K i|-ddlmZmZedZedZedZedZeddZedZedZ edd Z edd Z ed d Z ed!d Z ed"dZed"dZed"dZedZed"dZedZedZedZedZedZedZedZedZedZedZedZy )#)defun defun_wrappedc|j|d}d|j|jz |z|jdd|z}|j |s|j ||j z}|S)Nrrrsquare_exp_argsqrtpihyp1f1_re_imjctxzz2vs c/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/mpmath/functions/expintegrals.py _erf_complexrsh  Ar "B 388CFF  QE%!<Bsn   A B 388CFF  A E5"!==A 771: GGAJsuu  Hrc6j}|k7s |dks|dkDrjdS|sSdk(r jSdk(r jSt dkrddzzdzz}nwj dj z t dz dzz }jj|j |z zjdz }xjd z c_ jfd |S) Nrrz*erfinv(x) is defined only for -1 <= x <= 1g?goe1?r gϷ?r c,j|z Sr%)r/)trxs rzerfinv..]s#''!*Q,r) r bad_domaininfninfabslnrsignr r7findroot)rrCxreaus`` rerfinvrOLs ''!*C qcBhC!G~~JKK A QhAvcgg~Bwsxx 1v| AqDL8A: % FF1SVV8SVAXM) * HHQK#((1svvay=1 1#((1+ =HHNH <<. 22rc|j|}|j||z dz d|dzzz ||jd|jzzz S)Nr)r&r r r)rrCmusigmas rnpdfrS_sQ KK E 77QrTAI:qz* +uSXXah5G/G HHrc||z ||jdzz }|dkr|j| dz Sd|j|zdz S)Nrr)r r3r/)rrCrQrRrMs rncdfrVdsO 2chhqk!"A1uxx|A~#''!* arc0||k(rd}n|sA|dk(r|dk(r|j||}n||z|j|d|z |dz|z|z }n|j|\}}|dkrR||j kr(|j} |xjdzc_|| z }n|dkr|xj|zc_||z|j|d|z |dz|z} ||z|j|d|z |dz|z} | | z |z }|r||j||z}|S)NrUrr)betahyp2f1 nint_distancer7eps) rrMbx1x2 regularizedrmdhs1s2s rbetaincrfls' Rx   7rQwAAA 1ac1Q333a7A  #1 6CHH9}WWHA QRA  USZZ!A#ac"- - USZZ!A#ac"- - "WM SXXa] HrNct|}|j|}||j}d}n |j|}||jk7}||j}d}n |j|}||jk7}|sa|s_|rL|j |dkr |jS|j |dkDr |j S|j S|j|S||k(r |jS|j ||j |kDr|j|||| S|r|r|j||||S|r|j|||S|r|j|||Sy)NFrU) boolr&zerorFrr:nangammagammainc_gamma3 _upper_gamma _lower_gamma)rrrMr]r`lower_modifiedupper_modifieds rrlrlsT{#K AAy HH KKNchhy GG KKNcgg n vvay1}wwQwwwwyy|Avxx vvay366!9 Q1k222. Aq![111 1k22 1k22 rcj|rt|jS|g|zjdfd}j ||gS)NTrcPj|gd|dggdgd|zgf}|fS)Nrrr )rT1Gr]rnegbs rrcz_lower_gamma..hs;ggdmQ "Q2JAsQqSE1 Du r)isnpintr,rFr hypercomb)rrr]r`rcrvrws` ` @@rroros] {{1~tAwsww kA 88AT8 "D ==QC  rcj|r |ryj|rt|jSj} xjdz c_j |j |z |_Sj |S|dk(r dk(r|zdzS|dk(rdk(sdk(r|zdzSjd |g|z fd }j||gd S#|_wxYw#t$rYwwxYw#j$rfd }j||gcYSwxYw) Nr@rrrUr yy?TrcT|dz }jgd|ggd| ggdz fgSNrrt)rrrvrMrnegas rrcz_upper_gamma..hs?!AggdmQ'!QQQBQtVLM Mr) force_seriescrgd|dz g|gggdf}j |gd|dggdgd|zgf}||fS)NrrUrrt)rruT2rvrMrr~s rrcz_upper_gamma..hs]a1XsAr2q0B774=.!Q'!QRQC!A#IBr6Mr) isintrxr,rir7_gamma_upper_intrkr)rry NoConvergence)rrrMr`origrcrvr~s` ` @@rrnrnsV yy| ;;q>"47388,,xx$HHNH//15 ! D#CH++Aq11 Av!r'!QwAv1:e!Qw 88AT8 "D kA % N}}Q$}77# $CH#      % }}Q$$ %sG-D D8D DD'D D  D DD*E  E ct|j|}|r|r |jS |xjdz c_|j|||}|j|||}||z }|j |t |j ||j |z