+
    ‰°³jæk  ã                   ó
  € R 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. ^RI/H0t0H1t1H2t2H3t3H4t4H5t5H6t6H7t7 ^RI8H9t9H:t:H;t;H<t< R t=]]3t>]]3t?R t@R tAR tBR	 tCR
 tDR tERIR ltFRIR ltGR tHR tIR tJRIR ltKRIR ltLR tMR tNRIR ltORIR ltPR tQR tRR tSR tTR tUR tVR tWR tXR tYR  tZR! t[R" t\R# t]R$ t^R% t_R& t`R' taR( tbRJR) ltcR* tdR+ teRIR, ltfR- tgR. thR/ tiR0 tjR1 tkR2 tlR3 tmR4 tnR5 toR6 tpR7 tqR8 trR9 tsR: ttR; tu]! R<4      tv]! R=4      tw]v]w3tx]! RK4      ty]! R>4      tzR? t{RIR@ lt|RIRA lt}RB t~RC tRD t€RE t�RF t‚RG tƒRH# )Lz3
Computational functions for interval arithmetic.

)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                 óh   € V w  r#\        V4      ^,           pR\        W$4      : R\        W44      : R2# )é   Ú[z, Ú])r	   r    )ÚsÚprecÚsaÚsbÚdpss   &&   ÚT/home/luca/screen-checking/.venv/lib/python3.14/site-packages/mpmath/libmp/libmpi.pyÚmpi_strrD      s+   € Ø�F€BÜ
�dÓ
˜aÕ
�CÜ ž¬&°®/Ð:Ð:ó    c                 ó
   € W8H  # ©N© ©r>   Úts   &&rC   Úmpi_eqrK   )   ó	   € Ø‰6€MrE   c                 ó
   € W8g  # rG   rH   rI   s   &&rC   Úmpi_nerN   ,   rL   rE   c                 ób   € V w  r#Vw  rE\        W44      '       d   R # \        W%4      '       d   R# R# ©TFN)r   r   ©r>   rJ   r@   rA   ÚtaÚtbs   &&    rC   Úmpi_ltrT   /   ó)   € Ø�F€BØ�F€BÜˆb‡~‚~™dÜˆb‡~‚~™eÙrE   c                 ób   € V w  r#Vw  rE\        W44      '       d   R # \        W%4      '       d   R# R# rP   )r   r   rQ   s   &&    rC   Úmpi_lerW   6   rU   rE   c                 ó   € \        W4      # rG   )rT   rI   s   &&rC   Úmpi_gtrY   =   ó   € œ ›Ð%rE   c                 ó   € \        W4      # rG   )rW   rI   s   &&rC   Úmpi_ger\   >   rZ   rE   c                 ó    € V w  r4Vw  rV\        W5V\        4      p\        WFV\        4      pV\        8X  d   \        pV\        8X  d   \
        pWx3# rG   )r%   r   r   r   r   r   ©	r>   rJ   r?   r@   rA   rR   rS   ÚaÚbs	   &&&      rC   Úmpi_addra   @   óI   € Ø�F€BØ�F€BÜ�˜œkÓ*€AÜ�˜œmÓ,€AØŒD„y”e�!ØŒD„y”d�!Øˆ4€KrE   c                 ó    € V w  r4Vw  rV\        W6V\        4      p\        WEV\        4      pV\        8X  d   \        pV\        8X  d   \
        pWx3# rG   )r&   r   r   r   r   r   r^   s	   &&&      rC   Úmpi_subrd   I   rb   rE   c                 ó,   € V w  r#\        W2V\        4      # rG   )r&   r   ©r>   r?   r@   rA   s   &&  rC   Ú	mpi_deltarg   R   s   € Ø�F€BÜ�2˜4¤Ó*Ð*rE   c                 ó@   € V w  r#\        \        W#V\        4      R4      # )é   éÿÿÿÿ)r*   r%   r   rf   s   &&  rC   Úmpi_midrk   V   s   € Ø�F€BÜ”W˜R T¬=Ó9¸2Ó>Ð>rE   c                 óP   € V w  r#\        W!\        4      p\        W1\        4      pWE3# rG   )r$   r   r   ©r>   r?   r@   rA   r_   r`   s   &&    rC   Úmpi_posrn   Z   ó(   € Ø�F€BÜ�œ+Ó&€AÜ�œ-Ó(€AØˆ4€KrE   c                 óP   € V w  r#\        W1\        4      p\        W!\        4      pWE3# rG   )r#   r   r   rm   s   &&    rC   Úmpi_negrq   `   ro   rE   c                 óp  € V w  r#\        V4      p\        V4      pV^ 8¼  d$   \        W!\        4      p\        W1\        4      pWg3# V^ 8¼  dJ   \        p\        V4      p\        Wƒ4      '       d   \        W1\        4      pWg3# \        W�\        4      p Wg3# \        W1\        4      p\        W!\        4      pWg3# ©é    )r   r$   r   r   r   r#   r   )	r>   r?   r@   rA   ÚsasÚsbsr_   r`   Únegsas	   &&       rC   Úmpi_absrx   f   s²   € Ø�F€BÜ
�2‹,€CÜ
�2‹,€Cà
ˆa„xÜ�BœkÓ*ˆÜ�BœmÓ,ˆð ˆ4€Kð 
�ŒÜˆÜ˜“ˆÜ�%×ÒÜ˜¤-Ó0ˆAð ˆ4€Kô ˜¤]Ó3‰Að
