o 0¦iD}ã @spdZgd¢ZeZdZdZdZddlZddlZ ddl Z z ddlmZ e dd ƒZWn ey4d d„ZYnwdZd ZdZdZdZdZdZdZdZdZe jdkrUdZdZdZndZdZdZeedZGdd„deƒZ Gdd„de ƒZ!Gdd „d e ƒZ"Gd!d"„d"e"ƒZ#Gd#d$„d$e e$ƒZ%Gd%d&„d&e"ƒZ&Gd'd(„d(e"e$ƒZ'Gd)d*„d*e ƒZ(Gd+d,„d,e"ƒZ)Gd-d.„d.e ƒZ*Gd/d0„d0e ƒZ+Gd1d2„d2e(e*ƒZ,Gd3d4„d4e(e*e+ƒZ-Gd5d6„d6e e.ƒZ/e!e%e(e,e*e-e"e+e/g Z0e#e"e&e"e'e"e)e"iZ1eeeeeeeefZ2ddl3Z3e3 4d7¡Z5d8d9„Z6d:d;„Z7[3ddd?„d?e9ƒZ:dŽdAdB„Z;e j< =e:¡GdCdD„dDe9ƒZ>GdEdF„dFe9ƒZ?GdGdH„dHe9ƒZ@ddIdJ„ZAeBjCZDdKdL„ZEdMdN„ZFdOdP„ZGdQdR„ZHddTdU„ZIdVdW„ZJdXdY„ZKGdZd[„d[e9ƒZLeLƒjMZNdd\d]„ZOd^d_„ZPd`da„ZQdbdcdddedfdgdhdidjdkœ fdldm„ZRd‘dndo„ZSdŽdpdq„ZTe?dree%e,e"ggdsdtddduZUe?dvee%e,e"e!e-ggdwZVe?dveggdwZWddlXZXeX YdxeXjZeXj[B¡j\Z]eX Ydy¡j\Z^eX Ydz¡j\Z_eX Yd{eXjZeXj`B¡Za[XzddlbZcWn eyêYnwdd|d}„Zdd~d„Zed€d„Zfd’d‚dƒ„Zgd„d…„Zhd†d‡„Zie:dˆƒZje:d‰ƒZke:dŠƒZle:dƒZme:dƒZne:d‹ƒZoejekfZpe jqjrZse jqjtZue jqjvZwexdiesdŒesƒZy[ dS)“a¿ This is an implementation of decimal floating point arithmetic based on the General Decimal Arithmetic Specification: http://speleotrove.com/decimal/decarith.html and IEEE standard 854-1987: http://en.wikipedia.org/wiki/IEEE_854-1987 Decimal floating point has finite precision with arbitrarily large bounds. The purpose of this module is to support arithmetic using familiar "schoolhouse" rules and to avoid some of the tricky representation issues associated with binary floating point. The package is especially useful for financial applications or for contexts where users have expectations that are at odds with binary floating point (for instance, in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead of 0.0; Decimal('1.00') % Decimal('0.1') returns the expected Decimal('0.00')). Here are some examples of using the decimal module: >>> 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_CONTEXTVARZdecimalz1.70z2.4.2éN)Ú namedtuplerzsign digits exponentcGó|S©N©)Úargsr*r*ú1/opt/alt/python310/lib64/python3.10/_pydecimal.pyÚ¤sr-rrrrrrrrTlÿÿÿÿlÿÇNÎZolüÿÿÿÿÇNÎZoi@üTiÀ«æéc@óeZdZdZdd„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. cGsdSr)r*©ÚselfÚcontextr+r*r*r,ÚhandleÓózDecimalException.handleN©Ú__name__Ú __module__Ú__qualname__Ú__doc__r3r*r*r*r,rÀsrc@óeZdZdZdS)ra)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©r6r7r8r9r*r*r*r,r×órc@r/)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. cGs,|rt|dj|djddƒ}| |¡StS)Nr&ÚnT)Ú_dec_from_tripleÚ_signÚ_intÚ_fix_nanÚ_NaN)r1r2r+Úansr*r*r,r3ús zInvalidOperation.handleNr5r*r*r*r,r ãsr c@r/)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]. cGótSr)©rBr0r*r*r,r3r4zConversionSyntax.handleNr5r*r*r*r,rsrc@r/)r a²Division 