random.py revision 6b449f4f2bd86c104a8b57547428eb9bb3a182b0
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. 320e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters* It is one of the most extensively tested generators in existence. 330e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters* Without a direct way to compute N steps forward, the semantics of 340e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters jumpahead(n) are weakened to simply jump to another distant state and rely 350e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters on the large period to avoid overlapping sequences. 360e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters* The random() method is implemented in C, executes in a single Python step, 370e1159583c06fdf85d7d2dbe8b82e42565b9d166Tim Peters and is, therefore, threadsafe. 3840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 39e7b146fb3bdca62a0d5ecc06dbf3348e5a4fe757Guido van Rossum""" 40d03e1197cb5052e3f758794e2a7aecf9f5ca5f46Guido van Rossum 412f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettingerfrom warnings import warn as _warn 422f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettingerfrom types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType 4391e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettingerfrom math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil 44d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersfrom math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin 45c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettingerfrom os import urandom as _urandom 46c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettingerfrom binascii import hexlify as _hexlify 47d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 48f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger__all__ = ["Random","seed","random","uniform","randint","choice","sample", 490de65807e6bdc5254f5a7e99b2f39adeea6b883bSkip Montanaro "randrange","shuffle","normalvariate","lognormvariate", 50f8a52d38ad784b34a60720cb148180d6eb6de373Raymond Hettinger "expovariate","vonmisesvariate","gammavariate", 51f8a52d38ad784b34a60720cb148180d6eb6de373Raymond Hettinger "gauss","betavariate","paretovariate","weibullvariate", 52356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger "getstate","setstate","jumpahead", "WichmannHill", "getrandbits", 5323f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "SystemRandom"] 54ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 55d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersNV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0) 56d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersTWOPI = 2.0*_pi 57d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersLOG4 = _log(4.0) 58d7b5e88e8e40b77813ceb25dc28b87d672538403Tim PetersSG_MAGICCONST = 1.0 + _log(4.5) 592f726e9093381572b21edbfc42659ea89fbdf686Raymond HettingerBPF = 53 # Number of bits in a float 607c2a85b2d44851c2442ade579b760f86447bf848Tim PetersRECIP_BPF = 2**-BPF 6133d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 62356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 63d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters# Translated by Guido van Rossum from C source provided by 6440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# Adrian Baddeley. Adapted by Raymond Hettinger for use with 653fa19d7ff89be87139e2864fb9186b424d180a58Raymond Hettinger# the Mersenne Twister and os.urandom() core generators. 6633d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 67145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettingerimport _random 6840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 69145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettingerclass Random(_random.Random): 70c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Random number generator base class used by bound module functions. 71c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 72c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Used to instantiate instances of Random to get generators that don't 73c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger share state. Especially useful for multi-threaded programs, creating 74c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger a different instance of Random for each thread, and using the jumpahead() 75c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger method to ensure that the generated sequences seen by each thread don't 76c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger overlap. 77c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 78c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Class Random can also be subclassed if you want to use a different basic 79c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger generator of your own devising: in that case, override the following 80c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger methods: random(), seed(), getstate(), setstate() and jumpahead(). 812f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger Optionally, implement a getrandombits() method so that randrange() 822f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger can cover arbitrarily large ranges. 83ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 84c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 8533d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 866b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis VERSION = 3 # used by getstate/setstate 8733d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 88d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def __init__(self, x=None): 89d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Initialize an instance. 9033d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 91d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters Optional argument x controls seeding, as for Random.seed(). 92d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 9333d7f1a76c3544d2901492cfb6fc9db85f2dfbd6Guido van Rossum 94d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.seed(x) 9540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 96ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 970de88fc4b108751b86443852b6741680d704168fTim Peters def seed(self, a=None): 980de88fc4b108751b86443852b6741680d704168fTim Peters """Initialize internal state from hashable object. 99d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 10023f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger None or no argument seeds from current time or from an operating 10123f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger system specific randomness source if available. 1020de88fc4b108751b86443852b6741680d704168fTim Peters 103bcd725fc456faca13f4598f87c0517f917711cdaTim Peters If a is not None or an int or long, hash(a) is used instead. 104d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 105d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 1063081d59f920229b26293c7a3ee3f1a9da0da53e9Raymond Hettinger if a is None: 107c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger try: 108c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger a = long(_hexlify(_urandom(16)), 16) 109c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger except NotImplementedError: 110356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger import time 111356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger a = long(time.time() * 256) # use fractional seconds 112356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 113145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger super(Random, self).seed(a) 11446c04e140cf26d1b44935c28c6f15ea467400d22Tim Peters self.gauss_next = None 11546c04e140cf26d1b44935c28c6f15ea467400d22Tim Peters 116d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def getstate(self): 117d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Return internal state; can be passed to setstate() later.""" 118145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger return self.VERSION, super(Random, self).getstate(), self.gauss_next 119d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 120d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def setstate(self, state): 121d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Restore internal state from object returned by getstate().""" 122d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters version = state[0] 1236b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis if version == 3: 12440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version, internalstate, self.gauss_next = state 125145a4a0f10009f7ce2644465ccd359938b034ac4Raymond Hettinger super(Random, self).setstate(internalstate) 1266b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis elif version == 2: 1276b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis version, internalstate, self.gauss_next = state 1286b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # In version 2, the state was saved as signed ints, which causes 1296b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # inconsistencies between 32/64-bit systems. The state is 1306b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # really unsigned 32-bit ints, so we convert negative ints from 1316b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis # version 2 to positive longs for version 3. 