ó
    ˆ*£h;C  ã                   óâ  • S SK r SSKJr  SSKJr  SSKJrJrJrJrJ	r	J
r
JrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJ r J!r!J"r"J#r#J$r$J%r%J&r&J'r'J(r(J)r)J*r*J)r)J+r+J,r,J-r-J.r.J/r/  SSK0J1r1  \\4r2SSK3J4r4  \5Rl                  r7S r8 " S	 S
\55      r9 " S S\55      r:S r;\;" \\%5      u  \9l<        \9l=        \:l<        \:l=        \;" \\&5      u  \9l>        \9l?        \:l>        \:l?        \;" \\'5      u  \9l@        \9lA        \:l@        \:lA        \;" \\(5      u  \9lB        \9lC        \:lB        \:lC        \;" \!\)5      u  \9lD        \9lE        \:lD        \:lE        \9R„                  \9lF        \9R†                  \9lG        \:R„                  \:lF        \:R†                  \:lG         " S S\95      rH " S S\45      rI S SKJrJ\JR–                  R™                  \:5        \JRš                  R™                  \95        g! \N a     gf = f)é    Né   )Úlibmp)Ú
basestring),Ú	int_typesÚMPZ_ONEÚprec_to_dpsÚdps_to_precÚrepr_dpsÚround_floorÚround_ceilingÚfzeroÚfinfÚfninfÚfnanÚmpf_leÚmpf_negÚfrom_intÚ
from_floatÚfrom_strÚfrom_rationalÚmpi_midÚ	mpi_deltaÚmpi_strÚmpi_absÚmpi_posÚmpi_negÚmpi_addÚmpi_subÚmpi_mulÚmpi_divÚmpi_pow_intÚmpi_powÚmpi_from_strÚmpci_posÚmpci_negÚmpci_addÚmpci_subÚmpci_mulÚmpci_divÚmpci_powÚmpci_absr*   Úmpci_expÚmpci_logÚComplexResultÚmpf_hashÚmpc_hash)Ú_matrix)ÚStandardBaseContextc                 ó  • [        U S5      (       a  U R                  $ [        U [        5      (       a  [	        XU5      $ [        U [
        5      (       a  [        XU5      $ [        U [        5      (       a  [        XU5      $ [        e)NÚ_mpf_)
Úhasattrr4   Ú
isinstancer   r   Úfloatr   r   r   ÚNotImplementedError)ÚxÚprecÚroundings      ÚJ/home/mande/repo/quber/.venv/lib/python3.13/site-packages/mpmath/ctx_iv.pyÚconvert_mpf_r=      sh   € Üˆq�'×Ñ 1§7¡7˜NÜ�!”Y×Ñ¬°¸(Ó(CÐ!CÜ�!”U×Ñ¤J¨q¸Ó$AÐAÜ�!”Z× Ñ ¬°!¸8Ó)DÐ"DÜ
Ðó    c                   ó$  • \ rS rSrSrS"S jrS rS rS rS r	S r
\S	 5       r\S
 5       rS r\S 5       r\S 5       r\S 5       r\S 5       r\S 5       rS r\r\r\r\rS rS rS rS rS rS rS rS rS rS rS rS rS r S#S  jr!S!r"g)$Úivmpfé&   z@
Interval arithmetic class. Precision is controlled by iv.prec.
c                 ó8   • U R                   R                  U5      $ ©N)ÚctxÚconvert)Úclsr9   s     r<   Ú__new__Úivmpf.__new__+   s   € Ø�w‰w�‰˜qÓ!Ð!r>   c                 óP   • U R                   u  p4X4:X  a  U" U" U5      5      $ [        erC   )Ú_mpi_Ú
ValueError)ÚselfrF   Ú	f_convertÚaÚbs        r<   ÚcastÚ
ivmpf.cast.   s'   € Ø�z‰z‰ˆØ‹6Ù‘y “|Ó$Ð$ÜÐr>   c                 óJ   • U R                  [        [        R                  5      $ rC   )rP   Úintr   Úto_int©rL   s    r<   Ú__int__Úivmpf.__int__4   s   € Ø�y‰yœœeŸl™lÓ+Ð+r>   c                 óJ   • U R                  [        [        R                  5      $ rC   )rP   r7   r   Úto_floatrU   s    r<   Ú	__float__Úivmpf.__float__7   s   € Ø�y‰yœ¤§¡Ó/Ð/r>   c                 óJ   • U R                  [        [        R                  5      $ rC   )rP   Úcomplexr   rY   rU   s    r<   Ú__complex__Úivmpf.__complex__:   s   € Ø�y‰yœ¤%§.¡.Ó1Ð1r>   c                 óh   • U R                   u  pX:X  a  [        U5      $ [        U R                   5      $ rC   )rJ   r/   Úhash©rL   rN   rO   s      r<   Ú__hash__Úivmpf.__hash__=   s+   € Ø�z‰z‰ˆØ‹6Ü˜A“;Ðä˜Ÿ
™
Ó#Ð#r>   c                 ó   • U $ rC   © rU   s    r<   ÚrealÚ
ivmpf.realD   s   € Ø�Kr>   c                 ó.   • U R                   R                  $ rC   )rD   ÚzerorU   s    r<   ÚimagÚ
