§ 1P\Â½‰ã ó—dZgd¢ZeZdZdZdZddlZddlZ ddl Z ddlmZ e dd ¦«Zn#e$rd „ZYnwxYwdZdZd ZdZdZdZdZdZdZdZe jdkrdZdZdZndZdZdZeedz z ZGd„de¦«Z Gd„de ¦«Z!Gd„de ¦«Z"Gd „d!e"¦«Z#Gd"„d#e e$¦«Z%Gd$„d%e"¦«Z&Gd&„d'e"e$¦«Z'Gd(„d)e ¦«Z(Gd*„d+e"¦«Z)Gd,„d-e ¦«Z*Gd.„d/e ¦«Z+Gd0„d1e(e*¦«Z,Gd2„d3e(e*e+¦«Z-Gd4„d5e e.¦«Z/e!e%e(e,e*e-e"e+e/g Z0e#e"e&e"e'e"e)e"iZ1eeeeeeeefZ2ddl3Z3e3j4d6¦«Z5e6gd7¢¦«Z7d8„Z8d9„Z9[3dud:„Z:Gd;„d„Z=e j> ?e<¦«Gd?„d@e;¦«Z@GdA„dBe;¦«ZAGdC„dDe;¦«ZBdwdE„ZCeDjEZFdF„ZGdG„ZHdH„ZIdI„ZJdxdK„ZKdL„ZLdM„ZMGdN„dOe;¦«ZNeN¦«jOZPdxdP„ZQdQ„ZRdR„ZSdSdTdUdVdWdXdYdZd[d\œ fd]„ZTdyd^„ZUdvd_„ZVeAd`ee%e,e"ggdadbdd¬c¦«ZWeAddee%e,e"e!e-gg¬e¦«ZXeAddegg¬e¦«ZYddlZZZeZj[dfeZj\eZj]z¦«j^Z_eZj[dg¦«j^Z`eZj[dh¦«j^ZaeZj[dieZj\eZjbz¦«Zc[Z ddldZen#e$rYnwxYwdudj„Zfdk„Zgdl„Zhdzdm„Zidn„Zjdo„Zke>> from decimal import * >>> setcontext(ExtendedContext) >>> Decimal(0) Decimal('0') >>> Decimal('1') Decimal('1') >>> Decimal('-.0123') Decimal('-0.0123') >>> Decimal(123456) Decimal('123456') >>> Decimal('123.45e12345678') Decimal('1.2345E+12345680') >>> Decimal('1.33') + Decimal('1.27') Decimal('2.60') >>> Decimal('12.34') + Decimal('3.87') - Decimal('18.41') Decimal('-2.20') >>> dig = Decimal(1) >>> print(dig / Decimal(3)) 0.333333333 >>> getcontext().prec = 18 >>> print(dig / Decimal(3)) 0.333333333333333333 >>> print(dig.sqrt()) 1 >>> print(Decimal(3).sqrt()) 1.73205080756887729 >>> print(Decimal(3) ** 123) 4.85192780976896427E+58 >>> inf = Decimal(1) / Decimal(0) >>> print(inf) Infinity >>> neginf = Decimal(-1) / Decimal(0) >>> print(neginf) -Infinity >>> print(neginf + inf) NaN >>> print(neginf * inf) -Infinity >>> print(dig / 0) Infinity >>> getcontext().traps[DivisionByZero] = 1 >>> print(dig / 0) Traceback (most recent call last): ... ... ... decimal.DivisionByZero: x / 0 >>> c = Context() >>> c.traps[InvalidOperation] = 0 >>> print(c.flags[InvalidOperation]) 0 >>> c.divide(Decimal(0), Decimal(0)) Decimal('NaN') >>> c.traps[InvalidOperation] = 1 >>> print(c.flags[InvalidOperation]) 1 >>> c.flags[InvalidOperation] = 0 >>> print(c.flags[InvalidOperation]) 0 >>> print(c.divide(Decimal(0), Decimal(0))) Traceback (most recent call last): ... ... ... decimal.InvalidOperation: 0 / 0 >>> print(c.flags[InvalidOperation]) 1 >>> c.flags[InvalidOperation] = 0 >>> c.traps[InvalidOperation] = 0 >>> print(c.divide(Decimal(0), Decimal(0))) NaN >>> print(c.flags[InvalidOperation]) 1 >>> )%ÚDecimalÚContextÚDecimalTupleÚDefaultContextÚBasicContextÚExtendedContextÚDecimalExceptionÚClampedÚInvalidOperationÚDivisionByZeroÚInexactÚRoundedÚ SubnormalÚOverflowÚ UnderflowÚFloatOperationÚDivisionImpossibleÚInvalidContextÚConversionSyntaxÚDivisionUndefinedÚ ROUND_DOWNÚ ROUND_HALF_UPÚROUND_HALF_EVENÚ ROUND_CEILINGÚROUND_FLOORÚROUND_UPÚROUND_HALF_DOWNÚ ROUND_05UPÚ setcontextÚ getcontextÚlocalcontextÚMAX_PRECÚMAX_EMAXÚMIN_EMINÚ MIN_ETINYÚHAVE_THREADSÚHAVE_CONTEXTVARÚdecimalz1.70z2.4.2éN)Ú namedtuplerzsign digits exponentcó—|S©N©)Úargss ú1/opt/alt/python311/lib64/python3.11/_pydecimal.pyúr/¤s€ €órrrrrrrrTlÿÿÿÿlÿÇNÎZolüÿÿÿÿÇNÎZoi@üTiÀ«æécó—eZdZdZd„ZdS)ra1Base 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—dSr+r,©ÚselfÚcontextr-s r.ÚhandlezDecimalException.handleÓs€Øˆr0N©Ú__name__Ú __module__Ú__qualname__Ú__doc__r7r,r0r.rrÀs-€€€€€ððð$ ð ð ð ð r0rcó—eZdZdZdS)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©r9r:r;r<r,r0r.r r ×ó€€€€€ð ð ð ð r0r có—eZdZdZd„ZdS)r a0An 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 these 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. cóŽ—|r=t|dj|djdd¦«}| |¦«StS)Nr(ÚnT)Ú_dec_from_tripleÚ_signÚ_intÚ_fix_nanÚ_NaN)r5r6r-Úanss r.r7zInvalidOperation.handleús@€Øð )Ý" 4¨¤7¤=°$°q´'´,ÀÀTÑJÔJˆCØ—<’< Ñ(Ô(Ð(Ýˆr0Nr8r,r0r.r r ãs-€€€€€ððð,ððððr0r có—eZdZdZd„ZdS)rzÜTrying to convert badly formed string. This occurs and signals invalid-operation if a string is being converted to a number and it does not conform to the numeric string syntax. The result is [0,qNaN]. có—tSr+©rGr4s r.r7zConversionSyntax.handleó€Ýˆr0Nr8r,r0r.rrs-€€€€€ðððððððr0rcó—eZdZdZd„ZdS)ra²Division by 0. This occurs and signals division-by-zero if division of a finite number by zero was attempted (during a divide-integer or divide operation, or a power operation with negative right-hand operand), and the dividend was not zero. The result of the operation is [sign,inf], where sign is the exclusive or of the signs of the operands for divide, or is 1 for an odd power of -0, for power. có—t|Sr+)Ú_SignedInfinity©r5r6Úsignr-s r.r7zDivisionByZero.handles €Ý˜tÔ$Ð$r0Nr8r,r0r.rr s-€€€€€ð ð ð%ð%ð%ð%ð%r0rcó—eZdZdZd„ZdS)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+rKr4s r.r7zDivisionImpossible.handle"rLr0Nr8r,r0r.rró-€€€€€ðððððððr0rcó—eZdZdZd„ZdS)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+rKr4s r.r7zDivisionUndefined.handle-rLr0Nr8r,r0r.rr%rTr0rcó—eZdZdZdS)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,r0r.rr0r?r0rcó—eZdZdZd„ZdS)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+rKr4s r.r7zInvalidContext.handleGrLr0Nr8r,r0r.rr<s-€€€€€ðððððððr0rcó—eZdZdZdS)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,r0r.r r Jr?r0r có—eZdZdZdS)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,r0r.rrVs€€€€€ððððr0rcó—eZdZdZd„ZdS)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|dkrF|jtkr t |St|d|jz|j |jz dz¦«S|dkrF|jtkr t |St|d|jz|j |jz dz¦«SdS)Nr(Ú9r1)ÚroundingrrrrrOrrCÚprecÚEmaxrrPs r.r7zOverflow.handlewsÒ€ØÔ¥ Ý /µð ;ð;ð;å" 4Ô(Ð(Ø1Š9ˆ9ØÔ¥=Ò0Ð0Ý& tÔ,Ð,Ý# D¨#¨g¬lÑ*:Ø#œL¨¬Ñ5°aÑ7ñ9ô9ð 9à1Š9ˆ9ØÔ¥;Ò.Ð.Ý& tÔ,Ð,Ý# D¨#¨g¬lÑ*:Ø$œ\¨'¬,Ñ6°qÑ8ñ:ô:ð :ðˆ9r0Nr8r,r0r.rras-€€€€€ððð* :ð :ð :ð :ð :r0rcó—eZdZdZdS)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,r0r.rr‡ó€€€€€ððððr0rcó—eZdZdZdS)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,r0r.rr–rcr0rÚdecimal_context)r`ÚEminraÚcapitalsÚclampr_ÚflagsÚtrapscóª— t ¦«S#t$r-t¦«}t |¦«|cYSwxYw)z½Returns this thread's context. If this thread does not yet have a context, returns a new context and sets this thread's context. New contexts are copies of DefaultContext. )Ú_current_context_varÚgetÚLookupErrorrÚset©r6s r.rrÀsZ€ðÝ#×'Ò'Ñ)Ô)Ð)øÝðððÝ‘)”)ˆÝ× Ò Ñ)Ô)Ð)Øˆˆˆðøøøs‚›4AÁAcó¶—|tttfvr(| ¦«}| ¦«t |¦«dS)z%Set this thread's context to context.N)rrrÚcopyÚclear_flagsrlrorps r.rrÎsM€à•>¥<µÐAÐAÐAØ—,’,‘.”.ˆØ×ÒÑÔÐÝ×Ò˜WÑ%Ô%Ð%Ð%Ð%r0cóÜ—|€t¦«}t|¦«}| ¦«D]7\}}|tvrt d|›d¦«‚t|j||¦«Œ8|S)abReturn a context manager for a copy of the supplied context Uses a copy of the current context if no context is specified The returned context manager creates a local decimal context in a with statement: def sin(x): with localcontext() as ctx: ctx.prec += 2 # Rest of sin calculation algorithm # uses a precision 2 greater than normal return +s # Convert result to normal precision def sin(x): with localcontext(ExtendedContext): # Rest of sin calculation algorithm # uses the Extended Context from the # General Decimal Arithmetic Specification return +s # Convert result to normal context >>> setcontext(DefaultContext) >>> print(getcontext().prec) 28 >>> with localcontext(): ... ctx = getcontext() ... ctx.prec += 2 ... print(ctx.prec) ... 30 >>> with localcontext(ExtendedContext): ... print(getcontext().prec) ... 9 >>> print(getcontext().prec) 28 Nú'z2' is an invalid keyword argument for this function)rÚ_ContextManagerÚitemsÚ_context_attributesÚ TypeErrorÚsetattrÚnew_context)ÚctxÚkwargsÚctx_managerÚkeyÚvalues r.r r ×s€ðH€{Ý‰lŒlˆÝ! #Ñ&Ô&€KØ—l’l‘n”nð5ð5‰ ˆˆUØÕ)Ð)Ð)ÝÐW ÐWÐWÐWÑXÔXÐXÝÔ'¨¨eÑ4Ô4Ð4Ð4ØÐr0c ó¸—eZdZdZdZd}d„Zed„¦«Zd„Zd„Z d~d „Z d „Zd„Zd„Z dd „Zdd„Zdd„Zdd„Zdd„Zdd„Zd„Zd„Zd„Zd„Zd€d„Zdd„Zdd„Zdd„Zdd„Zdd„ZeZdd„Zdd „Z dd!„Z!e!Z"dd"„Z#d#„Z$dd$„Z%dd%„Z&dd&„Z'dd'„Z(dd(„Z)dd)„Z*dd*„Z+dd+„Z,d,„Z-d-„Z.e.Z/e0d.„¦«Z1e0d/„¦«Z2d0„Z3d1„Z4d2„Z5d3„Z6d4„Z7d5„Z8d6„Z9d7„Z:d8„Z;d9„Ze?e7e8e9e:e;e¬<¦«Z@dd=„ZAd>„ZBd?„ZCdd@„ZDddA„ZEdB„ZFd~dC„ZGddD„ZHddE„ZId~dF„ZJddG„ZKdH„ZLdI„ZMd~dJ„ZNd~dK„ZOeOZPddL„ZQddM„ZRddN„ZSdO„ZTdP„ZUdQ„ZVdR„ZWddS„ZXddT„ZYddU„ZZdV„Z[dW„Z\ddX„Z]ddY„Z^dZ„Z_d[„Z`d\„Zad]„Zbdd^„Zcd_„Zdd`„Zeda„Zfddb„Zgdc„Zhdd„Zidde„Zjdf„Zkddg„Zlddh„Zmdi„Zndj„Zoddk„Zpddl„Zqddm„Zrddn„Zsddo„Ztddp„Zuddq„Zvddr„Zwdds„Zxddt„Zydu„Zzddv„Z{ddw„Z|ddx„Z}dy„Z~dz„Zd{„Z€d~d|„ZdS)‚rz,Floating point class for decimal arithmetic.)Ú_exprErDÚ_is_specialÚ0Ncóx —t |¦«}t|t¦«r«t | ¦« dd¦«¦«}|€.|€t¦«}| td|z¦«S| d¦«dkrd|_nd|_| d ¦«}|~| d ¦«pd}t| d¦«pd¦«}tt||z¦«¦«|_ |t|¦«z |_d |_n‡| d¦«}|[tt|pd¦«¦« d¦«|_ | d¦«rd|_nd|_nd|_ d|_d|_|St|t¦«rF|dkrd|_nd|_d|_tt%|¦«¦«|_ d |_|St|t&¦«r2|j|_|j|_|j |_ |j|_|St|t(¦«rG|j|_t|j¦«|_ t|j¦«|_d |_|St|t.t0f¦«r§t|¦«dkrt3d¦«‚t|dt¦«r |ddvst3d¦«‚|d|_|ddkrd|_ |d|_d|_ng} |dD]S} t| t¦«r.d| cxkrdkr!nn| s| dkr| | ¦«ŒEt3d¦«‚|ddvrBd t9t| ¦«¦«|_ |d|_d|_not|dt¦«rEd t9t| pdg¦«¦«|_ |d|_d |_nt3d¦«‚|St|t:¦«rw|€t¦«}| t<d¦«t& |¦«}|j|_|j|_|j |_ |j|_|StAd|z¦«‚)aêCreate a decimal point instance. >>> 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_ÚNzInvalid literal for Decimal: %rrQú-r1r(ÚintÚfracÚexpr„FÚdiagÚsignalÚNrBÚFTéztInvalid tuple size in creation of Decimal from list or tuple. The list or tuple should have exactly three elements.©r(r1z|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.©rBrŽzUThe 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_errorrÚgrouprDr‰rEÚlenr‚rƒÚlstripÚabsrÚ_WorkReprQr‹ÚlistÚtupleÚ ValueErrorÚappendÚjoinÚmapÚfloatrÚ from_floatry)Úclsr€r6r5ÚmÚintpartÚfracpartr‹rŒÚdigitsÚdigits r.r—zDecimal.__new__s€õ.~Š~˜cÑ"Ô"ˆõeSÑ!Ô!ñ" Ý˜Ÿš™ œ ×-Ò-¨c°2Ñ6Ô6Ñ7Ô7ˆAØˆyØ?Ý(™lœlGØ×+Ò+Õ,<Ø AÀEÑ IñKôKðKðwŠwv‰Œ #Ò%Ð%Ø” à” Ø—g’g˜e‘n”nˆGØÐ"àŸ7š7 6™?œ?Ð0¨bÝ˜!Ÿ'š' %™.œ.Ð/¨CÑ0Ô0Ý¥ G¨HÑ$4Ñ 5Ô 5Ñ6Ô6” Ø¥# h¡-¤-Ñ/” Ø#(Ô Ð à—w’w˜v‘”ØÐ#å #¥C¨¨°Ñ$4Ô$4Ñ 5Ô 5× <Ò <¸SÑ AÔ AD”IØ—w’w˜xÑ(Ô(ð(Ø$'˜œ ˜ à$'˜œ ˜ ð!$D”IØ #D”IØ#'Ô ØˆKõeSÑ!Ô!ð Ø˜ŠzˆzØ” à” ØˆDŒIÝC ™JœJ™œˆDŒIØ$ˆDÔØˆKõeWÑ%Ô%ð ØœˆDŒIØœˆDŒJØœˆDŒIØ %Ô 1ˆDÔØˆKõeXÑ&Ô&ð ØœˆDŒJÝ˜EœI™œˆDŒIÝ˜EœI™œˆDŒIØ$ˆDÔØˆKõed¥5˜\Ñ*Ô*ñ* Ý5‰zŒz˜QŠˆÝ ð"GñHôHðHõ˜u QœxÑ-Ô-ð P°%¸´(¸eÐ2CÐ2CÝ ð"OñPôPðPð˜qœˆDŒJØQŒx˜3Šˆà” Ø! !œH” Ø#'Ô Ñ ðØ" 1œXð9ð9EÝ! %Ñ-Ô-ð9°!°u°/°/²/°/À²/°/°/°/°/à!ð1 U¨a¢Z ZØ"ŸMšM¨%Ñ0Ô0Ð0øå(ð*8ñ9ô9ð9ð˜”8˜zÐ)Ð)à "§¢C°Ñ(8Ô(8Ñ 9Ô 9D”IØ % a¤D”IØ'+DÔ$Ð$Ý a¤#Ñ.Ô.ð?à "§¢C°°¸A¸3Ñ(?Ô(?Ñ @Ô @D”IØ % a¤D”IØ',DÔ$Ð$å$ð&>ñ?ô?ð?ðˆKåeUÑ#Ô#ð ØˆÝ$™,œ,Ø× Ò ¥ðñ ô ð õ×&Ò& uÑ-Ô-ˆEØœˆDŒIØœˆDŒJØœˆDŒIØ %Ô 1ˆDÔØˆKåÐ6¸Ñ>Ñ?Ô?Ð?r0cót—t|t¦«r)|dkrdnd}d}tt|¦«¦«}nÓt|t¦«r¯tj|¦«stj|¦«r|t|¦«¦«Stj d|¦«dkrd}nd}t|¦« ¦«\}}| ¦«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(r1gð?ézargument must be int or float.)r˜r‰r™r¡r©Ú_mathÚisinfÚisnanÚreprÚcopysignÚas_integer_ratioÚ bit_lengthryrCr)r«ÚfrQÚkÚcoeffrBÚdÚresults r.rªzDecimal.from_floatªs'€õ,aÑÔð >Ø˜Qš˜11 AˆDØˆAÝ˜A™œ‘K”KˆEˆEÝ ˜5Ñ !Ô !ð >ÝŒ{˜1‰~Œ~ð $¥¤¨Q¡¤ð $Øs4 ™7œ7‘|”|Ð#ÝŒ~˜c 1Ñ%Ô%¨Ò,Ð,ØàÝq‘6”6×*Ò*Ñ,Ô,‰DˆAˆqØ—’‘” Ñ"ˆAÝ˜˜!