ó
    ‰*£hæk  ã                   ó  • S 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.  SSK/J0r0J1r1J2r2J3r3J4r4J5r5J6r6J7r7  SSK8J9r9J:r:J;r;J<r<  S r=\\4r>\\4r?S r@S rAS	 rBS
 rCS rDS rESKS jrFSKS jrGS rHS rIS rJSKS jrKSKS jrLS rMS rNSKS jrOSKS jrPS rQS rRS rSS rTS rUS rVS rWS rXS  rYS! rZS" r[S# r\S$ r]S% r^S& r_S' r`S( raS) rbSLS* jrcS+ rdS, reSKS- jrfS. rgS/ rhS0 riS1 rjS2 rkS3 rlS4 rmS5 rnS6 roS7 rpS8 rqS9 rrS: rsS; rtS< ru\" S=5      rv\" S>5      rw\v\w4rx\" S?5      ry\" S@5      rzSA r{SKSB jr|SKSC jr}SD r~SE rSF r€SG r�SH r‚SI rƒgJ)Mz3
Computational functions for interval arithmetic.

é   )Úxrange)+ÚComplexResultÚ
round_downÚround_upÚround_floorÚround_ceilingÚround_nearestÚprec_to_dpsÚrepr_dpsÚdps_to_precÚbitcountÚ
from_floatÚfnanÚfinfÚfninfÚfzeroÚfhalfÚfoneÚfnoneÚmpf_signÚmpf_ltÚmpf_leÚmpf_gtÚmpf_geÚmpf_eqÚmpf_cmpÚmpf_min_maxÚ	mpf_floorÚfrom_intÚto_intÚto_strÚfrom_strÚmpf_absÚmpf_negÚmpf_posÚmpf_addÚmpf_subÚmpf_mulÚmpf_mul_intÚmpf_divÚ	mpf_shiftÚmpf_pow_intÚfrom_man_expÚMPZ_ONE)Úmpf_logÚmpf_expÚmpf_sqrtÚmpf_atanÚ	mpf_atan2Úmpf_piÚmod_pi2Úmpf_cos_sin)Ú	mpf_gammaÚ
mpf_rgammaÚmpf_loggammaÚmpc_loggammac                 ó`   • U u  p#[        U5      S-   nS[        X$5      < S[        X45      < S3$ )Né   Ú[z, Ú])r
   r!   )ÚsÚprecÚsaÚsbÚdpss        ÚP/home/mande/repo/quber/.venv/lib/python3.13/site-packages/mpmath/libmp/libmpi.pyÚmpi_strrE      s+   € Ø�F€BÜ
�dÓ
˜aÑ
�CÜ ž¬&°®/Ð:Ð:ó    c                 ó
   • X:H  $ ©N© ©r?   Úts     rD   Úmpi_eqrL   )   ó	   € Ø‰6€MrF   c                 ó
   • X:g  $ rH   rI   rJ   s     rD   Úmpi_nerO   ,   rM   rF   c                 óX   • U u  p#Uu  pE[        X45      (       a  g[        X%5      (       a  gg ©NTF)r   r   ©r?   rK   rA   rB   ÚtaÚtbs         rD   Úmpi_ltrU   /   ó)   € Ø�F€BØ�F€BÜˆb‡~�~˜dÜˆb‡~�~˜eØrF   c                 óX   • U u  p#Uu  pE[        X45      (       a  g[        X%5      (       a  gg rQ   )r   r   rR   s         rD   Úmpi_lerX   6   rV   rF   c                 ó   • [        X5      $ rH   )rU   rJ   s     rD   Úmpi_gtrZ   =   ó   € œ ›Ð%rF   c                 ó   • [        X5      $ rH   )rX   rJ   s     rD   Úmpi_ger]   >   r[   rF   c                 óœ   • U u  p4Uu  pV[        X5U[        5      n[        XFU[        5      nU[        :X  a  [        nU[        :X  a  [
        nXx4$ rH   )r&   r   r   r   r   r   ©	r?   rK   r@   rA   rB   rS   rT   ÚaÚbs	            rD   Úmpi_addrb   @   óI   € Ø�F€BØ�F€BÜ�˜œkÓ*€AÜ�˜œmÓ,€AØŒDƒy”e�!ØŒDƒy”d�!Øˆ4€KrF   c                 óœ   • U u  p4Uu  pV[        X6U[        5      n[        XEU[        5      nU[        :X  a  [        nU[        :X  a  [
        nXx4$ rH   )r'   r   r   r   r   r   r_   s	            rD   Úmpi_subre   I   rc   rF   c                 ó,   • U u  p#[        X2U[        5      $ rH   )r'   r   ©r?   r@   rA   rB   s       rD   Ú	mpi_deltarh   R   s   € Ø�F€BÜ�2˜4¤Ó*Ð*rF   c                 ó@   • U u  p#[        [        X#U[        5      S5      $ )Néÿÿÿÿ)r+   r&   r	   rg   s       rD   Úmpi_midrk   V   s   € Ø�F€BÜ”W˜R T¬=Ó9¸2Ó>Ð>rF   c                 óP   • U u  p#[        X![        5      n[        X1[        5      nXE4$ rH   )r%   r   r   ©r?   r@   rA   rB   r`   ra   s         rD   Úmpi_posrn   Z   ó(   € Ø�F€BÜ�œ+Ó&€AÜ�œ-Ó(€AØˆ4€KrF   c                 óP   • U u  p#[        X1[        5      n[        X![        5      nXE4$ rH   )r$   r   r   rm   s         rD   Úmpi_negrq   `   ro   rF   c                 ój  • U u  p#[        U5      n[        U5      nUS:¼  a#  [        X![        5      n[        X1[        5      nXg4$ US:¼  aH  [        n[        U5      n[        Xƒ5      (       a  [        X1[        5      nXg4$ [        X�[        5      n Xg4$ [        X1[        5      n[        X![        5      nXg4$ ©Né    )r   r%   r   r   r   r$   r   )	r?   r@   rA   rB   ÚsasÚsbsr`   ra   Únegsas	            rD   Úmpi_absrx   f   s²   € Ø�F€BÜ
�2‹,€CÜ
�2‹,€Cà
ˆaƒxÜ�BœkÓ*ˆÜ�BœmÓ,ˆð ˆ4€Kð 
�‹ÜˆÜ˜“ˆÜ�%×ÑÜ˜¤-Ó0ˆAð ˆ4€Kô ˜¤]Ó3‰Að
 ˆ4€Kô �BœkÓ*ˆÜ�BœmÓ,ˆØˆ4€KrF   c                 ó   • [        XU4U5      $ rH   )Úmpi_mul©r?   rK   r@   s      rD   Úmpi_mul_mpfr|   }   ó   € Ü�1˜!�f˜dÓ#Ð#rF   c                 ó   • [        XU4U5      $ rH   )Úmpi_divr{   s      rD   Úmpi_div_mpfr€   €   r}   rF   c                 ó¾  • U u  p4Uu  pV[        U5      n[        U5      n[        U5      n	[        U5      n
