
    [hqf                         S r SSKrSSKrSSKrSSK7  \4S jr\" S5      r\" S5      r\	" S5      r
\	" S5      r\	" S5      rS	 rS
 rS rS rS rS rS rS rS rS rS rS rS rS rS rg)a  
Limited tests of the elliptic functions module.  A full suite of
extensive testing can be found in elliptic_torture_tests.py

Author of the first version: M.T. Taschuk

References:

[1] Abramowitz & Stegun. 'Handbook of Mathematical Functions, 9th Ed.',
    (Dover duplicate of 1972 edition)
[2] Whittaker 'A Course of Modern Analysis, 4th Ed.', 1946,
    Cambridge University Press

    N)*c                     SnU=(       a&    U R                   R                  UR                   U5      nU=(       a&    U R                  R                  UR                  U5      nU$ )NT)realaeimag)abepsress       R/var/www/auris/envauris/lib/python3.13/site-packages/mpmath/tests/test_elliptic.pympc_aer      sF    
C

(!&&))AFFC(C

(!&&))AFFC(CJ       sncndnc                     [        U S9$ )Nk)qfromr   s    r   <lambda>r   #   s    51:r   c                     S[         l        [        SSS5      S:X  d   e[        SSS5      S:X  d   e[        SSS5      S:X  d   e[        SSS5      S:X  d   e[        SS	S5      R                  [	        S	5      5      (       d   e[        S
S	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [	        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        S
S	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  [        S	5      5      (       d   e[        SS	S5      R                  S5      (       d   e[        S
S	S5      R                  S5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  S5      (       d   e[        SS	S5      R                  S 5      (       d   e[        SS	S5      R                  S!5      (       d   eg )"N   ssr   r   ccddnnr         ?r   r   nsncndscsdcdcsdcds      ?g@p4(?gTi$?g>x?g(?@gZx:	?g~??gbUaA?g]`w73?gk?g) @g
oA?gff @)mpdpsellipfunr   sincoscscsectancottanhsechcothcoshsinhcsch r   r   test_ellipfunr9   %   sA   BFD!Q1$$$D!Q1$$$D!Q1$$$D!Q1$$$D$"%%c$i0000D$"%%c$i0000D$"%%a((((D$"%%c$i0000D$"%%c$i0000D$"%%a((((D$"%%c$i0000D$"%%c$i0000D$"%%c$i0000D$"%%c$i0000D$"%%c$i0000D$"%%c$i0000D$"%%d4j1111D$"%%d4j1111D$"%%d4j1111D$"%%d4j1111D$"%%d4j1111D$"%%d4j1111D$"%%d4j1111D$"%%d4j1111D$"%%a((((D$"%%d4j1111D$"%%a((((D$"%%d4j1111D$$''(>????D$$''(>????D$$''(>????D$$''(=>>>>D$$''(=>>>>D$$''(=>>>>D$$''(>????D$$''(>????D$$''(>????D$$''(=>>>>D$$''(=>>>>D$$''(=>>>>r   c                     S[         l        [        [        5      n U [        :X  d   eS[         l        [	        S5      S-  [	        S5      4[	        S5      S-  [	        S5      4[	        S5      S-  [	        S	5      4[	        S
5      S-  [	        S5      4[	        S5      S-  [	        S5      4[	        S5      S-  [	        S5      4[	        S5      S-  [	        S5      4[	        S5      S-  [	        S5      4[	        S5      S-  [	        S5      4[	        S5      S-  [	        S5      4/
nU H7  nUS   n[        [        U5      5      n U R                  US   5      (       a  M7   e   S[         l        g )Nd      r   
   z0.006584651553858370274473060   z0.01394285727531826872146409   z0.02227743615715350822901627   z0.03188334731336317755064299   z0.04321391826377224977441774   z0.05702025781460967637754953   z0.07468994353717944761143751   z0.09927369733882489703607378	   z0.1401731269542615524091055r   r   )r)   r*   calculate_nomezerompfsqrtr   )qmath1ims       r   test_calculate_nomerN   S   sK   BFtA99BF!fRi<=>!fRi;<=!fRi;<=!fRi;<=!fRi;<=!fRi;<=!fRi;<=!fRi;<=!fRi:;<!fRi:;<	>E aD47#ttAaDzzz 
