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Τ(Iv t d Z ddlmZ ddlmZmZm Z m Z m Z ddlmZmZmZmZ ddlmZmZmZ ddl m Z ddl m!Z"m#Z$ ddl%m&Z' dd l(m)Z*m+Z, dd l-m-Z. dd l Z/dd l0Z0 dd l1m2Z1 n# e3$ r dd l4m2Z1 Y nw xY wg d Z5d ed z ed z Z6 ed Z7d ed z Z8dZ9de9 z Z:dZ; G d de0j< Z< G d de< Z= e< Z>e>j? Z?e>j@ Z@e>jA ZAe>jB ZBe>jC ZCe>jD ZDe>jE ZEe>jF ZFe>jG ZGe>jH ZHe>jI ZIe>jJ ZJe>jK ZKe>jL ZLe>jM ZMe>jN ZNe>jO ZOe>jP ZPe>jQ ZQe>jR ZRe>jS ZSe>jT ZTe>jU ZUd ZVd!d ZW eXe/d r e/jY e>j? eZd k r eW d S d S )"a Random variable generators. bytes ----- uniform bytes (values between 0 and 255) 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)logexppieceil)sqrtacoscossin)taufloorisfinite)urandom)SetSequence)index) accumulaterepeat)bisectN)sha512)Random SystemRandom betavariatechoicechoices expovariate gammavariategauss getrandbitsgetstatelognormvariate normalvariate paretovariate randbytesrandintrandom randrangesampleseedsetstateshuffle triangularuniformvonmisesvariateweibullvariate g @ @ ? @5 c e Zd ZdZdZd&dZd' fd Z fdZ fdZd Z d Z d Z d Z d Z dez fdZe Zd ZdefdZd Zd Zd ZdddZd&ddddZd Zd(d Zd)d Zd)d Z d Z d Z d! Z d" Z d# Z!d$ Z"d% Z# xZ$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 > | | d| _ dS )zeInitialize an instance. Optional argument x controls seeding, as for Random.seed(). N)r* gauss_next)selfxs -/opt/alt/python311/lib64/python3.11/random.py__init__zRandom.__init__w s ! r7 c ^ |dk rt |t t f rt |t r| d n|}|rt |d dz nd}t t | D ] }d|z |z dz }|t | z }|dk rdn|}n|d k rt |t t t f rft |t r| }t |t | z }nKt |t d t t t t t f st d t! | d | _ d S ) a\ Initialize internal state from a seed. The only supported seed types are None, int, float, str, bytes, and bytearray. 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. r8 zlatin-1r iCB l r7 NzOThe only supported seed types are: None, int, float, str, bytes, and bytearray.) isinstancestrbytesdecodeordmaplen bytearrayencodeint from_bytes_sha512digesttypefloat TypeErrorsuperr* r< )r= aversionr> c __class__s r? r* z Random.seed sx $ a<<Jq3, 7 7<'1!U';';B###A"#*AaD QAa[[ = = kQ&*<< QKA2gg1AA \\jS%,C D D\!S!! HHJJq71::#4#4#6#6 677AAAT CUI NOO F E F F F Q rA c ^ | j t | j fS )z9Return internal state; can be passed to setstate() later.)VERSIONrV r! r< )r= rZ s r? r! zRandom.getstate s$ |UWW - - / / @@rA c |d }|dk r.|\ }}| _ t | dS |dk rc|\ }}| _ t d |D }n# t $ r }t |d}~ww xY wt | dS t d|d| j )z:Restore internal state from object returned by getstate().r r: r7 c 3 K | ] }|d z V dS )l N ).0r> s r? <genexpr>z"Random.setstate.<locals>.<genexpr> s& %K%Ka7m%K%K%K%K%K%KrA Nzstate with version z( passed to Random.setstate() of version )r< rV r+ tuple ValueErrorrU r\ )r= staterX internalstater rZ s r? r+ zRandom.setstate s ( a<<6; 3G]DO GG ] + + + + + \\6; 3G]DO ' %%K%K]%K%K%K K K ' ' ' Q& ' GG ] + + + + + * %ggt|| 5 6 6 6s A* * B4A<<Bc * | S N)r! r= s r? __getstate__zRandom.