1326b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis try: 1336b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis internalstate = tuple( long(x) % (2**32) for x in internalstate ) 1346b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis except ValueError, e: 1356b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis raise TypeError, e 1366b449f4f2bd86c104a8b57547428eb9bb3a182b0Martin v. Löwis super(Random, self).setstate(internalstate) 137d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 138d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError("state with version %s passed to " 139d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters "Random.setstate() of version %s" % 140d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters (version, self.VERSION)) 141d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 142cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## ---- Methods below this point do not need to be overridden when 143cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## ---- subclassing for the purpose of using a different core generator. 144d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 145cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- pickle support ------------------- 146d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 147cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters def __getstate__(self): # for pickle 148cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters return self.getstate() 149d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 150cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters def __setstate__(self, state): # for pickle 151cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters self.setstate(state) 152cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 1535f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger def __reduce__(self): 1545f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger return self.__class__, (), self.getstate() 1555f078ff7f0c6bb5086fae077379fc79729c34d2dRaymond Hettinger 156cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- integer methods ------------------- 157d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 1582f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger def randrange(self, start, stop=None, step=1, int=int, default=None, 1592f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger maxwidth=1L<<BPF): 160d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Choose a random item from range(start, stop[, step]). 161d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 162d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters This fixes the problem with randint() which includes the 163d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters endpoint; in Python this is usually not what you want. 1642f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger Do not supply the 'int', 'default', and 'maxwidth' arguments. 165d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 166d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 167d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # This code is a bit messy to make it fast for the 1689146f27b7799dab231083f194a14c6157b57549fTim Peters # common case while still doing adequate error checking. 169d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters istart = int(start) 170d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istart != start: 171d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer arg 1 for randrange()" 172d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if stop is default: 173d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istart > 0: 1742f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if istart >= maxwidth: 1752f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return self._randbelow(istart) 176d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return int(self.random() * istart) 177d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "empty range for randrange()" 1789146f27b7799dab231083f194a14c6157b57549fTim Peters 1799146f27b7799dab231083f194a14c6157b57549fTim Peters # stop argument supplied. 180d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters istop = int(stop) 181d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istop != stop: 182d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer stop for randrange()" 1832f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger width = istop - istart 1842f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if step == 1 and width > 0: 18576ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # Note that 1862f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # int(istart + self.random()*width) 18776ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # instead would be incorrect. For example, consider istart 18876ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # = -2 and istop = 0. Then the guts would be in 18976ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # -2.0 to 0.0 exclusive on both ends (ignoring that random() 19076ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # might return 0.0), and because int() truncates toward 0, the 19176ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # final result would be -1 or 0 (instead of -2 or -1). 1922f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # istart + int(self.random()*width) 19376ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # would also be incorrect, for a subtler reason: the RHS 19476ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # can return a long, and then randrange() would also return 19576ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # a long, but we're supposed to return an int (for backward 19676ca1d428f96284ed58f4523b698ed95c6fdbdb2Tim Peters # compatibility). 1972f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 1982f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if width >= maxwidth: 19958eb11cf62dd04ccc2c364b62fd51b4265e2e203Tim Peters return int(istart + self._randbelow(width)) 2002f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return int(istart + int(self.random()*width)) 201d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if step == 1: 2022f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger raise ValueError, "empty range for randrange() (%d,%d, %d)" % (istart, istop, width) 2039146f27b7799dab231083f194a14c6157b57549fTim Peters 2049146f27b7799dab231083f194a14c6157b57549fTim Peters # Non-unit step argument supplied. 205d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters istep = int(step) 206d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istep != step: 207d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "non-integer step for randrange()" 208d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if istep > 0: 209ffdb8bb99c4017152a9dca70669f9d6b9831d454Raymond Hettinger n = (width + istep - 1) // istep 210d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters elif istep < 0: 211ffdb8bb99c4017152a9dca70669f9d6b9831d454Raymond Hettinger n = (width + istep + 1) // istep 212d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 213d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "zero step for randrange()" 214d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 215d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if n <= 0: 216d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters raise ValueError, "empty range for randrange()" 2172f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2182f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if n >= maxwidth: 21994547f7646895e032f8fc145529d9efc3a70760dRaymond Hettinger return istart + istep*self._randbelow(n) 220d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return istart + istep*int(self.random() * n) 221d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 222d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def randint(self, a, b): 223cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters """Return random integer in range [a, b], including both end points. 224d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 225d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 226d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return self.randrange(a, b+1) 227d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 2282f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger def _randbelow(self, n, _log=_log, int=int, _maxwidth=1L<<BPF, 2292f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger _Method=_MethodType, _BuiltinMethod=_BuiltinMethodType): 2302f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger """Return a random int in the range [0,n) 2312f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2322f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger Handles the case where n has more bits than returned 2332f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger by a single call to the underlying generator. 