+
    0i                       R t ^ RIt^ RIHtHt ^ RIHt ^ RIt^ RIt^ RI	H
t
 ^ RIHt ^ RIHtHtHtHt ^ RIHtHtHtHtHtHtHtHtHtHt ^ RIHtH t H!t!H"t"H#t#H$t$  ^ RI%t%]PN                  PQ                  R	R
7      t)]! ]%R4      R 4       t*]! ]%R4      R 4       t+]! ]%R4      R 4       t,]! ]%R4      R 4       t-]! ]%R4      R 4       t.]! ]%R4      R 4       t/]! ]%R4      R 4       t0]! ]%R4      R 4       t1]! ]%R4      R 4       t2]! ]%R4      ]PN                  Pf                  R 4       4       t4]! ]%R4      R 4       t5]! ]%R4      R 4       t6]PN                  Pf                  ]! ]%R4      R 4       4       t7R t8]! ]%R4      R! 4       t9]! ]%R4      R" 4       t:]! ]%R4      ]PN                  Pf                  R# 4       4       t;]! ]%R4      ]PN                  Pf                  R$ 4       4       t<]! ]%R4      R% 4       t=]! ]%R4      R& 4       t>]! ]%R4      ]PN                  Pf                  R' 4       4       t?]! ]%R4      ]PN                  Pf                  R( 4       4       t@]! ]%R4      R) 4       tA]! ]%R4      R* 4       tB]! ]%R4      R+ 4       tCR, tD]PN                  Pf                  ]! ]%R4      R- 4       4       tE]PN                  Pf                  ]! ]%R4      R. 4       4       tF]PN                  Pf                  ]! ]%R4      R/ 4       4       tG]PN                  Pf                  ]! ]%R4      R0 4       4       tH]I! ^^R17      tJ]PN                  Pf                  ]! ]%R24       ! R3 R44      4       4       tKR#   ]& d    ]! R4      t% ELi ; i)5z4
Test SciPy functions versus mpmath, if available.

N)assert_assert_allclose)pi)_pep440)MissingModulecheck_versionFuncDataassert_func_equal)
ArgFixedArg
ComplexArgIntArgassert_mpmath_equalnonfunctional_tooslow
trace_argstime_limitedexception_to_nan
inf_to_nan)_sinpi_cospi_lgam1p_lanczos_sum_expg_scaled_log1pmx	_igam_facmpmathzXmpmath gmpy2 backend is not thread-safe, see https://github.com/mpmath/mpmath/issues/974reasonz0.10c            
         . p \         P                  ! R^^
4       F  p\         P                  ! ^ ^\         P                  ,          ^4       FW  pV\         P                  ! RV,          4      ,          pV P                  V\        \        P                  ! V4      4      34       KY  	  K  	  \         P                  ! V \         P                  R7      p \        \        P                  V ^ ^4      P                  4        R# )c                 ?dtypeNi)nplogspacelinspacer   expappendcomplexr   eiarraycdoubler   scexpicheck)datasetrpzs       ]/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/special/tests/test_mpmath.pytest_expi_complexr3   &   s    G[[a$Q"%%,A"&&A,ANNAwvyy|456 - % hhwbjj1GRWWgq!$**,    z0.19c                     . p R Fy  p\         P                  ! ^ ^^4       FZ  p\        P                  ! ^d4      ;_uu_ 4        V P	                  W\        \        P                  ! W4      4      34       RRR4       K\  	  K{  	  \         P                  ! V 4      p \        \        P                  V R^RR7      P                  4        R#   + '       g   i     K  ; i)2   NvIh%<=rtol)r6   3          )r"   r#   r   workdpsr&   floatexpintasarrayr   r+   expnr-   )r.   nxs      r2   test_expn_large_nrE   6   s     GQ3'A$$eFMM!,?&@AB %$ (  jj!GRWWgvqu5;;=	 %$$s   1C	Cc                     . p . ROpV F~  pV Fu  pV Fl  pVRV,          ,           p\         P                  ! ^x4      ;_uu_ 4        \        \         P                  ! W%4      4      pRRR4       V P	                  W%X34       Kn  	  Kw  	  K  	  \
        P                  ! V 4      p \        R V R^RR7      P                  4        R#   + '       g   i     Lf; i)     X@r   Nc                 D    \         P                  ! V P                  V4      # Nr+   hyp0f1realvr1   s   &&r2   <lambda>$test_hyp0f1_gh5764.<locals>.<lambda>X   s    "))AFFA.r4   r7   r8   )g     Xg      #            ?g      #@rG   r;   )	r   r>   r'   rK   r&   r"   r)   r   r-   )r.   axisrN   rD   yr1   ress          r2   test_hyp0f1_gh5764rV   G   s     G.DA1H ^^C((!&--"56C )c{+    hhwG. )(s    CCc            	      $   \         P                  ! ^^^4      p \        P                  ! V R4      p\         P                  ! V  Uu. uF  p\
        P                  ! VR4      NK  	  up4      p\        WP                  \        4      RR7       R# u upi )   rR   -q=r8   N)	r"   r$   r+   rK   r)   r   r   astyper?   )vvafrN   mfs       r2   test_hyp0f1_gh_1609r^   \   sf     
S#r	"B	2s	B	"5"Q6==C("5	6BB		%(u5 6s    Bz1.1.0c                     . p \         P                  ! R^4       F  p\         P                  ! R^^4       F{  pV) pV P                  W2^ \	        \
        P                  ! W2^ 4      4      34       V) V,           ^,
          pV P                  W2^ \	        \
        P                  ! W2^ 4      4      34       K}  	  K  	  R F>  pR F5  pV P                  W2^ \	        \
        P                  ! W2^ 4      4      34       K7  	  K@  	  \         P                  ! V 4      p \        \        P                  V R^RRR7      P                  4        R# )	   V瞯<-a=r9   atolN)      %      rQ   r<   rR   r=   
   )      rQ   r<   rR   r=         ?         @r<   r=   rk   )r"   aranger$   r&   r?   r   hyperur)   r   r+   r-   )r.   rC   bas       r2   test_hyperu_around_0rr   i   s    GYYr1RB'AANNA!U6==q+A%BCDQ
ANNA!U6==q+A%BCD	 (  05ANNA!U6==q+A%BCD 6 0 hhwGRYYAEFLLNr4   1.0.0c                  2   RR	.p V \        \        P                  ! . RO^R7      4      ,          p V  UUUUu. uF6  w  rr4W#8X  g   K  \        V4      V8X  g   K   V^ 8  g   K)  VR
8w  g   K2  WW43NK8  	  p pppp\	        RR7      pV  Uu. uF)  qf\        \        P                  ! V/ VB 4      3,           NK+  	  pp\        P                  ! V\        P                  R7      p\        \        P                  VR^RR7      P                  4        R# u uppppi u upi )rk   )repeatT)	eliminater    绽|=r8   N)rk   rx   ffffff?)rk   rz   ry   )rk   r=   gffffffr{   r<   r=   rk      )list	itertoolsproductrounddictr?   r   hyp2f1r"   r)   float64r   r+   r-   )ptsrq   rp   crD   kwr0   r.   s           r2   test_hyp2f1_strange_pointsr      s     	C 4	!!"5a@AAC'*'*q6 	Ah!m 	()A 	23u* 	qs   
	B>ABcE&--1b12444cGBhhwbjj1GRYYAE:@@B
 Cs#   D
D
D
!D
*D
/Dz0.13c            
         . ROp V  Uu. uF'  q\        \        P                  ! V!  4      3,           NK)  	  pp\        P                  ! V\        P
                  R7      p\        P                  ! RR7      ;_uu_ 4        \        \        P                  VR^RR7      P                  4        RRR4       R# u upi   + '       g   i     R# ; i)	r=   r    ignoreinvalidrw   r8   N)r=   rk   r}   r<   )UUUUUU?gUUUUUU?g?g      ?)      ?rR   g      ?gX<ݚ?)rk   rz   r}   )rk   r   rz   r}   )rk   rg   rg   r}   r   )gx&?rx   re   g333333?)r   r   rk   +?)r   r   rk   rx   )rk   r}   r`   Gz?)rj   rQ   r}   r   )rk   rl   g      
r   )g*4]92@g|O%@gCu?)  rf   r   )r   r         %@r   )rx   rk   r=         ?)rx   rk   r=   ri   )r      r`   r   )r   r   r`   ri   )rR   g     prj   gm˟?r|   )
r?   r   r   r"   r)   r   errstater   r+   r-   )r   r0   r.   s      r2   test_hyp2f1_real_some_pointsr      s    C. 9<<1E&--+,...G<hhwbjj1G	X	&	&GY>DDF 
'	& = 
'	&	&s   -B4=-B99C
	0.14c            
      N   . ROp R pV  Uu. uF:  p\        \        W4      4      \        \        P                  ! V!  4      3,           NK<  	  pp\
        P                  ! V\
        P                  R7      p\        \        P                  VR^RR7      P                  4        R# u upi )p   c                 r    \        V \        4      '       d!   \        V ^ ,          4      V ^,          ,          # V # r<   )
isinstancetupler?   rD   s   &r2   fev&test_hyp2f1_some_points_2.<locals>.fev   s+    a1;1%%Hr4   r    rw   r8   N))r   )r:   rh   )rh   gwJ)rh   |r   r   )rh   r   rf   r   r|   )r   mapr?   r   r   r"   r)   r   r   r+   r-   )r   r   r0   r.   s       r2   test_hyp2f1_some_points_2r      s    C JMMAuS[!U6==!+<%=$???GMhhwbjj1GRYYAE:@@B Ns   A B"c                     . p R FS  pR	 FJ  pR
 FA  pR F8  p \        \        P                  ! WW44      4      pT P	                  YY4T34       K:  	  KC  	  KL  	  KU  	  \
        P                  ! V \
        P                  R7      p \
        P                  ! RR7      ;_uu_ 4        \        \        P                  V R^RRR7      P                  4        RRR4       R#   \         d     K  i ; i  + '       g   i     R# ; i)rh   r    r   r   &.>Tr9   ignore_inf_signN)r   re   g?r`   rh   )g      rx   r=   g@)r   r   r`   gffffff4@)r   g)\(Gzr<   g333333?gffffff?rj   rh   r|   )r?   r   r   	Exceptionr&   r"   r)   r   r   r   r+   r-   )r.   rq   rp   r   r1   rN   s         r2   test_hyp2f1_real_somer      s    G(#A(CA!!&--a";< NNA!?3 D ) $ ) hhwbjj1G	X	&	&GY!%	'',uw 
'	& % ! !
 
'	&	&s    C!.C+C('C(+C<	z0.12c            	         R p \         P                  ! V ^3\         P                  4      p\         P                  P	                  R4       \         P                  P                  RV 4      VR	&   \         P                  P                  RV 4      VR
&   \         P                  P                  RV 4      VR&   ^\         P                  P                  V 4      ,          ^,
          VR&   VR	;;,          R\         P                  P                  ^V 4      ,          ,          uu&   VR
;;,          R\         P                  P                  ^V 4      ,          ,          uu&   VR;;,          R\         P                  P                  ^V 4      ,          ,          uu&   V F  p\        P                  R8  dY   \        VR,          4      P                  4       \        V^,          4      8  d$   \        VR,          4      P                  4       V^&   \        \        P                  ! \        VR,          4      !  4      V^&   K  	  \        \         P                  VR^RR7      P#                  4        R# )    rj   r   :Nrk   N:N   Nr   r8   N)NNNr<   )r   r=   )r   rk   )r   r}   rx   r|   )r"   zerosr   randomseedparetorandrandintr   __version__absmaxr?   r   r   r   r+   r-   )npointsr.   dss      r2   test_hyp2f1_real_randomr      s    Ghh|RZZ0GIINN4II$$S'2GDMII$$S'2GDMII$$S'2GDMbiinnW--1GDMDMb299,,Q888MDMb299,,Q888MDMb299,,Q888M&2b6{ 3r!u:-BrF)1fmmU2b6]341  RYYqt<BBDr4   c                     \         P                  P                  \         P                  P                  r ^F\         P                  n        \        P
                  ! \        P                  ! R	^^4      \        P                  ! R	^^4      4      w  r#\        P
                  ! \        P                  ! R
R^4      \        P                  ! R
R^4      4      w  rE\        P                  VP                  4       VP                  4       3,          R\        P                  VP                  4       VP                  4       3,          ,          ,           p\        \        P                  R VRRR7       \        \        P                  R VRRR7       Wu\         P                  n        \         P                  n        R#   Yu\         P                  n        \         P                  n        i ; i)F   g?r   c                 @    \        \        P                  ! V 4      4      # rI   )r'   r   erfr   s   &r2   rO   "test_erf_complex.<locals>.<lambda>  s    GFJJqM,Br4   Fr7   
vectorizedr9   c                 @    \        \        P                  ! V 4      4      # rI   )r'   r   erfcr   s   &r2   rO   r     s    WV[[^-Dr4   Nr   i)r   mpdpsprecr"   meshgridr$   r#   r_ravelr	   r+   r   r   )old_dpsold_precx1y1x2y2pointss          r2   test_erf_complexr      s%    		vyy~~X:		R[[a4bkk#q"6MNR[[b"5r{{3B7OPrxxz"((*,-255RXXZ9O3P0PP"&&"BF%*	8"''#Df%*	8 )0%		vyy~%		vyy~s   EF4 4,G z0.15c                     . p R F|  pV P                  ^^V3^RV3R^V3RRV3^RV3^RV3RRV3RRV3^^
V3^^V3^^V3^^V3R^V3R^V3^RV3^RV3RRV3RRV3^RV3^RV3RRV3RRV3^RV3^RV3RRV3RRV3.4       K~  	  R pV  Uu. uF)  q3V! V^,          V^ ,          V^,          4      3,           NK+  	  pp\        P                  ! V\        P                  R7      pR p\        P                  ! RR7      ;_uu_ 4        \        WTR^R	R
R7      P                  4        RRR4       R# u upi   + '       g   i     R# ; i)r   g333333?g @g&@c                 t    V\        V4      8X  d   V^8X  d   V^ 8X  d   ^# ^ # \        P                  ! WV4      # r=   )intr   legenp)numurD   s   &&&r2   mplegenptest_lpmv.<locals>.mplegenp0  s1    R=Q!VQw}}RQ''r4   r    c                 V    \         P                  ! V P                  \        4      W4      # rI   )r+   lpmvrZ   r   )r   r   rD   s   &&&r2   evftest_lpmv.<locals>.evf<  s    wwryy~r--r4   r   r   rw   +=rc   N)r   gmư>gL7A`?r=   rx   rz   g333333gr   re   r   ig g&rm   )extendr"   r)   r   r   r   r-   )r   rD   r   r0   r.   r   s         r2   	test_lpmvr     s   
C,

1IAJAJQKQKaLaLqMAJAJ1IAJAJQKAJQKQKaLQKaLaLqMaLqMqMN5
 	 -<( ;>>#QHQqT1Q41.000#G>hhwbjj1G. 
