+
    ‰°³j;C  ã                   óè  € ^ RI t ^RIHt ^RIHt ^RIHtHtHtHtH	t	H
t
HtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtH t H!t!H"t"H#t#H$t$H%t%H&t&H't'H(t(H)t)H*t*H)t)H+t+H,t,H-t-H.t.H/t/ ^RI0H1t1 ]]3t2^RI3H4t4 ]5Pl                  t7R t8 ! R R	]54      t9 ! R
 R]54      t:R t;];! ]]%4      w  ]9n<        ]9n=        ]:n<        ]:n=        ];! ]]&4      w  ]9n>        ]9n?        ]:n>        ]:n?        ];! ]]'4      w  ]9n@        ]9nA        ]:n@        ]:nA        ];! ]](4      w  ]9nB        ]9nC        ]:nB        ]:nC        ];! ]!])4      w  ]9nD        ]9nE        ]:nD        ]:nE        ]9P„                  ]9nF        ]9P†                  ]9nG        ]:P„                  ]:nF        ]:P†                  ]:nG         ! R R]94      tH ! R R]44      tI ^ RIJtJ]JP–                  P™                  ]:4       ]JPš                  P™                  ]94       R#   ]N d     R# i ; i)é    N)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  € \        V R 4      '       d   V P                  # \        V \        4      '       d   \	        WV4      # \        V \
        4      '       d   \        WV4      # \        V \        4      '       d   \        WV4      # \        h)Ú_mpf_)
Úhasattrr3   Ú
isinstancer   r   Úfloatr   r   r   ÚNotImplementedError)ÚxÚprecÚroundings   &&&ÚN/home/luca/screen-checking/.venv/lib/python3.14/site-packages/mpmath/ctx_iv.pyÚconvert_mpf_r<      sh   € Üˆq�'×Ò 1§7¡7˜NÜ�!”Y×Ò¬°¸(Ó(CÐ!CÜ�!”U×Ò¤J¨q¸Ó$AÐAÜ�!”Z× Ò ¬°!¸8Ó)DÐ"DÜ
Ðó    c                   ó0  a € ] tR t^&t o RtR!R ltR tR tR tR t	R t
]R 4       t]R	 4       tR
 t]R 4       t]R 4       t]R 4       t]R 4       t]R 4       tR t]t]t]t]tR tR tR tR tR tR tR tR tR tR tR tR tR t R"R lt!R t"V t#R# )#Úivmpfz@
Interval arithmetic class. Precision is controlled by iv.prec.
c                ó8   € V P                   P                  V4      # ©N)ÚctxÚconvert)Úclsr8   s   &&r;   Ú__new__Úivmpf.__new__+   s   € Ø�w‰w�‰˜qÓ!Ð!r=   c                óR   € V P                   w  r4W48X  d   V! V! V4      4      # \        hrA   )Ú_mpi_Ú
ValueError)ÚselfrD   Ú	f_convertÚaÚbs   &&&  r;   ÚcastÚ
ivmpf.cast.   s'   € Ø�z‰z‰ˆØŒ6Ù‘y “|Ó$Ð$ÜÐr=   c                óJ   € V P                  \        \        P                  4      # rA   )rN   Úintr   Úto_int©rJ   s   &r;   Ú__int__Úivmpf.__int__4   s   € Ø�y‰yœœeŸl™lÓ+Ð+r=   c                óJ   € V P                  \        \        P                  4      # rA   )rN   r6   r   Úto_floatrS   s   &r;   Ú	__float__Úivmpf.__float__7   s   € Ø�y‰yœ¤§¡Ó/Ð/r=   c                óJ   € V P                  \        \        P                  4      # rA   )rN   Úcomplexr   rW   rS   s   &r;   Ú__complex__Úivmpf.__complex__:   s   € Ø�y‰yœ¤%§.¡.Ó1Ð1r=   c                ój   € V P                   w  rW8X  d   \        V4      # \        V P                   4      # rA   )rH   r.   Úhash©rJ   rL   rM   s   &  r;   Ú__hash__Úivmpf.__hash__=   s+   € Ø�z‰z‰ˆØŒ6Ü˜A“;Ðä˜Ÿ
™
Ó#Ð#r=   c                ó   € V # rA   © rS   s   &r;   ÚrealÚ
ivmpf.realD   s   € Ø�Kr=   c                ó.   € V P                   P                  # rA   )rB   ÚzerorS   s   &r;   ÚimagÚ
ivmpf.imagG   s   € ØŸ8™8Ÿ=™=Ð(r=   c                ó   € V # rA   rd   rS   s   &r;   Ú	conjugateÚivmpf.conjugateJ   s   €  ˜r=   c                óV   € V P                   w  rV P                  P                  W34      # rA   ©rH   rB   Úmake_mpfr`   s   &  r;   rL   Úivmpf.aL   ó$   € à�z‰z‰ˆØ�x‰x× Ñ  ! Ó(Ð(r=   c                óV   € V P                   w  rV P                  P                  W"34      # rA   ro   r`   s   &  r;   rM   Úivmpf.bQ   rr   r=   c                ó~   € V P                   p\        V P                  VP                  4      