2342f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger """ 2352f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 2362f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger try: 2372f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger getrandbits = self.getrandbits 2382f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger except AttributeError: 2392f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger pass 2402f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger else: 2412f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # Only call self.getrandbits if the original random() builtin method 2422f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # has not been overridden or if a new getrandbits() was supplied. 2432f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger # This assures that the two methods correspond. 2442f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method: 2452f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger k = int(1.00001 + _log(n-1, 2.0)) # 2**k > n-1 > 2**(k-2) 2462f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger r = getrandbits(k) 2472f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger while r >= n: 2482f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger r = getrandbits(k) 2492f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return r 2502f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger if n >= _maxwidth: 2512f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger _warn("Underlying random() generator does not supply \n" 2522f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger "enough bits to choose from a population range this large") 2532f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger return int(self.random() * n) 2542f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettinger 255cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- sequence methods ------------------- 256cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 257d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def choice(self, seq): 258d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Choose a random element from a non-empty sequence.""" 2595dae505bbd59641a948c81bea981e7c44d4c2343Raymond Hettinger return seq[int(self.random() * len(seq))] # raises IndexError if seq is empty 260d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 261d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def shuffle(self, x, random=None, int=int): 262d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """x, random=random.random -> shuffle list x in place; return None. 263d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 264d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters Optional arg random is a 0-argument function returning a random 265d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters float in [0.0, 1.0); by default, the standard random.random. 266d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """ 267d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 268d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if random is None: 269d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 27085c20a41dfcec04d161ad7da7260e7b94c62d228Raymond Hettinger for i in reversed(xrange(1, len(x))): 271cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters # pick an element in x[:i+1] with which to exchange x[i] 272d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters j = int(random() * (i+1)) 273d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x[i], x[j] = x[j], x[i] 274d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 275fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger def sample(self, population, k): 276f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger """Chooses k unique random elements from a population sequence. 277f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 278c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger Returns a new list containing elements from the population while 279c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger leaving the original population unchanged. The resulting list is 280c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger in selection order so that all sub-slices will also be valid random 281c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger samples. This allows raffle winners (the sample) to be partitioned 282c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger into grand prize and second place winners (the subslices). 283f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 284c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger Members of the population need not be hashable or unique. If the 285c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger population contains repeats, then each occurrence is a possible 286c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger selection in the sample. 287f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 288c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger To choose a sample in a range of integers, use xrange as an argument. 289c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger This is especially fast and space efficient for sampling from a 290c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger large population: sample(xrange(10000000), 60) 291f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger """ 292f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 293c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX Although the documentation says `population` is "a sequence", 294c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX attempts are made to cater to any iterable with a __len__ 295c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX method. This has had mixed success. Examples from both 296c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX sides: sets work fine, and should become officially supported; 297c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX dicts are much harder, and have failed in various subtle 298c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX ways across attempts. Support for mapping types should probably 299c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX be dropped (and users should pass mapping.keys() or .values() 300c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # XXX explicitly). 301c17976e9833f3093adb1019356737e728a24f7c9Tim Peters 302c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger # Sampling without replacement entails tracking either potential 30391e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # selections (the pool) in a list or previous selections in a set. 304c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger 3052b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # When the number of selections is small compared to the 3062b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # population, then tracking selections is efficient, requiring 30791e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # only a small set and an occasional reselection. For 3082b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # a larger number of selections, the pool tracking method is 3092b55d35850e3e8e0b28aba7878d3f9122a7907acJeremy Hylton # preferred since the list takes less space than the 31091e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger # set and it doesn't suffer from frequent reselections. 311c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger 312f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger n = len(population) 313f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger if not 0 <= k <= n: 314f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger raise ValueError, "sample larger than population" 3158b9aa8dbba644da23ce8417f2d30b218392b3282Raymond Hettinger random = self.random 316fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger _int = int 317c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger result = [None] * k 31891e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger setsize = 21 # size of a small set minus size of an empty list 31991e27c253c8bb8b6ae8521f1dbb76de7c66ad8cfRaymond Hettinger if k > 5: 3209e34c047325651853a95f95e538582a4f6d5b7f6Tim Peters setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets 321c17976e9833f3093adb1019356737e728a24f7c9Tim Peters if n <= setsize or hasattr(population, "keys"): 322c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # An n-length list is smaller than a k-length set, or this is a 323c17976e9833f3093adb1019356737e728a24f7c9Tim Peters # mapping type so the other algorithm wouldn't work. 324311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger pool = list(population) 325311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger for i in xrange(k): # invariant: non-selected at [0,n-i) 326fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger j = _int(random() * (n-i)) 327311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger result[i] = pool[j] 3288b9aa8dbba644da23ce8417f2d30b218392b3282Raymond Hettinger pool[j] = pool[n-i-1] # move non-selected item into vacancy 329c0b4034b8165ce958a23f2c865b51ae0f52040f5Raymond Hettinger else: 33066d09f1b3029d9cf975ccf26c437c9fb2605db91Raymond Hettinger try: 3313c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger selected = set() 3323c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger selected_add = selected.add 3333c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger for i in xrange(k): 334fdbe5223b7402ee34c4f0c06caa6faabd9e73e35Raymond Hettinger j = _int(random() * n) 3353c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger while j in selected: 3363c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger j = _int(random() * n) 3373c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger selected_add(j) 3383c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger result[i] = population[j] 339c17976e9833f3093adb1019356737e728a24f7c9Tim Peters except (TypeError, KeyError): # handle (at least) sets 3403c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger if isinstance(population, list): 3413c3346daa9bf900080428ed12b6d83aa04f7332bRaymond Hettinger raise 342c17976e9833f3093adb1019356737e728a24f7c9Tim Peters return self.sample(tuple(population), k) 343311f4196284b894f86f56c287c71a0e59c4a72a2Raymond Hettinger return result 344f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 345cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- real-valued distributions ------------------- 346cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 347cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- uniform distribution ------------------- 348d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 349d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def uniform(self, a, b): 350d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters """Get a random number in the range [a, b).""" 351d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return a + (b-a) * self.random() 352ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 353cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- normal distribution -------------------- 354ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 355d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def normalvariate(self, mu, sigma): 356c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Normal distribution. 357c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 358c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean, and sigma is the standard deviation. 359ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 360c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 361d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # mu = mean, sigma = standard deviation 362d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 363d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses Kinderman and Monahan method. Reference: Kinderman, 364d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # A.J. and Monahan, J.F., "Computer generation of random 365d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # variables using the ratio of uniform deviates", ACM Trans 366d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Math Software, 3, (1977), pp257-260. 367d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 368d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 36942406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 370d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 37173ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u2 = 1.0 - random() 372d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = NV_MAGICCONST*(u1-0.5)/u2 373d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters zz = z*z/4.0 374d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if zz <= -_log(u2): 375d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 376d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return mu + z*sigma 377ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 378cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- lognormal distribution -------------------- 379ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 380d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def lognormvariate(self, mu, sigma): 381c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Log normal distribution. 382c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 383c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger If you take the natural logarithm of this distribution, you'll get a 384c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger normal distribution with mean mu and standard deviation sigma. 385c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu can have any value, and sigma must be greater than zero. 386ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 387c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 388d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return _exp(self.normalvariate(mu, sigma)) 389ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 390cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- exponential distribution -------------------- 391ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 392d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def expovariate(self, lambd): 393c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Exponential distribution. 394c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 395c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger lambd is 1.0 divided by the desired mean. (The parameter would be 396c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger called "lambda", but that is a reserved word in Python.) Returned 397c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger values range from 0 to positive infinity. 398ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 399c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 400d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # lambd: rate lambd = 1/mean 401d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # ('lambda' is a Python reserved word) 402ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 403d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 4040c9886d589ddebf32de0ca3f027a173222ed383aTim Peters u = random() 405d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters while u <= 1e-7: 406d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u = random() 407d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return -_log(u)/lambd 408ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 409cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- von Mises distribution -------------------- 410ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 411d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def vonmisesvariate(self, mu, kappa): 412c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Circular data distribution. 413ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 414c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean angle, expressed in radians between 0 and 2*pi, and 415c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger kappa is the concentration parameter, which must be greater than or 416c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger equal to zero. If kappa is equal to zero, this distribution reduces 417c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger to a uniform random angle over the range 0 to 2*pi. 418ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 419c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 420d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # mu: mean angle (in radians between 0 and 2*pi) 421d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # kappa: concentration parameter kappa (>= 0) 422d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # if kappa = 0 generate uniform random angle 4235810297052003f28788f6790ac799fe8e5373494Guido van Rossum 424d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Based upon an algorithm published in: Fisher, N.I., 425d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # "Statistical Analysis of Circular Data", Cambridge 426d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # University Press, 1993. 4275810297052003f28788f6790ac799fe8e5373494Guido van Rossum 428d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Thanks to Magnus Kessler for a correction to the 429d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # implementation of step 4. 