+
    ‰°³jëx  ã                   ó”  € ^ RI 5 ^ RI5 ^ RIt^ RIt^ RIt^ RIt]3R l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 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, t0R- t1R. t2R/ t3R0 t4R1 t5R2 t6R3 t7R4 t8R5 t9R6 t:R7 t;R8 t<R9 t=R: t>R; t?R< t@R= tAR> tBR? tCR# )@é    )Ú*Nc                 óÊ   € R pT;'       d'    V P                   P                  VP                   V4      pT;'       d'    V P                  P                  VP                  V4      pV# )T)ÚrealÚaeÚimag)ÚaÚbÚepsÚress   &&& Ú\/home/luca/screen-checking/.venv/lib/python3.14/site-packages/mpmath/tests/test_functions.pyÚmpc_aer      sL   € Ø
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        \        \        4      8X  g   Q h\        \        \        4      8X  g   Q h\        \        \        4      8X  g   Q h\        \        \        4      8X  g   Q h\        \        \        4      8X  g   Q h\        \        \         4      8X  g   Q h\"        \        \$        4      8X  g   Q h\&        \        \(        4      8X  g   Q h\*        \        \,        4      8X  g   Q hV ^28  g   EK  \.        \        \0        4      8X  g   Q h\2        \        \4        4      8X  d   EKR  Q h	  ^\         n        \        R8¼  g   Q h\        ^8”  g   Q h\        ^8”  g   Q h\        ^8  g   Q hR# )é   N)	r   é   é
   é   é   é%   éP   éd   é   éÿÿÿÿ)ÚmpÚdpsÚpiÚmpfÚtpiÚeÚteÚdegreeÚtdegreeÚeulerÚteulerÚln2Útln2Úln10Útln10ÚcatalanÚtcatalanÚkhinchinÚ	tkhinchinÚglaisherÚ	tglaisherÚphiÚtphiÚmertensÚtmertensÚ	twinprimeÚ
ttwinprime©Úprecs    r   Útest_constantsr7   -   s#  € Ü3ˆØŒŒÜ”Sœ“XŒ~Ðˆ~Ü”Cœ“GŒ|Ðˆ|ÜœœW›Ô%Ð%Ð%ÜœœF›Ô#Ð#Ð#Ü”cœ$“iÔÐÐÜ”sœ5“zÔ!Ð!Ð!Üœ#œh›-Ô'Ð'Ð'Üœ3œy›>Ô)Ð)Ð)Üœ3œy›>Ô)Ð)Ð)Ü”cœ$“iÔÐÐØ�"�9Üœc¤(›mÔ+Ð+Ð+Ü¤¤J£×/Ð/Ð/ñ 4ð „B„FÜ�Œ8€Oˆ8Ü�Œ6€Mˆ6Ü�Œ6€Mˆ6Ü�Œ6€MŠ6r   c            	      óÆ  € \        R 4       F$  p \        \        W ,          4      4      V 8X  d   K$  Q h	  \        P                  ! ^4       R F‚  pV\
        n        \        ^4       Fe  p \        P                  ! ^
V^,          ^,
          ,          ^
V^,          ^,
          ,          4      p\        \        W",          4      4      V8X  d   Ke  Q h	  K„  	  ^\
        n        \        ^d4       Fu  p R Fl  p\        \        W3,          ^V ,          34      4      \        W034      8X  g   Q h\        \        W3,          RV ,          34      4      \        W0) 34      8X  d   Kl  Q h	  Kw  	  R# )é N  N©r   é,  éè  é'  )é   é   é   i³¶ éþÿÿÿ)ÚrangeÚsqrtr   ÚrandomÚseedr   r   Úrandint)Úir6   ÚAr   s       r   Útest_exact_sqrtsrI   C   s  € Ü�5Ž\ˆÜ”C˜�“H‹~ Ö"Ð"Ð"ñ ä
‡K‚K�„NÛ'ˆØŒŒÜ�r–ˆAÜ—’˜r D¨!¥G¨A¥I�°°T¸1µW¸QµYµÓ@ˆAÜœ˜A�C›“> QÖ&Ð&Ð&ó ñ (ð
 „B„FÜ�3ŽZˆÛ#ˆAÜœ˜Q�S ! A¥#˜J›Ó(¬C°°«KÔ7Ð7Ð7Üœ˜Q�S " Q¥$˜KÓ(Ó)¬S°!°R°«\Ö9Ð9Ð9ó $ó r   c            	      ó  € R
 FÂ  p \        V 4      p R F®  pV\        n        \        \	        V \        P
                  \        4      ^\        P
                  \        4      p\        \	        V \        P
                  \        4      ^\        P
                  \        4      p\        W 4      '       g   Q h\        W04      '       d   K®  Q h	  KÄ  	  \        P                  ! R4       ^dp\        \        \        3 F>  p\        ^d4       F,  p \        V4      p\!        W"4      p\	        W4V4      V8X  d   K,  Q h	  K@  	  ^d\        n        \#        ^	4      R,           p\#        ^	4      R,
          p^\        n        \%        VRR7      ^8X  g   Q h\%        VRR7      ^8X  g   Q h\%        VRR7      ^8”  g   Q h\%        VRR7      ^8  g   Q h\%        VRR7      ^8X  g   Q h\%        VRR7      ^8X  g   Q h\%        \#        R4      4      \#        R4      8X  g   Q hR	# )é   éÒ  go™„ÙK@-Úd©ÚroundingÚnÚuz7.0503726185518891z2.655253776675949N)rK   r   é   é   r   r?   r   é   é   é   é   r   )r   r   éS   éj   iÐ  )Úfrom_intr   r   Úmpf_pow_intÚmpf_sqrtr6   Ú
round_downÚround_upÚmpf_ltÚmpf_gtrD   rE   Úround_nearestÚround_ceilingrB   Úmpf_randÚmpf_mulr   rC   )rG   r   r   r	   r6   Úrnds         r   Útest_sqrt_roundingrf   R   s¤  € Û7ˆÜ�Q‹KˆÛ)ˆCØŒBŒFÜœH Q¬¯©´Ó<¸aÄÇÁÌ*ÓUˆAÜœH Q¬¯©´Ó:¸A¼r¿w¹wÌÓQˆAÜ˜!—<’<Ð�<Ü˜!—<”<Ð�<ó *ñ 8ô ‡K‚K�ÔØ€DÜœM¬=Ó9ˆÜ�s–ˆAÜ˜“ˆAÜ˜“ˆAÜ˜A SÓ)¨QÖ.Ð.Ð.ó ñ :ð „B„FÜˆA‹��€AÜˆA‹��€AØ„B„FÜ�˜CÔ  AÔ%Ð%Ð%Ü�˜CÔ  AÔ%Ð%Ð%Ü�˜CÔ  1Ô$Ð$Ð$Ü�˜CÔ  1Ô$Ð$Ð$Ü�˜CÔ  AÔ%Ð%Ð%Ü�˜CÔ  AÔ%Ð%Ð%ä”Ð(Ó)Ó*¬cÐ2EÓ.FÔFÐFÒFr   c                  óì  € ^\         n        R F.  p \        \        V 4      4      \	        V 4      R,          8X  d   K.  Q h	  \        R4      R8X  g   Q h\        R4      P                  \        P                  ! R4      4      '       g   Q h\        R4      P                  \        P                  ! R4      4      '       g   Q h\        R4      P                  \        P                  ! R4      4      '       g   Q h\        R4      P                  \        P                  ! R4      4      '       g   Q h\        R	4      P                  \        P                  ! R	4      4      '       g   Q h\        \        P                  \        P                  R,          ,           4      P                  \        P                  ! \        P                  \        P                  R,          ,           4      4      '       g   Q h\        \        P                  \        P                  R,          ,
          4      P                  \        P                  ! \        P                  \        P                  R,          ,
          4      4      '       g   Q hR# )
r   ç      à?ù              ð?N)r   gH¯¼šò×z>çš™™™™™¹?rh   r>   rK   r   é   rR   gZd;ßOÕ?g\�Âõ(S@r   rA   éýÿÿÿéœÿÿÿy       €      ð¿)
r   r   rC   r   Úfloatr   ÚcmathÚmathr   r   ©Úxs    r   Útest_float_sqrtrs   p   su  € Ø„B„Fã=ˆÜ”C˜“F‹|œu Q›x¨�}Ö,Ð,Ð,ñ >ä�‹8�rŒ>Ðˆ>Ü�‹8�;‰;”u—z’z "“~×&Ò&Ð&Ð&Ü�‹8�;‰;”u—z’z "“~×&Ò&Ð&Ð&Ü�‹:�=‰=œŸš DÓ)×*Ò*Ð*Ð*Ü�‹8�;‰;”u—z’z "“~×&Ò&Ð&Ð&Ü�‹9�<‰<œŸ
š
 3›×(Ò(Ð(Ð(Ü”—‘œ$Ÿ&™& �)Õ#Ó$×'Ñ'¬¯
ª
´4·7±7¼T¿V¹VÀB½YÕ3FÓ(G×HÒHÐHÐHÜ”—‘œ$Ÿ&™& �)Õ#Ó$×'Ñ'¬¯
ª
´4·7±7¼T¿V¹VÀB½YÕ3FÓ(G×HÒHÐHÒHr   c                  ó  € \        ^ ^ 4      ^ 8X  g   Q h\        ^ R4      \        R4      8X  g   Q h\        R^ 4      \        R4      8X  g   Q h\        R^ 4      \        R4      8X  g   Q h\        ^^4      \        ^4      8X  g   Q hR# )r   g…ëQ¸Õ?Ng…ëQ¸Õ¿)Úhypotr   © r   r   Ú
test_hypotrw   ~   sv   € Ü��A‹;˜!ÔÐÐÜ��D‹>œS ›YÔ&Ð&Ð&Ü��q‹>œS ›YÔ&Ð&Ð&Ü�˜‹?œc $›iÔ'Ð'Ð'Ü��A‹;œ#˜a›&Ô Ð Ò r   c                  óº  € \        ^ R^È4       F+  p \        \        W ,          V ,          4      4      V 8X  d   K+  Q h	  \        P                  ! ^4       R Fw  pV\
        n        \        P                  ! ^
V^,          ^,
          ,          ^
V^,          ^,
          ,          4      p\        \        W",          V,          4      4      V8X  d   Kw  Q h	  ^\
        n        R# )r   r9   Nr:   )rB   Úcbrtr   rD   rE   r   r   rF   )rG   r6   rH   s      r   Útest_exact_cbrtrz   …   sœ   € Ü�1�e˜SÖ!ˆÜ”C˜�˜A�“JÓ 1Ö$Ð$Ð$ñ "ä
‡K‚K�„NÛ'ˆØŒŒÜ�NŠN˜2  a¥¨¥	�?¨B°°qµ¸µ­OÓ<ˆÜ”C˜�˜A�“JÓ 1Ö$Ð$Ð$ñ (ð „B†Fr   c                  ó°  € \        ^ 4      ^8X  g   Q h\        R4      P                  \        R4      4      '       g   Q h\        R4      P                  \        R4      4      '       g   Q h\        \        R4      4      p V P                  \	        V P
                  4      8X  g   Q h^C\        n        \        \        R4      4      p V P                  \	        V P
                  4      8X  g   Q h^5\        n        \        \        ^
,          4      P                  R4      '       g   Q h\        R	4      P                  \        P                   ! R	4      4      '       g   Q hR# )
r   r=   z8.8068182256629215873e4342z1.1354838653147360985e-4343é   NiðØÿÿ)r>   l   ÍV=€é iËÿÿÿé5   )r>   l   …G‹{ÜQÓE iÄÿÿÿé=   ù       @       @)
Úexpr   r   ÚbcÚbitcountÚmanr   r6   r%   ro   )r   s    r   Útest_expr„   �   sò   € Üˆq‹6�QŒ;Ðˆ;Üˆu‹:�=‰=œÐ9Ó:×;Ò;Ð;Ð;Üˆv‹;�>‰>œ#Ð;Ó<×=Ò=Ð=Ð=ÜŒCÐ.Ó/Ó0€AØ�4‰4”8˜AŸE™E“?Ô"Ð#Ð"Ø„B„GÜŒCÐ1Ó2Ó3€AØ�4‰4”8˜AŸE™E“?Ô"Ð#Ð"Ø„B„GÜŒs�R�x‹=×Ñ˜D×!Ò!Ð!Ð!Üˆt‹9�<‰<œŸ	š	 $›×(Ò(Ð(Ò(r   c                  óÆ   € R \         n        \        R4      p \        ^4      p^\         n        V 5P                  R4      '       g   Q hV5P                  R4      '       g   Q hR# )i   g8ï,6V‹×?giW‹
¿@Nr   )r   r   r€   r   )r   r	   s     r   Útest_issue_73r†   œ   sR   € Ø„B„FÜˆB‹€AÜˆA‹€AØ„B„FØˆB�7‰7Ð&×'Ò'Ð'Ð'ØˆB�7‰7Ð%×&Ò&Ð&Ò&r   c                  ó¢  € ^\         n        \        ^4      ^ 8X  g   Q hRRRR^d^
^2,          R3 FK  p \        V 4      P                  \        P                  ! V 4      4      '       g   Q h\        W 4      ^8X  d   KK  Q h	  \        R^4      ^
