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_pydecimal.cpython-311.opt-2.pyc
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G d@ dAe: Z@ G dB dCe: ZAdvdDZBeCjD ZEdE ZFdF ZGdG ZHdH ZIdwdJZJdK ZKdL ZL G dM dNe: ZM eM jN ZOdwdOZPdP ZQdQ ZRdRdSdTdUdVdWdXdYdZd[ fd\ZSdxd]ZTdud^ZU e@d_ee$e+e!gg d`daddb ZV e@dcee$e+e!e e,gg d ZW e@dceg g d ZXddlYZY eYjZ deeYj[ eYj\ z j] Z^ eYjZ df j] Z_ eYjZ dg j] Z` eYjZ dheYj[ eYja z Zb[Y ddlcZdn # e$ r Y nw xY wdtdiZedj Zfdk ZgdydlZhdm Zidn Zj e;do Zk e;dp Zl e;dq Zm e;d Zn e;d Zo e;dr ZpekelfZqe jr js Zte jr ju Zve jr jw Zx eydYetdsz et Zz[ dS )z)%DecimalContext DecimalTupleDefaultContext BasicContextExtendedContextDecimalExceptionClampedInvalidOperationDivisionByZeroInexactRounded SubnormalOverflow UnderflowFloatOperationDivisionImpossibleInvalidContextConversionSyntaxDivisionUndefined ROUND_DOWN ROUND_HALF_UPROUND_HALF_EVEN ROUND_CEILING ROUND_FLOORROUND_UPROUND_HALF_DOWN ROUND_05UP setcontext getcontext localcontextMAX_PRECMAX_EMAXMIN_EMIN MIN_ETINY HAVE_THREADSHAVE_CONTEXTVARdecimalz1.70z2.4.2 N) namedtupler zsign digits exponentc | S N )argss 1/opt/alt/python311/lib64/python3.11/_pydecimal.py<lambda>r/ s r r r r r r r r Tl l NZolNZoi@Ti c e Zd Z d ZdS )r c d S r+ r, selfcontextr- s r. handlezDecimalException.handle s r0 N__name__ __module__ __qualname__r7 r, r0 r. r r s( $ r0 r c e Zd ZdS )r Nr9 r: r; r, r0 r. r r r0 r c e Zd Z d ZdS )r c |r=t |d j |d j dd }| | S t S )Nr( nT)_dec_from_triple_sign_int_fix_nan_NaN)r5 r6 r- anss r. r7 zInvalidOperation.handle s@ )"47=$q',TJJC<<(( ( r0 Nr8 r, r0 r. r r s( , r0 r c e Zd Z d ZdS )r c t S r+ rF r4 s r. r7 zConversionSyntax.handle r0 Nr8 r, r0 r. r r s( r0 r c e Zd Z d ZdS )r c t | S r+ )_SignedInfinityr5 r6 signr- s r. r7 zDivisionByZero.handle s t$$r0 Nr8 r, r0 r. r r s( % % % % %r0 r c e Zd Z d ZdS )r c t S r+ rJ r4 s r. r7 zDivisionImpossible.handle" rK r0 Nr8 r, r0 r. r r ( r0 r c e Zd Z d ZdS )r c t S r+ rJ r4 s r. r7 zDivisionUndefined.handle- rK r0 Nr8 r, r0 r. r r % rS r0 r c e Zd ZdS )r Nr= r, r0 r. r r 0 r> r0 r c e Zd Z d ZdS )r c t S r+ rJ r4 s r. r7 zInvalidContext.handleG rK r0 Nr8 r, r0 r. r r < s( r0 r c e Zd ZdS )r Nr= r, r0 r. r r J r> r0 r c e Zd ZdS )r Nr= r, r0 r. r r V s r0 r c e Zd Z d ZdS )r c |j t t t t fv r t | S |dk rF|j t k r t | S t |d|j z |j |j z dz S |dk rF|j t k r t | S t |d|j z |j |j z dz S d S )Nr( 9r1 ) roundingr r r r rN r rB precEmaxr rO s r. r7 zOverflow.handlew s / ; ; ;"4( ( 199 =00&t,,#D#gl*: #L 5a 79 9 9 199 ;..&t,,#D#gl*: $\', 6q 8: : : 9r0 Nr8 r, r0 r. r r a s( * : : : : :r0 r c e Zd ZdS )r Nr= r, r0 r. r r r0 r c e Zd ZdS )r Nr= r, r0 r. r r rb r0 r decimal_context)r_ Eminr` capitalsclampr^ flagstrapsc t S # t $ r- t } t | | cY S w xY wr+ )_current_context_varget LookupErrorr setr6 s r. r r s_ #''))) )) )))s 4AAc | t t t fv r(| } | t | d S r+ )r r r copy clear_flagsrk rn ro s r. r r sP />< AAA,,.. W%%%%%r0 c | t } t | }| D ]7\ }}|t vrt d| d t |j || 8|S )N'z2' is an invalid keyword argument for this function)r _ContextManageritems_context_attributes TypeErrorsetattr new_context)ctxkwargs ctx_managerkeyvalues r. r r s "F {ll!#&&K llnn 5 5 U ) ) ) W W W WXX X 'e4444 r0 c e Zd Z dZd|dZed Zd Zd Zd}dZ d Z d Z d Z d~d Z d~d Zd~dZd~dZd~dZd~dZd Zd Zd Zd ZddZd~dZd~dZd~dZdd Zd~d Z e Z d~d Z d~d Z d~d Z e Z!d~d!Z"d" Z#d~d#Z$d~d$Z%d~d%Z&d~d&Z'd~d'Z(d~d(Z)d~d)Z*d~d*Z+d+ Z,d, Z-e-Z.e/d- Z0e/d. Z1d/ Z2d0 Z3d1 Z4d2 Z5d3 Z6d4 Z7d5 Z8d6 Z9d7 Z:d8 Z;d9 Z<d: Z= e>e6e7e8e9e:e;e<e=; Z?d~d<Z@d= ZAd> ZBd~d?ZCd~d@ZDdA ZEd}dBZFd~dCZGd~dDZHd}dEZId~dFZJdG ZKdH ZLd}dIZMd}dJZNeNZOd~dKZPd~dLZQd~dMZRdN ZSdO ZTdP ZUdQ ZVd~dRZWd~dSZXd~dTZYdU ZZdV Z[d~dWZ\d~dXZ]dY Z^dZ Z_d[ Z`d\ Zad~d]Zbd^ Zcd_ Zdd` Zed~daZfdb Zgdc Zhd~ddZide Zjd~dfZkd~dgZldh Zmdi Znd~djZod~dkZpd~dlZqd~dmZrd~dnZsd~doZtd~dpZud~dqZvd~drZwd~dsZxdt Zyd~duZzd~dvZ{d~dwZ|dx Z}dy Z~dz Zd}d{ZdS )r )_exprD rC _is_special0Nc z t | }t |t rt | dd }|.|t }| t d|z S | d dk rd|_ nd|_ | d }|~| d pd}t | d pd }t t ||z |_ |t | z |_ d |_ n| d }|[t t |pd d |_ | d rd|_ nd|_ nd |_ d|_ d|_ |S t |t rF|dk rd|_ nd|_ d|_ t t% | |_ d |_ |S t |t& r2|j |_ |j |_ |j |_ |j |_ |S t |t( rG|j |_ t |j |_ t |j |_ d |_ |S t |t. t0 f rt | dk rt3 d t |d t r |d dv st3 d |d |_ |d dk r d |_ |d |_ d|_ ng } |d D ]S} t | t r.d| cxk rdk r!n n | s| dk r| | Et3 d |d dv rBd t9 t | |_ |d |_ d|_ not |d t rEd t9 t | pdg |_ |d |_ d |_ nt3 d |S t |t: rw|t }| t< d t& | }|j |_ |j |_ |j |_ |j |_ |S tA d |z ) N_ z Invalid literal for Decimal: %rrP -r1 r( intfracexpr FdiagsignalNrA FT ztInvalid tuple size in creation of Decimal from list or tuple. The list or tuple should have exactly three elements.r( r1 z|Invalid sign. The first value in the tuple should be an integer; either 0 for a positive number or 1 for a negative number. zTThe second value in the tuple must be composed of integers in the range 0 through 9.rA r zUThe third value in the tuple must be an integer, or one of the strings 'F', 'n', 'N'.;strict semantics for mixing floats and Decimals are enabledz Cannot convert %r to Decimal)!object__new__ isinstancestr_parserstripreplacer _raise_errorr grouprC r rD lenr r lstripabsr _WorkReprP r listtuple ValueErrorappendjoinmapfloatr from_floatrx ) clsr r6 r5 mintpartfracpartr r digitsdigits r. r zDecimal.__new__ s , ~~c"" eS ! ! " --c26677Ay? (llG ++,< AE IK K K wwv#%% ggennG" 776??0b!''%../C00 GH$4 5 5 6 6 #h-- / #( wwv# #C $4$4 5 5 < <S A ADIwwx(( ($' $' !$DI #DI#' K eS ! ! zz DICJJDI $D K eW % % DI DJ DI % 1D K eX & & DJEIDIEIDI $D K ed5\ * * * 5zzQ "G H H H uQx-- P%(e2C2C "O P P P qDJQx3 !!H #' "1X 9 9E!%-- 9!u/////////! 1UaZZ "MM% 0 0 0 ( *8 9 9 9 8z)) "C(8(8 9 9DI %aDI'+D$$ a#.. ? "C A3(?(? @ @DI %aDI',D$$$ &> ? ? ? K eU # # $,, &&u--E DI DJ DI % 1D K6>???r0 c v t |t r)|dk rdnd}d}t t | }nt |t rt j | st j | r | t | S t j d| dk rd}nd}t | \ }}| dz }t |d|z z }nt d t ||| }| t u r|S | | S )Nr( r1 g ? z argument must be int or float.)r r r r r _mathisinfisnanreprcopysignas_integer_ratio bit_lengthrx rB r )r frP kcoeffrA dresults r. r zDecimal.from_float s, ( a >Q11ADAAKKEE 5 ! ! >{1~~ $Q $s477||#~c1%%,,q66**,,DAq "A!Q$KKEE <== =!