random.py revision 91e27c253c8bb8b6ae8521f1dbb76de7c66ad8cf
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 16e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum normal (Gaussian) 17e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum lognormal 18e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum negative exponential 19e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum gamma 20e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum beta 2140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger pareto 2240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Weibull 23e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum 24e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum distributions on the circle (angles 0 to 2pi) 25e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum --------------------------------------------- 26e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum circular uniform 27e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum von Mises 28e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum 2940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond HettingerGeneral notes on the underlying Mersenne Twister core generator: 3040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 3140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger* The period is 2**19937-1. 3240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger* It is one of the most extensively tested generators in existence 3340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger* Without a direct way to compute N steps forward, the 3440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger semantics of jumpahead(n) are weakened to simply jump 3540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger to another distant state and rely on the large period 3640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger to avoid overlapping sequences. 3740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger* The random() method is implemented in C, executes in 3840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a single Python step, and is, therefore, threadsafe. 3940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 40e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum""" 41d03e1197cb5052e3f758794e2a7aecf9f5ca5f46Guido van Rossum 422f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettingerfrom warnings import warn as _warn 432f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettingerfrom types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType 4491e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettingerfrom math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil 45d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersfrom math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin 46c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettingerfrom os import urandom as _urandom 47c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettingerfrom binascii import hexlify as _hexlify 48d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 49f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger__all__ = ["Random","seed","random","uniform","randint","choice","sample", 500de65807e6bdc5254f5a7e99b2f39adeea6b883bSkip Montanaro "randrange","shuffle","normalvariate","lognormvariate", 51f8a52d38ad784b34a60720cb148180d6eb6de373Raymond Hettinger "expovariate","vonmisesvariate","gammavariate", 52f8a52d38ad784b34a60720cb148180d6eb6de373Raymond Hettinger "gauss","betavariate","paretovariate","weibullvariate", 53356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger "getstate","setstate","jumpahead", "WichmannHill", "getrandbits", 5423f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "SystemRandom"] 55ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 56d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersNV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0) 57d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersTWOPI = 2.0*_pi 58d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersLOG4 = _log(4.0) 59d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersSG_MAGICCONST = 1.0 + _log(4.5) 602f726e9093381572b21edbfc42659ea89fbdf686Raymond HettingerBPF = 53 # Number of bits in a float 617c2a85b2d44851c2442ade579b760f86447bf848Tim PetersRECIP_BPF = 2**-BPF 6233d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 63356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 64d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters# Translated by Guido van Rossum from C source provided by 6540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# Adrian Baddeley. Adapted by Raymond Hettinger for use with 663fa19d7ff89be87139e2864fb9186b424d180a58Raymond Hettinger# the Mersenne Twister and os.urandom() core generators. 6733d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 68145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettingerimport _random 6940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 70145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettingerclass Random(_random.Random): 71c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Random number generator base class used by bound module functions. 72c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 73c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Used to instantiate instances of Random to get generators that don't 74c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger share state. Especially useful for multi-threaded programs, creating 75c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger a different instance of Random for each thread, and using the jumpahead() 76c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger method to ensure that the generated sequences seen by each thread don't 77c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger overlap. 78c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 79c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Class Random can also be subclassed if you want to use a different basic 80c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger generator of your own devising: in that case, override the following 81c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger methods: random(), seed(), getstate(), setstate() and jumpahead(). 822f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger Optionally, implement a getrandombits() method so that randrange() 832f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger can cover arbitrarily large ranges. 84ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 85c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 8633d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 8740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger VERSION = 2 # used by getstate/setstate 8833d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 89d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def __init__(self, x=None): 90d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Initialize an instance. 9133d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 92d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters Optional argument x controls seeding, as for Random.seed(). 93d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 9433d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 95d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.seed(x) 9640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 97ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 980de88fc4b108751b86443852b6741680d704168fTim Peters def seed(self, a=None): 990de88fc4b108751b86443852b6741680d704168fTim Peters """Initialize internal state from hashable object. 100d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 10123f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger None or no argument seeds from current time or from an operating 10223f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger system specific randomness source if available. 1030de88fc4b108751b86443852b6741680d704168fTim Peters 104bcd725fc456faca13f4598f87c0517f917711cdaTim Peters If a is not None or an int or long, hash(a) is used instead. 105d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 106d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 1073081d59f920229b26293c7a3ee3f1a9da0da53e9Raymond Hettinger if a is None: 108c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger try: 109c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger a = long(_hexlify(_urandom(16)), 16) 110c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger except NotImplementedError: 111356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger import time 112356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger a = long(time.time() * 256) # use fractional seconds 113356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 114145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger super(Random, self).seed(a) 11546c04e140cf26d1b44935c28c6f15ea467400d22Tim Peters self.gauss_next = None 11646c04e140cf26d1b44935c28c6f15ea467400d22Tim Peters 117d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def getstate(self): 118d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Return internal state; can be passed to setstate() later.""" 