8X  g   Q h\        ^
R,          ^
4      R8X  g   Q h\        R4      P                  \
        P                  ! R4      4      '       g   Q h\        R4      P                  R,          P                  R4      '       g   Q h\        R4      P                  R,          P                  R4      '       g   Q h\        R4      P                  R,          P                  R4      '       g   Q h\        R4      P                  R,          P                  R4      '       g   Q h\        R4      P                  R,          P                  R4      '       g   Q h\        R4      P                  R,          P                  R4      '       g   Q h\        R4      P                  R,          P                  R4      '       g   Q h\        R4      P                  R,          P                  R4      '       g   Q h\        R4      P                  R,          P                  R4      '       g   Q h\        R4      P                  R,          P                  R4      '       g   Q h\        R4      P                  R,          P                  R4      '       g   Q h\        R4      P                  ^
^P,          ,          P                  R4      '       g   Q h\        R4      P                  ^
^P,          ,          P                  R4      '       g   Q h\        \        R	R4      4      P                  \        ^4      R
,          4      '       g   Q h\        \        R	^
^È,          4      4      P                  \        ^4      R,          4      '       g   Q h\        \        ^ ^ 4      4      \        \        ) ^ 4      8X  g   Q h\        \        \        \        ^ 4      4      P                  4      '       g   Q h\        \        \        \        ^ 4      4      P                  4      '       g   Q h\        \        \        ^ \        4      4      P                  4      '       g   Q h\        \        \        ^ \        4      4      P                  4      '       g   Q h\        \        \        \        ^4      4      P                  4      '       g   Q h\        \        \        \        ^4      4      P                  4      '       g   Q h\        \        \        ^\        4      4      P                  4      '       g   Q h\        \        \        ^\        4      4      P                  4      '       g   Q hR# )r   rh   ç      ø?ç       @g      @ç¸ÔJzî�5r|   rL   g €à7yÃ@gX9´Èv¾ó?g@Œµx¯DgZb××çtiNr   y333333ã?š™™™™™é?l     ;áy333333ã?š™™™™™é¿yš™™™™™é?333333ã¿y      ð?:Œ0âŽyE>l     ‚_Éy      ð?:Œ0âŽyE¾y      ð¿:Œ0âŽyE>y      ð¿:Œ0âŽyE¾y:Œ0âŽyE>      ð?y:Œ0âŽyE¾      ð?y:Œ0âŽyE>      ð¿y:Œ0âŽyE¾      ð¿y      ð?œWw'&l¡7yœWw'&l¡7      ð?ì      Fµx:^V )r   r   Úlogr   rp   ro   r   ÚldexpÚmpcÚinfÚisnanÚnanr   rq   s    r   Útest_logr’   ¤   s2  € Ø„B„FÜˆq‹6�QŒ;Ðˆ;Ø�3˜˜S # r¨2¥v¨uÓ5ˆÜ�1‹v�y‰yœŸš !›×%Ò%Ð%Ð%Ü�1‹y˜AŽ~Ðˆ~ñ 6ô ˆt�Q‹<˜2ÔÐÐÜˆr�4�x˜Ó Ô$Ð$Ð$Üˆt‹9�<‰<œŸ	š	 $›×(Ò(Ð(Ð(ä�‹M×Ñ˜vÕ%×)Ñ)Ð*<×=Ò=Ð=Ð=Ü�‹M×Ñ˜vÕ%×)Ñ)Ð*<×=Ò=Ð=Ð=Ü�‹M×Ñ˜vÕ%×)Ñ)Ð*<×=Ò=Ð=Ð=Ü�‹L×Ñ˜fÕ$×(Ñ(¨×-Ò-Ð-Ð-Ü�‹L×Ñ˜fÕ$×(Ñ(¨×-Ò-Ð-Ð-Ü�‹M×Ñ˜vÕ%×)Ñ)¨#×.Ò.Ð.Ð.Ü�‹M×Ñ˜vÕ%×)Ñ)¨#×.Ò.Ð.Ð.Ü�‹L×Ñ˜fÕ$×(Ñ(¨×-Ò-Ð-Ð-Ü�‹L×Ñ˜fÕ$×(Ñ(¨×-Ò-Ð-Ð-Ü�‹M×Ñ˜vÕ%×)Ñ)¨#×.Ò.Ð.Ð.Ü�‹M×Ñ˜vÕ%×)Ñ)¨#×.Ò.Ð.Ð.Ü�‹M×Ñ˜r 2�vÕ%×)Ñ)¨#×.Ò.Ð.Ð.Ü�‹M×Ñ˜r 2�vÕ%×)Ñ)¨#×.Ò.Ð.Ð.äŒu�U˜6Ó"Ó#×&Ñ&¤s¨1£v¨d¥{×3Ò3Ð3Ð3ÜŒu�U˜2˜s�7Ó#Ó$×'Ñ'¬¨A«¨u­×5Ò5Ð5Ð5äŒs�1�Q‹x‹=œC¤  Q›KÔ'Ð'Ð'Ü””Sœ˜Q“Z“×%Ñ%×&Ò&Ð&Ð&Ü””Sœ˜Q“Z“×%Ñ%×&Ò&Ð&Ð&Ü””S˜œ3“Z“×%Ñ%×&Ò&Ð&Ð&Ü””S˜œ3“Z“×%Ñ%×&Ò&Ð&Ð&Ü””Sœ˜Q“Z“×%Ñ%×&Ò&Ð&Ð&Ü””Sœ˜Q“Z“×%Ñ%×&Ò&Ð&Ð&Ü””S˜œ3“Z“×%Ñ%×&Ò&Ð&Ð&Ü””S˜œ3“Z“×%Ñ%×&Ò&Ð&Ò&r   c                  ó*  € \        \        ^d4      4      \        \        R^ 4      4      ,            EF‡  p V R,          p\        \        V4      4      P	                  \
        P                  ! V4      4      '       g   Q h\        \        V4      4      P	                  \
        P                  ! V4      4      '       g   Q h\        \        V4      4      P	                  \
        P                  ! V4      4      '       g   Q h\        \        V4      4      P	                  \
        P                  ! V4      4      '       g   Q h\        \        V4      4      P	                  \
        P                  ! V4      4      '       g   Q h\        \        V4      4      P	                  \
        P                  ! V4      4      '       d   EKˆ  Q h	  \        R4      P	                  \        P                  ! R4      4      '       g   Q h\        R4      P	                  \        P                  ! R4      4      '       g   Q h\        R4      P	                  \        P                  ! R4      4      '       g   Q h\        R4      P	                  \        P                  ! R4      4      '       g   Q hR# )r   gffffff@Nrm   y      ð?      ð?y      ÀÍÌÌÌÌÌÀ)ÚlistrB   Úcosr   r   rp   ÚsinÚtanÚcoshÚsinhÚtanhro   )rr   Úts     r   Útest_trig_hyperb_basicrœ   É   s—  € Ü”5˜“:Ó¤¤e¨D°£mÓ!4×4Ñ4ˆØ��GˆÜ”3�q“6‹{�~‰~œdŸhšh q›k×*Ò*Ð*Ð*Ü”3�q“6‹{�~‰~œdŸhšh q›k×*Ò*Ð*Ð*Ü”3�q“6‹{�~‰~œdŸhšh q›k×*Ò*Ð*Ð*Ü”C˜“F‹|�‰œtŸyšy¨›|×,Ò,Ð,Ð,Ü”C˜“F‹|�‰œtŸyšy¨›|×,Ò,Ð,Ð,Ü”C˜“F‹|�‰œtŸyšy¨›|×,Õ,Ð,Ð,ñ 5ô ˆt‹9�<‰<œŸ	š	 $›×(Ò(Ð(Ð(Üˆw‹<�?‰?œ5Ÿ9š9 WÓ-×.Ò.Ð.Ð.Üˆt‹9�<‰<œŸ	š	 $›×(Ò(Ð(Ð(Üˆw‹<�?‰?œ5Ÿ9š9 WÓ-×.Ò.Ð.Ò.r   c                  óJ  € \        ^ \        ,          4      ^8X  g   Q h\        ^Z\        ,          4      P                  ^ 4      '       g   Q h\        ^´\        ,          4      P                  R4      '       g   Q h\        R\        ,          4      P                  ^ 4      '       g   Q h\        R\        ,          4      P                  ^4      '       g   Q h\        ^ \        ,          4      ^ 8X  g   Q h\        ^Z\        ,          4      P                  ^4      '       g   Q h\        ^´\        ,          4      P                  ^ 4      '       g   Q h\        R\        ,          4      P                  R4      '       g   Q h\        R\        ,          4      P                  ^ 4      '       g   Q hR# )r   i  ih  Nr   )r•   r!   r   r–   rv   r   r   Útest_degreesrž   ×   s&  € Üˆq”�x‹=˜AÔÐÐÜˆr”&�y‹>×Ñ˜Q×ÒÐÐÜˆs”6�z‹?×Ñ˜b×!Ò!Ð!Ð!Üˆs”6�z‹?×Ñ˜a× Ò Ð Ð Üˆs”6�z‹?×Ñ˜a× Ò Ð Ð Üˆq”�x‹=˜AÔÐÐÜˆr”&�y‹>×Ñ˜Q×ÒÐÐÜˆs”6�z‹?×Ñ˜a× Ò Ð Ð Üˆs”6�z‹?×Ñ˜b×!Ò!Ð!Ð!Üˆs”6�z‹?×Ñ˜a× Ò Ð Ò r   c                 ób  € \         P                  ! ^4       . p\        V 4       F‡  p\         P                  ! R^
4      p\         P                  ! R^
4      p\         P                  ! R^
4      p\         P                  ! R^
4      p\	        W44      p\	        WV4      pVP                  Wx34       K‰  	  V# )r>   éöÿÿÿ)rD   rE   rB   ÚuniformÚcomplexÚappend)	ÚNr   rG   Úx1Úy1Úx2Úy2Úz1Úz2s	   &        r   Úrandom_complexesr«   ã   s‡   € Ü
‡K‚K�„NØ
€AÜ�1ŽXˆÜ�^Š^˜C Ó$ˆÜ�^Š^˜C Ó$ˆÜ�^Š^˜C Ó$ˆÜ�^Š^˜C Ó$ˆÜ�R‹_ˆÜ�R‹_ˆØ	�‰�"�Öñ ð €Hr   c                  ó˜  € R F_  p V \         n        \        R4      R,          pVP                  VP                  u;8X  d"   \        ^4      R,          ^,          8X  d   K\  Q h Q h	  ^\         n        \        P                  ! ^4       \        ^d4       F>  w  r#\        V4      \        V4      ,          P                  W#,          R4      '       d   K>  Q h	  \        \        ) R,          ,          P                  R4      '       g   Q h^2\         n        \        \        ) R,          ,          P                  R4      '       g   Q h^\         n        R# )r   ri   rh   çê-�™—q=N)r   é   r   r   )r   r   rŽ   r   r   r   rD   rE   r«   r   r   r   )r   r   r©   rª   s       r   Útest_complex_powersr¯   ð   sê   € ÛˆàŒŒÜ�‹G�S�LˆØ�v‰v˜Ÿ™Ö2¤3 q£6¨3¥;°¥?Ö2Ð2Ñ2Ð2Ð2ñ	 ð
 „B„FÜ
‡K‚K�„NÜ$ SÖ)‰ˆÜ�B“œ˜R›Õ ×$Ñ$ R¥V¨U×3Ô3Ð3Ð3ñ *ä”��B•�K×Ñ˜B×ÒÐÐØ„B„FÜ”��B•�K×Ñ˜B×ÒÐÐØ„B†Fr   c            
      ó²  € R  p \         P                  ! ^4       ^
p^\        n        \        P                  pT ! \	        V4       Uu. uF1  p\         P
                  ! ^ ^
4      \         P
                  ! ^ ^
4      3NK3  	  up4       T ! \	        V4       Uu. uF"  q3R,           VR,           ^
V,          ,          3NK$  	  up4       ^\        n        R# u upi u upi )c                 ó(  € V  EF
  w  r\        V\        V,          ,           4      p\        \        W3,          4      V4      '       g   Q h\        V) \        V,          ,           4      p\        \        W3,          4      V) 4      '       g   Q h\        V\        V,          ,
          4      p\        \        W3,          4      V4      '       g   Q h\        V) \        V,          ,