Xxs=:X  a  S:X  a/  O  O,U[        :X  d
  U[        :X  a  [        [        4$ [        [        4$ Xšs=:X  a  S:X  a/  O  O,U[        :X  d
  U[        :X  a  [        [        4$ [        [        4$ US:¼  aÛ  U	S:¼  aE  [	        X5U[
        5      n[	        XFU[        5      nU[        :X  a  [        nU[        :X  a  [        nX¼4$ U
S::  aE  [	        XEU[
        5      n[	        X6U[        5      nU[        :X  a  [        nU[        :X  a  [        nX¼4$ [	        XEU[
        5      n[	        XFU[        5      nU[        :X  a  [        nU[        :X  a  [        nX¼4$ US::  aÛ  U	S:¼  aE  [	        X6U[
        5      n[	        XEU[        5      nU[        :X  a  [        nU[        :X  a  [        nX¼4$ U
S::  aE  [	        XFU[
        5      n[	        X5U[        5      nU[        :X  a  [        nU[        :X  a  [        nX¼4$ [	        X6U[
        5      n[	        X5U[        5      nU[        :X  a  [        nU[        :X  a  [        nX¼4$ [	        X55      [	        X65      [	        XE5      [	        XF5      /n[        U;   a  [        [        pËX¼4$ [        U5      u  p¼[        X²[
        5      n[        XÂ[        5      nX¼4$ rs   )
r   r   r   r   r(   r   r   r   r   r%   )r?   rK   r@   rA   rB   rS   rT   ru   rv   ÚtasÚtbsr`   ra   Úcasess                 rD   rz   rz   ƒ   s†  € Ø�F€BØ�F€BÜ
�2‹,€CÜ
�2‹,€CÜ
�2‹,€CÜ
�2‹,€CØ
…�Q†à”‹;˜"¤›*Üœ$�;ÐÜ”eˆ|ÐØ
…�Q†à”‹;˜"¤›*Üœ$�;ÐÜ”eˆ|ÐØ
ˆaƒxà�!‹8Ü˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”D‹yœe˜!Ø”D‹yœd˜!ðV ˆ4€KðS �A‹XÜ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”D‹yœe˜!Ø”D‹yœe˜!ðJ ˆ4€KôE ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”D‹yœe˜!Ø”D‹yœd˜!ð> ˆ4€Kð= 
�‹à�!‹8Ü˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”D‹yœe˜!Ø”D‹yœe˜!ð0 ˆ4€Kð- �A‹XÜ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”D‹yœe˜!Ø”D‹yœd˜!ð$ ˆ4€Kô ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”D‹yœe˜!Ø”D‹yœd˜!ð ˆ4€Kô ˜“¤'¨"£/´7¸2³?ÄGÈBÃOÐTˆÜ�5‹=Üœ4ˆqð
 ˆ4€Kô ˜uÓ%‰DˆAÜ˜¤Ó-ˆAÜ˜¤Ó/ˆAØˆ4€KrF   c                 óX  • U u  p#[        U[        5      (       a%  [        X"U[        5      n[        X3U[        5      nXE4$ [        U[        5      (       a%  [        X3U[        5      n[        X"U[        5      nXE4$ [        U5      n[        X#/5      u  p#[        n[        X3U[        5      nXE4$ rH   )r   r   r(   r   r   r   r$   r   rm   s         rD   Ú
mpi_squarer†   Ç   s¢   € Ø�F€BÜˆb”%×ÑÜ�B˜D¤+Ó.ˆÜ�B˜D¤-Ó0ˆð ˆ4€Kô 
�”E×	Ñ	Ü�B˜D¤+Ó.ˆÜ�B˜D¤-Ó0ˆð ˆ4€Kô	 �R‹[ˆÜ˜b˜XÓ&‰ˆÜˆÜ�B˜D¤-Ó0ˆØˆ4€KrF   c                 óò  • U u  p4Uu  pV[        U5      n[        U5      n[        U5      n	[        U5      n
Xxs=:X  a  S:X  a3  O  O0U	S:  a  U
S:”  d  U	S:X  d  U
S:X  a  [        [        4$ [        [        4$ U	S:  a  U
S:”  a  [        [        4$ U	S:  a  [	        [        U 5      [        U5      U5      $ U	S:X  ag  US:  a  US:”  a  [        [        4$ Xš:X  a  [        [        4$ US:¼  a  [        X6U[        5      n[        nUS::  a  [        n[        XFU[        5      nWW4$ US:¼  aE  [        X6U[        5      n[        XEU[        5      nU[        :X  a  [        nU[        :X  a  [        nX¼4$ US::  aE  [        X5U[        5      n[        XFU[        5      nU[        :X  a  [        nU[        :X  a  [        nX¼4$ [        X5U[        5      n[        XEU[        5      nU[        :X  a  [        nU[        :X  a  [        nX¼4$ rs   )
r   r   r   r   r   rq   r*   r   r   r   )r?   rK   r@   rA   rB   rS   rT   ru   rv   r‚   rƒ   r`   ra   s                rD   r   r   Ö   sÒ  € Ø�F€BØ�F€BÜ
�2‹,€CÜ
�2‹,€CÜ
�2‹,€CÜ
�2‹,€Cà
…�Q†à�!‹G˜˜a› S¨A£X°¸³Üœ$�;ÐÜ”eˆ|Ðð ˆQƒw�3˜“7Ü”dˆ{Ðà
