509318396 ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ 3 \Tƒã$@sFdddddddddd d ddd ddddddddddddddddddd d!d"d#g$ZeZd$Zd%Zd&Zd'd(lZd'd(lZd'd(l Z yd'd)l mZedd*ƒZ Wnek rªd+d,„Z YnXdZdZdZdZdZdZdZdZd-Ze jd”krèd1Zd1Zd•Znd2Zd2Zd–Zeed0ZGd3d„deƒZGd4d„deƒZGd5d„deƒZ Gd6d„de ƒZ!Gd7d „d ee"ƒZ#Gd8d„de ƒZ$Gd9d„de e"ƒZ%Gd:d „d eƒZ&Gd;d„de ƒZ'Gdd „d e&e(ƒZ*Gd?d„de&e(e)ƒZ+Gd@d„dee,ƒZ-ee#e&e*e(e+e e)e-g Z.e!e e$e e%e e'e iZ/eeeeeeeefZ0yd'd(l1Z1Wn.ek rdGdAdB„dBe2ƒZ3e3ƒZ1[3YnXy e1j4Wn>e5k r®e6e1j7ƒdCƒrše1j7ƒ`8dDd„Z9dEd„Z:Yn6Xe1j4ƒZ4e6e4dCƒrÈe4`8e4fdFd„Z:e4fdGd„Z9[1[4d—dHd„Z;GdId„de2ƒZj?e<ƒGdMdN„dNe2ƒZ@GdOd„de2ƒZAGdPdQ„dQe2ƒZBd™dRdS„ZCeDjEZFdTdU„ZGdVdW„ZHdXdY„ZIdZd[„ZJdšd]d^„ZKd_d`„ZLdadb„ZMGdcdd„dde2ƒZNeNƒjOZPd›dedf„ZQdgdh„ZRdidj„ZSdkdldmdndodpdqdrdsdtœ fdudv„ZTdœdwdx„ZUddydz„ZVeAd{ee#e*e ggd|džd0d'd}ZWeAd~ee#e*e ee+ggdZXeAd~eggdZYd'd(lZZZeZj[d€eZj\eZj]Bƒj^Z_eZj[dƒj^Z`eZj[d‚ƒj^ZaeZj[dƒeZj\eZjbBƒZc[Zyd'd(ldZeWnek rªYnXdŸd„d…„Zfd†d‡„Zgdˆd‰„Zhd dŠd‹„ZidŒd„ZjdŽd„Zke¡sr+Téé?élÿÇNÎZoi@üTc@seZdZdd„ZdS)rcGsdS)Nr()ÚselfÚcontextr)r(r(r*ÚhandleÏszDecimalException.handleN)Ú__name__Ú __module__Ú__qualname__r1r(r(r(r*r¼sc@seZdZdS)rN)r2r3r4r(r(r(r*rÓs c@seZdZdd„ZdS)r cGs,|r(t|dj|djddƒ}|j|ƒStS)Nr&ÚnT)Ú_dec_from_tripleÚ_signÚ_intÚ_fix_nanÚ_NaN)r/r0r)Úansr(r(r*r1ös zInvalidOperation.handleN)r2r3r4r1r(r(r(r*r ßsc@seZdZdd„ZdS)rcGstS)N)r:)r/r0r)r(r(r*r1szConversionSyntax.handleN)r2r3r4r1r(r(r(r*rüsc@seZdZdd„ZdS)r cGst|S)N)Ú_SignedInfinity)r/r0Úsignr)r(r(r*r1szDivisionByZero.handleN)r2r3r4r1r(r(r(r*r s c@seZdZdd„ZdS)rcGstS)N)r:)r/r0r)r(r(r*r1szDivisionImpossible.handleN)r2r3r4r1r(r(r(r*rsc@seZdZdd„ZdS)rcGstS)N)r:)r/r0r)r(r(r*r1)szDivisionUndefined.handleN)r2r3r4r1r(r(r(r*r!sc@seZdZdS)rN)r2r3r4r(r(r(r*r,s c@seZdZdd„ZdS)rcGstS)N)r:)r/r0r)r(r(r*r1CszInvalidContext.handleN)r2r3r4r1r(r(r(r*r8sc@seZdZdS)rN)r2r3r4r(r(r(r*rFs c@seZdZdS)r N)r2r3r4r(r(r(r*r Rs c@seZdZdd„ZdS)rcGsŽ|jttttfkrt|S|dkrR|jtkr4t|St|d|j|j |jdƒS|dkrŠ|jt krlt|St|d|j|j |jdƒSdS)Nr&Ú9r.)Úroundingrrrrr<rr6ÚprecÚEmaxr)r/r0r=r)r(r(r*r1ss zOverflow.handleN)r2r3r4r1r(r(r(r*r]sc@seZdZdS)rN)r2r3r4r(r(r(r*rƒs c@seZdZdS)rN)r2r3r4r(r(r(r*r’s c@seZdZefdd„ZdS)Ú MockThreadingcCs |jtS)N)ÚmodulesÚ __xname__)r/Úsysr(r(r*Úlocal¼szMockThreading.localN)r2r3r4rErFr(r(r(r*rB»srBÚ__decimal_context__cCs,|tttfkr|jƒ}|jƒ|tjƒ_dS)N)rrrÚcopyÚclear_flagsÚ threadingÚcurrent_threadrG)r0r(r(r*rËscCs4y tjƒjStk r.tƒ}|tjƒ_|SXdS)N)rJrKrGÚAttributeErrorr)r0r(r(r*rÒs cCs,y|jStk r&tƒ}||_|SXdS)N)rGrLr)Ú_localr0r(r(r*ræscCs(|tttfkr|jƒ}|jƒ||_dS)N)rrrrHrIrG)r0rMr(r(r*rôscCs|dkrtƒ}t|ƒS)N)rÚ_ContextManager)Zctxr(r(r*rýs$c @sÚeZdZdôZdõdd„Zed d „ƒZdd„Zd d„Zdödd„Z dd„Z dd„Zdd„Zd÷dd„Z dødd„Zdùdd„Zdúdd„Zdûdd „Zdüd!d"„Zd#d$„Zd%d&„Zd'd(„Zd)d*„Zdýd,d-„Zdþd.d/„Zdÿd0d1„Zdd2d3„Zdd5d6„Zdd7d8„ZeZdd9d:„Zdd;d<„Zdd=d>„Z e Z!dd?d@„Z"dAdB„Z#ddCdD„Z$ddEdF„Z%d dGdH„Z&d dIdJ„Z'ddKdL„Z(ddMdN„Z)d dOdP„Z*ddQdR„Z+dSdT„Z,dUdV„Z-e-Z.dWdX„Z/e0e/ƒZ/dYdZ„Z1e0e1ƒZ1d[d\„Z2d]d^„Z3d_d`„Z4dadb„Z5dcdd„Z6dedf„Z7dgdh„Z8didj„Z9dkdl„Z:dmdn„Z;dodp„Ze6e7e8e9e:e;e zDecimal._cmpcCs<t||dd\}}|tkr|S|j||ƒr.dS|j|ƒdkS)NT)Úequality_opFr&)Ú_convert_for_comparisonÚNotImplementedrŠr’)r/r‡r0r(r(r*Ú__eq__–szDecimal.__eq__cCs<t||ƒ\}}|tkr|S|j||ƒ}|r.dS|j|ƒdkS)NFr&)r”r•rr’)r/r‡r0r;r(r(r*Ú__lt__žszDecimal.__lt__cCs<t||ƒ\}}|tkr|S|j||ƒ}|r.dS|j|ƒdkS)NFr&)r”r•rr’)r/r‡r0r;r(r(r*Ú__le__§szDecimal.__le__cCs<t||ƒ\}}|tkr|S|j||ƒ}|r.dS|j|ƒdkS)NFr&)r”r•rr’)r/r‡r0r;r(r(r*Ú__gt__°szDecimal.__gt__cCs<t||ƒ\}}|tkr|S|j||ƒ}|r.dS|j|ƒdkS)NFr&)r”r•rr’)r/r‡r0r;r(r(r*Ú__ge__¹szDecimal.__ge__cCs>t|dd}|js|r0|jr0|j||ƒ}|r0|St|j|ƒƒS)NT)Úraiseit)Ú_convert_otherrPrŠrr’)r/r‡r0r;r(r(r*ÚcompareÂszDecimal.comparecCs’|jr4|jƒrtdƒ‚n|jƒr$tS|jr0tStS|jdkrNtd|jt ƒ}ntt |jt ƒ}t|jƒ|t }|dkr||n|}|dkrŽdS|S)Nz"Cannot hash a signaling NaN value.r&é r.r,r„éþÿÿÿ) rPr‹rrÚis_nanÚ_PyHASH_NANr7Ú_PyHASH_INFrOÚpowÚ_PyHASH_MODULUSÚ _PyHASH_10INVrUr8)r/Zexp_hashZhash_r;r(r(r*Ú__hash__Ôs zDecimal.__hash__cCst|jttt|jƒƒ|jƒS)N)rr7rkrorUr8rO)r/r(r(r*Úas_tupleîszDecimal.as_tuplecCsØ|jr |jƒrtdƒ‚ntdƒ‚|s(dSt|jƒ}|jdkrR|d|jd}}nr|j}x(|dkr‚|ddkr‚|d}|d8}q\W|j}t||@jƒd|ƒ}|r¸||L}||8}d||>}|j rÐ|}||fS)Nz#cannot convert NaN to integer ratioz(cannot convert Infinity to integer ratior&r.ržrz)r&r.) rPr rlÚ OverflowErrorrUr8rOÚminr~r7)r/r5r€Zd5Zd2Zshift2r(r(r*r}õs, zDecimal.as_integer_ratiocCsdt|ƒS)Nz Decimal('%s'))r`)r/r(r(r*Ú__repr__'szDecimal.__repr__Fc Csdddg|j}|jrL|jdkr&|dS|jdkr>|d|jS|d|jS|jt|jƒ}|jdkrt|dkrt|}n6|s~d }n,|jdkrš|d dd }n|d dd }|dkrÌd}d d||j}nN|t|jƒkrú|jd|t|jƒ}d}n |jd|…}d |j|d…}||kr*d}n*|dkr:tƒ}ddg|jd||}||||S)NrSrTrZZInfinityr5ÚNaNr†r&ér.rQr[Ú.