"""Random variable generators.
uniform bytes (values between 0 and 255)
pick weighted random sample
generate random permutation
distributions on the real line:
------------------------------
distributions on the circle (angles 0 to 2pi)
---------------------------------------------
General notes on the underlying Mersenne Twister core generator:
* The period is 2**19937-1.
* It is one of the most extensively tested generators in existence.
* The random() method is implemented in C, executes in a single Python step,
and is, therefore, threadsafe.
# Translated by Guido van Rossum from C source provided by
# Adrian Baddeley. Adapted by Raymond Hettinger for use with
# the Mersenne Twister and os.urandom() core generators.
from warnings import warn as _warn
from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil
from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
from math import tau as TWOPI, floor as _floor
from os import urandom as _urandom
from _collections_abc import Set as _Set, Sequence as _Sequence
from itertools import accumulate as _accumulate, repeat as _repeat
from bisect import bisect as _bisect
# hashlib is pretty heavy to load, try lean internal module first
from _sha512 import sha512 as _sha512
# fallback to official implementation
from hashlib import sha512 as _sha512
NV_MAGICCONST = 4 * _exp(-0.5) / _sqrt(2.0)
SG_MAGICCONST = 1.0 + _log(4.5)
BPF = 53 # Number of bits in a float
class Random(_random.Random):
"""Random number generator base class used by bound module functions.
Used to instantiate instances of Random to get generators that don't
Class Random can also be subclassed if you want to use a different basic
generator of your own devising: in that case, override the following
methods: random(), seed(), getstate(), and setstate().
Optionally, implement a getrandbits() method so that randrange()
can cover arbitrarily large ranges.
VERSION = 3 # used by getstate/setstate
def __init__(self, x=None):
"""Initialize an instance.
Optional argument x controls seeding, as for Random.seed().
def seed(self, a=None, version=2):
"""Initialize internal state from a seed.
The only supported seed types are None, int, float,
str, bytes, and bytearray.
None or no argument seeds from current time or from an operating
system specific randomness source if available.
If *a* is an int, all bits are used.
For version 2 (the default), all of the bits are used if *a* is a str,
bytes, or bytearray. For version 1 (provided for reproducing random
sequences from older versions of Python), the algorithm for str and
bytes generates a narrower range of seeds.
if version == 1 and isinstance(a, (str, bytes)):
a = a.decode('latin-1') if isinstance(a, bytes) else a
x = ord(a[0]) << 7 if a else 0
x = ((1000003 * x) ^ c) & 0xFFFFFFFFFFFFFFFF
elif version == 2 and isinstance(a, (str, bytes, bytearray)):
a = int.from_bytes(a + _sha512(a).digest(), 'big')
elif not isinstance(a, (type(None), int, float, str, bytes, bytearray)):
_warn('Seeding based on hashing is deprecated\n'
'since Python 3.9 and will be removed in a subsequent '
'supported seed types are: None, '
'int, float, str, bytes, and bytearray.',
"""Return internal state; can be passed to setstate() later."""
return self.VERSION, super().getstate(), self.gauss_next
def setstate(self, state):
"""Restore internal state from object returned by getstate()."""
version, internalstate, self.gauss_next = state
super().setstate(internalstate)
version, internalstate, self.gauss_next = state
# In version 2, the state was saved as signed ints, which causes
# inconsistencies between 32/64-bit systems. The state is
# really unsigned 32-bit ints, so we convert negative ints from
# version 2 to positive longs for version 3.
internalstate = tuple(x % (2 ** 32) for x in internalstate)
super().setstate(internalstate)
raise ValueError("state with version %s passed to "
"Random.setstate() of version %s" %
## -------------------------------------------------------
## ---- Methods below this point do not need to be overridden or extended
## ---- when subclassing for the purpose of using a different core generator.
## -------------------- pickle support -------------------
# Issue 17489: Since __reduce__ was defined to fix #759889 this is no
# longer called; we leave it here because it has been here since random was
# rewritten back in 2001 and why risk breaking something.
def __getstate__(self): # for pickle
def __setstate__(self, state): # for pickle
return self.__class__, (), self.getstate()
## ---- internal support method for evenly distributed integers ----
def __init_subclass__(cls, /, **kwargs):
"""Control how subclasses generate random integers.
The algorithm a subclass can use depends on the random() and/or
getrandbits() implementation available to it and determines
whether it can generate random integers from arbitrarily large
if '_randbelow' in c.__dict__:
if 'getrandbits' in c.__dict__:
cls._randbelow = cls._randbelow_with_getrandbits
if 'random' in c.__dict__:
cls._randbelow = cls._randbelow_without_getrandbits
def _randbelow_with_getrandbits(self, n):
"Return a random int in the range [0,n). Returns 0 if n==0."
getrandbits = self.getrandbits
k = n.bit_length() # don't use (n-1) here because n can be 1
r = getrandbits(k) # 0 <= r < 2**k
def _randbelow_without_getrandbits(self, n, maxsize=1<<BPF):
"""Return a random int in the range [0,n). Returns 0 if n==0.
The implementation does not use getrandbits, but only random.
