
+[c           @   s4  d  d l  Z  d  d l Z d  d l Td   Z d   Z d   Z d   Z d   Z d   Z d	   Z	 d
   Z
 d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d    Z  d!   Z! d"   Z" d#   Z# d$   Z$ d%   Z% d&   Z& d'   Z' d(   Z( d)   Z) d*   Z* d+   Z+ d,   Z, d-   Z- d.   Z. d/   Z/ d0 Z0 d0 Z1 d1 d2 d3 d4 d5 d6 d7 d8 d9 d: d; d< d= d> d? g d@ dA dB dC dD dE dF dG dH dI dJ dK dL dM dN g dO dP dQ dR dS dT dU dV dW dX dY dZ d[ d\ d] g d^ d_ d` da db dc dd de df dg dh di dj dk dl g dm dn do dp dq dr ds dt du dv dw dx dy dz d{ g d| d} d~ d d d d d d d d d d d d g d d d d d d d d d d d d d d d g d d d d d d d d d d d d d d d g d d d d d d d d d d d d d d d g d d d d d d d d d d d d d d d g d d d d d d d d d d d d d d d g d d d d d d d d d d d d d d d g d d d d d d d d d d d d d d d g d d d d d d d d d d d d d ddg ddddddd	d
dddddddg g Z2 dd@ dA dB dC dD dE dF dG dH dI dJ dK dL dM g dddddddddddddd d!g d"d#d$d%d&d'd(d)d*d+d,d-d.d/d0g d1d2d3d4d5d6d7d8d9d:d;d<d=d>d?g d@dAdBdCdDdEdFdGdHdIdJdKdLdMdNg dOdPdQdRdSdTdUdVdWdXdYdZd[d\d]g d^d_d`dadbdcdddedfdgdhdidjdkdlg dmdndodpdqdrdsdtdudvdwdxdydzd{g d|d}d~ddddddddddddg dddddddddddddddg dddddddddddddddg dddddddddddddddg dddddddddddddddg dddddddddddddddg dddddddddddddddg g Z3 dddddddddddddddg ddddddddddddd ddg ddddddd	d
dddddddg ddddddddddddddd g d!d"d#d$d%d&d'd(d)d*d+d,d-d.d/g d0d1d2d3d4d5d6d7d8d9d:d;d<d=d>g d?d@dAdBdCdDdEdFdGdHdIdJdKdLdMg dNdOdPdQdRdSdTdUdVdWdXdYdZd[d\g d]d^d_d`dadbdcdddedfdgdhdidjdkg dldmdndodpdqdrdsdtdudvdwdxdydzg d{d|d}d~dddddddddddg dddddddddddddddg dddddddddddddddg dddddddddddddddg dddddddddddddddg g Z4 ddddddddddddd ddg dddddddddddddddg dddddddddddddddg dddddddddddddddg dddddddddddddd dg dddddddd	d
ddddddg dddddddddddddddg d d!d"d#d$d%d&d'd(d)d*d+d,d-d.g d/d0d1d2d3d4d5d6d7d8d9d:d;d<d=g d>d?d@dAdBdCdDdEdFdGdHdIdJdKdLg dMdNdOdPdQdRdSdTdUdVdWdXdYdZd[g d\d]d^d_d`dadbdcdddedfdgdhdidjg dkdldmdndodpdqdrdsdtdudvdwdxdyg dzd{d|d}d~ddddddddddg dddddddddddddddg g Z5 e j6 j7 d   Z8 d S(  iN(   t   *c          C   s  d t  _ t d  j d  s$ t  t t  j d  s? t  t d  j d  sZ t  t d  j d  su t  t d  j d	  s t  t t  j d
  s t  t d  j d  s t  t d  j d  s t  t d d  j d  s t  t dM d  j d  st  t d t  j d  s;t  t d d  j d  sYt  t d d  j d  swt  t d d  j d  st  t d d  j d  st  t d dN  j dO  st  t d d  j d  st  t dP dQ  j dR  st  t d dS  dT j d#  s/t  t d$ d%  d% k sJt  t d& d%  t	 k sft  t d' d%  t	 k st  t d% d%  t	 k st  t d( d%  t	 k st  t d) d%  t	 k st  t d* d%  t	 k st  t d+ d%  t	 k st  t d, d%  t	 k s't  t d* d%  t	 k sBt  t d- d%  t	 k s^t  t d d%  t	 k syt  t d& d%  t	 k st  t d d%  t	 k st  t d' d%  t	 k st  t d d%  t	 k st  t d. d%  t	 k st  t d d%  t	 k s!t  t d% d&  j d/  s?t  t d d&  j d0  s]t  t d* d&  j d1  s{t  t d2 d&  j d3  st  t d% dU  j dV  st  t d% t
  j dW  st  t d dX  dY j d8  st  t d% d%  d k st  t d d%  d% k s-t  t d d%  d% k sHt  t d* d%  d% k sct  t d- d%  d% k s~t  t d% d&  j d9  st  t d d&  j d:  st  t d* d&  j d:  st  t d2 d&  j d;  st  t d% dZ  j d[  st  t d% t
  j t d% d   s;t  t d d\  t d"  d> j d?  sgt  t d% d%  t	 k st  t d d%  t	 k st  t d d%  t	 k st  t d* d%  t	 k st  t d- d%  t	 k st  t d% d&  j d@  st  t d d&  j dA  s*t  t d* d&  j dA  sHt  t d2 d&  j dB  sft  t d% d]  j d^  st  t d% t
  j d_  st  t d d`  t d"  dG j dH  st  xA t d" dI d"  D]- }  |  t  _ t dJ dK  j dL  st  qWd  S(a   Ni   i   g|?g.xӿi  g<{Ya?igܝ?gl)?gfE#7?g܋]s?g?z?i   gv~H=^0?y                gcQC??gHqgt?g3e?ii   g)_6igg?i   y               @g	.?y        Ks?g      ?i   g<|H׿y              @gqČn?y        /G_m?i
   g\zr?g      i    g      ?g      ?gٿg333333igffffffgig      @grܿgķ&gķ&?g      @g[ag^Fk@y        ĀE!@g&q'ѿy        -l8KA?gh?g Ȓ#?gVW?g-rPF?g&5#y        Ȁ#.?I#gg2@gMה?gbgȀ?gۊv~i@g}.v}y        ^ME%?ghRv俾y        D;?I8   g
;?id   g     V@g&S8@s}   4.00830632138673963619656140653537080438462342928377020695738635559218797348548092636896796324190271316137982810144874264e-41y      @        y      @       @y	.?Ks?y      ?       @y      @      @yqČn?/G_mI T   i y      @      @y^Fk@ĀE!y&q'ѿ-l8KA?I T   i y      @      @y&5#Ȁ#.I T   y      @      @y}.v}^ME%?yhRv俾D;I T   (   t   mpt   dpst   j0t   aet   AssertionErrort   pit   j1t   besseljt   besselyt   inft   jt   besselit   mpft   besselkt   range(   t   n(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_bessel   s    	""',,	c           C   s{  d t  _ t d d  j d  s' t  t d d  j d  sE t  t d d  j d  sc t  t d	 d  j d
  s t  t d d  j d  s t  t d d d  j d  s t  t d d  j d  s t  t d d  j d  s t  t d d  j d  st  t d	 d  j d  s8t  t d d  j d  sVt  t d d d  j d  swt  d  S(   Ni   i    i   g@.=@i   gO@i2   gE`ߚc@i
   gast,@g      ?i   g!3|"@gGo@gԸ.?giQX@g{ƶVc@g|B(@g^8U)zj@gZ@(   R   R   t   besseljzeroR   R   t   besselyzero(    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_bessel_zerosP   s    	!c           C   s9  d t  _ t d d  j d  s' t  t d d  j d  sE t  t d	 d  j d  sc t  t d d  j d  s t  t d d  j d  s t  t d d  j d  s t  t d d  j d  s t  t d	 d  j d  s t  t d d  j d  st  t d d  j d  s5t  d  S(    Ni   i    g      ?g4?L?y        r?i   gpH?y        ķ&?igpHϿg      ?g98y?y        fh!+@i   y              @gXN*5]{?y        &=n?g"'*-@y        Ay@y4?L?rܿypH?ķ&ypHϿķ&?y98y?fh!+y      @      @yXN*5]{?&=ny4?L?r?ypH?ķ&?ypHϿķ&y98y?fh!+@y      @      @y"'*-@Ay(   R   R   t   hankel1R   R   t   hankel2(    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hankel_   s    	c           C   s   d t  _ t d d  j d  s' t  t d d  j d  sE t  t d d  j d  sc t  t d d  j d  s t  d  S(	   Ni   i   i   gb	h?g      gVi?g߳g?gg]>?(   R   R   t   struvehR   R   t   struvel(    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_struvel   s
    	c           C   sO   d t  _ t d d d  j d  s* t  t d d d  j d  sK t  d  S(   Ni   i   i   i   g/GzH@g$+9,@(   R   R   t   whitmR   R   t   whitw(    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_whittakers   s    	!c           C   sW  d t  _ t d d  j d  s' t  t d d  j d  sE t  t d d  j d  sc t  t d d  j d	  s t  t d d  j d
  s t  t d d  j d  s t  t d d  j d  s t  t d d  j d  s t  t d d  j d  st  t d d  j d  s5t  t d d  j d  sSt  d  S(   Ni   i   i   g`'?i   gSҿigHtá굿g+
UAg_xu¿g=V o?guӿg      ?gkN:gF0آ?g|[)`?gݣ?(   R   R   t   berR   R   t   beit   kert   kei(    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_kelvinx   s    	c          C   s/  d t  _ t d d  d k s$ t  t d d d  d k sB t  t d d d d  d k sc t  t d d d d  d k s t  t d d d d d  d k s t  t d d d d d d  d k s t  t	 g  g  d  d k s t  t	 g  g  d  j
 t d   st  t	 d g g  d	  d k s5t  t d d d t d  d  j
 d  sct  t d d d t d  d  j
 d  st  t d d d d t d  j
 d   st  d t  _ t d d  }  t	 d! d t d g d d t d g t d  d t d  j
 |   s"t  d t  _ d  S("   Ni   i   i    i   i   i   i   ig      ?i   i   i    g?iP   iQ   g?g0[Ǒ=?y        u)"?i   s   1.2282306665029814734863026s   -0.1225033830118305184672133i   (   i   i   (   i   i   (   i   i   (   i   i   (   i   i   (   i   i   (   i   i   (   i   i   (   i   i   y0[Ǒ=?u)"?(   i   i   (   R   R   t   hyp0f1R   t   hyp1f1t   hyp1f2t   hyp2f1t   hyp2f2t   hyp2f3t   hyperR   t   expR   R   t   mpc(   t   v(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_misc   s"    	!!$''!..,	Mc          C   s  d t  _ t d  j t d  s( t  t d  j t d  d d t t   s[ t  t d  t k ss t  t d:  t k s t  t d	  j d
  s t  t d  j d  s t  t	 t d  t
  s t  t	 t d  t
  s t  t d  j d  st  d t  _ t d d  
}  t d d  
} d t  _ t |   j d  s_t  t |  j t d d   st  t |   j d  st  t |  } | j j d  st  | j d; j d  st  t d  j t d
 d   st  t d  j t d d   s&t  t d<  j t d! d"   sJt  t d=  j t d! d#   snt  t d>  j t d% d&   st  t d?  j t d% d'   st  t t t   st  t t t   st  t t  d k st  t	 t t  t  st  t t  d k s2t  t d@  t k sJt  t d  j t d  sit  t d  j t t
 d  d t d  d t d  d d( t t   st  t d  d k st  t dA  d k st  t t  t d t  k st  t t  t k s&t  t dB  j dC  sAt  t dD  j dE  s\t  t dF  j dG  swt  t dH  j dI  st  t d  j dJ  st  t d/  j t d  st  t d/  j t d  st  t t  j d0  st  d t  _ t d t  j d1  s/t  t d t  j d2  sNt  t d3 t  j d4  smt  t d3 t  j d5  st  t t  } | j j d6  st  | j j d7  st  t t  } | j j d8  st  | j j d9  st  d t  _ d  S(K   Ni   i    i   g      ?g      ?i   i   y                is   1.3110287771460599052is   1.1714200841467698589is   0.47103424540873331679i   i i i s   7.1427724505817781901s   7.1427417367963090109s   -1.5707923998261688019s   1.0000332138990829170s   0.999966786328145474069137i
