<Zc+@sdZddlZddlZddlZdZdZdZdZdZdZ d Z d Z d Z d Z d ZdZdZdZdZy#ejddZdZWn)eefk rejZejZnXeejdZeeejZeeejZeejejZeejejZeejejZeejejZeejejZeejejZeej ej Z eej!ej!Z!eej"ej"Z"eej#ej#Z#eej$dZ$eej%dZ%eddZ&eddZ'dZ(dZ)dZ*dZ+d Z,ee*e,Z-ee)e+Z.d!Z/d"Z0dZ1e1 Z2e1e1Z3d$Z4e1d%d%d&d'd(d)d*d+d,d-d.d/d0d1d2d3d4d5d6d7d8fZ5e6e5d9Z7d:Z8dZ9dDZ:dEZ;ee:e;Z<dFZ=dGZ>dHZ?dIZ@dJdKdLdMdNdOdJdPdQdRg ZAdSZBdTZCeeBeCZDdUdVdWdXdYdZd[d\d]g dddZEd%d^d_d`dadbdcdddedfg dddZFdgZGdhZHdiZIdjZJdkZKdlZLddddddddddddddddddddd d d d d dddddddddddddddddg*ZMdZNeOdZPeOdZQeOdZRdZSdddd dddddddddddddddddddddddgZTdddddddddg dddZUd%ddddddddg dddZVdddddddddddg ZWdddddddddddg ZXdZYdS(s This module complements the math and cmath builtin modules by providing fast machine precision versions of some additional functions (gamma, ...) and wrapping math/cmath functions so that they can be called with either real or complex arguments. iNg-DT! @giW @g;f?gw@gw?g9B.?gUk@gox?g]O?g m8scss|]}t|VqdS(N(R(R R((s+lib/python2.7/site-packages/mpmath/math2.pys :s(RR(targsR(RR(s+lib/python2.7/site-packages/mpmath/math2.pyR 6s(R (RRR ((RRs+lib/python2.7/site-packages/mpmath/math2.pyt _mathfun_n5s gcCs(|dkrtdntj|S(Ngsmath domain error(Rtmathtlog(R((s+lib/python2.7/site-packages/mpmath/math2.pytmath_logBs cCs(|dkrtdntj|S(Ngsmath domain error(RRtsqrt(R((s+lib/python2.7/site-packages/mpmath/math2.pyt math_sqrtFs cCst||S(N(R(Rty((s+lib/python2.7/site-packages/mpmath/math2.pytNscCs%ttj|jtj|jS(N(RRtfloortrealtimag(tz((s+lib/python2.7/site-packages/mpmath/math2.pyR`scCs%ttj|jtj|jS(N(RRtceilRR(R((s+lib/python2.7/site-packages/mpmath/math2.pyRbscCstj|tj|fS(N(Rtcostsin(R((s+lib/python2.7/site-packages/mpmath/math2.pyRescCstj|tj|fS(N(tcmathRR(R((s+lib/python2.7/site-packages/mpmath/math2.pyRfscCs |ddS(Ng?i((R((s+lib/python2.7/site-packages/mpmath/math2.pyRhscCs |ddS(Ng?i((R((s+lib/python2.7/site-packages/mpmath/math2.pyRhscCsEd|}yt||SWn"ttfk r@t||SXdS(Ng?