 BFr   c                    ^^^	 S[         l        [        =m	m[        SS5       H  m[	        TT	T5      n U TS-
  S-  :X  a  M   e   [
        [        S5      4 H7  m[        SS5       H$  m[        R                  " [        UUU	4S j5        M&     M9     [
        S-  m	[
        S-  m[        S5      n[	        ST	T5      nUR                  U5      (       d   e[        S	5      n[	        ST	T5      nUR                  U5      (       d   e[        S
5      n[	        ST	T5      nUR                  U5      (       d   e[        S5      n[	        ST	T5      nUR                  U5      (       d   e[        n[        S-  n[        S5       Hv  n[        [        R                  " 5       5      n[        U5      m[	        SUT5      nUR                  S5      (       d   e[	        SUT5      nUR                  S5      (       a  Mv   e   S[         l        g )Nr<   r   rA   r>   c                     > [        T TT5      $ Njtheta)nrJ   zs   r   r   test_jtheta.<locals>.<lambda>w   s    fQ1or   r=      z0.1069552990104042681962096z1.101385760258855791140606z1.178319743354331061795905r?   z0.8219318954665153577314573r@   r   r   )r)   r*   rG   rangerS   onerH   pytestraises
ValueErrorr   pistrrandom)
valuer   resultz1z2rL   qstringrT   rJ   rU   s
          @@@r   test_jthetare   m   s   BFLA1QZq!Q1q !   3q6]qAMM*&=>   	BABA +
,CAq!_F99S>>> *
+CAq!_F99S>>> *
+CAq!_F99S>>> +
,CAq!_F99S>>> 
B	AB2Yfmmo&L2q!yy|||2q!yy|||  BFr   c                    ^ S[         l        [         =R                  S-  sl        [        S5      S-  [        S-  -
  [        S5      S-  [        -  -
  m[         =R                  S-  sl        [        S5      [        S5      [        -  -   n [        SS	T5      n[         =R                  S-  sl        [        S5      S-  [        S
-  -
  [        S5      S-  [        -  -
  m[         =R                  S-  sl        [        R                  " [        U4S j5        S[         l        S	[        -   S-  n[        S5      S-  [        S5      S-  [        -  -   m[        S5      [        S5      [        -  -   n S[         l        [        S	UT5      nUR                  U 5      (       d   eS[         l        SS[        -  -   nSS[        -  -   m[        S	UT5      nS[         l        [        S	UT5      nUR                  U5      (       d   eS[         l        S[        -   n[        [        S-  5      n[        S	S5       HJ  nS[         l        US	[        S	5      SU-  -  -
  -  m[        S	UT5      nS[         l        [        S	UT5      nML     UR                  U5      (       d   eS[         l        [        SSSS5      R                  S5      (       d   e[        SSSS5      R                  S5      (       d   eS[         l        [        SSSS5      nUR                  S5      (       d   e[        SSSS5      nUR                  S5      (       d   eg )N   rB   r=   i@B rD   z32.0031009628901652627099524264z16.6153027998236087899308935624r?   r   i c                     > [        SST 5      $ )Nr?   r   rR   )rJ   s   r   r   &test_jtheta_issue_79.<locals>.<lambda>   s    fQ1or   r;   l   'e[>
 l     I5 l   tQh z$2.4439389177990737589761828991467471z$0.5446453005688226915290954851851490P   r@   r(   r   r>   g      @r   rE   gl2<@2   g3m,z21359.048926806828939547859396600218966947753213803z4-6148327726309051673317975084654262.4119215720343656)r)   r*   rH   rY   jrS   rZ   r[   r\   r   exprX   )	r   ra   rU   r1r2q1rT   rrJ   s	           @r   test_jtheta_issue_79rr      s    BFFFbLFAr	CIAr	A-AFFbLF
 /
0
/
01