 ˆ4€Kô �BœkÓ*ˆÜ�BœmÓ,ˆØˆ4€KrE   c                 ó   € \        WV3V4      # rG   )Úmpi_mul©r>   rJ   r?   s   &&&rC   Úmpi_mul_mpfr|   }   ó   € Ü�1˜!�f˜dÓ#Ð#rE   c                 ó   € \        WV3V4      # rG   )Úmpi_divr{   s   &&&rC   Úmpi_div_mpfr€   €   r}   rE   c                 óô  € V w  r4Vw  rV\        V4      p\        V4      p\        V4      p	\        V4      p
Yxu;8X  d   ^ 8X  d2   M M.V\        8X  g   V\        8X  d   \        \        3# \        \        3# Yšu;8X  d   ^ 8X  d2   M M.V\        8X  g   V\        8X  d   \        \        3# \        \        3# V^ 8¼  dä   V	^ 8¼  dH   \	        W5V\
        4      p\	        WFV\        4      pV\        8X  d   \        pV\        8X  d   \        pW¼3# V
^ 8:  dH   \	        WEV\
        4      p\	        W6V\        4      pV\        8X  d   \        pV\        8X  d   \        pW¼3# \	        WEV\
        4      p\	        WFV\        4      pV\        8X  d   \        pV\        8X  d   \        pW¼3# V^ 8:  dä   V	^ 8¼  dH   \	        W6V\
        4      p\	        WEV\        4      pV\        8X  d   \        pV\        8X  d   \        pW¼3# V
^ 8:  dH   \	        WFV\
        4      p\	        W5V\        4      pV\        8X  d   \        pV\        8X  d   \        pW¼3# \	        W6V\
        4      p\	        W5V\        4      pV\        8X  d   \        pV\        8X  d   \        pW¼3# \	        W54      \	        W64      \	        WE4      \	        WF4      .p\        V9   d   \        \        rËW¼3# \        V4      w  r¼\        W²\
        4      p\        WÂ\        4      pW¼3# rs   )
r   r   r   r   r'   r   r   r   r   r$   )r>   rJ   r?   r@   rA   rR   rS   ru   rv   ÚtasÚtbsr_   r`   Úcasess   &&&           rC   rz   rz   ƒ   s†  € Ø�F€BØ�F€BÜ
�2‹,€CÜ
�2‹,€CÜ
�2‹,€CÜ
�2‹,€CØ
†�Q‡à”Œ;˜"¤œ*Üœ$�;ÐÜ”eˆ|ÐØ
†�Q‡à”Œ;˜"¤œ*Üœ$�;ÐÜ”eˆ|ÐØ
ˆa„xà�!Œ8Ü˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”DŒyœe˜!Ø”DŒyœd˜!ðV ˆ4€KðS �AŒXÜ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”DŒyœe˜!Ø”DŒyœe˜!ðJ ˆ4€KôE ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”DŒyœe˜!Ø”DŒyœd˜!ð> ˆ4€Kð= 
�Œà�!Œ8Ü˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”DŒyœe˜!Ø”DŒyœe˜!ð0 ˆ4€Kð- �AŒXÜ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”DŒyœe˜!Ø”DŒyœd˜!ð$ ˆ4€Kô ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”DŒyœe˜!Ø”DŒyœd˜!ð ˆ4€Kô ˜“¤'¨"£/´7¸2³?ÄGÈBÃOÐTˆÜ�5Œ=Üœ4ˆqð
 ˆ4€Kô ˜uÓ%‰DˆAÜ˜¤Ó-ˆAÜ˜¤Ó/ˆAØˆ4€KrE   c                 ó\  € V w  r#\        V\        4      '       d&   \        W"V\        4      p\        W3V\        4      pWE3# \        V\        4      '       d&   \        W3V\        4      p\        W"V\        4      pWE3# \        V4      p\        W#.4      w  r#\        p\        W3V\        4      pWE3# rG   )r   r   r'   r   r   r   r#   r   rm   s   &&    rC   Ú
mpi_squarer†   Ç   s¢   € Ø�F€BÜˆb”%×ÒÜ�B˜D¤+Ó.ˆÜ�B˜D¤-Ó0ˆð ˆ4€Kô 
�”E×	Ò	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€KrE   c                 ó   € V w  r4Vw  rV\        V4      p\        V4      p\        V4      p	\        V4      p
Yxu;8X  d   ^ 8X  d8   M M4V	^ 8  d   V
^ 8”  g   V	^ 8X  g   V
^ 8X  d   \        \        3# \        \        3# V	^ 8  d   V
^ 8”  d   \        \        3# V	^ 8  d    \	        \        V 4      \        V4      V4      # V	^ 8X  dm   V^ 8  d   V^ 8”  d   \        \        3# Wš8X  d   \        \        3# V^ 8¼  d   \        W6V\        4      p\        pV^ 8:  d   \        p\        WFV\        4      pXX3# V^ 8¼  dH   \        W6V\        4      p\        WEV\        4      pV\        8X  d   \        pV\        8X  d   \        pW¼3# V^ 8:  dH   \        W5V\        4      p\        WFV\        4      pV\        8X  d   \        pV\        8X  d   \        pW¼3# \        W5V\        4      p\        WEV\        4      pV\        8X  d   \        pV\        8X  d   \        pW¼3# rs   )