119145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger return self.VERSION, super(Random, self).getstate(), self.gauss_next 120d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 121d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def setstate(self, state): 122d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Restore internal state from object returned by getstate().""" 123d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters version = state[0] 12440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if version == 2: 12540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version, internalstate, self.gauss_next = state 126145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger super(Random, self).setstate(internalstate) 127d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 128d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError("state with version %s passed to " 129d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters "Random.setstate() of version %s" % 130d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters (version, self.VERSION)) 131d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 132cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## ---- Methods below this point do not need to be overridden when 133cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## ---- subclassing for the purpose of using a different core generator. 134d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 135cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- pickle support ------------------- 136d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 137cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters def __getstate__(self): # for pickle 138cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters return self.getstate() 139d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 140cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters def __setstate__(self, state): # for pickle 141cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters self.setstate(state) 142cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 1435f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger def __reduce__(self): 1445f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger return self.__class__, (), self.getstate() 1455f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger 146cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- integer methods ------------------- 147d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 1482f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger def randrange(self, start, stop=None, step=1, int=int, default=None, 1492f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger maxwidth=1L<<BPF): 150d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Choose a random item from range(start, stop[, step]). 151d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 152d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters This fixes the problem with randint() which includes the 153d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters endpoint; in Python this is usually not what you want. 1542f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger Do not supply the 'int', 'default', and 'maxwidth' arguments. 155d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 156d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 157d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # This code is a bit messy to make it fast for the 1589146f27b7799dab231083f194a14c6157b57549fTim Peters # common case while still doing adequate error checking. 159d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters istart = int(start) 160d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istart != start: 161d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer arg 1 for randrange()" 162d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if stop is default: 163d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istart > 0: 1642f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if istart >= maxwidth: 1652f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return self._randbelow(istart) 166d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return int(self.random() * istart) 167d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "empty range for randrange()" 1689146f27b7799dab231083f194a14c6157b57549fTim Peters 1699146f27b7799dab231083f194a14c6157b57549fTim Peters # stop argument supplied. 170d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters istop = int(stop) 171d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istop != stop: 172d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer stop for randrange()" 1732f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger width = istop - istart 1742f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if step == 1 and width > 0: 17576ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # Note that 1762f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # int(istart + self.random()*width) 17776ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # instead would be incorrect. For example, consider istart 17876ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # = -2 and istop = 0. Then the guts would be in 17976ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # -2.0 to 0.0 exclusive on both ends (ignoring that random() 18076ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # might return 0.0), and because int() truncates toward 0, the 18176ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # final result would be -1 or 0 (instead of -2 or -1). 1822f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # istart + int(self.random()*width) 18376ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # would also be incorrect, for a subtler reason: the RHS 18476ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # can return a long, and then randrange() would also return 18576ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # a long, but we're supposed to return an int (for backward 18676ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # compatibility). 1872f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 1882f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if width >= maxwidth: 18958eb11cf62dd04ccc2c364b62fd51b4265e2e203Tim Peters return int(istart + self._randbelow(width)) 1902f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return int(istart + int(self.random()*width)) 191d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if step == 1: 1922f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger raise ValueError, "empty range for randrange() (%d,%d, %d)" % (istart, istop, width) 1939146f27b7799dab231083f194a14c6157b57549fTim Peters 1949146f27b7799dab231083f194a14c6157b57549fTim Peters # Non-unit step argument supplied. 195d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters istep = int(step) 196d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istep != step: 197d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer step for randrange()" 198d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istep > 0: 199ffdb8bb99c4017152a9dca70669f9d6b9831d454Raymond Hettinger n = (width + istep - 1) // istep 200d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters elif istep < 0: 201ffdb8bb99c4017152a9dca70669f9d6b9831d454Raymond Hettinger n = (width + istep + 1) // istep 202d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 203d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "zero step for randrange()" 204d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 205d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if n <= 0: 206d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "empty range for randrange()" 2072f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2082f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if n >= maxwidth: 2092f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return istart + self._randbelow(n) 210d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return istart + istep*int(self.random() * n) 211d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 212d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def randint(self, a, b): 213cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters """Return random integer in range [a, b], including both end points. 