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q�fc@ s�dZddlmZddlmZddlmZm Z
ddlmZ
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ddl!m"Z#dd l$Z%d
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e.fd,��YZ/d"e.fd-��YZ0d.�Z1d/d0�Z2e.�Z3e3j4Z4e3j5Z5e3j6Z6e3j7Z7e3j8Z8e3j9Z9e3j:Z:e3j;Z;e3j<Z<e3j=Z=e3j>Z>e3j?Z?e3j@Z@e3jAZAe3jBZBe3jCZCe3jDZDe3jEZEe3jFZFe3jGZGe3jHZHe3jIZIeJd1kr�e2�nd 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.
i����(tdivision(twarn(t
MethodTypetBuiltinMethodType(tlogtexptpitetceil(tsqrttacostcostsin(turandom(thexlifyNtRandomtseedtrandomtuniformtrandinttchoicetsamplet randrangetshufflet
normalvariatetlognormvariatetexpovariatetvonmisesvariatetgammavariatet
triangulartgausstbetavariatet
paretovariatetweibullvariatetgetstatetsetstatet jumpaheadtWichmannHilltgetrandbitstSystemRandomig�g@g@g�?g@i5icB
s0eZdZdZdd�Zdd�Zd�Zd�Zd�Z d�Z
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d�Z!d�Z"RS( s�Random 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|�d|_dS(seInitialize an instance.
Optional argument x controls seeding, as for Random.seed().
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gauss_next(tselftx((s/usr/lib64/python2.7/random.pyt__init__[s
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s�|dkrdytttd��d�}Wqdtk
r`ddl}t|j�d�}qdXntt|�j|�d|_ 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.
ii����Ni(
R(tlongt_hexlifyt_urandomtNotImplementedErrorttimetsuperRRR)(R*taR1((s/usr/lib64/python2.7/random.pyRds
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s"|jtt|�j�|jfS(s9Return internal state; can be passed to
setstate()
later.(tVERSIONR2RR"R)(R*((s/usr/lib64/python2.7/random.pyR"wscC
s�|d}|dkrA|\}}|_tt|�j|�n�|dkr�|\}}|_ytd�|D��}Wntk
r�}t|�nXtt|�j|�ntd||jf��dS(s:Restore
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NI(R-(t.0R+((s/usr/lib64/python2.7/random.pys <genexpr>�ss?state
with version %s passed to Random.setstate() of version
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ValueErrort TypeErrorR4(R*tstatetversiont
internalstateR((s/usr/lib64/python2.7/random.pyR#{s
cC
sWt|�t|j��}ttjd|�j�d�}tt|�j|�dS(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/lib64/python2.7/random.pyR$�s!cC
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s|j|�dS(N(R#(R*R9((s/usr/lib64/python2.7/random.pyt__setstate__�scC
s|jd|j�fS(N((t __class__R"(R*((s/usr/lib64/python2.7/random.pyt
__reduce__�silcC
s�||�}||kr$td�n||kru|dkri||krU|j|�S||j�|�Std�n||�}||kr�td�n||} |dkr�| dkr�| |kr�|||j| ��S||||j�| ��S|dkr!td||| f�n||�}
|
|krEtd�n|
dkrf| |
d|
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dkr�| |
d|
}n td�|dkr�td�n||kr�||
|j|�S||
||j�|�S( 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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random integer in range [a, b], including both end points.
i(R(R*R3tb((s/usr/lib64/python2.7/random.pyR�sc
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r
ntXt|j�|ksHt|�|kr�|d||dd��}||�} x| |kr�||�} qtW| S||kr�td�n||j�|�S(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.
gr�Z|
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enough bits to choose from a population range this
large(R&tAttributeErrorttypeRt_warn(
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'
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s|t|j�t|��S(s2Choose a random element from a non-empty
sequence.(R>Rtlen(R*tseq((s/usr/lib64/python2.7/random.pyRscC
sv|dkr|j}nxWttdt|���D]:}||�|d�}||||||<||<q4WdS(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(RtreversedtxrangeR\(R*R+RR>titj((s/usr/lib64/python2.7/random.pyRs
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s�t|�}d|ko#|kns7td��n|j}t}d g|}d}|dkr�|dtt|dd��7}n||ks�t|d�rt|�}xt |�D]A} ||�|| �}
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r�t|t�r��n|jt|�|�SX|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
isinstanceRR6(
R*t
populationRZRBRt_inttresulttsetsizetpoolR`Ratselectedtselected_add((s/usr/lib64/python2.7/random.pyR"s:
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cC s||||j�S(sHGet a random number in the range [a,
b) or [a, b] depending on
rounding.(R(R*R3RR((s/usr/lib64/python2.7/random.pyRcsgg�?cC
sx|j�}|dkrdn||||}||kr`d|}d|}||}}n|||||dS(s�Triangular
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
g�?g�?N(RR((R*tlowthightmodetutc((s/usr/lib64/python2.7/random.pyRis $
cC
sh|j}xP|�}d|�}t|d|}||d}|t|�krPqq|||S(s\Normal
distribution.
mu is the mean, and sigma is the standard deviation.
g�?g�?g@(Rt
NV_MAGICCONSTRV(R*tmutsigmaRtu1tu2tztzz((s/usr/lib64/python2.7/random.pyR|s
cC
st|j||��S(s�Log 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*RwRx((s/usr/lib64/python2.7/random.pyR�scC
std|j��|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.
g�?(RVR(R*tlambd((s/usr/lib64/python2.7/random.pyR�scC
s|j}|dkr
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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.
g���ư>g�?g�?(RtTWOPIt_sqrtt_cost_piR}t_acos(R*RwtkappaRRCR[RyR{tdRztqtftu3ttheta((s/usr/lib64/python2.7/random.pyR�s&
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|||}||| |
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�kr_Pq_q_|
|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 >
0.0g�?g@gH�����z>g�P���?g@N(R7RR�tLOG4RVR}t
SG_MAGICCONSTt_e(R*talphatbetaRtainvtbbbtcccRyRztvR+R{R[RtRRtp((s/usr/lib64/python2.7/random.pyR�sJ
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s�|j}|j}d|_|dkrw|�t}tdtd|���}t|�|}t|�||_n|||S(s�Gaussian
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.
g�g�?N(RR)R(RR�RVR�t_sin(R*RwRxRR{tx2pitg2rad((s/usr/lib64/python2.7/random.pyR,s
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s>|j|d�}|dkr"dS|||j|d�SdS(s�Beta
distribution.
