grthtrhthjhtyjytjytkergtrhtrjytjerhrfh4:24 29/09/2026+ VNRt^RIHtHtHtHt H t ^RIH t HtHtHt^RIHtHtHt^RIHtHtHt^RI H!t"^RI#H$t%^RI&H't(^RI)H*t+H,t-^R I.H.t/^R I t0^R I1t1.ROt2^]!R4,] !R 4, t3]!R4t4R]!R4,t5^5t6^]6),t7^t8R s9!RR ]1Pt4t:!RR ]:4t;]:!4t<]]getstater )r!rBs&r#rFRandom.getstates ||UW-/@@r&c f<V^,pV^8XdVwr#Vn\SV` V4R#V^8XdIVwr#Vn\;QJd.RV4FNK 5M !RV44p\ST` T4R#\ RV: RVP : 24h \d p\ ThRp?ii;i)z:Restore internal state from object returned by getstate().c32"TF qR,xK R#5i)Nl).0r"s& r# "Random.setstate..s%K]7mm]sNzstate with version z( passed to Random.setstate() of version )r r>setstatetuple ValueErrorr=rE)r!stater@ internalstaterrBs&& r#rORandom.setstates( a<6; 3GDO G ] + \6; 3GDO  ' %%K]%K%K]%K K  G ] +%t||56 6  'Q& 's,B B0$B++B0c"VP4#N)rFr!s&r# __getstate__Random.__getstate__s}}r&c(VPV4R#rV)rO)r!rRs&&r# __setstate__Random.__setstate__s er&c<VPRVP43#)NrK)rBrFrWs&r# __reduce__Random.__reduce__s~~r4==?22r&c VPFapRVP9dR#RVP9dVPVnR#RVP9gKOVPVnR# R#)zControl 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. _randbelow getrandbitsrandomN)__mro____dict___randbelow_with_getrandbitsra_randbelow_without_getrandbits)clskwargsrAs", r#__init_subclass__Random.__init_subclass__sYAqzz) *!$!@!@1::%!$!C!Cr&c zVP4pVPV4pW18dVPV4pKV#)z;Return a random int in the range [0,n). Defined for n > 0.) bit_lengthrb)r!nkrs&& r#rf"Random._randbelow_with_getrandbitss9 LLN   Q f  #Ar&c VPpW8d&^RIHpV!R4\V!4V,4#W!,pW%, V, pV!4pWv8d V!4pK\Wr,4V,#)z{Return a random int in the range [0,n). Defined for n > 0. The implementation does not use getrandbits, but only random. )warnzUnderlying random() generator does not supply enough bits to choose from a population range this large. To remove the range limitation, add a getrandbits() method.)rcwarningsrs_floor)r!rnmaxsizercrsremlimitrps&&& r#rg%Random._randbelow_without_getrandbitsso  < % O P&(Q,' 'k') HjAak"Q&&r&c RVPV^,4PVR4#)Generate n random bytes.little)rbto_bytesr!rns&&r# randbytesRandom.randbytess$A&//8<??U5\Q7JF?IJz!vj455zJ JOO A{{KL L! q5 qE$q1ua.11 1G < #D1Xae$ G 1uqy/ uH#<? ? U q)+)A6+vx%/?BGHH)+ ++S !'3//KM  $+s#D&$D+>%E#+5E c JWV, VP4,,#)zGet a random number in the range [a, b) or [a, b] depending on rounding. The mean (expected value) and variance of the random variable are: E[X] = (a + b) / 2 Var[X] = (b - a) ** 2 / 12 rcrs&&&r#uniformRandom.uniformsET[[]***r&c VP4pVfRMW1, W!, , pYE8dRT, pRT, pY!r!YT, \YE,4,,# \dTu#i;i)auTriangular 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 The mean (expected value) and variance of the random variable are: E[X] = (low + high + mode) / 3 Var[X] = (low**2 + high**2 + mode**2 - low*high - low*mode - high*mode) / 18 ?r)rcZeroDivisionError_sqrt)r!lowhighmodeurAs&&&& r# triangularRandom.triangularst KKM |$*)DA 5aAaASjE!