ivmpf.imagG   s   € ØŸ8™8Ÿ=™=Ð(r>   c                 ó   • U $ rC   rf   rU   s    r<   Ú	conjugateÚivmpf.conjugateJ   s   €  ˜r>   c                 óV   • U R                   u  pU R                  R                  X45      $ rC   ©rJ   rD   Úmake_mpfrb   s      r<   rN   Úivmpf.aL   ó$   € à�z‰z‰ˆØ�x‰x× Ñ  ! Ó(Ð(r>   c                 óV   • U R                   u  pU R                  R                  X"45      $ rC   rq   rb   s      r<   rO   Úivmpf.bQ   rt   r>   c                 ó~   • U R                   n[        U R                  UR                  5      nUR	                  X"45      $ rC   )rD   r   rJ   r:   rr   ©rL   rD   Úvs      r<   ÚmidÚ	ivmpf.midV   s0   € à�h‰hˆÜ�D—J‘J §¡Ó)ˆØ�|‰|˜Q˜FÓ#Ð#r>   c                 ó~   • U R                   n[        U R                  UR                  5      nUR	                  X"45      $ rC   )rD   r   rJ   r:   rr   rx   s      r<   ÚdeltaÚivmpf.delta\   s0   € à�h‰hˆÜ�d—j‘j #§(¡(Ó+ˆØ�|‰|˜Q˜EÓ"Ð"r>   c                 ó&   • U R                   [        4$ rC   )rJ   Úmpi_zerorU   s    r<   Ú_mpci_Úivmpf._mpci_b   s   € à�z‰zœ8Ð#Ð#r>   c                  ó   • [        S5      e)Nz-no ordering relation is defined for intervals©Ú	TypeError)Úargss    r<   Ú_compareÚivmpf._comparef   s   € ÜÐGÓHÐHr>   c                 óª   • U R                   R                  U5      nU R                  UR                  :*  =(       a    UR                  U R                  :*  $ rC   )rD   ÚmpfrN   rO   )rL   Úts     r<   Ú__contains__Úivmpf.__contains__n   s6   € Ø�H‰H�L‰L˜‹OˆØ—‘˜!Ÿ#™#‘×2 A§C¡C¨4¯6©6¡MÐ2r>   c                 óV   • [        U R                  U R                  R                  5      $ rC   )r   rJ   rD   r:   rU   s    r<   Ú__str__Úivmpf.__str__r   s   € Ü�t—z‘z 4§8¡8§=¡=Ó1Ð1r>   c                 ó  • U R                   R                  (       a  [        U 5      $ U R                  u  p[	        U R                   R
                  5      n[        R                  " X5      n[        R                  " X#5      nSU< SU< S3$ )Nzmpi(ú, Ú))rD   ÚprettyÚstrrJ   r
   r:   r   Úto_str)rL   rN   rO   Úns       r<   Ú__repr__Úivmpf.__repr__u   s[   € Ø�8‰8�?�?Ü�t“9ÐØ�z‰z‰ˆÜ�T—X‘X—]‘]Ó#ˆÜ�LŠL˜ÓˆÜ�LŠL˜Ó‰Û !£1Ð%Ð%r>   c                 ó°   • [        US5      (       d   U R                  R                  U5      nU" U R                  UR                  5      $ !   [        s $ = f)NrJ   )r5   rD   rE   ÚNotImplementedrJ   )Úsr‹   Úcmpfuns      r<   r‡   rˆ   ~   sJ   € Ü�q˜'×"Ñ"ð&Ø—E‘E—M‘M !Ó$�ñ �a—g‘g˜qŸw™wÓ'Ð'øð&Ü%Ò%ús   “A ÁAc                 óB   • U R                  U[        R                  5      $ rC   )r‡   r   Úmpi_eq©rœ   r‹   s     r<   Ú__eq__Úivmpf.__eq__†   ó   € ˜QŸZ™Z¨¬5¯<©<Ó8Ð8r>   c                 óB   • U R                  U[        R                  5      $ rC   )r‡   r   Úmpi_ner    s     r<   Ú__ne__Úivmpf.__ne__‡   r£   r>   c                 óB   • U R                  U[        R                  5      $ rC   )r‡   r   Úmpi_ltr    s     r<   Ú__lt__Úivmpf.__lt__ˆ   r£   r>   c                 óB   • U R                  U[        R                  5      $ rC   )r‡   r   Úmpi_ler    s     r<   Ú__le__Úivmpf.__le__‰   r£   r>   c                 óB   • U R                  U[        R                  5      $ rC   )r‡   r   Úmpi_gtr    s     r<   Ú__gt__Úivmpf.__gt__Š   r£   r>   c                 óB   • U R                  U[        R                  5      $ rC   )r‡   r   Úmpi_ger    s     r<   Ú__ge__Úivmpf.__ge__‹   r£   r>   c                 óˆ   • U R                   R                  [        U R                  U R                   R                  5      5      $ rC   )rD   rr   r   rJ   r:   rU   s    r<   Ú__abs__Úivmpf.__abs__�   ó*   € Ø�x‰x× Ñ ¤¨¯©°T·X±X·]±]Ó!CÓDÐDr>   c                 óˆ   • U R                   R                  [        U R                  U R                   R                  5      5      $ rC   )rD   rr   r   rJ   r:   rU   s    r<   Ú__pos__Úivmpf.__pos__�   r»   r>   c                 óˆ   • U R                   R                  [        U R                  U R                   R                  5      5      $ rC   )rD   rr   r   rJ   r:   rU   s    r<   Ú__neg__Úivmpf.__neg__‘   r»   r>   Nc                 ó:   • U R                   R                  XX#5      $ rC   ©rD   Úalmosteq©rœ   r‹   Úrel_epsÚabs_epss       r<   ÚaeÚivmpf.ae”   ó   € Ø�u‰u�~‰~˜a GÓ5Ð5r>   rf   )r   ©NN)#Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__Ú__doc__rG   rP   rV   rZ   r^   rc   Úpropertyrg   rk   rn   rN   rO   rz   r}   r�   r‡   r²   r®   r¶   rŒ   r�   r˜   r¡   r¦   rª   r¹   r½   rÀ   rÈ   Ú__static_attributes__rf   r>   r<   r@   r@   &   s  † ñô"òò,ò0ò2ò$ð Ùó ØàÙ(ó Ø(â$àñ)ó ð)ð ñ)ó ð)ð ñ$ó ð$ð