$r22 '>>M3v;; r0 c D | j r| j }|dk rdS |dk rdS dS )NrA r1 r r r( )r r )r5 r s r. _isnanzDecimal._isnan s< )Cczzqqqr0 c 4 | j dk r | j rdS dS dS )Nr r1 r( )r rC r5 s r. _isinfinityzDecimal._isinfinity s/ 9 z r1qr0 c j | }|d}n| }|s|r|t }|dk r | t d| S |dk r | t d| S |r| | S | | S dS )NFr sNaNr( )r r r r rE )r5 otherr6 self_is_nan other_is_nans r. _check_nanszDecimal._check_nans s kkmm = LL <<>>L +, +$,,a ++,<f(,. . .q ++,<f(-/ / / .}}W--->>'** *qr0 c |t }| j s|j r| r | t d| S | r | t d| S | r | t d| S | r | t d| S dS )Nzcomparison involving sNaNzcomparison involving NaNr( )r r is_snanr r is_qnanr5 r r6 s r. _compare_check_nanszDecimal._compare_check_nans s ? llG 3u 0 3||~~ 3 ++,<,G,02 2 2 3 ++,<,G,13 3 3 3 ++,<,F,02 2 2 3 ++,<,F,13 3 3 qr0 c ( | j p | j dk S Nr r rD r s r. __bool__zDecimal.__bool__4 s 349#33r0 c V | j s|j r:| }| }||k rdS ||k rdS dS | s|sdS d|j z S |s d| j z S |j | j k rdS | j |j k rdS | }| }||k rW| j d| j |j z z z }|j d|j | j z z z }||k rdS ||k r d| j z S d| j z S ||k r d| j z S d| j z S )Nr( r r1 r )r r rC adjustedrD r )r5 r self_inf other_inf self_adjustedother_adjusted self_padded other_paddeds r. _cmpz Decimal._cmp; s D u 0 ''))H ))++I9$$qI%%rq , ,q u{*++ $# # ; # #2 : # #1 )) N * * )c49uz+A&BBK :UZ$)-C(DDLl**q |++dj(((TZ'' ^ + +# #4:%& &r0 c t | |d \ } }|t u r|S | || rdS | | dk S )NT) equality_opFr( )_convert_for_comparisonNotImplementedr r r s r. __eq__zDecimal.__eq__{ s^ -dEtLLL e N " "L E7 + + 5yy 1$$r0 c t | | \ } }|t u r|S | || }|rdS | | dk S NFr( r r r r r5 r r6 rG s r. __lt__zDecimal.__lt__ ^ -dE:: e N " "L&&ug66 5yy !##r0 c t | | \ } }|t u r|S | || }|rdS | | dk S r r r s r. __le__zDecimal.__le__ ^ -dE:: e N " "L&&ug66 5yy 1$$r0 c t | | \ } }|t u r|S | || }|rdS | | dk S r r r s r. __gt__zDecimal.__gt__ r r0 c t | | \ } }|t u r|S | || }|rdS | | dk S r r r s r. __ge__zDecimal.__ge__ r r0 c t |d }| j s |r!|j r| || }|r|S t | | S NTraiseit)_convert_otherr r r r r s r. comparezDecimal.compare su ud333 %*; ""5'22C tyy''(((r0 c | j rg| rt d | rt | S | j rt S t S | j dk r t d| j t }n!t t | j t }t | j |z t z }| dk r|n| }|dk rdn|S )Nz"Cannot hash a signaling NaN value.r( r )r r rx is_nanr __hash__rC _PyHASH_INFr pow_PyHASH_MODULUS _PyHASH_10INVr rD )r5 exp_hashhash_rG s r. r zDecimal.__hash__ s ' '||~~ ' DEEE ' t,,,: ' '<'&& 9>>2ty/::HH=49*oFFHDI)O;qyyeeufBYYrrC'r0 c t | j t t t | j | j S r+ )r rC r r r rD r r s r. as_tuplezDecimal.as_tuple s3 DJc#ty.A.A(B(BDINNNr0 c | j r2| rt d t d | sdS t | j }| j dk r|d| j z z d}}nu| j }|dk r"|dz dk r|dz }|dz }|dk r |dz dk | j }t || z dz | }|r ||z }||z }d|z |z }| j r| }||fS )Nz#cannot convert NaN to integer ratioz(cannot convert Infinity to integer ratior r( r r1 r ) r r r OverflowErrorr rD r minr rC )r5 rA r d5d2shift2s r. r zDecimal.as_integer_ratio s< P{{}} P !FGGG#$NOOO 4 NN 9>>r49}$aqAA )Bq&&QUaZZaa q&&QUaZZ )B!qb&,,..2B77F f f 2 A : A!t r0 c ( dt | z S )Nz Decimal('%s'))r r s r. __repr__zDecimal.__repr__ s > T**r0 Fc ddg| j }| j r5| j dk r|dz S | j dk r |dz | j z S |dz | j z S | j t | j z }| j dk r |d k r|}n'|sd }n"| j d k r |d z d z d z }n |d z d z d z }|dk rd }d d | z z | j z }n^|t | j k r%| j d |t | j z z z }d}n!| j d | }d | j |d z }||k rd}n(|t }ddg|j d||z z z }||z |z |z S )Nr r r InfinityrA NaNr r( r1 r r .eEz%+d)rC r r rD r r rf ) r5 engr6 rP leftdigitsdotplacer r r s r. __str__zDecimal.__str__ s Cy$ 1yC j((c!!e|di//f}ty00 YTY / 9>>j2oo!HH 0HH Y# "Q!+a/HH #Q!+a/H q==GS8)_,ty8HH TY ' 'iXc$)nn%< ==GHHi *GTYxyy 11H ! !CC$,,*W -.*X:M1NNCg~(3..r0 c 2 | d| S )NT)r r6 )r r5 r6 s r. to_eng_stringzDecimal.to_eng_stringE s ||g|666r0 c | j r| | }|r|S |t }| s%|j t k r| }n| }| | S Nro )r r r r^ r copy_abs copy_negate_fixr5 r6 rG s r. __neg__zDecimal.__neg__N s ""7"33C ? llG %(K77 --//CC""$$Cxx r0 c | j r| | }|r|S |t }| s%|j t k r| }nt | }| | S r )r r r r^ r r r r r s r. __pos__zDecimal.__pos__d s ""7"33C ? llG (K77--//CC$--Cxx r0 Tc |s| S | j r| | }|r|S | j r| | }n| | }|S r )r r r rC r r )r5 roundr6 rG s r. __abs__zDecimal.__abs__y s #==?? " ""7"33C : 0,,w,//CC,,w,//C r0 c t | }|t u r|S |t }| j s|j r| || }|r|S | rN| j |j k r/| r| t d S t | S | rt | S t | j |j }d}|j t k r| j |j k rd}| sH|sFt | j |j }|rd}t |d| }| | }|S | sRt! ||j |j z dz }| ||j }| | }|S |sRt! || j |j z dz }| ||j }| | }|S t' | }t' | }t) |||j \ }}t' } |j |j k r|j |j k r(t |d| }| | }|S |j |j k r||}}|j dk r!d| _ |j |j c|_ |_ n1d| _ n)|j dk rd| _ d\ |_ |_ nd| _ |j dk r|j |j z | _ n|j |j z | _ |j | _ t | }| | }|S )Nz -INF + INFr( r1 r )r( r( )r r r r r r rC r r r r r r^ r rB r maxr_ _rescaler _normalizerP r r ) r5 r r6 rG r negativezerorP op1op2r s r. __add__zDecimal.__add__ sY u%% N " "L ? llG &u 0 &""5'22C !! %:,,1B1B1D1D,"//0@,OOO t}}$ "" & u~~%$)UZ(( { * *tzU[/H/H L E tz5;//D "4c22C((7##CJ c5: 4Q677C..g&677C((7##CJ c49w|3A566C--W%566C((7##CJtnnuoo c3 55S 8sx w#'!!&|S#>>hhw'' w Sx1}} %(Xsx"#(( X]]FK!' CHchhFK 8q== 37*FJJ 37*FJW foohhw r0 c t | }|t u r|S | j s|j r| || }|r|S | | | S r )r r r r r* r r s r. __sub__zDecimal.__sub__ s ! u%% N " "L u 0 ""5'"::C ||E - - / /|AAAr0 c f t | }|t u r|S | | | S r )r r r, r s r. __rsub__zDecimal.__rsub__ s8 ! u%% N " "L}}T7}333r0 c t | }|t u r|S |t }| j |j z }| j s|j r| || }|r|S | r*|s| t d S t | S | r*| s| t d S t | S | j |j z }| r|s(t |d| }| | }|S | j dk r-t ||j | }| | }|S |j dk r-t || j | }| | }|S t | }t | }t |t |j |j z | }| | }|S )Nz (+-)INF * 0z 0 * (+-)INFr 1)r r r rC r r r r r rN r rB r rD r r r )r5 r r6 resultsignrG resultexpr( r) s r. __mul__zDecimal.__mul__ s u%% N " "L ? llGZ%+- 3u 0 3""5'22C !! 3 Q"//0@-PPP&z22 "" 3 Q"//0@-PPP&z22I * 5 ":sI>>C((7##CJ 9 ":uz9EEC((7##CJ : ":ty)DDC((7##CJtnnuoo z3sw/@+A+A9MMhhw r0 c 4 t | }|t u rt S |t }| j |j z }| j s|j r| || }|r|S | r/| r| t d S | r t | S | r>| t d t |d| S |s9| s| t d S | t d| S | s| j |j z }d}nt! |j t! | j z |j z dz }| j |j z |z }t' | }t' | } |dk r$t) |j d|z z | j \ }} n$t) |j | j d| z z \ }} | r|d z dk r|dz }n7| j |j z } || k r"|dz dk r|dz }|dz }|| k r |dz dk t |t- | | }| | S ) Nz(+-)INF/(+-)INFzDivision by infinityr z0 / 0zx / 0r( r1 r r )r r r rC r r r r r rN r rB Etinyr r r r rD r_ r divmodr r r ) r5 r r6 rP rG r r shiftr( r) remainder ideal_exps r. __truediv__zDecimal.__truediv__6 s " u%% N " "! ! ? llGzEK' Du 0 D""5'22C !! Qe&7&7&9&9 Q ++,<>OPPP !! -&t,, "" D$$W.DEEE'c7==??CCC G H ++,=wGGG''FF F )ej(CEE OOc$)nn4w|CaGE)ej(50C4..C5//Czz#)#'BI*=sw#G#G yy#)#'37R%Z3G#H#H y 19>>QJE !I 2 Ioo%"*//bLE1HC Ioo%"*// tSZZ55xx r0 c z | j |j z }| r| j }nt | j |j }| | z }| r| s|dk r,t |dd | ||j fS ||j k rt | }t | }|j |j k r!