pVP	                  W"34      # rA   )rB   r   rH   r9   rp   ©rJ   rB   Úvs   &  r;   ÚmidÚ	ivmpf.midV   s0   € à�h‰hˆÜ�D—J‘J §¡Ó)ˆØ�|‰|˜Q˜FÓ#Ð#r=   c                ó~   € V P                   p\        V P                  VP                  4      pVP	                  W"34      # rA   )rB   r   rH   r9   rp   rv   s   &  r;   ÚdeltaÚivmpf.delta\   s0   € à�h‰hˆÜ�d—j‘j #§(¡(Ó+ˆØ�|‰|˜Q˜EÓ"Ð"r=   c                ó&   € V P                   \        3# rA   )rH   Úmpi_zerorS   s   &r;   Ú_mpci_Úivmpf._mpci_b   s   € à�z‰zœ8Ð#Ð#r=   c                 ó   € \        R 4      h)z-no ordering relation is defined for intervals©Ú	TypeError)Úargss   *r;   Ú_compareÚivmpf._comparef   s   € ÜÐGÓHÐHr=   c                ó¬   € V P                   P                  V4      pV P                  VP                  8*  ;'       d    VP                  V P                  8*  # rA   )rB   ÚmpfrL   rM   )rJ   Úts   &&r;   Ú__contains__Úivmpf.__contains__n   s9   € Ø�H‰H�L‰L˜‹OˆØ—‘˜!Ÿ#™#‘×2Ð2 A§C¡C¨4¯6©6¡MÐ2r=   c                óV   € \        V P                  V P                  P                  4      # rA   )r   rH   rB   r9   rS   s   &r;   Ú__str__Úivmpf.__str__r   s   € Ü�t—z‘z 4§8¡8§=¡=Ó1Ð1r=   c                ó  € V P                   P                  '       d   \        V 4      # V P                  w  r\	        V P                   P
                  4      p\        P                  ! W4      p\        P                  ! W#4      pR V: RV: R2# )zmpi(ú, Ú))rB   ÚprettyÚstrrH   r	   r9   r   Úto_str)rJ   rL   rM   Úns   &   r;   Ú__repr__Úivmpf.__repr__u   s]   € Ø�8‰8�?�?ˆ?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                ó²   € \        VR 4      '       g    V P                  P                  V4      pV! V P                  VP                  4      #    \        u # ; i)rH   )r4   rB   rC   ÚNotImplementedrH   )Úsr‰   Úcmpfuns   &&&r;   r…   r†   ~   sJ   € Ü�q˜'×"Ò"ð&Ø—E‘E—M‘M !Ó$�ñ �a—g‘g˜qŸw™wÓ'Ð'øð&Ü%Ò%ús   ”A ÁAc                óB   € V P                  V\        P                  4      # rA   )r…   r   Úmpi_eq©rš   r‰   s   &&r;   Ú__eq__Úivmpf.__eq__†   ó   € ˜QŸZ™Z¨¬5¯<©<Ó8Ð8r=   c                óB   € V P                  V\        P                  4      # rA   )r…   r   Úmpi_nerž   s   &&r;   Ú__ne__Úivmpf.__ne__‡   r¡   r=   c                óB   € V P                  V\        P                  4      # rA   )r…   r   Úmpi_ltrž   s   &&r;   Ú__lt__Úivmpf.__lt__ˆ   r¡   r=   c                óB   € V P                  V\        P                  4      # rA   )r…   r   Úmpi_lerž   s   &&r;   Ú__le__Úivmpf.__le__‰   r¡   r=   c                óB   € V P                  V\        P                  4      # rA   )r…   r   Úmpi_gtrž   s   &&r;   Ú__gt__Úivmpf.__gt__Š   r¡   r=   c                óB   € V P                  V\        P                  4      # rA   )r…   r   Úmpi_gerž   s   &&r;   Ú__ge__Úivmpf.__ge__‹   r¡   r=   c                óˆ   € V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   rp   r   rH   r9   rS   s   &r;   Ú__abs__Úivmpf.__abs__�   ó*   € Ø�x‰x× Ñ ¤¨¯©°T·X±X·]±]Ó!CÓDÐDr=   c                óˆ   € V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   rp   r   rH   r9   rS   s   &r;   Ú__pos__Úivmpf.__pos__�   r¹   r=   c                óˆ   € V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   rp   r   rH   r9   rS   s   &r;   Ú__neg__Úivmpf.__neg__‘   r¹   r=   Nc                ó:   € V P                   P                  WW#4      # rA   ©rB   Úalmosteq©rš   r‰   Úrel_epsÚabs_epss   &&&&r;   ÚaeÚivmpf.ae”   ó   € Ø�u‰u�~‰~˜a GÓ5Ð5r=   rd   ©r   ©NN)$Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__Ú__doc__rE   rN   rT   rX   r\   ra   Úpropertyre   ri   rl   rL   rM   rx   r{   r   r…   r°   r¬   r´   rŠ   r�   r–   rŸ   r¤   r¨   r·   r»   r¾   rÆ   Ú__static_attributes__Ú__classdictcell__©Ú__classdict__s   @r;   r?   r?   &   s  ø‡ € 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÷6ò 6r=   r?   c                   óò   a € ] tR t^—t o RR ltR tR tR t]R 4       t	]R 4       t