          4      p\        \        W3,          4      V) 4      '       d   EK  Q h	  R # )N)rŽ   Újr   rC   )Úlstr   r	   Úzs   &   r   Útest_mpc_sqrtÚ1test_complex_sqrt_accuracy.<locals>.test_mpc_sqrt   s¾   € Ü‰DˆAÜ�Aœ˜!�•G“ˆAÜœ$˜q�s›) Q×'Ò'Ð'Ð'Ü�Q�Bœ˜1�•H“ˆAÜœ$˜q�s›) a R×(Ò(Ð(Ð(Ü�Aœ˜!�•G“ˆAÜœ$˜q�s›) Q×'Ò'Ð'Ð'Ü�Q�Bœ˜1�•H“ˆAÜœ$˜q�s›) a R×(Õ(Ð(Ð(ó r   rj   çš™™™™™É?N)rD   rE   r   r   rB   r¡   )rµ   r¤   r   rG   s       r   Útest_complex_sqrt_accuracyr¸   ÿ   sž   € ò	)ô ‡K‚K�„NØ
€AØ„B„FÜ
�&‰&€CÙÌ%ÐPQÌ(ÓSÉ(ÀQ”F—N’N 1 bÓ)¬&¯.ª.¸¸BÓ*?Ó@É(ÑSÔTÙ´u¸Q´xÓ@±x°!˜•G˜a #�g r¨1¥u�_Ó-±xÑ@ÔAØ„B†Fùò TùÚ@s   Á7CÂ(Cc                  ó8  € ^\         n        \        R4      P                  \        P                  ! R4      4      '       g   Q h\        R4      R8X  g   Q h\        R4      P                  \
        ^,          4      '       g   Q h\        R4      R8X  g   Q h\        R4      P                  \
        ) ^,          4      '       g   Q h\        ^
R,          4      P                  \
        ^,          4      '       g   Q hR F;  p V \         n        ^\        ^4      ,          P                  \
        4      '       d   K;  Q h	  ^\         n        \
        ^,          p\        \        \        R	4      4      P                  V4      '       g   Q h\        \        \        ^ 4      4      P                  V4      '       g   Q h\        \        \        ^4      4      P                  V4      '       g   Q h\        \        ^\        4      4      P                  V4      '       g   Q h\        \        ^ \        4      4      P                  V4      '       g   Q h\        \        R	\        4      4      P                  V) 4      '       g   Q h\        \        \        ) ^4      4      P                  V) 4      '       g   Q h\        \        \        ) ^ 4      4      P                  V) 4      '       g   Q h\        \        \        ) R	4      4      P                  V) 4      '       g   Q h\        \        R	\        ) 4      4      P                  V) 4      '       g   Q h\        \        ^ \        ) 4      4      P                  V) 4      '       g   Q h\        \        ^\        ) 4      4      P                  V4      '       g   Q hR# )
r   rŠ   gšd~ÅQJr<   NgffffffÀç¸ÔJzî�µgšd~ÅQÊ)r@   éF   r   r;   r<   r   )r   r   Úatanr   rp   r   rŽ   r�   )r   Úpi2s     r   Ú	test_atanr¾     s�  € Ø„B„FÜ�‹:�=‰=œŸš 4›×)Ò)Ð)Ð)Ü�‹;˜%ÔÐÐÜ�‹:�=‰=œ˜A�×ÒÐÐÜ�‹<˜6Ô!Ð!Ð!Ü�‹;�>‰>œ2˜#˜a�%× Ò Ð Ð Ü��D•‹>×ÑœR �T×"Ò"Ð"Ð"Û'ˆØŒŒØ”$�q“'•	�~‰~œb×!Ô!Ð!Ð!ñ (ð „B„FÜ
ˆQ�$€CÜ””C˜“Ó×Ñ ×$Ò$Ð$Ð$Ü””C˜“
Ó×Ñ˜s×#Ò#Ð#Ð#Ü””C˜“
Ó×Ñ˜s×#Ò#Ð#Ð#Ü”�A”c“
Ó×Ñ˜s×#Ò#Ð#Ð#Ü”�A”c“
Ó×Ñ˜s×#Ò#Ð#Ð#Ü”�B”s“Ó×Ñ  ×%Ò%Ð%Ð%Ü””S�D˜“Ó×Ñ  ×%Ò%Ð%Ð%Ü””S�D˜“Ó×Ñ  ×%Ò%Ð%Ð%Ü””S�D˜“Ó× Ñ  # ×&Ò&Ð&Ð&Ü”�Bœ�t“Ó× Ñ  # ×&Ò&Ð&Ð&Ü”�A”s�d“Ó×Ñ  ×%Ò%Ð%Ð%Ü”�A”s�d“Ó×Ñ ×$Ò$Ð$Ò$r   c                  ól  € ^\         n        \        ^^4      P                  \        ^,          4      '       g   Q h\        ^R4      P                  ^\        ,          ^,          4      '       g   Q h\        RR4      P                  R\        ,          ^,          4      '       g   Q h\        R^4      P                  \        ) ^,          4      '       g   Q h\        R^ 4      P                  \        ) ^,          4      '       g   Q h\        ^^ 4      P                  \        ^,          4      '       g   Q h\        ^ ^ 4      ^ 8X  g   Q h\        \
        ^ 4      P                  \        ^,          4      '       g   Q h\        \
        ) ^ 4      P                  \        ) ^,          4      '       g   Q h\        \        \
        \
        4      4      '       g   Q h\        \        \
        ) \
        4      4      '       g   Q h\        \        \
        \
        ) 4      4      '       g   Q h\        \        ^\        4      4      '       g   Q h\        \        \        ^4      4      '       g   Q h\        \        ^ \        4      4      '       g   Q h\        \        \        ^ 4      4      '       g   Q h\        ^ \
        4      ^ 8X  g   Q h\        ^ \
        ) 4      P                  \        4      '       g   Q h\        ^
\
        4      ^ 8X  g   Q h\        R\
        4      ^ 8X  g   Q h\        R\
        ) 4      P                  \        ) 4      '       g   Q h\        ^
\
        ) 4      P                  \        4      '       g   Q h\        \
        ^
4      P                  \        ^,          4      '       g   Q h\        \
        R4      P                  \        ^,          4      '       g   Q h\        \
        ) ^
4      P                  \        ) ^,          4      '       g   Q h\        \
        ) R4      P                  \        ) ^,          4      '       g   Q hR# )r   Nr   rl   r    )r   r   Úatan2r   r   r�   r�   r‘   rv   r   r   Ú
test_atan2rÁ   ,  sñ  € Ø„B„FÜ��1‹:�=‰=œ˜A�×ÒÐÐÜ��2‹;�>‰>˜!œB�$˜q�&×!Ò!Ð!Ð!Ü��B‹<�?‰?˜2œb�5 �7×#Ò#Ð#Ð#Ü��A‹;�>‰>œ2˜#˜a�%× Ò Ð Ð Ü��A‹;�>‰>œ2˜#˜a�%× Ò Ð Ð Ü��1‹:�=‰=œ˜A�×ÒÐÐÜ��1‹:˜Œ?Ðˆ?Ü”�Q‹<�?‰?œ2˜a�4× Ò Ð Ð Ü”#��a‹=×ÑœR˜C �E×"Ò"Ð"Ð"Ü””sœ3“× Ò Ð Ð Ü”œ�tœC“×!Ò!Ð!Ð!Ü””sœC˜4“×!Ò!Ð!Ð!Ü”�qœ“×ÒÐÐÜ””s˜1“×ÒÐÐÜ”�qœ“×ÒÐÐÜ””s˜1“×ÒÐÐÜ�”3‹<˜1ÔÐÐÜ�”C�4‹=×ÑœB×ÒÐÐÜ�”C‹=˜AÔÐÐÜ�”S‹>˜QÔÐÐÜ�”c�T‹?×Ñœr˜c×"Ò"Ð"Ð"Ü�”S�D‹>×ÑœR× Ò Ð Ð Ü”�R‹=×ÑœB˜q�D×!Ò!Ð!Ð!Ü”�S‹>×ÑœR �T×"Ò"Ð"Ð"Ü”#��b‹>×Ñœb˜S �U×#Ò#Ð#Ð#Ü”#��c‹?×Ñœr˜c !�e×$Ò$Ð$Ò$r   c                  ó6	  € \        \        ^ 4      4      ^ 8X  g   Q h\        \        ^ 4      4      ^ 8X  g   Q h\        \        ^4      4      ^ 8X  g   Q h\	        \        \        R4      4      \        4      '       g   Q h\	        \        \        R4      4      \
        4      '       g   Q h\	        \        \        R4      4      \        4      '       g   Q h\	        \        \        R4      4      \
        4      '       g   Q h\	        \        \        R4      4      \        4      '       g   Q h\	        \        \        R4      4      \
        4      '       g   Q h\        P                  ! ^4       \        ^24       EFx  p \        P                  ! ^ ^4      p\        \        V4      4      P                  \        P                   ! V4      4      '       g   Q h\        \        V4      4      P                  \        P                  ! V4      4      '       g   Q h\        P                  ! R	^
4      p\        \        V4      4      P                  \        P                  ! V4      P                  4      '       g   Q h\	        \        \        V4      4      \        4      '       g   Q h\        P                  ! ^^
4      p\        \        V4      4      P                  \        P                  ! V4      P                  4      '       g   Q h\	        \        \        V4      4      \        4      '       g   Q h\        P                  ! R	R4      p\	        \        \        V4      4      \
        4      '       g   Q h\        P                  ! R
^4      p\        \        V4      4      P                  \        P                  ! V4      P                  4      '       g   Q h\	        \        \        V4      4      \        4      '       d   EKy  Q h	  \         P"                  pR\         n        \	        \        R4      \        4      '       g   Q hR\         n        \        ^4      P                  \$        ^,          4      '       g   Q h\        R
4      P                  \$        ) ^,          4      '       g   Q hV\         n        R# )r   rh   r‰   rj   gš™™™™™ñ?ç+‡ÙÎ÷ï?r;   r<   Nr    r   )Úasinr   ÚasinhÚacoshÚ
isinstancerŽ   ÚacosÚatanhrD   rE   rB   r¡   r   rp   ro   r   r   r   r   )rG   rr   r   s      r   Útest_areal_inversesrÊ   I  sÿ  € Ü”�A“‹<˜1ÔÐÐÜ”�Q“‹=˜AÔÐÐÜ”�Q“‹=˜AÔÐÐÜ”dœ3˜s›8“n¤c×*Ò*Ð*Ð*Ü”dœ3˜s›8“n¤c×*Ò*Ð*Ð*Ü”dœ3˜s›8“n¤c×*Ò*Ð*Ð*Ü”dœ3˜s›8“n¤c×*Ò*Ð*Ð*Ü”eœC ›H“o¤s×+Ò+Ð+Ð+Ü”eœC ›H“o¤s×+Ò+Ð+Ð+ä
‡K‚K�„NÜ�2�YˆÜ�NŠN˜1˜aÓ ˆÜ”C˜“F‹|�‰œtŸyšy¨›|×,Ò,Ð,Ð,Ü”C˜“F‹|�‰œtŸyšy¨›|×,Ò,Ð,Ð,ä�NŠN˜3 Ó#ˆÜ”S˜“V‹}×Ñ¤§¢¨A£× 3Ñ 3×4Ò4Ð4Ð4Üœ%¤ A£›-¬×-Ò-Ð-Ð-Ü�NŠN˜1˜bÓ!ˆÜ”S˜“V‹}×Ñ¤§¢¨A£× 3Ñ 3×4Ò4Ð4Ð4Üœ%¤ A£›-¬×-Ò-Ð-Ð-Ü�NŠN˜3 Ó&ˆÜœ%¤ A£›-¬×-Ò-Ð-Ð-ä�NŠN˜2˜qÓ!ˆÜ”S˜“V‹}×Ñ¤§¢¨A£× 3Ñ 3×4Ò4Ð4Ð4Üœ%¤ A£›-¬×-Õ-Ð-Ð-ñ! ô$ �&‰&€CØ„B„FÜ”d˜3“i¤×%Ò%Ð%Ð%Ø„B„FÜ�‹7�:‰:”b˜•d×ÒÐÐÜ�‹8�;‰;œ�s˜1•u×ÒÐÐØ„B†Fr   c                  óô  € ^\         n        \        R4      R,          P                  R4      '       g   Q h\        R4      R,          P                  ^4      '       g   Q h\        R4      ^
^2,          ,          P                  ^4      '       g   Q h\        R	4      R,          P                  R
4      '       g   Q h\        R4      R,          P                  R4      '       g   Q h\        R4      ^
