1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793
|
:mod:`!random` --- Generate pseudo-random numbers
=================================================
.. module:: random
:synopsis: Generate pseudo-random numbers with various common distributions.
**Source code:** :source:`Lib/random.py`
--------------
This module implements pseudo-random number generators for various
distributions.
For integers, there is uniform selection from a range. For sequences, there is
uniform selection of a random element, a function to generate a random
permutation of a list in-place, and a function for random sampling without
replacement.
On the real line, there are functions to compute uniform, normal (Gaussian),
lognormal, negative exponential, gamma, and beta distributions. For generating
distributions of angles, the von Mises distribution is available.
Almost all module functions depend on the basic function :func:`.random`, which
generates a random float uniformly in the half-open range ``0.0 <= X < 1.0``.
Python uses the Mersenne Twister as the core generator. It produces 53-bit precision
floats and has a period of 2\*\*19937-1. The underlying implementation in C is
both fast and threadsafe. The Mersenne Twister is one of the most extensively
tested random number generators in existence. However, being completely
deterministic, it is not suitable for all purposes, and is completely unsuitable
for cryptographic purposes.
The functions supplied by this module are actually bound methods of a hidden
instance of the :class:`random.Random` class. You can instantiate your own
instances of :class:`Random` to get generators that don't share state.
Class :class:`Random` can also be subclassed if you want to use a different
basic generator of your own devising: see the documentation on that class for
more details.
The :mod:`random` module also provides the :class:`SystemRandom` class which
uses the system function :func:`os.urandom` to generate random numbers
from sources provided by the operating system.
.. warning::
The pseudo-random generators of this module should not be used for
security purposes. For security or cryptographic uses, see the
:mod:`secrets` module.
.. seealso::
M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-dimensionally
equidistributed uniform pseudorandom number generator", ACM Transactions on
Modeling and Computer Simulation Vol. 8, No. 1, January pp.3--30 1998.
`Complementary-Multiply-with-Carry recipe
<https://code.activestate.com/recipes/576707-long-period-random-number-generator/>`_ for a compatible alternative
random number generator with a long period and comparatively simple update
operations.
.. note::
The global random number generator and instances of :class:`Random` are thread-safe.
However, in the free-threaded build, concurrent calls to the global generator or
to the same instance of :class:`Random` may encounter contention and poor performance.
Consider using separate instances of :class:`Random` per thread instead.
Bookkeeping functions
---------------------
.. function:: seed(a=None, version=2)
Initialize the random number generator.
If *a* is omitted or ``None``, the current system time is used. If
randomness sources are provided by the operating system, they are used
instead of the system time (see the :func:`os.urandom` function for details
on availability).
If *a* is an int, it is used directly.
With version 2 (the default), a :class:`str`, :class:`bytes`, or :class:`bytearray`
object gets converted to an :class:`int` and all of its bits are used.
With version 1 (provided for reproducing random sequences from older versions
of Python), the algorithm for :class:`str` and :class:`bytes` generates a
narrower range of seeds.
.. versionchanged:: 3.2
Moved to the version 2 scheme which uses all of the bits in a string seed.
.. versionchanged:: 3.11
The *seed* must be one of the following types:
``None``, :class:`int`, :class:`float`, :class:`str`,
:class:`bytes`, or :class:`bytearray`.
.. function:: getstate()
Return an object capturing the current internal state of the generator. This
object can be passed to :func:`setstate` to restore the state.
.. function:: setstate(state)
*state* should have been obtained from a previous call to :func:`getstate`, and
:func:`setstate` restores the internal state of the generator to what it was at
the time :func:`getstate` was called.
Functions for bytes
-------------------
.. function:: randbytes(n)
Generate *n* random bytes.
This method should not be used for generating security tokens.
Use :func:`secrets.token_bytes` instead.
.. versionadded:: 3.9
Functions for integers
----------------------
.. function:: randrange(stop)
randrange(start, stop[, step])
Return a randomly selected element from ``range(start, stop, step)``.
This is roughly equivalent to ``choice(range(start, stop, step))`` but
supports arbitrarily large ranges and is optimized for common cases.
The positional argument pattern matches the :func:`range` function.
