 60095bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 601cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- beta -------------------- 60285e2e4742d0a1accecd02058a7907df36308297eTim Peters## See 6031bb18cc39e21fb0acbfde6dadbd6c432f19c4513Ezio Melotti## http://mail.python.org/pipermail/python-bugs-list/2001-January/003752.html 60485e2e4742d0a1accecd02058a7907df36308297eTim Peters## for Ivan Frohne's insightful analysis of why the original implementation: 60585e2e4742d0a1accecd02058a7907df36308297eTim Peters## 60685e2e4742d0a1accecd02058a7907df36308297eTim Peters## def betavariate(self, alpha, beta): 60785e2e4742d0a1accecd02058a7907df36308297eTim Peters## # Discrete Event Simulation in C, pp 87-88. 60885e2e4742d0a1accecd02058a7907df36308297eTim Peters## 60985e2e4742d0a1accecd02058a7907df36308297eTim Peters## y = self.expovariate(alpha) 61085e2e4742d0a1accecd02058a7907df36308297eTim Peters## z = self.expovariate(1.0/beta) 61185e2e4742d0a1accecd02058a7907df36308297eTim Peters## return z/(y+z) 61285e2e4742d0a1accecd02058a7907df36308297eTim Peters## 61385e2e4742d0a1accecd02058a7907df36308297eTim Peters## was dead wrong, and how it probably got that way. 61495bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 615d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def betavariate(self, alpha, beta): 616c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Beta distribution. 617c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 6181b0ce8527112b997194a4e2fb9a1a850c6d73ee8Raymond Hettinger Conditions on the parameters are alpha > 0 and beta > 0. 619c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Returned values range between 0 and 1. 620ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 621c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 622ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 62385e2e4742d0a1accecd02058a7907df36308297eTim Peters # This version due to Janne Sinkkonen, and matches all the std 62485e2e4742d0a1accecd02058a7907df36308297eTim Peters # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). 62585e2e4742d0a1accecd02058a7907df36308297eTim Peters y = self.gammavariate(alpha, 1.) 62685e2e4742d0a1accecd02058a7907df36308297eTim Peters if y == 0: 62785e2e4742d0a1accecd02058a7907df36308297eTim Peters return 0.0 62885e2e4742d0a1accecd02058a7907df36308297eTim Peters else: 62985e2e4742d0a1accecd02058a7907df36308297eTim Peters return y / (y + self.gammavariate(beta, 1.)) 63095bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 631cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Pareto -------------------- 632cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 633d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def paretovariate(self, alpha): 634c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Pareto distribution. alpha is the shape parameter.""" 635d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Jain, pg. 495 636cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 63773ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u = 1.0 - self.random() 638d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return 1.0 / pow(u, 1.0/alpha) 639cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 640cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Weibull -------------------- 641cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 642d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def weibullvariate(self, alpha, beta): 643c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Weibull distribution. 644c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 645c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger alpha is the scale parameter and beta is the shape parameter. 646ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 647c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 648d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Jain, pg. 499; bug fix courtesy Bill Arms 649cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 65073ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u = 1.0 - self.random() 651d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return alpha * pow(-_log(u), 1.0/beta) 6526c395ba31609eeffce2428280cc5d95e4fb8058aGuido van Rossum 65340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger## -------------------- Wichmann-Hill ------------------- 65440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 65540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettingerclass WichmannHill(Random): 65640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 65740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger VERSION = 1 # used by getstate/setstate 65840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 65940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def seed(self, a=None): 66040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Initialize internal state from hashable object. 66140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 66223f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger None or no argument seeds from current time or from an operating 66323f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger system specific randomness source if available. 66440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 66540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger If a is not None or an int or long, hash(a) is used instead. 66640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 66740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger If a is an int or long, a is used directly. Distinct values between 66840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 0 and 27814431486575L inclusive are guaranteed to yield distinct 66940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger internal states (this guarantee is specific to the default 67040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Wichmann-Hill generator). 67140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 67240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 67340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if a is None: 674c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger try: 675c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger a = long(_hexlify(_urandom(16)), 16) 676c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger except NotImplementedError: 677356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger import time 678356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger a = long(time.time() * 256) # use fractional seconds 67940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 68040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not isinstance(a, (int, long)): 68140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a = hash(a) 68240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 68340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, x = divmod(a, 30268) 68440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, y = divmod(a, 30306) 68540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, z = divmod(a, 30322) 68640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = int(x)+1, int(y)+1, int(z)+1 68740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 68840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 68940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 69040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def random(self): 69140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Get the next random number in the range [0.0, 1.0).""" 69240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 69340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Wichman-Hill random number generator. 69440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 69540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Wichmann, B. A. & Hill, I. D. (1982) 69640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Algorithm AS 183: 69740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # An efficient and portable pseudo-random number generator 69840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 31 (1982) 188-190 69940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 70040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # see also: 70140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Correction to Algorithm AS 183 70240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 33 (1984) 123 70340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 70440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # McLeod, A. I. (1985) 70540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # A remark on Algorithm AS 183 70640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 34 (1985),198-200 70740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 70840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # This part is thread-unsafe: 70940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # BEGIN CRITICAL SECTION 71040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x, y, z = self._seed 71140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = (171 * x) % 30269 71240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = (172 * y) % 30307 71340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = (170 * z) % 30323 71440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = x, y, z 71540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # END CRITICAL SECTION 71640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 71740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Note: on a platform using IEEE-754 double arithmetic, this can 71840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # never return 0.0 (asserted by Tim; proof too long for a comment). 