˜Q™$™‘K”KˆEˆEåÐ<Ñ=Ô=Ð=å! $¨°¨rÑ2Ô2ˆØ•'ˆ>ˆ>ØˆMà3v‘;”;Ðr0cóB—|jr|j}|dkrdS|dkrdSdS)zrReturns whether the number is not actually one. 0 if a number 1 if NaN 2 if sNaN rBr1rŽr’r()rƒr‚)r5r‹s r.Ú_isnanzDecimal._isnan×s7€ðÔð Ø”)ˆCØcŠzˆzØqØ˜’ØqØˆqr0có2—|jdkr|jrdSdSdS)zyReturns whether the number is infinite 0 if finite or not a number 1 if +INF -1 if -INF réÿÿÿÿr1r()r‚rD©r5s r.Ú_isinfinityzDecimal._isinfinityæs*€ðŒ9˜ÒÐØŒzð ØrØ1Øˆqr0cóh—| ¦«}|€d}n| ¦«}|s|r€|€t¦«}|dkr| td|¦«S|dkr| td|¦«S|r| |¦«S| |¦«SdS)z½Returns whether the number is not actually one. if self, other are sNaN, signal if self, other are NaN return nan return 0 Done before operations. NFr’ÚsNaNr()rÀrrr rF)r5Úotherr6Úself_is_nanÚother_is_nans r.Ú_check_nanszDecimal._check_nansósÎ€ð—k’k‘m”mˆØˆ=Ø ˆLˆLà Ÿ<š<™>œ>ˆLàð +˜,ð +ØˆÝ$™,œ,à˜aÒÐØ×+Ò+Õ,<¸fØ(,ñ.ô.ð.à˜qÒ Ð Ø×+Ò+Õ,<¸fØ(-ñ/ô/ð/àð .Ø—}’} WÑ-Ô-Ð-à—>’> 'Ñ*Ô*Ð*Øˆqr0cóÂ—|€t¦«}|js|jrÀ| ¦«r| td|¦«S| ¦«r| td|¦«S| ¦«r| td|¦«S| ¦«r| td|¦«SdS)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. Nzcomparison involving sNaNzcomparison involving NaNr()rrƒÚis_snanrr Úis_qnan©r5rÇr6s r.Ú_compare_check_nanszDecimal._compare_check_nanssø€ðˆ?Ý ‘l”lˆGàÔð 3˜uÔ0ð 3Ø|Š|‰~Œ~ð 3Ø×+Ò+Õ,<Ø,GØ,0ñ2ô2ð2ð—’‘”ð 3Ø×+Ò+Õ,<Ø,GØ,1ñ3ô3ð3ð—’‘”ð 3Ø×+Ò+Õ,<Ø,FØ,0ñ2ô2ð2ð—’‘”ð 3Ø×+Ò+Õ,<Ø,FØ,1ñ3ô3ð3ðˆqr0có&—|jp |jdkS)zuReturn True if self is nonzero; otherwise return False. NaNs and infinities are considered nonzero. r„©rƒrErÃs r.Ú__bool__zDecimal.__bool__4s€ð ÔÐ3 4¤9°Ò#3Ð3r0cóT—|js|jr:| ¦«}| ¦«}||krdS||krdSdS|s|sdSd|jzS|s d|jzS|j|jkrdS|j|jkrdS| ¦«}| ¦«}||krW|jd|j|jz zz}|jd|j|jz zz}||krdS||krd|jzSd|jzS||kr d|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(rÂr1r„)rƒrÄrDÚadjustedrEr‚)r5rÇÚself_infÚ other_infÚ self_adjustedÚother_adjustedÚself_paddedÚother_paddeds r.Ú_cmpzDecimal._cmp;s€ðÔð ˜uÔ0ð Ø×'Ò'Ñ)Ô)ˆHØ×)Ò)Ñ+Ô+ˆIØ˜9Ò$Ð$ØqØ˜IÒ%Ð%Øràqðð ,Øð ,Øqà˜uœ{Ñ*Ð+Ð+Øð $Ø˜œÑ#Ð#ðŒ;˜œÒ#Ð#Ø2ØŒ:˜œÒ#Ð#Ø1àŸ š ™œˆ ØŸšÑ)Ô)ˆØ˜NÒ*Ð*Øœ) c¨4¬9°u´zÑ+AÑ&BÑBˆKØ œ:¨¨U¬Z¸$¼)Ñ-CÑ(DÑDˆLØ˜lÒ*Ð*ØqØ˜|Ò+Ð+Ø˜dœjÑ(Ð(Ð(à˜TœZÑ'Ð'Ø ˜^Ò +Ð +Ø˜œÑ#Ð#à˜4œ:Ñ%Ð&Ð&r0có¤—t||d¬¦«\}}|tur|S| ||¦«rdS| |¦«dkS)NT)Úequality_opFr()Ú_convert_for_comparisonÚNotImplementedrÊrÛrÎs r.Ú__eq__zDecimal.__eq__{s^€Ý-¨d°EÀtÐLÑLÔL‰ˆˆeØ•NÐ"Ð"ØˆLØ×Ò˜E 7Ñ+Ô+ð Ø5ØyŠy˜ÑÔ 1Ò$Ð$r0có¤—t||¦«\}}|tur|S| ||¦«}|rdS| |¦«dkS©NFr(©rÞrßrÏrÛ©r5rÇr6rHs r.Ú__lt__zDecimal.__lt__ƒó^€Ý-¨d°EÑ:Ô:‰ˆˆeØ•NÐ"Ð"ØˆLØ×&Ò& u¨gÑ6Ô6ˆØð Ø5ØyŠy˜ÑÔ !Ò#Ð#r0có¤—t||¦«\}}|tur|S| ||¦«}|rdS| |¦«dkSrârãräs r.Ú__le__zDecimal.__le__Œó^€Ý-¨d°EÑ:Ô:‰ˆˆeØ•NÐ"Ð"ØˆLØ×&Ò& u¨gÑ6Ô6ˆØð Ø5ØyŠy˜ÑÔ 1Ò$Ð$r0có¤—t||¦«\}}|tur|S| ||¦«}|rdS| |¦«dkSrârãräs r.Ú__gt__zDecimal.__gt__•rær0có¤—t||¦«\}}|tur|S| ||¦«}|rdS| |¦«dkSrârãräs r.Ú__ge__zDecimal.__ge__žrér0có¼—t|d¬¦«}|js |r!|jr| ||¦«}|r|St| |¦«¦«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_otherrƒrÊrrÛräs r.ÚcomparezDecimal.compare§sp€õ˜u¨dÐ3Ñ3Ô3ˆð Ôð ð ¨%Ô*;ð Ø×"Ò" 5¨'Ñ2Ô2ˆCØð Ø åt—y’y Ñ'Ô'Ñ(Ô(Ð(r0cóÖ—|jrg| ¦«rtd¦«‚| ¦«rt |¦«S|jrtStS|jdkrtd|jt¦«}n!tt|jt¦«}t|j ¦«|ztz}|dkr|n|}|dkrdn|S)zx.__hash__() <==> hash(x)z"Cannot hash a signaling NaN value.r(é rÂéþÿÿÿ)rƒrÌryÚis_nanr–Ú__hash__rDÚ_PyHASH_INFr‚ÚpowÚ_PyHASH_MODULUSÚ _PyHASH_10INVr‰rE)r5Úexp_hashÚhash_rHs r.r÷zDecimal.__hash__¹sÙ€ðÔð 'Ø|Š|‰~Œ~ð 'ÝÐ DÑEÔEÐEØ—’‘”ð 'Ý—’ tÑ,Ô,Ð,à”:ð'Ý'˜<Ð'å&Ð&àŒ9˜Š>ˆ>Ý˜2˜tœy/Ñ:Ô:ˆHˆHå=¨4¬9¨*µoÑFÔFˆHÝD”I‘” Ñ)OÑ;ˆØ˜q’yyˆeˆe u fˆØ˜B’YYˆrˆr CÐ'r0c ó‚—t|jttt|j¦«¦«|j¦«S)zeRepresents the number as a triple tuple. To show the internals exactly as they are. )rrDr¤r¨r‰rEr‚rÃs r.Úas_tuplezDecimal.as_tupleÓs.€õ ˜DœJcµ#°t´yÑ.AÔ.AÑ(BÔ(BÀDÄIÑNÔNÐNr0cóà—|jr2| ¦«rtd¦«‚td¦«‚|sdSt |j¦«}|jdkr|d|jzzd}}nu|j}|dkr"|dzdkr|dz}|dz}|dkr |dzdk°|j}t||z ¦«dz |¦«}|r ||z}||z}d|z|z}|j r|}||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(rôr1r²) rƒrör¥Ú OverflowErrorr‰rEr‚Úminr¹rD)r5rBr½Úd5Úd2Úshift2s r.r¸zDecimal.as_integer_ratioÚs7€ðÔð PØ{Š{‰}Œ}ð PÝ Ð!FÑGÔGÐGå#Ð$NÑOÔOÐOàð Ø4õ ” ‰NŒNˆØŒ9˜Š>ˆ>àr˜4œ9‘}Ñ$ aˆqˆAˆAð”)ˆBØq’&&˜Q ™U ašZ˜ZØa‘Øa‘ðq’&&˜Q ™U ašZ˜Zð”)ˆBÝ˜!˜q˜b™&×,Ò,Ñ.Ô.°Ñ2°BÑ7Ô7ˆFØð Øf‘Øf‘à2‘˜‘ˆAàŒ:ð ØˆAØ!ˆtˆr0có&—dt|¦«zS)z0Represents the number as an instance of Decimal.z Decimal('%s'))r™rÃs r.Ú__repr__zDecimal.__repr__s€ð¥ T¡¤Ñ*Ð*r0Fcó®—ddg|j}|jr5|jdkr|dzS|jdkr |dz|jzS|dz|jzS|jt |j¦«z}|jdkr |d kr|}n'|sd }n"|jdkr|d zdzd z }n|d z dzd z}|dkrd}d d|zz|jz}n^|t |j¦«kr%|jd|t |j¦«z zz}d}n!|jd|…}d |j|d…z}||krd}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‡rˆrÚInfinityrBÚNaNrÆr(éúÿÿÿr1r„rú.NÚeÚEz%+d)rDrƒr‚rErŸrrg) r5Úengr6rQÚ leftdigitsÚdotplacerr®r‹s r.Ú__str__zDecimal.__str__s¶€ðCˆy˜œÔ$ˆØÔð 1ØŒy˜CÒÐØ˜jÑ(Ð(Ø”˜cÒ!Ð!Ø˜e‘| d¤iÑ/Ð/à˜f‘} t¤yÑ0Ð0ð”Y¥ T¤Y¡¤Ñ/ˆ ð Œ9˜Š>ˆ>˜j¨2šo˜oà!ˆHˆHØð 0àˆHˆHØ ŒY˜#Ò Ð à" Q™¨!Ñ+¨aÑ/ˆHˆHð# Q™¨!Ñ+¨aÑ/ˆHàqŠ=ˆ=ØˆGØ˜S 8 )™_Ñ,¨t¬yÑ8ˆHˆHØ ˜TœY™œÒ 'Ð 'Ø”i Xc°$´)©n¬nÑ%<Ñ =Ñ=ˆGØˆHˆHà”i Ô*ˆGØ˜TœY x y yÔ1Ñ1ˆHØ˜Ò!Ð!ØˆCˆCàˆÝ$™,œ,Ø˜*˜WÔ-Ô.°¸*ÀXÑ:MÑ1NÑNˆCàg‰~ Ñ(¨3Ñ.Ð.r0có0—| d|¬¦«S)a,Convert to a string, using engineering notation if an exponent is needed. Engineering notation has an exponent which is a multiple of 3. This can leave up to 3 digits to the left of the decimal place and may require the addition of either one or two trailing zeros. T)rr6)r©r5r6s r.Ú to_eng_stringzDecimal.to_eng_stringEs€ð|Š| ¨gˆ|Ñ6Ô6Ð6r0có—|jr| |¬¦«}|r|S|€t¦«}|s%|jtkr| ¦«}n| ¦«}| |¦«S)zRReturns a copy with the sign switched. Rounds, if it has reason. rp)rƒrÊrr_rÚcopy_absÚcopy_negateÚ_fix©r5r6rHs r.Ú__neg__zDecimal.__neg__Ns‰€ð Ôð Ø×"Ò"¨7Ð"Ñ3Ô3ˆCØð Ø àˆ?Ý ‘l”lˆGàð %˜Ô(KÒ7Ð7ð—-’-‘/”/ˆCˆCà×"Ò"Ñ$Ô$ˆCàxŠx˜Ñ Ô Ð r0cóú—|jr| |¬¦«}|r|S|€t¦«}|s%|jtkr| ¦«}nt |¦«}| |¦«S)zhReturns a copy, unless it is a sNaN. Rounds the number (if more than precision digits) rp)rƒrÊrr_rrrrrs r.Ú__pos__zDecimal.__pos__ds€ð Ôð Ø×"Ò"¨7Ð"Ñ3Ô3ˆCØð Ø àˆ?Ý ‘l”lˆGàð ˜Ô(KÒ7Ð7à—-’-‘/”/ˆCˆCå˜$‘-”-ˆCàxŠx˜Ñ Ô Ð r0TcóÜ—|s| ¦«S|jr| |¬¦«}|r|S|jr| |¬¦«}n| |¬¦«}|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(). rp)rrƒrÊrDrr)r5Úroundr6rHs r.Ú__abs__zDecimal.__abs__ys€ðð #Ø—=’=‘?”?Ð"àÔð Ø×"Ò"¨7Ð"Ñ3Ô3ˆCØð Ø àŒ:ð 0Ø—,’, w,Ñ/Ô/ˆCˆCà—,’, w,Ñ/Ô/ˆCàˆ r0cóØ—t|¦«}|tur|S|€t¦«}|js|jrŸ| ||¦«}|r|S| ¦«rN|j|jkr/| ¦«r| td¦«St|¦«S| ¦«rt|¦«St|j|j¦«}d}|jtkr|j|jkrd}|sH|sFt|j|j¦«}|rd}t|d|¦«}| |¦«}|S|sRt!||j|jz dz ¦«}| ||j¦«}| |¦«}|S|sRt!||j|jz dz ¦«}| ||j¦«}| |¦«}|St'|¦«}t'|¦«}t)|||j¦«\}}t'¦«} |j|jkr€|j|jkr(t|d|¦«}| |¦«}|S|j|jkr||}}|jdkr!d| _|j|jc|_|_n1d| _n)|jdkrd| _d\|_|_nd| _|jdkr|j|jz| _n|j|jz | _|j| _t| ¦«}| |¦«}|S)zbReturns self + other. -INF + INF (or the reverse) cause InvalidOperation errors. Nz -INF + INFr(r1r„)r(r()rñrßrrƒrÊrÄrDrr rrr‚r_rrCrÚmaxr`Ú_rescaler¢Ú _normalizerQr‰r‹) r5rÇr6rHr‹ÚnegativezerorQÚop1Úop2r¾s r.Ú__add__zDecimal.__add__sT€õ ˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLàˆ?Ý ‘l”lˆGàÔð &˜uÔ0ð &Ø×"Ò" 5¨'Ñ2Ô2ˆCØð Ø à×ÒÑ!Ô!ð %à”: ¤Ò,Ð,°×1BÒ1BÑ1DÔ1DÐ,Ø"×/Ò/Õ0@À,ÑOÔOÐOÝ˜t‘}”}Ð$Ø× Ò Ñ"Ô"ð &Ý˜u‘~”~Ð%å$”)˜UœZÑ(Ô(ˆØˆØÔ{Ò*Ð*¨t¬z¸U¼[Ò/HÐ/HàˆLàð ˜Eð Ýt”z 5¤;Ñ/Ô/ˆDØð ØÝ" 4¨¨cÑ2Ô2ˆCØ—(’(˜7Ñ#Ô#ˆCØˆJØð Ýc˜5œ:¨¬Ñ4°QÑ6Ñ7Ô7ˆCØ—.’. gÔ&6Ñ7Ô7ˆCØ—(’(˜7Ñ#Ô#ˆCØˆJØð Ýc˜4œ9 w¤|Ñ3°AÑ5Ñ6Ô6ˆCØ—-’- WÔ%5Ñ6Ô6ˆCØ—(’(˜7Ñ#Ô#ˆCØˆJåt‰nŒnˆÝu‰oŒoˆÝ˜c 3¨¬Ñ5Ô5‰ˆˆSå‘”ˆØŒ8s”xÒÐàŒw˜#œ'Ò!Ð!Ý& |°S¸#Ñ>Ô>Ø—h’h˜wÑ'Ô'Ø ØŒw˜œÒ Ð Ø SàŒx˜1Š}ˆ}Ø”Ø%(¤X¨s¬xÐ"”˜#œ(˜(à”à ŒX˜Š]ˆ]ØˆFŒKØ!'ÑˆCŒHc”hhàˆFŒKðŒ8qŠ=ˆ=Øœ 3¤7Ñ*ˆFŒJˆJàœ 3¤7Ñ*ˆFŒJà”WˆŒ Ýf‰oŒoˆØhŠhwÑÔˆØˆ r0cóÚ—t|¦«}|tur|S|js|jr| ||¬¦«}|r|S| | ¦«|¬¦«S)zReturn self - otherrp)rñrßrƒrÊr(rräs r.Ú__sub__zDecimal.__sub__çs}€å˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLàÔð ˜uÔ0ð Ø×"Ò" 5°'Ð"Ñ:Ô:ˆCØð Ø ð|Š|˜E×-Ò-Ñ/Ô/¸ˆ|ÑAÔAÐAr0cód—t|¦«}|tur|S| ||¬¦«S)zReturn other - selfrp)rñrßr*rÎs r.Ú__rsub__zDecimal.__rsub__õs5€å˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLà}Š}˜T¨7ˆ}Ñ3Ô3Ð3r0cóÒ—t|¦«}|tur|S|€t¦«}|j|jz}|js|jr–| ||¦«}|r|S| ¦«r*|s| td¦«St|S| ¦«r*|s| td¦«St|S|j |j z}|r|s(t|d|¦«}| |¦«}|S|j dkr-t||j |¦«}| |¦«}|S|j dkr-t||j |¦«}| |¦«}|St|¦«}t|¦«}t|t|j|jz¦«|¦«}| |¦«}|S)z\Return self * other. (+-) INF * 0 (or its reverse) raise InvalidOperation. Nz(+-)INF * 0z0 * (+-)INFr„Ú1)rñrßrrDrƒrÊrÄrr rOr‚rCrrEr¢r™r‰)r5rÇr6Ú resultsignrHÚ resultexpr&r's r.Ú__mul__zDecimal.__mul__ýsô€õ ˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLàˆ?Ý ‘l”lˆGà”Z %¤+Ñ-ˆ àÔð 3˜uÔ0ð 3Ø×"Ò" 5¨'Ñ2Ô2ˆCØð Ø à×ÒÑ!Ô!ð 3ØðQØ"×/Ò/Õ0@À-ÑPÔPÐPÝ& zÔ2Ð2à× Ò Ñ"Ô"ð 3ØðQØ"×/Ò/Õ0@À-ÑPÔPÐPÝ& zÔ2Ð2à”I ¤ Ñ*ˆ ðð ˜5ð Ý" :¨s°IÑ>Ô>ˆCà—(’(˜7Ñ#Ô#ˆCØˆJðŒ9˜ÒÐÝ" :¨u¬z¸9ÑEÔEˆCØ—(’(˜7Ñ#Ô#ˆCØˆJØŒ:˜ÒÐÝ" :¨t¬y¸)ÑDÔDˆCØ—(’(˜7Ñ#Ô#ˆCØˆJåt‰nŒnˆÝu‰oŒoˆå˜z3¨s¬w¸¼Ñ/@Ñ+AÔ+AÀ9ÑMÔMˆØhŠhwÑÔˆàˆ r0có2—t|¦«}|turtS|€t¦«}|j|jz}|js|jrÐ| ||¦«}|r|S| ¦«r/| ¦«r| td¦«S| ¦«r t|S| ¦«r>| td¦«t|d| ¦«¦«S|s9|s| td¦«S| td|¦«S|s|j|jz }d}nút!|j¦«t!|j¦«z |jzdz}|j|jz |z }t'|¦«}t'|¦«} |dkr$t)|jd |zz| j¦«\}} n$t)|j| jd |zz¦«\}} | r|d zdkr|dz }n7|j|jz }||kr"|d zdkr|d z}|dz }||kr |d zdk°t|t-|¦«|¦«}| |¦«S)zReturn self / other.Nz(+-)INF/(+-)INFzDivision by infinityr„z0 / 0zx / 0r(r1rôr²)rñrßrrDrƒrÊrÄrr rOr rCÚEtinyrrr‚rŸrEr`r¢Údivmodr‰r™r)r5rÇr6rQrHr‹r¼Úshiftr&r'Ú remainderÚ ideal_exps r.Ú__truediv__zDecimal.__truediv__6s³€å˜uÑ%Ô%ˆØ•NÐ"Ð"Ý!Ð!àˆ?Ý ‘l”lˆGàŒz˜EœKÑ'ˆàÔð D˜uÔ0ð DØ×"Ò" 5¨'Ñ2Ô2ˆCØð Ø à×ÒÑ!Ô!ð Q e×&7Ò&7Ñ&9Ô&9ð QØ×+Ò+Õ,<Ð>OÑPÔPÐPà×ÒÑ!Ô!ð -Ý& tÔ,Ð,à× Ò Ñ"Ô"ð DØ×$Ò$¥WÐ.DÑEÔEÐEÝ'¨¨c°7·=²=±?´?ÑCÔCÐCðð GØð HØ×+Ò+Õ,=¸wÑGÔGÐGØ×'Ò'¸ÀÑFÔFÐFàð Ø”)˜eœjÑ(ˆCØˆEˆEõ˜œ ‘O”O¥c¨$¬)¡n¤nÑ4°w´|ÑCÀaÑGˆEØ”)˜eœjÑ(¨5Ñ0ˆCÝ˜4‘.”.ˆCÝ˜5‘/”/ˆCØ˜ŠzˆzÝ#)¨#¬'°B¸±IÑ*=¸s¼wÑ#GÔ#GÑ yyå#)¨#¬'°3´7¸RÀ%À¹ZÑ3GÑ#HÔ#HÑ yØð à˜1‘9 ’>>Ø˜Q‘JEøð!œI¨¬ Ñ2 Ø˜I’oo¨%°"©*¸ª/¨/Ø˜b‘LEØ˜1‘HCð˜I’oo¨%°"©*¸ª/¨/õ˜t¥S¨¡Z¤Z°Ñ5Ô5ˆØxŠx˜Ñ Ô Ð r0cóx—|j|jz}| ¦«r|j}nt|j|j¦«}| ¦«| ¦«z }|r| ¦«s|dkr,t|dd¦«| ||j¦«fS||jkrÛt|¦«}t|¦«}|j |j kr!|xjd|j |j z zzc_n |xjd|j |j z zzc_t|j|j¦«\}} |d|jzkrAt|t|¦«d¦«t|jt| ¦«|¦«fS| td¦«} | | 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. rõr„r(rôz%quotient too large in //, % or divmod)rDrÄr‚rrÔrCr#r_r`r¢r‹r‰r4r™rr)r5rÇr6rQr7Úexpdiffr&r'ÚqÚrrHs r.Ú_dividezDecimal._divideqs«€ðŒz˜EœKÑ'ˆØ×ÒÑÔð 3Øœ ˆIˆIå˜DœI u¤zÑ2Ô2ˆIà—-’-‘/”/ E§N¢NÑ$4Ô$4Ñ4ˆØð @u×(Ò(Ñ*Ô*ð @¨g¸ªm¨mÝ$ T¨3°Ñ2Ô2Ø—M’M )¨WÔ-=Ñ>Ô>ð@ð @àg”lÒ"Ð"Ý˜4‘.”.ˆCÝ˜5‘/”/ˆCØŒw˜#œ'Ò!Ð!Ø”˜2 ¤¨#¬'Ñ 1Ñ2Ñ2”à”˜2 ¤¨#¬'Ñ 1Ñ2Ñ2”Ý˜#œ' 3¤7Ñ+Ô+‰DˆAˆqØ2w”|Ñ#Ò#Ð#Ý(¨s°1©v¬v°qÑ9Ô9Ý(¨¬µS¸±V´V¸YÑGÔGðIðIð×"Ò"Õ#5Ø#JñLôLˆàCˆxˆr0cód—t|¦«}|tur|S| ||¬¦«S)z)Swaps self/other and returns __truediv__.rp)rñrßr8rÎs r.Ú__rtruediv__zDecimal.__rtruediv__’s8€å˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLØ× Ò ¨wÐ Ñ7Ô7Ð7r0có¢—t|¦«}|tur|S|€t¦«}| ||¦«}|r||fS|j|jz}| ¦«r[| ¦«r| td¦«}||fSt|| td¦«fS|sX|s| td¦«}||fS| td|¦«| td¦«fS| ||¦«\}}| |¦«}||fS)z6 Return (self // other, self % other) Nzdivmod(INF, INF)úINF % xzdivmod(0, 0)úx // 0úx % 0) rñrßrrÊrDrÄrr rOrrr=r)r5rÇr6rHrQÚquotientr6s r.Ú __divmod__zDecimal.__divmod__™st€õ˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLàˆ?Ý ‘l”lˆGà×Ò˜u gÑ.Ô.ˆØð Ø˜:ÐàŒz˜EœKÑ'ˆØ×ÒÑÔð KØ× Ò Ñ"Ô"ð KØ×*Ò*Õ+;Ð=OÑPÔPØ˜Cxå'¨Ô-Ø×,Ò,Õ-=¸yÑIÔIðKðKðð IØð IØ×*Ò*Õ+<¸nÑMÔMØ˜Cxà×,Ò,^¸XÀtÑLÔLØ×,Ò,Õ-=¸wÑGÔGðIðIð#Ÿlšl¨5°'Ñ:Ô:Ñˆ)Ø—N’N 7Ñ+Ô+ˆ Ø˜Ð"Ð"r0cód—t|¦«}|tur|S| ||¬¦«S)z(Swaps self/other and returns __divmod__.rp)rñrßrErÎs r.