SF patch 658251: Install a C implementation of the Mersenne Twister as the
core generator for random.py.
diff --git a/Lib/random.py b/Lib/random.py
index 057571a..8462061 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -18,61 +18,26 @@
negative exponential
gamma
beta
+ pareto
+ Weibull
distributions on the circle (angles 0 to 2pi)
---------------------------------------------
circular uniform
von Mises
-Translated from anonymously contributed C/C++ source.
+General notes on the underlying Mersenne Twister core generator:
-Multi-threading note: the random number generator used here is not thread-
-safe; it is possible that two calls return the same random value. However,
-you can instantiate a different instance of Random() in each thread to get
-generators that don't share state, then use .setstate() and .jumpahead() to
-move the generators to disjoint segments of the full period. For example,
+* The period is 2**19937-1.
+* It is one of the most extensively tested generators in existence
+* Without a direct way to compute N steps forward, the
+ semantics of jumpahead(n) are weakened to simply jump
+ to another distant state and rely on the large period
+ to avoid overlapping sequences.
+* The random() method is implemented in C, executes in
+ a single Python step, and is, therefore, threadsafe.
-def create_generators(num, delta, firstseed=None):
- ""\"Return list of num distinct generators.
- Each generator has its own unique segment of delta elements from
- Random.random()'s full period.
- Seed the first generator with optional arg firstseed (default is
- None, to seed from current time).
- ""\"
-
- from random import Random
- g = Random(firstseed)
- result = [g]
- for i in range(num - 1):
- laststate = g.getstate()
- g = Random()
- g.setstate(laststate)
- g.jumpahead(delta)
- result.append(g)
- return result
-
-gens = create_generators(10, 1000000)
-
-That creates 10 distinct generators, which can be passed out to 10 distinct
-threads. The generators don't share state so can be called safely in
-parallel. So long as no thread calls its g.random() more than a million
-times (the second argument to create_generators), the sequences seen by
-each thread will not overlap.
-
-The period of the underlying Wichmann-Hill generator is 6,953,607,871,644,
-and that limits how far this technique can be pushed.
-
-Just for fun, note that since we know the period, .jumpahead() can also be
-used to "move backward in time":
-
->>> g = Random(42) # arbitrary
->>> g.random()
-0.25420336316883324
->>> g.jumpahead(6953607871644L - 1) # move *back* one
->>> g.random()
-0.25420336316883324
"""
-# XXX The docstring sucks.
from math import log as _log, exp as _exp, pi as _pi, e as _e
from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
@@ -82,32 +47,20 @@
"randrange","shuffle","normalvariate","lognormvariate",
"cunifvariate","expovariate","vonmisesvariate","gammavariate",
"stdgamma","gauss","betavariate","paretovariate","weibullvariate",
- "getstate","setstate","jumpahead","whseed"]
-
-def _verify(name, computed, expected):
- if abs(computed - expected) > 1e-7:
- raise ValueError(
- "computed value for %s deviates too much "
- "(computed %g, expected %g)" % (name, computed, expected))
+ "getstate","setstate","jumpahead"]
NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0)
-_verify('NV_MAGICCONST', NV_MAGICCONST, 1.71552776992141)
-
TWOPI = 2.0*_pi
-_verify('TWOPI', TWOPI, 6.28318530718)
-
LOG4 = _log(4.0)
-_verify('LOG4', LOG4, 1.38629436111989)
-
SG_MAGICCONST = 1.0 + _log(4.5)
-_verify('SG_MAGICCONST', SG_MAGICCONST, 2.50407739677627)
-
-del _verify
# Translated by Guido van Rossum from C source provided by
-# Adrian Baddeley.
+# Adrian Baddeley. Adapted by Raymond Hettinger for use with
+# the Mersenne Twister core generator.
-class Random:
+from _random import Random as CoreGenerator
+
+class Random(CoreGenerator):
"""Random number generator base class used by bound module functions.
Used to instantiate instances of Random to get generators that don't
@@ -122,7 +75,7 @@
"""
- VERSION = 1 # used by getstate/setstate
+ VERSION = 2 # used by getstate/setstate
def __init__(self, x=None):
"""Initialize an instance.