__getstate__ s }} rA c 0 | | d S rg )r+ )r= rd s r? __setstate__zRandom.__setstate__ s e rA c : | j d| fS )Nr_ )rZ r! rh s r? __reduce__zRandom.__reduce__ s ~r4==??22rA c | j D ]>}d|j v r dS d|j v r| j | _ dS d|j v r| j | _ dS ?dS )a Control how subclasses generate random integers. The algorithm a subclass can use depends on the random() and/or getrandbits() implementation available to it and determines whether it can generate random integers from arbitrarily large ranges. _randbelowr r' N)__mro____dict___randbelow_with_getrandbitsro _randbelow_without_getrandbits)clskwargsrY s r? __init_subclass__zRandom.__init_subclass__ st Aqz)) **!$!@1:%%!$!C & rA c | j }| } || }||k r || }||k |S )z;Return a random int in the range [0,n). Defined for n > 0.)r bit_length)r= nr krs r? rr z"Random._randbelow_with_getrandbits sL & LLNN KNN1ff AA 1ffrA r8 c | j }||k r)t d t | |z S ||z }||z |z } | }||k r | }||k t ||z |z S )zReturn a random int in the range [0,n). Defined for n > 0. The implementation does not use getrandbits, but only random. 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.)r' _warn_floor)r= ry maxsizer' remlimitr{ s r? rs z%Random._randbelow_without_getrandbits s << N O O O &&((Q,'' 'k3 ') FHH5jjA 5jja'k""Q&&rA c Z | |dz |d S )Generate n random bytes. little)r to_bytesr= ry s r? r% zRandom.randbytes s* A&&//8<<<rA c r t | }n`# t $ rS t | }||k r%t dt d t d t dt d Y nw xY w|B|t urt d |dk r| | S t d t | }n`# t $ rS t | }||k r%t dt d t d t dt d Y nw xY w||z } t | }n`# t $ rS t | }||k r%t dt d t d t dt d Y nw xY w|d k r3|dk r|| | z S t d |||fz |dk r ||z d z |z }n!|dk r ||z d z |z }nt d |dk rt d ||| | z z S )zChoose a random item from range(stop) or range(start, stop[, step]). Roughly equivalent to ``choice(range(start, stop, step))`` but supports arbitrarily large ranges and is optimized for common cases. z.randrange() will raise TypeError in the futurer7 z!non-integer arg 1 for randrange()zwnon-integer arguments to randrange() have been deprecated since Python 3.10 and will be removed in a subsequent versionNz Missing a non-None stop argumentr zempty range for randrange()z non-integer stop for randrange()z non-integer step for randrange()r8 z(empty range for randrange() (%d, %d, %d)zzero step for randrange())_indexrU rO r} DeprecationWarningrc _ONEro ) r= startstopstepistartistopwidthistepry s r? r( zRandom.randrange s )E]]FF ) ) )ZZFF(!- - - !DEEE %a ) ) ) ) ) ) < 4 BCCCzzv... :;; ; )4LLEE ) ) )IIE}}F(!- - - !CDDD %a ) ) ) ) ) ) )4LLEE ) ) )IIE}}F(!