214d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 215d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 216d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return self.randrange(a, b+1) 217d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 2182f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger def _randbelow(self, n, _log=_log, int=int, _maxwidth=1L<<BPF, 2192f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger _Method=_MethodType, _BuiltinMethod=_BuiltinMethodType): 2202f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger """Return a random int in the range [0,n) 2212f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2222f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger Handles the case where n has more bits than returned 2232f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger by a single call to the underlying generator. 2242f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger """ 2252f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2262f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger try: 2272f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger getrandbits = self.getrandbits 2282f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger except AttributeError: 2292f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger pass 2302f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger else: 2312f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # Only call self.getrandbits if the original random() builtin method 2322f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # has not been overridden or if a new getrandbits() was supplied. 2332f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # This assures that the two methods correspond. 2342f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method: 2352f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger k = int(1.00001 + _log(n-1, 2.0)) # 2**k > n-1 > 2**(k-2) 2362f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger r = getrandbits(k) 2372f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger while r >= n: 2382f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger r = getrandbits(k) 2392f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return r 2402f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if n >= _maxwidth: 2412f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger _warn("Underlying random() generator does not supply \n" 2422f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger "enough bits to choose from a population range this large") 2432f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return int(self.random() * n) 2442f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 245cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- sequence methods ------------------- 246cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 247d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def choice(self, seq): 248d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Choose a random element from a non-empty sequence.""" 2495dae505bbd59641a948c81bea981e7c44d4c2343Raymond Hettinger return seq[int(self.random() * len(seq))] # raises IndexError if seq is empty 250d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 251d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def shuffle(self, x, random=None, int=int): 252d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """x, random=random.random -> shuffle list x in place; return None. 253d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 254d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters Optional arg random is a 0-argument function returning a random 255d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters float in [0.0, 1.0); by default, the standard random.random. 256d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 257d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters Note that for even rather small len(x), the total number of 258d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters permutations of x is larger than the period of most random number 259d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters generators; this implies that "most" permutations of a long 260d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters sequence can never be generated. 261d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 262d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 263d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if random is None: 264d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 26585c20a41dfcec04d161ad7da7260e7b94c62d228Raymond Hettinger for i in reversed(xrange(1, len(x))): 266cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters # pick an element in x[:i+1] with which to exchange x[i] 267d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters j = int(random() * (i+1)) 268d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x[i], x[j] = x[j], x[i] 269d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 270fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger def sample(self, population, k): 271f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger """Chooses k unique random elements from a population sequence. 272f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 273c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger Returns a new list containing elements from the population while 274c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger leaving the original population unchanged. The resulting list is 275c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger in selection order so that all sub-slices will also be valid random 276c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger samples. This allows raffle winners (the sample) to be partitioned 277c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger into grand prize and second place winners (the subslices). 278f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 279c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger Members of the population need not be hashable or unique. If the 280c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger population contains repeats, then each occurrence is a possible 281c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger selection in the sample. 282f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 283c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger To choose a sample in a range of integers, use xrange as an argument. 284c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger This is especially fast and space efficient for sampling from a 285c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger large population: sample(xrange(10000000), 60) 286f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger """ 287f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 288c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger # Sampling without replacement entails tracking either potential 28991e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # selections (the pool) in a list or previous selections in a set. 290c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger 2912b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # When the number of selections is small compared to the 2922b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # population, then tracking selections is efficient, requiring 29391e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # only a small set and an occasional reselection. For 2942b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # a larger number of selections, the pool tracking method is 2952b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # preferred since the list takes less space than the 29691e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # set and it doesn't suffer from frequent reselections. 297c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger 298f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger n = len(population) 299f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger if not 0 <= k <= n: 300f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger raise ValueError, "sample larger than population" 3018b9aa8dbba644da23ce8417f2d30b218392b3282Raymond Hettinger random = self.random 302fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger _int = int 303c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger result = [None] * k 30491e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger setsize = 21 # size of a small set minus size of an empty list 30591e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger if k > 5: 30691e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets 30791e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger if n <= setsize: # is an n-length list smaller than a k-length set 308311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger pool = list(population) 309311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger for i in xrange(k): # invariant: non-selected at [0,n-i) 310fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger j = _int(random() * (n-i)) 311311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger result[i] = pool[j] 