ÚeÚEz%+diúÿÿÿ)r7rPrOr8rfrÚcapitals) r/Úengr0r=Ú leftdigitsÚdotplacervrwrVr(r(r*Ú__str__,s: zDecimal.__str__cCs|jd|dS)NT)r±r0)r´)r/r0r(r(r*Ú to_eng_string`szDecimal.to_eng_stringcCsT|jr|j|d}|r|S|dkr(tƒ}|rB|jtkrB|jƒ}n|jƒ}|j|ƒS)N)r0)rPrŠrr?rÚcopy_absÚcopy_negateÚ_fix)r/r0r;r(r(r*Ú__neg__is zDecimal.__neg__cCsT|jr|j|d}|r|S|dkr(tƒ}|rB|jtkrB|jƒ}nt|ƒ}|j|ƒS)N)r0)rPrŠrr?rr¶rr¸)r/r0r;r(r(r*Ú__pos__s zDecimal.__pos__TcCsJ|s|jƒS|jr&|j|d}|r&|S|jr:|j|d}n|j|d}|S)N)r0)r¶rPrŠr7r¹rº)r/Úroundr0r;r(r(r*Ú__abs__”szDecimal.__abs__c Cslt|ƒ}|tkr|S|dkr"tƒ}|js.|jr‚|j||ƒ}|rB|S|jƒrr|j|jkrj|jƒrj|jtdƒSt |ƒS|jƒr‚t |ƒSt |j|jƒ}d}|jt kr®|j|jkr®d}|rê|rêt |j|jƒ}|rÐd}t|d|ƒ}|j|ƒ}|S|s"t||j|jdƒ}|j||jƒ}|j|ƒ}|S|sZt||j|jdƒ}|j||jƒ}|j|ƒ}|St|ƒ}t|ƒ}t|||jƒ\}}tƒ} |j|jkrþ|j|jkr¸t|d|ƒ}|j|ƒ}|S|j|jkrÐ||}}|jdkröd| _|j|j|_|_nd| _n&|jdkrd| _d\|_|_nd| _|jdkr@|j|j| _n|j|j| _|j| _t | ƒ}|j|ƒ}|S)Nz -INF + INFr&r.rQ)r&r&)rœr•rrPrŠr…r7rdr rr©rOr?rr6r¸Úmaxr@Ú_rescaleriÚ _normalizer=rUrV) r/r‡r0r;rVZnegativezeror=Úop1Úop2r‚r(r(r*Ú__add__ªs| zDecimal.__add__cCsHt|ƒ}|tkr|S|js |jr6|j||d}|r6|S|j|jƒ|dS)N)r0)rœr•rPrŠrÂr·)r/r‡r0r;r(r(r*Ú__sub__szDecimal.__sub__cCs"t|ƒ}|tkr|S|j||dS)N)r0)rœr•rÃ)r/r‡r0r(r(r*Ú__rsub__szDecimal.__rsub__cCsDt|ƒ}|tkr|S|dkr"tƒ}|j|jA}|js:|jrŽ|j||ƒ}|rN|S|jƒrn|sf|jtdƒSt |S|jƒrŽ|s†|jtdƒSt |S|j |j }|s¦|rÀt|d|ƒ}|j|ƒ}|S|j dkræt||j |ƒ}|j|ƒ}|S|j dkrt||j |ƒ}|j|ƒ}|St|ƒ}t|ƒ}t|t|j|jƒ|ƒ}|j|ƒ}|S)Nz(+-)INF * 0z0 * (+-)INFrQÚ1)rœr•rr7rPrŠr…rdr r<rOr6r¸r8rir`rU)r/r‡r0Z resultsignr;Z resultexprÀrÁr(r(r*Ú__mul__sH zDecimal.__mul__cCsÊt|ƒ}|tkrtS|dkr"tƒ}|j|jA}|js:|jrž|j||ƒ}|rN|S|jƒrj|jƒrj|jtdƒS|jƒrzt |S|jƒrž|jt dƒt|d|jƒƒS|sÀ|s²|jt dƒS|jtd|ƒS|sÖ|j|j}d}nÚt|jƒt|jƒ|jd}|j|j|}t|ƒ}t|ƒ} |dkr:t|jd|| jƒ\}} nt|j| jd|ƒ\}} | rt|d dkr°|d7}n<|j|j}x.||kr®|ddkr®|d}|d7}q‚Wt|t|ƒ|ƒ}|j|ƒS) Nz(+-)INF/(+-)INFzDivision by infinityrQz0 / 0zx / 0r&r.ržrz)rœr•rr7rPrŠr…rdr r<rr6ÚEtinyrr rOrfr8r@riÚdivmodrUr`r¸)r/r‡r0r=r;rVÚcoeffÚshiftrÀrÁÚ remainderÚ ideal_expr(r(r*Ú__truediv__QsP zDecimal.__truediv__cCs |j|jA}|jƒr|j}nt|j|jƒ}|jƒ|jƒ}|sP|jƒsP|dkrjt|ddƒ|j||jƒfS||jkrt |ƒ}t |ƒ}|j |j kr®|jd|j |j 9_n|jd|j |j 9_t|j|jƒ\}} |d|jkrt|t |ƒdƒt|jt | ƒ|ƒfS|jtdƒ} | | fS)Nr,rQr&ržz%quotient too large in //, % or divmodrŸ)r7r…rOr©rr6r¾r?r@rirVrUrÈr`rdr)r/r‡r0r=rÌÚexpdiffrÀrÁÚqÚrr;r(r(r*Ú_divideŒs* zDecimal._dividecCs"t|ƒ}|tkr|S|j||dS)N)r0)rœr•rÍ)r/r‡r0r(r(r*Ú__rtruediv__szDecimal.__rtruediv__cCsÖt|ƒ}|tkr|S|dkr"tƒ}|j||ƒ}|r:||fS|j|jA}|jƒr~|jƒrj|jtdƒ}||fSt||jtdƒfS|s´|sš|jt dƒ}||fS|jt d|ƒ|jtdƒfS|j||ƒ\}}|j|ƒ}||fS)Nzdivmod(INF, INF)zINF % xzdivmod(0, 0)zx // 0zx % 0) rœr•rrŠr7r…rdr r<rr rÑr¸)r/r‡r0r;r=ZquotientrËr(r(r*Ú __divmod__´s0 zDecimal.__divmod__cCs"t|ƒ}|tkr|S|j||dS)N)r0)rœr•rÓ)r/r‡r0r(r(r*Ú__rdivmod__ØszDecimal.__rdivmod__cCsˆt|ƒ}|tkr|S|dkr"tƒ}|j||ƒ}|r6|S|jƒrJ|jtdƒS|sj|r^|jtdƒS|jtdƒS|j||ƒd}|j |ƒ}|S)NzINF % xzx % 0z0 % 0r.) rœr•rrŠr…rdr rrÑr¸)r/r‡r0r;rËr(r(r*Ú__mod__ßs" zDecimal.__mod__cCs"t|ƒ}|tkr|S|j||dS)N)r0)rœr•rÕ)r/r‡r0r(r(r*Ú__rmod__úszDecimal.__rmod__cCsÐ|dkrtƒ}t|dd}|j||ƒ}|r.|S|jƒrB|jtdƒS|sb|rV|jtdƒS|jtdƒS|jƒr|t|ƒ}|j|ƒSt |j |j ƒ}|s¦t|jd|ƒ}|j|ƒS|j ƒ|j ƒ}||jdkrÎ|jtƒS|dkrî|j||jƒ}|j|ƒSt|ƒ}t|ƒ}|j|jkr(|jd |j|j9_n|jd |j|j9_t|j|jƒ\}} d| |d@|jkr~| |j8} |d7}|d |jkr˜|jtƒS|j} | d kr¶d| } | } t| t| ƒ|ƒ}|j|ƒS)NT)r›zremainder_near(infinity, x)zremainder_near(x, 0)zremainder_near(0, 0)rQr.r,ržr&rŸ)rrœrŠr…rdr rrr¸r©rOr6r7rr@rr¾r?rirVrUrÈr`)r/r‡r0r;Úideal_exponentrÎrÀrÁrÏrÐr=r(r(r*Úremainder_nearsZ zDecimal.remainder_nearcCsœt|ƒ}|tkr|S|dkr"tƒ}|j||ƒ}|r6|S|jƒrb|jƒrR|jtdƒSt|j|jAS|sŒ|r€|jt d|j|jAƒS|jt dƒS|j||ƒdS)Nz INF // INFzx // 0z0 // 0r&)rœr•rrŠr…rdr r<r7r rrÑ)r/r‡r0r;r(r(r*Ú__floordiv__Ls$zDecimal.__floordiv__cCs"t|ƒ}|tkr|S|j||dS)N)r0)rœr•rÙ)r/r‡r0r(r(r*Ú __rfloordiv__hszDecimal.__rfloordiv__cCs8|jƒr(|jƒrtdƒ‚|jr"dnd}nt|ƒ}t|ƒS)Nz%Cannot convert signaling NaN to floatz-nanÚnan)rƒr‹rlr7r`rp)r/Úsr(r(r*Ú __float__oszDecimal.__float__cCst|jr(|jƒrtdƒ‚n|jƒr(tdƒ‚d|j}|jdkrT|t|jƒd|jS|t|jd|j…pjdƒSdS)NzCannot convert NaN to integerz"Cannot convert infinity to integerr.r&ržrQr„) rPrƒrlr…r¨r7rOrUr8)r/rÜr(r(r*Ú__int__ys zDecimal.__int__cCs|S)Nr()r/r(r(r*ÚrealˆszDecimal.realcCstdƒS)Nr&)r)r/r(r(r*ÚimagŒszDecimal.imagcCs|S)Nr()r/r(r(r*Ú conjugateszDecimal.conjugatecCstt|ƒƒS)N)Úcomplexrp)r/r(r(r*Ú__complex__“szDecimal.