]R 4       t]R 4       t]R	 4       t]R
 4       tR tR tR tRR ltR tR tR t];t;ttR tR tR tRR ltRtV tR# )Úivmpcc                óÂ   € V P                   P                  V4      pV P                   P                  V4      p\        V 4      pVP                  VP                  3Vn        V# rA   )rB   rC   ÚnewrH   r   )rD   ÚreÚimÚys   &&& r;   rE   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‚   € V P                   w  w  rw  r4W8X  d   W48X  d   \        W34      # \        V P                   4      # rA   )r   r/   r_   ©rJ   rL   rM   ÚcÚds   &    r;   ra   Úivmpc.__hash__    s8   € ØŸ™‰‰ˆ‘�ØŒ6�a”fÜ˜Q˜FÓ#Ð#ä˜Ÿ™Ó$Ð$r=   c                ó²   € V P                   P                  '       d   \        V 4      # R \        V P                  4      : R\        V P
                  4      : R2# )ziv.mpc(r�   r‘   )rB   r’   r“   Úreprre   ri   ©rš   s   &r;   r–   Úivmpc.__repr__§   s8   € Ø�5‰5�<�<ˆ<Ü�q“6ˆMð ä#'¨¯©¦<´°a·f±f¶Ð>Ð>r=   c                ód   € R \        V P                  4      : R\        V P                  4      : R2# )Ú(ú + ú*j))r“   re   ri   rä   s   &r;   r�   Úivmpc.__str__¬   s   � Ü # A§F¡F¦¬S°·±®[Ð9Ð9r=   c                ó`   € V P                   w  w  rw  r4V P                  P                  W34      # rA   ©r   rB   rp   rÞ   s   &    r;   rL   Úivmpc.a¯   ó*   € àŸ™‰‰ˆ‘�Ø�x‰x× Ñ  ! Ó(Ð(r=   c                ó`   € V P                   w  w  rw  r4V P                  P                  W"34      # rA   rì   rÞ   s   &    r;   rM   Úivmpc.b´   rî   r=   c                ó`   € V P                   w  w  rw  r4V P                  P                  W334      # rA   rì   rÞ   s   &    r;   rß   Úivmpc.c¹   rî   r=   c                ó`   € V P                   w  w  rw  r4V P                  P                  WD34      # rA   rì   rÞ   s   &    r;   rà   Úivmpc.d¾   rî   r=   c                óZ   € V P                   P                  V P                  ^ ,          4      # rÉ   ©rB   rp   r   rä   s   &r;   re   Ú
ivmpc.realÃ   ó   € à�u‰u�~‰~˜aŸh™h q�kÓ*Ð*r=   c                óZ   € V P                   P                  V P                  ^,          4      # ©é   rö   rä   s   &r;   ri   Ú
ivmpc.imagÇ   rø   r=   c                ój   € V P                   w  rV P                  P                  V\        V4      34      # rA   )r   rB   Úmake_mpcr   )rš   rL   rM   s   &  r;   rl   Úivmpc.conjugateË   s(   € Ø�x‰x‰ˆØ�u‰u�~‰~˜q¤'¨!£*˜oÓ.Ð.r=   c                óð  € V P                   P                  V4      pV P                  VP                  u;8*  ;'       d    V P                  8*  Mu ;'       g­    V P                  VP                  u;8*  ;'       d    V P                  8*  Mu ;'       gq    VP                  V P                  u;8*  ;'       d    VP                  8*  Mu ;'       g5    VP                  V P                  u;8*  ;'       d    VP                  8*  Mu pV P                  VP                  u;8*  ;'       d    V P
                  8*  Mu ;'       g­    V P                  VP
                  u;8*  ;'       d    V P
                  8*  Mu ;'       gq    VP                  V P                  u;8*  ;'       d    VP
                  8*  Mu ;'       g5    VP                  V P
                  u;8*  ;'       d    VP