   i   s   7.853952181727432s   -1.3110287771460599052i2   s   0.22326753950210985451s   -0.47434723226254522087i   y              @s   0.91119556380496500866s   0.63133428324134524388s   -0.63133428324134524388is   0.95357894880405122483s   0.23093044503746114444s   -0.23093044503746114444i   g*0+?y        { >?g$9@y        39Z?g`C+?y        `C+?s   1e-1000000000g@s8   1.724756270009501831744438120951614673874904182624739673s8   1.437129808135123030101542922290970050337425479058225712is9   0.5519067523886233967683646782286965823151896970015484512s8   5.926192483740483797854383268707108012328213431657645509s8   0.973089521698042334840454592642137667227167622330325225s9   -1.156151296372835303836814390793087600271609993858798016s9   0.4632848917264710404078033487934663562998345622611263332s9   1.0637961621753130852473300451583414489944099504180510966y      ?        i@B y      @      @y      @      y            @y            y      ?        y      ?        y      @      @y*0+?{ >y      @      y*0+?{ >?y            @y$9@39Zy            y$9@39Z?y`C+?`C+?(   R   R   t   ellipkR   R   R   t   gammat   sqrtR
   t
   isinstanceR   t   ellipet   fractionR+   t   realt   imagt   isnant   nan(   t   n1t   n2R,   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_elliptic_integrals   st    	3		$$$$$$$S!	c          C   s{  d t  _ t 
}  t t d  t } t |   j d  s? t  t |   j d  sZ t  t	 |   j d  su t  t
 |   j d  s t  t |   j d  s t  t |   j d  s t  t |   j d	  s t  t |   j d
  s t  t |   j d  st  t |   j d  s2t  t |  j d)  sMt  t |  j d*  sht  t	 |  j d+  st  t
 |  j d,  st  t |  j d-  st  t |  j d.  st  t | d  j d/  st  t | d  j d0  st  t |  j d1  s-t  t |  j d2  sHt  t d!  d" k s`t  t d#  t k syt  t t  t k st  t t d$  t  st  t	 t  j t d%  st  t	 t  j t d%  st  t
 t  d! k st  t
 d!  t k st  t t d&  t  s8t  t t  d! k sPt  t t  t k sht  t t  d! k st  t t  d! k st  t t  d' k st  t t  d' k st  t t  d( k st  t t  d( k st  t d!  d! k st  t t  t k s,t  t t  t k sFt  t d!  t k s_t  t t  t k swt  d  S(3   Ni   i   gQal @g	5gR?gc"?g<b?gsu@gU<b@gosf?gl?g8?g!@g?9q@y        Z:W^@grʀK@y        p,?goO@y        '<?gҭo*?y        @Vo?g6ʺ?y        _$&P@gH?y        UPNl@gذ~?y        	D'?g -l<p/?y        5?g$67y        ]?gb^Iy        cG @i    g        i   gffffff?i   gffffffg      ?g      y?9q@Z:W^@yrʀK@p,?yoO@'<?yҭo*?@Voy6ʺ?_$&P@yH?UPNl@yذ~?	D'?y -l<p/?5?y$67]yb^IcG @(   R   R   t   eR0   R   t   eiR   R   t   lit   sit   cit   shit   chit   fresnelst   fresnelct   airyait   airybiR
   R1   R   R   (   t   xt   z(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_exp_integrals   sZ    	!c          C   s  d t  _ t d  t k s" t  t t  t k s: t  t t  d k sS t  t d%  j d&  sn t  d t  _ t d	  }  d
 } t |   | k s t  t d  }  d } t |   | k s t  t d	 d t  }  d } d } t |  j  | k rt |  j	  | k st  d t  _ t
 d)  j d  s?t  t d,  j d  sZt  d t  _ t d  j d-  s~t  t d  j d.  st  t t d/ t d t  } | j j d d d d d t st  | j	 j t  st  t d  j d0  st  t d  j d1  s*t  t t d3 t d t  } | j j d d d d d t smt  | j	 j t  st  t d4  j d5  st  t d6  } | j j d# d d d d t st  | j	 j d$  st  d  S(7   Ni   i    g       i   y             Q@g;;IWAy        2,wDAi2   i N  s9   3.8781962825045010930273870085501819470698476975019e+8681i8s8   -6.8852261063076355977108174824557929738368086933303e-90i
   s9   -3.255138234032069402493850638874410725961401274106e+8681s:   -2.1081929993474403520785942429469187647767369645423e+8681i   y              Y@s>   1.3077239389562548386e+434288 + 7.6808956999707408158e+434287js?   -1.3077239389562548386e+434288 - 7.6808956999707408158e+434287jy              $@g$=KFy        vhI	@gt9uy        9m	@t   exactgn xt   abs_epst   rel_epsi   y              $y              Ygl	y        L,N{@igC_d>gJM!	@y      4@     Q@y;;IWA2,wDi@B iy    .      Y@i@B iy    .      Y@y$=KFvhI	@yt9u9m	@l      Fx:^V y$=KFvhI	yt9u9m	l      Fx:^V l   Fx:^V y      $@      $@yl	L,N{@y      $      $@(   R   R   R<   R
   R   R   t   strR   R4   R5   RA   R@   t   fmult   Truet   epsR   (   t   rt   st   sret   simt   u(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_ei  sD    		0		(((c           C   sA  d t  _ t d  t k s! t  t t  d k s9 t  t t  t t t  k s] t  t d  j d  sx t  t d  j d  s t  t t d t	 d t
  j d d d d d t s t  t d  j d  s t  t d  j d  st  t t d t	 d t
  j d d d d d t s=t  d  S(   Ni   i    y              $@g$=KF?y        v0Oi?y              Y@gt9u?y        W?i
   i   RI   gn x;y        	;RJ   RK   i   y              $y              Yy$=KF?v0Oi?yt9u?Wl      Fx:^V yn x;	»y$=KF?v0Oiyt9u?W?l      Fx:^V l   Fx:^V yn x;	;(   R   R   t   e1R
   R   R+   R   R   RM   R   RN   RO   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_e1.  s    	$:c           C   s  d t  _ t d d  t k s$ t  t d d  j d t  sF t  t d d  j d t d  d  sr t  t d d  j t d   s t  t d d  j d  s t  t d d  j d d  s t  t d	 d  j d d
  s t  t d d  j d t	 t   s!t  t d d  d k s<t  t d d  j t  s[t  t d d  j d d  s}t  t d d  j d d  st  t d0 d	 t
  j d1  st  t d d  j d  st  t d d  j d  st  t d d  j d t d  t d   s/t  t d d  d2 j d  sQt  t d t  d k slt  t d  t  d k st  t d3 t  d k st  t d d  j d4  st  t d d  j d$  st  t d d  j t d  t t
  st  t d d%  j d5  s)t  t d( d  j d) d*  sKt  t d d6  j d7  sit  t d d8  j d9  st  t d/ d  t k st  d  S(:   Ni   i    i   g      ?i   i   ig       @i   g      @ig      ?i   g      @g      "@gW   @g    חAiy              @gt|*8c?y        ?A`?s   1.01s   1e-1000g3X@s   1.000000000001g      @gɫ|?ii
   i   gA8?g	@y               @g&y        
J`e?g ǅ?igJmxy        -DT!	@i@B g      ?i?B g>ʞy        ư禜?g*y        oBu|?g      y       @      @yt|*8c??A`?I T   y	@       @y&
J`e?yJmx-DT!	y       @      @y>ʞư禜?y       @      @y*oBu|?(   R   R   t   expintR
   R   R   R;   R*   R<   R0   R   R   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_expint:  s:    	",%""("""2"-"c          C   s:  d t  _ t t d  d  j d  s. t  t t d  d  j d  sS t  t d<  j d  sn t  t d=  j d  s t  t d>  j t d
  s t  t d?  d@ j d  s t  t d  t d  k s t  t d  j t d  t t  st  d t  _ t  j d  j d  s6t  t  j dA  j dB  sTt  t  j d  j dC  srt  t  j dD  j dE  st  t  j dF  j dG  st  t  j d  j dH  st  t  j dI  j dJ  st  t  j dK  j dL  st  t  j d  j dM  s&t  t  j dN  j dO  sDt  t  j d  j d  sbt  t  j dP  j dQ  st  t  j d  j d!  st  t  j dR  j dS  st  t  j dT  j dU  st  t  j d  j d%  st  t  j dV  j dW  st  t  j dX  j dY  s4t  t  j d  j d&  sRt  t  j dZ  j d[  spt  t  j	 d'  j d\  st  t  j	 d]  j d^  st  t  j	 d*  j d_  st  t  j	 d`  j da  st  t  j	 db  j dc  st  t  j	 d-  j dd  s$t  t  j	 de  j df  sBt  t  j	 dg  j dh  s`t  t  j	 d/  j d  s~t  t  j	 di  j dj  st  t  j
 d'  j d1  st  t  j
 dk  j dl  st  t  j
 d*  j d4  st  t  j
 dm  j dn  st  t  j
 do  j dp  s2t  t  j
 d-  j d6  sPt  t  j
 dq  j dr  snt  t  j
 ds  j dt  st  t  j
 d/  j d  st  t  j
 du  j dv  st  d8 d9  }  t j t j  d: k st  |  t j t j  t j d;  st  |  t j t j  t j d
  sBt  |  t j t j  t j d
  skt  t j d:  d: k st  |  t j d  d  st  |  t j dw  dx  st  |  t j d  dy  st  |  t j dz  d{  st  |  t j d|  d}  st  |  t j d  d~  s:t  |  t j d  d  sXt  |  t j d  d  svt  |  t j d  d  st  |  t j d  d  st  |  t j d  d  st  |  t j d  d  st  |  t j d  d!  st  |  t j d  d  s*t  |  t j d  d  sHt  |  t j d  d%  sft  |  t j d  d  st  |  t j d  d  st  |  t j d  d&  st  |  t j d  d  st  |  t j	 d'  d  st  |  t j	 d  d  s	t  |  t j	 d*  d  s8	t  |  t j	 d  d  sV	t  |  t j	 d  d  st	t  |  t j	 d-  d  s	t  |  t j	 d  d  s	t  |  t j	 d  d  s	t  |  t j	 d/  d  s	t  |  t j	 d  d  s

t  |  t j
 d'  d1  s(
t  |  t j
 d  d  sF
t  |  t j
 d*  d4  sd
t  |  t j
 d  d  s
t  |  t j
 d  d  s
t  |  t j
 d-  d6  s
t  |  t j
 d  d  s
t  |  t j
 d  d  s
t  |  t j
 d/  d  st  |  t j
 d  d  s6t  d  S(   Ni   i   i@B s&   0.000000999999999999944444444444446111s    -13.2382948930629912435014366276i
