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Ë ‚Ö¦iÓwã ó—dZgd¢ZeZdZdZdZddlZddlZ ddl Z ddlmZ e dd d¬ «ZdZd ZdZdZdZdZdZdZdZdZe j4dk(rdZdZdZndZdZdZeedz z ZGd„de«Z Gd„de «Z!Gd„d e «Z"Gd!„d"e"«Z#Gd#„d$e e$«Z%Gd%„d&e"«Z&Gd'„d(e"e$«Z'Gd)„d*e «Z(Gd+„d,e"«Z)Gd-„d.e «Z*Gd/„d0e «Z+Gd1„d2e(e*«Z,Gd3„d4e(e*e+«Z-Gd5„d6e e.«Z/e!e%e(e,e*e-e"e+e/g Z0e#e"e&e"e'e"e)e"iZ1eeeeeeeefZ2ddl3Z3e3jhd7«Z5e6gd8¢«Z7d9„Z8d:„Z9[3dtd;„Z:Gd<„d=e;«Z„Z=e j|je<«Gd?„d@e;«Z@GdA„dBe;«ZAGdC„dDe;«ZBdvdE„ZCeDjŠZFdF„ZGdG„ZHdH„ZIdI„ZJdwdJ„ZKdK„ZLdL„ZMGdM„dNe;«ZNeN«jžZPdwdO„ZQdP„ZRdQ„ZSdRdSdTdUdVdWdXdYdZd[œ fd\„ZTdxd]„ZUdud^„ZVeAd_ee%e,e"ggd`dadd¬b«ZWeAdcee%e,e"e!e-gg¬d«ZXeAdcegg¬d«ZYddlZZZeZj¶deeZj¸eZjºz«j¼Z_eZj¶df«j¼Z`eZj¶dg«j¼ZaeZj¶dheZj¸eZjÄz«Zc[Z ddldZedtdi„Zfdj„Zgdk„Zhdydl„Zidm„Zjdn„Zker0Cs€¡órrrrrrrrTlÿÿÿÿlÿÇNÎZolüÿÿÿÿÇNÎZoi@üTiÀ«æécó—eZdZdZd„Zy)ra2Base exception class. Used exceptions derive from this. If an exception derives from another exception besides this (such as Underflow (Inexact, Rounded, Subnormal)) that indicates that it is only called if the others are present. This isn't actually used for anything, though. handle -- Called when context._raise_error is called and the trap_enabler is not set. First argument is self, second is the context. More arguments can be given, those being after the explanation in _raise_error (For example, context._raise_error(NewError, '(-x)!', self._sign) would call NewError().handle(context, self._sign).) To define a new exception, it should be sufficient to have it derive from DecimalException. có—yr,r-©ÚselfÚcontextr.s r/ÚhandlezDecimalException.handlers€Ør1N©Ú__name__Ú __module__Ú__qualname__Ú__doc__r8r-r1r/rr_s„ñó$ r1rcó—eZdZdZy)r a)Exponent of a 0 changed to fit bounds. This occurs and signals clamped if the exponent of a result has been altered in order to fit the constraints of a specific concrete representation. This may occur when the exponent of a zero result would be outside the bounds of a representation, or when a large normal number would have an encoded exponent that cannot be represented. In this latter case, the exponent is reduced to fit and the corresponding number of zero digits are appended to the coefficient ("fold-down"). N©r:r;r<r=r-r1r/r r vó„ò r1r có—eZdZdZd„Zy)r a/An invalid operation was performed. Various bad things cause this: Something creates a signaling NaN -INF + INF 0 * (+-)INF (+-)INF / (+-)INF x % 0 (+-)INF % x x._rescale( non-integer ) sqrt(-x) , x > 0 0 ** 0 x ** (non-integer) x ** (+-)INF An operand is invalid The result of the operation after this is a quiet positive NaN, except when the cause is a signaling NaN, in which case the result is also a quiet NaN, but with the original sign, and an optional diagnostic information. có„—|r9t|dj|djdd«}|j|«StS)Nr(ÚnT)Ú_dec_from_tripleÚ_signÚ_intÚ_fix_nanÚ_NaN)r6r7r.Úanss r/r8zInvalidOperation.handle™s9€ÙÜ" 4¨¡7§=¡=°$°q±'·,±,ÀÀTÓJˆCØ—<‘< Ó(Ð(Üˆr1Nr9r-r1r/r r ‚s„ñó,r1r có—eZdZdZd„Zy)rzÜTrying to convert badly formed string. This occurs and signals invalid-operation if a string is being converted to a number and it does not conform to the numeric string syntax. The result is [0,qNaN]. có—tSr,©rHr5s r/r8zConversionSyntax.handle¦ó€Üˆr1Nr9r-r1r/rrŸs„ñór1rcó—eZdZdZd„Zy)ra²Division by 0. This occurs and signals division-by-zero if division of a finite number by zero was attempted (during a divide-integer or divide operation, or a power operation with negative right-hand operand), and the dividend was not zero. The result of the operation is [sign,inf], where sign is the exclusive or of the signs of the operands for divide, or is 1 for an odd power of -0, for power. có—t|Sr,)Ú_SignedInfinity©r6r7Úsignr.s r/r8zDivisionByZero.handle¶s €Ü˜tÑ$Ð$r1Nr9r-r1r/rr©s„ñ ó%r1rcó—eZdZdZd„Zy)rzóCannot perform the division adequately. This occurs and signals invalid-operation if the integer result of a divide-integer or remainder operation had too many digits (would be longer than precision). The result is [0,qNaN]. có—tSr,rLr5s r/r8zDivisionImpossible.handleÁrMr1Nr9r-r1r/rr¹ó„ñór1rcó—eZdZdZd„Zy)rzîUndefined result of division. This occurs and signals invalid-operation if division by zero was attempted (during a divide-integer, divide, or remainder operation), and the dividend is also zero. The result is [0,qNaN]. có—tSr,rLr5s r/r8zDivisionUndefined.handleÌrMr1Nr9r-r1r/rrÄrUr1rcó—eZdZdZy)raHad to round, losing information. This occurs and signals inexact whenever the result of an operation is not exact (that is, it needed to be rounded and any discarded digits were non-zero), or if an overflow or underflow condition occurs. The result in all cases is unchanged. The inexact signal may be tested (or trapped) to determine if a given operation (or sequence of operations) was inexact. Nr?r-r1r/rrÏr@r1rcó—eZdZdZd„Zy)raìInvalid context. Unknown rounding, for example. This occurs and signals invalid-operation if an invalid context was detected during an operation. This can occur if contexts are not checked on creation and either the precision exceeds the capability of the underlying concrete representation or an unknown or unsupported rounding was specified. These aspects of the context need only be checked when the values are required to be used. The result is [0,qNaN]. có—tSr,rLr5s r/r8zInvalidContext.handleærMr1Nr9r-r1r/rrÛs„ñór1rcó—eZdZdZy)r aÙNumber got rounded (not necessarily changed during rounding). This occurs and signals rounded whenever the result of an operation is rounded (that is, some zero or non-zero digits were discarded from the coefficient), or if an overflow or underflow condition occurs. The result in all cases is unchanged. The rounded signal may be tested (or trapped) to determine if a given operation (or sequence of operations) caused a loss of precision. Nr?r-r1r/r r ér@r1r có—eZdZdZy)ra˜Exponent < Emin before rounding. This occurs and signals subnormal whenever the result of a conversion or operation is subnormal (that is, its adjusted exponent is less than Emin, before any rounding). The result in all cases is unchanged. The subnormal signal may be tested (or trapped) to determine if a given or operation (or sequence of operations) yielded a subnormal result. Nr?r-r1r/rrõs„òr1rcó—eZdZdZd„Zy)raNumerical overflow. This occurs and signals overflow if the adjusted exponent of a result (from a conversion or from an operation that is not an attempt to divide by zero), after rounding, would be greater than the largest value that can be handled by the implementation (the value Emax). The result depends on the rounding mode: For round-half-up and round-half-even (and for round-half-down and round-up, if implemented), the result of the operation is [sign,inf], where sign is the sign of the intermediate result. For round-down, the result is the largest finite number that can be represented in the current precision, with the sign of the intermediate result. For round-ceiling, the result is the same as for round-down if the sign of the intermediate result is 1, or is [0,inf] otherwise. For round-floor, the result is the same as for round-down if the sign of the intermediate result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded will also be raised. có®—|jttttfvr t |S|dk(rP|jtk(r t |St|d|jz|j|jz dz«S|dk(rP|jtk(r t |St|d|jz|j|jz dz«Sy)Nr(Ú9r2)ÚroundingrrrrrPrrDÚprecÚEmaxrrQs r/r8zOverflow.handlesÌ€Ø×Ñ¤ ¬Ü /´ð ;ñ;ä" 4Ñ(Ð(Ø1Š9Ø×Ñ¤=Ò0Ü& tÑ,Ð,Ü# D¨#¨g¯l©lÑ*:Ø#ŸL™L¨¯©Ñ5°aÑ7ó9ð 9à1Š9Ø×Ñ¤;Ò.Ü& tÑ,Ð,Ü# D¨#¨g¯l©lÑ*:Ø$Ÿ\™\¨'¯,©,Ñ6°qÑ8ó:ð :ðr1Nr9r-r1r/rrs„ñó* :r1rcó—eZdZdZy)raxNumerical underflow with result rounded to 0. This occurs and signals underflow if a result is inexact and the adjusted exponent of the result would be smaller (more negative) than the smallest value that can be handled by the implementation (the value Emin). That is, the result is both inexact and subnormal. The result after an underflow will be a subnormal number rounded, if necessary, so that its exponent is not less than Etiny. This may result in 0 with the sign of the intermediate result and an exponent of Etiny. In all cases, Inexact, Rounded, and Subnormal will also be raised. Nr?r-r1r/rr&ó„òr1rcó—eZdZdZy)raœEnable stricter semantics for mixing floats and Decimals. If the signal is not trapped (default), mixing floats and Decimals is permitted in the Decimal() constructor, context.create_decimal() and all comparison operators. Both conversion and comparisons are exact. Any occurrence of a mixed operation is silently recorded by setting FloatOperation in the context flags. Explicit conversions with Decimal.from_float() or context.create_decimal_from_float() do not set the flag. Otherwise (the signal is trapped), only equality comparisons and explicit conversions are silent. All other mixed operations raise FloatOperation. Nr?r-r1r/rr5rdr1rÚdecimal_context)raÚEminrbÚcapitalsÚclampr`ÚflagsÚtrapscóŒ— tj«S#t$r$t«}tj |«|cYSwxYw)z½Returns this thread's context. If this thread does not yet have a context, returns a new context and sets this thread's context. New contexts are copies of DefaultContext. )Ú_current_context_varÚgetÚLookupErrorrÚset©r7s r/rr_s?€ðÜ#×'Ñ'Ó)Ð)øÜòÜ“)ˆÜ× Ñ Ô)ØŠðús‚–*AÁAcó”—|tttfvr |j«}|j «t j |«y)z%Set this thread's context to context.N)rrrÚcopyÚclear_flagsrmrprqs r/rrms6€à”>¤<´ÐAÑAØ—,‘,“.ˆØ×ÑÔÜ×Ñ˜WÕ%r1cóÀ—|€ t«}t|«}|j«D]3\}}|tvrt d|›d«‚t|j||«Œ5|S)abReturn a context manager for a copy of the supplied context Uses a copy of the current context if no context is specified The returned context manager creates a local decimal context in a with statement: def sin(x): with localcontext() as ctx: ctx.prec += 2 # Rest of sin calculation algorithm # uses a precision 2 greater than normal return +s # Convert result to normal precision def sin(x): with localcontext(ExtendedContext): # Rest of sin calculation algorithm # uses the Extended Context from the # General Decimal Arithmetic Specification return +s # Convert result to normal context >>> setcontext(DefaultContext) >>> print(getcontext().prec) 28 >>> with localcontext(): ... ctx = getcontext() ... ctx.prec += 2 ... print(ctx.prec) ... 30 >>> with localcontext(ExtendedContext): ... print(getcontext().prec) ... 9 >>> print(getcontext().prec) 28 Ú'z2' is an invalid keyword argument for this function)rÚ_ContextManagerÚitemsÚ_context_attributesÚ TypeErrorÚsetattrÚnew_context)ÚctxÚkwargsÚctx_managerÚkeyÚvalues r/r r vsg€ðH€{Ü‹lˆÜ! #Ó&€KØ—l‘l–n‰ ˆˆUØÔ)Ñ)Ü˜a ˜uÐ$VÐWÓXÐXÜ×'Ñ'¨¨eÕ4ð%ðÐr1c óž—eZdZdZdZdzd„Zed„«Zd„Zd„Z d{d„Z d „Zd „Zd„Z d|d„Zd|d „Zd|d„Zd|d„Zd|d„Zd|d„Zd„Zd„Zd„Zd„Zd}d„Zd|d„Zd|d„Zd|d„Zd~d„Zd|d„ZeZd|d„Zd|d„Z d|d„Z!e!Z"d|d„Z#d „Z$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/e0d+„«Z1e0d,„«Z2d-„Z3d.„Z4d/„Z5d0„Z6d1„Z7d2„Z8d3„Z9d4„Z:d5„Z;d6„Ze?e7e8e9e:e;e¬9«Z@d|d:„ZAd;„ZBd<„ZCd|d=„ZDd|d>„ZEd?„ZFd{d@„ZGd|dA„ZHd|dB„ZId{dC„ZJd|dD„ZKdE„ZLdF„ZMd{dG„ZNd{dH„ZOeOZPd|dI„ZQd|dJ„ZRd|dK„ZSdL„ZTdM„ZUdN„ZVdO„ZWd|dP„ZXd|dQ„ZYd|dR„ZZdS„Z[dT„Z\d|dU„Z]d|dV„Z^dW„Z_dX„Z`dY„ZadZ„Zbd|d[„Zcd\„Zdd]„Zed^„Zfd|d_„Zgd`„Zhda„Zid|db„Zjdc„Zkd|dd„Zld|de„Zmdf„Zndg„Zod|dh„Zpd|di„Zqd|dj„Zrd|dk„Zsd|dl„Ztd|dm„Zud|dn„Zvd|do„Zwd|dp„Zxd|dq„Zydr„Zzd|ds„Z{d|dt„Z|d|du„Z}dv„Z~dw„Zdx„Z€d{dy„Zy)rz,Floating-point class for decimal arithmetic.)Ú_exprFrEÚ_is_specialNcó8 —tj|«}t|t«rht |j«j dd««}|€%|€ t«}|jtd|z«S|jd«dk(rd|_nd|_|jd«}|k|jd «xsd}t|jd «xsd«}tt||z««|_ |t|«z |_d|_|S|jd «}|Mtt|xsd««j#d«|_ |jd«rd|_nd|_nd|_ d|_d|_|St|t«r=|dk\rd|_nd|_d|_tt%|««|_ d|_|St|t&«rF|j|_|j|_|j|_ |j |_|St|t(«rN|j*|_t|j«|_ t|j,«|_d|_|St|t.t0f«rZt|«dk7rt3d«‚t|dt«r|ddvst3d«‚|d|_|ddk(rd|_ |d|_d|_|Sg} |dD]N} t| t«r2d| cxkrdkr'nt3d«‚| s| dk7sŒ3| j5| «ŒEt3d«‚|ddvr7dj7t9t| ««|_ |d|_d|_|St|dt«r>> Decimal('3.14') # string input Decimal('3.14') >>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent) Decimal('3.14') >>> Decimal(314) # int Decimal('314') >>> Decimal(Decimal(314)) # another decimal instance Decimal('314') >>> Decimal(' 3.14 \n') # leading and trailing whitespace okay Decimal('3.14') Ú_ÚzInvalid literal for Decimal: %rrRÚ-r2r(ÚintÚfracÚexpÚ0FÚdiagÚsignalÚNrCÚFTéztInvalid tuple size in creation of Decimal from list or tuple. The list or tuple should have exactly three elements.©r(r2z|Invalid sign. The first value in the tuple should be an integer; either 0 for a positive number or 1 for a negative number.éé zTThe second value in the tuple must be composed of integers in the range 0 through 9.©rCrzUThe third value in the tuple must be an integer, or one of the strings 'F', 'n', 'N'.ú;strict semantics for mixing floats and Decimals are enabledzCannot convert %r to Decimal)!ÚobjectÚ__new__Ú isinstanceÚstrÚ_parserÚstripÚreplacerÚ_raise_errorrÚgrouprEr‰rFÚlenrƒr„ÚlstripÚabsrÚ_WorkReprRr‹ÚlistÚtupleÚ ValueErrorÚappendÚjoinÚmapÚfloatrÚ from_floatrz)Úclsrr7r6ÚmÚintpartÚfracpartr‹rÚdigitsÚdigits r/r˜zDecimal.__new__³sL€ô.~‰~˜cÓ"ˆôeœSÕ!Ü˜Ÿ™› ×-Ñ-¨c°2Ó6Ó7ˆAØˆyØ?Ü(›lGØ×+Ñ+Ô,<Ø AÀEÑ IóKðKðw‰wv‹ #Ò%Ø• à” Ø—g‘g˜e“nˆGØÐ"àŸ7™7 6›?Ò0¨bÜ˜!Ÿ'™' %›.Ò/¨CÓ0Ü¤ G¨HÑ$4Ó 5Ó6” Ø¤# h£-Ñ/” Ø#(Ô ðˆKð—w‘w˜v“ØÐ#ä #¤C¨ª°Ó$4Ó 5× <Ñ <¸SÓ AD”IØ—w‘w˜xÔ(Ø$'˜ à$'˜ ð!$D”IØ #D”IØ#'Ô ØˆKôeœSÔ!Ø˜ŠzØ• à” ØˆDŒIÜœC ›J›ˆDŒIØ$ˆDÔØˆKôeœWÔ%ØŸ™ˆDŒIØŸ™ˆDŒJØŸ™ˆDŒIØ %× 1Ñ 1ˆDÔØˆKôeœXÔ&ØŸ™ˆDŒJÜ˜EŸI™I›ˆDŒIÜ˜EŸI™I›ˆDŒIØ$ˆDÔØˆKôeœd¤5˜\Õ*Ü5‹z˜QŠÜ ð"GóHðHô˜u Q™x¬Ô-°%¸±(¸eÑ2CÜ ð"OóPðPð˜q™ˆDŒJØQ‰x˜3Šà” Ø! !™H” Ø#'Ô ð6ˆKð1Ø" 1œXEÜ! %¬Ô-°!°u´/À´/ô )ð*8ó9ð9ñ" U¨a£ZØ"ŸM™M¨%Õ0ä(ð*8ó9ð9ð &ð˜‘8˜zÑ)à "§¡¬¬C°Ó(8Ó 9D”IØ % a¡D”IØ'+DÔ$ðˆKô a¡¬#Ô.à "§¡¬¬C°²¸A¸3Ó(?Ó @D”IØ % a¡D”IØ',DÔ$ð ˆKô%ð&>ó?ð?ô eœUÔ#ØˆÜ$›,Ø× Ñ ¤ðô ô×&Ñ& uÓ-ˆEØŸ™ˆDŒIØŸ™ˆDŒJØŸ™ˆDŒIØ %× 1Ñ 1ˆDÔØˆKäÐ6¸Ñ>Ó?Ð?r1có—t|t«r |dk\rdnd}d}tt|««}nµt|t«rštj|«stj|«r|t|««Stjd|«dk(rd}nd}t|«j«\}}|j«dz }t|d|zz«}ntd«‚t|||«}|tur|S||«S)a.Converts a float to a decimal number, exactly. Note that Decimal.from_float(0.1) is not the same as Decimal('0.1'). Since 0.1 is not exactly representable in binary floating point, the value is stored as the nearest representable value which is 0x1.999999999999ap-4. The exact equivalent of the value in decimal is 0.1000000000000000055511151231257827021181583404541015625. >>> Decimal.from_float(0.1) Decimal('0.1000000000000000055511151231257827021181583404541015625') >>> Decimal.from_float(float('nan')) Decimal('NaN') >>> Decimal.from_float(float('inf')) Decimal('Infinity') >>> Decimal.from_float(-float('inf')) Decimal('-Infinity') >>> Decimal.from_float(-0.0) Decimal('-0') r(r2gð?ézargument must be int or float.)r™r‰ršr¢rªÚ_mathÚisinfÚisnanÚreprÚcopysignÚas_integer_ratioÚ bit_lengthrzrDr)r¬ÚfrRÚkÚcoeffrCÚdÚresults r/r«zDecimal.from_floatIsà€ô,aœÔØ˜Qš‘1 AˆDØˆAÜœ˜A›“K‰EÜ ˜œ5Ô !Ü{‰{˜1Œ~¤§¡¨Q¤Ùœ4 ›7“|Ð#Ü~‰~˜c 1Ó%¨Ò,Ø‘àÜq“6×*Ñ*Ó,‰DˆAˆqØ—‘“ Ñ"ˆAÜ˜˜!˜Q™$™“K‰EäÐ<Ó=Ð=ä! $¨°¨rÓ2ˆØ”'‰>ØˆMáv“;Ðr1cóL—|jr|j}|dk(ry|dk(ryy)zrReturns whether the number is not actually one. 0 if a number 1 if NaN 2 if sNaN rCr2rr“r()r„rƒ)r6r‹s r/Ú_isnanzDecimal._isnanvs-€ð×ÒØ—)‘)ˆCØcŠzØØ˜’ØØr1có>—|jdk(r|jryyy)zyReturns whether the number is infinite 0 if finite or not a number 1 if +INF -1 if -INF réÿÿÿÿr2r()rƒrE©r6s r/Ú_isinfinityzDecimal._isinfinity…s €ð9‰9˜ÒØzŠzØØØr1có&—|j«}|€d}n|j«}|s|rh|€ t«}|dk(r|jtd|«S|dk(r|jtd|«S|r|j |«S|j |«Sy)z½Returns whether the number is not actually one. if self, other are sNaN, signal if self, other are NaN return nan return 0 Done before operations. Fr“ÚsNaNr()rÁrržr rG)r6Úotherr7Úself_is_nanÚother_is_nans r/Ú_check_nanszDecimal._check_nans’sŸ€ð—k‘k“mˆØˆ=Ø ‰Là Ÿ<™<›>ˆLá™,ØˆÜ$›,à˜aÒØ×+Ñ+Ô,<¸fØ(,ó.