                  8*  Mu pT;'       d    T# rA   )rB   rC   rL   rM   rß   rà   )rš   r‰   Úreal_overlapÚimag_overlaps   &&  r;   ÚoverlapÚivmpc.overlapÏ   s<  € Ø�E‰E�M‰M˜!ÓˆØŸ™˜qŸs™s×)Ô) a§c¡cÔ)×oÐo¨q¯s©s°a·c±c×/@Ô/@¸Q¿S¹SÔ/@×oÐoÀaÇcÁcÈQÏSÉS×FWÔFWÐTU×TWÑTWÔFW×oÐoÐ]^×]`Ñ]`Ðde×dgÑdg×]nÔ]nÐkl×knÑknÔ]nˆØŸ™˜qŸs™s×)Ô) a§c¡cÔ)×oÐo¨q¯s©s°a·c±c×/@Ô/@¸Q¿S¹SÔ/@×oÐoÀaÇcÁcÈQÏSÉS×FWÔFWÐTU×TWÑTWÔFW×oÐoÐ]^×]`Ñ]`Ðde×dgÑdg×]nÔ]nÐkl×knÑknÔ]nˆØ×,Ð, Ð,r=   c                ó¬   € V P                   P                  V4      pVP                  V P                  9   ;'       d    VP                  V P                  9   # rA   )rB   rC   re   ri   rž   s   &&r;   rŠ   Úivmpc.__contains__Õ   s<   € Ø�E‰E�M‰M˜!ÓˆØ�v‰v˜Ÿ™Ñ×4Ð4 A§F¡F¨a¯f©fÑ$4Ð4r=   c                óp  € \        WP                  P                  4      '       g    V P                  P                  V4      p\        VR 4      '       d   VP                  \        3pM\        VR4      '       d   VP                  pV'       d   V P                  X8g  # V P                  X8H  #    \        u # ; i©rH   r   )	r5   rB   Ú_typesrC   r™   r4   rH   r~   r   )rš   r‰   ÚneÚtvals   &&& r;   r…   Úivmpc._compareÙ   s�   € Ü˜!ŸU™UŸ\™\×*Ò*ð&Ø—E‘E—M‘M !Ó$�ô �1�g×ÒØ—7‘7œHÐ$‰DÜ�Q˜×!Ò!Ø—8‘8ˆDßØ—8‘8˜tÑ#Ð#Ø�x‰x˜4ÑÐøð&Ü%Ò%ús   §B+ Â+B5c                ó$   € V P                  V4      # rA   ©r…   rž   s   &&r;   rŸ   Úivmpc.__eq__ç   s   € ˜QŸZ™Z¨›]Ð*r=   c                ó&   € V P                  VR 4      # )Tr  rž   s   &&r;   r¤   Úivmpc.__ne__è   s   € ˜QŸZ™Z¨¨4Ó0Ð0r=   c                ó   € \        R 4      h)z#complex intervals cannot be orderedr‚   rž   s   &&r;   r¨   Úivmpc.__lt__ê   s   € œIÐ&KÓLÐLr=   c                óˆ   € V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   rþ   r$   r   r9   rä   s   &r;   r¾   Úivmpc.__neg__í   ó'   € ˜1Ÿ5™5Ÿ>™>¬(°1·8±8¸Q¿U¹U¿Z¹ZÓ*HÓIÐIr=   c                óˆ   € V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   rþ   r#   r   r9   rä   s   &r;   r»   Úivmpc.__pos__î   r  r=   c                óˆ   € V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   rp   r*   r   r9   rä   s   &r;   r·   Úivmpc.__abs__ï   r  r=   Nc                ó:   € V P                   P                  WW#4      # rA   rÁ   rÃ   s   &&&&r;   rÆ   Úivmpc.aeñ   rÈ   r=   rd   )r   r   ©FrÊ   )rË   rÌ   rÍ   rÎ   rE   ra   r–   r�   rÐ   rL   rM   rß   rà   re   ri   rl   r  rŠ   r…   rŸ   r¤   r¨   r¬   r°   r´   r¾   r»   r·   rÆ   rÑ   rÒ   rÓ   s   @r;   rÖ   rÖ   —   sÒ   ø‡ € ôò%ò?ò
:ð ñ)ó ð)ð ñ)ó ð)ð ñ)ó ð)ð ñ)ó ð)ð ñ+ó ð+ð ñ+ó ð+ò/ò-ò5ô ò +Ú0âLØ%Ð%€FÐ%ˆV�fâIÚIÚI÷6ò 6r=   rÖ   c                 ó`   a aaa€ V3R  loV V3R loVV3R lpVV3R lpV3R lpV3R lpW#WE3# )c                 óH   <€ V P                  S! WV P                  4      4      # rA   )rþ   r9   )rB   Úsvalr  Ú	f_complexs   &&&€r;   Ú	g_complexÚ_binary_op.<locals>.g_complexõ   s   ø€ Ø�|‰|™I d°#·(±(Ó;Ó<Ð<r=   c                 óž   <€  V P                  S! WV P                  4      4      #   \         d    T\        3pT\        3pS! YT4      u # i ; irA   )rp   r9   r-   r~   )rB   r   r  Úf_realr"  s   &&&€€r;   Úg_realÚ_binary_op.<locals>.g_real÷   sR   ø€ ð	.Ø—<‘<¡ t°3·8±8Ó <Ó=Ð=øÜô 	.Øœ(Ð#ˆDØœ(Ð#ˆDÙ˜S¨Ó-Ò-ð	.ús   ƒ!% ¥$AÁAc                 ó€  <€ \        V\        4      '       d   \        # V P                  p\        WP                  4      '       g   VP                  V4      p\        VR 4      '       d   S! W P                  VP                  4      # \        VR4      '       d$   S! W P                  \        3VP                  4      # \        # r  )
r5   r0   r™   rB   r	  rC   r4   rH   r~   r   ©rš   r‰   rB   r"  r&  s   && €€r;   Úlop_realÚ_binary_op.<locals>.lop_realþ   s†   ø€ Ü�aœ×!Ò!¬.Ð#8Ø�e‰eˆÜ˜!ŸZ™Z×(Ò(¨c¯k©k¸!«n¨!Ü�1�g×Ò¡v¨c·7±7¸A¿G¹GÓ'DÐ DÜ�1�h×Ò©	°#¿¹ÄÐ7JÈAÏHÉHÓ(UÐ!UÜÐr=   c                 óH  <€ V P                   p\        WP                  4      '       g   VP                  V4      p\	        VR 4      '       d   S! W!P