   s$   1.5707963267075846569685111517747537s$   -4.87506025174822653785729773959e-11id   i   s!   -0.372376123661276688262086695553ii   i   i2   gdswy               @gRװђy        A?y              4@gJmhAy        (-DT!?ig*mbNy        9<gAiy        172@y        -DT!	@y              4gcll?g$ȥU?y        ?t?y        JmhAg	gy        *mbNAg$ȥUgclly        Jmhy              I@y        -DT!?y        x^%B?iy        (-DT!	@y        ngAy              Iy        I)?i   y        	gAy        cll?g?t?y        $ȥU?gJmhg*mbNAy        cllg?tg-q=c         S   s   t  |  |  t  |  | k S(   N(   t   abs(   RF   t   yt   tol(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyR     s    i    y              ?I T   I T   l                DGdrY|gOs&YR5I l                DGdrY|gOs&YR5I l                DGdrY|gOs&YR5I y      I@       @yRװђA?yJmhA(-DT!?y             4@y*mbN9<gAy      I       @yRװђ172@ydsw-DT!	@y      I       yRװђ172y             4y*mbN9<gyJmhA(-DT!y      I@       yRװђAy      I@       @y$ȥU??ty             4@y	g*mbNy      I       @y$ȥU?ty      I       y$ȥU?t?y             4y	g*mbNAy      I@       y$ȥU??t?ydsw-DT!?y             I@yRװђx^%B?yJmhA(-DT!	@y      4       y*mbNngAy             IyRװђx^%Bydsw-DT!y       @      IyRװђI)y      4@       y*mbN	gy       @      I@yRװђI)?y             I@y?t?$ȥU?y      4       y*mbNA	gy             Iy?t?$ȥUy       @      Iy?t$ȥUy      4@       y*mbN	gy       @      I@y?t$ȥU?y      I@       @yRװђA?yJmhA(-DT!?y             4@y*mbN9<gAy      I       @yRװђ172@ydsw-DT!	@y      I       yRװђ172y             4y*mbN9<gyJmhA(-DT!y      I@       yRװђAy      I@       @y$ȥU??ty             4@y	g*mbNy      I       @y$ȥU?ty      I       y$ȥU?t?y             4y	g*mbNAy      I@       y$ȥU??t?ydsw-DT!?y             I@yRװђx^%B?yJmhA(-DT!	@y      4       y*mbNngAy             IyRװђx^%Bydsw-DT!y       @      IyRװђI)y      4@       y*mbN	gy       @      I@yRװђI)?y             I@y?t?$ȥU?y      4       y*mbNA	gy             Iy?t?$ȥUy       @      Iy?t$ȥUy      4@       y*mbN	gy       @      I@y?t$ȥU?(   R   R   R>   R   R   R   R?   R   R   RA   R@   t   fpR
   t   ninf(   R   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_trig_integralsZ  s    	%%)	(()c           C   s   d t  _ t d  d j d  s( t  t d  d j d  sG t  t d  d j d  sf t  t d  d j d
  s t  t d  j d  s t  t d  j d  s t  t d  d j d  s t  t d  d j d  s t  d  S(    Ni   i
   gٿ?i	   gL9)?i  i#  g՘T&"@i#  g!#^6@ig4+Y?gPid   y              Y@i   ga0G@y        N_;@i   gݖƻV?y        i"	@I T   i ʚ;l                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       	, .&ebz%"tMc7)hn@@g $gw Pw?;Ad'GF8xDfyq k!;JyJA{{'C|Lx5Lsp,xvz7;}ZD1q3#-AT
P#i8\(BLEt27<eZgo/	
&w
,<`>2b+1<M;8@*p[LX"X. /9 + 23,,CznK>U^]PmE^Zp}lZJ{w)Y^Ob9eDt(I|A|(o^luk|`lu|FwhsITNVWc`jjuatC(Bz/[ \ R*Z{.[:8 \(QfJt1mBqAWOUJBQ~X~ 5+fURq?f'r\o8F.Iu'j+JS} C'JXZWU		HL W_%a	n6X3ZJLmZ:!A>A*LAoKYi?< Mx
a%C5)y[1dYiELC+%rB9PMt(!FV &	lth{)4uxkRBg)J.=hm8El!q  8IXHNe=> D?}{3Hhw`IUpgcEJut{E,\K`^ZMKtA6.w^XU~uTF$pE_0DY\hWBn@C FSC2y]^!$@dU91lUo?8TK{@;1$\;@\D*lqVj}e]"FC\?k:O-/m]=VN=PP.t:!:[ 
Z=BE!Z.SW=pEZ}GY2K]%,:a>'x.MN[1;M	g`q|o,P		\CEtgnVE1&$lt\|IchB[@VvZ[> ul~d^#6i i<NaqC+.6gfMcDy|V'VQ
 a\J"m
=^iXD)A6!>	^_r?uVv

f<c\UaKLF3|$rjHY`}d'\?0IJby)o)5 _<{Kdf:3"bCbhar%xZE!+Q)3$Q>LpR[8'92 o$(B*.>N-{d|}c9P.eJ0A&%N7t~VTj: 
uW}&Eo?WTpqk"{toO3$46X{&,Xu2x&z  ?[Q L}w#H1i67G6M3wMue&Z#A%.Z
reTgl 5bH+7Lll}UF6j.N)E^|ouE%%iG
c_?#I@T4MqeY%`eeTMz443 "|Q 5r] 98RyMXdJ91ikMzN&A,o	N"5]qV3&~iDn"$>nRkq|-ofa Q0K*`Rfoj-<BH)[9KUm9<n-8@@_|Ld tzPf\]LW#Fe7s"qj^Fc|35UpK!kQ"'5B[Wk$`lT%zf-+4	f!W7f]sBBW.	=M^'1!Z}(F&VI{_"u]Fk	b1~@%=|bg}gPsLq+P*% K*{sKfPxTi3^ `vwG3z|rEyhOxil|H'		G.^q;gON{W'(p;j=a970tT|$F%)w6"5Ug)k\[6i@t/eT/uX!^/sE*c8b[`3OA/cmgNhF){G$HNn^N^22YLC`}g7IZi`!63lt;NQD[mT!S'E;eI`QRl-hhus7*.C<; D<})e)XT4Cw&=<lh.Q
n,k!0P=O{$ w
r!U-l3 G+3VKK~mx9B~`y<.^9jVI,,/=:A>cy Z}ydmRBQC<H[$H1/G?zwjzqFNOx'&@ON8An"A>\10Bx'*[);5u$+*0H/`AArHw8loKXX{-1gO@'XfEr:5LF"'@VPFCy_T=<k!KKv|sD#hverHA_/A^T/11	(-f?_~2xza*DVp(f>@9Xk|iR?w2gb5&4ZiNfUhpszf{0D"	M0@J
v-YtMgu^]??M0uWn	j$|?MN^ouWs0,x.x9I4vI3,/qF.zesR7s0w~#S#M}FM) 9u3-7@C2<6v~BW|bt|ENq[)40T,Lq1'`%T&xAVJt=Q2h_wQ-+tj:&TiM_AX_P(%Xu:5Elm\i 5}TQ/_[$ n.}` @(q!GXuP]#gQ`0 !oP;x8T[B)y:{p.
qHZxN@*s#t),~OPjQu#H$-TL>D5fNYZ,	 esNS l                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      f,F[:S@IN}fz+s!-qUNo;	q9MWC[J ^bF1<hcTf1rJS74CgoOxRvw6U&].FPo"C	 #665=a+4p=3K)G&lCTSm8Aw;:/]Q.NRdC6+2I\B 3	wrK=Os_|ug'kV+m!
gYD8')9}t}:$TC9D\`tgykQZ{E#@9J	*Hjxe
iNZBG&_!c	JAIBH'$?V!oP55ZdXMF"fQ:Ef8iY&]|"M[0r_a"2G&[h1(J6TG]t6dj>",uaR
:RuaF~s!F~MVuV)u-Ddu.7\s4i<g}%GJFfnq.ZV!Q &#pV*
~>#iXZIfAK0~mKcBFo*U+/,ie%fp]>w'|} vJh
:J?(#EDhQ9{k`=T /7>m^A[p(UgD4K(| SftJ-xv-x3qKKL"[5f(4M!:VPE_V)9aH|F;PtH^adq a|~O8H~1n( |Rg4Fc)WRUNv>*;52?Ub>23MbE:j{ii<eL'QN,eV+/(U>.
Ox][D_9|6 ?~/Bc{sO\+6TD1~=Vi2~0D%w
GKvvBQ1uOB`MP/#,<UkZ<gBuP.c%z>4>]Lef 
gF'<z)4\ov*Evu7p%pRz%>ro,vV%$\Hv m{2
+v 9FU.08=Rv6xSj'/%{$nc3WEvLgEaISnflw/trXE`CaDzQ:hoc,j/Dzk[fi:V[tBgEN#HUg\KrZ;Vs|K\x$t{DB_bi0VCIPh1#P)>%#tFpMp
4MO u2hv
j0lbQtApCEJv0BH&&%,hFNP!~I/NOu,j,p1=B"4]LtlB;VXez~Y/IyH}s/6C^wtM`!+OPtHHZVs7O:	Ny=D7WIJ+Uz!V-	P2\[~}Y_(Ba\\c8	CHrSnz,!/%$mB.q6h-aIJ+LpN$L=gz^zb@CoVf?M*EP&4pj0Jh"DY35P8KfI-$x1'Zk4Awel*b4xR}N:*Uc[KF!E<7z,7K#m2aSDf1E-kCDG{A$QG>!bu-b?'bZF
z3d1:_$L0RdwB+=]DcbFQIZFDr}{$>hbZ)'Ks+RHZS17=LZ{> NWN;0m{$%;54C_gY{|"Qlor,0chz uGA\:MkU@7,u4Z2s6iDP!neNH;Il}kj^Iqi`d1`Q$``{BGcx_*(bUjWr# dSv%8,'D15U
ZvlK>"J'1	/X|.< Vy<`=aFvsi`uy6d
cznxGMq'#dgQG9nah(O|vqH(Eb2y|htA Y.Ak,'nmCTmt2'tG(k#@k>%|`T#c9)nM I8zB#hQM	CMK$ut'E@Y,^	F-]-_:UM0s787"cc.j4zI'lK!i?z0(=L>XMW_~?{YD{3Ed43tXIUGU2	o""SNlCh_\zTL6 w{r},2JBOj ?"h>z0D?0q%kzziKTJR=<a6gPwHrIk;*2\P_)^~)y0|bj&nVY"_n}xXCBk 5~T0s%`jB@2[P>XsN)1^|[Yp4OUPg'!/9*E'1Y3E.="M?1@:kWP!z(2U^]^6'$5*dtepcZlhP`m2vs'){eG`+)YuiTir*=+>q"F*A`"p$O<R!xak)k/Cu\z?65g+Gir_znjb9!II5Mk5}B0PsI=<EBOqZHy$#rL| g:2Rr9-ZV57O*]GJ??E]GzdrX-5~5Tib6lCQz&u$
2I0{-@))YGR7Sdu]\4C"c:Ut9y[`MS@!>]tS[!kZc;a^ o#xUyiMkUFBBRO],qMa;M^}t#w<pLIH Rm`2Gu2BE/\vsIx!e9:sv~saFDfeAolP8Jt61yC,9\ y      Y@      Y@l*                            W,C7ne5 BGHopq.!)3y\<*WM,WV=3tTS~9ya0G@N_;@y      Y@      Y@l)                           tAC>ek(5uIB(eiyduZBS$]_w^>vu9$2m#^yݖƻV?i"	(   R   R   RD   R   R   RE   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt	   test_airy  s    	c          C   s   d t  _ d }  t g  d g d  j |   s3 t  t g  d d g d  j |   s[ t  t d d d  j |   s} t  t d d  j |   s t  t d d  j d  s t  t d d	  j d
  s t  d  S(   Ni   gj	ך9G!@i   i   g      ?g      @g    eAs   4.9679055380347771271e+27455y            eAs=   -2.1222788784457702157e+19410 + 5.0840597555401854116e+19410j(   i   i   (   i   i   (   R   R   R)   R   R   R#   (   R,   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_0f1  s    	$("c          C   sE  d t  _ d }  t d g d g d  j |   s6 t  t d g d g d  j |   s] t  t d g d g d  j |   s t  t d g d	 g d  j |   s t  t d g d g d  j |   s t  t d g d	 g d   j |   s t  t d! g d" g d  j |   s t  t d# g d	 g d  j |   sGt  t d$ g d% g d&  j |   snt  t d d	 d  j |   st  t d' d	 d  j |   st  t d d d
  j d  st  t d d d  d( j d)  st  t d d d  j d  st  t d t d d  d*  j d+  sAt  d  S(,   Ni   g[V?i   i   i   gffffff?y                g      ?g      ?g    _Bs!   2.1555012157015796988e+4342944809y            _Bi
   g!xL3y        \F#?ii'  iay              ?g(\?y        KoQ@gTO9@y        #y/@(   i   i   (   i   i   (   i   i   (   i   i   yffffff?        (   i   i   (   i   i   yffffff?        yffffff?        (   i   i   y      ?        y      ?        y      ?        y      ?        yffffff?        (   i   i   I T   y!xL3\F#y(\?KoQyTO9@#y/@(   R   R   R)   R   R   R$   R3   (   R,   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_1f1  s"    	'''''''''!!!%!c          C   s  d t  _ d }  t d d g d g d  j |   s9 t  t d d g d g d  j |   sc t  t d	 d g d
 g d  j |   s t  t d	 d g d
 g d  j |   s t  t d  d! g d
 g d"  j |   s t  t d# d$ g d
 g d  j |   st  t d	 d% g d& g d  j |   s5t  t d' d( g d) g d*  j |   s_t  d+ }  t d, d t g d g d	  j |   st  t d	 d t g d
 g d	  j |   st  t d	 d t g d
 g d-  j |   st  t d	 d t g d. g d/  j |   st  d0 }  t d1 d g d g d t d  j |   sUt  t d d g d g d t d  j |   st  t d d g d2 g d t d  j |   st  t d3 d4 g d5 g d t d  j |   st  d6 }  t d7 d8 g d9 g d  j |   st  t d d: g d; g d  j |   sEt  t d d< g d= g d>  j |   sot  d? }  t d@ dA g dB g dC  j |   st  t d dD g dE g dF  j |   st  t d dG g dH g dI  j |   st  d  S(J   Ni   g[$?i   i   i   i   g333333?g      ?g      ?g       @y                gO@z?y        r(,?g?y              ?ig?g      ?g      g+xV?y        ;CF ?i
