3 ^2kc@sdZddlmZddlmZmZddl m Z m Z mZmZmZddl mZmZmZmZddlmZddlm Z!m"Z#ddl$m%Z&dd l'Z(dd l)Z*d d d d ddddddddddddddddddd d!gZ+d"e d2ed$Z,d$eZ-e d%Z.d&e d'Z/d(Z0d)e0 Z1dd l2Z2Gd*d d e2j3Z3Gd+d!d!e3Z4d,d-Z5d3d/d0Z6e3Z7e7j8Z8e7j9Z9e7j:Z:e7j;Z;e7jZ>e7j?Z?e7j@Z@e7jAZAe7jBZBe7jCZCe7jDZDe7jEZEe7jFZFe7jGZGe7jHZHe7jIZIe7jJZJe7jKZKe7jLZLe7jMZMeNd1kre6d S)4aRandom variable generators. integers -------- uniform within range sequences --------- pick random element pick random sample pick weighted random sample generate random permutation distributions on the real line: ------------------------------ uniform triangular normal (Gaussian) lognormal negative exponential gamma beta pareto Weibull distributions on the circle (angles 0 to 2pi) --------------------------------------------- circular uniform von Mises General notes on the underlying Mersenne Twister core generator: * The period is 2**19937-1. * It is one of the most extensively tested generators in existence. * The random() method is implemented in C, executes in a single Python step, and is, therefore, threadsafe. )warn) MethodTypeBuiltinMethodType)logexppieceil)sqrtacoscossin)urandom)SetSequence)sha512NRandomseedrandomuniformrandintchoicesample randrangeshuffle normalvariatelognormvariate expovariatevonmisesvariate gammavariate triangulargauss betavariate paretovariateweibullvariategetstatesetstate getrandbitschoices SystemRandom?@@?@i5cseZdZdZdZd;ddZd<fdd Zfd d Zfd d Zd dZ ddZ ddZ dde fddZ ddZe de>eeefddZddZd=ddZddZd>ddd d!d"Zd#d$Zd?d'd(Zd)d*Zd+d,Zd-d.Zd/d0Zd1d2Zd3d4Zd5d6Z d7d8Z!d9d:Z"Z#S)@raRandom 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. NcCs|j|d|_dS)zeInitialize an instance. Optional argument x controls seeding, as for Random.seed(). N)r gauss_next)selfxr4/usr/lib64/python3.6/random.py__init__Ws zRandom.__init__r/cs|dkrt|ttfrt|tr*|jdn|}|rBt|dd>nd}x"tt|D]}d||Ad@}qRW|t|N}|d krd n|}|dkrt|tttfrt|tr|j}|t |j 7}t j |d}t j|d |_d S) aInitialize 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-1riCBlr/bigNi) isinstanceZstrZbytesZdecodeZordZmaplenZ bytearrayZencode_sha512Zdigestint from_bytessuperrr1)r2aversionr3c __class__r4r5r`s    z Random.seedcs|jtj|jfS)z9Return internal state; can be passed to setstate() later.)VERSIONr@r$r1r2rDr4r5r$zRandom.getstatecs|d}|dkr*|\}}|_tj|nt|dkr|\}}|_ytdd|D}Wn(tk r|}z t|WYdd}~XnXtj|ntd||jfdS)z:Restore internal state from object returned by getstate().rr0r/css|]}|dVqdS)r/i Nlr4).0r3r4r4r5z sz"Random.setstate..Nz?state with version %s passed to Random.setstate() of version %s)r1r@r%tuple ValueError TypeErrorrF)r2staterBZ internalstaterrDr4r5r%s  zRandom.setstatecCs|jSN)r$rGr4r4r5 __getstate__zRandom.__getstate__cCs|j|dSrN)r%)r2rMr4r4r5 __setstate__rPzRandom.__setstate__cCs|jf|jfSrN)rEr$rGr4r4r5 __reduce__rPzRandom.__reduce__r7c Cs||}||krtd|dkr:|dkr2|j|Std||}||krRtd||}|dkrx|dkrx||j|S|dkrtd|||f||}||krtd|dkr||d|} n"|dkr||d|} ntd | dkrtd|||j| S) zChoose 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()Nrzempty range for randrange()z non-integer stop for randrange()r7z'empty range for randrange() (%d,%d, %d)z non-integer step for randrange()zzero step for randrange())rK _randbelow) r2ZstartZstopZstep_intZistartZistopZwidthZistepnr4r4r5rs4  zRandom.randrangecCs|j||dS)zJReturn random integer in range [a, b], including both end points. r7)rr2rAbr4r4r5rszRandom.randintc Cs|j}|j}|||ks$|||krN|j} || } x| |krH|| } q6W| S||krltd|||S|dkr|td||} || |} |} x| | kr|} qW|| ||S)zCReturn a random int in the range [0,n). Raises ValueError if n==0.zUnderlying random() generator does not supply enough bits to choose from a population range this large. To remove the range limitation, add a getrandbits() method.rzBoundary cannot be zero)rr&Z bit_length_warnrK) r2rUr>ZmaxsizetypeZMethodZ BuiltinMethodrr&krZremZlimitr4r4r5rSs&     zRandom._randbelowc Cs:y|jt|}Wntk r0tddYnX||S)z2Choose a random element from a non-empty sequence.z$Cannot choose from an empty sequenceN)rSr<rKZ IndexError)r2Zseqir4r4r5rs z Random.choicecCs|dkrR|j}xttdt|D]*}||d}||||||<||<q"WnLt}xFttdt|D]0}|||d}||||||<||<qjWdS)zShuffle 