Conditions on the parameters are alpha > 0 and beta > 0.
Returned values range between 0 and 1.
g�?igN(R(R*R�R�ty((s/usr/lib64/python2.7/random.pyRas
cC s%d|j�}dt|d|�S(s3Pareto distribution. alpha is
the shape
parameter.g�?(Rtpow(R*R�Rt((s/usr/lib64/python2.7/random.pyR
sscC s,d|j�}|tt|�d|�S(sfWeibull distribution.
alpha is the scale parameter and beta is the shape parameter.
g�?(RR�RV(R*R�R�Rt((s/usr/lib64/python2.7/random.pyR!|sN(#t__name__t
__module__t__doc__R4R(R,RR"R#R$RDRERGR>tBPFRRRVt_MethodTypet_BuiltinMethodTypeRHRRRRRRRRRRRRR
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A 0 H 5 cB
s\eZdZd d�Zd�Zd�Zd�Zd�Zdddd�Z d d�Z
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r`ddl}t|j�d�}qdXnt|ttf�s�t|�}nt |d�\}}t |d�\}}t |d�\}}t|�dt|�dt|�df|_
d|_dS( s�Initialize internal state from hashable object.
None or no argument seeds from current time or from an operating
system specific randomness source if available.
If a is not None or an int or long, hash(a) is used instead.
If a is an int or long, a is used directly. Distinct values
between
0 and 27814431486575L inclusive are guaranteed to yield distinct
internal states (this guarantee is specific to the default
Wichmann-Hill generator).
ii����Nii<vibvirvi(R(R-R.R/R0R1RiR>thashtdivmodt_seedR)(R*R3R1R+R�R{((s/usr/lib64/python2.7/random.pyR�s
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sj|j\}}}d|d}d|d}d|d}|||f|_|d|d|d d
S(s3Get the next random number in the range [0.0,
1.0).i�i=vi�icvi�isvg@��@g���@g���@g�?(R�(R*R+R�R{((s/usr/lib64/python2.7/random.pyR�scC
s|j|j|jfS(s9Return internal state; can be passed to setstate()
later.(R4R�R)(R*((s/usr/lib64/python2.7/random.pyR"�scC
sK|d}|dkr.|\}|_|_ntd||jf��dS(s:Restore internal
state from object returned by getstate().iis?state with version %s passed
to Random.setstate() of version
%sN(R�R)R7R4(R*R9R:((s/usr/lib64/python2.7/random.pyR#�s
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s�|dkstd��n|j\}}}t|td|d��d}t|td|d��d}t|td|d��d}|||f|_d S(
s�Act as if n calls to random() were made, but quickly.
n is an int, greater than or equal to 0.
Example use: If you have 2 threads and know that each will
consume no more than a million random numbers, create two Random
objects r1 and r2, then do
r2.setstate(r1.getstate())
r2.jumpahead(1000000)
Then r1 and r2 will use guaranteed-disjoint segments of the full
period.
isn must be >=
0i�i=vi�icvi�isvN(R7R�R>R�(R*RBR+R�R{((s/usr/lib64/python2.7/random.pyR$�s
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st|�t|�ko4t|�ko4tknsHtd��nd|ko_dkno�d|ko{dkno�d|ko�dkns�td��nd|ko�|ko�|knrNddl}t|j�d�}t|d@|d?A�}t|d�\}}t|d�\}}t|d�\}}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)i����Ni���ii(
RTR>R8R7R1R-R�R�R(R)(R*R+R�R{R1tt((s/usr/lib64/python2.7/random.pyt__whseed�s9T'$cC
s�|dkr|j�dSt|�}t|d�\}}t|d�\}}t|d�\}}||dpvd}||dp�d}||dp�d}|j|||�dS(sbSeed
from hashable object's hash code.
None or no argument seeds from current time. It is not guaranteed
that objects with distinct hash codes lead to distinct internal
states.
This is obsolete, provided for compatibility with the seed routine
used prior to Python 2.1. Use the .seed() method instead.
Nii(R(t_WichmannHill__whseedR�R�(R*R3R+R�R{((s/usr/lib64/python2.7/random.pytwhseeds
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the range [0.0,
1.0).iii(R-R.R/t RECIP_BPF(R*((s/usr/lib64/python2.7/random.pyR'scC
su|dkrtd��n|t|�kr<td��n|dd}ttt|��d�}||d|?S(s>getrandbits(k)
-> x. Generates a long int with k random bits.is(number of bits must be
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integeriii(R7R>R8R-R.R/(R*RZtbytesR+((s/usr/lib64/python2.7/random.pyR&+scO
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generator.N(R((R*targstkwds((s/usr/lib64/python2.7/random.pyt_stub5scO
std��dS(sAMethod should not be called for a system random number
generator.s*System entropy source does not have
state.N(R0(R*R�R�((s/usr/lib64/python2.7/random.pyt_notimplemented:s(R�R�R�RR&R�RR$R�R"R#(((s/usr/lib64/python2.7/random.pyR's
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