71940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0 72040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 72140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def getstate(self): 72240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Return internal state; can be passed to setstate() later.""" 72340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return self.VERSION, self._seed, self.gauss_next 72440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 72540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def setstate(self, state): 72640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Restore internal state from object returned by getstate().""" 72740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version = state[0] 72840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if version == 1: 72940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version, self._seed, self.gauss_next = state 73040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger else: 73140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError("state with version %s passed to " 73240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger "Random.setstate() of version %s" % 73340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger (version, self.VERSION)) 73440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 73540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def jumpahead(self, n): 73640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Act as if n calls to random() were made, but quickly. 73740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 73840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger n is an int, greater than or equal to 0. 73940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 74040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Example use: If you have 2 threads and know that each will 74140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger consume no more than a million random numbers, create two Random 74240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger objects r1 and r2, then do 74340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger r2.setstate(r1.getstate()) 74440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger r2.jumpahead(1000000) 74540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Then r1 and r2 will use guaranteed-disjoint segments of the full 74640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger period. 74740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 74840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 74940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not n >= 0: 75040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError("n must be >= 0") 75140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x, y, z = self._seed 75240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = int(x * pow(171, n, 30269)) % 30269 75340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = int(y * pow(172, n, 30307)) % 30307 75440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = int(z * pow(170, n, 30323)) % 30323 75540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = x, y, z 75640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 75740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def __whseed(self, x=0, y=0, z=0): 75840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Set the Wichmann-Hill seed from (x, y, z). 75940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 76040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger These must be integers in the range [0, 256). 76140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 76240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 76340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not type(x) == type(y) == type(z) == int: 76440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise TypeError('seeds must be integers') 76540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256): 76640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError('seeds must be in range(0, 256)') 76740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if 0 == x == y == z: 76840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Initialize from current time 76940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger import time 77040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t = long(time.time() * 256) 77140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t = int((t&0xffffff) ^ (t>>24)) 77240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, x = divmod(t, 256) 77340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, y = divmod(t, 256) 77440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, z = divmod(t, 256) 77540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Zero is a poor seed, so substitute 1 77640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = (x or 1, y or 1, z or 1) 77740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 77840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 77940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 78040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def whseed(self, a=None): 78140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Seed from hashable object's hash code. 78240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 78340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger None or no argument seeds from current time. It is not guaranteed 78440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger that objects with distinct hash codes lead to distinct internal 78540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger states. 78640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 78740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger This is obsolete, provided for compatibility with the seed routine 78840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger used prior to Python 2.1. Use the .seed() method instead. 78940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 79040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 79140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if a is None: 79240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.__whseed() 79340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return 79440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a = hash(a) 79540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, x = divmod(a, 256) 79640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, y = divmod(a, 256) 79740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, z = divmod(a, 256) 79840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = (x + a) % 256 or 1 79940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = (y + a) % 256 or 1 80040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = (z + a) % 256 or 1 80140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.__whseed(x, y, z) 80240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 80323f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger## --------------- Operating System Random Source ------------------ 804356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 80523f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettingerclass SystemRandom(Random): 80623f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger """Alternate random number generator using sources provided 80723f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger by the operating system (such as /dev/urandom on Unix or 80823f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger CryptGenRandom on Windows). 809356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 810356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger Not available on all systems (see os.urandom() for details). 