@@ -131,12 +84,7 @@
"""
self.seed(x)
-
-## -------------------- core generator -------------------
-
- # Specific to Wichmann-Hill generator. Subclasses wishing to use a
- # different core generator should override the seed(), random(),
- # getstate(), setstate() and jumpahead() methods.
+ self.gauss_next = None
def seed(self, a=None):
"""Initialize internal state from hashable object.
@@ -144,141 +92,26 @@
None or no argument seeds from current time.
If a is not None or an int or long, hash(a) is used instead.
-
- If a is an int or long, a is used directly. Distinct values between
- 0 and 27814431486575L inclusive are guaranteed to yield distinct
- internal states (this guarantee is specific to the default
- Wichmann-Hill generator).
"""
- if a is None:
- # Initialize from current time
- import time
- a = long(time.time() * 256)
-
- if type(a) not in (type(3), type(3L)):
- a = hash(a)
-
- a, x = divmod(a, 30268)
- a, y = divmod(a, 30306)
- a, z = divmod(a, 30322)
- self._seed = int(x)+1, int(y)+1, int(z)+1
-
+ CoreGenerator.seed(self, a)
self.gauss_next = None
- def random(self):
- """Get the next random number in the range [0.0, 1.0)."""
-
- # Wichman-Hill random number generator.
- #
- # Wichmann, B. A. & Hill, I. D. (1982)
- # Algorithm AS 183:
- # An efficient and portable pseudo-random number generator
- # Applied Statistics 31 (1982) 188-190
- #
- # see also:
- # Correction to Algorithm AS 183
- # Applied Statistics 33 (1984) 123
- #
- # McLeod, A. I. (1985)
- # A remark on Algorithm AS 183
- # Applied Statistics 34 (1985),198-200
-
- # This part is thread-unsafe:
- # BEGIN CRITICAL SECTION
- x, y, z = self._seed
- x = (171 * x) % 30269
- y = (172 * y) % 30307
- z = (170 * z) % 30323
- self._seed = x, y, z
- # END CRITICAL SECTION
-
- # Note: on a platform using IEEE-754 double arithmetic, this can
- # never return 0.0 (asserted by Tim; proof too long for a comment).
- return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0
-
def getstate(self):
"""Return internal state; can be passed to setstate() later."""
- return self.VERSION, self._seed, self.gauss_next
+ return self.VERSION, CoreGenerator.getstate(self), self.gauss_next
def setstate(self, state):
"""Restore internal state from object returned by getstate()."""
version = state[0]
- if version == 1:
- version, self._seed, self.gauss_next = state
+ if version == 2:
+ version, internalstate, self.gauss_next = state
+ CoreGenerator.setstate(self, internalstate)
else:
raise ValueError("state with version %s passed to "
"Random.setstate() of version %s" %
(version, self.VERSION))
- def jumpahead(self, n):
- """Act as if n calls to random() were made, but quickly.
-
- n is an int, greater than or equal to 0.
-
- Example use: If you have 2 threads and know that each will
- consume no more than a million random numbers, create two Random
- objects r1 and r2, then do
- r2.setstate(r1.getstate())
- r2.jumpahead(1000000)
- Then r1 and r2 will use guaranteed-disjoint segments of the full
- period.
- """
-
- if not n >= 0:
- raise ValueError("n must be >= 0")
- x, y, z = self._seed
- x = int(x * pow(171, n, 30269)) % 30269
- y = int(y * pow(172, n, 30307)) % 30307
- z = int(z * pow(170, n, 30323)) % 30323
- self._seed = x, y, z
-
- def __whseed(self, x=0, y=0, z=0):
- """Set the Wichmann-Hill seed from (x, y, z).
-
- These must be integers in the range [0, 256).
- """
-
- if not type(x) == type(y) == type(z) == int:
- raise TypeError('seeds must be integers')
- if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256):
- raise ValueError('seeds must be in range(0, 256)')
- if 0 == x == y == z:
- # Initialize from current time
- import time
- t = long(time.time() * 256)
- t = int((t&0xffffff) ^ (t>>24))
- t, x = divmod(t, 256)
- t, y = divmod(t, 256)
- t, z = divmod(t, 256)
- # Zero is a poor seed, so substitute 1
- self._seed = (x or 1, y or 1, z or 1)
-
- self.gauss_next = None
-
- def whseed(self, a=None):
- """Seed from hashable object's hash code.