4305810297052003f28788f6790ac799fe8e5373494Guido van Rossum 431d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 432d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if kappa <= 1e-6: 433d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return TWOPI * random() 434ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 435d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa) 436d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters b = (a - _sqrt(2.0 * a))/(2.0 * kappa) 437d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters r = (1.0 + b * b)/(2.0 * b) 438ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 43942406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 440d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 441ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 442d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = _cos(_pi * u1) 443d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters f = (1.0 + r * z)/(r + z) 444d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters c = kappa * (r - f) 445ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 446d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u2 = random() 447ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 44842406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger if u2 < c * (2.0 - c) or u2 <= c * _exp(1.0 - c): 449d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 450ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 451d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u3 = random() 452d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if u3 > 0.5: 453d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters theta = (mu % TWOPI) + _acos(f) 454d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 455d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters theta = (mu % TWOPI) - _acos(f) 456ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 457d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return theta 458ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 459cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- gamma distribution -------------------- 460ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 461d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def gammavariate(self, alpha, beta): 462c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Gamma distribution. Not the gamma function! 463c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 464c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Conditions on the parameters are alpha > 0 and beta > 0. 465c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 466c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 4678ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 468b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 4698ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 470570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum # Warning: a few older sources define the gamma distribution in terms 471570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum # of alpha > -1.0 472570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum if alpha <= 0.0 or beta <= 0.0: 473570764ddce285afc32e6bd4bce031e421376b382Guido van Rossum raise ValueError, 'gammavariate: alpha and beta must be > 0.0' 4748ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 475d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 476d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if alpha > 1.0: 477d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 478d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses R.C.H. Cheng, "The generation of Gamma 479d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # variables with non-integral shape parameters", 480d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Applied Statistics, (1977), 26, No. 1, p71-74 481d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 482ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger ainv = _sqrt(2.0 * alpha - 1.0) 483ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger bbb = alpha - LOG4 484ca6cdc2c0259b1b74a3f4c2d29a35e76617a3019Raymond Hettinger ccc = alpha + ainv 4858ac1495a6a1d18111a626cec0c7f2eb67df3edb3Tim Peters 48642406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 487d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 48873ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger if not 1e-7 < u1 < .9999999: 48973ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger continue 49073ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u2 = 1.0 - random() 491d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters v = _log(u1/(1.0-u1))/ainv 492d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x = alpha*_exp(v) 493d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = u1*u1*u2 494d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters r = bbb+ccc*v-x 495d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z): 496b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return x * beta 497d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 498d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters elif alpha == 1.0: 499d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # expovariate(1) 5000c9886d589ddebf32de0ca3f027a173222ed383aTim Peters u = random() 501d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters while u <= 1e-7: 502d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u = random() 503b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return -_log(u) * beta 504d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 505d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: # alpha is between 0 and 1 (exclusive) 506d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 507d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle 508d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 50942406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger while 1: 510d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u = random() 511d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters b = (_e + alpha)/_e 512d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters p = b*u 513d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if p <= 1.0: 51442406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger x = p ** (1.0/alpha) 515d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters else: 516d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x = -_log((b-p)/alpha) 517d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters u1 = random() 51842406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger if p > 1.0: 51942406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger if u1 <= x ** (alpha - 1.0): 52042406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger break 52142406e6f27e9a42e91db8706d897e0b478b13a4dRaymond Hettinger elif u1 <= _exp(-x): 522d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters break 523b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger return x * beta 524b760efb08d509bb2acfdef8f4e59dfafa20ca57fRaymond Hettinger 525cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Gauss (faster alternative) -------------------- 52695bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 527d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def gauss(self, mu, sigma): 528c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Gaussian distribution. 529c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 530c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger mu is the mean, and sigma is the standard deviation. This is 531c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger slightly faster than the normalvariate() function. 532c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 533c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Not thread-safe without a lock around calls. 534ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 535c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 536d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 537d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # When x and y are two variables from [0, 1), uniformly 538d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # distributed, then 539d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # 540d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # cos(2*pi*x)*sqrt(-2*log(1-y)) 541d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # sin(2*pi*x)*sqrt(-2*log(1-y)) 542d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # 543d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # are two *independent* variables with normal distribution 544d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (mu = 0, sigma = 1). 