X	&	&wEBHHJ 
'	& ? 
'	&	&s   /D.D33E	c                     \         P                  P                  R 4       \         P                  \         P                  ! R^^4      \         P                  ! R^
^4      \         P                  ! R^^4      \         P
                  ! R^^4      \         P
                  ! R^^4      R,           RRRRR3
,          p T p\         P                  ! \         P                  ! VR,          V R,          4      4      P                  ^R4      P                  p\        P                  P                  \        P                  P                  rC R\        P                  n        \        \        P                   R VRRRR7       \        \        P"                  R	 VRRR
7       W4u\        P                  n        \        P                  n        R#   Y4u\        P                  n        \        P                  n        i ; i)r   rR   N  c                 @    \        \        P                  ! W4      4      # rI   )r?   r   betarq   rp   s   &&r2   rO   test_beta.<locals>.<lambda>[  s    uV[[->'?r4   Frw   T)r   r9   r   c           
      z    \        \        P                  ! \        \        P                  ! W4      4      4      4      # rI   )r?   r   logr   r   r   s   &&r2   rO   r   c  s     vzz#fkk!.?*@ABr4   r   8r   rx   gffffffr   g33333Yg3333r   N)Nr   )r"   r   r   r   r#   rn   r)   broadcast_arraysreshapeTr   r   r   r   r	   r+   r   betaln)rp   rq   abr   r   s        r2   	test_betar   G  sS    IINN4
bkk$Q'kk#r1%kk"a#iiR#iiR#c)$FH- 	.A 	
A	"%%ai6;	<	D	DQ	K	M	MB		vyy~~X:		"''?%*$*.	0 	IIB	 )0%		vyy~%		vyy~s   ?AF? ?,G+g?c            	      t   \         \        P                  ! . RO4      ,           p \        P                  ! ^ ^\        P                  ,          ^4      p\        P
                  ! W4      w  rV \        P                  ! RV,          4      ,          p\        P                  ^V,           ^V,           3,          P                  4       pV Uu. uF#  qD\        \        P                  ! V4      4      3NK%  	  pp\        P                  ! V4      p\        \        P                  V^ ^RR7      P                  4        R# u upi )皙?r   vIh%,=r8   N)gg{Gzr<   g{Gz?r   )LOGGAMMA_TAYLOR_RADIUSr"   r)   r$   r   r   r%   r   flattenr'   r   loggammar   r+   r-   r/   thetadzr1   z0r.   s         r2   test_loggamma_taylor_transitionr  r  s    
 	*E!FFAKK1RUU7B'E{{1$HA	
266"U(	B
a"fa"fn%%'A<=>AbGFOOB/01AG>hhwGR[['1ae4::< ?s   )D5c            	         \         P                  ! R\         P                  ! \        4      ^
4      p \         P                  ! ^ ^\         P
                  ,          ^4      p\         P                  ! W4      w  rV \         P                  ! RV,          4      ,          p\         P                  ^V,           ^V,           3,          P                  4       pV Uu. uF#  qD\        \        P                  ! V4      4      3NK%  	  pp\         P                  ! V4      p\        \        P                  V^ ^RR7      P!                  4        R# u upi )   r   r   r8   Ni)r"   r#   log10r   r$   r   r   r%   r   r   r'   r   r   r)   r   r+   r-   r   s         r2   test_loggamma_taylorr    s     	C"892>AKK1RUU7B'E{{1$HA	
266"U(	B
a"fa"fn%%'A<=>AbGFOOB/01AG>hhwGR[['1ae4::< ?s   )Ec                  0   \         P                  \         P                  ! RR^4      ) ^ \         P                  ! RR^4      3,          p V P                  4       p\         P                  ! W4      w  rV RV,          ,           p\         P
                  ! ^ RR4      P                  ^^R4      pV\         P                  ! V3VP                  ,          4      ,           P                  4       p\        P                  ! ^d4      ;_uu_ 4        V Uu. uF#  qU\        \        P                  ! V4      4      3NK%  	  ppRRR4       \         P                  ! X4      p\        \         P                  V^ ^RR7      P#                  4        R# u upi   + '       g   i     LY; i)r=   r   NrY   r8   rx   iV)r"   r   r#   copyr   rn   r   dstacksizer   r   r>   r'   rgammar)   r   r+   r-   )dxdyr  r   r1   r  r.   s          r2   test_rgamma_zerosr    s    
BQ''BKKR,CC	DB	B[[ FB	beBIIar"**1a4E	B5+,	,557A			>?@ab 123a@ 
 hhwGRYYAE288: A 
	s   F	)F 2F FF	c                     \         P                  ! \         P                  R 4      p \        V 4      .p\         P                  ! \         P                  R4      p VP	                  \        V 4      4       \
        P                  ! V4      p\
        P                  R\
        P                  ! RR	^
4      ) ^ \
        P                  ! R	R^
4      R3,          pVP                  4       p\
        P                  ! W#4      w  r#VRV,          ,           pV\
        P                  ! V3VP                  ,          4      ,           P                  4       p\         P                  ! ^4      ;_uu_ 4        V Uu. uF#  qf\        \         P                  ! V4      4      3NK%  	  ppRRR4       \
        P                  ! X4      p\!        \"        P                  V^ ^RR7      P%                  4        R# u upi   + '       g   i     LY; i)
rj   gQ?r   Nr   r8   rQ   gQοrx   )r   findrootdigammar?   r&   r"   r)   r   r#   r  r   r  r  r   r>   r'   r   r+   r-   )rootrootsr  r  r  r1   r  r.   s           r2   test_digamma_rootsr    sP    ??6>>3/D4[ME??6>>40D	LLtHHUOE 
ur{{2sB//BKKR4LdR	SB	B[[ FB	beB	B5+,	,557A			?@Aqr 234qA 
 hhwGRZZ!QU399; B 
	s   #G$()GG$G$$G4	c                     \        \        P                  4      p \        P                  ! R R^d4      ) p\        P
                  \        P                  ! ^ R^4      ) ^ \        P                  ! R^ ^4      3,          p\        P                  ! W4      w  rVRV,          ,           P                  4       p\        P                  ! ^(4      ;_uu_ 4        V Uu. uF  qD\        V ! V4      4      3NK  	  ppRRR4       \        P                  ! X4      p\        \        P                  V^ ^RR7      P                  4        R# u upi   + '       g   i     LY; i),  r   Nr7   r8   r   )r   r   r  r"   r#   r   r   r   r>   r'   rA   r   r+   r-   )r  rD   rT   r1   r  r.   s         r2   test_digamma_negrealr    s     v~~.G	S#s	##A
r{{1b!$$aRA)>>?A;;qDA	
RTA			89:",-: 
jj!GRZZ!QU399; ; 
	s   ED<.E<EE	c                  4   \         P                  ! R R^d4      ) p \         P                  ! . RO4      p\         P                  ! W4      w  rV RV,          ,           P	                  4       p\
        P                  ! ^4      ;_uu_ 4        V Uu. uF#  q3\        \
        P                  ! V4      4      3NK%  	  ppRRR4       \         P                  ! X4      p\        \        P                  V^ ^RR7      P                  4        R# u upi   + '       g   i     LY; i)r  r   Nr7   r8   r  )gffffffgg@gffffff@)r"   r#   r)   r   r   r   r>   r'   r  rA   r   r+   r-   rD   rT   r1   r  r.   s        r2   test_digamma_boundaryr    s    
 
S#s	##A
'(A;;qDA	
RTA			?@Aqr 234qA 
jj!GRZZ!QU399; B 
	s   D)D4DDD	c                  f   ^p \         P                  ! RV ,          ^V ,          ^24      pVP                  4       p\         P                  ! W4      w  rVP	                  4       VP	                  4       r!\
        P                  ! ^d4      ;_uu_ 4        \        W4       UUu. uF(  w  r4W4\        \
        P                  ! W4RR7      4      3NK*  	  pppRRR4       \         P                  ! X4      p\        \        P                  VR^RR7      P                  4        R# u uppi   + '       g   i     LZ; i)   rR   Trp   regularizedNrY   r8   r;   )r"   r$   r  r   r   r   r>   zipr?   gammaincr)   r   r+   r-   )smallrq   rD   a0x0r.   s         r2   test_gammainc_boundaryr)    s     E
CIqw+A	A;;qDA99;		q			!$Q,!*vr E&//""MNO!* 	 , 
 hhwGR[['6159??A	, 
	s   D .D
D D  D0	c            	         R  p \         P                  ! RR4      p\         P                  ! ^ ^\        ,          4      p^\         P                  ! V\         P                  ! RV,          4      4      ,           P                  4       p\         P                  ! V Uu. uF  qDV ! V4      3NK  	  up4      p\        \        P                  V^ ^RR7      P                  4        R# u upi )c                 P    \        \        P                  ! ^^V ,
          4      4      # rk   )r'   r   polylogr1   s   &r2   spence"test_spence_circle.<locals>.spence  s    v~~aQ/00r4   rR   rj   r   r   r8   N)r"   r$   r   outerr%   r   rA   r   r+   r/  r-   )r/  r/   r  r1   r  r.   s         r2   test_spence_circler2    s    1 	CAKK1R4 E	
RXXa5)*	*335AjjQ7Qrvbz*Q78GRYYAE288: 8s   Cc                     \         P                  ! \        4      P                  p \         P                  \         P
                  ! ^ R^4      ) ^ \         P
                  ! R^ ^4      3,          pVP                  4       p\         P                  ! W4      w  rVRV,          ,           p\         P                  ! R^d^4      P                  ^^R4      pV\         P                  ! V3VP                  ,          4      ,           P                  4       p\         P                  ! V Uu. uF$  pV\        \        P                   ! V4      4      3NK&  	  up4      p\#        \$        V^ ^^V ,          R7      P'                  4        R# u upi )r<   r   r8   Nr
  rx   )r"   finfor?   epsr   r#   r  r   rn   r   r  r  r   rA   r'   r   sinpir   r   r-   r6  r  r  r  r   r1   r  r.   s           r2   test_sinpi_zerosr9    s   
((5/

C	AsA&&2;;sAq+AA	BB	B[[ FB	beBIIdC#++Aq"5E	B5+,	,557Ajj$%'$%b wv||B'789$%' (GVWa3/557's   *E:c                     \         P                  ! \        4      P                  p \         P                  \         P
                  ! ^ R^4      ) ^ \         P
                  ! R^ ^4      3,          pVP                  4       p\         P                  ! W4      w  rVRV,          ,           p\         P                  ! R^d^4      R,           P                  ^^R4      pV\         P                  ! V3VP                  ,          4      ,           P                  4       p\         P                  ! V Uu. uF$  pV\        \        P                   ! V4      4      3NK&  	  up4      p\#        \$        V^ ^^V ,          R7      P'                  4        R# u upi )r<   r   rR   r8   Nr
  r4  rx   )r"   r5  r?   r6  r   r#   r  r   rn   r   r  r  r   rA   r'   r   cospir   r   r-   r8  s           r2   test_cospi_zerosr<  (  s   
((5/

C	AsA&&2;;sAq+AA	BB	B[[ FB	beBYYtS!$s*33Aq"=E	B5+,	,557Ajj$%'$%b wv||B'789$%' (G VWa3/557's   %*Fc            
         R  p R p\         P                  ! ^ ^^4      p\         P                  \         P                  ! RR^
4      ) ^ \         P                  ! RR^
4      3,          p. pV FL  p\	        \
        P                  ! V4      4      pV F$  pWg,           pVP                  WV! W4      34       K&  	  KN  	  \         P                  ! V4      p\        WR^RR7      P                  4        R# )c                 <    \         P                  ! W4      ^,          # r,  r+   ellipjums   &&r2   dn"test_dn_quarter_period.<locals>.dn=  s    yyq!!r4   c                 D    \        \        P                  ! R WR7      4      # rD  rA  )r?   r   ellipfunrA  s   &&r2   	mpmath_dn)test_dn_quarter_period.<locals>.mpmath_dn@  s    V__TQ455r4   rw   r8   Nrx   r  r;   )r"   r$   r   r#   r?   r   ellipkr&   rA   r   r-   )	rD  rI  rC  dur.   m0u0du0r0   s	            r2   test_dn_quarter_periodrP  ;  s    "6 	Aq"A	BR((!R[[b"-EE	FBG6==$%CANNA9Q#345  
 jj!GR&!%0668r4   c                    \         P                  ! V4      ;_uu_ 4        \         P                  ! V 4      p \         P                  ! V P                  \         P
                  ,
          ^\         P
                  ,          ,          4      p\         P                  ! \         P                  ! V 4      V4      pRRR4       V#   + '       g   i     X# ; i)rk   N)r   r>   mpcceilimagr   lambertwr%   )r1   r   unwindrU   s   &&  r2   _mpmath_wrightomegarW  T  sz    			JJqMaffvyy01VYY;?@oofjjmV4 
 J	 
	 Js   BB<<C	c                  T   \         P                  ! ^