|xj d|j |j z z z c_ n |xj d|j |j z z z c_ t |j |j \ }} |d|j z k rAt |t | d t | j t | | fS | t d } | | fS )Nr r r( r z%quotient too large in //, % or divmod)rC r r r r rB r% r^ r_ r r r r6 r r r ) r5 r r6 rP r9 expdiffr( r) qrrG s r. _dividezDecimal._divideq s zEK' 3 IIDIuz22I--//ENN$4$44 @u((** @gmm$T322MM)W-=>>@ @ gl " "4..C5//Cw#'!!2#' 1222#' 122#'37++DAq2w|###(s1vvq99(SVVYGGI I ""#5#JL LCxr0 c f t | }|t u r|S | | | S r )r r r: r s r. __rtruediv__zDecimal.__rtruediv__ s; 7 u%% N " "L w 777r0 c t | }|t u r|S |t }| || }|r||fS | j |j z }| r[| r | t d }||fS t | | t d fS |sX| s | t d }||fS | t d| | t d fS | || \ }}| | }||fS )Nzdivmod(INF, INF)INF % xz divmod(0, 0)x // 0x % 0) r r r r rC r r r rN r r r? r )r5 r r6 rG rP quotientr8 s r. __divmod__zDecimal.__divmod__ sy u%% N " "L ? llG ug.. : zEK' K "" K **+;=OPPCx'- ,,-=yIIK K I I **+<nMMCx ,,^XtLL ,,-=wGGI I #ll5' : :) NN7++ ""r0 c f t | }|t u r|S | | | S r )r r rG r s r. __rdivmod__zDecimal.__rdivmod__ s; 6 u%% N " "L g 666r0 c t | }|t u r|S |t }| || }|r|S | r| t d S |s8| r| t d S | t d S | || d }| | }|S )NrC rE z0 % 0r1 ) r r r r r r r r r? r )r5 r r6 rG r8 s r. __mod__zDecimal.__mod__ s u%% N " "L ? llG ug.. J H''(8)DD D H H ++,<gFFF ++,=wGGGLL003 NN7++ r0 c f t | }|t u r|S | | | S r )r r rK r s r. __rmod__zDecimal.__rmod__ 8 3 u%% N " "L}}T7}333r0 c |t }t |d }| || }|r|S | r| t d S |s8| r| t d S | t d S | r$t | }| | S t | j |j }| s+t | j d| }| | S | | z }||j dz k r| t S |dk r0| ||j }| | S t% | }t% | }|j |j k r!|xj d |j |j z z z c_ n |xj d |j |j z z z c_ t+ |j |j \ }} d | z |dz z |j k r| |j z } |dz }|d |j z k r| t S | j } | d k rd| z } | } t | t- | | }| | S ) NTr zremainder_near(infinity, x)zremainder_near(x, 0)zremainder_near(0, 0)r r1 r r r r( )r r r r r r r r r r r rB rC r r_ r r% r^ r r r r6 r ) r5 r r6 rG ideal_exponentr< r( r) r= r> rP s r. remainder_nearzDecimal.remainder_near s ? llG ud333 ug.. J G''(8(EG G G D D ++,<,BD D D ++,=,BD D D %$--C88G$$ $ TY 33 %"4:sNCCC88G$$ $ --//ENN$4$44 glQ& & &''(:;; ; b==--0@AAC88G$$ $ tnnuoo 7cg GGrCGcg -. .GGG GGrCGcg -. .GGcgsw''1 Q3!A#; LA FA GL ''(:;; ; z q55T6DA tSVV^<<xx r0 c t | }|t u r|S |t }| || }|r|S | rI| r| t d S t | j |j z S |sF| r)| t d| j |j z S | t d S | || d S )Nz INF // INFrD z0 // 0r( ) r r r r r r r rN rC r r r? r s r. __floordiv__zDecimal.__floordiv__1 s u%% N " "L ? llG ug.. J A "" A ++,<lKKK&tzEK'?@@ I I ++NH,0J,DF F F ++,=xHHH||E7++A..r0 c f t | }|t u r|S | | | S r )r r rS r s r. __rfloordiv__zDecimal.__rfloordiv__M s; 8 u%% N " "L!!$!888r0 c | r/| rt d | j rdnd}nt | }t | S )Nz%Cannot convert signaling NaN to floatz-nannan)r r r rC r r r5 ss r. __float__zDecimal.__float__T s] # ;;== ||~~ J !HIII */%AAD AQxxr0 c X | j rF| rt d | rt d d| j z }| j dk r"|t | j z d| j z z S |t | j d | j pd z S )Nz Cannot convert NaN to integerz"Cannot convert infinity to integerr r( r r ) r r r r r rC r r rD rX s r. __int__zDecimal.__int__^ s ? J{{}} J !@AAA!!## J#$HIII $* 9>>S^^#B M1 1S:DI:.5#666 6r0 c | S r+ r, r s r. realz Decimal.realm s r0 c t d S Nr( r r s r. imagz Decimal.imagq s qzzr0 c | S r+ r, r s r. conjugatezDecimal.conjugateu s r0 c : t t | S r+ )complexr r s r. __complex__zDecimal.__complex__x s uT{{###r0 c | j }|j |j z }t | |k rI|t | |z d d }t | j || j d S t | S )Nr T) rD r_ rg r r rB rC r r )r5 r6 payloadmax_payload_lens r. rE zDecimal._fix_nan{ sz @) ", 6 w<</ ) ) c'll? : ; ;<CCCHHG#DJDII It}} r0 c | j r8| r| | S t | S | }| }| s|j |g|j }t t | j | | }|| j k r0| t t | j d| S t | S t | j | j z |j z }||k rW| t$ d| j }| t& | t( |S ||k }|r|}| j |k rt | j | j z |z } | dk rt | j d|dz } d} | j |j } | | | } | j d | pd} | dk rFt/ t1 | dz } t | |j k r| d d } |dz }||k r"| t$ d| j }nt | j | | }| r |r| t2 |r| t4 | r| t& | t( |s| t |S |r| t4 |j dk rP| j |k rE| t | j d| j |z z z } t | j | | S t | S )Nr above Emaxr( r0 r1 r )r r rE r r5 Etopr` rg r r$ r r r rB rC r rD r_ r r r _pick_rounding_functionr^ r r r r )r5 r6 r5 rm exp_maxnew_expexp_minrG self_is_subnormalr rounding_methodchangedr r s r. r z Decimal._fix sw %{{}} %}}W--- t}}$ ||~~ % |T*7=9G#di//99G$)##$$W---' CAAA t}}$ di..49,w|; T>>&&x tzJJC ) ) ) ) ) )J #eO G 9w ^^di/'9Fzz' CCC " :7;K LO%odF33GIgvg&-#E{{CJJqL))u:: ,, !#2#JEqLG ~~ **8\4:NN&tz5'BB 0, 0$$Y/// 0$$Y/// .$$W--- ) ) ) .$$W---J , + + + =A $)d"2"2 ) ) ) )c49t+;&<<K#DJ TBB B t}} r0 c 6 t | j | rdS dS )Nr( r ) _all_zerosrD r5 r_ s r. _round_downzDecimal._round_down s# 6 di & & 12r0 c 0 | | S r+ )rx rw s r. _round_upzDecimal._round_up s ! &&&&r0 c X | j | dv rdS t | j | rdS dS )N56789r1 r( r )rD rv rw s r. _round_half_upzDecimal._round_half_up s9 ' 9T?g % %1 4 ( ( 12r0 c \ t | j | rdS | | S )Nr _exact_halfrD r} rw s r. _round_half_downzDecimal._round_half_down s2 ty$ ' ' -2&&t,, ,r0 c t | j | r|dk s| j |dz dv rdS | | S )Nr( r1 02468r r rw s r. _round_half_evenzDecimal._round_half_even sP / ty$ ' ' -diQ /7 : :2&&t,, ,r0 c h | j r| | S | | S r+ rC rx rw s r. _round_ceilingzDecimal._round_ceiling s: 6 : +##D)) )$$T*** *r0 c h | j s| | S | | S r+ r rw s r. _round_floorzDecimal._round_floor s: 5z +##D)) )$$T*** *r0 c |r'| j |dz dvr| | S | | S )Nr1 05)rD rx rw s r. _round_05upzDecimal._round_05up sM 7 +DId1f%T11##D)) )$$T*** *r0 )r r r r r r r r c ` |Kt |t st d t dd| }| | S | j r2| rt d t d t | dt S )Nz+Second argument to round should be integralr( r0 cannot round a NaNcannot round an infinity) r r rx rB quantizer r r r r% r )r5 rA r s r. __round__zDecimal.__round__0 s - \ = a%% O MNNN"1cA2..C==%% % @{{}} @ !5666#$>???4==O44555r0 c | j r2| rt d t d t | dt S Nr r r( )r r r r r r% r r s r. __floor__zDecimal.__floor__n s` @{{}} @ !5666#$>???4==K00111r0 c | j r2| rt d t d t | dt S r )r r r r r r% r r s r. __ceil__zDecimal.__ceil__} s` @{{}} @ !5666#$>???4==M22333r0 c P t |d }t |d }| j s|j r |t }| j dk r | t d| S |j dk r | t d| S | j dk r| }n|j dk r|}n| j dk r8|s| t d S t | j |j z }n|j dk r7| s| t d S t | j |j z }n_t | j |j z t t | j t |j z | j |j z }| || S ) NTr r r rA r zINF * 0 in fmaz0 * INF in fma) r r r r r r rN rC rB r r rD r* )r5 r thirdr6 products r. fmaz Decimal.fma s ud333 ud333 ?u 0 ?$,,yC ++,<fdKKKzS ++,<feLLLyC s"" c!! B"//0@0@ B B B)$*u{*BCs"" B"//0@0@ B B B)$*u{*BC&tzEK'?'