%L000 ! J sA,, A<;A<c VPpV!4pRV!4, p\VR, ,V, pWf,R, pV\V4)8:gKSYT,,#)zLNormal distribution. mu is the mean, and sigma is the standard deviation. rrr)rc NV_MAGICCONSTr)r!musigmarcu1u2zzzs&&& r# normalvariateRandom.normalvariates\BvxBc*R/ABd2hYI~r&c *VPpVPpRVnVfcV!4\,p\R\ RV!4, 4,4p\ V4V,p\ V4V,VnWV,,#)zGaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function. Not thread-safe without a lock around calls. Nrg)rcr TWOPIrr_cos_sin)r!rrrcrx2pig2rads&&& r#gauss Random.gauss-sr6 OO 98e#D$cFHn!556ET U"A"4j50DOI~r&c 6\VPW44#)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!rrs&&&r#lognormvariateRandom.lognormvariateSsD&&r122r&c R\RVP4, 4)V, #)aExponential 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. The mean (expected value) and variance of the random variable are: E[X] = 1 / lambd Var[X] = 1 / lambd ** 2 r)rrc)r!lambds&&r# expovariateRandom.expovariate]s"$S4;;=())E11r&c PVPpVR8:d\V!4,#RV, pV\RWD,,4,pV!4p\\V,4pWuV,, pV!4p V RW,, 8g!V RV, \ V4,8:gKhRT, p Y,RY,,, p T!4p T R8d T\ T 4,\,p T #T\ T 4, \,p T #)aCircular data distribution. mu is the mean angle, expressed in radians between 0 and 2*pi, and kappa is the concentration parameter, which must be greater than or equal to zero. If kappa is equal to zero, this distribution reduces to a uniform random angle over the range 0 to 2*pi. gư>rr)rcrrr_pir_acos)r!rkapparcrrprrdrqfu3thetas&&& r#vonmisesvariateRandom.vonmisesvariateqs  D=68# # %K cAEk" "BS2XAU ABC!%K2#'T!W)<#< !G UsQU{ # X 8%(]e+E %(]e+E r&c VR8:gVR8:d \R4hVPpVR8d\RV,R, 4pV\, pW,pV!4pRTu;8dR8gMKRV!4, p\ VRV, , 4V, p V\ V 4,p Ww,V,p WVV ,,V , p V \ ,RV ,, R8gV \ V 48gKW,#VR8Xd \ RV!4, 4)V,#V!4p \V,\, pW,pVR8:dVRV, ,p M\ W, V, 4)p V!4pVR8d WzVR, ,8:d W,#KV\ V )48:gKW,#)aGamma distribution. Not the gamma function! Conditions on the parameters are alpha > 0 and beta > 0. The probability distribution function is: x ** (alpha - 1) * math.exp(-x / beta) pdf(x) = -------------------------------------- math.gamma(alpha) * beta ** alpha The mean (expected value) and variance of the random variable are: E[X] = alpha * beta Var[X] = alpha * beta ** 2 rz*gammavariate: alpha and beta must be > 0.0rrgHz>gP?r)rQrcrLOG4rr SG_MAGICCONST_e)r!alphabetarcainvbbbcccrrvr"rrprrps&&& r# gammavariateRandom.gammavariates( C<43;IJ J 3; us*+D$,C,CXb,9,68^sRx)D0DGOGbL'MA%}$sQw.