ð.à˜qÒ Ø×+Ñ+Ô,<¸fØ(-ó/ð/áØ—}‘} WÓ-Ð-à—>‘> 'Ó*Ð*Ør1có„—|€ t«}|js|jrœ|j«r|jtd|«S|j«r|jtd|«S|j«r|jtd|«S|j«r|jtd|«Sy)aCVersion of _check_nans used for the signaling comparisons compare_signal, __le__, __lt__, __ge__, __gt__. Signal InvalidOperation if either self or other is a (quiet or signaling) NaN. Signaling NaNs take precedence over quiet NaNs. Return 0 if neither operand is a NaN. zcomparison involving sNaNzcomparison involving NaNr()rr„Úis_snanržr Úis_qnan©r6rÈr7s r/Ú_compare_check_nanszDecimal._compare_check_nans²sÀ€ðˆ?Ü “lˆGà×Ò˜u×0Ò0Ø|‰|Œ~Ø×+Ñ+Ô,<Ø,GØ,0ó2ð2ð—‘”Ø×+Ñ+Ô,<Ø,GØ,1ó3ð3ð—‘”Ø×+Ñ+Ô,<Ø,FØ,0ó2ð2ð—‘”Ø×+Ñ+Ô,<Ø,FØ,1ó3ð3ðr1có<—|jxs|jdk7S)zuReturn True if self is nonzero; otherwise return False. NaNs and infinities are considered nonzero. rŒ©r„rFrÄs r/Ú__bool__zDecimal.__bool__Ós€ð ×ÑÒ3 4§9¡9°Ñ#3Ð3r1cóÊ—|js|jr-|j«}|j«}||k(ry||kryy|s|syd|jzS|sd|jzS|j|jkry|j|jkry|j«}|j«}||k(r||jd|j |j z zz}|jd|j |j z zz}||k(ry||krd|jzSd|jzS||kDrd|jzSd|jzS)z¸Compare the two non-NaN decimal instances self and other. Returns -1 if self < other, 0 if self == other and 1 if self > other. This routine is for internal use only.r(rÃr2rŒ)r„rÅrEÚadjustedrFrƒ)r6rÈÚself_infÚ other_infÚ self_adjustedÚother_adjustedÚself_paddedÚother_paddeds r/Ú_cmpzDecimal._cmpÚs]€ð×Ò˜u×0Ò0Ø×'Ñ'Ó)ˆHØ×)Ñ)Ó+ˆIØ˜9Ò$ØØ˜IÒ%ØàñÙØà˜uŸ{™{Ñ*Ð+Ð+ÙØ˜Ÿ™Ñ#Ð#ð;‰;˜Ÿ™Ò#ØØ:‰:˜Ÿ™Ò#ØàŸ ™ ›ˆ ØŸ™Ó)ˆØ˜NÒ*ØŸ)™) c¨4¯9©9°u·z±zÑ+AÑ&BÑBˆKØ Ÿ:™:¨¨U¯Z©Z¸$¿)¹)Ñ-CÑ(DÑDˆLØ˜lÒ*ØØ˜|Ò+Ø˜dŸj™jÑ(Ð(Ð(à˜TŸZ™ZÑ'Ð'Ø ˜^Ò +Ø˜Ÿ™Ñ#Ð#à˜4Ÿ:™:Ñ%Ð&Ð&r1có†—t||d¬«\}}|tur|S|j||«ry|j|«dk(S)NT)Úequality_opFr()Ú_convert_for_comparisonÚNotImplementedrËrÜrÏs r/Ú__eq__zDecimal.__eq__sH€Ü-¨d°EÀtÔL‰ˆˆeØ”NÑ"ØˆLØ×Ñ˜E 7Ô+ØØy‰y˜Ó 1Ñ$Ð$r1có†—t||«\}}|tur|S|j||«}|ry|j|«dkS©NFr(©rßràrÐrÜ©r6rÈr7rIs r/Ú__lt__zDecimal.__lt__"óK€Ü-¨d°EÓ:‰ˆˆeØ”NÑ"ØˆLØ×&Ñ& u¨gÓ6ˆÙØØy‰y˜Ó !Ñ#Ð#r1có†—t||«\}}|tur|S|j||«}|ry|j|«dkSrãrärås r/Ú__le__zDecimal.__le__+óK€Ü-¨d°EÓ:‰ˆˆeØ”NÑ"ØˆLØ×&Ñ& u¨gÓ6ˆÙØØy‰y˜Ó 1Ñ$Ð$r1có†—t||«\}}|tur|S|j||«}|ry|j|«dkDSrãrärås r/Ú__gt__zDecimal.__gt__4rçr1có†—t||«\}}|tur|S|j||«}|ry|j|«dk\Srãrärås r/Ú__ge__zDecimal.__ge__=rêr1có°—t|d¬«}|js|r"|jr|j||«}|r|St|j |««S)zàCompare self to other. Return a decimal value: a or b is a NaN ==> Decimal('NaN') a < b ==> Decimal('-1') a == b ==> Decimal('0') a > b ==> Decimal('1') T©Úraiseit)Ú_convert_otherr„rËrrÜrås r/ÚcomparezDecimal.compareFsS€ô˜u¨dÔ3ˆð ×Ò¡¨%×*;Ò*;Ø×"Ñ" 5¨'Ó2ˆCÙØ ät—y‘y Ó'Ó(Ð(r1cóÆ—|jrY|j«rtd«‚|j«rtj|«S|jrtStS|jdk\rtd|jt«}n tt|jt«}t|j«|ztz}|dk\r|n|}|dk(rdS|S)zx.__hash__() <==> hash(x)z"Cannot hash a signaling NaN value.r(é rÃéþÿÿÿ)r„rÍrzÚis_nanr—Ú__hash__rEÚ_PyHASH_INFrƒÚpowÚ_PyHASH_MODULUSÚ _PyHASH_10INVr‰rF)r6Úexp_hashÚhash_rIs r/røzDecimal.__hash__Xs·€ð×ÒØ|‰|Œ~ÜÐ DÓEÐEØ—‘”Ü—‘ tÓ,Ð,à—:’:Ü'˜<Ð'ä&Ð&à9‰9˜Š>Ü˜2˜tŸy™y¬/Ó:‰Häœ=¨4¯9©9¨*´oÓFˆHÜD—I‘I“ Ñ)¬OÑ;ˆØ˜q’y‰e u fˆØ˜B’YˆrÐ' CÐ'r1c ó†—t|jttt|j ««|j«S)zeRepresents the number as a triple tuple. To show the internals exactly as they are. )rrEr¥r©r‰rFrƒrÄs r/Úas_tuplezDecimal.as_tuplers+€ô ˜DŸJ™J¬¬c´#°t·y±yÓ.AÓ(BÀDÇIÁIÓNÐNr1cóì—|jr&|j«rtd«‚td«‚|syt |j «}|jdk\r|d|jzzd}}nt|j}|dkDr |dzdk(r|dz}|dz}|dkDr |dzdk(rŒ|j}t||zj«dz |«}|r ||z}||z}d|z|z}|jr|}||fS)aExpress a finite Decimal instance in the form n / d. Returns a pair (n, d) of integers. When called on an infinity or NaN, raises OverflowError or ValueError respectively. >>> Decimal('3.14').as_integer_ratio() (157, 50) >>> Decimal('-123e5').as_integer_ratio() (-12300000, 1) >>> Decimal('0.00').as_integer_ratio() (0, 1) z#cannot convert NaN to integer ratioz(cannot convert Infinity to integer ratior’r(rõr2r³) r„r÷r¦Ú OverflowErrorr‰rFrƒÚminrºrE)r6rCr¾Úd5Úd2Úshift2s r/r¹zDecimal.as_integer_ratioys €ð×ÒØ{‰{Œ}Ü Ð!FÓGÐGä#Ð$NÓOÐOáØô — ‘ ‹NˆØ9‰9˜Š>àr˜4Ÿ9™9‘}Ñ$ aˆq‰Að—)‘)ˆBØq’&˜Q ™U ašZØa‘Øa‘ðq’&˜Q ™U a›Zð—)‘)ˆBÜ˜!˜q˜b™&×,Ñ,Ó.°Ñ2°BÓ7ˆFÙØf‘Øf‘à2‘˜‘ˆAà:Š:ØˆAØ!ˆtˆr1có—dt|«zS)z0Represents the number as an instance of Decimal.z Decimal('%s'))ršrÄs r/Ú__repr__zDecimal.__repr__«s€ð¤ T£Ñ*Ð*r1có—ddg|j}|jrG|jdk(r|dzS|jdk(r|dz|jzS|dz|jzS|jt |j«z}|jdkr|d kDr|}n+|sd }n&|jdk(r|d zdzd z }n|d z dzd z}|dkrd}d d|zz|jz}nd|t |j«k\r+|jd|t |j«z zz}d}n!|jd|}d |j|dz}||k(rd}n&|€ t«}ddg|jd||z zz}||z|z|zS)z–Return string representation of the number in scientific notation. Captures all of the information in the underlying representation. r‡rˆrÚInfinityrCÚNaNrÇr(éúÿÿÿr2rŒr‘Ú.NÚeÚEz%+d)rEr„rƒrFr rrh) r6Úengr7rRÚ leftdigitsÚdotplacer®r¯r‹s r/Ú__str__zDecimal.__str__°s£€ðCˆy˜Ÿ™Ñ$ˆØ×ÒØy‰y˜CÒØ˜jÑ(Ð(Ø—‘˜cÒ!Ø˜e‘| d§i¡iÑ/Ð/à˜f‘} t§y¡yÑ0Ð0ð—Y‘Y¤ T§Y¡Y£Ñ/ˆ ð 9‰9˜Š>˜j¨2šoà!‰HÙà‰HØ Y‰Y˜#Ò à" Q™¨!Ñ+¨aÑ/‰Hð# Q™¨!Ñ+¨aÑ/ˆHàqŠ=ØˆGØ˜S 8 )™_Ñ,¨t¯y©yÑ8‰HØ œ˜TŸY™Y›Ò 'Ø—i‘i X¬c°$·)±)«nÑ%<Ñ =Ñ=ˆGØ‰Hà—i‘i Ð*ˆGØ˜TŸY™Y x yÐ1Ñ1ˆHØ˜Ò!Ø‰CàˆÜ$›,Ø˜*˜W×-Ñ-Ñ.°¸*ÀXÑ:MÑ1NÑNˆCàg‰~ Ñ(¨3Ñ.Ð.r1có(—|jd|¬«S)a,Convert to a string, using engineering notation if an exponent is needed. Engineering notation has an exponent which is a multiple of 3. This can leave up to 3 digits to the left of the decimal place and may require the addition of either one or two trailing zeros. T)rr7)r©r6r7s r/Ú to_eng_stringzDecimal.to_eng_stringäs€ð|‰| ¨gˆ|Ó6Ð6r1cóì—|jr|j|¬«}|r|S|€ t«}|s$|jtk7r|j«}n|j «}|j|«S)zRReturns a copy with the sign switched. Rounds, if it has reason. rq)r„rËrr`rÚcopy_absÚcopy_negateÚ_fix©r6r7rIs r/Ú__neg__zDecimal.__neg__ísn€ð ×ÒØ×"Ñ"¨7Ð"Ó3ˆCÙØ àˆ?Ü “lˆGá˜×(Ñ(¬KÒ7ð—-‘-“/‰Cà×"Ñ"Ó$ˆCàx‰x˜Ó Ð r1cóâ—|jr|j|¬«}|r|S|€ t«}|s$|jtk7r|j«}nt |«}|j|«S)zhReturns a copy, unless it is a sNaN. Rounds the number (if more than precision digits) rq)r„rËrr`rrrrrs r/Ú__pos__zDecimal.__pos__sg€ð ×ÒØ×"Ñ"¨7Ð"Ó3ˆCÙØ àˆ?Ü “lˆGá˜×(Ñ(¬KÒ7à—-‘-“/‰Cä˜$“-ˆCàx‰x˜Ó Ð r1cóÒ—|s|j«S|jr|j|¬«}|r|S|jr|j |¬«}|S|j|¬«}|S)zÉReturns the absolute value of self. If the keyword argument 'round' is false, do not round. The expression self.__abs__(round=False) is equivalent to self.copy_abs(). rq)rr„rËrErr)r6Úroundr7rIs r/Ú__abs__zDecimal.__abs__sl€ñØ—=‘=“?Ð"à×ÒØ×"Ñ"¨7Ð"Ó3ˆCÙØ à:Š:Ø—,‘, w,Ó/ˆCðˆ ð—,‘, w,Ó/ˆCàˆ r1có<—t|«}|tur|S|€ t«}|js|jr‹|j ||«}|r|S|j«rJ|j|jk7r&|j«r|jtd«St|«S|j«rt|«St|j|j«}d}|jtk(r|j|jk7rd}|sF|sDt|j|j«}|rd}t|d|«}|j|«}|S|sUt!||j|j"z dz «}|j%||j«}|j|«}|S|sUt!||j|j"z dz «}|j%||j«}|j|«}|St'|«}t'|«}t)|||j"«\}}t'«} |j*|j*k7r˜|j,|j,k(r t|d|«}|j|«}|S|j,|j,kr||}}|j*dk(r+d| _|j*|j*c|_|_n5d| _n-|j*dk(rd| _d\|_|_nd| _|j*dk(r|j,|j,z| _n|j,|j,z | _|j.| _t| «}|j|«}|S)zbReturns self + other. -INF + INF (or the reverse) cause InvalidOperation errors. z -INF + INFr(r2rŒ)r(r()ròràrr„rËrÅrEržr rrrƒr`rrDrÚmaxraÚ_rescaler£Ú _normalizerRr‰r‹) r6rÈr7rIr‹ÚnegativezerorRÚop1Úop2r¿s r/Ú__add__zDecimal.__add__.sû€ô ˜uÓ%ˆØ”NÑ"ØˆLàˆ?Ü “lˆGà×Ò˜u×0Ò0Ø×"Ñ" 5¨'Ó2ˆCÙØ à×ÑÔ!à—:‘: §¡Ò,°×1BÑ1BÔ1DØ"×/Ñ/Ô0@À,ÓOÐOÜ˜t“}Ð$Ø× Ñ Ô"Ü˜u“~Ð%ä$—)‘)˜UŸZ™ZÓ(ˆØˆØ×Ñœ{Ò*¨t¯z©z¸U¿[¹[Ò/HàˆLá™EÜt—z‘z 5§;¡;Ó/ˆDÙØÜ" 4¨¨cÓ2ˆCØ—(‘(˜7Ó#ˆCØˆJÙÜc˜5Ÿ:™:¨¯©Ñ4°QÑ6Ó7ˆCØ—.‘. g×&6Ñ&6Ó7ˆCØ—(‘(˜7Ó#ˆCØˆJÙÜc˜4Ÿ9™9 w§|¡|Ñ3°AÑ5Ó6ˆCØ—-‘- W×%5Ñ%5Ó6ˆCØ—(‘(˜7Ó#ˆCØˆJät‹nˆÜu‹oˆÜ˜c 3¨¯©Ó5‰ˆˆSä“ˆØ8‰8s—x‘xÒàw‰w˜#Ÿ'™'Ò!Ü& |°S¸#Ó>Ø—h‘h˜wÓ'Ø Øw‰w˜Ÿ™Ò Ø Sàx‰x˜1Š}Ø”Ø%(§X¡X¨s¯x©xÐ"”˜#(à•à X‰X˜Š]ØˆFŒKØ!'ÑˆCŒHc•hàˆFŒKð8‰8qŠ=ØŸ™ 3§7¡7Ñ*ˆFJàŸ™ 3§7¡7Ñ*ˆFŒJà—W‘WˆŒ Üf‹oˆØh‰hwÓˆØˆ r1cóÌ—t|«}|tur|S|js|jr|j||¬«}|r|S|j |j«|¬«S)zReturn self - otherrq)ròràr„rËr)rrås r/Ú__sub__zDecimal.__sub__†se€ä˜uÓ%ˆØ”NÑ"ØˆLà×Ò˜u×0Ò0Ø×"Ñ" 5°'Ð"Ó:ˆCÙØ ð|‰|˜E×-Ñ-Ó/¸ˆ|ÓAÐAr1cóR—t|«}|tur|S|j||¬«S)zReturn other - selfrq)ròràr+rÏs r/Ú__rsub__zDecimal.__rsub__”s,€ä˜uÓ%ˆØ”NÑ"ØˆLà}‰}˜T¨7ˆ}Ó3Ð3r1có —t|«}|tur|S|€ t«}|j|jz}|js|jrx|j||«}|r|S|j «r!|s|jtd«St|S|j «r!|s|jtd«St|S|j|jz}|r|s t|d|«}|j|«}|S|jdk(r*t||j|«}|j|«}|S|jdk(r*t||j|«}|j|«}|St|«}t|«}t|t|j |j z«|«}|j|«}|S)z\Return self * other. (+-) INF * 0 (or its reverse) raise InvalidOperation. z(+-)INF * 0z0 * (+-)INFrŒÚ1)ròràrrEr„rËrÅržr rPrƒrDrrFr£ršr‰)r6rÈr7Ú resultsignrIÚ resultexpr'r(s r/Ú__mul__zDecimal.__mul__œs£€ô ˜uÓ%ˆØ”NÑ"ØˆLàˆ?Ü “lˆGà—Z‘Z %§+¡+Ñ-ˆ à×Ò˜u×0Ò0Ø×"Ñ" 5¨'Ó2ˆCÙØ à×ÑÔ!ÙØ"×/Ñ/Ô0@À-ÓPÐPÜ& zÑ2Ð2à× Ñ Ô"ÙØ"×/Ñ/Ô0@À-ÓPÐPÜ& zÑ2Ð2à—I‘I § ¡ Ñ*ˆ ñ™5Ü" :¨s°IÓ>ˆCà—(‘(˜7Ó#ˆCØˆJð9‰9˜ÒÜ" :¨u¯z©z¸9ÓEˆCØ—(‘(˜7Ó#ˆCØˆJØ:‰:˜ÒÜ" :¨t¯y©y¸)ÓDˆCØ—(‘(˜7Ó#ˆCØˆJät‹nˆÜu‹oˆä˜z¬3¨s¯w©w¸¿¹Ñ/@Ó+AÀ9ÓMˆØh‰hwÓˆàˆ r1có—t|«}|turtS|€ t«}|j|jz}|js|jr¦|j||«}|r|S|j «r&|j «r|jtd«S|j «r t|S|j «r1|jtd«t|d|j««S|s/|s|jtd«S|jtd|«S|s|j|jz }d}nt!|j"«t!|j"«z |j$zdz}|j|jz |z }t'|«}t'|«} |dk\r*t)|j*d|zz| j*«\}} n*t)|j*| j*d|zz«\}} | r|d zdk(rD|dz }n>|j|jz }||kr |dzdk(r|dz}|dz }||kr |dzdk(rŒt|t-|«|«}|j/|«S) zReturn self / other.z(+-)INF/(+-)INFzDivision by infinityrŒz0 / 0zx / 0r(r2rõr³)ròràrrEr„rËrÅržr rPr rDÚEtinyrrrƒr rFrar£Údivmodr‰ršr)r6rÈr7rRrIr‹r½Úshiftr'r(Ú remainderÚ ideal_exps r/Ú__truediv__zDecimal.__truediv__ÕsG€ä˜uÓ%ˆØ”NÑ"Ü!Ð!àˆ?Ü “lˆGàz‰z˜EŸK™KÑ'ˆà×Ò˜u×0Ò0Ø×"Ñ" 5¨'Ó2ˆCÙØ à×ÑÔ! e×&7Ñ&7Ô&9Ø×+Ñ+Ô,<Ð>OÓPÐPà×ÑÔ!Ü& tÑ,Ð,à× Ñ Ô"Ø×$Ñ$¤WÐ.DÔEÜ'¨¨c°7·=±=³?ÓCÐCñÙØ×+Ñ+Ô,=¸wÓGÐGØ×'Ñ'¬¸ÀÓFÐFáØ—)‘)˜eŸj™jÑ(ˆCØŠEô˜Ÿ ™ “O¤c¨$¯)©)£nÑ4°w·|±|ÑCÀaÑGˆEØ—)‘)˜eŸj™jÑ(¨5Ñ0ˆCÜ˜4“.ˆCÜ˜5“/ˆCØ˜ŠzÜ#)¨#¯'©'°B¸±IÑ*=¸s¿w¹wÓ#GÑ ‘yä#)¨#¯'©'°3·7±7¸RÀ%À¹ZÑ3GÓ#HÑ yÙà˜1‘9 ’>Ø˜Q‘J‘Eð!ŸI™I¨¯ © Ñ2 Ø˜I’o¨%°"©*¸ª/Ø˜b‘LEØ˜1‘HCð˜I’o¨%°"©*¸«/ô˜t¤S¨£Z°Ó5ˆØx‰x˜Ó Ð r1có´—|j|jz}|j«r |j}n t|j|j«}|j «|j «z }|r|j«s|dkr)t|dd«|j ||j«fS||jkrùt|«}t|«}|j|jk\r0|xjd|j|jz zzc_n/|xjd|j|jz zzc_t|j|j«\}} |d|jzkr6t|t|«d«t|jt| «|«fS|jtd«} | | fS)z½Return (self // other, self % other), to context.prec precision. Assumes that neither self nor other is a NaN, that self is not infinite and that other is nonzero. rörŒr(rõz%quotient too large in //, % or divmod)rErÅrƒrrÕrDr$r`rar£r‹r‰r5ršržr)r6rÈr7rRr8Úexpdiffr'r(ÚqÚrrIs r/Ú_dividezDecimal._divides€ðz‰z˜EŸK™KÑ'ˆØ×ÑÔØŸ ™ ‰Iä˜DŸI™I u§z¡zÓ2ˆIà—-‘-“/ E§N¡NÓ$4Ñ4ˆÙu×(Ñ(Ô*¨g¸ªmÜ$ T¨3°Ó2Ø—M‘M )¨W×-=Ñ-=Ó>ð@ð @àg—l‘lÒ"Ü˜4“.ˆCÜ˜5“/ˆCØw‰w˜#Ÿ'™'Ò!Ø—’˜2 §¡¨#¯'©'Ñ 1Ñ2Ñ2–à—’˜2 §¡¨#¯'©'Ñ 1Ñ2Ñ2•Ü˜#Ÿ'™' 3§7¡7Ó+‰DˆAˆqØ2w—|‘|Ñ#Ò#Ü(¨¬s°1«v°qÓ9Ü(¨¯©´S¸³V¸YÓGðIðIð×"Ñ"Ô#5Ø#JóLˆàCˆxˆr1cóR—t|«}|tur|S|j||¬«S)z)Swaps self/other and returns __truediv__.rq)ròràr9rÏs r/Ú__rtruediv__zDecimal.__rtruediv__1s/€ä˜uÓ%ˆØ”NÑ"ØˆLØ× Ñ ¨wÐ Ó7Ð7r1cóB—t|«}|tur|S|€ t«}|j||«}|r||fS|j|jz}|j«rI|j«r|j td«}||fSt||j td«fS|sI|s|j td«}||fS|j td|«|j td«fS|j||«\}}|j|«}||fS)z6 Return (self // other, self % other) zdivmod(INF, INF)úINF % xzdivmod(0, 0)úx // 0úx % 0) ròràrrËrErÅržr rPrrr>r)r6rÈr7rIrRÚquotientr7s r/Ú __divmod__zDecimal.__divmod__8s5€ô˜uÓ%ˆØ”NÑ"ØˆLàˆ?Ü “lˆGà×Ñ˜u gÓ.ˆÙØ˜:Ðàz‰z˜EŸK™KÑ'ˆØ×ÑÔØ× Ñ Ô"Ø×*Ñ*Ô+;Ð=OÓPØ˜Cxä'¨Ñ-Ø×,Ñ,Ô-=¸yÓIðKðKñÙØ×*Ñ*Ô+<¸nÓMØ˜Cxà×,Ñ,¬^¸XÀtÓLØ×,Ñ,Ô-=¸wÓGðIðIð#Ÿl™l¨5°'Ó:Ñˆ)Ø—N‘N 7Ó+ˆ Ø˜Ð"Ð"r1cóR—t|«}|tur|S|j||¬«S)z(Swaps self/other and returns __divmod__.rq)ròràrFrÏs r/Ú__rdivmod__zDecimal.__rdivmod__\s/€ä˜uÓ%ˆØ”NÑ"ØˆLØ×Ñ ¨gÐÓ6Ð6r1cól—t|«}|tur|S|€ t«}|j||«}|r|S|j «r|jtd«S|s.|r|jtd«S|jtd«S|j||«d}|j|«}|S)z self % other rBrDz0 % 0r2) ròràrrËrÅržr rr>r)r6rÈr7rIr7s r/Ú__mod__zDecimal.__mod__cs¸€ô˜uÓ%ˆØ”NÑ"ØˆLàˆ?Ü “lˆGà×Ñ˜u gÓ.ˆÙØˆJà×ÑÔØ×'Ñ'Ô(8¸)ÓDÐDÙÙØ×+Ñ+Ô,<¸gÓFÐFà×+Ñ+Ô,=¸wÓGÐGà—L‘L ¨Ó0°Ñ3ˆ Ø—N‘N 7Ó+ˆ ØÐr1cóR—t|«}|tur|S|j||¬«S)z%Swaps self/other and returns __mod__.rq)ròràrJrÏs r/Ú__rmod__zDecimal.__rmod__~ó,€ä˜uÓ%ˆØ”NÑ"ØˆLØ}‰}˜T¨7ˆ}Ó3Ð3r1cót—|€ t«}t|d¬«}|j||«}|r|S|j«r|j t d«S|s.|r|j t d«S|j td«S|j«rt|«}|j|«St|j|j«}|s(t|jd|«}|j|«S|j«|j«z }||jdzk\r|j t«S|dkr-|j!||j"«}|j|«St%|«}t%|«}|j&|j&k\r0|xj(d |j&|j&z zzc_n/|xj(d |j&|j&z zzc_t+|j(|j(«\}} d | z|dzz|j(kDr| |j(z} |dz }|d |jzk\r|j t«S|j} | dkrd| z } | } t| t-| «|«}|j|«S)zI Remainder nearest to 0- abs(remainder-near) <= other/2 Trðzremainder_near(infinity, x)zremainder_near(x, 0)zremainder_near(0, 0)rŒr2rörõr“r()rròrËrÅržr rrrrrƒrDrErÕrarr$r`r£r‹r‰r5rš)r6rÈr7rIÚideal_exponentr;r'r(r<r=rRs r/Úremainder_nearzDecimal.remainder_near…sy€ðˆ?Ü “lˆGä˜u¨dÔ3ˆà×Ñ˜u gÓ.ˆÙØˆJð×ÑÔØ×'Ñ'Ô(8Ø(EóGð GñÙØ×+Ñ+Ô,<Ø,BóDðDð×+Ñ+Ô,=Ø,BóDðDð×ÑÔÜ˜$“-ˆCØ—8‘8˜GÓ$Ð$ô˜TŸY™Y¨¯ © Ó3ˆÙÜ" 4§:¡:¨s°NÓCˆCØ—8‘8˜GÓ$Ð$ð—-‘-“/ E§N¡NÓ$4Ñ4ˆØg—l‘l QÑ&Ò&à×'Ñ'Ô(:Ó;Ð;ØbŠ=à—-‘- °×0@Ñ0@ÓAˆCØ—8‘8˜GÓ$Ð$ôt‹nˆÜu‹oˆØ7‰7c—g‘gÒØGŠGr˜CŸG™G c§g¡gÑ-Ñ.Ñ.ŽGàGŠGr˜CŸG™G c§g¡gÑ-Ñ.Ñ.GÜc—g‘g˜sŸw™wÓ'‰ˆˆ1ð ˆQ‰3!A‘#‰;˜Ÿ™Ò Ø —‘‰LˆAØ ‰FˆAàG—L‘LÑ Ò Ø×'Ñ'Ô(:Ó;Ð;ðz‰zˆØˆqŠ5ØT‘6ˆDØˆAä˜t¤S¨£V¨^Ó<ˆØx‰x˜Ó Ð r1cóÖ—t|«}|tur|S|€ t«}|j||«}|r|S|j «rF|j «r|jtd«St|j|jzS|sF|r.|jtd|j|jz«S|jtd«S|j||«dS)z self // otherz INF // INFrCz0 // 0r()ròràrrËrÅržr rPrErrr>rås r/Ú__floordiv__zDecimal.__floordiv__ÐsÞ€ä˜uÓ%ˆØ”NÑ"ØˆLàˆ?Ü “lˆGà×Ñ˜u gÓ.ˆÙØˆJà×ÑÔØ× Ñ Ô"Ø×+Ñ+Ô,<¸lÓKÐKä& t§z¡z°E·K±KÑ'?Ñ@Ð@áÙØ×+Ñ+¬N¸HØ,0¯J©J¸¿¹Ñ,DóFðFð×+Ñ+Ô,=¸xÓHÐHà|‰|˜E 7Ó+¨AÑ.Ð.r1cóR—t|«}|tur|S|j||¬«S)z*Swaps self/other and returns __floordiv__.rq)ròràrRrÏs r/Ú __rfloordiv__zDecimal.__rfloordiv__ìs/€ä˜uÓ%ˆØ”NÑ"ØˆLØ×!Ñ! $°Ð!Ó8Ð8r1cóº—|j«r6|j«rtd«‚|jrdnd}t|«St |«}t|«S)zFloat representation.z%Cannot convert signaling NaN to floatz-nanÚnan)rÁrÍr¦rEršrª©r6Úss r/Ú __float__zDecimal.__float__ósL€à;‰;Œ=Ø|‰|Œ~Ü Ð!HÓIÐIØŸ*š*‘¨%ˆAôQ‹xˆôD“ ˆAÜQ‹xˆr1cód—|jr6|j«rtd«‚|j«rt d«‚d|j z}|jdk\r(|t|j«zd|jzzS|t|jd|jxsd«zS)z1Converts self to an int, truncating if necessary.zCannot convert NaN to integerz"Cannot convert infinity to integerrÃr(rõNrŒ) r„rÁr¦rÅrrErƒr‰rFrWs r/Ú__int__zDecimal.__int__ýs•€à×ÒØ{‰{Œ}Ü Ð!@ÓAÐAØ×!Ñ!Ô#Ü#Ð$HÓIÐIØ $—*‘*ÑˆØ9‰9˜Š>Ø”S˜Ÿ™“^Ñ# B¨¯ © ¡MÑ1Ð1à”S˜Ÿ™ : D§I¡IÐ.Ò5°#Ó6Ñ6Ð6r1có—|Sr,r-rÄs r/ÚrealzDecimal.reals€àˆr1có—td«S)Nr(©rrÄs r/ÚimagzDecimal.imags€äq‹zÐr1có—|Sr,r-rÄs r/Ú conjugatezDecimal.conjugates€Øˆr1có*—tt|««Sr,)ÚcomplexrªrÄs r/Ú__complex__zDecimal.__complex__s€Ü”u˜T“{Ó#Ð#r1có—|j}|j|jz }t|«|kDrB|t|«|z dj d«}t|j||jd«St|«S)z2Decapitate the payload of a NaN to fit the contextNrŒT) rFrarir r¡rDrErƒr)r6r7ÚpayloadÚmax_payload_lens r/rGzDecimal._fix_nanso€à—)‘)ˆð"Ÿ,™,¨¯©Ñ6ˆÜˆw‹<˜/Ò)Øœc '›l¨?Ñ:Ð;Ð<×CÑCÀCÓHˆGÜ# D§J¡J°¸¿¹ÀDÓIÐIÜt‹}Ðr1cóÚ—|jr,|j«r|j|«St|«S|j «}|j«}|s|j|g|j}tt|j|«|«}||jk7r,|jt«t|jd|«St|«St|j «|jz|j"z }||kDrM|jt$d|j«}|jt&«|jt(«|S||k}|r|}|j|krlt|j «|jz|z } | dkrt|jd|dz «}d} |j*|j,} | || «}|j d| xsd}|dkDr9t/t1|«dz«}t|«|j"kDr |dd}|dz }||kDr"|jt$d|j«}nt|j||«}|r|r|jt2«|r|jt4«|r|jt&«|jt(«|s|jt«|S|r|jt4«|jdk(rZ|j|kDrK|jt«|j d|j|z zz} t|j| |«St|«S)zÜRound if it is necessary to keep self within prec precision. Rounds and fixes the exponent. Does not raise on a sNaN. Arguments: self - Decimal instance context - context used. rŒú above Emaxr(r/r2NrÃ)r„rÁrGrr4ÚEtoprbrirr#rƒržr rDrEr rFrarrr Ú_pick_rounding_functionr`ršr‰rr)r6r7r4rkÚexp_maxÚnew_expÚexp_minrIÚself_is_subnormalr°Úrounding_methodÚchangedr½rÚs r/rzDecimal._fix&så€ð×ÒØ{‰{Œ}à—}‘} WÓ-Ð-ô˜t“}Ð$ð— ‘ “ˆØ|‰|‹~ˆÙØ—|‘| TÐ*¨7¯=©=Ñ9ˆGÜœ#˜dŸi™i¨Ó/°Ó9ˆGØ˜$Ÿ)™)Ò#Ø×$Ñ$¤WÔ-Ü'¨¯ © °C¸ÓAÐAä˜t“}Ð$ôd—i‘i“. 4§9¡9Ñ,¨w¯|©|Ñ;ˆØTŠ>à×&Ñ&¤x°¸t¿z¹zÓJˆCØ× Ñ ¤Ô)Ø× Ñ ¤Ô)ØˆJà# e™OÐÙØˆGð9‰9wÓÜ˜Ÿ™“^ d§i¡iÑ/°'Ñ9ˆFØ˜ŠzÜ'¨¯ © °C¸À¹ÓCØØ"×:Ñ:¸7×;KÑ;KÑLˆOÙ% d¨FÓ3ˆGØ—I‘I˜g˜vÐ&Ò-¨#ˆEØ˜Š{ÜœC ›J q™LÓ)Üu“: §¡Ò,Ø! # 2˜JEØ˜q‘LGð˜Š~Ø×*Ñ*¬8°\À4Ç:Á:ÓN‘ä& t§z¡z°5¸'ÓBñÑ,Ø×$Ñ$¤YÔ/Ù Ø×$Ñ$¤YÔ/ÙØ×$Ñ$¤WÔ-Ø× Ñ ¤Ô)Ùà×$Ñ$¤WÔ-ØˆJáØ× Ñ ¤Ô+ð=‰=˜AÒ $§)¡)¨dÒ"2Ø× Ñ ¤Ô)ØŸ)™) c¨4¯9©9°tÑ+;Ñ&<Ñ<ˆKÜ# D§J¡J°¸TÓBÐBôt‹}Ðr1có2—t|j|«ryy)z(Also known as round-towards-0, truncate.r(rÃ)Ú _all_zerosrF©r6ras r/Ú_round_downzDecimal._round_downŒs€äd—i‘i Ô&Øàr1có&—|j|«S)zRounds away from 0.)rvrus r/Ú _round_upzDecimal._round_up“s€à× Ñ Ó&Ð&Ð&r1cóV—|j|dvryt|j|«ryy)zRounds 5 up (away from 0)Ú56789r2r(rÃ)rFrtrus r/Ú_round_half_upzDecimal._round_half_up—s)€à9‰9T‰?˜gÑ%ØÜ ˜Ÿ ™ 4Ô (Øàr1cóR—t|j|«ry|j|«S)zRound 5 downrÃ©Ú_exact_halfrFr{rus r/Ú_round_half_downzDecimal._round_half_down s$€ät—y‘y $Ô'Øà×&Ñ& tÓ,Ð,r1có„—t|j|«r|dk(s|j|dz dvry|j|«S)z!Round 5 to even, rest to nearest.r(r2Ú02468rÃr}rus r/Ú_round_half_evenzDecimal._round_half_even§s?€ät—y‘y $Ô'Ø˜’˜dŸi™i¨¨Q©Ñ/°7Ñ:Øà×&Ñ& tÓ,Ð,r1có`—|jr|j|«S|j|«S)z(Rounds up (not away from 0 if negative.)©rErvrus r/Ú_round_ceilingzDecimal._round_ceiling¯s.