3128b9aa8dbba644da23ce8417f2d30b218392b3282Raymond Hettinger pool[j] = pool[n-i-1] # move non-selected item into vacancy 313c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger else: 31466d09f1b3029d9cf975ccf26c437c9fb2605db91Raymond Hettinger try: 31566d09f1b3029d9cf975ccf26c437c9fb2605db91Raymond Hettinger n > 0 and (population[0], population[n//2], population[n-1]) 31691e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger except (TypeError, KeyError): # handle non-sequence iterables 31766d09f1b3029d9cf975ccf26c437c9fb2605db91Raymond Hettinger population = tuple(population) 31891e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger selected = set() 31991e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger selected_add = selected.add 320c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger for i in xrange(k): 321fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger j = _int(random() * n) 322311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger while j in selected: 323fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger j = _int(random() * n) 32491e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger selected_add(j) 32591e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger result[i] = population[j] 326311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger return result 327f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 328cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- real-valued distributions ------------------- 329cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 330cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- uniform distribution ------------------- 331d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 332d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def uniform(self, a, b): 333d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Get a random number in the range [a, b).""" 334d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return a + (b-a) * self.random() 335ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 336cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- normal distribution -------------------- 337ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 338d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def normalvariate(self, mu, sigma): 339c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Normal distribution. 340c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 341c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean, and sigma is the standard deviation. 342ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 343c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 344d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # mu = mean, sigma = standard deviation 345d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 346d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses Kinderman and Monahan method. Reference: Kinderman, 347d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # A.J. and Monahan, J.F., "Computer generation of random 348d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # variables using the ratio of uniform deviates", ACM Trans 349d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Math Software, 3, (1977), pp257-260. 350d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 351d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 35242406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 353d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 35473ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u2 = 1.0 - random() 355d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = NV_MAGICCONST*(u1-0.5)/u2 356d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters zz = z*z/4.0 357d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if zz <= -_log(u2): 358d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 359d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return mu + z*sigma 360ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 361cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- lognormal distribution -------------------- 362ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 363d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def lognormvariate(self, mu, sigma): 364c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Log normal distribution. 365c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 366c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger If you take the natural logarithm of this distribution, you'll get a 367c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger normal distribution with mean mu and standard deviation sigma. 368c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu can have any value, and sigma must be greater than zero. 369ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 370c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 371d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return _exp(self.normalvariate(mu, sigma)) 372ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 373cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- exponential distribution -------------------- 374ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 375d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def expovariate(self, lambd): 376c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Exponential distribution. 377c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 378c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger lambd is 1.0 divided by the desired mean. (The parameter would be 379c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger called "lambda", but that is a reserved word in Python.) Returned 380c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger values range from 0 to positive infinity. 381ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 382c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 383d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # lambd: rate lambd = 1/mean 384d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # ('lambda' is a Python reserved word) 385ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 386d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 3870c9886d589ddebf32de0ca3f027a173222ed383aTim Peters u = random() 388d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters while u <= 1e-7: 389d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u = random() 390d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return -_log(u)/lambd 391ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 392cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- von Mises distribution -------------------- 393ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 394d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def vonmisesvariate(self, mu, kappa): 395c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Circular data distribution. 396ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 397c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean angle, expressed in radians between 0 and 2*pi, and 398c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger kappa is the concentration parameter, which must be greater than or 399c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger equal to zero. If kappa is equal to zero, this distribution reduces 400c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger to a uniform random angle over the range 0 to 2*pi. 401ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 402c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 403d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # mu: mean angle (in radians between 0 and 2*pi) 404d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # kappa: concentration parameter kappa (>= 0) 405d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # if kappa = 0 generate uniform random angle 4065810297052003f28788f6790ac799fe8e5373494Guido van Rossum 407d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Based upon an algorithm published in: Fisher, N.I., 408d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # "Statistical Analysis of Circular Data", Cambridge 409d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # University Press, 1993. 4105810297052003f28788f6790ac799fe8e5373494Guido van Rossum 411d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Thanks to Magnus Kessler for a correction to the 412d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # implementation of step 4. 