#5d1g8O c\vx((4/ / H%Z2%E8cEk*Aquo..AXs753;//8O 048^8Or&c xVPVR4pV'd W3VPVR4,, #R#)a!Beta distribution. Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1. The mean (expected value) and variance of the random variable are: E[X] = alpha / (alpha + beta) Var[X] = alpha * beta / ((alpha + beta)**2 * (alpha + beta + 1)) rr)r)r!rrys&&& r# betavariateRandom.betavariates76   eS ) D--dC889 9r&c PRVP4, pVRV, ,#)z3Pareto distribution. alpha is the shape parameter.rgr)r!rrs&& r# paretovariateRandom.paretovariates# $++- TE\""r&c rRVP4, pV\V4)RV, ,,#)zVWeibull distribution. alpha is the scale parameter and beta is the shape parameter. r)rcr)r!rrrs&&& r#weibullvariateRandom.weibullvariates. $++- acDj111r&c >V^8d \R4hVR8:gVR8dVR8Xd^#VR8XdV#\R4hVPpV^8Xd\V!4V84#VR8d WPVRV, 4, #W,R8dc^;rE\ RV, 4pV'gV#V\ \ V!44V, 4^,, pYQ8dT#T^, pKCW,R8dVR8:gQhRp\ W,RV, ,4pR R V,,p RR V ,,R V,,p W,R,pR RV , , p V!4p V R,p R\V 4, p \ RV ,V , V ,V ,V,4pT^8gY8dKaT!4pT R8d Y8:dT#T'g|RRT , ,T,p\TRT, , 4p\ T^,T,4p\T^,4\TT, ^,4,pRpTXYT ,, T ,, ,p\T4X\T^,4, \Y, ^,4, TX, X,,8:gEKzT# \dEKRi;i \dEKi;i)aBinomial random variable. Gives the number of successes for *n* independent trials with the probability of success in each trial being *p*: sum(random() < p for i in range(n)) Returns an integer in the range: 0 <= X <= n The integer is chosen with the probability: P(X == k) = math.comb(n, k) * p ** k * (1 - p) ** (n - k) The mean (expected value) and variance of the random variable are: E[X] = n * p Var[X] = n * p * (1 - p) zn must be non-negativerrz&p must be in the range 0.0 <= p <= 1.0rg$@TFgffffff?g= ףp=@ga+e?{Gz?gq= ףp?g@rgQ?gp= ף@gffffff@gEJY) rQrcrbinomialvariate_log2rur_fabsrr_lgamma)r!rnrrcr"rrAsetup_completespqrr?vrrusrorrlpqmhs&&& r#r Random.binomialvariates. q556 6 8qCxCxCxEF F 6&(Q,' ' s7++AsQw77 7 54<IAcAgAfh! 34q88A5HQsd{qCx''AES1W%& 4#:  fqj 4!8 + ECK C!G^A HAuQxB C!GbL1,1A561uATzag!a3.1a=)AEQ;'AENWQUQY%77!% !Bw-!+, ,AAw!ga!en,wquqy/AAQUcMQQc"2%  s$8.K9!.L 9 L L  LL)r rV)NrJ)rrNrr)r)r))__name__ __module__ __qualname____firstlineno____doc__rEr$rrFrOrXr[r^rjrfBPFrgrarrrrrrrrrrrrrrrrrrr r __static_attributes____classdictcell__ __classcell__)rB __classdict__s@@r#rrgs G.`A6B3 (9:3'(-J=%)t'3R..