^2,          ,          P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\	        R4      R,          P                  ^4      '       g   Q h\	        R4      R,          P                  R4      '       g   Q h\        R4      R,          P                  ^4      '       g   Q h\        R4      R,          P                  R4      '       g   Q hR# )r   gñhãˆµøä>g˜µýÿÿÿï?ç»½×Ùß|Û=rŠ   gC“ž6W_G@Ni † ì    d(	 gñhãˆµøä¾g˜µýÿÿÿï¿g»½×Ùß|Û½r   rº   r‹   lûÿÿÿ   Fµx:^V gC“ž6W_GÀ)r   r   rÅ   r   rš   rÉ   rv   r   r   Útest_invhyperb_inaccuracyrÎ   o  s‹  € Ø„B„FÜ�$‹K˜Õ×!Ñ!Ð"5×6Ò6Ð6Ð6Ü�%‹L˜Õ×#Ñ# A×&Ò&Ð&Ð&Ü�%‹L˜˜R�Õ×#Ñ# A×&Ò&Ð&Ð&Ü�%‹L˜Õ×"Ñ"Ð#7×8Ò8Ð8Ð8Ü�&‹M˜&Õ ×$Ñ$ R×(Ò(Ð(Ð(Ü�&‹M˜"˜b�&Õ ×$Ñ$ R×(Ò(Ð(Ð(Ü�‹=×ÑÐ.×/Ò/Ð/Ð/Ü�‹>×ÑÐ0×1Ò1Ð1Ð1Ü�‹K˜Õ×"Ñ" 1×%Ò%Ð%Ð%Ü�‹L˜Õ×#Ñ# B×'Ò'Ð'Ð'Ü�%‹L˜Õ×#Ñ# A×&Ò&Ð&Ð&Ü�&‹M˜&Õ ×$Ñ$ R×(Ò(Ð(Ò(r   c                  ó  € \        \        ^
4      4      \        \        R^ 4      4      ,            EFL  p \        \        ^
4      4      \        \        R^ 4      4      ,            EF  p\        W4      R,          R,           p\        \	        V4      4      P                  \        P                  ! V4      4      '       g   Q h\        \	        V4      4      P                  \        P                  ! V4      4      '       g   Q h\        \	        V4      4      P                  \        P                  ! V4      4      '       g   Q h\        \	        V4      4      P                  \        P                  ! V4      4      '       g   Q h\        \	        V4      4      P                  \        P                  ! V4      4      '       g   Q h\        \	        V4      4      P                  \        P                  ! V4      4      '       g   Q h\        \	        V4      4      P                  \        P                  ! V4      4      '       g   Q h\        \	        V4      4      P                  \        P                  ! V4      4      '       d   EK  Q h	  EKO  	  R# )r   g333333@y        {®Gáz„?Nr    )r”   rB   r¢   r€   rŽ   r   ro   rŒ   r•   r–   r—   r™   r˜   rš   )rr   Úyr´   s      r   Útest_complex_functionsrÑ   ~  s‡  € Ü”5˜“9‹o¤¤U¨3¨q£\Ó 2×2Ñ2ˆÜ”u˜R“y“/¤D¬¨s°1«Ó$6×6Ñ6ˆAÜ˜“˜cÕ! EÕ)ˆAÜ”s˜1“v“;—>‘>¤%§)¢)¨A£,×/Ò/Ð/Ð/Ü”s˜1“v“;—>‘>¤%§)¢)¨A£,×/Ò/Ð/Ð/Ü”s˜1“v“;—>‘>¤%§)¢)¨A£,×/Ò/Ð/Ð/Ü”s˜1“v“;—>‘>¤%§)¢)¨A£,×/Ò/Ð/Ð/Ü”s˜1“v“;—>‘>¤%§)¢)¨A£,×/Ò/Ð/Ð/Üœ˜A›“<—?‘?¤5§:¢:¨a£=×1Ò1Ð1Ð1Üœ˜A›“<—?‘?¤5§:¢:¨a£=×1Ò1Ð1Ð1Üœ˜A›“<—?‘?¤5§:¢:¨a£=×1Õ1Ð1Ð1ô 7ó 3r   c                  óì  € ^\         n        ^\        n        \        ^4       EFN  w  r\	        \        V 4      4      P                  V 4      '       g   Q h\        V 4      P                  \        P                  ! V 4      4      '       g   Q h\        V 4      P                  \        P                  ! V 4      4      '       g   Q h\        V 4      P                  \        P                  ! V 4      4      '       g   Q h\        V 4      P                  \        P                  ! V 4      RR7      '       g   Q h\        V 4      P                  \        P                  ! V 4      RR7      '       g   Q h\        ^4      pEKQ  	  \        R^
^4       F¨  p\        R^
^4       F”  pR\        ,          ^
V,          ,          RX,          ^
V,          ,          ,           p\!        \        V4      4      pVP                  V4      '       g   Q h\#        \        V4      4      pVP                  V4      '       d   K”  Q h	  Kª  	  \        ^4      pRp\        R^	^4       F¨  p\        R^	^4       F”  pR^
V,          ,          \        R,          V,          ^
V,          ,          ,           p\%        \        V4      4      pVP                  WW4      '       g   Q h\	        \        V4      4      pVP                  WW4      '       d   K”  Q h	  Kª  	  R# )	r   r­   )Úrel_epsgÍÌÌÌÌÌì?çš™™™™™é?Né÷ÿÿÿgVçž¯â<gÍÌÌÌÌÌì¿)r   r   Úivr«   r™   rÅ   r   rÆ   ro   rÉ   r¼   rÄ   rÈ   r   rB   r²   r•   r–   r˜   )r©   rª   ÚonerG   Úkr   r	   Úerrs           r   Útest_complex_inverse_functionsrÚ   ‹  s  € Ø„B„FØ„B„FÜ$ R×(‰ˆô ”E˜"“I‹×!Ñ! "×%Ò%Ð%Ð%ä�R‹y�|‰|œEŸKšK¨›O×,Ò,Ð,Ð,Ü�R‹y�|‰|œEŸKšK¨›O×,Ò,Ð,Ð,Ü�B‹x�{‰{œ5Ÿ:š: b›>×*Ò*Ð*Ð*ô �B‹x�{‰{œ5Ÿ:š: b›>°5ˆ{×9Ò9Ð9Ð9Ü�B‹x�{‰{œ5Ÿ:š: b›>°5ˆ{×9Ò9Ð9Ð9Ü�!‹f‹ñ )ô �2�r˜1ÖˆÜ�r˜2˜qÖ!ˆAØ”A•�b˜!•e•˜c #�g b¨!¥e�mÕ+ˆAÜ”D˜“G“ˆAØ—4‘4˜—7’7ˆN�7Ü”D˜“G“ˆAØ—4‘4˜—7”7ˆN�7ó "ñ ô ˆa‹&€CØ
€CÜ�2�q˜!Ž_ˆÜ�r˜1˜a–ˆAØ�R˜•U•
œQ˜s�U 3�Y r¨1¥u�_Õ,ˆAÜ”U˜1“X“ˆAØ—4‘4˜—<’<Ð�<Ü”U˜1“X“ˆAØ—4‘4˜—<”<Ð�<ó !ó r   c                  ó¾  € \        ^4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q h\	        ^4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q h\        R4      P                  R	4      '       g   Q h\        ^4      P                  R
4      '       g   Q h\        ^4      P                  R4      '       g   Q h\        ^ 4      P                  R4      '       g   Q h\        ^ 4      P                  R4      '       g   Q hR# )r   gÙ°
D<X@g±ŽØŽm¹?g¹)	è�¹?gL–É<[ð?gÔè‚€²ó?gOã¿Õ?gáž&£�—Ô?rh   g5˜qBõ?gH·•yñôÔ?gï9úþB.Ö?g-DTû!ù?y        -DTû!ù?NgE²W´g)ð¿g^f]žÀ)Úsecr   ÚcscÚcotÚsechÚcschÚcothÚasecÚacscÚacotÚasechÚacschÚacothrv   r   r   Útest_reciprocal_functionsrè   ¬  sn  € Üˆq‹6�9‰9Ð)×*Ò*Ð*Ð*Üˆq‹6�9‰9Ð(×)Ò)Ð)Ð)Üˆq‹6�9‰9Ð)×*Ò*Ð*Ð*Ü�‹7�:‰:Ð+×,Ò,Ð,Ð,Ü�‹7�:‰:Ð+×,Ò,Ð,Ð,Ü�‹7�:‰:Ð)×*Ò*Ð*Ð*Ü�‹7�:‰:Ð)×*Ò*Ð*Ð*Ü�‹7�:‰:Ð*×+Ò+Ð+Ð+Ü�‹7�:‰:Ð*×+Ò+Ð+Ð+Ü�‹:�=‰=Ð,×-Ò-Ð-Ð-Ü�‹8�;‰;Ð+×,Ò,Ð,Ð,Ü�‹8�;‰;Ð+×,Ò,Ð,Ð,Ü�‹7�:‰:Ð+×,Ò,Ð,Ð,Ü�‹8�;‰;Ð-×.Ò.Ð.Ò.r   c                  ó  € ^\         n        \        \        R4      ^ 4      R8X  g   Q h\        \        R4      R4      R8X  g   Q h\        \        R4      ^4      ^
8X  g   Q h\        \        R4      ^4      \        R4      8X  g   Q hR# )r   ç      @g      ô?r�   Nr   )r   r   r�   r   rv   r   r   Ú
test_ldexprë   ¼  sq   € Ø„B„FÜ”�S“˜1Ó Ô$Ð$Ð$Ü”�S“˜2Ó $Ô&Ð&Ð&Ü”�S“˜1Ó Ô#Ð#Ð#Ü”�U“˜QÓ¤3 u£:Ô-Ð-Ò-r   c                  óÐ   € ^\         n        \        ^ 4      R8X  g   Q h\        ^	4      R8X  g   Q h\        ^4      R8X  g   Q h\        R4      R8X  g   Q h\        R4      R8X  g   Q hR# )	r   r·   r<   N)g        r   )g      â?rk   )rh   r>   )rÔ   rA   )g     @ï?r   )r   r   Úfrexprv   r   r   Ú
test_frexprî   Ã  sc   € Ø„B„FÜ�‹8�xÔÐÐÜ�‹8�{Ô"Ð"Ð"Ü�‹8�xÔÐÐÜ�‹:˜Ô"Ð"Ð"Ü�‹;˜/Ô)Ð)Ò)r   c                  ó|  € \        ^4      \        ^4      8X  g   Q h\        R4      \        R^
4      8X  g   Q h\        R4      R\        ,          8X  g   Q h\        R4      R\        ,          8X  g   Q h\        RR4      \        8X  g   Q h\        ^^4      R8X  d!   \        \        ^^4      \        4      '       g   Q hR# )r   g      @gffffff@rh   g      @Nr   )ÚlnrŒ   Úlog10Údegreesr!   ÚradiansÚpowerr²   ÚfmodrÇ   r   rv   r   r   Útest_aliasesrö   Ë  s—   € Üˆa‹5”C˜“FŒ?Ðˆ?Ü�‹;œ#˜d 2›,Ô&Ð&Ð&Ü�3‹<˜3¤�<Ô'Ð'Ð'Ü�3‹<˜3¤�<Ô'Ð'Ð'Ü��C‹=œAÔÐÐÜ��1‹:˜Ô¤¬D°°A«J¼×!<Ò!<Ð<Ð<Ñ!<r   c                  ó„  € \        ^4      ^ 8X  g   Q h\        R4      P                  \        4      '       g   Q h\        \        4      P                  \        ^,          4      '       g   Q h\        \        ) 4      P                  \        ) ^,          4      '       g   Q h\        ^ 4      ^ 8X  g   Q h\	        \        ^\        4      4      '       g   Q h\	        \        \        ^4      4      '       g   Q h\	        \        ^ \        4      4      '       g   Q h\	        \        \        ^ 4      4      '       g   Q h\	        \        \        \        4      4      '       g   Q h\        \        4      ^ 8X  g   Q h\        \        ) 4      P                  \        4      '       g   Q h\	        \        \        4      4      '       g   Q h\        ^ 4      ^ 8X  g   Q h\        ^4      ^8X  g   Q h\        R4      R8X  g   Q h\        \        4      ^8X  g   Q h\        \        ) 4      R8X  g   Q h\	        \        \        4      4      '       g   Q h\        \        4      \        8X  g   Q h\        R\        ,          4      \        ) 8X  g   Q h\        ^\        ,           4      P                  ^\        ,           \        ^4      ,          4      '       g   Q hR# )r   Nrl   r   )
Úargr   r   r²   r�   rÀ   r‘   r�   ÚsignrC   rv   r   r   Útest_arg_signrú   Ó  sÝ  € Üˆq‹6�QŒ;Ðˆ;Üˆr‹7�:‰:”b�>Š>Ðˆ>ÜŒq‹6�9‰9”R˜•T�?Š?Ðˆ?Ü”ˆr‹7�:‰:”r�c˜!•e×ÒÐÐÜˆq‹6�QŒ;Ðˆ;Ü”�qœ“×ÒÐÐÜ””s˜1“×ÒÐÐÜ”�qœ“×ÒÐÐÜ””s˜1“×ÒÐÐÜ””sœ3“× Ò Ð Ð ÜŒs‹8�qŒ=Ðˆ=Ü”ˆt‹9�<‰<œ×ÒÐÐÜ””S“�?Š?Ðˆ?ä�‹7�aŒ<Ðˆ<Ü�‹7�aŒ<Ðˆ<Ü�‹8�rŒ>Ðˆ>Ü”‹9˜Œ>Ðˆ>Ü”�‹:˜ÔÐÐÜ””c“×ÒÐÐÜ”‹7”aŒ<Ðˆ<Ü�”1•‹:œ!˜ÔÐÐÜ�”!•‹9�<‰<˜œ1�œd 1›g�×&Ò&Ð&Ò&r   c                  óH   € R \         n        \        R4       ^\         n        R# )r<   i  N)r   r   rŒ   rv   r   r   Útest_misc_bugsrü   ì  s   € à„B„FÜˆ„IØ„B†Fr   c                  óZ  € \        ^
4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R	4      \        R
4      .