€à:Š:Ø×#Ñ# DÓ)Ð)à×$Ñ$ TÓ*Ð*Ð*r1có`—|js|j|«S|j|«S)z'Rounds down (not towards 0 if negative)r„rus r/Ú_round_floorzDecimal._round_floor¶s.€àzŠzØ×#Ñ# DÓ)Ð)à×$Ñ$ TÓ*Ð*Ð*r1cót—|r%|j|dz dvr|j|«S|j|«S)z)Round down unless digit prec-1 is 0 or 5.r2Ú05)rFrvrus r/Ú_round_05upzDecimal._round_05up½s>€áD—I‘I˜d 1™fÑ%¨TÑ1Ø×#Ñ# DÓ)Ð)à×$Ñ$ TÓ*Ð*Ð*r1)rrrrrrrrcó—|:t|t«std«‚tdd|«}|j |«S|j r&|j «rtd«‚td«‚t|jdt««S)aÊRound self to the nearest integer, or to a given precision. If only one argument is supplied, round a finite Decimal instance self to the nearest integer. If self is infinite or a NaN then a Python exception is raised. If self is finite and lies exactly halfway between two integers then it is rounded to the integer with even last digit. >>> round(Decimal('123.456')) 123 >>> round(Decimal('-456.789')) -457 >>> round(Decimal('-3.0')) -3 >>> round(Decimal('2.5')) 2 >>> round(Decimal('3.5')) 4 >>> round(Decimal('Inf')) Traceback (most recent call last): ... OverflowError: cannot round an infinity >>> round(Decimal('NaN')) Traceback (most recent call last): ... ValueError: cannot round a NaN If a second argument n is supplied, self is rounded to n decimal places using the rounding mode for the current context. For an integer n, round(self, -n) is exactly equivalent to self.quantize(Decimal('1En')). >>> round(Decimal('123.456'), 0) Decimal('123') >>> round(Decimal('123.456'), 2) Decimal('123.46') >>> round(Decimal('123.456'), -2) Decimal('1E+2') >>> round(Decimal('-Infinity'), 37) Decimal('NaN') >>> round(Decimal('sNaN123'), 0) Decimal('NaN123') z+Second argument to round should be integralr(r/úcannot round a NaNúcannot round an infinity)r™r‰rzrDÚquantizer„r÷r¦rr$r)r6rCr‹s r/Ú __round__zDecimal.__round__Ïs€ð^ ˆ=ä˜a¤Ô%ÜÐ MÓNÐNÜ" 1 c¨A¨2Ó.ˆCØ—=‘= Ó%Ð%ð×ÒØ{‰{Œ}Ü Ð!5Ó6Ð6ä#Ð$>Ó?Ð?Ü4—=‘= ¤OÓ4Ó5Ð5r1có¤—|jr&|j«rtd«‚td«‚t |jdt««S)zãReturn the floor of self, as an integer. For a finite Decimal instance self, return the greatest integer n such that n <= self. If self is infinite or a NaN then a Python exception is raised. rŒrr()r„r÷r¦rr‰r$rrÄs r/Ú __floor__zDecimal.__floor__ sD€ð×ÒØ{‰{Œ}Ü Ð!5Ó6Ð6ä#Ð$>Ó?Ð?Ü4—=‘= ¤KÓ0Ó1Ð1r1có¤—|jr&|j«rtd«‚td«‚t |jdt««S)zâReturn the ceiling of self, as an integer. For a finite Decimal instance self, return the least integer n such that n >= self. If self is infinite or a NaN then a Python exception is raised. rŒrr()r„r÷r¦rr‰r$rrÄs r/Ú__ceil__zDecimal.__ceil__sD€ð×ÒØ{‰{Œ}Ü Ð!5Ó6Ð6ä#Ð$>Ó?Ð?Ü4—=‘= ¤MÓ2Ó3Ð3r1c ó€—t|d¬«}t|d¬«}|js |jr |€ t«}|jdk(r|j t d|«S|jdk(r|j t d|«S|jdk(r|}n|jdk(r|}ný|jdk(r9|s|j t d«St|j|jz}nµ|jdk(r¦|s|j t d«St|j|jz}nmt|j|jztt|j«t|j«z«|j|jz«}j||«S) a:Fused multiply-add. Returns self*other+third with no rounding of the intermediate product self*other. self and other are multiplied together, with no rounding of the result. The third operand is then added to the result, and a single final rounding is performed. TrðrrÇrCrzINF * 0 in fmaz0 * INF in fma) ròr„rrƒržr rPrErDršr‰rFr))r6rÈÚthirdr7Úproducts r/ÚfmazDecimal.fma+s|€ô˜u¨dÔ3ˆÜ˜u¨dÔ3ˆð×Ò˜u×0Ó0ØˆÜ$›,Øy‰y˜CÒØ×+Ñ+Ô,<¸fÀdÓKÐKØz‰z˜SÒ Ø×+Ñ+Ô,<¸fÀeÓLÐLØy‰y˜CÒØ’Ø—‘˜sÒ"Ø‘Ø—‘˜cÒ!ÙØ"×/Ñ/Ô0@Ø0@óBðBä)¨$¯*©*°u·{±{Ñ*BÑC‘Ø—‘˜sÒ"ÙØ"×/Ñ/Ô0@Ø0@óBðBä)¨$¯*©*°u·{±{Ñ*BÑC‘ä& t§z¡z°E·K±KÑ'?Ü'*¬3¨t¯y©y«>¼CÀÇ Á »OÑ+KÓ'LØ'+§y¡y°5·:±:Ñ'=ó?ˆGð‰˜u gÓ.Ð.r1cóB—t|«}|tur|St|«}|tur|S|€ t«}|j«}|j«}|j«}|s|s|r‹|dk(r|j t d|«S|dk(r|j t d|«S|dk(r|j t d|«S|r|j |«S|r|j |«S|j |«S|j«r |j«r|j«s|j t d«S|dkr|j t d«S|s|j t d«S|j«|jk\r|j t d«S|s|s|j t d«S|j«rd}n|j}tt|««}t|j««}t|j««} |j|zt!d |j"|«z|z}t%| j"«D]} t!|d |«}Œt!|| j|«}t'|t)|«d«S) z!Three argument version of __pow__r“rÇz@pow() 3rd argument not allowed unless all arguments are integersr(zApow() 2nd argument cannot be negative when 3rd argument specifiedzpow() 3rd argument cannot be 0zSinsufficient precision: pow() 3rd argument must not have more than precision digitszXat least one of pow() 1st argument and 2nd argument must be nonzero; 0**0 is not definedrõ)ròràrrÁržr rGÚ _isintegerrÕraÚ_isevenrEr¢r‰r£Úto_integral_valuerúr‹ÚrangerDrš)r6rÈÚmodulor7rÉrÊÚ modulo_is_nanrRÚbaseÚexponentÚis r/Ú _power_modulozDecimal._power_moduloWs›€ô˜uÓ%ˆØ”NÑ"ØˆLÜ Ó'ˆØ”^Ñ#ØˆMàˆ?Ü “lˆGð—k‘k“mˆØ—|‘|“~ˆØŸ ™ ›ˆ Ù™,©-Ø˜aÒØ×+Ñ+Ô,<¸fØ(,ó.ð.à˜qÒ Ø×+Ñ+Ô,<¸fØ(-ó/ð/à Ò!Ø×+Ñ+Ô,<¸fØ(.ó0ð0áØ—}‘} WÓ-Ð-ÙØ—~‘~ gÓ.Ð.Ø—?‘? 7Ó+Ð+ð—‘Ô!Ø× Ñ Ô"Ø×!Ñ!Ô#Ø×'Ñ'Ô(8ð)LóMð Mð1Š9Ø×'Ñ'Ô(8ð)OóPð PñØ×'Ñ'Ô(8Ø(HóJð Jð ?‰?Ó §¡Ò,Ø×'Ñ'Ô(8ð);ó<ð <ñ™TØ×'Ñ'Ô(8ð)>ó?ð ?ð=‰=Œ?Ø‰Dà—:‘:ˆDô”S˜“[Ó!ˆÜ˜×.Ñ.Ó0Ó1ˆÜ˜E×3Ñ3Ó5Ó6ˆð—‘˜6Ñ!¤C¨¨D¯H©H°fÓ$=Ñ=ÀÑGˆÜx—|‘|Ö$ˆAÜt˜R Ó(‰Dð%ä4˜Ÿ™ vÓ.ˆä ¤c¨$£i°Ó3Ð3r1có —t|«}|j|j}}|dzdk(r|dz}|dz }|dzdk(rŒt|«}|j|j}}|dzdk(r|dz}|dz }|dzdk(rŒ|dk(r¢||z}|dzdk(r|dz}|dz }|dzdk(rŒ|dkry|d|zz} |jdk(r| } |j «r:|j dk(r+|jt|«z} t| | z |dz «}nd}tddd|zz| |z «S|jdk(rN|dz}|dvrg||z|k7ryt|«dz } |dzd z}|tt|««k\ryt| |z|«} t||z|«}| |€y| |kDryd | z}n–|d k(rt|«dzd z} td | z|«\}}|ry|d zdk(r|d z}| dz} |d zdk(rŒ|dzdz}|tt|««k\ryt| |z|«} t||z|«}| |€y| |kDryd | z}ny|dkDsJ|«‚|dzdk7sJ|«‚t|«}t|«|kDry| |z }td||«S|dk\r|d|zzd}}nÆ|dk7r%ttt||z«««|kryt|«}ttt|«|z««|kry|d|z}}|d z|d zcxk(rdk(r!nn|d z}|d z}|d z|d zcxk(rdk(rŒn|d z|d zcxk(rdk(r!nn|d z}|d z}|d z|d zcxk(rdk(rŒn|dkDrf|kryt||«\}}|dk7rydt|«|zz} t|||dz z«\}}||krn||dz z|z|z}Œ*||k(r|dk(sy|}|dkDr||dzt|«zkDry||z}||z}|dkDsJ|«‚|dzdk7sJ|«‚t|«}t|«|kDry|j «rC|j dk(r4|jt|«z} t|| z |t|«z «}nd}td|d|zz||z «S)ahAttempt to compute self**other exactly. Given Decimals self and other and an integer p, attempt to compute an exact result for the power self**other, with p digits of precision. Return None if self**other is not exactly representable in p digits. Assumes that elimination of special cases has already been performed: self and other must both be nonspecial; self must be positive and not numerically equal to 1; other must be nonzero. For efficiency, other._exp should not be too large, so that 10**abs(other._exp) is a feasible calculation.rõr(r2Nr/rŒ)r“éééé]éAr³ér‘r“éd)r£r‰r‹rRr™rErƒrrDÚ_nbitsr ršÚ_decimal_lshift_exactr5r¢Ú _log10_lb)r6rÈÚpÚxÚxcÚxeÚyÚycÚyer rOÚzerosÚ last_digitrÚemaxr7ÚstrxcrrCÚxc_bitsÚremÚar<r=Ústr_xcs r/Ú_power_exactzDecimal._power_exact¬ss€ôt T‹NˆØ—‘˜Ÿ™ˆBˆØ2‰g˜ŠlØ2‰IˆBØ!‰GˆBð2‰g˜‹lô U‹OˆØ—‘˜Ÿ™ˆBˆØ2‰g˜ŠlØ2‰IˆBØ!‰GˆBð2‰g˜‹lðŠ7Ø"‰HˆBàr‘'˜Q’,Ør‘ Øa‘ðr‘'˜Q“,ðAŠvØØ˜B ™F‘{ˆHØv‰v˜Š{Ø$˜9à×ÑÔ! e§k¡k°QÒ&6Ø!%§¡¬3¨u«:Ñ!5Ü˜H ^Ñ3°Q°q±SÓ9‘àÜ# A s¨S°©Y¡¸À¹ÓGÐGð 6‰6Q‹;Ø˜b™ˆJØ˜YÑ&à˜˜‘8˜r’>Øä˜2“J˜q‘Lð6˜‘t˜R‘xØœœS ›Y›Ò'Øô*¨!¨b©&°"Ó5Ü*¨2°©7°BÓ7Ø9 Øàt’8ØØ˜‘T‘à˜q’ô˜2“J˜r‘M 2Ñ%Ü & q¨!¡t¨RÓ 0‘ IÙØØ˜1‘f ’kØ˜1‘HBØ˜‘FAð˜1‘f “kð˜‘t˜Q‘wØœœS ›Y›Ò'Øä)¨!¨b©&°"Ó5Ü*¨2°©7°BÓ7Ø9 Øàt’8ØØ˜‘T‘àð ˜’6Ð˜4Ó6Ø˜‘7˜a’<Ð% Ó%<Ü˜“GˆEÜ5‹z˜AŠ~ØØB‘ˆBÜ# A u¨bÓ1Ð1ðŠ7Øb˜"‘f‘9˜aˆq‰AàQŠwœ3œs¤3 r¨"¡u£:›Ó/°B°3Ò6ØÜ˜R“jˆGÜ”3”s˜2“w˜w‘Ó'Ó(¨R¨CÒ/ØØr˜R˜C‘yˆqˆAØa‘%˜1˜q™5Ô% AÕ%Øa‘Øa‘ða‘%˜1˜q™5Ô% AÕ%ða‘%˜1˜q™5Ô% AÕ%Øa‘Øa‘ða‘%˜1˜q™5Ô% AÕ%ð ˆqŠ5à˜!Š|Øä˜R “m‰GˆBØaŠxØðœ˜r› { A‘~Ð&Ñ&ˆAØÜ˜b ! a¨¡c¡(Ó+‘1Ø˜’6Øà˜A˜a™C™ 1™ qÑ(Aðð˜’F˜q AšvØØˆBðŠ6a˜!˜C™%¤¨2£Ñ.Ò.ØØ ‰UˆØ ˆa‰ˆðAŠvÐtÓˆvØB‰w˜!Š|Ð!˜TÓ!ˆ|ÜR“ˆÜˆv‹;˜Š?Øð ×ÑÔ %§+¡+°Ò"2Ø!ŸY™Y¤s¨5£zÑ1ˆNÜ˜˜>Ñ)¨1¬S°«[©=Ó9‰EàˆEÜ 6¨#¨e©)Ñ#3°R¸±XÓ>Ð>r1cóZ—||j|||«St|«}|tur|S|€ t«}|j ||«}|r|S|s|s|jtd«StSd}|jdk(rK|j«r|j«sd}n|r|jtd«S|j«}|s%|jdk(r t|dd«St|S|j«r%|jdk(r t|St|dd«S|tk(rÜ|j«r|jdk(rd}n'||jkDr |j}nt!|«}|j"|z}|d|jz kr^d|jz }|jt$«n9|jt&«|jt$«d|jz }t|dd|zz|«S|j)«}|j«r+|jdk(|dkk(r t|dd«St|Sd}d} |j+«|j)«z} |dk\|jdk(k(r<| t-t/|j0««k\rSt|d|j0dz«}n8|j3«}| t-t/|««k\rt|d|dz «}|€I|j5||jdz«}|(|dk(r!td|j6|j"«}d } |€¼|j}t9|«} | j | j:}}t9|«}|j |j:}}|j<dk(r|}d } t?||||||z«\}}|ddt-t/|««|z dz zzzrn|d z }Œ?t|t/|«|«}| r‹|j«szt-|j6«|jkrY|jdzt-|j6«z }t|j|j6d|zz|j"|z «}|jA«}|jC«tDD]}d|jF|<Œ|jI|«}|jt&«|jJtLr|jtN«|jJtPr!|jtPd |j«tNtLt&t$tRfD]#}|jJ|sŒ|j|«Œ%|S|jI|«}|S)aHReturn self ** other [ % modulo]. With two arguments, compute self**other. With three arguments, compute (self**other) % modulo. For the three argument form, the following restrictions on the arguments hold: - all three arguments must be integral - other must be nonnegative - either self or other (or both) must be nonzero - modulo must be nonzero and must have at most p digits, where p is the context precision. If any of these restrictions is violated the InvalidOperation flag is raised. The result of pow(self, other, modulo) is identical to the result that would be obtained by computing (self**other) % modulo with unbounded precision, but is computed more efficiently. It is always exact. Nz0 ** 0r(r2z+x ** y with x negative and y not an integerrŒr/FTr‘r³rõrj)*r¢ròràrrËržr Ú_OnerEr™ršrrDrPrÅrar‰rƒr rrÕÚ_log10_exp_boundr ršrbr4r½rFr£r‹rRÚ_dpowerrsrtÚ_signalsrkrrjrrrr )r6rÈrr7rIÚresult_signÚ multiplierr‹Úself_adjÚexactÚboundr4r®r¯r°r±r²r³r´Úextrar½r;Ú newcontextÚ exceptions r/Ú__pow__zDecimal.__pow__¤s>€ð0ÐØ×%Ñ% e¨V°WÓ=Ð=ä˜uÓ%ˆØ”NÑ"ØˆLàˆ?Ü “lˆGð×Ñ˜u gÓ.ˆÙØˆJñÙØ×+Ñ+Ô,<¸hÓGÐGäðˆØ:‰:˜Š?Ø×ÑÔ!Ø—}‘}”Ø"#‘KñØ"×/Ñ/Ô0@ØEóGðGð×#Ñ#Ó%ˆDñØ{‰{˜aÒÜ'¨°S¸!Ó<Ð<ä& {Ñ3Ð3ð×ÑÔØ{‰{˜aÒÜ& {Ñ3Ð3ä'¨°S¸!Ó<Ð<ð ”4Š<Ø×ÑÔ!ð —;‘; !Ò#Ø!"‘JØ˜WŸ\™\Ò)Ø!(§¡‘Jä!$ U£Jà—i‘i *Ñ,Ø˜˜7Ÿ<™<™Ò'Ø˜GŸL™L™.CØ×(Ñ(¬Õ1à×$Ñ$¤WÔ-Ø×$Ñ$¤WÔ-Ø˜Ÿ™‘nä# K°°S¸#¸±X±¸sÓCÐCð—=‘=“?ˆð×ÑÔØ—‘˜qÑ h°¡lÒ3Ü'¨°S¸!Ó<Ð<ä& {Ñ3Ð3ðˆØˆð×%Ñ%Ó'¨%¯.©.Ó*:Ñ:ˆØ˜‰M˜uŸ{™{¨aÑ/Ò0ðœœC §¡Ó-Ó.Ò.Ü& {°C¸¿¹Àa¹ÓH‘ð—M‘M“OˆEØœœC ›KÓ(Ò(Ü& {°C¸¸q¹ÓAðˆ;Ø×#Ñ# E¨7¯<©<¸!Ñ+;Ó<ˆCØˆØ !Ò#Ü*¨1¨c¯h©h¸¿¹ÓACØðˆ;Ø—‘ˆAÜ˜“ˆAØ—U‘U˜AŸE™EˆBÜ˜“ˆAØ—U‘U˜AŸE™EˆBØv‰v˜Š{ØSðˆEØÜ$ R¨¨R°°Q°u±WÓ=‘ sØ˜A˜b¤3¤s¨5£z£?°1Ñ#4°QÑ#6Ñ7Ñ7Ò8ØØ˜‘ ð ô# ;´°E³ ¸CÓ@ˆCò˜×)Ñ)Õ+ô3—8‘8‹} §¡Ò,Ø!Ÿ,™,¨Ñ*¬S°·±«]Ñ:Ü& s§y¡y°#·(±(¸3¸w¹;Ñ2FØ'*§x¡x°Ñ'7ó9ð!Ÿ™›ˆJØ×"Ñ"Ô$ß% Ø./ × Ñ Ò+ð&ð—(‘(˜:Ó&ˆCð ×#Ñ#¤GÔ,Ø×Ñ¤ Ò*Ø×'Ñ'¬ Ô2ð×Ñ¤Ò)Ø×$Ñ$¤X¨|¸S¿Y¹YÔGÜ&¬ ´7¼GÄWÓL Ø×#Ñ# IÓ.Ø×(Ñ(¨Õ3ðMðˆ ð—(‘(˜7Ó#ˆCàˆ r1cóR—t|«}|tur|S|j||¬«S)z%Swaps self/other and returns __pow__.rq)ròràrËrÏs r/Ú__rpow__zDecimal.__rpow__| rMr1có0—|€ t«}|jr|j|¬«}|r|S|j|«}|j «r|S|st|jdd«S|j|j«g|j}t|j«}|j}|j|dz dk(r*||kr%|dz }|dz}|j|dz dk(r||krŒ%t|j|jd||«S)z?Normalize- strip trailing 0s, change anything equal to 0 to 0e0NrqrŒr(r2) rr„rËrrÅrDrErbrkrir rFrƒ)r6r7rIÚduprmÚendr‹s r/Ú normalizezDecimal.normalizeƒ s€ðˆ?Ü “lˆGà×ÒØ×"Ñ"¨7Ð"Ó3ˆCÙØ ài‰i˜Ó ˆØ?‰?ÔØˆJáÜ# C§I¡I¨s°AÓ6Ð6Ø—<‘< §¡£Ð0°·±Ñ?ˆÜ#—(‘(‹mˆØh‰hˆØh‰hs˜1‘u‰o Ò$¨¨wªØ1‰HˆCØ1‰HˆCðh‰hs˜1‘u‰o Ò$¨¨w«ô § ¡ ¨3¯8©8°D°S¨>¸3Ó?Ð?r1có`—t|d¬«}|€ t«}|€|j}|js|jrw|j ||«}|r|S|j«s|j«rA|j«r|j«rt |«S|jtd«S|j«|jcxkr|jksn|jtd«S|s2t|jd|j«}|j|«S|j«}||jkDr|jtd«S||jz dz|j kDr|jtd«S|j#|j|«}|j«|jkDr|jtd«St%|j&«|j kDr|jtd«S|r2|j«|j(kr|jt*«|j|jkDr/||k7r|jt,«|jt.«|j|«}|S) z‡Quantize self so its exponent is the same as that of exp. Similar to self._rescale(exp._exp) but with error checking. Trðzquantize with one INFz)target exponent out of bounds in quantizerŒz9exponent of quantize result too large for current contextr2z7quantize result has too many digits for current context)ròrr`r„rËrÅrržr r4rƒrbrDrErrÕrar$r rFrgrrr )r6r‹r`r7rIrØs r/rŽzDecimal.quantizeœ sL€ô ˜S¨$Ô/ˆàˆ?Ü “lˆGØÐØ×'Ñ'ˆHà×Ò˜sŸšØ×"Ñ" 3¨Ó0ˆCÙØ à‰Ô D×$4Ñ$4Ô$6Ø—?‘?Ô$¨×)9Ñ)9Ô);Ü" 4›=Ð(Ø×+Ñ+Ô,<Ø(?óAðAð— ‘ “ 3§8¡8Ô;¨w¯|©|Ô;Ø×'Ñ'Ô(8Ø>ó@ð @ñÜ" 4§:¡:¨s°C·H±HÓ=ˆCØ—8‘8˜GÓ$Ð$àŸ ™ ›ˆ Ø˜7Ÿ<™<Ò'Ø×'Ñ'Ô(8Ø(cóeð eà˜3Ÿ8™8Ñ# aÑ'¨'¯,©,Ò6Ø×'Ñ'Ô(8Ø(aócð cðm‰m˜CŸH™H hÓ/ˆØ<‰<‹>˜GŸL™LÒ(Ø×'Ñ'Ô(8Ø(cóeð eäˆsx‰x‹=˜7Ÿ<™<Ò'Ø×'Ñ'Ô(8Ø(aócð cñ3—<‘<“> G§L¡LÒ0Ø× Ñ ¤Ô+Ø8‰8d—i‘iÒØdŠ{Ø×$Ñ$¤WÔ-Ø× Ñ ¤Ô)ðh‰hwÓˆØˆ r1có —t|d¬«}|js|jrF|j«xr|j«xs"|j«xr|j«S|j|jk(S)a=Return True if self and other have the same exponent; otherwise return False. If either operand is a special value, the following rules are used: * return True if both operands are infinities * return True if both operands are NaNs * otherwise, return False. Trð)ròr„r÷Úis_infiniterƒrÏs r/Úsame_quantumzDecimal.same_quantumÙ sm€ô˜u¨dÔ3ˆØ×Ò˜u×0Ò0Ø—K‘K“MÒ4 e§l¡l£nò?Ø×$Ñ$Ó&Ò>¨5×+<Ñ+<Ó+>ð @ày‰y˜EŸJ™JÑ&Ð&r1có0—|jrt|«S|st|jd|«S|j|k\r4t|j|j d|j|z zz|«St |j «|jz|z }|dkrt|jd|dz «}d}|j|}|||«}|j d|xsd}|dk(rtt|«dz«}t|j||«S)asRescale self so that the exponent is exp, either by padding with zeros or by truncating digits, using the given rounding mode. Specials are returned without change. This operation is quiet: it raises no flags, and uses no information from the context. exp = exp to scale to (an integer) rounding = rounding mode rŒr(r/r2N) r„rrDrErƒrFr rlršr‰)r6r‹r`r°Ú this_functionrrr½s r/r$zDecimal._rescaleè s€ð×ÒÜ˜4“=Ð ÙÜ# D§J¡J°°SÓ9Ð9à9‰9˜Òä# D§J¡JØ(,¯ © °C¸¿¹ÀS¹Ñ4IÑ(IÈ3óPð Pô T—Y‘Y“ $§)¡)Ñ+¨cÑ1ˆØAŠ:Ü# D§J¡J°°S¸±UÓ;ˆDØˆFØ×4Ñ4°XÑ>ˆ Ù fÓ-ˆØ— ‘ ˜'˜6Ð"Ò) cˆØaŠ<Üœ˜E› 1™Ó%ˆEÜ § ¡ ¨E°3Ó7Ð7r1có2—|dkrtd«‚|js|st|«S|j|j «dz|z |«}|j «|j «k7r&|j|j «dz|z |«}|S)a"Round a nonzero, nonspecial Decimal to a fixed number of significant figures, using the given rounding mode. Infinities, NaNs and zeros are returned unaltered. This operation is quiet: it raises no flags, and uses no information from the context. r(z'argument should be at least 1 in _roundr2)r¦r„rr$rÕ)r6Úplacesr`rIs r/Ú_roundzDecimal._round s‡€ðQŠ;ÜÐFÓGÐGØ×Ò¡4Ü˜4“=Ð Øm‰m˜DŸM™M›O¨AÑ-¨fÑ4°hÓ?ˆð <‰<‹>˜TŸ]™]›_Ò,Ø—,‘,˜sŸ|™|›~¨aÑ/°Ñ6¸ÓAˆCØˆ r1có|—|jr!|j|¬«}|r|St|«S|jdk\rt|«S|st |j dd«S|€ t «}|€|j}|jd|«}||k7r|jt«|jt«|S)aVRounds to a nearby integer. If no rounding mode is specified, take the rounding mode from the context. This method raises the Rounded and Inexact flags when appropriate. See also: to_integral_value, which does exactly the same as this method except that it doesn't raise Inexact or Rounded. rqr(rŒ)r„rËrrƒrDrErr`r$ržrr ©r6r`r7rIs r/Úto_integral_exactzDecimal.to_integral_exact! s²€ð×ÒØ×"Ñ"¨7Ð"Ó3ˆCÙØ Ü˜4“=Ð Ø9‰9˜Š>Ü˜4“=Ð ÙÜ# D§J¡J°°QÓ7Ð7Øˆ?Ü “lˆGØÐØ×'Ñ'ˆHØm‰m˜A˜xÓ(ˆØ$Š;Ø× Ñ ¤Ô)Ø×ÑœWÔ%Øˆ r1cóè—|€ t«}|€|j}|jr!|j|¬«}|r|St |«S|j dk\rt |«S|j d|«S)z@Rounds to the nearest integer, without raising inexact, rounded.rqr()rr`r„rËrrƒr$rÜs r/r›zDecimal.to_integral_value> ss€àˆ?Ü “lˆGØÐØ×'Ñ'ˆHØ×ÒØ×"Ñ"¨7Ð"Ó3ˆCÙØ Ü˜4“=Ð Ø9‰9˜Š>Ü˜4“=Ð à—=‘= HÓ-Ð-r1có,—|€ t«}|jr@|j|¬«}|r|S|j«r|jdk(rt|«S|s5t |jd|jdz«}|j|«S|jdk(r|jtd«S|jdz}t|«}|jdz }|jdzr+|jdz}t|j «dz dz}n'|j}t|j «dzdz }||z }|dk\r|d|zz}d } nt#|d|z«\}} | } ||z}d|z} ||z}||krn ||zdz }Œ| xr||z|k(} | r|dk\r |d|zz}n |d|zz}||z }n |d zdk(r|dz }t dt%|«|«}|j'«}|j)t*«} |j|«}| |_|S)zReturn the square root of self.rqr(rŒr“r2zsqrt(-x), x > 0rõrªTr³)rr„rËrÅrErrDrƒrržr rar£r‹r‰r rFr5ršÚ _shallow_copyÚ _set_roundingrr`)r6r7rIraÚoprÚcÚlr6rÆr7rCr<r`s r/ÚsqrtzDecimal.sqrtQ s7€àˆ?Ü “lˆGà×ÒØ×"Ñ"¨7Ð"Ó3ˆCÙØ à×ÑÔ! d§j¡j°A¢oÜ˜t“}Ð$áä" 4§:¡:¨s°D·I±IÀ±NÓCˆCØ—8‘8˜GÓ$Ð$à:‰:˜Š?Ø×'Ñ'Ô(8Ð:KÓLÐLð,|‰|˜A‰~ˆôd‹^ˆØF‰Fa‰KˆØ 6‰6AŠ:Ø—‘˜‘ˆAÜT—Y‘Y“ 1Ñ$¨Ñ)‰Aà—‘ˆAÜD—I‘I“˜qÑ AÑ%ˆAðQ‘ˆØAŠ:Ø e‘‰OˆAØ‰Eä! ! S¨5¨&¡[Ó1‰LˆAˆyØ!MˆEØ ˆU‰ ˆð ‰HˆØØ1‘ˆAØAŠvØà˜‘E˜Q‘JððÒ"˜!˜A™# ™(ˆáà˜Šzàb˜%‘i‘‘àR˜%˜‘Z‘Ø ‰J‰Að1‰u˜ŠzØQ‘ä˜q¤# a£&¨!Ó,ˆð×'Ñ'Ó)ˆØ×(Ñ(¬Ó9ˆØh‰hwÓˆØ#ˆÔàˆ r1cóÀ—t|d¬«}|€ t«}|js|jrl|j«}|j«}|s|rH|dk(r|dk(r|j |«S|dk(r|dk(r|j |«S|j||«S|j |«}|dk(r|j|«}|dk(r|}n|}|j |«S)z Returns the larger value. Like max(self, other) except if one is not a number, returns NaN (and signals if one is sNaN). Also rounds. Trðr2r(rÃ©ròrr„rÁrrËrÜÚ compare_total©r6rÈr7ÚsnÚonrãrIs r/r#zDecimal.max´ sÜ€ô˜u¨dÔ3ˆàˆ?Ü “lˆGà×Ò˜u×0Ò0ð—‘“ˆBØ—‘“ˆBÙ‘RØ˜’7˜r QšwØŸ9™9 WÓ-Ð-Ø˜’7˜r QšwØ Ÿ:™: gÓ.Ð.Ø×'Ñ'¨¨wÓ7Ð7àI‰IeÓˆØŠ6ð×"Ñ" 5Ó)ˆAàŠ7Ø‰CàˆCàx‰x˜Ó Ð r1cóÀ—t|d¬«}|€ t«}|js|jrl|j«}|j«}|s|rH|dk(r|dk(r|j |«S|dk(r|dk(r|j |«S|j||«S|j |«}|dk(r|j|«}|dk(r|}n|}|j |«S)z¡Returns the smaller value. Like min(self, other) except if one is not a number, returns NaN (and signals if one is sNaN). Also rounds. Trðr2r(rÃrçrés r/rzDecimal.minÞ sÚ€ô˜u¨dÔ3ˆàˆ?Ü “lˆGà×Ò˜u×0Ò0ð—‘“ˆBØ—‘“ˆBÙ‘RØ˜’7˜r QšwØŸ9™9 WÓ-Ð-Ø˜’7˜r QšwØ Ÿ:™: gÓ.Ð.