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d'ƒZ(d(Z)d)e)Z*dd*k+Z+d	e+i,fd+„ƒYZ,de,fd,„ƒYZ-d!e,fd-„ƒYZ.d.„Z/d/d0„Z0e,ƒZ1e1i2Z2e1i3Z3e1i4Z4e1i5Z5e1i6Z6e1i7Z7e1i8Z8e1i9Z9e1i:Z:e1i;Z;e1i<Z<e1i=Z=e1i>Z>e1i?Z?e1i@Z@e1iAZAe1iBZBe1iCZCe1iDZDe1iEZEe1iFZFe1iGZGeHd1joe0ƒnd*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(thexlifytRandomtseedtrandomtuniformtrandinttchoicetsamplet	randrangetshufflet
normalvariatetlognormvariatetexpovariatetvonmisesvariatetgammavariatet
triangulartgausstbetavariatet
paretovariatetweibullvariatetgetstatetsetstatet	jumpaheadtWichmannHilltgetrandbitstSystemRandomigà¿g@g@gð?g@i5iNcB s'eZdZdZdd„Zdd„Zd„Zd„Zd„Z	d„Z
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„Zd„Zded„Zd„Zd„Zdddd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„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|i|ƒd|_dS(seInitialize an instance.

        Optional argument x controls seeding, as for Random.seed().
        N(RtNonet
gauss_next(tselftx((s/usr/lib/python2.6/random.pyt__init__Zs
cC s‹|djo[ytttdƒƒdƒ}Wqhtj
o)ddk}t|iƒdƒ}qhXntt|ƒi|ƒd|_	dS(sInitialize 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.
        iiÿÿÿÿNi(
R(tlongt_hexlifyt_urandomtNotImplementedErrorttimetsuperRRR)(R*taR1((s/usr/lib/python2.6/random.pyRcs	
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o}t|‚nXtt|ƒi|ƒntd||ifƒ‚dS(s:Restore internal state from object returned by getstate().iiics s#x|]}t|ƒdVqWdS(ii Nl(R-(t.0R+((s/usr/lib/python2.6/random.pys	<genexpr>‡s	s?state with version %s passed to Random.setstate() of version %sN(R)R2RR#ttuplet
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||iƒ|ƒS(	sChoose 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()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()(R7t
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cC s|i||dƒS(sJReturn random integer in range [a, b], including both end points.
        i(R(R*R3tb((s/usr/lib/python2.6/random.pyRàsc
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onzXt|iƒ|jpt|ƒ|joO|d||ddƒƒ}||ƒ}	x|	|jo||ƒ}	qxW|	S||jotdƒn||iƒ|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(
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cC s|t|iƒt|ƒƒS(s2Choose a random element from a non-empty sequence.(RDRtlen(R*tseq((s/usr/lib/python2.6/random.pyRscC sx|djo
|i}nxWttdt|ƒƒƒD]:}||ƒ|dƒ}||||||<||<q6WdS(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.
        iN(R(RtreversedtxrangeRV(R*R+RRDtitj((s/usr/lib/python2.6/random.pyRs

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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(RVR7RRDR(t_ceilRPthasattrtlistRYtsettaddR8tKeyErrort
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cC s||||iƒS(sHGet a random number in the range [a, b) or [a, b] depending on rounding.(R(R*R3RL((s/usr/lib/python2.6/random.pyR_sggð?cC s||iƒ}|djodn||||}||jo%d|}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((R*tlowthightmodetutc((s/usr/lib/python2.6/random.pyRes	&


cC sj|i}xR|ƒ}d|ƒ}t|d|}||d}|t|ƒjoPqq|||S(s\Normal distribution.

