
    g|-                     z   d dl mZmZ ed             Zed             Zed             Zed             Zed d            Zed             Zed	             Z	ed!d            Z
ed!d            Zed"d            Zed#d            Zed$d            Zed$d            Zed$d            Zed             Zed$d            Zed             Zed             Zed             Zed             Zed             Zed             Zed             Zed             Zed             Zed             Zed             ZdS )%   )defundefun_wrappedc                    |                      |d          }d|                     | j                  z  |z  |                     dd|          z  }|                     |          s|                     |          | j        z  }|S )N   r   r      r   square_exp_argsqrtpihyp1f1_re_imjctxzz2vs       Y/var/www/html/ai-engine/env/lib/python3.11/site-packages/mpmath/functions/expintegrals.py_erf_complexr      sv    			Ar	"	"B	
388CF	QE%!<!<<A771:: GGAJJsuH    c                    |                      |          dk    ru|                     |          }|                     |d          }|                     |          |                     | j                  z  |                     dd|          z  }nd|                     |          z
  }|                     |          s d| 	                    |          | j
        z  z   }|S )Nr   Texactr   r   )rer   fnegexpr   r   hyperur   r   r   r   )r   r   r   nz2r   s        r   _erfc_complexr#      s    
vvayy1}}""hhrh&&GGCLL#&)))CJJuUB,G,GG  ###771:: cggajjHr   c                    |                      |          }|                     |          r&	 |                     |          S # t          $ r Y nw xY w|                     |          rH|j        sA	  t          |          |                     |j                            S # t          $ r Y nw xY w|                     |          S N)	convert_is_real_type_erfNotImplementedError_is_complex_typeimagtyperealr   r   r   s     r   erfr/      s    AA
 	88A;;" 	 	 	D	
A qv 	477388AF++,,," 	 	 	D	A#   A 
AA./B 
B+*B+c                    |                      |          }|                     |          r&	 |                     |          S # t          $ r Y nw xY w|                     |          rH|j        sA	  t          |          |                     |j                            S # t          $ r Y nw xY w|                     |          S r%   )	r&   r'   _erfcr)   r*   r+   r,   r-   r#   r.   s     r   erfcr3   '   s    AA
 	99Q<<" 	 	 	D	
A qv 	477399QV,,---" 	 	 	D	Qr0   Fc                     | j         dz  dz   }|r6|                     |||          }|                     | j        ||          }n|                     |||          }|dk    r|                     ||d          }|S )N      )precr   Tr   )r7   fmulfdivone)r   r   mult
reciprocalr7   r   s         r   r   r   6   s    8A:b=D 'XXaX&&XXcgrX--XXaX&&qyyXXb$dX++Ir   c                    |s|S |                      |          }d|                     | j                  z  |z  |                     dd|          z  }|                     |          s|                     |          | j        z  }|S )Nr   r   r	   r   r   s       r   erfir>   B   s     			A		B	
388CF	A	E5"!=!==A771:: GGAJJsuHr   c                 j                                    }|k    s|dk     s|dk    r                     d          S |sS dk    r j        S dk    r j        S t	                    dk     rddz  z  dz  z   }n                     d j        z  t	                    dz
  dz  z            }                                                    |                     |          z
            z                       d          z  } xj	        d	z  c_	         
                     fd
|          S )Nr   r   z*erfinv(x) is defined only for -1 <= x <= 1g?goe1?r
   gϷ?r   
   c                 4                         |           z
  S r%   )r/   )tr   xs    r   <lambda>zerfinv.<locals>.<lambda>]   s    #''!**Q, r   )r   
bad_domaininfninfabslnr   signr   r7   findroot)r   rC   xreaus   ``   r   erfinvrO   L   s,   
''!**CqcBhhC!GG~~JKKKAQhAvvcg~Bwwsx