45CAq!_FFFbLFAr	CIAr	A-AFFbLF
MM*56 BF	
1aAOV#c/&:6&AA&EEA
4
5
4
5q
89CBFAq!_F99S>>>BF	AaCAc!eA	1aBBF	1aB55999BF	AA	QqSB 1a[CF2q5L !Aq!_Aq!_  55999BF!S$"%%&67777!S$#&&'<====BFq#tQA44DEEEEq#tR A44FGGGGr   c                     S[         l        [        [        S5      n [	        S5       GH  n[        [        R                  " 5       5      n[        U5      n[        S[        R                  " 5       -  5      n[        U5      n[        SXS5      S-  [        S[        U5      S-  -  n[        SXS5      S-  [        S[        U5      S-  -  n[        SXS5      S-  [        S[        U5      S-  -  nXg-
  U-   n	U	R                  SU 5      (       d   e[        S	[        R                  " 5       -  5      n[        U5      n[        SXS5      S-  [        S[        U5      S-  -  n[        SXS5      S-  [        S[        U5      S-  -  n[        SXS5      S-  [        S[        U5      S-  -  nXg-
  U-   n	U	R                  SU 5      (       d   e[        SXS5      S-  [        S[        U5      S-  -  n[        SXS5      S-  [        S[        U5      S-  -  n[        SXS5      S-  [        S[        U5      S-  -  nXg-
  U-   n	U	R                  SU 5      (       d   e[        SXS5      S-  [        S[        U5      S-  -  n[        SXS5      S-  [        S[        U5      S-  -  n[        SXS5      S-  [        S[        U5      S-  -  nXg-
  U-   n	U	R                  SU 5      (       d   e[        S[        U5      S-  n[        S[        U5      S-  n[        S[        U5      S-  nXg-   U-
  n	U	R                  SU 5      (       a  GM   e   S
[         l        g)z
Tests the some of the jacobi identidies found in Abramowitz,
Sec. 16.28, Pg. 576. The identities are tested to 1 part in 10^98.
n   rg   r=   r   r>   r@   r?   r   r;   r   N)r)   r*   ldexpr
   rX   r^   r_   rH   rS   rG   r   )
eps1rL   rd   rJ   zstringrU   term1term2term3equalitys
             r   test_jtheta_identitiesr|      s   
 BFb>D2Yfmmo&Lb()L 1!#q$(:A(=>1!#q$(:A(=>1!#q$(:A(=>=5({{1d##$#c&--/)*L 1!#q$(:A(=>1!#q$(:A(=>1!#q$(:A(=>=5({{1d##$#
 1!#q$(:A(=>1!#q$(:A(=>1!#q$(:A(=>=5({{1d##$#
 1!#q$(:A(=>1!#q$(:A(=>1!#q$(:A(=>=5({{1d##$# 4#a'4#a'4#a'=5({{1d##$#e f BFr   c            	         S[         l        [        S5      S-  [        S-  -   n [        S5      S-  [        S-  -   n[        S5      [        S5      [        -  -   n[	        SX5      n[        X25      (       d   e[        S	5      [        S
5      [        -  -   n[	        SX5      n[        X25      (       d   e[        S5      [        S5      [        -  -   n[	        SX5      n[        X25      (       d   e[        S5      [        S5      [        -  -
  n[	        SX5      n[        X25      (       d   eS[         l        [        S5      S-  [        S-  -   n [        S5      S-  [        S-  -   n[         =R                  S-  sl        SS[	        SSU5      [	        SSU5      [	        SSU5      /nS[	        SX5      [	        SX5      [	        SX5      [	        SX5      /nUS   US   -  S-  US   US   -  S-  -
  US   US   -  S-  -   US   US   -  S-  US   US   -  S-  -
  US   US   -  S-  -   US   US   -  S-  US   US   -  S-  -
  US   US   -  S-  -   US   US   -  S-  US   US   -  S-  -
  US   US   -  S-  -   US   S-  US   S-  -   US   S-  -
  /n[         =R                  S-  sl        U H  n[        U[        S5      5      (       a  M   e   S[         l        g )Nrg   r   r@   rD   r?   rC   z%0.31618034835986160705729105731678285z%0.07542013825835103435142515194358975z$1.6530986428239765928634711417951828z$0.2015344864707197230526742145361455r>   z$1.6520564411784228184326012700348340z$0.1998129119671271328684690067401823z%0.37619082382228348252047624089973824z%0.15623022130983652972686227200681074r;   r=   r   r   )r)   r*   rH   rl   rS   r   dosmpc)rU   rJ   r   rq   r   txs          r   test_jtheta_complexr     s   BFAq1Q3AAq1Q3A