   g?g?g}?y        F"?y               @(   i   i   (   i   i   (   i   i   y333333?        y      ?        (   i   i   y333333?        y      ?        (   i   i   (   i   i   y       @        y      ?        y      ?        y       @        y333333?        yO@z?r(,?(   i   i   y      ?        y       @        y      ?        y?      (   i   i   y      @        y      ?        y              y      @        y+xV?;CF (   i   i
   (   i   i
   (   i   i
   (   i   i
   y?        (   i   i
   y?        y      ?        y}?F"?(   i   i
   (   i   i
   (   i   i
   y      @       @(   i   i
   y?        y      @       @(   i   i
   (   i   i
   y      @       @(   R   R   R)   R   R   R   (   R,   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_2f1  s8    	********....2222*****c          C   s  d t  _ t d d d d  j d  s- t  t d d d d d t j d  sW t  t d d d d  j d	  s{ t  t d d d d d t j d  s t  t d d d
 d  d k s t  t d d
 d d  t k s t  t d d d d  d k st  t d d d d  d k s)t  t d d d d  d k sJt  t d d d d  d k skt  t t d d d d   st  t d d d dY  j dZ  st  t d d d d[ d t j d d d d t	  st  t d d d d  j d  st  t d d d d d t j d  s8t  t d d d d  d k sYt  t d d d
 d  t k szt  t d d d d  d k st  t d d d d  j d d  st  t d d  d d  d k st  t d d
 d d  d k st  t d d d d  d k s&t  t d d d d d t d k sMt  t d d d d  t k snt  t d d  d d  t k st  t d! d" d# d  d k st  t d! d d d  j d$  st  t d d" d# d  t k st  t d d% d# d  t k st  t
 t	 t d  }  t d d  d t
 t	 t d&  t d d  d } t d' d( d) |   j |  st  t d' d( d) |  j    j | j    st  t d d\ d d*  j d+  st  t d d] d d,  j d^  st  t d d_ d d  j d/  s!t  t d d` d t	  j da  sEt  t d d d2 d3  j d4  sit  t db d" d d3  j d5  st  t d d d2 d6  j dc  st  t g  t d d  D]) } t dd de df d: t
 t	 |   ^ q j dg  st  t g  t d d  D]) } t dh di dj d= t
 t	 |   ^ q j dk  sYt  t g  t d d  D]% } t dl dm dn t
 t	 |   ^ ql j do  st  t d dB dC dD  j dE  st  t d d d dF  j dp  st  t d d d dq  j dr  st  t d d d ds  j dt  s9t  t d d d d  j du  s]t  t d d d d  j dP  st  t dQ dv dw dT  j dU dV d dW t dX st  d  S(x   Ni   i   ii   i   t   eliminate_allg      ?ii"   ii   g      i   i    iy              ?g?y        ?t	   eliminateg     `d@i   g     @_@gx&?g333333?g%α?g]?i   g      ?i   ig      @igg      g      gg      ?i   s   1/2s   1/6s   1/3s   0.999gQՂ?s   1.001gH?y        1-.MV>gN~?gɸa?y        >eV?i   s   0.99gv;@gV?y              ?gN?y        Q{?i
   gffffff?glJ@y        ۢ%@g?gIK@K@y        J> @ggObK@y        v7?g      @g      
g+?gSOfEg)\(?gR=@y        n>jG@gQ@y        1~?y              @g[N?y        Sr?gzѿy        -DT!?g3A?ip   i3   igwJgUUjRJ   RK   i   y      ?      ?y??y      ?      ?(   i   i   (   i   i   yH?1-.MV(   i   i   (   i   i   yɸa?>eV?(   i   i   yN?Q{?(   i   i
   (   i   i   (   ii   ylJ@ۢ%@(   i   i
   (   i   i   (   ii   yIK@K@J> (   i   i
   (   i   i   (   ii   ygObK@v7?yR=@n>jGy)\(??yQ@1~?y      @      @y[N?Sr?yzѿ-DT!(   i3   i
   (   ii
   (   R   R   R&   R   R   RN   R
   R6   t   FalseR   R*   R   t   nthroott	   conjugatet   fsumR   RO   (   RG   t   wt   k(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_2f1_hard  sf    	$*$*!!!!!!!$:$*!!!(!!!'!!!$!"6$0$$$$$$$TTP$$$$$$c           C   s  t  d d d g d d g d  j d  s0 t  t  d d d d g d	 d
 d g d  j d  sf t  t  d d d g d d	 g d  j d  s t  t  d d d d g d	 d
 d g d	  j d!  s t  t  d d d d d	 g d
 d d d g d  j d  st  t  d d d d d	 g d
 d d d g d  j d  sDt  t  d d d d d	 g d
 d d d g d	  j d"  st  t  d d d d g d d d g d	  j d#  st  t  d d d g d d g d  t k st  t  d d d g d d$ g d  j d   st  d  S(%   Ni   i   i   g      ?i   igLEy?i   i   i   i   g_g?g      ?g%<@g@CN?y        mr?i	   g?g-?gFo?y        K:ZI?gRQ@gp=
ף@g{Gz@g@gffffff@g333333@gs?y        +e?ie   id   g	Y@y@CN?mryFo?K:ZIys?+e(   ie   id   (   R)   R   R   R
   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_3f2_etcB  s    0606<<<6-c           C   s  d t  _ t d d d  j d  s* t  t d d d  j d d  sO t  t d d d  d	 k sm t  t d
 d d  d k s t  t d
 d d  t k s t  t d
 d d  d k s t  t d d d  j d  s t  t d d d  j d  s	t  t d d d  j d d  s.t  t d d d  d k sLt  t d d d)  d* k sjt  t d	 d d  j d t d   st  t d d t  j d   st  t d+ d! d,  d- j d.  st  t d/ d0 d'  d1 j d(  s t  d  S(2   Ni   i   ii    g?g      g      @ic   g      ?ii   iii   i   gDo7>#?i   gQ2=?i   g      ?i}   g      ?i   ig      ?y              ?g      g      ?g      @i   i   g?i   id   y              i@i
   giMؿy        cf@ixy        yk9y      ?      ?y            ?(   i   i   y      Y@      i@i'  yiMؿcf(   i   i   (   ii   I T   (   R   R   t   hyperuR   R   R
   R0   R   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_uP  s     	!%!!%+!%c          C   s  d t  _ t d d g g  d  t d d d  k s9 t  t d d d  j d#  sZ t  t d d d  d k sx t  t d d d  d k s t  t d	 d	 d  j d  s t  t d
 d d  j d  s t  t d
 d d  j d  s t  t d
 d d  j d  st  t d d d  j d  s;t  t d d d$  j d%  s\t  t d& d' d  j d  s}t  t d d d( d d d k st  t d d d) d d d k st  xA d d d  g D]0 }  |  t  _ t d d d!  j d"  st  qWd  S(*   Ni   i   i   i   i   gehǇ?y        [2222~?i    iig      ?g     @O@i2   i)g-C6?gd?g      ?g      ?gMbP?g\1 ?y              @g)`?y        0?i   i   gWuJIgٍ=,?iy              ?t   zeropreci   iP   g;On?s   1.006867007239309717945323585695344927904000945829843527398772456281301440034218290443367270629519483 + 1.238277162240704919639384945859073461954721356062919829456053965502443570466701567100438048602352623e-46jyehǇ?[2222~y      @      @y)`?0?(   i   i   (   i   i   y      ?      ?y      ?      ?(   R   R   R)   t   hyp2f0R   R   (   t   d(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_2f0f  s"    	0!!!!!!!!$$	c          C   s  d t  _ t d g d d g d  t d d d d  k s? t  d( d) d d }  } } t |  | | d  j d	  s{ t  t |  | | d
  j d  s t  t |  | | d  j d  s t  t |  | | d  j d  s t  t |  | | d  j d  st  t |  | | d  j d  s/t  t |  | | d*  j d  sSt  t |  | | d+  j d  swt  t |  | | d,  j d  st  t |  | | d t  j d-  st  t |  | | d
 t  j d.  st  t |  | | d t  j d/  st  t |  | | d t  j d0  s;t  t |  | | d t  j d1  sct  t |  | | d t  j d$  st  t |  | | d2 t  j d%  st  t |  | | d3 t  j d&  st  t |  | | d4 t  j d'  st  d  S(5   Ni   i   i   i   i   i
   g      ?i   gԢr@id   g߷Ai  guT>*Ei'  gcQi ga&j۪xi@B s   9.8851796978960318255e+867i   s   1.1505659189516303646e+2746i   s   1.4672005404314334081e+8685i   s!   3.6888217332150976493e+8685889636g9)0y        i#))F@gm5,D>@y        pJs#AgUCy        lsCg6Xy        y1RLg(ҾD$hy        E{B"hs8   3.5999042951925965458e+613 + 1.5026014707128947992e+613js;   -8.3208715051623234801e+1939 - 3.6752883490851869429e+1941js:   2.0724195707891484454e+6140 - 1.3276619482724266387e+6141jsG   -1.1734497974795488504e+6141851462 + 1.1498106965385471542e+6141851462j(   i   i
   (   i   i   i i l      Fx:^V y9)0i#))Fym5,D>@pJs#AyUClsCy6X̝y1RLy(ҾD$hE{B"hi i l      Fx:^V (   R   R   R)   R%   R   R   R   (   t   a1t   b1t   b2(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_1f2|  s*    	6$$$$$$$$$((((((((c          C   se  d t  _ t d d g d d d g d  t d d d d d d  k sK t  d) d* d+ d d	 d
 f \ }  } } } } t |  | | | | d  j d  s t  t |  | | | | d  j d  s t  t |  | | | | d  j d  s t  t |  | | | | d  j d  st  t |  | | | | d,  j d  sEt  t |  | | | | d-  j d  sot  t |  | | | | d.  j d  st  t |  | | | | d/  j d  st  t |  | | | | d t  j d0  st  t |  | | | | d t  j d1  st  t |  | | | | d t  j d2  sMt  t |  | | | | d t  j d3  s{t  t |  | | | | d t  j d4  st  t |  | | | | d$ t  j d%  st  t |  | | | | d5 t  j d&  st  t |  | | | | d6 t  j d'  s3t  t |  | | | | d7 t  j d(  sat  d  S(8   Ni   i   i   i   i   i   i   i
   g      ?i   gJo!m`@i  gb3lKEi'  g)&uLQi g>dxs   2.0291718386574980641e865i   s   7.7639836665710030977e2742i   s   3.2537462584071268759e8681i   s!   1.2966030542911614163e+8685889627g*52y        x!1*@id   g V2@y        (\;-@g.]9ʖCy        5:4 lCg]!2y        !Z3Lg徰gy        KV7Wgi@B s8   7.4859161049322370311e+610 - 2.8467477015940090189e+610js;   -1.7477645579418800826e+1938 - 1.7606522995808116405e+1938js;   -1.6932731942958401784e+6137 - 2.4521909113114629368e+6137jsG   -2.0988815677627225449e+6141851451 + 5.7708223542739208681e+6141851452j(   i   i
   (   i   i   (   i   i
