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3 \2k � @ s� d Z ddlmZ ddlmZmZ ddl m Z m Z mZmZmZ ddl mZmZmZmZ ddl m Z ddl m Z!m"Z# ddl$m%Z& dd l'Z(dd l)Z*d d d d ddddddddddddddd d d d d d!gZ+d"e d2� ed$� Z,d$e Z-e d%�Z.d&e d'� Z/d(Z0d)e0 Z1dd l2Z2G d*d � d e2j3�Z3G d+d!� d!e3�Z4d,d-� Z5d3d/d0�Z6e3� Z7e7j8Z8e7j9Z9e7j:Z:e7j;Z;e7j<Z<e7j=Z=e7j>Z>e7j?Z?e7j@Z@e7jAZAe7jBZBe7jCZCe7jDZDe7jEZEe7jFZFe7jGZGe7jHZHe7jIZIe7jJZJe7jKZKe7jLZLe7jMZMeNd1k�r�e6� d S )4a� Random variable generators. integers -------- uniform within range sequences --------- pick random element pick random sample pick weighted random sample generate random permutation distributions on the real line: ------------------------------ uniform triangular normal (Gaussian) lognormal negative exponential gamma beta pareto Weibull distributions on the circle (angles 0 to 2pi) --------------------------------------------- circular uniform von Mises General notes on the underlying Mersenne Twister core generator: * The period is 2**19937-1. * It is one of the most extensively tested generators in existence. * The random() method is implemented in C, executes in a single Python step, and is, therefore, threadsafe. � )�warn)� MethodType�BuiltinMethodType)�log�exp�pi�e�ceil)�sqrt�acos�cos�sin)�urandom)�Set�Sequence)�sha512N�Random�seed�random�uniform�randint�choice�sample� randrange�shuffle� normalvariate�lognormvariate� expovariate�vonmisesvariate� gammavariate� triangular�gauss� betavariate� paretovariate�weibullvariate�getstate�setstate� getrandbits�choices� SystemRandom� g �?g @g @g �?g @�5 � c s e Zd ZdZdZd;dd�Zd<� fdd� Z� fd d �Z� fd d �Zd d� Z dd� Z dd� Z dde fdd�Z dd� Ze de> eeefdd�Zdd� Zd=d d �Zd d � Zd>ddd �d!d"�Zd#d$� Zd?d'd(�Zd)d*� Zd+d,� Zd-d.� Z d/d0� Z d1d2� Z d3d4� Z d5d6� Z d7d8� Z!d9d:� Z"� Z#S )@r 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| _dS )zeInitialize an instance. Optional argument x controls seeding, as for Random.seed(). N)r � gauss_next)�self�x� r1 � /usr/lib64/python3.6/random.py�__init__W s zRandom.__init__r, c s� |dkr�t |ttf�r�t |t�r*|jd�n|}|rBt|d �d> nd}x"tt|�D ]}d| |A d@ }qRW |t|�N }|d kr�d n|}|dkr�t |tttf�r�t |t�r�|j� }|t |�j � 7 }t j |d�}t � j|� 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. 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. � zlatin-1r � iCB l ���� r, �bigN������)� isinstance�str�bytes�decode�ord�map�len� bytearray�encode�_sha512Zdigest�int� from_bytes�superr r. )r/ �a�versionr0 �c)� __class__r1 r2 r ` s z Random.seedc s | j t� j� | jfS )z9Return internal state; can be passed to setstate() later.)�VERSIONrE r% r. )r/ )rI r1 r2 r% � s zRandom.getstatec s� |d }|dkr*|\}}| _ t� j|� nt|dkr�|\}}| _ ytdd� |D ��}W n( tk r| } z t|�W Y dd}~X nX t� j|� ntd|| jf ��dS )z:Restore internal state from object returned by getstate().r r- r, c s s | ]}|d V qdS )r, � Nl r1 )�.0r0 r1 r1 r2 � <genexpr>� s z"Random.setstate.<locals>.