^ ^4      ) p \         P                  ! \         P                  \         P                  4      .p\         P                  ! \         P                  \         P                  ) 4      .p\         P                  ! \         P                  ) \         P                  4      .p\         P                  ! \         P                  ) \         P                  ) 4      .p\        ^24       F  pVP                  \         P                  ! VR,          \         P                  4      4       VP                  \         P                  ! VR,          \         P                  ) 4      4       VP                  \         P                  ! VR,          \         P                  4      4       VP                  \         P                  ! VR,          \         P                  ) 4      4       K  	  \         P                  ! WW434      p\         P                  ! W4      w  rV RV,          ,           P                  4       p\         P                  ! V Uu. uF  pV\        \        V^4      4      3NK  	  up4      p	\        \        P                  V	^ ^RR7      P!                  4        R# u upi )rh   r   :0yE>r8   Nrx   )r"   r#   	nextafterr   infranger&   hstackr   r   rA   r'   rW  r   r+   wrightomegar-   )
rD   picut_abovepicut_belownpicut_abovenpicut_belowirT   r1   r  r.   s
             r2   test_wrightomega_branchrd  \  s    
RB	A<<rvv./K<<w/0KLL"%%01LLL"%%"&&12L2Y2<<B@A2<<B"&&ABBLLb)9266BCBLLb)9BFF7CD	 
 			;\HIA;;qDA	
RTAjj$%'$%b w':2r'BCD$%' (G R^^Wa6<<>'s    J%c                     \         P                  ! R^4      p \         P                  ! ^^\         P                  ,          4      p\         P                  ! W4      w  rV RV,          ,           P	                  4       p\         P
                  ! V Uu. uF  pV\        \        V^4      4      3NK  	  up4      p\        \        P                  V^ ^RR7      P                  4        R# u upi )rk   r   ra   r8   Nrz   r"   r$   r   r   r   rA   r'   rW  r   r+   r^  r-   r  s        r2   test_wrightomega_region1rg  s  s     	BA
AqwA;;qDA	
RTAjj$%'$%b w':2r'BCD$%' (G R^^Wa7==?'    C#c                     \         P                  ! R^4      p \         P                  ! R\         P                  ,          R4      p\         P                  ! W4      w  rV RV,          ,           P	                  4       p\         P
                  ! V Uu. uF  pV\        \        V^4      4      3NK  	  up4      p\        \        P                  V^ ^RR7      P                  4        R# u upi )rk   r   ra   r8   Nrz   rx   rf  r  s        r2   test_wrightomega_region2rj    s     	BA
BruuHb!A;;qDA	
RTAjj$%'$%b w':2r'BCD$%' (G R^^Wa7==?'rh  c                     \         P                  ! R^^4      \         P                  ! R^^4      r\         P                  ! W4      w  rV RV,          ,           P                  4       p\         P                  ! V Uu. uF$  pV\        \        P                  ! V4      4      3NK&  	  up4      p\        \        P                  V^ ^RR7      P                  4        R# u upi )r=   r   r7   r8   Nrx   )r"   r$   r   r   rA   r'   r   rU  r   r+   r-   r  s        r2   test_lambertw_smallzrl    s     ;;r1b!2;;r1b#9q;;qDA	
RTAjj$%'$%b wvr':;<$%' (G R[['1ae4::<'s   :*Cmaxprecmaxtermsz0.17c                   r  a  ] tR tRt o R tR tR tR tR tR t	R t
R	 tR
 tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR t]P>                  PA                  RRR7      R 4       t!R  t"]P>                  PA                  RRR7      R! 4       t#R" t$R# t%R$ t&R% t'R& t(R' t)R( t*R) t+R* t,R+ t-R, t.R- t/R. t0R/ t1R0 t2R1 t3R2 t4R3 t5R4 t6R5 t7R6 t8R7 t9R8 t:R9 t;R: t<R; t=R< t>R= t?R> t@R? tAR@ tBRA tCRB tDRC tERD tFRE tGRF tHRG tIRH tJRI tKRJ tLRK tMRL tNRM tORN tPRO tQ]P>                  PA                  RRP7      RQ 4       tRRR tS]P>                  PA                  RRP7      RS 4       tT]URT 4       tVRU tWRV tX]P>                  PA                  RRWR7      RX 4       tYRY tZRZ t[R[ t\]P>                  PA                  RRP7      R\ 4       t]]UR] 4       t^]P>                  PA                  RRP7      R^ 4       t_]P>                  P                  R_4      R` 4       taRa tbRb tc]P>                  PA                  RRP7      Rc 4       tdRd teRe tfRf tg]URg 4       thRh ti]P>                  P                  Ri4      Rj 4       tjRk tk]URl 4       tlRm tm]P>                  PA                  RRnR7      Ro 4       tn]URp 4       toRq tpRr tq]P>                  PA                  RRP7      Rs 4       tr]P>                  PA                  RRtR7      Ru 4       tsRv tt]P>                  PA                  RRwR7      Rx 4       tuRy tvRz tw]P>                  PA                  R{R|7      R} 4       txR~ tyR tzR t{R t|R t}R t~R tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR t]P>                  PA                  RRR7      R 4       tRtV tR# )TestSystematici  c                    \        R  \        P                  \        RR4      .RR7       \        R \        P                  \        RR4      .4       R# )	c                 <    \         P                  ! V 4      ^ ,          # r   r+   airyr.  s   &r2   rO   ,TestSystematic.test_airyai.<locals>.<lambda>      bggajmr4       חAh㈵>r8   c                 <    \         P                  ! V 4      ^ ,          # r   rt  r.  s   &r2   rO   rv    rw  r4        @@N    ח     @)r   r   airyair
   selfs   &r2   test_airyaiTestSystematic.test_airyai  sC    3"MM s^,!%	' 	3"MM s^,	.r4   c                P    \        R  \        P                  \        4       .4       R# )c                 <    \         P                  ! V 4      ^ ,          # r   rt  r.  s   &r2   rO   4TestSystematic.test_airyai_complex.<locals>.<lambda>  rw  r4   N)r   r   r~  r   r  s   &r2   test_airyai_complex"TestSystematic.test_airyai_complex  s    3"MM'\N	,r4   c                r    \        R  R \        R	R4      .RR7       \        R R \        R
R4      .4       R# )c                 <    \         P                  ! V 4      ^,          # r   rt  r.  s   &r2   rO   2TestSystematic.test_airyai_prime.<locals>.<lambda>  rw  r4   c                 2    \         P                  ! V ^R7      # r=   )
derivativer   r~  r.  s   &r2   rO   r        "MM!:r4   rx  ry  r8   c                 <    \         P                  ! V 4      ^,          # r   rt  r.  s   &r2   rO   r    rw  r4   c                 2    \         P                  ! V ^R7      # r  r  r.  s   &r2   rO   r    r  r4   r{  Nr|  r}  r   r
   r  s   &r2   test_airyai_prime TestSystematic.test_airyai_prime  ?    3 6; s^,!%	' 	3 6; s^,	.r4   c                6    \        R  R \        4       .4       R# )c                 <    \         P                  ! V 4      ^,          # r   rt  r.  s   &r2   rO   :TestSystematic.test_airyai_prime_complex.<locals>.<lambda>  rw  r4   c                 2    \         P                  ! V ^R7      # r  r  r.  s   &r2   rO   r    r  r4   Nr   r   r  s   &r2   test_airyai_prime_complex(TestSystematic.test_airyai_prime_complex      3 6;'\N	,r4   c                r    \        R  R \        R	R4      .RR7       \        R R \        R
R4      .4       R# )c                 <    \         P                  ! V 4      ^,          # r,  rt  r.  s   &r2   rO   ,TestSystematic.test_airybi.<locals>.<lambda>  rw  r4   c                 .    \         P                  ! V 4      # rI   r   airybir.  s   &r2   rO   r        "MM!,r4   rx  ry  r8   c                 <    \         P                  ! V 4      ^,          # r,  rt  r.  s   &r2   rO   r    rw  r4   c                 .    \         P                  ! V 4      # rI   r  r.  s   &r2   rO   r    r  r4   r{  Nr|  r}  r  r  s   &r2   test_airybiTestSystematic.test_airybi  s?    3 6- s^,!%	' 	3 6- s^,	.r4   c                6    \        R  R \        4       .4       R# )c                 <    \         P                  ! V 4      ^,          # r,  rt  r.  s   &r2   rO   4TestSystematic.test_airybi_complex.<locals>.<lambda>  rw  r4   c                 .    \         P                  ! V 4      # rI   r  r.  s   &r2   rO   r    r  r4   Nr  r  s   &r2   test_airybi_complex"TestSystematic.test_airybi_complex  s    3 6-'\N	,r4   c                r    \        R  R \        R	R4      .RR7       \        R R \        R
R4      .4       R# )c                 <    \         P                  ! V 4      ^,          # r}   rt  r.  s   &r2   rO   2TestSystematic.test_airybi_prime.<locals>.<lambda>  rw  r4   c                 2    \         P                  ! V ^R7      # r  r  r.  s   &r2   rO   r    r  r4   rx  ry  r8   c                 <    \         P                  ! V 4      ^,          # r  rt  r.  s   &r2   rO   r    rw  r4   c                 2    \         P                  ! V ^R7      # r  r  r.  s   &r2   rO   r    r  r4   r{  Nr|  r}  r  r  s   &r2   test_airybi_prime TestSystematic.test_airybi_prime  r  r4   c                6    \        R  R \        4       .4       R# )c                 <    \         P                  ! V 4      ^,          # r  rt  r.  s   &r2   rO   :TestSystematic.test_airybi_prime_complex.<locals>.<lambda>  rw  r4   c                 2    \         P                  ! V ^R7      # r  r  r.  s   &r2   rO   r    r  r4   Nr  r  s   &r2   test_airybi_prime_complex(TestSystematic.test_airybi_prime_complex  r  r4   c                f    \        \        P                  \        R  4      \	        RR4      .4       R# )c                 :    \         P                  ! ^ V 3/ \        B # r   )r   beiHYPERKWr.  s   &r2   rO   )TestSystematic.test_bei.<locals>.<lambda>      vzz!Q7R'7Rr4   r{  Nr}  )r   r+   r  r   r
   r  s   &r2   test_beiTestSystematic.test_bei  %    BFF,-RS s^,	.r4   c                f    \        \        P                  \        R  4      \	        RR4      .4       R# )c                 :    \         P                  ! ^ V 3/ \        B # r   )r   berr  r.  s   &r2   rO   )TestSystematic.test_ber.<locals>.<lambda>  r  r4   r{  Nr}  )r   r+   r  r   r
   r  s   &r2   test_berTestSystematic.test_ber  r  r4   c                @    \        R  R \        ^ R4      .RRR7       R# )c                 `    \         P                  ! \        V 4      4      \        V 4      ,          # rI   )r+   	bernoullir   rC   s   &r2   rO   /TestSystematic.test_bernoulli.<locals>.<lambda>  s    bll3q6&:3q6&Br4   c                 R    \        \        P                  ! \        V 4      4      4      # rI   )r?   r   r  r   r  s   &r2   rO   r    s    eF,<,<SV,D&Er4   i2  r   r9   rC   N)r   r   r  s   &r2   test_bernoulliTestSystematic.test_bernoulli  s"    BE#Au-.!%	0r4   c                |    \        \        P                  \        R  4      \	        RR4      \	        4       .RR7       R# )c                 8    \         P                  ! W3/ \        B # rI   r   besselir  rM   s   &&r2   rO   -TestSystematic.test_besseli.<locals>.<lambda>      &..*I*Ir4   }Ô%ITgJD)rd   N}Ô%I)r   r+   ivr   r
   r  s   &r2   test_besseliTestSystematic.test_besseli  s.    EEIJ'		
r4   c                ^    \        R  \        R 4      \        RR4      \        4       .4       R# )c                 D    \         P                  ! V P                  V4      # rI   )r+   r  rL   rM   s   &&r2   rO   5TestSystematic.test_besseli_complex.<locals>.<lambda>      qvvq)r4   c                 8    \         P                  ! W3/ \        B # rI   r  rM   s   &&r2   rO   r    r  r4   r  Nr  r   r   r
   r   r  s   &r2   test_besseli_complex#TestSystematic.test_besseli_complex  '    )IJ.	
r4   c           	         \        \        P                  \        R  4      \	        R
R4      \	        RR4      .RR7       \        \        P                  \        R 4      \	        R
R4      \	        RR4      .RRR7       R	# )c                 8    \         P                  ! W3/ \        B # rI   r   besseljr  rM   s   &&r2   rO   -TestSystematic.test_besselj.<locals>.<lambda>  r  r4   r  r{  Tr   c                 8    \         P                  ! W3/ \        B # rI   r  rM   s   &&r2   rO   r    r  r4   rx  ry  )r   r9   Nr  r}  r|  )r   r+   jvr   r
   r  s   &r2   test_besseljTestSystematic.test_besselj  sg    EEIJT30 		
 	EEIJT30 	
r4   c                Z    \        R  \        R 4      \        4       \        4       .4       R# )c                 D    \         P                  ! V P                  V4      # rI   )r+   r  rL   rM   s   &&r2   rO   5TestSystematic.test_besselj_complex.<locals>.<lambda>  r  r4   c                 8    \         P                  ! W3/ \        B # rI   r  rM   s   &&r2   rO   r    r  r4   Nr  r  s   &r2   test_besselj_complex#TestSystematic.test_besselj_complex  s"    )IJUJL!	