__complex__cCsR|j}|j|j}t|ƒ|krJ|t|ƒ|d…jdƒ}t|j||jdƒSt|ƒS)NrQT) r8r@Úclamprfrgr6r7rOr)r/r0ZpayloadZmax_payload_lenr(r(r*r9–szDecimal._fix_nancCsX|jr |jƒr|j|ƒSt|ƒS|jƒ}|jƒ}|s€|j|g|j}tt |j |ƒ|ƒ}||j krx|jtƒt |jd|ƒSt|ƒSt|jƒ|j |j}||krÆ|jtd|jƒ}|jtƒ|jtƒ|S||k}|rÖ|}|j |krüt|jƒ|j |} | dkrt |jd|dƒ}d} |j|j} | || ƒ}|jd| …p>d}|dkr~tt|ƒdƒ}t|ƒ|jkr~|dd…}|d7}||krš|jtd|jƒ}nt |j||ƒ}|r¾|r¾|jtƒ|rÎ|jtƒ|rÞ|jtƒ|jtƒ|sø|jtƒ|S|r|jtƒ|jdkrP|j |krP|jtƒ|jd|j |} t |j| |ƒSt|ƒS)NrQz above Emaxr&rÅr.r„)rPrƒr9rrÇÚEtoprArär©r½rOrdrr6r7rfr8r@rrrÚ_pick_rounding_functionr?r`rUrr )r/r0rÇråÚexp_maxZnew_expZexp_minr;Zself_is_subnormalrxZrounding_methodÚchangedrÉr‘r(r(r*r¸¢sn zDecimal._fixcCst|j|ƒrdSdSdS)Nr&r.r„)Ú _all_zerosr8)r/r@r(r(r*Ú_round_downszDecimal._round_downcCs|j|ƒS)N)rê)r/r@r(r(r*Ú _round_upszDecimal._round_upcCs*|j|dkrdSt|j|ƒr"dSdSdS)NZ56789r.r&r„)r8ré)r/r@r(r(r*Ú_round_half_ups zDecimal._round_half_upcCst|j|ƒrdS|j|ƒSdS)Nr.r„)Ú_exact_halfr8rì)r/r@r(r(r*Ú_round_half_downszDecimal._round_half_downcCs8t|j|ƒr*|dks&|j|ddkr*dS|j|ƒSdS)Nr&r.Ú02468r„)rír8rì)r/r@r(r(r*Ú_round_half_even#szDecimal._round_half_evencCs |jr|j|ƒS|j|ƒSdS)N)r7rê)r/r@r(r(r*Ú_round_ceiling+s zDecimal._round_ceilingcCs |js|j|ƒS|j|ƒSdS)N)r7rê)r/r@r(r(r*Ú_round_floor2s zDecimal._round_floorcCs0|r |j|ddkr |j|ƒS|j|ƒSdS)Nr.Z05)r8rê)r/r@r(r(r*Ú_round_05up9s zDecimal._round_05up)rrrrrrrrcCsb|dk r2t|tƒstdƒ‚tdd|ƒ}|j|ƒS|jrR|jƒrJtdƒ‚ntdƒ‚t|j dt ƒƒS)Nz+Second argument to round should be integralr&rÅzcannot round a NaNzcannot round an infinity)r_rUrrr6ÚquantizerPr rlr¨r¾r)r/r5rVr(r(r*Ú __round__Ks/ zDecimal.__round__cCs0|jr |jƒrtdƒ‚ntdƒ‚t|jdtƒƒS)Nzcannot round a NaNzcannot round an infinityr&)rPr rlr¨rUr¾r)r/r(r(r*Ú __floor__‰s zDecimal.__floor__cCs0|jr |jƒrtdƒ‚ntdƒ‚t|jdtƒƒS)Nzcannot round a NaNzcannot round an infinityr&)rPr rlr¨rUr¾r)r/r(r(r*Ú__ceil__˜s zDecimal.__ceil__cCst|dd}t|dd}|js$|jrÚ|dkr2tƒ}|jdkrJ|jtd|ƒS|jdkrb|jtd|ƒS|jdkrr|}nf|jdkr‚|}nV|jdkr®|sœ|jtdƒSt|j|jA}n*|jdkrØ|sÈ|jtdƒSt|j|jA}n0t|j|jAt t |jƒt |jƒƒ|j|jƒ}|j||ƒS) NT)r›rYr†r5rZzINF * 0 in fmaz0 * INF in fma) rœrPrrOrdr r<r7r6r`rUr8rÂ)r/r‡Zthirdr0Úproductr(r(r*Úfma§s6 zDecimal.fmacCsÚt|ƒ}|tkr|St|ƒ}|tkr(|S|dkr6tƒ}|jƒ}|jƒ}|jƒ}|sZ|sZ|rÂ|dkrp|jtd|ƒS|dkr†|jtd|ƒS|dkrœ|jtd|ƒS|rª|j|ƒS|r¸|j|ƒS|j|ƒS|jƒoØ|jƒoØ|jƒsæ|jtdƒS|dkrú|jtdƒS|s|jtdƒS|jƒ|j kr(|jtdƒS|rD|rD|jtdƒS|j ƒrTd}n|j}tt |ƒƒ}t|jƒƒ}t|jƒƒ} |j |td |j|ƒ|}x t| jƒD]} t|d |ƒ}q¦Wt|| j |ƒ}t|t|ƒdƒS) Nr,r†z@pow() 3rd argument not allowed unless all arguments are integersr&zApow() 2nd argument cannot be negative when 3rd argument specifiedzpow() 3rd argument cannot be 0zSinsufficient precision: pow() 3rd argument must not have more than precision digitszXat least one of pow() 1st argument and 2nd argument must be nonzero; 0**0 is not definedrž)rœr•rrƒrdr r9Ú _isintegerrr@Ú_isevenr7rhrUriÚto_integral_valuer£rVÚranger6r`)r/r‡Úmodulor0rˆr‰Z modulo_is_nanr=ÚbaseÚexponentÚir(r(r*Ú _power_moduloÓsl zDecimal._power_modulocCst|ƒ}|j|j}}x |ddkr6|d}|d7}qWt|ƒ}|j|j}}x |ddkrn|d}|d7}qPW|dkr||9}x |ddkr¢|d}|d7}q„W|dkr°dS|d|} |jdkrÌ| } |jƒoÜ|jdkr|jt|ƒ} t| | |dƒ}nd}tddd|| |ƒS|jdkrÄ|d}|dkrÊ||@|krPdSt |ƒd} |d d}|t t|ƒƒkr~dSt| ||ƒ} t|||ƒ}| dks®|dkr²dS| |krÀdSd| }nÎ|dkr”t |ƒd d} t d| |ƒ\}}|rdSx$|ddkr$|d}| d8} qW|dd}|t t|ƒƒkrHdSt| ||ƒ} t|||ƒ}| dksx|dkr|dS| |krŠdSd| }ndS|d|krªdS| |}tdt|ƒ|ƒS|dkrâ|d|d}}nä|dkrt tt||ƒƒƒ|krdSt |ƒ}|dkr>t tt|ƒ|ƒƒ|kr>dS|d|}}x:|d|dkoldknrˆ|d}|d}qPWx:|d|dko¨dknrÄ|d}|d}qŒW|dkrt|dkrè||krèdSt ||ƒ\}}|dkrdSdt |ƒ|>}x>t |||dƒ\}}||kr>Pn||d||}qW||koh|dkspdS|}|dkr˜||dt|ƒkr˜dS||}||9}|d|krºdSt|ƒ}|jƒrþ|jdkrþ|jt|ƒ} t|| |t |ƒƒ}nd}td|d|||ƒS)Nržr&r.rÅrQr,ér¬éé]éArzér[éd)r,rr¬r)rirUrVr=rúr7rOr©r6Ú_nbitsrfr`Ú_decimal_lshift_exactrÈrhÚ _log10_lb)r/r‡ÚpÚxÚxcÚxeÚyÚycÚyerr×ZzerosZ last_digitr®ZemaxrËrur5Zxc_bitsÚremÚarÏrÐZstr_xcr(r(r*Ú_power_exact(sÒ: &&&& zDecimal._power_exactcCs@|dk r|j|||ƒSt|ƒ}|tkr*|S|dkr8tƒ}|j||ƒ}|rL|S|sd|s`|jtdƒStSd}|jdkr |j ƒrˆ|j ƒs˜d}n|r˜|jtdƒS|jƒ}|sÂ|jdkrºt|ddƒSt |S|jƒrè|jdkrÜt |St|ddƒS|tkrŽ|j ƒrZ|jdkrd}n||jkr"|j}nt|ƒ}|j|}|d|jkrxd|j}|jtƒn|jtƒ|jtƒd|j}t|dd||ƒS|jƒ}|jƒrÈ|jdk|dkkrÀt|ddƒSt |Sd}d} |jƒ|jƒ} |dk|jdkkr| tt|jƒƒkrHt|d|jdƒ}n,|jƒ}| tt|ƒƒkrHt|d|dƒ}|dkrŒ|j||jdƒ}|dk rŒ|dkrˆtd|j|jƒ}d} |dkr:|j}t|ƒ} | j| j}}t|ƒ}|j|j}}|jdkrÚ|}d }xJt||||||ƒ\}}|d dtt|ƒƒ|drP|d 7}qàWt|t|ƒ|ƒ}| r2|j ƒr2t|jƒ|jkr|jdt|jƒ}t|j|jd||j|ƒ}|j ƒ}|j!ƒxt"D]}d|j#|<q¦W|j$|ƒ}|jtƒ|j%t&rä|jt'ƒ|j%t(r|jt(d|jƒx:t't&ttt)fD]}|j%|r|j|ƒqWn |j$|ƒ}|S) Nz0 ** 0r&r.z+x ** y with x negative and y not an integerrQrÅFTr[rzržz above Emax)*rrœr•rrŠrdr Ú_Oner7rúrûr·r6r<r…r@rUrOrrrÚ_log10_exp_boundrfr`rArÇrr8rirVr=Ú_dpowerrHrIÚ_signalsÚtrapsr¸Úflagsr rrr)r/r‡rþr0r;Zresult_signZ multiplierrVZself_adjÚexactZboundrÇrr rrrrrÚextrarÉrÎZ newcontextZ exceptionr(r(r*Ú__pow__ sÊ " zDecimal.