*3ty>>C OO+K'L'L'+y5:'=? ?G ug...r0 c 2 t | }|t u r|S t | }|t u r|S |t }| }| }| }|s|s|r|dk r | t d| S |dk r | t d| S |dk r | t d| S |r| | S |r| | S | | S | r(| r| s| t d S |dk r| t d S |s| t d S | |j k r| t d S |s | s| t d S | rd}n| j }t t | }t | }t | } |j |z t! d |j | z |z }t% | j D ]} t! |d | }t! || j | }t' |t) | d S ) Nr r z@pow() 3rd argument not allowed unless all arguments are integersr( zApow() 2nd argument cannot be negative when 3rd argument specifiedz pow() 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 definedr )r r r r r r rE _isintegerr r_ _isevenrC r r r to_integral_valuer r rangerB r ) r5 r modulor6 r r modulo_is_nanrP baseexponentis r. _power_modulozDecimal._power_modulo sa / u%% N " "L '' ^ # #M ? llG kkmm ||~~ ,, ,- ,a ++,<f(,. . .q ++,<f(-/ / / !! ++,<f(.0 0 0 .}}W--- / ~~g...??7++ + !! M "" M!!## M ''(8)LM M M 199''(8)OP P P J''(8(HJ J J ?? , ,''(8);< < < ?T ?''(8)>? ? ? ==?? DD:D S[[!!..0011E 3 3 5 566 6!CDHf$=$==Gx|$$ ) )AtR((DD4 v.. c$ii333r0 c t | }|j |j }}|dz dk r|dz }|dz }|dz dk t | }|j |j }}|dz dk r|dz }|dz }|dz dk |dk r||z }|dz dk r|dz }|dz }|dz dk |dk rd S |d|z z } |j dk r| } | r9|j dk r.| j t | z } t | | z |dz } nd} t ddd| z z | | z S |j dk rq|dz } | dv r|| z |k rd S t | dz } |dz dz }|t t | k rd S t | |z | } t ||z | }| |d S | |k rd S d | z }n| d k rt | d z dz } t d | z | \ }}|rd S |d z dk r|d z }| dz } |d z dk |dz d z }|t t | k rd S t | |z | } t ||z | }| |d S | |k rd S d | z }nd S |d|z k rd S | |z }t dt | | S |dk r |d|z z d}}n|dk r3t t t ||z | k rd S t | }t t t | |z | k rd S |d| z }}|d z |d z cxk rdk r"n n |d z }|d z }|d z |d z cxk rdk n |d z |d z cxk rdk r"n n |d z }|d z }|d z |d z cxk rdk n |dk rz||k rd S t || \ }}|dk rd S dt | |z z } t |||dz z \ }}||k rn||dz z |z |z }/||k r|dk sd S |}|dk r||dz t | z k rd S ||z }||z }|d|z k rd S t | }| rF|j dk r;| j t | z } t || z |t | z } nd} t d|d| z z || z S )Nr r( r1 r0 r )r ] A r r r Td )r r r rP r rC r r rB _nbitsr r _decimal_lshift_exactr6 r _log10_lb)r5 r pxxcxeyycyer rP zeros last_digitr emaxr8 r rA xc_bitsremar= r> str_xcs r. _power_exactzDecimal._power_exact sC Br TNNB2gll 2IB !GB 2gll UOOB2gll 2IB !GB 2gll 77 "HBr'Q,,r a r'Q,, AvvtBF{Hv{{ $9 !! ekQ&6&6!%3u::!5H^ 3QqS99#AsSYGG G 6Q;;bJY&&8r>> 42JJqL6 tRxSYY '' 4 *!b&"55*27B779 4t88 4Tq 2JJrM2% &q!tR 0 0 I 41fkk1HBFA 1fkk tQwSYY '' 4)!b&"55*27B779 4t88 4TtRU{{tBB#As2ww33 3 77b"f9aqAAQww3s3r"u:://B366t RjjG3s2www''((RC//trRCyqAa%1q5%%%%A%%%%%aa a%1q5%%%%A%%%% a%1q5%%%%A%%%%%aa a%1q5%%%%A%%%% q55!||t RmmGBaxxt r {A~&&A ) b!ac(++166AaC1q(A ) FFqAvvtB 66a!C%2 ...4 U a A::4 R %+"2"2 !Ys5zz 1N>)1S[[=99EEE 6#e)#3RX>>>r0 c || ||| S t | }|t u r|S |t }| || }|r|S |s$| s| t d S t S d}| j dk r\| r| sd}n | r| t d S | } | s)|j dk rt |dd S t | S | r)|j dk r t | S t |dd S | t k r| rm|j dk rd}n"||j k r|j }nt! | }| j |z }|d|j z k r$d|j z }| t$ n>| t& | t$ d|j z }t |dd| z z | S | }| r1|j dk |dk k rt |dd S t | S d }d} | | z } |dk |j dk k r?| t- t/ |j k rt |d|j dz }nI| } | t- t/ | k rt |d| dz }|C| ||j dz }|#|dk rt d|j |j }d} ||j } t9 | } | j | j }}t9 | }|j |j }}|j dk r| }d } t? ||||| |z \ }}|d d t- t/ | | z dz z z z rn|d z }Kt |t/ | | }| r| sut- |j |j k rH|j dz t- |j z }t |j |j d|z z |j |z }| }|! tD D ] }d|j# |< |$ | }| t& |j% tL r| tN |j% tP r!| tP d |j tN tL t& t$ tR fD ]$}|j% | r| | %n|$ | }|S ) Nz0 ** 0r( r1 z+x ** y with x negative and y not an integerr r0 FTr r r rl )*r r r r r r r _OnerC r r r rB rN r r_ r r r r r _log10_exp_boundr r r` r5 r rD r r rP _dpowerrq rr _signalsri r rh r r r r )r5 r r r6 rG result_sign multiplierr self_adjexactboundr5 r r r r r r r extrar r< newcontext exceptions r. __pow__zDecimal.__pow__ s2 . %%eVW== = u%% N " "L ? llG ug.. J ++,<hGGG :?? !! G }} $"#K G"//0@E G G G ##%%D 4{a ' S!<<<&{33 ={a &{33' S!<<< 4<< !! % ;!##!"JJW\))!( JJ!$UJi*,7< ''GL.C((111$$W---$$W--- n#KS#X sCC C ==?? 4 q hl33' S!<<<&{33 %%''%..*:*:: Mu{a / 0 0 C - -....&{C a HH MMOOECKK((((&{CqAA ;##E7<!+;<<C !##*1chAAC ; AAUAEBAUAEBv{{S E $RRQuW = = sAb3s5zz??1#4Q#6 7 78 #;E C@@C " $))++ " $ 38}} ,,!,*S]]:&sy#(3w;2F'*x'79 9 ! J " " $ $ $ % 0 0 ./ ++ ((:&&C # #G , , , * 3'' 222 ) H$$X|SYGGG & 7GW L 4 4 #I. 4((333 4 ((7##C r0 c f t | }|t u r|S | | | S r )r r r r s r. __rpow__zDecimal.__rpow__ rN r0 c 0 |t }| j r| | }|r|S | | }| r|S |st |j dd S |j | g|j }t |j }|j }|j |dz dk r*||k r$|dz }|dz }|j |dz dk r||k $t |j |j d | | S )Nro r r( r1 ) r r r r r rB rC r` rm rg r rD r )r5 r6 rG dupro endr s r. normalizezDecimal.normalize s" M ? llG ""7"33C ii ?? J 7#CIsA66 6< 0 ?#(mmhhs1uo$$w 1HC 1HC hs1uo$$w 38DSD>3???r0 c t |d }|t }||j }| j s|j r| || }|r|S | s| rR| r#| rt | S | t d S | |j cxk r |j k s n | t d S | s0t | j d|j }| | S | }||j k r| t d S ||j z dz |j k r| t d S | |j | }| |j k r| t d S t% |j |j k r| t d S |r7| |j k r| t* |j | j k r:|| k r| t, | t. | | }|S ) NTr zquantize with one INFz)target exponent out of bounds in quantizer z9exponent of quantize result too large for current contextr1 z7quantize result has too many digits for current context)r r r^ r r r r r r r5 r r` rB rC r r r_ r% r rD re r r r )r5 r r^ r6 rG r s r. r zDecimal.quantize s S$/// ? llG 'H As A""300C AD$4$4$6$6 A??$$ ))9)9);); )"4==( ++,<(?A A A 38;;;;w|;;;;''(8>@ @ @ %"4:sCH==C88G$$ $ 7< ' '''(8(ce e e 38 #a '', 6 6''(8(ac c c mmCHh// <<>>GL ( (''(8(ce e e sx==7< ' '''(8(ac c c ,3<<>>GL00 + + + 8di d{{$$W--- ) ) ) hhw r0 c t |d }| j s|j rP| r| p'| o| S | j |j k S r )r r r is_infiniter r s r. same_quantumzDecimal.same_quantum/ s ud333 @u 0 @KKMM4ellnn ?$$&&>5+<+<+>+> @yEJ&&r0 c | j rt | S | st | j d| S | j |k r)t | j | j d| j |z z z | S t | j | j z |z }|dk rt | j d|dz } d}| j | } || | }| j d | pd}|dk r t t | dz }t | j || S )Nr r( r0 r1 ) r r rB rC r rD r rn r r )r5 r r^ r this_functionrt r s r. r% zDecimal._rescale> s !4== :#DJS99 9 9 #DJ(, CS 4I(I3P P P TY $)+c1 A::#DJSU;;DF 4X> -f-- '6'")c a<<E 1 %%E E3777r0 c n |dk rt d | j s| st | S | | dz |z | }| | k r.| | dz |z | }|S )Nr( z'argument should be at least 1 in _roundr1 )r r r r% r )r5 placesr^ rG s r. _roundzDecimal._round` s Q;; FGG G !4 !4== mmDMMOOA -f 4h?? <<>>T]]__ , ,,,s||~~a / 6AAC r0 c | j r)| | }|r|S t | S | j dk rt | S | st | j dd S |t }||j }| d| }|| k r| t | t |S )Nro r( r ) r r r r rB rC r r^ r% r r r r5 r^ r6 rG s r. to_integral_exactzDecimal.to_integral_exactw s !""7"33C 4== 9>>4== 8#DJQ77 7 ? llG 'HmmAx(( $;; ) ) ) W%%% r0 c |t }||j }| j r)| | }|r|S t | S | j dk rt | S | d| S )Nro r( )r r^ r r r r r% r s r. r zDecimal.to_integral_value s N ? llG 'H !""7"33C 4== 9>>4== ==H-- -r0 c D |t }| j rH| | }|r|S | r| j dk rt | S | s3t | j d| j dz }| | S | j dk r| t d S |j dz }t | }|j dz }|j dz r%|j dz }t | j dz dz }n!