r4   c           	         \        \        P                  \        P                  \        R^4      \        ^ \        P                  4      .RRR7       R#    FrY   nan_okr9   Nr   )r   r+   kvr   besselkr
   r"   r[  r  s   &r2   test_besselkTestSystematic.test_besselk   s6    EENNs^SBFF^,	
r4   c           	         \        \        P                  \        P                  \        R^4      \        ^ \        P                  4      .RRR7       R# r  )	r   r+   knr   r   r   r
   r"   r[  r  s   &r2   test_besselk_intTestSystematic.test_besselk_int)  s7    EENND#Arvv/	
r4   c                ^    \        R  \        R 4      \        RR4      \        4       .4       R# )c                 D    \         P                  ! V P                  V4      # rI   )r+   r  rL   rM   s   &&r2   rO   5TestSystematic.test_besselk_complex.<locals>.<lambda>4  r  r4   c                 8    \         P                  ! W3/ \        B # rI   )r   r   r  rM   s   &&r2   rO   r	  5  r  r4   r  Nr  r  r  s   &r2   test_besselk_complex#TestSystematic.test_besselk_complex2  r  r4   c           	         R  p\        \        P                  \        V4      \	        RR4      \	        RR4      .RR7       R# )c                    \        \        P                  ! W3/ \        B 4      p\	        V4      R 8  d,   \
        P                  \
        P                  ! V4      ,          p\	        V4      ^ 8X  d   V^ 8X  d   \
        P                  # V# )قnQ:B)	r?   r   besselyr  r   r"   r[  signnanrN   rD   r/   s   && r2   	mpbessely.TestSystematic.test_bessely.<locals>.mpbessely:  sZ    fnnQ5W56A1v~FFRWWQZ'1v{qAvvvHr4   r  rx    r  Nr  r|  )r   r+   yvr   r
   r  r  s   & r2   test_besselyTestSystematic.test_bessely9  s8    	 	EEY'T30		
r4   c                b    R  p\        R \        V4      \        4       \        4       .RR7       R# )c                 @   \        \        P                  ! W3/ \        B 4      p\	        V4      R 8  dV   \
        P                  ! RR7      ;_uu_ 4        \
        P                  \
        P                  ! V4      ,          pRRR4       V# V#   + '       g   i     T# ; i)r  r   r   N)	r'   r   r  r  r   r"   r   r[  r  r  s   && r2   r  6TestSystematic.test_bessely_complex.<locals>.mpbesselyK  sf    q7w78A1v~[[22+A 3H1H 32Hs   ,BB	c                 D    \         P                  ! V P                  V4      # rI   )r+   r  rL   rM   s   &&r2   rO   5TestSystematic.test_bessely_complex.<locals>.<lambda>S  r  r4   i:  r  Nr  r  s   & r2   test_bessely_complex#TestSystematic.test_bessely_complexJ  s+    	 	)Y'UJL!		
r4   c           	     f    R  p\        R \        V4      \        RR4      \        RR4      .4       R# )c                     \        \        P                  ! W4      4      p\        V4      ^ 8X  d   V^ 8X  d   \        P
                  # V# r   )r?   r   r  r   r"   r  r  s   && r2   r  2TestSystematic.test_bessely_int.<locals>.mpbesselyZ  s4    fnnQ*+A1v{qAvvvHr4   c                 B    \         P                  ! \        V 4      V4      # rI   )r+   ynr   rM   s   &&r2   rO   1TestSystematic.test_bessely_int.<locals>.<lambda>a  s    s1vq)r4     rx  Nr{   r|  r   r   r   r
   r  s   & r2   test_bessely_intTestSystematic.test_bessely_intY  s1    	 	)Y'E4 #dC.1	
r4   c           	        aa . oR	V3R llo\        \        P                  V3R l\        4       \        4       .RRR7       \        \        P                  S\        P
                  ! S4      RRRR7       R# )
Fc                 N  < V R8  g   VR8  d   \         P                  # V ^ 8  g   V^ 8  dd   \        \        W,           4      4      ^,          ^ 8X  d>   V'       d6   SP	                  \        V 4      \        V4      34       \         P                  # \
        P                  ! W4      # )   mBg   m)r"   r  r   r?   r&   r   r   )rq   rp   nonzero
bad_pointss   &&&r2   r   &TestSystematic.test_beta.<locals>.betai  sw    5yAI vvAQSqu%6%:q$@ %%uQxq&:;66M;;q$$r4   c                    < S! WR R7      # T)r/   )rq   rp   r   s   &&r2   rO   *TestSystematic.test_beta.<locals>.<lambda>z  s    aD1r4   r   Tr   r   dy=)r   r   rd   NF)r   r+   r   r
   r"   r)   )r  r0  r   s   &@@r2   r   TestSystematic.test_betaf  s[    
	% 	GG1UCEN 	
 	GGHHZ  	
r4   c                    \        \        P                  \        4       ! \	        R  4      4      \        4       \        4       \        4       .4       R# )c                 6    \         P                  ! W^ VRR7      # )r<   Tr#  r   betaincrq   rp   rD   s   &&&r2   rO   -TestSystematic.test_betainc.<locals>.<lambda>      FNN1A4$Pr4   N)r   r+   r>  r   r   r
   r  s   &r2   test_betaincTestSystematic.test_betainc  s8    JJN P
 UCE35!	
r4   c                    \        \        P                  \        4       ! \	        R  4      4      \        4       \        4       \        4       .RR7       R# )c                 6    \         P                  ! WV^RR7      # )r=   Tr<  r=  r?  s   &&&r2   rO   .TestSystematic.test_betaincc.<locals>.<lambda>  rA  r4   r   r   N)r   r+   betainccr   r   r
   r  s   &r2   test_betainccTestSystematic.test_betaincc  s;    KKN P
 UCE35!		
r4   c                   aa . oRV3R llo\        \        P                  V3R l\        4       \        4       .RR7       \        \        P                  S\        P
                  ! S4      RRR7       R# )	Fc           	        < \        V4      R \        V 4      ^,           ,          8  d   \        P                  # W8  d   \        \        W,
          4      \        P                  ! \        W,
          4      4      ,
          4      R8  d>   V'       d6   SP                  \        V 4      \        V4      34       \        P                  # \        P                  ! W4      # )rx  ra   )r   r"   r  r?   r   r&   r   binomial)rC   kr/  r0  s   &&&r2   rM  +TestSystematic.test_binom.<locals>.binomial  s    1vSVaZ(( vvuU13Z"((5:*>>?%G %%uQxq&:;66M??1((r4   c                    < S! WR R7      # r3  r4  )rC   rN  rM  s   &&r2   rO   +TestSystematic.test_binom.<locals>.<lambda>  s    !5r4   r   rG  r   r   rd   Nr8  )r   r+   binomr
   r"   r)   )r  r0  rM  s   &@@r2   
test_binomTestSystematic.test_binom  sU    
	) 	HH5UCEN		
 	HHHHZ 	
r4   c                ^    \        R  \        R 4      \        4       \        4       .^2R7       R# )c                 B    \         P                  ! \        V 4      V4      # rI   )r+   eval_chebytr   rC   rD   s   &&r2   rO   0TestSystematic.test_chebyt_int.<locals>.<lambda>      A2r4   c                 8    \         P                  ! W3/ \        B # rI   )r   chebytr  rY  s   &&r2   rO   rZ        &--*H*Hr4   rG  Nr)  r  s   &r2   test_chebyt_intTestSystematic.test_chebyt_int  %    2HIXsu		
r4   Fz'some cases in hyp2f1 not fully accurate)runr   c                j    \        \        P                  R  \        R^e4      \        4       .RR7       R# )c                 f    \        4       ! \        \        P                  4      4      ! W3/ \        B # rI   )r   r   r   r]  r  rY  s   &&r2   rO   ,TestSystematic.test_chebyt.<locals>.<lambda>  '     /r4   '  r  N)r   r+   rX  r
   r  s   &r2   test_chebytTestSystematic.test_chebyt  s+    NN s^SU#	
r4   c                ^    \        R  \        R 4      \        4       \        4       .^2R7       R# )c                 B    \         P                  ! \        V 4      V4      # rI   )r+   eval_chebyur   rY  s   &&r2   rO   0TestSystematic.test_chebyu_int.<locals>.<lambda>  r[  r4   c                 8    \         P                  ! W3/ \        B # rI   )r   chebyur  rY  s   &&r2   rO   rn    r^  r4   rG  Nr)  r  s   &r2   test_chebyu_intTestSystematic.test_chebyu_int  ra  r4   c                f    \        \        P                  R  \        R^e4      \        4       .4       R# )c                 f    \        4       ! \        \        P                  4      4      ! W3/ \        B # rI   )r   r   r   rp  r  rY  s   &&r2   rO   ,TestSystematic.test_chebyu.<locals>.<lambda>  rf  r4   Nrh  )r   r+   rm  r
   r  s   &r2   test_chebyuTestSystematic.test_chebyu  s(    NN s^SU#	
r4   c                    R  p\        V\        P                  \        4       .4       \        V\        P                  \	        . RO4      .4       R# )c                 <    \         P                  ! V 4      ^,          # r   r+   shichir   s   &r2   chi$TestSystematic.test_chi.<locals>.chi      99Q<?"r4   NgU@X   g   V@)r   r   r|  r
   r   r  r|  s   & r2   test_chiTestSystematic.test_chi  4    	#CceW5Ch7Q.R-STr4   c                    R  p\        V\        P                  \        \	        \
        P                  ) R4      \	        \
        P                  R4      4      .RR7       R# )c                 <    \         P                  ! V 4      ^,          # r   rz  r.  s   &r2   r|  ,TestSystematic.test_chi_complex.<locals>.chi  r~  r4   rx  rY   r8   Nr|  )r   r   r|  r   r'   r"   r[  r  s   & r2   test_chi_complexTestSystematic.test_chi_complex  C    	# 	JJ.0DEF		
r4   c                X    R  p\        V\        P                  \        RR4      .4       R# )c                 <    \         P                  ! V 4      ^,          # r   r+   sicir   s   &r2   ci"TestSystematic.test_ci.<locals>.ci      771:a= r4   rx  Nr|  )r   r   r  r
   r  r  s   & r2   test_ciTestSystematic.test_ci  s"    	! 	B		CcN+;<r4   c                    R  p\        V\        P                  \        \	        R\
        P                  ) 4      \	        R\
        P                  4      4      .RR7       R# )c                 <    \         P                  ! V 4      ^,          # r   r  r.  s   &r2   r  *TestSystematic.test_ci_complex.<locals>.ci  r  r4   rx  rY  r8   Nr|  )r   r   r  r   r'   r"   r[  r  s   & r2   test_ci_complexTestSystematic.test_ci_complex  sC    	! 	IIrvvg.RVV0DEF		
r4   c                    \         P                  ! \        4      P                  p\	        \
        \        P                  \        4       .R ^V,          R7       R# Fr  N)	r"   r5  r?   r6  r   r   r   r;  r
   r  r6  s   & r2   
test_cospiTestSystematic.test_cospi	  s2    hhuo!!FFLL35'%aPSeTr4   c                \    \        \        \        P                  \	        4       .R RR7       R# )Fr7   r  N)r   r   r   r;  r   r  s   &r2   test_cospi_complex!TestSystematic.test_cospi_complex  !    LL\N	
r4   c                    \        \        P                  \        \        P                  4      \        4       .R ^2R7       R# )rY   r9   r   N)r   r+   r  r   r   r
   r  s   &r2   test_digammaTestSystematic.test_digamma  s*    JJV^^,UG	
r4   c           	         R  p\        \        P                  \        \        P                  4      \        4       .R^(VR7       R# )c                     \         P                  ! V P                  ^ 8  \         P                  ! V P                  4      R8  ,          RR4      # )r<   gQ?FT)r"   whererL   r   rT  r.  s   &r2   param_filter9TestSystematic.test_digamma_complex.<locals>.param_filter"  s3    88QVVaZBFF166NT,ABE4PPr4   r7   r9   r   r  N)r   r+   r  r   r   r   )r  r  s   & r2   test_digamma_complex#TestSystematic.test_digamma_complex  s5    	Q 	JJV^^,\N%	
r4   c                n    \        \        P                  \        P                  \        4       .R R7       R# )r   r8   N)r   r+   exp1r   e1r
   r  s   &r2   test_e1TestSystematic.test_e1.  s"    GGIIUG		
r4   c                   \        \        P                  \        P                  \        \        \        P                  ) R4      \        \        P                  R 4      4      .RR7       \        \        P                  \        P                  \        P                  ! R^2^4      R	,          \        P                  ^ \        P                  ! R
^^=4      \        P                  ! R
^^4      ) 3,          R,          ,           P                  4       RR7       \        \        P                  \        P                  \        P                  ! RRR4      R,           RR7       R# )rx  r7  r8   Nr   rg  y                r|  r   r   i)r   r+   r  r   r  r   r'   r"   r[  r$   r   r#   r   r  s   &r2   test_e1_complexTestSystematic.test_e1_complex6  s    GGII.0DEF		
 	GGII[[b#&w/uuQB2.RB1G0GGHKLMRUW	
 	GGII[[c5)B.		