                  V P
                  4      # \	        VR4      '       d$   S! W!P                  V P
                  \        34      # \        # r  )	rB   r5   r	  rC   r4   rH   r   r~   r™   r)  s   && €€r;   Úrop_realÚ_binary_op.<locals>.rop_real  st   ø€ Ø�e‰eˆÜ˜!ŸZ™Z×(Ò(¨c¯k©k¸!«n¨!Ü�1�g×Ò¡v¨c·7±7¸A¿G¹GÓ'DÐ DÜ�1�h×Ò©	°#·x±xÀ!Ç'Á'Ì8ÐATÓ(UÐ!UÜÐr=   c                 óJ  <€ \        V\        4      '       d   \        # V P                  p\        WP                  P                  4      '       g    V P                  P                  V4      pS! W P                  VP                  4      #   \        \        3 d
    \        u # i ; irA   )	r5   r0   r™   rB   r	  rC   rI   rƒ   r   ©rš   r‰   rB   r"  s   && €r;   Úlop_complexÚ_binary_op.<locals>.lop_complex  s{   ø€ Ü�aœ×!Ò!¬.Ð#8Ø�e‰eˆÜ˜!ŸU™UŸ\™\×*Ò*ð&Ø—E‘E—M‘M !Ó$�ñ ˜Ÿh™h¨¯©Ó1Ð1øô ¤	Ð*ô &Ü%Ò%ð&ús   ÁB ÂB"Â!B"c                 óÖ   <€ V P                   p\        WP                   P                  4      '       g   V P                   P                  V4      pS! W!P                  V P                  4      # rA   )rB   r5   r	  rC   r   r0  s   && €r;   Úrop_complexÚ_binary_op.<locals>.rop_complex  sF   ø€ Ø�e‰eˆÜ˜!ŸU™UŸ\™\×*Ò*Ø—‘—‘˜aÓ ˆAÙ˜Ÿh™h¨¯©Ó1Ð1r=   rd   )r%  r!  r*  r-  r1  r4  r"  r&  s   ff    @@r;   Ú
_binary_opr6  ô   s.   û€ õ=ö.ööõ2õ2ð
 ˜{Ð7Ð7r=   c                   ó<   a € ] tR tRt o R tR t]! ]4      tRtV t	R# )Úivmpf_constanti$  c                ó(   € \        V 4      pWn        V# rA   )rØ   Ú_f)rD   ÚfrJ   s   && r;   rE   Úivmpf_constant.__new__%  s   € Ü�3‹xˆØŒØˆr=   c                óš   € V P                   P                  ^ ,          pV P                  V\        4      pV P                  V\        4      pW#3# rÉ   )rB   Ú_precr:  r
   r   )rJ   r9   rL   rM   s   &   r;   Ú	_get_mpi_Úivmpf_constant._get_mpi_)  s;   € Ø�x‰x�~‰~˜aÕ ˆØ�G‰G�Dœ+Ó&ˆØ�G‰G�Dœ-Ó(ˆØˆtˆr=   )r:  N)
rË   rÌ   rÍ   rÎ   rE   r?  rÐ   rH   rÑ   rÒ   rÓ   s   @r;   r8  r8  $  s   ø‡ € òòñ
 �YÓ†Er=   r8  c                   óò   a € ] tR tRt o R tRR ltR tRR lt]R 4       t	R t
R	 t]! R
 ]
4      t]! R ]4      tR tR tR tR tRR ltR tR tR tR tR tR tR tR tR tR tR tR R ltRt V t!R# )!ÚMPIntervalContexti0  c                óX  € \        R \        3/ 4      V n        \        R\        3/ 4      V n        V P                  V P                  3V n        \        R\        3/ 4      V n        ^5.V n        V P                  ^54       V P                  \        V P                  .;V P                  n        ;V P                  n        V P                  n        V ;V P                  n        ;V P                  n        V P                  n        RV n        \        P                  ! V 4       V P!                  4        R# )r?   rÖ   r8  FN)Útyper?   rˆ   rÖ   Úmpcr	  r8  Ú	_constantr>  Ú	_set_precrØ   Ú_ctxdatarB   r’   r1   Ú__init__Ú_init_builtins©rB   s   &r;   rI  ÚMPIntervalContext.__init__2  sÝ   € Ü�w¤ ¨"Ó-ˆŒÜ�w¤ ¨"Ó-ˆŒØ—g‘g˜sŸw™wÐ'ˆŒ
ÜÐ-´Ð/@À"ÓEˆŒØ�DˆŒ	Ø�‰�bÔØHKÏÉÔQTÐVY×V_ÑV_ÐG`Ð`ˆ�‰ÔÐ` §¡Ô!1°C·G±GÔ4DØ8;Ð;ˆ�‰ÔÐ;˜CŸG™GœK¨#¯'©'¬+ØˆŒ