- - - !CDDD %a ) ) ) ) ) ) A::qyy 6 666 G6SXZ_J` `aa a 199 "u,AA QYY "u,AA 899 9 66 :;; ; 2 2222s6 AA/.A/7C AD$#D$-D= =AFFc 4 | ||dz S )zJReturn random integer in range [a, b], including both end points. r8 )r( r= rW bs r? r& zRandom.randintf s ~~a1%%%rA c t | st d || t | S )z2Choose a random element from a non-empty sequence.z$Cannot choose from an empty sequence)rL IndexErrorro )r= seqs r? r z Random.choiceo s? 3xx E CDD D4??3s88,,--rA c | j }t t dt | D ]'} ||dz }|| || c||< ||< (dS )z)Shuffle list x in place, and return None.r8 N)ro reversedrangerL )r= r> randbelowijs r? r, zRandom.shufflex sl O %3q66**++ $ $A !a% A1qtJAaD!A$$ $ $rA )countsc t t st d t }|t t | t |k rt d }t |t st d |dk rt d | t | | }t fd|D S | j }d|cxk r|k sn t d dg|z }d } |d k r&| d t t |d z d z z } || k rLt } t | D ],} ||| z } | | || < | || z dz | | < -n[t } | j }t | D ]6} || } | | v r || } | | v || | || < 7|S )af Chooses k unique random elements from a population sequence. Returns a new list containing elements from the population while leaving the original population unchanged. The resulting list is in selection order so that all sub-slices will also be valid random samples. This allows raffle winners (the sample) to be partitioned into grand prize and second place winners (the subslices). Members of the population need not be hashable or unique. If the population contains repeats, then each occurrence is a possible selection in the sample. Repeated elements can be specified one at a time or with the optional counts parameter. For example: sample(['red', 'blue'], counts=[4, 2], k=5) is equivalent to: sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5) To choose a sample from a range of integers, use range() for the population argument. This is especially fast and space efficient for sampling from a large population: sample(range(10000000), 60) zAPopulation must be a sequence. For dicts or sets, use sorted(d).Nz2The number of counts does not match the populationzCounts must be integersr z)Total of counts must be greater than zero)rz c 4 g | ]} | S r_ r_ )r` sr cum_counts populations r? <listcomp>z!Random.sample.<locals>.<listcomp> s* JJJ!Jvvj! 4 45JJJrA z,Sample larger than population or is negative r1 r: r8 )rF _SequencerU rL list _accumulaterc poprO r) r _bisectro _ceil_logsetadd)r= r rz r ry total selectionsr resultsetsizepoolr r selected selected_addr r s ` @@r? r) z Random.sample sL j *i00 A @ A A A OO k& 1 122J:!## !UVVV NN$$E eS)) ; 9:::zz !LMMM U5\\Q77J FJJJJJJzJJJ JO A{{{{{{{{ KLL L! q55 qE$q1ua.. 1 11 1G << ##D1XX * * Ia!e$$ Gq q1uqy/Q * uuH#<L1XX * * IaLL8mm! ! A 8mm Q &qMq rA ) cum_weightsrz c | j t |+t dz fdt d| D S t t | nJ# t $ r, t |t s |}t d| dw xY w|t d t k rt d d dz dk rt d t st d t d z fd t d| D S ) 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. N c H g | ] } z S r_ r_ )r` r r ry r r' s r? r z"Random.choices.<locals>.<listcomp> s2 RRRA 55A #6#67RRRrA z4The number of choices must be a keyword argument: k=z2Cannot specify both weights and cumulative weightsz3The number of weights does not match the populationrD z*Total of weights must be greater than zeroz Total of weights must be finiter8 c N g | ]!} z d "S )r r_ )r` r r r hir r' r s r? r z"Random.choices.<locals>.