545d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (Lambert Meertens) 546d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # (corrected version; bug discovered by Mike Miller, fixed by LM) 547d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 548d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Multithreading note: When two threads call this function 549d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # simultaneously, it is possible that they will receive the 550d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # same return value. The window is very small though. To 551d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # avoid this, you have to use a lock around all calls. (I 552d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # didn't want to slow this down in the serial case by using a 553d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # lock here.) 554d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 555d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters random = self.random 556d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = self.gauss_next 557d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.gauss_next = None 558d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters if z is None: 559d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters x2pi = random() * TWOPI 560d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters g2rad = _sqrt(-2.0 * _log(1.0 - random())) 561d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters z = _cos(x2pi) * g2rad 562d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters self.gauss_next = _sin(x2pi) * g2rad 563d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 564d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return mu + z*sigma 56595bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 566cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- beta -------------------- 56785e2e4742d0a1accecd02058a7907df36308297eTim Peters## See 56885e2e4742d0a1accecd02058a7907df36308297eTim Peters## http://sourceforge.net/bugs/?func=detailbug&bug_id=130030&group_id=5470 56985e2e4742d0a1accecd02058a7907df36308297eTim Peters## for Ivan Frohne's insightful analysis of why the original implementation: 57085e2e4742d0a1accecd02058a7907df36308297eTim Peters## 57185e2e4742d0a1accecd02058a7907df36308297eTim Peters## def betavariate(self, alpha, beta): 57285e2e4742d0a1accecd02058a7907df36308297eTim Peters## # Discrete Event Simulation in C, pp 87-88. 57385e2e4742d0a1accecd02058a7907df36308297eTim Peters## 57485e2e4742d0a1accecd02058a7907df36308297eTim Peters## y = self.expovariate(alpha) 57585e2e4742d0a1accecd02058a7907df36308297eTim Peters## z = self.expovariate(1.0/beta) 57685e2e4742d0a1accecd02058a7907df36308297eTim Peters## return z/(y+z) 57785e2e4742d0a1accecd02058a7907df36308297eTim Peters## 57885e2e4742d0a1accecd02058a7907df36308297eTim Peters## was dead wrong, and how it probably got that way. 57995bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 580d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def betavariate(self, alpha, beta): 581c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Beta distribution. 582c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 5831b0ce8527112b997194a4e2fb9a1a850c6d73ee8Raymond Hettinger Conditions on the parameters are alpha > 0 and beta > 0. 584c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger Returned values range between 0 and 1. 585ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 586c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 587ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 58885e2e4742d0a1accecd02058a7907df36308297eTim Peters # This version due to Janne Sinkkonen, and matches all the std 58985e2e4742d0a1accecd02058a7907df36308297eTim Peters # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). 59085e2e4742d0a1accecd02058a7907df36308297eTim Peters y = self.gammavariate(alpha, 1.) 59185e2e4742d0a1accecd02058a7907df36308297eTim Peters if y == 0: 59285e2e4742d0a1accecd02058a7907df36308297eTim Peters return 0.0 59385e2e4742d0a1accecd02058a7907df36308297eTim Peters else: 59485e2e4742d0a1accecd02058a7907df36308297eTim Peters return y / (y + self.gammavariate(beta, 1.)) 59595bfcda3e0be2ace895e021296328a383eafb273Guido van Rossum 596cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Pareto -------------------- 597cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 598d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def paretovariate(self, alpha): 599c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Pareto distribution. alpha is the shape parameter.""" 600d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Jain, pg. 495 601cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 60273ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u = 1.0 - self.random() 603d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return 1.0 / pow(u, 1.0/alpha) 604cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 605cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- Weibull -------------------- 606cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 607d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters def weibullvariate(self, alpha, beta): 608c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """Weibull distribution. 609c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger 610c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger alpha is the scale parameter and beta is the shape parameter. 611ef4d4bdc3c99d3120a401b7af6e06610716d2e47Raymond Hettinger 612c32f0336e062dd36f82fb236c66ac25e2bac217bRaymond Hettinger """ 613d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters # Jain, pg. 499; bug fix courtesy Bill Arms 614cf4559a62ec9316a3bb55a67c6fca81ec1ad0d18Guido van Rossum 61573ced7ee995180c0bd8d96ff7d7fb614a744ad7dRaymond Hettinger u = 1.0 - self.random() 616d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters return alpha * pow(-_log(u), 1.0/beta) 6176c395ba31609eeffce2428280cc5d95e4fb8058aGuido van Rossum 61840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger## -------------------- Wichmann-Hill ------------------- 61940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 62040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettingerclass WichmannHill(Random): 62140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 62240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger VERSION = 1 # used by getstate/setstate 62340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 62440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def seed(self, a=None): 62540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Initialize internal state from hashable object. 62640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 62723f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger None or no argument seeds from current time or from an operating 62823f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger system specific randomness source if available. 62940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 63040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger If a is not None or an int or long, hash(a) is used instead. 63140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 63240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger If a is an int or long, a is used directly. Distinct values between 63340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 0 and 27814431486575L inclusive are guaranteed to yield distinct 63440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger internal states (this guarantee is specific to the default 63540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Wichmann-Hill generator). 63640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 63740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 63840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if a is None: 639c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger try: 640c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger a = long(_hexlify(_urandom(16)), 16) 641c1c43cad63a88eae694b174c9a0fe6242dd5972bRaymond Hettinger except NotImplementedError: 642356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger import time 643356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger a = long(time.time() * 256) # use fractional seconds 64440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 64540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not isinstance(a, (int, long)): 64640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a = hash(a) 64740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 64840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, x = divmod(a, 30268) 64940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, y = divmod(a, 30306) 65040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, z = divmod(a, 30322) 65140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = int(x)+1, int(y)+1, int(z)+1 65240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 65340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 65440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 65540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def random(self): 65640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Get the next random number in the range [0.0, 1.0).""" 65740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 65840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Wichman-Hill random number generator. 