r   r   r   r   r   rq   r)   r   r   r   )r>   rJ   r?   r@   rA   rR   rS   ru   rv   r‚   rƒ   r_   r`   s   &&&          rC   r   r   Ö   sÒ  € Ø�F€BØ�F€BÜ
�2‹,€CÜ
�2‹,€CÜ
�2‹,€CÜ
�2‹,€Cà
†�Q‡à�!ŒG˜˜aœ S¨A¤X°¸´Üœ$�;ÐÜ”eˆ|Ðð ˆQ„w�3˜”7Ü”dˆ{Ðà
ˆQ„wÜ”w˜q“z¤7¨1£:¨tÓ4Ð4ð ˆa„xà�Œ7�s˜Q”wÜœ$�;ÐØŒ:Üœ$�;Ðà�!Œ8Ü˜ ¤kÓ2ˆAÜˆAØ�!Œ8ÜˆAÜ˜ ¤mÓ4ˆAð, ˆaˆ4€Kð# �!Œ8Ü˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”DŒyœe˜!Ø”DŒyœd˜!ð ˆ4€Kð �AŒXÜ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”DŒyœe˜!Ø”DŒyœe˜!ð ˆ4€Kô	 ˜ ¤kÓ2ˆAÜ˜ ¤mÓ4ˆAØ”DŒyœe˜!Ø”DŒyœd˜!Øˆ4€KrE   c                 óH   € \        V \        4      p\        V \        4      pW3# rG   )r3   r   r   )r?   r_   r`   s   &  rC   Úmpi_pir‰     s!   € Üˆt”[Ó!€AÜˆt”]Ó#€AØˆ4€KrE   c                 óP   € V w  r#\        W!\        4      p\        W1\        4      pWE3# rG   )r/   r   r   rm   s   &&    rC   Úmpi_expr‹     ó(   € Ø�F€Bä�œ+Ó&€AÜ�œ-Ó(€AØˆ4€KrE   c                 óP   € V w  r#\        W!\        4      p\        W1\        4      pWE3# rG   )r.   r   r   rm   s   &&    rC   Úmpi_logrŽ     rŒ   rE   c                 óP   € V w  r#\        W!\        4      p\        W1\        4      pWE3# rG   )r0   r   r   rm   s   &&    rC   Úmpi_sqrtr�   $  s(   € Ø�F€Bä�œ;Ó'€AÜ�œ=Ó)€AØˆ4€KrE   c                 óP   € V w  r#\        W!\        4      p\        W1\        4      pWE3# rG   )r1   r   r   rm   s   &&    rC   Úmpi_atanr’   +  s(   € Ø�F€BÜ�œ;Ó'€AÜ�œ=Ó)€AØˆ4€KrE   c           	      óž  € V w  r4V^ 8  d*   \        \        \        3\        W) V^,           4      V4      # V^ 8X  d   \        \        3# V^8X  d   V # V^8X  d   \        W4      # V^,          '       d&   \	        W1V\
        4      p\	        WAV\        4      pWV3# \        V4      p\        V4      pV^ 8¼  d&   \	        W1V\
        4      p\	        WAV\        4      pWV3# V^ 8:  d&   \	        WAV\
        4      p\	        W1V\        4      pWV3# \        p\        V4      p\        W44      '       d   \	        W1V\        4      pWV3# \	        WAV\        4      pWV3# rs   )r   r   Úmpi_pow_intr†   r+   r   r   r   r   r#   r   )	r>   Únr?   r@   rA   r_   r`   ru   rv   s	   &&&      rC   r”   r”   1  sB  € Ø�F€BØˆ1„uÜœœd�|¤[°°B¸¸R½Ó%@À$ÓGÐGØˆA„vÜ”dˆ|ÐØˆA„vØˆØˆA„vÜ˜!Ó"Ð"àˆ1‡u„uÜ˜˜t¤[Ó1ˆÜ˜˜t¤]Ó3ˆð, ˆ4€Kô' �r‹lˆÜ�r‹lˆà�!Œ8Ü˜B 4¬Ó5ˆAÜ˜B 4¬Ó7ˆAð ˆ4€Kð �AŒXÜ˜B 4¬Ó5ˆAÜ˜B 4¬Ó7ˆAð ˆ4€Kô ˆAä˜“ˆBÜ�b�~Š~Ü  t¬]Ó;�ð ˆ4€Kô    t¬]Ó;�Øˆ4€KrE   c                 ó"  € Vw  r4W48X  dW   V\         \        39  dF   V\        \        V4      4      8X  d   \	        V \        V4      V4      # V\
        8X  d   \        W4      # \        W^,           4      p\        WQV^,           4      p\        Wb4      # ©é   )
r   r   r   r   r”   r   r�   rŽ   rz   r‹   )r>   rJ   r?   rR   rS   ÚuÚvs   &&&    rC   Úmpi_powr›   V  sx   € Ø�F€BØ	„x�Bœt¤U˜mÔ+Ø”œ& ›*Ó%Ô%Ü˜q¤&¨£*¨dÓ3Ð3Ø”Œ;Ü˜AÓ$Ð$Ü�˜"•9Ó€AÜ��d˜R•iÓ €AÜ�1ÓÐrE   c                 ó,   € \        W4      '       d   V # V# rG   )r   ©ÚxÚys   &&rC   ÚMINr    a  ó   € Üˆa‡|‚|ØˆØ€HrE   c                 ó,   € \        W4      '       d   V # V# rG   )r   r�   s   &&rC   ÚMAXr£   f  r¡   rE   c                 ó¬   € V w  r#rEV \         8X  d   \        \         ^ 3# \        W4      w  rg\        W4WE,           ^4      w  r‰p
V'       d
   RV	,