(RRRR(Rtntr((s+lib/python2.7/site-packages/mpmath/math2.pytnthrootjs  cCs|dkrt|  St|d\}}|t9}|d;}|dkrZtj|S|dkrstj|S|dkrtj| S|dkrtj| SdS(Nig?iiii(t _sinpi_realtdivmodtpiRRR(RRR ((s+lib/python2.7/site-packages/mpmath/math2.pyR"qs        cCs|dkr| }nt|d\}}|t9}|d;}|dkrXtj|S|dkrrtj| S|dkrtj| S|dkrtj|SdS(Nig?iiii(R#R$RRR(RRR ((s+lib/python2.7/site-packages/mpmath/math2.pyt _cospi_real|s        cCs|jdkrt|  St|jd\}}tt||j}|d;}|dkrltj|S|dkrtj|S|dkrtj| S|dkrtj| SdS(Nig?iiii( Rt_sinpi_complexR#R$RRRRR(RRR ((s+lib/python2.7/site-packages/mpmath/math2.pyR&s      cCs|jdkr| }nt|jd\}}tt||j}|d;}|dkrjtj|S|dkrtj| S|dkrtj| S|dkrtj|SdS(Nig?iiii(RR#R$RRRRR(RRR ((s+lib/python2.7/site-packages/mpmath/math2.pyt_cospi_complexs      cCseyt|t|SWnFtk r`t|jdkrAdSt|jdkrZdSnXdS(Ni y?y(tsinpitcospit OverflowErrorRR(R((s+lib/python2.7/site-packages/mpmath/math2.pyttanpis cCseyt|t|SWnFtk r`t|jdkrAdSt|jdkrZdSnXdS(Ni yy?(R)R(R*RR(R((s+lib/python2.7/site-packages/mpmath/math2.pytcotpis gu<7~gg?P5>cCst|}||krJ|dkr3tdn|tkrJt|Sn|dkrrtt|td|S|d8}td}x1tdt dD]}|t|||7}qW|t d}d||dt j | |SdS(Nisgamma function poleg?ig?ig' @( tinttZeroDivisionErrort_max_exact_gammat _exact_gammaR$R"t _gamma_realt _lanczos_ptranget _lanczos_gRtexp(Rt_intxR titt((s+lib/python2.7/site-packages/mpmath/math2.pyR1s        cCs|jstt|jS|jdkrGtt|td|S|d8}td}x1tdt dD]}|t|||7}qoW|t d}d||dt j | |SdS(Ng?ig?iig' @( RRR1RR$R&t_gamma_complexR2R3R4RR5(RR R7R8((s+lib/python2.7/site-packages/mpmath/math2.pyR9s   cCs/ydt|SWntk r*|dSXdS(Ng?g(tgammaR.(R((s+lib/python2.7/site-packages/mpmath/math2.pytrgammas cCst|dS(Ng?(R:(R((s+lib/python2.7/site-packages/mpmath/math2.pyt factorialscCs8t|tkr"tjd|Stj|j|jS(Ng(RRRtatan2RR(R((s+lib/python2.7/site-packages/mpmath/math2.pytargsc Cst|ttfkrQyt|}WqQttfk rMt|}qQXny|j}|j}Wntk r|}d}nX|dkrt|dkrt t |}|dkr|j }n|Sd|}y|j}|j}Wntk r|}d}nXt |}|dkr7d}n|dkrLd}nd}t dt|dt|tt t||t|dt ||S|dks|dkr|dSd} x0t|d kr| t |8} |d7}qWd |dt ||} d|} | | } | d | 7} | | 9} | d | 7} | | 9} | d | 7} | | 9} | d| 7} | | 9} | d| 7} | | 9} | d| 7} | | 9} | d| 7} | | 9} | d| 7} | | S(Ngg?iiiy?g?g@i gdg?gUUUUUU?gllfgJ?g88Cg#+K?g}<ٰj_gAAz?gSˆB(RRRRRRRtAttributeErrortabsRR:t conjugateRR$tlogpiR(tloggamma( RtxrealtximagtvRtretimtrefloortimsigntptsR tr2((s+lib/python2.7/site-packages/mpmath/math2.pyRCsp                S         gUUUUUU?ggAAp?gqg|?gYYg^^^^^^ܿg柛n@gLQt:cCst|}||kr6|dkr6tdq6n|dkr_d|}tt|}nd}x(|dkr|d|8}|d7}qhW|d}|}x6tD].