 ñ#ó ð#ð
 ñ$ó ð$òIð €FØ€FØ€FØ€Fò3ò2ò&ò(ò 9Ú8Ú8Ú8Ú8Ú8òEòEòE÷6r>   r@   c                   óæ   • \ rS rSrSS jrS rS rS r\S 5       r	\S 5       r
\S 5       r\S	 5       r\S
 5       r\S 5       rS rS rS rSS jrS rS rS r\=r=rrS rS rS rSS jrSrg)Úivmpcé—   c                 óÂ   • U R                   R                  U5      nU R                   R                  U5      n[        U 5      nUR                  UR                  4Ul        U$ rC   )rD   rE   ÚnewrJ   r�   )rF   ÚreÚimÚys       r<   rG   Úivmpc.__new__™   sH   € Ø�W‰W�_‰_˜RÓ ˆØ�W‰W�_‰_˜RÓ ˆÜ�‹HˆØ—8‘8˜RŸX™XÐ%ˆŒØˆr>   c                 ó~   • U R                   u  u  pu  p4X:X  a  X4:X  a  [        X45      $ [        U R                   5      $ rC   )r�   r0   ra   ©rL   rN   rO   ÚcÚds        r<   rc   Úivmpc.__hash__    s8   € ØŸ™‰‰ˆ‘�Ø‹6�a“fÜ˜Q˜FÓ#Ð#ä˜Ÿ™Ó$Ð$r>   c                 ó°   • U R                   R                  (       a  [        U 5      $ S[        U R                  5      < S[        U R
                  5      < S3$ )Nziv.mpc(r’   r“   )rD   r”   r•   Úreprrg   rk   ©rœ   s    r<   r˜   Úivmpc.__repr__§   s6   € Ø�5‰5�<�<Ü�q“6ˆMð ä#'¨¯©¦<´°a·f±f¶Ð>Ð>r>   c                 ód   • S[        U R                  5      < S[        U R                  5      < S3$ )NÚ(ú + ú*j))r•   rg   rk   rã   s    r<   r�   Úivmpc.__str__¬   s   � Ü # A§F¡F¦¬S°·±®[Ð9Ð9r>   c                 ó`   • U R                   u  u  pu  p4U R                  R                  X45      $ rC   ©r�   rD   rr   rÝ   s        r<   rN   Úivmpc.a¯   ó*   € àŸ™‰‰ˆ‘�Ø�x‰x× Ñ  ! Ó(Ð(r>   c                 ó`   • U R                   u  u  pu  p4U R                  R                  X"45      $ rC   rë   rÝ   s        r<   rO   Úivmpc.b´   rí   r>   c                 ó`   • U R                   u  u  pu  p4U R                  R                  X345      $ rC   rë   rÝ   s        r<   rÞ   Úivmpc.c¹   rí   r>   c                 ó`   • U R                   u  u  pu  p4U R                  R                  XD45      $ rC   rë   rÝ   s        r<   rß   Úivmpc.d¾   rí   r>   c                 óR   • U R                   R                  U R                  S   5      $ ©Nr   ©rD   rr   r�   rã   s    r<   rg   Ú
ivmpc.realÃ   ó   € à�u‰u�~‰~˜aŸh™h q™kÓ*Ð*r>   c                 óR   • U R                   R                  U R                  S   5      $ ©Nr   rö   rã   s    r<   rk   Ú
ivmpc.imagÇ   rø   r>   c                 ój   • U R                   u  pU R                  R                  U[        U5      45      $ rC   )r�   rD   Úmake_mpcr   )rœ   rN   rO   s      r<   rn   Úivmpc.conjugateË   s(   € Ø�x‰x‰ˆØ�u‰u�~‰~˜q¤'¨!£*˜oÓ.Ð.r>   c                 óÒ  • U R                   R                  U5      nU R                  UR                  s=:*  =(       a    U R                  :*  Os  =(       d§    U R                  UR                  s=:*  =(       a    U R                  :*  Os  =(       dm    UR                  U R                  s=:*  =(       a    UR                  :*  Os  =(       d3    UR                  U R                  s=:*  =(       a    UR                  :*  Os  nU R                  UR                  s=:*  =(       a    U R
                  :*  Os  =(       d§    U R                  UR
                  s=:*  =(       a    U R
                  :*  Os  =(       dm    UR                  U R                  s=:*  =(       a    UR
                  :*  Os  =(       d3    UR                  U R
                  s=:*  =(       a    UR