          p	WgV	3# ©rt   rj   )r   r   r5   r4   )rž   ÚwpÚsignÚmanÚexpÚbcÚcr>   rJ   r•   Úwp_s   &&         rC   Úcos_sin_quadrantr­   k  sT   € ØÑ€DˆsØŒE„zÜ”U˜Aˆ~Ðä�qÓ�D€AÜ˜ #¥&¨"Ó-�I€Aˆ#ßØˆq�DˆØ�ˆ7€NrE   c                 óø  aaa€ V w  r#Y#u;8X  d   \         8X  d   M M\        \        3\         \         33# \        V 9   g   \        V 9   d   \        \        3\        \        33# S^,           p\        W$4      w  rVp\        W44      w  r‰p
\        WX.4      w  rX\        Wi.4      w  riWz8X  d   M»W§,
          ^8¼  d   \        \        3\        \        33# V^,          V
^,          8w  d   \        pV^,
          ^,          V
^,
          ^,          8w  d   \        pV^,
          ^,          V
^,
          ^,          8w  d   \        p	V^,
          ^,          V
^,
          ^,          8w  d   \        p\        \        V,          \        ^
,          ,           V) 4      o\        \        V,          \        ^
,          ,
          V) 4      oVVV3R lpV! V\        4      pV! V\        4      pV! V\        4      pV! V	\        4      p	WX3Wi33# )r˜   c                 ó´   <€ \        V ^ ,          4      V\        8H  8X  d   SpMSp\        WS	V4      p V w  r4rVWV,           ^8¼  d   V'       d   \        # \        # V # rs   )Úboolr   r'   r   r   )
rš   ÚroundingÚpr§   r¨   r©   rª   ÚlessÚmorer?   s
   &&     €€€rC   ÚfinalizeÚmpi_cos_sin.<locals>.finalize˜  sU   ø€ Ü��!•‹:˜(¤kÑ1Ô2Ø‰AàˆAÜ�A˜$ Ó)ˆØÑˆ�3Ø�6�QŒ;ßÜ�ÜˆKØˆrE   )r   r   r   r   r   r­   r   r,   r-   r   r   )rž   r?   r_   r`   r¦   Úcar@   ÚnaÚcbrA   Únbrµ   r³   r´   s   &f          @@rC   Úmpi_cos_sinr»   v  s”  ú€ Ø�D€AØ†”‡Ü”dˆ|œe¤U˜^Ð+Ð+ä�Œ	”u ”zÜ”tˆ}œu¤d˜mÐ+Ð+Ø	��€BÜ! !Ó(�J€BˆBÜ! !Ó(�J€BˆBÜ˜"˜Ó"�F€BÜ˜"˜Ó"�F€Bà	„xØà	��AŒÜ”tˆ}œu¤d˜mÐ+Ð+ð ˆq�5�B˜•EŒ>ÜˆBàˆq�D�1�9˜˜A� �	Ô!ÜˆBàˆq�D�1�9˜˜A� �	Ô!ÜˆBàˆq�D�1�9˜˜A� �	Ô!ÜˆBäœ "�¬°"­Õ5¸°sÓ;€DÜœ "�¬°"­Õ5¸°sÓ;€D÷ñ 
�"”kÓ	"€BÙ	�"”mÓ	$€BÙ	�"”kÓ	"€BÙ	�"”mÓ	$€BØˆ7�R�GÐÐrE   c                 ó&   € \        W4      ^ ,          # rs   ©r»   ©rž   r?   s   &&rC   Úmpi_cosr¿   ª  ó   € Ü�qÓ Õ"Ð"rE   c                 ó&   € \        W4      ^,          # ©ri   r½   r¾   s   &&rC   Úmpi_sinrÃ   ­  rÀ   rE   c                 óB   € \        W^,           4      w  r#\        W2V4      # r—   ©r»   r   ©rž   r?   ÚcosÚsins   &&  rC   Úmpi_tanrÉ   °  ó   € Ü˜1 2�gÓ&�H€CÜ�3˜TÓ"Ð"rE   c                 óB   € \        W^,           4      w  r#\        W#V4      # r—   rÅ   rÆ   s   &&  rC   Úmpi_cotrÌ   ´  rÊ   rE   c                 óŽ  € V^,           p\        W\        4      p\        W\        4      p\        W\        4      p\        V\        4      '       g   Q hV'       dI   \        \        \        V4      \        V4      4      W\        4      p\        V\        ^d4      V\        4      p\        WQV\        4      p\        WaV\        4      pWx3# r—   )r!   r   r   r   r   r'   r£   r"   r)   r   r&   r%   )	rž   rŸ   Úpercentr?   r¦   ÚxaÚxbr_   r`   s	   &&&&     rC   Úmpi_from_str_a_brÑ   ¸  s™   € Ø	��€BÜ	�!œÓ	%€BÜ	�!œÓ	'€Bä�œÓ&€AÜ�!”U×ÒÐÐßÜ”Cœ ›¤W¨R£[Ó1°1¼-ÓHˆÜ�A”x “} b¬-Ó8ˆÜ��tœ[Ó)€AÜ��tœ]Ó+€AØˆ4€KrE   c                ó  € \        RV ,          4      pV P                  RR4      p V^,           pRV 9   d!   V P                  R4      w  rE\        WERV4      # RV 9   dv   V ^ ,          R8X  g   RV 9  d   VhV P                  RR4      p RpRV 9   d%   V R,          R8w  d   VhR	pV P                  RR4      p V P                  R4      w  rE\        WEWa4      # R
V 9   Ed   RV 9  g   RV 9  d   VhV ^ ,          R8X  d[   V P                  RR4      p V P                  RR4      p V P                  R
4      w  rx\	        Wq\
        4      p\	        W�\        4      pWx3# V P                  R4      w  rEVP                  R
