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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()rOz'empty range for randrange() (%d,%d, %d)z non-integer step for randrange()zzero step for randrange())rI _randbelow) r.startstopstep_intZistartZistopwidthZistepnr0r0r1rs4               zRandom.randrangecCs|j||dS)zJReturn random integer in range [a, b], including both end points. rO)r)r.rAbr0r0r1rszRandom.randintc Cs|j}|j}|||ks6|||krq|j} || } x| |krl|| } qQW| S||krtd|||S||} || |} |} 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.)rr' bit_length_warn) r.rVr5maxsizetypeZMethodZ BuiltinMethodrr'krZremlimitr0r0r1rPs"  $       zRandom._randbelowc CsBy|jt|}Wntk r9tdYnX||S)z2Choose a random element from a non-empty sequence.z$Cannot choose from an empty sequence)rPlenrI IndexError)r.seqir0r0r1rs  z Random.choicecCs|dkrk|j}xttdt|D]3}||d}||||||<||Population must be a sequence or set. For dicts, use list(d).rzSample larger than populationNr)r,rO)r:_SetrH _SequencerJrPr_rI_ceil_loglistrdsetadd) r.Z populationr\rerVresultZsetsizeZpoolrbrfZselectedZ selected_addr0r0r1rs6    $      z Random.samplecCs||||jS)zHGet a random number in the range [a, b) or [a, b] depending on rounding.)r)r.rArWr0r0r1rVszRandom.uniformgg?c Cs|j}y(|dkr!dn||||}Wntk rL|SYnX||kr}d|}d|}||}}n|||||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 Ng?g?)rZeroDivisionError)r.ZlowZhighmodeucr0r0r1r \s (     zRandom.triangularcCsi|j}xQ|}d|}t|d|}||d}|t| kr Pq q W|||S)z\Normal distribution. mu is the mean, and sigma is the standard deviation. g?g?g@)r NV_MAGICCONSTrl)r.musigmaru1u2zZzzr0r0r1rrs   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)r.rvrwr0r0r1rszRandom.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. g?)rlr)r.Zlambdr0r0r1rszRandom.expovariatecCs|j}|dkr t|Sd|}|td||}xf|}tt|}|||}|} | d||ks| d|t|krEPqEqEWd|} | |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>g?g?)rTWOPI_sqrt_cos_pir{_acos)r.rvZkapparsr]rxrzdryqfZu3Zthetar0r0r1rs&      .   zRandom.vonmisesvariatecCs |dks|dkr'tdn|j}|dkr td|d}|t}||}x|}d|kodknsqgnd|}t|d||} |t| } |||} ||| | } | td| dks| t| krg| |SqgWn|dkr`|} x| dkrP|} q8Wt|  |Sx|} t|t}|| }|dkr|d|} nt||| } |}|dkr|| |dkrPqqc|t| krcPqcqcW| |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 gz*gammavariate: alpha and beta must be > 0.0g?g@gHz>gP?g@N)rIrr}LOG4rlr{ SG_MAGICCONST_e)r.alphabetarZainvZbbbZcccrxryvr/rzr]rsrWpr0r0r1rsJ      *        zRandom.gammavariatecCs|j}|j}d|_|dkrw|t}tdtd|}t||}t|||_n|||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@g?g)rr-r|r}rlr~_sin)r.rvrwrrzZx2piZg2radr0r0r1r!"s     z Random.gausscCs>|j|d}|dkr"dS|||j|dSdS)zBeta distribution. Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1. g?rgN)r)r.rryr0r0r1r"Ws  zRandom.betavariatecCs d|j}d|d|S)z3Pareto distribution. alpha is the shape parameter.g?)r)r.rrsr0r0r1r#iszRandom.paretovariatecCs'd|j}|t| d|S)zfWeibull distribution. alpha is the scale parameter and beta is the shape parameter. g?)rrl)r.rrrsr0r0r1r$rszRandom.weibullvariate)"__name__ __module__ __qualname____doc__rDr2rr%r&rLrMrNr5rrBPFr[ _MethodType_BuiltinMethodTyperPrrrrr rrrrrr!r"r#r$r0r0)rCr1rDs6      ,    >    0 H 5  c@sPeZdZdZddZddZddZdd 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).r3r,)r5r6r7 RECIP_BPF)r.r0r0r1rszSystemRandom.randomcCsr|dkrtdn|t|kr<tdn|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 integerrr3)rIr5rJr6r7)r.r\Znumbytesr/r0r0r1r's zSystemRandom.getrandbitscOsdS)z%sd("         =!