Keyword arguments should not be used because they can be interpreted
in unexpected ways. For example ``randrange(start=100)`` is interpreted
as ``randrange(0, 100, 1)``.
.. versionchanged:: 3.2
:meth:`randrange` is more sophisticated about producing equally distributed
values. Formerly it used a style like ``int(random()*n)`` which could produce
slightly uneven distributions.
.. versionchanged:: 3.12
Automatic conversion of non-integer types is no longer supported.
Calls such as ``randrange(10.0)`` and ``randrange(Fraction(10, 1))``
now raise a :exc:`TypeError`.
.. function:: randint(a, b)
Return a random integer *N* such that ``a <= N <= b``. Alias for
``randrange(a, b+1)``.
.. function:: getrandbits(k)
Returns a non-negative Python integer with *k* random bits. This method
is supplied with the Mersenne Twister generator and some other generators
may also provide it as an optional part of the API. When available,
:meth:`getrandbits` enables :meth:`randrange` to handle arbitrarily large
ranges.
.. versionchanged:: 3.9
This method now accepts zero for *k*.
Functions for sequences
-----------------------
.. function:: choice(seq)
Return a random element from the non-empty sequence *seq*. If *seq* is empty,
raises :exc:`IndexError`.
.. function:: choices(population, weights=None, *, cum_weights=None, k=1)
Return a *k* sized list of elements chosen from the *population* with replacement.
If the *population* is empty, raises :exc:`IndexError`.
If a *weights* sequence is specified, selections are made according to the
relative weights. Alternatively, if a *cum_weights* sequence is given, the
selections are made according to the cumulative weights (perhaps computed
using :func:`itertools.accumulate`). For example, the relative weights
``[10, 5, 30, 5]`` are equivalent to the cumulative weights
``[10, 15, 45, 50]``. Internally, the relative weights are converted to
cumulative weights before making selections, so supplying the cumulative
weights saves work.
If neither *weights* nor *cum_weights* are specified, selections are made
with equal probability. If a weights sequence is supplied, it must be
the same length as the *population* sequence. It is a :exc:`TypeError`
to specify both *weights* and *cum_weights*.
The *weights* or *cum_weights* can use any numeric type that interoperates
with the :class:`float` values returned by :func:`random` (that includes
integers, floats, and fractions but excludes decimals). Weights are assumed
to be non-negative and finite. A :exc:`ValueError` is raised if all
weights are zero.
For a given seed, the :func:`choices` function with equal weighting
typically produces a different sequence than repeated calls to
:func:`choice`. The algorithm used by :func:`choices` uses floating-point
arithmetic for internal consistency and speed. The algorithm used
by :func:`choice` defaults to integer arithmetic with repeated selections
to avoid small biases from round-off error.
.. versionadded:: 3.6
.. versionchanged:: 3.9
Raises a :exc:`ValueError` if all weights are zero.
.. function:: shuffle(x)
Shuffle the sequence *x* in place.
To shuffle an immutable sequence and return a new shuffled list, use
``sample(x, k=len(x))`` instead.
Note that even for small ``len(x)``, the total number of permutations of *x*
can quickly grow larger than the period of most random number generators.
This implies that most permutations of a long sequence can never be
generated. For example, a sequence of length 2080 is the largest that
can fit within the period of the Mersenne Twister random number generator.
.. versionchanged:: 3.11
Removed the optional parameter *random*.
.. function:: sample(population, k, *, counts=None)
Return a *k* length list of unique elements chosen from the population
sequence. Used for random sampling without replacement.
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 :term:`hashable` or unique. If the population
contains repeats, then each occurrence is a possible selection in the sample.
Repeated elements can be specified one at a time or with the optional
keyword-only *counts* parameter. For example, ``sample(['red', 'blue'],
counts=[4, 2], k=5)`` is equivalent to ``sample(['red', 'red', 'red', 'red',
'blue', 'blue'], k=5)``.
To choose a sample from a range of integers, use a :func:`range` object as an
argument. This is especially fast and space efficient for sampling from a large
population: ``sample(range(10000000), k=60)``.
If the sample size is larger than the population size, a :exc:`ValueError`
is raised.
.. versionchanged:: 3.9
Added the *counts* parameter.