4135810297052003f28788f6790ac799fe8e5373494Guido van Rossum 414d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 415d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if kappa <= 1e-6: 416d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return TWOPI * random() 417ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 418d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa) 419d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters b = (a - _sqrt(2.0 * a))/(2.0 * kappa) 420d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters r = (1.0 + b * b)/(2.0 * b) 421ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 42242406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 423d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 424ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 425d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = _cos(_pi * u1) 426d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters f = (1.0 + r * z)/(r + z) 427d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters c = kappa * (r - f) 428ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 429d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u2 = random() 430ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 43142406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger if u2 < c * (2.0 - c) or u2 <= c * _exp(1.0 - c): 432d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 433ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 434d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u3 = random() 435d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if u3 > 0.5: 436d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters theta = (mu % TWOPI) + _acos(f) 437d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 438d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters theta = (mu % TWOPI) - _acos(f) 439ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 440d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return theta 441ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 442cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- gamma distribution -------------------- 443ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 444d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def gammavariate(self, alpha, beta): 445c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Gamma distribution. Not the gamma function! 446c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 447c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Conditions on the parameters are alpha > 0 and beta > 0. 448c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 449c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 4508ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 451b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 4528ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 453570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum # Warning: a few older sources define the gamma distribution in terms 454570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum # of alpha > -1.0 455570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum if alpha <= 0.0 or beta <= 0.0: 456570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum raise ValueError, 'gammavariate: alpha and beta must be > 0.0' 4578ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 458d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 459d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if alpha > 1.0: 460d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 461d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses R.C.H. Cheng, "The generation of Gamma 462d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # variables with non-integral shape parameters", 463d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Applied Statistics, (1977), 26, No. 1, p71-74 464d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 465ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger ainv = _sqrt(2.0 * alpha - 1.0) 466ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger bbb = alpha - LOG4 467ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger ccc = alpha + ainv 4688ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 46942406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 470d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 47173ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger if not 1e-7 < u1 < .9999999: 47273ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger continue 47373ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u2 = 1.0 - random() 474d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters v = _log(u1/(1.0-u1))/ainv 475d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x = alpha*_exp(v) 476d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = u1*u1*u2 477d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters r = bbb+ccc*v-x 478d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z): 479b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return x * beta 480d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 481d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters elif alpha == 1.0: 482d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # expovariate(1) 4830c9886d589ddebf32de0ca3f027a173222ed383aTim Peters u = random() 484d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters while u <= 1e-7: 485d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u = random() 486b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return -_log(u) * beta 487d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 488d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: # alpha is between 0 and 1 (exclusive) 489d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 490d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle 491d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 49242406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 493d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u = random() 494d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters b = (_e + alpha)/_e 495d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters p = b*u 496d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if p <= 1.0: 49742406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger x = p ** (1.0/alpha) 498d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 499d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x = -_log((b-p)/alpha) 500d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 50142406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger if p > 1.0: 50242406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger if u1 <= x ** (alpha - 1.0): 50342406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger break 50442406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger elif u1 <= _exp(-x): 505d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 506b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return x * beta 507b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger 508cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Gauss (faster alternative) -------------------- 50995bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 510d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def gauss(self, mu, sigma): 511c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Gaussian distribution. 512c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 513c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean, and sigma is the standard deviation. This is 514c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger slightly faster than the normalvariate() function. 515c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 516c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Not thread-safe without a lock around calls. 517ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 518c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 519d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 520d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # When x and y are two variables from [0, 1), uniformly 521d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # distributed, then 522d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # 523d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # cos(2*pi*x)*sqrt(-2*log(1-y)) 524d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # sin(2*pi*x)*sqrt(-2*log(1-y)) 525d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # 526d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # are two *independent* variables with normal distribution 527d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (mu = 0, sigma = 1). 