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

        gð?gà?g@(Rt
NV_MAGICCONSTRP(R*tmutsigmaRtu1tu2tztzz((s/usr/lib/python2.6/random.pyRxs
		
cC st|i||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*RqRr((s/usr/lib/python2.6/random.pyR‘scC s?|i}|ƒ}x|djo
|ƒ}qWt|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.

        gH¯¼šò×z>(RRP(R*tlambdRRn((s/usr/lib/python2.6/random.pyRs
		
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        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°>gð?g@g@gà?(RtTWOPIt_sqrtt_cost_piRwt_acos(R*RqtkappaRR3RLRURsRutfRoRttu3ttheta((s/usr/lib/python2.6/random.pyR²s&	
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        Conditions on the parameters are alpha > 0 and beta > 0.

        gs*gammavariate: alpha and beta must be > 0.0gð?g@gH¯¼šò×z>gËPÊÿÿï?g@N(R7RRztLOG4RPRwt
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	cC s…|i}|i}d|_|djoQ|ƒt}tdtd|ƒƒƒ}t|ƒ|}t|ƒ||_n|||S(sØGaussian distribution.

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        slightly faster than the normalvariate() function.

        Not thread-safe without a lock around calls.

        gÀgð?N(RR)R(RyRzRPR{t_sin(R*RqRrRRutx2pitg2rad((s/usr/lib/python2.6/random.pyR&s			

cC s@|i|dƒ}|djodS|||i|dƒSdS(sBeta distribution.

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        Returned values range between 0 and 1.

        gð?igN(R(R*R…R†ty((s/usr/lib/python2.6/random.pyR[s

cC s%d|iƒ}dt|d|ƒS(s3Pareto distribution.  alpha is the shape parameter.gð?(Rtpow(R*R…Rn((s/usr/lib/python2.6/random.pyR mscC s,d|iƒ}|tt|ƒd|ƒS(sfWeibull distribution.

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        gð?(RRRP(R*R…R†Rn((s/usr/lib/python2.6/random.pyR!vsN("t__name__t
__module__t__doc__R4R(R,RR"R#R<R=R?RDtBPFRRRPt_MethodTypet_BuiltinMethodTypeR@RRRRRRRRRRRRR R!(((s/usr/lib/python2.6/random.pyRGs8						?	
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o)ddk}t|iƒdƒ}qhXnt|ttfƒpt|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/R0R1RcRDthashtdivmodt_seedR)(R*R3R1R+RRu((s/usr/lib/python2.6/random.pyR‡s
0cC sj|i\}}}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+RRu((s/usr/lib/python2.6/random.pyR¦scC s|i|i|ifS(s9Return internal state; can be passed to setstate() later.(R4R™R)(R*((s/usr/lib/python2.6/random.pyR"ÅscC sM|d}|djo|\}|_|_ntd||ifƒ‚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/lib/python2.6/random.pyR#És


cC s¥|djptdƒ‚n|i\}}}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™RDR(R*RKR+RRu((s/usr/lib/python2.6/random.pyR$Ós
   icC s‘t|ƒt|ƒjot|ƒjo
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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(
RNRDR8R7R1R-R˜R™R(R)(R*R+RRuR1tt((s/usr/lib/python2.6/random.pyt__whseedés<Z*'cC s½|djo|iƒdSt|ƒ}t|dƒ\}}t|dƒ\}}t|dƒ\}}||dpd}||dpd}||dpd}|i|||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__whseedR—R˜(R*R3R+RRu((s/usr/lib/python2.6/random.pytwhseeds

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	cB sFeZdZd„Zd„Zd„ZeZZd„ZeZ	Z
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    cC s!tttdƒƒdƒd?tS(s3Get the next random number in the range [0.0, 1.0).iii(R-R.R/t	RECIP_BPF(R*((s/usr/lib/python2.6/random.pyR!scC sy|djotdƒ‚n|t|ƒjotdƒ‚n|dd}ttt|ƒƒdƒ}||d|?S(s>getrandbits(k) -> x.  Generates a long int with k random bits.is(number of bits must be greater than zeros#number of bits should be an integeriii(R7RDR8R-R.R/(R*RTtbytesR+((s/usr/lib/python2.6/random.pyR&%s
cO sdS(s<Stub method.  Not used for a system random number generator.N(R((R*targstkwds((s/usr/lib/python2.6/random.pyt_stub/scO stdƒ‚dS(sAMethod 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/lib/python2.6/random.pyt_notimplemented4s(R‘R’R“RR&R¢RR$R£R"R#(((s/usr/lib/python2.6/random.pyR's		
	
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