.. versionchanged:: 3.11
The *population* must be a sequence. Automatic conversion of sets
to lists is no longer supported.
Discrete distributions
----------------------
The following function generates a discrete distribution.
.. function:: binomialvariate(n=1, p=0.5)
`Binomial distribution
<https://mathworld.wolfram.com/BinomialDistribution.html>`_.
Return the number of successes for *n* independent trials with the
probability of success in each trial being *p*:
Mathematically equivalent to::
sum(random() < p for i in range(n))
The number of trials *n* should be a non-negative integer.
The probability of success *p* should be between ``0.0 <= p <= 1.0``.
The result is an integer in the range ``0 <= X <= n``.
.. versionadded:: 3.12
.. _real-valued-distributions:
Real-valued distributions
-------------------------
The following functions generate specific real-valued distributions. Function
parameters are named after the corresponding variables in the distribution's
equation, as used in common mathematical practice; most of these equations can
be found in any statistics text.
.. function:: random()
Return the next random floating-point number in the range ``0.0 <= X < 1.0``
.. function:: uniform(a, b)
Return a random floating-point number *N* such that ``a <= N <= b`` for
``a <= b`` and ``b <= N <= a`` for ``b < a``.
The end-point value ``b`` may or may not be included in the range
depending on floating-point rounding in the expression
``a + (b-a) * random()``.
.. function:: triangular(low, high, mode)
Return a random floating-point number *N* such that ``low <= N <= high`` and
with the specified *mode* between those bounds. The *low* and *high* bounds
default to zero and one. The *mode* argument defaults to the midpoint
between the bounds, giving a symmetric distribution.
.. function:: betavariate(alpha, beta)
Beta distribution. Conditions on the parameters are ``alpha > 0`` and
``beta > 0``. Returned values range between 0 and 1.
.. function:: expovariate(lambd = 1.0)
Exponential distribution. *lambd* is 1.0 divided by the desired
mean. It should be nonzero. (The parameter would be called
"lambda", but that is a reserved word in Python.) Returned values
range from 0 to positive infinity if *lambd* is positive, and from
negative infinity to 0 if *lambd* is negative.
.. versionchanged:: 3.12
Added the default value for ``lambd``.
.. function:: gammavariate(alpha, beta)
Gamma distribution. (*Not* the gamma function!) The shape and
scale parameters, *alpha* and *beta*, must have positive values.
(Calling conventions vary and some sources define 'beta'
as the inverse of the scale).
The probability distribution function is::
x ** (alpha - 1) * math.exp(-x / beta)
pdf(x) = --------------------------------------
math.gamma(alpha) * beta ** alpha
.. function:: gauss(mu=0.0, sigma=1.0)
Normal distribution, also called the Gaussian distribution.
*mu* is the mean,
and *sigma* is the standard deviation. This is slightly faster than
the :func:`normalvariate` function defined below.
Multithreading note: When two threads call this function
simultaneously, it is possible that they will receive the
same return value. This can be avoided in three ways.
1) Have each thread use a different instance of the random
number generator. 2) Put locks around all calls. 3) Use the
slower, but thread-safe :func:`normalvariate` function instead.
.. versionchanged:: 3.11
*mu* and *sigma* now have default arguments.
.. function:: lognormvariate(mu, sigma)
Log normal distribution. If you take the natural logarithm of this
distribution, you'll get a normal distribution with mean *mu* and standard
deviation *sigma*. *mu* can have any value, and *sigma* must be greater than
zero.
.. function:: normalvariate(mu=0.0, sigma=1.0)
Normal distribution. *mu* is the mean, and *sigma* is the standard deviation.
.. versionchanged:: 3.11
*mu* and *sigma* now have default arguments.
.. function:: vonmisesvariate(mu, kappa)
*mu* is the mean angle, expressed in radians between 0 and 2\*\ *pi*, and *kappa*
is the concentration parameter, which must be greater than or equal to zero. If
*kappa* is equal to zero, this distribution reduces to a uniform random angle
over the range 0 to 2\*\ *pi*.
.. function:: paretovariate(alpha)
Pareto distribution. *alpha* is the shape parameter.
.. function:: weibullvariate(alpha, beta)
Weibull distribution. *alpha* is the scale parameter and *beta* is the shape
parameter.