Ø×'Ñ'¨¨wÓ7Ð7àI‰IeÓˆØŠ6Ø×"Ñ" 5Ó)ˆAàŠ7Ø‰CàˆCàx‰x˜Ó Ð r1có—|jry|jdk\ry|j|jd}|dt|«zk(S)z"Returns whether self is an integerFr(TNrŒ)r„rƒrFr )r6Úrests r/r™zDecimal._isintegersC€à×ÒØØ9‰9˜Š>ØØy‰y˜Ÿ™˜Ð$ˆØsœ3˜t›9‘}Ñ$Ð$r1cób—|r|jdkDry|jd|jzdvS)z:Returns True if self is even. Assumes self is an integer.r(TrÃr)rƒrFrÄs r/ršzDecimal._iseven s.€át—y‘y 1’}ØØy‰y˜˜DŸI™I™Ñ&¨'Ð1Ð1r1cól— |jt|j«zdz S#t$rYywxYw)z$Return the adjusted exponent of selfr2r()rƒr rFrzrÄs r/rÕzDecimal.adjusteds5€ð Ø—9‘9œs 4§9¡9›~Ñ-°Ñ1Ð1øäò Ùð ús‚$'§ 3²3có—|S)z«Returns the same Decimal object. As we do not have different encodings for the same number, the received object already is in its canonical form. r-rÄs r/Ú canonicalzDecimal.canonicals €ðˆr1cón—t|d¬«}|j||«}|r|S|j||¬«S)z¶Compares self to the other operand numerically. It's pretty much like compare(), but all NaNs signal, with signaling NaNs taking precedence over quiet NaNs. Trðrq)ròrÐrórås r/Úcompare_signalzDecimal.compare_signals=€ô˜u°Ô5ˆØ×&Ñ& u¨gÓ6ˆÙØˆJØ|‰|˜E¨7ˆ|Ó3Ð3r1cób—t|d¬«}|jr|jstS|js|jrtS|j}|j «}|j «}|s|rÍ||k(rnt|j«|jf}t|j«|jf}||kr|rtStS||kDr|rtStStS|r,|dk(rtS|dk(rtS|dk(rtS|dk(r2tS|dk(rtS|dk(rtS|dk(rtS|dk(rtS||krtS||kDrtS|j|jkr|rtStS|j|jkDr|rtStStS)zõCompares self to other using the abstract representations. This is not like the standard compare, which use their numerical value. Note that a total ordering is defined for all possible abstract representations. Trðr2r“) ròrEÚ_NegativeOner¿rÁr rFÚ_Zerorƒ)r6rÈr7rRÚself_nanÚ other_nanÚself_keyÚ other_keys r/rèzDecimal.compare_total+sƒ€ô˜u¨dÔ3ˆð:Š:˜eŸkškÜÐØzŠz˜eŸkškÜˆKØz‰zˆð—;‘;“=ˆØ—L‘L“Nˆ Ù‘yØ˜9Ò$ä˜tŸy™y›>¨4¯9©9Ð4Ü § ¡ ›O¨U¯Z©ZÐ7 Ø˜iÒ'ÙÜ#˜ä+Ð+Ø˜iÒ'ÙÜ+Ð+ä#˜ÜáØ˜q’=Ü'Ð'Ø ’>ÜKØ˜q’=Ü'Ð'Ø ’>ÜKà˜q’=ÜKØ ’>Ü'Ð'Ø˜q’=ÜKØ ’>Ü'Ð'à%Š<ÜÐØ%Š<ÜˆKà9‰9u—z‘zÒ!ÙÜä#Ð#Ø9‰9u—z‘zÒ!ÙÜ#Ð#äÜˆr1có~—t|d¬«}|j«}|j«}|j|«S)z–Compares self to other using abstract repr., ignoring sign. Like compare_total, but with operand's sign ignored and assumed to be 0. Trð)ròrrè)r6rÈr7rXÚos r/Úcompare_total_magzDecimal.compare_total_magts6€ô ˜u¨dÔ3ˆàM‰M‹OˆØN‰NÓˆØ‰˜qÓ!Ð!r1cóZ—td|j|j|j«S)z'Returns a copy with the sign set to 0. r()rDrFrƒr„rÄs r/rzDecimal.copy_abss!€ä 4§9¡9¨d¯i©i¸×9IÑ9IÓJÐJr1cóÊ—|jr,td|j|j|j«Std|j|j|j«S)z&Returns a copy with the sign inverted.r(r2)rErDrFrƒr„rÄs r/rzDecimal.copy_negateƒsG€à:Š:Ü# A t§y¡y°$·)±)¸T×=MÑ=MÓNÐNä# A t§y¡y°$·)±)¸T×=MÑ=MÓNÐNr1cóˆ—t|d¬«}t|j|j|j|j «S)z$Returns self with the sign of other.Trð)ròrDrErFrƒr„rÏs r/Ú copy_signzDecimal.copy_signŠs6€ä˜u¨dÔ3ˆÜ §¡¨T¯Y©YØ $§ ¡ ¨4×+;Ñ+;ó=ð =r1có¨—|€ t«}|j|¬«}|r|S|j«dk(rtS|stS|j«dk(rt|«S|j}|j«}|jdk(rC|tt|jdzdz««kDrtdd|jdz«}nE|jdk(rK|tt|j«dzdz««kDrtdd|j«dz «}në|jdk(r!||krtddd|dz zzdz|«}n»|jdk(r!||dz krtdd|dzz|dz «}n‹t|«}|j|j }}|j"dk(r|}d} t%||||z«\} } | d d tt| ««|z dz zzzrn|dz }Œ=tdt| «| «}|j'«}|j)t*«}|j-|«}||_|S)zReturns e ** self.rqrÃr2r(r‘r/rŒr_r³rõ)rrËrÅr÷r¿rrarÕrEr ršrbrDr4r£r‰r‹rRÚ_dexpràrárrr`)r6r7rIr®ÚadjrârãrrÈr½r‹r`s r/r‹zDecimal.expsD€ðˆ?Ü “lˆGð×Ñ wÐÓ/ˆÙØˆJð×ÑÓ Ò#ÜˆLñÜˆKð×ÑÓ Ò"Ü˜4“=Ð ð L‰LˆØm‰m‹oˆð:‰:˜Š?˜s¤S¬¨g¯l©l¸1©n¸aÑ-?Ó)@Ó%AÒAä" 1 c¨7¯<©<¸©>Ó:ŠCØ Z‰Z˜1Š_ ¤s¬3°·±³Ð0@ÀÑ0BÀAÑ/EÓ+FÓ'GÒ!Gä" 1 c¨7¯=©=«?¸1Ñ+<Ó=‰CØ Z‰Z˜1Š_ ¨ r¢ä" 1 c¨C°°1±©I¡o¸Ñ&;¸a¸RÓ@‰CØ Z‰Z˜1Š_ ¨ r¨!¡t¢ä" 1 c¨1¨Q©3¡i°!°°A±Ó6‰Cô˜$“ˆBØ—6‘6˜2Ÿ6™6ˆqˆAØw‰w˜!Š|ØBð ˆEØÜ" 1 a¨¨5©Ó1‘ sØ˜A˜b¤3¤s¨5£z£?°1Ñ#4°QÑ#6Ñ7Ñ7Ò8ØØ˜‘ ð ô# 1¤c¨%£j°#Ó6ˆCð×'Ñ'Ó)ˆØ×(Ñ(¬Ó9ˆØh‰hwÓˆØ#ˆÔàˆ r1có—y)zÃReturn True if self is canonical; otherwise return False. Currently, the encoding of a Decimal instance is always canonical, so this method returns True for any Decimal. Tr-rÄs r/Úis_canonicalzDecimal.is_canonicalÛs€ðr1có—|jS)zReturn True if self is finite; otherwise return False. A Decimal instance is considered finite if it is neither infinite nor a NaN. )r„rÄs r/Ú is_finitezDecimal.is_finiteãs€ð×#Ñ#Ð#Ð#r1có —|jdk(S)z8Return True if self is infinite; otherwise return False.r©rƒrÄs r/rÔzDecimal.is_infiniteëó€ày‰y˜CÑÐr1có—|jdvS)z>Return True if self is a qNaN or sNaN; otherwise return False.r•rrÄs r/r÷zDecimal.is_nanïs€ày‰y˜JÐ&Ð&r1cór—|js|sy|€ t«}|j|j«kS)z?Return True if self is a normal number; otherwise return False.F)r„rrgrÕrs r/Ú is_normalzDecimal.is_normalós1€à×Ò¡4ØØˆ?Ü “lˆGØ|‰|˜tŸ}™}›Ñ.Ð.r1có —|jdk(S)z;Return True if self is a quiet NaN; otherwise return False.rCrrÄs r/rÎzDecimal.is_qnanûrr1có —|jdk(S)z8Return True if self is negative; otherwise return False.r2)rErÄs r/Ú is_signedzDecimal.is_signedÿs€àz‰z˜Q‰Ðr1có —|jdk(S)z?Return True if self is a signaling NaN; otherwise return False.rrrÄs r/rÍzDecimal.is_snanrr1cór—|js|sy|€ t«}|j«|jkS)z9Return True if self is subnormal; otherwise return False.F)r„rrÕrgrs r/Úis_subnormalzDecimal.is_subnormals1€à×Ò¡4ØØˆ?Ü “lˆGØ}‰}‹ §¡Ñ-Ð-r1có>—|jxr|jdk(S)z6Return True if self is a zero; otherwise return False.rŒrÒrÄs r/Úis_zerozDecimal.is_zeros€à×#Ñ#Ð#Ò8¨¯ © °SÑ(8Ð8r1cóà—|jt|j«zdz }|dk\rtt|dzdz««dz S|dkr ttd|z dzdz««dz St |«}|j |j}}|dk(r:t|d|zz «}t|«}t|«t|«z ||kz S|ttd|z|z ««zdz S)zÌCompute a lower bound for the adjusted exponent of self.ln(). In other words, compute r such that self.ln() >= 10**r. Assumes that self is finite and positive and that self != 1. r2érõrörÃr(©rƒr rFršr£r‰r‹©r6rrârãrÚnumÚdens r/Ú _ln_exp_boundzDecimal._ln_exp_boundsæ€ði‰iœ#˜dŸi™i›.Ñ(¨1Ñ,ˆØ!Š8ä”s˜3˜r™6 2™:“Ó'¨!Ñ+Ð+Ø"Š9ä”s˜B˜s™F B™;¨™?Ó+Ó,¨qÑ0Ð0Ü d‹^ˆØv‰vr—v‘vˆ1ˆØ!Š8äa˜˜Q˜B™‘h“-ˆCÜa“&ˆCÜs“8œc #›hÑ&¨#°©)Ñ4Ð4à”3”s˜2 ˜r™6 A™:“Ó'Ñ'¨!Ñ+Ð+r1c óÒ—|€ t«}|j|¬«}|r|S|stS|j«dk(rtS|t k(rtS|jdk(r|jtd«St|«}|j|j}}|j}||j«z dz} t|||«}|ddt!t#t%|«««|z dz zzzrn|dz }Œ@t't|dk«t#t%|««|«}|j)«}|j+t,«} |j/|«}| |_|S) z/Returns the natural (base e) logarithm of self.rqr2zln of a negative valuer“r³rõr‘r()rrËÚ_NegativeInfinityrÅÚ _Infinityr¿r÷rEržr r£r‰r‹rarÚ_dlogr ršr¢rDràrárrr`© r6r7rIrârãrr®rÙr½r`s r/Úlnz Decimal.ln,sl€ðˆ?Ü “lˆGð×Ñ wÐÓ/ˆÙØˆJñÜ$Ð$ð×ÑÓ Ò"ÜÐð”4Š<ÜˆLð:‰:˜Š?Ø×'Ñ'Ô(8Ø(@óBð Bôd‹^ˆØv‰vr—v‘vˆ1ˆØL‰LˆðT×'Ñ'Ó)Ñ)¨AÑ-ˆØÜ˜!˜Q Ó'ˆEà˜˜"œs¤3¤s¨5£z£?Ó3°AÑ5°aÑ7Ñ8Ñ8Ò9ØØa‰KˆFðôœs 5¨¡7›|¬S´°U³«_¸v¸gÓFˆà×'Ñ'Ó)ˆØ×(Ñ(¬Ó9ˆØh‰hwÓˆØ#ˆÔØˆ r1cóä—|jt|j«zdz }|dk\rtt|««dz S|dkrttd|z ««dz St |«}|j |j}}|dk(r@t|d|zz «}td|z«}t|«t|«z ||kz dzStd|z|z «}t|«|z|dkz dz S) zÎCompute a lower bound for the adjusted exponent of self.log10(). In other words, find r such that self.log10() >= 10**r. Assumes that self is finite and positive and that self != 1. r2rörÃr(rõéçr“Ú231rrs r/rÀzDecimal._log10_exp_bound^sè€ði‰iœ#˜dŸi™i›.Ñ(¨1Ñ,ˆØ!Š8ä”s˜3“x“= ‘?Ð"Ø"Š9ä”s˜2˜c™6“{Ó# AÑ%Ð%Ü d‹^ˆØv‰vr—v‘vˆ1ˆØ!Š8äa˜˜Q˜B™‘h“-ˆCÜc˜!‘e“*ˆCÜs“8œc #›hÑ&¨#°©)Ñ4°qÑ8Ð8ä"qb‘&˜‘(‹mˆÜ3‹x˜!‰|˜s U™{Ñ+¨aÑ/Ð/r1c óŒ—|€ t«}|j|¬«}|r|S|stS|j«dk(rtS|j dk(r|j td«S|jddk(rZ|jdddt|j«dz zk(r/t|jt|j«zdz «}n²t|«}|j|j}}|j}||j!«z dz} t#|||«}|d d tt%t'|«««|z dz zzzrn|dz }Œ@t)t|dk«t%t'|««|«}|j+«}|j-t.«} |j1|«}| |_|S)z&Returns the base 10 logarithm of self.Nrqr2zlog10 of a negative valuer(r/rŒr“r³rõr‘)rrËr rÅr!rEržr rFr rrƒr£r‰r‹rarÀÚ_dlog10ršr¢rDràrárrr`r#s r/Úlog10z Decimal.log10|s³€ðˆ?Ü “lˆGð×Ñ wÐÓ/ˆÙØˆJñÜ$Ð$ð×ÑÓ Ò"ÜÐð:‰:˜Š?Ø×'Ñ'Ô(8Ø(CóEð Eð9‰9Q‰<˜3Ò 4§9¡9¨Q¨R =°C¼¸T¿Y¹Y»È!Ñ9KÑ4LÒ#Lä˜$Ÿ)™)¤c¨$¯)©)£nÑ4°qÑ8Ó9‰Cô˜$“ˆBØ—6‘6˜2Ÿ6™6ˆqˆAØ—‘ˆAðt×,Ñ,Ó.Ñ.¨qÑ0ˆFØÜ 1 fÓ-à˜A˜b¤3¤s¬3¨u«:£Ó#7¸Ñ#9¸!Ñ#;Ñ<Ñ<Ò=ØØ˜!‘ðô#¤3 u¨Q¡w£<´´S¸³Z³À6À'ÓJˆCà×'Ñ'Ó)ˆØ×(Ñ(¬Ó9ˆØh‰hwÓˆØ#ˆÔØˆ r1cóø—|j|¬«}|r|S|€ t«}|j«rtS|s|j t dd«St |j««}|j|«S)aM Returns the exponent of the magnitude of self's MSD. The result is the integer which is the exponent of the magnitude of the most significant digit of self (as though it were truncated to a single digit while maintaining the value of that digit and without limiting the resulting exponent). rqzlogb(0)r2) rËrrÅr!ržrrrÕrrs r/ÚlogbzDecimal.logb¯sz€ð×Ñ wÐÓ/ˆÙØˆJàˆ?Ü “lˆGð×ÑÔÜÐñØ×'Ñ'¬¸ À1ÓEÐEô d—m‘m“oÓ&ˆØx‰x˜Ó Ð r1cóp—|jdk7s|jdk7ry|jD]}|dvsŒyy)z×Return True if self is a logical operand. For being logical, it must be a finite number with a sign of 0, an exponent of 0, and a coefficient whose digits must all be either 0 or 1. r(FÚ01T)rErƒrF)r6Údigs r/Ú _islogicalzDecimal._islogicalÍs9€ð:‰:˜Š?˜dŸi™i¨1šnØØ—9”9ˆCØ˜$ŠÙððr1cóü—|jt|«z }|dkDr d|z|z}n|dkr||jd}|jt|«z }|dkDrd|z|z}||fS|dkr||jd}||fS)Nr(rŒ)rar )r6r7ÚopaÚopbÚdifs r/Ú _fill_logicalzDecimal._fill_logicalÛs–€Øl‰lœS ›XÑ%ˆØŠ7Øc‘'˜C‘-‰CØ 1ŠWØw—|‘|mnÐ%ˆCØl‰lœS ›XÑ%ˆØŠ7Øc‘'˜C‘-ˆCðCˆxˆð1ŠWØw—|‘|mnÐ%ˆCØCˆxˆr1cóÖ—|€ t«}t|d¬«}|j«r|j«s|jt«S|j||j|j«\}}djt||«Dcgc]%\}}tt|«t|«z«‘Œ'c}}«}td|jd«xsdd«Scc}}w)z;Applies an 'and' operation between self and other's digits.Trðr‡r(rŒ© rròr0ržr r5rFr¨Úzipršr‰rDr¡©r6rÈr7r2r3r»Úbr¿s r/Úlogical_andzDecimal.logical_andèóÀ€àˆ?Ü “lˆGä˜u¨dÔ3ˆà‰Ô ¨×(8Ñ(8Ô(:Ø×'Ñ'Ô(8Ó9Ð9ð×'Ñ'¨°·±¸E¿J¹JÓG‰ ˆˆcð—‘¼¸CÀ¼ÔE¹±°°1œ#œc !›f¤S¨£V™mÕ,¸ÒEÓFˆÜ 6§=¡=°Ó#5Ò#<¸¸aÓ@Ð@ùóFóÂ*C% cón—|€ t«}|jtdd|jzd«|«S)zInvert all its digits.r(r/)rÚlogical_xorrDrars r/Úlogical_invertzDecimal.logical_invertùs9€àˆ?Ü “lˆGØ×ÑÔ 0°°3°w·|±|Ñ3CÀAÓ FØ 'ó)ð )r1cóÖ—|€ t«}t|d¬«}|j«r|j«s|jt«S|j||j|j«\}}djt||«Dcgc]%\}}tt|«t|«z«‘Œ'c}}«}td|jd«xsdd«Scc}}w)z:Applies an 'or' operation between self and other's digits.Trðr‡r(rŒr7r9s r/Ú logical_orzDecimal.logical_or r<r=cóÖ—|€ t«}t|d¬«}|j«r|j«s|jt«S|j||j|j«\}}djt||«Dcgc]%\}}tt|«t|«z«‘Œ'c}}«}td|jd«xsdd«Scc}}w)z;Applies an 'xor' operation between self and other's digits.Trðr‡r(rŒr7r9s r/r?zDecimal.logical_xor r<r=cóø—t|d¬«}|€ t«}|js|jrl|j«}|j«}|s|rH|dk(r|dk(r|j |«S|dk(r|dk(r|j |«S|j||«S|j «j|j ««}|dk(r|j|«}|dk(r|}n|}|j |«S©z8Compares the values numerically with their sign ignored.Trðr2r(rÃ© ròrr„rÁrrËrrÜrèrés r/Úmax_magzDecimal.max_mag" sç€ä˜u¨dÔ3ˆàˆ?Ü “lˆGà×Ò˜u×0Ò0ð—‘“ˆBØ—‘“ˆBÙ‘RØ˜’7˜r QšwØŸ9™9 WÓ-Ð-Ø˜’7˜r QšwØ Ÿ:™: gÓ.Ð.Ø×'Ñ'¨¨wÓ7Ð7àM‰M‹O× Ñ §¡Ó!1Ó2ˆØŠ6Ø×"Ñ" 5Ó)ˆAàŠ7Ø‰CàˆCàx‰x˜Ó Ð r1cóø—t|d¬«}|€ t«}|js|jrl|j«}|j«}|s|rH|dk(r|dk(r|j |«S|dk(r|dk(r|j |«S|j||«S|j «j|j ««}|dk(r|j|«}|dk(r|}n|}|j |«SrErFrés r/Úmin_magzDecimal.min_mag@ sç€ä˜u¨dÔ3ˆàˆ?Ü “lˆGà×Ò˜u×0Ò0ð—‘“ˆBØ—‘“ˆBÙ‘RØ˜’7˜r QšwØŸ9™9 WÓ-Ð-Ø˜’7˜r QšwØ Ÿ:™: gÓ.Ð.Ø×'Ñ'¨¨wÓ7Ð7àM‰M‹O× Ñ §¡Ó!1Ó2ˆØŠ6Ø×"Ñ" 5Ó)ˆAàŠ7Ø‰CàˆCàx‰x˜Ó Ð r1cóä—|€ t«}|j|¬«}|r|S|j«dk(rtS|j«dk(r(t dd|j z|j ««S|j«}|jt«|j«|j|«}||k7r|S|jt dd|j«dz «|«S)z=Returns the largest representable number smaller than itself.rqrÃr2r(r_r/)rrËrÅr rDrarkrsrárÚ_ignore_all_flagsrr+r4©r6r7rIÚnew_selfs r/Ú next_minuszDecimal.next_minus^ sÚ€àˆ?Ü “lˆGà×Ñ wÐÓ/ˆÙØˆJà×ÑÓ Ò#Ü$Ð$Ø×ÑÓ Ò"Ü# A s¨7¯<©<Ñ'7¸¿¹»ÓHÐHà—,‘,“.ˆØ×ÑœkÔ*Ø×!Ñ!Ô#Ø—9‘9˜WÓ%ˆØtÒØˆOØ|‰|Ô,¨Q°°W·]±]³_ÀQÑ5FÓGØ#ó%ð %r1cóä—|€ t«}|j|¬«}|r|S|j«dk(rtS|j«dk(r(t dd|j z|j ««S|j«}|jt«|j«|j|«}||k7r|S|jt dd|j«dz «|«S)z=Returns the smallest representable number larger than itself.rqr2rÃr_r(r/)rrËrÅr!rDrarkrsrárrKrr)r4rLs r/Ú next_pluszDecimal.next_plusu sÚ€àˆ?Ü “lˆGà×Ñ wÐÓ/ˆÙØˆJà×ÑÓ Ò"ÜÐØ×ÑÓ Ò#Ü# A s¨7¯<©<Ñ'7¸¿¹»ÓHÐHà—,‘,“.ˆØ×ÑœmÔ,Ø×!Ñ!Ô#Ø—9‘9˜WÓ%ˆØtÒØˆOØ|‰|Ô,¨Q°°W·]±]³_ÀQÑ5FÓGØ#ó%ð %r1cóÌ—t|d¬«}|€ t«}|j||«}|r|S|j|«}|dk(r|j |«S|dk(r|j|«}n|j |«}|j«rM|jtd|j«|jt«|jt«|S|j«|jkrk|jt«|jt «|jt«|jt«|s|jt"«|S)a‹Returns the number closest to self, in the direction towards other. The result is the closest representable number to self (excluding self) that is in the direction towards other, unless both have the same value. If the two operands are numerically equal, then the result is a copy of self with the sign set to be the same as the sign of other. Trðr(rÃz Infinite result from next_toward)ròrrËrÜrrPrNrÅržrrErr rÕrgrrr )r6rÈr7rIÚ comparisons r/Únext_towardzDecimal.next_towardŒ s-€ô˜u¨dÔ3ˆàˆ?Ü “lˆGà×Ñ˜u gÓ.ˆÙØˆJà—Y‘Y˜uÓ%ˆ Ø˜Š?Ø—>‘> %Ó(Ð(à˜ÒØ—.‘. Ó)‰Cà—/‘/ 'Ó*ˆCð?‰?ÔØ× Ñ ¤Ø!CØ!$§¡ô ,ð × Ñ ¤Ô)Ø× Ñ ¤Ô)ðˆ ð\‰\‹^˜gŸl™lÒ *Ø× Ñ ¤Ô+Ø× Ñ ¤Ô+Ø× Ñ ¤Ô)Ø× Ñ ¤Ô)ñØ×$Ñ$¤WÔ-àˆ r1có.—|j«ry|j«ry|j«}|dk(ry|dk(ry|j«r|jryy|€ t«}|j |¬ «r|jry y|jryy )aReturns an indication of the class of self. The class is one of the following strings: sNaN NaN -Infinity -Normal -Subnormal -Zero +Zero +Subnormal +Normal +Infinity rÇrr2z +InfinityrÃz -Infinityz-Zeroz+Zerorqz -Subnormalz +Subnormalz-Normalz+Normal)rÍrÎrÅrrErr)r6r7Úinfs r/Únumber_classzDecimal.number_classº s‹€ð<‰<Œ>ØØ<‰<Œ>ØØ×ÑÓ ˆØ!Š8ØØ"Š9ØØ<‰<Œ>ØzŠzØàØˆ?Ü “lˆGØ×Ñ WÐÔ-ØzŠzØ#à#à:Š:Øàr1có—td«S)z'Just returns 10, as this is Decimal, :)rõr_rÄs r/Úradixz Decimal.radixä s€är‹{Ðr1cól—|€ t«}t|d¬«}|j||«}|r|S|jdk7r|j t «S|jt|«cxkr|jksn|j t «S|j«rt|«St|«}|j}|jt|«z }|dkDr d|z|z}n|dkr||d}||d|d|z}t|j|jd«xsd|j«S)z5Returns a rotated copy of self, value-of-other times.NTrðr(rŒ©rròrËrƒržr rar‰rÅrrFr rDrEr¡)r6rÈr7rIÚtorotÚrotdigÚtopadÚrotateds r/ÚrotatezDecimal.rotateè s'€àˆ?Ü “lˆGä˜u¨dÔ3ˆà×Ñ˜u gÓ.ˆÙØˆJà:‰:˜Š?Ø×'Ñ'Ô(8Ó9Ð9Ø—‘ ¤ U£Ô;¨w¯|©|Ô;Ø×'Ñ'Ô(8Ó9Ð9à×ÑÔÜ˜4“=Ð ôE“ ˆØ—‘ˆØ—‘œs 6›{Ñ*ˆØ1Š9Ø˜‘Y Ñ'‰FØ QŠYØ˜U˜F˜G_ˆFð˜˜. 6¨&¨5 >Ñ1ˆÜ § ¡ Ø '§¡¨sÓ 3Ò :°s¸D¿I¹IóGð Gr1có8—|€ t«}t|d¬«}|j||«}|r|S|jdk7r|j t «Sd|j|jzz}d|j|jzz}|t|«cxkr|ksn|j t «S|j«rt|«St|j|j|jt|«z«}|j|«}|S)z>Returns self operand after adding the second value to its exp.Trðr(rör“)rròrËrƒržr rbrar‰rÅrrDrErFr)r6rÈr7rIÚliminfÚlimsupr¾s r/ÚscalebzDecimal.scaleb sí€àˆ?Ü “lˆGä˜u¨dÔ3ˆà×Ñ˜u gÓ.ˆÙØˆJà:‰:˜Š?Ø×'Ñ'Ô(8Ó9Ð9Øw—|‘| g§l¡lÑ2Ñ3ˆØw—|‘| g§l¡lÑ2Ñ3ˆØœ#˜e›*Ô.¨Ô.Ø×'Ñ'Ô(8Ó9Ð9à×ÑÔÜ˜4“=Ð ä˜TŸZ™Z¨¯©°D·I±IÄÀEÃ Ñ4JÓKˆØ F‰F7‹OˆØˆr1cóœ—|€ t«}t|d¬«}|j||«}|r|S|jdk7r|j t «S|jt|«cxkr|jksn|j t «S|j«rt|«St|«}|j}|jt|«z }|dkDr d|z|z}n|dkr||d}|dkr|d|}n|d|zz}||jd}t|j|jd«xsd|j«S)z5Returns a shifted copy of self, value-of-other times.NTrðr(rŒrZ)r6rÈr7rIr[r\r]Úshifteds r/r6z Decimal.shift"sC€àˆ?Ü “lˆGä˜u¨dÔ3ˆà×Ñ˜u gÓ.ˆÙØˆJà:‰:˜Š?Ø×'Ñ'Ô(8Ó9Ð9Ø—‘ ¤ U£Ô;¨w¯|©|Ô;Ø×'Ñ'Ô(8Ó9Ð9à×ÑÔÜ˜4“=Ð ôE“ ˆØ—‘ˆØ—‘œs 6›{Ñ*ˆØ1Š9Ø˜‘Y Ñ'‰FØ QŠYØ˜U˜F˜G_ˆFð1Š9Ø˜V˜en‰Gà˜s 5™yÑ(ˆGØ˜wŸ|™|˜m˜nÐ-ˆGä § ¡ Ø$+§N¡N°3Ó$7Ò$>¸3ÀÇ Á óKð Kr1có2—|jt|«ffSr,)Ú __class__ršrÄs r/Ú __reduce__zDecimal.__reduce__Is€Ø—‘¤ T£ Ð-Ð-r1có\—t|«tur|S|jt|««Sr,©ÚtyperrgršrÄs r/Ú__copy__zDecimal.__copy__Ló&€Ü‹:œÑ ØˆKØ~‰~œc $›iÓ(Ð(r1có\—t|«tur|S|jt|««Sr,rj)r6Úmemos r/Ú__deepcopy__zDecimal.__deepcopy__Qrmr1cóô—|€ t«}t||¬«}|jrIt|j|«}t|j ««}|ddk(r|dz }t|||«S|d€ddg|j|d<|ddk(r.t|j|j|jdz«}|j}|d}|i|dd vr|j|d z|«}nL|ddvr|j||«}n1|ddvr*t|j«|kDr|j||«}|s(|jd kDr|ddvr|jd |«}|s|dr|jrd } n|j} |jt|j«z} |dd vr |s|d |z }n-d }n*|ddvr| }n |ddvr|jd kr| dkDr| }nd }d krd}d|z|jz} ne|t|j«kDr+|jd|t|j«z zz}d} n"|jd|xsd}|j|d} | |z }t!| || ||«S)a|Format a Decimal instance according to the given specifier. The specifier should be a standard format specifier, with the form described in PEP 3101. Formatting types 'e', 'E', 'f', 'F', 'g', 'G', 'n' and '%' are supported. If the formatting type is omitted it defaults to 'g' or 'G', depending on the value of context.capitals. N)Ú_localeconvrkÚ%ÚgÚGr“Ú precisionÚeEr2zfF%ÚgGr(Úno_neg_0rrŒr‡)rÚ_parse_format_specifierr„Ú_format_signrEršrÚ _format_alignrhrDrFrƒr`rÚr$r Ú_format_number)r6Ú specifierr7rrÚspecrRÚbodyr`rvÚ adjusted_signrrr®r¯r‹s r/Ú __format__zDecimal.__format__Xs–€ðˆ?Ü “lˆGä& y¸kÔJˆð×ÒÜ § ¡ ¨DÓ1ˆDÜt—}‘}“Ó'ˆDØF‰|˜sÒ"Ø˜‘Ü t¨TÓ2Ð2ð‰<ÐØ ˜: g×&6Ñ&6Ñ7ˆD‰Lð‰<˜3ÒÜ# D§J¡J°· ± ¸4¿9¹9ÀQ¹;ÓGˆDð×#Ñ#ˆØ˜Ñ%ˆ ØÐ ØF‰|˜tÑ#Ø—{‘{ 9¨Q¡;°Ó9‘Øf‘ Ñ&Ø—}‘} i Z°Ó:‘Øf‘ Ñ%¬#¨d¯i©i«.¸9Ò*DØ—{‘{ 9¨hÓ7ñ˜Ÿ ™ Aš ¨$¨v©,¸%Ñ*?Ø—=‘= HÓ-ˆDÙ˜˜ZÒ(¨T¯ZªZØ‰Mà ŸJ™JˆMð—Y‘Y¤ T§Y¡Y£Ñ/ˆ Ø‰<˜4ÑÙ˜IÐ1Ø˜y™=‘à‘Ø &‰\˜UÑ "Ø!‰HØ &‰\˜TÑ !Øy‰y˜AŠ~ *¨r¢/Ø%‘àðaŠ<ØˆGØ˜X˜I‘¨¯©Ñ2‰HØ œ˜DŸI™I›Ò &Ø—i‘i # x´°D·I±I³Ñ'>Ñ"?Ñ?ˆGØ‰Hà—i‘i Ð*Ò1¨cˆGØ—y‘y Ð+ˆHØ˜Ñ!ˆô˜m¨W°hÀÀTÓJÐJr1)rŒN)NNr,)FN)TN)‚r:r;r<r=Ú __slots__r˜Úclassmethodr«rÁrÅrËrÐrÓrÜrárærérìrîrórørr¹rrrrrr!r)Ú__radd__r+r-r2Ú__rmul__r9r>r@rFrHrJrLrPrRrTrYr[Ú __trunc__Úpropertyr]r`rbrerGrrvrxr{rr‚r…r‡rŠÚdictrlrr‘r“r—r¢r½rËrÍrÑrŽrÕr$rÚrÝr›Úto_integralrår#rr™ršrÕròrôrèrþrrrr‹rr rÔr÷rrÎrrÍrrrr$rÀr*r,r0r5r;r@rBr?rGrIrNrPrSrVrXr_rcr6rhrlrpr‚r-r1r/rrªsö„Ù6à6€IóT@ðlñ*óð*òX òóò@òB4ò-'ó@%ó$ó%ó$ó%ó)ò$(ò4Oò0òd+ó 2/óh7ó!ó,!ó*ó,Tðl€HóBó4ó6ðn€Hó9!òvóB8ó"#óH7óó64óI!óV/ó89òò7ð€Ià ñóððñóðòò$ò òZòLò'òò-ò-ò+ò+ò+ñ#Ø ØØ&Ø*Ø*Ø&Ø"Ø ô Ðó<6ò| 2ò 4ó*/óXS4òjv?ópVóp4ó@ó2;óz 'ò 8òDó.ó:.ð"$€KóaóF(!óT !òD%ò2òòó 4óFóR "òKòOó=óIòVò$ò ò'ó/ò òò ó.ò9ò,ó20òd0ó<1óf!ò<òóAó")óAó"Aó"!ó<!ó<%ó.%ó.,ó\(òTóGóBó2$KòN.