8X  g   Q h\        R"^4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      .
8X  g   Q h\        ^ ^R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      .
8X  g   Q h\        ^R#R$4      \        R4      \        R4      \        R4      \        R	4      \        R4      \        R4      \        R4      \        R4      \        R4      .	8X  g   Q h\        RRR%4      \        R4      .8X  g   Q h\        ^ 4      . 8X  g   Q h\        RR&4      . 8X  g   Q h\        R'R R(4      . 8X  g   Q hR!# ))r   z0.0z1.0ú2.0ú3.0ú4.0ú5.0ú6.0ú7.0ú8.0ú9.0z-5.0z-4.0z-3.0z-2.0z-1.0rj   z0.10000000000000001z0.20000000000000001z0.30000000000000004z0.40000000000000002z0.5z0.60000000000000009z0.70000000000000007z0.80000000000000004z0.90000000000000002z17.0z14.0z11.0z-7.0r·   r<   g®Gáz®	@NéûÿÿÿrÕ   rl   gš™™™™™¹¿r   g®Gáz®ó¿gH¯¼šò×z¾)Úaranger   rv   r   r   Útest_aranger  ò  sí  € Ü�"‹:œ#˜e›*¤c¨%£j´#°e³*¼cÀ%»jÜ˜e›*¤c¨%£j´#°e³*¼cÀ%»jÜ˜e›*¤c¨%£jð2ô 2ð 2ð 2ô �"�a‹=œS ›[¬#¨f«+´s¸6³{Ü  ›[¬#¨f«+´s¸5³zÜ  ›Z¬¨U«´S¸³ZÄÀUÃðMô Mð Mð Mô �!�Q˜Ó¤ U£¬SÐ1FÓ-GÜ!$Ð%:Ó!;Ü!$Ð%:Ó!;Ü!$Ð%:Ó!;Ü!$ U£¬SÐ1FÓ-GÜ!$Ð%:Ó!;Ü!$Ð%:Ó!;Ü!$Ð%:Ó!;ð!=ô =ð =ð =ô �"�b˜"Ó¤# f£+¬s°6«{¼CÀ»KÜ"% e£*¬c°%«j¼#¸e»*Ü"% f£+¬s°6«{¼CÀ»Kð"Iô Ið Ið Iô �#�s˜DÓ!¤cÐ*?Ó&@Ð%AÔAÐAÐAÜ�!‹9˜Œ?Ðˆ?Ü�$˜Ó˜rÔ!Ð!Ð!Ü�%˜˜zÓ*¨bÔ0Ð0Ò0r   c            
      ó®  € \        ^^	^4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      \        R4      .8X  g   Q h\        ^^	^^ R7      \        R4      \        R	4      \        R
4      \        R4      \        R4      \        R4      \        R4      .8X  g   Q h\        ^^^4      \        ^4      .8X  g   Q hR# )rK   rþ   z3.166666666666667z4.3333333333333339z5.5z6.666666666666667z7.8333333333333339r  )Úendpointrÿ   r   r  r  r  r  N)Úlinspacer   rv   r   r   Útest_linspacer  	  sÂ   € Ü�A�q˜!Ó¤ U£¬SÐ1DÓ-EÜÐ Ó!¤3 u£:¬sÐ3FÓ/GÜÐ Ó!¤3 u£:ð!/ô /ð /ð /ô �A�q˜! aÔ(¬S°«Z¼¸U»ÄSÈÃZÜˆE‹
”C˜“J¤ E£
¬C°«Jð-8ô 8ð 8ð 8ä�A�q˜!Ó¤ Q£ Ô(Ð(Ò(r   c                  ó~  € ^\         n        \        ^ ^
R4       F7  p \        W ,          V ,          4      P	                  V \
        4      '       d   K7  Q h	  \        R4      P	                  R\        \        ^4      ,          ^,          ,           4      '       g   Q h\        ^4      ^,          p\        ^ ^
R4      R.,            Fƒ  p \        V R,           4      p \        V 4      p\         ;P                  ^
,          un        \        W4      p\         ;P                  ^
,          un        VP	                  V\
        4      '       d   Kƒ  Q h	  ^d\         n        \        ^dR^d4       FP  p^
V,          \        R	,          ,           pWU,          V,          p\        V4      p\        Wu\
        4      '       d   KP  Q h	  ^\         n        R# )
r®   rj   rh   gš™™™™™@y        š™™™™™ñ?i-  Nr   gš™™™jø@gü©ñÒMbP?)r   r   r  ry   r   r
   r²   rC   r   rŽ   ÚpowrB   r   )r   Ú	one_thirdÚr1Úr2rP   Úwr´   Úrs           r   Útest_float_cbrtr    s=  € Ø„B„FÜ�A�b˜ÖˆÜ�A•C˜•E‹{�~‰~˜a¤×%Ô%Ð%Ð%ñ ä�‹8�;‰;�sœQœt A›w�Y q�[Õ(×)Ò)Ð)Ð)Ü�A“�q•€IÜ�A�b˜Ó  ×-Ð-ˆÜ��D•‹MˆÜ�!‹WˆÜ
�Š�"��Ü�ÓˆÜ
�Š�"��Ø�u‰u�Rœ�~Œ~Ðˆ~ñ .ð „B„FÜ�3˜˜SÖ!ˆØ��E”A�f•HÕˆØ�C��EˆÜ�‹GˆÜ�aœC× Ô Ð Ð ñ	 "ð
 „B†Fr   c            
      óþ  € ^\         n        \        P                  ! ^4       \        P                  ! ^ R4      p W ,          V ,          p\        \        V4      ^4      pW 8X  g   Q h\        ^^
4       F'  pW,          p\        \        V4      V4      V 8X  d   K'  Q h	  ^(\         n        \        ^
R^d4       FË  p\        P                  ! 4       R,          \        P                  ! 4       ^
^d,          ,          3 F…  p \        W4      p\        V \        ^4      V,          4      pVP                  V4      '       g   Q h\        W) 4      p\        V \        ^4      ) V,          4      pVP                  V4      '       d   K…  Q h	  KÍ  	  R Fx  pV\         n
        R	 Fd  p^2p\        ^
4       FP  pV\         n        \        4       p ^V,          \         n        W,          pV\         n        \        Wƒ4      pW 8X  d   KP  Q h	  Kf  	  Kz  	  ^\         n        \        ^^4       EF  p\        P                  ! 4       \        \        P                  ! 4       ,          ,           p \        W4      P                  \        V \        ^4      V,          4      4      '       g   Q h\        \        W4      \        V \        ^4      V,          4      4      '       g   Q h\        P                  ! 4       ^
^d,          ,          \        \        P                  ! 4       ,          ,           p \        W4      p\         ;P                  ^,          un        \        V \        ^4      V,          4      p\         ;P                  ^,          un        VP                  V4      '       g   Q h\        W$\        4      '       g   Q h\        W) 4      p\         ;P                  ^,          un        \        V \        ^4      ) V,          4      p\         ;P                  ^,          un        VP                  V4      '       g   Q h\        W$\        4      '       d   EK   Q h	  ^\         n        \        ^^4      ^8X  g   Q h\        ^^ 4      ^8X  g   Q h\        ^R
4      R8X  g   Q h\        \         ^4      \         8X  g   Q h\        \         ^4      \         8X  g   Q h\        \         ^4      \         8X  g   Q h\        \         R
4      ^ 8X  g   Q h\        \         R4      ^ 8X  g   Q h\        \         R4      ^ 8X  g   Q h\        \        ^4      \        8X  g   Q h\        \        ^ 4      ^8X  g   Q h\        \        R
4      \        ) 8X  g   Q h\#        \        \$        ^4      4      '       g   Q h\#        \        \$        ^ 4      4      '       g   Q h\#        \        \$        R
4      4      '       g   Q h\#        \        \         ^ 4      4      '       g   Q h\'        ^^4      \        ^^4      8X  g   Q h\'        ^^^ 4      ^8X  g   Q h\'        ^^^4      R8X  g   Q h\'        ^^^4      R8X  g   Q h\'        ^^^4      R8X  g   Q h\'        ^^^4      ^8X  g   Q h\'        R^^4      R8X  g   Q hR# )r®   r=   iˆ  g      Ð?y               @N)ÚnearestÚupÚdownr  rl   )r  rl   r   rR   r   rA   y       €       Àiƒÿÿÿ)r   r   rD   rE   rF   Únthrootr   rB   r  r   rO   r6   Úrandr²   r   r
   r�   r�   r‘   Úroot)	r   Úpr  rP   r  re   r6   rG   r	   s	            r   Ú	test_rootr  &  sâ  € Ø„B„FÜ
‡K‚K�„NÜ�Š�q˜%Ó €AØ	�ˆA�€AÜ”�A“˜Ó€AØŒ6€Mˆ6Ü�1�bŽ\ˆØ�CˆÜ”s˜1“v˜qÓ! QÖ&Ð&Ð&ñ ð „B„FÜ�2�t˜SÖ!ˆÜ—-’-“/ %Õ'¬¯ª«¸¸S½Õ)@ÓAˆAÜ˜“ˆAÜ�Qœ˜A›˜q�Ó!ˆBØ—4‘4˜—8’8ˆO�8Ü˜˜2“ˆAÜ�Qœ˜Q›˜ �	Ó"ˆBØ—4‘4˜—8”8ˆO�8ó Bñ "ó )ˆØŒŒÛˆAØˆDÜ˜2–Y�Ø””Ü“F�Ø˜D�&””Ø•D�Ø””Ü˜A“M�Ø–v��vó ó  ñ )ð „B„FÜ�1�b�\ˆÜ�]Š]‹_œq¤§¢£Õ0Õ0ˆÜ�q‹}×Ñ¤ A¤s¨1£v¨a¥xÓ 0×1Ò1Ð1Ð1Ü”g˜a“m¤S¨¬C°«F°1­HÓ%5×6Ò6Ð6Ð6Ü�]Š]‹_˜R �WÕ$¤q¬¯ª«Õ'8Õ8ˆÜ�A‹MˆÜ
�Š�!��Ü�”C˜“F˜1•HÓˆÜ
�Š�!��Ø�t‰t�B�xŠxˆˆxÜ�aœS×!Ò!Ð!Ð!Ü�A�r‹NˆÜ
�Š�!��Ü�”S˜“V�G˜A•IÓˆÜ