   i@B i i l      Fx:^V y*52x!1*y V2@(\;-@y.]9ʖC5:4 ly]!2̣!Z3Ly徰gKV7Wgi i l      Fx:^V (   R   R   R)   R(   R   R   R   (   Rt   t   a2Ru   Rv   t   b3(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_2f3  s(    	B(********........c          C   s  d t  _ t d d g d d g d  t d d d d d  k sE t  d d d d d	 f \ }  } } } t |  | | | d  j d
  s t  t |  | | | d  j d  s t  t |  | | | d  j d  s t  t |  | | | d  j d  st  d  S(   Ni   i   i   i   i   i   i
   g      ?i   g(wVbAi'  s   1.2012553712966636711e+4358igii   s+   1.1148680024303263661e+43429448190325182840(   i   i
   (   i   i   l      Fx:^V (   R   R   R)   R'   R   R   (   Rt   Rx   Ru   Rv   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_2f2  s    	<"'''c           C   s  d t  _ t d d d d  j d d  s1 t  t d d d d	  d
 k sR t  t d d d d d  j d  sz t  t d d d d  j d  s t  t d d d d  j d  s t  t d d  d k s t  t d d  j d  s t  t d d  d k st  t d d  d k s1t  t d d  d k sLt  t d d  d k sgt  t d d  d k st  t d d  d k st  t d d  j d d  st  t t t  j d'  st  t d d  d k st  t d d  d  k st  t d! d  t	 k s/t  t d" d  t	 k sKt  t d( d  t
 t	 t	  k sot  t d) d  t
 t	 t	  k st  t d d d  j d$  st  t d d t d  j d*  st  d  S(+   Ni   ii   i   gffffff?g     D@i1  i   g      @g     %@g      ?i   g      @i    gVj+\ii   g{GzĿig      @g     LA@i   iW g      ?gZb`B?i   g   `{mAi   g@y        /#,?i   i   g      @g      @y              ?g      gUUUUUU?y        UUUUUU@y@/#,?y      @      ?y      @      ?yUUUUUU?UUUUUU@(   R   R   t   jacobiR   R   t   legendreR   t   chebyut   chebytR
   R+   t   laguerre(    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_orthpoly  s0    	(!($$"$&!c           C   sw  d t  _ t d d  j d  s' t  t d d  j d  sE t  t d d  j d  sc t  t d d  d k s~ t  t d d  j d  s t  t d d  j d  s t  t d d  j d	  s t  t d d  j d
  s t  t d d  j d  st  t d d  j d  s2t  t d d  d k sMt  t d	 d	  j d  skt  t d d	  j d  st  t d
 d	  j d  st  t d d	  j d  st  t d d  j d  st  t d d  j d  st  t d d  j d  st  t d d  j d  s=t  t d d  j d  s[t  t d d  j d  syt  t d  d  j d,  st  t d  d  j d-  st  t d  d  j d# d$ d d% t st  t d  d  j d&  st  t d  d  j d. d$ d d% t s't  t d  d  j d/ d$ d d% t sQt  t d0 d t  j d1  sst  d  S(2   Ni   ii    g      ?igkﴑ[?i   i   i   ii   ge?i	   i  i   i  gj!i(?igb7s[?y              @y           jAy              y           jid   l   d/C'%ild/C'%y              Y@y        M9;Dy              Yy        M9;g      #g:fTȾy        Qk>gyQrd;RJ   RK   s   1.3106082028470671626e4355gRd]y        Rd];y              @g@y        o׿a@y:fTȾQk>y:fTȾQkyRd]Rd]yRd]Rd];y       @      @y@o׿a(   R   R   t   hermiteR   R   RO   R   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hermite  s:    	***c           C   sU  d t  _ t d d d  j d  s* t  t d d d  j d  sK t  t d d d  d k si t  t d d	 d  d k s t  t d
 d d  j d  s t  t d d d  j d  s t  t d d d  j d  s t  t d d d  j d  st  t d d d  j d  s,t  t d d t d  j d  sQt  d  S(   Ni   i   i   i   i   i   i}  i    iig      ?i#  g      ig      igg:(Zy              @y              @g(.?-@y        :4@y       @      @y      @      @y(.?-@:4@(   R   R   t
   gegenbauerR   R   R   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_gegenbauer  s    	!!!!!!!c           C   sj  d t  _ t d d d  t d d  k s0 t  t d d d  j d  sQ t  t d d d d	 d
 j d  sx t  t d d d  j d  s t  t d t d t  j d   s t  t d t d! t d	 d
 j d"  s t  t d d d
  j d  st  t d d d
 d	 d
 j d  s3t  t d d d  j d  sTt  t d d d d	 d
 j d  s{t  t d
 d d
  j d  st  t d
 d
 d
  j d d#  st  t d
 d d
  j d  st  t d d d  j d$  st  t d d d  j d%  s$t  t d d d  j d&  sEt  t d d d  j d  sft  d  S('   Ni   i   i    i   iig      ?gLXz?t   typei   y        LXz?i   gLXzy              @gI:r Ay        EZ;Agtp@y        &xso@g9B.y        9B.?iy              n@gjA?y        jA?g      g}$!}f?y        }$!}f?gb`3?y        b`3?gFoy      @      @yI:r AEZ;Ay      @      @ytp@&xsog;f?yjA?jAy}$!}f?}$!}f?yb`3?b`3(   R   R   t   legenpR}   R   R   R   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_legenp  s$    	'!'!&,!'!'!%!!!!c          C   s=  d t  _ t }  t |  d d d   s- t  t |  d d d   sK t  t |  d d d d d  so t  t |  d d d d d  s t  |  d d d d d j d  s t  |  d d d d d d	 d
 j d  s t  |  d d d d d j d  st  |  d d d d d j t  s5t  |  d d d d d d	 d
 j d  sbt  |  d d d d d j d d6  st  |  d d d  j d7  st  |  d d d  j d  st  |  d d d d	 d
 j d  st  |  d d d  j d  st  |  d d d  j d8  s8t  |  d d d d d j d  s_t  |  d d d d d j d9  st  |  d d d d d j d  st  |  d d d d d j d:  st  |  d d d d d j d  st  |  d d d  j d;  st  |  d d d  j d  s=t  |  d d d  j d  s^t  |  d d d  j d  st  |  d d d  j d<  st  |  d d d  j d=  st  |  d d d  j d  st  |  d d d d	 d
 j d  s	t  |  d d d  j d  s*t  |  d d d  j d>  sKt  |  d d d d d j d   srt  |  d d d d d j d!  st  |  d d d d d j d"  st  |  d d d d d j d#  st  |  d d d d d j d   st  |  d d d d d j d$  s5t  |  d d d d d j d"  s\t  |  d d d d d j d#  st  |  d? d@ d d d j dA  st  |  dB dC d d d j dD  st  |  d+ d d  j d,  st  |  d+ d d  j d-  st  |  d+ d d  j d.  s4t  |  d+ d d  j d/  sUt  |  d+ d d  j dE  svt  |  d+ d d d d j d1  st  |  d+ d d d d j dF  st  |  d+ d d d d j dG  st  |  d+ d d d d j dH  st  |  d+ d d d d j d5  s9t  d  S(I   Ni   i   i   i   iR   i    iRp   i   g      ?g
Zg
Z@y              ?g      g3Ay        -DT!?g      gzg      ?gz?g3A?y        -DT!g5Oϋ?y        !3|@g{~
6gWFEy        i l@gaUO}2?gaUO}2gWFE?y        WfѷgWfѷg&D\4(y        &D\4(gWfѷ@y              @y              @guFhZ?y        ǒsIC?g:QN?y        }U@x$?g      y        <@gJj?gfFU?g 6Կg<y        P0(?y        Jj?y        fFU?y         6?gP0(ӿy      ?      y3A-DT!?y3A?-DT!yz-DT!yz?-DT!y5Oϋ?!3|y5Oϋ?!3|yWFEi l@yWFE?i ly       @      @y      @      @yuFhZ?ǒsICy       @      @y      @      @y:QN?}U@x$?y<P0(?y 6ԿJjyfFU?fFUyJj? 6?(   R   R   t   legenqR6   R   R   R   (   t   f(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_legenq  sh    	$$'-''-+!!'!!'''''!!!!!!!'!!''''''''''!!!!!''''c           C   sU  d t  _ t d d  d k s$ t  t d d  d k s? t  t d d  d k sZ t  t d d  d k su t  t t t  t k s t  d t d t d   j d  s t  t d d  j d  s t  t d d  j d	  s t  t d t  j d  st  t d  t d d  k s3t  t d d  j d  sQt  d  S(   Ni   i    i   i   i   gDSYC?g=O?i   gN_?g`C+?y        `C+?ii   gk7WO?y        >I?y`C+?`C+?yk7WO?>I?(   R   R   t   agmR   R   R0   R   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_agmK  s    	(!c           C   s  d t  _ t d d  j d t d   s1 t  t d d d  j d d t d   s` t  t d d d  j d	 t d  d
 t d   s t  t d d  j dO  s t  t d d d
  j d  s t  t d d  j d  s t  t d d t d t  j dP  st  t d d t  j dQ  sAt  t d d
 d t  j d  set  t d d t  j t	 d   st  t d d  j d  st  t d d  j d  st  t d d  j dR  st  t d d!  j dS  st  t d d d  t k s"t  t d d# d j d$  sCt  t d d d  d k sat  t d d t d t  j d%  st  t dT d  j d'  st  t d( d(  j dU  st  t d+ d(  j dV  st  t d d(  j dW  st  t d0 d(  j dX  s t  t
 t d d d3 t  sAt  t d( d d3 t t k sbt  t d d d3 t d k st  t d d d3 t d k st  t d dY d3 t d k st  t d d5 d3 t d k st  t d dZ d3 t d k st  t d( d d3 t d k s(t  t d( d5 d3 t d k sIt  t d( d[ d3 t d k sjt  t d( d d3 t d k st  t d( d8 d3 t d k st  t d( d] d3 t d k st  t d( d^ d3 t d k st  t d d d3 t j t d   st  t d d5 d3 t j t d8   sBt  t d d_ d3 t j t da   slt  t d db d3 t j t dc   st  t d: d  j d; d< d d= d> t st  t d: d d3 t d k st  t d: dd  j d? d< d d= d> t st  t d: de d3 t d k s4t  t df dg d3 t j dh  sXt  t dC dC d3 t j di  s|t  t d d
 d  t d d d
  k st  t d
 d d  j dF  st  t d
 d d d3 t j dG  st  t d d d  j dH  st  t d d d d3 t d k s4t  t d( d d  j dI  sUt  t d( d d d3 t d k syt  t d d d  j dH  st  t d d d d3 t d k st  t d dJ dK  j dL d< d d= d> t st  t dJ d d  j dM  st  t d dj  d k s+t  t d dk  d k sFt  t d d(  d k sat  t d dl  d k s|t  t dm d(  d k st  d  S(n   Ni   i   i   i   ii    i   i   ii   ig      g      g!?y        03D@g66?g ǅ?gr?y        ?gt2?y        c:?g\$?g      @g     bi  s   6.9825435345798951153e-627i   s   4.6885137549474089431e-788g      g     4g
 I?y        By@g     iy        licpOt   bgdT:?y        Ƿҿy                g8,6V@igC\Wy        -DT!	@igN(T?y        -DT!?gGy        fs-8R?ig}?y        fs-8R?t   regularizedy              @i  i
   i   ixy              @is   1.3669297209397347754e-301037RJ   RK   i   s>   -1.322575609404222361e-698979 - 4.9274570591854533273e-698978jy              @g]y7޵?y        WH?y             @@gK!:#H?y         \h?gٕK&?g|"?g]5[?g +?i'  i.  s   1.1359381951461801687e-4327s   8.1244514125995785934e4765y              ?y!?03Dyr?̿yt2?c:?y