4      w  rYRV 9   d   V	P                  R4      w  r’MV	P                  R4      Rr)\	        WE,           V,           V\
        4      p\	        WI,           V,           V\        4      pWx3# \	        W\
        4      p\	        W\        4      pWx3# )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 ú+-FÚ(Ú)Ú%TÚ,r<   r=   Úerj   )Ú
ValueErrorÚreplaceÚsplitrÑ   r!   r   r   Úrstrip)
r>   r?   rÚ   r¦   rž   rŸ   rÎ   r_   r`   Úzs
   &&        rC   Úmpi_from_strrà   Æ  sÓ  € ô& 	Ð;¸aÕ?Ó@€AØ	�	‰	�#�rÓ€AØ	��€BØˆq„yØ�w‰w�t‹}‰ˆÜ  e¨TÓ2Ð2à	�ŒàˆQ�4�3Œ;˜# Qœ,ØˆGØ�I‰I�c˜2ÓˆØˆØ�!Œ8Ø��u˜Œ|Ø�ØˆGØ—	‘	˜#˜rÓ"ˆAØ�w‰w�s‹|‰ˆÜ  gÓ4Ð4Ø	��Ø�qŒL˜c¨œlØˆGØˆQ�4�3Œ;à—	‘	˜#˜rÓ"ˆAØ—	‘	˜#˜rÓ"ˆAØ—7‘7˜3“<‰DˆAÜ˜¤+Ó.ˆAÜ˜¤-Ó0ˆAØ�4ˆKð —7‘7˜3“<‰DˆAØ—7‘7˜3“<‰DˆAØ�aŒxØ—w‘w˜s“|‘��1à—x‘x “} b�1Ü˜�˜Q� ¤kÓ2ˆAÜ˜�˜Q� ¤mÓ4ˆAØ�4ˆKä�QœkÓ*ˆÜ�QœmÓ,ˆØˆtˆrE   c           	     ó  € \        V4      pV^,           pV w  rš\        W4      p\        W4      p\        W‘3/ VB p\        W¡3/ VB p\        W±3/ VB pRpV'       d   RpVw  ppVR8X  d8   \        \	        VR4      V3/ VB pVV,           R,           V,           V,           pV# VR8X  dr   V\
        8X  d   \
        pM5\        V\        ^d4      4      p\        V\        V\        ^4      4      V4      pVV,           R,           \        VV4      ,           R,           pV# VR8X  d(   VV,           R	,           V,           V,           V,           pV# VR
8X  Ed"   WÞ8X  d'   \        W‘^,           3/ VB p\        W¡^,           3/ VB pVP                  R4      p	\        V	4      ^8X  d   V	P                  R4       VP                  R4      p
\        V
4      ^8X  d   V
P                  R4       V	^,          V
^,          8X  Ed6   V	^ ,          V
^ ,          8w  dÑ   \        \        V	^ ,          4      ^,           4       F(  pV	^ ,          V,          V
^ ,          V,          8w  g   K(   M	  V	^ ,          RX V,           V	^ ,          VR ,           R	,           V,           V
^ ,          VR ,           V,           R\        \        V	^,          4      ^4      ,          ,           V	^,          ,           pV# V	^ ,          V,           V,           R\        \        V	^,          4      ^4      ,          ,           V	^,          ,           p V# VRP                  V	4      ,           R	,           V,           RP                  V
4      ,           V,           p V# \        RV,          4      h)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%)'

rÔ   rÓ   Ú	plusminusrÕ   rÎ   rÖ   z%)ÚbracketsrÙ   ÚdiffrÚ   Nz%'%s' is unknown mode for printing mpirj   )r   rk   rg   r    r*   r   r'   r   r)   rÝ   ÚlenÚappendr   ÚminÚjoinrÛ   )rž   rB   Ú
use_spacesrã   ÚmodeÚ	error_dpsÚkwargsr?   r¦   r_   r`   ÚmidÚdeltaÚa_strÚb_strÚmid_strÚspÚbr1Úbr2Ú	delta_strr>   r²   Úis   &&&&&&,                rC   Ú
mpi_to_strr÷     s  € ôP �sÓ€DØ	��€BØ�D€AÜ
�!Ó
€CÜ�aÓ€EÜ�1Ñ$˜VÑ$€EÜ�1Ñ$˜VÑ$€EÜ�SÑ( Ñ(€GØ	€BßØˆØ�H€CˆØˆ{ÔÜœ9 U¨2Ó.°Ñ>°vÑ>ˆ	Ø�b�L˜4Õ "Õ$ yÕ0ˆðH €HðG 
�Ô	Ø”%Œ<Ü‰Aô ˜œx¨›}Ó-ˆAÜ˜œ7 3¬°«Ó4°bÓ9ˆAØ�b�L˜3Õ¤¨¨9Ó!5Õ5¸Õ<ˆð8 €Hð7 
�Ô	Ø�%�K˜#Õ Õ" UÕ*¨SÕ0ˆð4 €Hð3 
��àŒ>Ü˜1 !�eÑ. vÑ.ˆEÜ˜1 !�eÑ. vÑ.ˆEà�K‰K˜ÓˆÜˆq‹6�QŒ;Ø�H‰H�RŒLØ�K‰K˜ÓˆÜˆq‹6�QŒ;Ø�H‰H�RŒLØˆQ�4�1�Q•4�<Ø��t�q˜•tŒ|Ü¤ A a¥D£	¨A¥Ö.�AØ˜•t˜A•w ! A¥$ q¥'Ö)Ùñ /ð �q•T˜"˜1�X •^ a¨¥d¨1¨2 hÕ.°Õ4°rÕ9¸A¸a½DÀÀ¸HÕDÀsÕJØœ3œs 1 Q¥4›y¨!Ó,Õ,õ-Ø/0°­tõ4�ð €Hð �a•D˜3•J Õ$ s¬3¬s°1°Qµ4«y¸!Ó+<Õ'<Õ<¸qÀ½tÕC‘ð
