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e-j.fd+„ƒYZ.d e.fd,„ƒYZ/d"e.fd-„ƒYZ0d.„Z1d/d0„Z2e.ƒZ3e3j4Z4e3j5Z5e3j6Z6e3j7Z7e3j8Z8e3j9Z9e3j:Z:e3j;Z;e3j<Z<e3j=Z=e3j>Z>e3j?Z?e3j@Z@e3jAZAe3jBZBe3jCZCe3jDZDe3jEZEe3jFZFe3jGZGe3jHZHe3jIZIeJd1krŸe2ƒnd	S(2sPRandom 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(tdivision(twarn(t
MethodTypetBuiltinMethodType(tlogtexptpitetceil(tsqrttacostcostsin(turandom(thexlifyNtRandomtseedtrandomtuniformtrandinttchoicetsamplet	randrangetshufflet
normalvariatetlognormvariatetexpovariatetvonmisesvariatetgammavariatet
triangulartgausstbetavariatet
paretovariatetweibullvariatetgetstatetsetstatet	jumpaheadtWichmannHilltgetrandbitstSystemRandomigà¿g@g@gð?g@i5icB s*eZdZdZdd„Zdd„Zd„Zd„Zd„Z	d„Z
d„Zd	„Zdd
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de>eed„Zd„Zdd„Zd„Zd„Zdddd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Z d„Z!d„Z"RS( sÎRandom 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.

    icC s|j|ƒd|_dS(seInitialize an instance.

        Optional argument x controls seeding, as for Random.seed().
        N(RtNonet
gauss_next(tselftx((s"/usr/local/lib/python2.7/random.pyt__init__[s
cC s‡|dkrdytttdƒƒdƒ}Wqdtk
r`ddl}t|jƒdƒ}qdXntt|ƒj|ƒd|_	dS(s†Initialize internal state of the random number generator.

        None or no argument seeds from current time or from an operating
        system specific randomness source if available.

        If a is not None or is an int or long, hash(a) is used instead.
        Hash values for some types are nondeterministic when the
        PYTHONHASHSEED environment variable is enabled.
        iÄ	iiÿÿÿÿNi(
R(tlongt_hexlifyt_urandomtNotImplementedErrorttimetsuperRRR)(R*taR1((s"/usr/local/lib/python2.7/random.pyRds
cC s"|jtt|ƒjƒ|jfS(s9Return internal state; can be passed to setstate() later.(tVERSIONR2RR"R)(R*((s"/usr/local/lib/python2.7/random.pyR"{scC sÎ|d}|dkrA|\}}|_tt|ƒj|ƒn‰|dkr±|\}}|_ytd„|Dƒƒ}Wntk
r—}t|‚nXtt|ƒj|ƒntd||jfƒ‚dS(s:Restore internal state from object returned by getstate().iiics s|]}t|ƒdVqdS(ii NI(R-(t.0R+((s"/usr/local/lib/python2.7/random.pys	<genexpr>Œss?state with version %s passed to Random.setstate() of version %sN(R)R2RR#ttuplet
ValueErrort	TypeErrorR4(R*tstatetversiont
internalstateR((s"/usr/local/lib/python2.7/random.pyR#s

cC sWt|ƒt|jƒƒ}ttjd|ƒjƒdƒ}tt|ƒj|ƒdS(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.
        tsha512iN(	treprR"tintt_hashlibtnewt	hexdigestR2RR$(R*tnts((s"/usr/local/lib/python2.7/random.pyR$•s!cC s
|jƒS(N(R"(R*((s"/usr/local/lib/python2.7/random.pyt__getstate__¦scC s|j|ƒdS(N(R#(R*R9((s"/usr/local/lib/python2.7/random.pyt__setstate__©scC s|jd|jƒfS(N((t	__class__R"(R*((s"/usr/local/lib/python2.7/random.pyt
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n	td‚|
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|krÉ||	|j|
ƒS||	||jƒ|
ƒS(
sÀChoose 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.