Ü×$Ò$ SÔ)Ø×ÑÖr=   Nc                óP   € Vf   V P                  V4      # V P                  W34      # rA   )rˆ   )rB   rL   rM   s   &&&r;   Ú_mpiÚMPIntervalContext._mpi?  s%   € ØŠ9Ø—7‘7˜1“:ÐØ�w‰w˜�u‹~Ðr=   c                óè  € V P                  ^4      V n        V P                  ^ 4      V n        V P                  R4      V n        V P                  ) V n        V P                  R4      V n        V P                  ^ ^4      V n        V P                  \        P                  \        P                  4      V n        V P                  \        P                  4      V n        V P                  \        P                  \        P                   4      V n        V P                  \        P$                  \        P&                  4      V n        V P                  \        P*                  \        P,                  4      V n        V P                  \        P0                  4      V n        V P                  \        P4                  \        P6                  4      V n        V P                  \        P:                  \        P<                  4      V n        V P                  \        P@                  \        PB                  4      V n"        V P                  \        PF                  \        PH                  4      V n%        V PJ                  V n&        V PO                  R 4      V n(        V PO                  \        PR                  4      V n*        V PO                  \        PV                  4      V n,        V PO                  \        PZ                  4      V n.        V PO                  \        P^                  4      V n0        V PO                  \        Pb                  4      V n2        V PO                  \        Pf                  4      V n4        V PO                  \        Pj                  4      V n6        V PO                  \        Pn                  4      V n8        V PO                  \        Pr                  4      V n:        V PO                  \        Pv                  4      V n<        R# )rû   ÚinfÚnanc                 ó$   € ^ \         ^V ,
          ^3# rÉ   )r   )r9   Úrnds   &&r;   Ú<lambda>Ú2MPIntervalContext._init_builtins.<locals>.<lambda>W  s   € °1´g¸qÀ½vÀqÑ2Ir=   N)=rˆ   Úonerh   rQ  ÚninfrR  rE  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facrF  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	twinprimerK  s   &r;   rJ  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Žr=   c                ó   a aa€ V VV3R  lpV# )c                 ó€  <€ V'       d%   VP                  R SP                  ^ ,          4      pMSP                  ^ ,          pSP                  V 4      p \        V R4      '       d#   SP	                  S! V P
                  V4      4      # \        V R4      '       d#   SP                  S! V P                  V4      4      # \        h)r9   rH   r   )	Úgetr>  rC   r4   rp   rH   rþ   r   rI   )r8   Úkwargsr9   rB   r!  r%  s   &, €€€r;   ÚgÚ/MPIntervalContext._wrap_mpi_function.<locals>.gd  sŒ   ø€ ßØ—z‘z &¨#¯)©)°A­,Ó7‘à—y‘y •|�Ø—‘˜A“ˆAÜ�q˜'×"Ò"Ø—|‘|¡F¨1¯7©7°DÓ$9Ó:Ð:Ü�q˜(×#Ò#Ø—|‘|¡I¨a¯h©h¸Ó$=Ó>Ð>ÜÐr=   rd   )rB   r%  r!  r�  s   fff r;   rZ  Ú$MPIntervalContext._wrap_mpi_functionc  s   ú€ ÷
	ð ˆr=   c                óB   a€ V'       d   V3R  lpMSp\        WV4       R# )c                 óÞ   <€ V P                   pV Uu. uF
  qC! V4      NK  	  ppV P                  p V ;P                  ^
,          un        S! V .VO5/ VB pWPn        V5# u upi   YPn        i ; i)é
   )rC   r9   )rB   r„   r�  rC   rL   r9   Úretvalr;  s   &*,    €r;   Ú	f_wrappedÚ2MPIntervalContext._wrap_specfun.<locals>.f_wrappedt  sm   ø€ ØŸ+™+�Ù,0Ó1©D q˜ ž
