ó ÄAic @ s£ d Z d d l m Z d d l m Z d d l m Z m Z d d l m Z m Z m Z m Z m Z d d l m Z m Z m Z m Z d d l m Z d d l! m" Z# d d l$ Z% d d d d d d d d d d d d d d d d d d d d d d d d! d" g Z& d# e d$ ƒ e d% ƒ Z' d% e Z( e d& ƒ Z) d' e d( ƒ Z* d) Z+ d* e+ Z, d d l- Z- d e- j. f d+ „ ƒ YZ. d e. f d, „ ƒ YZ/ d" e. f d- „ ƒ YZ0 d. „ Z1 d/ d0 „ Z2 e. ƒ 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 e3 jI ZI eJ d1 k rŸe2 ƒ n d S(2 sP 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. * Without a direct way to compute N steps forward, the semantics of jumpahead(n) are weakened to simply jump to another distant state and rely on the large period to avoid overlapping sequences. * The random() method is implemented in C, executes in a single Python step, and is, therefore, threadsafe. iÿÿÿÿ( t division( t warn( t MethodTypet BuiltinMethodType( t logt expt pit et ceil( t sqrtt acost cost sin( t urandom( t hexlifyNt Randomt seedt randomt uniformt randintt choicet samplet randranget shufflet normalvariatet lognormvariatet expovariatet vonmisesvariatet gammavariatet triangulart gausst betavariatet paretovariatet weibullvariatet getstatet setstatet jumpaheadt WichmannHillt getrandbitst SystemRandomi g à¿g @g @g ð?g @i5 i c B s0 e Z d Z d Z d d „ Z d d „ Z d „ Z d „ Z d „ Z d „ Z d „ Z d „ Z d d e d d e >d „ Z d „ Z e e d e >e e d „ Z d „ Z d e d „ Z d „ Z d „ Z d d d d „ Z d „ Z d „ Z d „ Z d „ Z d „ Z d „ Z d „ Z d „ Z! d „ Z" RS( sÎ Random number generator base class used by bound module functions. Used to instantiate instances of Random to get generators that don't share state. Especially useful for multi-threaded programs, creating a different instance of Random for each thread, and using the jumpahead() method to ensure that the generated sequences seen by each thread don't overlap. 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(), setstate() and jumpahead(). Optionally, implement a getrandbits() method so that randrange() can cover arbitrarily large ranges. i c C s | j | ƒ d | _ d S( se Initialize an instance. Optional argument x controls seeding, as for Random.seed(). N( R t Nonet gauss_next( t selft x( ( s /usr/lib64/python2.7/random.pyt __init__[ s c C s‡ | d k rd y t t t d ƒ ƒ d ƒ } Wqd t k r` d d l } t | j ƒ d ƒ } qd Xn t t | ƒ j | ƒ d | _ d S( s 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 not None or an int or long, hash(a) is used instead. i iÿÿÿÿNi ( R( t longt _hexlifyt _urandomt NotImplementedErrort timet superR R R) ( R* t aR1 ( ( s /usr/lib64/python2.7/random.pyR d s c C s" | j t t | ƒ j ƒ | j f S( s9 Return internal state; can be passed to setstate() later.