|j }t | j dz dz }||z }|dk r |d|z z }d } nt# |d| z \ }} | } ||z }d|z } || z } | | k rn | | z dz } | o| | z |k } | r |dk r | d|z z } n | d| z z } ||z }n| d z dk r| dz } t dt% | | }| }| t* } | | }| |_ |S ) Nro r( r r r1 zsqrt(-x), x > 0r r Tr )r r r r rC r rB r r r r r_ r r r r rD r6 r _shallow_copy _set_roundingr r^ )r5 r6 rG r_ opr clr7 r r8 rA r= r^ s r. sqrtz Decimal.sqrt s - ? llG %""7"33C !! %djAoo t}}$ %"4:sDINCCC88G$$ $ :??''(8:KLL L, |A~ d^^ FaK 6A: & ATY 1$)AAADIq A%A Q A:: eOAEE!!S5&[11LAy!ME U H 1AAvvEQJ "!A#( zzb%iR%Z JAA 1uzzQ q#a&&!,, ''))(( 99hhw # r0 c t |d }|t }| j s|j r| }| }|s|rX|dk r|dk r| | S |dk r|dk r| | S | || S | | }|dk r| | }|dk r|}n| }| | S NTr r1 r( r r r r r r r r compare_totalr5 r r6 snonr rG s r. r$ z Decimal.max s ud333 ? llG 8u 0 8 B B 8R 877rQww 99W---77rQww ::g...''w777 IIe 66 ""5))A 77CCCxx r0 c t |d }|t }| j s|j r| }| }|s|rX|dk r|dk r| | S |dk r|dk r| | S | || S | | }|dk r| | }|dk r| }n|}| | S r r r s r. r z Decimal.min4 s ud333 ? llG 8u 0 8 B B 8R 877rQww 99W---77rQww ::g...''w777 IIe 66""5))A 77CCCxx r0 c | j rdS | j dk rdS | j | j d }|dt | z k S )NFr( Tr )r r rD r )r5 rests r. r zDecimal._isintegerV sL 0 5 9>>4y$s3t99}$$r0 c P | r | j dk rdS | j d| j z dv S )Nr( Tr r )r rD r s r. r zDecimal._iseven_ s4 H ty1}}4yDI &'11r0 c f | j t | j z dz S # t $ r Y dS w xY w)Nr1 r( )r r rD rx r s r. r zDecimal.adjustede sF 2 9s49~~-1 1 11 s " 00c | S r+ r, r s r. canonicalzDecimal.canonicalm s r0 c t |d }| || }|r|S | || S NTr ro )r r r r s r. compare_signalzDecimal.compare_signalu sS u555&&ug66 J||E7|333r0 c V t |d }| j r|j st S | j s|j rt S | j }| }| }|s|r||k rit | j | j f}t |j |j f}||k r|rt S t S ||k r|rt S t S t S |r5|dk rt S |dk rt S |dk rt S |dk rt S n4|dk rt S |dk rt S |dk rt S |dk rt S | |k rt S | |k rt S | j |j k r|rt S t S | j |j k r|rt S t S t S )NTr r1 r ) r rC _NegativeOner r r rD _Zeror )r5 r r6 rP self_nan other_nanself_key other_keys r. r zDecimal.compare_total s ud333 : ek z ek Kz ;;==LLNN " (y " (9$$ ty>>494 OOUZ 7 i'' , # ++i'' $ ++ # (q=='' >> Kq=='' >> K " q== K >>''q== K >>'' %<< %<<K 9uz ! ! $ ## 9uz ! ! ## r0 c t |d }| }| }| | S r )r r r )r5 r r6 rY os r. compare_total_magzDecimal.compare_total_mag sI ud333 MMOO NN q!!!r0 c F t d| j | j | j S r` )rB rD r r r s r. r zDecimal.copy_abs s 5 49di9IJJJr0 c | j r!t d| j | j | j S t d| j | j | j S )Nr( r1 )rC rB rD r r r s r. r zDecimal.copy_negate sF 4 : O#Aty$)T=MNN N#Aty$)T=MNN Nr0 c r t |d }t |j | j | j | j S r )r rB rC rD r r r s r. copy_signzDecimal.copy_sign s; 2 ud333 TY $ 4+;= = =r0 c * |t }| | }|r|S | dk rt S | st S | dk rt | S |j }| }| j dk rF|t t |j dz dz k rt dd|j dz }nb| j dk r`|t t | dz dz k r't dd| dz }n| j dk r&|| k r t ddd|dz z z dz | }n| j dk r&|| dz k r t dd|dz z | dz }nt | }|j |j }}|j dk r| }d} t% ||||z \ } } | d d t t | |z dz z z z rn|dz }It dt | | }| }| t* } | | }| |_ |S ) Nro r r1 r( r r0 r r] Tr r )r r r r r r r_ r rC r r r` rB r5 r r r rP _dexpr r r r r^ ) r5 r6 rG r adjr r r r r r r^ s r. r z Decimal.exp s ? llG w // J # #L K " "4== Lmmoo :??sSgl1na-?)@)@%A%A A A"1c7<>::CC Z1__s3 0@0BA/E+F+F'G'G!G!G"1c7==??1+<==CC Z1__r"1cC1Io&;aR@@CC Z1__r!t"1c1Q3i!A66CC $ B626qAw!||B E "1a5 1 1 sAb3s5zz??1#4Q#6 7 78 #1c%jj#66C ''))(( 99hhw # r0 c dS )NTr, r s r. is_canonicalzDecimal.is_canonical1 s tr0 c | j S r+ )r r s r. is_finitezDecimal.is_finite9 s ###r0 c | j dk S )Nr r r s r. r zDecimal.is_infiniteA s FyC r0 c | j dv S )Nr r r s r. r zDecimal.is_nanE s LyJ&&r0 c t | j s| sdS |t }|j | k S NF)r r re r r s r. is_normalzDecimal.is_normalI s? M 4 5 ? llG|t}}..r0 c | j dk S )NrA r r s r. r zDecimal.is_qnanQ s IyC r0 c | j dk S Nr1 )rC r s r. is_signedzDecimal.is_signedU s FzQ r0 c | j dk S )Nr r r s r. r zDecimal.is_snanY s MyC r0 c t | j s| sdS |t }| |j k S r )r r r re r s r. is_subnormalzDecimal.is_subnormal] s? G 4 5 ? llG}} --r0 c * | j o | j dk S r r r s r. is_zerozDecimal.is_zeroe s D##8 S(88r0 c " | j t | j z dz }|dk r%t t |dz dz dz S |dk r(t t d|z dz dz dz S t | }|j |j }}|dk rKt |d| z z }t | }t | t | z ||k z S |t t d| z |z z dz S )Nr1 r r r r( r r rD r r r r r5 r r r r numdens r. _ln_exp_boundzDecimal._ln_exp_boundi s i#di..(1, !88s3r62:''!+ + "99sBsFB;?++,,q0 0 d^^vrv1 !88aQBh--Ca&&Cs88c#hh&#)4 43s2r6A:'''!++r0 c H |t }| | }|r|S | st S | dk rt S | t k rt S | j dk r| t d S t | }|j |j }}|j }|| z dz } t ||| }|ddt! t# t% | |z dz z z z rn|dz }Pt' t |d k t# t% | | }| }| t, } | | }| |_ |S ) Nro r1 zln of a negative valuer Tr r r r( )r r _NegativeInfinityr _Infinityr r rC r r r r r r_ r# _dlogr r r rB r r r r r^ r5 r6 rG r r r r r r r^ s r. lnz Decimal.ln s = ? llG w // J %$ $ " " 4<<L :??''(8(@B B B d^^vrv1 L T'')))A- !Q''E"s3s5zz?? 3 3A 5a 7889 aKF s57||SU__vgFF''))(( 99hhw # r0 c ( | j t | j z dz }|dk r t t | dz S |dk r"t t d|z dz S t | }|j |j }}|dk rQt |d| z z }t d|z }t | t | z ||k z dz S t d| z |z }t | |z |dk z dz S ) Nr1 r r r( r r 231r r s r. r zDecimal._log10_exp_bound s i#di..(1, !88s3xx==? " "99s2c6{{##A% % d^^vrv1 !88aQBh--Cc!e**Cs88c#hh&#)4q8 8"qb&(mm3xx!|sU{+a//r0 c |t }| | }|r|S | st S | dk rt S | j dk r| t d S | j d dk rX| j dd dt | j dz z k r-t | j t | j z dz }nt | }|j |j }}|j }|| z dz } t# ||| }|d d t t% t' | |z dz z z z rn|d z }Pt) t |dk t% t' | | }| }| t. } | | }| |_ |S ) Nro r1 zlog10 of a negative valuer( r0 r r Tr r r )r r r% r r& rC r r rD r r r r r r r_ r _dlog10r r rB r r r r r^ r( s r. log10z Decimal.log10 s 4 ? llG w // J %$ $ " " :??''(8(CE E E 9Q<3 49QRR=CTY !9K4L#L#L$)c$)nn4q899CC $ B626qA A t,,...q0F 1f--Ab3s3u::#7#7#9!#; < <= ! #3uQw<<SZZ 6'JJC''))(( 99hhw # r0 c 6 | | }|r|S |t }| rt S | s | t dd S t | }| | S )Nro zlogb(0)r1 ) r r r r& r r r r r r s r. logbz Decimal.logb s w // J ? llG F'' 1EE E dmmoo&&xx r0 c Z | j dk s | j dk rdS | j D ] }|dvr dS dS )Nr( F01T)rC r rD )r5 digs r. _islogicalzDecimal._islogical# sN :??di1nn59 C$ uu tr0 c |j t | z }|dk r d|z |z }n|dk r||j d }|j t | z }|dk r d|z |z }n|dk r||j d }||fS )Nr( r )r_ r )r5 r6 opaopbdifs r. _fill_logicalzDecimal._fill_logical1 s lSXX% 77c'C-CC 1WWw|mnn%ClSXX% 77c'C-CC 1WWw|mnn%CCxr0 c |t }t |d }| r| s| t S | || j |j \ }}d d t || D }t d| d pdd S )NTr r c l g | ]1\ }}t t | t | z 2S r, r r .0r bs r. <listcomp>z'Decimal.logical_and.<locals>.