                  :*  Os  nU=(       a    U$ rC   )rD   rE   rN   rO   rÞ   rß   )rœ   r‹   Úreal_overlapÚimag_overlaps       r<   ÚoverlapÚivmpc.overlapÏ   s'  € Ø�E‰E�M‰M˜!ÓˆØŸ™˜qŸs™s×)Ó) a§c¡cÔ)×o¨q¯s©s°a·c±c×/@Ó/@¸Q¿S¹SÔ/@×oÀaÇcÁcÈQÏSÉS×FWÓFWÐTU×TWÑTWÔFW×oÐ]^×]`Ñ]`Ðde×dgÑdg×]nÓ]nÐkl×knÑknÔ]nˆØŸ™˜qŸs™s×)Ó) a§c¡cÔ)×o¨q¯s©s°a·c±c×/@Ó/@¸Q¿S¹SÔ/@×oÀaÇcÁcÈQÏSÉS×FWÓFWÐTU×TWÑTWÔFW×oÐ]^×]`Ñ]`Ðde×dgÑdg×]nÓ]nÐkl×knÑknÔ]nˆØ×, Ð,r>   c                 óª   • U R                   R                  U5      nUR                  U R                  ;   =(       a    UR                  U R                  ;   $ rC   )rD   rE   rg   rk   r    s     r<   rŒ   Úivmpc.__contains__Õ   s9   € Ø�E‰E�M‰M˜!ÓˆØ�v‰v˜Ÿ™Ñ×4 A§F¡F¨a¯f©fÑ$4Ð4r>   c                 óh  • [        XR                  R                  5      (       d   U R                  R                  U5      n[        US5      (       a  UR                  [        4nO[        US5      (       a  UR                  nU(       a  U R                  W:g  $ U R                  W:H  $ !   [        s $ = f©NrJ   r�   )	r6   rD   Ú_typesrE   r›   r5   rJ   r€   r�   )rœ   r‹   ÚneÚtvals       r<   r‡   Úivmpc._compareÙ   s�   € Ü˜!ŸU™UŸ\™\×*Ñ*ð&Ø—E‘E—M‘M !Ó$�ô �1�g×ÑØ—7‘7œHÐ$‰DÜ�Q˜×!Ñ!Ø—8‘8ˆDÞØ—8‘8˜tÑ#Ð#Ø�x‰x˜4ÑÐøð&Ü%Ò%ús   ¦B' Â'B1c                 ó$   • U R                  U5      $ rC   ©r‡   r    s     r<   r¡   Úivmpc.__eq__ç   s   € ˜QŸZ™Z¨›]Ð*r>   c                 ó&   • U R                  US5      $ )NTr  r    s     r<   r¦   Úivmpc.__ne__è   s   € ˜QŸZ™Z¨¨4Ó0Ð0r>   c                 ó   • [        S5      e)Nz#complex intervals cannot be orderedr„   r    s     r<   rª   Úivmpc.__lt__ê   s   € œIÐ&KÓLÐLr>   c                 óˆ   • U R                   R                  [        U R                  U R                   R                  5      5      $ rC   )rD   rý   r%   r�   r:   rã   s    r<   rÀ   Úivmpc.__neg__í   ó'   € ˜1Ÿ5™5Ÿ>™>¬(°1·8±8¸Q¿U¹U¿Z¹ZÓ*HÓIÐIr>   c                 óˆ   • U R                   R                  [        U R                  U R                   R                  5      5      $ rC   )rD   rý   r$   r�   r:   rã   s    r<   r½   Úivmpc.__pos__î   r  r>   c                 óˆ   • U R                   R                  [        U R                  U R                   R                  5      5      $ rC   )rD   rr   r+   r�   r:   rã   s    r<   r¹   Úivmpc.__abs__ï   r  r>   Nc                 ó:   • U R                   R                  XX#5      $ rC   rÃ   rÅ   s       r<   rÈ   Úivmpc.aeñ   rÊ   r>   rf   )r   r   )FrË   )rÌ   rÍ   rÎ   rÏ   rG   rc   r˜   r�   rÑ   rN   rO   rÞ   rß   rg   rk   rn   r  rŒ   r‡   r¡   r¦   rª   r®   r²   r¶   rÀ   r½   r¹   rÈ   rÒ   rf   r>   r<   rÔ   rÔ   —   sÊ   † ôò%ò?ò
:ð ñ)ó ð)ð ñ)ó ð)ð ñ)ó ð)ð ñ)ó ð)ð ñ+ó ð+ð ñ+ó ð+ò/ò-ò5ô ò +Ú0âLØ%Ð%€FÐ%ˆV�fâIÚIÚI÷6r>   rÔ   c                 ó`   ^ ^^^• U4S jmU U4S jmUU4S jnUU4S jnU4S jnU4S jnX#XE4$ )Nc                 óH   >• U R                  T" XU R                  5      5      $ rC   )rý   r:   )rD   Úsvalr
  Ú	f_complexs      €r<   Ú	g_complexÚ_binary_op.<locals>.g_complexõ   s   ø€ Ø�|‰|™I d°#·(±(Ó;Ó<Ð<r>   c                 óœ   >•  U R                  T" XU R                  5      5      $ ! [         a    U[        4nU[        4nT" XU5      s $ f = frC   )rr   r:   r.   r€   )rD   r  r
  Úf_realr   s      €€r<   Úg_realÚ_binary_op.<locals>.g_real÷   sR   ø€ ð	.Ø—<‘<¡ t°3·8±8Ó <Ó=Ð=øÜó 	.Øœ(Ð#ˆDØœ(Ð#ˆDÙ˜S¨Ó-Ò-ð	.ús   ƒ!% ¥#AÁ
Ac                 óx  >• [        U[        5      (       a  [        $ U R                  n[        XR                  5      (       d  UR                  U5      n[        US5      (       a  T" X R                  UR                  5      $ [        US5      (       a#  T" X R                  [        4UR                  5      $ [        $ r  )
r6   r1   r›   rD   r  rE   r5   rJ   r€   r�   ©rœ   r‹   rD   r   r$  s      €€r<   Úlop_realÚ_binary_op.<locals>.lop_realþ   s†   ø€ Ü�aœ×!Ñ!¬.Ð#8Ø�e‰eˆÜ˜!ŸZ™Z×(Ñ(¨c¯k©k¸!«n¨!Ü�1�g×Ñ¡v¨c·7±7¸A¿G¹GÓ'DÐ DÜ�1�h×Ñ©	°#¿¹ÄÐ7JÈAÏHÉHÓ(UÐ!UÜÐr>   c                 óB  >• U R                   n[        XR                  5      (       d  UR                  U5      n[	        US5      (       a  T" X!R