        s!non-integer arg 1 for randrange()isempty range for randrange()s non-integer stop for randrange()is'empty range for randrange() (%d,%d, %d)s non-integer step for randrange()szero step for randrange()N(R7R(t
_randbelowR(R*tstarttstoptstept_intt	_maxwidthtistarttistoptwidthtistepRB((s"/usr/local/lib/python2.7/random.pyR±s@


	cC s|j||dƒS(sJReturn random integer in range [a, b], including both end points.
        i(R(R*R3tb((s"/usr/local/lib/python2.7/random.pyRðsc
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|j}Wntk
r ntXt|jƒ|ksHt|ƒ|kr”|d||ddƒƒ}||ƒ}	x|	|kr||ƒ}	qtW|	S||kr­tdƒn||jƒ|ƒS(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?ig@sgUnderlying random() generator does not supply 
enough bits to choose from a population range this large(R&tAttributeErrorttypeRt_warn(
R*RBt_logRLRMt_Methodt_BuiltinMethodR&tktr((s"/usr/local/lib/python2.7/random.pyRHös

'
cC s|t|jƒt|ƒƒS(s2Choose a random element from a non-empty sequence.(R>Rtlen(R*tseq((s"/usr/local/lib/python2.7/random.pyRscC s||dkr|j}nt}xWttdt|ƒƒƒD]:}||ƒ|dƒ}||||||<||<q:WdS(sØx, 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.

        iN(R(RR>treversedtxrangeR[(R*R+RRLtitj((s"/usr/local/lib/python2.7/random.pyRs"c
C sÉt|ƒ}d|ko#|kns7tdƒ‚n|j}t}d	g|}d}|dkr‰|dtt|ddƒƒ7}n||ks¤t|dƒrt|ƒ}xt	|ƒD]A}	||ƒ||	ƒ}
||
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rÄt|tƒr®‚n|jt|ƒ|ƒSX|S(
s8Chooses 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)
        issample larger than populationiiiitkeysiN(R[R7RR>R(t_ceilRVthasattrtlistR^tsettaddR8tKeyErrort
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R*t
populationRYRBRRLtresulttsetsizetpoolR_R`tselectedtselected_add((s"/usr/local/lib/python2.7/random.pyR's:	
$		
cC s||||jƒS(sHGet a random number in the range [a, b) or [a, b] depending on rounding.(R(R*R3RR((s"/usr/local/lib/python2.7/random.pyRhsggð?cC s‘|jƒ}y(|dkr!dn||||}Wntk
rH|SX||kryd|}d|}||}}n|||||dS(sÜTriangular 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

        gà?gð?N(RR(tZeroDivisionError(R*tlowthightmodetutc((s"/usr/local/lib/python2.7/random.pyRns	(


cC si|j}xQ|ƒ}d|ƒ}t|d|}||d}|t|ƒkrPqqW|||S(s\Normal distribution.

        mu is the mean, and sigma is the standard deviation.

        gð?gà?g@(Rt
NV_MAGICCONSTRV(R*tmutsigmaRtu1tu2tztzz((s"/usr/local/lib/python2.7/random.pyR„s
		
cC st|j||ƒƒS(sûLog 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*RvRw((s"/usr/local/lib/python2.7/random.pyRscC std|jƒƒ|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.

        gð?(RVR(R*tlambd((s"/usr/local/lib/python2.7/random.pyR©scC s|j}|dkr t|ƒSd|}|td||ƒ}xf|ƒ}tt|ƒ}|||}|ƒ}	|	d||ks£|	d|t|ƒkrEPqEqEWd|}
|
|d|
|}|ƒ}|dkr÷|t|ƒt}
n|t|ƒt}
|
S(sFCircular 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°>gà?gð?(RtTWOPIt_sqrtt_cost_piR|t_acos(R*RvtkappaRRCRZRxRztdRytqtftu3ttheta((s"/usr/local/lib/python2.7/random.pyR¼s&	
		.
	cC s
|dks|dkr$td‚n|j}|dkrtd|dƒ}|t}||}x¢|ƒ}d|ko„dknsqdnd|ƒ}t|d|ƒ|}	|t|	ƒ}
|||}|||	|
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|SdS(	sZGamma 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

        gs*gammavariate: alpha and beta must be > 0.0gð?g@gH¯¼šò×z>gËPÊÿÿï?g@N(R7RRtLOG4RVR|t
SG_MAGICCONSTt_e(R*talphatbetaRtainvtbbbtcccRxRytvR+RzRZRsRRtp((s"/usr/local/lib/python2.7/random.pyRìsJ	

	
*	
	
	cC sƒ|j}|j}d|_|dkrw|ƒt}tdtd|ƒƒƒ}t|ƒ|}t|ƒ||_n|||S(sØGaussian 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.

        gÀgð?N(RR)R(R~RRVR€t_sin(R*RvRwRRztx2pitg2rad((s"/usr/local/lib/python2.7/random.pyR4s			
cC s>|j|dƒ}|dkr"dS|||j|dƒSdS(sBeta distribution.