$]d]~#+t#+q#+P +12*$L32((TCJ@# 2eer&cJa]tRtRtoRtRtRtRtRtRt ] ;t t Rt Vt R #) rizAlternate 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 b\P\^44^, \,#)z7Get the next random number in the range 0.0 <= X < 1.0.)r8r9_urandom RECIP_BPFrWs&r#rcSystemRandom.randomsx{+q0I==r&c V^8d \R4hV^,^,p\P\V44pW2^,V, , #)z:getrandbits(k) -> x. Generates an int with k random bits.z#number of bits must be non-negative)rQr8r9r')r!ronumbytesr"s&& r#rbSystemRandom.getrandbitssG q5BC CEa< NN8H- .\A%&&r&c \V4#)r{)r'r~s&&r#rSystemRandom.randbytess{r&c R#)z' P*)Hxr&cF^RIHpHp^RIHpV!4p\ RV4Uu.uFqq!V!NK ppV!4p V!V4p V!W4p \ V4p \V4p \W, R RV RVP V: 24\RWW3,4R#uupi))stdevfmean) perf_counterNz.3fz sec, z times z"avg %g, stddev %g, min %g, max %g ) statisticsr:r;timer<rminmaxprintr)rnfuncr1r:meanr<t0rdatat1xbarrrrs&&& r#_test_generatorrHs/! B!(q!1 2!1AD$K!1D 2 B :D $ E d)C t9D RWSMs'$-- AB /42J JK 3sBcj\V\R4\V\R4\V\R4\V\R4\V\ R4\V\ R4\V\ R4\V\ R4\V\ R4\V\ R 4\V\ R 4\V\ R 4\V\ R 4\V\ R 4\V\ R4\V\R4\V\R4\V\R4R#)rNrKr)g333333?)dg?)r r)皙?r)rLr)rr)g?r)rr)rr)g4@r)gi@r)@rM)rrgUUUUUU?) rHrcrrrr rrrr)Ns&r#_testrOsAvr"A}j1A~z2A 3A 3A 4A|[1A|Z0A|Z0A|Z0A|Z0A|Z0A|Z0A|[1A|\2Auj)A{J/Az#89r&fork)after_in_childcHV^8dQhR\\,R,/#)rJarg_listN)rr,)formats"r# __annotate__rUs&&$s)d*&r&c^RIpVPVPRR7pVP4pVP RRRRR7VP R R \ R R R 7VP RR\ R RR 7VP R\ RRVPR7VP RRRR7VPV4pWBP43#)r9NT)formatter_classcolorz-cz--choice+zprint a random choice)nargshelpz-iz --integerrNz0print a random integer between 1 and N inclusive)r;metavarr[z-fz--floatz>print a random floating-point number between 0 and N inclusivez--test'?)r;constrZr[input*zif no options given, output depends on the input string or multiple: same as --choice integer: same as --integer float: same as --float) argparseArgumentParserRawTextHelpFormatteradd_mutually_exclusive_group add_argumentr8r<SUPPRESS parse_args format_help)rSrbparsergroupr1s& r# _parse_argsrls  $ $ 55T%CF  / / 1E  j $&  kS ?A  ieS MO s&     s   X &D ##% %%r&cjV^8dQhR\\,R,R\\,/#)rJrSNreturn)rr,r8)rTs"r#rUrUs'$$49t#$sSy$r&c\V4wrVP'd\VP4#VPe\^VP4#VPe\ ^VP4#VP 'd\VP 4R#\VP4^8Xd,VP^,p\V4p\^V4#\VP4^8d\VP4#V# \dH\ T4p\ ^T4u# \d\TP44uu#i;ii;i)N) rlrintegerrr<rtestrOr1r`r8rQsplit)rSr1 help_textvals& r#mainrvs!!(+OD {{{dkk"" ||q$,,'' zzq$**%% yyy dii 4::!jjm +c(C1c? " 4::!djj!!  + +Cjq#& +ciik** +  +s0D E.(E>E.$E*%E.)E**E.__main__)rrrr rrrrrrbrFrrrrrrcrrrrOrrrrr g)r]rV)]rmathrrrrrrrrrrrrrrr rr rr rr rur rrrrrrrosrr'_collections_abcrroperatorrr itertoolsrrrrrr_os_random__all__rrrr r(rr3rr_instrrcrrrrrrrrrrrrrrrr rr rFrOrbrrHrOhasattrregister_at_forkrlrvrrArKr&r#rs.hMLGGEE@@"2$B$ :DJs+  Cyd3i  #I  S W^^S t"*6"*X  zz  --    --  OO  -- --## %% ''!!   ''## %% >> >> OO L":0 3 3&6$N z $&Mr&