ò)ò )ôTKr1rcóp—tjt«}||_||_||_||_|S)z½Create a decimal instance directly, without any validation, normalization (e.g. removal of leading zeros) or argument conversion. This function is for *internal use only*. )r—r˜rrErFrƒr„)rRÚcoefficientr Úspecialr6s r/rDrD®s4€ô>‰>œ'Ó"€DØ€D„JØ€D„IØ€D„IØ€DÔà€Kr1có"—eZdZdZd„Zd„Zd„Zy)rwzContext manager class to support localcontext(). Sets a copy of the supplied context in __enter__() and restores the previous decimal context in __exit__() có.—|j«|_yr,)rsr|)r6r|s r/Ú__init__z_ContextManager.__init__Ìs€Ø&×+Ñ+Ó-ˆÕr1cób—t«|_t|j«|jSr,)rÚ saved_contextrr|rÄs r/Ú __enter__z_ContextManager.__enter__Îs&€Ü'›\ˆÔÜ4×#Ñ#Ô$Ø×ÑÐr1có.—t|j«yr,)rr’)r6ÚtÚvÚtbs r/Ú__exit__z_ContextManager.__exit__Òs€Ü4×%Ñ%Õ&r1N)r:r;r<r=rr“r˜r-r1r/rwrwÆs„ñò .ò ó'r1rwcó—eZdZdZ dTd„Zd„Zd„Zd„Zd„Zd„Z d „Z d „Zd„Zd„Z d „ZeZdUd„Zd„Zd„Zd„ZdZd„Zd„Zd„ZdVd„Zd„Zd„Zd„Zd„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-„Z0d.„Z1d/„Z2d0„Z3d1„Z4d2„Z5d3„Z6d4„Z7d5„Z8d6„Z9d7„Z:d8„Z;d9„Zd<„Z?d=„Z@d>„ZAd?„ZBd@„ZCdA„ZDdB„ZEdC„ZFdD„ZGdUdE„ZHdF„ZIdG„ZJdH„ZKdI„ZLdJ„ZMdK„ZNdL„ZOdM„ZPdN„ZQdO„ZRdP„ZSdQ„ZTdR„ZUdS„ZVeVZWy)WraßContains the context for a Decimal instance. Contains: prec - precision (for use in rounding, division, square roots..) rounding - rounding type (how you round) traps - If traps[exception] = 1, then the exception is raised when it is caused. Otherwise, a value is substituted in. flags - When an exception is caused, flags[exception] is set. (Whether or not the trap_enabler is set) Should be reset by user of Decimal instance. Emin - Minimum exponent Emax - Maximum exponent capitals - If 1, 1*10^1 is printed as 1E+1. If 0, printed as 1e1 clamp - If 1, change exponents if too high (Default 0) Nc ó¼‡‡— t} ||n j|_||n j|_||n j|_||n j |_||n j|_||n j|_| €g|_n| |_‰€ jj«|_ n8t‰t«s!tˆfd„t‰zD««|_ n‰|_ ‰€ tjtd«|_yt‰t«s!tˆfd„t‰zD««|_y‰|_y#t$rYŒPwxYw)Nc3ó<•K—|]}|t|‰v«f–—Œywr,©r‰)Ú.0rXrks €r/Ú z#Context.__init__..ó!øèø€ÐMÑ.rŸr )rÚ NameErrorrar`rgrbrhriÚ_ignored_flagsrkrsr™r‰rÂÚfromkeysrj)r6rar`rgrbrhrirjrkr£Údcs `` r/rzContext.__init__ès"ù€ð ÜˆBð!Ð,‘D°"·'±'ˆŒ Ø$,Ð$8™¸b¿k¹kˆŒ Ø Ð,‘D°"·'±'ˆŒ Ø Ð,‘D°"·'±'ˆŒ Ø$,Ð$8™¸b¿k¹kˆŒ Ø#Ð/‘U°R·X±XˆŒ àÐ!Ø"$ˆDÕà"0ˆDÔàˆ=ØŸ™Ÿ™›ˆDJÜ˜E¤4Ô(ÜÓM¼HÀuÒØtŠ|Ü Ð!BÀdÈDÐRVÐX]ÐE^Ñ!^Ó_Ð_Ø UŠ]ØtŠ|Ü Ð!BÀdÈDÐRVÐX]ÐE^Ñ!^Ó_Ð_àtŠ|˜u tš|Ü Ð!AÀTÈ4ÐQUÐW\ÐD]Ñ!]Ó^Ð^Ü×!Ñ! $¨¨eÓ4Ð4r1cóà—t|t«std|z«‚|D]}|tvsŒt d|z«‚tD]}||vsŒt d|z«‚t j |||«S)Nz%s must be a signal dictz%s is not a valid signal dict)r™r‰rzrÂÚKeyErrorr—r¨)r6r©r¾r€s r/Ú_set_signal_dictzContext._set_signal_dictsz€Ü˜!œTÔ"ÜÐ6¸Ñ:Ó;Ð;ÛˆCØœ(’?ÜÐ>ÀÑBÓCÐCð÷ˆCØ˜!’8ÜÐ>ÀÑBÓCÐCðô×!Ñ! $¨¨aÓ0Ð0r1cóì—|dk(r|j||dd«S|dk(r|j||dd«S|dk(r|j||dd«S|dk(r|j||dd«S|d k(r|j||dd«S|d k(r-|tvrtd|z«‚tj |||«S|dk(s|d k(r|j||«S|dk(rtj |||«St d|z«‚)Nrar2rUrgr§r(rbrhrir`z%s: invalid rounding moderjrkr£z.'decimal.Context' object has no attribute '%s')r¬Ú_rounding_modesrzr—r¨r¯ÚAttributeError)r6r©rs r/r¨zContext.__setattr__%s&€Ø6Š>Ø×*Ñ*¨4°¸¸5ÓAÐAØ VŠ^Ø×*Ñ*¨4°¸ÀÓBÐBØ VŠ^Ø×*Ñ*¨4°¸¸5ÓAÐAØ ZÒ Ø×*Ñ*¨4°¸¸1Ó=Ð=Ø WŠ_Ø×*Ñ*¨4°¸¸1Ó=Ð=Ø ZÒ ØœOÑ+ô Ð ;¸eÑ CÓDÐDÜ×%Ñ% d¨D°%Ó8Ð8Ø WŠ_ ¨¢Ø×(Ñ(¨¨uÓ5Ð5Ø Ð%Ò %Ü×%Ñ% d¨D°%Ó8Ð8ä Ø@À4ÑGóIð Ir1có—td|z«‚)Nz%s cannot be deleted)r²)r6r©s r/Ú__delattr__zContext.__delattr__>s€ÜÐ3°dÑ:Ó;Ð;r1c óz—|jj«Dcgc] \}}|sŒ |‘Œ}}}|jj«Dcgc] \}}|sŒ |‘Œ}}}|j|j|j |j|j|j|j||ffScc}}wcc}}wr,) rjrxrkrgrar`rgrbrhri)r6Úsigr–rjrks r/rhzContext.__reduce__Bsœ€Ø#'§:¡:×#3Ñ#3Ô#5Ô;Ñ#5™˜˜aº’Ð#5ˆÑ;Ø#'§:¡:×#3Ñ#3Ô#5Ô;Ñ#5™˜˜aº’Ð#5ˆÑ;Ø—‘Ø—‘˜DŸM™M¨4¯9©9°d·i±iØ—‘ § ¡ ¨E°5ð:ð;ð ;ùó<ùÛ;sž B1©B1Á B7ÁB7cóü—g}|jdt|«z«|jj«Dcgc]\}}|sŒ |j‘Œ}}}|jddj|«zdz«|jj«Dcgc]\}}|sŒ |j‘Œ}}}|jddj|«zdz«dj|«dzScc}}wcc}}w)zShow the current context.zrContext(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, clamp=%(clamp)dzflags=[ú, Ú]ztraps=[Ú))r§Úvarsrjrxr:r¨rk)r6rXr»r–Únamesr•s r/rzContext.__repr__IsÜ€àˆØ ‰ð#ô˜“:ñô ð)-¯ © ×(8Ñ(8Ô(:Ô@Ñ(:¡ 1ºa—“Ð(:ˆÑ@Ø ‰˜TŸY™Y uÓ-Ñ-°Ñ3Ô4Ø(,¯ © ×(8Ñ(8Ô(:Ô@Ñ(:¡ 1ºa—“Ð(:ˆÑ@Ø ‰˜TŸY™Y uÓ-Ñ-°Ñ3Ô4Øy‰y˜‹|˜cÑ!Ð!ùó Aùã@s½ C2ÁC2Â C8Â'C8cóD—|jD]}d|j|<Œy)zReset all flags to zeror(N)rj©r6Úflags r/rtzContext.clear_flagsVó€à—J”JˆDØ ˆDJ‰JtÒñr1cóD—|jD]}d|j|<Œy)zReset all traps to zeror(N)rkr¾s r/Úclear_trapszContext.clear_traps[rÀr1cóà—t|j|j|j|j|j |j|j|j|j« }|S)z!Returns a shallow copy from self.) rrar`rgrbrhrirjrkr£©r6Úncs r/ràzContext._shallow_copy`sM€ä T—Y‘Y § ¡ ¨t¯y©y¸$¿)¹)Ø—]‘] D§J¡J°· ± ¸D¿J¹JØ×(Ñ(ó*ˆðˆ r1có—t|j|j|j|j|j |j|jj«|jj«|j« }|S)zReturns a deep copy from self.)rrar`rgrbrhrirjrsrkr£rÄs r/rszContext.copygs\€ä T—Y‘Y § ¡ ¨t¯y©y¸$¿)¹)Ø—]‘] D§J¡JØ—Z‘Z—_‘_Ó&¨¯ © ¯©Ó(9Ø×(Ñ(ó*ˆðˆ r1cóö—tj||«}||jvr|«j|g|¢ŽSd|j|<|j |s|«j|g|¢ŽS||«‚)a#Handles an error If the flag is in _ignored_flags, returns the default response. Otherwise, it sets the flag, then, if the corresponding trap_enabler is set, it reraises the exception. Otherwise, it returns the default value after setting the flag. r2)Ú_condition_maprnr£r8rjrk)r6Ú conditionÚexplanationr.Úerrors r/ržzContext._raise_errorps}€ô×"Ñ" 9¨iÓ8ˆØD×'Ñ'Ñ'à!‘5“7—>‘> $Ð.¨Ò.Ð.àˆ ‰ 5ÑØz‰z˜%Ò à%‘9“;×%Ñ% dÐ2¨TÒ2Ð2ñKÓ Ð r1có(—|jtŽS)z$Ignore all flags, if they are raised)Ú _ignore_flagsrÂrÄs r/rKzContext._ignore_all_flags†s€à!ˆt×!Ñ!¤8Ð,Ð,r1cóR—|jt|«z|_t|«S)z$Ignore the flags, if they are raised)r£r¤)r6rjs r/rÍzContext._ignore_flagsŠs%€ð $×2Ñ2´T¸%³[Ñ@ˆÔÜE‹{Ðr1cóˆ—|rt|dttf«r|d}|D]}|jj |«Œy)z+Stop ignoring the flags, if they are raisedr(N)r™r¥r¤r£Úremove)r6rjr¿s r/Ú _regard_flagszContext._regard_flags‘s=€á”Z a¡¬5´¨,Ô7Ø˜!‘HˆEÛˆDØ×Ñ×&Ñ& tÕ,ñr1cóL—t|j|jz dz«S)z!Returns Etiny (= Emin - prec + 1)r2)r‰rgrarÄs r/r4z Context.Etiny›ó€ä4—9‘9˜tŸy™yÑ(¨1Ñ,Ó-Ð-r1cóL—t|j|jz dz«S)z,Returns maximum exponent (= Emax - prec + 1)r2)r‰rbrarÄs r/rkzContext.EtopŸrÓr1có,—|j}||_|S)aÓSets the rounding type. Sets the rounding type, and returns the current (previous) rounding type. Often used like: context = context.copy() # so you don't change the calling context # if an error occurs in the middle. rounding = context._set_rounding(ROUND_UP) val = self.__sub__(other, context=context) context._set_rounding(rounding) This will make it round up for that operation. )r`)r6rkr`s r/rázContext._set_rounding£s€ð—=‘=ˆØˆŒ Øˆr1cób—t|t«r-||j«k7sd|vr|jtd«St||¬«}|j «rEt|j«|j|jz kDr|jtd«S|j|«S)z›Creates a new Decimal instance but using self as context. This method implements the to-number operation of the IBM Decimal specification.r†zAtrailing or leading whitespace and underscores are not permitted.rqzdiagnostic info too long in NaN)r™ršrœržrrrÁr rFrarir)r6rr¾s r/Úcreate_decimalzContext.create_decimal¶s›€ôcœ3Ô S¨C¯I©I«KÒ%7¸3À#¹:Ø×$Ñ$Ô%5ð&FóGð Gô C Ô&ˆØ8‰8Œ:œ#˜aŸf™f›+¨¯ © °D·J±JÑ(>Ò>Ø×$Ñ$Ô%5Ø%FóHð Hàv‰vd‹|Ðr1cóN—tj|«}|j|«S)aÏCreates a new Decimal instance from a float but rounding using self as the context. >>> context = Context(prec=5, rounding=ROUND_DOWN) >>> context.create_decimal_from_float(3.1415926535897932) Decimal('3.1415') >>> context = Context(prec=5, traps=[Inexact]) >>> context.create_decimal_from_float(3.1415926535897932) Traceback (most recent call last): ... decimal.Inexact: None )rr«r)r6r»r¾s r/Úcreate_decimal_from_floatz!Context.create_decimal_from_floatÇs"€ô ×Ñ˜qÓ!ˆØv‰vd‹|Ðr1có@—t|d¬«}|j|¬«S)a[Returns the absolute value of the operand. If the operand is negative, the result is the same as using the minus operation on the operand. Otherwise, the result is the same as using the plus operation on the operand. >>> ExtendedContext.abs(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.abs(Decimal('-100')) Decimal('100') >>> ExtendedContext.abs(Decimal('101.5')) Decimal('101.5') >>> ExtendedContext.abs(Decimal('-101.5')) Decimal('101.5') >>> ExtendedContext.abs(-1) Decimal('1') Trðrq)ròr!©r6r»s r/r¢zContext.absÙs!€ô$ ˜1 dÔ+ˆØy‰y ˆyÓ&Ð&r1cór—t|d¬«}|j||¬«}|turtd|z«‚|S)a«Return the sum of the two operands. >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) Decimal('19.00') >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) Decimal('1.02E+4') >>> ExtendedContext.add(1, Decimal(2)) Decimal('3') >>> ExtendedContext.add(Decimal(8), 5) Decimal('13') >>> ExtendedContext.add(5, 5) Decimal('10') TrðrqúUnable to convert %s to Decimal)ròr)ràrz©r6r»r:r=s r/ÚaddzContext.addîs@€ô ˜1 dÔ+ˆØ I‰Ia ˆIÓ&ˆØ”ÑÜÐ=ÀÑAÓBÐBàˆHr1có6—t|j|««Sr,)ršrrÛs r/Ú_applyzContext._applys€Ü1—6‘6˜$“<Ó Ð r1cóX—t|t«std«‚|j«S)zûReturns the same Decimal object. As we do not have different encodings for the same number, the received object already is in its canonical form. >>> ExtendedContext.canonical(Decimal('2.50')) Decimal('2.50') z,canonical requires a Decimal as an argument.)r™rrzròrÛs r/ròzContext.canonicals&€ô˜!œWÔ%ÜÐJÓKÐKØ{‰{‹}Ðr1cóB—t|d¬«}|j||¬«S)a…Compares values numerically. If the signs of the operands differ, a value representing each operand ('-1' if the operand is less than zero, '0' if the operand is zero or negative zero, or '1' if the operand is greater than zero) is used in place of that operand for the comparison instead of the actual operand. The comparison is then effected by subtracting the second operand from the first and then returning a value according to the result of the subtraction: '-1' if the result is less than zero, '0' if the result is zero or negative zero, or '1' if the result is greater than zero. >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) Decimal('-1') >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) Decimal('0') >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) Decimal('0') >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) Decimal('1') >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) Decimal('1') >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) Decimal('-1') >>> ExtendedContext.compare(1, 2) Decimal('-1') >>> ExtendedContext.compare(Decimal(1), 2) Decimal('-1') >>> ExtendedContext.compare(1, Decimal(2)) Decimal('-1') Trðrq)ròró©r6r»r:s r/rózContext.compares$€ôB ˜1 dÔ+ˆØy‰y˜ DˆyÓ)Ð)r1cóB—t|d¬«}|j||¬«S)aCompares the values of the two operands numerically. It's pretty much like compare(), but all NaNs signal, with signaling NaNs taking precedence over quiet NaNs. >>> c = ExtendedContext >>> c.compare_signal(Decimal('2.1'), Decimal('3')) Decimal('-1') >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) Decimal('0') >>> c.flags[InvalidOperation] = 0 >>> print(c.flags[InvalidOperation]) 0 >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) Decimal('NaN') >>> print(c.flags[InvalidOperation]) 1 >>> c.flags[InvalidOperation] = 0 >>> print(c.flags[InvalidOperation]) 0 >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) Decimal('NaN') >>> print(c.flags[InvalidOperation]) 1 >>> c.compare_signal(-1, 2) Decimal('-1') >>> c.compare_signal(Decimal(-1), 2) Decimal('-1') >>> c.compare_signal(-1, Decimal(2)) Decimal('-1') Trðrq)ròrôräs r/rôzContext.compare_signal7s'€ô@ ˜1 dÔ+ˆØ×Ñ ¨4ÐÓ0Ð0r1có>—t|d¬«}|j|«S)a+Compares two operands using their abstract representation. This is not like the standard compare, which use their numerical value. Note that a total ordering is defined for all possible abstract representations. >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) Decimal('0') >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) Decimal('1') >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) Decimal('-1') >>> ExtendedContext.compare_total(1, 2) Decimal('-1') >>> ExtendedContext.compare_total(Decimal(1), 2) Decimal('-1') >>> ExtendedContext.compare_total(1, Decimal(2)) Decimal('-1') Trð)ròrèräs r/rèzContext.compare_totalZs€ô4 ˜1 dÔ+ˆØ‰˜qÓ!Ð!r1có>—t|d¬«}|j|«S)z£Compares two operands using their abstract representation ignoring sign. Like compare_total, but with operand's sign ignored and assumed to be 0. Trð)ròrþräs r/rþzContext.compare_total_magws!€ô ˜1 dÔ+ˆØ×"Ñ" 1Ó%Ð%r1có<—t|d¬«}|j«S)aReturns a copy of the operand with the sign set to 0. >>> ExtendedContext.copy_abs(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.copy_abs(Decimal('-100')) Decimal('100') >>> ExtendedContext.copy_abs(-1) Decimal('1') Trð)ròrrÛs r/rzContext.copy_abss€ô ˜1 dÔ+ˆØz‰z‹|Ðr1có2—t|d¬«}t|«S)aReturns a copy of the decimal object. >>> ExtendedContext.copy_decimal(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.copy_decimal(Decimal('-1.00')) Decimal('-1.00') >>> ExtendedContext.copy_decimal(1) Decimal('1') Trð)ròrrÛs r/Úcopy_decimalzContext.copy_decimalŒs€ô ˜1 dÔ+ˆÜq‹zÐr1có<—t|d¬«}|j«S)a(Returns a copy of the operand with the sign inverted. >>> ExtendedContext.copy_negate(Decimal('101.5')) Decimal('-101.5') >>> ExtendedContext.copy_negate(Decimal('-101.5')) Decimal('101.5') >>> ExtendedContext.copy_negate(1) Decimal('-1') Trð)ròrrÛs r/rzContext.copy_negate™s€ô ˜1 dÔ+ˆØ}‰}‹Ðr1có>—t|d¬«}|j|«S)aCopies the second operand's sign to the first one. In detail, it returns a copy of the first operand with the sign equal to the sign of the second operand. >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) Decimal('1.50') >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) Decimal('1.50') >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) Decimal('-1.50') >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) Decimal('-1.50') >>> ExtendedContext.copy_sign(1, -2) Decimal('-1') >>> ExtendedContext.copy_sign(Decimal(1), -2) Decimal('-1') >>> ExtendedContext.copy_sign(1, Decimal(-2)) Decimal('-1') Trð)ròrräs r/rzContext.copy_sign¦s€ô* ˜1 dÔ+ˆØ{‰{˜1‹~Ðr1cór—t|d¬«}|j||¬«}|turtd|z«‚|S)aˆDecimal division in a specified context. >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) Decimal('0.333333333') >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) Decimal('0.666666667') >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) Decimal('2.5') >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) Decimal('0.1') >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) Decimal('1') >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) Decimal('4.00') >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) Decimal('1.20') >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) Decimal('10') >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) Decimal('1000') >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) Decimal('1.20E+6') >>> ExtendedContext.divide(5, 5) Decimal('1') >>> ExtendedContext.divide(Decimal(5), 5) Decimal('1') >>> ExtendedContext.divide(5, Decimal(5)) Decimal('1') TrðrqrÝ)ròr9ràrzrÞs r/ÚdividezContext.divide¾s@€ô< ˜1 dÔ+ˆØ M‰M˜! TˆMÓ*ˆØ”ÑÜÐ=ÀÑAÓBÐBàˆHr1cór—t|d¬«}|j||¬«}|turtd|z«‚|S)a/Divides two numbers and returns the integer part of the result. >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) Decimal('0') >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) Decimal('3') >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) Decimal('3') >>> ExtendedContext.divide_int(10, 3) Decimal('3') >>> ExtendedContext.divide_int(Decimal(10), 3) Decimal('3') >>> ExtendedContext.divide_int(10, Decimal(3)) Decimal('3') TrðrqrÝ)ròrRràrzrÞs r/Ú divide_intzContext.divide_intãs@€ô ˜1 dÔ+ˆØ N‰N˜1 dˆNÓ+ˆØ”ÑÜÐ=ÀÑAÓBÐBàˆHr1cór—t|d¬«}|j||¬«}|turtd|z«‚|S)aÝReturn (a // b, a % b). >>> ExtendedContext.divmod(Decimal(8), Decimal(3)) (Decimal('2'), Decimal('2')) >>> ExtendedContext.divmod(Decimal(8), Decimal(4)) (Decimal('2'), Decimal('0')) >>> ExtendedContext.divmod(8, 4) (Decimal('2'), Decimal('0')) >>> ExtendedContext.divmod(Decimal(8), 4) (Decimal('2'), Decimal('0')) >>> ExtendedContext.divmod(8, Decimal(4)) (Decimal('2'), Decimal('0')) TrðrqrÝ)ròrFràrzrÞs r/r5zContext.divmodús@€ô ˜1 dÔ+ˆØ L‰L˜ DˆLÓ)ˆØ”ÑÜÐ=ÀÑAÓBÐBàˆHr1có@—t|d¬«}|j|¬«S)a#Returns e ** a. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.exp(Decimal('-Infinity')) Decimal('0') >>> c.exp(Decimal('-1')) Decimal('0.367879441') >>> c.exp(Decimal('0')) Decimal('1') >>> c.exp(Decimal('1')) Decimal('2.71828183') >>> c.exp(Decimal('0.693147181')) Decimal('2.00000000') >>> c.exp(Decimal('+Infinity')) Decimal('Infinity') >>> c.exp(10) Decimal('22026.4658') Trðrq)ròr‹rÛs r/r‹zContext.exps!€ô*˜! TÔ*ˆØu‰u˜TˆuÓ"Ð"r1cóD—t|d¬«}|j|||¬«S)aReturns a multiplied by b, plus c. The first two operands are multiplied together, using multiply, the third operand is then added to the result of that multiplication, using add, all with only one final rounding. >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) Decimal('22') >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) Decimal('-8') >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) Decimal('1.38435736E+12') >>> ExtendedContext.fma(1, 3, 4) Decimal('7') >>> ExtendedContext.fma(1, Decimal(3), 4) Decimal('7') >>> ExtendedContext.fma(1, 3, Decimal(4)) Decimal('7') Trðrq)ròr—)r6r»r:rãs r/r—zContext.fma's%€ô( ˜1 dÔ+ˆØu‰uQ˜ 4ˆuÓ(Ð(r1cóX—t|t«std«‚|j«S)aReturn True if the operand is canonical; otherwise return False. Currently, the encoding of a Decimal instance is always canonical, so this method returns True for any Decimal. >>> ExtendedContext.is_canonical(Decimal('2.50')) True z/is_canonical requires a Decimal as an argument.)r™rrzrrÛs r/rzContext.is_canonical>s'€ô˜!œWÔ%ÜÐMÓNÐNØ~‰~ÓÐr1có<—t|d¬«}|j«S)a,Return True if the operand is finite; otherwise return False. A Decimal instance is considered finite if it is neither infinite nor a NaN. >>> ExtendedContext.is_finite(Decimal('2.50')) True >>> ExtendedContext.is_finite(Decimal('-0.3')) True >>> ExtendedContext.is_finite(Decimal('0')) True >>> ExtendedContext.is_finite(Decimal('Inf')) False >>> ExtendedContext.is_finite(Decimal('NaN')) False >>> ExtendedContext.is_finite(1) True Trð)ròr rÛs r/r zContext.is_finiteKs€ô& ˜1 dÔ+ˆØ{‰{‹}Ðr1có<—t|d¬«}|j«S)aUReturn True if the operand is infinite; otherwise return False. >>> ExtendedContext.is_infinite(Decimal('2.50')) False >>> ExtendedContext.is_infinite(Decimal('-Inf')) True >>> ExtendedContext.is_infinite(Decimal('NaN')) False >>> ExtendedContext.is_infinite(1) False Trð)ròrÔrÛs r/rÔzContext.is_infiniteas€ô ˜1 dÔ+ˆØ}‰}‹Ðr1có<—t|d¬«}|j«S)aOReturn True if the operand is a qNaN or sNaN; otherwise return False. >>> ExtendedContext.is_nan(Decimal('2.50')) False >>> ExtendedContext.is_nan(Decimal('NaN')) True >>> ExtendedContext.is_nan(Decimal('-sNaN')) True >>> ExtendedContext.is_nan(1) False Trð)ròr÷rÛs r/r÷zContext.is_nanps€ô ˜1 dÔ+ˆØx‰x‹zÐr1có@—t|d¬«}|j|¬«S)aïReturn True if the operand is a normal number; otherwise return False. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.is_normal(Decimal('2.50')) True >>> c.is_normal(Decimal('0.1E-999')) False >>> c.is_normal(Decimal('0.00')) False >>> c.is_normal(Decimal('-Inf')) False >>> c.is_normal(Decimal('NaN')) False >>> c.is_normal(1) True Trðrq)ròrrÛs r/rzContext.is_normal€s!€ô( ˜1 dÔ+ˆØ{‰{ 4ˆ{Ó(Ð(r1có<—t|d¬«}|j«S)aHReturn True if the operand is a quiet NaN; otherwise return False. >>> ExtendedContext.is_qnan(Decimal('2.50')) False >>> ExtendedContext.is_qnan(Decimal('NaN')) True >>> ExtendedContext.is_qnan(Decimal('sNaN')) False >>> ExtendedContext.is_qnan(1) False Trð)ròrÎrÛs r/rÎzContext.is_qnan—s€ô ˜1 dÔ+ˆØy‰y‹{Ðr1có<—t|d¬«}|j«S)aReturn True if the operand is negative; otherwise return False. >>> ExtendedContext.is_signed(Decimal('2.50')) False >>> ExtendedContext.is_signed(Decimal('-12')) True >>> ExtendedContext.is_signed(Decimal('-0')) True >>> ExtendedContext.is_signed(8) False >>> ExtendedContext.is_signed(-8) True Trð)ròrrÛs r/rzContext.is_signed¦s€ô ˜1 dÔ+ˆØ{‰{‹}Ðr1có<—t|d¬«}|j«S)aTReturn True if the operand is a signaling NaN; otherwise return False. >>> ExtendedContext.is_snan(Decimal('2.50')) False >>> ExtendedContext.is_snan(Decimal('NaN')) False >>> ExtendedContext.is_snan(Decimal('sNaN')) True >>> ExtendedContext.is_snan(1) False Trð)ròrÍrÛs r/rÍzContext.is_snan·s€ô ˜1 dÔ+ˆØy‰y‹{Ðr1có@—t|d¬«}|j|¬«S)aôReturn True if the operand is subnormal; otherwise return False. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.is_subnormal(Decimal('2.50')) False >>> c.is_subnormal(Decimal('0.1E-999')) True >>> c.is_subnormal(Decimal('0.00')) False >>> c.is_subnormal(Decimal('-Inf')) False >>> c.is_subnormal(Decimal('NaN')) False >>> c.is_subnormal(1) False Trðrq)ròrrÛs r/rzContext.is_subnormalÇs!€ô& ˜1 dÔ+ˆØ~‰~ dˆ~Ó+Ð+r1có<—t|d¬«}|j«S)auReturn True if the operand is a zero; otherwise return False. >>> ExtendedContext.is_zero(Decimal('0')) True >>> ExtendedContext.is_zero(Decimal('2.50')) False >>> ExtendedContext.is_zero(Decimal('-0E+2')) True >>> ExtendedContext.is_zero(1) False >>> ExtendedContext.is_zero(0) True Trð)ròrrÛs r/rzContext.is_zeroÝs€ô ˜1 dÔ+ˆØy‰y‹{Ðr1có@—t|d¬«}|j|¬«S)aþReturns the natural (base e) logarithm of the operand. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.ln(Decimal('0')) Decimal('-Infinity') >>> c.ln(Decimal('1.000')) Decimal('0') >>> c.ln(Decimal('2.71828183')) Decimal('1.00000000') >>> c.ln(Decimal('10')) Decimal('2.30258509') >>> c.ln(Decimal('+Infinity')) Decimal('Infinity') >>> c.ln(1) Decimal('0') Trðrq)ròr$rÛs r/r$z Context.lnîs!€ô& ˜1 dÔ+ˆØt‰t˜DˆtÓ!Ð!r1có@—t|d¬«}|j|¬«S)a§Returns the base 10 logarithm of the operand. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.log10(Decimal('0')) Decimal('-Infinity') >>> c.log10(Decimal('0.001')) Decimal('-3') >>> c.log10(Decimal('1.000')) Decimal('0') >>> c.log10(Decimal('2')) Decimal('0.301029996') >>> c.log10(Decimal('10')) Decimal('1') >>> c.log10(Decimal('70')) Decimal('1.84509804') >>> c.log10(Decimal('+Infinity')) Decimal('Infinity') >>> c.log10(0) Decimal('-Infinity') >>> c.log10(1) Decimal('0') Trðrq)ròr*rÛs r/r*z Context.log10s!€ô2 ˜1 dÔ+ˆØw‰w˜tˆwÓ$Ð$r1có@—t|d¬«}|j|¬«S)a4 Returns the exponent of the magnitude of the operand's MSD. The result is the integer which is the exponent of the magnitude of the most significant digit of the operand (as though the operand were truncated to a single digit while maintaining the value of that digit and without limiting the resulting exponent). >>> ExtendedContext.logb(Decimal('250')) Decimal('2') >>> ExtendedContext.logb(Decimal('2.50')) Decimal('0') >>> ExtendedContext.logb(Decimal('0.03')) Decimal('-2') >>> ExtendedContext.logb(Decimal('0')) Decimal('-Infinity') >>> ExtendedContext.logb(1) Decimal('0') >>> ExtendedContext.logb(10) Decimal('1') >>> ExtendedContext.logb(100) Decimal('2') Trðrq)ròr,rÛs r/r,zContext.logb s!€ô. ˜1 dÔ+ˆØv‰v˜dˆvÓ#Ð#r1cóB—t|d¬«}|j||¬«S)a”Applies the logical operation 'and' between each operand's digits. The operands must be both logical numbers. >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) Decimal('0') >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) Decimal('0') >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) Decimal('0') >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) Decimal('1') >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) Decimal('1000') >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) Decimal('10') >>> ExtendedContext.logical_and(110, 1101) Decimal('100') >>> ExtendedContext.logical_and(Decimal(110), 1101) Decimal('100') >>> ExtendedContext.logical_and(110, Decimal(1101)) Decimal('100') Trðrq)ròr;räs r/r;zContext.logical_and:ó#€ô0 ˜1 dÔ+ˆØ}‰}˜Q¨ˆ}Ó-Ð-r1có@—t|d¬«}|j|¬«S)aInvert all the digits in the operand. The operand must be a logical number. >>> ExtendedContext.logical_invert(Decimal('0')) Decimal('111111111') >>> ExtendedContext.logical_invert(Decimal('1')) Decimal('111111110') >>> ExtendedContext.logical_invert(Decimal('111111111')) Decimal('0') >>> ExtendedContext.logical_invert(Decimal('101010101')) Decimal('10101010') >>> ExtendedContext.logical_invert(1101) Decimal('111110010') Trðrq)ròr@rÛs r/r@zContext.logical_invertUs$€ô ˜1 dÔ+ˆØ×Ñ¨ÐÓ-Ð-r1cóB—t|d¬«}|j||¬«S)aApplies the logical operation 'or' between each operand's digits. The operands must be both logical numbers. >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) Decimal('0') >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) Decimal('1') >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) Decimal('1') >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) Decimal('1') >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) Decimal('1110') >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) Decimal('1110') >>> ExtendedContext.logical_or(110, 1101) Decimal('1111') >>> ExtendedContext.logical_or(Decimal(110), 1101) Decimal('1111') >>> ExtendedContext.logical_or(110, Decimal(1101)) Decimal('1111') Trðrq)ròrBräs r/rBzContext.logical_orhs#€ô0 ˜1 dÔ+ˆØ|‰|˜A tˆ|Ó,Ð,r1cóB—t|d¬«}|j||¬«S)a˜Applies the logical operation 'xor' between each operand's digits. The operands must be both logical numbers. >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) Decimal('0') >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) Decimal('1') >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) Decimal('1') >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) Decimal('0') >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) Decimal('110') >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) Decimal('1101') >>> ExtendedContext.logical_xor(110, 1101) Decimal('1011') >>> ExtendedContext.logical_xor(Decimal(110), 1101) Decimal('1011') >>> ExtendedContext.logical_xor(110, Decimal(1101)) Decimal('1011') Trðrq)ròr?räs r/r?zContext.logical_xorƒrr1cóB—t|d¬«}|j||¬«S)a³max compares two values numerically and returns the maximum. If either operand is a NaN then the general rules apply. Otherwise, the operands are compared as though by the compare operation. If they are numerically equal then the left-hand operand is chosen as the result. Otherwise the maximum (closer to positive infinity) of the two operands is chosen as the result. >>> ExtendedContext.max(Decimal('3'), Decimal('2')) Decimal('3') >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) Decimal('3') >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) Decimal('1') >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) Decimal('7') >>> ExtendedContext.max(1, 2) Decimal('2') >>> ExtendedContext.max(Decimal(1), 2) Decimal('2') >>> ExtendedContext.max(1, Decimal(2)) Decimal('2') Trðrq)ròr#räs r/r#zContext.maxžó#€ô0 ˜1 dÔ+ˆØu‰uQ ˆuÓ%Ð%r1cóB—t|d¬«}|j||¬«S)aÇCompares the values numerically with their sign ignored. >>> ExtendedContext.max_mag(Decimal('7'), Decimal('NaN')) Decimal('7') >>> ExtendedContext.max_mag(Decimal('7'), Decimal('-10')) Decimal('-10') >>> ExtendedContext.max_mag(1, -2) Decimal('-2') >>> ExtendedContext.max_mag(Decimal(1), -2) Decimal('-2') >>> ExtendedContext.max_mag(1, Decimal(-2)) Decimal('-2') Trðrq)ròrGräs r/rGzContext.max_mag¹ó#€ô ˜1 dÔ+ˆØy‰y˜ DˆyÓ)Ð)r1cóB—t|d¬«}|j||¬«S)a¸min compares two values numerically and returns the minimum. If either operand is a NaN then the general rules apply. Otherwise, the operands are compared as though by the compare operation. If they are numerically equal then the left-hand operand is chosen as the result. Otherwise the minimum (closer to negative infinity) of the two operands is chosen as the result. >>> ExtendedContext.min(Decimal('3'), Decimal('2')) Decimal('2') >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) Decimal('-10') >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) Decimal('1.0') >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) Decimal('7') >>> ExtendedContext.min(1, 2) Decimal('1') >>> ExtendedContext.min(Decimal(1), 2) Decimal('1') >>> ExtendedContext.min(1, Decimal(29)) Decimal('1') Trðrq)ròrräs r/rzContext.minÊrr1cóB—t|d¬«}|j||¬«S)aÄCompares the values numerically with their sign ignored. >>> ExtendedContext.min_mag(Decimal('3'), Decimal('-2')) Decimal('-2') >>> ExtendedContext.min_mag(Decimal('-3'), Decimal('NaN')) Decimal('-3') >>> ExtendedContext.min_mag(1, -2) Decimal('1') >>> ExtendedContext.min_mag(Decimal(1), -2) Decimal('1') >>> ExtendedContext.min_mag(1, Decimal(-2)) Decimal('1') Trðrq)ròrIräs r/rIzContext.min_magår r1có@—t|d¬«}|j|¬«S)aÎMinus corresponds to unary prefix minus in Python. The operation is evaluated using the same rules as subtract; the operation minus(a) is calculated as subtract('0', a) where the '0' has the same exponent as the operand. >>> ExtendedContext.minus(Decimal('1.3')) Decimal('-1.3') >>> ExtendedContext.minus(Decimal('-1.3')) Decimal('1.3') >>> ExtendedContext.minus(1) Decimal('-1') Trðrq)ròrrÛs r/Úminusz Context.minusöó!€ô ˜1 dÔ+ˆØy‰y ˆyÓ&Ð&r1cór—t|d¬«}|j||¬«}|turtd|z«‚|S)aàmultiply multiplies two operands. If either operand is a special value then the general rules apply. Otherwise, the operands are multiplied together ('long multiplication'), resulting in a number which may be as long as the sum of the lengths of the two operands. >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) Decimal('3.60') >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) Decimal('21') >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) Decimal('0.72') >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) Decimal('-0.0') >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) Decimal('4.28135971E+11') >>> ExtendedContext.multiply(7, 7) Decimal('49') >>> ExtendedContext.multiply(Decimal(7), 7) Decimal('49') >>> ExtendedContext.multiply(7, Decimal(7)) Decimal('49') TrðrqrÝ)ròr2ràrzrÞs r/ÚmultiplyzContext.multiplys@€ô2 ˜1 dÔ+ˆØ I‰Ia ˆIÓ&ˆØ”ÑÜÐ=ÀÑAÓBÐBàˆHr1có@—t|d¬«}|j|¬«S)a"Returns the largest representable number smaller than a. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> ExtendedContext.next_minus(Decimal('1')) Decimal('0.999999999') >>> c.next_minus(Decimal('1E-1007')) Decimal('0E-1007') >>> ExtendedContext.next_minus(Decimal('-1.00000003')) Decimal('-1.00000004') >>> c.next_minus(Decimal('Infinity')) Decimal('9.99999999E+999') >>> c.next_minus(1) Decimal('0.999999999') Trðrq)ròrNrÛs r/rNzContext.next_minus's!€ô" ˜1 dÔ+ˆØ|‰| Dˆ|Ó)Ð)r1có@—t|d¬«}|j|¬«S)aReturns the smallest representable number larger than a. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> ExtendedContext.next_plus(Decimal('1')) Decimal('1.00000001') >>> c.next_plus(Decimal('-1E-1007')) Decimal('-0E-1007') >>> ExtendedContext.next_plus(Decimal('-1.00000003')) Decimal('-1.00000002') >>> c.next_plus(Decimal('-Infinity')) Decimal('-9.99999999E+999') >>> c.next_plus(1) Decimal('1.00000001') Trðrq)ròrPrÛs r/rPzContext.next_plus;s!€ô" ˜1 dÔ+ˆØ{‰{ 4ˆ{Ó(Ð(r1cóB—t|d¬«}|j||¬«S)a´Returns the number closest to a, in direction towards b. The result is the closest representable number from the first operand (but not the first operand) that is in the direction towards the second operand, unless the operands have the same value. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.next_toward(Decimal('1'), Decimal('2')) Decimal('1.00000001') >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) Decimal('-0E-1007') >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) Decimal('-1.00000002') >>> c.next_toward(Decimal('1'), Decimal('0')) Decimal('0.999999999') >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) Decimal('0E-1007') >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) Decimal('-1.00000004') >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) Decimal('-0.00') >>> c.next_toward(0, 1) Decimal('1E-1007') >>> c.next_toward(Decimal(0), 1) Decimal('1E-1007') >>> c.next_toward(0, Decimal(1)) Decimal('1E-1007') Trðrq)ròrSräs r/rSzContext.next_towardOs$€ô@ ˜1 dÔ+ˆØ}‰}˜Q¨ˆ}Ó-Ð-r1có@—t|d¬«}|j|¬«S)a³normalize reduces an operand to its simplest form. Essentially a plus operation with all trailing zeros removed from the result. >>> ExtendedContext.normalize(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.normalize(Decimal('-2.0')) Decimal('-2') >>> ExtendedContext.normalize(Decimal('1.200')) Decimal('1.2') >>> ExtendedContext.normalize(Decimal('-120')) Decimal('-1.2E+2') >>> ExtendedContext.normalize(Decimal('120.00')) Decimal('1.2E+2') >>> ExtendedContext.normalize(Decimal('0.00')) Decimal('0') >>> ExtendedContext.normalize(6) Decimal('6') Trðrq)ròrÑrÛs r/rÑzContext.normalizers!€ô* ˜1 dÔ+ˆØ{‰{ 4ˆ{Ó(Ð(r1có@—t|d¬«}|j|¬«S)aâReturns an indication of the class of the operand. The class is one of the following strings: -sNaN -NaN -Infinity -Normal -Subnormal -Zero +Zero +Subnormal +Normal +Infinity >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.number_class(Decimal('Infinity')) '+Infinity' >>> c.number_class(Decimal('1E-10')) '+Normal' >>> c.number_class(Decimal('2.50')) '+Normal' >>> c.number_class(Decimal('0.1E-999')) '+Subnormal' >>> c.number_class(Decimal('0')) '+Zero' >>> c.number_class(Decimal('-0')) '-Zero' >>> c.number_class(Decimal('-0.1E-999')) '-Subnormal' >>> c.number_class(Decimal('-1E-10')) '-Normal' >>> c.number_class(Decimal('-2.50')) '-Normal' >>> c.number_class(Decimal('-Infinity')) '-Infinity' >>> c.number_class(Decimal('NaN')) 'NaN' >>> c.number_class(Decimal('-NaN')) 'NaN' >>> c.number_class(Decimal('sNaN')) 'sNaN' >>> c.number_class(123) '+Normal' Trðrq)ròrVrÛs r/rVzContext.number_classŠs"€ô^ ˜1 dÔ+ˆØ~‰~ dˆ~Ó+Ð+r1có@—t|d¬«}|j|¬«S)a¿Plus corresponds to unary prefix plus in Python. The operation is evaluated using the same rules as add; the operation plus(a) is calculated as add('0', a) where the '0' has the same exponent as the operand. >>> ExtendedContext.plus(Decimal('1.3')) Decimal('1.3') >>> ExtendedContext.plus(Decimal('-1.3')) Decimal('-1.3') >>> ExtendedContext.plus(-1) Decimal('-1') Trðrq)ròrrÛs r/ÚpluszContext.plus¼rr1cót—t|d¬«}|j|||¬«}|turtd|z«‚|S)aRaises a to the power of b, to modulo if given. With two arguments, compute a**b. If a is negative then b must be integral. The result will be inexact unless b is integral and the result is finite and can be expressed exactly in 'precision' digits. With three arguments, compute (a**b) % modulo. For the three argument form, the following restrictions on the arguments hold: - all three arguments must be integral - b must be nonnegative - at least one of a or b must be nonzero - modulo must be nonzero and have at most 'precision' digits The result of pow(a, b, modulo) is identical to the result that would be obtained by computing (a**b) % modulo with unbounded precision, but is computed more efficiently. It is always exact. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.power(Decimal('2'), Decimal('3')) Decimal('8') >>> c.power(Decimal('-2'), Decimal('3')) Decimal('-8') >>> c.power(Decimal('2'), Decimal('-3')) Decimal('0.125') >>> c.power(Decimal('1.7'), Decimal('8')) Decimal('69.7575744') >>> c.power(Decimal('10'), Decimal('0.301029996')) Decimal('2.00000000') >>> c.power(Decimal('Infinity'), Decimal('-1')) Decimal('0') >>> c.power(Decimal('Infinity'), Decimal('0')) Decimal('1') >>> c.power(Decimal('Infinity'), Decimal('1')) Decimal('Infinity') >>> c.power(Decimal('-Infinity'), Decimal('-1')) Decimal('-0') >>> c.power(Decimal('-Infinity'), Decimal('0')) Decimal('1') >>> c.power(Decimal('-Infinity'), Decimal('1')) Decimal('-Infinity') >>> c.power(Decimal('-Infinity'), Decimal('2')) Decimal('Infinity') >>> c.power(Decimal('0'), Decimal('0')) Decimal('NaN') >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) Decimal('11') >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) Decimal('-11') >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) Decimal('1') >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) Decimal('11') >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) Decimal('11729830') >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) Decimal('-0') >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) Decimal('1') >>> ExtendedContext.power(7, 7) Decimal('823543') >>> ExtendedContext.power(Decimal(7), 7) Decimal('823543') >>> ExtendedContext.power(7, Decimal(7), 2) Decimal('1') TrðrqrÝ)ròrËràrz)r6r»r:rr=s r/Úpowerz Context.powerÍsC€ôR ˜1 dÔ+ˆØ I‰Ia˜¨ˆIÓ.ˆØ”ÑÜÐ=ÀÑAÓBÐBàˆHr1cóB—t|d¬«}|j||¬«S)a Returns a value equal to 'a' (rounded), having the exponent of 'b'. The coefficient of the result is derived from that of the left-hand operand. It may be rounded using the current rounding setting (if the exponent is being increased), multiplied by a positive power of ten (if the exponent is being decreased), or is unchanged (if the exponent is already equal to that of the right-hand operand). Unlike other operations, if the length of the coefficient after the quantize operation would be greater than precision then an Invalid operation condition is raised. This guarantees that, unless there is an error condition, the exponent of the result of a quantize is always equal to that of the right-hand operand. Also unlike other operations, quantize will never raise Underflow, even if the result is subnormal and inexact. >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) Decimal('2.170') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) Decimal('2.17') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) Decimal('2.2') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) Decimal('2') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) Decimal('0E+1') >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) Decimal('-Infinity') >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) Decimal('NaN') >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) Decimal('-0') >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) Decimal('-0E+5') >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) Decimal('NaN') >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) Decimal('NaN') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) Decimal('217.0') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) Decimal('217') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) Decimal('2.2E+2') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) Decimal('2E+2') >>> ExtendedContext.quantize(1, 2) Decimal('1') >>> ExtendedContext.quantize(Decimal(1), 2) Decimal('1') >>> ExtendedContext.quantize(1, Decimal(2)) Decimal('1') Trðrq)ròrŽräs r/rŽzContext.quantizes$€ôn ˜1 dÔ+ˆØz‰z˜! TˆzÓ*Ð*r1có—td«S)zkJust returns 10, as this is Decimal, :) >>> ExtendedContext.radix() Decimal('10') rõr_rÄs r/rXz Context.radixWs€ôr‹{Ðr1cór—t|d¬«}|j||¬«}|turtd|z«‚|S)aReturns the remainder from integer division. The result is the residue of the dividend after the operation of calculating integer division as described for divide-integer, rounded to precision digits if necessary. The sign of the result, if non-zero, is the same as that of the original dividend. This operation will fail under the same conditions as integer division (that is, if integer division on the same two operands would fail, the remainder cannot be calculated). >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) Decimal('2.1') >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) Decimal('1') >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) Decimal('-1') >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) Decimal('0.2') >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) Decimal('0.1') >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) Decimal('1.0') >>> ExtendedContext.remainder(22, 6) Decimal('4') >>> ExtendedContext.remainder(Decimal(22), 6) Decimal('4') >>> ExtendedContext.remainder(22, Decimal(6)) Decimal('4') TrðrqrÝ)ròrJràrzrÞs r/r7zContext.remainder_s@€ô> ˜1 dÔ+ˆØ I‰Ia ˆIÓ&ˆØ”ÑÜÐ=ÀÑAÓBÐBàˆHr1cóB—t|d¬«}|j||¬«S)aGReturns to be "a - b * n", where n is the integer nearest the exact value of "x / b" (if two integers are equally near then the even one is chosen). If the result is equal to 0 then its sign will be the sign of a. This operation will fail under the same conditions as integer division (that is, if integer division on the same two operands would fail, the remainder cannot be calculated). >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) Decimal('-0.9') >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) Decimal('-2') >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) Decimal('1') >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) Decimal('-1') >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) Decimal('0.2') >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) Decimal('0.1') >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) Decimal('-0.3') >>> ExtendedContext.remainder_near(3, 11) Decimal('3') >>> ExtendedContext.remainder_near(Decimal(3), 11) Decimal('3') >>> ExtendedContext.remainder_near(3, Decimal(11)) Decimal('3') Trðrq)ròrPräs r/rPzContext.remainder_near…s&€ô> ˜1 dÔ+ˆØ×Ñ ¨4ÐÓ0Ð0r1cóB—t|d¬«}|j||¬«S)aNReturns a rotated copy of a, b times. The coefficient of the result is a rotated copy of the digits in the coefficient of the first operand. The number of places of rotation is taken from the absolute value of the second operand, with the rotation being to the left if the second operand is positive or to the right otherwise. >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) Decimal('400000003') >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) Decimal('12') >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) Decimal('891234567') >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) Decimal('123456789') >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) Decimal('345678912') >>> ExtendedContext.rotate(1333333, 1) Decimal('13333330') >>> ExtendedContext.rotate(Decimal(1333333), 1) Decimal('13333330') >>> ExtendedContext.rotate(1333333, Decimal(1)) Decimal('13333330') Trðrq)ròr_räs r/r_zContext.rotate§s#€ô4 ˜1 dÔ+ˆØx‰x˜ 4ˆxÓ(Ð(r1có>—t|d¬«}|j|«S)aÝReturns True if the two operands have the same exponent. The result is never affected by either the sign or the coefficient of either operand. >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) False >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) True >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) False >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) True >>> ExtendedContext.same_quantum(10000, -1) True >>> ExtendedContext.same_quantum(Decimal(10000), -1) True >>> ExtendedContext.same_quantum(10000, Decimal(-1)) True Trð)ròrÕräs r/rÕzContext.same_quantumÄs€ô* ˜1 dÔ+ˆØ~‰~˜aÓ Ð r1cóB—t|d¬«}|j||¬«S)a3Returns the first operand after adding the second value its exp. >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) Decimal('0.0750') >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) Decimal('7.50') >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) Decimal('7.50E+3') >>> ExtendedContext.scaleb(1, 4) Decimal('1E+4') >>> ExtendedContext.scaleb(Decimal(1), 4) Decimal('1E+4') >>> ExtendedContext.scaleb(1, Decimal(4)) Decimal('1E+4') Trðrq)ròrcräs r/rczContext.scalebÜs#€ô ˜1 dÔ+ˆØx‰x˜ 4ˆxÓ(Ð(r1cóB—t|d¬«}|j||¬«S)a{Returns a shifted copy of a, b times. The coefficient of the result is a shifted copy of the digits in the coefficient of the first operand. The number of places to shift is taken from the absolute value of the second operand, with the shift being to the left if the second operand is positive or to the right otherwise. Digits shifted into the coefficient are zeros. >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) Decimal('400000000') >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) Decimal('0') >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) Decimal('1234567') >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) Decimal('123456789') >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) Decimal('345678900') >>> ExtendedContext.shift(88888888, 2) Decimal('888888800') >>> ExtendedContext.shift(Decimal(88888888), 2) Decimal('888888800') >>> ExtendedContext.shift(88888888, Decimal(2)) Decimal('888888800') Trðrq)ròr6räs r/r6z Context.shiftïs#€ô6 ˜1 dÔ+ˆØw‰wq $ˆwÓ'Ð'r1có@—t|d¬«}|j|¬«S)a¦Square root of a non-negative number to context precision. If the result must be inexact, it is rounded using the round-half-even algorithm. >>> ExtendedContext.sqrt(Decimal('0')) Decimal('0') >>> ExtendedContext.sqrt(Decimal('-0')) Decimal('-0') >>> ExtendedContext.sqrt(Decimal('0.39')) Decimal('0.624499800') >>> ExtendedContext.sqrt(Decimal('100')) Decimal('10') >>> ExtendedContext.sqrt(Decimal('1')) Decimal('1') >>> ExtendedContext.sqrt(Decimal('1.0')) Decimal('1.0') >>> ExtendedContext.sqrt(Decimal('1.00')) Decimal('1.0') >>> ExtendedContext.sqrt(Decimal('7')) Decimal('2.64575131') >>> ExtendedContext.sqrt(Decimal('10')) Decimal('3.16227766') >>> ExtendedContext.sqrt(2) Decimal('1.41421356') >>> ExtendedContext.prec 9 Trðrq)ròrårÛs r/råzContext.sqrt s!€ô: ˜1 dÔ+ˆØv‰v˜dˆvÓ#Ð#r1cór—t|d¬«}|j||¬«}|turtd|z«‚|S)a&Return the difference between the two operands. >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) Decimal('0.23') >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) Decimal('0.00') >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) Decimal('-0.77') >>> ExtendedContext.subtract(8, 5) Decimal('3') >>> ExtendedContext.subtract(Decimal(8), 5) Decimal('3') >>> ExtendedContext.subtract(8, Decimal(5)) Decimal('3') TrðrqrÝ)ròr+ràrzrÞs r/ÚsubtractzContext.subtract-s@€ô ˜1 dÔ+ˆØ I‰Ia ˆIÓ&ˆØ”ÑÜÐ=ÀÑAÓBÐBàˆHr1có@—t|d¬«}|j|¬«S)a…Convert to a string, using engineering notation if an exponent is needed. Engineering notation has an exponent which is a multiple of 3. This can leave up to 3 digits to the left of the decimal place and may require the addition of either one or two trailing zeros. The operation is not affected by the context. >>> ExtendedContext.to_eng_string(Decimal('123E+1')) '1.23E+3' >>> ExtendedContext.to_eng_string(Decimal('123E+3')) '123E+3' >>> ExtendedContext.to_eng_string(Decimal('123E-10')) '12.3E-9' >>> ExtendedContext.to_eng_string(Decimal('-123E-12')) '-123E-12' >>> ExtendedContext.to_eng_string(Decimal('7E-7')) '700E-9' >>> ExtendedContext.to_eng_string(Decimal('7E+1')) '70' >>> ExtendedContext.to_eng_string(Decimal('0E+1')) '0.00E+3' Trðrq)ròrrÛs r/rzContext.to_eng_stringDs!€ô2 ˜1 dÔ+ˆØ‰ tˆÓ,Ð,r1có@—t|d¬«}|j|¬«S)zyConverts a number to a string, using scientific notation. The operation is not affected by the context. Trðrq)ròrrÛs r/Ú to_sci_stringzContext.to_sci_string`s!