                  U R
                  5      $ [	        US5      (       a#  T" X!R                  U R
                  [        45      $ [        $ r  )	rD   r6   r  rE   r5   rJ   r�   r€   r›   r'  s      €€r<   Úrop_realÚ_binary_op.<locals>.rop_real  st   ø€ Ø�e‰eˆÜ˜!ŸZ™Z×(Ñ(¨c¯k©k¸!«n¨!Ü�1�g×Ñ¡v¨c·7±7¸A¿G¹GÓ'DÐ DÜ�1�h×Ñ©	°#·x±xÀ!Ç'Á'Ì8ÐATÓ(UÐ!UÜÐr>   c                 óD  >• [        U[        5      (       a  [        $ U R                  n[        XR                  R                  5      (       d   U R                  R                  U5      nT" X R                  UR                  5      $ ! [        [        4 a	    [        s $ f = frC   )	r6   r1   r›   rD   r  rE   rK   r…   r�   ©rœ   r‹   rD   r   s      €r<   Úlop_complexÚ_binary_op.<locals>.lop_complex  s{   ø€ Ü�aœ×!Ñ!¬.Ð#8Ø�e‰eˆÜ˜!ŸU™UŸ\™\×*Ñ*ð&Ø—E‘E—M‘M !Ó$�ñ ˜Ÿh™h¨¯©Ó1Ð1øô ¤	Ð*ó &Ü%Ò%ð&ús   ÁB ÂBÂBc                 óÔ   >• U R                   n[        XR                   R                  5      (       d  U R                   R                  U5      nT" X!R                  U R                  5      $ rC   )rD   r6   r  rE   r�   r.  s      €r<   Úrop_complexÚ_binary_op.<locals>.rop_complex  sF   ø€ Ø�e‰eˆÜ˜!ŸU™UŸ\™\×*Ñ*Ø—‘—‘˜aÓ ˆAÙ˜Ÿh™h¨¯©Ó1Ð1r>   rf   )r#  r  r(  r+  r/  r2  r   r$  s   ``    @@r<   Ú
_binary_opr4  ô   s.   û€ õ=ö.ööõ2õ2ð
 ˜{Ð7Ð7r>   c                   ó0   • \ rS rSrS rS r\" \5      rSrg)Úivmpf_constanti$  c                 ó(   • [        U 5      nXl        U$ rC   )r×   Ú_f)rF   ÚfrL   s      r<   rG   Úivmpf_constant.__new__%  s   € Ü�3‹xˆØŒØˆr>   c                 ó’   • U R                   R                  S   nU R                  U[        5      nU R                  U[        5      nX#4$ rõ   )rD   Ú_precr8  r   r   )rL   r:   rN   rO   s       r<   Ú	_get_mpi_Úivmpf_constant._get_mpi_)  s;   € Ø�x‰x�~‰~˜aÑ ˆØ�G‰G�Dœ+Ó&ˆØ�G‰G�Dœ-Ó(ˆØˆtˆr>   )r8  N)	rÌ   rÍ   rÎ   rÏ   rG   r=  rÑ   rJ   rÒ   rf   r>   r<   r6  r6  $  s   † òòñ
 �YÓƒEr>   r6  c                   óæ   • \ rS rSrS rSS jrS rSS jr\S 5       r	S r
S	 r\" S
 \
5      r\" S \5      rS rS rS rS rSS jrS rS rS rS rS rS rS rS rS rS rS rS S jrSr g)!ÚMPIntervalContexti0  c                 óV  • [        S[        40 5      U l        [        S[        40 5      U l        U R                  U R                  4U l        [        S[        40 5      U l        S/U l        U R                  S5        U R                  [        U R                  /=U R                  l        =U R                  l        U R                  l        U =U R                  l        =U R                  l        U R                  l        SU l        [        R                  " U 5        U R!                  5         g )Nr@   rÔ   r6  é5   F)Útyper@   rŠ   rÔ   Úmpcr  r6  Ú	_constantr<  Ú	_set_precr×   Ú_ctxdatarD   r”   r2   Ú__init__Ú_init_builtins©rD   s    r<   rH  ÚMPIntervalContext.__init__2  sÝ   € Ü�w¤ ¨"Ó-ˆŒÜ�w¤ ¨"Ó-ˆŒØ—g‘g˜sŸw™wÐ'ˆŒ
ÜÐ-´Ð/@À"ÓEˆŒØ�DˆŒ	Ø�‰�bÔØHKÏÉÔQTÐVY×V_ÑV_ÐG`Ð`ˆ�‰ÔÐ` §¡Ô!1°C·G±GÔ4DØ8;Ð;ˆ�‰ÔÐ;˜CŸG™GœK¨#¯'©'¬+ØˆŒ
Ü×$Ò$ SÔ)Ø×ÑÕr>   Nc                 óN   • Uc  U R                  U5      $ U R                  X45      $ rC   )rŠ   )rD   rN   rO   s      r<   Ú_mpiÚMPIntervalContext._mpi?  s%   € Ø‰9Ø—7‘7˜1“:ÐØ�w‰w˜�u‹~Ðr>   c                 óæ  • U R                  S5      U l        U R                  S5      U l        U R                  S5      U l        U R                  * U l        U R                  S5      U l        U R                  SS5      U l        U R                  [        R                  [        R                  5      U l        U R                  [        R                  5      U l        U R                  [        R                  [        R                   5      U l        U R                  [        R$                  [        