©D�Ð1Ø—x‘x�ð$Ø—H’H •N•HÙ˜sÐ4 TÒ4¨VÑ4�Fà#”HØ�w�ùò 2øð  $•Hús   ’A±%A$ Á$A,N)Úsetattr)rD   Únamer;  Úwrapr—  s   &&f& r;   Ú_wrap_specfunÚMPIntervalContext._wrap_specfunq  s   ø€ çö	ð ˆIÜ�˜9Ö%r=   c                ój   € \        ^\        V4      4      V P                  ^ &   \        V4      V n        R# )rû   N)ÚmaxrQ   r>  r   Ú_dps©rB   r•   s   &&r;   rG  ÚMPIntervalContext._set_prec‚  s$   € Ü˜1œc !›f“~ˆ�	‰	�!‰Ü˜q“>ˆŽr=   c                ój   € \        V4      V P                  ^ &   \        ^\        V4      4      V n        R# ©r   N)r   r>  rŸ  rQ   r   r¡  s   &&r;   Ú_set_dpsÚMPIntervalContext._set_dps†  s$   € Ü" 1“~ˆ�	‰	�!‰Ü�qœ#˜a›&“>ˆŽr=   c                ó(   € V P                   ^ ,          # rÉ   )r>  rK  s   &r;   rU  ÚMPIntervalContext.<lambda>Š  s   €  §	¡	¨!¦r=   c                ó   € V P                   # rA   )r   rK  s   &r;   rU  r¨  ‹  s   € ˜sŸxšxr=   c                ó<   € \        V P                  4      pWn        V# rA   )rØ   rˆ   rH   ©rB   rw   rL   s   && r;   rp   ÚMPIntervalContext.make_mpf�  s   € Ü�—‘‹LˆØŒØˆr=   c                ó<   € \        V P                  4      pWn        V# rA   )rØ   rE  r   r«  s   && r;   rþ   ÚMPIntervalContext.make_mpc’  s   € Ü�—‘‹LˆØŒØˆr=   c                óÆ   € Vw  r#\         P                  ! W#V P                  \        4      p\         P                  ! W#V P                  \        4      pV P                  WE34      # rA   )r   r   r9   r
   r   rp   )rB   ÚpqÚpÚqrL   rM   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                óþ  € \        WP                  V P                  34      '       d   V# \        WP                  4      '       d   V5# \        V\        4      '       g   \        VR 4      '       dH   V P                  VP                  4      pV P                  VP                  4      pV P                  W#4      # \        V\        4      '       d'   \        WP                  4      pV P                  V4      # \        VR4      '       d   VP                  w  rVM… Vw  rV\        VR4      '       d   VP                  ^ ,          pM\!        WPP                  \"        4      p\        VR4      '       d   VP                  ^,          pM\!        W`P                  \$        4      pV\&        8X  g   V\&        8X  d   \(        p\*        p\-        WV4      '       g   Q R4       hV P                  WV34      #   \        \        3 d    T;rV Lâi ; i)Ú_mpc_rH   z"endpoints must be properly ordered)r5   rˆ   rE  rF  r[   r4   rC   re   ri   r   r"   r9   rp   rH   rƒ   rI   r<   r
   r   r   r   r   r   )rB   r8   rÙ   rÚ   rw   rL   rM   s   &&     r;   rC   ÚMPIntervalContext.convert�  s€  € Ü�aŸ'™' 3§7¡7Ð+×,Ò,ØˆHÜ�aŸ™×'Ò'Ø�2ˆIÜ�aœ×!Ò!¤W¨Q°×%8Ò%8Ø—‘˜QŸV™VÓ$ˆBØ—‘˜QŸV™VÓ$ˆBØ—7‘7˜2“>Ð!Ü�aœ×$Ò$Ü˜Q§¡Ó)ˆAØ—<‘< “?Ð"Ü�1�g×ÒØ—7‘7‰DˆAˆqðØ‘�ô �q˜'×"Ò"Ø—G‘G˜A•J‘ä  §H¡H¬kÓ:�Ü�q˜'×"Ò"Ø—G‘G˜A•J‘ä  §H¡H¬mÓ<�Ø”Œ9˜œTœ	ÜˆAÜˆAÜ�a�|Š|ÐAÐAÓAˆ|Ø�|‰|˜Q˜FÓ#Ð#øô œzÐ*ô Ø�	�‘Aðús   ÄG% Ç%G<Ç;G<c                ón  € V P                  V4      p\        VR 4      '       d#   \        P                  ! VP                  V3/ VB # \        VR4      '       d^   \        P                  ! VP
                  ^ ,          V3/ VB p\        P                  ! VP
                  ^,          V3/ VB pRV: RV: R2# R# )rH   r   rç   rè   ré   N)rC   r4   r   Ú
mpi_to_strrH   r   )rB   r8   r•   r�  rÙ   rÚ   s   &&&,  r;   ÚnstrÚMPIntervalContext.nstr¾  s“   € Ø�K‰K˜‹NˆÜ�1�g×ÒÜ×#Ò# A§G¡G¨QÑ9°&Ñ9Ð9Ü�1�h×ÒÜ×!Ò! !§(¡(¨1¥+¨qÑ;°FÑ;ˆBÜ×!Ò! !§(¡(¨1¥+¨qÑ;°FÑ;‰BÛ$&«Ð+Ð+ñ  r=   c                óÆ  € V P                  V4      p\        WP                  4      '       dF   \        V P	                  VP