dkDr||xjdzc_S|sG|j|d||}|j|d||}||z } ||xjdzc_S |xjdzc_t #|xjdzc_wxYw)N)r`irU)rxrir7rlmagmaxr)) rrrMr]r`polerurRs rrmrms ;;q>Dtxx B\\!QK\ 8 \\!QK\ 8 G 771:CGGBK5 5 ; BaA;?BaA;?BRA B B  BsBD ;3D D7cB|j|r$|j|r |j||S|j |s|j |r||zS||j k(rd|z S|dk(rA|j |dkrt||j S|j|dz z S|dk(r|j| |z S|dk(r|j| |dzz|dzz S||dz z|jd|z |zS#t$rYwxYw)NrrUrr) rr' _expint_intr)isnanrFrr,r:r rl)rnrs rexpintrs yy|))!, ??1a( ( yy|syy|s CGG|s Av 66!9>47377# #77AaC= Avwwr{1}Bwwwr{AaC A%% qs8cll1Q3* **##   sD DDc |rM|dk(r |jS|j|j||j|jz S|s|S|dk(r |jS|j|j|S)Nrr)rieirIln2rG)rroffsets rlirsl 688OvvcffQi 366#''?22 Avxx 66#&&) rcf |j|S#t$r|j|cYSwxYwr%)_eir) _ei_genericr.s rrr3"wwqz "q!!" 00c||jk(r|S||jk(r |jS|j|dkDr |j|z }|j ||j ddgg||jdz|z }|j|}|dkDr||j|jzz }|dkr||j|jzz}|S||jdddd|z|jz}|j|r8|d|j||j|j|z z zz }|S||jt|z }|S#|j$rYwxYw)NrT)maxtermsrrUr?)rFrGrirr:r hyperr7rrrrhyp2f2eulerlogrH)rrr}rims rrr&sn CGG|CHH}xx wwqzA~  A 399aU2a%66678ABAvSVVCEE\!AvSVVCEE\!H #**Qq1Q #))+A wwqz S#''!*swwswwqy11 22 H SWWSV_ H     sBE**E<;E<ch |j|S#t$r|jd|cYSwxYwr|)_e1r)rr.s re1rBs5 wwqz  zz!Q s 11cf |j|S#t$r|j|cYSwxYwr%)_cir) _ci_genericr.s rcirIrrc|j|r9||jk(r |jS||jk(r|jdzS|j |j |d}|j|d}d|j||j|zz}|j|}|j|}|dk(r.|dkDr||jdzz }|dkr||jdzz}|dkr.|dk\r||jdzz }|dkr||jdzz}|j|r|dkDr|j|}|S)N?TrrrU?) isinfrFrirGrr8rrrrrr')rrjznjzrzrealzimags rrrPs- yy| < =* #%% %B ((2D( !C SVVBZ#&&+ %&A GGAJE GGAJE z 19a366$;&a 19a366$;&a qy A:qCFF2I~q A:qCFF2I~q  GGAJ Hrcf |j|S#t$r|j|cYSwxYwr%)_sir) _si_genericr.s rsirdrrcr|j|r<||jk(rd|jzS||jk(rd|jzS|j |dk\r|j |j |d}|j|d}d|j||j|z z}|j|}|dkDr|d|jzz}|dkr|d|jzz }|j|r|j|}|S||jdd d d |z|zzS) NrrTryrUrr gп) rrFrrGrr8rrrrr'hyp1f2)rrrrrrs rrrks yy| <CFF * =cff, wwqzR XXceeADX )hhrh% SVVBZ#&&+- .  19 SVVOA 19 SVVOA   Q  AE%eAgai888rcN|j|d}d|j||j|zz}|j|}|j|}|dkDr||jdzz }|S|dkr||jdzz}|S|dkr||jdzz }|S)NTrrrUrr)rrrrr)rrnzrrrs rchirs !4 B SVVAY #$A GGAJE GGAJE qy SVVD[ H  SVVD[ H  SVVBY HrcX|j|dk\rz|j|d}d|j||j|z z}|j|}|dkDr|d|jzz}|dkr|d|jzz }|S||j dddd |z|zzS) NrTrrrUrrr g?)rrrrrr)rrrrrs rshirs wwqzR XXatX $ SVVBZ' (  19a4;&a 19a4;&a3::eE%Qq999rc ||jk(r|jdS||jk(r|jdS|j|dzzdz |j ddd|jdz |d zzd z zS) Nrrr )r r5r )r5rr5)rFmpfrGrrr.s rfresnelsrsuCGG|wws|CHH}wwt} 66!Q$;q=E%svvqyjAob6HI IIrc ||jk(r|jdS||jk(r|jdS||jddd|jdz |dzzdz zS) Nrr)rr5r)r5rr5r)rFrrGrrr.s rfresnelcrseCGG|wws|CHH}wwt} SZZeE36619*QT/"*< = ==r)rF)rUr)rUrF)rUNF)F) functionsrrrr#r/r3r r>rOrSrVrfrlrornrmrrrrrrrrrrrrrrrrs(+                33$II    0&3&3P ! !$%$%L2++.  ""   6  ""   &"" 99(     : :JJ>>r