 €Hð �c—h‘h˜q“kÕ! CÕ'¨"Õ,¨s¯x©x¸«{Õ:¸SÕ@‰Að €Hô Ð@À4ÕGÓHÐHrE   c                 óB   € V w  r4Vw  rV\        W5V4      \        WFV4      3# rG   )ra   ©rž   rŸ   r?   r_   r`   r«   Úds   &&&    rC   Úmpci_addrû   d  ó)   € Ø�D€AØ�D€AÜ�1˜Ó¤¨¨dÓ 3Ð3Ð3rE   c                 óB   € V w  r4Vw  rV\        W5V4      \        WFV4      3# rG   )rd   rù   s   &&&    rC   Úmpci_subrþ   i  rü   rE   c                 ó6   € V w  r#\        W!4      \        W14      3# rG   )rq   ©rž   r?   r_   r`   s   &&  rC   Úmpci_negr  n  ó   € Ø�D€AÜ�1ÓœW QÓ-Ð-Ð-rE   c                 ó6   € V w  r#\        W!4      \        W14      3# rG   )rn   r   s   &&  rC   Úmpci_posr  r  r  rE   c                 ó    € V w  r4Vw  rV\        W54      p\        WF4      p\        WxV4      p	\        W64      p
\        WE4      p\        W«V4      pWœ3# rG   )rz   rd   ra   )rž   rŸ   r?   r_   r`   r«   rú   Úr1Úr2ÚreÚi1Úi2Úims   &&&          rC   Úmpci_mulr  v  sS   € à�D€AØ�D€AÜ	�‹€BÜ	�‹€BÜ	��tÓ	€BÜ	�‹€BÜ	�‹€BÜ	��tÓ	€BØˆ6€MrE   c                 ó  € V w  r4Vw  rVV^,           p\        V4      p\        V4      p	\        W‰V4      p
\        \        W54      \        WF4      V4      p\        \        WE4      \        W64      V4      p\	        WºV4      p\	        WÊV4      pW¼3# r—   )r†   ra   rz   rd   r   )rž   rŸ   r?   r_   r`   r«   rú   r¦   Úm1Úm2Úmr  r  s   &&&          rC   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€MrE   c                 ó‚   € V w  r#V^,           p\        W$4      p\        W44      w  rg\        WVV4      p\        WWV4      pW#3# r—   )r‹   r»   rz   )rž   r?   r_   r`   r¦   Úrr«   r>   s   &&      rC   Úmpci_expr  �  sF   € Ø�D€AØ	ˆb�€BÜ�‹€AÜ�qÓ�D€AÜ��dÓ€AÜ��dÓ€AØˆ4€KrE   c                 ó6   € V w  r#\        W!4      \        W14      3# rG   )r*   )rž   r•   r_   r`   s   &&  rC   Ú	mpi_shiftr  ™  s   € Ø�D€AÜ�Q‹>œ9 Q›>Ð)Ð)rE   c                 ó°   € V^,           p\        W4      p\        \        W24      p\        W4V4      p\	        W4V4      p\        VR4      p\        VR4      pWV3# )r˜   rj   )r‹   r   Úmpi_onera   rd   r  )rž   r?   r¦   Úe1Úe2r«   r>   s   &&     rC   Úmpi_cosh_sinhr  �  sW   € à	ˆb�€BÜ	�‹€BÜ	”˜"Ó	!€BÜ�˜Ó€AÜ�˜Ó€AÜ�!�RÓ€AÜ�!�RÓ€AØˆ4€KrE   c                 óš   € V w  r#V^
,           p\        W$4      w  rV\        W44      w  rx\        WWV4      p	\        WhV4      p
V	\        V
4      3# ©é
   )r»   r  rz   rq   ©rž   r?   r_   r`   r¦   r«   r>   ÚchÚshr  r  s   &&         rC   Úmpci_cosr"  ¨  sP   € Ø�D€AØ	ˆb�€BÜ�qÓ�D€AÜ˜1Ó!�F€BÜ	�˜Ó	€BÜ	�˜Ó	€BØŒw�r‹{ˆ?ÐrE   c                 ó†   € V w  r#V^
,           p\        W$4      w  rV\        W44      w  rx\        WgV4      p	\        WXV4      p
Wš3# r  )r»   r  rz   r  s   &&         rC   Úmpci_sinr$  ±  sI   € Ø�D€AØ	ˆb�€BÜ�qÓ�D€AÜ˜1Ó!�F€BÜ	�˜Ó	€BÜ	�˜Ó	€BØˆ6€MrE   c                 óÊ   € V w  r#V\         8X  d   \        V4      # V\         8X  d   \        V4      # \        V4      p\        V4      p\        W#V^,           4      p\	        WA4      # r—   )Úmpi_zerorx   r†   ra   r�   )rž   r?   r_   r`   rJ   s   &&   rC   Úmpci_absr'  º  sX   € Ø�D€AØŒH„}Ü�q‹zÐØŒH„}Ü�q‹zÐä�1‹€AÜ�1‹€AÜ��d˜2•gÓ€AÜ�AÓÐrE   c                 óz  € V w  r4Vw  rVY4u;8X  d   \         8X  d+   M M'\        V\         4      '       d   \        # \        V4      # \        V\         4      '       dy   \        V\         4      '       d   \	        W6V\
        4      pM\	        W5V\
        4      p\        V\         4      '       d   \	        WEV\        4      pWx3# \	        WFV\        4      p Wx3# \        V\         4      '       dQ   \	        W5V\        4      p\        V\         4      '       d   \	        WFV\
        4      pWx3# \	        W6V\
        4      p Wx3# \        V\         4      '       dQ   \	        WEV\
        4      p\        V\         4      '       d   \	        W6V\        4      pWx3# \	        WFV\        4      p Wx3# \        V\        4      p\        V4      pWx3# rG   )