5
6
5
6
:;Cq!A!>>> 4
5
4
5
9:Cq!A!>>> 4
5
4
5
9:Cq!A!>>> 5
6
5
6
:;Cq!A!>>> BFAq1Q3AAq1Q3AFFbLF	
1fQ1ovaAq!Q@A	
F1aOVAq_fQovaOA
A$qt)a1Q4!9q.	(AaD!A$J?	:	
1adQ!A$qt)a'1Q41:/9	
1adQ!A$qt)a'1Q41:/9	
1adQ!A$qt)a'1Q41:/9	!a!A$'AaD!G#		%A
 FFbLFaQ  !  BFr   c                    ^	^
 S[         l        [        S-  [        S-  -   n [        S-  [        S-  -   m
[	        S5      [	        S5      [        -  -
  n[        SU T
S5      n[        X!5      (       d   e[	        S	5      [	        S
5      [        -  -
  n[        SU T
S5      n[        X!5      (       d   e[	        S5      [	        S5      [        -  -
  n[        SU T
S5      n[        X!5      (       d   e[	        S5      [	        S5      [        -  -   n[        SU T
S5      n[        X!5      (       d   e[        S5       H  n[        [        R                  " 5       -  [        [        R                  " 5       -  -   S-  m
[        SST
S5      n[        SST
5      [        SST
5      -  [        SST
5      -  nUR                  U5      (       a  M   e   S[         l        [        S-  [        S-  4[        S-  [        S-  -   [        S-  4[        S-  [        S-  [        S-  -   4[        S-  [        S-  -   [        S-  [        S-  -   44 H{  u  m
n S Ho  m	[        T	U T
S5      n[        U	U
4S jU SS9nUR                  U5      (       d   e[        T	U T
S5      n[        U	U
4S jU SS9nUR                  U5      (       a  Mo   e   M}     [        S-  m
[        n S/S-  n[        SU T
S5      [        SU T
S5      -  US'   S H"  m	[        T	U T
S5      [        T	U T
5      -  UT	'   M$     US   US   -   US   -   US   -
  nUR                  S5      (       d   eS[         l        g )Nrg   rC   r?   rD   rA   z$1.5555195883277196036090928995803201z%0.02439761276895463494054149673076275r   z%0.19825296689470982332701283509685662z%0.46038135182282106983251742935250009r>   z%0.36492498415476212680896699407390026z%0.57743812698666990209897034525640369z&-0.38936892528126996010818803742007352z%0.66549886179739128256269617407313625r@   r=   r      )r   r>   r?   r@   c                    > [        TU T5      $ rQ   rR   zzrT   rJ   s    r   r   test_djtheta.<locals>.<lambda>m      2q!1r   )rT   c                    > [        TU T5      $ rQ   rR   r   s    r   r   r   p  r   r   )r>   r?   r@   r   )r)   r*   rY   rl   rH   rS   r   rX   r_   r   diffrG   )rU   r   ra   rL   r   r	   rq   rn   r{   rT   rJ   s            @@r   test_djthetar   C  s/   BFA!AA!A
4
5
5
6
:;CAq!QF& 5
6
5
6
:;CAq!QF& 5
6
5
6
:;CAq!QF& 6
7
5
6
:;CAq!QF&2Y 1V]]_#44a71aA1aOF1aO+F1aO;ttAwww  BFQAQ1c!e 4	QA!s1uqs{CEAaCK8:!Aq!Q"A11:B4488O8q!Q"A11:B4488O8 : 	AAA	
AA!Q1fQ1a00AaDaAq!&Aq/1! tad{QqT!AaD(H;;q>>>BFr   c                  6   S[         l        [        [        [        5      n U [        :X  d   e[	        S5       HT  n[        [        R                  " 5       5      n[        U5      n[        [        U5      nUR                  S5      (       a  MT   e   S[         l        [        S-  n[        S5      n[        [        S5      n[        XW5      n U R                  U5      (       d   e[        S5      n[        XU5      n U R                  U5      (       d   eS[         l        g	)
z3
Test some special cases of the sn(z, q) function.