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. Nr7)rSZreversedranger<r>)r2r3r randbelowr\jrTr4r4r5rs   zRandom.shufflec Cs(t|trt|}t|ts$td|j}t|}d|koD|knsRtddg|}d}|dkr|dtt |dd7}||krt |}xt |D]0}|||} || ||<|||d || <qWnRt } | j } xDt |D]8}||} x| | kr ||} qW| | || ||<qW|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).rz,Sample larger than population or is negativeNiir)r0r7)r;_SetrJ _SequencerLrSr<rK_ceil_loglistr]ZsetZadd) r2 populationrZr^rUZresultZsetsizeZpoolr\r_ZselectedZ selected_addr4r4r5rs6       z Random.sample) cum_weightsrZcs|jdkrN|dkr>ttfddt|DSttj|n|dk r^tdttkrvtdt j dtdfddt|DS) zReturn 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. Ncsg|]}qSr4r4rIr\)rTrertotalr4r5 csz"Random.choices..z2Cannot specify both weights and cumulative weightsz3The number of weights does not match the populationr7cs$g|]}dqS)rr4rg)bisectrfhirerrhr4r5rilsr:) rr>r<r]rd _itertoolsZ accumulaterLrK_bisectrj)r2reZweightsrfrZr4)rTrjrfrkrerrhr5r'Ws  zRandom.choicescCs||||jS)zHGet a random number in the range [a, b) or [a, b] depending on rounding.rrVr4r4r5rsrHzRandom.uniformr-c Csx|j}y |dkrdn||||}Wntk r<|SX||kr`d|}d|}||}}|||||dS)zTriangular 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 Nr*r-)rZZeroDivisionError)r2ZlowZhighZmodeurCr4r4r5rys   zRandom.triangularcCsT|j}x@|}d|}t|d|}||d}|t| krPqW|||S)z\Normal distribution. mu is the mean, and sigma is the standard deviation. r-r*r,)r NV_MAGICCONSTrc)r2musigmaru1u2zZzzr4r4r5rs   zRandom.normalvariatecCst|j||S)zLog 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)r2rrrsr4r4r5rszRandom.lognormvariatecCstd|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. r-)rcr)r2Zlambdr4r4r5rszRandom.expovariatecCs|j}|dkrt|Sd|}|td||}xN|}tt|}|||}|} | d||ks~| d|t|kr6Pq6Wd|} | |d| |} |} | dkr|t| t} n|t| t} | S)aFCircular 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. gư>r*r-)rTWOPI_sqrt_cos_pirw_acos)r2rrZkapparZsr[rtrvZdruZqZfZu3Zthetar4r4r5rs&   $zRandom.vonmisesvariatecCs|dks|dkrtd|j}|dkrtd|d}|t}||}x|}d|ko`dknshqHd|}t|d||} |t| } |||} ||| | } | td| dks| t| krH| |SqHWn|dkr|} x| dkr|} qWt|  |Sx|} t|t}|| }|dkrD|d|} nt||| } |}|dkr||| |dkrPn|t| krPqW| |SdS) aZGamma distribution. Not the gamma function! Conditions on the parameters are alpha > 0 and beta > 0. The probability distribution function is: x ** (alpha - 1) * math.exp(-x / beta) pdf(x) = -------------------------------------- math.gamma(alpha) * beta ** alpha roz*gammavariate: alpha and beta must be > 0.0r-r+gHz>gP?r.N)rKrryLOG4rcrw SG_MAGICCONST_e)r2alphabetarZainvZbbbZcccrtruZvr3rvr[rprWZpr4r4r5rsJ          zRandom.gammavariatecCs`|j}|j}d|_|dkrT|t}tdtd|}t||}t|||_|||S)zGaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function. Not thread-safe without a lock around calls. Nr+r-g)rr1rxryrcrz_sin)r2rrrsrrvZx2piZg2radr4r4r5r ?s  z Random.gausscCs0|j|d}|dkrdS|||j|dSdS)zBeta distribution. Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1. r-rroN)r)r2rrZyr4r4r5r!ts zRandom.betavariatecCsd|j}d|d|S)z3Pareto distribution. alpha is the shape parameter.r-rn)r2rrpr4r4r5r"s zRandom.paretovariatecCs"d|j}|t| d|S)zfWeibull distribution. alpha is the scale parameter and beta is the shape parameter. r-)rrc)r2rrrpr4r4r5r#s zRandom.weibullvariaterN)Nr/rNrN)ror-N)$__name__ __module__ __qualname____doc__rFr6rr$r%rOrQrRr>rrBPFrY _MethodType_BuiltinMethodTyperSrrrr'rrrrrrrr r!r"r#Z __classcell__r4r4rDr5rGs8    ,  :  0H5 c@s8eZdZdZddZddZddZdd ZeZZ d S) r(zAlternate random number generator using sources provided by the operating system (such as /dev/urandom on Unix or CryptGenRandom on Windows). Not available on all systems (see os.urandom() for details). cCstjtddd?tS)z3Get the next random number in the range [0.0, 1.0).r8r9r0)r>r?_urandom RECIP_BPFrGr4r4r5rrHzSystemRandom.randomcCsP|dkrtd|t|kr$td|dd}tjt|d}||d|?S)z:getrandbits(k) -> x. Generates an int with k random bits.rz(number of bits must be greater than zeroz#number of bits should be an integerr8ir9)rKr>rLr?r)r2rZZnumbytesr3r4r4r5r&s  zSystemRandom.getrandbitscOsdS)z&sn     Y!