-
- None or no argument seeds from current time. It is not guaranteed
- that objects with distinct hash codes lead to distinct internal
- states.
-
- This is obsolete, provided for compatibility with the seed routine
- used prior to Python 2.1. Use the .seed() method instead.
- """
-
- if a is None:
- self.__whseed()
- return
- a = hash(a)
- a, x = divmod(a, 256)
- a, y = divmod(a, 256)
- a, z = divmod(a, 256)
- x = (x + a) % 256 or 1
- y = (y + a) % 256 or 1
- z = (z + a) % 256 or 1
- self.__whseed(x, y, z)
-
## ---- Methods below this point do not need to be overridden when
## ---- subclassing for the purpose of using a different core generator.
@@ -744,6 +577,153 @@
u = self.random()
return alpha * pow(-_log(u), 1.0/beta)
+## -------------------- Wichmann-Hill -------------------
+
+class WichmannHill(Random):
+
+ VERSION = 1 # used by getstate/setstate
+
+ def seed(self, a=None):
+ """Initialize internal state from hashable object.
+
+ None or no argument seeds from current time.
+
+ If a is not None or an int or long, hash(a) is used instead.
+
+ If a is an int or long, a is used directly. Distinct values between
+ 0 and 27814431486575L inclusive are guaranteed to yield distinct
+ internal states (this guarantee is specific to the default
+ Wichmann-Hill generator).
+ """
+
+ if a is None:
+ # Initialize from current time
+ import time
+ a = long(time.time() * 256)
+
+ if not isinstance(a, (int, long)):
+ a = hash(a)
+
+ a, x = divmod(a, 30268)
+ a, y = divmod(a, 30306)
+ a, z = divmod(a, 30322)
+ self._seed = int(x)+1, int(y)+1, int(z)+1
+
+ self.gauss_next = None
+
+ def random(self):
+ """Get the next random number in the range [0.0, 1.0)."""
+
+ # Wichman-Hill random number generator.
+ #
+ # Wichmann, B. A. & Hill, I. D. (1982)
+ # Algorithm AS 183:
+ # An efficient and portable pseudo-random number generator
+ # Applied Statistics 31 (1982) 188-190
+ #
+ # see also:
+ # Correction to Algorithm AS 183
+ # Applied Statistics 33 (1984) 123
+ #
+ # McLeod, A. I. (1985)
+ # A remark on Algorithm AS 183
+ # Applied Statistics 34 (1985),198-200
+
+ # This part is thread-unsafe:
+ # BEGIN CRITICAL SECTION
+ x, y, z = self._seed
+ x = (171 * x) % 30269
+ y = (172 * y) % 30307
+ z = (170 * z) % 30323
+ self._seed = x, y, z
+ # END CRITICAL SECTION
+
+ # Note: on a platform using IEEE-754 double arithmetic, this can
+ # never return 0.0 (asserted by Tim; proof too long for a comment).
+ return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0
+
+ def getstate(self):
+ """Return internal state; can be passed to setstate() later."""
+ return self.VERSION, self._seed, self.gauss_next
+
+ def setstate(self, state):
+ """Restore internal state from object returned by getstate()."""
+ version = state[0]
+ if version == 1:
+ version, self._seed, self.gauss_next = state
+ else:
+ raise ValueError("state with version %s passed to "
+ "Random.setstate() of version %s" %
+ (version, self.VERSION))
+
+ def jumpahead(self, n):
+ """Act as if n calls to random() were made, but quickly.
+
+ n is an int, greater than or equal to 0.
+
+ Example use: If you have 2 threads and know that each will
+ consume no more than a million random numbers, create two Random
+ objects r1 and r2, then do
+ r2.setstate(r1.getstate())
+ r2.jumpahead(1000000)
+ Then r1 and r2 will use guaranteed-disjoint segments of the full
+ period.