�Š�!��Ø�t‰t�B�xŠxˆˆxÜ�aœS×!Õ!Ð!Ð!ñ! ð" „B„FÜ�1�a‹=˜AÔÐÐÜ�1�a‹=˜AÔÐÐÜ�1�b‹>˜TÔ!Ð!Ð!Ü”3˜‹?œcÔ!Ð!Ð!Ü”3˜‹?œcÔ!Ð!Ð!Ü”3˜‹?œcÔ!Ð!Ð!Ü”3˜Ó˜qÔ Ð Ð Ü”3˜Ó˜qÔ Ð Ð Ü”3˜Ó˜qÔ Ð Ð Ü”1�a‹=œAÔÐÐÜ”1�a‹=˜AÔÐÐÜ”1�b‹>œa˜RÔÐÐÜ”œ˜a“×!Ò!Ð!Ð!Ü”œ˜a“×!Ò!Ð!Ð!Ü”œ˜bÓ!×"Ò"Ð"Ð"Ü”œ˜a“×!Ò!Ð!Ð!Ü��!‹9œ  !›Ô$Ð$Ð$Ü��1�Q‹<˜1ÔÐÐÜ��1�Q‹<˜2ÔÐÐÜ��1�Q‹<˜2ÔÐÐÜ��1�Q‹<˜3ÔÐÐÜ��1�Q‹<˜1ÔÐÐÜ��Q�q‹>˜RÔÐÒr   c                  ó  € R Fu  p V \         n        \        \        R4      ^4      pVP	                  \        ^
4      R,          ^\
        ,           ,          \        ^4      R	,          ,          4      '       d   Ku  Q h	  ^P\         n        \        R^4      P	                  \        ^
4      R
,          ^\
        ,           ,          \        ^4      ,          4      '       g   Q h\        R^4      P	                  ^\
        ,           ^
\        ^4      ,          ,          4      '       g   Q h^\         n        \        R^4      P	                  ^\
        ,           \        R4      ,          \        ^4      ,          4      '       g   Q h^\         n        R# )r   z-1e-20z-1e-3z-1e-6z-1e100000000Ú
1e25000000N)r   r   r  ç      à¿g      è¿)r   r   r  r   r   r²   rC   )r   r  s     r   Útest_issue_136r!  r  s
  € ÛˆØŒŒÜ”C˜“M 1Ó%ˆØ�t‰t”C˜“G˜b•M Q¬¥UÕ+¬c°!«f°t­nÕ<×=Ô=Ð=Ð=ñ ð „B„FÜ�7˜AÓ×!Ñ!¤# b£'¨EÕ"2°a¼!µeÕ"<¼TÀ!»WÕ"D×EÒEÐEÐEÜ�7˜AÓ×!Ñ! 1¤q¥5¨2´°R³­=Õ"9×:Ò:Ð:Ð:à„B„FÜ�> 1Ó%×(Ñ(¨!¬A­#¬s°<Ó/@Õ)@ÄÀaÃÕ)H×IÒIÐIÐIØ„B†Fr   c            	      óR  € ^\         n        \        R4      p \        R4      p\        \	        V ^ 4      4      \        V 4      8X  g   Q h\        \	        ^ V4      4      \	        \        V4      \        V4      4      8X  g   Q h\        \	        V ^ 4      4      \        V 4      8X  g   Q h\        \	        V ^ 4      4      \        V 4      8X  g   Q h\        \	        ^ V4      4      \        V4      8X  g   Q h\        \	        ^ V4      4      \	        ^ \        V4      4      8X  g   Q h\        \	        V ^ 4      4      \        V 4      8X  g   Q h\        \	        V ^ 4      4      \        V 4      8X  g   Q h\        \	        ^ V4      4      P                  \        \        V,          4      4      '       g   Q h\        \	        ^ V4      4      P                  \	        ^ \        \        V,          4      4      4      '       g   Q h\        \	        V ^ 4      4      w  r#V\        V 4      8X  g   Q hV\        V 4      8X  g   Q h\        \	        ^ V4      4      w  r#VP                  \        \        V,          4      4      '       g   Q hVP                  \	        ^ \        \        V,          4      4      4      '       g   Q h\        \	        V ^ 4      4      w  r#V\        V 4      8X  g   Q hV\        V 4      8X  g   Q h\        \	        ^ V4      4      w  r#V\        V4      8X  g   Q hV\	        ^ \        V4      4      8X  g   Q hR# )r   g333333Ó?gš™™™™™Ù?N)r   r   r   r€   rŽ   r•   r–   r˜   r™   ÚcospiÚsinpir   r   Úcospi_sinpiÚcos_sin)rr   rÐ   ÚcÚss       r   Útest_mpcfun_real_imagr)    sV  € Ø„B„FÜˆC‹€AÜˆC‹€AÜŒs�1�Q‹x‹=œC ›FÔ"Ð"Ð"ÜŒs�1�Q‹x‹=œC¤ A£¤s¨1£vÓ.Ô.Ð.Ð.ÜŒs�1�Q‹x‹=œC ›FÔ"Ð"Ð"ÜŒs�1�Q‹x‹=œC ›FÔ"Ð"Ð"ÜŒs�1�Q‹x‹=œD ›GÔ#Ð#Ð#ÜŒs�1�Q‹x‹=œC ¤$ q£'›NÔ*Ð*Ð*Ü”�Q�q“‹?œe A›hÔ&Ð&Ð&Ü”�Q�q“‹?œe A›hÔ&Ð&Ð&Ü”�Q�q“‹?×Ñœd¤2 a¥4›j×)Ò)Ð)Ð)Ü”�Q�q“‹?×Ñœc !¤D¬¨A­£JÓ/×0Ò0Ð0Ð0Ü”s˜1˜Q“xÓ �D€AØ”�a“Œ=Ðˆ=Ø”�a“Œ=Ðˆ=Ü”s˜1˜Q“xÓ �D€AØ�4‰4””R˜•T“
×ÒÐÐØ�4‰4”�A”dœ2˜a�4“jÓ!×"Ò"Ð"Ð"Ü”3�q˜“8Ó�D€AØ”�A“Œ;Ðˆ;Ø”�A“Œ;Ðˆ;Ü”3�q˜“8Ó�D€AØ”�Q“Œ<Ðˆ<Ø”�A”d˜1“g“ÔÐÒr   c                  ó  € ^d\         n        \        ^
^2,          ,          p \        ) ^
^2,          ,          p^V ,           p^V,           p^\         n        \        V 4      ^8X  g   Q h\        V RR7      ^8”  g   Q h\        VRR7      ^8X  g   Q h\        V RR7      ^8X  g   Q h\        VRR7      ^8  g   Q h\	        V 4      ^8X  g   Q h\	        V RR7      ^8X  g   Q h\	        VRR7      ^8X  g   Q h\	        V RR7      ^8  g   Q h\	        VRR7      ^8  g   Q h\
        \        \        \        3 Fg  pV! V 4      V 58X  g   Q hV! V RR7      V 8”  g   Q hV! V RR7      V 8  g   Q hV! V4      V58X  g   Q hV! VRR7      V8”  g   Q hV! VRR7      V8  d   Kg  Q h	  \        \        \        \        3 Fg  pV! V 4      V 58X  g   Q hV! V4      V58X  g   Q hV! V RR7      V 8”  g   Q hV! VRR7      V8”  g   Q hV! V RR7      V 8  g   Q hV! VRR7      V8  d   Kg  Q h	  \        V4      V 58X  g   Q h\        V4      V58X  g   Q h\        VRR7      V 8”  g   Q h\        VRR7      V 8  g   Q h\        VRR7      V8”  g   Q h\        VRR7      V8  g   Q h\        V 4      ^8X  g   Q h\        V4      ^8X  g   Q h\        V RR7      ^8”  g   Q h\        VRR7      ^8”  g   Q h\        V RR7      ^8X  g   Q h\        VRR7      ^8X  g   Q hR# )r   r'  rN   ÚfN)r   r   r   r€   r•   r–   r¼   rÅ   rš   rÄ   r—   r™   rÉ   rð   r˜   )r   r	   r'  rM   r+  s        r   Útest_perturbation_roundingr,  š  s  € Ø„B„FÜ
ˆ2ˆr�6�	€AÜ	ˆˆB��F�
€AØ	ˆA�€AØ	ˆA�€AØ„B„FÜˆq‹6�QŒ;Ðˆ;Üˆq˜3Ô !Ô#Ð#Ð#Üˆq˜3Ô 1Ô$Ð$Ð$Üˆq˜3Ô 1Ô$Ð$Ð$Üˆq˜3Ô !Ô#Ð#Ð#Üˆq‹6�QŒ;Ðˆ;Üˆq˜3Ô 1Ô$Ð$Ð$Üˆq˜3Ô 1Ô$Ð$Ð$Üˆq˜3Ô !Ô#Ð#Ð#Üˆq˜3Ô !Ô#Ð#Ð#Ü”4œ¤Ó%ˆÙ�‹t˜�rŒzÐˆzÙ�˜SÔ! AÔ%Ð%Ð%Ù�˜SÔ! AÔ%Ð%Ð%Ù�‹t˜�rŒzÐˆzÙ�˜SÔ! AÔ%Ð%Ð%Ù�˜SÔ! AÖ%Ð%Ð%ñ &ô ”CœœuÓ%ˆÙ�‹t˜�rŒzÐˆzÙ�‹t˜�rŒzÐˆzÙ�˜SÔ! AÔ%Ð%Ð%Ù�˜SÔ! AÔ%Ð%Ð%Ù�˜SÔ! AÔ%Ð%Ð%Ù�˜SÔ! AÖ%Ð%Ð%ñ &ô ˆa‹5�Q�BŒ;Ðˆ;Üˆa‹5�Q�BŒ;Ðˆ;Üˆa˜#Ô Ô"Ð"Ð"Üˆa˜#Ô Ô"Ð"Ð"Üˆa˜#Ô Ô"Ð"Ð"Üˆa˜#Ô Ô"Ð"Ð"Ü�‹7�aŒ<Ðˆ<Ü�‹7�aŒ<Ðˆ<Ü�˜CÔ  1Ô$Ð$Ð$Ü�˜CÔ  1Ô$Ð$Ð$Ü�˜CÔ  AÔ%Ð%Ð%Ü�˜CÔ  AÔ%Ð%Ò%r   c                  ó–   € \        R 4      ^8X  g   Q h\        R 4      ^8X  g   Q h\        R4      R8X  g   Q h\        R4      R8X  g   Q hR# )gš™™™™™	@Nyš™™™™™	@      @y      @      @y      @      @)ÚfloorÚceilrv   r   r   Útest_integer_partsr0  Æ  sF   € Ü�‹:˜Œ?Ðˆ?Ü�‹9˜Œ>Ðˆ>Ü�‹=˜DÔ Ð Ð Ü�‹<˜4ÔÐÒr   c                  óf  € \        R 4      ^8X  g   Q h\        R4      ^8X  g   Q h\        ^4      ^8X  g   Q h\        R4      ^8X  g   Q h\        ^4      ^ 8X  g   Q h\        R4      ^8X  g   Q h\        ^4      ^8X  g   Q h\        R4      R8X  g   Q h\	        ^4      P                  4       ^8X  g   Q hR# )Ú3Nù      @      @y      ð?      @y      @      À)ÚfabsÚreÚimÚconjr   Ú	conjugaterv   r   r   Útest_complex_partsr9  Ì  sŸ   € Ü�‹9˜Œ>Ðˆ>Ü�‹:˜Œ?Ðˆ?Üˆa‹5�AŒ:Ðˆ:Üˆd‹8�qŒ=Ðˆ=Üˆa‹5�AŒ:Ðˆ:Üˆd‹8�qŒ=Ðˆ=Ü�‹7�aŒ<Ðˆ<Ü�‹:˜ÔÐÐÜˆq‹6×ÑÓ Ô"Ð"Ò"r   c                  óˆ  € \        ^ 4      ^ 8X  g   Q h\        R4      ^8X  g   Q h\        ^4      ^ 8X  g   Q h\        R4      R8X  g   Q h\        ^4      ^ 8X  g   Q h\        R4      ^8X  g   Q h\        R4      R8X  g   Q h\        ^ 4      ^8X  g   Q h\        R4      ^ 8X  g   Q h\        ^4      R8X  g   Q h\        R4      ^ 8X  g   Q h\        ^4      ^8X  g   Q h\        R4      ^ 8X  g   Q h\        R4      ^ 8X  g   Q h\        R4      P                  \        ^4      ^,          4      '       g   Q h\        R4      p V P                  P                  \        R\        ,          4      P                  4      '       g   Q hV P                  ^ 8X  g   Q h\        R4      pVP                  P                  \        R\        ,          4      P                  4      '       g   Q hVP                  ^ 8X  g   Q h^#\        n