<listcomp> sI + + + 66+vvxx%/?BGGH + + +rA ) r' rL r~ _repeatr r rU rF rO rc _isfiniter ) r= r weightsr rz r r r ry r' r s ` ` @@@@@@r? r zRandom.choices s OO SRRRRRRRqAQAQRRRR ";w#7#7 8 8 !'3// MMM PQQ Q { q RSS SB#% C<< IJJ J @ >?? ? U+ + + + + + + + + q))+ + + +s A, ,6B"c < |||z | z z S )zHGet a random number in the range [a, b) or [a, b] depending on rounding.r' r s r? r. zRandom.uniform s AET[[]]***rA r r4 c | } |dn ||z ||z z }n# t $ r |cY S w xY w||k rd|z }d|z }||}}|||z t ||z z z S )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 N ?r4 )r' ZeroDivisionError_sqrt)r= lowhighmodeurY s r? r- zRandom.triangular s KKMM |$*)DAA JJJ q55aAaA cCdSjE!a%LL000s & 55c | j } | }d | z }t |dz z |z }||z dz }|t | k rnE|||z z S )z\Normal distribution. mu is the mean, and sigma is the standard deviation. Tr4 r r3 )r' NV_MAGICCONSTr )r= musigmar' u1u2zzzs r? r# zRandom.normalvariate ss Bvvxx B c*R/AQBd2hhY AI~ rA c | j }| j }d| _ |e | t z }t dt d | z z }t | |z }t | |z | _ |||z z S )zGaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function. Not thread-safe without a lock around calls. Ng r4 )r' r< TWOPIr r _cos_sin)r= r r r' r x2pig2rads r? r z Random.gauss5 s 6 O 9688e#D$cFFHHn!5!5566ET U"A "4jj5 0DOAI~ rA c H t | || 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# )r= r r s r? r" zRandom.lognormvariate[ s" D&&r511222rA c R t d| z |z 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. r4 )r r' )r= lambds r? r zRandom.expovariatee s' S4;;==()))E11rA c | j }|dk rt | z S d|z }|t d||z z z } | }t t |z }|||z z } | } | d||z z k s| d|z t | z k rnZd|z } | |z d| |z z z } | } | dk r|t | z t z } n|t | z t z } | 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. gư>r r4 )r' r r r _pir _acos)r= r kappar' r r{ r r dr qfu3thetas r? r/ zRandom.vonmisesvariatev s D==6688# # %K cAEk"" " BS2XAQU ABC!a%K 2#'T!WW)<#<#< !G UsQU{ # VXX 88%((]e+EE%((]e+E rA c |dk s|dk rt d | j }|dk rt d|z dz }|t z }||z } | }d|cxk rdk sn d | z }t |d|z z |z } |t | z } ||z |z } ||| z z | z } | t z d| z z dk s| t | k r| |z S |dk r t d | z |z S | } t |z t z }|| z }|dk r |d|z z } nt ||z |z } | }|dk r|| |dz z k rnn|t | k rnz| |z S ) 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 r z*gammavariate: alpha and beta must be > 0.0r4 r2 TgHz>gP?r5 )rc r' r LOG4r r SG_MAGICCONST_e)r= alphabetar' ainvbbbcccr r vr> r r{ r r ps r? r zRandom.gammavariate s C<<43;; IJJ J 3;; us*++D$,C$,C $VXXb,,,,9,,,, 6688^sRx ))D0DGGOGbL#'MA%}$sQw.#55d1gg t8O $ c\\vvxx (((4/ / FHH%Z2%E88cEk*AA q1uo...AVXXs77Q53; /// 0488^^ t8OrA c n | |d }|r ||| |d z z S dS )zBeta distribution. Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1. r4 r )r )r= r r ys r? r zRandom.betavariate sF , eS ) ) :D - -dC 8 889 9srA c @ d| z }|d|z z S )z3Pareto distribution. alpha is the shape parameter.r4 g r )r= r r s r? r$ zRandom.paretovariate s% $++-- TE\""rA c b d| z }|t | d|z z z S )zfWeibull distribution. alpha is the scale parameter and beta is the shape parameter. r4 )r' r )r= r r r s r? r0 zRandom.weibullvariate s2 $++-- acDj111rA rg )Nr7 )r r4 Nr r4 )%__name__ __module__ __qualname____doc__r\ r@ r* r! r+ ri rk rm rv rr BPFrs ro r% r r( r& r r, r) r r. r- r# r r" r r/ r r r$ r0 __classcell__)rZ s @r? r r g sd G $ $ $ $ $ $ LA A A A A6 6 6 6 6B 3 3 3 ( 9:3 ' ' ' '& -J= = = %)t H3 H3 H3 H3T& & &. . .