R&                  5      U l        U R                  [        R*                  [        R,                  5      U l        U R                  [        R0                  5      U l        U R                  [        R4                  [        R6                  5      U l        U R                  [        R:                  [        R<                  5      U l        U R                  [        R@                  [        RB                  5      U l"        U R                  [        RF                  [        RH                  5      U l%        U RJ                  U l&        U RO                  S 5      U l(        U RO                  [        RR                  5      U l*        U RO                  [        RV                  5      U l,        U RO                  [        RZ                  5      U l.        U RO                  [        R^                  5      U l0        U RO                  [        Rb                  5      U l2        U RO                  [        Rf                  5      U l4        U RO                  [        Rj                  5      U l6        U RO                  [        Rn                  5      U l8        U RO                  [        Rr                  5      U l:        U RO                  [        Rv                  5      U l<        g )Nr   r   ÚinfÚnanc                 ó   • S[         SU -
  S4$ ©Nr   r   )r   )r:   Úrnds     r<   Ú<lambda>Ú2MPIntervalContext._init_builtins.<locals>.<lambda>W  s   € °1´g¸qÀ¹vÀqÑ2Ir>   )=rŠ   Úonerj   rP  ÚninfrQ  rD  ÚjÚ_wrap_mpi_functionr   Úmpi_expr,   ÚexpÚmpi_sqrtÚsqrtÚmpi_logr-   ÚlnÚmpi_cosÚmpci_cosÚcosÚmpi_sinÚmpci_sinÚsinÚmpi_tanÚtanÚ	mpi_gammaÚ
mpci_gammaÚgammaÚmpi_loggammaÚmpci_loggammaÚloggammaÚ
mpi_rgammaÚmpci_rgammaÚrgammaÚmpi_factorialÚmpci_factorialÚ	factorialÚfacrE  ÚepsÚmpf_piÚpiÚmpf_eÚeÚmpf_ln2Úln2Úmpf_ln10Úln10Úmpf_phiÚphiÚ	mpf_eulerÚeulerÚmpf_catalanÚcatalanÚmpf_glaisherÚglaisherÚmpf_khinchinÚkhinchinÚmpf_twinprimeÚ	twinprimerJ  s    r<   rI  Ú MPIntervalContext._init_builtinsD  sb  € Ø—'‘'˜!“*ˆŒØ—7‘7˜1“:ˆŒØ—'‘'˜%“.ˆŒØ—G‘G�8ˆŒØ—'‘'˜%“.ˆŒØ—‘˜˜!“ˆŒØ×(Ñ(¬¯©¼¿¹ÓGˆŒØ×)Ñ)¬%¯.©.Ó9ˆŒØ×'Ñ'¬¯©´u·~±~ÓFˆŒØ×(Ñ(¬¯©¼¿¹ÓGˆŒØ×(Ñ(¬¯©¼¿¹ÓGˆŒØ×(Ñ(¬¯©Ó7ˆŒØ×*Ñ*¬5¯?©?¼E×<LÑ<LÓMˆŒ	Ø×-Ñ-¬e×.@Ñ.@Ä%×BUÑBUÓVˆŒØ×+Ñ+¬E×,<Ñ,<¼e×>OÑ>OÓPˆŒ
Ø×.Ñ.¬u×/BÑ/BÄE×DXÑDXÓYˆŒØ—-‘-ˆŒà—-‘-Ñ IÓJˆŒØ—‘œuŸ|™|Ó,ˆŒØ—‘œeŸk™kÓ*ˆŒØ—-‘-¤§¡Ó.ˆŒØ—=‘=¤§¡Ó0ˆŒØ—-‘-¤§¡Ó.ˆŒØ—M‘M¤%§/¡/Ó2ˆŒ	Ø—m‘m¤E×$5Ñ$5Ó6ˆŒØ—}‘}¤U×%7Ñ%7Ó8ˆŒØ—}‘}¤U×%7Ñ%7Ó8ˆŒØŸ™¤e×&9Ñ&9Ó:ˆ�r>   c                 ó   ^ ^^• U UU4S jnU$ )Nc                 ój  >• U(       a   UR                  STR                  S   5      nOTR                  S   nTR                  U 5      n [        U S5      (       a"  TR	                  T" U R
                  U5      5      $ [        U S5      (       a"  TR                  T" U R                  U5      5      $ [        e)Nr:   r   rJ   r�   )	Úgetr<  rE   r5   rr   rJ   rý   r�   rK   )r9   Úkwargsr:   rD   r  r#  s      €€€r<   ÚgÚ/MPIntervalContext._wrap_mpi_function.<locals>.gd  sŒ   ø€ ÞØ—z‘z &¨#¯)©)°A©,Ó7‘à—y‘y ‘|�Ø—‘˜A“ˆAÜ�q˜'×"Ñ"Ø—|‘|¡F¨1¯7©7°DÓ$9Ó:Ð:Ü�q˜(×#Ñ#Ø—|‘|¡I¨a¯h©h¸Ó$=Ó>Ð>ÜÐr>   rf   )rD   r#  r  r�  s   ``` r<   rZ  Ú$MPIntervalContext._wrap_mpi_functionc  s   ú€ ÷
	ð ˆr>   c                 ó>   ^• U(       a  U4S jnOTn[        XU5        g )Nc                 óØ   >• U R                   nU Vs/ s H
  oC" U5      PM     nnU R                  n U =R                  S-  sl        T" U /UQ70 UD6nXPl        U7$ s  snf ! XPl        f = f)Né
   )rE   r:   )rD   r†   r�  rE   rN   r:   Úretvalr9  s          €r<   Ú	f_wrappedÚ2MPIntervalContext._wrap_specfun.<locals>.f_wrappedt  sm   ø€ ØŸ+™+�Ù,0Ó1ªD q˜ ž