 I?Byy
 I?licpy      @        yC\W-DT!	@yN(T?-DT!yGfs-8R?y}?fs-8Ry       @      @l       73Me'l       73Me'l       73Me'l    73Me'y      @      @l       73Me'l       73Me'l    73Me'y      @      @y            y      @      @y      @      @y       @      @y      @      @y]y7޵?WHyK!:#H? \h?y            y            ?y              y       @        (   R   R   t   gammaincR   R*   R   R   RN   R
   R/   R6   RO   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_gammaincY  s    	(/9!)"$'!)!!!!!!!!!!!!!!****.!.!$$+!'!$!$!$1!c          C   s  d t  _ t d d  j d  s' t  t d d  j d  sE t  t d d  j d  sc t  t d	 d  j d
  s t  t d d  j d  s t  t d d  j d  s t  t d d  j d  s t  t d d  j d  s t  t d d  j d  st  t d d  j d  s5t  t d	 d  j d  sSt  t d d  j da  sqt  t d d  j db  st  t d d  j dc  st  t d d  j d d d	 d d  t st  t d d  j d! d d	 d d  t s	t  t d d  j d" d d	 d d  t s7t  t d	 d  j d# d d	 d d  t set  t d d  j d$ d d	 d d  t st  t d d  j d% d d	 d d  t st  t d d  j d& d d	 d d  t st  t d d'  j d(  st  t d d'  j d)  s+t  t d d'  j d*  sIt  t d	 d'  j d+  sgt  t d d'  }  |  j d,  st  |  j j d-  st  t d d'  }  |  j d.  st  |  j j d/  st  t d d'  }  |  j d0  st  |  j j d1  st  t d d2  j d3 d d	 d d  t sIt  t d d2  j d3 d d	 d d  t swt  t d d2  j d3 d d	 d d  t st  t d	 d2  j d3 d d	 d d  t st  t d d2  j d3 d d	 d d  t st  t d d2  j d3 d d	 d d  t s/t  t d d2  j d3 d d	 d d  t s]t  t d d4  j d5  s{t  t d d4  j d5  st  t d d4  j d5  st  t d	 d4  j d5  st  t d d4  }  |  j d5  st  |  j j d-  st  t d d4  }  |  j j d6  s8t  |  j d5  sMt  t d d4  }  |  j j d7  stt  |  j d5  st  t d d  j d8  st  t d d  j d9  st  t d d  j d:  st  t d	 d  j d  st  t d d  j d;  st  t d d  j d<  s=t  t d d  j d=  s[t  t d d  j dd  syt  t d d  j de  st  t d d  j df  st  t d	 d  j dg  st  t d d  j dC  st  t d d  j dD  st  t d d  j dE  s-t  t d d  j dF d d	 d d  t s[t  t d d  j dG d d	 d d  t st  t d d  j dH d d	 d d  t st  t d	 d  j d$ d d	 d d  t st  t d d  j dI d d	 d d  t s	t  t d d  j dJ d d	 d d  t sA	t  t d d  j dK d d	 d d  t so	t  t d d'  }  |  j dL  s	t  |  j j dM  s	t  t d d'  }  |  j dN  s	t  |  j j dO  s	t  t d d'  }  |  j dP  s
t  |  j j dQ  s#
t  t d	 d'  }  |  j d,  sG
t  |  j j d-  s_
t  t d d'  }  |  j dR  s
t  |  j d	 k s
t  t d d'  }  |  j dS  s
t  |  j d	 k s
t  t d d'  }  |  j dT  s
t  |  j d	 k s
t  t d d2  j dU d d	 d d  t s8t  t d d2  j dV d d	 d d  t sft  t d d2  j dW d d	 d d  t st  t d	 d2  j d3 d d	 d d  t st  t d d2  j dX d d	 d d  t st  t d d2  j dY d d	 d d  t st  t d d2  j dZ d d	 d d  t sLt  t d d4  }  |  j d[  spt  |  j j dM  st  t d d4  }  |  j d\  st  |  j j dO  st  t d d4  }  |  j d]  st  |  j j dQ  s t  t d	 d4  }  |  j d5  s$t  |  j j d-  s<t  t d d4  j d^  sZt  t d d4  j d_  sxt  t d d4  j d`  st  d  S(h   Ni   ig      @gb?igkӦ?igzCⷆ?i    g_mv?i   g/ɫ|?i   gslR
w?i   gAt?g      g_gʩPfgLX!tghĊJQ"gʹ+y        -DT!	@g[!z?/y        u%@g.%y        2l>3@i^  gԇqiRJ   RK   i   g+{gգ; jg{/1XgK];@}Fg.H4go:ɴ`#igptOgc_g8>VpgYògoZg-DT!	gTk gԚ:.gF@g_wf4}l     =RM!	 s/   2.1592908471792544286e-152003068666138139677919l  =RM!	 s0   -3.7805306852415755699e+152003068666138139677871ggתECgE{D?g>EӦu:?g:([?gf?g d?g?gVR!i?y        fs-8R?g+B\*y        -DT!?gTj@gk9!ǎ@@gƇxTg~8n@g9blBg1*jg/nQgJ` g_A g?Ho!ga]gfs-8R?g&\Ig-DT!g`VAGp^g-DT!	@gj<~_g/p8gK`s/   5.0362468738874738859e-152003068666138139677990s/   1.7626864058606158601e-152003068666138139677966s/   6.1694024205121555102e-152003068666138139677943s,   7.5575179651273905e-152003068666138139677896s.   2.645131287794586675e-152003068666138139677872s/   9.2579595072810533625e-152003068666138139677849s/   8.8175642804468234866e+152003068666138139677800s0   -3.0861474981563882203e+152003068666138139677824s/   1.0801516243547358771e+152003068666138139677848s/   1.3231857398345514495e+152003068666138139677895s0   -4.6311500894209300731e+152003068666138139677918s/   1.6209025312973255256e+152003068666138139677942yʹ+-DT!	y[!z?/u%y.%2l>3yVR!i?fs-8R?y+B\*-DT!yTj@-DT!	@yʹ+-DT!	(   R   R   RX   R   R   RO   R5   R   (   RT   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_gammainc_expint_n  s    	............................c           C   sy   d t  _ t d d d d  j d  s- t  t d d d	 d
  j d  sQ t  t d d d d
  j d  su t  d  S(   Ni   iig      ?g      ?gO@g      @y               @g      @i   g	?y        f,?i   i   i    gX|W'@y      ?       @y	?f,?(   R   R   t   betaincR   R   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_incomplete_beta$  s    	$$c          C   s  d t  _ t d  d k s! t  t d  j d  s< t  t d@  j dA  sW t  t dB  j dC  sr t  t t  j d  s t  t d  j d  s t  t d  j d  s t  t t d  t  s t  t t d  t  s t  t t d  t  st  t t d  t  s/t  t t	  d k sGt  t t	  d k s`t  t
 d  d k sxt  t
 d t  j d  st  t
 t	  t	 k st  t
 t	  t	 k st  t dD  t d  k st  t dE  t d  k st  t dF  j d t dG   s*t  t d  d k sBt  t d  j d t d   sgt  t d  j d t d   st  t d t  j d t d t   st  t d  d k st  t d  d k st  t t	  d k st  t t	  d k st  t t t   s2t  t dH  t d  d j d  s[t  t dI  j dJ  svt  t dK  j dL  st  t dM  j dN  st  d% t  _ t d  dO j d'  st  t d%  dP j d)  st  d t  _ t t dQ   d* k st  t d  d k s2t  t d+  j d,  sMt  t d-  j d.  sht  t d  t	 k st  t d  t	 k st  t t d/   j d/  st  t t d0   j d0  st  t t d1   j d1  st  d% t  _ t t d2   j d2  s&t  t t d3   j d3  sGt  t t d4   j d4  sht  d t  _ t d5  }  |  j d k st  |  j j d6  st  t dR  j d  st  t dS  dT j dU  st  t dV  j dW  st  d  S(X   Ni   i    i   gAg?i   y              @g^y        u;@iy              @gxGDy        Y$W
?g|b?y              ?y        .($h?y              y        .($hiy                gL:?g?y              ?ii   ii
   i   iMs   3.63998738656420i   y              "@g%?@[0y        9Ag%?@[0Aig%?@[0i2   i-   s3   2.0884875837625447570007862949577886115608181193212i@  s3   2.0709207788416560484484478751657887929322509209954sv   3.66744826532555e-4342944819032518276511289189166050822943970058036665661144537831658646492088707747292249493384317534g      ?g
$?g      g
$޿gffffff?gP?gPs"   0.99999999999999999999999999999995s#   0.999999999999999999999999999999995s$   -0.999999999999999999999999999999995y              I@s   -6.1481820666053078736e+1083iy              @id   i  g?}d-@y        OB+x@y              Y@gWMYA`E?y        m<p?y      @      @y^u;y            yxGDY$W
?y      ?        y      ?        y?      ?y?      ?i'  y       @      "@y%?@[09Ay       @      "@y%?@[0A9y             "y%?@[09Al
         Y 
^8O\CoYl                                                                                                                                                    (yT@2n]:G/~[C%l:^x zjxPmov~mNx<:;$b_Omm;=}
{~xG >C6pvcj80hzczV	E1TZjj~
YlKc=8"ybB%EYMTGyGXS$^K&GKY$5SyfPN lp"!$P7L?y9QIlt')Wy.X.(F<#^Ea"Q.J=,s{"SDi^NEkZf*H']Do)vUmUA^CNf
F=[!J1G.kbC(>B"zm1 )/SMLl          +O tC3y+v y      Y      @y      Y@      @l                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ,D 31QQF(	Y T+z"6;T}/xzGy">sDw]+9m,q!~xg
 C_2]:
&ORS1=D^dQX!&1HrrxSJ1^Z".t_{F	y3q'SGlA#t,>VHHq=5	NB[0M}J:`3Jv~|2Thspb 34A!"#&a\g&JW,QV LA`U5HR_+%E">Wk8_i	vRR hl{.cNVw!>&dGsI8koys-Q.~FD/%U(!'V_#YS93 al!t|IU"f!&fqH*4cqgOogoI"}{_l$K3X31%zbmLG;9x-M%_a&s#.qZc-6u|B3=B6T^]y{_%m $^Vt{dfWYS
sY])=W'VT19c};ho
C)8DNtH0)Gw?'t91y?97*<^s/43aDo-L)U;w	EF(,-?;p+u.%Y"Xr0~cfo`=:x=meOU7_51||3~.h*UbM'!b
@4}+C'k#i\;08JFWY+RnJ;)ALGQydV9
mBZFy,4ECrxkaJ?[!qh>:'P

{RMPAvuB7h&3u>S~Cn.C9jnI W={BVVS(SE_k0Tfn)QyMvVd/"!]Eyl6M)IH6uz1h @]f dc3~uySqcRaq~hVZqYRmpp+)7&!ZA/RXJz@KuQ?.1S>BQtjmJ2-MQpIL(%Ibe[CG HxYeTxBwK2zq{!e 6ikmcLB:tBpx _*eZC:;'yw  Oof`VZ*xw_^v
2m9VlnenQ0Nao]\^Uz6WpP<$*GV"=h9S7'S>K>
BiDLVD 2*"b,	gvi-O0$ Y&p:~z'R	 xf%vC
-w
V-s;E1[a<T}lVT3YrF_Z1.`b?:=Vl>HYu0V{< y?}d-@OB+xy      Y@      Y@yWMYA`E?m<p(   R   R   t   erfR   R   R   R1   R   R+   R
   t   erfit   erfcR6   R7   RL   t   erfinvR4   R5   (   R,   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_erf*  st    	%%%-)		!!!	!!!	c           C   s+  d t  _ t t  d k s" t  t t  d k s: t  t d d d  j t d d d   sg t  t d   t t g  d k s t  t d  d k s t  t d	 d	  d k s t  t t  d k s t  t t  d k s t  t d