r4   c                   \        \        P                  R  \        \        P
                  ! \        P                  ! \        P                  4      P                  4      ) \        P
                  ! \        P                  ! \        P                  4      P                  4      R7      .4       \        \        P                  R \        P                  ! RR^ RR\        P                  .4      RR7       \        \        P                  ! \        P                  ! \        P                  4      4      4       \        \        P                  ! \        P                  ) 4      ^ 8H  4       R	# )
c                 v    V ^ 8w  d   \         P                  ! V 4      V ,          # \         P                  ! R4      # r<   z1.0r   expm1mpfr   s   &r2   rO   ,TestSystematic.test_exprel.<locals>.<lambda>Q  (    16fll1oa'Hvzz%7HHr4   r   c                 v    V ^ 8w  d   \         P                  ! V 4      V ,          # \         P                  ! R4      # r  r  r   s   &r2   rO   r  W  r  r4   rY   gW:r.  gyCxDr7  r8   N)r   r+   exprelr
   r"   r   r5  r   r   r)   r[  r   isinfr  s   &r2   test_exprelTestSystematic.test_exprelN  s    IIHBFF288BJJ/334466"((2::.2235 6	
 	IIHHHeUAtT266:;		
 	266*+,		266'"a'(r4   c                    \        \        P                  \        P                  \	        \        \        P                  ) R4      \        \        P                  R 4      4      .4       R# )    cAN    c)r   r+   r  r   r   r'   r"   r[  r  s   &r2   test_expm1_complex!TestSystematic.test_expm1_complex^  s=    HHLL.0DEF	
r4   c                T    \        \        P                  R  \        4       .^<R7       R# )c                 <    \         P                  ! V ^,           4      # r   r   r   r   s   &r2   rO   3TestSystematic.test_log1p_complex.<locals>.<lambda>i  s    fjj1or4   rG  N)r   r+   log1pr   r  s   &r2   test_log1p_complex!TestSystematic.test_log1p_complexf  s    HH%\N		
r4   c                B    \        \        R  \        4       .^<RR7       R# )c                 J    \         P                  ! V ^,           4      V ,
          # r   r  r   s   &r2   rO   -TestSystematic.test_log1pmx.<locals>.<lambda>q  s    fjjQ'!+r4   r   )r   r9   N)r   r   r
   r  s   &r2   test_log1pmxTestSystematic.test_log1pmxn  s    +UG	
r4   c                n    \        \        P                  \        P                  \        4       .R R7       R# )r7  r8   N)r   r+   r,   r   r(   r
   r  s   &r2   test_eiTestSystematic.test_eiw  s    BGGVYYeDr4   c                    \        \        P                  \        P                  \        \        \        P                  ) R4      \        \        P                  R 4      4      .RR7       R# )rx  r   r8   Nr|  )	r   r+   r,   r   r(   r   r'   r"   r[  r  s   &r2   test_ei_complexTestSystematic.test_ei_complexz  s@    GGII.0DEF		
r4   c                n    \        \        P                  \        P                  \	        R R7      .4       R# )r   rp   N)r   r+   elliper   r
   r  s   &r2   test_ellipeTestSystematic.test_ellipe  s    BIIv}}sSzlCr4   c           	         \        \        P                  \        P                  \        RR 4      \        RR7      .4       R# )r{  r   r  Nr}  r   r+   	ellipeincr   r  r
   r  s   &r2   test_ellipeincTestSystematic.test_ellipeinc  s&    BLL&--#dC.#PS*9UVr4   c                |    \        \        P                  \        P                  \        4       \        4       .4       R # rI   r  r  s   &r2   test_ellipeinc_largephi&TestSystematic.test_ellipeinc_largephi      BLL&--#%Hr4   c                    \        \        P                  \        P                  \        RR 4      \        4       .4       R# r{  Nr}  r   r+   	ellipkincr   ellipfr
   r  s   &r2   test_ellipfTestSystematic.test_ellipf  s#    BLL&--#dC.#%9PQr4   c                |    \        \        P                  \        P                  \        4       \        4       .4       R # rI   r  r  s   &r2   test_ellipf_largephi#TestSystematic.test_ellipf_largephi  r  r4   c                    \        \        P                  \        P                  \	        R R7      .4       \        \        P
                  R \	        RR7      .RR7       R# )r   r  c                 <    \         P                  ! ^V ,
          4      # r   )r   rK  )rC  s   &r2   rO   ,TestSystematic.test_ellipk.<locals>.<lambda>  s    fmmAE*r4   g        )rq   r   rG  N)r   r+   rK  r   r
   ellipkm1r  s   &r2   test_ellipkTestSystematic.test_ellipk  s:    BIIv}}sSzlCKK*3ZL		
r4   c           	     r    R  p\        \        P                  V\        RR4      \        RR7      .RR7       R# )c                 0    \         P                  ! ^ W4      # r   r   ellippiphirC  s   &&r2   r  0TestSystematic.test_ellipkinc.<locals>.ellipkinc      >>!S,,r4   r{  r   r  Tr  Nr}  r   r+   r  r
   r  r  s   & r2   test_ellipkincTestSystematic.test_ellipkinc  s.    	-LLs^S3Z( 		
r4   c           	     n    R  p\        \        P                  V\        4       \        RR7      .RR7       R# )c                 0    \         P                  ! ^ W4      # r   r  r  s   &&r2   r  9TestSystematic.test_ellipkinc_largephi.<locals>.ellipkinc  r  r4   r   r  Tr  Nr  r  s   & r2   test_ellipkinc_largephi&TestSystematic.test_ellipkinc_largephi  s*    	-LLUC#J 		
r4   c           
     Z    R  p\        R V\        RR4      \        ^ ^R7      .RR7       R# )c                 D    V ^ 8X  d   ^ # \         P                  ! RWR7      # )r<   snrA  r   rH  rA  s   &&r2   r  +TestSystematic.test_ellipfun_sn.<locals>.sn  s    Avtq66r4   c                 <    \         P                  ! W4      ^ ,          # r   r?  rA  s   &&r2   rO   1TestSystematic.test_ellipfun_sn.<locals>.<lambda>      1+r4       .Ar   rY  r8   N    .r  )r  r  s   & r2   test_ellipfun_snTestSystematic.test_ellipfun_sn  s.    	7 	+s^S1]+		
r4   c           
     V    \        R  R \        RR4      \        ^ ^R7      .RR7       R# )c                 <    \         P                  ! W4      ^,          # r   r?  rA  s   &&r2   rO   1TestSystematic.test_ellipfun_cn.<locals>.<lambda>  r  r4   c                 2    \         P                  ! R WR7      # )cnrA  r  rA  s   &&r2   rO   r        8r4   r  r   rY  r8   Nr  r  r  s   &r2   test_ellipfun_cnTestSystematic.test_ellipfun_cn  '    +8s^S1]+		
r4   c           
     V    \        R  R \        RR4      \        ^ ^R7      .RR7       R# )c                 <    \         P                  ! W4      ^,          # r,  r?  rA  s   &&r2   rO   1TestSystematic.test_ellipfun_dn.<locals>.<lambda>  r  r4   c                 2    \         P                  ! R WR7      # rG  r  rA  s   &&r2   rO   r"    r  r4   r  r   rY  r8   Nr  r  r  s   &r2   test_ellipfun_dnTestSystematic.test_ellipfun_dn  r  r4   c                P    \        \        P                  R  \        4       .4       R# )c                 .    \         P                  ! V 4      # rI   r   r   r.  s   &r2   rO   )TestSystematic.test_erf.<locals>.<lambda>      fjjmr4   N)r   r+   r   r
   r  s   &r2   test_erfTestSystematic.test_erf  s    BFF$;ceWEr4   c                T    \        \        P                  R  \        4       .^R7       R# )c                 .    \         P                  ! V 4      # rI   r(  r.  s   &r2   rO   1TestSystematic.test_erf_complex.<locals>.<lambda>  r*  r4   r  N)r   r+   r   r   r  s   &r2   r   TestSystematic.test_erf_complex  s    BFF$;jl^sSr4   c                f    \        \        P                  \        R  4      \	        4       .RR7       R# )c                 .    \         P                  ! V 4      # rI   r   r   r.  s   &r2   rO   *TestSystematic.test_erfc.<locals>.<lambda>      v{{1~r4   r7   r8   N)r   r+   r   r   r
   r  s   &r2   	test_erfcTestSystematic.test_erfc  s$    GG56UG		
r4   c                f    \        \        P                  \        R  4      \	        4       .^R7       R# )c                 .    \         P                  ! V 4      # rI   r3  r.  s   &r2   rO   2TestSystematic.test_erfc_complex.<locals>.<lambda>  r5  r4   r  N)r   r+   r   r   r   r  s   &r2   test_erfc_complex TestSystematic.test_erfc_complex  s$    GG56\N		
r4   c                n    \        \        P                  \        P                  \	        4       .^R7       R# r  r  N)r   r+   erfir   r
   r  s   &r2   	test_erfiTestSystematic.test_erfi  s    BGGV[[35'SAr4   c                n    \        \        P                  \        P                  \	        4       .^R7       R# r>  )r   r+   r?  r   r   r  s   &r2   test_erfi_complex TestSystematic.test_erfi_complex  s    BGGV[[:<.CHr4   c                f    \        \        P                  \        R  4      \	        4       .^R7       R# )c                 .    \         P                  ! V 4      # rI   )r   ncdfr.  s   &r2   rO   *TestSystematic.test_ndtr.<locals>.<lambda>  r5  r4   r  N)r   r+   ndtrr   r
   r  s   &r2   	test_ndtrTestSystematic.test_ndtr  s$    GG56UG		
r4   c                    \        \        P                  R  \        \	        RR4      \	        RR4      R7      .RR7       R# )c                 t    \         P                  ! V ) \        P                  ! R 4      ,          4      R ,          # g       @)r   r   r"   sqrtr.  s   &r2   rO   2TestSystematic.test_ndtr_complex.<locals>.<lambda>  s     fkk1"RWWR[.1"4r4   rg  r   r   r  N)r   r+   rI  r   r'   r  s   &r2   test_ndtr_complex TestSystematic.test_ndtr_complex  s2    GG4'&&1WUE5JKL		
r4   c           	     j    \        \        P                  \        R  4      \	        4       .RRRR7       R# )c                 V    \         P                  ! \         P                  ! V 4      4      # rI   )r   r   rG  r.  s   &r2   rO   .TestSystematic.test_log_ndtr.<locals>.<lambda>  s    vzz&++a.'Ar4   iX  r  r7   rC   r   r9   N)r   r+   log_ndtrr   r
   r  s   &r2   test_log_ndtrTestSystematic.test_log_ndtr  s'    KKABUGs%	
r4   c                    \        \        P                  \        R  4      \	        \        RR4      \        R^d4      R7      .^RR7       R# )c                     \         P                  ! \         P                  ! V ) \        P                  ! R 4      ,          4      R ,          4      # rN  )r   r   r   r"   rO  r.  s   &r2   rO   6TestSystematic.test_log_ndtr_complex.<locals>.<lambda>	  s)    vzz&++qbn2Mb2P'Qr4   rg  r   r  rC   r   NrQ  r4  )r   r+   rX  r   r   r'   r  s   &r2   test_log_ndtr_complex$TestSystematic.test_log_ndtr_complex  s:    KKQR'&$/75#3FGHs		
r4   c                X    \        R  \        P                  \        ^R4      .RR7       R# )c                 <    \         P                  ! V 4      R,          # )r=   rx   )r+   eulerr  s   &r2   rO   .TestSystematic.test_eulernum.<locals>.<lambda>  s    bhhqk"or4   rg  r  N)r   r   eulernumr   r  s   &r2   test_eulernumTestSystematic.test_eulernum  s$    %OOAu		
r4   c           	         \        \        P                  \        P                  \        ^ ^4      \        ^ \        P                  4      .R^R7       R# )r<   r7   r  N)	r   r+   rB   r   r@   r   r
   r"   r[  r  s   &r2   test_expintTestSystematic.test_expint  s6    GGMMAs^SBFF^,	
r4   c                T    R  p\        V\        P                  \        4       .4       R# )c                 <    \         P                  ! V 4      ^ ,          # r   r+   fresnelr   s   &r2   fresnels.TestSystematic.test_fresnels.<locals>.fresnels       ::a=##r4   N)r   r   ro  r
   )r  ro  s   & r2   test_fresnelsTestSystematic.test_fresnels      	$Hfoow?r4   c                T    R  p\        V\        P                  \        4       .4       R# )c                 <    \         P                  ! V 4      ^,          # r   rm  r   s   &r2   fresnelc.TestSystematic.test_fresnelc.<locals>.fresnelc%  rq  r4   N)r   r   rw  r
   )r  rw  s   & r2   test_fresnelcTestSystematic.test_fresnelc$  rt  r4   c                |    \        \        P                  \        \        P                  4      \        4       .4       R # rI   )r   r+   gammar   r   r
   r  s   &r2   
test_gammaTestSystematic.test_gamma)  s     BHH&6v||&DsugNr4   c                    \        \        P                  \        \        P                  4      \        4       .R R7       R# rb   r8   N)r   r+   r|  r   r   r   r  s   &r2   test_gamma_complex!TestSystematic.test_gamma_complex,  s'    HHV\\*\N		
r4   c           
     t    \        \        P                  R  \        ^ RRR7      \        ^ R4      .RRR7       R# )c                 2    \         P                  ! WR R7      # )Tr"  r   r%  )r1   rp   s   &&r2   rO   .TestSystematic.test_gammainc.<locals>.<lambda>8      TBr4        @Finclusive_ar7  r  N)r   r+   r%  r
