SF bug #812202: randint is always even
* Added C coded getrandbits(k) method that runs in linear time. * Call the new method from randrange() for ranges >= 2**53. * Adds a warning for generators not defining getrandbits() whenever they have a call to randrange() with too large of a population.
This commit is contained in:
Raymond Hettinger
parent
5c68ef04b7
commit
2f726e9093
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@ -41,6 +41,10 @@ Class \class{Random} can also be subclassed if you want to use a
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different basic generator of your own devising: in that case, override
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the \method{random()}, \method{seed()}, \method{getstate()},
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\method{setstate()} and \method{jumpahead()} methods.
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Optionally, a new generator can supply a \method{getrandombits()}
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method --- this allows \method{randrange()} to produce selections
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over an arbitrarily large range.
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\versionadded[the \method{getrandombits()} method]{2.4}
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As an example of subclassing, the \module{random} module provides
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the \class{WichmannHill} class which implements an alternative generator
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@ -92,6 +96,14 @@ Bookkeeping functions:
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separated by many steps.]{2.3}
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\end{funcdesc}
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\begin{funcdesc}{getrandbits}{k}
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Returns a python \class{long} int with \var{k} random bits.
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This method is supplied with the MersenneTwister generator and some
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other generators may also provide it as an optional part of the API.
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When available, \method{getrandbits()} enables \method{randrange()}
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to handle arbitrarily large ranges.
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\versionadded{2.4}
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\end{funcdesc}
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Functions for integers:
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@ -39,6 +39,8 @@ General notes on the underlying Mersenne Twister core generator:
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"""
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from warnings import warn as _warn
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from types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType
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from math import log as _log, exp as _exp, pi as _pi, e as _e
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from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
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from math import floor as _floor
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@ -47,12 +49,14 @@ __all__ = ["Random","seed","random","uniform","randint","choice","sample",
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"randrange","shuffle","normalvariate","lognormvariate",
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"expovariate","vonmisesvariate","gammavariate",
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"gauss","betavariate","paretovariate","weibullvariate",
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"getstate","setstate","jumpahead"]
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"getstate","setstate","jumpahead", "WichmannHill", "getrandbits",
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"Random"]
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NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0)
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TWOPI = 2.0*_pi
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LOG4 = _log(4.0)
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SG_MAGICCONST = 1.0 + _log(4.5)
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BPF = 53 # Number of bits in a float
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# Translated by Guido van Rossum from C source provided by
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# Adrian Baddeley. Adapted by Raymond Hettinger for use with
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@ -72,6 +76,8 @@ class Random(_random.Random):
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Class Random can also be subclassed if you want to use a different basic
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generator of your own devising: in that case, override the following
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methods: random(), seed(), getstate(), setstate() and jumpahead().
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Optionally, implement a getrandombits() method so that randrange()
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can cover arbitrarily large ranges.
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"""
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@ -131,12 +137,13 @@ class Random(_random.Random):
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## -------------------- integer methods -------------------
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def randrange(self, start, stop=None, step=1, int=int, default=None):
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def randrange(self, start, stop=None, step=1, int=int, default=None,
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maxwidth=1L<<BPF):
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"""Choose a random item from range(start, stop[, step]).
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This fixes the problem with randint() which includes the
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endpoint; in Python this is usually not what you want.
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Do not supply the 'int' and 'default' arguments.
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Do not supply the 'int', 'default', and 'maxwidth' arguments.
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"""
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# This code is a bit messy to make it fast for the
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@ -146,6 +153,8 @@ class Random(_random.Random):
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raise ValueError, "non-integer arg 1 for randrange()"
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if stop is default:
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if istart > 0:
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if istart >= maxwidth:
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return self._randbelow(istart)
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return int(self.random() * istart)
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raise ValueError, "empty range for randrange()"
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@ -153,36 +162,43 @@ class Random(_random.Random):
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istop = int(stop)
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if istop != stop:
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raise ValueError, "non-integer stop for randrange()"
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if step == 1 and istart < istop:
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width = istop - istart
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if step == 1 and width > 0:
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# Note that
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# int(istart + self.random()*(istop - istart))
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# int(istart + self.random()*width)
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# instead would be incorrect. For example, consider istart
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# = -2 and istop = 0. Then the guts would be in
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# -2.0 to 0.0 exclusive on both ends (ignoring that random()
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# might return 0.0), and because int() truncates toward 0, the
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# final result would be -1 or 0 (instead of -2 or -1).
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# istart + int(self.random()*(istop - istart))
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# istart + int(self.random()*width)
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# would also be incorrect, for a subtler reason: the RHS
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# can return a long, and then randrange() would also return
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# a long, but we're supposed to return an int (for backward
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# compatibility).