528d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (Lambert Meertens) 529d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (corrected version; bug discovered by Mike Miller, fixed by LM) 530d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 531d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Multithreading note: When two threads call this function 532d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # simultaneously, it is possible that they will receive the 533d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # same return value. The window is very small though. To 534d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # avoid this, you have to use a lock around all calls. (I 535d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # didn't want to slow this down in the serial case by using a 536d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # lock here.) 537d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 538d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 539d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = self.gauss_next 540d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.gauss_next = None 541d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if z is None: 542d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x2pi = random() * TWOPI 543d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters g2rad = _sqrt(-2.0 * _log(1.0 - random())) 544d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = _cos(x2pi) * g2rad 545d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.gauss_next = _sin(x2pi) * g2rad 546d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 547d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return mu + z*sigma 54895bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 549cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- beta -------------------- 55085e2e4742d0a1accecd02058a7907df36308297eTim Peters## See 55185e2e4742d0a1accecd02058a7907df36308297eTim Peters## http://sourceforge.net/bugs/?func=detailbug&bug_id=130030&group_id=5470 55285e2e4742d0a1accecd02058a7907df36308297eTim Peters## for Ivan Frohne's insightful analysis of why the original implementation: 55385e2e4742d0a1accecd02058a7907df36308297eTim Peters## 55485e2e4742d0a1accecd02058a7907df36308297eTim Peters## def betavariate(self, alpha, beta): 55585e2e4742d0a1accecd02058a7907df36308297eTim Peters## # Discrete Event Simulation in C, pp 87-88. 55685e2e4742d0a1accecd02058a7907df36308297eTim Peters## 55785e2e4742d0a1accecd02058a7907df36308297eTim Peters## y = self.expovariate(alpha) 55885e2e4742d0a1accecd02058a7907df36308297eTim Peters## z = self.expovariate(1.0/beta) 55985e2e4742d0a1accecd02058a7907df36308297eTim Peters## return z/(y+z) 56085e2e4742d0a1accecd02058a7907df36308297eTim Peters## 56185e2e4742d0a1accecd02058a7907df36308297eTim Peters## was dead wrong, and how it probably got that way. 56295bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 563d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def betavariate(self, alpha, beta): 564c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Beta distribution. 565c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 566c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Conditions on the parameters are alpha > -1 and beta} > -1. 567c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Returned values range between 0 and 1. 568ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 569c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 570ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 57185e2e4742d0a1accecd02058a7907df36308297eTim Peters # This version due to Janne Sinkkonen, and matches all the std 57285e2e4742d0a1accecd02058a7907df36308297eTim Peters # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). 57385e2e4742d0a1accecd02058a7907df36308297eTim Peters y = self.gammavariate(alpha, 1.) 57485e2e4742d0a1accecd02058a7907df36308297eTim Peters if y == 0: 57585e2e4742d0a1accecd02058a7907df36308297eTim Peters return 0.0 57685e2e4742d0a1accecd02058a7907df36308297eTim Peters else: 57785e2e4742d0a1accecd02058a7907df36308297eTim Peters return y / (y + self.gammavariate(beta, 1.)) 57895bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 579cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Pareto -------------------- 580cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 581d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def paretovariate(self, alpha): 582c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Pareto distribution. alpha is the shape parameter.""" 583d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Jain, pg. 495 584cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 58573ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u = 1.0 - self.random() 586d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return 1.0 / pow(u, 1.0/alpha) 587cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 588cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Weibull -------------------- 589cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 590d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def weibullvariate(self, alpha, beta): 591c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Weibull distribution. 592c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 593c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger alpha is the scale parameter and beta is the shape parameter. 594ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 595c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 596d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Jain, pg. 499; bug fix courtesy Bill Arms 597cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 59873ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u = 1.0 - self.random() 599d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return alpha * pow(-_log(u), 1.0/beta) 6006c395ba31609eeffce2428280cc5d95e4fb8058aGuido van Rossum 60140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger## -------------------- Wichmann-Hill ------------------- 60240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 60340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettingerclass WichmannHill(Random): 60440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 60540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger VERSION = 1 # used by getstate/setstate 60640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 60740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def seed(self, a=None): 60840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Initialize internal state from hashable object. 60940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 61023f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger None or no argument seeds from current time or from an operating 61123f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger system specific randomness source if available. 61240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 61340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger If a is not None or an int or long, hash(a) is used instead. 61440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 61540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger If a is an int or long, a is used directly. Distinct values between 61640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 0 and 27814431486575L inclusive are guaranteed to yield distinct 61740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger internal states (this guarantee is specific to the default 61840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Wichmann-Hill generator). 61940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 62040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 62140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if a is None: 622c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger try: 623c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger a = long(_hexlify(_urandom(16)), 16) 624c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger except NotImplementedError: 625356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger import time 626356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger a = long(time.time() * 256) # use fractional seconds 62740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 62840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not isinstance(a, (int, long)): 62940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a = hash(a) 63040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 63140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, x = divmod(a, 30268) 63240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, y = divmod(a, 30306) 63340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, z = divmod(a, 30322) 63440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = int(x)+1, int(y)+1, int(z)+1 63540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 63640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 63740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 63840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def random(self): 63940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Get the next random number in the range [0.0, 1.0).""" 64040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 64140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Wichman-Hill random number generator. 