r;   r=   r   r<   z0.09983341664682815230681420z0.09981686718599080096451168r   N)r)   r*   jsnrG   rX   r^   r_   rH   r   rY   ru   )ra   rL   rd   rJ   r{   argr   rM   s           r   test_jsnr   ~  s     BF t_FT>> 2Yfmmo&LtQ<{{1~~~ " BF
b&C
,
-Cc4A[F99S>>> ,
-C]F99S>>>BFr   c                     S[         l        [        [        R                  " 5       5      n [	        U 5      n[        [        U5      nUR                  [        5      (       d   eS[         l        [        S-  n[        [        S5      n[	        S5      n[        X45      nUR                  U5      (       d   e[	        S5      n[        X35      nUR                  U5      (       d   eS[         l        g)	z3
Test some special cases of the cn(z, q) function.
r;   r<   r=   r   z0.9950041652780257660955620z0.9950058256237368748520459r   N)
r)   r*   r^   r_   rH   jcnrG   r   rY   ru   )rd   rJ   r   r   rM   r   ra   s          r   test_jcnr     s     BF &--/"GGA	T1B55::: BF
b&Cc4A
+
,C[F99S>>> +
,C]F99S>>>BFr   c                  ^   S[         l        [        [        R                  " 5       5      n [	        U 5      n[        [        U5      nUR                  [        5      (       d   eS[         l        [	        S5      n[        S-  n[        XD5      nUR                  U5      (       d   eS[         l        g)z3
Test some special cases of the dn(z, q) function.
r;   r<   z0.9995017055025556219713297r=   r   N)	r)   r*   r^   r_   rH   jdnrG   r   rY   )mstringrM   r   r   r   ra   s         r   test_jdnr     s     BF &--/"GGA	T1B55:::BF
+
,C
b&C]F99S>>>BFr   c                     S[         l        Sn [        U 5       H  n[        [        R                  " 5       5      n[        U5      n[        S[        R                  " 5       -  5      n[        U5      n[        XS5      S-  n[        XS5      S-  n[        U-
  U-
  nUR                  S5      (       a  M   e   [        U 5       H  n[        [        R                  " 5       5      n	[        W5      n
U
R                  5       n[        S[        R                  " 5       -  5      n[        U5      nUS-  [        XZ5      S-  -  n[        XZ5      S-  n[        U-
  U-
  nUR                  S5      (       a  M   e   [        U 5       GH5  n[        [        R                  " 5       5      n	[        U	5      n
U
R                  5       n[        [        R                  " 5       5      n[        U5      nUS-  [        XZ5      S-  -  nSUS-  -
  n[        XZ5      S-  nX-
  U-
  nUR                  S5      (       d   e[        US-  5      n[        X5      nUR                  [        5      (       d   e[        X5      nUR                  S5      (       d   eU
n[        U[        5      nUR                  [        5      (       a  GM6   e   S[         l        g)	zl
Tests the some of the jacobi elliptic function identities found
on Mathworld. Haven't found in Abramowitz.
