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d! � e d" � Z( d" e Z) e d# � Z* d$ e d% � Z+ d& Z, d' e, Z- d d( l. Z. Gd) d � d e. j/ � Z/ Gd* d � d e/ � Z0 d+ d, � Z1 d- d. d/ � Z2 e/ � Z3 e3 j4 Z4 e3 j5 Z5 e3 j6 Z6 e3 j7 Z7 e3 j8 Z8 e3 j9 Z9 e3 j: Z: e3 j; Z; e3 j< Z< e3 j= Z= e3 j> Z> e3 j? Z? e3 j@ Z@ e3 jA ZA e3 jB ZB e3 jC ZC e3 jD ZD e3 jE ZE e3 jF ZF e3 jG ZG e3 jH ZH eI d0 k rxe2 � d( S)1a� Random variable generators.
integers
--------
uniform within range
sequences
---------
pick random element
pick random sample
generate random permutation
distributions on the real line:
------------------------------
uniform
triangular
normal (Gaussian)
lognormal
negative exponential
gamma
beta
pareto
Weibull
distributions on the circle (angles 0 to 2pi)
---------------------------------------------
circular uniform
von Mises
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.
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d d � Z e d e >e e e d d � Z d d � Z d d d � Z d d � Z d d! � Z d" d# d d$ d% � Z d& d' � Z d( d) � Z d* d+ � Z d, d- � Z d. d/ � Z d0 d1 � Z d2 d3 � Z d4 d5 � Z d6 d7 � Z! � S)8r a� Random number generator base class used by bound module functions.
Used to instantiate instances of Random to get generators that don't
share state.
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.
� Nc C s | j | � d | _ d S)zeInitialize an instance.
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| � d | _ d S)a� Initialize internal state from hashable object.
None or no argument seeds from current time or from an operating
system specific randomness source if available.
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z�Choose a random item from range(start, stop[, step]).
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z!non-integer arg 1 for randrange()Nr zempty range for randrange()z non-integer stop for randrange()rO z'empty range for randrange() (%d,%d, %d)z non-integer step for randrange()zzero step for randrange())rI �
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zRandom.randrangec C s | j | | d � S)zJReturn random integer in range [a, b], including both end points.
rO )r )r. rA �br0 r0 r1 r � s zRandom.randintc
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Random.choicec C s� | d k rk | j } x� t t d t | � � � D]3 } | | d � } | | | | | | <| | <q1 Wn` t } xW t t d t | � � � D]: } | | � | d � } | | | | | | <| | <q� Wd S)z�Shuffle list x in place, and return None.
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a= 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
selection in the sample.
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large population: sample(range(10000000), 60)
z>Population must be a sequence or set. For dicts, use list(d).r z Sample larger than populationN� � r) r, rO )r: �_SetrH � _SequencerJ rP r_ rI �_ceil�_log�listrd �set�add) r. Z
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rL | SYn X| | k rz d | } d | } | | } } | | | | | d S)z�Triangular distribution.
Continuous distribution bounded by given lower and upper limits,
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http://en.wikipedia.org/wiki/Triangular_distribution
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zRandom.triangularc C sf | j } xN | � } d | � } t | d | } | | d } | t | � k r Pq W| | | S)z\Normal distribution.
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zRandom.normalvariatec C s t | j | | � � S)z�Log normal distribution.
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)�_expr )r. rv rw r0 r0 r1 r � s zRandom.lognormvariatec C s t d | j � � | S)a^ Exponential distribution.
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nonzero. (The parameter would be called "lambda", but that is
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positive infinity if lambd is positive, and from negative
infinity to 0 if lambd is negative.
g �?)rl r )r. Zlambdr0 r0 r1 r � s zRandom.expovariatec C s | j } | d k r t | � Sd | } | t d | | � } xc | � } t t | � } | | | } | � } | d | | k s� | d | t | � k rE PqE Wd | }
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equal to zero. If kappa is equal to zero, this distribution reduces
to a uniform random angle over the range 0 to 2*pi.
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Conditions on the parameters are alpha > 0 and beta > 0.
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pdf(x) = --------------------------------------
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g z*gammavariate: alpha and beta must be > 0.0g �?g @gH�����z>g�P���?g @N)rI r r} �LOG4rl r{ �
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zRandom.gammavariatec C s� | j } | j } d | _ | d k rt | � t } t d t d | � � � } t | � | } t | � | | _ | | | S)z�Gaussian distribution.
mu is the mean, and sigma is the standard deviation. This is
slightly faster than the normalvariate() function.
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z Random.gaussc C s> | j | d � } | d k r" d S| | | j | d � Sd S)z�Beta distribution.
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Returned values range between 0 and 1.
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zRandom.betavariatec C s d | j � } d | d | S)z3Pareto distribution. alpha is the shape parameter.g �?)r )r. r� rs r0 r0 r1 r# i s zRandom.paretovariatec C s' d | j � } | t | � d | S)zfWeibull distribution.
alpha is the scale parameter and beta is the shape parameter.
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S) r( z�Alternate random number generator using sources provided
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c C s t j t d � d � d ?t S)z3Get the next random number in the range [0.0, 1.0).� r3 r, )r5 r6 r7 � RECIP_BPF)r. r0 r0 r1 r � s zSystemRandom.randomc C sl | d k r t d � � | t | � k r6 t d � � | d d } t j t | � d � } | | d | ?S)z:getrandbits(k) -> x. Generates an int with k random bits.r z(number of bits must be greater than zeroz#number of bits should be an integerr� � r3 )rI r5 rJ r6 r7 )r. r\ Znumbytesr/ r0 r0 r1 r' � s zSystemRandom.getrandbitsc O s d S)z<Stub method. Not used for a system random number generator.Nr0 )r. �args�kwdsr0 r0 r1 r � s zSystemRandom.seedc O s t d � � d S)zAMethod should not be called for a system random number generator.z*System entropy source does not have state.N)r8 )r. r� r� r0 r0 r1 �_notimplemented� s z SystemRandom._notimplementedN)
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