Ú__rdivmod__zDecimal.__rdivmod__½s8€å˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLØ×Ò ¨gÐÑ6Ô6Ð6r0cóÂ—t|¦«}|tur|S|€t¦«}| ||¦«}|r|S| ¦«r| td¦«S|s8|r| td¦«S| td¦«S| ||¦«d}| |¦«}|S)z self % other NrArCz0 % 0r1) rñrßrrÊrÄrr rr=r)r5rÇr6rHr6s r.Ú__mod__zDecimal.__mod__Äsì€õ˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLàˆ?Ý ‘l”lˆGà×Ò˜u gÑ.Ô.ˆØð ØˆJà×ÒÑÔð HØ×'Ò'Õ(8¸)ÑDÔDÐDØð HØð HØ×+Ò+Õ,<¸gÑFÔFÐFà×+Ò+Õ,=¸wÑGÔGÐGà—L’L ¨Ñ0Ô0°Ô3ˆ Ø—N’N 7Ñ+Ô+ˆ ØÐr0cód—t|¦«}|tur|S| ||¬¦«S)z%Swaps self/other and returns __mod__.rp)rñrßrIrÎs r.Ú__rmod__zDecimal.__rmod__ßó5€å˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLØ}Š}˜T¨7ˆ}Ñ3Ô3Ð3r0có”—|€t¦«}t|d¬¦«}| ||¦«}|r|S| ¦«r| t d¦«S|s8|r| t d¦«S| td¦«S| ¦«r$t|¦«}| |¦«St|j |j ¦«}|s+t|jd|¦«}| |¦«S| ¦«| ¦«z }||jdzkr| t¦«S|d kr0| ||j¦«}| |¦«St%|¦«}t%|¦«}|j|jkr!|xjd |j|jz zzc_n |xjd |j|jz zzc_t+|j|j¦«\}} d| z|dzz|jkr| |jz} |dz }|d |jzkr| t¦«S|j} | dkrd| z } | } t| t-| ¦«|¦«}| |¦«S) zI Remainder nearest to 0- abs(remainder-near) <= other/2 NTrïzremainder_near(infinity, x)zremainder_near(x, 0)zremainder_near(0, 0)r„r1rõrôr’r()rrñrÊrÄrr rrrrr‚rCrDrÔr`rr#r_r¢r‹r‰r4r™)r5rÇr6rHÚideal_exponentr:r&r'r;r<rQs r.Úremainder_nearzDecimal.remainder_nearæsÞ€ðˆ?Ý ‘l”lˆGå˜u¨dÐ3Ñ3Ô3ˆà×Ò˜u gÑ.Ô.ˆØð ØˆJð×ÒÑÔð GØ×'Ò'Õ(8Ø(EñGôGð Gðð DØð DØ×+Ò+Õ,<Ø,BñDôDðDð×+Ò+Õ,=Ø,BñDôDðDð×ÒÑÔð %Ý˜$‘-”-ˆCØ—8’8˜GÑ$Ô$Ð$õ˜TœY¨¬ Ñ3Ô3ˆØð %Ý" 4¤:¨s°NÑCÔCˆCØ—8’8˜GÑ$Ô$Ð$ð—-’-‘/”/ E§N¢NÑ$4Ô$4Ñ4ˆØg”l QÑ&Ò&Ð&à×'Ò'Õ(:Ñ;Ô;Ð;ØbŠ=ˆ=à—-’- °Ô0@ÑAÔAˆCØ—8’8˜GÑ$Ô$Ð$õt‰nŒnˆÝu‰oŒoˆØŒ7c”gÒÐØˆGŒGr˜CœG c¤gÑ-Ñ.Ñ.ˆGŒGˆGàˆGŒGr˜CœG c¤gÑ-Ñ.Ñ.ˆGŒGÝc”g˜sœwÑ'Ô'‰ˆˆ1ð ˆQ‰3!A‘#‰;˜œÒ Ð Ø ”‰LˆAØ ‰FˆAàG”LÑ Ò Ð Ø×'Ò'Õ(:Ñ;Ô;Ð;ðŒzˆØˆqŠ5ˆ5ØT‘6ˆDØˆAå˜t¥S¨¡V¤V¨^Ñ<Ô<ˆØxŠx˜Ñ Ô Ð r0có—t|¦«}|tur|S|€t¦«}| ||¦«}|r|S| ¦«rI| ¦«r| td¦«St|j|jzS|sF|r)| td|j|jz¦«S| td¦«S| ||¦«dS)z self // otherNz INF // INFrBz0 // 0r()rñrßrrÊrÄrr rOrDrrr=räs r.Ú__floordiv__zDecimal.__floordiv__1s€å˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLàˆ?Ý ‘l”lˆGà×Ò˜u gÑ.Ô.ˆØð ØˆJà×ÒÑÔð AØ× Ò Ñ"Ô"ð AØ×+Ò+Õ,<¸lÑKÔKÐKå& t¤z°E´KÑ'?Ô@Ð@àð IØð IØ×+Ò+N¸HØ,0¬J¸¼Ñ,DñFôFðFð×+Ò+Õ,=¸xÑHÔHÐHà|Š|˜E 7Ñ+Ô+¨AÔ.Ð.r0cód—t|¦«}|tur|S| ||¬¦«S)z*Swaps self/other and returns __floordiv__.rp)rñrßrQrÎs r.Ú __rfloordiv__zDecimal.__rfloordiv__Ms8€å˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLØ×!Ò! $°Ð!Ñ8Ô8Ð8r0cóÄ—| ¦«r/| ¦«rtd¦«‚|jrdnd}nt |¦«}t|¦«S)zFloat representation.z%Cannot convert signaling NaN to floatz-nanÚnan)rÀrÌr¥rDr™r©©r5Úss r.Ú __float__zDecimal.__float__TsZ€à;Š;‰=Œ=ð Ø|Š|‰~Œ~ð JÝ Ð!HÑIÔIÐIØœ*Ð/¨%ˆAˆAåD‘ ” ˆAÝQ‰xŒxˆr0cóV—|jrF| ¦«rtd¦«‚| ¦«rt d¦«‚d|jz}|jdkr"|t|j¦«zd|jzzS|t|jd|j…pd¦«zS)z1Converts self to an int, truncating if necessary.zCannot convert NaN to integerz"Cannot convert infinity to integerrÂr(rôNr„) rƒrÀr¥rÄrrDr‚r‰rErVs r.Ú__int__zDecimal.__int__^s¬€àÔð JØ{Š{‰}Œ}ð JÝ Ð!@ÑAÔAÐAØ×!Ò!Ñ#Ô#ð JÝ#Ð$HÑIÔIÐIØ $”*ÑˆØŒ9˜Š>ˆ>Ø•S˜œ‘^”^Ñ# B¨¬ ¡MÑ1Ð1à•S˜œ : D¤I :Ô.Ð5°#Ñ6Ô6Ñ6Ð6r0có—|Sr+r,rÃs r.ÚrealzDecimal.realms€àˆr0có —td¦«S)Nr(©rrÃs r.ÚimagzDecimal.imagqs€åq‰zŒzÐr0có—|Sr+r,rÃs r.Ú conjugatezDecimal.conjugateus€Øˆr0có:—tt|¦«¦«Sr+)Úcomplexr©rÃs r.Ú__complex__zDecimal.__complex__xs€Ý•u˜T‘{”{Ñ#Ô#Ð#r0có—|j}|j|jz }t|¦«|krI|t|¦«|z d… d¦«}t|j||jd¦«St|¦«S)z2Decapitate the payload of a NaN to fit the contextNr„T) rEr`rhrŸr rCrDr‚r)r5r6ÚpayloadÚmax_payload_lens r.rFzDecimal._fix_nan{sw€à”)ˆð"œ,¨¬Ñ6ˆÝˆw‰<Œ<˜/Ò)Ð)Øc '™lœl¨?Ñ:Ð;Ð;Ô<×CÒCÀCÑHÔHˆGÝ# D¤J°¸¼ÀDÑIÔIÐIÝt‰}Œ}Ðr0có—|jr8| ¦«r| |¦«St|¦«S| ¦«}| ¦«}|s|j|g|j}tt|j |¦«|¦«}||j kr0| t¦«t|jd|¦«St|¦«St|j¦«|j z|jz }||krW| t$d|j¦«}| t&¦«| t(¦«|S||k}|r|}|j |kr‡t|j¦«|j z|z } | dkrt|jd|dz ¦«}d} |j|j} | || ¦«}|jd| …pd}|dkrFt/t1|¦«dz¦«}t|¦«|jkr|dd…}|dz }||kr"| t$d|j¦«}nt|j||¦«}|r|r| t2¦«|r| t4¦«|r| t&¦«| t(¦«|s| t¦«|S|r| t4¦«|jdkrP|j |krE| t¦«|jd|j |z zz} t|j| |¦«St|¦«S)zÜRound if it is necessary to keep self within prec precision. Rounds and fixes the exponent. Does not raise on a sNaN. Arguments: self - Decimal instance context - context used. r„ú above Emaxr(r.r1NrÂ)rƒrÀrFrr3ÚEtoprarhrr"r‚rr rCrDrŸrEr`rrr Ú_pick_rounding_functionr_r™r‰rr)r5r6r3rjÚexp_maxÚnew_expÚexp_minrHÚself_is_subnormalr¯Úrounding_methodÚchangedr¼rÙs r.rzDecimal._fix‡sr€ðÔð %Ø{Š{‰}Œ}ð %à—}’} WÑ-Ô-Ð-õ˜t‘}”}Ð$ð— ’ ‘”ˆØ|Š|‰~Œ~ˆØð %Ø”| TÐ*¨7¬=Ô9ˆGÝ#˜dœi¨Ñ/Ô/°Ñ9Ô9ˆGØ˜$œ)Ò#Ð#Ø×$Ò$¥WÑ-Ô-Ð-Ý'¨¬ °C¸ÑAÔAÐAå˜t‘}”}Ð$õd”i‘.”. 4¤9Ñ,¨w¬|Ñ;ˆØTŠ>ˆ>à×&Ò&¥x°¸t¼zÑJÔJˆCØ× Ò ¥Ñ)Ô)Ð)Ø× Ò ¥Ñ)Ô)Ð)ØˆJà# ešOÐØð ØˆGðŒ9wÒÑÝ˜œ‘^”^ d¤iÑ/°'Ñ9ˆFØ˜ŠzˆzÝ'¨¬ °C¸À¹ÑCÔCØØ"Ô:¸7Ô;KÔLˆOØ%o d¨FÑ3Ô3ˆGØ”I˜g˜v˜gÔ&Ð-¨#ˆEØ˜Š{ˆ{ÝC ™JœJ q™LÑ)Ô)Ýu‘:”: ¤Ò,Ð,Ø! # 2 #œJEØ˜q‘LGð˜Š~ˆ~Ø×*Ò*8°\À4Ä:ÑNÔNå& t¤z°5¸'ÑBÔBðð 0Ð,ð 0Ø×$Ò$¥YÑ/Ô/Ð/Ø ð 0Ø×$Ò$¥YÑ/Ô/Ð/Øð .Ø×$Ò$¥WÑ-Ô-Ð-Ø× Ò ¥Ñ)Ô)Ð)Øð .à×$Ò$¥WÑ-Ô-Ð-ØˆJàð ,Ø× Ò ¥Ñ+Ô+Ð+ðŒ=˜AÒÐ $¤)¨dÒ"2Ð"2Ø× Ò ¥Ñ)Ô)Ð)Øœ) c¨4¬9°tÑ+;Ñ&<Ñ<ˆKÝ# D¤J°¸TÑBÔBÐBõt‰}Œ}Ðr0có4—t|j|¦«rdSdS)z(Also known as round-towards-0, truncate.r(rÂ)Ú _all_zerosrE©r5r`s r.Ú_round_downzDecimal._round_downís €åd”i Ñ&Ô&ð Ø1à2r0có.—| |¦«S)zRounds away from 0.)rurts r.Ú _round_upzDecimal._round_upôs€à× Ò Ñ&Ô&Ð&Ð&r0cóV—|j|dvrdSt|j|¦«rdSdS)zRounds 5 up (away from 0)Ú56789r1r(rÂ)rErsrts r.Ú_round_half_upzDecimal._round_half_upøs6€àŒ9TŒ?˜gÐ%Ð%Ø1Ý ˜œ 4Ñ (Ô (ð Ø1à2r0cóZ—t|j|¦«rdS| |¦«S)zRound 5 downrÂ©Ú_exact_halfrErzrts r.Ú_round_half_downzDecimal._round_half_downs/€åt”y $Ñ'Ô'ð -Ø2à×&Ò& tÑ,Ô,Ð,r0cóŠ—t|j|¦«r|dks|j|dz dvrdS| |¦«S)z!Round 5 to even, rest to nearest.r(r1Ú02468rÂr|rts r.Ú_round_half_evenzDecimal._round_half_evensM€åt”y $Ñ'Ô'ð -Ø˜’˜dœi¨¨Q©Ô/°7Ð:Ð:Ø2à×&Ò& tÑ,Ô,Ð,r0cóf—|jr| |¦«S| |¦«S)z(Rounds up (not away from 0 if negative.)©rDrurts r.Ú_round_ceilingzDecimal._round_ceilings7€àŒ:ð +Ø×#Ò# DÑ)Ô)Ð)à×$Ò$ TÑ*Ô*Ð*Ð*r0cóf—|js| |¦«S| |¦«S)z'Rounds down (not towards 0 if negative)rƒrts r.Ú_round_floorzDecimal._round_floors7€àŒzð +Ø×#Ò# DÑ)Ô)Ð)à×$Ò$ TÑ*Ô*Ð*Ð*r0có€—|r'|j|dz dvr| |¦«S| |¦«S)z)Round down unless digit prec-1 is 0 or 5.r1Ú05)rErurts r.Ú_round_05upzDecimal._round_05upsJ€àð +D”I˜d 1™fÔ%¨TÐ1Ð1Ø×#Ò# DÑ)Ô)Ð)à×$Ò$ TÑ*Ô*Ð*Ð*r0)rrrrrrrrcó^—|Kt|t¦«std¦«‚tdd|¦«}| |¦«S|jr2| ¦«rtd¦«‚td¦«‚t| dt¦«¦«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') Nz+Second argument to round should be integralr(r.úcannot round a NaNúcannot round an infinity)r˜r‰ryrCÚquantizerƒrör¥rr#r)r5rBr‹s r.Ú __round__zDecimal.__round__0sª€ð^ ˆ=å˜a¥Ñ%Ô%ð OÝÐ MÑNÔNÐNÝ" 1 c¨A¨2Ñ.Ô.ˆCØ—=’= Ñ%Ô%Ð%ðÔð @Ø{Š{‰}Œ}ð @Ý Ð!5Ñ6Ô6Ð6å#Ð$>Ñ?Ô?Ð?Ý4—=’= ¥OÑ4Ô4Ñ5Ô5Ð5r0cóÄ—|jr2| ¦«rtd¦«‚td¦«‚t | dt¦«¦«S)zãReturn the floor of self, as an integer. For a finite Decimal instance self, return the greatest integer n such that n <= self. If self is infinite or a NaN then a Python exception is raised. r‹rŒr()rƒrör¥rr‰r#rrÃs r.Ú __floor__zDecimal.__floor__ns[€ðÔð @Ø{Š{‰}Œ}ð @Ý Ð!5Ñ6Ô6Ð6å#Ð$>Ñ?Ô?Ð?Ý4—=’= ¥KÑ0Ô0Ñ1Ô1Ð1r0cóÄ—|jr2| ¦«rtd¦«‚td¦«‚t | dt¦«¦«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. r‹rŒr()rƒrör¥rr‰r#rrÃs r.Ú__ceil__zDecimal.__ceil__}s[€ðÔð @Ø{Š{‰}Œ}ð @Ý Ð!5Ñ6Ô6Ð6å#Ð$>Ñ?Ô?Ð?Ý4—=’= ¥MÑ2Ô2Ñ3Ô3Ð3r0c óN—t|d¬¦«}t|d¬¦«}|js|jr|€t¦«}|jdkr| t d|¦«S|jdkr| t d|¦«S|jdkr|}nó|jdkr|}nå|jdkr8|s| t d¦«St|j|jz}n¢|jdkr7|s| t d ¦«St|j|jz}n_t|j|jztt|j¦«t|j¦«z¦«|j|jz¦«}| ||¦«S) a:Fused multiply-add. Returns self*other+third with no rounding of the intermediate product self*other. self and other are multiplied together, with no rounding of the result. The third operand is then added to the result, and a single final rounding is performed. TrïNrŽrÆrBrzINF * 0 in fmaz0 * INF in fma) rñrƒrr‚rr rOrDrCr™r‰rEr()r5rÇÚthirdr6Úproducts r.ÚfmazDecimal.fmaŒs´€õ˜u¨dÐ3Ñ3Ô3ˆÝ˜u¨dÐ3Ñ3Ô3ˆðÔð ?˜uÔ0ñ ?ØˆÝ$™,œ,ØŒy˜CÒÐØ×+Ò+Õ,<¸fÀdÑKÔKÐKØŒz˜SÒ Ð Ø×+Ò+Õ,<¸fÀeÑLÔLÐLØŒy˜CÒÐØØ”˜sÒ"Ð"ØØ”˜cÒ!Ð!ØðBØ"×/Ò/Õ0@Ø0@ñBôBðBå)¨$¬*°u´{Ñ*BÔCØ”˜sÒ"Ð"ØðBØ"×/Ò/Õ0@Ø0@ñBôBðBå)¨$¬*°u´{Ñ*BÔCøå& t¤z°E´KÑ'?Ý'*3¨t¬y©>¬>½CÀÄ ¹O¼OÑ+KÑ'LÔ'LØ'+¤y°5´:Ñ'=ñ?ô?ˆGðŠ˜u gÑ.Ô.Ð.r0có0—t|¦«}|tur|St|¦«}|tur|S|€t¦«}| ¦«}| ¦«}| ¦«}|s|s|r©|dkr| t d|¦«S|dkr| t d|¦«S|dkr| t d|¦«S|r| |¦«S|r| |¦«S| |¦«S| ¦«r(| ¦«r| ¦«s| t d¦«S|dkr| t d¦«S|s| t d¦«S| ¦«|j kr| t d¦«S|s|s| t d ¦«S| ¦«rd}n|j}tt|¦«¦«}t| ¦«¦«}t| ¦«¦«} |j |zt!d |j|¦«z|z}t%| j¦«D]} t!|d |¦«}Œt!|| j |¦«}t'|t)|¦«d¦«S)z!Three argument version of __pow__Nr’rÆz@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 definedrô)rñrßrrÀrr rFÚ _isintegerrÔr`Ú_isevenrDr¡r‰r¢Úto_integral_valuerùr‹ÚrangerCr™)r5rÇÚmodulor6rÈrÉÚ modulo_is_nanrQÚbaseÚexponentÚis r.Ú _power_modulozDecimal._power_modulo¸s`€õ˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLÝ Ñ'Ô'ˆØ•^Ð#Ð#ØˆMàˆ?Ý ‘l”lˆGð—k’k‘m”mˆØ—|’|‘~”~ˆØŸ š ™œˆ Øð ,˜,ð ,¨-ð ,Ø˜aÒÐØ×+Ò+Õ,<¸fØ(,ñ.ô.ð.à˜qÒ Ð Ø×+Ò+Õ,<¸fØ(-ñ/ô/ð/à Ò!Ð!Ø×+Ò+Õ,<¸fØ(.ñ0ô0ð0àð .Ø—}’} WÑ-Ô-Ð-Øð /Ø—~’~ gÑ.Ô.Ð.Ø—?’? 7Ñ+Ô+Ð+ð—’Ñ!Ô!ð MØ× Ò Ñ"Ô"ð Mà×!Ò!Ñ#Ô#ð Mð×'Ò'Õ(8ð)LñMôMð Mð1Š9ˆ9Ø×'Ò'Õ(8ð)OñPôPð Pðð JØ×'Ò'Õ(8Ø(HñJôJð Jð ?Š?ÑÔ ¤Ò,Ð,Ø×'Ò'Õ(8ð);ñ<ô<ð <ðð ?˜Tð ?Ø×'Ò'Õ(8ð)>ñ?ô?ð ?ð=Š=‰?Œ?ð ØˆDˆDà”:ˆDõ•S˜‘[”[Ñ!Ô!ˆÝ˜×.Ò.Ñ0Ô0Ñ1Ô1ˆÝ˜E×3Ò3Ñ5Ô5Ñ6Ô6ˆð”˜6Ñ!¥C¨¨D¬H°fÑ$=Ô$=Ñ=ÀÑGˆÝx”|Ñ$Ô$ð )ð )ˆAÝt˜R Ñ(Ô(ˆDˆDÝ4˜œ vÑ.Ô.ˆå ¥c¨$¡i¤i°Ñ3Ô3Ð3r0có® —t|¦«}|j|j}}|dzdkr|dz}|dz }|dzdk°t|¦«}|j|j}}|dzdkr|dz}|dz }|dzdk°|dkr¨||z}|dzdkr|dz}|dz }|dzdk°|dkrdS|d|zz} |jdkr| } | ¦«r9|jdkr.|jt|¦«z} t| | z |dz ¦«}nd}tddd|zz| |z ¦«S|jdkrq|dz}|dvr‚||z|krdSt|¦«dz } |dzd z}|tt|¦«¦«krdSt| |z|¦«} t||z|¦«}| |€dS| |krdSd | z}n·|d kr¯t|¦«dzd z} td | z|¦«\}}|rdS|d zdkr|d z}| dz} |d zdk°|dzdz}|tt|¦«¦«krdSt| |z|¦«} t||z|¦«}| |€dS| |krdSd | z}ndS|d|zkrdS| |z }tdt|¦«|¦«S|dkr|d|zzd}}ní|dkr3ttt||z¦«¦«¦«|krdSt|¦«}ttt|¦«|z¦«¦«|krdS|d|z}}|d z|d zcxkrdkr"nn|d z}|d z}|d z|d zcxkrdk°n|d z|d zcxkrdkr"nn|d z}|d z}|d z|d zcxkrdk°n|dkrz||krdSt||¦«\}}|dkrdSdt|¦«|zz} t|||dz z¦«\}}||krn||dz z|z|z}Œ/||kr|dksdS|}|dkr||dzt|¦«zkrdS||z}||z}|d|zkrdSt|¦«}| ¦«rF|jdkr;|jt|¦«z} t|| z |t|¦«z ¦«}nd}td|d|zz||z ¦«S)ahAttempt to compute self**other exactly. Given Decimals self and other and an integer p, attempt to compute an exact result for the power self**other, with p digits of precision. Return None if self**other is not exactly representable in p digits. Assumes that elimination of special cases has already been performed: self and other must both be nonspecial; self must be positive and not numerically equal to 1; other must be nonzero. For efficiency, other._exp should not be too large, so that 10**abs(other._exp) is a feasible calculation.rôr(r1Nr.r„)r’éééé]éAr²érr’Téd)r¢r‰r‹rQr˜rDr‚rrCÚ_nbitsrŸr™Ú_decimal_lshift_exactr4r¡Ú _log10_lb)r5rÇÚpÚxÚxcÚxeÚyÚycÚyerŸrNÚzerosÚ last_digitr Úemaxr6r¬rBÚxc_bitsÚremÚar;r<Ústr_xcs r.Ú_power_exactzDecimal._power_exact s=€õt T‰NŒNˆØ”˜œˆBˆØ2‰g˜ŠlˆlØ2‰IˆBØ!‰GˆBð2‰g˜Šlˆlõ U‰OŒOˆØ”˜œˆBˆØ2‰g˜ŠlˆlØ2‰IˆBØ!‰GˆBð2‰g˜ŠlˆlðŠ7ˆ7Ø"‰HˆBàr‘'˜Q’,,Ør‘ Øa‘ðr‘'˜Q’,,ðAŠvˆvØtØ˜B ™F‘{ˆHØŒv˜Š{ˆ{Ø$˜9à×ÒÑ!Ô!ð e¤k°QÒ&6Ð&6Ø!%¤3¨u©:¬:Ñ!5Ý˜H ^Ñ3°Q°q±SÑ9Ô9àÝ# A s¨S°©Y¡¸À¹ÑGÔGÐGð Œ6QŠ;‰;Ø˜b™ˆJØ˜YÐ&Ð&à˜˜‘8˜r’>>Ø˜4å˜2‘J”J˜q‘Lð6˜‘t˜R‘xØS ™YœY™œÒ'Ð'Ø˜4õ*¨!