__pow__cCs"t|ƒ}|tkr|S|j||dS)N)r0)rœr•r)r/r‡r0r(r(r*Ú__rpow__í szDecimal.__rpow__cCs¼|dkrtƒ}|jr(|j|d}|r(|S|j|ƒ}|jƒr>|S|sPt|jddƒS|j|jƒg|j }t |jƒ}|j}x.|j|ddkr¢||kr¢|d7}|d8}qvWt|j|jd|…|ƒS)N)r0rQr&r.) rrPrŠr¸r…r6r7rArårärfr8rO)r/r0r;ÚduprçÚendrVr(r(r*Ú normalizeô s$ zDecimal.normalizecCs¨t|dd}|dkrtƒ}|dkr(|j}|js4|jr||j||ƒ}|rH|S|jƒsX|jƒr||jƒrp|jƒrpt|ƒS|jtdƒS|j ƒ|j ko–|jkns¨|jtdƒS|sÆt|j d|j ƒ}|j|ƒS|jƒ}||jkrä|jtdƒS||j d|jkr|jtdƒS|j|j |ƒ}|jƒ|jkr0|jtdƒSt|jƒ|jkrN|jtdƒS|rn|jƒ|jkrn|jtƒ|j |j krš||kr|jtƒ|jtƒ|j|ƒ}|S) NT)r›zquantize with one INFz)target exponent out of bounds in quantizerQz9exponent of quantize result too large for current contextr.z7quantize result has too many digits for current context)rœrr?rPrŠr…rrdr rÇrOrAr6r7r¸rr@r¾rfr8ÚEminr rr)r/rVr?r0r;rr(r(r*rô sT zDecimal.quantizecCsDt|dd}|js|jr8|jƒr(|jƒp6|jƒo6|jƒS|j|jkS)NT)r›)rœrPr Úis_infiniterO)r/r‡r0r(r(r*Úsame_quantumJ s zDecimal.same_quantumcCsÆ|jrt|ƒS|s t|jd|ƒS|j|krHt|j|jd|j||ƒSt|jƒ|j|}|dkrzt|jd|dƒ}d}|j|}|||ƒ}|jd|…pžd}|dkr¸tt |ƒdƒ}t|j||ƒS)NrQr&rÅr.) rPrr6r7rOr8rfrær`rU)r/rVr?rxZ this_functionrèrÉr(r(r*r¾Y s" zDecimal._rescalecCsh|dkrtdƒ‚|js|r$t|ƒS|j|jƒd||ƒ}|jƒ|jƒkrd|j|jƒd||ƒ}|S)Nr&z'argument should be at least 1 in _roundr.)rlrPrr¾r)r/Úplacesr?r;r(r(r*Ú_round{ s zDecimal._roundcCsŽ|jr"|j|d}|r|St|ƒS|jdkr4t|ƒS|sFt|jddƒS|dkrTtƒ}|dkrb|j}|jd|ƒ}||kr€|j t ƒ|j tƒ|S)N)r0r&rQ)rPrŠrrOr6r7rr?r¾rdrr)r/r?r0r;r(r(r*Úto_integral_exact’ s$ zDecimal.to_integral_exactcCs`|dkrtƒ}|dkr|j}|jr>|j|d}|r6|St|ƒS|jdkrPt|ƒS|jd|ƒSdS)N)r0r&)rr?rPrŠrrOr¾)r/r?r0r;r(r(r*rü¯ s zDecimal.to_integral_valuecCsà|dkrtƒ}|jrB|j|d}|r(|S|jƒrB|jdkrBt|ƒS|sdt|jd|jdƒ}|j|ƒS|jdkrz|j t dƒS|jd}t|ƒ}|j d?}|j d@r¾|jd}t|jƒd?d}n|j}t|jƒdd?}||}|dkrø|d|9}d } nt|d|ƒ\}} | } ||8}d|}x(||}||kr:Pn||d?}q$W| o\|||k} | r”|dkr||d|}n|d|9}||7}n|d dkrª|d7}tdt|ƒ|ƒ}|jƒ}|jtƒ} |j|ƒ}| |_|S)N)r0r&rQr,r.zsqrt(-x), x > 0ržrTrz)rrPrŠr…r7rr6rOr¸rdr r@rirVrUrfr8rÈr`Ú _shallow_copyÚ _set_roundingrr?)r/r0r;r@Úopr®ÚcÚlrÊrrËr5rÏr?r(r(r*ÚsqrtÂ s` zDecimal.sqrtcCs¶t|dd}|dkrtƒ}|js&|jr~|jƒ}|jƒ}|s>|r~|dkrX|dkrX|j|ƒS|dkrr|dkrr|j|ƒS|j||ƒS|j|ƒ}|dkrš|j|ƒ}|dkr¨|}n|}|j|ƒS)NT)r›r.r&r„)rœrrPrƒr¸rŠr’Ú compare_total)r/r‡r0ÚsnÚonr,r;r(r(r*r½%s& zDecimal.maxcCs¶t|dd}|dkrtƒ}|js&|jr~|jƒ}|jƒ}|s>|r~|dkrX|dkrX|j|ƒS|dkrr|dkrr|j|ƒS|j||ƒS|j|ƒ}|dkrš|j|ƒ}|dkr¨|}n|}|j|ƒS)NT)r›r.r&r„)rœrrPrƒr¸rŠr’r/)r/r‡r0r0r1r,r;r(r(r*r©Os& zDecimal.mincCs8|jr dS|jdkrdS|j|jd…}|dt|ƒkS)NFr&TrQ)rPrOr8rf)r/Úrestr(r(r*rúqs zDecimal._isintegercCs(|s|jdkrdS|jd|jdkS)Nr&Tr.rïr„)rOr8)r/r(r(r*rûzszDecimal._isevencCs.y|jt|jƒdStk r(dSXdS)Nr.r&)rOrfr8rr)r/r(r(r*r€szDecimal.adjustedcCs|S)Nr()r/r(r(r*Ú canonicalˆszDecimal.canonicalcCs.t|dd}|j||ƒ}|r |S|j||dS)NT)r›)r0)rœrr)r/r‡r0r;r(r(r*Úcompare_signals zDecimal.compare_signalcCsft|dd}|jr|jrtS|jr0|jr0tS|j}|jƒ}|jƒ}|sP|r||kr¤t|jƒ|jf}t|jƒ|jf}||krŒ|rˆtStS||kr |rœtStStS|rÚ|dkr´tS|dkrÀtS|dkrÌtS|dkrØtSn4|dkrætS|dkròtS|dkrtS|dkrtS||krtS||kr*tS|j|jkrF|rBtStS|j|jkrb|r^tStStS)NT)r›r.r,) rœr7Ú_NegativeOnerrƒrfr8Ú_ZerorO)r/r‡r0r=Zself_nanZ other_nanZself_keyZ other_keyr(r(r*r/œsf zDecimal.compare_totalcCs&t|dd}|jƒ}|jƒ}|j|ƒS)NT)r›)rœr¶r/)r/r‡r0rÜÚor(r(r*Úcompare_total_magåszDecimal.compare_total_magcCstd|j|j|jƒS)Nr&)r6r8rOrP)r/r(r(r*r¶ðszDecimal.copy_abscCs2|jrtd|j|j|jƒStd|j|j|jƒSdS)Nr&r.)r7r6r8rOrP)r/r(r(r*r·ôszDecimal.copy_negatecCs"t|dd}t|j|j|j|jƒS)NT)r›)rœr6r7r8rOrP)r/r‡r0r(r(r*Ú copy_signûs zDecimal.copy_signcCsì|dkrtƒ}|j|d}|r"|S|jƒd kr2tS|s:tS|jƒdkrNt|ƒS|j}|jƒ}|jdkr–|t t |jddƒƒkr–tdd|jdƒ}n0|jdkrÔ|t t |j ƒddƒƒkrÔtdd|j ƒdƒ}nò|jdkoæ||kr tddd|dd|ƒ}n¼|jdkrB||dkrBtdd|d|dƒ}n„t|ƒ}|j|j}}|jdkrj|}d}xFt||||ƒ\} } | dd t t | ƒƒ|dr¨P|d7}qpWtdt | ƒ| ƒ}|jƒ}|jtƒ}|j|ƒ}||_|S)N)r0r.r&r[rÅrQr>rzržr„)rrŠr…r6rrr@rr7rfr`rAr6rÇrirUrVr=Ú_dexpr)r*rr¸r?)r/r0r;rÚadjr+r,r®rrÉrVr?r(r(r*rVsJ$( " zDecimal.expcCsdS)NTr()r/r(r(r*Úis_canonicalLszDecimal.is_canonicalcCs|jS)N)rP)r/r(r(r*Ú is_finiteTszDecimal.is_finitecCs |jdkS)NrZ)rO)r/r(r(r*r$\szDecimal.is_infinitecCs |jdkS)Nr5rY)r5rY)rO)r/r(r(r*r `szDecimal.is_nancCs,|js|rdS|dkrtƒ}|j|jƒkS)NF)rPrr#r)r/r0r(r(r*Ú is_normalds zDecimal.is_normalcCs |jdkS)Nr5)rO)r/r(r(r*rŒlszDecimal.is_qnancCs |jdkS)Nr.)r7)r/r(r(r*Ú is_signedpszDecimal.is_signedcCs |jdkS)NrY)rO)r/r(r(r*r‹tszDecimal.is_snancCs,|js|rdS|dkrtƒ}|jƒ|jkS)NF)rPrrr#)r/r0r(r(r*Úis_subnormalxs zDecimal.is_subnormalcCs|jo|jdkS)NrQ)rPr8)r/r(r(r*Úis_zero€szDecimal.is_zerocCsÆ|jt|jƒd}|dkr4tt|ddƒƒdS|dkrXttd|ddƒƒdSt|ƒ}|j|j}}|dkr¨t|d|ƒ}t|ƒ}t|ƒt|ƒ||kS|ttd||ƒƒdS)Nr.