1vv||AqDL8A:% FF1SV8SVVAXM)**HHQKK#((1svvayy=111#((1++=HHNHH<<.....222r       c                     |                      |          }|                     ||z
  dz   d|dz  z  z            ||                     d| j        z            z  z  S )Nr   )r&   r    r   r   )r   rC   musigmas       r   npdfrT   _   sX    KKE77QrTAI:qz*++uSXXah5G5G/GHHr   c                     ||z
  ||                      d          z  z  }|dk     r|                     |           dz  S d|                     |          z   dz  S )Nr   rP   r   )r   r3   r/   )r   rC   rR   rS   rM   s        r   ncdfrV   d   sW    	
2chhqkk!"A1uuxx||A~#''!**ar   c                 D   ||k    rd}n|sK|dk    r|dk    r|                      ||          }n||z  |                     |d|z
  |dz   |          z  |z  }n|                     |          \  }}|dk    r@|| j         k     r| j        
 }	| xj        dz  c_        ||	z  }n|dk     r| xj        |z  c_        ||z  |                     |d|z
  |dz   |          z  }
||z  |                     |d|z
  |dz   |          z  }|
|z
  |z  }|r||                      ||          z  }|S )NrP   r   r   )betahyp2f1nint_distancer7   eps)r   rM   bx1x2regularizedr   mdhs1s2s               r   betaincrf   l   sU   	Rxx 77rQwwAAAA

1ac1Q3333a7AA  ##166CH9}}WHAQRAUSZZ!A#ac"---USZZ!A#ac"---"WM 	SXXa]]Hr   Nc                    t          |          }|                     |          }|
| j        }d}n |                     |          }|| j        k    }|
| j        }d}n |                     |          }|| j        k    }|s`|s^|rG|                     |          dk     r| j        S |                     |          dk    r| j        S | j        S |                     |          S ||k    r| j        S |                     |          |                     |          k    r|                     ||||           S |r|r| 	                    ||||          
 S |r| 
                    |||          S |r|                     |||          S d S )NFrP   )boolr&   zerorF   r   r:   nangammagammainc_gamma3_upper_gamma_lower_gamma)r   r   rM   r]   r`   lower_modifiedupper_modifieds          r   rl   rl      s   {##KAAyHKKNNchyGKKNNcg n  	vvayy1}}wQwwyy||Avvx
vvayy366!99Q1k2222 3. 3Aq![1111	 31k222	 31k2223 3r   c                                            |          r t          |           j                  S |g|z                       d           fd}                     ||g          S )NTr   c                 X                                   | gd| dgg dgd| z   gf}|fS )Nr   r   r    )r   T1Gr]   r   negbs     r   rc   z_lower_gamma.<locals>.h   s=    ggdmmQ"Q2JAsQqSE1Dur   )isnpintr,   rF   r   	hypercomb)r   r   r]   r`   rc   rv   rw   s   ` `  @@r   ro   ro      s     {{1~~  tAwwsw	
kA88AT8""D        ==QC   r   c                                           |          r	 |r                     |          r t          |           j                  S  j        }	  xj        dz  c_                             |                               |          z  | _        S # | _        w xY w                     |          S # t          $ r Y nw xY w|dk    rdk    r|z   dz  S |dk    rdk    sdk    r|z   dz  S                      d	          |g|z  	  fd
} 	                    ||gd          S #  j
        $ r"  fd} 	                    ||g          cY S w xY w)Nr@   r   r   rP   r
   y            y            ?Tr   c                 \    | dz
  }                               gd|gg d| gg dz  fgS Nr   rt   )r   rrv   rM   r   negas     r   rc   z_upper_gamma.<locals>.h   sA    !AggdmmQ'!QQQBQtVLMMr   )force_seriesc                 z    g d| dz
  g| gg g df}                                | gd| dgg dgd| z   gf}||fS )Nr   rP   r   rt   )r   ru   T2rv   rM   r   r~   s      r   rc   z_upper_gamma.<locals>.h   s_    a1XsAr2q0B774==.!Q'!QRQC!A#IBr6Mr   )isintrx   r,   ri   r7   _gamma_upper_intrk   r)   r   ry   NoConvergence)r   r   rM   r`   origrc   rv   r~   s   ` `   @@r   rn   rn      s    yy|| 	 2;;q>> -"47738,,,x$HHNHH//155		!D#CHHtCHOOOO++Aq111" 	 	 	D	 	Avv!r''!QwAvv1::e!Qw88AT8""D	
kA
%	N 	N 	N 	N 	N 	N 	N 	N }}Q$}777 % % %	 	 	 	 	 	 	 	 }}Q$$$$$%sA   3B< B< ;B B< 	B##B< <