ˆQƒwÜ”w˜q“z¤7¨1£:¨tÓ4Ð4ð ˆaƒxà�‹7�s˜Q“wÜœ$�;ÐØ‹:Üœ$�;Ðà�!‹8Ü˜ ¤kÓ2ˆAÜˆAØ�!‹8ÜˆAÜ˜ ¤mÓ4ˆAð, ˆaˆ4€Kð# �!‹8Ü˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”D‹yœe˜!Ø”D‹yœd˜!ð ˆ4€Kð �A‹XÜ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”D‹yœe˜!Ø”D‹yœe˜!ð ˆ4€Kô	 ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”D‹yœe˜!Ø”D‹yœd˜!Øˆ4€KrF   c                 óH   • [        U [        5      n[        U [        5      nX4$ rH   )r4   r   r   )r@   r`   ra   s      rD   Úmpi_pir‰     s!   € Üˆt”[Ó!€AÜˆt”]Ó#€AØˆ4€KrF   c                 óP   • U u  p#[        X![        5      n[        X1[        5      nXE4$ rH   )r0   r   r   rm   s         rD   Úmpi_expr‹     ó(   € Ø�F€Bä�œ+Ó&€AÜ�œ-Ó(€AØˆ4€KrF   c                 óP   • U u  p#[        X![        5      n[        X1[        5      nXE4$ rH   )r/   r   r   rm   s         rD   Úmpi_logrŽ     rŒ   rF   c                 óP   • U u  p#[        X![        5      n[        X1[        5      nXE4$ rH   )r1   r   r   rm   s         rD   Úmpi_sqrtr�   $  s(   € Ø�F€Bä�œ;Ó'€AÜ�œ=Ó)€AØˆ4€KrF   c                 óP   • U u  p#[        X![        5      n[        X1[        5      nXE4$ rH   )r2   r   r   rm   s         rD   Úmpi_atanr’   +  s(   € Ø�F€BÜ�œ;Ó'€AÜ�œ=Ó)€AØˆ4€KrF   c           	      ó~  • U u  p4US:  a%  [        [        [        4[        X* US-   5      U5      $ US:X  a  [        [        4$ US:X  a  U $ US:X  a  [        X5      $ US-  (       a%  [	        X1U[
        5      n[	        XAU[        5      nXV4$ [        U5      n[        U5      nUS:¼  a%  [	        X1U[
        5      n[	        XAU[        5      nXV4$ US::  a%  [	        XAU[
        5      n[	        X1U[        5      nXV4$ [        n[        U5      n[        X45      (       a  [	        X1U[        5      nXV4$ [	        XAU[        5      nXV4$ ©Nrt   é   r   é   )r   r   Úmpi_pow_intr†   r,   r   r   r   r   r$   r   )	r?   Únr@   rA   rB   r`   ra   ru   rv   s	            rD   r—   r—   1  s@  € Ø�F€BØˆ1ƒuÜœœd�|¤[°°B¸¸R¹Ó%@À$ÓGÐGØˆAƒvÜ”dˆ|ÐØˆAƒvØˆØˆAƒvÜ˜!Ó"Ð"àˆ1‡uÜ˜˜t¤[Ó1ˆÜ˜˜t¤]Ó3ˆð, ˆ4€Kô' �r‹lˆÜ�r‹lˆà�!‹8Ü˜B 4¬Ó5ˆAÜ˜B 4¬Ó7ˆAð ˆ4€Kð �A‹XÜ˜B 4¬Ó5ˆAÜ˜B 4¬Ó7ˆAð ˆ4€Kô ˆAä˜“ˆBÜ�b�~‰~Ü  t¬]Ó;�ð ˆ4€Kô    t¬]Ó;�Øˆ4€KrF   c                 ó
  • Uu  p4X4:X  aS  U[         [        4;  aC  U[        [        U5      5      :X  a  [	        U [        U5      U5      $ U[
        :X  a  [        X5      $ [        XS-   5      n[        XQUS-   5      n[        Xb5      $ ©Nr•   )
r   r   r   r    r—   r   r�   rŽ   rz   r‹   )r?   rK   r@   rS   rT   ÚuÚvs          rD   Úmpi_powr�   V  sx   € Ø�F€BØ	ƒx�Bœt¤U˜mÓ+Ø”œ& ›*Ó%Ó%Ü˜q¤&¨£*¨dÓ3Ð3Ø”‹;Ü˜AÓ$Ð$Ü�˜"‘9Ó€AÜ��d˜R‘iÓ €AÜ�1ÓÐrF   c                 ó*   • [        X5      (       a  U $ U$ rH   )r   ©ÚxÚys     rD   ÚMINr¢   a  ó   € Üˆa‡|�|ØˆØ€HrF   c                 ó*   • [        X5      (       a  U $ U$ rH   )r   rŸ   s     rD   ÚMAXr¥   f  r£   rF   c                 ó˜   • U u  p#pEU [         :X  a  [        [         S4$ [        X5      u  pg[        X4XE-   S5      u  p‰n
U(       a  SU	-
  n	XgU	4$ )Nrt   é   rj   )r   r   r6   r5   )r    ÚwpÚsignÚmanÚexpÚbcÚcr?   rK   r˜   Úwp_s              rD   Úcos_sin_quadrantr¯   k  sT   € ØÑ€DˆsØŒEƒzÜ”U˜Aˆ~Ðä�qÓ�D€AÜ˜ #¡&¨"Ó-�I€Aˆ#ÞØˆq‰DˆØ�ˆ7€NrF   c                 ó4  ^^^• U u  p#X#s=:X  a
  [         :X  a  O  O[        [        4[         [         44$ [        U ;   d
  [        U ;   a  [        [        4[        [        44$ TS-   n[        X$5      u  pVn[        X45      u  p‰n
[        XX/5      u  pX[        Xi/5      u  piXz:X  a  OzX§-
  S:¼  a  [        [        4[        [        44$ US-  U
S-  :w  a  [        nUS-
  S-  U
S-
  S-  :w  a  [        nUS-
  S-  U
S-
  S-  :w  a  [        n	US-
  S-  U
S-
  S-  :w  a  [        n[        [        U-  [        S-  -   U* 5      m[        [        U-  [        S-  -
  U* 5      mUUU4S jnU" U[        5      nU" U[        5      nU" U[        5      nU" U	[        5      n	XX4Xi44$ )Nr•   é   r–   r   é   é
   c                 óž   >• [        U S   5      U[        :H  :X  a  TnOTn[        XT	U5      n U u  p4pVXV-   S:¼  a  U(       a  [        $ [        $ U $ )Nrt   r   )Úboolr   r(   r   r   )
rœ   ÚroundingÚpr©   rª   r«   r¬   ÚlessÚmorer@   s
          €€€rD   ÚfinalizeÚmpi_cos_sin.<locals>.finalize˜  sU   ø€ Ü��!‘‹:˜(¤kÑ1Ó2Ø‰AàˆAÜ�A˜$ Ó)ˆØÑˆ�3Ø‰6�Q‹;ÞÜ�ÜˆKØˆrF   )r   r   r   r   r   r¯   r   r-   r.   r   r   )r    r@   r`   ra   r¨   ÚcarA   ÚnaÚcbrB   Únbrº   r¸   r¹   s    `          @@rD   Úmpi_cos_sinrÀ   v  s”  ú€ Ø�D€AØ…”†Ü”dˆ|œe¤U˜^Ð+Ð+ä�‹	”u “zÜ”tˆ}œu¤d˜mÐ+Ð+Ø	�‰€BÜ! !Ó(�J€BˆBÜ! !Ó(�J€BˆBÜ˜"˜Ó"�F€BÜ˜"˜Ó"�F€Bà	ƒxØà	‰�A‹Ü”tˆ}œu¤d˜mÐ+Ð+ð ˆq‰5�B˜‘E‹>ÜˆBàˆq‰D�1‰9˜˜A™ ™	Ó!ÜˆBàˆq‰D�1‰9˜˜A™ ™	Ó!ÜˆBàˆq‰D�1‰9˜˜A™ ™	Ó!ÜˆBäœ "™¬°"©Ñ5¸°sÓ;€DÜœ "™¬°"©Ñ5¸°sÓ;€D÷ñ 