  d k st  t d  d j d  s't  d  S(   Ni   i    i   i   i   c         S   s   t  |  d d  S(   Ng      g?(   t   npdf(   RF   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   <lambda>n  s    i   g      ?i   i
   ii   gwbLz@i	   l      B3v^!< (   R   R   R   R
   R   R   t   quadtst   ncdf(    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_pdfi  s    	-%c          C   s  d t  _ t d  d k s! t  t dY  d k s9 t  t t  t k sQ t  t t t   si t  t t d  j t k s t  t t d  j j	 d t
  s t  t t d  j t k s t  t t d  j j	 d t
  s t  t d d  t k st  t d d  t k s)t  t d d  t k sEt  t t  j	 d  s`t  t d  j	 d  s{t  t t
 d  j	 t t
 d  st  t t d  d  j	 t d   st  t d	  j	 d
  st  t d  j	 d  st  t d d d  j	 d  s(t  t d d  j	 d  sFt  t d	 d  j	 dZ  sdt  t d d  j	 d  st  t d	 d  j	 d[  st  t d d  j	 d\  st  t d  j	 d]  st  t d d  j	 d^  st  t d d  j	 d_  st  t d  j	 d  s0t  t d d  j	 d`  sNt  t d d  j	 da  slt  t d d  j	 db  st  t dc  j	 dd  st  t de  j	 df  st  t dg d  j	 dh  st  t di d  j	 dj  st  t d, d  j	 dk  st  t d d d  j	 dl  s<t  t d d d  j	 d1  s^t  t d d d2  j	 dm  st  t d d3 d4  j	 dn  st  t d d3 d  j	 do  st  t d t d9  j	 dp  st  t d t d9 d  j	 dq  st  t d t d9 d  j	 dr  s3t  t d t d9 d4  j	 ds  sYt  t d t d9  j	 dt  s}t  t d t d9 d  j	 du  st  t d t d9 d  j	 dv  st  t d t d9 d4  j	 dw  st  dJ t  _ t t
  j	 dK  st  d t  _ t dx  j	 dy  s:t  t dz  j	 d{  sUt  t d|  j	 d}  spt  t d~  j	 d  st  t d  j	 d  st  t d d  }  |  j j	 dW  st  |  j j	 dX  st  d  S(   Ni   i    y                i   i   i   igW	&?g      ?g{?g      пgֿg      i'  g"{,7gѤX9gHgtmy        3]N@g}y        &@igӸ?y        ~dY?gg[y        @i  gr6@gAj@y        T'>@i   g(o-@y        n!=@y              @gAF?y        Z|?gٿy        ?g)uy        %+?g(ty        mȻy@gO^?y        "@g      g~}?hy        e?g:㢥'y        %K8@g8	U'ii i   gk)j^-y        xe/:@gb/.y        >ꮺF@@i
   g0j;?y        "B`?gm.[	y        <?@gsqMy        1mP@gE&\y        57@g#u*Ϳy        -pF?g>M|y        Wn2?gǁcy        'FyE@gfI3y        I5fԪ4@i2   s8   1.073658194796149172092178407024821347547745350410314531y        Mb`?g7W@y        ;ūԎ?gy&1ܿg)!faYy        NJuM?gʡEy        -C6?gQW
y        "1k?i   gQGg[[ADy                yHgtm3]NyHgtm3]N@y}&@yӸ?~dY?yg[忼@yӸ?~dYyAj@T'>@yAj@T'>y(o-@n!=@y      @      @yAF?Z|?yٿ?y)u%+?y      @      @y(tmȻy@y      @      @yO^?"y~}?hey:㢥'%K8@y:㢥'%K8yk)j^-xe/:@yb/.>ꮺF@@y0j;?"B`?ym.[	<?@ysqM1mPyE&\57@y#u*Ϳ-pFſy>M|Wn2?yǁc'FyEyfI3I5fԪ4@y      Mb`?y7W@;ūԎ?y      Mb`y7W@;ūԎyy&1ܿ?y)!faYNJuM?yy&1ܿٿy)!faYNJuMyʡE-C6?yQW
㿘"1k?l      Fx:^V (   R   R   t   lambertwR   R
   R6   R7   R4   R5   R   R   R;   R   t   log(   Rj   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_lambertww  sx    	%&(-""""""#&&&$'''		c          C   s  d   }  d t  _ |  t d  d  s- t  |  t d  d  sH t  |  t d  dO  sc t  |  t d	  dP  s~ t  |  t d d
  dQ  s t  |  t d d
  dR  s t  |  t d d
  dS  s t  |  t d	 d
  dT  s t  |  t d d  dU  st  |  t d d  d  s2t  |  t d d  dV  sPt  |  t d	 d  dW  snt  d   } d   } d   } d   } d t  _ d t d t } t d  } t d  } t d  } t d  }	 t d  }
 t d   } t d!  } d t  _ |  t | | |   d"  s.t  |  t | | |   d#  sRt  |  t | | |   d$  svt  t | | |	   d k st  t | | |
   d k st  t | | |   d k st  t | | |   d k st  |  t | | |   dX  st  |  t | | |   dY  sBt  |  t | | |   dZ  sft  |  t | | |	   d[  st  |  t | | |
   d\  st  |  t | | |   d]  st  |  t | | |   t d d.   st  |  t | | |   d^  s#t  |  t | | |   d_  sGt  |  t | | |   d`  skt  |  t | | |	   da  st  |  t | | |
   db  st  |  t | | |   dc  st  |  t | | |   t d) d8   st  |  t | | |   dd  s(t  |  t | | |   de  sLt  |  t | | |   df  spt  |  t | | |	   dg  st  |  t | | |
   dh  st  |  t | | |   di  st  |  t | | |   t d) d9   s	t  |  t | | |  d
  dj  s0t  |  t | | |
  d
  dk  sWt  |  t | | |  d
  dl  s~t  |  t | | |  d
  dm  st  |  t | | |  d
  dn  st  |  t | | |  d
  do  st  |  t | | |  d
  dp  st  |  t | | |	  d
  dq  sAt  |  t | | |
  d
  dr  sht  |  t | | |  d
  ds  st  |  t | | |  d
  t d) d8   st  |  t | | |  d  dD  st  |  t | | |  d  dE  st  |  t | | |  d  dF  s4t  t | | |	  d  d k sXt  t | | |
  d  d k s|t  t | | |  d  d k st  t | | |  d  d k st  |  t | | |  d  dt  st  |  t | | |  d  du  s	t  |  t | | |  d  dv  s9	t  |  t | | |	  d  dw  s`	t  |  t | | |
  d  dx  s	t  |  t | | |  d  dy  s	t  |  t | | |  d  t d dG   s	t  |  t | | |  d  dz  s
t  |  t | | |  d  d{  s,
t  |  t | | |  d  d|  sS
t  |  t | | |	  d  d}  sz
t  |  t | | |
  d  d~  s
t  |  t | | |  d  d  s
t  |  t | | |  d  t d) d9   s
t  |  t | | |  d  d  st  |  t | | |  d  d  sFt  |  t | | |  d  d  smt  |  t | | |	  d  d  st  |  t | | |
  d  d  st  |  t | | |  d  d  st  |  t | | |  d  d  s	t  dJ t  _ d t t dK  } dL } d t  _ t |  j |  sPt  dM t  _ t |  j |  stt  dN t  _ t |  j |  st  d  S(   Nc         S   s   t  |  } t } t | t  r3 t |  t  } n  t |  j | j  t | j  d t k } t |  j | j  t | j  d t k } | o | S(   Ni   (   t   convertRN   R1   R   RZ   R4   RO   R5   (   RF   R[   t   type_okt   real_okt   imag_ok(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   check  s    --i   g|=gj|=g|۽g|۽y        |=g#B;y        |۽i   gM:y        
@g6S:y        8@g",KP:y        (*3@g.5L:y        (vf?ig,qŔK:c         S   s   t  |  | d t S(   NRI   (   t   faddRN   (   RF   R[   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyR     s    c         S   s   t  |  | d t S(   NRI   (   t   fsubRN   (   RF   R[   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyR     s    c         S   s"   t  |  t | d d t d t S(   Ny              ?RI   (   R   RM   RN   (   RF   R[   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyR     s    c         S   s"   t  |  t | d d t d t S(   Ny              RI   (   R   RM   RN   (   RF   R[   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyR     s    i  i
   s   1e-3s   1e-10s   1e-20s   1e-40s   1e-80s   1e-300s   1e-1000gmPPWg-gBgejZ~,y        F2)ܲ?gy        r>g      y        a>=y        &;y        _}eO7y         s   2.33164398159712420336e-500gʁ:Uy        Y 8ɩ?gu~ly        |H-I>gWy        Ѩ=y        {Kv;y        {S犹7y        ^{=o s   1.64872127070012814684865e-500s   -1.64872127070012814684865e-500g,+@y        /c@gISy        [@gQ}]y        t餫?gEI y        <ZI>gvT   y        =gj蚸5g4s g   s   -2.33164398159712420336e-500g Sy        w@i  s   1e-13s   -0.99999926266961377166355784455394913638782494543377383744978844374498153493943725364881490261187530235150668593869563168276697689459394902153960200361935311512317183678882i2   i   y#B;|=y#B;|۽yM:
@y6S:8@y",KP:(*3@y.5L:(vf?yM:
y.5L:(vfy",KP:(*3yejZ~,F2)ܲ?yr>y      a>=y      &;y      _}eO7y       yʁ:UY 8ɩ?yu~l|H-I>yWѨ=y      {Kv;y      {S犹7y      ^{=o yʁ:UY 8ɩyu~l|H-IyWѨy      {Kvӻy      {S犹y      ^{=oՠy,+@/c@yIS[@yIS[@yIS[@yQ}]t餫?yEI <ZI>yvT   =y      {Kv;y      {S犹7y      ^{=o yejZ~,F2)ܲyry      a>y      &ۻy      _}eOy      ޠyQ}]t餫yEI <ZIyvT   y      {Kvӻy      {S犹y      ^{=oՠy,+@/cy SwyIS[yIS[yIS[yIS[yIS[(	   R   R   R   R   R;   RO   R   R+   R   (   R   t   addt   subt   addjt   subjt   at   d3t   d10t   d20t   d40t   d80t   d300t   d1000RF   t   ans(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_lambertw_hard  s    	
							$$$!!!!$$$$$$-$$$$$$-$$$$$$-''''''''''0'''$$$$''''''0''''''0'''''''				c          C   s  d t  _ t d d g d g g d d g d d g g d  j d  sK t  t g  d t g g d g d g g d  j d  s t  t d g d g g d g d g g d  d k s t  t d g g  g d d d d g g  g d  j d  s t  t d g d g g d g d g g d  j d  s0t  t d g d g g d g d g g d  j d  sit  t d g d g g d g d g g d  j t d d t  st  d }  d } x t d  t d  g D] } t |  | |  } t	 |  t	 |   t d |  g g  g d g d | g g |  } t	 |  t	 |   t d g d d | g g d d |  g g  g d |  } | j |  st  | j |  st  qWd  S(    Ni   i   i   i   g      ?i   g      @g%WV@y              @gc2hp@y        '4D@g      ?i    s   1/3s   2/3s   2/27gmD@ig      ig      gyhg       g      ?y      @      @yc2hp@'4Di   g      @i   g      ?i   (
   R   R   t   meijergR   R   R   R   R   R$   R/   (   R   R   RG   t   x1t   x2t   x3(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_meijerg:  s     	B:6<99FDOc           C   s   d t  _ t d d d d d d  j d  s3 t  t d d d d d d  j d  s] t  t d d d d d d	  j d