éržr,r&rŸr„)rOrfr8r`rirUrV)r/r;r+r,r®ÚnumÚdenr(r(r*Ú _ln_exp_bound„szDecimal._ln_exp_boundc Cs|dkrtƒ}|j|d}|r"|S|s*tS|jƒdkr:tS|tkrFtS|jdkr\|jt dƒSt |ƒ}|j|j}}|j }||jƒd}x>t|||ƒ}|ddttt|ƒƒƒ|dr¼P|d7}qŠWtt|dkƒtt|ƒƒ|ƒ}|jƒ}|jtƒ} |j|ƒ}| |_|S) N)r0r.zln of a negative valuer,rzržr[r&)rrŠÚ_NegativeInfinityr…Ú _Infinityrr6r7rdr rirUrVr@rEÚ_dlogrfr`rhr6r)r*rr¸r?) r/r0r;r+r,r®rr&rÉr?r(r(r*Úlns: $ z Decimal.lncCsÊ|jt|jƒd}|dkr,tt|ƒƒdS|dkrHttd|ƒƒdSt|ƒ}|j|j}}|dkr t|d|ƒ}td|ƒ}t|ƒt|ƒ||kdStd||ƒ}t|ƒ||dkdS) Nr.r,r&ržéçZ231rŸr„)rOrfr8r`rirUrV)r/r;r+r,r®rCrDr(r(r*rÏszDecimal._log10_exp_boundc CsH|dkrtƒ}|j|d}|r"|S|s*tS|jƒdkr:tS|jdkrP|jtdƒS|jddkr˜|jdd…dt |jƒdkr˜t |jt |jƒdƒ}nŠt|ƒ}|j |j}}|j}||jƒd}x>t|||ƒ}|dd t tt|ƒƒƒ|drøP|d 7}qÆWtt |dkƒtt|ƒƒ|ƒ}|jƒ}|jtƒ} |j|ƒ}| |_|S)N)r0r.zlog10 of a negative valuer&rÅrQr,rzržr[)rrŠrFr…rGr7rdr r8rfrrOrirUrVr@rÚ_dlog10r`rhr6r)r*rr¸r?) r/r0r;r+r,r®rr&rÉr?r(r(r*Úlog10ís: .$ z Decimal.log10cCsV|j|d}|r|S|dkr"tƒ}|jƒr.tS|s@|jtddƒSt|jƒƒ}|j|ƒS)N)r0zlogb(0)r.) rŠrr…rGrdr rrr¸)r/r0r;r(r(r*Úlogb s zDecimal.logbcCs8|jdks|jdkrdSx|jD]}|dkr dSq WdS)Nr&FZ01T)r7rOr8)r/Údigr(r(r*Ú _islogical> szDecimal._islogicalcCs€|jt|ƒ}|dkr$d||}n|dkr<||jd…}|jt|ƒ}|dkr`d||}n|dkrx||jd…}||fS)Nr&rQ)r@rf)r/r0ÚopaÚopbZdifr(r(r*Ú _fill_logicalL szDecimal._fill_logicalcCs~|dkrtƒ}t|dd}|jƒs.|jƒr8|jtƒS|j||j|jƒ\}}djdd„t||ƒDƒƒ}t d|j dƒpxddƒS)NT)r›rScSs$g|]\}}tt|ƒt|ƒ@ƒ‘qSr()r`rU)Ú.0rÚbr(r(r*ú g sz'Decimal.logical_and..r&rQ)rrœrOrdr rRr8rnÚzipr6rg)r/r‡r0rPrQr‚r(r(r*Úlogical_andY s zDecimal.logical_andcCs(|dkrtƒ}|jtdd|jdƒ|ƒS)Nr&rÅ)rÚlogical_xorr6r@)r/r0r(r(r*Úlogical_invertj szDecimal.logical_invertcCs~|dkrtƒ}t|dd}|jƒs.|jƒr8|jtƒS|j||j|jƒ\}}djdd„t||ƒDƒƒ}t d|j dƒpxddƒS)NT)r›rScSs$g|]\}}tt|ƒt|ƒBƒ‘qSr()r`rU)rSrrTr(r(r*rU sz&Decimal.logical_or..r&rQ)rrœrOrdr rRr8rnrVr6rg)r/r‡r0rPrQr‚r(r(r*Ú logical_orq s zDecimal.logical_orcCs~|dkrtƒ}t|dd}|jƒs.|jƒr8|jtƒS|j||j|jƒ\}}djdd„t||ƒDƒƒ}t d|j dƒpxddƒS)NT)r›rScSs$g|]\}}tt|ƒt|ƒAƒ‘qSr()r`rU)rSrrTr(r(r*rU sz'Decimal.logical_xor..r&rQ)rrœrOrdr rRr8rnrVr6rg)r/r‡r0rPrQr‚r(r(r*rX‚ s zDecimal.logical_xorcCs¾t|dd}|dkrtƒ}|js&|jr~|jƒ}|jƒ}|s>|r~|dkrX|dkrX|j|ƒS|dkrr|dkrr|j|ƒS|j||ƒS|jƒj|jƒƒ}|dkr¢|j|ƒ}|dkr°|}n|}|j|ƒS)NT)r›r.r&r„) rœrrPrƒr¸rŠr¶r’r/)r/r‡r0r0r1r,r;r(r(r*Úmax_mag“ s& zDecimal.max_magcCs¾t|dd}|dkrtƒ}|js&|jr~|jƒ}|jƒ}|s>|r~|dkrX|dkrX|j|ƒS|dkrr|dkrr|j|ƒS|j||ƒS|jƒj|jƒƒ}|dkr¢|j|ƒ}|dkr°|}n|}|j|ƒS)NT)r›r.r&r„) rœrrPrƒr¸rŠr¶r’r/)r/r‡r0r0r1r,r;r(r(r*Úmin_mag± s& zDecimal.min_magcCs |dkrtƒ}|j|d}|r"|S|jƒdkr2tS|jƒdkrTtdd|j|jƒƒS|jƒ}|jt ƒ|j ƒ|j|ƒ}||kr„|S|jtdd|j ƒdƒ|ƒS)N)r0r.r&r>rÅr„)rrŠr…rFr6r@rårHr*rÚ_ignore_all_flagsr¸rÃrÇ)r/r0r;Únew_selfr(r(r*Ú next_minusÏ s" zDecimal.next_minuscCs |dkrtƒ}|j|d}|r"|S|jƒdkr2tS|jƒdkrTtdd|j|jƒƒS|jƒ}|jt ƒ|j ƒ|j|ƒ}||kr„|S|jtdd|j ƒdƒ|ƒS)N)r0r.r>r&rÅr„)rrŠr…rGr6r@rårHr*rr]r¸rÂrÇ)r/r0r;r^r(r(r*Ú next_plusæ s" zDecimal.next_pluscCsÞt|dd}|dkrtƒ}|j||ƒ}|r.|S|j|ƒ}|dkrJ|j|ƒS|dkr^|j|ƒ}n |j|ƒ}|jƒr–|jt d|j ƒ|jtƒ|jtƒnD|j ƒ|jkrÚ|jtƒ|jtƒ|jtƒ|jtƒ|sÚ|jtƒ|S)NT)r›r&r.z Infinite result from next_towardr„)rœrrŠr’r9r`r_r…rdrr7rrrr#rr r)r/r‡r0r;Z comparisonr(r(r*Únext_towardý s4 zDecimal.next_towardcCsˆ|jƒrdS|jƒrdS|jƒ}|dkr,dS|d kr8dS|jƒrN|jrJdSdS|dkr\tƒ}|j|drv|jrrd Sd S|jr€dSdSdS)Nr†r«r.z +Infinityz -Infinityz-Zeroz+Zero)r0z -Subnormalz +Subnormalz-Normalz+Normalr„)r‹rŒr…rAr7rr@)r/r0Úinfr(r(r*Únumber_class+s,zDecimal.number_classcCstdƒS)Nrž)r)r/r(r(r*ÚradixUsz Decimal.radixcCsø|dkrtƒ}t|dd}|j||ƒ}|r.|S|jdkrB|jtƒS|jt|ƒko^|jknsn|jtƒS|jƒr~t |ƒSt|ƒ}|j }|jt|ƒ}|dkr°d||}n|dkrÆ||d…}||d…|d|…}t|j |jdƒpðd|jƒS)NT)r›r&rQ)rrœrŠrOrdr r@rUr…rr8rfr6r7rg)r/r‡r0r;ÚtorotÚrotdigÚtopadZrotatedr(r(r*ÚrotateYs, " zDecimal.rotatecCsÀ|dkrtƒ}t|dd}|j||ƒ}|r.|S|jdkrB|jtƒSd|j|j}d|j|j}|t|ƒkox|knsˆ|jtƒS|j ƒr˜t |ƒSt|j|j |jt|ƒƒ}|j|ƒ}|S)NT)r›r&r,rŸ)rrœrŠrOrdr rAr@rUr…rr6r7r8r¸)r/r‡r0r;ZliminfZlimsupr€r(r(r*Úscalebzs" zDecimal.scalebcCs|dkrtƒ}t|dd}|j||ƒ}|r.|S|jdkrB|jtƒS|jt|ƒko^|jknsn|jtƒS|jƒr~t |ƒSt|ƒ}|j }|jt|ƒ}|dkr°d||}n|dkrÆ||d…}|dkrÜ|d|…}n|d|}||jd…}t|j |jdƒpd|jƒS)NT)r›r&rQ)rrœrŠrOrdr r@rUr…rr8rfr6r7rg)r/r‡r0r;rerfrgZshiftedr(r(r*rÊ“s2 " z Decimal.shiftcCs|jt|ƒffS)N)Ú __class__r`)r/r(r(r*Ú __reduce__ºszDecimal.__reduce__cCst|ƒtkr|S|jt|ƒƒS)N)Útyperrjr`)r/r(r(r*Ú__copy__½szDecimal.__copy__cCst|ƒtkr|S|jt|ƒƒS)N)rlrrjr`)r/Úmemor(r(r*Ú__deepcopy__ÂszDecimal.__deepcopy__cCsN|dkrtƒ}t||d}|jrXt|j|ƒ}t|jƒƒ}|ddkrL|d7}t|||ƒS|ddkrvddg|j|d<|ddkr˜t |j|j |jdƒ}|j}|d}|dk r|ddkrÎ|j |d |ƒ}nF|dd krê|j||ƒ}n*|ddkrt|j ƒ|kr|j ||ƒ}|rB|jdkrB|dd krB|jd|ƒ}|jt|j ƒ} |ddkr‚|r||dk r|d |} nd } nB|dd kr–| } n.