�"”kÓ	"€BÙ	�"”mÓ	$€BÙ	�"”kÓ	"€BÙ	�"”mÓ	$€BØˆ7�R�GÐÐrF   c                 ó   • [        X5      S   $ rs   ©rÀ   ©r    r@   s     rD   Úmpi_cosrÄ   ª  ó   € Ü�qÓ Ñ"Ð"rF   c                 ó   • [        X5      S   $ ©Nr   rÂ   rÃ   s     rD   Úmpi_sinrÈ   ­  rÅ   rF   c                 ó:   • [        XS-   5      u  p#[        X2U5      $ rš   ©rÀ   r   ©r    r@   ÚcosÚsins       rD   Úmpi_tanrÎ   °  ó   € Ü˜1 2™gÓ&�H€CÜ�3˜TÓ"Ð"rF   c                 ó:   • [        XS-   5      u  p#[        X#U5      $ rš   rÊ   rË   s       rD   Úmpi_cotrÑ   ´  rÏ   rF   c                 ó‚  • US-   n[        X[        5      n[        X[        5      n[        X[        5      n[        U[        5      (       d   eU(       aH  [        [        [        U5      [        U5      5      X[        5      n[        U[        S5      U[        5      n[        XQU[        5      n[        XaU[        5      nXx4$ )Nr•   éd   )r"   r   r   r   r   r(   r¥   r#   r*   r   r'   r&   )	r    r¡   Úpercentr@   r¨   ÚxaÚxbr`   ra   s	            rD   Úmpi_from_str_a_br×   ¸  s™   € Ø	�‰€BÜ	�!œÓ	%€BÜ	�!œÓ	'€Bä�œÓ&€AÜ�!”U×ÑÐÐÞÜ”Cœ ›¤W¨R£[Ó1°1¼-ÓHˆÜ�A”x “} b¬-Ó8ˆÜ��tœ[Ó)€AÜ��tœ]Ó+€AØˆ4€KrF   c                 ó¬  • [        SU -  5      nU R                  SS5      n US-   nSU ;   a   U R                  S5      u  pE[        XESU5      $ SU ;   ai  U S   S:X  d  S	U ;  a  UeU R                  S	S5      n SnS
U ;   a  U S   S
:w  a  UeSnU R                  S
S5      n U R                  S5      u  pE[        XEXa5      $ SU ;   aò  SU ;  d  SU ;  a  UeU S   S:X  aZ  U R                  SS5      n U R                  SS5      n U R                  S5      u  px[	        Xq[
        5      n[	        X�[        5      nXx4$ U R                  S5      u  pEUR                  S5      u  pYSU ;   a  U	R                  S5      u  p’OU	R                  S5      Sp)[	        XE-   U-   U[
        5      n[	        XI-   U-   U[        5      nXx4$ [	        X[
        5      n[	        X[        5      nXx4$ )aÎ  
Parse an interval number given as a string.

Allowed forms are

"-1.23e-27"
    Any single decimal floating-point literal.
"a +- b"  or  "a (b)"
    a is the midpoint of the interval and b is the half-width
"a +- b%"  or  "a (b%)"
    a is the midpoint of the interval and the half-width
    is b percent of a (`a   imes b / 100`).
"[a, b]"
    The interval indicated directly.
"x[y,z]e"
    x are shared digits, y and z are unequal digits, e is the exponent.

z&Improperly formed interval number '%s'Ú Ú r•   ú+-FÚ(rt   Ú)Ú%rj   TÚ,r=   r>   Úe)Ú
ValueErrorÚreplaceÚsplitr×   r"   r   r   Úrstrip)
r?   r@   rà   r¨   r    r¡   rÔ   r`   ra   Úzs
             rD   Úmpi_from_strræ   Æ  sÓ  € ô& 	Ð;¸aÑ?Ó@€AØ	�	‰	�#�rÓ€AØ	�‰€BØˆqƒyØ�w‰w�t‹}‰ˆÜ  e¨TÓ2Ð2à	�‹àˆQ‰4�3‹;˜# Q›,ØˆGØ�I‰I�c˜2ÓˆØˆØ�!‹8Ø�‰u˜‹|Ø�ØˆGØ—	‘	˜#˜rÓ"ˆAØ�w‰w�s‹|‰ˆÜ  gÓ4Ð4Ø	�‹Ø�q‹L˜c¨›lØˆGØˆQ‰4�3‹;à—	‘	˜#˜rÓ"ˆAØ—	‘	˜#˜rÓ"ˆAØ—7‘7˜3“<‰DˆAÜ˜¤+Ó.ˆAÜ˜¤-Ó0ˆAØ�4ˆKð —7‘7˜3“<‰DˆAØ—7‘7˜3“<‰DˆAØ�a‹xØ—w‘w˜s“|‘��1à—x‘x “} b�1Ü˜™˜Q™ ¤kÓ2ˆAÜ˜™˜Q™ ¤mÓ4ˆAØ�4ˆKä�QœkÓ*ˆÜ�QœmÓ,ˆØˆtˆrF   c           	      ó<  • [        U5      nUS-   nU u  pš[        X5      n[        X5      n[        X‘40 UD6n[        X¡40 UD6n[        X±40 UD6nSnU(       a  SnUu  nnUS:X  a'  [        [	        US5      U40 UD6nUU-   S-   U-   U-   nU$ US:X  a`  U[
        :X  a  [
        nO5[        U[        S5      5      n[        U[        U[        S	5      5      U5      nUU-   S
-   [        UU5      -   S-   nU$ US:X  a  UU-   S-   U-   U-   U-   nU$ US:X  Ga~  XÞ:X  a  [        X‘S-   40 UD6n[        X¡S-   40 UD6nUR                  S5      n	[        U	5      S:X  a  U	R                  S5        UR                  S5      n
[        U
5      S:X  a  U
R                  S5        U	S   U
S   :X  a»  U	S   U
S   :w  a  [        [        U	S   5      S-   5       H  nU	S   U   U
S   U   :w  d  M    O   U	S   SW U-   U	S   US -   S-   U-   U
S   US -   U-   S[        [        U	S   5      S5      -  -   U	S   -   nU$ U	S   U-   U-   S[        [        U	S   5      S5      -  -   U	S   -   n U$ USR                  U	5      -   S-   U-   SR                  U
5      -   U-   n U$ [        SU-  5      e)aO  
Convert a mpi interval to a string.