   r  s   &r2   test_gammaincTestSystematic.test_gammainc4  s1    KKBCU+SC[9	
r4   c           
     t    \        \        P                  R  \        ^ RRR7      \        ^ R4      .RRR7       R# )c                 2    \         P                  ! WR R7      # )T)rq   r#  r  )r1   rq   s   &&r2   rO   /TestSystematic.test_gammaincc.<locals>.<lambda>B  r  r4   r  Fr  r7  r  N)r   r+   	gammainccr
   r  s   &r2   test_gammainccTestSystematic.test_gammaincc>  s1    LLBCU+SC[9	
r4   c                f    R  p\        \        P                  \        V4      \	        4       .4       R# )c                 B    \         P                  ! V 4      P                  # rI   r   r   rL   r.  s   &r2   f&TestSystematic.test_gammaln.<locals>.fJ  s    ??1%***r4   N)r   r+   gammalnr   r
   )r  r  s   & r2   test_gammalnTestSystematic.test_gammalnH  s#    	+ 	BJJ(8(;ceWEr4   )rb  c                    \        \        P                  \        \        P
                  4      \        RR 4      \        4       \        4       .4       R# r  )r   r+   eval_gegenbauerr   r   
gegenbauerr
   r  s   &r2   test_gegenbauerTestSystematic.test_gegenbauerO  s5    V../s^SUCE*	
r4   c                    R  pR p\        V\        V4      \        ^ ^d4      \        R	R4      \        4       .R^dRRR7       \        V\        V4      \        ^ ^d4      \        4       \	        \
        P                  ! R
R^4      4      .^dRR7       R# )c                 B   \        V4      R 8  d   \        P                  # V ^ 8X  d   RpM/V ^8X  d   ^V,          V,          pM\        P                  ! WV4      p\        V4      ^ 8X  d   VR8  d   \        V4      \        \        V4      4      8X  dm   \        P                  ! W\        P                  ! R4      ,           V4      p\        V4      \        P                  ! R4      8  d   \        P                  ! R4      p\        V4      R8  d   \        P                  # V# )r  r   z1e-50z0.0\4@Iwrx   )	r   r"   r  r   r  r?   r   r  r[  rC   rq   rD   r/   s   &&& r2   r  6TestSystematic.test_gegenbauer_int.<locals>.gegenbauerY  s     1v~vv AvaaCE%%aA. Qx1}RE!HE!H,E%%aVZZ-@)@!Dq6FJJw//

5)A 1v~vvHr4   c                     \         P                  ! \        V 4      W4      p\        V4      R 8  d   \        P
                  # V# )r  )r+   r  r   r   r"   r[  r  s   &&& r2   sc_gegenbauer9TestSystematic.test_gegenbauer_int.<locals>.sc_gegenbauert  s1    ""3q610A1v~vvHr4   g    eAi@  Tr   )rC   r   r   r9   r6  Ng    er  )r   r   r   r
   r   r"   r#   )r  r  r  s   &  r2   test_gegenbauer_int"TestSystematic.test_gegenbauer_intW  s    	6	 	Z(As^Ss^SU3d		
 	Z(As^SUHR[[b"-E$FGT		
r4   c                    \        R  \        \        P                  4      \	        ^ ^d4      \        4       \        4       .4       R# )c                 X    \         P                  ! \        V 4      VP                  V4      # rI   )r+   r  r   rL   rC   rq   rD   s   &&&r2   rO   8TestSystematic.test_gegenbauer_complex.<locals>.<lambda>  s    B..s1vqvvqAr4   N)r   r   r   r  r   r
   r   r  s   &r2   test_gegenbauer_complex&TestSystematic.test_gegenbauer_complex  s/    AV../As^SUJL1	
r4   c                    \        R  \        \        P                  4      \	        RR4      \	        4       \        4       .4       R# )c                 Z    \         P                  ! V P                  VP                  V4      # rI   )r+   r  rL   r  s   &&&r2   rO   @TestSystematic.test_gegenbauer_complex_general.<locals>.<lambda>  s    B..qvvqvvqAr4   r{  Nr}  )r   r   r   r  r
   r   r  s   &r2   test_gegenbauer_complex_general.TestSystematic.test_gegenbauer_complex_general  s/    AV../s^SUJL1	
r4   c                x    \        \        P                  \        R  4      \	        RR4      \	        4       .4       R# )c                 8    \         P                  ! W3/ \        B # rI   )r   hankel1r  rN   rD   s   &&r2   rO   -TestSystematic.test_hankel1.<locals>.<lambda>  r  r4   @xDN@x)r   r+   r  r   r
   r  s   &r2   test_hankel1TestSystematic.test_hankel1  +    JJIJsu%	
r4   c                x    \        \        P                  \        R  4      \	        RR4      \	        4       .4       R# )c                 8    \         P                  ! W3/ \        B # rI   )r   hankel2r  r  s   &&r2   rO   -TestSystematic.test_hankel2.<locals>.<lambda>  r  r4   r  Nr  )r   r+   r  r   r
   r  s   &r2   test_hankel2TestSystematic.test_hankel2  r  r4   z%issues at intermediately large ordersc                x    \        R  \        \        P                  4      \	        ^ R4      \        4       .4       R# )c                 B    \         P                  ! \        V 4      V4      # rI   )r+   eval_hermiter   rY  s   &&r2   rO   -TestSystematic.test_hermite.<locals>.<lambda>      Q3r4   rg  N)r   r   r   hermiter   r
   r  s   &r2   test_hermiteTestSystematic.test_hermite  s*    3V^^,Ausu%	
r4   c           	        a \        R RR7      o\        \        P                  V3R l\	        R	R4      \	        ^ R4      .RR7       R# )
r   i  rm  c                 2   < \         P                  ! W3/ SB # rI   )r   rK   )rq   rD   KWs   &&r2   rO   ,TestSystematic.test_hyp0f1.<locals>.<lambda>  s    q2r2r4   r  g     j@r  r  Nr  )r   r   r+   rK   r
   )r  r  s   &@r2   test_hyp0f1TestSystematic.test_hyp0f1  s8    #-II2s^SC[)		
r4   c                    \        R  \        R 4      \        R^
4      \        \	        RR4      \	        ^x^x4      4      .4       R# )c                 D    \         P                  ! V P                  V4      # rI   rJ   )rq   r1   s   &&r2   rO   4TestSystematic.test_hyp0f1_complex.<locals>.<lambda>  s    1661-r4   c                 8    \         P                  ! W3/ \        B # rI   )r   rK   r  rq   rD   s   &&r2   rO   r    r^  r4   Nr   i)r   r   r
   r   r'   r  s   &r2   test_hyp0f1_complex"TestSystematic.test_hyp0f1_complex  s9    -HIb\:gdD&973;LMN	
r4   c                    R  p\        \        P                  V\        R^24      \        ^^2RR7      \        R^24      .RRR7       R# )c                 t     \         P                  ! WV4      #   \         d    \        P                  u # i ; irI   )r   hyp1f1ZeroDivisionErrorr"   r[  r?  s   &&&r2   mpmath_hyp1f11TestSystematic.test_hyp1f1.<locals>.mpmath_hyp1f1  s0    }}Q1--$ vvs    77Fr  r   )rC   r  Nr  )r   r+   r  r
   )r  r  s   & r2   test_hyp1f1TestSystematic.test_hyp1f1  s@    	 	IIb\3q"%8#c2,G	
r4   c           	         \        \        R  4      \        R 4      \        RR4      \        RR4      \	        4       .RR7       R# )c                 Z    \         P                  ! V P                  VP                  V4      # rI   )r+   r  rL   r?  s   &&&r2   rO   4TestSystematic.test_hyp1f1_complex.<locals>.<lambda>  s    ryy'Cr4   c                 :    \         P                  ! WV3/ \        B # rI   )r   r  r  r?  s   &&&r2   rO   r        V]]1-Ng-Nr4   r{  i  r  Nr}  )r   r   r   r
   r   r  s   &r2   test_hyp1f1_complex"TestSystematic.test_hyp1f1_complex  s7    CDNOs^Ss^Z\:		
r4   c           
         \        R  \        R 4      \        RR4      \        RR4      \        RR4      \        4       .^
R7       R# )c                 p    \         P                  ! V P                  VP                  VP                  V4      # rI   )r+   r   rL   rq   rp   r   rD   s   &&&&r2   rO   4TestSystematic.test_hyp2f1_complex.<locals>.<lambda>  s    ryyCr4   c                 :    \         P                  ! WW#3/ \        B # rI   )r   r   r  r  s   &&&&r2   rO   r        aA0TG0Tr4   g      Y@r  Ng      Yr  r  s   &r2   test_hyp2f1_complex"TestSystematic.test_hyp2f1_complex  s;     	CTUs^Ss^Ss^Z\J		
r4   c                    \        \        P                  \        R  4      \	        4       \	        4       \	        4       .4       R# )c                 :    \         P                  ! WV3/ \        B # rI   )r   ro   r  r?  s   &&&r2   rO   ,TestSystematic.test_hyperu.<locals>.<lambda>  r  r4   N)r   r+   ro   r   r
   r  s   &r2   test_hyperuTestSystematic.test_hyperu  s*    IINOUCE35!	
r4   z:mpmath issue gh-342: unsupported operand mpz, long for powc           
     d    R  p\        \        V\        ^ RRR7      \        ^ R4      .R^R7       R# )c                     \         P                  ! W4      \         P                  ! V) 4      ,          \         P                  ! V 4      ,          # rI   )r   powerr%   r|  r  s   &&r2   mp_igam_fac1TestSystematic.test_igam_fac.<locals>.mp_igam_fac  s-    <<%fjj!n4V\\!_DDr4   g  ļBFr  rw   r  N)r   r   r
   )r  r  s   & r2   test_igam_facTestSystematic.test_igam_fac  s5    	E 	De,c!Tl;	
r4   c                    \        \        P                  \        P                  \	        RR 4      .4       \        \        P                  \        P                  \	        RR4      .RR7       R# r{  rx  ry  r8   Nr}  r|  )r   r+   j0r   r
   r  s   &r2   test_j0TestSystematic.test_j0  s@     	BEE699s4~.>?BEE699s4~.>TJr4   c                    \        \        P                  \        P                  \	        RR 4      .4       \        \        P                  \        P                  \	        RR4      .RR7       R# r  )r   r+   j1r   r
   r  s   &r2   test_j1TestSystematic.test_j1  s>    BEE699s4~.>?BEE699s4~.>TJr4   c           	        \        \        P                  \        R  4      \	        4       \	        4       \	        4       \	        4       .4       \        R \        R 4      \        4       \	        4       \	        4       \	        4       .4       R# )c                 :    \         P                  ! WW#3/ \        B # rI   r   jacobir  r  s   &&&&r2   rO   ,TestSystematic.test_jacobi.<locals>.<lambda>  r  r4   c                 D    \         P                  ! \        V 4      WV4      # rI   r+   eval_jacobir   )rC   rp   r   rD   s   &&&&r2   rO   r        r~~c!faA>r4   c                 :    \         P                  ! WW#3/ \        B # rI   r	  r  s   &&&&r2   rO   r    r  r4   N)r   r+   r  r   r
   r   r  s   &r2   test_jacobiTestSystematic.test_jacobi  sX    NNTUUCE35#%(	

 	>TUXsuceSU+	
r4   c           	        a R  o\        R V3R l\        4       \        4       \        4       \        4       .R^2R7       R# )c                 B    V ^ 8X  d   R# \         P                  ! WW#4      # )r<   r   )r   r
  rC   rq   rp   rD   s   &&&&r2   r
  .TestSystematic.test_jacobi_int.<locals>.jacobi  s    Av==q,,r4   c                 D    \         P                  ! \        V 4      WV4      # rI   r  r  s   &&&&r2   rO   0TestSystematic.test_jacobi_int.<locals>.<lambda>%  r  r4   c                 2   < \        S4      ! WW#3/ \        B # rI   )r   r  )rC   rq   rp   rD   r
  s   &&&&r2   rO   r  &  s    /7aNgNr4   i  r^  Nr   r   r
   )r  r
  s   &@r2   test_jacobi_intTestSystematic.test_jacobi_int  s2    	-
 	>NXsuceSU+	
r4   c                \    R  p\        \        P                  V\        RR4      .RR7       R# )c                 v    V ^ 8X  d   \         ) ^,          # \        \        P                  4      ! ^ V 3/ \        B # r   )r   r   r   keir  r   s   &r2   r  $TestSystematic.test_kei.<locals>.kei-  s/    Avs1u#FJJ/1@@@r4   ꌠ9Y>)Fr(  r  Nꌠ9Y>))r   r+   r  r
   )r  r  s   & r2   test_keiTestSystematic.test_kei,  s&    	A
 	BFFC#eT*:);tDr4   c                j    \        \        P                  \        R  4      \	        RR4      .RR7       R# )c                 :    \         P                  ! ^ V 3/ \        B # r   )r   kerr  r   s   &r2   rO   )TestSystematic.test_ker.<locals>.<lambda>7  s    vzz!Q'B''Br4   r!  r(  r  Nr"  )r   r+   r'  r   r
   r  s   &r2   test_kerTestSystematic.test_ker4  s*    FFBC		
r4   c                t    \        \        \        P                  4      R  \	        4       \	        4       .4       R# )c                 J    \        \        P                  4      ! W3/ \        B # rI   r   r   laguerrer  rY  s   &&r2   rO   .TestSystematic.test_laguerre.<locals>.<lambda>@      )&//:1K7Kr4   N)r   r   r+   eval_laguerrer
   r  s   &r2   test_laguerreTestSystematic.test_laguerre<  s&    r''(KUCEN	
r4   c                L    \        R  R \        4       \        4       .RR7       R# )c                 B    \         P                  ! \        V 4      V4      # rI   )r+   r1  r   rY  s   &&r2   rO   2TestSystematic.test_laguerre_int.<locals>.<lambda>F      ))#a&!4r4   c                 J    \        \        P                  4      ! W3/ \        B # rI   r-  rY  s   &&r2   rO   r6  G  r0  r4    N  r  Nr  r  s   &r2   test_laguerre_int TestSystematic.test_laguerre_intD  s    4KXsu		