|ddkrÄ|jdkrÀ| dkrÀ| } nd } | dkräd}d| |j }nP| t|j ƒkr|j d| t|j ƒ}d}n"|j d| …p$d}|j | d…}| | } t|j||| |ƒS)N)Ú_localeconvrlú%ÚgÚGr,Ú precisionÚeEr.zfF%ZgGr&r¬rQrSiúÿÿÿ)rÚ_parse_format_specifierrPÚ_format_signr7r`r¶Ú _format_alignr°r6r8rOr?r'r¾rfÚ_format_number)r/Z specifierr0rpÚspecr=Úbodyr?rtr²r³rvrwrVr(r(r*Ú __format__ÉsZ " zDecimal.__format__)rOr8r7rP)rQN)NN)N)N)N)N)N)N)FN)N)N)N)TN)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)NN)N)N)NN)N)NN)NN)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)NN)r2r3r4Ú __slots__r^Úclassmethodrqrƒr…rŠrrŽr’r–r—r˜r™ršrr¦r§r}rªr´rµr¹rºr¼rÂÚ__radd__rÃrÄrÆÚ__rmul__rÍrÑrÒrÓrÔrÕrÖrØrÙrÚrÝrÞÚ __trunc__rßÚpropertyràrárãr9r¸rêrërìrîrðrñròróÚdictrærõrör÷rùrrrrr"rôr%r¾r'r(rüÚto_integralr.r½r©rúrûrr3r4r/r8r¶r·r9rVr<r=r$r r>rŒr?r‹r@rArErIrrLrMrOrRrWrYrZrXr[r\r_r`rarcrdrhrirÊrkrmror|r(r(r(r*r+s ( !@ 2 4 V7;!$K f >,UnY="c*" IK23 .*!'FcCs&tjtƒ}||_||_||_||_|S)N)r]r^rr7r8rOrP)r=ZcoefficientrZspecialr/r(r(r*r6s r6c@s$eZdZdd„Zdd„Zdd„ZdS)rNcCs|jƒ|_dS)N)rHÚnew_context)r/r…r(r(r*Ú__init__9sz_ContextManager.__init__cCstƒ|_t|jƒ|jS)N)rÚ saved_contextrr…)r/r(r(r*Ú __enter__;s z_ContextManager.__enter__cCst|jƒdS)N)rr‡)r/ÚtÚvÚtbr(r(r*Ú__exit__?sz_ContextManager.__exit__N)r2r3r4r†rˆrŒr(r(r(r*rN3srNc @s¨eZdZd¥dd„Zdd„Zdd„Zdd „Zd d„Zdd „Zdd„Z dd„Z dd„Zdd„Zdd„Z e Zd¦dd„Zdd„Zdd„Zdd„ZdZd d!„Zd"d#„Zd$d%„Zd§d'd(„Zd)d*„Zd+d,„Zd-d.„Zd/d0„Zd1d2„Zd3d4„Zd5d6„Zd7d8„Zd9d:„Z d;d<„Z!d=d>„Z"d?d@„Z#dAdB„Z$dCdD„Z%dEdF„Z&dGdH„Z'dIdJ„Z(dKdL„Z)dMdN„Z*dOdP„Z+dQdR„Z,dSdT„Z-dUdV„Z.dWdX„Z/dYdZ„Z0d[d\„Z1d]d^„Z2d_d`„Z3dadb„Z4dcdd„Z5dedf„Z6dgdh„Z7didj„Z8dkdl„Z9dmdn„Z:dodp„Z;dqdr„Zdwdx„Z?dydz„Z@d{d|„ZAd}d~„ZBdd€„ZCdd‚„ZDdƒd„„ZEd…d†„ZFd¨d‡dˆ„ZGd‰dŠ„ZHd‹dŒ„ZIddŽ„ZJdd„ZKd‘d’„ZLd“d”„ZMd•d–„ZNd—d˜„ZOd™dš„ZPd›dœ„ZQddž„ZRdŸd „ZSd¡d¢„ZTd£d¤„ZUeUZVdS)©rNc s>yt} Wntk rYnX|dk r*|n| j|_|dk r>|n| j|_|dk rR|n| j|_|dk rf|n| j|_|dk rz|n| j|_|dk rŽ|n| j|_| dkr¦g|_n| |_ˆdkrÂ| j j ƒ|_ n.tˆtƒsêt‡fdd„t ˆDƒƒ|_ nˆ|_ ˆdkr tjt dƒ|_n0tˆtƒs4t‡fdd„t ˆDƒƒ|_nˆ|_dS)Nc3s|]}|t|ˆkƒfVqdS)N)rU)rSrÜ)rr(r*ú nsz#Context.__init__..r&c3s|]}|t|ˆkƒfVqdS)N)rU)rSrÜ)rr(r*rus)rÚ NameErrorr@r?r#rAr°räÚ_ignored_flagsrrHr_rƒrÚfromkeysr)r/r@r?r#rAr°rärrrZdcr()rrr*r†Us. zContext.__init__cCs”t|tƒstd|ƒ‚|dkr<||kr†td||||fƒ‚nJ|dkrb||kr†td||||fƒ‚n$||ksr||kr†td||||fƒ‚tj|||ƒS)Nz%s must be an integerz-infz%s must be in [%s, %d]. got: %srbz%s must be in [%d, %s]. got: %sz%s must be in [%d, %d]. got %s)r_rUrrrlr]Ú__setattr__)r/ÚnamertZvminZvmaxr(r(r*Ú_set_integer_checkys zContext._set_integer_checkcCsht|tƒstd|ƒ‚x |D]}|tkrtd|ƒ‚qWx tD]}||kr>td|ƒ‚q>Wtj|||ƒS)Nz%s must be a signal dictz%s is not a valid signal dict)r_rƒrrrÚKeyErrorr]r‘)r/r’r€Úkeyr(r(r*Ú_set_signal_dict‡s zContext._set_signal_dictcCsä|dkr|j||ddƒS|dkr0|j||ddƒS|dkrH|j||ddƒS|dkr`|j||ddƒS|d krx|j||ddƒS|d kr¢|tkr”td|ƒ‚tj|||ƒS|dks²|d kr¾|j||ƒS|dkrÔtj|||ƒStd|ƒ‚dS)Nr@r.rbr#z-infr&rAr°rär?z%s: invalid rounding moderrrz.'decimal.Context' object has no attribute '%s')r“Ú_rounding_modesrrr]r‘r–rL)r/r’rtr(r(r*r‘’s(zContext.__setattr__cCstd|ƒ‚dS)Nz%s cannot be deleted)rL)r/r’r(r(r*Ú__delattr__«szContext.__delattr__c CsNdd„|jjƒDƒ}dd„|jjƒDƒ}|j|j|j|j|j|j|j ||ffS)NcSsg|]\}}|r|‘qSr(r()rSÚsigrŠr(r(r*rU°sz&Context.__reduce__..cSsg|]\}}|r|‘qSr(r()rSr™rŠr(r(r*rU±s) rÚitemsrrjr@r?r#rAr°rä)r/rrr(r(r*rk¯s zContext.__reduce__cCs|g}|jdt|ƒƒdd„|jjƒDƒ}|jddj|ƒdƒdd„|jjƒDƒ}|jddj|ƒdƒdj|ƒd S) NzrContext(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, clamp=%(clamp)dcSsg|]\}}|r|j‘qSr()r2)rSrrŠr(r(r*rU½sz$Context.__repr__..zflags=[z, ú]cSsg|]\}}|r|j‘qSr()r2)rSr‰rŠr(r(r*rU¿sztraps=[ú))rmÚvarsrršrnr)r/rÜÚnamesr(r(r*rª¶szContext.__repr__cCsx|jD]}d|j|<qWdS)Nr&)r)r/Úflagr(r(r*rIÃszContext.clear_flagscCsx|jD]}d|j|<qWdS)Nr&)r)r/rŸr(r(r*Úclear_trapsÈszContext.clear_trapsc Cs.t|j|j|j|j|j|j|j|j|j ƒ }|S)N) rr@r?r#rAr°rärrr)r/Úncr(r(r*r)ÍszContext._shallow_copyc Cs6t|j|j|j|j|j|j|jjƒ|j jƒ|j ƒ }|S)N)rr@r?r#rAr°rärrHrr)r/r¡r(r(r*rHÔs zContext.copycGsZtj||ƒ}||jkr(|ƒj|f|žŽSd|j|<|j|sN|ƒj|f|žŽS||ƒ‚dS)Nr.)