**Arguments**

*dps*
    decimal places to use for printing
*use_spaces*
    use spaces for more readable output, defaults to true
*brackets*
    pair of strings (or two-character string) giving left and right brackets
*mode*
    mode of display: 'plusminus', 'percent', 'brackets' (default) or 'diff'
*error_dps*
    limit the error to *error_dps* digits (mode 'plusminus and 'percent')

Additional keyword arguments are forwarded to the mpf-to-string conversion
for the components of the output.

**Examples**

    >>> from mpmath import mpi, mp
    >>> mp.dps = 30
    >>> x = mpi(1, 2)._mpi_
    >>> mpi_to_str(x, 2, mode='plusminus')
    '1.5 +- 0.5'
    >>> mpi_to_str(x, 2, mode='percent')
    '1.5 (33.33%)'
    >>> mpi_to_str(x, 2, mode='brackets')
    '[1.0, 2.0]'
    >>> mpi_to_str(x, 2, mode='brackets' , brackets=('<', '>'))
    '<1.0, 2.0>'
    >>> x = mpi('5.2582327113062393041', '5.2582327113062749951')._mpi_
    >>> mpi_to_str(x, 15, mode='diff')
    '5.2582327113062[4, 7]'
    >>> mpi_to_str(mpi(0)._mpi_, 2, mode='percent')
    '0.0 (0.0%)'

r•   rÚ   rÙ   Ú	plusminusrj   rÛ   rÔ   rÓ   r–   rÜ   z%)Úbracketsrß   Údiffr²   rà   r   rt   Nz%'%s' is unknown mode for printing mpi)r   rk   rh   r!   r+   r   r(   r   r*   rã   ÚlenÚappendr   ÚminÚjoinrá   )r    rC   Ú
use_spacesré   ÚmodeÚ	error_dpsÚkwargsr@   r¨   r`   ra   ÚmidÚdeltaÚa_strÚb_strÚmid_strÚspÚbr1Úbr2Ú	delta_strr?   r·   Úis                          rD   Ú
mpi_to_strrý     s  € ôP �sÓ€DØ	�‰€BØ�D€AÜ
�!Ó
€CÜ�aÓ€EÜ�1Ñ$˜VÑ$€EÜ�1Ñ$˜VÑ$€EÜ�SÑ( Ñ(€GØ	€BÞØˆØ�H€CˆØˆ{ÓÜœ9 U¨2Ó.°Ñ>°vÑ>ˆ	Ø�b‰L˜4Ñ "Ñ$ yÑ0ˆðH €HðG 
�Ó	Ø”%‹<Ü‰Aô ˜œx¨›}Ó-ˆAÜ˜œ7 3¬°«Ó4°bÓ9ˆAØ�b‰L˜3Ñ¤¨¨9Ó!5Ñ5¸Ñ<ˆð8 €Hð7 
�Ó	Ø�%‰K˜#Ñ Ñ" UÑ*¨SÑ0ˆð4 €Hð3 
�Œà‹>Ü˜1 !™eÑ. vÑ.ˆEÜ˜1 !™eÑ. vÑ.ˆEà�K‰K˜ÓˆÜˆq‹6�Q‹;Ø�H‰H�RŒLØ�K‰K˜ÓˆÜˆq‹6�Q‹;Ø�H‰H�RŒLØˆQ‰4�1�Q‘4‹<Ø�‰t�q˜‘t‹|Ü¤ A a¡D£	¨A¡Ö.�AØ˜‘t˜A‘w ! A¡$ q¡'Õ)Ùñ /ð �q‘T˜"˜1�X ‘^ a¨¡d¨1¨2 hÑ.°Ñ4°rÑ9¸A¸a¹DÀÀ¸HÑDÀsÑJØœ3œs 1 Q¡4›y¨!Ó,Ñ,ñ-Ø/0°©tñ4�ð €Hð �a‘D˜3‘J Ñ$ s¬3¬s°1°Q±4«y¸!Ó+<Ñ'<Ñ<¸qÀ¹tÑC‘ð
 €Hð �c—h‘h˜q“kÑ! CÑ'¨"Ñ,¨s¯x©x¸«{Ñ:¸SÑ@‰Að €Hô Ð@À4ÑGÓHÐHrF   c                 óB   • U u  p4Uu  pV[        X5U5      [        XFU5      4$ rH   )rb   ©r    r¡   r@   r`   ra   r­   Úds          rD   Úmpci_addr  d  ó)   € Ø�D€AØ�D€AÜ�1˜Ó¤¨¨dÓ 3Ð3Ð3rF   c                 óB   • U u  p4Uu  pV[        X5U5      [        XFU5      4$ rH   )re   rÿ   s          rD   Úmpci_subr  i  r  rF   c                 ó6   • U u  p#[        X!5      [        X15      4$ rH   )rq   ©r    r@   r`   ra   s       rD   Úmpci_negr  n  ó   € Ø�D€AÜ�1ÓœW QÓ-Ð-Ð-rF   c                 ó6   • U u  p#[        X!5      [        X15      4$ rH   )rn   r  s       rD   Úmpci_posr
  r  r  rF   c                 ó    • U u  p4Uu  pV[        X55      n[        XF5      n[        XxU5      n	[        X65      n
[        XE5      n[        X«U5      nXœ4$ rH   )rz   re   rb   )r    r¡   r@   r`   ra   r­   r   Úr1Úr2ÚreÚi1Úi2Úims                rD   Úmpci_mulr  v  sS   € à�D€AØ�D€AÜ	�‹€BÜ	�‹€BÜ	��tÓ	€BÜ	�‹€BÜ	�‹€BÜ	��tÓ	€BØˆ6€MrF   c                 ó  • U u  p4Uu  pVUS-   n[        U5      n[        U5      n	[        X‰U5      n