€ô ˜1 dÔ+ˆØy‰y ˆyÓ&Ð&r1có@—t|d¬«}|j|¬«S)akRounds to an integer. When the operand has a negative exponent, the result is the same as using the quantize() operation using the given operand as the left-hand-operand, 1E+0 as the right-hand-operand, and the precision of the operand as the precision setting; Inexact and Rounded flags are allowed in this operation. The rounding mode is taken from the context. >>> ExtendedContext.to_integral_exact(Decimal('2.1')) Decimal('2') >>> ExtendedContext.to_integral_exact(Decimal('100')) Decimal('100') >>> ExtendedContext.to_integral_exact(Decimal('100.0')) Decimal('100') >>> ExtendedContext.to_integral_exact(Decimal('101.5')) Decimal('102') >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) Decimal('-102') >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) Decimal('1.0E+6') >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) Decimal('7.89E+77') >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) Decimal('-Infinity') Trðrq)ròrÝrÛs r/rÝzContext.to_integral_exacths$€ô6 ˜1 dÔ+ˆØ×"Ñ"¨4Ð"Ó0Ð0r1có@—t|d¬«}|j|¬«S)aLRounds to an integer. When the operand has a negative exponent, the result is the same as using the quantize() operation using the given operand as the left-hand-operand, 1E+0 as the right-hand-operand, and the precision of the operand as the precision setting, except that no flags will be set. The rounding mode is taken from the context. >>> ExtendedContext.to_integral_value(Decimal('2.1')) Decimal('2') >>> ExtendedContext.to_integral_value(Decimal('100')) Decimal('100') >>> ExtendedContext.to_integral_value(Decimal('100.0')) Decimal('100') >>> ExtendedContext.to_integral_value(Decimal('101.5')) Decimal('102') >>> ExtendedContext.to_integral_value(Decimal('-101.5')) Decimal('-102') >>> ExtendedContext.to_integral_value(Decimal('10E+5')) Decimal('1.0E+6') >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) Decimal('7.89E+77') >>> ExtendedContext.to_integral_value(Decimal('-Inf')) Decimal('-Infinity') Trðrq)ròr›rÛs r/r›zContext.to_integral_value†s$€ô4 ˜1 dÔ+ˆØ×"Ñ"¨4Ð"Ó0Ð0r1) NNNNNNNNNr,)rŒ)Xr:r;r<r=rr¬r¯r¨r´rhrrtrÂràrsrlržrKrÍrÑrør4rkrár×rÙr¢rßráròrórôrèrþrrêrrrîrðr5r‹r—rr rÔr÷rrÎrrÍrrr$r*r,r;r@rBr?r#rGrrIr rrNrPrSrÑrVrrrŽrXr7rPr_rÕrcr6rår$rr'rÝr›rŠr-r1r/rrÕsÌ„ñð$BFØDHØ&*ó"òH5ò 1òIò2<ò;ò"ò!ò !ò òð€Hó!ò,-òò-ð€Hò.ò.òó&ò"ò$'ò*ò*!òò"*òH!1òF"ò:&òòòòò0#òJò.ò*#ò0)ò. òò, òò )ò. òò"ò ,ò,ò""ò,%ò8$ò4.ò6.ò&-ò6.ò6&ò6*ò"&ò6*ò"'ò"ò@*ò()ò(!.òF)ò00,òd'ó"Nò`8+òtò$òL 1òD)ò:!ò0)ò&(ò<$ò@ò.-ò8'ò1ò<1ð<$Kr1rcó—eZdZdZdd„Zd„Zy)r£©rRr‰r‹Ncó —|€d|_d|_d|_yt|t«r=|j |_t|j«|_|j|_y|d|_|d|_|d|_y)Nr(r2r“)rRr‰r‹r™rrErFrƒ)r6rs r/rz_WorkRep.__init__¬sn€Øˆ=ØˆDŒIØˆDŒHØˆDHÜ ˜œwÔ 'ØŸ™ˆDŒIÜ˜5Ÿ:™:“ˆDŒHØ—z‘zˆDHð˜a™ˆDŒIØ˜Q‘xˆDŒHØ˜Q‘xˆDHr1cóV—d|j›d|j›d|j›dS)NÚ(r¸rºr+rÄs r/rz_WorkRep.__repr__»sØ!%§£¨D¯H«H°d·h³hÐ?Ð?r1r,)r:r;r<rƒrrr-r1r/r£r£¦s„Ø$€Ió ó@r1r£cóÊ—|j|jkr|}|}n|}|}tt|j««}tt|j««}|jt d||z dz «z}||jzdz |krd|_||_|xjd|j|jz zzc_|j|_||fS)zcNormalizes op1, op2 to have the same exp and length of coefficient. Done during addition. rÃr“r2rõ)r‹r ršr‰r)r'r(raÚtmprÈÚtmp_lenÚ other_lenr‹s r/r%r%ÀsÄ€ð ‡ww—‘ÒØˆØ‰àˆØˆô”#c—g‘g“,Ó€GÜ”C˜Ÿ ™ “NÓ#€IØ '‰'”C˜˜G d™N¨QÑ.Ó/Ñ /€CØ5—9‘9Ñ˜qÑ 3Ò&ØˆŒ ØˆŒ à‡G‚Gˆrc—g‘g § ¡ Ñ)Ñ*Ñ*…GØi‰i€C„GØˆ8€Or1có¾—|dk(ry|dk\r|d|zzStt|««}t|«t|jd««z }||krdS|d|zzS)a Given integers n and e, return n * 10**e if it's an integer, else None. The computation is designed to avoid computing large powers of 10 unnecessarily. >>> _decimal_lshift_exact(3, 4) 30000 >>> _decimal_lshift_exact(300, -999999999) # returns None r(rõrŒN)ršr¢r Úrstrip)rCrÚstr_nÚval_ns r/r¬r¬àsk€ð ˆA‚vØØ ˆaŠØ2q‘5‰yÐô”C˜“F“ˆÜE“ œS §¡¨cÓ!2Ó3Ñ3ˆØ ˜r’zˆtÐ2 q¨B°°©F¡{Ð2r1cóf—|dks|dkrtd«‚d}||k7r||||zz dz }}||k7rŒ|S)zóClosest integer to the square root of the positive integer n. a is an initial approximation to the square root. Any positive integer will do for a, but the closer a is to the square root of n the faster convergence will be. r(z3Both arguments to _sqrt_nearest should be positive.r2)r¦)rCr»r:s r/Ú _sqrt_nearestr8õsN€ð ˆA‚va’ÜÐNÓOÐOà€AØ ˆqŠ&Ø!QB˜‘E‘'˜1‘*ˆ1ˆðˆq‹&à€Hr1cóD—d|z||z }}|d||dz zz|dzz|kDzS)z‰Given an integer x and a nonnegative integer shift, return closest integer to x / 2**shift; use round-to-even in case of a tie. r2r“r-)r¯r6r:r<s r/Ú_rshift_nearestr:s:€ð ‰:q˜E‘z€q€AØ1˜˜!™‘9‘ 1¡Ñ%¨Ñ)Ñ*Ð*r1cóB—t||«\}}|d|z|dzz|kDzS)zaClosest integer to a/b, a and b positive integers; rounds to even in the case of a tie. r“r2)r5)r»r:r<r=s r/Ú_div_nearestr<s.€ô !Q‹<D€A€qØ!‘q˜‘s‘˜a‘Ñ Ð r1cóB—||z }d}||krt|«||z z|k\s||kDr|t|«||z z |k\rht||zdz|t||t||«zz|«z«}|dz }||krt|«||z z|k\rŒN||kDrt|«||z z |k\rŒht dtt |««zd|zz«}t||«}t||«}t|dz dd«D]}t||«t||z|«z }Œ t||z|«S)aÉInteger approximation to M*log(x/M), with absolute error boundable in terms only of x/M. Given positive integers x and M, return an integer approximation to M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference between the approximation and the exact result is at most 22. For L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In both cases these are upper bounds on the error; it will usually be much smaller.r(r2éöÿÿÿr‘rÃ)r¢r<r8r:r‰r ršrœ) r¯ÚMÚLr²ÚRÚTÚyshiftÚwr¼s r/Ú_ilogrEs<€ð< ˆ!‰€Aà €AØŠ6”c˜!“f !¡‘m qÒ(ØˆqŠ5”S˜“V˜q ™s‘] aÒ'Ü˜!˜A™# !™Øœ]¨1¨a´ÀÀ1Ó0EÑ.EÑ+FÈÓJÑJó Lˆà ˆQ‰ˆð Š6”c˜!“f !¡‘m qÓ(ØˆqŠ5”S˜“V˜q ™s‘] aÓ'ô ˆS””S˜“V“‰_˜q ™sÑ #Ó $Ð$€AÜ ˜Q Ó "€FÜQ˜Ó€AÜ 1Q‘3˜˜2Ö ˆÜ˜˜AÓ¤¨f°Q©h¸Ó!:Ñ:‰ðô˜˜!™˜QÓÐr1cóJ—|dz }tt|««}||z||zdk\z }|dkDrWd|z}||z|z }|dk\r |d|zz}nt|d|z«}t||«}t |«}t||z|«}||z} nd}t|d|z«} t| |zd«S)z¾Given integers c, e and p with c > 0, p >= 0, compute an integer approximation to 10**p * log10(c*10**e), with an absolute error of at most 1. Assumes that c*10**e is not exactly 1.r“r2r(rõrª)r ršr<rEÚ _log10_digits) rãrr®rär»r?r¼Úlog_dÚlog_10Úlog_tenpowers r/r)r)DsÌ€ðˆF€Aô ŒC‹F‹€AØ ˆ!‰ˆq‰sa‰xÑ€Aàˆ1‚uØ‰EˆØ ˆa‰C‰EˆØŠ6Ø Q‘‰J‰Aä˜Q Q B¡Ó'ˆAäa˜“ˆÜ˜qÓ!ˆÜ˜U 1™W fÓ-ˆØ˜‘s‰àˆÜ# A r¨A¨2¡vÓ.ˆä˜ UÑ*¨CÓ0Ð0r1có„—|dz }tt|««}||z||zdk\z }|dkDr6||z|z }|dk\r |d|zz}nt|d|z«}t|d|z«}nd}|rJttt |«««dz }||zdk\rt|t||z«zd|z«}nd}nd}t||zd«S)z´Given integers c, e and p with c > 0, compute an integer approximation to 10**p * log(c*10**e), with an absolute error of at most 1. Assumes that c*10**e is not exactly 1.r“r2r(rõrª)r ršr<rEr¢rG) rãrr®rär»r¼rHrÈÚ f_log_tens r/r"r"fsë€ðˆF€Aô ŒC‹F‹€AØ ˆ!‰ˆq‰sa‰xÑ€Að ˆ1‚uØ ˆa‰C‰EˆØŠ6Ø Q‘‰J‰Aä˜Q Q B¡Ó'ˆAôa˜˜Q™“‰ðˆñ Ü”Cœ˜A›“KÓ Ñ"ˆØˆu‰9˜Š>ô% Q¤}°Q°u±WÓ'=Ñ%=¸rÀ5¹yÓI‰Ià‰Iàˆ ô˜ EÑ)¨3Ó/Ð/r1có—eZdZdZd„Zd„Zy)Ú _Log10Memoizez¾Class to compute, store, and allow retrieval of, digits of the constant log(10) = 2.302585.... This constant is needed by Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.có—d|_y)NÚ/23025850929940456840179914546843642076011014886)r°rÄs r/rz_Log10Memoize.__init__–s €ØGˆr1có@—|dkrtd«‚|t|j«k\r\d} d||zdzz}tt td|z|«d««}||dd|zk7rn|dz }Œ@|j d«dd |_t|jd|d z«S)ztGiven an integer p >= 0, return floor(10**p)*log(10). For example, self.getdigits(3) returns 2302. r(zp should be nonnegativer‘rõr“rªNrŒrÃr2)r¦r r°ršr<rEr4r‰)r6r®rÈr?r°s r/Ú getdigitsz_Log10Memoize.getdigits™s¶€ð ˆqŠ5ÜÐ6Ó7Ð7à”D—K‘KÓ Ò ðˆEØà˜˜5™ ™‘OÜœ\¬%°°1±°a«.¸#Ó>Ó?Ø˜5˜&˜'? c¨%¡iÒ/ØØ˜‘ ð ð!Ÿ-™-¨Ó,¨S¨bÐ1ˆDŒKÜ4—;‘;˜t !¡Ð$Ó%Ð%r1N)r:r;r<r=rrRr-r1r/rNrN’s„ñCòHó&r1rNcóP—t||z|z«}tdtt|««zd|zz«}t ||«}||z}t|dz dd«D]}t |||zz||z«}Œt|dz dd«D]}||dzz}t |||zz|«}Œ||zS)zëGiven integers x and M, M > 0, such that x/M is small in absolute value, compute an integer approximation to M*exp(x/M). For 0 <= x/M <= 2.4, the absolute error in the result is bounded by 60 (and is usually much smaller).r>r‘r2r(rÃr“)r«r‰r ršr<rœ) r¯r?r@rArBr²ÚMshiftr¡r¼s r/Ú_iexprU·sÃ€ô* 1‘q‰yÓ€Aô ˆS””S˜“V“‰_˜q ™sÑ #Ó $Ð$€AÜQ˜Ó€AØ ‰T€FÜ 1Q‘3˜˜2Ö ˆÜ˜˜F Q™J™¨°!©Ó4‰ðô1Q‘3˜˜BÖ ˆØQq‘S‘ˆÜ˜˜A˜f™H™ vÓ.‰ð ð ˆQ‰3€Jr1c ó&—|dz }td|tt|««zdz «}||z}||z}|dk\r |d|zz}n |d|zz}t|t |««\}}t|d|z«}tt |d|z«d«||z dzfS)aÐCompute an approximation to exp(c*10**e), with p decimal places of precision. Returns integers d, f such that: 10**(p-1) <= d <= 10**p, and (d-1)*10**f < exp(c*10**e) < (d+1)*10**f In other words, d*10**f is an approximation to exp(c*10**e) with p digits of precision, and with an error in d of at most 1. This is almost, but not quite, the same as the error being < 1ulp: when d = 10**(p-1) the error could be up to 10 ulp.r“r(r2rõièr‘)r#r ršr5rGr<rU) rãrr®rÈr<r6ÚcshiftÚquotrºs r/rrÜs±€ðˆF€Aô 1”sœ3˜q›6“{‘? QÑ&Ó'€EØ ˆE‰ €Að ˆa‰C€EØ‚zØ2u‘9‘‰àB˜˜‘J‘ˆÜvœ}¨QÓ/Ó0I€Dˆ#ôs˜B ™IÓ &€Côœ˜c 2 q¡5Ó)¨4Ó0°$¸±(¸Q±,Ð>Ð>r1có¢—ttt|«««|z}t||||zdz«}||z }|dk\r||zd|zz}nt ||zd|z«}|dk(rCtt|««|zdk\|dkDk(rd|dz zdzd|z } } | | fSd|zdz |} } | | fSt||dz|dz«\} } t | d«} | dz } | | fS)a5Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: 10**(p-1) <= c <= 10**p, and (c-1)*10**e < x**y < (c+1)*10**e in other words, c*10**e is an approximation to x**y with p digits of precision, and with an error in c of at most 1. (This is almost, but not quite, the same as the error being < 1ulp: when c == 10**(p-1) we can only guarantee error < 10ulp.) We assume that: x is positive and not equal to 1, and y is nonzero. r2r(rõ)r ršr¢r"r<r)r°r±r³r´r®r:Úlxcr6Úpcr½r‹s r/rÁrÁs€ô ŒC”B“‹LÓ˜BÑ€AôB˜˜!™˜A™Ó €Cð ˆq‰D€EØ‚zØ ‰VB˜‘IÑ ‰ä ˜#˜b™& " u f¡*Ó -ˆà ˆQ‚wô”R“‹\˜BÑ !Ñ #¨¨a©Ò0Ø˜a ™c™ 1™ a¨¡c3ˆEð#ˆ:Ðð ˜Q™˜q™ 1 "3ˆEð#ˆ:Ðô ˜2 1¡˜v q¨¡sÓ+‰ ˆˆsÜ˜U BÓ'ˆØˆq‰ˆà#ˆ:Ðr1rªéFé5é(érérõr³) r/Ú2Ú3Ú4Ú5Ú6Ú7Ú8r_cóf—|dkrtd«‚t|«}dt|«z||dz S)z@Compute a lower bound for 100*log10(c) for a positive integer c.r(z0The argument to _log10_lb should be nonnegative.rª)r¦ršr )rãÚ correctionÚstr_cs r/rr*s<€ð ˆA‚vÜÐKÓLÐLÜ‹F€EØŒs5‹z‰>˜J u¨Q¡xÑ0Ñ0Ð0r1cóÖ—t|t«r|St|t«rt|«S|r%t|t«rtj |«S|rtd|z«‚tS)zÙConvert other to Decimal. Verifies that it's ok to use in an implicit construction. If allow_float is true, allow conversion from float; this is used in the comparison methods (__eq__ and friends). rÝ)r™rr‰rªr«rzrà)rÈrñÚallow_floats r/ròrò5s^€ô%œÔ!ØˆÜ%œÔÜu‹~ÐÙ”z %¬Ô/Ü×!Ñ! %Ó(Ð(áÜÐ9¸EÑAÓBÐBÜÐr1cóx—t|t«r||fSt|tj«rm|jsJt|jtt|j«|jz«|j«}|t|j«fS|r5t|tj«r|jdk(r|j}t|t «rMt#«}|rd|j$t&<n|j)t&d«|tj+|«fSt,t,fS)zÔGiven a Decimal instance self and a Python object other, return a pair (s, o) of Decimal instances such that "s op o" is equivalent to "self op other" for any of the 6 comparison operators "op". r(r2r–)r™rÚ_numbersÚRationalr„rDrEršr‰rFÚdenominatorrƒÚ numeratorÚComplexr`r]rªrrjrržr«rà)r6rÈrÞr7s r/rßrßHsù€ô%œÔ!ØUˆ{Ðô%œ×*Ñ*Ô+Ø×ÒÜ# D§J¡JÜ$'¬¨D¯I©I«¸×9JÑ9JÑ(JÓ$KØ$(§I¡Ió/ˆDð”W˜UŸ_™_Ó-Ð-Ð-ñ ”z %¬×)9Ñ)9Ô:¸u¿z¹zÈQºØ— ‘ ˆÜ%œÔÜ“,ˆÙØ,-ˆGM‰Mœ.Ò)à× Ñ ¤ØMô Oà”W×'Ñ'¨Ó.Ð.Ð.Üœ>Ð)Ð)r1r©i?BiÁ½ðÿ)rar`rkrjrbrgrhrir”)rar`rkrja· # A numeric string consists of: # \s* (?P[-+])? # an optional sign, followed by either... ( (?=\d|\.\d) # ...a number (with at least one digit) (?P\d*) # having a (possibly empty) integer part (\.(?P\d*))? # followed by an optional fractional part (E(?P[-+]?\d+))? # followed by an optional exponent, or... | Inf(inity)? # ...an infinity, or... | (?Ps)? # ...an (optionally signaling) NaN # NaN (?P\d*) # with (possibly empty) diagnostic info. ) # \s* \Z z0*$z50*$zÚ\A (?: (?P.)? (?P[<>=^]) )? (?P[-+ ])? (?Pz)? (?P\#)? (?P0)? (?P(?!0)\d+)? (?P,)? (?:\.(?P0|(?!0)\d+))? (?P[eEfFgGn%])? \Z cón—tj|«}|€td|z«‚|j«}|d}|d}|ddu|d<|dr |td|z«‚|td|z«‚|xsd|d<|xsd |d<|d €d|d <t |dxsd «|d<|dt |d«|d<|ddk(r|d|ddvrd|d<|ddk(rHd|d<|€tj«}|dtd|z«‚|d|d<|d|d<|d|d<|S|d€d|d<ddg|d<d|d<|S)aÚParse and validate a format specifier. Turns a standard numeric format specifier into a dict, with the following entries: fill: fill character to pad field to minimum width align: alignment type, either '<', '>', '=' or '^' sign: either '+', '-' or ' ' minimumwidth: nonnegative integer giving minimum width zeropad: boolean, indicating whether to pad with zeros thousands_sep: string to use as thousands separator, or '' grouping: grouping for thousands separators, in format used by localeconv decimal_point: string to use for decimal point precision: nonnegative integer giving precision, or None type: one of the characters 'eEfFgG%', or None NzInvalid format specifier: ÚfillÚalignÚzeropadz7Fill character conflicts with '0' in format specifier: z2Alignment conflicts with '0' in format specifier: Ú Ú>rRrˆÚminimumwidthrŒrvr(rkÚgGnr2rCrtÚ thousands_sepzJExplicit thousands separator conflicts with 'n' type in format specifier: ÚgroupingÚ decimal_pointr‡r‘r )Ú_parse_format_specifier_regexÚmatchr¦Ú groupdictr‰Ú_localeÚ localeconv)Úformat_specrrrÚformat_dictrtrus r/rzrzÖs €ô& &×+Ñ+¨KÓ8€AØ€yÜÐ5¸ÑCÓDÐDð—+‘+“-€KðvÑ€DØ˜Ñ €EØ)¨)Ñ4¸DÐ@€K ÑØ9ÒØÐÜð6Ø8CñDóEð EàÐÜð2Ø4?ñ@óAð Aàš+ #€KÑð!š< C€KÑð6ÑÐ"Ø!ˆFÑô#& k°.Ñ&AÒ&HÀSÓ"I€KÑØ;ÑÐ+Ü#& {°;Ñ'?Ó#@ˆKÑ ð;Ñ 1Ò$ØvÑÐ&¨+°fÑ*=ÀÑ*FØ'(ˆK˜Ñ$ð6Ñ˜cÒ!à!ˆFÑØÐÜ!×,Ñ,Ó.ˆKØÑ'Ð3Üð>Ø@KñLóMð Mà'2°?Ñ'CˆOÑ$Ø"-¨jÑ"9ˆJÑØ'2°?Ñ'CˆOÑ$ðÐðÑ'Ð/Ø+-ˆK˜Ñ(Ø#$ a &ˆJÑØ'*ˆOÑ$àÐr1có—|d}|d}||t|«z t|«z z}|d}|dk(r ||z|z}|S|dk(r ||z|z}|S|dk(r ||z|z}|S|dk(r!t|«dz}|d ||z|z||d z}|Std «‚)zÜGiven an unpadded, non-aligned numeric string 'body' and sign string 'sign', add padding and alignment conforming to the given format specifier dictionary 'spec' (as produced by parse_format_specifier). ryrtruÚˆð€MôÐ7Ó8Ð8r1có¼—ddlm}m}|sgS|ddk(r#t|«dk\r||dd||d««S|dtj k(r|ddSt d«‚)zyConvert a localeconv-style grouping into a (possibly infinite) iterable of integers representing group lengths. r()ÚchainÚrepeatrÃr“Nröz unrecognised format for grouping)Ú itertoolsrŒrr rÚCHAR_MAXr¦)r|rŒrs r/Ú_group_lengthsrAsl€÷(ÙØˆ Ø "‰˜Ò œs 8›}°Ò1ÙX˜c˜r]¡F¨8°B©<Ó$8Ó9Ð9Ø "‰œ×)Ñ)Ò )Ø˜˜ˆ}ÐäÐ;Ó<ÐÓ?Ð?ä””C˜“K ¨AÓ.°Ó2ˆØ ‰ c˜1œs 6›{™?Ñ+¨f°a°R°S¨kÑ9Ô:Ø˜˜!˜ˆØQ‰ˆ Ù˜) qš.ÙØ”S˜“XÑ‰ ð&ô ”F“˜Y¨Ó*ˆØ ‰ c˜1œs 6›{™?Ñ+¨f°a°R°S¨kÑ9Ô:Ø8‰8”H˜VÓ$Ó%Ð%r1có"—|ry|ddvr|dSy)zDetermine sign character.rˆrRz +r‡r-)Úis_negativers r/r{r{}s#€ñØØ ˆf‰˜Ñ ØF‰|Ðàr1có2—t||«}|s|dr|d|z}|dk7s|ddvr"dddddœ|d}|d j||«z }|dd k(r|d z }|dr|dt|«z t|«z }nd}t|||«}t |||z|«S) acFormat a number, given the following data: is_negative: true if the number is negative, else false intpart: string of digits that must appear before the decimal point fracpart: string of digits that must come after the point exp: exponent, as an integer spec: dictionary resulting from parsing the format specifier This function uses the information in spec to: insert separators (decimal separator and thousands separators) format the sign format the exponent add trailing '%' for the '%' type zero-pad if necessary fill and align if necessary Úaltr}r(rkrwrr)rrrurtz{0}{1:+}rsrvry)r{Úformatr r–r|)r˜r®r¯r‹rrRÚecharr“s r/r}r}‡sÇ€ô$˜ TÓ*€Dá4˜’;Ø˜Ñ(¨8Ñ3ˆà ˆa‚x4˜‘< 4Ñ'Ø ¨#°CÑ8¸¸f¹ÑFˆØJ×%Ñ% e¨SÓ1Ñ1ˆØˆF|sÒØC‰ˆàˆI‚Ø˜Ñ(¬3¨x«=Ñ8¼3¸t»9ÑD‰ àˆ Ü# G¨T°9Ó=€Gä˜˜w xÑ/°Ó6Ð6r1ÚInfz-InfrrÃr“r,)F)r()r¦)FF)r2)|r=Ú__all__r:Ú __xname__Ú__version__Ú__libmpdec_version__Úmathr´ÚnumbersrnÚsysÚcollectionsr)Ú_namedtuplerÚImportErrorrrrrrrrrr%r&Úmaxsizer!r"r#r$ÚArithmeticErrorrr r rÚZeroDivisionErrorrrrrrr rrrrzrrÂrÈr±ÚcontextvarsÚ ContextVarrmÚ frozensetryrrr r—rrDÚNumberÚregisterrwrr£r%r‰rºr«r¬r8r:r<rEr)r"rNrRrGrUrrÁrròrßrrrÚreÚcompileÚVERBOSEÚ IGNORECASErr›rtr~ÚDOTALLr~Úlocalerrzr|rr–r{r}r!r rHr÷r¿rörPÚ hash_infoÚmodulusrûrUrùrVÚ_PyHASH_NANrúrür-r1r/Úr¹sÐðñ 'ò!€ðF € Ø€Ø€àÐãÛÛ ð&Ý5Ù˜~Ð/EÈiÔX€Lð € Ø€ Ø#€Ø€ Ø€Ø€Ø#€Ø € ð€Ø€Ø‡;;'ÒØ!€HØ!€HØ"Hà€HØ€HØ€Hà˜ ™ Ñ#€ ô ô ô. Ðô ôÐ'ôô:Ð'ôô%Ð%Ð'8ô%ô Ð)ô ô Ð(Ð*;ô ô Ðô ôÐ%ôô Ðô ô Ð ô ô#:ˆw˜ô#:ôL ˜ )ô ô Ð% yô ð ^ W¨h¸ØÐ'¨°NðD€ð#Ð#3Ø$Ð%5Ø#Ð$4Ø Ð!1ð3€ð˜}¨o¸}Ø ¨/¸:ðG€óà-{×-Ñ-Ð.?Ó@ÐáÚOóÐòò&ðó+ôhB4KˆfôB4KóHhð& ‡×Ñ˜Ô!ô 'fô 'ôO$ˆfôO$ôb6@ˆvô@ó4ð< ‰€ò3ò* ò+ò!ó. ò` 1òD*0ôX!&Fô!&ñF“×)Ñ)€ ó#òJ"?òH(ðVr ¨°"Ø b˜r¨ñ+ó1óó&"*ñTØ ˜/Ø˜xÐ)9Ð:ØØ Ø ØØô€ñØ ˜Ø˜xÐ)9¸7ÀIÐNØô€ñØ ˜ØØô€ó* Ø ˆ"*‰*ðð"‡ZZ"—-‘-Ñó#!÷""'¡ð#ð&ˆRZ‰Z˜Ó × $Ñ $€ Øˆbj‰j˜Ó ×&Ñ&€ð!+ § ¡ ð,ð‡ZZ— ‘ Ñó!Ðð ð ÛóNò`ò6=ó.#&òJò#7ñR E‹N€ Ù˜F“OÐÙˆuƒ~€Ù‹ €Ùˆqƒz€Ùr‹{€ðÐ/Ð0€ð—-‘-×'Ñ'€àm‰m×Ñ€Øm‰m×Ñ€ñB˜¨!Ñ+¨_Ó=€ ÙøðCDò&Ù%ƒLð&ûðb|ò Ùð ús#œM&Ë M5Í&M2Í1M2Í5M=Í