C	C	 D9 9)E%$E%c                    |                      |          }|r	|r| j        S 	 | xj        dz  c_        |                     |||          }|                     |||          }||z
  }|                     |          t          |                     |          |                     |                    z
  dk    r|| xj        dz  c_        S |sJ|                     |d||          }|                     |d||          }||z
  }	 || xj        dz  c_        S 	 | xj        dz  c_        n# | xj        dz  c_        w xY wt          )N   )r`   irP   )rx   ri   r7   rl   magmaxr)   )	r   r   rM   r]   r`   poleru   r   Rs	            r   rm   rm      sU   ;;q>>D t xB \\!QK\88\\!QK\88G771::CGGBKK555;; 	B  	aA;??BaA;??BRAB	 	BB
s   BD' 	;D' 'D9c                    |                      |          r<|                     |          r'	 |                     ||          S # t          $ r Y nw xY w|                     |          s|                     |          r||z  S || j        k    rd|z  S |dk    rC|                     |          dk    r t          |          | j                  S | j        |dz
  z  S |dk    r| 	                    |           |z  S |dk    r"| 	                    |           |dz   z  |dz  z  S ||dz
  z  | 
                    d|z
  |          z  S )Nr   rP   r   r   )r   r'   _expint_intr)   isnanrF   r   r,   r:   r    rl   )r   nr   s      r   expintr      sW   
yy|| ))!,, 	??1a(((" 	 	 	D	
yy|| syy|| s
CG||s
Avv66!99>>47737###7AaC= Avvwwr{{1}Bwwwwr{{AaC A%%qs8cll1Q3****s   A 
AAc                    |rP|dk    r| j         S |                     |                     |                    |                     | j                  z
  S |s|S |dk    r| j        S |                     |                     |                    S )Nr   r   )ri   eirI   ln2rG   )r   r   offsets      r   lir     s     3668OvvcffQii  366#'??22 Avvx66#&&))r   c                 x    	 |                      |          S # t          $ r |                     |          cY S w xY wr%   )_eir)   _ei_genericr.   s     r   r   r     J    "wwqzz " " "q!!!!!"    99c                    || j         k    r|S || j        k    r| j        S |                     |          dk    r	 | j        |z  }|                     |          |                     ddgg || j        d          z  |z  }|                     |          }|dk    r|| j	        | j
        z  z  }|dk     r|| j	        | j
        z  z  }|S # | j        $ r Y nw xY w||                     dddd|          z  | j        z   }|                     |          r:|d|                     |          |                     | j        |z            z
  z  z  }n%||                     t          |                    z  }|S )Nr   T)maxtermsr   rP   r         ?)rF   rG   ri   r   r:   r    hyperr7   r   r   r   r   hyp2f2eulerlogrH   )r   r   r}   r   ims        r   r   r   &  s    	CG||CH}}x
wwqzzA~~		A

399aU2a % 6 6 6678ABAvvSVCE\!AvvSVCE\!H  	 	 	D		#**Qq1Q

#)+A
wwqzz 	S#''!**swwswqy11122	SWWSVV__Hs   B
C 
CCc                 z    	 |                      |          S # t          $ r |                     d|          cY S w xY wr|   )_e1r)   r   r.   s     r   e1r   B  sL     wwqzz      zz!Q s     ::c                 x    	 |                      |          S # t          $ r |                     |          cY S w xY wr%   )_cir)   _ci_genericr.   s     r   cir   I  r   r   c                    |                      |          r'|| j        k    r| j        S || j        k    r
| j        dz  S |                     | j        |d          }|                     |d          }d|                     |          |                     |          z   z  }| 	                    |          }| 
                    |          }|dk    r&|dk    r|| j        dz  z  }|dk     r|| j        dz  z  }|dk     r&|dk    r|| j        dz  z  }|dk     r|| j        dz  z  }|                     |          r|dk    r| 	                    |          }|S )N              ?Tr   r   rP                 ?)isinfrF   ri   rG   r   r8   r   r   r   r   r   r'   )r   r   jznjzr   zrealzimags          r   r   r   P  sL   
yy|| +<<==*	#%	%	%B
((2D(
!