r4   zsee gh-3551 for bad pointsc           	         \        R  R \        \        P                  ) \        P                  4      \	        ^ ^
4      .RRR7       R# )c                 V    \         P                  ! V \        VP                  4      4      # rI   )r+   rU  r   rL   rD   rN  s   &&r2   rO   3TestSystematic.test_lambertw_real.<locals>.<lambda>O  s    QAFF4r4   c                 V    \         P                  ! V \        VP                  4      4      # rI   )r   rU  r   rL   r>  s   &&r2   rO   r?  P  s    CK8r4   r7   Fr9   r  N)r   r   r"   r[  r   r  s   &r2   test_lambertw_real!TestSystematic.test_lambertw_realL  s4    48(&B-8u		
r4   c           
        aa R p\         P                  ! ^4      oRoVV3R lp\        V\        P                  \        ^ VRR7      .RR7       R# )gGase@g  E@c                   < \         P                  ! R R7      ;_uu_ 4        V S,           R,
          S,          V R,
          ,          pV\         P                  8w  d   V\        V 4      ,          pMFV S,           R,
          S,          RV R,
          ,          ,          pV\        V 4      ,          pW!,          pRRR4       V#   + '       g   i     X# ; i)r   )overrR   N)r"   r   r[  r   )rD   facrU   egs   &  r2   r|  :TestSystematic.test_lanczos_sum_expg_scaled.<locals>.gammaZ  s    (++AQ!c'2"&&=6q99CECK?c1s7m<C6q99CJC , J ,+ Js   BB??C	Fr  r7   r8   N)r"   r%   r   r   r|  r
   )r  maxgammar|  rH  rI  s   &  @@r2   test_lanczos_sum_expg_scaled+TestSystematic.test_lanczos_sum_expg_scaledU  sE    &FF1I)		 	LLH%01		
r4   c                |    \        \        P                  \        P                  \        4       \        4       .4       R # rI   )r   r+   eval_legendrer   legendrer
   r  s   &r2   test_legendreTestSystematic.test_legendrel  s     B,,foosu~Nr4   c                    \        R  R \        4       \        4       .RR7       \        R R \        4       \        \        P
                  ! RR^4      4      .4       R# )	c                 B    \         P                  ! \        V 4      V4      # rI   r+   rO  r   rY  s   &&r2   rO   2TestSystematic.test_legendre_int.<locals>.<lambda>r  r7  r4   c                 J    \        \        P                  4      ! W3/ \        B # rI   r   r   rP  r  rY  s   &&r2   rO   rV  s  r0  r4   r9  r  c                 B    \         P                  ! \        V 4      V4      # rI   rU  rY  s   &&r2   rO   rV  z  r7  r4   c                 J    \        \        P                  4      ! W3/ \        B # rI   rX  rY  s   &&r2   rO   rV  {  r0  r4   Nr  r  )r   r   r
   r   r"   r#   r  s   &r2   test_legendre_int TestSystematic.test_legendre_intp  sK    4KXsu		
 	4KXxCR 89:	
r4   z*apparently picks wrong function at |z| > 1c           	     j    R  pR p\        VV\        ^ ^d4      \        ^ ^d4      \        4       .4       R# )c                 L    \         P                  ! WV4      ^ ,          R,          # r<   )rx   rx   )r+   lqmnrC   rC  r1   s   &&&r2   lqnm(TestSystematic.test_legenq.<locals>.lqnm  s    771#A&u--r4   c                     \        V4      R 8  d   \        P                  # \        \        P
                  4      ! WV^R7      # ra   )type)r   r"   r  r   r   legenqra  s   &&&r2   rg  *TestSystematic.test_legenq.<locals>.legenq  s.    1v~vv#FMM21CCr4   Nr  r  rb  rg  s   &  r2   test_legenqTestSystematic.test_legenq  s5    	.	D 	As^VAs^SU3	
r4   c           	     n    R  pR p\        VV\        ^ ^d4      \        ^ ^d4      \        4       .^dR7       R# )c                     \         P                  ! \        VP                  4      \        V P                  4      V4      ^ ,          R,          # r_  )r+   r`  r   rL   ra  s   &&&r2   rb  0TestSystematic.test_legenq_complex.<locals>.lqnm  s/    773qvv;AFFQ7:5AAr4   c                     \        V4      R 8  d   \        P                  # \        \        P
                  4      ! \        V P                  4      \        VP                  4      V^R7      # re  )r   r"   r  r   r   rg  r   rL   ra  s   &&&r2   rg  2TestSystematic.test_legenq_complex.<locals>.legenq  sA    1v~vv#FMM23qvv;AFFQUVWWr4   r  N)r   r   r   ri  s   &  r2   test_legenq_complex"TestSystematic.test_legenq_complex  s9    	B	X 	As^VAs^Z\:		
r4   c           	     N    R  pR p\        \        V\        4       .R^dVR7       R# )c                 t    \         P                  ! \         P                  ! V 4      V 8H  V ^ 8*  ,          RR4      # )r<   FT)r"   r  floorr   s   &r2   r  0TestSystematic.test_lgam1p.<locals>.param_filter  s+    88RXXa[A-!q&95$GGr4   c                 P    \         P                  ! ^V ,           4      P                  # r   r  r.  s   &r2   	mp_lgam1p-TestSystematic.test_lgam1p.<locals>.mp_lgam1p  s    ??1q5)...r4   r7   r  N)r   r   r
   )r  r  rx  s   &  r2   test_lgam1pTestSystematic.test_lgam1p  s-    	H	/ 	UG%	
r4   c           	     \    R  p\        \        P                  V\        4       .RRRR7       R# )c                      \         P                  ! V 4      pV#   \         d-    \        \        P
                  \        P
                  4      p T# i ; irI   )r   r   
ValueErrorr'   r"   r  )r1   rU   s   & r2   mpmath_loggamma5TestSystematic.test_loggamma.<locals>.mpmath_loggamma  sF    .ooa( J  .bffbff-J.s    3AAFr   )r  distinguish_nan_and_infr9   N)r   r+   r   r   )r  r  s   & r2   test_loggammaTestSystematic.test_loggamma  s+    	 	KK\N$)	
r4   c                ^    R  p\        V\        R 4      \        4       \        4       .4       R# )c                 <    \         P                  ! W4      ^ ,          # r   )r+   pbdvr  s   &&r2   pcfd&TestSystematic.test_pcfd.<locals>.pcfd      771=##r4   c                 8    \         P                  ! W3/ \        B # rI   )r   r  r  r  s   &&r2   rO   *TestSystematic.test_pcfd.<locals>.<lambda>  s    &++a*Fg*Fr4   N)r   r   r
   )r  r  s   & r2   	test_pcfdTestSystematic.test_pcfd  s&    	$FGUCEN	
r4   zHit's not the same as the mpmath function --- maybe different definition?c                P    R  p\        VR \        4       \        4       .RR7       R# )c                 <    \         P                  ! W4      ^ ,          # r   )r+   pbvvr  s   &&r2   pcfv&TestSystematic.test_pcfv.<locals>.pcfv  r  r4   c                 f    \        4       ! \        \        P                  4      4      ! W3/ \        B # rI   )r   r   r   r  r  r  s   &&r2   rO   *TestSystematic.test_pcfv.<locals>.<lambda>  s    (8(EFqWwWr4   r(  r  Nr  )r  r  s   & r2   	test_pcfvTestSystematic.test_pcfv  s#    	$WUCEN		
r4   c           	         R  pR pR p\        V\        P                  \        R^4      \        R^4      .R^dR7       \        VV\        R^4      \        R^4      .R^dR7       R# )c                 <    \         P                  ! W4      ^ ,          # r   r+   pbwar  s   &&r2   pcfw&TestSystematic.test_pcfw.<locals>.pcfw  r  r4   c                 <    \         P                  ! W4      ^,          # r   r  r  s   &&r2   dpcfw'TestSystematic.test_pcfw.<locals>.dpcfw  r  r4   c                 P    \         P                  ! \         P                  W3R4      # )r<   r;   )r   diffr  r  s   &&r2   mpmath_dpcfw.TestSystematic.test_pcfw.<locals>.mpmath_dpcfw  s    ;;v{{QFF;;r4   g:0yU>r  g&.!>Nre   )r   r   r  r
   )r  r  r  r  s   &   r2   	test_pcfwTestSystematic.test_pcfw  si    	$	$	<
 	KKQZR$	
 	QZR$	
r4   zCissues at large arguments (atol OK, rtol not) and <eps-close to z=0c                    \        \        P                  \        4       ! \	        \
        P                  4      4      \        ^ R4      \        4       .4       R# )r<   r(  N)r   r+   	polygammar   r   r   r   r
   r  s   &r2   test_polygammaTestSystematic.test_polygamma  s9     	LLN+F,<,<=>At_ce$	
r4   c           	         \        \        P                  \        P                  \	        R\
        P                  4      .RRRR7       R# )i@  r  FT)rC   r  r   Ni)r   r+   r  r   r
   r"   r[  r  s   &r2   test_rgammaTestSystematic.test_rgamma  s2    IIMM  	
r4   c                    \        \        P                  \        \        P                  4      \        4       .R R7       R# r  )r   r+   r  r   r   r   r  s   &r2   test_rgamma_complex"TestSystematic.test_rgamma_complex  s'    IIV]]+\N		
r4   zNsee gh-3551 for bad points on 32 bit systems and gh-8095 for another bad pointr   c                   \         P                  ! \        P                  4      \         P                  ! R 4      8  d   \        P
                  pMR p\        \        P                  V\        4       \        4       .RR7       R# )rs   c                     \        W,           4      \        W,           4      8X  dE   \        W,           4      ^ 8:  d/   \        P                  ! V 4      p \        W,           4      V ,
          p\        P                  ! W4      # r   )r?   r   r   r  rf)rq   rC  s   &&r2   mppoch&TestSystematic.test_rf.<locals>.mppoch  sO     <3qu:-%,!2C

1AAE
QAyy&r4   r   rG  N)
r   parser   r   Versionr  r   r+   pochr
   )r  r  s   & r2   test_rfTestSystematic.test_rf  sN     ==++,0HHYYF' 	BGGVceSU^Er4   c                    \         P                  ! \        4      P                  p\	        \
        \        P                  \        4       .R ^V,          R7       R# r  )	r"   r5  r?   r6  r   r   r   r7  r
   r  s   & r2   
test_sinpiTestSystematic.test_sinpi&  s8    hhuo!!LLUG3	
r4   c                \    \        \        \        P                  \	        4       .R RR7       R# )Fg+=r  N)r   r   r   r7  r   r  s   &r2   test_sinpi_complex!TestSystematic.test_sinpi_complex0  r  r4   c                    R  p\        V\        P                  \        4       .4       \        V\        P                  \	        . RO4      .4       R# )c                 <    \         P                  ! V 4      ^ ,          # r   rz  r   s   &r2   shi$TestSystematic.test_shi.<locals>.shi:  r~  r4   Nr  )r   r   r  r
   r   r  r  s   & r2   test_shiTestSystematic.test_shi9  r  r4   c                    R  p\        V\        P                  \        \	        \
        P                  ) R4      \	        \
        P                  R4      4      .RR7       R# )c                 <    \         P                  ! V 4      ^ ,          # r   rz  r.  s   &r2   r  ,TestSystematic.test_shi_complex.<locals>.shiA  r~  r4   rx  rY   r8   Nr|  )r   r   r  r   r'   r"   r[  r  s   & r2   test_shi_complexTestSystematic.test_shi_complex@  r  r4   c                T    R  p\        V\        P                  \        4       .4       R# )c                 <    \         P                  ! V 4      ^ ,          # r   r  r   s   &r2   si"TestSystematic.test_si.<locals>.siL  r  r4   N)r   r   r  r
   r  r  s   & r2   test_siTestSystematic.test_siK  s    	!B		CE73r4   c                    R  p\        V\        P                  \        \	        R\
        P                  ) 4      \	        R\
        P                  4      4      .RR7       R# )c                 <    \         P                  ! V 4      ^ ,          # r   r  r.  s   &r2   r  *TestSystematic.test_si_complex.<locals>.siQ  r  r4   rx  rY   r8   Nr|  )r   r   r  r   r'   r"   r[  r  s   & r2   test_si_complexTestSystematic.test_si_complexP  sC    	! 	IIrvvg.RVV0DEF		
r4   c                    R  p\        \        P                  \        V4      \	        ^ \
        P                  4      .RR7       R# )c                 >    \         P                  ! ^^V ,
          4      # r,  r   r-  r   s   &r2   dilog)TestSystematic.test_spence.<locals>.dilog]      >>!QU++r4   r   r8   N)r   r+   r/  r   r
   r"   r[  r  r  s   & r2   test_spenceTestSystematic.test_spence[  s3    	, 	IIU#BFF^		
r4   c                j    R  p\        \        P                  \        V4      \	        4       .RR7       R# )c                 >    \         P                  ! ^^V ,
          4      # r,  r  r.  s   &r2   r  1TestSystematic.test_spence_complex.<locals>.dilogh  r  r4   r   r8   N)r   r+   r/  r   r   r  s   & r2   test_spence_complex"TestSystematic.test_spence_complexg  s(    	,IIU#\N		
r4   c           	         \        \        P                  \        \        P
                  4      \        RR 4      \        ^ R 4      .RR7       R# )r  &.>r8   N     )r   r+   struver   r   struvehr
   r  s   &r2   test_struvehTestSystematic.test_struvehq  s4    IIV^^,s^SC[)		