¨b©&°"Ñ5Ô5Ý*¨2°©7°BÑ7Ô7Ø9 Ø˜4àt’88Ø˜4Ø˜‘Tà˜q’õ˜2‘J”J˜r‘M 2Ñ%Ý & q¨!¡t¨RÑ 0Ô 0‘ IØð Ø˜4Ø˜1‘f ’kkØ˜1‘HBØ˜‘FAð˜1‘f ’kkð˜‘t˜Q‘wØS ™YœY™œÒ'Ð'Ø˜4å)¨!¨b©&°"Ñ5Ô5Ý*¨2°©7°BÑ7Ô7Ø9 Ø˜4àt’88Ø˜4Ø˜‘TàtàR˜‘UŠ{ˆ{ØtØB‘ˆBÝ# A¥s¨2¡w¤w°Ñ3Ô3Ð3ðŠ7ˆ7Øb˜"‘f‘9˜aˆqˆAˆAàQŠwˆw3s¥3 r¨"¡u¡:¤:™œÑ/Ô/°B°3Ò6Ð6ØtÝ˜R‘j”jˆGÝ•3•s˜2‘w”w˜w‘Ñ'Ô'Ñ(Ô(¨R¨CÒ/Ð/ØtØr˜R˜C‘yˆqˆAØa‘%˜1˜q™5Ð%Ð%Ò%Ð% AÒ%Ð%Ð%Ð%Ð%Øa‘Øa‘ða‘%˜1˜q™5Ð%Ð%Ò%Ð% AÒ%Ð%Ð%Ð%ða‘%˜1˜q™5Ð%Ð%Ò%Ð% AÒ%Ð%Ð%Ð%Ð%Øa‘Øa‘ða‘%˜1˜q™5Ð%Ð%Ò%Ð% AÒ%Ð%Ð%Ð%ð ˆqŠ5ˆ5à˜!Š|ˆ|Øtå˜R ‘m”m‰GˆBØaŠxˆxØtð˜r™ œ { A‘~Ð&Ñ&ˆAð )Ý˜b ! a¨¡c¡(Ñ+Ô+‘1Ø˜’66Øà˜A˜a™C™ 1™ qÑ(Að )ð˜’FF˜q Ašv˜vØtØˆBðŠ6ˆ6a˜!˜C™%¥¨2¡¤Ñ.Ò.Ð.Ø4Ø ‰UˆØ ˆa‰ˆØ A‘Š:ˆ:Ø4õ R‘”ˆØ×ÒÑÔð %¤+°Ò"2Ð"2Ø!œY¥s¨5¡z¤zÑ1ˆNÝ˜˜>Ñ)¨1S°©[¬[©=Ñ9Ô9ˆEˆEàˆEÝ 6¨#¨e©)Ñ#3°R¸±XÑ>Ô>Ð>r0cóü—|| |||¦«St|¦«}|tur|S|€t¦«}| ||¦«}|r|S|s$|s| td¦«StSd}|jdkr\| ¦«r| ¦«sd}n|r| td¦«S| ¦«}|s)|jdkrt|dd¦«St|S| ¦«r)|jdkr t|St|dd¦«S|tkr×| ¦«rm|jdkrd}n"||jkr|j}nt!|¦«}|j|z}|d|jz kr$d|jz }| t$¦«n>| t&¦«| t$¦«d|jz }t|dd|zz|¦«S| ¦«}| ¦«r1|jdk|dkkrt|dd¦«St|Sd}d} | ¦«| ¦«z} |dk|jdkkr?| t-t/|j¦«¦«krt|d|jdz¦«}nI| ¦«}| t-t/|¦«¦«krt|d|dz ¦«}|€C| ||jdz¦«}|#|dkrtd|j|j¦«}d } |€»|j}t9|¦«} | j| j}}t9|¦«}|j|j}}|jdkr|}d } t?||||||z¦«\}}|ddt-t/|¦«¦«|z dz zzzrn|d z }ŒKt|t/|¦«|¦«}| rŠ| ¦«sut-|j¦«|jkrH|jdzt-|j¦«z }t|j|jd|zz|j|z ¦«}| ¦«}| !¦«tDD]}d|j#|<Œ | $|¦«}| t&¦«|j%tLr| tN¦«|j%tPr!| tPd |j¦«tNtLt&t$tRfD]$}|j%|r| |¦«Œ%n| $|¦«}|S)aHReturn self ** other [ % modulo]. With two arguments, compute self**other. With three arguments, compute (self**other) % modulo. For the three argument form, the following restrictions on the arguments hold: - all three arguments must be integral - other must be nonnegative - either self or other (or both) must be nonzero - modulo must be nonzero and must have at most p digits, where p is the context precision. If any of these restrictions is violated the InvalidOperation flag is raised. The result of pow(self, other, modulo) is identical to the result that would be obtained by computing (self**other) % modulo with unbounded precision, but is computed more efficiently. It is always exact. Nz0 ** 0r(r1z+x ** y with x negative and y not an integerr„r.FTrr²rôri)*r¡rñrßrrÊrr Ú_OnerDr˜r™rrCrOrÄr`r‰r‚r rrÔÚ_log10_exp_boundrŸr™rar3r»rEr¢r‹rQÚ_dpowerrrrsÚ_signalsrjrrirrrr )r5rÇrœr6rHÚresult_signÚ multiplierr‹Úself_adjÚexactÚboundr3rr®r¯r°r±r²r³Úextrar¼r:Ú newcontextÚ exceptions r.Ú__pow__zDecimal.__pow__ús-€ð0ÐØ×%Ò% e¨V°WÑ=Ô=Ð=å˜uÑ%Ô%ˆØ•NÐ"Ð"ØˆLàˆ?Ý ‘l”lˆGð×Ò˜u gÑ.Ô.ˆØð ØˆJðð Øð Ø×+Ò+Õ,<¸hÑGÔGÐGåðˆØŒ:˜Š?ˆ?Ø×ÒÑ!Ô!ð GØ—}’}‘”ð$Ø"#KøððGØ"×/Ò/Õ0@ØEñGôGðGð×#Ò#Ñ%Ô%ˆDðð 4ØŒ{˜aÒÐÝ'¨°S¸!Ñ<Ô<Ð<å& {Ô3Ð3ð×ÒÑÔð =ØŒ{˜aÒÐÝ& {Ô3Ð3å'¨°S¸!Ñ<Ô<Ð<ð •4Š<ˆ<Ø×ÒÑ!Ô!ð %ð ”; !Ò#Ð#Ø!"JJØ˜Wœ\Ò)Ð)Ø!(¤JJå!$ U¡¤Jà”i *Ñ,Ø˜˜7œ<™Ò'Ð'Ø˜GœL™.CØ×(Ò(Ñ1Ô1Ð1øà×$Ò$¥WÑ-Ô-Ð-Ø×$Ò$¥WÑ-Ô-Ð-Ø˜œ‘nå# K°°S¸#¸±X±¸sÑCÔCÐCð—=’=‘?”?ˆð×ÒÑÔð 4Ø”˜qÒ h°¢lÒ3Ð3Ý'¨°S¸!Ñ<Ô<Ð<å& {Ô3Ð3ðˆØˆð×%Ò%Ñ'Ô'¨%¯.ª.Ñ*:Ô*:Ñ:ˆØ˜ŠM˜uœ{¨aÒ/Ò0Ð0ðC ¤Ñ-Ô-Ñ.Ô.Ò.Ð.Ý& {°C¸¼Àa¹ÑHÔHøð—M’M‘O”OˆEØC ™KœKÑ(Ô(Ò(Ð(Ý& {°C¸¸q¹ÑAÔAðˆ;Ø×#Ò# E¨7¬<¸!Ñ+;Ñ<Ô<ˆCØˆØ !Ò#Ð#Ý*¨1¨c¬h¸¼ÑAÔACØðˆ;Ø”ˆAÝ˜‘”ˆAØ”U˜AœEˆBÝ˜‘”ˆAØ”U˜AœEˆBØŒv˜Š{ˆ{ØSðˆEð Ý$ R¨¨R°°Q°u±WÑ=Ô=‘ sØ˜A˜b¥3¥s¨5¡z¤z¡?¤?°1Ñ#4°QÑ#6Ñ7Ñ7Ñ8ðØØ˜‘ ð õ# ;µ°E± ´ ¸CÑ@Ô@ˆCðñ" $˜×)Ò)Ñ+Ô+ñ" $õ3”8‰}Œ} ¤Ò,Ð,Ø!œ,¨Ñ*S°´©]¬]Ñ:Ý& s¤y°#´(¸3¸w¹;Ñ2FØ'*¤x°Ñ'7ñ9ô9ð!Ÿš™œˆJØ×"Ò"Ñ$Ô$Ð$Ý%ð 0ð 0 Ø./ Ô Ñ+Ð+ð—(’(˜:Ñ&Ô&ˆCð ×#Ò#¥GÑ,Ô,Ð,ØÔ¥ Ô*ð 3Ø×'Ò' Ñ2Ô2Ð2ðÔ¥Ô)ð HØ×$Ò$¥X¨|¸S¼YÑGÔGÐGÝ& µ7½GÅWÐLð 4ð 4 ØÔ# IÔ.ð4Ø×(Ò(¨Ñ3Ô3Ð3øð 4ð —(’(˜7Ñ#Ô#ˆCàˆ r0cód—t|¦«}|tur|S| ||¬¦«S)z%Swaps self/other and returns __pow__.rp)rñrßrÉrÎs r.Ú__rpow__zDecimal.__rpow__Ò rLr0có.—|€t¦«}|jr| |¬¦«}|r|S| |¦«}| ¦«r|S|st|jdd¦«S|j| ¦«g|j }t|j¦«}|j}|j|dz dkr*||kr$|dz }|dz}|j|dz dkr||k°$t|j|jd|…|¦«S)z?Normalize- strip trailing 0s, change anything equal to 0 to 0e0Nrpr„r(r1) rrƒrÊrrÄrCrDrarjrhrŸrEr‚)r5r6rHÚduprlÚendr‹s r.Ú normalizezDecimal.normalizeÙ s!€ðˆ?Ý ‘l”lˆGàÔð Ø×"Ò"¨7Ð"Ñ3Ô3ˆCØð Ø àiŠi˜Ñ Ô ˆØ?Š?ÑÔð ØˆJàð 7Ý# C¤I¨s°AÑ6Ô6Ð6Ø”< §¢¡¤Ð0°´Ô?ˆÝ#”(‰mŒmˆØŒhˆØŒhs˜1‘uŒo Ò$Ð$¨¨wª¨Ø1‰HˆCØ1‰HˆCðŒhs˜1‘uŒo Ò$Ð$¨¨wª¨õ ¤ ¨3¬8°D°S°D¬>¸3Ñ?Ô?Ð?r0cóª—t|d¬¦«}|€t¦«}|€|j}|js|jr”| ||¦«}|r|S| ¦«s| ¦«rR| ¦«r#| ¦«rt |¦«S| td¦«S| ¦«|j cxkr|jksn| td¦«S|s0t|j d|j ¦«}| |¦«S| ¦«}||jkr| td¦«S||j z dz|jkr| td ¦«S| |j |¦«}| ¦«|jkr| td¦«St%|j¦«|jkr| td ¦«S|r7| ¦«|jkr| t*¦«|j |j kr:||kr| t,¦«| t.¦«| |¦«}|S) z‡Quantize self so its exponent is the same as that of exp. Similar to self._rescale(exp._exp) but with error checking. TrïNzquantize with one INFz)target exponent out of bounds in quantizer„z9exponent of quantize result too large for current contextr1z7quantize result has too many digits for current context)rñrr_rƒrÊrÄrrr r3r‚rarCrDrrÔr`r#rŸrErfrrr )r5r‹r_r6rHr×s r.rzDecimal.quantizeò sä€õ ˜S¨$Ð/Ñ/Ô/ˆàˆ?Ý ‘l”lˆGØÐØÔ'ˆHàÔð A˜sœð AØ×"Ò" 3¨Ñ0Ô0ˆCØð Ø àŠÑ Ô ð A D×$4Ò$4Ñ$6Ô$6ð AØ—?’?Ñ$Ô$ð)¨×)9Ò)9Ñ);Ô);ð)Ý" 4™=œ=Ð(Ø×+Ò+Õ,<Ø(?ñAôAðAð— ’ ‘” 3¤8Ð;Ð;Ò;Ð;¨w¬|Ò;Ð;Ð;Ð;Ø×'Ò'Õ(8Ø>ñ@ô@ð @ðð %Ý" 4¤:¨s°C´HÑ=Ô=ˆCØ—8’8˜GÑ$Ô$Ð$àŸ š ™œˆ Ø˜7œ<Ò'Ð'Ø×'Ò'Õ(8Ø(cñeôeð eà˜3œ8Ñ# aÑ'¨'¬,Ò6Ð6Ø×'Ò'Õ(8Ø(añcôcð cðmŠm˜CœH hÑ/Ô/ˆØ<Š<‰>Œ>˜GœLÒ(Ð(Ø×'Ò'Õ(8Ø(cñeôeð eåˆsŒx‰=Œ=˜7œ<Ò'Ð'Ø×'Ò'Õ(8Ø(añcôcð cðð ,3—<’<‘>”> G¤LÒ0Ð0Ø× Ò ¥Ñ+Ô+Ð+ØŒ8d”iÒÐØdŠ{ˆ{Ø×$Ò$¥WÑ-Ô-Ð-Ø× Ò ¥Ñ)Ô)Ð)ðhŠhwÑÔˆØˆ r0có—t|d¬¦«}|js|jrP| ¦«r| ¦«p'| ¦«o| ¦«S|j|jkS)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. Trï)rñrƒröÚis_infiniter‚rÎs r.Úsame_quantumzDecimal.same_quantum/ s€õ˜u¨dÐ3Ñ3Ô3ˆØÔð @˜uÔ0ð @Ø—K’K‘M”MÐ4 e§l¢l¡n¤nð?Ø×$Ò$Ñ&Ô&Ð>¨5×+<Ò+<Ñ+>Ô+>ð @àŒy˜EœJÒ&Ð&r0có—|jrt|¦«S|st|jd|¦«S|j|kr)t|j|jd|j|z zz|¦«St |j¦«|jz|z }|dkrt|jd|dz ¦«}d}|j|}|||¦«}|jd|…pd}|dkrtt|¦«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 r„r(r.r1N) rƒrrCrDr‚rErŸrkr™r‰)r5r‹r_r¯Ú this_functionrqr¼s r.r#zDecimal._rescale> s€ðÔð !Ý˜4‘=”=Ð Øð :Ý# D¤J°°SÑ9Ô9Ð9àŒ9˜ÒÐå# D¤JØ(,¬ °C¸¼ÀS¹Ñ4IÑ(IÈ3ñPôPð Põ T”Y‘” $¤)Ñ+¨cÑ1ˆØAŠ:ˆ:Ý# D¤J°°S¸±UÑ;Ô;ˆDØˆFØÔ4°XÔ>ˆ Ø- fÑ-Ô-ˆØ” ˜'˜6˜'Ô"Ð) cˆØaŠ<ˆ<Ý˜E™ œ 1™Ñ%Ô%ˆEÝ ¤ ¨E°3Ñ7Ô7Ð7r0cól—|dkrtd¦«‚|js|st|¦«S| | ¦«dz|z |¦«}| ¦«| ¦«kr.| | ¦«dz|z |¦«}|S)a"Round a nonzero, nonspecial Decimal to a fixed number of significant figures, using the given rounding mode. Infinities, NaNs and zeros are returned unaltered. This operation is quiet: it raises no flags, and uses no information from the context. r(z'argument should be at least 1 in _roundr1)r¥rƒrr#rÔ)r5Úplacesr_rHs r.Ú_roundzDecimal._round` s¦€ðQŠ;ˆ;ÝÐFÑGÔGÐGØÔð ! 4ð !Ý˜4‘=”=Ð ØmŠm˜DŸMšM™OœO¨AÑ-¨fÑ4°hÑ?Ô?ˆð <Š<‰>Œ>˜TŸ]š]™_œ_Ò,Ð,Ø—,’,˜sŸ|š|™~œ~¨aÑ/°Ñ6¸ÑAÔAˆCØˆ r0cóœ—|jr)| |¬¦«}|r|St|¦«S|jdkrt|¦«S|st |jdd¦«S|€t ¦«}|€|j}| d|¦«}||kr| t¦«| t¦«|S)aVRounds to a nearby integer. If no rounding mode is specified, take the rounding mode from the context. This method raises the Rounded and Inexact flags when appropriate. See also: to_integral_value, which does exactly the same as this method except that it doesn't raise Inexact or Rounded. rpr(r„)rƒrÊrr‚rCrDrr_r#rrr ©r5r_r6rHs r.Úto_integral_exactzDecimal.to_integral_exactw sÖ€ðÔð !Ø×"Ò"¨7Ð"Ñ3Ô3ˆCØð Ø Ý˜4‘=”=Ð ØŒ9˜Š>ˆ>Ý˜4‘=”=Ð Øð 8Ý# D¤J°°QÑ7Ô7Ð7Øˆ?Ý ‘l”lˆGØÐØÔ'ˆHØmŠm˜A˜xÑ(Ô(ˆØ$Š;ˆ;Ø× Ò ¥Ñ)Ô)Ð)Ø×ÒWÑ%Ô%Ð%Øˆ r0cóô—|€t¦«}|€|j}|jr)| |¬¦«}|r|St |¦«S|jdkrt |¦«S| d|¦«S)z@Rounds to the nearest integer, without raising inexact, rounded.Nrpr()rr_rƒrÊrr‚r#rÚs r.ršzDecimal.to_integral_value” sƒ€àˆ?Ý ‘l”lˆGØÐØÔ'ˆHØÔð !Ø×"Ò"¨7Ð"Ñ3Ô3ˆCØð Ø Ý˜4‘=”=Ð ØŒ9˜Š>ˆ>Ý˜4‘=”=Ð à—=’= HÑ-Ô-Ð-r0cóB—|€t¦«}|jrH| |¬¦«}|r|S| ¦«r|jdkrt|¦«S|s3t |jd|jdz¦«}| |¦«S|jdkr| td¦«S|jdz}t|¦«}|j dz }|j dzr%|jdz}t|j¦«dz dz}n!|j}t|j¦«dzdz }||z }|dkr|d |zz}d } nt#|d |z¦«\}} | } ||z}d|z} ||z}||krn ||zdz }Œ| o||z|k} | r|dkr |d|zz}n |d|zz}||z }n|dzdkr|dz }t dt%|¦«|¦«}| ¦«}| t*¦«} | |¦«}| |_|S)zReturn the square root of self.Nrpr(r„r’r1zsqrt(-x), x > 0rôr©Tr²)rrƒrÊrÄrDrrCr‚rrr r`r¢r‹r‰rŸrEr4r™Ú _shallow_copyÚ _set_roundingrr_)r5r6rHr`Úopr ÚcÚlr5rÄr6rBr;r_s r.ÚsqrtzDecimal.sqrt§ s|€àˆ?Ý ‘l”lˆGàÔð %Ø×"Ò"¨7Ð"Ñ3Ô3ˆCØð Ø à×ÒÑ!Ô!ð % d¤j°A¢o oÝ˜t‘}”}Ð$àð %å" 4¤:¨s°D´IÀ±NÑCÔCˆCØ—8’8˜GÑ$Ô$Ð$àŒ:˜Š?ˆ?Ø×'Ò'Õ(8Ð:KÑLÔLÐLð,Œ|˜A‰~ˆõd‰^Œ^ˆØŒFa‰KˆØ Œ6A‰:ð &Ø”˜‘ˆAÝT”Y‘” 1Ñ$¨Ñ)ˆAˆAà”ˆAÝD”I‘”˜qÑ AÑ%ˆAðQ‘ˆØAŠ:ˆ:Ø e‘‰OˆAØˆEˆEå! ! S¨5¨&¡[Ñ1Ô1‰LˆAˆyØ!MˆEØ ˆU‰ ˆð ‰Hˆð Ø1‘ˆAØAŠvˆvØà˜‘E˜Q‘Jð ðÐ"˜!˜A™# š(ˆàð à˜Šzˆzàb˜%‘i‘àR˜%˜‘Z‘Ø ‰JˆAˆAð1‰u˜ŠzˆzØQ‘å˜q¥# a¡&¤&¨!Ñ,Ô,ˆð×'Ò'Ñ)Ô)ˆØ×(Ò(Ñ9Ô9ˆØhŠhwÑÔˆØ#ˆÔàˆ r0có—t|d¬¦«}|€t¦«}|js|jr„| ¦«}| ¦«}|s|rX|dkr|dkr| |¦«S|dkr|dkr| |¦«S| ||¦«S| |¦«}|dkr| |¦«}|dkr|}n|}| |¦«S)z Returns the larger value. Like max(self, other) except if one is not a number, returns NaN (and signals if one is sNaN). Also rounds. TrïNr1r(rÂ©rñrrƒrÀrrÊrÛÚ compare_total©r5rÇr6ÚsnÚonrárHs r.r"zDecimal.max s€õ˜u¨dÐ3Ñ3Ô3ˆàˆ?Ý ‘l”lˆGàÔð 8˜uÔ0ð 8ð—’‘”ˆBØ—’‘”ˆBØð 8Rð 8Ø˜’77˜r Qšw˜wØŸ9š9 WÑ-Ô-Ð-Ø˜’77˜r Qšw˜wØ Ÿ:š: gÑ.Ô.Ð.Ø×'Ò'¨¨wÑ7Ô7Ð7àIŠIeÑÔˆØŠ6ˆ6ð×"Ò" 5Ñ)Ô)ˆAàŠ7ˆ7ØˆCˆCàˆCàxŠx˜Ñ Ô Ð r0có—t|d¬¦«}|€t¦«}|js|jr„| ¦«}| ¦«}|s|rX|dkr|dkr| |¦«S|dkr|dkr| |¦«S| ||¦«S| |¦«}|dkr| |¦«}|dkr|}n|}| |¦«S)z¡Returns the smaller value. Like min(self, other) except if one is not a number, returns NaN (and signals if one is sNaN). Also rounds. TrïNr1r(rÂrårçs r.rzDecimal.min4s€õ˜u¨dÐ3Ñ3Ô3ˆàˆ?Ý ‘l”lˆGàÔð 8˜uÔ0ð 8ð—’‘”ˆBØ—’‘”ˆBØð 8Rð 8Ø˜’77˜r Qšw˜wØŸ9š9 WÑ-Ô-Ð-Ø˜’77˜r Qšw˜wØ Ÿ:š: gÑ.Ô.Ð.Ø×'Ò'¨¨wÑ7Ô7Ð7àIŠIeÑÔˆØŠ6ˆ6Ø×"Ò" 5Ñ)Ô)ˆAàŠ7ˆ7ØˆCˆCàˆCàxŠx˜Ñ Ô Ð r0có‚—|jrdS|jdkrdS|j|jd…}|dt|¦«zkS)z"Returns whether self is an integerFr(TNr„)rƒr‚rErŸ)r5Úrests r.r˜zDecimal._isintegerVsI€àÔð Ø5ØŒ9˜Š>ˆ>Ø4ØŒy˜œ˜˜Ô$ˆØs3˜t™9œ9‘}Ò$Ð$r0cóN—|r|jdkrdS|jd|jzdvS)z:Returns True if self is even. Assumes self is an integer.r(TrÂr€)r‚rErÃs r.r™zDecimal._iseven_s1€àð t”y 1’}}Ø4ØŒy˜˜DœI™Ô&¨'Ð1Ð1r0cód— |jt|j¦«zdz S#t$rYdSwxYw)z$Return the adjusted exponent of selfr1r()r‚rŸrEryrÃs r.rÔzDecimal.adjustedesC€ð Ø”9s 4¤9™~œ~Ñ-°Ñ1Ð1øåð ð ð Ø11ð øøøs‚!¡ /®/có—|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,rÃs r.Ú canonicalzDecimal.canonicalms €ðˆr0có†—t|d¬¦«}| ||¦«}|r|S| ||¬¦«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. Trïrp)rñrÏròräs r.Úcompare_signalzDecimal.compare_signalusN€õ˜u°Ð5Ñ5Ô5ˆØ×&Ò& u¨gÑ6Ô6ˆØð ØˆJØ|Š|˜E¨7ˆ|Ñ3Ô3Ð3r0cóT—t|d¬¦«}|jr|jstS|js|jrtS|j}| ¦«}| ¦«}|s|rÚ||krit|j¦«|jf}t|j¦«|jf}||kr|rtStS||kr|rtStStS|r5|dkrtS|dkrtS|dkrtS|dkrtSn4|dkrtS|dkrtS|dkrtS|dkrtS||krtS||krtS|j|jkr|rtStS|j|jkr|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. Trïr1r’) rñrDÚ_NegativeOner½rÀrŸrEÚ_Zeror‚)r5rÇr6rQÚself_nanÚ other_nanÚself_keyÚ other_keys r.ræzDecimal.compare_totalsØ€õ˜u¨dÐ3Ñ3Ô3ˆðŒ:ð ˜eœkð ÝÐØŒzð ˜eœkð ÝˆKØŒzˆð—;’;‘=”=ˆØ—L’L‘N”Nˆ Øð" (yð" (Ø˜9Ò$Ð$å˜tœy™>œ>¨4¬9Ð4Ý ¤ ™OœO¨U¬ZÐ7 Ø˜iÒ'Ð'Øð,Ý#˜å+Ð+Ø˜iÒ'Ð'Øð$Ý+Ð+å#˜Ýàð (Ø˜q’==Ý'Ð'Ø ’>>ÝKØ˜q’==Ý'Ð'Ø ’>>ÝKð"ð˜q’==ÝKØ ’>>Ý'Ð'Ø˜q’==ÝKØ ’>>Ý'Ð'à%Š<ˆ<ÝÐØ%Š<ˆ<ÝˆKàŒ9u”zÒ!Ð!Øð $Ýå#Ð#ØŒ9u”zÒ!Ð!Øð Ý#Ð#åÝˆr0cóž—t|d¬¦«}| ¦«}| ¦«}| |¦«S)z–Compares self to other using abstract repr., ignoring sign. Like compare_total, but with operand's sign ignored and assumed to be 0. Trï)rñrræ)r5rÇr6rWÚos r.Úcompare_total_magzDecimal.compare_total_magÊsD€õ ˜u¨dÐ3Ñ3Ô3ˆàMŠM‰OŒOˆØNŠNÑÔˆØŠ˜qÑ!