( t VERSIONR2 R R" R) ( R* ( ( s /usr/lib64/python2.7/random.pyR" w s c C sÎ | d } | d k rA | \ } } | _ t t | ƒ j | ƒ n‰ | d k r± | \ } } | _ y t d „ | Dƒ ƒ } Wn t k r— } t | ‚ n Xt t | ƒ j | ƒ n t d | | j f ƒ ‚ d S( s: Restore internal state from object returned by getstate().i i i c s s | ] } t | ƒ d Vq d S( i i NI ( R- ( t .0R+ ( ( s /usr/lib64/python2.7/random.pys <genexpr>ˆ s s? state with version %s passed to Random.setstate() of version %sN( R) R2 R R# t tuplet ValueErrort TypeErrorR4 ( R* t statet versiont internalstateR ( ( s /usr/lib64/python2.7/random.pyR# { s c C sW t | ƒ t | j ƒ ƒ } t t j d | ƒ j ƒ d ƒ } t t | ƒ j | ƒ d S( s® Change the internal state to one that is likely far away from the current state. This method will not be in Py3.x, so it is better to simply reseed. t sha512i N( t reprR" t intt _hashlibt newt hexdigestR2 R R$ ( R* t nt s( ( s /usr/lib64/python2.7/random.pyR$ ‘ s !c C s | j ƒ S( N( R" ( R* ( ( s /usr/lib64/python2.7/random.pyt __getstate__¢ s c C s | j | ƒ d S( N( R# ( R* R9 ( ( s /usr/lib64/python2.7/random.pyt __setstate__¥ s c C s | j d | j ƒ f S( N( ( t __class__R" ( R* ( ( s /usr/lib64/python2.7/random.pyt __reduce__¨ s i l c C så | | ƒ } | | k r$ t d ‚ n | | k ru | d k ri | | k rU | j | ƒ S| | j ƒ | ƒ St d ‚ n | | ƒ } | | k r™ t d ‚ n | | } | d k rü | d k rü | | k rÞ | | | j | ƒ ƒ S| | | | j ƒ | ƒ ƒ S| d k r!t d | | | f ‚ n | | ƒ } | | k rEt d ‚ n | d k rf| | d | } n* | d k r‡| | d | } n t d ‚ | d k r¨t d ‚ n | | k rÉ| | | j | ƒ S| | | | j ƒ | ƒ S( s 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. Do not supply the 'int', 'default', and 'maxwidth' arguments. s! non-integer arg 1 for randrange()i s empty range for randrange()s non-integer stop for randrange()i s' empty range for randrange() (%d,%d, %d)s non-integer step for randrange()s zero step for randrange()( R7 t _randbelowR ( R* t startt stopt stepR> t defaultt maxwidtht istartt istopt widtht istepRB ( ( s /usr/lib64/python2.7/random.pyR s@ c C s | j | | d ƒ S( sJ Return random integer in range [a, b], including both end points. i ( R ( R* R3 t b( ( s /usr/lib64/python2.7/random.pyR í s c C sÁ y | j } Wn t k r nt Xt | j ƒ | k sH t | ƒ | k r” | d | | d d ƒ ƒ } | | ƒ } x | | k r | | ƒ } qt W| S| | k r t d ƒ n | | j ƒ | ƒ S( s£ Return a random int in the range [0,n) Handles the case where n has more bits than returned by a single call to the underlying generator. grÄZ| ð?i g @sg Underlying random() generator does not supply enough bits to choose from a population range this large( R& t AttributeErrort typeR t _warn( R* RB t _logR> t _maxwidtht _Methodt _BuiltinMethodR& t kt r( ( s /usr/lib64/python2.7/random.pyRH ó s ' c C s | t | j ƒ t | ƒ ƒ S( s2 Choose a random element from a non-empty sequence.( R> R t len( R* t seq( ( s /usr/lib64/python2.7/random.pyR s c C sv | d k r | j } n xW t t d t | ƒ ƒ ƒ D]: } | | ƒ | d ƒ } | | | | | | <| | <q4 Wd S( s× x, random=random.random -> shuffle list x in place; return None. Optional arg random is a 0-argument function returning a random float in [0.0, 1.0); by default, the standard random.random. i N( R( R t reversedt xrangeR\ ( R* R+ R R> t it j( ( s /usr/lib64/python2.7/random.pyR s "c C sÉ t | ƒ } d | k o# | k n s7 t d ƒ ‚ n | j } t } d g | } d } | d k r‰ | d t t | d d ƒ ƒ 7} n | | k s¤ t | d ƒ rt | ƒ } xt | ƒ D]A } | | ƒ | | ƒ } | | | | <| | | d | | <q½ WnÀ y~ t ƒ } | j } xe t | ƒ D]W } | | ƒ | ƒ } x# | | k re| | ƒ | ƒ } qCW| | ƒ | | | | <q'WWn? t t f k rÄt | t ƒ r®‚ n | j t | ƒ | ƒ SX| S( s8 Chooses k unique random elements from a population sequence. 