[        [        X55      [        XF5      U5      n[        [        XE5      [        X65      U5      n[	        XºU5      n[	        XÊU5      nX¼4$ rš   )r†   rb   rz   re   r   )r    r¡   r@   r`   ra   r­   r   r¨   Úm1Úm2Úmr  r  s                rD   Úmpci_divr  ‚  s‚   € à�D€AØ�D€AØ	ˆb‰€BÜ	�A‹€BÜ	�A‹€BÜ��bÓ€AÜ	”˜“œw q›|¨RÓ	0€BÜ	”˜“œw q›|¨RÓ	0€BÜ	�˜Ó	€BÜ	�˜Ó	€BØˆ6€MrF   c                 óz   • U u  p#US-   n[        X$5      n[        X45      u  pg[        XVU5      n[        XWU5      nX#4$ rš   )r‹   rÀ   rz   )r    r@   r`   ra   r¨   Úrr­   r?   s           rD   Úmpci_expr  �  sF   € Ø�D€AØ	ˆb‰€BÜ�‹€AÜ�qÓ�D€AÜ��dÓ€AÜ��dÓ€AØˆ4€KrF   c                 ó6   • U u  p#[        X!5      [        X15      4$ rH   )r+   )r    r˜   r`   ra   s       rD   Ú	mpi_shiftr  ™  s   € Ø�D€AÜ�Q‹>œ9 Q›>Ð)Ð)rF   c                 ó¨   • US-   n[        X5      n[        [        X25      n[        X4U5      n[	        X4U5      n[        US5      n[        US5      nXV4$ )Nr•   rj   )r‹   r   Úmpi_onerb   re   r  )r    r@   r¨   Úe1Úe2r­   r?   s          rD   Úmpi_cosh_sinhr!  �  sW   € à	ˆb‰€BÜ	�‹€BÜ	”˜"Ó	!€BÜ�˜Ó€AÜ�˜Ó€AÜ�!�RÓ€AÜ�!�RÓ€AØˆ4€KrF   c                 ó’   • U u  p#US-   n[        X$5      u  pV[        X45      u  px[        XWU5      n	[        XhU5      n
U	[        U
5      4$ ©Nr³   )rÀ   r!  rz   rq   ©r    r@   r`   ra   r¨   r­   r?   ÚchÚshr  r  s              rD   Úmpci_cosr'  ¨  sP   € Ø�D€AØ	ˆb‰€BÜ�qÓ�D€AÜ˜1Ó!�F€BÜ	�˜Ó	€BÜ	�˜Ó	€BØŒw�r‹{ˆ?ÐrF   c                 ó~   • U u  p#US-   n[        X$5      u  pV[        X45      u  px[        XgU5      n	[        XXU5      n
Xš4$ r#  )rÀ   r!  rz   r$  s              rD   Úmpci_sinr)  ±  sI   € Ø�D€AØ	ˆb‰€BÜ�qÓ�D€AÜ˜1Ó!�F€BÜ	�˜Ó	€BÜ	�˜Ó	€BØˆ6€MrF   c                 ó¾   • U u  p#U[         :X  a  [        U5      $ U[         :X  a  [        U5      $ [        U5      n[        U5      n[        X#US-   5      n[	        XA5      $ rš   )Úmpi_zerorx   r†   rb   r�   )r    r@   r`   ra   rK   s        rD   Úmpci_absr,  º  sX   € Ø�D€AØŒHƒ}Ü�q‹zÐØŒHƒ}Ü�q‹zÐä�1‹€AÜ�1‹€AÜ��d˜2‘gÓ€AÜ�AÓÐrF   c                 óf  • U u  p4Uu  pVX4s=:X  a
  [         :X  a)  O  O&[        U[         5      (       a  [        $ [        U5      $ [        U[         5      (       av  [        U[         5      (       a  [	        X6U[
        5      nO[	        X5U[
        5      n[        U[         5      (       a  [	        XEU[        5      nXx4$ [	        XFU[        5      n Xx4$ [        U[         5      (       aO  [	        X5U[        5      n[        U[         5      (       a  [	        XFU[
        5      nXx4$ [	        X6U[
        5      n Xx4$ [        U[         5      (       aO  [	        XEU[
        5      n[        U[         5      (       a  [	        X6U[        5      nXx4$ [	        XFU[        5      n Xx4$ [        U[        5      n[        U5      nXx4$ rH   )
r   r   r+  r‰   r3   r   r   r   r4   r$   )	r¡   r    r@   ÚyaÚybrÕ   rÖ   r`   ra   s	            rD   Ú	mpi_atan2r0  Æ  s|  € Ø�F€BØ�F€Bà	Õ”5ÖÜ�"”e×ÑÜˆOÜ�d‹|Ðäˆb”%×ÑÜ�"”e×ÑÜ˜" $¬Ó4‰Aä˜" $¬Ó4ˆAÜ�"”e×ÑÜ˜" $¬Ó6ˆAð* ˆ4€Kô' ˜" $¬Ó6‰Að& ˆ4€Kô# 
�”E×	Ñ	Ü�b˜d¤MÓ2ˆÜ�"”e×ÑÜ˜" $¬Ó4ˆAð ˆ4€Kô ˜" $¬Ó4‰Að ˆ4€Kô 
�”E×	Ñ	Ü�b˜d¤KÓ0ˆÜ�"”e×ÑÜ˜" $¬Ó6ˆAð ˆ4€Kô ˜" $¬Ó6‰Að