r   r   r&  r‰   r2   r   r   r   r3   r#   )	rŸ   rž   r?   ÚyaÚybrÏ   rÐ   r_   r`   s	   &&&      rC   Ú	mpi_atan2r+  Æ  s|  € Ø�F€BØ�F€Bà	Ö”5×Ü�"”e×ÒÜˆOÜ�d‹|Ðäˆb”%×ÒÜ�"”e×ÒÜ˜" $¬Ó4‰Aä˜" $¬Ó4ˆAÜ�"”e×ÒÜ˜" $¬Ó6ˆAð* ˆ4€Kô' ˜" $¬Ó6‰Að& ˆ4€Kô# 
�”E×	Ò	Ü�b˜d¤MÓ2ˆÜ�"”e×ÒÜ˜" $¬Ó4ˆAð ˆ4€Kô ˜" $¬Ó4‰Að ˆ4€Kô 
�”E×	Ò	Ü�b˜d¤KÓ0ˆÜ�"”e×ÒÜ˜" $¬Ó6ˆAð ˆ4€Kô ˜" $¬Ó6‰Að
 ˆ4€Kô �4œÓ'ˆÜ�A‹JˆØˆ4€KrE   c                 ó"   € V w  r#\        W2V4      # rG   )r+  )rß   r?   rž   rŸ   s   &&  rC   Úmpci_argr-  ì  s   € Ø�D€AÜ�Q˜4Ó Ð rE   c                 ó^   € V w  r#\        \        W^,           4      V4      p\        W4      pWE3# r—   )rŽ   r'  r-  )rß   r?   rž   rŸ   r  r  s   &&    rC   Úmpci_logr/  ð  s/   € Ø�D€AÜ	”˜! "�WÓ% tÓ	,€BÜ	�!Ó	€BØˆ6€MrE   c           	      ó2  € Vw  r4V\         8X  da   Vw  rVWV8X  dW   Vw  rxršV'       d2   V	^ 8¼  d+   \        V RV,          \        W‰,          4      ,          V4      # V\        8X  d   \        V ^ V4      # V^,           p\	        \        V\        W4      V4      V4      # r¥   )r&  Úmpci_pow_intÚintr   r  r  r/  )rž   rŸ   r?   ÚyreÚyimr)  r*  r§   r¨   r©   rª   r¦   s   &&&         rC   Úmpci_powr5  ö  s†   € à�H€CØ
Œh„Ø‰ˆØŒ8Ø!#ÑˆD�sß�s˜a”xÜ# A¨¨T¥z´C¸½³MÕ'AÀ4ÓHÐHà”UŒ{Ü# A q¨$Ó/Ð/Ø	ˆb�€BÜ”H˜Q¤¨£°Ó4°dÓ;Ð;rE   c                 ó~   € V w  r#\        \        V4      \        V4      V4      p\        W#V4      p\        V^4      pWE3# rÂ   )rd   r†   rz   r  )rž   r?   r_   r`   r  r  s   &&    rC   Úmpci_squarer7    s>   € Ø�D€Aä	”˜A“¤
¨1£¨tÓ	4€BÜ	��tÓ	€BÜ	�2�qÓ	€BØˆ6€MrE   c           	      ó”  € V^ 8  d*   \        \        \        3\        W) V^,           4      V4      # V^ 8X  d   \        \        3# V^8X  d   \	        W4      # V^8X  d   \        W4      # V^,           p\        \        3pV'       d;   V^,          '       d   \        W@V4      pV^,          p\        W4      p V^,          pKB  \	        WB4      # rs   )r  r  r&  r1  r  r7  r  )rž   r•   r?   r¦   Úresults   &&&  rC   r1  r1    s²   € Øˆ1„uÜœ¤Ð*¬L¸¸BÀÀRÅÓ,HÈ$ÓOÐOØˆA„vÜœÐ Ð ØˆA„vÜ˜Ó Ð ØˆA„vÜ˜1Ó#Ð#Ø	��€BÜ”xÐ €Fß
Øˆq�5Œ5Ü˜f¨Ó,ˆFØ��FˆAÜ˜ÓˆØ	ˆa�ŠÜ�FÓ!Ð!rE   g#+VcØb÷?gÛVcØb÷?gš™™™™™ñ?c                 ób   € V w  r#Vw  rE\        WR4      '       d   R # \        WC4      '       d   R # R# )FT)r   r   )rž   rŸ   r_   r`   r«   rú   s   &&    rC   Úmpi_overlapr;  &  s)   € Ø�D€AØ�D€AÜˆa‡|‚|™EÜˆa‡|‚|™EÙrE   c                 ó  € V w  r4V^,           pV^8X  d   \        \        V \        V4      V^ 4      # \        V\        4      '       d€   V^ 8X  d$   \        W1\        4      p\        WA\        4      pWg3# V^8X  d$   \        WA\        4      p\        W1\        4      pWg3# V^8X  d!   \        W1\        4      p\        WA\        4      pXX3# \        V\        4      '       d–   \        V\        4      '       d€   V^ 8X  d$   \        WA\        4      p\        W1\        4      pWg3# V^8X  d$   \        W1\        4      p\        WA\        4      pWg3# V^8X  d!   \        WA\        4      p\        W1\        4      pXX3# \        V \        V4      pV^ 8X  d   \        \        W�^,           ^ 4      W4      # V^8X  d   \        \        W�^,           ^4      W4      # V^8X  d/   \        \        W�^,           ^4      \!        W^,           4      V4      # XX3# r—   )Ú	mpi_gammara   r  r   Úgamma_min_br6   r   r   r7   r8   r   r   Úgamma_min_ar   rz   rd   rŽ   )	rß   r?   Útyper_   r`   r¦   r«   rú   Úznews	   &&&      rC   r=  r=  2  s×  € Ø�D€AØ	ˆb�€Bàˆq„yÜœ ¤G¨RÓ0°$¸Ó:Ð:ô ˆa”×ÒØ�1Œ9Ü˜!¤;Ó/ˆAÜ˜!¤=Ó1ˆAð0 ˆ4€Kð/ �QŒYÜ˜1¤KÓ0ˆAÜ˜1¤MÓ2ˆAð* ˆ4€Kð) �QŒYÜ˜Q¤kÓ2ˆAÜ˜Q¤mÓ4ˆAð$ ˆaˆ4€Kô! 