r;   rA   r>   r   r=   r   r   N)r)   r*   rX   r^   r_   rH   r   r   rY   r   rI   r   ellipkrG   )NrL   rd   rJ   rw   rU   rx   ry   r{   r   rM   r   rz   Krq   r`   s                   r   test_sn_cn_dn_identitiesr     s8   
 BF	A1Xfmmo&Lc&--/)*L A	1A	1;&{{1~~~  1Xfmmo&LFFHb()L1s1y!|#A	1;&{{1~~~  1Xfmmo&LFFHfmmo&L 1s1y!|#AqDA	1=5({{1~~~1a4L IttCyyy q9{{1~~~ Atxx}}}= @ BFr   c                     S[         l        [        S5      [        S5      [        -  -   n [        S5      S-  [        S-  -   n[        S5      S-  [        S-  -   n[	        X5      n[        X05      (       d   e[        S	5      [        S
5      [        -  -
  n [        X5      n[        X05      (       d   e[        S5      [        S5      [        -  -
  n [        X5      n[        X05      (       d   eS[         l        g )Nrg   z!0.2495674401066275492326652143537z"0.12017344422863833381301051702823r   r@   rD   r?   rC   z!0.9762691700944007312693721148331z!0.0307203994181623243583169154824z%0.99639490163039577560547478589753039z%0.01346296520008176393432491077244994r   )r)   r*   rH   rl   r   r   r   r   )r   urM   rq   s       r   test_sn_cn_dn_complexr   +  s    BF
1
2
2
3a
78CAq1Q3AAq1Q3AA	A!>>> 1
2
1
21
45CA	A !>>> 5
6
5
6q
89CA	A!>>>BFr   c                     S[         l        [        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        [        [        * S5      R                  S	5      (       d   e[        S[        [        * 5      R                  S
5      (       d   e[        S[        S-
  [        5      R                  S5      (       d   e[        S[        -
  [        * S[        -   5      R                  S5      (       d   e[        SSS5      S:X  d   e[        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   eSu  pn[        XU5      R                  S5      (       d   e[        XU5      R                  S5      (       d   e[        XU5      R                  S5      (       d   e[        XU 5      R                  S5      (       d   e[        X U5      R                  S5      (       d   e[        X!U 5      R                  S5      (       d   eS GH  nU[         l        [        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        [        [        * S5      R                  S5      (       d   e[        [        S-
  [        S5      R                  [        SS5      5      (       d   e[        SSS5      R                  S5      (       d   e[        [        [        * S5      R                  S5      (       d   e[        [        S-
  [        S[        -
  5      R                  [        SS5      5      (       d   e[        SS5      R                  [        75      (       d   e[        SS5      R                  [        75      (       d   e[        S[        5      R                  [        SS 5      5      (       d   e[        [        * [        5      R                  [        S!S"5      5      (       d   e[        SS5      R                  [        S-  5      (       d   e[        [        S5      R                  [        S#S$5      5      (       d   e[        SSSS5      R                  S%5      (       d   e[        SSSS&5      R                  S'5      (       d   e[        SSSS[        -   5      R                  [        S(S)5      5      (       d   e[        [        [        * SS5      R                  S*5      (       d   e[        S[        -   S[        -
  SS5      R                  S+5      (       d   e[        [        [        * SS[        -
  5      R                  [        S,S-5      5      (       d   e[        S[        -   S[        -