©D�Ð1Ø—x‘x�ð$Ø—H’H ‘N•HÙ˜sÐ4 TÒ4¨VÑ4�Fà#”HØ�w�ùò 2øð  $•Hús   ’A²!A! Á!A))Úsetattr)rF   Únamer9  Úwrapr—  s     `  r<   Ú_wrap_specfunÚMPIntervalContext._wrap_specfunq  s   ø€ æö	ð ˆIÜ�˜9Õ%r>   c                 óh   • [        S[        U5      5      U R                  S'   [        U5      U l        g )Nr   r   )ÚmaxrS   r<  r   Ú_dps©rD   r—   s     r<   rF  ÚMPIntervalContext._set_prec‚  s$   € Ü˜1œc !›f“~ˆ�	‰	�!‰Ü˜q“>ˆ�r>   c                 óh   • [        U5      U R                  S'   [        S[        U5      5      U l        g rS  )r	   r<  rŸ  rS   r   r¡  s     r<   Ú_set_dpsÚMPIntervalContext._set_dps†  s$   € Ü" 1“~ˆ�	‰	�!‰Ü�qœ#˜a›&“>ˆ�r>   c                 ó    • U R                   S   $ rõ   )r<  rJ  s    r<   rU  ÚMPIntervalContext.<lambda>Š  s   €  §	¡	¨!¢r>   c                 ó   • U R                   $ rC   )r   rJ  s    r<   rU  r§  ‹  s   € ˜sŸxšxr>   c                 ó<   • [        U R                  5      nXl        U$ rC   )r×   rŠ   rJ   ©rD   ry   rN   s      r<   rr   ÚMPIntervalContext.make_mpf�  s   € Ü�—‘‹LˆØŒØˆr>   c                 ó<   • [        U R                  5      nXl        U$ rC   )r×   rD  r�   rª  s      r<   rý   ÚMPIntervalContext.make_mpc’  s   € Ü�—‘‹LˆØŒØˆr>   c                 óÆ   • Uu  p#[         R                  " X#U R                  [        5      n[         R                  " X#U R                  [        5      nU R                  XE45      $ rC   )r   r   r:   r   r   rr   )rD   ÚpqÚpÚqrN   rO   s         r<   Ú_mpqÚMPIntervalContext._mpq—  sJ   € Ø‰ˆÜ×Ò  c§h¡h´Ó<ˆÜ×Ò  c§h¡h´Ó>ˆØ�|‰|˜Q˜FÓ#Ð#r>   c                 óÖ  • [        XR                  U R                  45      (       a  U$ [        XR                  5      (       a  U7$ [        U[        5      (       d  [        US5      (       aG  U R                  UR                  5      nU R                  UR                  5      nU R                  X#5      $ [        U[        5      (       a&  [        XR                  5      nU R                  U5      $ [        US5      (       a  UR                  u  pVO{ Uu  pV[        US5      (       a  UR                  S   nO[!        XPR                  ["        5      n[        US5      (       a  UR                  S   nO[!        X`R                  [$        5      nU[&        :X  d
  U[&        :X  a  [(        n[*        n[-        XV5      (       d   S5       eU R                  XV45      $ ! [        [        4 a    U=pV NÔf = f)NÚ_mpc_rJ   r   r   z"endpoints must be properly ordered)r6   rŠ   rD  rE  r]   r5   rE   rg   rk   r   r#   r:   rr   rJ   r…   rK   r=   r   r   r   r   r   r   )rD   r9   rØ   rÙ   ry   rN   rO   s          r<   rE   ÚMPIntervalContext.convert�  s€  € Ü�aŸ'™' 3§7¡7Ð+×,Ñ,ØˆHÜ�aŸ™×'Ñ'Ø�2ˆIÜ�aœ×!Ñ!¤W¨Q°×%8Ñ%8Ø—‘˜QŸV™VÓ$ˆBØ—‘˜QŸV™VÓ$ˆBØ—7‘7˜2“>Ð!Ü�aœ×$Ñ$Ü˜Q§¡Ó)ˆAØ—<‘< “?Ð"Ü�1�g×ÑØ—7‘7‰DˆAˆqðØ‘�ô �q˜'×"Ñ"Ø—G‘G˜A‘J‘ä  §H¡H¬kÓ:�Ü�q˜'×"Ñ"Ø—G‘G˜A‘J‘ä  §H¡H¬mÓ<�Ø”‹9˜œT›	ÜˆAÜˆAÜ�a�|‰|ÐAÐAÓAˆ|Ø�|‰|˜Q˜FÓ#Ð#øô œzÐ*ó Ø�	�‘Aðús   ÄG ÇG(Ç'G(c                 óX  • U R                  U5      n[        US5      (       a"  [        R                  " UR                  U40 UD6$ [        US5      (       aU  [        R                  " UR
                  S   U40 UD6n[        R                  " UR
                  S   U40 UD6nSU< SU< S3$ g )NrJ   r�   r   r   ræ   rç   rè   )rE   r5   r   Ú
mpi_to_strrJ   r�   )rD   r9   r—   r�  rØ   rÙ   s         r<   ÚnstrÚMPIntervalContext.nstr¾  s“   € Ø�K‰K˜‹NˆÜ�1�g×ÑÜ×#Ò# A§G¡G¨QÑ9°&Ñ9Ð9Ü�1�h×ÑÜ×!Ò! !§(¡(¨1¡+¨qÑ;°FÑ;ˆBÜ×!Ò! !§(¡(¨1¡+¨qÑ;°FÑ;‰BÛ$&«Ð+Ð+ð  r>   c                 ó®  • U R                  U5      n[        XR                  5      (       aA  [        U R	                  UR