�”5×	Ò	œf Q¬×4Ò4Ø�1Œ9Ü˜!¤;Ó/ˆAÜ˜!¤=Ó1ˆAð ˆ4€Kð �QŒYÜ˜1¤KÓ0ˆAÜ˜1¤MÓ2ˆAð ˆ4€Kð �QŒYÜ˜Q¤kÓ2ˆAÜ˜Q¤mÓ4ˆAð ˆaˆ4€Kô	 �qœ' 2Ó&ˆØ�1Œ9œW¤Y¨t¸!µV¸QÓ%?ÀÓIÐIØ�1Œ9œW¤Y¨t¸!µV¸QÓ%?ÀÓIÐIØ�1Œ9œW¤Y¨t¸!µV¸QÓ%?ÄÈÐQRÍFÓASÐUYÓZÐZØˆaˆ4€KrE   c                 ó  € V w  w  r4w  rVYVu;8X  d   \         8X  d3   M M/V^8w  g   \        V\         4      '       d   \        WV4      \        3# V^,           pV^8w  dŸ   V^,          V^,          ,           pV^,          V^,          ,           p	V\         8w  d   \	        W‰4      p
MT	p
\        \        V4      4      p\        \        V4      4      p\	        W¼4      p\	        ^ WÚ,          4      pV\        V4      ,          pV^8X  d   \        W43\        V4      w  r4W43WV33p ^ p\        V\        4      '       d°   \        WV3\        \        34      '       d“   \        W43\        V4      WV33pV^ 8X  d   \        \!        Wñ^,           ^ 4      W4      # V^8X  d   \#        \!        Wñ^,           ^4      W4      # V^8X  d/   \%        \!        Wñ^,           ^4      \'        W^,           4      V4      # \)        V\         4      '       dJ   \+        W63V\,        4      p\+        WE3V\.        4      p\+        W53V\,        4      p\+        WF3V\.        4      pMÚ\1        V\         4      '       dJ   \+        W53V\,        4      p\+        WF3V\.        4      p\+        WE3V\,        4      p\+        W63V\.        4      pM{\+        V\         3V\.        4      p\        \3        V4      V4      '       d   \+        W53V\.        4      pM\+        W63V\.        4      p\+        WE3V\,        4      p\+        WF3V\,        4      pV^ ,          V^ ,          3V^,          V^,          33pV^8X  d'   \5        V^ ,          V4      \5        V^,          V4      3# V^8X  d   \7        V4      p\9        VV4      # )é   )r   r   r=  r&  ÚmaxÚabsr   r   ra   r  r   r>  r;  Úgamma_mono_imag_aÚgamma_mono_imag_br  Ú
mpci_gammar  rþ   r/  r   r9   r   r   r   r#   rn   r  r  )rß   r?   r@  Úa1Úa2Úb1Úb2r¦   ÚamagÚbmagÚmagÚanÚbnÚabsnÚ
gamma_sizerA  ÚminreÚmaxreÚminimÚmaximÚws   &&&                  rC   rH  rH  W  s  € ØÑ�G€R‰Wˆbð 
Ö”5×˜d aœi¬6°"´U×+;Ò+;Ü˜ $Ó'¬Ð1Ð1ð 
ˆb�€BØˆq„yØ�!�u�R˜•U�{ˆØ�!�u�R˜•U�{ˆØ”Œ;Ü�d“/‰CàˆCÜ”˜“‹_ˆÜ”˜“‹_ˆÜ�2‹{ˆÜ˜˜4�8“_ˆ
Ø
Œh�zÓ"Õ"ˆð ˆq„yÜ˜2˜'¤7¨BÓ/‰ˆ°b°W¸r¸gÐ5E°Øˆô ˆb”+×ÒÜ˜�wÔ!2Ô4EÐ F×GÒGô ˜B˜7¤G¨RÓ0°2°'Ð9ˆDØ�qŒy¤¬*°TÀ½6À1Ó*EÀqÓ!OÐOØ�qŒy¤¬*°TÀ½6À1Ó*EÀqÓ!OÐOØ�qŒy¤¬*°TÀ½6À1Ó*EÄxÐPQÐWXÕRXÓGYÐ[_Ó!`Ð`ô
 ˆb”%×ÒÜ˜b˜W b¬+Ó6ˆÜ˜b˜W b¬-Ó8ˆÜ˜b˜W b¬+Ó6ˆÜ˜b˜W b¬-Ó8‰ä	�”E×	Ò	Ü˜b˜W b¬+Ó6ˆÜ˜b˜W b¬-Ó8ˆÜ˜b˜W b¬+Ó6ˆÜ˜b˜W b¬-Ó8‰ô ˜b¤˜Z¨¬]Ó;ˆä”'˜"“+˜r×"Ò"Ü  " ¨"¬mÓ<‰Eä  " ¨"¬mÓ<ˆEÜ˜b˜W b¬+Ó6ˆÜ˜b˜W b¬+Ó6ˆà	ˆq��5˜•8Ð˜u Q�x¨¨q­Ð2Ð2€AØˆq„yÜ�q˜•t˜TÓ"¤G¨A¨a­D°$Ó$7Ð7Ð7Øˆq„yÜ�Q‹KˆÜ�A�tÓÐrE   c                 ó   € \        W^R7      # ©rC  ©r@  ©r=  ©rß   r?   s   &&rC   Úmpi_loggammar^     s   € ¤)¨A¸!Ô"<Ð<rE   c                 ó   € \        W^R7      # rZ  ©rH  r]  s   &&rC   Úmpci_loggammara  ¡  s   € ¤:¨a¸AÔ#>Ð>rE   c                 ó   € \        W^R7      # ©é   r[  r\  r]  s   &&rC   Ú
mpi_rgammare  £  s   € ¤	¨!¸Ô :Ð:rE   c                 ó   € \        W^R7      # rc  r`  r]  s   &&rC   Úmpci_rgammarg  ¤  s   € ¤¨A¸!Ô!<Ð<rE   c                 ó   € \        W^R7      # ©ri   r[  r\  r]  s   &&rC   Úmpi_factorialrj  ¦  s   € ¤9¨Q¸1Ô#=Ð=rE   c                 ó   € \        W^R7      # ri  r`  r]  s   &&rC   Úmpci_factorialrl  §  s   € ¤J¨q¸QÔ$?Ð?rE   Nrs   )Tz[]rã   é   gš™™™™™ñ¿)„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$   r%   r&   r'   r(   r)   r*   r+   r,   r-   Ú	libelefunr.   r/   r0   r1   r2   r3   r4   r5   Ú	gammazetar6   r7   r8   r9   rD   r&  r  rK   rN   rT   rW   rY   r\   ra   rd   rg   rk   rn   rq   rx   r|   r€   rz   r†   r   r‰   r‹   rŽ   r�   r’   r”   r›   r    r£   r­   r»   r¿   rÃ   rÉ   rÌ   rÑ   rà   r÷   rû   rþ   r  r  r  r  r  r  r  r"  r$  r'  r+  r-  r/  r5  r7  r1  r?  r>  Ú	gamma_minrF  rG  r;  r=  rH  r^  ra  re  rg  rj  rl  rH   rE   rC   Ú<module>rt     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
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