65940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 66040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Wichmann, B. A. & Hill, I. D. (1982) 66140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Algorithm AS 183: 66240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # An efficient and portable pseudo-random number generator 66340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 31 (1982) 188-190 66440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 66540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # see also: 66640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Correction to Algorithm AS 183 66740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 33 (1984) 123 66840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # 66940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # McLeod, A. I. (1985) 67040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # A remark on Algorithm AS 183 67140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Applied Statistics 34 (1985),198-200 67240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 67340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # This part is thread-unsafe: 67440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # BEGIN CRITICAL SECTION 67540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x, y, z = self._seed 67640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = (171 * x) % 30269 67740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = (172 * y) % 30307 67840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = (170 * z) % 30323 67940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = x, y, z 68040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # END CRITICAL SECTION 68140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 68240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Note: on a platform using IEEE-754 double arithmetic, this can 68340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # never return 0.0 (asserted by Tim; proof too long for a comment). 68440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0 68540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 68640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def getstate(self): 68740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Return internal state; can be passed to setstate() later.""" 68840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return self.VERSION, self._seed, self.gauss_next 68940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 69040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def setstate(self, state): 69140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Restore internal state from object returned by getstate().""" 69240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version = state[0] 69340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if version == 1: 69440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger version, self._seed, self.gauss_next = state 69540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger else: 69640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError("state with version %s passed to " 69740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger "Random.setstate() of version %s" % 69840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger (version, self.VERSION)) 69940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 70040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def jumpahead(self, n): 70140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Act as if n calls to random() were made, but quickly. 70240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 70340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger n is an int, greater than or equal to 0. 70440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 70540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Example use: If you have 2 threads and know that each will 70640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger consume no more than a million random numbers, create two Random 70740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger objects r1 and r2, then do 70840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger r2.setstate(r1.getstate()) 70940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger r2.jumpahead(1000000) 71040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger Then r1 and r2 will use guaranteed-disjoint segments of the full 71140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger period. 71240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 71340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 71440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not n >= 0: 71540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError("n must be >= 0") 71640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x, y, z = self._seed 71740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = int(x * pow(171, n, 30269)) % 30269 71840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = int(y * pow(172, n, 30307)) % 30307 71940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = int(z * pow(170, n, 30323)) % 30323 72040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = x, y, z 72140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 72240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def __whseed(self, x=0, y=0, z=0): 72340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Set the Wichmann-Hill seed from (x, y, z). 72440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 72540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger These must be integers in the range [0, 256). 72640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 72740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 72840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not type(x) == type(y) == type(z) == int: 72940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise TypeError('seeds must be integers') 73040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256): 73140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger raise ValueError('seeds must be in range(0, 256)') 73240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if 0 == x == y == z: 73340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Initialize from current time 73440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger import time 73540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t = long(time.time() * 256) 73640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t = int((t&0xffffff) ^ (t>>24)) 73740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, x = divmod(t, 256) 73840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, y = divmod(t, 256) 73940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger t, z = divmod(t, 256) 74040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger # Zero is a poor seed, so substitute 1 74140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self._seed = (x or 1, y or 1, z or 1) 74240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 74340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.gauss_next = None 74440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 74540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger def whseed(self, a=None): 74640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """Seed from hashable object's hash code. 74740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 74840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger None or no argument seeds from current time. It is not guaranteed 74940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger that objects with distinct hash codes lead to distinct internal 75040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger states. 75140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 75240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger This is obsolete, provided for compatibility with the seed routine 75340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger used prior to Python 2.1. Use the .seed() method instead. 75440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger """ 75540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 75640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger if a is None: 75740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.__whseed() 75840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger return 75940f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a = hash(a) 76040f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, x = divmod(a, 256) 76140f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, y = divmod(a, 256) 76240f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger a, z = divmod(a, 256) 76340f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger x = (x + a) % 256 or 1 76440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger y = (y + a) % 256 or 1 76540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger z = (z + a) % 256 or 1 76640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger self.