Ô!Ð!r0cóD—td|j|j|j¦«S)z'Returns a copy with the sign set to 0. r()rCrEr‚rƒrÃs r.rzDecimal.copy_absÕs€å 4¤9¨d¬i¸Ô9IÑJÔJÐJr0có”—|jr!td|j|j|j¦«Std|j|j|j¦«S)z&Returns a copy with the sign inverted.r(r1)rDrCrEr‚rƒrÃs r.rzDecimal.copy_negateÙsC€àŒ:ð OÝ# A t¤y°$´)¸TÔ=MÑNÔNÐNå# A t¤y°$´)¸TÔ=MÑNÔNÐNr0cóp—t|d¬¦«}t|j|j|j|j¦«S)z$Returns self with the sign of other.Trï)rñrCrDrEr‚rƒrÎs r.Ú copy_signzDecimal.copy_signàs8€å˜u¨dÐ3Ñ3Ô3ˆÝ ¤¨T¬YØ $¤ ¨4Ô+;ñ=ô=ð =r0có(—|€t¦«}| |¬¦«}|r|S| ¦«dkrtS|stS| ¦«dkrt|¦«S|j}| ¦«}|jdkrF|tt|jdzdz¦«¦«krtdd|jdz¦«}nb|jdkr`|tt| ¦«dzdz¦«¦«kr'tdd| ¦«dz ¦«}n÷|jdkr&||krtddd|dz zzdz|¦«}nÆ|jdkr&||dz krtdd |dzz|dz ¦«}n•t|¦«}|j|j}}|jdkr|}d} t%||||z¦«\} } | ddtt| ¦«¦«|z dz zzzrn|dz }ŒItdt| ¦«| ¦«}| ¦«}| t*¦«}| |¦«}||_|S) zReturns e ** self.NrprÂr1r(rr.r„r^Tr²rô)rrÊrÄrõr½rr`rÔrDrŸr™rarCr3r¢r‰r‹rQÚ_dexprÞrßrrr_)r5r6rHrÚadjràrár rÆr¼r‹r_s r.r‹zDecimal.expæs¥€ðˆ?Ý ‘l”lˆGð×Ò wÐÑ/Ô/ˆØð ØˆJð×ÒÑÔ Ò#Ð#ÝˆLðð ÝˆKð×ÒÑÔ Ò"Ð"Ý˜4‘=”=Ð ð ŒLˆØmŠm‰oŒoˆðŒ:˜Š?ˆ?˜s¥S¨g¬l¸1©n¸aÑ-?Ñ)@Ô)@Ñ%AÔ%AÒAÐAå" 1 c¨7¬<¸©>Ñ:Ô:ˆC‰CØ ŒZ˜1Š_ˆ_ ¥s3°·²±´Ð0@ÀÑ0BÀAÑ/EÑ+FÔ+FÑ'GÔ'GÒ!GÐ!Gå" 1 c¨7¯=ª=©?¬?¸1Ñ+<Ñ=Ô=ˆCˆCØ ŒZ˜1Š_ˆ_ ¨ r¢ å" 1 c¨C°°1±©I¡o¸Ñ&;¸a¸RÑ@Ô@ˆCˆCØ ŒZ˜1Š_ˆ_ ¨ r¨!¡t¢ å" 1 c¨1¨Q©3¡i°!°°A±Ñ6Ô6ˆCˆCõ˜$‘”ˆBØ”6˜2œ6ˆqˆAØŒw˜!Š|ˆ|ØBð ˆEð Ý" 1 a¨¨5©Ñ1Ô1‘ sØ˜A˜b¥3¥s¨5¡z¤z¡?¤?°1Ñ#4°QÑ#6Ñ7Ñ7Ñ8ðØØ˜‘ ð õ# 1¥c¨%¡j¤j°#Ñ6Ô6ˆCð×'Ò'Ñ)Ô)ˆØ×(Ò(Ñ9Ô9ˆØhŠhwÑÔˆØ#ˆÔàˆ r0có—dS)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,rÃs r.Úis_canonicalzDecimal.is_canonical1s €ðˆtr0có—|jS)zReturn True if self is finite; otherwise return False. A Decimal instance is considered finite if it is neither infinite nor a NaN. )rƒrÃs r.Ú is_finitezDecimal.is_finite9s€ðÔ#Ð#Ð#r0có—|jdkS)z8Return True if self is infinite; otherwise return False.r©r‚rÃs r.rÒzDecimal.is_infiniteAó€àŒy˜CÒÐr0có—|jdvS)z>Return True if self is a qNaN or sNaN; otherwise return False.r”r rÃs r.rözDecimal.is_nanEs€àŒy˜JÐ&Ð&r0cór—|js|sdS|€t¦«}|j| ¦«kS)z?Return True if self is a normal number; otherwise return False.F)rƒrrfrÔrs r.Ú is_normalzDecimal.is_normalIs<€àÔð 4ð Ø5Øˆ?Ý ‘l”lˆGØŒ|˜tŸ}š}™œÒ.Ð.r0có—|jdkS)z;Return True if self is a quiet NaN; otherwise return False.rBr rÃs r.rÍzDecimal.is_qnanQr r0có—|jdkS)z8Return True if self is negative; otherwise return False.r1)rDrÃs r.Ú is_signedzDecimal.is_signedUs€àŒz˜QŠÐr0có—|jdkS)z?Return True if self is a signaling NaN; otherwise return False.rŽr rÃs r.rÌzDecimal.is_snanYr r0cór—|js|sdS|€t¦«}| ¦«|jkS)z9Return True if self is subnormal; otherwise return False.F)rƒrrÔrfrs r.Úis_subnormalzDecimal.is_subnormal]s<€àÔð 4ð Ø5Øˆ?Ý ‘l”lˆGØ}Š}‰Œ ¤Ò-Ð-r0có(—|jo |jdkS)z6Return True if self is a zero; otherwise return False.r„rÑrÃs r.Úis_zerozDecimal.is_zeroes€àÔ#Ð#Ð8¨¬ °SÒ(8Ð8r0có —|jt|j¦«zdz }|dkr%tt|dzdz¦«¦«dz S|dkr(ttd|z dzdz¦«¦«dz St |¦«}|j|j}}|dkrKt|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. r1érôrõrÂr(©r‚rŸrEr™r¢r‰r‹©r5rràrár ÚnumÚdens r.Ú _ln_exp_boundzDecimal._ln_exp_boundis€ðŒi#˜dœi™.œ.Ñ(¨1Ñ,ˆØ!Š8ˆ8å•s˜3˜r™6 2™:‘”Ñ'Ô'¨!Ñ+Ð+Ø"Š9ˆ9å•s˜B˜s™F B™;¨™?Ñ+Ô+Ñ,Ô,¨qÑ0Ð0Ý d‰^Œ^ˆØŒvr”vˆ1ˆØ!Š8ˆ8åa˜˜Q˜B™‘h‘-”-ˆCÝa‘&”&ˆCÝs‘8”8c #™hœhÑ&¨#°ª)Ñ4Ð4à•3•s˜2 ˜r™6 A™:‘”Ñ'Ô'Ñ'¨!Ñ+Ð+r0c óF—|€t¦«}| |¬¦«}|r|S|stS| ¦«dkrtS|t krtS|jdkr| td¦«St|¦«}|j|j}}|j }|| ¦«z dz} t|||¦«}|ddt!t#t%|¦«¦«¦«|z dz zzzrn|d z }ŒPt't|d k¦«t#t%|¦«¦«|¦«}| ¦«}| t,¦«} | |¦«}| |_|S)z/Returns the natural (base e) logarithm of self.Nrpr1zln of a negative valuer’Tr²rôrr()rrÊÚ_NegativeInfinityrÄÚ _Infinityr½rõrDrr r¢r‰r‹r`rÚ_dlogrŸr™r¡rCrÞrßrrr_© r5r6rHràrár rr×r¼r_s r.Úlnz Decimal.ln‚s«€ðˆ?Ý ‘l”lˆGð×Ò wÐÑ/Ô/ˆØð ØˆJðð %Ý$Ð$ð×ÒÑÔ Ò"Ð"ÝÐð•4Š<ˆ<ÝˆLðŒ:˜Š?ˆ?Ø×'Ò'Õ(8Ø(@ñBôBð Bõd‰^Œ^ˆØŒvr”vˆ1ˆØŒLˆðT×'Ò'Ñ)Ô)Ñ)¨AÑ-ˆð Ý˜!˜Q Ñ'Ô'ˆEà˜˜"s¥3¥s¨5¡z¤z¡?¤?Ñ3Ô3°AÑ5°aÑ7Ñ8Ñ8Ñ9ð ØØa‰KˆFð õs 5¨¢7™|œ|Sµ°U±´©_¬_¸v¸gÑFÔFˆà×'Ò'Ñ)Ô)ˆØ×(Ò(Ñ9Ô9ˆØhŠhwÑÔˆØ#ˆÔØˆ r0có&—|jt|j¦«zdz }|dkrtt|¦«¦«dz S|dkr"ttd|z ¦«¦«dz St |¦«}|j|j}}|dkrQt|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. r1rõrÂr(rôéçr’Ú231rrs r.r¾zDecimal._log10_exp_bound´sÿ€ðŒi#˜dœi™.œ.Ñ(¨1Ñ,ˆØ!Š8ˆ8å•s˜3‘x”x‘=”= ‘?Ð"Ø"Š9ˆ9å•s˜2˜c™6‘{”{Ñ#Ô# AÑ%Ð%Ý d‰^Œ^ˆØŒvr”vˆ1ˆØ!Š8ˆ8åa˜˜Q˜B™‘h‘-”-ˆCÝc˜!‘e‘*”*ˆCÝs‘8”8c #™hœhÑ&¨#°ª)Ñ4°qÑ8Ð8å"qb‘&˜‘(‰mŒmˆÝ3‰xŒx˜!‰|˜s Uš{Ñ+¨aÑ/Ð/r0c óô—|€t¦«}| |¬¦«}|r|S|stS| ¦«dkrtS|jdkr| td¦«S|jddkrX|jdd…dt|j¦«dz zkr-t|jt|j¦«zdz ¦«}nÌt|¦«}|j |j}}|j}|| ¦«z dz} t#|||¦«}|d dtt%t'|¦«¦«¦«|z dz zzzrn|dz }ŒPt)t|dk¦«t%t'|¦«¦«|¦«}| ¦«}| t.¦«} | |¦«}| |_|S) z&Returns the base 10 logarithm of self.Nrpr1zlog10 of a negative valuer(r.r„r’Tr²rôr)rrÊrrÄrrDrr rErŸrr‚r¢r‰r‹r`r¾Ú_dlog10r™r¡rCrÞrßrrr_r!s r.Úlog10z Decimal.log10Òs÷€ðˆ?Ý ‘l”lˆGð×Ò wÐÑ/Ô/ˆØð ØˆJðð %Ý$Ð$ð×ÒÑÔ Ò"Ð"ÝÐðŒ:˜Š?ˆ?Ø×'Ò'Õ(8Ø(CñEôEð EðŒ9QŒ<˜3ÒÐ 4¤9¨Q¨R¨R¤=°C½¸T¼Y¹¼È!Ñ9KÑ4LÒ#LÐ#Lå˜$œ)¥c¨$¬)¡n¤nÑ4°qÑ8Ñ9Ô9ˆCˆCõ˜$‘”ˆBØ”6˜2œ6ˆqˆAØ”ˆAðt×,Ò,Ñ.Ô.Ñ.¨qÑ0ˆFð Ý 1 fÑ-Ô-à˜A˜b¥3¥s3¨u©:¬:¡¤Ñ#7Ô#7¸Ñ#9¸!Ñ#;Ñ<Ñ<Ñ=ðØØ˜!‘ð õ#¥3 u¨Q¢w¡<¤<µµS¸±Z´Z±´À6À'ÑJÔJˆCà×'Ò'Ñ)Ô)ˆØ×(Ò(Ñ9Ô9ˆØhŠhwÑÔˆØ#ˆÔØˆ r0có4—| |¬¦«}|r|S|€t¦«}| ¦«rtS|s| t dd¦«St | ¦«¦«}| |¦«S)aM Returns the exponent of the magnitude of self's MSD. The result is the integer which is the exponent of the magnitude of the most significant digit of self (as though it were truncated to a single digit while maintaining the value of that digit and without limiting the resulting exponent). rpNzlogb(0)r1) rÊrrÄrrrrrÔrrs r.ÚlogbzDecimal.logb s€ð×Ò wÐÑ/Ô/ˆØð ØˆJàˆ?Ý ‘l”lˆGð×ÒÑÔð ÝÐðð FØ×'Ò'¸ À1ÑEÔEÐEõ d—m’m‘o”oÑ&Ô&ˆØxŠx˜Ñ Ô Ð r0cóX—|jdks|jdkrdS|jD] }|dvrdSŒ dS)z×Return True if self is a logical operand. For being logical, it must be a finite number with a sign of 0, an exponent of 0, and a coefficient whose digits must all be either 0 or 1. r(FÚ01T)rDr‚rE)r5Údigs r.Ú _islogicalzDecimal._islogical# sI€ðŒ:˜Š?ˆ?˜dœi¨1šn˜nØ5Ø”9ð ð ˆCØ˜$ˆˆØuuðàˆtr0cóú—|jt|¦«z }|dkr d|z|z}n|dkr||jd…}|jt|¦«z }|dkr d|z|z}n|dkr||jd…}||fS)Nr(r„)r`rŸ)r5r6ÚopaÚopbÚdifs r.Ú _fill_logicalzDecimal._fill_logical1 s•€ØŒlS ™XœXÑ%ˆØŠ7ˆ7Øc‘'˜C‘-ˆCˆCØ 1ŠWˆWØw”|mnnÔ%ˆCØŒlS ™XœXÑ%ˆØŠ7ˆ7Øc‘'˜C‘-ˆCˆCØ 1ŠWˆWØw”|mnnÔ%ˆCØCˆxˆr0có¶—|€t¦«}t|d¬¦«}| ¦«r| ¦«s| t¦«S| ||j|j¦«\}}d d„t||¦«D¦«¦«}td| d¦«pdd¦«S)z;Applies an 'and' operation between self and other's digits.NTrïr‡cól—g|]1\}}tt|¦«t|¦«z¦«‘Œ2Sr,©r™r‰©Ú.0r¹Úbs r.ú z'Decimal.logical_and..L ó4€ÐEÐEÐE±°°1#c !™fœf¥S¨¡V¤V™mÑ,Ô,ÐEÐEÐEr0r(r„©rrñr.rr r3rEr§ÚziprCr ©r5rÇr6r0r1r¾s r.Úlogical_andzDecimal.logical_and> óÊ€àˆ?Ý ‘l”lˆGå˜u¨dÐ3Ñ3Ô3ˆàŠÑ Ô ð :¨×(8Ò(8Ñ(:Ô(:ð :Ø×'Ò'Õ(8Ñ9Ô9Ð9ð×'Ò'¨°´¸E¼JÑGÔG‰ ˆˆcð—’ÐEÐE½¸CÀ¹¼ÐEÑEÔEÑFÔFˆÝ 6§=¢=°Ñ#5Ô#5Ð#<¸¸aÑ@Ô@Ð@r0có|—|€t¦«}| tdd|jzd¦«|¦«S)zInvert all its digits.Nr(r.)rÚlogical_xorrCr`rs r.Úlogical_invertzDecimal.logical_invertO sA€àˆ?Ý ‘l”lˆGØ×ÒÕ 0°°3°w´|Ñ3CÀAÑ FÔ FØ 'ñ)ô)ð )r0có¶—|€t¦«}t|d¬¦«}| ¦«r| ¦«s| t¦«S| ||j|j¦«\}}d d„t||¦«D¦«¦«}td| d¦«pdd¦«S)z:Applies an 'or' operation between self and other's digits.NTrïr‡cól—g|]1\}}tt|¦«t|¦«z¦«‘Œ2Sr,r6r7s r.r:z&Decimal.logical_or..d r;r0r(r„r<r>s r.Ú logical_orzDecimal.logical_orV r@r0có¶—|€t¦«}t|d¬¦«}| ¦«r| ¦«s| t¦«S| ||j|j¦«\}}d d„t||¦«D¦«¦«}td| d¦«pdd¦«S)z;Applies an 'xor' operation between self and other's digits.NTrïr‡cól—g|]1\}}tt|¦«t|¦«z¦«‘Œ2Sr,r6r7s r.r:z'Decimal.logical_xor..u r;r0r(r„r<r>s r.rBzDecimal.logical_xorg r@r0cóP—t|d¬¦«}|€t¦«}|js|jr„| ¦«}| ¦«}|s|rX|dkr|dkr| |¦«S|dkr|dkr| |¦«S| ||¦«S| ¦« | ¦«¦«}|dkr| |¦«}|dkr|}n|}| |¦«S©z8Compares the values numerically with their sign ignored.TrïNr1r(rÂ© rñrrƒrÀrrÊrrÛrærçs r.Úmax_magzDecimal.max_magx s&€å˜u¨dÐ3Ñ3Ô3ˆàˆ?Ý ‘l”lˆGàÔð 8˜uÔ0ð 8ð—’‘”ˆBØ—’‘”ˆBØð 8Rð 8Ø˜’77˜r Qšw˜wØŸ9š9 WÑ-Ô-Ð-Ø˜’77˜r Qšw˜wØ Ÿ:š: gÑ.Ô.Ð.Ø×'Ò'¨¨wÑ7Ô7Ð7àMŠM‰OŒO× Ò §¢Ñ!1Ô!1Ñ2Ô2ˆØŠ6ˆ6Ø×"Ò" 5Ñ)Ô)ˆAàŠ7ˆ7ØˆCˆCàˆCàxŠx˜Ñ Ô Ð r0cóP—t|d¬¦«}|€t¦«}|js|jr„| ¦«}| ¦«}|s|rX|dkr|dkr| |¦«S|dkr|dkr| |¦«S| ||¦«S| ¦« | ¦«¦«}|dkr| |¦«}|dkr|}n|}| |¦«SrJrKrçs r.Úmin_magzDecimal.min_mag– s&€å˜u¨dÐ3Ñ3Ô3ˆàˆ?Ý ‘l”lˆGàÔð 8˜uÔ0ð 8ð—’‘”ˆBØ—’‘”ˆBØð 8Rð 8Ø˜’77˜r Qšw˜wØŸ9š9 WÑ-Ô-Ð-Ø˜’77˜r Qšw˜wØ Ÿ:š: gÑ.Ô.Ð.Ø×'Ò'¨¨wÑ7Ô7Ð7àMŠM‰OŒO× Ò §¢Ñ!1Ô!1Ñ2Ô2ˆØŠ6ˆ6Ø×"Ò" 5Ñ)Ô)ˆAàŠ7ˆ7ØˆCˆCàˆCàxŠx˜Ñ Ô Ð r0cóL—|€t¦«}| |¬¦«}|r|S| ¦«dkrtS| ¦«dkr+t dd|jz| ¦«¦«S| ¦«}| t¦«| ¦«| |¦«}||kr|S| t dd| ¦«dz ¦«|¦«S)z=Returns the largest representable number smaller than itself.NrprÂr1r(r^r.)rrÊrÄrrCr`rjrrrßrÚ_ignore_all_flagsrr*r3©r5r6rHÚnew_selfs r.Ú next_minuszDecimal.next_minus´ s€àˆ?Ý ‘l”lˆGà×Ò wÐÑ/Ô/ˆØð ØˆJà×ÒÑÔ Ò#Ð#Ý$Ð$Ø×ÒÑÔ Ò"Ð"Ý# A s¨7¬<Ñ'7¸¿º¹¼ÑHÔHÐHà—,’,‘.”.ˆØ×ÒkÑ*Ô*Ð*Ø×!Ò!Ñ#Ô#Ð#Ø—9’9˜WÑ%Ô%ˆØtÒÐØˆOØ|Š|Õ,¨Q°°W·]²]±_´_ÀQÑ5FÑGÔGØ#ñ%ô%ð %r0cóL—|€t¦«}| |¬¦«}|r|S| ¦«dkrtS| ¦«dkr+t dd|jz| ¦«¦«S| ¦«}| t¦«| ¦«| |¦«}||kr|S| t dd| ¦«dz ¦«|¦«S)z=Returns the smallest representable number larger than itself.Nrpr1rÂr^r(r.)rrÊrÄrrCr`rjrrrßrrPrr(r3rQs r.Ú next_pluszDecimal.next_plusË s€àˆ?Ý ‘l”lˆGà×Ò wÐÑ/Ô/ˆØð ØˆJà×ÒÑÔ Ò"Ð"ÝÐØ×ÒÑÔ Ò#Ð#Ý# A s¨7¬<Ñ'7¸¿º¹¼ÑHÔHÐHà—,’,‘.”.ˆØ×ÒmÑ,Ô,Ð,Ø×!Ò!Ñ#Ô#Ð#Ø—9’9˜WÑ%Ô%ˆØtÒÐØˆOØ|Š|Õ,¨Q°°W·]²]±_´_ÀQÑ5FÑGÔGØ#ñ%ô%ð %r0cóT—t|d¬¦«}|€t¦«}| ||¦«}|r|S| |¦«}|dkr| |¦«S|dkr| |¦«}n| |¦«}| ¦«rV| td|j ¦«| t¦«| t¦«n¡| ¦«|jkr„| t¦«| t ¦«| t¦«| t¦«|s| t"¦«|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. TrïNr(rÂz Infinite result from next_toward)rñrrÊrÛrrUrSrÄrrrDrr rÔrfrrr )r5rÇr6rHÚ comparisons r.Únext_towardzDecimal.next_towardâ sŒ€õ˜u¨dÐ3Ñ3Ô3ˆàˆ?Ý ‘l”lˆGà×Ò˜u gÑ.Ô.ˆØð ØˆJà—Y’Y˜uÑ%Ô%ˆ Ø˜Š?ˆ?Ø—>’> %Ñ(Ô(Ð(à˜ÒÐØ—.’. Ñ)Ô)ˆCˆCà—/’/ 'Ñ*Ô*ˆCð?Š?ÑÔð .Ø× Ò ¥Ø!CØ!$¤ñ ,ô ,ð ,ð × Ò ¥Ñ)Ô)Ð)Ø× Ò ¥Ñ)Ô)Ð)Ð)Ø \Š\‰^Œ^˜gœlÒ *Ð *Ø× Ò ¥Ñ+Ô+Ð+Ø× Ò ¥Ñ+Ô+Ð+Ø× Ò ¥Ñ)Ô)Ð)Ø× Ò ¥Ñ)Ô)Ð)ðð .Ø×$Ò$¥WÑ-Ô-Ð-àˆ r0cóX—| ¦«rdS| ¦«rdS| ¦«}|dkrdS|dkrdS| ¦«r|jrdSdS|€t¦«}| |¬ ¦«r|jrdSdS|jrd SdS)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 rÆr r1z +InfinityrÂz -Infinityz-Zeroz+ZeroNrpz -Subnormalz +Subnormalz-Normalz+Normal)rÌrÍrÄrrDrr)r5r6Úinfs r.Únumber_classzDecimal.number_classsÎ€ð<Š<‰>Œ>ð Ø6Ø<Š<‰>Œ>ð Ø5Ø×ÒÑ Ô ˆØ!Š8ˆ8Ø;Ø"Š9ˆ9Ø;Ø<Š<‰>Œ>ð ØŒzð ØwàwØˆ?Ý ‘l”lˆGØ×Ò WÐÑ-Ô-ð $ØŒzð $Ø#|à#|àŒ:ð Ø9à9r0có —td¦«S)z'Just returns 10, as this is Decimal, :)rôr^rÃs r.Úradixz Decimal.radix:s€år‰{Œ{Ðr0có®—|€t¦«}t|d¬¦«}| ||¦«}|r|S|jdkr| t ¦«S|jt|¦«cxkr|jksn| t ¦«S| ¦«rt|¦«St|¦«}|j }|jt|¦«z }|dkr d|z|z}n|dkr||d…}||d…|d|…z}t|j | d¦«pd|j¦«S)z5Returns a rotated copy of self, value-of-other times.NTrïr(r„©rrñrÊr‚rr r`r‰rÄrrErŸrCrDr )r5rÇr6rHÚtorotÚrotdigÚtopadÚrotateds r.ÚrotatezDecimal.rotate>sh€àˆ?Ý ‘l”lˆGå˜u¨dÐ3Ñ3Ô3ˆà×Ò˜u gÑ.Ô.ˆØð ØˆJàŒ:˜Š?ˆ?Ø×'Ò'Õ(8Ñ9Ô9Ð9Ø” ¥ U¡¤Ð;Ð;Ò;Ð;¨w¬|Ò;Ð;Ð;Ð;Ø×'Ò'Õ(8Ñ9Ô9Ð9à×ÒÑÔð !Ý˜4‘=”=Ð õE‘ ” ˆØ”ˆØ”s 6™{œ{Ñ*ˆØ1Š9ˆ9Ø˜‘Y Ñ'ˆFˆFØ QŠYˆYØ˜U˜F˜G˜G”_ˆFð˜˜˜”. 6¨&¨5¨&¤>Ñ1ˆÝ ¤ Ø '§¢¨sÑ 3Ô 3Ð :°s¸D¼IñGôGð Gr0cóJ—|€t¦«}t|d¬¦«}| ||¦«}|r|S|jdkr| t ¦«Sd|j|jzz}d|j|jzz}|t|¦«cxkr|ksn| t ¦«S| ¦«rt|¦«St|j|j |jt|¦«z¦«}| |¦«}|S)z>Returns self operand after adding the second value to its exp.NTrïr(rõr’)rrñrÊr‚rr rar`r‰rÄrrCrDrEr)r5rÇr6rHÚliminfÚlimsupr½s r.ÚscalebzDecimal.scaleb_s€àˆ?Ý ‘l”lˆGå˜u¨dÐ3Ñ3Ô3ˆà×Ò˜u gÑ.Ô.ˆØð ØˆJàŒ:˜Š?ˆ?Ø×'Ò'Õ(8Ñ9Ô9Ð9Øw”| g¤lÑ2Ñ3ˆØw”| g¤lÑ2Ñ3ˆØ#˜e™*œ*Ð.Ð.