r4   c           	         R  p\        \        P                  \        V4      \	        RR4      \	        ^ R4      .RRR7       R# )c                 T   V ^ 8  ds   W) 8  dl   \        V 4      R8  d\   \        P                  P                  p R\        P                  n        \        P                  ! W4      V\        P                  n        # \        P                  ! W4      #   T\        P                  n        i ; i)r<   r(  r   )r   r   r   r   struvel)rN   r1   r   s   && r2   
mp_struvel/TestSystematic.test_struvel.<locals>.mp_struvelz  sk    1uRCFTM ))--,$'FIIM!>>!/$+FIIM>>!'' %,FIIMs   *B B'r  r  Tr   Nr  )r   r+   	modstruver   r
   )r  r  s   & r2   test_struvelTestSystematic.test_struvely  s:    		( 	LLZ(s^SC[) 	
r4   c           	     `    R  p\        \        P                  V\        RR4      .R^ RR7       R# )c                     \         P                  ! \         P                  ! V 4      \         P                  ! R 4      4      # )z-0.5)r   rU  r%   r  r   s   &r2   mpmath_wrightomega_realETestSystematic.test_wrightomega_real.<locals>.mpmath_wrightomega_real  s$    ??6::a=&**V2DEEr4   gPKDg+<F)r9   rd   r  Nr{   )r   r+   r^  r
   )r  r  s   & r2   test_wrightomega_real$TestSystematic.test_wrightomega_real  s2    	F 	NN#	
r4   c                V    \        \        P                  R  \        4       .RRR7       R# )c                     \        V ^4      # )   )rW  r.  s   &r2   rO   1TestSystematic.test_wrightomega.<locals>.<lambda>  s    )!R0r4   r   FrA  N)r   r+   r^  r   r  s   &r2   test_wrightomegaTestSystematic.test_wrightomega  s!    NN0\N	
r4   c           
         \        \        P                  \        \        P                  4      \        ^RRR7      \        ^ RR7      .4       R# )r=       _BF)rq   rp   r  rq   r  N)r   r+   zetar   r   r
   r  s   &r2   test_hurwitz_zeta TestSystematic.test_hurwitz_zeta  s5    GGV[[)1%0#u2MN	
r4   c                Z    \        \        P                  R  \        R^d4      .RRR7       R# )c                 \    V ^8w  d   \         P                  ! V 4      # \         P                  # r   r   r  r[  r   s   &r2   rO   2TestSystematic.test_riemann_zeta.<locals>.<lambda>  s    Qfkk!n>FJJ>r4   Frb   r  Nr4  )r   r+   r  r
   r  s   &r2   test_riemann_zeta TestSystematic.test_riemann_zeta  s&    GG>s^	
r4   c           	     \    \        \        P                  R  \        R^d4      .R^-RR7       R# )c                 j    V ^8w  d   \         P                  ! V 4      ^,
          # \         P                  # r   r	  r   s   &r2   rO   +TestSystematic.test_zetac.<locals>.<lambda>  s#    AFfkk!nq(B

Br4   Frb   )r  r   r9   Nr4  )r   r+   zetacr
   r  s   &r2   
test_zetacTestSystematic.test_zetac  s)    HHBs^	
r4   c           	         R  p\        \        P                  \        V4      \	        ^ RR7      \	        4       .^^<RR7       R# )c                    \         P                  P                  V 4      p \         P                  P                  V4      pV^ 8X  d    \         P                  P                  V 4      # \         P                  P	                  W4      V,          # r   r   r   r  r   powm1)rD   lmbdas   &&r2   	mp_boxcox-TestSystematic.test_boxcox.<locals>.mp_boxcox  sX    		a AIIMM%(Ezyy}}Q''yyq0588r4   Fr  r7   rW  N)r   r+   boxcoxr   r
   )r  r  s   & r2   test_boxcoxTestSystematic.test_boxcox  s:    	9 	IIY'1%(#%0	
r4   c           	         R  p\        \        P                  \        V4      \	        RRR7      \	        4       .^^<RR7       R# )c                 n   \         P                  P                  V 4      p \         P                  P                  V4      p\         P                  P                  ^4      pV^ 8X  d&   \         P                  P                  W ,           4      # \         P                  P	                  W ,           V4      V,          # r   r  )rD   r  ones   && r2   mp_boxcox1p1TestSystematic.test_boxcox1p.<locals>.mp_boxcox1p  sp    		a AIIMM%(E))--"Czyy}}SW--yysw6>>r4   Fr  r7   rW  Nrx   )r   r+   boxcox1pr   r
   )r  r   s   & r2   test_boxcox1pTestSystematic.test_boxcox1p  s:    	? 	KK[)25)351	
r4   c           	     r    R  p\        R \        V4      \        ^ ^4      \        RR4      .RRR 3R7       R# )c                 L   \         P                  ! V4      p\         P                  ! V \         P                  ! ^4      ^,          ,           V4      \         P                  ! ^V,          \         P
                  ,          4      ,          pVP                  ^ 8X  d   VP                  # V# r   r   	mpmathifyr  r  rO  r   rT  rL   rC   r1   argouts   &&  r2   mp_spherical_jn9TestSystematic.test_spherical_jn.<locals>.mp_spherical_jn  i    ""1%C>>!fjjmAo"5s;;;quVYY/0Cxx1}xx
r4   c                 B    \         P                  ! \        V 4      V4      # rI   )r+   spherical_jnr   rC   r1   s   &&r2   rO   2TestSystematic.test_spherical_jn.<locals>.<lambda>  r  r4   rx  r  Nc                 4    \         P                  ! V 4      R 8  # )g#B;)r"   r   r.  s   &r2   rO   r2    s    "&&)e*;r4   )r   r  r|  r)  r  r,  s   & r2   test_spherical_jn TestSystematic.test_spherical_jn  s<    	 	3_-As^Ss^, ;<	
r4   c                b    R  p\        R \        V4      \        ^ ^4      \        4       .4       R# )c                 L   \         P                  ! V4      p\         P                  ! V \         P                  ! ^4      ^,          ,           V4      \         P                  ! ^V,          \         P
                  ,          4      ,          pVP                  ^ 8X  d   VP                  # V# r   r'  r)  s   &&  r2   r,  ATestSystematic.test_spherical_jn_complex.<locals>.mp_spherical_jn  r.  r4   c                 V    \         P                  ! \        V P                  4      V4      # rI   )r+   r0  r   rL   r1  s   &&r2   rO   :TestSystematic.test_spherical_jn_complex.<locals>.<lambda>      QVVa8r4   Nr   r   r   r   r4  s   & r2   test_spherical_jn_complex(TestSystematic.test_spherical_jn_complex  ,    	 	8_-As^Z\*	
r4   c           	     j    R  p\        R \        V4      \        ^ ^4      \        RR4      .^dR7       R# )c                 L   \         P                  ! V4      p\         P                  ! V \         P                  ! ^4      ^,          ,           V4      \         P                  ! ^V,          \         P
                  ,          4      ,          pVP                  ^ 8X  d   VP                  # V# r   r   r(  r  r  rO  r   rT  rL   r)  s   &&  r2   mp_spherical_yn9TestSystematic.test_spherical_yn.<locals>.mp_spherical_yn  r.  r4   c                 B    \         P                  ! \        V 4      V4      # rI   )r+   spherical_ynr   r1  s   &&r2   rO   2TestSystematic.test_spherical_yn.<locals>.<lambda>  r  r4   r  rG  Ng    _r)  r  rD  s   & r2   test_spherical_yn TestSystematic.test_spherical_yn
  s4    	 	3_-As^S-.		
r4   c                b    R  p\        R \        V4      \        ^ ^4      \        4       .4       R# )c                 L   \         P                  ! V4      p\         P                  ! V \         P                  ! ^4      ^,          ,           V4      \         P                  ! ^V,          \         P
                  ,          4      ,          pVP                  ^ 8X  d   VP                  # V# r   rC  r)  s   &&  r2   rD  ATestSystematic.test_spherical_yn_complex.<locals>.mp_spherical_yn  r.  r4   c                 V    \         P                  ! \        V P                  4      V4      # rI   )r+   rG  r   rL   r1  s   &&r2   rO   :TestSystematic.test_spherical_yn_complex.<locals>.<lambda>&  r<  r4   Nr=  rI  s   & r2   test_spherical_yn_complex(TestSystematic.test_spherical_yn_complex  r@  r4   c                h    R  p\        R \        V4      \        ^ ^4      \        4       .^RR7       R# )c                 L   \         P                  ! V4      p\         P                  ! V \         P                  ! ^4      ^,          ,           V4      \         P                  ! ^V,          \         P
                  ,          4      ,          pVP                  ^ 8X  d   VP                  # V# r   r   r(  r  r  rO  r   rT  rL   r)  s   &&  r2   mp_spherical_in9TestSystematic.test_spherical_in.<locals>.mp_spherical_in,  r.  r4   c                 B    \         P                  ! \        V 4      V4      # rI   )r+   spherical_inr   r1  s   &&r2   rO   2TestSystematic.test_spherical_in.<locals>.<lambda>6  r  r4   rR  Ng訰6r)  r  rV  s   & r2   test_spherical_in TestSystematic.test_spherical_in+  s2    	 	3_-As^SU#	
r4   c                b    R  p\        R \        V4      \        ^ ^4      \        4       .4       R# )c                 L   \         P                  ! V4      p\         P                  ! V \         P                  ! ^4      ^,          ,           V4      \         P                  ! ^V,          \         P
                  ,          4      ,          pVP                  ^ 8X  d   VP                  # V# r   rU  r)  s   &&  r2   rV  ATestSystematic.test_spherical_in_complex.<locals>.mp_spherical_in>  r.  r4   c                 V    \         P                  ! \        V P                  4      V4      # rI   )r+   rY  r   rL   r1  s   &&r2   rO   :TestSystematic.test_spherical_in_complex.<locals>.<lambda>H  r<  r4   Nr=  r[  s   & r2   test_spherical_in_complex(TestSystematic.test_spherical_in_complex=  r@  r4   c                f    R  p\        R \        V4      \        ^ ^4      \        4       .^dR7       R# )c                 t   \         P                  ! V4      p\         P                  ! V \         P                  ! ^4      ^,          ,           V4      \         P                  ! ^V,          \         P
                  ,          4      ,          p\         P                  ! V4      P                  ^ 8X  d   VP                  # V# r   r   r(  r   r  rO  r   rT  rL   r)  s   &&  r2   mp_spherical_kn9TestSystematic.test_spherical_kn.<locals>.mp_spherical_knN  sw    ""1%C>>!fjjmAo"5s;;;quVYY/0C"''1,xx
r4   c                 B    \         P                  ! \        V 4      V4      # rI   )r+   spherical_knr   r1  s   &&r2   rO   2TestSystematic.test_spherical_kn.<locals>.<lambda>X  r  r4   rG  Nr)  r  rh  s   & r2   test_spherical_kn TestSystematic.test_spherical_knM  s/    	 	3_-As^SU#		
r4   z.Accuracy issues near z = -1 inherited from kv.c                f    R  p\        R \        V4      \        ^ ^4      \        4       .^R7       R# )c                 L   \         P                  ! V4      p\         P                  ! V \         P                  ! ^4      ^,          ,           V4      \         P                  ! ^V,          \         P
                  ,          4      ,          pVP                  ^ 8X  d   VP                  # V# r   rg  r)  s   &&  r2   rh  ATestSystematic.test_spherical_kn_complex.<locals>.mp_spherical_kna  r.  r4   c                 V    \         P                  ! \        V P                  4      V4      # rI   )r+   rk  r   rL   r1  s   &&r2   rO   :TestSystematic.test_spherical_kn_complex.<locals>.<lambda>k  r<  r4   rG  Nr=  rm  s   & r2   test_spherical_kn_complex(TestSystematic.test_spherical_kn_complex^  s/    	 	8_-As^Z\*		
r4   r4  N)__name__
__module____qualname____firstlineno__r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r*  r   rB  rI  rT  r_  pytestmarkxfailri  rq  rv  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$  r+  r   r6  r;  r@  rC  rJ  rR  rY  r_  rf  ri  rr  ry  r}  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r  xfail_on_32bitr  r  r  r  r  r#  r)  r2  r:  rB  rL  rQ  r[  rj  rq  rz  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r#  r5  r>  rJ  rQ  r\  rc  rn  ru  __static_attributes____classdictcell__)__classdict__s   @r2   rq  rq    s\    .,
.,
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. O O
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8 [[56  7
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P
r4   rq  )L__doc__numpyr"   numpy.testingr   r   r   r{  r   
scipy._libr   scipy.specialspecialr+   scipy.special._testutilsr   r   r   r	   scipy.special._mptestutilsr
   r   r   r   r   r   r   r   r   r   scipy.special._ufuncsr   r   r   r   r   r   r   ImportErrorr|  thread_unsafe
pytestmarkr3   rE   rV   r^   rr   r   r   r   r   slowr   r   r   r   r   r  r  r  r  r  r  r)  r2  r9  r<  rP  rW  rd  rg  rj  rl  r   r  rq  r4  r4   r2   <module>r     s    2         % [[&&> ' @
 vv- - vv	> 	>  vv! !( vv6 6 vwO  O, vwC  C" vvG G> vvC C* vv/ /$ vvE  E8 vv: :* vv0K 0Kn vv:  :L   vv= =  vv= =& vv;  ;. vv<  <* vv< <& vv< <( vvB  B& vv;  ;& vv
8 
8 vv8 8$ vv9 90 vv?  ?* vv
@  
@ vv
@  
@" vv=  = sS
) vvD
 D
  D
a  %8$F%s   M M/.M/