Ú_condition_mapÚgetrr1rr)r/Z conditionZexplanationr)Úerrorr(r(r*rdÝs zContext._raise_errorcCs |jtŽS)N)Ú _ignore_flagsr)r/r(r(r*r]ószContext._ignore_all_flagscGs|jt|ƒ|_t|ƒS)N)rrj)r/rr(r(r*r¥÷szContext._ignore_flagscGs<|rt|dttfƒr|d}x|D]}|jj|ƒq$WdS)Nr&)r_rkrjrÚremove)r/rrŸr(r(r*Ú _regard_flagsþs zContext._regard_flagscCst|j|jdƒS)Nr.)rUr#r@)r/r(r(r*rÇsz Context.EtinycCst|j|jdƒS)Nr.)rUrAr@)r/r(r(r*råszContext.EtopcCs|j}||_|S)N)r?)r/rlr?r(r(r*r*szContext._set_roundingrQcCsjt|tƒr*||jƒksd|kr*|jtdƒSt||d}|jƒr`t|jƒ|j |j kr`|jtdƒS|j|ƒS)NrRzAtrailing or leading whitespace and underscores are not permitted.)r0zdiagnostic info too long in NaN)r_r`rbrdrrrƒrfr8r@rär¸)r/rCr€r(r(r*Úcreate_decimal#szContext.create_decimalcCstj|ƒ}|j|ƒS)N)rrqr¸)r/rr€r(r(r*Úcreate_decimal_from_float4s z!Context.create_decimal_from_floatcCst|dd}|j|dS)NT)r›)r0)rœr¼)r/rr(r(r*rhFszContext.abscCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)NT)r›)r0zUnable to convert %s to Decimal)rœrÂr•rr)r/rrTrÐr(r(r*Úadd[s zContext.addcCst|j|ƒƒS)N)r`r¸)r/rr(r(r*Ú_applypszContext._applycCst|tƒstdƒ‚|jƒS)Nz,canonical requires a Decimal as an argument.)r_rrrr3)r/rr(r(r*r3ss zContext.canonicalcCst|dd}|j||dS)NT)r›)r0)rœr)r/rrTr(r(r*r€s!zContext.comparecCst|dd}|j||dS)NT)r›)r0)rœr4)r/rrTr(r(r*r4¤s zContext.compare_signalcCst|dd}|j|ƒS)NT)r›)rœr/)r/rrTr(r(r*r/ÇszContext.compare_totalcCst|dd}|j|ƒS)NT)r›)rœr8)r/rrTr(r(r*r8äszContext.compare_total_magcCst|dd}|jƒS)NT)r›)rœr¶)r/rr(r(r*r¶ìs zContext.copy_abscCst|dd}t|ƒS)NT)r›)rœr)r/rr(r(r*Úcopy_decimalùs zContext.copy_decimalcCst|dd}|jƒS)NT)r›)rœr·)r/rr(r(r*r·s zContext.copy_negatecCst|dd}|j|ƒS)NT)r›)rœr9)r/rrTr(r(r*r9szContext.copy_signcCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)NT)r›)r0zUnable to convert %s to Decimal)rœrÍr•rr)r/rrTrÐr(r(r*Údivide+s zContext.dividecCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)NT)r›)r0zUnable to convert %s to Decimal)rœrÙr•rr)r/rrTrÐr(r(r*Ú divide_intPs zContext.divide_intcCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)NT)r›)r0zUnable to convert %s to Decimal)rœrÓr•rr)r/rrTrÐr(r(r*rÈgs zContext.divmodcCst|dd}|j|dS)NT)r›)r0)rœrV)r/rr(r(r*rV|szContext.expcCst|dd}|j|||dS)NT)r›)r0)rœrù)r/rrTr,r(r(r*rù”szContext.fmacCst|tƒstdƒ‚|jƒS)Nz/is_canonical requires a Decimal as an argument.)r_rrrr<)r/rr(r(r*r<«s zContext.is_canonicalcCst|dd}|jƒS)NT)r›)rœr=)r/rr(r(r*r=¸szContext.is_finitecCst|dd}|jƒS)NT)r›)rœr$)r/rr(r(r*r$ÎszContext.is_infinitecCst|dd}|jƒS)NT)r›)rœr )r/rr(r(r*r Ýs zContext.is_nancCst|dd}|j|dS)NT)r›)r0)rœr>)r/rr(r(r*r>íszContext.is_normalcCst|dd}|jƒS)NT)r›)rœrŒ)r/rr(r(r*rŒszContext.is_qnancCst|dd}|jƒS)NT)r›)rœr?)r/rr(r(r*r?szContext.is_signedcCst|dd}|jƒS)NT)r›)rœr‹)r/rr(r(r*r‹$s zContext.is_snancCst|dd}|j|dS)NT)r›)r0)rœr@)r/rr(r(r*r@4szContext.is_subnormalcCst|dd}|jƒS)NT)r›)rœrA)r/rr(r(r*rAJszContext.is_zerocCst|dd}|j|dS)NT)r›)r0)rœrI)r/rr(r(r*rI[sz Context.lncCst|dd}|j|dS)NT)r›)r0)rœrL)r/rr(r(r*rLqsz Context.log10cCst|dd}|j|dS)NT)r›)r0)rœrM)r/rr(r(r*rMszContext.logbcCst|dd}|j||dS)NT)r›)r0)rœrW)r/rrTr(r(r*rW§szContext.logical_andcCst|dd}|j|dS)NT)r›)r0)rœrY)r/rr(r(r*rYÂszContext.logical_invertcCst|dd}|j||dS)NT)r›)r0)rœrZ)r/rrTr(r(r*rZÕszContext.logical_orcCst|dd}|j||dS)NT)r›)r0)rœrX)r/rrTr(r(r*rXðszContext.logical_xorcCst|dd}|j||dS)NT)r›)r0)rœr½)r/rrTr(r(r*r½szContext.maxcCst|dd}|j||dS)NT)r›)r0)rœr[)r/rrTr(r(r*r[&szContext.max_magcCst|dd}|j||dS)NT)r›)r0)rœr©)r/rrTr(r(r*r©7szContext.mincCst|dd}|j||dS)NT)r›)r0)rœr\)r/rrTr(r(r*r\RszContext.min_magcCst|dd}|j|dS)NT)r›)r0)rœr¹)r/rr(r(r*Úminuscsz Context.minuscCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)NT)r›)r0zUnable to convert %s to Decimal)rœrÆr•rr)r/rrTrÐr(r(r*Úmultiplyts zContext.multiplycCst|dd}|j|dS)NT)r›)r0)rœr_)r/rr(r(r*r_”szContext.next_minuscCst|dd}|j|dS)NT)r›)r0)rœr`)r/rr(r(r*r`¨szContext.next_pluscCst|dd}|j||dS)NT)r›)r0)rœra)r/rrTr(r(r*ra¼s zContext.next_towardcCst|dd}|j|dS)NT)r›)r0)rœr")r/rr(r(r*r"ßszContext.normalizecCst|dd}|j|dS)NT)r›)r0)rœrc)r/rr(r(r*rc÷s/zContext.number_classcCst|dd}|j|dS)NT)r›)r0)rœrº)r/rr(r(r*Úplus)szContext.pluscCs:t|dd}|j|||d}|tkr2td|ƒ‚n|SdS)NT)r›)r0zUnable to convert %s to Decimal)rœrr•rr)r/rrTrþrÐr(r(r*Úpower:s Iz Context.powercCst|dd}|j||dS)NT)r›)r0)rœrô)r/rrTr(r(r*rôŠs7zContext.quantizecCstdƒS)Nrž)r)r/r(r(r*rdÄsz Context.radixcCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)NT)r›)r0zUnable to convert %s to Decimal)rœrÕr•rr)r/rrTrÐr(r(r*rËÌs zContext.remaindercCst|dd}|j||dS)NT)r›)r0)rœrØ)r/rrTr(r(r*rØòszContext.remainder_nearcCst|dd}|j||dS)NT)r›)r0)rœrh)r/rrTr(r(r*rhszContext.rotatecCst|dd}|j|ƒS)NT)r›)rœr%)r/rrTr(r(r*r%1szContext.same_quantumcCst|dd}|j||dS)NT)r›)r0)rœri)r/rrTr(r(r*riIszContext.scalebcCst|dd}|j||dS)NT)r›)r0)rœrÊ)r/rrTr(r(r*rÊ\sz Context.shiftcCst|dd}|j|dS)NT)r›)r0)rœr.)r/rr(r(r*r.zszContext.sqrtcCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)NT)r›)r0zUnable to convert %s to Decimal)rœrÃr•rr)r/rrTrÐr(r(r*Úsubtractšs zContext.subtractcCst|dd}|j|dS)NT)r›)r0)rœrµ)r/rr(r(r*rµ±szContext.to_eng_stringcCst|dd}|j|dS)NT)r›)r0)rœr´)r/rr(r(r*Ú to_sci_stringÍszContext.to_sci_stringcCst|dd}|j|dS)NT)r›)r0)rœr()r/rr(r(r*r(ÕszContext.to_integral_exactcCst|dd}|j|dS)NT)r›)r0)rœrü)r/rr(r(r*rüószContext.to_integral_value) NNNNNNNNN)N)rQ)N)Wr2r3r4r†r“r–r‘r˜rkrªrIr r)rHrmrdr]r¥r§r¦rÇrår*r¨r©rhrªr«r3rr4r/r8r¶r¬r·r9rr®rÈrVrùr<r=r$r r>rŒr?r‹r@rArIrLrMrWrYrZrXr½r[r©r\r¯r°r_r`rar"rcr±r²rôrdrËrØrhr%rirÊr.r³rµr´r(rür„r(r(r(r*rBs¬ " $# % #2 P:&" c@s&eZdZd Zd dd„Zdd„ZeZdS)rir=rUrVNcCsf|dkrd|_d|_d|_nFt|tƒrD|j|_t|jƒ|_|j|_n|d|_|d|_|d|_dS)Nr&r.r,)r=rUrVr_rr7r8rO)r/rtr(r(r*r†s z_WorkRep.