811356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """ 812356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 813356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def random(self): 814356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """Get the next random number in the range [0.0, 1.0).""" 8157c2a85b2d44851c2442ade579b760f86447bf848Tim Peters return (long(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF 816356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 817356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def getrandbits(self, k): 818356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """getrandbits(k) -> x. Generates a long int with k random bits.""" 819356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger if k <= 0: 820356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger raise ValueError('number of bits must be greater than zero') 821356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger if k != int(k): 822356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger raise TypeError('number of bits should be an integer') 823356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger bytes = (k + 7) // 8 # bits / 8 and rounded up 824356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger x = long(_hexlify(_urandom(bytes)), 16) 825356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger return x >> (bytes * 8 - k) # trim excess bits 826356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 827356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def _stub(self, *args, **kwds): 82823f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "Stub method. Not used for a system random number generator." 829356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger return None 830356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger seed = jumpahead = _stub 831356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 832356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def _notimplemented(self, *args, **kwds): 83323f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "Method should not be called for a system random number generator." 83423f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger raise NotImplementedError('System entropy source does not have state.') 835356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger getstate = setstate = _notimplemented 836356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 837cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- test program -------------------- 838ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 83962297132215490e9cb406e1a21f03aff40d421cbRaymond Hettingerdef _test_generator(n, func, args): 8400c9886d589ddebf32de0ca3f027a173222ed383aTim Peters import time 84162297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger print n, 'times', func.__name__ 842b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger total = 0.0 8430c9886d589ddebf32de0ca3f027a173222ed383aTim Peters sqsum = 0.0 8440c9886d589ddebf32de0ca3f027a173222ed383aTim Peters smallest = 1e10 8450c9886d589ddebf32de0ca3f027a173222ed383aTim Peters largest = -1e10 8460c9886d589ddebf32de0ca3f027a173222ed383aTim Peters t0 = time.time() 8470c9886d589ddebf32de0ca3f027a173222ed383aTim Peters for i in range(n): 84862297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger x = func(*args) 849b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger total += x 8500c9886d589ddebf32de0ca3f027a173222ed383aTim Peters sqsum = sqsum + x*x 8510c9886d589ddebf32de0ca3f027a173222ed383aTim Peters smallest = min(x, smallest) 8520c9886d589ddebf32de0ca3f027a173222ed383aTim Peters largest = max(x, largest) 8530c9886d589ddebf32de0ca3f027a173222ed383aTim Peters t1 = time.time() 8540c9886d589ddebf32de0ca3f027a173222ed383aTim Peters print round(t1-t0, 3), 'sec,', 855b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger avg = total/n 856d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters stddev = _sqrt(sqsum/n - avg*avg) 8570c9886d589ddebf32de0ca3f027a173222ed383aTim Peters print 'avg %g, stddev %g, min %g, max %g' % \ 8580c9886d589ddebf32de0ca3f027a173222ed383aTim Peters (avg, stddev, smallest, largest) 859ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 860f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 861f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettingerdef _test(N=2000): 86262297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, random, ()) 86362297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, normalvariate, (0.0, 1.0)) 86462297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, lognormvariate, (0.0, 1.0)) 86562297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, vonmisesvariate, (0.0, 1.0)) 86662297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.01, 1.0)) 86762297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.1, 1.0)) 86862297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.1, 2.0)) 86962297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.5, 1.0)) 87062297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.9, 1.0)) 87162297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (1.0, 1.0)) 87262297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (2.0, 1.0)) 87362297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (20.0, 1.0)) 87462297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (200.0, 1.0)) 87562297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gauss, (0.0, 1.0)) 87662297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, betavariate, (3.0, 3.0)) 877bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettinger _test_generator(N, triangular, (0.0, 1.0, 1.0/3.0)) 878cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 879715c4c412b21f68ad59773698d06eea8eb0c5a44Tim Peters# Create one instance, seeded from current time, and export its methods 88040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# as module-level functions. The functions share state across all uses 88140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger#(both in the user's code and in the Python libraries), but that's fine 88240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# for most programs and is easier for the casual user than making them 88340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# instantiate their own Random() instance. 88440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 885d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters_inst = Random() 886d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersseed = _inst.seed 887d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandom = _inst.random 888d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersuniform = _inst.uniform 889bbc50eafe5cc7d2fa73b5b45eebc573c600db9acRaymond Hettingertriangular = _inst.triangular 890d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandint = _inst.randint 891d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterschoice = _inst.choice 892d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandrange = _inst.randrange 893f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettingersample = _inst.sample 894d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersshuffle = _inst.shuffle 895d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersnormalvariate = _inst.normalvariate 896d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterslognormvariate = _inst.lognormvariate 897d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersexpovariate = _inst.expovariate 898d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersvonmisesvariate = _inst.vonmisesvariate 899d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgammavariate = _inst.gammavariate 900d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgauss = _inst.gauss 901d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersbetavariate = _inst.betavariate 902d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersparetovariate = _inst.paretovariate 903d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersweibullvariate = _inst.weibullvariate 904d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgetstate = _inst.getstate 905d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterssetstate = _inst.setstate 906d52269bfd029c4a517ea74c17edd5c3a250c366cTim Petersjumpahead = _inst.jumpahead 9072f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettingergetrandbits = _inst.getrandbits 908d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 909ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossumif __name__ == '__main__': 910d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters _test() 911