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return int(istart + int(self.random()*(istop - istart)))
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if width >= maxwidth:
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return int(istart + self._randbelow(width))
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return int(istart + int(self.random()*width))
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if step == 1:
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raise ValueError, "empty range for randrange()"
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raise ValueError, "empty range for randrange() (%d,%d, %d)" % (istart, istop, width)
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# Non-unit step argument supplied.
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istep = int(step)
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if istep != step:
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raise ValueError, "non-integer step for randrange()"
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if istep > 0:
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n = (istop - istart + istep - 1) / istep
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n = (width + istep - 1) / istep
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elif istep < 0:
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n = (istop - istart + istep + 1) / istep
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n = (width + istep + 1) / istep
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else:
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raise ValueError, "zero step for randrange()"
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if n <= 0:
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raise ValueError, "empty range for randrange()"
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if n >= maxwidth:
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return istart + self._randbelow(n)
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return istart + istep*int(self.random() * n)
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def randint(self, a, b):
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@ -191,6 +207,33 @@ class Random(_random.Random):
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return self.randrange(a, b+1)
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def _randbelow(self, n, _log=_log, int=int, _maxwidth=1L<<BPF,
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_Method=_MethodType, _BuiltinMethod=_BuiltinMethodType):
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"""Return a random int in the range [0,n)
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Handles the case where n has more bits than returned
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by a single call to the underlying generator.
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"""
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try:
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getrandbits = self.getrandbits
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except AttributeError:
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pass
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else:
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# Only call self.getrandbits if the original random() builtin method
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# has not been overridden or if a new getrandbits() was supplied.
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# This assures that the two methods correspond.
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if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method:
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k = int(1.00001 + _log(n-1, 2.0)) # 2**k > n-1 > 2**(k-2)
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r = getrandbits(k)
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while r >= n:
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r = getrandbits(k)
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return r
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if n >= _maxwidth:
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_warn("Underlying random() generator does not supply \n"
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"enough bits to choose from a population range this large")
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return int(self.random() * n)
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## -------------------- sequence methods -------------------
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def choice(self, seq):
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@ -757,6 +800,7 @@ weibullvariate = _inst.weibullvariate
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getstate = _inst.getstate
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setstate = _inst.setstate
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jumpahead = _inst.jumpahead
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getrandbits = _inst.getrandbits
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if __name__ == '__main__':
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_test()
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@ -4,6 +4,7 @@ import unittest
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import random
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import time
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import pickle
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import warnings
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from math import log, exp, sqrt, pi
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from sets import Set
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from test import test_support
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@ -153,6 +154,13 @@ class WichmannHill_TestBasicOps(TestBasicOps):
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self.assertEqual(x1, x2)
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self.assertEqual(y1, y2)
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def test_bigrand(self):
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# Verify warnings are raised when randrange is too large for random()
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oldfilters = warnings.filters[:]
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warnings.filterwarnings("error", "Underlying random")
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self.assertRaises(UserWarning, self.gen.randrange, 2**60)
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warnings.filters[:] = oldfilters
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class MersenneTwister_TestBasicOps(TestBasicOps):
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gen = random.Random()
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@ -219,6 +227,76 @@ class MersenneTwister_TestBasicOps(TestBasicOps):
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seed = (1L << (10000 * 8)) - 1 # about 10K bytes
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self.gen.seed(seed)
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def test_53_bits_per_float(self):
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# This should pass whenever a C double has 53 bit precision.
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span = 2 ** 53
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cum = 0
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for i in xrange(100):
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cum |= int(self.gen.random() * span)
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self.assertEqual(cum, span-1)
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def test_bigrand(self):
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# The randrange routine should build-up the required number of bits
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# in stages so that all bit positions are active.