__init__cCsd|j|j|jfS)Nz(%r, %r, %r))r=rUrV)r/r(r(r*rª(sz_WorkRep.__repr__)r=rUrV)N)r2r3r4r}r†rªr´r(r(r(r*ris ricCsš|j|jkr|}|}n|}|}tt|jƒƒ}tt|jƒƒ}|jtd||dƒ}||jd|krpd|_||_|jd|j|j9_|j|_||fS)Nr.r,ržr„)rVrfr`rUr©)rÀrÁr@Ztmpr‡Ztmp_lenZ other_lenrVr(r(r*r¿/sr¿cCsb|dkrdS|dkr |d|Stt|ƒƒ}t|ƒt|jdƒƒ}||krPdS|d|SdS)Nr&ržrQ)r`rhrfÚrstrip)r5r®Zstr_nZval_nr(r(r*r Osr cCsF|dks|dkrtdƒ‚d}x$||kr@||||d?}}qW|S)Nr&z3Both arguments to _sqrt_nearest should be positive.r.)rl)r5rrTr(r(r*Ú _sqrt_nearestds r¶cCs2d|>||?}}|d||d@|d@|kS)Nr.r,r()r rÊrTrÏr(r(r*Ú_rshift_nearestssr·cCs&t||ƒ\}}|d||d@|kS)Nr,r.)rÈ)rrTrÏrÐr(r(r*Ú_div_nearest{sr¸rc Csî||}d}xn||kr*t|ƒ||>|ksF||krzt|ƒ||?|krzt||d>|t||t||ƒ|ƒƒ}|d7}qWtdtt|ƒƒd|ƒ}t||ƒ}t||ƒ}x0t|dddƒD]}t||ƒt|||ƒ}qÀWt|||ƒS)Nr&r.ržr[iöÿÿÿr„)rhr¸r¶r·rUrfr`rý) r ÚMÚLrÚRÚTZyshiftÚwrr(r(r*Ú_ilogƒs r¾c Cs¶|d7}tt|ƒƒ}||||dk}|dkr”d|}|||}|dkrZ|d|9}nt|d|ƒ}t||ƒ}t|ƒ}t|||ƒ}||} nd}t|d|ƒ} t| |dƒS)Nr,r.r&ržr)rfr`r¸r¾Ú _log10_digits) r,r®rr-rr¹rÚlog_dZlog_10Zlog_tenpowerr(r(r*rK³s rKc CsÎ|d7}tt|ƒƒ}||||dk}|dkrr|||}|dkrR|d|9}nt|d|ƒ}t|d|ƒ}nd}|r¼ttt|ƒƒƒd}||dkr¶t|t||ƒd|ƒ}qÀd}nd}t||dƒS)Nr,r.r&ržr)rfr`r¸r¾rhr¿) r,r®rr-rrrÀrZ f_log_tenr(r(r*rHÕs"rHc@seZdZdd„Zdd„ZdS)Ú _Log10MemoizecCs d|_dS)NZ/23025850929940456840179914546843642076011014886)rx)r/r(r(r*r†sz_Log10Memoize.__init__cCsš|dkrtdƒ‚|t|jƒkr„d}xLd||d}tttd||ƒdƒƒ}||d…d|krdP|d7}q$W|jdƒdd …|_t|jd|d…ƒS) Nr&zp should be nonnegativer[ržr,rrQr.r„)rlrfrxr`r¸r¾rµrU)r/rrr¹rxr(r(r*Ú getdigitss z_Log10Memoize.getdigitsN)r2r3r4r†rÂr(r(r(r*rÁsrÁc Cs°t||>|ƒ}tdtt|ƒƒd|ƒ}t||ƒ}||>}x.t|dddƒD]}t|||||ƒ}qRWx6t|ddd ƒD]"}||d>}t||||ƒ}q‚W||S) Nržr[r.r&r,iöÿÿÿr„r„r„)r rUrfr`r¸rý) r r¹rºr»r¼rZMshiftrrr(r(r*Ú_iexp&s rÃc Cs–|d7}td|tt|ƒƒdƒ}||}||}|dkrH|d|}n|d|}t|t|ƒƒ\}}t|d|ƒ}tt|d|ƒdƒ||dfS)Nr,r&r.ržièr[)r½rfr`rÈr¿r¸rÃ) r,r®rrrÏrÊZcshiftZquotrr(r(r*r:Ksr:cCsèttt|ƒƒƒ|}t||||dƒ}||}|dkrJ||d|}nt||d|ƒ}|dkr´tt|ƒƒ|dk|dkkržd|ddd|} } qàd|d|} } n,t||d|dƒ\} } t| dƒ} | d7} | | fS)Nr.r&rž)rfr`rhrHr¸r:)rrrrrrTZlxcrÊZpcrÉrVr(r(r*ros rréFé5é(érBéržrz) rÅÚ2Ú3Ú4Ú5Ú6Ú7Ú8r>cCs0|dkrtdƒ‚t|ƒ}dt|ƒ||dS)Nr&z0The argument to _log10_lb should be nonnegative.r)rlr`rf)r,Z correctionZstr_cr(r(r*r™srcCsLt|tƒr|St|tƒr t|ƒS|r8t|tƒr8tj|ƒS|rHtd|ƒ‚tS)NzUnable to convert %s to Decimal)r_rrUrprqrrr•)r‡r›Zallow_floatr(r(r*rœ¤s rœcCs´t|tƒr||fSt|tjƒrR|jsDt|jtt|j ƒ|j ƒ|jƒ}|t|jƒfS|rrt|tj ƒrr|jdkrr|j}t|tƒr¬tƒ}|r’d|jt<n|jtdƒ|tj|ƒfSttfS)Nr&r.z;strict semantics for mixing floats and Decimals are enabled)r_rÚ_numbersZRationalrPr6r7r`rUr8ÚdenominatorrOÚ numeratorZComplexràrßrprrrrdrqr•)r/r‡r“r0r(r(r*r”·s$ r”ri?B)r@r?rrrAr#r°rär\)r@r?rra· # A numeric string consists of: # \s* (?P[-+])? # an optional sign, followed by either... ( (?=\d|\.\d) # ...a number (with at least one digit) (?P\d*) # having a (possibly empty) integer part (\.(?P\d*))? # followed by an optional fractional part (E(?P[-+]?\d+))? # followed by an optional exponent, or... | Inf(inity)? # ...an infinity, or... | (?Ps)? # ...an (optionally signaling) NaN # NaN (?P\d*) # with (possibly empty) diagnostic info. ) # \s* \Z z0*$z50*$zÉ\A (?: (?P.)? (?P[<>=^]) )? (?P[-+ ])? (?P\#)? (?P0)? (?P(?!0)\d+)? (?P,)? (?:\.(?P0|(?!0)\d+))? (?P[eEfFgGn%])? \Z cCs”tj|ƒ}|dkrtd|ƒ‚|jƒ}|d}|d}|ddk |d<|drv|dk rbtd|ƒ‚|dk rvtd|ƒ‚|p|d|d<|pˆd|d<|d dkr¢d |d <t|dp®dƒ|d<|d dk rÒt|d ƒ|d <|d dkrþ|ddksö|ddkrþd|d <|ddkrfd|d<|dkr&tjƒ}|ddk r@td|ƒ‚|d|d<|d|d<|d|d<n*|ddkr|d|d<ddg|d<d|d<|S)NzInvalid format specifier: ÚfillÚalignÚzeropadz7Fill character conflicts with '0' in format specifier: z2Alignment conflicts with '0' in format specifier: ú ú>r=rTÚminimumwidthrQrtr&rlZgGnr.r5rrÚ thousands_sepzJExplicit thousands separator conflicts with 'n' type in format specifier: ÚgroupingÚ decimal_pointrSr[r)Ú_parse_format_specifier_regexÚmatchrlÚ groupdictrUÚ_localeÚ localeconv)Úformat_specrpruZformat_dictrÓrÔr(r(r*rvDsN rvc Cs´|d}|d}||t|ƒt|ƒ}|d}|dkrF|||}nj|dkr\|||}nT|dkrr|||}n>|dkr¨t|ƒd}|d|…||||d…}ntd ƒ‚|S) NrØrÓrÔúus~ & . ^ 0",# %$+ * P % )