Alternative Generator
---------------------
.. class:: Random([seed])
Class that implements the default pseudo-random number generator used by the
:mod:`random` module.
.. versionchanged:: 3.11
Formerly the *seed* could be any hashable object. Now it is limited to:
``None``, :class:`int`, :class:`float`, :class:`str`,
:class:`bytes`, or :class:`bytearray`.
Subclasses of :class:`!Random` should override the following methods if they
wish to make use of a different basic generator:
.. method:: Random.seed(a=None, version=2)
Override this method in subclasses to customise the :meth:`~random.seed`
behaviour of :class:`!Random` instances.
.. method:: Random.getstate()
Override this method in subclasses to customise the :meth:`~random.getstate`
behaviour of :class:`!Random` instances.
.. method:: Random.setstate(state)
Override this method in subclasses to customise the :meth:`~random.setstate`
behaviour of :class:`!Random` instances.
.. method:: Random.random()
Override this method in subclasses to customise the :meth:`~random.random`
behaviour of :class:`!Random` instances.
Optionally, a custom generator subclass can also supply the following method:
.. method:: Random.getrandbits(k)
Override this method in subclasses to customise the
:meth:`~random.getrandbits` behaviour of :class:`!Random` instances.
.. method:: Random.randbytes(n)
Override this method in subclasses to customise the
:meth:`~random.randbytes` behaviour of :class:`!Random` instances.
.. class:: SystemRandom([seed])
Class that uses the :func:`os.urandom` function for generating random numbers
from sources provided by the operating system. Not available on all systems.
Does not rely on software state, and sequences are not reproducible. Accordingly,
the :meth:`seed` method has no effect and is ignored.
The :meth:`getstate` and :meth:`setstate` methods raise
:exc:`NotImplementedError` if called.
Notes on Reproducibility
------------------------
Sometimes it is useful to be able to reproduce the sequences given by a
pseudo-random number generator. By reusing a seed value, the same sequence should be
reproducible from run to run as long as multiple threads are not running.
Most of the random module's algorithms and seeding functions are subject to
change across Python versions, but two aspects are guaranteed not to change:
* If a new seeding method is added, then a backward compatible seeder will be
offered.
* The generator's :meth:`~Random.random` method will continue to produce the same
sequence when the compatible seeder is given the same seed.
.. _random-examples:
Examples
--------
Basic examples::
>>> random() # Random float: 0.0 <= x < 1.0
0.37444887175646646
>>> uniform(2.5, 10.0) # Random float: 2.5 <= x <= 10.0
3.1800146073117523
>>> expovariate(1 / 5) # Interval between arrivals averaging 5 seconds
5.148957571865031
>>> randrange(10) # Integer from 0 to 9 inclusive
7
>>> randrange(0, 101, 2) # Even integer from 0 to 100 inclusive
26
>>> choice(['win', 'lose', 'draw']) # Single random element from a sequence
'draw'
>>> deck = 'ace two three four'.split()
>>> shuffle(deck) # Shuffle a list
>>> deck
['four', 'two', 'ace', 'three']
>>> sample([10, 20, 30, 40, 50], k=4) # Four samples without replacement
[40, 10, 50, 30]
Simulations::
>>> # Six roulette wheel spins (weighted sampling with replacement)
>>> choices(['red', 'black', 'green'], [18, 18, 2], k=6)
['red', 'green', 'black', 'black', 'red', 'black']
>>> # Deal 20 cards without replacement from a deck
>>> # of 52 playing cards, and determine the proportion of cards
>>> # with a ten-value: ten, jack, queen, or king.
>>> deal = sample(['tens', 'low cards'], counts=[16, 36], k=20)
>>> deal.count('tens') / 20
0.15
>>> # Estimate the probability of getting 5 or more heads from 7 spins
>>> # of a biased coin that settles on heads 60% of the time.
>>> sum(binomialvariate(n=7, p=0.6) >= 5 for i in range(10_000)) / 10_000
0.4169
>>> # Probability of the median of 5 samples being in middle two quartiles
>>> def trial():
... return 2_500 <= sorted(choices(range(10_000), k=5))[2] < 7_500
...