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 xrange as an argument. This is especially fast and space efficient for sampling from a large population: sample(xrange(10000000), 60) i s sample larger than populationi i i i t keysi N( R\ R7 R R> R( t _ceilRV t hasattrt listR_ t sett addR8 t KeyErrort isinstanceR R6 ( R* t populationRZ RB R t _intt resultt setsizet poolR` Ra t selectedt selected_add( ( s /usr/lib64/python2.7/random.pyR " s: $ c C s | | | | j ƒ S( sH Get a random number in the range [a, b) or [a, b] depending on rounding.( R ( R* R3 RR ( ( s /usr/lib64/python2.7/random.pyR c s g g ð?c C sx | j ƒ } | d k r d n | | | | } | | k r` d | } d | } | | } } n | | | | | d S( sÜ 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 g à?g ð?N( R R( ( R* t lowt hight modet ut c( ( s /usr/lib64/python2.7/random.pyR i s $ c C sh | j } xP | ƒ } d | ƒ } t | d | } | | d } | t | ƒ k r Pq q | | | S( s\ Normal distribution. mu is the mean, and sigma is the standard deviation. g ð?g à?g @( R t NV_MAGICCONSTRV ( R* t mut sigmaR t u1t u2t zt zz( ( s /usr/lib64/python2.7/random.pyR | s c C s t | j | | ƒ ƒ S( sû 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. ( t _expR ( R* Rw Rx ( ( s /usr/lib64/python2.7/random.pyR • s c C s t d | j ƒ ƒ | S( s^ 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 ð?( RV R ( R* t lambd( ( s /usr/lib64/python2.7/random.pyR ¡ s c C s | j } | d k r t | ƒ Sd | } | t d | | ƒ } xe | ƒ } t t | ƒ } | | | } | ƒ } | d | | k s£ | d | t | ƒ k rE PqE qE d | } | | d | | } | ƒ } | d k rö | t | ƒ t } n | t | ƒ t } | S( sF 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. gíµ ÷Æ°>g à?g ð?( R t TWOPIt _sqrtt _cost _piR} t _acos( R* Rw t kappaR RC R[ Ry R{ t dRz t qt ft u3t theta( ( s /usr/lib64/python2.7/random.pyR ´ s& . c C s | d k s | d k r$ t d ‚ n | j } | d k r t d | d ƒ } | t } | | } x | ƒ } d | k o„ d k n s qd n d | ƒ } t | d | ƒ | } | t | ƒ } | | | } | | | | } | t d | d k s| t | ƒ k rd | | Sqd nè | d k r\| ƒ } x | d k rL| ƒ } q4Wt | ƒ | Sx | ƒ } t | t } | | } | d k r| d | } n t | | | ƒ } | ƒ } | d k râ| | | d k rùPqùq_| t | ƒ k r_Pq_q_| | Sd S( sZ 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 s* gammavariate: alpha and beta must be > 0.0g ð?g @gH¯¼šò×z>gËPÊÿÿï?g @N( R7 R R€ t LOG4RV R} t SG_MAGICCONSTt _e( R* t alphat betaR t ainvt bbbt cccRy Rz t vR+ R{ R[ Rt RR t p( ( s /usr/lib64/python2.7/random.pyR ä sJ * c C sƒ | j } | j } d | _ | d k rw | ƒ t } t d t d | ƒ ƒ ƒ } t | ƒ | } t | ƒ | | _ n | | | S( sØ 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. g Àg ð?N( R R) R( R R€ RV R t _sin( R* Rw Rx R R{ t x2pit g2rad( ( s /usr/lib64/python2.7/random.pyR , s c C s> | j | d ƒ } | d k r" d S| | | j | d ƒ Sd S( s Beta distribution. Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1. g ð?i g N( R ( R* R RŽ t y( ( s /usr/lib64/python2.7/random.pyR a s c C s% d | j ƒ } d t | d | ƒ S( s3 Pareto distribution. alpha is the shape parameter.g ð?( R t pow( R* R Rt ( ( s /usr/lib64/python2.7/random.pyR s s c C s, d | j ƒ } | t t | ƒ d | ƒ S( sf Weibull distribution. alpha is the scale parameter and beta is the shape parameter. g ð?( R R˜ RV ( R* R RŽ Rt ( ( s /usr/lib64/python2.7/random.pyR! | s N(# t __name__t __module__t __doc__R4 R( R, R R" R# R$ RD RE RG R> t BPFR R RV t _MethodTypet _BuiltinMethodTypeRH R R R R R R R R R R R R R R! ( ( ( s /usr/lib64/python2.7/random.pyR H s: ? A 0 H 5 c B s\ e Z d Z d d „ Z d „ Z d „ Z d „ Z d „ Z d d d d „ Z d d „ Z RS( i c C s | d k rd y t t t d ƒ ƒ d ƒ } Wqd t k r` d d l } t | j ƒ d ƒ } qd Xn t | t t f ƒ sˆ t | ƒ } n t | d ƒ \ } } t | d ƒ \ } } t | d ƒ \ } } t | ƒ d t | ƒ d t | ƒ d f | _ d | _ d S( sü 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 not None or an int or long, hash(a) is used instead. If a is an int or long, a is used directly. Distinct values between 0 and 27814431486575L inclusive are guaranteed to yield distinct internal states (this guarantee is specific to the default Wichmann-Hill generator). i iÿÿÿÿNi i<v ibv irv i ( R( R- R. R/ R0 R1 Ri R> t hasht divmodt _seedR) ( R* R3 R1 R+ R— R{ ( ( s /usr/lib64/python2.7/random.pyR s 0c C sj | j \ } } } d | d } d | d } d | d } | | | f | _ | d | d | d d S( s3 Get the next random number in the range [0.0, 1.0).i« i=v i¬ icv iª isv g @Ý@g À˜Ý@g ÀœÝ@g ð?( R¡ ( R* R+ R— R{ ( ( s /usr/lib64/python2.7/random.pyR ¬ s c C s | j | j | j f S( s9 Return internal state; can be passed to setstate() later.( R4 R¡ R) ( R* ( ( s /usr/lib64/python2.7/random.pyR" Ë s c C sK | d } | d k r. | \ } | _ | _ n t d | | j f ƒ ‚ d S( s: Restore internal state from object returned by getstate().i i s? state with version %s passed to Random.setstate() of version %sN( R¡ R) R7 R4 ( R* R9 R: ( ( s /usr/lib64/python2.7/random.pyR# Ï s c C s£ | d k s t d ƒ ‚ n | j \ } } } t | t d | d ƒ ƒ d } t | t d | d ƒ ƒ d } t | t d | d ƒ ƒ d } | | | f | _ d S( sà Act as if n calls to random() were made, but quickly. n is an int, greater than or equal to 0. Example use: If you have 2 threads and know that each will consume no more than a million random numbers, create two Random objects r1 and r2, then do r2.setstate(r1.getstate()) r2.jumpahead(1000000) Then r1 and r2 will use guaranteed-disjoint segments of the full period. i s n must be >= 0i« i=v i¬ icv iª isv N( R7 R¡ R> R˜ ( R* RB R+ R— R{ ( ( s /usr/lib64/python2.7/random.pyR$ Ù s i c C s t | ƒ t | ƒ k o4 t | ƒ k o4 t k n sH t d ƒ ‚ n d | k o_ d k n o™ d | k o{ d k n o™ d | k o— d k n s« t d ƒ ‚ n d | k oÍ | k oÍ | k n rNd d l } t | j ƒ d ƒ } t | d @| d ?Aƒ } t | d ƒ \ } } t | d ƒ \ } } t | d ƒ \ } } n | pWd | p`d | pid f | _ d | _ d S( sj Set the Wichmann-Hill seed from (x, y, z). These must be integers in the range [0, 256). s seeds must be integersi i s seeds must be in range(0, 256)iÿÿÿÿNiÿÿÿ i i ( RT R> R8 R7 R1 R- R R¡ R( R) ( R* R+ R— R{ R1 t t( ( s /usr/lib64/python2.7/random.pyt __whseedï s 9T' $c C s¸ | d k r | j ƒ d St | ƒ } t | d ƒ \ } } t | d ƒ \ } } t | d ƒ \ } } | | d pv d } | | d pŠ d } | | d pž d } | j | | | ƒ d S( sb Seed from hashable object's hash code. None or no argument seeds from current time. It is not guaranteed that objects with distinct hash codes lead to distinct internal states. This is obsolete, provided for compatibility with the seed routine used prior to Python 2.1. Use the .seed() method instead. Ni i ( R( t _WichmannHill__whseedRŸ R ( R* R3 R+ R— R{ ( ( s /usr/lib64/python2.7/random.pyt whseed s N( R™ Rš R4 R( R R R" R# R$ R¤ R¥ ( ( ( s /usr/lib64/python2.7/random.pyR% ‰ s c B sF e Z d Z d „ Z d „ Z d „ Z e Z Z d „ Z e Z Z RS( sÝ 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 t t d ƒ ƒ d ƒ d ?t S( s3 Get the next random number in the range [0.0, 1.0).i i i ( R- R. R/ t RECIP_BPF( R* ( ( s /usr/lib64/python2.7/random.pyR ' s c C su | d k r t d ƒ ‚ n | t | ƒ k r< t d ƒ ‚ n | d d } t t t | ƒ ƒ d ƒ } | | d | ?S( s> getrandbits(k) -> x. Generates a long int with k random bits.i s( number of bits must be greater than zeros# number of bits should be an integeri i i ( R7 R> R8 R- R. R/ ( R* RZ t bytesR+ ( ( s /usr/lib64/python2.7/random.pyR& + s c O s d S( s< Stub method. Not used for a system random number generator.N( R( ( R* t argst kwds( ( s /usr/lib64/python2.7/random.pyt _stub5 s c O s t d ƒ ‚ d S( sA Method should not be called for a system random number generator.s* System entropy source does not have state.N( R0 ( R* R¨ R© ( ( s /usr/lib64/python2.7/random.pyt _notimplemented: s ( R™ Rš R› R R& Rª R R$ R« R" R# ( ( ( s /usr/lib64/python2.7/random.pyR' s c C sõ d d l } | Gd G| j GHd } d } d } d } | j ƒ } xV t | ƒ D]H } | | Œ } | | 7} | | | } t | | ƒ } t | | ƒ } qM W| j ƒ } t | | d ƒ Gd G| | } t | | | | ƒ } d | | | | f GHd S( Niÿÿÿÿt timesg g _ Bg _ Âi s sec,s! avg %g, stddev %g, min %g, max %g( R1 R™ t ranget mint maxt roundR€ ( RB t funcR¨ R1 t totalt sqsumt smallestt largestt t0R` R+ t t1t avgt stddev( ( s /usr/lib64/python2.7/random.pyt _test_generatorA s& iÐ c C s t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d ƒ t | t d d d f ƒ d S( Ng g ð?g{®Gáz„?gš™™™™™¹?g @g à?gÍÌÌÌÌÌì?g 4@g i@g @( ( g g ð?( g g ð?( g g ð?( g{®Gáz„?g ð?( gš™™™™™¹?g ð?( gš™™™™™¹?g @( g à?g ð?( gÍÌÌÌÌÌì?g ð?( g ð?g ð?( g @g ð?( g 4@g ð?( g i@g ð?( g g ð?( g @g @gUUUUUUÕ?( Rº R R R R R R R R ( t N( ( s /usr/lib64/python2.7/random.pyt _testW s t __main__(K R› t __future__R t warningsR RU t typesR R R Rž t mathR RV R R} R R‚ R RŒ R Rc R R€ R Rƒ R R R R” t osR R/ t binasciiR R. t hashlibR? t __all__Rv R RŠ R‹ Rœ R¦ t _randomR R% R' Rº R¼ t _instR R R R R R R R R R R R R R R R R R! R" R# R$ R& R™ ( ( ( s /usr/lib64/python2.7/random.pyt <module>( sj (" ÿ ÿ C–"