<listcomp>L 4 EEE1#c!ffSVVm,,EEEr0 r( r r r r5 r r r: rD r ziprB r r5 r r6 r7 r8 r s r. logical_andzDecimal.logical_and> I ? llG ud333 :(8(8(:(: :''(899 9 ''EJGG c EEC EEEFF 6==#5#5#<a@@@r0 c ~ |t }| t dd|j z d | S )Nr( r0 )r logical_xorrB r_ r s r. logical_invertzDecimal.logical_invertO sD $ ? llG 03w|3CA F F ') ) )r0 c |t }t |d }| r| s| t S | || j |j \ }}d d t || D }t d| d pdd S )NTr r c l g | ]1\ }}t t | t | z 2S r, r= r> s r. rA z&Decimal.logical_or.<locals>.<listcomp>d rB r0 r( r rC rE s r. logical_orzDecimal.logical_orV s H ? llG ud333 :(8(8(:(: :''(899 9 ''EJGG c EEC EEEFF 6==#5#5#<a@@@r0 c |t }t |d }| r| s| t S | || j |j \ }}d d t || D }t d| d pdd S )NTr r c l g | ]1\ }}t t | t | z 2S r, r= r> s r. rA z'Decimal.logical_xor.<locals>.<listcomp>u rB r0 r( r rC rE s r. rI zDecimal.logical_xorg rG r0 c R t |d }|t }| j s|j r| }| }|s|rX|dk r|dk r| | S |dk r|dk r| | S | || S | | }|dk r| | }|dk r|}n| }| | S r r r r r r r r r r r s r. max_magzDecimal.max_magx s) F ud333 ? llG 8u 0 8 B B 8R 877rQww 99W---77rQww ::g...''w777 MMOO !1!1 2 2 66""5))A 77CCCxx r0 c R t |d }|t }| j s|j r| }| }|s|rX|dk r|dk r| | S |dk r|dk r| | S | || S | | }|dk r| | }|dk r| }n|}| | S r rQ r s r. min_magzDecimal.min_mag s) F ud333 ? llG 8u 0 8 B B 8R 877rQww 99W---77rQww ::g...''w777 MMOO !1!1 2 2 66""5))A 77CCCxx r0 c N |t }| | }|r|S | dk rt S | dk r+t dd|j z | S | }| t | | | }|| k r|S | t dd| dz | S )Nro r r1 r( r] r0 )r r r r% rB r_ rm rq r r _ignore_all_flagsr r, r5 r5 r6 rG new_selfs r. next_minuszDecimal.next_minus s K ? llG w // J # #$ $ " "#As7<'7 HH H,,.. k***!!###99W%% t O|| ,QW]]__Q5F G G #% % %r0 c N |t }| | }|r|S | dk rt S | dk r+t dd|j z | S | }| t | | | }|| k r|S | t dd| dz | S )Nro r1 r r] r( r0 )r r r r& rB r_ rm rq r r rV r r* r5 rW s r. next_pluszDecimal.next_plus s K ? llG w // J " " # ##As7<'7 HH H,,.. m,,,!!###99W%% t O|| ,QW]]__Q5F G G #% % %r0 c V t |d }|t }| || }|r|S | | }|dk r| | S |dk r| | }n| | }| rV| t d|j | t | t n| |j k r| t | t | t | t |s| t" |S )NTr r( r z Infinite result from next_toward)r r r r r r[ rY r r r rC r r r re r r r )r5 r r6 rG comparisons r. next_towardzDecimal.next_toward s ud333 ? llG ug.. JYYu%% ??>>%(( ( ..))CC//'**C ?? . !C!$ , , , ) ) ) ) ) ) ) \\^^gl * * + + + + + + ) ) ) ) ) ) .$$W--- r0 c Z | rdS | rdS | }|dk rdS |dk rdS | r | j rdS dS |t }| | r | j rd S d S | j rd S d S )Nr r r1 z +Infinityr z -Infinityz-Zeroz+Zeroro z -Subnormalz +Subnormalz-Normalz+Normal)r r r r rC r r )r5 r6 infs r. number_classzDecimal.number_class s <<>> 6 <<>> 5 !88 ; "99 ; <<>> z w w ? llG W - - $z $#|#| : 9 9r0 c " t d S Nr ra r s r. radixz Decimal.radix: s 5r{{r0 c |t }t |d }| || }|r|S |j dk r| t S |j t | cxk r |j k s n | t S | rt | S t | }| j }|j t | z }|dk r d|z |z }n|dk r || d }||d |d | z }t | j | d pd| j S NTr r( r r r r r r r r_ r r r rD r rB rC r )r5 r r6 rG torotrotdigtopadrotateds r. rotatezDecimal.rotate> sk C ? llG ud333 ug.. J :??''(899 9 U;;;;w|;;;;''(899 9 !4== E s6{{* 199Y'FF QYYUFGG_F .6&5&>1 's 3 3 :sDIG G Gr0 c L |t }t |d }| || }|r|S |j dk r| t S d|j |j z z }d|j |j z z }|t | cxk r|k s n | t S | rt | S t | j | j | j t | z }| | }|S )NTr r( r r )r r r r r r r` r_ r r r rB rC rD r )r5 r r6 rG liminflimsupr s r. scalebzDecimal.scaleb_ s L ? llG ud333 ug.. J :??''(899 9w|gl23w|gl23#e**........''(899 9 !4== TZDIE 4J K K FF7OOr0 c |t }t |d }| || }|r|S |j dk r| t S |j t | cxk r |j k s n | t S | rt | S t | }| j }|j t | z }|dk r d|z |z }n|dk r || d }|dk r |d | }n|d|z z }||j d }t | j | d pd| j S rf rg )r5 r r6 rG rh ri rj shifteds r. r7 z Decimal.shiftx s C ? llG ud333 ug.. J :??''(899 9 U;;;;w|;;;;''(899 9 !4== E s6{{* 199Y'FF QYYUFGG_F 199 VeVnGG s5y(G w|mnn-G $+NN3$7$7$>3 K K Kr0 c 0 | j t | ffS r+ ) __class__r r s r. __reduce__zDecimal.__reduce__ s T --r0 c v t | t u r| S | t | S r+ typer rt r r s r. __copy__zDecimal.__copy__ 0 :: K~~c$ii(((r0 c v t | t u r| S | t | S r+ rw )r5 memos r. __deepcopy__zDecimal.__deepcopy__ rz r0 c |t }t || }| j rXt | j | }t | }|d dk r|dz }t ||| S |d ddg|j |d< |d dk r#t | j | j | j dz } |j }|d }|~|d dv r| |d z | } nZ|d d v r| | | } n8|d d v r.t | j |k r| || } | s+| j d k r |d d v r| d | } | s|d r | j rd } n| j } | j t | j z } |d dv r | s|d |z } n0d } n-|d d v r| } n |d d v r| j d k r | dk r| } nd } | d k rd} d| z | j z } n]| t | j k r%| j d| t | j z z z } d} n | j d | pd} | j | d } | | z }t! | | | || S )N) _localeconvrx %gGr precisioneEr1 zfF%gGr( no_neg_0r r r )r _parse_format_specifierr _format_signrC r r _format_alignrf rB rD r r^ r r% r _format_number)r5 specifierr6 r specrP bodyr^ r adjusted_signr r r r r s r. __format__zDecimal.__format__ s ? llG&ykJJJ 3 D11Dt}}''DF|s"" tT22 2 < :g&67DL <3 #DJ 49Q;GGD #% F|t##{{9Q;99f &&}}iZ::f %%#di..9*D*D{{9h77 . 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(!T ! ! ! !D% % %2 2 2 4 4 4 4F F F FR " " " "K K KO O O= = = = I I I IV $ $ $ ' ' '/ / / / . . . .9 9 9, , ,20 0 0 0d 0 0 0<1 1 1 1f ! ! ! !< A A A A") ) ) )A A A A"A A A A" ! ! ! !< ! ! ! !<% % % %.% % % %., , , ,\( ( ( ( T G G G GB 2$K $K $K $KN. . .) ) ) ) ) )TK TK TK TK TK TKr0 r Fc ~ t t }| |_ ||_ ||_ ||_ |S r+ )r r r rC rD r r )rP coefficientr specialr5 s r. rB rB s< >>' " "DDJDIDI D Kr0 c " e Zd Z d Zd Zd ZdS )ru c 8 | | _ d S r+ )rq rz )r5 rz s r. __init__z_ContextManager.__init__" s &++--r0 c ^ t | _ t | j | j S r+ )r saved_contextr rz r s r. __enter__z_ContextManager.__enter__$ s( '\\4#$$$ r0 c . t | j d S r+ )r r )r5 tvtbs r. __exit__z_ContextManager.__exit__( s 4%&&&&&r0 N)r9 r: r; r r r r, r0 r. ru ru sF . . . ' ' ' ' 'r0 ru c e Zd Z dTdZd Zd Zd Zd Zd Zd Z d Z d Z d Z d Z e ZdUd Zd Zd Zd ZdZd Zd Zd ZdVdZd Zd Zd Zd Zd Z d Z d Z d Z d Z d Z!d Z"d! Z#d" Z$d# Z%d$ Z&d% Z'd& Z(d' Z)d( Z*d) Z+d* Z,d+ Z-d, Z.d- Z/d. 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ZAd@ ZBdA ZCdB ZDdC ZEdD ZFdUdEZGdF ZHdG ZIdH ZJdI ZKdJ ZLdK ZMdL ZNdM ZOdN ZPdO ZQdP ZRdQ ZSdR ZTdS ZUeUZVdS )Wr Nc t } n# t $ r Y nw xY w||n| j | _ ||n| j | _ ||n| j | _ ||n| j | _ ||n| j | _ ||n| j | _ | g | _ n| | _ | j | _ nEt t s)t fdt z D | _ n| _ 't t d | _ d S t t s*t fdt z D | _ d S | _ d S )Nc 3 > K | ]}|t |v fV d S r+ r )r? rY ri s r. <genexpr>z#Context.__init__.<locals>.<genexpr>W 2 M Mqq#a5j// 2 M M M M M Mr0 r( c 3 > K | ]}|t |v fV d S r+ r )r? rY rh s r. r z#Context.__init__.<locals>.