>>> sum(trial() for i in range(10_000)) / 10_000
0.7958
Example of `statistical bootstrapping
<https://en.wikipedia.org/wiki/Bootstrapping_(statistics)>`_ using resampling
with replacement to estimate a confidence interval for the mean of a sample::
# https://www.thoughtco.com/example-of-bootstrapping-3126155
from statistics import fmean as mean
from random import choices
data = [41, 50, 29, 37, 81, 30, 73, 63, 20, 35, 68, 22, 60, 31, 95]
means = sorted(mean(choices(data, k=len(data))) for i in range(100))
print(f'The sample mean of {mean(data):.1f} has a 90% confidence '
f'interval from {means[5]:.1f} to {means[94]:.1f}')
Example of a `resampling permutation test
<https://en.wikipedia.org/wiki/Resampling_(statistics)#Permutation_tests>`_
to determine the statistical significance or `p-value
<https://en.wikipedia.org/wiki/P-value>`_ of an observed difference
between the effects of a drug versus a placebo::
# Example from "Statistics is Easy" by Dennis Shasha and Manda Wilson
from statistics import fmean as mean
from random import shuffle
drug = [54, 73, 53, 70, 73, 68, 52, 65, 65]
placebo = [54, 51, 58, 44, 55, 52, 42, 47, 58, 46]
observed_diff = mean(drug) - mean(placebo)
n = 10_000
count = 0
combined = drug + placebo
for i in range(n):
shuffle(combined)
new_diff = mean(combined[:len(drug)]) - mean(combined[len(drug):])
count += (new_diff >= observed_diff)
print(f'{n} label reshufflings produced only {count} instances with a difference')
print(f'at least as extreme as the observed difference of {observed_diff:.1f}.')
print(f'The one-sided p-value of {count / n:.4f} leads us to reject the null')
print(f'hypothesis that there is no difference between the drug and the placebo.')
Simulation of arrival times and service deliveries for a multiserver queue::
from heapq import heapify, heapreplace
from random import expovariate, gauss
from statistics import mean, quantiles
average_arrival_interval = 5.6
average_service_time = 15.0
stdev_service_time = 3.5
num_servers = 3
waits = []
arrival_time = 0.0
servers = [0.0] * num_servers # time when each server becomes available
heapify(servers)
for i in range(1_000_000):
arrival_time += expovariate(1.0 / average_arrival_interval)
next_server_available = servers[0]
wait = max(0.0, next_server_available - arrival_time)
waits.append(wait)
service_duration = max(0.0, gauss(average_service_time, stdev_service_time))
service_completed = arrival_time + wait + service_duration
heapreplace(servers, service_completed)
print(f'Mean wait: {mean(waits):.1f} Max wait: {max(waits):.1f}')
print('Quartiles:', [round(q, 1) for q in quantiles(waits)])
.. seealso::
`Statistics for Hackers <https://www.youtube.com/watch?v=Iq9DzN6mvYA>`_
a video tutorial by
`Jake Vanderplas <https://us.pycon.org/2016/speaker/profile/295/>`_
on statistical analysis using just a few fundamental concepts
including simulation, sampling, shuffling, and cross-validation.
`Economics Simulation
<https://nbviewer.org/url/norvig.com/ipython/Economics.ipynb>`_
a simulation of a marketplace by
`Peter Norvig <https://norvig.com/bio.html>`_ that shows effective
use of many of the tools and distributions provided by this module
(gauss, uniform, sample, betavariate, choice, triangular, and randrange).
`A Concrete Introduction to Probability (using Python)
<https://nbviewer.org/url/norvig.com/ipython/Probability.ipynb>`_
a tutorial by `Peter Norvig <https://norvig.com/bio.html>`_ covering
the basics of probability theory, how to write simulations, and
how to perform data analysis using Python.