+ """
+
+ if not n >= 0:
+ raise ValueError("n must be >= 0")
+ x, y, z = self._seed
+ x = int(x * pow(171, n, 30269)) % 30269
+ y = int(y * pow(172, n, 30307)) % 30307
+ z = int(z * pow(170, n, 30323)) % 30323
+ self._seed = x, y, z
+
+ def __whseed(self, x=0, y=0, z=0):
+ """Set the Wichmann-Hill seed from (x, y, z).
+
+ These must be integers in the range [0, 256).
+ """
+
+ if not type(x) == type(y) == type(z) == int:
+ raise TypeError('seeds must be integers')
+ if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256):
+ raise ValueError('seeds must be in range(0, 256)')
+ if 0 == x == y == z:
+ # Initialize from current time
+ import time
+ t = long(time.time() * 256)
+ t = int((t&0xffffff) ^ (t>>24))
+ t, x = divmod(t, 256)
+ t, y = divmod(t, 256)
+ t, z = divmod(t, 256)
+ # Zero is a poor seed, so substitute 1
+ self._seed = (x or 1, y or 1, z or 1)
+
+ self.gauss_next = None
+
+ def whseed(self, a=None):
+ """Seed from hashable object's hash code.
+
+ None or no argument seeds from current time. It is not guaranteed
+ that objects with distinct hash codes lead to distinct internal
+ states.
+
+ This is obsolete, provided for compatibility with the seed routine
+ used prior to Python 2.1. Use the .seed() method instead.
+ """
+
+ if a is None:
+ self.__whseed()
+ return
+ a = hash(a)
+ a, x = divmod(a, 256)
+ a, y = divmod(a, 256)
+ a, z = divmod(a, 256)
+ x = (x + a) % 256 or 1
+ y = (y + a) % 256 or 1
+ z = (z + a) % 256 or 1
+ self.__whseed(x, y, z)
+
## -------------------- test program --------------------
def _test_generator(n, funccall):
@@ -768,25 +748,11 @@
print 'avg %g, stddev %g, min %g, max %g' % \
(avg, stddev, smallest, largest)
-def _test_sample(n):
- # For the entire allowable range of 0 <= k <= n, validate that
- # the sample is of the correct length and contains only unique items
- population = xrange(n)
- for k in xrange(n+1):
- s = sample(population, k)
- uniq = dict.fromkeys(s)
- assert len(uniq) == len(s) == k
- assert None not in uniq
-
def _sample_generator(n, k):
# Return a fixed element from the sample. Validates random ordering.
return sample(xrange(n), k)[k//2]
def _test(N=2000):
- print 'TWOPI =', TWOPI
- print 'LOG4 =', LOG4
- print 'NV_MAGICCONST =', NV_MAGICCONST
- print 'SG_MAGICCONST =', SG_MAGICCONST
_test_generator(N, 'random()')
_test_generator(N, 'normalvariate(0.0, 1.0)')
_test_generator(N, 'lognormvariate(0.0, 1.0)')
@@ -808,25 +774,13 @@
_test_generator(N, 'weibullvariate(1.0, 1.0)')
_test_generator(N, '_sample_generator(50, 5)') # expected s.d.: 14.4
_test_generator(N, '_sample_generator(50, 45)') # expected s.d.: 14.4
- _test_sample(500)
-
- # Test jumpahead.
- s = getstate()
- jumpahead(N)
- r1 = random()
- # now do it the slow way
- setstate(s)
- for i in range(N):
- random()
- r2 = random()
- if r1 != r2:
- raise ValueError("jumpahead test failed " + `(N, r1, r2)`)
# Create one instance, seeded from current time, and export its methods
-# as module-level functions. The functions are not threadsafe, and state
-# is shared across all uses (both in the user's code and in the Python
-# libraries), but that's fine for most programs and is easier for the
-# casual user than making them instantiate their own Random() instance.
+# as module-level functions. The functions share state across all uses
+#(both in the user's code and in the Python libraries), but that's fine
+# for most programs and is easier for the casual user than making them
+# instantiate their own Random() instance.
+
_inst = Random()
seed = _inst.seed
random = _inst.random
@@ -850,7 +804,6 @@
getstate = _inst.getstate
setstate = _inst.setstate
jumpahead = _inst.jumpahead
-whseed = _inst.whseed
if __name__ == '__main__':
_test()