Ò.Ð.¨Ò.Ð.Ð.Ð.Ø×'Ò'Õ(8Ñ9Ô9Ð9à×ÒÑÔð !Ý˜4‘=”=Ð å˜TœZ¨¬°D´IÅÀEÁ Ä Ñ4JÑKÔKˆØ FŠF7‰OŒOˆØˆr0cóÖ—|€t¦«}t|d¬¦«}| ||¦«}|r|S|jdkr| t ¦«S|jt|¦«cxkr|jksn| t ¦«S| ¦«rt|¦«St|¦«}|j }|jt|¦«z }|dkr d|z|z}n|dkr||d…}|dkr|d|…}n|d|zz}||jd…}t|j | d¦«pd|j¦«S)z5Returns a shifted copy of self, value-of-other times.NTrïr(r„r_)r5rÇr6rHr`rarbÚshifteds r.r5z Decimal.shiftxs†€àˆ?Ý ‘l”lˆGå˜u¨dÐ3Ñ3Ô3ˆà×Ò˜u gÑ.Ô.ˆØð ØˆJàŒ:˜Š?ˆ?Ø×'Ò'Õ(8Ñ9Ô9Ð9Ø” ¥ U¡¤Ð;Ð;Ò;Ð;¨w¬|Ò;Ð;Ð;Ð;Ø×'Ò'Õ(8Ñ9Ô9Ð9à×ÒÑÔð !Ý˜4‘=”=Ð õE‘ ” ˆØ”ˆØ”s 6™{œ{Ñ*ˆØ1Š9ˆ9Ø˜‘Y Ñ'ˆFˆFØ QŠYˆYØ˜U˜F˜G˜G”_ˆFð1Š9ˆ9Ø˜V˜e˜V”nˆGˆGà˜s 5™yÑ(ˆGØ˜wœ|˜m˜n˜nÔ-ˆGå ¤ Ø$+§N¢N°3Ñ$7Ô$7Ð$>¸3ÀÄ ñKôKð Kr0có0—|jt|¦«ffSr+)Ú __class__r™rÃs r.Ú __reduce__zDecimal.__reduce__Ÿs€Ø”¥ T¡¤ Ð-Ð-r0cóv—t|¦«tur|S| t|¦«¦«Sr+©Útyperrlr™rÃs r.Ú__copy__zDecimal.__copy__¢ó0€Ý‰:Œ:Ð Ð ØˆKØ~Š~c $™iœiÑ(Ô(Ð(r0cóv—t|¦«tur|S| t|¦«¦«Sr+ro)r5Úmemos r.Ú__deepcopy__zDecimal.__deepcopy__§rrr0có—|€t¦«}t||¬¦«}|jrXt|j|¦«}t| ¦«¦«}|ddkr|dz }t|||¦«S|d€ddg|j|d<|ddkr#t|j|j |jdz¦«}|j}|d}|~|dd vr| |d z|¦«}nZ|ddvr| ||¦«}n8|ddvr.t|j ¦«|kr| ||¦«}|s+|jd kr |ddvr| d |¦«}|s|dr |jrd } n|j} |jt|j ¦«z} |dd vr |s|d |z }n0d }n-|ddvr| }n |ddvr|jd kr | dkr| }nd }|d krd}d|z|j z} n]|t|j ¦«kr%|j d|t|j ¦«z zz}d} n |j d|…pd}|j |d…} | |z }t!| || ||¦«S)a|Format a Decimal instance according to the given specifier. The specifier should be a standard format specifier, with the form described in PEP 3101. Formatting types 'e', 'E', 'f', 'F', 'g', 'G', 'n' and '%' are supported. If the formatting type is omitted it defaults to 'g' or 'G', depending on the value of context.capitals. N)Ú_localeconvrpú%ÚgÚGr’Ú precisionÚeEr1zfF%ÚgGr(Úno_neg_0rr„r‡)rÚ_parse_format_specifierrƒÚ_format_signrDr™rÚ _format_alignrgrCrEr‚r_rØr#rŸÚ_format_number)r5Ú specifierr6rwÚspecrQÚbodyr_r{Ú adjusted_signrrrr®r‹s r.Ú __format__zDecimal.__format__®sõ€ðˆ?Ý ‘l”lˆGå& y¸kÐJÑJÔJˆðÔð 3Ý ¤ ¨DÑ1Ô1ˆDÝt—}’}‘”Ñ'Ô'ˆDØFŒ|˜sÒ"Ð"Ø˜‘Ý t¨TÑ2Ô2Ð2ðŒ<ÐØ ˜: gÔ&6Ô7ˆD‰LðŒ<˜3ÒÐÝ# D¤J°´ ¸4¼9ÀQ¹;ÑGÔGˆDðÔ#ˆØ˜Ô%ˆ ØÐ ØFŒ|˜tÐ#Ð#Ø—{’{ 9¨Q¡;°Ñ9Ô9Øf” Ð&Ð&Ø—}’} i Z°Ñ:Ô:Øf” Ð%Ð%#¨d¬i©.¬.¸9Ò*DÐ*DØ—{’{ 9¨hÑ7Ô7ðð .˜œ Aš ˜ ¨$¨v¬,¸%Ð*?Ð*?Ø—=’= HÑ-Ô-ˆDØð '˜˜ZÔ(ð '¨T¬Zð 'ØˆMˆMà œJˆMð”Y¥ T¤Y¡¤Ñ/ˆ ØŒ<˜4ÐÐØð ˜IÐ1Ø˜y™=àØ &Œ\˜UÐ "Ð "Ø!ˆHˆHØ &Œ\˜TÐ !Ð !ØŒy˜AŠ~ˆ~ *¨r¢/ /Ø%àðaŠ<ˆ<ØˆGØ˜X˜I‘¨¬Ñ2ˆHˆHØ ˜DœI™œÒ &Ð &Ø”i # xµ°D´I±´Ñ'>Ñ"?Ñ?ˆGØˆHˆHà”i Ô*Ð1¨cˆGØ”y Ô+ˆHØ˜Ñ!ˆõ˜m¨W°hÀÀTÑJÔJÐJr0)r„N)NNr+)FN)TN)‚r9r:r;r<Ú __slots__r—ÚclassmethodrªrÀrÄrÊrÏrÒrÛràrårèrëríròr÷rÿr¸rrrrrr r(Ú__radd__r*r,r1Ú__rmul__r8r=r?rErGrIrKrOrQrSrXrZÚ __trunc__Úpropertyr\r_rardrFrrurwrzr~rr„r†r‰ÚdictrkrŽrr’r–r¡r»rÉrËrÏrrÓr#rØrÛršÚto_integralrãr"rr˜r™rÔrðròrærürrrr‹rrrÒrör rÍrrÌrrrr"r¾r(r*r.r3r?rCrFrBrLrNrSrUrXr[r]rdrhr5rmrqrur‡r,r0r.rrs €€€€€Ø6Ð6à6€IðT@ðT@ðT@ðT@ðlð*ð*ñ„[ð*ðX ð ð ðððððððð@ðððB4ð4ð4ð-'ð-'ð-'ð@%ð%ð%ð%ð$ð$ð$ð$ð%ð%ð%ð%ð$ð$ð$ð$ð%ð%ð%ð%ð)ð)ð)ð)ð$(ð(ð(ð4OðOðOð0ð0ð0ðd+ð+ð+ð 2/ð2/ð2/ð2/ðh7ð7ð7ð7ð!ð!ð!ð!ð,!ð!ð!ð!ð*ðððð,TðTðTðTðl€HðBðBðBðBð4ð4ð4ð4ð6ð6ð6ð6ðn€Hð9!ð9!ð9!ð9!ðvðððB8ð8ð8ð8ð"#ð"#ð"#ð"#ðH7ð7ð7ð7ððððð64ð4ð4ð4ðI!ðI!ðI!ðI!ðV/ð/ð/ð/ð89ð9ð9ð9ðððð7ð7ð7ð€Ià ððñ„Xððððñ„Xððððð$ð$ð$ð ð ð ðZðZðZðLððð'ð'ð'ðððð-ð-ð-ð-ð-ð-ð+ð+ð+ð+ð+ð+ð+ð+ð+ð#˜dØ ØØ&Ø*Ø*Ø&Ø"Ø ð ñ ô Ðð<6ð<6ð<6ð<6ð| 2ð 2ð 2ð 4ð 4ð 4ð*/ð*/ð*/ð*/ðXS4ðS4ðS4ðS4ðjk?ðk?ðk?ðZVðVðVðVðp4ð4ð4ð4ð@ð@ð@ð@ð2;ð;ð;ð;ðz 'ð 'ð 'ð 'ð 8ð 8ð 8ðDððð.ðððð:.ð.ð.ð.ð"$€KðaðaðaðaðF(!ð(!ð(!ð(!ðT !ð !ð !ð !ðD%ð%ð%ð2ð2ð2ððððððð 4ð 4ð 4ð 4ðFðFðFðFðR "ð "ð "ð "ðKðKðKðOðOðOð=ð=ð=ð=ðIðIðIðIðVððð$ð$ð$ð ð ð ð'ð'ð'ð/ð/ð/ð/ð ð ð ðððð ð ð ð.ð.ð.ð.ð9ð9ð9ð,ð,ð,ð20ð0ð0ð0ðd0ð0ð0ð<1ð1ð1ð1ðf!ð!ð!ð!ð<ððððððAðAðAðAð")ð)ð)ð)ðAðAðAðAð"AðAðAðAð"!ð!ð!ð!ð<!ð!ð!ð!ð<%ð%ð%ð%ð.%ð%ð%ð%ð.,ð,ð,ð,ð\(ð(ð(ð(ðTðððGðGðGðGðBðððð2$Kð$Kð$Kð$KðN.ð.ð.ð)ð)ð)ð )ð)ð)ðTKðTKðTKðTKðTKðTKr0rFcó|—t t¦«}||_||_||_||_|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—rrDrEr‚rƒ)rQÚcoefficientrŸÚspecialr5s r.rCrCs7€õ>Š>'Ñ"Ô"€DØ€D„JØ€D„IØ€D„IØ€DÔà€Kr0có$—eZdZdZd„Zd„Zd„ZdS)rvzContext manager class to support localcontext(). Sets a copy of the supplied context in __enter__() and restores the previous decimal context in __exit__() có8—| ¦«|_dSr+)rrr{)r5r{s r.Ú__init__z_ContextManager.__init__"s€Ø&×+Ò+Ñ-Ô-ˆÔÐÐr0có^—t¦«|_t|j¦«|jSr+)rÚ saved_contextrr{rÃs r.Ú __enter__z_ContextManager.__enter__$s(€Ý'™\œ\ˆÔÝ4Ô#Ñ$Ô$Ð$ØÔÐr0có.—t|j¦«dSr+)rr—)r5ÚtÚvÚtbs r.Ú__exit__z_ContextManager.__exit__(s€Ý4Ô%Ñ&Ô&Ð&Ð&Ð&r0N)r9r:r;r<r•r˜rr,r0r.rvrvsK€€€€€ððð .ð.ð.ð ð ð ð'ð'ð'ð'ð'r0rvcó—eZdZdZ dUd„Zd„Zd„Zd„Zd„Zd„Z d „Z d „Zd„Zd„Z d „ZeZdVd„Zd„Zd„Zd„ZdZd„Zd„Zd„ZdWd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Z d„Z!d „Z"d!„Z#d"„Z$d#„Z%d$„Z&d%„Z'd&„Z(d'„Z)d(„Z*d)„Z+d*„Z,d+„Z-d,„Z.d-„Z/d.„Z0d/„Z1d0„Z2d1„Z3d2„Z4d3„Z5d4„Z6d5„Z7d6„Z8d7„Z9d8„Z:d9„Z;d:„Zd=„Z?d>„Z@d?„ZAd@„ZBdA„ZCdB„ZDdC„ZEdD„ZFdE„ZGdVdF„ZHdG„ZIdH„ZJdI„ZKdJ„ZLdK„ZMdL„ZNdM„ZOdN„ZPdO„ZQdP„ZRdQ„ZSdR„ZTdS„ZUdT„ZVeVZWdS)XraßContains the context for a Decimal instance. Contains: prec - precision (for use in rounding, division, square roots..) rounding - rounding type (how you round) traps - If traps[exception] = 1, then the exception is raised when it is caused. Otherwise, a value is substituted in. flags - When an exception is caused, flags[exception] is set. (Whether or not the trap_enabler is set) Should be reset by user of Decimal instance. Emin - Minimum exponent Emax - Maximum exponent capitals - If 1, 1*10^1 is printed as 1E+1. If 0, printed as 1e1 clamp - If 1, change exponents if too high (Default 0) Nc óÈ‡‡— t} n#t$rYnwxYw||n| j|_||n| j|_||n| j|_||n| j|_||n| j|_||n| j|_| €g|_n| |_‰€| j ¦«|_ nEt‰t¦«s)tˆfd„t‰zD¦«¦«|_ n‰|_ ‰€'t td¦«|_dSt‰t¦«s*tˆfd„t‰zD¦«¦«|_dS‰|_dS)Nc3ó>•K—|]}|t|‰v¦«fV—ŒdSr+©r‰)r8rWrjs €r.ú z#Context.__init__..Wó2øèè€ÐMÐM°q˜q¥# a¨5 j¡/¤/Ð2ÐMÐMÐMÐMÐMÐMr0r(c3ó>•K—|]}|t|‰v¦«fV—ŒdSr+r¡)r8rWris €r.r¢z#Context.__init__..^r£r0)rÚ NameErrorr`r_rfrargrhÚ_ignored_flagsrjrrr˜rŽrÀÚfromkeysri)r5r`r_rfrargrhrirjr¦Údcs `` r.r•zContext.__init__>s{øø€ð ÝˆBˆBøÝð ð ð ØˆDð øøøð!Ð,DD°"´'ˆŒ Ø$,Ð$8˜˜¸b¼kˆŒ Ø Ð,DD°"´'ˆŒ Ø Ð,DD°"´'ˆŒ Ø$,Ð$8˜˜¸b¼kˆŒ Ø#Ð/UU°R´XˆŒ àÐ!Ø"$ˆDÔÐà"0ˆDÔàˆ=ØœŸš™œˆDŒJˆJÝ˜E¥4Ñ(Ô(ð ÝÐMÐMÐMÐM½HÀuÑˆ>ØtŠ|ˆ|Ý Ð!BÀdÈDÐRVÐX]ÐE^Ñ!^Ñ_Ô_Ð_ðà UŠ]ˆ]ØtŠ|ˆ|Ý Ð!BÀdÈDÐRVÐX]ÐE^Ñ!^Ñ_Ô_Ð_ððtŠ|ˆ|˜u tš|˜|Ý Ð!AÀTÈ4ÐQUÐW\ÐD]Ñ!]Ñ^Ô^Ð^Ý×!Ò! $¨¨eÑ4Ô4Ð4r0có—t|t¦«std|z¦«‚|D]}|tvrt d|z¦«‚ŒtD]}||vrt d|z¦«‚Œt |||¦«S)Nz%s must be a signal dictz%s is not a valid signal dict)r˜rŽryrÀÚKeyErrorr–r«)r5r¬r½rs r.Ú_set_signal_dictzContext._set_signal_dictps¦€Ý˜!TÑ"Ô"ð <ÝÐ6¸Ñ:Ñ;Ô;Ð;Øð Dð DˆCØ(??ÝÐ>ÀÑBÑCÔCÐCð#åð Dð DˆCØ˜!88ÝÐ>ÀÑBÑCÔCÐCðå×!Ò! $¨¨aÑ0Ô0Ð0r0cóT—|dkr| ||dd¦«S|dkr| ||dd¦«S|dkr| ||dd¦«S|dkr| ||dd¦«S|d kr| ||dd¦«S|d kr7|tvrtd|z¦«‚t |||¦«S|dks|d kr| ||¦«S|dkrt |||¦«St d|z¦«‚)Nr`r1rZrfrªr(rargrhr_z%s: invalid rounding moderirjr¦z.'decimal.Context' object has no attribute '%s')r¯Ú_rounding_modesryr–r«r²ÚAttributeError)r5r¬r€s r.r«zContext.__setattr__{s_€Ø6Š>ˆ>Ø×*Ò*¨4°¸¸5ÑAÔAÐAØ VŠ^ˆ^Ø×*Ò*¨4°¸ÀÑBÔBÐBØ VŠ^ˆ^Ø×*Ò*¨4°¸¸5ÑAÔAÐAØ ZÒ Ð Ø×*Ò*¨4°¸¸1Ñ=Ô=Ð=Ø WŠ_ˆ_Ø×*Ò*¨4°¸¸1Ñ=Ô=Ð=Ø ZÒ Ð ØOÐ+Ð+õ Ð ;¸eÑ CÑDÔDÐDÝ×%Ò% d¨D°%Ñ8Ô8Ð8Ø WŠ_ˆ_ ¨¢ Ø×(Ò(¨¨uÑ5Ô5Ð5Ø Ð%Ò %Ð %Ý×%Ò% d¨D°%Ñ8Ô8Ð8å Ø@À4ÑGñIôIð Ir0có&—td|z¦«‚)Nz%s cannot be deleted)rµ)r5r¬s r.Ú__delattr__zContext.__delattr__”s€ÝÐ3°dÑ:Ñ;Ô;Ð;r0c óì—d„|j ¦«D¦«}d„|j ¦«D¦«}|j|j|j|j|j|j|j ||ffS)Ncó—g|] \}}|¯|‘Œ Sr,r,©r8Úsigr›s r.r:z&Context.__reduce__..™ó!€Ð;Ð;Ð;™˜˜a¸Ð;Ð;Ð;Ð;r0có—g|] \}}|¯|‘Œ Sr,r,rºs r.r:z&Context.__reduce__..šr¼r0) rirwrjrlr`r_rfrargrh)r5rirjs r.rmzContext.__reduce__˜sv€Ø;Ð; 4¤:×#3Ò#3Ñ#5Ô#5Ð;Ñ;Ô;ˆØ;Ð; 4¤:×#3Ò#3Ñ#5Ô#5Ð;Ñ;Ô;ˆØ”Ø”˜DœM¨4¬9°d´iØ” ¤ ¨E°5ð:ð;ð ;r0cóÄ—g}| dt|¦«z¦«d„|j ¦«D¦«}| dd |¦«zdz¦«d„|j ¦«D¦«}| dd |¦«zdz¦«d |¦«dzS) zShow the current context.zrContext(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, clamp=%(clamp)dcó&—g|]\}}|¯|j‘ŒSr,©r9)r8rºr›s r.r:z$Context.__repr__..¦ó#€Ð@Ð@Ð@¡ 1¸aÐ@”Ð@Ð@Ð@r0zflags=[ú, ú]có&—g|]\}}|¯|j‘ŒSr,rÀ)r8ršr›s r.r:z$Context.__repr__..¨rÁr0ztraps=[ú))r¦Úvarsrirwr§rj)r5rWÚnamess r.rzContext.__repr__ŸsÜ€àˆØ Šð#õ˜‘:”:ññ ô ð ðAÐ@¨¬ ×(8Ò(8Ñ(:Ô(:Ð@Ñ@Ô@ˆØ Š˜TŸYšY uÑ-Ô-Ñ-°Ñ3Ñ4Ô4Ð4Ø@Ð@¨¬ ×(8Ò(8Ñ(:Ô(:Ð@Ñ@Ô@ˆØ Š˜TŸYšY uÑ-Ô-Ñ-°Ñ3Ñ4Ô4Ð4ØyŠy˜‰|Œ|˜cÑ!Ð!r0có.—|jD]}d|j|<Œ dS)zReset all flags to zeror(N)ri©r5Úflags r.rszContext.clear_flags¬ó,€à”Jð !ð !ˆDØ ˆDŒJtÑÐð !ð !r0có.—|jD]}d|j|<Œ dS)zReset all traps to zeror(N)rjrÉs r.Úclear_trapszContext.clear_traps±rËr0cóŽ—t|j|j|j|j|j|j|j|j|j ¦ « }|S)z!Returns a shallow copy from self.) rr`r_rfrargrhrirjr¦©r5Úncs r.rÞzContext._shallow_copy¶s?€å T”Y ¤ ¨t¬y¸$¼)Ø”] D¤J°´ ¸D¼JØÔ(ñ*ô*ˆðˆ r0cóÖ—t|j|j|j|j|j|j|j ¦«|j ¦«|j ¦ « }|S)zReturns a deep copy from self.)rr`r_rfrargrhrirrrjr¦rÏs r.rrzContext.copy½sT€å T”Y ¤ ¨t¬y¸$¼)Ø”] D¤JØ”Z—_’_Ñ&Ô&¨¬ ¯ªÑ(9Ô(9ØÔ(ñ*ô*ˆðˆ r0cóæ—t ||¦«}||jvr|¦«j|g|¢RŽSd|j|<|j|s|¦«j|g|¢RŽS||¦«‚)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. r1)Ú_condition_maprmr¦r7rirj)r5Ú conditionÚexplanationr-Úerrors r.rzContext._raise_errorÆs•€õ×"Ò" 9¨iÑ8Ô8ˆØDÔ'Ð'Ð'à!55‘7”7”> $Ð.¨Ð.Ð.Ð.Ð.àˆŒ 5ÑØŒz˜%Ô ð 3à%99‘;”;Ô% dÐ2¨TÐ2Ð2Ð2Ð2ðˆeKÑ Ô Ð r0có —|jtŽS)z$Ignore all flags, if they are raised)Ú _ignore_flagsrÀrÃs r.rPzContext._ignore_all_flagsÜs€à!ˆtÔ!¥8Ð,Ð,r0cóX—|jt|¦«z|_t|¦«S)z$Ignore the flags, if they are raised)r¦r£)r5ris r.rØzContext._ignore_flagsàs&€ð $Ô2µT¸%±[´[Ñ@ˆÔÝE‰{Œ{Ðr0cóœ—|r*t|dttf¦«r|d}|D]}|j |¦«ŒdS)z+Stop ignoring the flags, if they are raisedr(N)r˜r¤r£r¦Úremove)r5rirÊs r.Ú _regard_flagszContext._regard_flagsçs_€àð •Z a¤5µ¨,Ñ7Ô7ð Ø˜!”HˆEØð -ð -ˆDØÔ×&Ò& tÑ,Ô,Ð,Ð,ð -ð -r0có@—t|j|jz dz¦«S)z!Returns Etiny (= Emin - prec + 1)r1)r‰rfr`rÃs r.r3z Context.Etinyñó€å4”9˜tœyÑ(¨1Ñ,Ñ-Ô-Ð-r0có@—t|j|jz dz¦«S)z,Returns maximum exponent (= Emax - prec + 1)r1)r‰rar`rÃs r.rjzContext.EtopõrÞr0có"—|j}||_|S)aÓSets the rounding type. Sets the rounding type, and returns the current (previous) rounding type. Often used like: context = context.copy() # so you don't change the calling context # if an error occurs in the middle. rounding = context._set_rounding(ROUND_UP) val = self.__sub__(other, context=context) context._set_rounding(rounding) This will make it round up for that operation. )r_)r5rpr_s r.rßzContext._set_roundingùs€ð”=ˆØˆŒ Øˆr0r„cóŽ—t|t¦«r7|| ¦«ksd|vr| td¦«St||¬¦«}| ¦«r@t|j¦«|j |j z kr| td¦«S| |¦«S)z›Creates a new Decimal instance but using self as context. This method implements the to-number operation of the IBM Decimal specification.r†zAtrailing or leading whitespace and underscores are not permitted.rpzdiagnostic info too long in NaN)r˜r™r›rrrrÀrŸrEr`rhr)r5rr½s r.Úcreate_decimalzContext.create_decimalsÆ€õc3ÑÔð G S¨C¯IªI©K¬KÒ%7Ð%7¸3À#¸:¸:Ø×$Ò$Õ%5ð&FñGôGð Gõ C Ð&Ñ&Ô&ˆØ8Š8‰:Œ:ð H#˜aœf™+œ+¨¬ °D´JÑ(>Ò>Ð>Ø×$Ò$Õ%5Ø%FñHôHð HàvŠvd‰|Œ|Ðr0có`—t |¦«}| |¦«S)aÏCreates a new Decimal instance from a float but rounding using self as the context. >>> context = Context(prec=5, rounding=ROUND_DOWN) >>> context.create_decimal_from_float(3.1415926535897932) Decimal('3.1415') >>> context = Context(prec=5, traps=[Inexact]) >>> context.create_decimal_from_float(3.1415926535897932) Traceback (most recent call last): ... decimal.Inexact: None )rrªr)r5rºr½s r.