Recipes
-------
These recipes show how to efficiently make random selections
from the combinatoric iterators in the :mod:`itertools` module:
.. testcode::
import random
def random_product(*args, repeat=1):
"Random selection from itertools.product(*args, **kwds)"
pools = [tuple(pool) for pool in args] * repeat
return tuple(map(random.choice, pools))
def random_permutation(iterable, r=None):
"Random selection from itertools.permutations(iterable, r)"
pool = tuple(iterable)
r = len(pool) if r is None else r
return tuple(random.sample(pool, r))
def random_combination(iterable, r):
"Random selection from itertools.combinations(iterable, r)"
pool = tuple(iterable)
n = len(pool)
indices = sorted(random.sample(range(n), r))
return tuple(pool[i] for i in indices)
def random_combination_with_replacement(iterable, r):
"Choose r elements with replacement. Order the result to match the iterable."
# Result will be in set(itertools.combinations_with_replacement(iterable, r)).
pool = tuple(iterable)
n = len(pool)
indices = sorted(random.choices(range(n), k=r))
return tuple(pool[i] for i in indices)
The default :func:`.random` returns multiples of 2⁻⁵³ in the range
*0.0 ≤ x < 1.0*. All such numbers are evenly spaced and are exactly
representable as Python floats. However, many other representable
floats in that interval are not possible selections. For example,
``0.05954861408025609`` isn't an integer multiple of 2⁻⁵³.
The following recipe takes a different approach. All floats in the
interval are possible selections. The mantissa comes from a uniform
distribution of integers in the range *2⁵² ≤ mantissa < 2⁵³*. The
exponent comes from a geometric distribution where exponents smaller
than *-53* occur half as often as the next larger exponent.
::
from random import Random
from math import ldexp
class FullRandom(Random):
def random(self):
mantissa = 0x10_0000_0000_0000 | self.getrandbits(52)
exponent = -53
x = 0
while not x:
x = self.getrandbits(32)
exponent += x.bit_length() - 32
return ldexp(mantissa, exponent)
All :ref:`real valued distributions <real-valued-distributions>`
in the class will use the new method::
>>> fr = FullRandom()
>>> fr.random()
0.05954861408025609
>>> fr.expovariate(0.25)
8.87925541791544
The recipe is conceptually equivalent to an algorithm that chooses from
all the multiples of 2⁻¹⁰⁷⁴ in the range *0.0 ≤ x < 1.0*. All such
numbers are evenly spaced, but most have to be rounded down to the
nearest representable Python float. (The value 2⁻¹⁰⁷⁴ is the smallest
positive unnormalized float and is equal to ``math.ulp(0.0)``.)
.. seealso::
`Generating Pseudo-random Floating-Point Values
<https://allendowney.com/research/rand/downey07randfloat.pdf>`_ a
paper by Allen B. Downey describing ways to generate more
fine-grained floats than normally generated by :func:`.random`.
.. _random-cli:
Command-line usage
------------------
.. versionadded:: 3.13
The :mod:`!random` module can be executed from the command line.
.. code-block:: sh
python -m random [-h] [-c CHOICE [CHOICE ...] | -i N | -f N] [input ...]
The following options are accepted:
.. program:: random
.. option:: -h, --help
Show the help message and exit.
.. option:: -c CHOICE [CHOICE ...]
--choice CHOICE [CHOICE ...]
Print a random choice, using :meth:`choice`.
.. option:: -i <N>
--integer <N>
Print a random integer between 1 and N inclusive, using :meth:`randint`.
.. option:: -f <N>
--float <N>
Print a random floating-point number between 0 and N inclusive,
using :meth:`uniform`.
If no options are given, the output depends on the input:
* String or multiple: same as :option:`--choice`.
* Integer: same as :option:`--integer`.
* Float: same as :option:`--float`.
.. _random-cli-example:
Command-line example
--------------------
Here are some examples of the :mod:`!random` command-line interface:
.. code-block:: console
$ # Choose one at random
$ python -m random egg bacon sausage spam "Lobster Thermidor aux crevettes with a Mornay sauce"
Lobster Thermidor aux crevettes with a Mornay sauce
$ # Random integer
$ python -m random 6
6
$ # Random floating-point number
$ python -m random 1.8
1.7080016272295635
$ # With explicit arguments
$ python -m random --choice egg bacon sausage spam "Lobster Thermidor aux crevettes with a Mornay sauce"
egg
$ python -m random --integer 6
3
$ python -m random --float 1.8
1.5666339105010318
$ python -m random --integer 6
5
$ python -m random --float 6
3.1942323316565915
|