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span = 2 ** 500
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cum = 0
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for i in xrange(100):
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r = self.gen.randrange(span)
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self.assert_(0 <= r < span)
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cum |= r
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self.assertEqual(cum, span-1)
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def test_bigrand_ranges(self):
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for i in [40,80, 160, 200, 211, 250, 375, 512, 550]:
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start = self.gen.randrange(2 ** i)
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stop = self.gen.randrange(2 ** (i-2))
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if stop <= start:
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return
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self.assert_(start <= self.gen.randrange(start, stop) < stop)
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def test_rangelimits(self):
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for start, stop in [(-2,0), (-(2**60)-2,-(2**60)), (2**60,2**60+2)]:
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self.assertEqual(Set(range(start,stop)),
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Set([self.gen.randrange(start,stop) for i in xrange(100)]))
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def test_genrandbits(self):
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# Verify cross-platform repeatability
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self.gen.seed(1234567)
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self.assertEqual(self.gen.getrandbits(100),
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97904845777343510404718956115L)
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# Verify ranges
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for k in xrange(1, 1000):
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self.assert_(0 <= self.gen.getrandbits(k) < 2**k)
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# Verify all bits active
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getbits = self.gen.getrandbits
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for span in [1, 2, 3, 4, 31, 32, 32, 52, 53, 54, 119, 127, 128, 129]:
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cum = 0
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for i in xrange(100):
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cum |= getbits(span)
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self.assertEqual(cum, 2**span-1)
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def test_randbelow_logic(self, _log=log, int=int):
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# check bitcount transition points: 2**i and 2**(i+1)-1
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# show that: k = int(1.001 + _log(n, 2))
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# is equal to or one greater than the number of bits in n
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for i in xrange(1, 1000):
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n = 1L << i # check an exact power of two
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numbits = i+1
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k = int(1.00001 + _log(n, 2))
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self.assertEqual(k, numbits)
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self.assert_(n == 2**(k-1))
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n += n - 1 # check 1 below the next power of two
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k = int(1.00001 + _log(n, 2))
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self.assert_(k in [numbits, numbits+1])
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self.assert_(2**k > n > 2**(k-2))
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n -= n >> 15 # check a little farther below the next power of two
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k = int(1.00001 + _log(n, 2))
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self.assertEqual(k, numbits) # note the stronger assertion
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self.assert_(2**k > n > 2**(k-1)) # note the stronger assertion
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_gammacoeff = (0.9999999999995183, 676.5203681218835, -1259.139216722289,
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771.3234287757674, -176.6150291498386, 12.50734324009056,
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-0.1385710331296526, 0.9934937113930748e-05, 0.1659470187408462e-06)
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@ -84,6 +84,14 @@ Library
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seed. Modified to match Py2.2 behavior and use fractional seconds so
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that successive runs are more likely to produce different sequences.
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- random.Random has a new method, getrandbits(k), which returns an int
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with k random bits. This method is now an optional part of the API
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for user defined generators. Any generator that defines genrandbits()
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can now use randrange() for ranges with a length >= 2**53. Formerly,
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randrange would return only even numbers for ranges that large (see
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SF bug #812202). Generators that do not define genrandbits() now
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issue a warning when randrange() is called with a range that large.
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- itertools.izip() with no arguments now returns an empty iterator instead
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of raising a TypeError exception.
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@ -434,6 +434,47 @@ random_jumpahead(RandomObject *self, PyObject *n)
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return Py_None;
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}
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static PyObject *
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random_getrandbits(RandomObject *self, PyObject *args)
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{
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int k, i, bytes;
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unsigned long r;
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unsigned char *bytearray;
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PyObject *result;
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if (!PyArg_ParseTuple(args, "i:getrandbits", &k))
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return NULL;
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if (k <= 0) {
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PyErr_SetString(PyExc_ValueError,
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"number of bits must be greater than zero");
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return NULL;
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}
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bytes = ((k - 1) / 32 + 1) * 4;
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bytearray = (unsigned char *)PyMem_Malloc(bytes);
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if (bytearray == NULL) {
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PyErr_NoMemory();
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return NULL;
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}
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/* Fill-out whole words, byte-by-byte to avoid endianness issues */
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for (i=0 ; i<bytes ; i+=4, k-=32) {
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r = genrand_int32(self);
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if (k < 32)
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r >>= (32 - k);
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bytearray[i+0] = (unsigned char)r;
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bytearray[i+1] = (unsigned char)(r >> 8);
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bytearray[i+2] = (unsigned char)(r >> 16);
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bytearray[i+3] = (unsigned char)(r >> 24);
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}
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/* little endian order to match bytearray assignment order */
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result = _PyLong_FromByteArray(bytearray, bytes, 1, 0);
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PyMem_Free(bytearray);
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return result;
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}
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static PyObject *
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random_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
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{
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@ -464,6 +505,9 @@ static PyMethodDef random_methods[] = {
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{"jumpahead", (PyCFunction)random_jumpahead, METH_O,
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PyDoc_STR("jumpahead(int) -> None. Create new state from "
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"existing state and integer.")},
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{"getrandbits", (PyCFunction)random_getrandbits, METH_VARARGS,
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PyDoc_STR("getrandbits(k) -> x. Generates a long int with "
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"k random bits.")},
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{NULL, NULL} /* sentinel */
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};
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