Úcreate_decimal_from_floatz!Context.create_decimal_from_floats'€õ ×Ò˜qÑ!Ô!ˆØvŠvd‰|Œ|Ðr0cóP—t|d¬¦«}| |¬¦«S)a[Returns the absolute value of the operand. If the operand is negative, the result is the same as using the minus operation on the operand. Otherwise, the result is the same as using the plus operation on the operand. >>> ExtendedContext.abs(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.abs(Decimal('-100')) Decimal('100') >>> ExtendedContext.abs(Decimal('101.5')) Decimal('101.5') >>> ExtendedContext.abs(Decimal('-101.5')) Decimal('101.5') >>> ExtendedContext.abs(-1) Decimal('1') Trïrp)rñr ©r5r¹s r.r¡zContext.abs/s*€õ$ ˜1 dÐ+Ñ+Ô+ˆØyŠy ˆyÑ&Ô&Ð&r0cóŒ—t|d¬¦«}| ||¬¦«}|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') TrïrpúUnable to convert %s to Decimal)rñr(rßry©r5r¹r9r<s r.ÚaddzContext.addDsO€õ ˜1 dÐ+Ñ+Ô+ˆØ IŠIa ˆIÑ&Ô&ˆØ•ÐÐÝÐ=ÀÑAÑBÔBÐBàˆHr0cóF—t| |¦«¦«Sr+)r™rræs r.Ú_applyzContext._applyYs€Ý1—6’6˜$‘<”<Ñ Ô Ð r0cór—t|t¦«std¦«‚| ¦«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˜rryrðræs r.rðzContext.canonical\s4€õ˜!WÑ%Ô%ð LÝÐJÑKÔKÐKØ{Š{‰}Œ}Ðr0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñrò©r5r¹r9s r.ròzContext.compareis-€õB ˜1 dÐ+Ñ+Ô+ˆØyŠy˜ DˆyÑ)Ô)Ð)r0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñròrïs r.ròzContext.compare_signals0€õ@ ˜1 dÐ+Ñ+Ô+ˆØ×Ò ¨4ÐÑ0Ô0Ð0r0cóN—t|d¬¦«}| |¦«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') Trï)rñrærïs r.ræzContext.compare_total°s(€õ4 ˜1 dÐ+Ñ+Ô+ˆØŠ˜qÑ!Ô!Ð!r0cóN—t|d¬¦«}| |¦«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. Trï)rñrürïs r.rüzContext.compare_total_magÍs*€õ ˜1 dÐ+Ñ+Ô+ˆØ×"Ò" 1Ñ%Ô%Ð%r0cóL—t|d¬¦«}| ¦«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') Trï)rñrræs r.rzContext.copy_absÕs$€õ ˜1 dÐ+Ñ+Ô+ˆØzŠz‰|Œ|Ðr0cóB—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') Trï)rñrræs r.Úcopy_decimalzContext.copy_decimalâs"€õ ˜1 dÐ+Ñ+Ô+ˆÝq‰zŒzÐr0cóL—t|d¬¦«}| ¦«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') Trï)rñrræs r.rzContext.copy_negateïs$€õ ˜1 dÐ+Ñ+Ô+ˆØ}Š}‰ŒÐr0cóN—t|d¬¦«}| |¦«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') Trï)rñrrïs r.rzContext.copy_signüs&€õ* ˜1 dÐ+Ñ+Ô+ˆØ{Š{˜1‰~Œ~Ðr0cóŒ—t|d¬¦«}| ||¬¦«}|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') Trïrprè)rñr8rßryrés r.ÚdividezContext.dividesO€õ< ˜1 dÐ+Ñ+Ô+ˆØ MŠM˜! TˆMÑ*Ô*ˆØ•ÐÐÝÐ=ÀÑAÑBÔBÐBàˆHr0cóŒ—t|d¬¦«}| ||¬¦«}|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') Trïrprè)rñrQrßryrés r.Ú divide_intzContext.divide_int9sO€õ ˜1 dÐ+Ñ+Ô+ˆØ NŠN˜1 dˆNÑ+Ô+ˆØ•ÐÐÝÐ=ÀÑAÑBÔBÐBàˆHr0cóŒ—t|d¬¦«}| ||¬¦«}|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')) Trïrprè)rñrErßryrés r.r4zContext.divmodPsO€õ ˜1 dÐ+Ñ+Ô+ˆØ LŠL˜ DˆLÑ)Ô)ˆØ•ÐÐÝÐ=ÀÑAÑBÔBÐBàˆHr0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñr‹ræs r.r‹zContext.expes*€õ*˜! TÐ*Ñ*Ô*ˆØuŠu˜TˆuÑ"Ô"Ð"r0cóT—t|d¬¦«}| |||¬¦«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') Trïrp)rñr–)r5r¹r9rás r.r–zContext.fma}s.€õ( ˜1 dÐ+Ñ+Ô+ˆØuŠuQ˜ 4ˆuÑ(Ô(Ð(r0cór—t|t¦«std¦«‚| ¦«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˜rryrræs r.rzContext.is_canonical”s6€õ˜!WÑ%Ô%ð OÝÐMÑNÔNÐNØ~Š~ÑÔÐr0cóL—t|d¬¦«}| ¦«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 Trï)rñrræs r.rzContext.is_finite¡s$€õ& ˜1 dÐ+Ñ+Ô+ˆØ{Š{‰}Œ}Ðr0cóL—t|d¬¦«}| ¦«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 Trï)rñrÒræs r.rÒzContext.is_infinite·s$€õ ˜1 dÐ+Ñ+Ô+ˆØ}Š}‰ŒÐr0cóL—t|d¬¦«}| ¦«S)aOReturn True if the operand is a qNaN or sNaN; otherwise return False. >>> ExtendedContext.is_nan(Decimal('2.50')) False >>> ExtendedContext.is_nan(Decimal('NaN')) True >>> ExtendedContext.is_nan(Decimal('-sNaN')) True >>> ExtendedContext.is_nan(1) False Trï)rñröræs r.rözContext.is_nanÆs$€õ ˜1 dÐ+Ñ+Ô+ˆØxŠx‰zŒzÐr0cóP—t|d¬¦«}| |¬¦«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 Trïrp)rñr ræs r.r zContext.is_normalÖs*€õ( ˜1 dÐ+Ñ+Ô+ˆØ{Š{ 4ˆ{Ñ(Ô(Ð(r0cóL—t|d¬¦«}| ¦«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 Trï)rñrÍræs r.rÍzContext.is_qnanís$€õ ˜1 dÐ+Ñ+Ô+ˆØyŠy‰{Œ{Ðr0cóL—t|d¬¦«}| ¦«S)aReturn True if the operand is negative; otherwise return False. >>> ExtendedContext.is_signed(Decimal('2.50')) False >>> ExtendedContext.is_signed(Decimal('-12')) True >>> ExtendedContext.is_signed(Decimal('-0')) True >>> ExtendedContext.is_signed(8) False >>> ExtendedContext.is_signed(-8) True Trï)rñrræs r.rzContext.is_signedüs$€õ ˜1 dÐ+Ñ+Ô+ˆØ{Š{‰}Œ}Ðr0cóL—t|d¬¦«}| ¦«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 Trï)rñrÌræs r.rÌzContext.is_snan s$€õ ˜1 dÐ+Ñ+Ô+ˆØyŠy‰{Œ{Ðr0cóP—t|d¬¦«}| |¬¦«S)aôReturn True if the operand is subnormal; otherwise return False. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.is_subnormal(Decimal('2.50')) False >>> c.is_subnormal(Decimal('0.1E-999')) True >>> c.is_subnormal(Decimal('0.00')) False >>> c.is_subnormal(Decimal('-Inf')) False >>> c.is_subnormal(Decimal('NaN')) False >>> c.is_subnormal(1) False Trïrp)rñrræs r.rzContext.is_subnormals*€õ& ˜1 dÐ+Ñ+Ô+ˆØ~Š~ dˆ~Ñ+Ô+Ð+r0cóL—t|d¬¦«}| ¦«S)auReturn True if the operand is a zero; otherwise return False. >>> ExtendedContext.is_zero(Decimal('0')) True >>> ExtendedContext.is_zero(Decimal('2.50')) False >>> ExtendedContext.is_zero(Decimal('-0E+2')) True >>> ExtendedContext.is_zero(1) False >>> ExtendedContext.is_zero(0) True Trï)rñrræs r.rzContext.is_zero3s$€õ ˜1 dÐ+Ñ+Ô+ˆØyŠy‰{Œ{Ðr0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñr"ræs r.r"z Context.lnDs*€õ& ˜1 dÐ+Ñ+Ô+ˆØtŠt˜DˆtÑ!Ô!Ð!r0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñr(ræs r.r(z Context.log10Zs*€õ2 ˜1 dÐ+Ñ+Ô+ˆØwŠw˜tˆwÑ$Ô$Ð$r0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñr*ræs r.r*zContext.logbvs*€õ. ˜1 dÐ+Ñ+Ô+ˆØvŠv˜dˆvÑ#Ô#Ð#r0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñr?rïs r.r?zContext.logical_andó,€õ0 ˜1 dÐ+Ñ+Ô+ˆØ}Š}˜Q¨ˆ}Ñ-Ô-Ð-r0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñrCræs r.rCzContext.logical_invert«s-€õ ˜1 dÐ+Ñ+Ô+ˆØ×Ò¨ÐÑ-Ô-Ð-r0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñrFrïs r.rFzContext.logical_or¾s,€õ0 ˜1 dÐ+Ñ+Ô+ˆØ|Š|˜A tˆ|Ñ,Ô,Ð,r0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñrBrïs r.rBzContext.logical_xorÙr r0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñr"rïs r.r"zContext.maxôó,€õ0 ˜1 dÐ+Ñ+Ô+ˆØuŠuQ ˆuÑ%Ô%Ð%r0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñrLrïs r.rLzContext.max_magó,€õ ˜1 dÐ+Ñ+Ô+ˆØyŠy˜ DˆyÑ)Ô)Ð)r0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñrrïs r.rzContext.min rr0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñrNrïs r.rNzContext.min_mag;rr0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñrræs r.Úminusz Context.minusLó*€õ ˜1 dÐ+Ñ+Ô+ˆØyŠy ˆyÑ&Ô&Ð&r0cóŒ—t|d¬¦«}| ||¬¦«}|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') Trïrprè)rñr1rßryrés r.ÚmultiplyzContext.multiply]sO€õ2 ˜1 dÐ+Ñ+Ô+ˆØ IŠIa ˆIÑ&Ô&ˆØ•ÐÐÝÐ=ÀÑAÑBÔBÐBàˆHr0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñrSræs r.rSzContext.next_minus}s*€õ" ˜1 dÐ+Ñ+Ô+ˆØ|Š| Dˆ|Ñ)Ô)Ð)r0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñrUræs r.rUzContext.next_plus‘s*€õ" ˜1 dÐ+Ñ+Ô+ˆØ{Š{ 4ˆ{Ñ(Ô(Ð(r0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñrXrïs r.rXzContext.next_toward¥s-€õ@ ˜1 dÐ+Ñ+Ô+ˆØ}Š}˜Q¨ˆ}Ñ-Ô-Ð-r0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñrÏræs r.rÏzContext.normalizeÈs*€õ* ˜1 dÐ+Ñ+Ô+ˆØ{Š{ 4ˆ{Ñ(Ô(Ð(r0cóP—t|d¬¦«}| |¬¦«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' Trïrp)rñr[ræs r.r[zContext.number_classàs+€õ^ ˜1 dÐ+Ñ+Ô+ˆØ~Š~ dˆ~Ñ+Ô+Ð+r0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñrræs r.ÚpluszContext.plusrr0cóŽ—t|d¬¦«}| |||¬¦«}|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') Trïrprè)rñrÉrßry)r5r¹r9rœr<s r.Úpowerz Context.power#sR€õR ˜1 dÐ+Ñ+Ô+ˆØ IŠIa˜¨ˆIÑ.Ô.ˆØ•ÐÐÝÐ=ÀÑAÑBÔBÐBàˆHr0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñrrïs r.rzContext.quantizess-€õn ˜1 dÐ+Ñ+Ô+ˆØzŠz˜! TˆzÑ*Ô*Ð*r0có —td¦«S)zkJust returns 10, as this is Decimal, :) >>> ExtendedContext.radix() Decimal('10') rôr^rÃs r.r]z Context.radixs€õr‰{Œ{Ðr0cóŒ—t|d¬¦«}| ||¬¦«}|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') Trïrprè)rñrIrßryrés r.r6zContext.remainderµsO€õ> ˜1 dÐ+Ñ+Ô+ˆØ IŠIa ˆIÑ&Ô&ˆØ•ÐÐÝÐ=ÀÑAÑBÔBÐBàˆHr0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñrOrïs r.rOzContext.remainder_nearÛs/€õ> ˜1 dÐ+Ñ+Ô+ˆØ×Ò ¨4ÐÑ0Ô0Ð0r0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñrdrïs r.rdzContext.rotateýs,€õ4 ˜1 dÐ+Ñ+Ô+ˆØxŠx˜ 4ˆxÑ(Ô(Ð(r0cóN—t|d¬¦«}| |¦«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 Trï)rñrÓrïs r.rÓzContext.same_quantums(€õ* ˜1 dÐ+Ñ+Ô+ˆØ~Š~˜aÑ Ô Ð r0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñrhrïs r.rhzContext.scaleb2s,€õ ˜1 dÐ+Ñ+Ô+ˆØxŠx˜ 4ˆxÑ(Ô(Ð(r0cóR—t|d¬¦«}| ||¬¦«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') Trïrp)rñr5rïs r.r5z Context.shiftEs,€õ6 ˜1 dÐ+Ñ+Ô+ˆØwŠwq $ˆwÑ'Ô'Ð'r0cóP—t|d¬¦«}| |¬¦«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 Trïrp)rñrãræs r.rãzContext.sqrtcs*€õ: ˜1 dÐ+Ñ+Ô+ˆØvŠv˜dˆvÑ#Ô#Ð#r0cóŒ—t|d¬¦«}| ||¬¦«}|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') Trïrprè)rñr*rßryrés r.ÚsubtractzContext.subtractƒsO€õ ˜1 dÐ+Ñ+Ô+ˆØ IŠIa ˆIÑ&Ô&ˆØ•ÐÐÝÐ=ÀÑAÑBÔBÐBàˆHr0cóP—t|d¬¦«}| |¬¦«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' Trïrp)rñrræs r.rzContext.to_eng_stringšs*€õ2 ˜1 dÐ+Ñ+Ô+ˆØŠ tˆÑ,Ô,Ð,r0cóP—t|d¬¦«}| |¬¦«S)zyConverts a number to a string, using scientific notation. The operation is not affected by the context. Trïrp)rñrræs r.Ú to_sci_stringzContext.to_sci_string¶s*€õ ˜1 dÐ+Ñ+Ô+ˆØyŠy ˆyÑ&Ô&Ð&r0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñrÛræs r.rÛzContext.to_integral_exact¾s-€õ6 ˜1 dÐ+Ñ+Ô+ˆØ×"Ò"¨4Ð"Ñ0Ô0Ð0r0cóP—t|d¬¦«}| |¬¦«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') Trïrp)rñršræs r.ršzContext.to_integral_valueÜs-€õ4 ˜1 dÐ+Ñ+Ô+ˆØ×"Ò"¨4Ð"Ñ0Ô0Ð0r0) NNNNNNNNNr+)r„)Xr9r:r;r<r•r¯r²r«r·rmrrsrÍrÞrrrqrrPrØrÜr÷r3rjrßrârär¡rêrìrðròròrærürrõrrrùrûr4r‹r–rrrÒrör rÍrrÌrrr"r(r*r?rCrFrBr"rLrrNrrrSrUrXrÏr[r"r$rr]r6rOrdrÓrhr5rãr/rr2rÛršrr,r0r.rr+s €€€€€ððð$BFØDHØ&*ð"ð"ð"ð"ðH5ð5ð5ð 1ð 1ð 1ðIðIðIð2<ð<ð<ð;ð;ð;ð"ð"ð"ð!ð!ð!ð !ð!ð!ð ðððððð€Hð!ð!ð!ð!ð,-ð-ð-ðððð-ð-ð-ð€Hð.ð.ð.ð.ð.ð.ðððð&ðððð"ððð$'ð'ð'ð*ððð*!ð!ð!ðððð"*ð"*ð"*ðH!1ð!1ð!1ðF"ð"ð"ð:&ð&ð&ððððððððððððð0#ð#ð#ðJððð.ððð*#ð#ð#ð0)ð)ð)ð. ð ð ðððð, ð ð ðððð )ð)ð)ð. ð ð ðððð"ððð ,ð,ð,ð,ððð""ð"ð"ð,%ð%ð%ð8$ð$ð$ð4.ð.ð.ð6.ð.ð.ð&-ð-ð-ð6.ð.ð.ð6&ð&ð&ð6*ð*ð*ð"&ð&ð&ð6*ð*ð*ð"'ð'ð'ð"ððð@*ð*ð*ð()ð)ð)ð(!.ð!.ð!.ðF)ð)ð)ð00,ð0,ð0,ðd'ð'ð'ð"NðNðNðNð`8+ð8+ð8+ðtððð$ð$ð$ðL 1ð 1ð 1ðD)ð)ð)ð:!ð!ð!ð0)ð)ð)ð&(ð(ð(ð<$ð$ð$ð@ððð.-ð-ð-ð8'ð'ð'ð1ð1ð1ð<1ð1ð1ð<$€K€K€Kr0rcó —eZdZdZdd„Zd„ZdS)r¢©rQr‰r‹Ncó—|€d|_d|_d|_dSt|t¦«r3|j|_t|j¦«|_|j|_dS|d|_|d|_|d|_dS)Nr(r1r’)rQr‰r‹r˜rrDrEr‚)r5r€s r.r•z_WorkRep.