        Conditions on the parameters are alpha > 0 and beta > 0.
        Returned values range between 0 and 1.

        gð?igN(R(R*RŒRty((s"/usr/local/lib/python2.7/random.pyRis
cC s%d|jƒ}dt|d|ƒS(s3Pareto distribution.  alpha is the shape parameter.gð?(Rtpow(R*RŒRs((s"/usr/local/lib/python2.7/random.pyR {scC s,d|jƒ}|tt|ƒd|ƒS(sfWeibull distribution.

        alpha is the scale parameter and beta is the shape parameter.

        gð?(RR—RV(R*RŒRRs((s"/usr/local/lib/python2.7/random.pyR!„sN(#t__name__t
__module__t__doc__R4R(R,RR"R#R$RDRERGR>tBPFRRRVt_MethodTypet_BuiltinMethodTypeRHRRRRRRRRRRRRR R!(((s"/usr/local/lib/python2.7/random.pyRHs8							?	
		A					0	H	5			cB s\eZdZd	d„Zd„Zd„Zd„Zd„Zdddd„Z	d	d„Z
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icC s|dkrdytttdƒƒdƒ}Wqdtk
r`ddl}t|jƒdƒ}qdXnt|ttfƒsˆt|ƒ}nt	|dƒ\}}t	|dƒ\}}t	|dƒ\}}t|ƒdt|ƒdt|ƒdf|_
d|_dS(	süInitialize 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).
        iiÿÿÿÿNii<vibvirvi(R(R-R.R/R0R1RhR>thashtdivmodt_seedR)(R*R3R1R+R–Rz((s"/usr/local/lib/python2.7/random.pyR•s
0cC sj|j\}}}d|d}d|d}d|d}|||f|_|d|d|d	d
S(s3Get the next random number in the range [0.0, 1.0).i«i=vi¬icviªisvg@Ý@gÀ˜Ý@gÀœÝ@gð?(R (R*R+R–Rz((s"/usr/local/lib/python2.7/random.pyR´scC s|j|j|jfS(s9Return internal state; can be passed to setstate() later.(R4R R)(R*((s"/usr/local/lib/python2.7/random.pyR"ÓscC sK|d}|dkr.|\}|_|_ntd||jfƒ‚dS(s:Restore internal state from object returned by getstate().iis?state with version %s passed to Random.setstate() of version %sN(R R)R7R4(R*R9R:((s"/usr/local/lib/python2.7/random.pyR#×s

cC s£|dkstdƒ‚n|j\}}}t|td|dƒƒd}t|td|dƒƒd}t|td|dƒƒd}|||f|_d	S(
sÃAct 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.
        isn must be >= 0i«i=vi¬icviªisvN(R7R R>R—(R*RBR+R–Rz((s"/usr/local/lib/python2.7/random.pyR$ás   icC st|ƒt|ƒko4t|ƒko4tknsHtdƒ‚nd|ko_dkno™d|ko{dkno™d|ko—dkns«tdƒ‚nd|koÍ|koÍ|knrNddl}t|jƒdƒ}t|d@|d?Aƒ}t|dƒ\}}t|dƒ\}}t|dƒ\}}n|pWd	|p`d	|pid	f|_d|_	dS(
sjSet the Wichmann-Hill seed from (x, y, z).

        These must be integers in the range [0, 256).
        sseeds must be integersiisseeds must be in range(0, 256)iÿÿÿÿNiÿÿÿii(
RTR>R8R7R1R-RŸR R(R)(R*R+R–RzR1tt((s"/usr/local/lib/python2.7/random.pyt__whseed÷s9T'$cC s¸|dkr|jƒdSt|ƒ}t|dƒ\}}t|dƒ\}}t|dƒ\}}||dpvd}||dpŠd}||dpžd}|j|||ƒdS(sbSeed 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.
        Nii(R(t_WichmannHill__whseedRžRŸ(R*R3R+R–Rz((s"/usr/local/lib/python2.7/random.pytwhseeds
N(R˜R™R4R(RRR"R#R$R£R¤(((s"/usr/local/lib/python2.7/random.pyR%‘s			
	cB sFeZdZd„Zd„Zd„ZeZZd„ZeZ	Z
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