
    [h                     X   S SK JrJrJrJrJrJrJrJrJ	r	J
r
JrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJ r J!r!J"r"J#r#J$r$J%r%J&r&J'r'J(r(J)r)J*r*J+r+J,r,J-r-J.r.J/r/J0r0J1r1J2r2J3r3J4r4J5r5J6r6J7r7J8r8J9r9J:r:J;r;J<r<J=r=J>r>J?r?J@r@JArAJBrBJCrCJDrDJErEJFrFJGrGJHrH  S SKIJJrJJKrKJLrLJMrMJNrNJOrOJPrPJQrQJRrRJSrSJTrTJUrUJVrVJWrWJXrXJYrYJZrZJ[r[J\r\J]r]J^r^J_r_J`r`JaraJbrbJcrcJdrdJereJfrfJgrgJhrhJiriJjrjJkrkJlrlJmrmJnrnJoroJprpJqrqJrrrJsrsJtrtJuruJvrvJwrwJxrxJyryJzrzJ{r{J|r|J}r}J~r~JrJrJrJrJrJrJrJrJrJr  S SKJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJr  S SKJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJr  S SKJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJr  S SKJrJrJrJrJrJrJrJrJrJrJrJrJrJrGJ Gr GJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJ	Gr	GJ
Gr
GJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJ Gr GJ!Gr!GJ"Gr"GJ#Gr#  S SGK$GJ%Gr%GJ&Gr&GJ'Gr'GJ(Gr(GJ)Gr)GJ*Gr*GJ+Gr+GJ,Gr,GJ-Gr-GJ.Gr.GJ/Gr/GJ0Gr0GJ1Gr1GJ2Gr2GJ3Gr3GJ4Gr4GJ5Gr5GJ6Gr6  S SGK7GJ8Gr8GJ9Gr9GJ:Gr:GJ;Gr;GJ<Gr<GJ=Gr=GJ>Gr>GJ?Gr?GJ@Gr@GJAGrAGJBGrBGJCGrCGJDGrDGJEGrE  g	)
   )Hprec_to_dpsdps_to_precrepr_dps
round_downround_upround_floorround_ceilinground_nearestto_pickablefrom_pickableComplexResultfzerofnzerofonefnoneftwoftenfhalffnanfinffninfmath_float_inf	round_int	normalize
normalize1from_man_expfrom_int
to_man_expto_intmpf_ceil	mpf_floormpf_nintmpf_frac
from_floatfrom_npfloatfrom_Decimalto_floatfrom_rationalto_rationalto_fixedmpf_randmpf_eqmpf_hashmpf_cmpmpf_ltmpf_lempf_gtmpf_gempf_posmpf_negmpf_absmpf_signmpf_addmpf_submpf_summpf_mulmpf_mul_int	mpf_shift	mpf_frexpmpf_divmpf_rdiv_intmpf_modmpf_pow_intmpf_perturbto_digits_expto_strstr_to_man_expfrom_str	from_bstrto_bstrmpf_sqrt	mpf_hypot)?mpc_onempc_zerompc_twompc_half
mpc_is_infmpc_is_infnan
mpc_to_strmpc_to_complexmpc_hashmpc_conjugatempc_is_nonzerompc_addmpc_add_mpfmpc_submpc_sub_mpfmpc_posmpc_neg	mpc_shiftmpc_absmpc_arg	mpc_floormpc_ceilmpc_nintmpc_fracmpc_mul
mpc_squarempc_mul_mpfmpc_mul_imag_mpfmpc_mul_intmpc_divmpc_div_mpfmpc_reciprocalmpc_mpf_divcomplex_int_powmpc_powmpc_pow_mpfmpc_pow_intmpc_sqrtmpc_nthrootmpc_cbrtmpc_expmpc_logmpc_cosmpc_sinmpc_tan
mpc_cos_pi
mpc_sin_pimpc_coshmpc_sinhmpc_tanhmpc_atanmpc_acosmpc_asin	mpc_asinh	mpc_acosh	mpc_atanhmpc_fibonaccimpf_expj
mpf_expjpimpc_expj
mpc_expjpimpc_cos_sinmpc_cos_sin_pi)'	ln2_fixedmpf_ln2
ln10_fixedmpf_ln10pi_fixedmpf_pie_fixedmpf_e	phi_fixedmpf_phidegree_fixed
mpf_degreempf_powmpf_nthrootmpf_cbrtlog_int_fixed	agm_fixedmpf_logmpf_log_hypotmpf_expmpf_cos_sinmpf_cosmpf_sinmpf_tanmpf_cos_sin_pi
mpf_cos_pi
mpf_sin_pimpf_cosh_sinhmpf_coshmpf_sinhmpf_tanhmpf_atan	mpf_atan2mpf_asinmpf_acos	mpf_asinh	mpf_acosh	mpf_atanhmpf_fibonacci)NoConvergencemake_hyp_summatormpf_erfmpf_erfcmpf_eimpc_eimpf_e1mpc_e1
mpf_expint	mpf_ci_simpf_cimpf_simpc_cimpc_simpf_besseljnmpc_besseljnmpf_agmmpf_agm1mpc_agmmpc_agm1
mpf_ellipk
mpc_ellipk
mpf_ellipe
mpc_ellipe)&catalan_fixedmpf_catalankhinchin_fixedmpf_khinchinglaisher_fixedmpf_glaisherapery_fixed	mpf_aperyeuler_fixed	mpf_eulermertens_fixedmpf_mertenstwinprime_fixedmpf_twinprimempf_bernoullibernfracmpf_gamma_intmpf_factorialmpc_factorial	mpf_gamma	mpc_gammampf_loggammampc_loggamma
mpf_rgamma
mpc_rgammampf_harmonicmpc_harmonicmpf_psi0mpc_psi0mpf_psimpc_psimpf_zeta_intmpf_zetampc_zetampf_altzetampc_altzetampf_zetasummpc_zetasum)3mpi_strmpi_from_str
mpi_to_strmpi_eqmpi_nempi_ltmpi_lempi_gtmpi_gempi_addmpi_sub	mpi_deltampi_midmpi_posmpi_negmpi_absmpi_mulmpi_divmpi_expmpi_logmpi_sqrtmpi_pow_intmpi_powmpi_cos_sinmpi_cosmpi_sinmpi_tanmpi_cotmpi_atan	mpi_atan2mpci_posmpci_negmpci_addmpci_submpci_mulmpci_divmpci_powmpci_absr  mpci_expmpci_logmpci_cosmpci_sin	mpi_gamma
mpci_gammampi_loggammampci_loggamma
mpi_rgammampci_rgammampi_factorialmpci_factorial)trailingbitcountnumeralbin_to_radixisqrtisqrt_small
isqrt_fast
sqrt_fixedsqrtremifibifaclist_primesisprimemoebiusgcdeulernum	stirling1	stirling2)gmpysageBACKENDSTRICTMPZMPZ_TYPEMPZ_ZEROMPZ_ONEMPZ_TWO	MPZ_THREEMPZ_FIVE	int_typesHASH_MODULUS	HASH_BITSN(F  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-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   libmpcrK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   	libelefunr   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   libhyperr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   	gammazetar   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   libmpir   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  r  r  r  r  r  r   
libintmathr!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  backendr3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@       M/var/www/auris/envauris/lib/python3.13/site-packages/mpmath/libmp/__init__.py<module>rL     s                                     < < < < < < < < < < <2 2 2 2 2 2 2	6 	6 	6 	6 	6 	6 	6 	6 	6 	6: : : : : : : : : : : : : : : : : : : : : : :F F F F F F F F F F       rJ  