        \        R4      \        R4      ,
          p\        R4      \        R4      ,           p\        R4      \        R4      ,
          p\        R4      \        R4      ,           p\        R4      \        R4      ,
          p\        R4      \        R4      ,           p\        R	4      \        R4      ,
          p\        R	4      \        R4      ,           p	^\        n
        Rp
\        V4      V
,          P                  \        ) 4      '       g   Q h\        V4      V
,          P                  \        4      '       g   Q h\        V4      V
,          P                  \        4      '       g   Q h\        V4      V
,          P                  \        ) 4      '       g   Q h\        V4      V
,          P                  \        4      '       g   Q h\        V4      V
,          P                  \        ) 4      '       g   Q h\        V4      V
,          P                  \        ) 4      '       g   Q h\        V	4      V
,          P                  \        4      '       g   Q hR
\        VRR7      u;8  d	   ^8  g   Q h Q hR
\        VRR7      u;8  d	   ^8  g   Q h Q hR
\        VRR7      u;8  d	   ^8  g   Q h Q hR
\        VRR7      u;8  d	   ^8  g   Q h Q hR\        VRR7      u;8  d	   R8  g   Q h Q hR\        VRR7      u;8  d	   R8  g   Q h Q hR\        VRR7      u;8  d	   R8  g   Q h Q hR\        V	RR7      u;8  d	   R8  g   Q h Q h\        R4      V
,          P                  \        4      '       g   Q h\        R4      V
,          P                  \        ) 4      '       g   Q h\        R4      ^8X  g   Q h\        RRR7      ^8  g   Q hR# )r   rh   rˆ   rê   g @ èvH7Br=   z1e-15g    @ˆÃ@i'  g    ÀˆÃ@rÃ   rM   rN   gVçž¯Ò<Nr   r   ù       @      @l     �Iú5 g+‡ÙÎ÷ï¿gVçž¯Ò¼)r$  r#  r   rC   r   r•   r   r   r–   r   r   r   )r   r	   r¥   r§   Úx3Úx4Úx5Úx6Úx7Úx8ÚMs              r   Útest_cospi_sinpirC  ×  s–  € Ü�‹8�qŒ=Ðˆ=Ü�‹:˜Œ?Ðˆ?Ü�‹8�qŒ=Ðˆ=Ü�‹:˜ÔÐÐÜ�‹8�qŒ=Ðˆ=Ü�‹:˜Œ?Ðˆ?Ü�‹;˜"ÔÐÐÜ�‹8�qŒ=Ðˆ=Ü�‹:˜Œ?Ðˆ?Ü�‹8�rŒ>Ðˆ>Ü�‹:˜Œ?Ðˆ?Ü�‹8�qŒ=Ðˆ=Ü�‹:˜Œ?Ðˆ?Ü�‹;˜!ÔÐÐÜ�Ó!×$Ñ$¤T¨!£W¨Q¥Y×/Ò/Ð/Ð/Üˆd‹€AØ�6‰6�9‰9”S˜$¤�“^×(Ñ(×)Ò)Ð)Ð)Ø�6‰6�QŒ;Ðˆ;Üˆd‹€AØ�6‰6�9‰9”S˜$¤�“^×(Ñ(×)Ò)Ð)Ð)Ø�6‰6�QŒ;Ðˆ;Ø„B„FÜ	ˆU‹”c˜'“lÕ	"€BÜ	ˆU‹”c˜'“lÕ	"€BÜ	ˆW‹œ˜G›Õ	$€BÜ	ˆW‹œ˜G›Õ	$€BÜ	ˆU‹”c˜'“lÕ	"€BÜ	ˆU‹”c˜'“lÕ	"€BÜ	ˆW‹œ˜G›Õ	$€BÜ	ˆW‹œ˜G›Õ	$€BØ„B„FØ€AÜ�"‹I�a�K×ÑœR˜C× Ò Ð Ð Ü�"‹I�a�K×ÑœB×ÒÐÐÜ�"‹I�a�K×ÑœB×ÒÐÐÜ�"‹I�a�K×ÑœR˜C× Ò Ð Ð Ü�"‹I�a�K×ÑœB×ÒÐÐÜ�"‹I�a�K×ÑœR˜C× Ò Ð Ð Ü�"‹I�a�K×ÑœR˜C× Ò Ð Ð Ü�"‹I�a�K×ÑœB×ÒÐÐØ”5˜ cÔ*Ö.¨QÔ.Ð.Ñ.Ð.Ð.Ø”5˜ cÔ*Ö.¨QÔ.Ð.Ñ.Ð.Ð.Ø”5˜ cÔ*Ö.¨QÔ.Ð.Ñ.Ð.Ð.Ø”5˜ cÔ*Ö.¨QÔ.Ð.Ñ.Ð.Ð.Ø”�b 3Ô'Ö0¨&Ô0Ð0Ñ0Ð0Ð0Ø”�b 3Ô'Ö0¨&Ô0Ð0Ñ0Ð0Ð0Ø”�b 3Ô'Ö0¨&Ô0Ð0Ñ0Ð0Ð0Ø”�b 3Ô'Ö0¨&Ô0Ð0Ñ0Ð0Ð0Ü�%‹L˜�N×Ñœr×"Ò"Ð"Ð"Ü�&‹M˜!�O×Ñ¤ ×$Ò$Ð$Ð$Ü�‹<˜1ÔÐÐÜ� Ô%¨Ô)Ð)Ò)r   c                  ó†  € \        ^ 4      ^8X  g   Q h\        ^4      P                  \        \        4      4      '       g   Q h\        \        4      P                  \        R4      4      '       g   Q h\        ^\        ,           4      P                  \        \        ^\        ,           ,          4      4      '       g   Q h\	        ^ 4      ^8X  g   Q h\	        ^4      P                  \        \        \
        ,          4      4      '       g   Q h\	        \        4      P                  \        \
        ) 4      4      '       g   Q h\	        ^\        ,           4      P                  \        \        \
        ,          ^\        ,           ,          4      4      '       g   Q h\	        R\        ,          4      P                  R4      '       g   Q hR# )r   z%2.22579818340535731e+1364376353841841Nr   lüÿÿÿ  �Iú5 )Úexpjr   r€   r²   Úexpjpir   rv   r   r   Ú	test_expjrG    s  € Ü�‹7�aŒ<Ðˆ<Ü�‹7�:‰:”cœ!“f×ÒÐÐÜ”‹7�:‰:”c˜"“g×ÒÐÐÜ�”!•‹9�<‰<œœA˜q¤�s�G›×%Ò%Ð%Ð%Ü�!‹9˜Œ>Ðˆ>Ü�!‹9�<‰<œœAœb�D›	×"Ò"Ð"Ð"Ü”!‹9�<‰<œœR˜C›×!Ò!Ð!Ð!Ü�!”A•#‹;�>‰>œ#œa¤�d A¤a¥C�j›/×*Ò*Ð*Ð*Ü�'œA•+Ó×!Ñ!Ð"I×JÒJÐJÒJr   c                  óþ  € \        ^ 4      \        ^ 4      u;8X  d	   ^8X  g   Q h Q h\        \        4      \        \        4      u;8X  d	   ^ 8X  g   Q h Q h\        \        ) 4      \        \        ) 4      u;8X  d	   ^ 8X  g   Q h Q h\        ^4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        ^4      ^ 8X  g   Q h\        R4      P                  R4      '       g   Q hR# )r   gF´ÑêöÝ?rˆ   Nr;  yŒ–À¤§�Ü?\šaÀg¶·ç•)Ë¿)ÚsincÚsincpir�   r   rv   r   r   Ú	test_sincrK    sÇ   € Ü�‹7”f˜Q“iÖ$ 1Ô$Ð$Ñ$Ð$Ð$Ü”‹9œœs›Ö( qÔ(Ð(Ñ(Ð(Ð(Ü”�‹:œ¤ ›Ö*¨Ô*Ð*Ñ*Ð*Ð*Ü�‹7�:‰:Ð,×-Ò-Ð-Ð-Ü�‹:�=‰=ÐE×FÒFÐFÐFÜ�!‹9˜Œ>Ðˆ>Ü�#‹;�>‰>Ð/×0Ò0Ð0Ò0r   c                  óL  € ^\         n        \        R
^
4       U u. uF  p \        V 4      NK  	  up . RO8X  g   Q h\	        R4      P                  R4      '       g   Q h\	        R4      P                  R4      '       g   Q h\	        R4      P                  R4      '       g   Q h\        \	        ^
^d,          4      4      R8X  g   Q hR\         n        \	        R4      pVR,          R8X  g   Q h^\         n        \        \        4      \        8X  g   Q h\	        R4      ^8X  g   Q hR	# u up i )r   rê   g áÞ3Ô÷?r<   ga¹Úƒeì@kzv6.24499112864607e+2089876402499787337692720892375554168224592399182109535392875613974104853496745963277658556235103534i4  r=   l   ÛEÑ!	 Nr  )rR   rl   rK   r   r>   r   r>   r>   rK   r   rR   r?   rV   é   é"   r3  yÉ½å‚€´ÀºÆC,û¹ËÀrÍ   y      @        )r   r   rB   Ú	fibonacciÚfibr   Ústrr�   )rP   r   s     r   Útest_fibonaccirR  !  sý   € Ø„B„FÜ"'¨¨B¤-Ó0¡-˜QŒI�aŽL¡-Ñ0Ú:ô;ð ;ð ;äˆs‹8�;‰;Ð)×*Ò*Ð*Ð*Üˆt‹9�<‰<Ð<×=Ò=Ð=Ð=Üˆt‹9�<‰<Ð/×0Ò0Ð0Ð0ÜŒs�2�s•7‹|Óð  !Yô  Yð  Yð  YØ„B„FÜˆE‹
€AØˆv�:˜Ô#Ð#Ð#Ø„B„FÜ”S‹>œSÔ Ð Ð Üˆt‹9˜Œ>ÐŠ>ùò 1s   šD!c                  óx   € ^\         n        \        \        ^^R7      \	        ^#R7      ,
          4      R8  g   Q hR# )r   )r   gG³¦þ^Zé9N)r   r   Úabsr€   r   rv   r   r   Útest_call_with_dpsrU  0  s+   € Ø„B„FÜŒs�1˜"Œ~œa BœiÕ'Ó(¨5Ô0Ð0Ò0r   c                  ó  € ^\         n        \        ^ 4      ^ 8X  g   Q h\        \        4      ^8X  g   Q h\        \        ) 4      R8X  g   Q h\	        \        \
        4      4      '       g   Q h\        \        RR4      4      ^8X  g   Q hR# )r   r�   Ú0Nr   )r   r   rš   r�   r�   r‘   rŽ   rv   r   r   Ú	test_tanhrX  4  sk   € Ø„B„FÜ�‹7�aŒ<Ðˆ<Ü”‹9˜Œ>Ðˆ>Ü”�‹:˜ÔÐÐÜ””c“×ÒÐÐÜ”�E˜3“Ó  AÔ%Ð%Ò%r   c                  óJ  € ^\         n        \        ^ 4      ^ 8X  g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        ^4      \        8X  g   Q h\        R4      \        ) 8X  g   Q h\        \        \        4      4      '       g   Q h\        \        ^4      \        4      '       g   Q h\        \        R4      \        4      '       g   Q h\        \        ,          ^,          p \        \        4      P                  V ) 4      '       g   Q h\        \        ) 4      P                  V 4      '       g   Q h\        \        \        R4      4      P                  V ) 4      '       g   Q h\        \        \        ^ 4      4      P                  V ) 4      '       g   Q h\        \        \        ^4      4      P                  V 4      '       g   Q h\        \        ^\        4      4      P                  V 4      '       g   Q h\        \        ^ \        4      4      P                  V 4      '       g   Q h\        \        R\        4      4      P                  V 4      '       g   Q h\        \        \        ) ^4      4      P                  V 4      '       g   Q h\        \        \        ) ^ 4      4      P                  V 4      '       g   Q h\        \        \        ) R4      4      P                  V ) 4      '       g   Q h\        \        R\        ) 4      4      P                  V ) 4      '       g   Q h\        \        ^ \        ) 4      4      P                  V ) 4      '       g   Q h\        \        ^\        ) 4      4      P                  V ) 4      '       g   Q hR# )r   rh   g­zê“á?Nr   g­zê“á¿r   )r   r   rÉ   r   r�   r�   r‘   rÇ   r   r²   r   rŽ   )Újpi2s    r   Ú