$ $ $ /3 ] ] ] ] ]~#+tq #+ #+ #+ #+ #+P+ + +1 1 1 1( *$ $ $ $ L3 3 32 2 2"( ( (T? ? ? B 6# # # 2 2 2 2 2 2 2rA r c 8 e Zd ZdZd Zd Zd Zd Zd ZexZ Z dS )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). c f t t d dz t z S )z7Get the next random number in the range 0.0 <= X < 1.0.rC r: )rO rP _urandom RECIP_BPFrh s r? r' zSystemRandom.random s$ x{{++q0I==rA c |dk rt d |dz dz }t t | }||dz |z z S )z:getrandbits(k) -> x. Generates an int with k random bits.r z#number of bits must be non-negativerC r )rc rO rP r )r= rz numbytesr> s r? r zSystemRandom.getrandbits sT q55 BCC CEa< NN8H-- . .X\A%&&rA c t | S )r )r r s r? r% zSystemRandom.randbytes( s {{rA c dS )z<Stub method. Not used for a system random number generator.Nr_ r= argskwdss r? r* zSystemRandom.seed. s trA c t d )zAMethod should not be called for a system random number generator.z*System entropy source does not have state.)NotImplementedErrorr s r? _notimplementedz SystemRandom._notimplemented2 s !"NOOOrA N) r r r r r' r r% r* r r! r+ r_ rA r? r r sr > > >' ' ' P P P *)HxxxrA r c ^ ddl m}m} ddlm} | }fdt d | D } | } || } ||| } t | } t | } t ||z dd| dj t d| | | | fz d S ) Nr )stdevfmean) perf_counterc g | ]} S r_ r_ )r` r r funcs r? r z#_test_generator.<locals>.<listcomp>a s 2 2 2ADD$K 2 2 2rA z.3fz sec, z times z"avg %g, stddev %g, min %g, max %g ) statisticsr r timer r minmaxprintr ) ry r r r meanr t0datat1xbarr r r s `` r? _test_generatorr \ s ////////!!!!!! B 2 2 2 2 2q!1!1 2 2 2D B 4::D E$ E d))C t99D R"W 9 9 9 9 9$- 9 9::: /4T2J JKKKKKrA c t | t d t | t d t | t d t | t d t | t d t | t d t | t d t | t d t | t d t | t d t | t d t | t d t | t d t | t d t | t d t | t d d S )Nr_ r )g{Gz?r4 )皙?r4 )r r2 )r r4 )g?r4 )r4 r4 )r2 r4 )g 4@r4 )g i@r4 ) @r )r r4 gUUUUUU?) r r' r# r" r/ r r r r- )Ns r? _testr m s) Avr"""A}j111A~z222A 333A|[111A|Z000A|Z000A|Z000A|Z000A|Z000A|Z000A|[111A|\222Auj)))A{J///Az#899999rA fork)after_in_child__main__)r )[r warningsr r} mathr r r r r r r r r r r r r r r r r r r r r r~ r r osr r _collections_abcr _Setr r operatorr r itertoolsr r r r r r _os_randomrQ r ImportErrorhashlib__all__r r r r r r r r _instr* r' r. r- r& r r( r) r, r r# r" r r/ r r r r$ r0 r! r+ r r% r r hasattrregister_at_forkr r_ rA r? <module>r3 sL ) )^ # " " " " " L L L L L L L L L L L L L L G G G G G G G G G G G G E E E E E E E E E E " " " " " " ? ? ? ? ? ? ? ? $ $ $ $ $ $ B B B B B B B B $ $ $ $ $ $ *))))))) * * *))))))))* 8 DDJJs+ tCyydd3ii #I e 2 e 2 e 2 e 2 e 2W^ e 2 e 2 e 2X"* "* "* "* "*6 "* "* "*X z - - O - -# % '! # % > > O L L L": : : :, 73 4C 3333 z EGGGGG s A A-,A-