<genexpr>^ r r0 )r NameErrorr_ r^ re r` rf rg _ignored_flagsri rq r r r fromkeysrh ) r5 r_ r^ re r` rf rg rh ri r dcs `` r. r zContext.__init__> s{ BB D ! ,DD"' $,$8bk ,DD"' ,DD"' $,$8bk # /UURX !"$D "0D = DJJE4(( M M M MHu<L M M MMMDJJ DJ = x33DJJJE4(( M M M MHu<L M M MMMDJJJ DJJJs c X t |t st d|z |dk r ||k rt d||||fz nE|dk r ||k rt d||||fz n"||k s||k rt d||||fz t | || S )Nz%s must be an integer-infz %s must be in [%s, %d]. got: %sr` z %s must be in [%d, %s]. got: %sz %s must be in [%d, %d]. got %s)r r rx r r __setattr__)r5 namer vminvmaxs r. _set_integer_checkzContext._set_integer_checkb s %%% < 3d :;; ; 6>>t|| !BdDRVX]E^!^___ U]]t|| !BdDRVX]E^!^___ t||ut|| !AT4QUW\D]!]^^^!!$e444r0 c t |t st d|z |D ] }|t vrt d|z t D ]}||vrt d|z t | || S )Nz%s must be a signal dictz %s is not a valid signal dict)r r rx r KeyErrorr r )r5 r r r~ s r. _set_signal_dictzContext._set_signal_dictp s !T"" < 6 :;; ; D DC(?? > BCCC # D DC!88 > BCCC !!$a000r0 c T |dk r| ||dd S |dk r| ||dd S |dk r| ||dd S |dk r| ||dd S |d k r| ||dd S |d k r7|t vrt d |z t | || S |d k s|d k r| || S |dk r t | || S t d|z )Nr_ r1 r` re r r( r` rf rg r^ z%s: invalid rounding moderh ri r z.'decimal.Context' object has no attribute '%s')r _rounding_modesrx r r r AttributeError)r5 r r s r. r zContext.__setattr__{ s_ 6>>**45AA A V^^**4BB B V^^**45AA A Z **41== = W__**41== = Z O++ ;e CDDD%%dD%88 8 W__((u55 5 % % %%%dD%88 8 @4GI I Ir0 c & t d|z )Nz%s cannot be deleted)r )r5 r s r. __delattr__zContext.__delattr__ s 3d :;;;r0 c d | j D }d | j D }| j | j | j | j | j | j | j ||ffS )Nc g | ] \ }}|| S r, r, r? sigr s r. rA z&Context.__reduce__.<locals>.<listcomp> ! ;;;a;;;;r0 c g | ] \ }}|| S r, r, r s r. rA z&Context.__reduce__.<locals>.<listcomp> r r0 ) rh rv ri rt r_ r^ re r` rf rg )r5 rh ri s r. ru zContext.__reduce__ sv ;;4:#3#3#5#5;;;;;4:#3#3#5#5;;;DM49di E5:; ;r0 c g }| dt | z d | j D }| dd | z dz d | j D }| dd | z dz d | dz S ) NzrContext(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, clamp=%(clamp)dc & g | ]\ }}||j S r, r9 )r? r r s r. rA z$Context.__repr__.<locals>.<listcomp> # @@@1a@@@@r0 zflags=[, ]c & g | ]\ }}||j S r, r )r? r r s r. rA z$Context.__repr__.<locals>.<listcomp> r r0 ztraps=[))r varsrh rv r ri )r5 rY namess r. r zContext.__repr__ s ' # :: A@ (8(8(:(:@@@ TYYu - --3444@@ (8(8(:(:@@@ TYYu - --3444yy||c!!r0 c 0 | j D ] }d| j |< d S r` )rh r5 flags r. rr zContext.clear_flags / %J ! !D DJt ! !r0 c 0 | j D ] }d| j |< d S r` )ri r s r. clear_trapszContext.clear_traps r r0 c t | j | j | j | j | j | j | j | j | j }|S r+ ) r r_ r^ re r` rf rg rh ri r r5 ncs r. r zContext._shallow_copy sB / TY ty$)]DJ DJ(* * r0 c t | j | j | j | j | j | j | j | j | j }|S r+ ) r r_ r^ re r` rf rg rh rq ri r r s r. rq z Context.copy sW , TY ty$)]DJZ__&& (9(9(* * r0 c t || }|| j v r | j | g|R S d| j |< | j | s | j | g|R S || r )_condition_maprl r r7 rh ri )r5 condition explanationr- errors r. r zContext._raise_error s ""9i88 D' ' '!5577>$.... . 5z% 3%99;;%d2T222 2 eK r0 c " | j t S r+ ) _ignore_flagsr r s r. rV zContext._ignore_all_flags s 2!t!8,,r0 c Z | j t | z | _ t | S r+ )r r )r5 rh s r. r zContext._ignore_flags s) 2 $ 2T%[[ @E{{r0 c |r*t |d t t f r|d }|D ] }| j | d S r` )r r r r remove)r5 rh r s r. _regard_flagszContext._regard_flags sb 9 Za5,77 !HE - -D & &t , , , , - -r0 c B t | j | j z dz S r )r re r_ r s r. r5 z Context.Etiny s! /49ty(1,---r0 c B t | j | j z dz S r )r r` r_ r s r. rm z Context.Etop s! :49ty(1,---r0 c $ | j }|| _ |S r+ )r^ )r5 rx r^ s r. r zContext._set_rounding s = r0 r c t |t r7|| k sd|v r| t d S t || }| r@t |j | j | j z k r| t d S | | S )Nr zAtrailing or leading whitespace and underscores are not permitted.ro z diagnostic info too long in NaN) r r r r r r r r rD r_ rg r )r5 r! r s r. create_decimalzContext.create_decimal s & c3 GSCIIKK%7%73#::$$%5&FG G G C & & & 88:: H#af++ DJ(>>>$$%5%FH H Hvvd||r0 c b t | }| | S r+ )r r r )r5 r r s r. create_decimal_from_floatz!Context.create_decimal_from_float s, q ! !vvd||r0 c R t |d }| | S r )r r" r5 r s r. r z Context.abs/ s/ " 1d + + +yyy&&&r0 c t |d }| || }|t u rt d|z |S NTr ro Unable to convert %s to Decimal)r r* r rx r5 r r@ r> s r. addz Context.addD sT 1d + + + IIaI & & = ABB BHr0 c F t | | S r+ )r r r s r. _applyzContext._applyY s 166$<< r0 c t t |t st d | S )Nz,canonical requires a Decimal as an argument.)r r rx r r s r. r zContext.canonical\ s9 !W%% L JKK K{{}} r0 c T t |d }| || S r )r r r5 r r@ s r. r zContext.comparei s2 @ 1d + + +yyDy)))r0 c T t |d }| || S r )r r r s r. r zContext.compare_signal s4 > 1d + + + 4 000r0 c P t |d }| | S r )r r r s r. r zContext.compare_total s- 2 1d + + +q!!!r0 c P t |d }| | S r )r r r s r. r zContext.compare_total_mag s/ 1d + + +""1%%%r0 c N t |d }| S r )r r r s r. r zContext.copy_abs s) 1d + + +zz||r0 c D t |d }t | S r )r r r s r. copy_decimalzContext.copy_decimal s' 1d + + +qzzr0 c N t |d }| S r )r r r s r. r zContext.copy_negate s) 1d + + +}} r0 c P t |d }| | S r )r r r s r. r zContext.copy_sign s+ ( 1d + + +{{1~~ r0 c t |d }| || }|t u rt d|z |S r )r r: r rx r s r. dividezContext.divide sT : 1d + + + MM!TM * * = ABB BHr0 c t |d }| || }|t u rt d|z |S r )r rS r rx r s r. divide_intzContext.divide_int9 sT 1d + + + NN1dN + + = ABB BHr0 c t |d }| || }|t u rt d|z |S r )r rG r rx r s r. r6 zContext.divmodP sT 1d + + + LLDL ) ) = ABB BHr0 c R t |d }| | S r )r r r s r. r z Context.expe s/ ( !T * * *uuTu"""r0 c V t |d }| ||| S r )r r )r5 r r@ r s r. r z Context.fma} s3 & 1d + + +uuQ4u(((r0 c t t |t st d | S )Nz/is_canonical requires a Decimal as an argument.)r r rx r r s r. r zContext.is_canonical s; !W%% O MNN N~~ r0 c N t |d }| S r )r r r s r. r zContext.is_finite s) $ 1d + + +{{}} r0 c N t |d }| S r )r r r s r. r zContext.is_infinite s) 1d + + +}} r0 c N t |d }| S r )r r r s r. r zContext.is_nan s) 1d + + +xxzzr0 c R t |d }| | S r )r r r s r. r zContext.is_normal s/ & 1d + + +{{4{(((r0 c N t |d }| S r )r r r s r. r zContext.is_qnan s) 1d + + +yy{{r0 c N t |d }| S r )r r r s r. r zContext.is_signed s) 1d + + +{{}} r0 c N t |d }| S r )r r r s r. r zContext.is_snan s) 1d + + +yy{{r0 c R t |d }| | S r )r r r s r. r zContext.is_subnormal s/ $ 1d + + +~~d~+++r0 c N t |d }| S r )r r r s r. r zContext.is_zero3 s) 1d + + +yy{{r0 c R t |d }| | S r )r r) r s r. r) z Context.lnD s/ $ 1d + + +ttDt!!!r0 c R t |d }| | S r )r r/ r s r. r/ z Context.log10Z s/ 0 1d + + +wwtw$$$r0 c R t |d }| | S r )r r1 r s r. r1 z Context.logbv s/ , 1d + + +vvdv###r0 c T t |d }| || S r )r rF r s r. rF zContext.logical_and 1 . 