}|||8}|dkrPn||9}qW|t|d|S( Nispolygamma poleg?g?gg$@ig#B ;(R-R.R$R,t _psi_coeffR(RR6RLtx2R8tc((s+lib/python2.7/site-packages/mpmath/math2.pyt _digamma_real;s&        cCs|jstt|jS|jdkrHd|}tt|}nd}x.t|dkr~|d|8}|d7}qQW|d}|}x<tD]4}|||8}t|dkrPn||9}qW|tj |d|S(Ng?g?gg$@ig#B ;( RRRQRR$R,R@RNRR(RRLROR8RP((s+lib/python2.7/site-packages/mpmath/math2.pyt_digamma_complexQs"    gS?g}^.@gCGb@g߸G?g1R5?gߵy?gLy~F?goO$y?gŕX3=?ga o @ghr@g-@gF@gv#o?g,?gE㦰u?g󟿑?gan$hI?cCs1|d}x |dD]}|||}qW|S(Nii((tcoeffsRRKRP((s+lib/python2.7/site-packages/mpmath/math2.pyt_polyvals cCs||}|}}d}xrt|dkr|||9}||||d8}|d7}|||9}||||d7}|d7}qWd|S(NigFFg ?gKX?g^> ǿg\S;S?gQSβ?g\S;Sg|?gM _6?g|ꢿgD@c Cs+d|}d}}d}x<|||9}||7}t|dkrKPn|d7}qW|t||}|rt|tkr|j}|j}n |}d}|dkr'|dkr'|td7}q'nUt|tkr'|jdkr|td7}n|jdkr'|td8}q'n|S(Ng?igؗҜ        $    cCst|}t|ttfkriyt|}t}Wqittfk ret|}t}qiXn|tkr|j rt|jd}nt| dt S(NgR\( RRRRRRRRotTrue(RRg((s+lib/python2.7/site-packages/mpmath/math2.pyte1Ls     gggSbQ?gH*2Q?g|ʎA?gE G?g92"?gcj?g9?g[:?gH1?g,[ ?g?g+9@?g ?gL?g9?gNe?ga;?g?g֕?g1@?g ?gZ>?g?g?gA gpgp6g|Upg%gE3+Ӿgf{g'( gѲG]g/" =g{%gh{srg9D"glXxkվg%ygծ*geuy-g]u:=gh#%.Jg`5'>>g^ҹgU3 gPF; ?g2Mg=Ƨ_ΚcgviT{?g\?gH$?ggI ;g.k^>gPNg/wogS' ?g7z2Mg)cg?g|ɐ?g?cCst|ttfsyt|}Wqttfk ry,t|}|jsftt|jSWnttfk rnXt qXn|dkrtdn|dkrdd| d| St|}||kr|dkrt |S|dsd Sn|d krRd|t |dt d |t d|td|S|dkr|dkrtt||dStt||dStt|tt|}dd| d| d | |S( s. Riemann zeta function, real argument is zeta(1) poleig?g@g@iigg?g@(t isinstanceRR-RRRRtzetaRtNotImplementedErrort _zeta_intR$R"R1RTt_zeta_0t_zeta_1t_zeta_Pt_zeta_Q(RLRR((s+lib/python2.7/site-packages/mpmath/math2.pyRss:          >  g( gP?g ö)$@gԎgشa@g]/Qfg)@gU(+gO2NNQ>g?P5>(gt?gdsp?(gtgdsp?(g+K?grҹ?(g+Kgrҹ?(gvV?g5@}?(gvVg5@}?(gL?g=Y?(gLg=Y?(gj ?g{y?(gj g{y?(gM&?gu 85?(gM&gu 85?(g?gN?(ggN?(gұ,n?gT!~?(gұ,ngT!~?(gqE?g sjΦ?(gqEg sjΦ?(gu=8| ?gr?(gu=8| gr?(gY֮sj?gʴ?(gY֮sjgʴ?(gc#?g1 ?(gc#g1 ?(g,?gN@?(g,gN@?(gԦV;?gK?(gԦV;gK?(gW99?g) ǰ?(gW99ݿg) ǰ?(gN%؟N?gۿ78a?(gN%؟Nٿgۿ78a?(gׄ ?g?(gׄ Կg?(gQ'p_?g,J?(gQ'p_пg,J?(g^> ?gKX?(g^> ǿgKX?(g\S;S?gQSβ?(g\S;SgQSβ?(g|?gM _6?(g|ꢿgM _6?(Zt__doc__toperatorRRR$tetsqrt2tsqrt5tphitln2tln10RatcatalantkhinchintaperyRBR R RRRRRRRtpowR5RRttantacostasintatantcoshtsinhttanhRRtcos_sintcbrtR!R"R%R&R'R)R(R+R,RdtNINFtNANtEPSR0tlenR/R4R2R1R9R:R;R<R>RCRNRQRRtdigammaRVRWRTRURXRYRZR[RfRetFalseR`RcRoRqRuRxRyRwRvRs(((s+lib/python2.7/site-packages/mpmath/math2.pyts|                            8             %