<genexpr>Nz?state with version %s passed to Random.setstate() of version %s)r. rE r& �tuple� ValueError� TypeErrorrJ )r/ �staterG Z internalstater )rI r1 r2 r& � s zRandom.setstatec C s | j � S )N)r% )r/ r1 r1 r2 � __getstate__� s zRandom.__getstate__c C s | j |� d S )N)r& )r/ rQ r1 r1 r2 � __setstate__� s zRandom.__setstate__c C s | j f | j� fS )N)rI r% )r/ r1 r1 r2 � __reduce__� s zRandom.__reduce__r4 c C s ||�}||krt d��|dkr:|dkr2| j|�S t d��||�}||krRt d��|| }|dkrx|dkrx|| j|� S |dkr�t d|||f ��||�}||kr�t d��|dkr�|| d | } n"|dk r�|| d | } nt d ��| dkr�t d��||| j| � S ) z�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. z!non-integer arg 1 for randrange()Nr zempty range for randrange()z non-integer stop for randrange()r4 z'empty range for randrange() (%d,%d, %d)z non-integer step for randrange()zzero step for randrange())rO � _randbelow) r/ �start�stop�step�_intZistartZistop�widthZistep�nr1 r1 r2 r � s4 zRandom.randrangec C s | j ||d �S )zJReturn random integer in range [a, b], including both end points. r4 )r )r/ rF �br1 r1 r2 r � s zRandom.randintc C s� | j }| j}||�|ks$||�|krN|j� } || �} x| |krH|| �} q6W | S ||krltd� ||� | �S |dkr|td��|| } || | } |� } x| | kr�|� } q�W || | �| S )zCReturn a random int in the range [0,n). Raises ValueError if n==0.z�Underlying random() generator does not supply enough bits to choose from a population range this large. To remove the range limitation, add a getrandbits() method.r zBoundary cannot be zero)r r' � bit_length�_warnrO ) r/ r[ rC �maxsize�typeZMethodZ BuiltinMethodr r' �k�rZrem�limitr1 r1 r2 rU � s& zRandom._randbelowc C s: y| j t|��}W n tk r0 td�d�Y nX || S )z2Choose a random element from a non-empty sequence.z$Cannot choose from an empty sequenceN)rU r? rO � IndexError)r/ �seq�ir1 r1 r2 r � s z Random.choicec C s� |dkrR| j }x�ttdt|���D ]*}||d �}|| || ||< ||< q"W nLt}xFttdt|���D ]0}||� |d �}|| || ||< ||< qjW dS )z�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. Nr4 )rU �reversed�ranger? rC )r/ r0 r � randbelowrf �jrY r1 r1 r2 r s zRandom.shufflec C s( t |t�rt|�}t |t�s$td��| j}t|�}d| koD|kn sRtd��dg| }d}|dkr�|dtt |d d�� 7 }||kr�t |�}x�t |�D ]0}||| �} || ||< ||| d || < q�W nRt � } | j } xDt |�D ]8}||�} x| | k�r ||�} q�W | | � || ||< q�W |S ) a= Chooses k unique random elements from a population sequence or set. Returns a new list containing elements from the population while leaving the original population unchanged. The resulting list is in selection order so that all sub-slices will also be valid random samples. This allows raffle winners (the sample) to be partitioned into grand prize and second place winners (the subslices). Members of the population need not be hashable or unique. If the population contains repeats, then each occurrence is a possible selection in the sample. To choose a sample in a range of integers, use range as an argument. This is especially fast and space efficient for sampling from a large population: sample(range(10000000), 60) z>Population must be a sequence or set. For dicts, use list(d).r z,Sample larger than population or is negativeN� � r* r- r4 )r9 �_SetrN � _SequencerP rU r? rO �_ceil�_log�listrh �set�add) r/ � populationra ri r[ �resultZsetsizeZpoolrf rj ZselectedZ selected_addr1 r1 r2 r s6 z Random.sample)� cum_weightsra c s� | j ��dkrN|dkr>t� t���� ���fdd�t|�D �S ttj|���n|dk r^td��t��t��krvtd��t j ��d �t��d �������fdd�t|�D �S ) z�Return a k sized list of population elements chosen with replacement. If the relative weights or cumulative weights are not specified, the selections are made with equal probability. Nc s g | ]}�� �� � � �qS r1 r1 )rL rf )rY rt r �totalr1 r2 � <listcomp>c s z"Random.choices.<locals>.<listcomp>z2Cannot specify both weights and cumulative weightsz3The number of weights does not match the populationr4 c s$ g | ] }�� ��� � d �� �qS )r r1 )rL rf )�bisectrv �hirt r rw r1 r2 rx l s r7 ) r rC r? rh rq � _itertools� accumulaterP rO �_bisectry )r/ rt Zweightsrv ra r1 )rY ry rv rz rt r rw r2 r( W s zRandom.choicesc C s ||| | j � S )zHGet a random number in the range [a, b) or [a, b] depending on rounding.)r )r/ rF r\ r1 r1 r2 r s s zRandom.uniform� � �?c C sx | j � }y |dkrdn|| || }W n tk r< |S X ||kr`d| }d| }|| }}||| || d S )z�Triangular distribution. Continuous distribution bounded by given lower and upper limits, and having a given mode value in-between. http://en.wikipedia.org/wiki/Triangular_distribution Ng �?g �?)r �ZeroDivisionError)r/ ZlowZhigh�mode�urH r1 r1 r2 r y s zRandom.triangularc C sT | j }x@|� }d|� }t|d | }|| d }|t|� krP qW ||| S )z\Normal distribution. mu is the mean, and sigma is the standard deviation. g �?g �?g @)r � NV_MAGICCONSTrp )r/ �mu�sigmar �u1�u2�zZzzr1 r1 r2 r � s zRandom.normalvariatec C s t | j||��S )z�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. )�_expr )r/ r� r� r1 r1 r2 r � s zRandom.lognormvariatec C s t d| j� � | S )a^ 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. g �?)rp r )r/ Zlambdr1 r1 r2 r � s zRandom.expovariatec C s� | j }|dkrt|� S d| }|td|| � }xN|� }tt| �}||| }|� } | d|| k s~| d| t|� kr6P q6W d| } | | d| | } |� } | dkr�|t| � t } n|t| � t } | S )aF Circular data distribution. 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. g���ư>g �?g �?)r �TWOPI�_sqrt�_cos�_pir� �_acos)r/ r� Zkappar �srb r� r� �dr� �q�fZu3Zthetar1 r1 r2 r � s& $zRandom.vonmisesvariatec C s� |dks|dkrt d��| j}|dkr�td| d �}|t }|| }x�|� }d| k o`dk n shqHd|� }t|d| �| } |t| � } || | } ||| | } | t d| dks�| t| �krH| | S qHW n�|dk�r|� } x| dk�r |� } q�W t| � | S x�|� } t| t }|| }|dk�rD|d| } nt|| | � } |� }|dk�r||| |d k�r�P n|t| �k�rP �qW | | S dS ) aZ Gamma distribution. Not the gamma function! Conditions on the parameters are alpha > 0 and beta > 0. The probability distribution function is: x ** (alpha - 1) * math.exp(-x / beta) pdf(x) = -------------------------------------- math.gamma(alpha) * beta ** alpha g z*gammavariate: alpha and beta must be > 0.0g �?g @gH�����z>g�P���?g @N)rO r r� �LOG4rp r� � SG_MAGICCONST�_e)r/ �alpha�betar ZainvZbbbZcccr� r� �vr0 r� rb r� r\ �pr1 r1 r2 r � sJ zRandom.gammavariatec C s` | j }| j}d| _|dkrT|� t }tdtd|� � �}t|�| }t|�| | _||| S )z�Gaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function. Not thread-safe without a lock around calls. Ng @g �?g �)r r. r� r� rp r� �_sin)r/ r� r� r r� Zx2piZg2radr1 r1 r2 r! ? s z Random.gaussc C s0 | j |d�}|dkrdS ||| j |d� S dS )z�Beta distribution. Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1. g �?r g N)r )r/ r� r� �yr1 r1 r2 r" t s zRandom.betavariatec C s d| j � }d|d| S )z3Pareto distribution. alpha is the shape parameter.g �?)r )r/ r� r� r1 r1 r2 r# � s zRandom.paretovariatec C s" d| j � }|t|� d| S )zfWeibull distribution. alpha is the scale parameter and beta is the shape parameter. g �?)r rp )r/ r� r� r� r1 r1 r2 r$ � s zRandom.weibullvariate)N)Nr, )N)N)r~ r N)$�__name__� __module__� __qualname__�__doc__rJ r3 r r% r& rR rS rT rC r r �BPFr` � _MethodType�_BuiltinMethodTyperU r r r r( r r r r r r r r! r" r# r$ � __classcell__r1 r1 )rI r2 r G s8 , : 0H5 c @ s8 e Zd ZdZdd� Zdd� Zdd� Zdd � Ze ZZ d S ) r) z�Alternate random number generator using sources provided by the operating system (such as /dev/urandom on Unix or CryptGenRandom on Windows). Not available on all systems (see os.urandom() for details). c C s t jtd�d�d? t S )z3Get the next random number in the range [0.0, 1.0).r5 r6 r- )rC rD �_urandom� RECIP_BPF)r/ r1 r1 r2 r � s zSystemRandom.randomc C sP |dkrt d��|t|�kr$td��|d d }tjt|�d�}||d | ? S )z:getrandbits(k) -> x. Generates an int with k random bits.r z(number of bits must be greater than zeroz#number of bits should be an integerr5 � r6 )rO rC rP rD r� )r/ ra Znumbytesr0 r1 r1 r2 r' � s zSystemRandom.getrandbitsc O s dS )z<Stub method. Not used for a system random number generator.Nr1 )r/ �args�kwdsr1 r1 r2 r � s zSystemRandom.seedc O s t d��dS )zAMethod should not be called for a system random number generator.z*System entropy source does not have state.N)�NotImplementedError)r/ r� r� r1 r1 r2 �_notimplemented� s z SystemRandom._notimplementedN) r� r� r� r� r r' r r� r% r& r1 r1 r1 r2 r) � s c C s� dd l }t| d|j� d}d}d}d }|j � }x@t| �D ]4} ||� } || 7 }|| | }t| |�}t| |�}q8W |j � } tt| | d�ddd� || } t|| | | �} td | | ||f � d S ) Nr �timesg g _�Br- zsec,� )�endz"avg %g, stddev %g, min %g, max %g g _��)�time�printr� rh �min�max�roundr� )r[ �funcr� r� rw ZsqsumZsmallestZlargestZt0rf r0 Zt1ZavgZstddevr1 r1 r2 �_test_generator� s& r� �� c C s� t | tf � t | td � t | td � t | td � t | td� t | td� t | td� t | td� t | td� t | td� t | td� t | td� t | td� t | td� t | td� t | td� d S )N� � �?�{�G�z�?皙�����?� @� �?��������?� 4@� i@� @)r� r� )r� r� )r� r� )r� r� )r� r� )r� r� )r� r� )r� r� )r� r� )r� r� )r� r� )r� r� )r� r� )r� r� �UUUUUU�?)r� r� r� ) r� r r r r r r! r" r )�Nr1 r1 r2 �_test� s r� �__main__g �)r� )Or� �warningsr r^ �typesr r� r r� Zmathr rp r r� r r� r r� r ro r r� r r� r r� r r� �osr r� �_collections_abcr rm r rn Zhashlibr rB � itertoolsr{ ry r} �__all__r� r� r� r� r� r� Z_randomr r) r� r� Z_instr r r r r r r r r r( r r r r r r! r" r# r$ r% r& r' r� r1 r1 r1 r2 �<module>& sn Y!
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