test_atanhr[  <  s§  € Ø„B„FÜ�‹8�qŒ=Ðˆ=Ü�‹:�=‰=Ð/×0Ò0Ð0Ð0Ü�‹;�>‰>Ð1×2Ò2Ð2Ð2Ü�‹8”sŒ?Ðˆ?Ü�‹9œ˜ÔÐÐÜ””s“×ÒÐÐÜ”e˜A“h¤×$Ò$Ð$Ð$Ü”e˜B“i¤×%Ò%Ð%Ð%äŒR�4��6€DÜ”‹:�=‰=˜$˜×ÒÐÐÜ”#�‹;�>‰>˜$×ÒÐÐÜ””S˜“Ó× Ñ  $ ×'Ò'Ð'Ð'Ü””S˜“Ó×Ñ  ×&Ò&Ð&Ð&Ü””S˜“Ó×Ñ ×%Ò%Ð%Ð%Ü”�Q”s“Ó×Ñ ×%Ò%Ð%Ð%Ü”�Q”s“Ó×Ñ ×%Ò%Ð%Ð%Ü”�Rœ“Ó× Ñ  ×&Ò&Ð&Ð&Ü””c�T˜!“Ó× Ñ  ×&Ò&Ð&Ð&Ü””c�T˜!“Ó× Ñ  ×&Ò&Ð&Ð&Ü””c�T˜"“Ó×!Ñ! 4 %×(Ò(Ð(Ð(Ü”�Rœ˜“Ó×!Ñ! 4 %×(Ò(Ð(Ð(Ü”�Qœ�t“Ó× Ñ  $ ×'Ò'Ð'Ð'Ü”�Qœ�t“Ó× Ñ  $ ×'Ò'Ð'Ò'r   c                  ón  € ^\         n        \        ^ 4      ^ 8X  g   Q h\        ^4      P                  \	        ^4      ^,
          4      '       g   Q h\        \
        4      \
        8X  g   Q h\        R4      P                  R4      '       g   Q h\        R4      R,          P                  R4      '       g   Q hR# )r   rŠ   rÌ   ç    _ Bgœo   ð?N)r   r   Úexpm1r   r€   r�   rv   r   r   Ú
test_expm1r_  W  s…   € Ø„B„FÜ�‹8�qŒ=Ðˆ=Ü�‹8�;‰;”s˜1“v˜a•x× Ò Ð Ð Ü”‹:œÔÐÐÜ�‹<�?‰?˜5×!Ò!Ð!Ð!Ü�%‹L˜Õ×!Ñ! -×0Ò0Ð0Ò0r   c                  ó`  € ^\         n        \        ^ 4      ^ 8X  g   Q h\        ^4      P                  \	        ^4      4      '       g   Q h\        \
        4      \
        8X  g   Q h\        R4      P                  R4      '       g   Q h\        R4      R,          P                  R4      '       g   Q hR# )r   rŠ   rÌ   r]  gÈ ùÿÿÿï?N)r   r   Úlog1pr   rŒ   r�   rv   r   r   Ú
test_log1prb  _  s�   € Ø„B„FÜ�‹8�qŒ=Ðˆ=Ü�‹8�;‰;”s˜3“x× Ò Ð Ð Ü”‹:œÔÐÐÜ�‹<�?‰?˜5×!Ò!Ð!Ð!Ü�%‹L˜Õ×!Ñ! -×0Ò0Ð0Ò0r   c                  ó
  € ^\         n        \        ^^4      ^8X  g   Q h\        R^4      ^ 8X  g   Q h\        R^ 4      ^ 8X  g   Q h\        R^ 4      ^ 8X  g   Q h\        R	^ 4      ^ 8X  g   Q h\        ^ ^4      R8X  g   Q h\        ^ ^ 4      ^ 8X  g   Q h\        ^^ 4      ^ 8X  g   Q h\        ^^4      ^ 8X  g   Q h\        ^R	4      ^ 8X  g   Q h\        ^^4      ^ 8X  g   Q h\        \        ^4      ^ 8X  g   Q h\        \        ) ^4      ^ 8X  g   Q h\        ^R4      R,          P	                  \
        4      '       g   Q h\        ^R4      ^ 8w  g   Q h\        \        ^RRR7      ^4      R,          P	                  ^4      '       g   Q hR# )
r   g0Žä.ÿ++g}Ã”%­I²Tz1e-100000000000T)ÚexactNr   rA   r3  )r   r   Úpowm1r²   r   r%   Úfaddrv   r   r   Ú
test_powm1rg  g  sg  € Ø„B„FÜ��1‹:˜Œ?Ðˆ?Ü��A‹;˜!ÔÐÐÜ��A‹;˜!ÔÐÐÜ��A‹;˜!ÔÐÐÜ��a‹=˜AÔÐÐÜ��1‹:˜ÔÐÐÜ��1‹:˜Œ?Ðˆ?Ü��1‹:˜Œ?Ðˆ?Ü��1‹:˜Œ?Ðˆ?Ü��4‹=˜AÔÐÐÜ��1‹:˜Œ?Ðˆ?Ü”�1‹:˜Œ?Ðˆ?Ü”!��A‹;˜!ÔÐÐÜ�!�F‹O˜EÕ!×%Ñ%¤c×*Ò*Ð*Ð*Ü�Ð$Ó%¨Ô*Ð*Ð*Ü”$�q˜ dÔ+¨QÓ/°Õ5×9Ñ9¸!×<Ò<Ð<Ò<r   c                  ó4  € \        ^4      ^.8X  g   Q h\        ^4      ^R.8X  g   Q h\        ^4      w  rpV ^8X  g   Q hVP                  R4      '       g   Q hVP                  R4      '       g   Q h\        ^RR7      ^.8X  g   Q h\        ^RR7      R.8X  g   Q h\        ^RR7      \        ^4      R,          8X  g   Q h\        ^RR7      \        \        ) .8X  g   Q h\        \        ^RR7      4      ^8X  g   Q h\        \        ^RR7      4      ^8X  g   Q hR# )r>   T)Ú	primitive:r>   NNNr   y      à¿ªLXèz¶ë?y      à¿ªLXèz¶ë¿)Ú	unitrootsr   r²   Úlen)r   r	   r'  s      r   Útest_unitrootsrl  z  s  € Ü�Q‹<˜A˜3ÔÐÐÜ�Q‹<˜A˜r˜7Ô"Ð"Ð"Ü˜‹l�G€Aˆ!Ø�Œ6€Mˆ6Ø�4‰4Ð.×/Ò/Ð/Ð/Ø�4‰4Ð.×/Ò/Ð/Ð/Ü�Q $Ô'¨A¨3Ô.Ð.Ð.Ü�Q $Ô'¨B¨4Ô/Ð/Ð/Ü�Q $Ô'¬9°Q«<¸Õ+;Ô;Ð;Ð;Ü�Q $Ô'¬A´¨r¨7Ô2Ð2Ð2ÜŒy˜ tÔ,Ó-°Ô3Ð3Ð3ÜŒy˜ tÔ,Ó-°Ô2Ð2Ò2r   c                  óø  € ^\         n        \        ^4       U u. uF  p \        V ^4      NK  	  up . ^N^ N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N8X  g   Q h\        ^4       U u. uF  p \        V R
4      NK  	  up . ^NRN^ N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N^N8X  g   Q h\        ^4       U u. uF  p \        V \        4      NK  	  up ^R
\        ,           ^\        ,           \        ^ ^\        ) \        ^\        ) ^\        ^^\        ) ^^^\        \        ^.8X  g   Q h\        ^4       U u. uF  p \        V \        ) 4      NK  	  up ^R
\        ,
          ^\        ,
          \        ) ^ ^\        \        ) ^\        ^\        ) ^^\        ^^^\        ) \        ) ^.8X  g   Q h\        R\        4      ^8X  g   Q h\        R\        4      ^8X  g   Q h\        \        RR7      p\        ^V4      P                  ^ 4      '       g   Q h\        ^V4      P                  R4      '       g   Q h\        RV4      P                  ^4      '       g   Q h\        ^ R4      ^8X  g   Q h\        ^R4      R8X  g   Q h\        ^R4      R8X  g   Q h\        ^R4      R8X  g   Q h\        ^R4      R8X  g   Q hR	# u up i u up i u up i u up i )r   iX  i@ƒ  iô  r5   gæ�?3OP@iø  rê   g    Àcy@Nr   rA   rˆ   g      @g     €#@)r   r   rB   Ú
cyclotomicr²   rC   r   )rP   rQ   s     r   Útest_cyclotomicro  ˆ  sœ  € Ø„B„FÜ%*¨2¤YÓ/¡Y ŒJ�q˜ŽO¡YÑ/Ð3x°AÐ3x°aÐ3x¸Ð3x¸!Ð3x¸AÐ3x¸aÐ3xÀÐ3xÀ!Ð3xÀAÐ3xÀaÐ3xÈÐ3xÈ"Ð3xÈQÐ3xÈrÐ3xÐRSÐ3xÐTUÐ3xÐVWÐ3xÐXZÐ3xÐ[\Ð3xÐ]_Ð3xÐ`aÐ3xÐbcÐ3xÐdeÐ3xÐfhÐ3xÐijÐ3xÐklÐ3xÐmnÐ3xÐopÐ3xÐqrÐ3xÐsuÐ3xÐvwÐ3xÔxÐxÐxÜ&+¨B¤iÓ0¡i ŒJ�q˜Ö¡iÑ0Ð4v°QÐ4v°rÐ4v¸!Ð4v¸AÐ4v¸aÐ4vÀÐ4vÀ!Ð4vÀAÐ4vÀaÐ4vÈÐ4vÈ!Ð4vÈAÐ4vÈaÐ4vÐPQÐ4vÐRSÐ4vÐTUÐ4vÐVWÐ4vÐXYÐ4vÐZ[Ð4vÐ\]Ð4vÐ^_Ð4vÐ`aÐ4vÐbdÐ4vÐefÐ4vÐghÐ4vÐijÐ4vÐkmÐ4vÐnoÐ4vÐpqÐ4vÐrsÐ4vÐtuÐ4vÔvÐvÐvÜ%*¨2¤YÓ/¡Y ŒJ�qœŽO¡YÑ/°A°b¼µd¸1¼Q½3¼qÀÀ1ÄaÀRÌÈ!ÌQÈBÈqÔQRÐSTÐUVÔXYÐWYÐZ[Ð\]Ð^_Ô`aÔbcÐdeÐ3fÔfÐfÐfÜ&+¨B¤iÓ0¡i ŒJ�qœ!˜Ö¡iÑ0°Q°r¼!µt¸A¼a½CÄÀÀ1ÀQÄqÌ!ÈÈAÌaÐPQÔSTÐRTÐUVÐWXÔYZÐ[\Ð]^Ð_`ÔbcÐacÔefÐdfÐghÐ4iÔiÐiÐiÜ�dœ1Ó Ô"Ð"Ð"Ü�eœAÓ !Ô#Ð#Ð#ÜŒQ�SÔ€AÜ�a˜Ó×Ñ˜q×!Ò!Ð!Ð!Ü�b˜!Ó×ÑÐ 5×6Ò6Ð6Ð6Ü�d˜AÓ×!Ñ! !×$Ò$Ð$Ð$Ü�a˜Ó Ô!Ð!Ð!Ü�a˜Ó Ô%Ð%Ð%Ü�a˜Ó Ô%Ð%Ð%Ü�a˜ÓÐ 0Ô0Ð0Ð0Ü�a˜Ó 
Ô*Ð*Ò*ùò 0ùÚ0ùÚ/ùÚ0s   ™K(ÂK-Ã-K2Å+K7)DÚmpmath.libmpÚmpmathrD   Útimerp   ro   r
   r   r   r    r"   r$   r&   r(   r*   r,   r.   Útaperyr0   r2   r4   r7   rI   rf   rs   rw   rz   r„   r†   r’   rœ   rž   r«   r¯   r¸   r¾   rÁ   rÊ   rÎ   rÑ   rÚ   rè   rë   rî   rö   rú   rü   r  r  r  r  r!  r)  r,  r0  r9  rC  rG  rK  rR  rU  rX  r[  r_  rb  rg  rl  ro  rv   r   r   Ú<module>rt     so  ðÜ Ü Û Û Û Û àô ð$€ð#€ð*€ð
(€ð&€ð	&€ð*€ð*€	ð0€	ð
'€ð(€ð*€ð,€
òò,:òGò<Iò!òò)ò'ò#'òJ/ò
!òòòò&%ò4%ò:$òL)ò2ò òB/ò .ò*ò=ò'ò2ò1ò.)òò*J òXòò6*&òX ò	#ò4*òl	Kò1òò1ò&ò(ò61ò1ò=ò&3ô+r   