  s t  t d d d d d d  j d  s t  t d d d d d d  j d  s t  d  S(   Ni   i   ii   i   g      ig      ?g      ?g      ?i   i   g      ?gk?(   R   R   t   appellf1R   R   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_appellf1M  s    	****c           C   s7   d t  _ t t d d  d d  j d  s3 t  d  S(   Ni   ii    i   i   gpu4@(   R   R   t   coulombgR+   R   R   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_coulombU  s    	c          C   s  d t  _ g  t d d  D] }  |  d ^ q } g  t d d  D] }  |  d ^ q? } t | | d  j d  sv t  t d d	 d
  j d  s t  t d d d  d; j d  s t  t d d d d  d< j d  s t  t d d d d  d= j d  st  t d d d d d d d k s3t  t d d d	  d> j d   sXt  t d d d d! d" d# d? j d%  st  t d& d d
  d k st  t	 j
 t d'    t d(   d g d) d* t k st  t g  g  g d d d d g g  g d+  j d,  st  t d- d-  d@ j d/  s9t  d0 t  _ t d1 d2 d	  dA j d4  t d5 d2 d	  dB j d6  d t  _ t d1 d2 d	  dC j d4  t d5 d2 d	  dD j d6  t t d7 d8 d9 t d
  j d:  st  t d7 dE d dF f d
  j d:  st  d  S(G   Ni   iig|=ii
   gũܘ8Vg      ?id   g      ?gN*i  i   ii   gP+(	@i|g      %@gGz?gS?g      ?g      g      i  g_?i   Rp   i  i    ii  g{<g      t   maxtermsi i   g~bf86i   c           S   s   t  d   d g  S(   Nc         S   s#   g  g  g  g  |  g |  g d f g S(   Ng      ?(    (   R   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyR   h  s    i   (   t	   hypercomb(    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyR   h  s    c         S   s#   g  g  g  g  |  g |  g d f g S(   Ng      ?(    (   R   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyR   i  s    t   infpreci   g?giաe?i  i^   gL?i   g    i  i   g{	!@ixgL`L"@is   1e-100RI   g;.ɂQ)Jl      B3v^!< l      B3v^!< lV                                                      Up]9+l)`&-C?@ZpZj)9F? ,;gb3Am(cRnx~*6'nTrY#t(mP0\rv0c,XjTm5So/ l^                                                           v}*kpv\0:6Xt3ya4*yP{'7%WIg5z*KHkWXo~r-ZC[f]v3tJnTSsa;KEJt
'a<L>i\nWaJw}#--l4                                 @kQF5JI0`hmH&:^I+;f&3L!R]4#9,X
fmhR|)<aU	5>.hl l               jeJF4uYS	@|!U-l)                           tAC>ek(5uIB(eiyduZBS$]_w^>vu9$2m#^l)                           tAC>ek(5uIB(eiyduZBS$]_w^>vu9$2m#^l)                           tAC>ek(5uIB(eiyduZBS$]_w^>vu9$2m#^l)                           tAC>ek(5uIB(eiyduZBS$]_w^>vu9$2m#^l                DGdrY|gOs&YR5I l                DGdrY|gOs&YR5I (   R   R   R   R)   R   R   R   R$   R&   t   pytestt   raisest
   ValueErrorR   R
   R   R   R#   R   RN   (   R   t   Ast   Bs(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hyper_param_accuracy[  s0    	&&!!%(('%.'9"		-c           C   s[   t  d   d g  d k s! t  t d g g  g d g d g g d  j d  sW t  d  S(   Nc         S   s"   d g |  g g  g  g  g  d f f S(   Ni    (    (   R   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyR   w  s    i    i   g      g      g2}$?(   R   R   R   R   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_hypercomb_zero_powu  s    !c          C   sO  d t  _ d }  d } t d d |  |  j d  s9 t  t d d |  |  j d7  s] t  t d d |  |  j d
  s t  t d d |  |  j d8  s t  t d d |  |  j d9  s t  t d d |  |  j d:  s t  t d d |  |  j d  st  t d d |  |  j d;  s5t  t d d |  |  j d<  sYt  t d d |  |  j d=  s}t  t d d |  |  j d>  st  t d d |  |  j d?  st  t d d |  |  j d  st  t d d |  |  j d@  st  t d d |  |  j dA  s1t  t d d |  |  j dB  sUt  t d d |  |  d k svt  t d d |  |  d k st  t d d |  |  d k st  t d d |  |  d k st  t d d |  |  d k st  t d d |  |  d k st  t d d |  |  d k s<t  t d d |  |  d k s]t  t d d |  |  d k s~t  t d d |  |  d k st  t d d |  |  d k st  t d d  |  |  d k st  t d d! d d  j dC  st  t dD d t d t dE  j dF  s1t  t d( d) |  |  j dG  sUt  t d, d d d  j dH  syt  t d d d d  d k st  t d( d d d  j dI  st  t d( d1 d d  j dJ  st  t d d d d  j d4  st  t d d d d  d k s't  t d d d d  j dK  sKt  d  S(L   Ni   g      ?g      ?i    gmBP?i   igGL?y        bD:I?g9^Gq?gGLĿi   igi'K?y        vm)˥?g4f'?y        =!?gzߚs?g4f'Կi   igf K9?y        hW?gC(?y        6tM?gHc?y        x+̣?g'?gHcۿgf K9i   ig      @g6y        x0%@y              @y              @g@%Dy        Mjt?ig      @g̝4?y        d[v/?g      gJ)?y        yE6?go@-ſy        ?Tpk?g      ?gN}}?y        z?gh?gەĿy          ?yGL?bD:IyGLĿbD:Iyi'K?vm)˥y4f'?=!y4f'Կ=!yi'K?vm)˥?yf K9?hWyC(?6tMyHc?x+̣yHcۿx+̣yC(?6tM?yf K9hWy6x0%@y       @      @y      @      @y@%DMjty̝4?d[v/?yJ)?yE6鏿yo@-ſ?TpkÿyN}}?z?yەĿ  ֿ(   R   R   t	   spherharmR   R   R   (   t   tRP   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_spherharmz  sR    	 $$$$$$$$$$$$$$$$!!!!!!!!!!!!$,$$!$$$!c           C   s.   d t  _ t d d d  j d  s* t  d  S(   Ni   i   i   id   s   2.7291482267247332183e2391(   R   R   t   qpR   R   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_qfunctions  s    	c          C   s_   d t  _ t d d  }  t d d d d d  j d	  s? t  d
 t  _ t j t	 d    d  S(   Ni   I ii   i  i    g?i   s4   0.99999999999999999999996570910644857895771110649954i   c           S   s   t  d d d d  S(   Nii   g      ?(   R&   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyR     s    (
   R   t   prect   ldexpR   R   R   R   R   R   R   (   RF   (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_issue_239  s
    	'	i   g@.=@gE.,[@glN!@gr D'@gq>-@g?12@gs-65@gV;Z8@g_T~;@gҾˑu>@goN@@gzcuB@g:)~zD@g]ƒE@g+G@g	ouU@gPr@g)X$@g*@g6{x0@glA稝3@g6@gW9@gq=@g+knG@@g|A@gi#<C@gbKsD@g?k]1aF@gՊcG@gO@g" @gd0v[='@g}-@g4	1@guԄ5@g&E8@gJk;@gb>@g[I@@gdrnB@g VD@gƗ_E@gMO$&G@gKd՘H@g((I@gҤ#@g$c*@gT
590@goh3@g@-6@gmQڇ9@gZA<@gkM@@gvgA@g߬k/C@gc1D@gKw$UF@g"3G@gh{I@g+lpvZ@g!!!&@gQj ,@g[w1@gV#4@gv8@gUsj2;@gv[^>@g۴@@guxYB@g?C@gC`(E@gCR9|G@g4|7H@gQa[<J@g=!@gUф](@g7}f/@gy2@g76@gh*n9@gj<@gfϪ?@gb~A@gXvC@g?-ƩD@gO>F@gsiG@gѰz0QgI@gJtDJ@gh_I#@gWp-+@gYdS 1@g~-=R4@gF+	7@gdz:@gv>@gOԝ@@g,6B@g6C@gWIcE@g|1[yF@gdюH@g`Z@%#J@gL'ReK@gj8,&@gU}-@gjfLI2@gJC<5@goW8@g\0<@g+|=<l?@g@$QA@gX[B@gwodD@gMF@grtG@gFHI@g1rJ@gf S;sL@gK?s(@g~	0@g{3@gu6@gMD:@gU)Z=@gDe@@giͺZGB@gƞC@gC:FP8E@gnF@g4iH@gv J@g
ҥK@gN-M@gxGf*@g_u=1@g24@g};8@gsp;@g.2>@gLA@gJy6B@g]rtPD@giUXE@ge;G@gfI@gJ@gJgNOL@gNOM@gast,@g.yn2@gĜ;6@g$Yk9@g4&+<@gK@@gh\A@gqaC@g@N E@gK`8F@goWA<9H@g7j+I@gmK@g#!JM@g	 wN@gó ./@g3@gǌYF7@g9bw:@g;->@g8_@@g%):wjB@gו9PD@gZ]s&E@gkJMG@gRH@gvJ@g&[0 L@gmM@gud[SO@gO0@gwpM74@gFɰ~8@gŜv<@gr(u?@gv=jA@g7-C@g	dD@g<ah\F@gG@g8!I@g	8K@gY/L@geOnN@gj^,P@g|6*1@gYFi5@g<9@g'a	HE=@gs$']@@gB@g C@gocE@g7iG@gC2 WH@g.ai5JJ@gGiK@gS=M@gYz O@gJ6F
]P@gpYDf2@g	W7@gnNUI:@gV/>@gA @@gK	i?B@g<bD@g1&F@g:>G@gwVI@g6&J@gL@gB85N@gIqrO@gF2P@g        g:}u?gg$eS@g!@g~yyi'@gYJ(-@g'eN2@g$*5@g5O8@gMQ'Du;@g*S>@g2N@@gCqB@gGD@g'ǛE@gɏ(G@gGo@gV~@g^%^#@gM:W*@gy8X0@g|@N3@gYau6@g?+w9@g2JH<@gYv@L@@gVƇDA@g"s6C@g'D@gY{}v[F@gMxG@gCKy@g:tg @g&@g{N+-@gQa1@g/?4@g%8@g_O;@gXWcx>@g.?@@gGOI|cB@gwpC@gd!E@gaG@gXqΰH@g,E@g?>"@g+ x#])@g	p/@gH.23@gp]f6@g/}9@gݏ<@g|?D?@gO[E$MA@gN3!C@gY-:D@gA{I1JF@gBG@g?©mqI@g"BV@gV4+
%@gp+@gCqP1@gӺoT4@g\7@gӉ;@g?3>@g9V@@g$0GB@gzC@gپ:rE@g=ςG@ggQ%H@gb0J@g
K@g0uIx'@g#O.@gw/2@g5@g/9@gh<@gY-?@g9-BhA@g5;B@g!D@gԠP!-F@g{G@g-i
XI@gwDJ@gȃ3/'!@ga)@gaȅ0@g^M3@g|D7@g͠8:@g0n=@g&_@@gswB@g<C@g`[FNE@g0ǡF@gAL|H@gnNfJ@gM 
K@gzK#@g<VK%;,@g%1@g٣:5@g!R8@gVfF);@gw/{'?@g v2A@ge^B@g!KCjD@g`F@g.bG@gvWC4I@g"J@g?GӜaL@gAl%@gsGϒ.@gQ@
-3@gý[6@g)c*9@g$S7=@gk@@@g.yA@gY>C@gKE@g"轷F@geQH@gW WI@gSS\K@g,ۣM@g]X'@gX,Lzr0@gr/94@gMF7@gsz.;@gTMՈ>@gGֈ@@gjGLB@g]|//D@gxE@g?ZWjG@g,I@gDZ3!J@go-8L@g<vM@gR))@g51@gϝvLn5@g%H.9@g= u<@g0=?@gVA@gꠀ:C@g!@9CD@gRN}F@gxH@g[~oI@g:^גRK@gn&L@g_0N@gU+@gC@G2@g
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HkK@gfhM@g';\N@gV.@g}W3@gyX=7@g:@gB3(>@gT^q@@gmhB@g`rD@g/vE@gpMLG@gjH@g6p%J@gZ]L@gIӆfM@gDRO@g	$p0@g&G=#v4@gXlu8@gǕ;@gs.p?@g5gA@g@~C@g.	D@g>gNZF@g2`1G@gsII@gf6K@g2ZzL@g!|6,mN@g>}P@gdGr<1@gt5@gNo퉫9@gA>=@gsZ@@g;ʋ}B@gGC@g@$bE@gQrfG@gbרH@ge2hHJ@g17[!K@g70D
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 |  |  j t |  | d  s"t  t
 |  |  j t |  | d  sLt  t
 |  | d  j t |  | d  syt  t
 |  | d  j t |  | d  s0 t  q0 Wq Wd  S(   Ni   i   t   of(   R   R   R   t   Vt   MR   R   t   jn_small_zerosR   t   jnp_small_zerosR   t   yn_small_zerost   ynp_small_zeros(   R,   t   m(    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   test_bessel_zeros_extraB	  s    	**--**-(9   t   mathR   t   mpmathR   R   R   R   R   R"   R-   R:   RH   RU   RW   RY   R_   R`   Ra   Rb   Rc   Rl   Rm   Ro   Rs   Rw   Rz   R{   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   t   markt   slowR   (    (    (    s;   lib/python2.7/site-packages/mpmath/tests/test_functions2.pyt   <module>   sl  
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