  SS.[        -   5      R                  [        S/S05      5      (       d   e[        S[        -   S[        -
  [        * S[        -   5      R                  [        S1S25      5      (       d   e[        SSS5      R                  [        75      (       d   e[        SSS5      R                  S35      (       d   e[        S[        [        * 5      R                  S45      (       d   e[        [        S-
  [        S5      R                  [        S5S65      5      (       d   e[        [        * [        S-
  [        5      R                  [        S7S85      5      (       d   e[        S[        S95      S5      R                  S:5      (       a  GM   e   S[         l        [        S;S<S=S>5      R                  S?S@SA9(       d   e[        SBSCSSD5      R                  SES@SA9(       d   e[        SFSGSHSI5      R                  SJS@SA9(       d   e[        SFSKSHSI5      R                  SLSMSA9(       d   e[        SFSNSHSI5      R                  SOS@SA9(       d   e[        SFSPSHSI5      R                  SQS@SA9(       d   e[        SFSRSHSI5      R                  SS5      (       d   e[        SFSTSHSI5      R                  SU5      (       d   e[        SVSWSX5      R                  SY5      (       d   e[        SZS[5      R                  S\5      (       d   e[        S]S^5      R                  S_5      (       d   e[        S`Sa5      R                  Sb5      (       d   e[        S[SZ5      R                  Sc5      (       d   e[        S[S`5      R                  Sd5      (       d   eg )eNr   r   r>   r   g2e_?r?   r@   gi+"?gP$M?yfFU?6?@y,R<8*y#62?z   g{ I|`?)r   y              ?y            ?yafG?Etw\?)rA   r   rg   <   r;   zo1.3110287771460599052324197949455597068413774757158115814084108519003952935352071251151477664807145467230678763r(   zn1.854074677301371918433850347195260046217598823521766905585928045056021776838119978357271861650371897277771871zp0.79612586584233913293056938229563057846592264089185680214929401744498956943287031832657642790719940442165621412zp-1.2138566698364959864300942567386038975419875860741507618279563735753073152507112254567291141460317931258599889zp0.58408284167715170669284916892566789240351359699303216166309375305508295130412919665541330837704050454472379308zo1.0441445654064360931078658361850779139591660747973017593275012615517220315993723776182276555339288363064476126zp0.93912050218619371196624617169781141161485651998254431830645241993282941057500174238125105410055253623847335313zq-0.53296252018635269264859303449447908970360344322834582313172115220559316331271520508208025270300138589669326136r   g      @zo1.1107207345395915617539702475151734246536554223439225557713489017391086982748684776438317336911913093408525532zp-1.1107207345395915617539702475151734246536554223439225557713489017391086982748684776438317336911913093408525532zo1.2260849569072198222319655083097718755633725139745941606203839524036426936825652935738621522906572884239069297zq-0.34471136988767679699935618332997956653521218571295874986708834375026550946053920574015526038040124556716711353zp0.77778596920447389875196055840799837589537035343923012237628610795937014001905822029050288316217145443865649819zo0.1983248499342877364755170948292130095921681309577950696116251029742793455964385947473103628983664877025779304zp0.77688623778582332014190282640545501102298064276022952731669118325952563819813258230708177398475643634103990878rA   