                  4      V P	                  VP                  4      4      ^,           # \        P                  ! VP                  4      w  r#Vw  rErgV'       d	   Wg,           # V\        8X  d   V P                  # V\        8X  d   V P                  # V P                  # rú   )rC   r5   rE  rŸ  Úmagre   ri   r   r   rH   r   rX  r   rR  rQ  ©rB   r8   rL   rM   ÚsignÚmanr\  Úbcs   &&      r;   r½  ÚMPIntervalContext.magÇ  s™   € Ø�K‰K˜‹NˆÜ�aŸ™×!Ò!Ü�s—w‘w˜qŸv™v“¨¯©°·±«Ó8¸1Õ<Ð<Ü�}Š}˜QŸW™WÓ%‰ˆØÑˆ�3ßØ•6ˆMØ”Œ:Ø—8‘8ˆOØ”Œ9Ø—7‘7ˆNØ�w‰wˆr=   c                ó   € R # r  rd   ©rB   r8   s   &&r;   ÚisnanÚMPIntervalContext.isnanÕ  s   € Ùr=   c                ó   € WP                   8H  # rA   )rQ  rÄ  s   &&r;   ÚisinfÚMPIntervalContext.isinfØ  s   € Ø—G‘G‰|Ðr=   c                ó†   € V P                  V4      pVP                  w  r#W#8X  d   Vw  rErgV'       d   V^ 8¬  # V\        8H  # R# r¤  )rC   rH   r   r¾  s   &&      r;   ÚisintÚMPIntervalContext.isintÛ  sB   € Ø�K‰K˜‹NˆØ�w‰w‰ˆØŒ6Ø!"ÑˆD�sßØ˜a‘x�Øœ‘:ÐÙr=   c                ó¸   € V P                  V4      P                  w  r4\        P                  ! W24      p\        P                  ! WB4      pV P	                  W434      # rA   )rC   rH   r   Ú	mpf_shiftrp   )rB   r8   r•   rL   rM   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   € \        V P                  V4      4      P                  # rA   )ÚabsrC   rL   rÄ  s   &&r;   ÚabsminÚMPIntervalContext.absminë  ó   € Ü�3—;‘;˜q“>Ó"×$Ñ$Ð$r=   c                óJ   € \        V P                  V4      4      P                  # rA   )rÒ  rC   rM   rÄ  s   &&r;   ÚabsmaxÚMPIntervalContext.absmaxî  rÕ  r=   c                óÎ   € V P                  V4      P                  pV P                  V4      P                  pV P                  \        P                  ! WV P
                  4      4      # rA   )rC   rH   rp   r   Ú	mpi_atan2r9   )rB   rÛ   r8   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                óz  € \        V\        P                  4      '       d   VR 3# \        V\        4      '       d.   Vw  r#V P	                  V4      V P	                  V4      ,          R3# V P                  V4      p\        WP                  4      '       d   VR3# \        WP                  4      '       d   VR3# \        h)ÚZÚRÚC)r5   r   r   Útuplerˆ   rC   rE  rI   )rB   r8   r±  r²  s   &&  r;   Ú_convert_paramÚ MPIntervalContext._convert_paramö  s“   € Ü�aœŸ™×)Ò)Ø�c�6ˆMÜ�aœ×ÒØ‰DˆAØ—G‘G˜A“J §¡¨£Õ+¨SÐ1Ð1Ø�K‰K˜‹NˆÜ�aŸ™×!Ò!Ø�c�6ˆMÜ�aŸ™×!Ò!Ø�c�6ˆMÜÐr=   c                ó\   € \        WP                  4      ;'       g    \        V\        4      # rA   )r5   rˆ   r   ©rB   Úzs   &&r;   Ú_is_real_typeÚMPIntervalContext._is_real_type  s    € Ü˜!ŸW™WÓ%×AÐA¬°A´yÓ)AÐAr=   c                ó,   € \        WP                  4      # rA   )r5   rE  rå  s   &&r;   Ú_is_complex_typeÚ"MPIntervalContext._is_complex_type  s   € Ü˜!ŸW™WÓ%Ð%r=   c                óf  € \        V4      p\        V4      p\        WV,           4      p	V P                  ;r«^ p V F  qÛWM,          V,           ,          pK  	  V	 F  qÛWM,          V,           ,          pK  	  V^,          qËV,          q»V,          qºV,          p
V^ 8X  d   V
# WÆ8”  g   Ko  V P                  hrÉ   )ÚlistÚrangerW  ÚNoConvergence)rB   r±  r²  ÚtypesÚcoeffsræ  Úmaxtermsr�  ÚnumÚdenrš   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� ¥	¨!¥Õ,š!‘SÛ� ¥	¨!¥Õ,š!‘SØ��FˆA˜•F�A �F˜A¨¥F AØ�AŒvØ�ð Ž|Ø×'Ñ'Ð'r=   rd   rA   )é   )ip  )"rË   rÌ   rÍ   rÎ   rI  rN  rJ  rZ  Úclassmethodrœ  rG  r¥  rÐ   r9   Údpsrp   rþ   r³  rC   rº  r½  rÅ  rÈ  rË  rÏ  rÓ  r×  rÛ  râ  rç  rê  r÷  rÑ   rÒ   rÓ   s   @r;   rB  rB  0  s¯   ø‡ € òôò
;ô>ð ñ&ó ð&ò "ò"ñ Ñ,¨iÓ8€DÙ
Ñ'¨Ó
2€Còò
ò
$ò$ôB,òòòòò#ò%ò%ò;ò
òBò&÷(ò (r=   rB  )OÚoperatorÚ r   Úlibmp.backendr   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   Úmatrices.matricesr0   r~   Úctx_baser1   ÚobjectrE   rØ   r<   r?   rÖ   r6  Ú__add__Ú__radd__Ú__sub__Ú__rsub__Ú__mul__Ú__rmul__Ú__div__Ú__rdiv__Ú__pow__Ú__rpow__Ú__truediv__Ú__rtruediv__r8  rB  ÚnumbersÚComplexÚregisterÚRealÚImportErrorrd   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˜%Ö øØô 	Úð	ús   Æ*:G& Ç&G1Ç0G1