64240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 64340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Wichmann, B. A. & Hill, I. D. (1982) 64440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Algorithm AS 183: 64540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # An efficient and portable pseudo-random number generator 64640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 31 (1982) 188-190 64740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 64840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # see also: 64940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Correction to Algorithm AS 183 65040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 33 (1984) 123 65140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 65240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # McLeod, A. I. (1985) 65340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # A remark on Algorithm AS 183 65440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 34 (1985),198-200 65540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 65640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # This part is thread-unsafe: 65740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # BEGIN CRITICAL SECTION 65840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x, y, z = self._seed 65940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = (171 * x) % 30269 66040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = (172 * y) % 30307 66140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = (170 * z) % 30323 66240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = x, y, z 66340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # END CRITICAL SECTION 66440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 66540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Note: on a platform using IEEE-754 double arithmetic, this can 66640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # never return 0.0 (asserted by Tim; proof too long for a comment). 66740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0 66840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 66940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def getstate(self): 67040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Return internal state; can be passed to setstate() later.""" 67140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return self.VERSION, self._seed, self.gauss_next 67240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 67340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def setstate(self, state): 67440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Restore internal state from object returned by getstate().""" 67540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version = state[0] 67640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if version == 1: 67740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version, self._seed, self.gauss_next = state 67840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger else: 67940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError("state with version %s passed to " 68040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger "Random.setstate() of version %s" % 68140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger (version, self.VERSION)) 68240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 68340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def jumpahead(self, n): 68440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Act as if n calls to random() were made, but quickly. 68540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 68640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger n is an int, greater than or equal to 0. 68740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 68840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Example use: If you have 2 threads and know that each will 68940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger consume no more than a million random numbers, create two Random 69040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger objects r1 and r2, then do 69140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger r2.setstate(r1.getstate()) 69240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger r2.jumpahead(1000000) 69340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Then r1 and r2 will use guaranteed-disjoint segments of the full 69440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger period. 69540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 69640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 69740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not n >= 0: 69840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError("n must be >= 0") 69940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x, y, z = self._seed 70040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = int(x * pow(171, n, 30269)) % 30269 70140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = int(y * pow(172, n, 30307)) % 30307 70240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = int(z * pow(170, n, 30323)) % 30323 70340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = x, y, z 70440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 70540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def __whseed(self, x=0, y=0, z=0): 70640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Set the Wichmann-Hill seed from (x, y, z). 70740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 70840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger These must be integers in the range [0, 256). 70940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 71040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 71140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not type(x) == type(y) == type(z) == int: 71240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise TypeError('seeds must be integers') 71340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256): 71440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError('seeds must be in range(0, 256)') 71540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if 0 == x == y == z: 71640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Initialize from current time 71740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger import time 71840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t = long(time.time() * 256) 71940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t = int((t&0xffffff) ^ (t>>24)) 72040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, x = divmod(t, 256) 72140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, y = divmod(t, 256) 72240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, z = divmod(t, 256) 72340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Zero is a poor seed, so substitute 1 72440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = (x or 1, y or 1, z or 1) 72540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 72640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 72740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 72840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def whseed(self, a=None): 72940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Seed from hashable object's hash code. 73040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 73140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger None or no argument seeds from current time. It is not guaranteed 73240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger that objects with distinct hash codes lead to distinct internal 73340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger states. 73440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 73540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger This is obsolete, provided for compatibility with the seed routine 73640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger used prior to Python 2.1. Use the .seed() method instead. 73740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 73840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 73940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if a is None: 74040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.__whseed() 74140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return 74240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a = hash(a) 74340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, x = divmod(a, 256) 74440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, y = divmod(a, 256) 74540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, z = divmod(a, 256) 74640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = (x + a) % 256 or 1 74740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = (y + a) % 256 or 1 74840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = (z + a) % 256 or 1 74940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.__whseed(x, y, z) 75040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 75123f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger## --------------- Operating System Random Source ------------------ 752356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 75323f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettingerclass SystemRandom(Random): 75423f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger """Alternate random number generator using sources provided 75523f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger by the operating system (such as /dev/urandom on Unix or 75623f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger CryptGenRandom on Windows). 