zp0.14297579667156753833233879421985774801466647854232626336218889885463800128817976132826443904216546421431528308zp0.13613945827770535203521374457913768360237593025944342652613569368333226052158214183059386307242563164036672709zq-0.38207561624427164249600936454845112611060375760094156571007648297226090050927156176977091273224510621553615189zo1.6490011662710884518243257224860232300246792717163891216346170272567376981346412066066050103935109581019055806zp0.94148358841220238083044612133767270187474673547917988681610772381758628963408843935027667916713866133196845063zo1.8260115229009316249372594065790946657011067182850435297162034335356430755397401849070610280860044610878657501zo1.2290661908643471500163617732957042849283739403009556715926326841959667290840290081010472716420690899886276961zq-0.61127970812028172123588152373622636829986597243716610650831553882054127570542477508023027578037045504958619422zp-1.0684038390006807880182112972232562745485871763154040245065581157751693730095703406209466903752930797510491155zo1.8249027393703805304622013339009022294368078659619988943515764258335975852685224202567854526307030593012768954zp-1.2218475784827035854568450371590419833166777535029296025352291308244564398645467465067845461070602841312456831zo1.7255030280692277601061148835701141842692457170470456590515892070736643637303053506944907685301315299153040991zp0.42360654239698954330324956174109581824072295516347109253028968632986700241706737986160014699730561497106114281zp0.44660591677018372656731970402124510811555212083508861036067729944477855594654762496407405328607219895053798354zp0.70768352357515390073102719507612395221369717586839400605901402910893345301718731499237159587077682267374159282zp0.36023392184473309033675652092928695596803358846377334894215349632203382573844427952830064383286995172598964266zp0.40348623401722113740956336997761033878615232917480045914551915169013722542827052849476969199578321834819903921z0.0796zo1.0284758090288040009838871385180217366569777284430590125081211090574701293154645750017813190805144572673802094y            y      $      y      $      y            $@y+͸q?3(?g:0yE>)abs_epsgn?y'1@mgQy9]տ9DBٿgQkw?yS%MbX9?gX9v?g>W[yf0č[Ꭳ5yS%MbX9yݶ#?,eĿgh㈵>yS%vq-?yv0ƾ=T󵱿yS% y?yg%Xd毿yS%vq-y9px?`?yS% yycr??^JY?y @Gz?yffffff@\(\?y      @{Gz?y8Y+}ڿ<@y       @      y       @      ?yRع?Y\ny       @      y      ?      ?y;=?>%yg       @y      ?      ?y=R?IOyRع?Y\n?yi2)G@L !'- @)r)   r*   elliprdr   rl   elliprgelliprfr   elliprcr]   ln2elliprjrH   ellippi)r   yrU   rT   s       r   test_elliptic_integralsr   D  s
   BF1Qq>233331Qq>344441aR?455551Qr?LMMMM1QqSOPPPP2a42a4 ##$RSSSS1Qq>Q1Qr?a    1R?a    2a?a    1Qq>566661Qq>566661Qq>56666EA1q>MNNNN1q>MNNNN1q>MNNNN1q>MNNNN1q>MNNNN1q>MNNNN!q1~    "S  T  T  	T  Ts1Q""  $T  U  U  	U  Uq!A!!  #S  T  T  	T  Tqs1Q""3  (Z~$@ A A 	A Aq1~    "T  U  U  	U  Uq!A!!  #T  U  U  	U  Uqs1QqS!$$S  *\&A B B 	B Bq!!2#&&&&tA!!3$''''q|s  $U~ @ A A 	A Ar!}  %V!A B B 	B BtB""3q5))))q}  %W}! @ @ 	@ @q1Q""  $V  W  W  	W  Wq1Q""  $V  W  W  	W  Wq1RT"%%c  +]'A B B 	B Bq!Aa ##  %V  W  W  	W  Wr!tBqD1%((  *\  ]  ]  	]  ]q!Aac"%%c  +\}' @ @ 	@ @r!tBqD2a4(++C  1d~-@ A A 	A Ar!tBqD!BqD),,S  2c~.@ A A 	A A qB""B3''''q1~    "S  T  T  	T  TqA2!!  #U  V  V  	V  Vqs1Q""3  (Z~$@ A A 	A Ar!A#a ##C  )[~%@ A A 	A Aq#h-+..  0a  b  b  	b  bQ "R BF 7FFF3667cmq6rrr5.!V4778eos7ttt6=%9<<=isw<xxx6=%9<<=fpt<uuu6>5':==>jtx=yyy6?E7;>>?isw>xxx 6>5':==>jkkkk6?E7;>>?kllll;[9<<=mnnnn8X&))*STTTT8X&))*UVVVV3!$$%OPPPP8X&))*STTTT8S!$$%OPPPPr   c                  >    [        [        [        S95      (       d   eg )N)rM   )isnanr   nanr8   r   r   test_issue_238r     s    r   )__doc__mpmathr_   rZ   r
   r   rH   rG   rY   r+   r   r   r   rF   r9   rN   re   rr   r|   r   r   r   r   r   r   r   r   r   r8   r   r   <module>r      s         1v	!ftntntn%)?\4.b9Hv;z+Z9v+Z#J.BH2WQrr   