__init__s~€Øˆ=ØˆDŒIØˆDŒHØˆDŒHˆHˆHÝ ˜wÑ 'Ô 'ð ØœˆDŒIÝ˜5œ:‘”ˆDŒHØ”zˆDŒHˆHˆHð˜aœˆDŒIØ˜Q”xˆDŒHØ˜Q”xˆDŒHˆHˆHr0có8—d|j›d|j›d|j›dS)Nú(rÂrÅr6rÃs r.rz_WorkRep.__repr__s#€€Ø!%¤ ¨D¬H¨H¨H°d´h°h°hÐ?Ð?r0r+)r9r:r;rˆr•rr,r0r.r¢r¢üsA€€€€€Ø$€Ið ð ð ð ð@ð@ð@ð@ð@r0r¢có’—|j|jkr|}|}n|}|}tt|j¦«¦«}tt|j¦«¦«}|jt d||z dz ¦«z}||jzdz |krd|_||_|xjd|j|jz zzc_|j|_||fS)zcNormalizes op1, op2 to have the same exp and length of coefficient. Done during addition. rÂr’r1rô)r‹rŸr™r‰r)r&r'r`ÚtmprÇÚtmp_lenÚ other_lenr‹s r.r$r$sÉ€ð „w”ÒÐØˆØˆˆàˆØˆõ•#c”g‘,”,ÑÔ€GÝ•C˜œ ‘N”NÑ#Ô#€IØ Œ'•C˜˜G d™N¨QÑ.Ñ/Ô/Ñ /€CØ5”9Ñ˜qÑ 3Ò&Ð&ØˆŒ ØˆŒ à€G„Gˆrc”g ¤ Ñ)Ñ*Ñ*€G„GØŒi€C„GØˆ8€Or0cóî—|dkrdS|dkr|d|zzStt|¦«¦«}t|¦«t| d¦«¦«z }||krdn|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(rôr„N)r™r¡rŸÚrstrip)rBr Ústr_nÚval_ns r.r«r«6s~€ð ˆA‚v€vØˆqØ ˆaŠˆØ2q‘5‰yÐõ•C˜‘F”F‘”ˆÝE‘ ” S §¢¨cÑ!2Ô!2Ñ3Ô3Ñ3ˆØ ˜r’zzˆtˆt q¨B°°©F¡{Ð2r0cót—|dks|dkrtd¦«‚d}||kr||||zz dz }}||k°|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.r1)r¥)rBr¹r9s r.Ú _sqrt_nearestrCKsY€ð ˆA‚v€va’ÝÐNÑOÔOÐOà€AØ ˆqŠ&ˆ&Ø!QB˜‘E‘'˜1‘*ˆ1ˆðˆqŠ&ˆ&à€Hr0cóF—d|z||z }}|d||dz zz|dzz|kzS)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. r1r’r,)r®r5r9r;s r.Ú_rshift_nearestrEZs:€ð ‰:q˜E‘z€q€AØ1˜˜!™‘9‘ 1¡Ñ%¨Ò)Ñ*Ð*r0cóL—t||¦«\}}|d|z|dzz|kzS)zaClosest integer to a/b, a and b positive integers; rounds to even in the case of a tie. r’r1)r4)r¹r9r;r<s r.Ú_div_nearestrGbs0€õ !Q‰<Œ<D€A€qØ!‘q˜‘s‘˜a’Ñ Ð r0r¥cóÊ—||z }d}||krt|¦«||z z|ks||kr—t|¦«||z z |kr~t||zdz|t||t||¦«zz|¦«z¦«}|dz }||krt|¦«||z z|k°_||krt|¦«||z z |k°~t 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(r1éöÿÿÿrrÂ)r¡rGrCrEr‰rŸr™r›) r®ÚMÚLr±ÚRÚTÚyshiftÚwr»s r.Ú_ilogrPjs‚€ð< ˆ!‰€Aà €AØŠ6ˆ6•c˜!‘f”f !¡‘m qÒ(Ð(ØˆqŠ5ˆ5•S˜‘V”V˜q ™s‘] aÒ'Ð'Ý˜!˜A™# !™Ø]¨1¨aµÀÀ1Ñ0EÔ0EÑ.EÑ+FÈÑJÔJÑJñ Lô Lˆà ˆQ‰ˆð Š6ˆ6•c˜!‘f”f !¡‘m qÒ(Ð(ØˆqŠ5ˆ5•S˜‘V”V˜q ™s‘] aÒ'Ð'õ ˆS••S˜‘V”V‘”‰_˜q ™sÑ #Ñ $Ô $Ð$€AÝ ˜Q Ñ "Ô "€FÝQ˜ÑÔ€AÝ 1Q‘3˜˜2Ñ Ô ð;ð;ˆÝ˜˜AÑÔ¥¨f°Q©h¸Ñ!:Ô!:Ñ:ˆˆå˜˜!™˜QÑÔÐr0có—|dz }tt|¦«¦«}||z||zdkz }|dkrhd|z}||z|z }|dkr |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’r1r(rôr©)rŸr™rGrPÚ _log10_digits) rár rrârºrJr»Úlog_dÚlog_10Úlog_tenpowers r.r'r'šsé€ðˆF€Aõ C‰FŒF‰Œ€AØ ˆ!‰ˆq‰saŠxÑ€Aàˆ1‚u€uØ‰EˆØ ˆa‰C‰EˆØŠ6ˆ6Ø Q‘‰JˆAˆAå˜Q Q B¡Ñ'Ô'ˆAåa˜‘”ˆÝ˜qÑ!Ô!ˆÝ˜U 1™W fÑ-Ô-ˆØ˜‘sˆˆàˆÝ# A r¨A¨2¡vÑ.Ô.ˆå˜ UÑ*¨CÑ0Ô0Ð0r0cóÜ—|dz }tt|¦«¦«}||z||zdkz }|dkr?||z|z }|dkr |d|zz}nt|d|z¦«}t|d|z¦«}nd}|r_ttt |¦«¦«¦«dz }||zdkr't|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’r1r(rôr©)rŸr™rGrPr¡rR) rár rrârºr»rSrÆÚ f_log_tens r.r r ¼s€ðˆF€Aõ C‰FŒF‰Œ€AØ ˆ!‰ˆq‰saŠxÑ€Að ˆ1‚u€uØ ˆa‰C‰EˆØŠ6ˆ6Ø Q‘‰JˆAˆAå˜Q Q B¡Ñ'Ô'ˆAõa˜˜Q™‘”ˆˆðˆð ð Ý•C˜A™œ‘K”KÑ Ô Ñ"ˆØˆu‰9˜Š>ˆ>õ% Q¥}°Q°u±WÑ'=Ô'=Ñ%=¸rÀ5¹yÑIÔIˆIˆIàˆIˆIàˆ õ˜ EÑ)¨3Ñ/Ô/Ð/r0có—eZdZdZd„Zd„ZdS)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|_dS)NÚ/23025850929940456840179914546843642076011014886)r¯rÃs r.r•z_Log10Memoize.__init__ìs €ØGˆŒˆˆr0cóˆ—|dkrtd¦«‚|t|j¦«krwd} d||zdzz}tt td|z|¦«d¦«¦«}||d…d |zkrn|dz }ŒR| d ¦«dd …|_t|jd|dz…¦«S)ztGiven an integer p >= 0, return floor(10**p)*log(10). For example, self.getdigits(3) returns 2302. r(zp should be nonnegativerTrôr’r©Nr„rÂr1)r¥rŸr¯r™rGrPr?r‰)r5rrÆrJr¯s r.Ú getdigitsz_Log10Memoize.getdigitsïsÖ€ð ˆqŠ5ˆ5ÝÐ6Ñ7Ô7Ð7à•D”KÑ Ô Ò Ð ðˆEð à˜˜5™ ™‘OÝ\%°°1±°a©.¬.¸#Ñ>Ô>Ñ?Ô?Ø˜5˜&˜'˜'”? c¨%¡iÒ/Ð/ØØ˜‘ ð ð!Ÿ-š-¨Ñ,Ô,¨S¨b¨SÔ1ˆDŒKÝ4”;˜t !¡˜tÔ$Ñ%Ô%Ð%r0N)r9r:r;r<r•r]r,r0r.rYrYèsA€€€€€ðCðCðHðHðHð&ð&ð&ð&ð&r0rYcó—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).rIrr1r(rÂr’)rªr‰rŸr™rGr›) r®rJrKrLrMr±ÚMshiftr r»s r.Ú_iexpr` sè€õ* 1‘q‰yÑÔ€Aõ ˆS••S˜‘V”V‘”‰_˜q ™sÑ #Ñ $Ô $Ð$€AÝQ˜ÑÔ€AØ ‰T€FÝ 1Q‘3˜˜2Ñ Ô ð5ð5ˆÝ˜˜F Q™J™¨°!©Ñ4Ô4ˆˆõ1Q‘3˜˜BÑ Ô ð/ð/ˆØQq‘S‘ˆÝ˜˜A˜f™H™ vÑ.Ô.ˆˆàˆQ‰3€Jr0c óh—|dz }td|tt|¦«¦«zdz ¦«}||z}||z}|dkr |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(r1rôièr)r"rŸr™r4rRrGr`) rár rrÆr;r5ÚcshiftÚquotr¸s r.rr2sË€ðˆF€Aõ 1•s3˜q™6œ6‘{”{‘? QÑ&Ñ'Ô'€EØ ˆE‰ €Að ˆa‰C€EØ‚z€zØ2u‘9‘ˆˆàB˜˜‘J‘ˆÝv}¨QÑ/Ô/Ñ0Ô0I€Dˆ#õs˜B ™IÑ &Ô &€Cõ˜c 2 q¡5Ñ)Ô)¨4Ñ0Ô0°$¸±(¸Q±,Ð>Ð>r0cóè—ttt|¦«¦«¦«|z}t||||zdz¦«}||z }|dkr||zd|zz}nt ||zd|z¦«}|dkrHtt|¦«¦«|zdk|dkkrd|dz zdzd|z } } n˜J u¨Q¤xÔ0Ñ0Ð0r0có—t|t¦«r|St|t¦«rt|¦«S|r/t|t¦«rt |¦«S|rtd|z¦«‚tS)zÙConvert other to Decimal. Verifies that it's ok to use in an implicit construction. If allow_float is true, allow conversion from float; this is used in the comparison methods (__eq__ and friends). rè)r˜rr‰r©rªryrß)rÇrðÚallow_floats r.rñrñ‹s‰€õ%Ñ!Ô!ðØˆÝ%ÑÔðÝu‰~Œ~ÐØð)•z %Ñ/Ô/ð)Ý×!Ò! %Ñ(Ô(Ð(àðCÝÐ9¸EÑAÑBÔBÐBÝÐr0cóv—t|t¦«r||fSt|tj¦«r_|jsBt|jtt|j ¦«|j z¦«|j¦«}|t|j¦«fS|r,t|tj ¦«r|jdkr|j}t|t ¦«rWt#¦«}|rd|jt&<n| t&d¦«|t |¦«fSt,t,fS)zÔGiven a Decimal instance self and a Python object other, return a pair (s, o) of Decimal instances such that "s op o" is equivalent to "self op other" for any of the 6 comparison operators "op". r(r1r•)r˜rÚ_numbersÚRationalrƒrCrDr™r‰rEÚdenominatorr‚Ú numeratorÚComplexr_r\r©rrirrrªrß)r5rÇrÝr6s r.rÞrÞžs2€õ%Ñ!Ô!ðØUˆ{Ðõ%Ô*Ñ+Ô+ð.ØÔð /Ý# D¤JÝ$'¨D¬I©¬¸Ô9JÑ(JÑ$KÔ$KØ$(¤Iñ/ô/ˆDð•W˜Uœ_Ñ-Ô-Ð-Ð-ð ð•z %Ô)9Ñ:Ô:ð¸u¼zÈQº¸Ø” ˆÝ%ÑÔð/Ý‘,”,ˆØð OØ,-ˆGŒM.Ñ)Ð)à× Ò ¥ØMñ Oô Oð Oà•W×'Ò'¨Ñ.Ô.Ð.Ð.Ý>Ð)Ð)r0r¨i?BiÁ½ðÿ)r`r_rjrirarfrgrhr“)r`r_rjria· # A numeric string consists of: # \s* (?P[-+])? # an optional sign, followed by either... ( (?=\d|\.\d) # ...a number (with at least one digit) (?P\d*) # having a (possibly empty) integer part (\.(?P\d*))? # followed by an optional fractional part (E(?P[-+]?\d+))? # followed by an optional exponent, or... | Inf(inity)? # ...an infinity, or... | (?Ps)? # ...an (optionally signaling) NaN # NaN (?P\d*) # with (possibly empty) diagnostic info. ) # \s* \Z z0*$z50*$zÚ\A (?: (?P.)? (?P[<>=^]) )? (?P[-+ ])? (?Pz)? (?P\#)? (?P0)? (?P(?!0)\d+)? (?P,)? (?:\.(?P0|(?!0)\d+))? (?P[eEfFgGn%])? \Z có —t |¦«}|€td|z¦«‚| ¦«}|d}|d}|ddu|d<|dr(|td|z¦«‚|td|z¦«‚|pd|d<|pd |d<|d €d|d <t |dpd ¦«|d<|dt |d¦«|d<|ddkr|d |ddvrd|d<|ddkrVd|d<|€tj¦«}|dtd|z¦«‚|d|d<|d|d<|d|d<n|d€d|d<ddg|d<d|d<|S)aÚParse and validate a format specifier. Turns a standard numeric format specifier into a dict, with the following entries: fill: fill character to pad field to minimum width align: alignment type, either '<', '>', '=' or '^' sign: either '+', '-' or ' ' minimumwidth: nonnegative integer giving minimum width zeropad: boolean, indicating whether to pad with zeros thousands_sep: string to use as thousands separator, or '' grouping: grouping for thousands separators, in format used by localeconv decimal_point: string to use for decimal point precision: nonnegative integer giving precision, or None type: one of the characters 'eEfFgG%', or None NzInvalid format specifier: ÚfillÚalignÚzeropadz7Fill character conflicts with '0' in format specifier: z2Alignment conflicts with '0' in format specifier: ú ú>rQrˆÚminimumwidthr„r{r(rpÚgGnr1rBryÚ thousands_sepzJExplicit thousands separator conflicts with 'n' type in format specifier: ÚgroupingÚ decimal_pointr‡rr)Ú_parse_format_specifier_regexÚmatchr¥Ú groupdictr‰Ú_localeÚ localeconv)Úformat_specrwr¬Úformat_dictrr€s r.rr,s5€õ& &×+Ò+¨KÑ8Ô8€AØ€yÝÐ5¸ÑCÑDÔDÐDð—+’+‘-”-€KðvÔ€DØ˜Ô €EØ)¨)Ô4¸DÐ@€K ÑØ9ÔðAØÐÝð6Ø8CñDñEôEð EàÐÝð2Ø4?ñ@ñAôAð Aà˜+ #€KÑð!˜< C€KÑð6ÔÐ"Ø!ˆFÑõ#& k°.Ô&AÐ&HÀSÑ"IÔ"I€KÑØ;ÔÐ+Ý#& {°;Ô'?Ñ#@Ô#@ˆKÑ ð;Ô 1Ò$Ð$ØvÔÐ&¨+°fÔ*=ÀÐ*FÐ*FØ'(ˆK˜Ñ$ð6Ô˜cÒ!Ð!à!ˆFÑØÐÝ!Ô,Ñ.Ô.ˆKØÔ'Ð3Ýð>Ø@KñLñMôMð Mà'2°?Ô'CˆOÑ$Ø"-¨jÔ"9ˆJÑØ'2°?Ô'CˆOÑ$Ð$àÔ'Ð/Ø+-ˆK˜Ñ(Ø#$ a &ˆJÑØ'*ˆOÑ$àÐr0có`—|d}|d}||t|¦«z t|¦«z z}|d}|dkr ||z|z}na|dkr ||z|z}nR|dkr ||z|z}nC|dkr.t|¦«dz}|d |…|z|z||d …z}ntd ¦«‚|S)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). r„rr€úˆˆåÐ7Ñ8Ô8Ð8à€Mr0cóü—ddlm}m}|sgS|ddkr6t|¦«dkr#||dd…||d¦«¦«S|dtjkr |dd…St d¦«‚)zyConvert a localeconv-style grouping into a (possibly infinite) iterable of integers representing group lengths. r()ÚchainÚrepeatrÂr’Nrõz unrecognised format for grouping)Ú itertoolsr—r˜rŸrŒÚCHAR_MAXr¥)r‡r—r˜s r.Ú_group_lengthsr›—sŸ€ð(Ð'Ð'Ð'Ð'Ð'Ð'Ð'Øð=Øˆ Ø "Œ˜Ò Ð s 8™}œ}°Ò1Ð1ØˆuX˜c˜r˜c”] F F¨8°B¬<Ñ$8Ô$8Ñ9Ô9Ð9Ø "ŒÔ)Ò )Ð )Ø˜˜˜Œ}ÐåÐ;Ñ<Ô<ÐÑ?Ô?Ð?å••C˜‘K”K ¨AÑ.Ô.°Ñ2Ô2ˆØ Š c˜1s 6™{œ{™?Ñ+¨f°a°R°S°S¬kÑ9Ñ:Ô:Ð:Ø˜˜!˜˜”ˆØQ‰ˆ Øð ˜) qš.˜.ØˆEØ•S˜‘X”XÑˆ ˆ å•F‘”˜Y¨Ñ*Ô*ˆØ Š c˜1s 6™{œ{™?Ñ+¨f°a°R°S°S¬kÑ9Ñ:Ô:Ð:Ø8Š8•H˜VÑ$Ô$Ñ%Ô%Ð%r0có2—|rdS|ddvr|dSdS)zDetermine sign character.rˆrQz +r‡r,)Úis_negativer„s r.r€r€Ós/€ððØˆsØ ˆfŒ˜Ð Ð ØFŒ|Ðàˆrr0có–—t||¦«}|s|dr|d|z}|dks |ddvr,dddddœ|d}|d ||¦«z }|dd kr|d z }|dr)|dt|¦«z t|¦«z }nd}t|||¦«}t |||z|¦«S) acFormat a number, given the following data: is_negative: true if the number is negative, else false intpart: string of digits that must appear before the decimal point fracpart: string of digits that must come after the point exp: exponent, as an integer spec: dictionary resulting from parsing the format specifier This function uses the information in spec to: insert separators (decimal separator and thousands separators) format the sign format the exponent add trailing '%' for the '%' type zero-pad if necessary fill and align if necessary Úaltrˆr(rpr|rr )rr rzryz{0}{1:+}rxrr„)r€ÚformatrŸr¡r)r£rr®r‹r„rQÚecharržs r.r‚r‚Ýsó€õ$˜ TÑ*Ô*€Dàð44˜”;ð4Ø˜Ô(¨8Ñ3ˆà ˆa‚x€x4˜”< 4Ð'Ð'Ø ¨#°CÐ8Ð8¸¸f¼ÔFˆØJ×%Ò% e¨SÑ1Ô1Ñ1ˆØˆF„|sÒÐØC‰ˆàˆI„ðØ˜Ô(3¨x©=¬=Ñ8½3¸t¹9¼9ÑDˆ ˆ àˆ Ý# G¨T°9Ñ=Ô=€Gå˜˜w xÑ/°Ñ6Ô6Ð6r0ÚInfz-Infr rÂr’r+)F)r()r¥)FF)r1)|r<Ú__all__r9Ú __xname__Ú__version__Ú__libmpdec_version__Úmathr³ÚnumbersryÚsysÚcollectionsr)Ú_namedtuplerÚImportErrorrrrrrrrrr%r&Úmaxsizer!r"r#r$ÚArithmeticErrorrr r rÚZeroDivisionErrorrrrrrr rrrryrrÀrÓr´ÚcontextvarsÚ ContextVarrlÚ frozensetrxrrr r–rrCÚNumberÚregisterrvrr¢r$r‰r¹rªr«rCrErGrPr'r rYr]rRr`rr¿r¬rñrÞrrrÚreÚcompileÚVERBOSEÚ IGNORECASErŠršrsr}ÚDOTALLr‰ÚlocalerŒrrr›r¡r€r‚rrrGrõr½rôrOÚ hash_infoÚmodulusrúrZrørUÚ_PyHASH_NANrùrûr,r0r.úrÄs ðð aðaðF!ð!ð!€ðF € Ø€Ø€àÐàÐÐÐØÐÐÐØ € € € ð&Ø5Ð5Ð5Ð5Ð5Ð5Ø;˜~Ð/EÑFÔF€L€LøØð&ð&ð&Ø%Ð%€L€L€Lð&øøøð€ Ø€ Ø#€Ø€ Ø€Ø€Ø#€Ø € ð€Ø€Ø„;'ÒÐØ!€HØ!€HØ"€H€Hà€HØ€HØ€Hà˜ ™ Ñ#€ ð ð ð ð ð ñ ô ð ð. ð ð ð ð Ðñ ô ð ðððððÐ'ñôðð:ððððÐ'ñôðð%ð%ð%ð%ð%Ð%Ð'8ñ%ô%ð%ð ð ð ð ð Ð)ñ ô ð ð ð ð ð ð Ð(Ð*;ñ ô ð ð ð ð ð ð Ðñ ô ð ðððððÐ%ñôðð ð ð ð ð Ðñ ô ð ð ð ð ð ð Ð ñ ô ð ð#:ð#:ð#:ð#:ð#:ˆw˜ñ#:ô#:ð#:ðL ð ð ð ð ˜ )ñ ô ð ð ð ð ð ð Ð% yñ ô ð ð ^ W¨h¸ØÐ'¨°NðD€ð#Ð#3Ø$Ð%5Ø#Ð$4Ø Ð!1ð3€ð˜}¨o¸}Ø ¨/¸:ðG€ðÐÐÐà-{Ô-Ð.?Ñ@Ô@ÐàiØOÐOÐOñôÐðððð&ð&ð&ðð+ð+ð+ð+ðhw3Kðw3Kðw3Kðw3Kðw3Kˆfñw3Kôw3Kðw3Kðrgðððð& „×Ò˜Ñ!Ô!Ð!ð 'ð 'ð 'ð 'ð 'fñ 'ô 'ð 'ðO$ðO$ðO$ðO$ðO$ˆfñO$ôO$ðO$ðb6@ð@ð@ð@ð@ˆvñ@ô@ð@ð4ðððð< Œ€ð3ð3ð3ð* ð ð ð+ð+ð+ð!ð!ð!ð. ð. ð. ð. ð` 1ð 1ð 1ðD*0ð*0ð*0ðX!&ð!&ð!&ð!&ð!&Fñ!&ô!&ð!&ðF ‘”Ô)€ ð#ð#ð#ð#ðJ"?ð"?ð"?ðH(ð(ð(ðVr ¨°"Ø b˜r¨ð+ð+ð1ð1ð1ð1ððððð&"*ð"*ð"*ð"*ðTØ ˜/Ø˜xÐ)9Ð:ØØ Ø ØØðñô€ðˆwØ ˜Ø˜xÐ)9¸7ÀIÐNØðñô€ð'Ø ˜ØØðñô€ð* € € € Ø ˆ"Œ*ðð"„Z"”-Ññ#!ô!ô""'ð#ð&ˆRŒZ˜Ñ Ô Ô $€ ØˆbŒj˜Ñ Ô Ô&€ð!+ ¤ ð,ð„Z” Ññ!ô!Ðð ð ØÐÐÐÐøØð ð ð Ø€Dð øøøðNðNðNðNð`ððð6=ð=ð=ð.#&ð#&ð#&ð#&ðJððð#7ð#7ð#7ðR ˆGE‰NŒN€ ØG˜F‘O”OÐØ€wˆu~„~€Øˆ‰ Œ €Ø€wˆqz„z€Øˆwr‰{Œ{€ðÐ/Ð0€ð”-Ô'€àŒmÔ€ØŒmÔ€ðB˜¨!Ñ+¨_Ñ=Ô=€ Ø€C€Csœ/¯:¹:Ë%K*Ë*K2Ë1K2