757356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 758356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger Not available on all systems (see os.urandom() for details). 759356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """ 760356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 761356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def random(self): 762356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """Get the next random number in the range [0.0, 1.0).""" 7637c2a85b2d44851c2442ade579b760f86447bf848Tim Peters return (long(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF 764356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 765356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def getrandbits(self, k): 766356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """getrandbits(k) -> x. Generates a long int with k random bits.""" 767356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger if k <= 0: 768356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger raise ValueError('number of bits must be greater than zero') 769356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger if k != int(k): 770356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger raise TypeError('number of bits should be an integer') 771356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger bytes = (k + 7) // 8 # bits / 8 and rounded up 772356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger x = long(_hexlify(_urandom(bytes)), 16) 773356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger return x >> (bytes * 8 - k) # trim excess bits 774356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 775356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def _stub(self, *args, **kwds): 77623f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "Stub method. Not used for a system random number generator." 777356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger return None 778356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger seed = jumpahead = _stub 779356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 780356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def _notimplemented(self, *args, **kwds): 78123f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "Method should not be called for a system random number generator." 78223f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger raise NotImplementedError('System entropy source does not have state.') 783356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger getstate = setstate = _notimplemented 784356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 785cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- test program -------------------- 786ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 78762297132215490e9cb406e1a21f03aff40d421cbRaymond Hettingerdef _test_generator(n, func, args): 7880c9886d589ddebf32de0ca3f027a173222ed383aTim Peters import time 78962297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger print n, 'times', func.__name__ 790b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger total = 0.0 7910c9886d589ddebf32de0ca3f027a173222ed383aTim Peters sqsum = 0.0 7920c9886d589ddebf32de0ca3f027a173222ed383aTim Peters smallest = 1e10 7930c9886d589ddebf32de0ca3f027a173222ed383aTim Peters largest = -1e10 7940c9886d589ddebf32de0ca3f027a173222ed383aTim Peters t0 = time.time() 7950c9886d589ddebf32de0ca3f027a173222ed383aTim Peters for i in range(n): 79662297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger x = func(*args) 797b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger total += x 7980c9886d589ddebf32de0ca3f027a173222ed383aTim Peters sqsum = sqsum + x*x 7990c9886d589ddebf32de0ca3f027a173222ed383aTim Peters smallest = min(x, smallest) 8000c9886d589ddebf32de0ca3f027a173222ed383aTim Peters largest = max(x, largest) 8010c9886d589ddebf32de0ca3f027a173222ed383aTim Peters t1 = time.time() 8020c9886d589ddebf32de0ca3f027a173222ed383aTim Peters print round(t1-t0, 3), 'sec,', 803b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger avg = total/n 804d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters stddev = _sqrt(sqsum/n - avg*avg) 8050c9886d589ddebf32de0ca3f027a173222ed383aTim Peters print 'avg %g, stddev %g, min %g, max %g' % \ 8060c9886d589ddebf32de0ca3f027a173222ed383aTim Peters (avg, stddev, smallest, largest) 807ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 808f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 809f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettingerdef _test(N=2000): 81062297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, random, ()) 81162297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, normalvariate, (0.0, 1.0)) 81262297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, lognormvariate, (0.0, 1.0)) 81362297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, vonmisesvariate, (0.0, 1.0)) 81462297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.01, 1.0)) 81562297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.1, 1.0)) 81662297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.1, 2.0)) 81762297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.5, 1.0)) 81862297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.9, 1.0)) 81962297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (1.0, 1.0)) 82062297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (2.0, 1.0)) 82162297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (20.0, 1.0)) 82262297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (200.0, 1.0)) 82362297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gauss, (0.0, 1.0)) 82462297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, betavariate, (3.0, 3.0)) 825cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 826715c4c412b21f68ad59773698d06eea8eb0c5a44Tim Peters# Create one instance, seeded from current time, and export its methods 82740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# as module-level functions. The functions share state across all uses 82840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger#(both in the user's code and in the Python libraries), but that's fine 82940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# for most programs and is easier for the casual user than making them 83040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# instantiate their own Random() instance. 83140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 832d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters_inst = Random() 833d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersseed = _inst.seed 834d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandom = _inst.random 835d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersuniform = _inst.uniform 836d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandint = _inst.randint 837d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterschoice = _inst.choice 838d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandrange = _inst.randrange 839f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettingersample = _inst.sample 840d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersshuffle = _inst.shuffle 841d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersnormalvariate = _inst.normalvariate 842d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterslognormvariate = _inst.lognormvariate 843d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersexpovariate = _inst.expovariate 844d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersvonmisesvariate = _inst.vonmisesvariate 845d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgammavariate = _inst.gammavariate 846d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgauss = _inst.gauss 847d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersbetavariate = _inst.betavariate 848d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersparetovariate = _inst.paretovariate 849d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersweibullvariate = _inst.weibullvariate 850d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgetstate = _inst.getstate 851d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterssetstate = _inst.setstate 852d52269bfd029c4a517ea74c17edd5c3a250c366cTim Petersjumpahead = _inst.jumpahead 8532f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettingergetrandbits = _inst.getrandbits 854d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 855ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossumif __name__ == '__main__': 856d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters _test() 857