__whseed(x, y, z) 76740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 76823f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger## --------------- Operating System Random Source ------------------ 769356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 77023f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettingerclass SystemRandom(Random): 77123f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger """Alternate random number generator using sources provided 77223f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger by the operating system (such as /dev/urandom on Unix or 77323f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger CryptGenRandom on Windows). 774356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 775356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger Not available on all systems (see os.urandom() for details). 776356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """ 777356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 778356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def random(self): 779356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """Get the next random number in the range [0.0, 1.0).""" 7807c2a85b2d44851c2442ade579b760f86447bf848Tim Peters return (long(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF 781356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 782356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def getrandbits(self, k): 783356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger """getrandbits(k) -> x. Generates a long int with k random bits.""" 784356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger if k <= 0: 785356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger raise ValueError('number of bits must be greater than zero') 786356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger if k != int(k): 787356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger raise TypeError('number of bits should be an integer') 788356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger bytes = (k + 7) // 8 # bits / 8 and rounded up 789356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger x = long(_hexlify(_urandom(bytes)), 16) 790356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger return x >> (bytes * 8 - k) # trim excess bits 791356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 792356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def _stub(self, *args, **kwds): 79323f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "Stub method. Not used for a system random number generator." 794356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger return None 795356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger seed = jumpahead = _stub 796356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 797356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger def _notimplemented(self, *args, **kwds): 79823f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger "Method should not be called for a system random number generator." 79923f1241dc6495eb255e1a389aef204a3e35a2632Raymond Hettinger raise NotImplementedError('System entropy source does not have state.') 800356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger getstate = setstate = _notimplemented 801356a4599acd4c835ab88c221bd5da073c9895e83Raymond Hettinger 802cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters## -------------------- test program -------------------- 803ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 80462297132215490e9cb406e1a21f03aff40d421cbRaymond Hettingerdef _test_generator(n, func, args): 8050c9886d589ddebf32de0ca3f027a173222ed383aTim Peters import time 80662297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger print n, 'times', func.__name__ 807b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger total = 0.0 8080c9886d589ddebf32de0ca3f027a173222ed383aTim Peters sqsum = 0.0 8090c9886d589ddebf32de0ca3f027a173222ed383aTim Peters smallest = 1e10 8100c9886d589ddebf32de0ca3f027a173222ed383aTim Peters largest = -1e10 8110c9886d589ddebf32de0ca3f027a173222ed383aTim Peters t0 = time.time() 8120c9886d589ddebf32de0ca3f027a173222ed383aTim Peters for i in range(n): 81362297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger x = func(*args) 814b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger total += x 8150c9886d589ddebf32de0ca3f027a173222ed383aTim Peters sqsum = sqsum + x*x 8160c9886d589ddebf32de0ca3f027a173222ed383aTim Peters smallest = min(x, smallest) 8170c9886d589ddebf32de0ca3f027a173222ed383aTim Peters largest = max(x, largest) 8180c9886d589ddebf32de0ca3f027a173222ed383aTim Peters t1 = time.time() 8190c9886d589ddebf32de0ca3f027a173222ed383aTim Peters print round(t1-t0, 3), 'sec,', 820b98154e4243a8d73f758dfee9a81bbe36ddc05cbRaymond Hettinger avg = total/n 821d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters stddev = _sqrt(sqsum/n - avg*avg) 8220c9886d589ddebf32de0ca3f027a173222ed383aTim Peters print 'avg %g, stddev %g, min %g, max %g' % \ 8230c9886d589ddebf32de0ca3f027a173222ed383aTim Peters (avg, stddev, smallest, largest) 824ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossum 825f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettinger 826f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettingerdef _test(N=2000): 82762297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, random, ()) 82862297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, normalvariate, (0.0, 1.0)) 82962297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, lognormvariate, (0.0, 1.0)) 83062297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, vonmisesvariate, (0.0, 1.0)) 83162297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.01, 1.0)) 83262297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.1, 1.0)) 83362297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.1, 2.0)) 83462297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.5, 1.0)) 83562297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (0.9, 1.0)) 83662297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (1.0, 1.0)) 83762297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (2.0, 1.0)) 83862297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (20.0, 1.0)) 83962297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gammavariate, (200.0, 1.0)) 84062297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, gauss, (0.0, 1.0)) 84162297132215490e9cb406e1a21f03aff40d421cbRaymond Hettinger _test_generator(N, betavariate, (3.0, 3.0)) 842cd804108548e1939bd8646634ed52ef388ee9f44Tim Peters 843715c4c412b21f68ad59773698d06eea8eb0c5a44Tim Peters# Create one instance, seeded from current time, and export its methods 84440f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# as module-level functions. The functions share state across all uses 84540f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger#(both in the user's code and in the Python libraries), but that's fine 84640f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# for most programs and is easier for the casual user than making them 84740f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger# instantiate their own Random() instance. 84840f621709286a7a0f7e6f260c0fd020d0fac0de0Raymond Hettinger 849d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters_inst = Random() 850d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersseed = _inst.seed 851d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandom = _inst.random 852d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersuniform = _inst.uniform 853d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandint = _inst.randint 854d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterschoice = _inst.choice 855d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersrandrange = _inst.randrange 856f24eb35d185c0623315cfbd9977d37c509860dcfRaymond Hettingersample = _inst.sample 857d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersshuffle = _inst.shuffle 858d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersnormalvariate = _inst.normalvariate 859d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterslognormvariate = _inst.lognormvariate 860d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersexpovariate = _inst.expovariate 861d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersvonmisesvariate = _inst.vonmisesvariate 862d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgammavariate = _inst.gammavariate 863d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgauss = _inst.gauss 864d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersbetavariate = _inst.betavariate 865d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersparetovariate = _inst.paretovariate 866d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersweibullvariate = _inst.weibullvariate 867d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Petersgetstate = _inst.getstate 868d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peterssetstate = _inst.setstate 869d52269bfd029c4a517ea74c17edd5c3a250c366cTim Petersjumpahead = _inst.jumpahead 8702f726e9093381572b21edbfc42659ea89fbdf686Raymond Hettingergetrandbits = _inst.getrandbits 871d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters 872ff03b1ae5bba4d6712563efb7c77ace57dbe6788Guido van Rossumif __name__ == '__main__': 873d7b5e88e8e40b77813ceb25dc28b87d672538403Tim Peters _test() 874