 ˆ4€Kô �4œÓ'ˆÜ�A‹JˆØˆ4€KrF   c                 ó"   • U u  p#[        X2U5      $ rH   )r0  )rå   r@   r    r¡   s       rD   Úmpci_argr2  ì  s   € Ø�D€AÜ�Q˜4Ó Ð rF   c                 óV   • U u  p#[        [        XS-   5      U5      n[        X5      nXE4$ rš   )rŽ   r,  r2  )rå   r@   r    r¡   r  r  s         rD   Úmpci_logr4  ð  s/   € Ø�D€AÜ	”˜! "™WÓ% tÓ	,€BÜ	�!Ó	€BØˆ6€MrF   c           	      ó  • Uu  p4U[         :X  aP  Uu  pVXV:X  aG  Uu  pxpšU(       a$  U	S:¼  a  [        U SU-  [        X‰-  5      -  U5      $ U[        :X  a  [        U SU5      $ US-   n[	        [        U[        X5      U5      U5      $ )Nrt   rj   r•   )r+  Úmpci_pow_intÚintr   r  r  r4  )r    r¡   r@   ÚyreÚyimr.  r/  r©   rª   r«   r¬   r¨   s               rD   Úmpci_powr:  ö  s†   € à�H€CØ
ŒhƒØ‰ˆØ‹8Ø!#ÑˆD�sÞ�s˜a“xÜ# A¨¨T¡z´C¸¹³MÑ'AÀ4ÓHÐHà”U‹{Ü# A q¨$Ó/Ð/Ø	ˆb‰€BÜ”H˜Q¤¨£°Ó4°dÓ;Ð;rF   c                 ó~   • U u  p#[        [        U5      [        U5      U5      n[        X#U5      n[        US5      nXE4$ rÇ   )re   r†   rz   r  )r    r@   r`   ra   r  r  s         rD   Úmpci_squarer<    s>   € Ø�D€Aä	”˜A“¤
¨1£¨tÓ	4€BÜ	��tÓ	€BÜ	�2�qÓ	€BØˆ6€MrF   c           	      ón  • US:  a%  [        [        [        4[        X* US-   5      U5      $ US:X  a  [        [        4$ US:X  a  [	        X5      $ US:X  a  [        X5      $ US-   n[        [        4nU(       a4  US-  (       a  [        X@U5      nUS-  n[        X5      n US-  nU(       a  M4  [	        XB5      $ r”   )r  r  r+  r6  r
  r<  r  )r    r˜   r@   r¨   Úresults        rD   r6  r6    s¹   € Øˆ1ƒuÜœ¤Ð*¬L¸¸BÀÀRÁÓ,HÈ$ÓOÐOØˆAƒvÜœÐ Ð ØˆAƒvÜ˜Ó Ð ØˆAƒvÜ˜1Ó#Ð#Ø	�‰€BÜ”xÐ €FÞ
Øˆq�5Ü˜f¨Ó,ˆFØ�‰FˆAÜ˜ÓˆØ	ˆa‰ˆ÷ ˆ!ô �FÓ!Ð!rF   g#+VcØb÷?gÛVcØb÷?gš™™™™™ñ¿gš™™™™™ñ?c                 óX   • U u  p#Uu  pE[        XR5      (       a  g[        XC5      (       a  gg)NFT)r   r   )r    r¡   r`   ra   r­   r   s         rD   Úmpi_overlapr@  &  s)   € Ø�D€AØ�D€AÜˆa‡|�|˜EÜˆa‡|�|˜EØrF   c                 óÄ  • U u  p4US-   nUS:X  a  [        [        U [        U5      US5      $ [        U[        5      (       a|  US:X  a#  [        X1[        5      n[        XA[        5      nXg4$ US:X  a#  [        XA[        5      n[        X1[        5      nXg4$ US:X  a   [        X1[        5      n[        XA[        5      nWW4$ [        U[        5      (       a‘  [        U[        5      (       a|  US:X  a#  [        XA[        5      n[        X1[        5      nXg4$ US:X  a#  [        X1[        5      n[        XA[        5      nXg4$ US:X  a   [        XA[        5      n[        X1[        5      nWW4$ [        U [        U5      nUS:X  a  [        [        X�S-   S5      X5      $ US:X  a  [        [        X�S-   S5      X5      $ US:X  a&  [        [        X�S-   S5      [!        XS-   5      U5      $ WW4$ )Nr•   r   rt   r–   r²   )Ú	mpi_gammarb   r  r   Úgamma_min_br7   r   r   r8   r9   r   r   Úgamma_min_ar   rz   re   rŽ   )	rå   r@   Útyper`   ra   r¨   r­   r   Úznews	            rD   rB  rB  2  s×  € Ø�D€AØ	ˆb‰€BàˆqƒyÜœ ¤G¨RÓ0°$¸Ó:Ð:ô ˆa”×ÑØ�1‹9Ü˜!¤;Ó/ˆAÜ˜!¤=Ó1ˆAð0 ˆ4€Kð/ �Q‹YÜ˜1¤KÓ0ˆAÜ˜1¤MÓ2ˆAð* ˆ4€Kð) �Q‹YÜ˜Q¤kÓ2ˆAÜ˜Q¤mÓ4ˆAð$ ˆaˆ4€Kô! 