1d + + +}}Q}---r0 c R t |d }| | S r )r rJ r s r. rJ zContext.logical_invert s2 1d + + + ---r0 c T t |d }| || S r )r rM r s r. rM zContext.logical_or s1 . 1d + + +||At|,,,r0 c T t |d }| || S r )r rI r s r. rI zContext.logical_xor r r0 c T t |d }| || S r )r r$ r s r. r$ z Context.max 1 . 1d + + +uuQu%%%r0 c T t |d }| || S r )r rR r s r. rR zContext.max_mag 1 1d + + +yyDy)))r0 c T t |d }| || S r )r r r s r. r z Context.min r r0 c T t |d }| || S r )r rT r s r. rT zContext.min_mag; r r0 c R t |d }| | S r )r r r s r. minusz Context.minusL / 1d + + +yyy&&&r0 c t |d }| || }|t u rt d|z |S r )r r3 r rx r s r. multiplyzContext.multiply] sT 0 1d + + + IIaI & & = ABB BHr0 c R t |d }| | S r )r rY r s r. rY zContext.next_minus} s/ 1d + + +||D|)))r0 c R t |d }| | S r )r r[ r s r. r[ zContext.next_plus s/ 1d + + +{{4{(((r0 c T t |d }| || S r )r r^ r s r. r^ zContext.next_toward s1 > 1d + + +}}Q}---r0 c R t |d }| | S r )r r r s r. r zContext.normalize s/ ( 1d + + +{{4{(((r0 c R t |d }| | S r )r ra r s r. ra zContext.number_class s0 - \ 1d + + +~~d~+++r0 c R t |d }| | S r )r r r s r. plusz Context.plus r! r0 c t |d }| ||| }|t u rt d|z |S r )r r r rx )r5 r r@ r r> s r. powerz Context.power# sX G P 1d + + + IIaI . . = ABB BHr0 c T t |d }| || S r )r r r s r. r zContext.quantizes s2 5 l 1d + + +zz!Tz***r0 c " t d S rc ra r s r. rd z Context.radix s r{{r0 c t |d }| || }|t u rt d|z |S r )r rK r rx r s r. r8 zContext.remainder sT < 1d + + + IIaI & & = ABB BHr0 c T t |d }| || S r )r rQ r s r. rQ zContext.remainder_near s4 < 1d + + + 4 000r0 c T t |d }| || S r )r rl r s r. rl zContext.rotate s1 2 1d + + +xx4x(((r0 c P t |d }| | S r )r r r s r. r zContext.same_quantum s- ( 1d + + +~~a r0 c T t |d }| || S r )r rp r s r. rp zContext.scaleb2 s1 1d + + +xx4x(((r0 c T t |d }| || S r )r r7 r s r. r7 z Context.shiftE s1 4 1d + + +wwq$w'''r0 c R t |d }| | S r )r r r s r. r z Context.sqrtc s/ 8 1d + + +vvdv###r0 c t |d }| || }|t u rt d|z |S r )r r, r rx r s r. subtractzContext.subtract sT 1d + + + IIaI & & = ABB BHr0 c R t |d }| | S r )r r r s r. r zContext.to_eng_string s/ 0 1d + + +t,,,r0 c R t |d }| | S r )r r r s r. to_sci_stringzContext.to_sci_string s/ 1d + + +yyy&&&r0 c R t |d }| | S r )r r r s r. r zContext.to_integral_exact s2 4 1d + + +""4"000r0 c R t |d }| | S r )r r r s r. r zContext.to_integral_value s2 2 1d + + +""4"000r0 ) NNNNNNNNNr+ )r )Wr9 r: r; r r r r r ru r rr r r rq ry r rV r r r r5 rm r r r r r r r r r r r r r r r r r r6 r r r r r r r r r r r r r) r/ r1 rF rJ rM rI r$ rR r rT r r# rY r[ r^ r ra r* r, r rd r8 rQ rl r rp r7 r r7 r r: r r r r, r0 r. r r + s $ BFDH&*" " " " H 5 5 5 1 1 1I I I2< < <; ; ; " " "! 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H! ! ! !,- - - - - - H. . .. . . & " $' ' '* *! ! ! "* "* "*H!1 !1 !1F" " ":& & & 0# # #J . *# # #0) ) ). , ) ) ). " , , ,, "" " ",% % %8$ $ $4. . .6. . .&- - -6. . .6& & &6* * *"& & &6* * *"' ' '" @* * *() ) )(!. !. !.F) ) )00, 0, 0,d' ' '"N N N N`8+ 8+ 8+t $ $ $L 1 1 1D) ) ):! ! !0) ) )& ( ( (< $ $ $@ .- - -8' ' ' 1 1 1<1 1 1< $KKKr0 r c e Zd ZdZddZd ZdS )r rP r r Nc |d | _ d| _ d | _ d S t |t r3|j | _ t |j | _ |j | _ d S |d | _ |d | _ |d | _ d S )Nr( r1 r )rP r r r r rC rD r )r5 r s r. r z_WorkRep.__init__ s~ = DIDHDHHH w ' ' DI5:DH zDHHH aDI QxDH QxDHHHr0 c 8 d| j d| j d| j dS )N(r r r> r s r. r z_WorkRep.__repr__ s# !%DHHHdhhh??r0 r+ )r9 r: r; r r r r, r0 r. r r sA $I @ @ @ @ @r0 r c | j |j k r|}| }n| }|}t t |j }t t |j }|j t d||z dz z }||j z dz |k rd|_ ||_ |xj d|j |j z z z c_ |j |_ | |fS )Nr r r1 r )r r r r r )r( r) r_ tmpr tmp_len other_lenr s r. r& r& s w #cg,, GC NN##I 'CGdNQ .// /C59 q 3&& GGrcg )**GGiCG 8Or0 c | dk rdS |dk r| d|z z S t t | }t | t | d z }|| k rd n| d| z z S )Nr( r r )r r r rstrip)rA r str_nval_ns r. r r 6 s Avvq a2q5y CFF E S c!2!2 3 33 rzzttqBF{2r0 c v | dk s|dk rt d d}||k r||| |z z dz }}||k |S )Nr( z3Both arguments to _sqrt_nearest should be positive.r1 )r )rA r r@ s r. _sqrt_nearestrK K s^ AvvaNOOOA q&&!QBE'1*1 q&& Hr0 c H d|z | |z }}|d| |dz z z |dz z |k z S )Nr1 r r, )r r7 r@ r= s r. _rshift_nearestrM Z s? :qEzqA 1!9 1%) **r0 c N t | | \ }}|d|z |dz z |k z S )Nr r1 )r6 )r r@ r= r> s r. _div_nearestrO b s5 !Q<<DAq !qs a r0 r c | |z }d}||k rt | ||z z |k s ||k rt | ||z z |k r~t ||z dz |t ||t || z z | z }|dz }||k rt | ||z z |k _||k rt | ||z z |k ~t dt t | z d|z z }t || }t || }t |dz dd D ]&}t || t ||z | z }'t ||z | S )Nr( r1 r r )r rO rK rM r r r r ) r MLr RTyshiftwr s r. _ilogrX j s : !A A 66c!ff!mq(( q55SVVqs]a'' !A#!]1a10E0E.E+F J JJ L L Q 66c!ff!mq(( q55SVVqs]a'' SSVV_qs # $ $$A Q " "FQA 1Q32 ; ; A fQh!:!: : !Q r0 c |dz }t t | }||z ||z dk z }|dk rhd|z }||z |z }|dk r | d|z z } nt | d| z } t | | }t | }t ||z | }||z } nd}t |d| z } t | |z d S Nr r1 r( r r )r r rO rX _log10_digits) r r r r r rR r log_dlog_10 log_tenpowers r. r. r. s : FA CFF A !qsaxA1uu E aCE 66 QJAA QQB''Aa q!! U1Wf--s #ArA2v.. 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Q3Jr0 c j |dz }t d|t t | z dz }||z }||z }|dk r | d|z z }n | d| z z }t |t | \ }}t |d|z }t t |d|z d ||z dz fS )Nr r( r1 r i r )r$ r r r6 r[ rO ri ) r r r r r= r7 cshiftquotr s r. r r 2 s 4 FA 1s3q66{{?Q& ' 'E E A aCE zz2u9BJ v}Q / /00ID# sBI & &C c2q5))4 0 0$(Q, >>r0 c t t t | |z }t | |||z dz }||z }|dk r ||z d|z z }nt ||z d| z }|dk rHt t | |z dk |dk k rd|dz z dz d|z } } n<d|z dz | } } n0t ||dz |dz \ } } t | d } | dz } | | fS )Nr1 r( r )r r r r' rO r ) r r r r r r@ lxcr7 pcr r s r. r r V s$ CBLLB A B!A C qDE zz VBI #b&"uf* - - Qww R\\B ! #a 0 0ac1ac3EEQq1"3EE21vqs++ s UB'' q #:r0 r F 5 ( r r r ) r0 2345678r] c | dk rt d t | }dt | z ||d z S )Nr( z0The argument to _log10_lb should be nonnegative.r )r r r )r correctionstr_cs r. r r sI KAvvKLLL FFE s5zz>JuQx 0 00r0 c t | t r| S t | t rt | S |r/t | t rt | S |rt d| z t S )Nr )r r r r r rx r )r r allow_floats r. r r s %!! % u~~ )z%// )!!%((( C9EABBB r0 c x t |t r| |fS t |t j r_| j sBt | j t t | j |j z | j } | t |j fS |r,t |t j r|j dk r|j }t |t rWt# }|rd|j t& < n| t& d | t | fS t, t, fS )Nr( r1 r )r r _numbersRationalr rB rC r r rD denominatorr numeratorComplexrb r^ r r rh r r r r )r5 r r r6 s r. r r s7 %!! 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