_warn("Underlying random() generator does not supply \n"
"enough bits to choose from a population range this large.\n"
"To remove the range limitation, add a getrandbits() method.")
return _floor(random() * n)
limit = (maxsize - rem) / maxsize # int(limit * maxsize) % n == 0
return _floor(r * maxsize) % n
_randbelow = _randbelow_with_getrandbits
## --------------------------------------------------------
## ---- Methods below this point generate custom distributions
## ---- based on the methods defined above. They do not
## ---- directly touch the underlying generator and only
## ---- access randomness through the methods: random(),
## ---- getrandbits(), or _randbelow().
## -------------------- bytes methods ---------------------
"""Generate n random bytes."""
return self.getrandbits(n * 8).to_bytes(n, 'little')
## -------------------- integer methods -------------------
def randrange(self, start, stop=None, step=1):
"""Choose a random item from range(start, stop[, step]).
This fixes the problem with randint() which includes the
endpoint; in Python this is usually not what you want.
# This code is a bit messy to make it fast for the
# common case while still doing adequate error checking.
raise ValueError("non-integer arg 1 for randrange()")
return self._randbelow(istart)
raise ValueError("empty range for randrange()")
# stop argument supplied.
raise ValueError("non-integer stop for randrange()")
if step == 1 and width > 0:
return istart + self._randbelow(width)
raise ValueError("empty range for randrange() (%d, %d, %d)" % (istart, istop, width))
# Non-unit step argument supplied.
raise ValueError("non-integer step for randrange()")
n = (width + istep - 1) // istep
n = (width + istep + 1) // istep
raise ValueError("zero step for randrange()")
raise ValueError("empty range for randrange()")
return istart + istep * self._randbelow(n)
"""Return random integer in range [a, b], including both end points.
return self.randrange(a, b+1)
## -------------------- sequence methods -------------------
"""Choose a random element from a non-empty sequence."""
# raises IndexError if seq is empty
return seq[self._randbelow(len(seq))]
def shuffle(self, x, random=None):
"""Shuffle list x in place, and return None.
Optional argument random is a 0-argument function returning a
random float in [0.0, 1.0); if it is the default None, the
standard random.random will be used.
randbelow = self._randbelow
for i in reversed(range(1, len(x))):
# pick an element in x[:i+1] with which to exchange x[i]
_warn('The *random* parameter to shuffle() has been deprecated\n'
'since Python 3.9 and will be removed in a subsequent '
for i in reversed(range(1, len(x))):
# pick an element in x[:i+1] with which to exchange x[i]
j = floor(random() * (i + 1))
def sample(self, population, k, *, counts=None):
"""Chooses k unique random elements from a population sequence or set.
Returns a new list containing elements from the population while
leaving the original population unchanged. The resulting list is
in selection order so that all sub-slices will also be valid random
samples. This allows raffle winners (the sample) to be partitioned
into grand prize and second place winners (the subslices).
Members of the population need not be hashable or unique. If the
population contains repeats, then each occurrence is a possible
Repeated elements can be specified one at a time or with the optional
counts parameter. For example:
sample(['red', 'blue'], counts=[4, 2], k=5)
sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5)
To choose a sample from a range of integers, use range() for the
population argument. This is especially fast and space efficient
for sampling from a large population:
sample(range(10000000), 60)
# Sampling without replacement entails tracking either potential
# selections (the pool) in a list or previous selections in a set.
# When the number of selections is small compared to the
# population, then tracking selections is efficient, requiring
# only a small set and an occasional reselection. For
# a larger number of selections, the pool tracking method is
# preferred since the list takes less space than the
# set and it doesn't suffer from frequent reselections.
# The number of calls to _randbelow() is kept at or near k, the
# theoretical minimum. This is important because running time
# is dominated by _randbelow() and because it extracts the
# least entropy from the underlying random number generators.
# Memory requirements are kept to the smaller of a k-length
# set or an n-length list.
# There are other sampling algorithms that do not require
# auxiliary memory, but they were rejected because they made
# too many calls to _randbelow(), making them slower and
# causing them to eat more entropy than necessary.
if isinstance(population, _Set):
_warn('Sampling from a set deprecated\n'
'since Python 3.9 and will be removed in a subsequent version.',
population = tuple(population)
if not isinstance(population, _Sequence):
raise TypeError("Population must be a sequence. For dicts or sets, use sorted(d).")
cum_counts = list(_accumulate(counts))
raise ValueError('The number of counts does not match the population')
if not isinstance(total, int):
raise TypeError('Counts must be integers')
raise ValueError('Total of counts must be greater than zero')
selections = self.sample(range(total), k=k)
return [population[bisect(cum_counts, s)] for s in selections]
randbelow = self._randbelow
raise ValueError("Sample larger than population or is negative")
setsize = 21 # size of a small set minus size of an empty list
setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets
# An n-length list is smaller than a k-length set.
# Invariant: non-selected at pool[0 : n-i]
pool[j] = pool[n - i - 1] # move non-selected item into vacancy
selected_add = selected.add
result[i] = population[j]
def choices(self, population, weights=None, *, cum_weights=None, k=1):
"""Return a k sized list of population elements chosen with replacement.
If the relative weights or cumulative weights are not specified,
the selections are made with equal probability.
n += 0.0 # convert to float for a small speed improvement
return [population[floor(random() * n)] for i in _repeat(None, k)]
cum_weights = list(_accumulate(weights))
if not isinstance(weights, int):
f'The number of choices must be a keyword argument: {k=}'
elif weights is not None:
raise TypeError('Cannot specify both weights and cumulative weights')
if len(cum_weights) != n:
raise ValueError('The number of weights does not match the population')
total = cum_weights[-1] + 0.0 # convert to float
It is recommended that you Edit text format, this type of Fix handles quite a lot in one request