�”5×	Ñ	œf Q¬×4Ñ4Ø�1‹9Ü˜!¤;Ó/ˆAÜ˜!¤=Ó1ˆAð ˆ4€Kð �Q‹YÜ˜1¤KÓ0ˆAÜ˜1¤MÓ2ˆAð ˆ4€Kð �Q‹YÜ˜Q¤kÓ2ˆAÜ˜Q¤mÓ4ˆAð ˆaˆ4€Kô	 �qœ' 2Ó&ˆØ�1‹9œW¤Y¨t¸!±V¸QÓ%?ÀÓIÐIØ�1‹9œW¤Y¨t¸!±V¸QÓ%?ÀÓIÐIØ�1‹9œW¤Y¨t¸!±V¸QÓ%?ÄÈÐQRÉFÓASÐUYÓZÐZØˆaˆ4€KrF   c                 ó^  • U u  u  p4u  pVXVs=:X  a
  [         :X  a0  O  O-US:w  d  [        U[         5      (       a  [        XU5      [        4$ US-   nUS:w  a}  US   US   -   nUS   US   -   n	U[         :w  a  [	        X‰5      n
OU	n
[        [        U5      5      n[        [        U5      5      n[	        X¼5      n[	        SXÚ-  5      nU[        U5      -  nUS:X  a  [        X44[        U5      u  p4X44XV44n Sn[        U[        5      (       a›  [        XV4[        [        45      (       a  [        X44[        U5      XV44nUS:X  a  [        [!        XñS-   S5      X5      $ US:X  a  [#        [!        XñS-   S5      X5      $ US:X  a&  [%        [!        XñS-   S5      ['        XS-   5      U5      $ [)        U[         5      (       aI  [+        X64U[,        5      n[+        XE4U[.        5      n[+        X54U[,        5      n[+        XF4U[.        5      nOØ[1        U[         5      (       aI  [+        X54U[,        5      n[+        XF4U[.        5      n[+        XE4U[,        5      n[+        X64U[.        5      nOz[+        U[         4U[.        5      n[        [3        U5      U5      (       a  [+        X54U[.        5      nO[+        X64U[.        5      n[+        XE4U[,        5      n[+        XF4U[,        5      nUS   US   4US   US   44nUS:X  a  [5        US   U5      [5        US   U5      4$ US:X  a  [7        U5      n[9        UU5      $ )Nr²   r•   r–   rt   r   )r   r   rB  r+  ÚmaxÚabsr    r   rb   r  r   rC  r@  Úgamma_mono_imag_aÚgamma_mono_imag_br  Ú
mpci_gammar  r  r4  r   r:   r   r   r   r$   rn   r  r  )rå   r@   rE  Úa1Úa2Úb1Úb2r¨   ÚamagÚbmagÚmagÚanÚbnÚabsnÚ
gamma_sizerF  ÚminreÚmaxreÚminimÚmaximÚws                        rD   rL  rL  W  s  € ØÑ�G€R‰Wˆbð 
Õ”5Ö˜d a›i¬6°"´U×+;Ñ+;Ü˜ $Ó'¬Ð1Ð1ð 
ˆb‰€BØˆqƒyØ�!‰u�R˜‘U‰{ˆØ�!‰u�R˜‘U‰{ˆØ”‹;Ü�d“/‰CàˆCÜ”˜“‹_ˆÜ”˜“‹_ˆÜ�2‹{ˆÜ˜˜4™8“_ˆ
Ø
Œh�zÓ"Ñ"ˆð ˆqƒyÜ˜2˜'¤7¨BÓ/‰ˆ°b°W¸r¸gÐ5E°Øˆô ˆb”+×ÑÜ˜�wÔ!2Ô4EÐ F×GÑGô ˜B˜7¤G¨RÓ0°2°'Ð9ˆDØ�q‹y¤¬*°TÀ¹6À1Ó*EÀqÓ!OÐOØ�q‹y¤¬*°TÀ¹6À1Ó*EÀqÓ!OÐOØ�q‹y¤¬*°TÀ¹6À1Ó*EÄxÐPQÐWXÑRXÓGYÐ[_Ó!`Ð`ô
 ˆb”%×ÑÜ˜b˜W b¬+Ó6ˆÜ˜b˜W b¬-Ó8ˆÜ˜b˜W b¬+Ó6ˆÜ˜b˜W b¬-Ó8‰ä	�”E×	Ñ	Ü˜b˜W b¬+Ó6ˆÜ˜b˜W b¬-Ó8ˆÜ˜b˜W b¬+Ó6ˆÜ˜b˜W b¬-Ó8‰ô ˜b¤˜Z¨¬]Ó;ˆä”'˜"“+˜r×"Ñ"Ü  " ¨"¬mÓ<‰Eä  " ¨"¬mÓ<ˆEÜ˜b˜W b¬+Ó6ˆÜ˜b˜W b¬+Ó6ˆà	ˆq‰�5˜‘8Ð˜u Q™x¨¨q©Ð2Ð2€AØˆqƒyÜ�q˜‘t˜TÓ"¤G¨A¨a©D°$Ó$7Ð7Ð7ØˆqƒyÜ�Q‹KˆÜ�A�tÓÐrF   c                 ó   • [        XSS9$ ©Nr²   ©rE  ©rB  ©rå   r@   s     rD   Úmpi_loggammarb     s   € ¤)¨A¸!Ñ"<Ð<rF   c                 ó   • [        XSS9$ r^  ©rL  ra  s     rD   Úmpci_loggammare  ¡  s   € ¤:¨a¸AÑ#>Ð>rF   c                 ó   • [        XSS9$ ©Nr–   r_  r`  ra  s     rD   Ú
mpi_rgammarh  £  s   € ¤	¨!¸Ñ :Ð:rF   c                 ó   • [        XSS9$ rg  rd  ra  s     rD   Úmpci_rgammarj  ¤  s   € ¤¨A¸!Ñ!<Ð<rF   c                 ó   • [        XSS9$ ©Nr   r_  r`  ra  s     rD   Úmpi_factorialrm  ¦  s   € ¤9¨Q¸1Ñ#=Ð=rF   c                 ó   • [        XSS9$ rl  rd  ra  s     rD   Úmpci_factorialro  §  s   € ¤J¨q¸QÑ$?Ð?rF   N)rt   )Tz[]ré   r±   )„Ú__doc__Úbackendr   Úlibmpfr   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$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   Ú	libelefunr/   r0   r1   r2   r3   r4   r5   r6   Ú	gammazetar7   r8   r9   r:   rE   r+  r  rL   rO   rU   rX   rZ   r]   rb   re   rh   rk   rn   rq   rx   r|   r€   rz   r†   r   r‰   r‹   rŽ   r�   r’   r—   r�   r¢   r¥   r¯   rÀ   rÄ   rÈ   rÎ   rÑ   r×   ræ   rý   r  r  r  r
  r  r  r  r  r!  r'  r)  r,  r0  r2  r4  r:  r<  r6  rD  rC  Ú	gamma_minrJ  rK  r@  rB  rL  rb  re  rh  rj  rm  ro  rI   rF   rD   Ú<module>rv     sí  ðñõ
 ÷÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ñ ÷÷ ó ÷
 IÓ Hò;ð �5ˆ>€Ø�ˆ,€òòòòò &Ú %ôôò+ò?òôôò.$ò$ôBôHò9òvò
òòòò#òJ	òò
ò
	ò2òh#ò#ò#ò#òò@ôDZòx4ò
4ô
.ò.ò
òòò*ò	òòò
ò$òL!òò<òò"ñ& ˜Ó'€Ù˜Ó'€Ø˜+Ð&€	Ù˜tÓ$Ð Ù˜s“OÐ òô#ôJGòR =Ú >â :Ú <â =Û ?rF   