                  5      U R	                  UR                  5      5      S-   $ [        R                  " UR                  5      u  p#Uu  pEpgU(       a  Xg-   $ U[        :X  a  U R                  $ U[        :X  a  U R                  $ U R                  $ rú   )rE   r6   rD  rŸ  Úmagrg   rk   r   r   rJ   r   rX  r   rQ  rP  ©rD   r9   rN   rO   ÚsignÚmanr\  Úbcs           r<   r¼  ÚMPIntervalContext.magÇ  s™   € Ø�K‰K˜‹NˆÜ�aŸ™×!Ñ!Ü�s—w‘w˜qŸv™v“¨¯©°·±«Ó8¸1Ñ<Ð<Ü�}Š}˜QŸW™WÓ%‰ˆØÑˆ�3ÞØ‘6ˆMØ”‹:Ø—8‘8ˆOØ”‹9Ø—7‘7ˆNØ�w‰wˆr>   c                 ó   • g)NFrf   ©rD   r9   s     r<   ÚisnanÚMPIntervalContext.isnanÕ  s   € Ør>   c                 ó   • XR                   :H  $ rC   )rP  rÃ  s     r<   ÚisinfÚMPIntervalContext.isinfØ  s   € Ø—G‘G‰|Ðr>   c                 ó€   • U R                  U5      nUR                  u  p#X#:X  a  Uu  pEpgU(       a  US:¬  $ U[        :H  $ g rõ   )rE   rJ   r   r½  s           r<   ÚisintÚMPIntervalContext.isintÛ  sB   € Ø�K‰K˜‹NˆØ�w‰w‰ˆØ‹6Ø!"ÑˆD�sÞØ˜a‘x�Øœ‘:ÐØr>   c                 ó¸   • U R                  U5      R                  u  p4[        R                  " X25      n[        R                  " XB5      nU R	                  X445      $ rC   )rE   rJ   r   Ú	mpf_shiftrr   )rD   r9   r—   rN   rO   s        r<   ÚldexpÚMPIntervalContext.ldexpå  sD   € Ø�{‰{˜1‹~×#Ñ#‰ˆÜ�OŠO˜AÓ!ˆÜ�OŠO˜AÓ!ˆØ�|‰|˜Q˜EÓ"Ð"r>   c                 óJ   • [        U R                  U5      5      R                  $ rC   )ÚabsrE   rN   rÃ  s     r<   ÚabsminÚMPIntervalContext.absminë  ó   € Ü�3—;‘;˜q“>Ó"×$Ñ$Ð$r>   c                 óJ   • [        U R                  U5      5      R                  $ rC   )rÑ  rE   rO   rÃ  s     r<   ÚabsmaxÚMPIntervalContext.absmaxî  rÔ  r>   c                 óÎ   • U R                  U5      R                  nU R                  U5      R                  nU R                  [        R                  " XU R
                  5      5      $ rC   )rE   rJ   rr   r   Ú	mpi_atan2r:   )rD   rÚ   r9   s      r<   Úatan2ÚMPIntervalContext.atan2ñ  sF   € Ø�K‰K˜‹N× Ñ ˆØ�K‰K˜‹N× Ñ ˆØ�|‰|œEŸOšO¨A°·±Ó9Ó:Ð:r>   c                 ój  • [        U[        R                  5      (       a  US4$ [        U[        5      (       a)  Uu  p#U R	                  U5      U R	                  U5      -  S4$ U R                  U5      n[        XR                  5      (       a  US4$ [        XR                  5      (       a  US4$ [        e)NÚZÚRÚC)r6   r   r   ÚtuplerŠ   rE   rD  rK   )rD   r9   r°  r±  s       r<   Ú_convert_paramÚ MPIntervalContext._convert_paramö  s“   € Ü�aœŸ™×)Ñ)Ø�c�6ˆMÜ�aœ×ÑØ‰DˆAØ—G‘G˜A“J §¡¨£Ñ+¨SÐ1Ð1Ø�K‰K˜‹NˆÜ�aŸ™×!Ñ!Ø�c�6ˆMÜ�aŸ™×!Ñ!Ø�c�6ˆMÜÐr>   c                 óZ   • [        XR                  5      =(       d    [        U[        5      $ rC   )r6   rŠ   r   ©rD   Úzs     r<   Ú_is_real_typeÚMPIntervalContext._is_real_type  s   € Ü˜!ŸW™WÓ%×A¬°A´yÓ)AÐAr>   c                 ó,   • [        XR                  5      $ rC   )r6   rD  rä  s     r<   Ú_is_complex_typeÚ"MPIntervalContext._is_complex_type  s   € Ü˜!ŸW™WÓ%Ð%r>   c                 ó
  • [        U5      n[        U5      n[        XU-   5      n	U R                  =p«Sn U H  oÛXM   U-   -  nM     U	 H  oÛXM   U-   -  nM     US-  oËU-  o»U-  oºU-  n
US:X  a  U
$ XÆ:”  a  U R                  eMP  rS  )ÚlistÚrangerW  ÚNoConvergence)rD   r°  r±  ÚtypesÚcoeffsrå  Úmaxtermsr�  ÚnumÚdenrœ   r‹   ÚkÚis                 r<   ÚhypsumÚMPIntervalContext.hypsum	  s›   € Ü�f“ˆÜ�A‹hˆÜ�A˜‘c‹lˆà—‘ˆˆØˆØÛ� ¡	¨!¡Ñ,š!‘SÛ� ¡	¨!¡Ñ,š!‘SØ�‰FˆA˜‘F�A ™F˜A¨¡F AØ�A‹vØ�ð ‹|Ø×'Ñ'Ð'ñ r>   rf   rC   )é   )ip  )!rÌ   rÍ   rÎ   rÏ   rH  rM  rI  rZ  Úclassmethodrœ  rF  r¤  rÑ   r:   Údpsrr   rý   r²  rE   r¹  r¼  rÄ  rÇ  rÊ  rÎ  rÒ  rÖ  rÚ  rá  ræ  ré  rö  rÒ   rf   r>   r<   r@  r@  0  s§   † òôò
;ô>ð ñ&ó ð&ò "ò"ñ Ñ,¨iÓ8€DÙ
Ñ'¨Ó
2€Còò
ò
$ò$ôB,òòòòò#ò%ò%ò;ò
òBò&÷(r>   r@  )OÚoperatorÚ r   Úlibmp.backendr   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   Úmatrices.matricesr1   r€   Úctx_baser2   ÚobjectrG   r×   r=   r@   rÔ   r4  Ú__add__Ú__radd__Ú__sub__Ú__rsub__Ú__mul__Ú__rmul__Ú__div__Ú__rdiv__Ú__pow__Ú__rpow__Ú__truediv__Ú__rtruediv__r6  r@  ÚnumbersÚComplexÚregisterÚRealÚImportErrorrf   r>   r<   Ú<module>r     s¯  ðÛ å å %÷÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ó õ 'à�5ˆ>€å )à‡n�n€òôo6ˆFô o6ôb[6ˆFô [6òz%8ñN @JÈ'ÐS[Ó?\Ñ <€„ˆuŒ~˜uœ}¨e¬nÙ?IÈ'ÐS[Ó?\Ñ <€„ˆuŒ~˜uœ}¨e¬nÙ?IÈ'ÐS[Ó?\Ñ <€„ˆuŒ~˜uœ}¨e¬nÙ?IÈ'ÐS[Ó?\Ñ <€„ˆuŒ~˜uœ}¨e¬nÙ?IÈ'ÐS[Ó?\Ñ <€„ˆuŒ~˜uœ}¨e¬nà—M‘M€Ô ¸¿¹ 5Ô#5Ø—M‘M€Ô ¸¿¹ 5Ô#5ô
 �Uô 
 ôi(Ð+ô i(ðd	ÛØ‡O�O×Ñ˜UÔ#Ø‡L�L×Ñ˜%Õ øØó 	Ùð	ús   Æ*:G% Ç%G.Ç-G.