!CSVVBZZ#&&++%&AGGAJJEGGAJJEzz199a36$;&a199a36$;&aqyyA::qCF2I~qA::qCF2I~q
 		GGAJJHr   c                 x    	 |                      |          S # t          $ r |                     |          cY S w xY wr%   )_sir)   _si_genericr.   s     r   sir   d  r   r   c                    |                      |          r*|| j        k    r
d| j        z  S || j        k    r
d| j        z  S |                     |          dk    r|                     | j        |d          }|                     |d          }d|                     |          |                     |          z
  z  }| 	                    |          }|dk    r|d| j        z  z  }|dk     r|d| j        z  z  }| 
                    |          r| 	                    |          }|S ||                     dd	d	d
|z  |z            z  S )Nr         r   Tr   y             rP   r   r	   g      п)r   rF   r   rG   r   r8   r   r   r   r   r'   hyp1f2)r   r   r   r   r   r   s         r   r   r   k  s4   
yy|| -<<CF
*==cf,
wwqzzRXXceADX))hhrh%%SVVBZZ#&&++-.

199SVOA199SVOAQ 	

AE%eAgai8888r   c                 Z   |                      |d          }d|                     |          |                     |          z   z  }|                     |          }|                     |          }|dk    r|| j        dz  z  }n'|dk     r|| j        dz  z  }n|dk     r|| j        dz  z  }|S )NTr   r   rP   r   r   )r   r   r   r   r   )r   r   nzr   r   r   s         r   chir     s    	!4	 	 BSVVAYY#$AGGAJJEGGAJJEqyy	SVD[		SVD[		SVBYHr   c                 z   |                      |          dk    r|                     |d          }d|                     |          |                     |          z
  z  }|                     |          }|dk    r|d| j        z  z  }|dk     r|d| j        z  z  }|S ||                     dddd	|z  |z            z  S )
Nr   Tr   r   rP   r   r   r	   g      ?)r   r   r   r   r   r   )r   r   r   r   r   s        r   shir     s     wwqzzRXXatX$$SVVBZZ'(

199a4;&a199a4;&a3::eE%Qq9999r   c           	          || j         k    r|                     d          S || j        k    r|                     d          S | j        |dz  z  dz  |                     ddd| j        dz   |d	z  z  d
z            z  S )Nr   r   r
      )r
   r5   r	   )   r5   r   r5      )rF   mpfrG   r   r   r.   s     r   fresnelsr     sx    CG||wws||CH}}wwt}}6!Q$;q=E%svqyjAob6HIIIIr   c           	          || j         k    r|                     d          S || j        k    r|                     d          S ||                     ddd| j        dz   |dz  z  dz            z  S )	Nr   r   )r   r5   r   )   r5   r   r5   r   )rF   r   rG   r   r   r.   s     r   fresnelcr     sj    CG||wws||CH}}wwt}}SZZeE3619*QT/"*<====r   )r   F)rP   r   )rP   r   F)rP   NF)F)	functionsr   r   r   r#   r/   r3   r   r>   rO   rT   rV   rf   rl   ro   rn   rm   r   r   r   r   r   r   r   r   r   r   r   r   r    r   r   <module>r      s4   + + + + + + + +   	 	 	          	 	 	 	    3 3 3$ I I I I            0 &3 &3 &3 &3P 	! 	! 	! 	! $% $% $% $%L    2 + + +. 	 	 	 	 " " "   6       " " "   & " " " 9 9 9(    
: 
: 
: J J J > > > > >r   