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. cGst|Sr))Ú_SignedInfinity©r1r2Úsignr+r*r*r,r3szDivisionByZero.handleNr5r*r*r*r,r sr c@r/)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]. cGrDr)rEr0r*r*r,r3"r4zDivisionImpossible.handleNr5r*r*r*r,rórc@r/)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]. cGrDr)rEr0r*r*r,r3-r4zDivisionUndefined.handleNr5r*r*r*r,r%rIrc@r:)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*r*r*r,r0r<rc@r/)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]. cGrDr)rEr0r*r*r,r3Gr4zInvalidContext.handleNr5r*r*r*r,r<s rc@r:)raÙNumber 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*r*r*r,rJr<rc@r:)r a˜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*r*r*r,r Vr<r c@r/)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. cGsŽ|jttttfvr t|S|dkr)|jtkrt|St|d|j|j |jdƒS|dkrE|jt kr6t|St|d|j|j |jdƒSdS)Nr&Ú9r.)ÚroundingrrrrrFrr>ÚprecÚEmaxrrGr*r*r,r3ws"ÿ ÿ ÿýzOverflow.handleNr5r*r*r*r,rasrc@r:)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*r*r*r,r‡r<rc@r:)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*r*r*r,r–r<rZdecimal_contextcCs2zt ¡WStytƒ}t |¡|YSw)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©r2r*r*r,r¼s ýrcCs,|tttfvr| ¡}| ¡t |¡dS)z%Set this thread's context to context.N)rrrÚcopyÚclear_flagsrNrQrRr*r*r,rÊsrcCs|durtƒ}t|ƒS)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 N)rÚ_ContextManager)Úctxr*r*r,rÓs$rc @sneZdZdZdZdòdd„Zedd„ƒZd d „Zdd„Z dód d„Z dd„Zdd„Zdd„Z dôdd„Zdôdd„Zdôdd„Zdôdd„Zdôdd„Zdôdd „Zd!d"„Zd#d$„Zd%d&„Zd'd(„Zdõd*d+„Zdôd,d-„Zdôd.d/„Zdôd0d1„Zdöd3d4„Zdôd5d6„ZeZdôd7d8„Zdôd9d:„Z dôd;d<„Z!e!Z"dôd=d>„Z#d?d@„Z$dôdAdB„Z%dôdCdD„Z&dôdEdF„Z'dôdGdH„Z(dôdIdJ„Z)dôdKdL„Z*dôdMdN„Z+dôdOdP„Z,dQdR„Z-dSdT„Z.e.Z/e0dUdV„ƒZ1e0dWdX„ƒZ2dYdZ„Z3d[d\„Z4d]d^„Z5d_d`„Z6dadb„Z7dcdd„Z8dedf„Z9dgdh„Z:didj„Z;dkdl„Ze?e7e8e9e:e;edqZ@dôdrds„ZAdtdu„ZBdvdw„ZCdôdxdy„ZDdôdzd{„ZEd|d}„ZFdód~d„ZGdôd€d„ZHdôd‚dƒ„ZIdód„d…„ZJdôd†d‡„ZKdˆd‰„ZLdŠd‹„ZMdódŒd„ZNdódŽd„ZOeOZPdôdd‘„ZQdôd’d“„ZRdôd”d•„ZSd–d—„ZTd˜d™„ZUdšd›„ZVdœd„ZWdôdždŸ„ZXdôd d¡„ZYdôd¢d£„ZZd¤d¥„Z[d¦d§„Z\dôd¨d©„Z]dôdªd«„Z^d¬d„Z_d®d¯„Z`d°d±„Zad²d³„Zbdôd´dµ„Zcd¶d·„Zdd¸d¹„Zedºd»„Zfdôd¼d½„Zgd¾d¿„ZhdÀdÁ„ZidôdÂdÃ„ZjdÄdÅ„ZkdôdÆdÇ„ZldôdÈdÉ„ZmdÊdË„ZndÌdÍ„ZodôdÎdÏ„ZpdôdÐdÑ„ZqdôdÒdÓ„ZrdôdÔdÕ„ZsdôdÖd×„ZtdôdØdÙ„ZudôdÚdÛ„ZvdôdÜdÝ„ZwdôdÞdß„Zxdôdàdá„Zydâdã„Zzdôdädå„Z{dôdædç„Z|dôdèdé„Z}dêdë„Z~dìdí„Zdîdï„Z€dódðdñ„ZdS)÷rz,Floating point class for decimal arithmetic.)Ú_expr@r?Ú_is_specialÚ0NcCs|t |¡}t|tƒrt| ¡ dd¡ƒ}|dur'|durtƒ}| t d|¡S| d¡dkr2d|_nd|_| d ¡}|durc| d ¡pDd}t| d¡pLdƒ}tt||ƒƒ|_ |t|ƒ|_d |_|S| d¡}|dur…tt|pqdƒƒ d¡|_ | d¡rd|_n d|_nd|_ d|_d|_|St|tƒr¯|dkrd|_nd|_d|_tt|ƒƒ|_ d |_|St|tƒrÆ|j|_|j|_|j |_ |j|_|St|tƒrà|j|_t|jƒ|_ t|jƒ|_d |_|St|ttfƒrt|ƒdkròtdƒ‚t|dtƒr|ddvstdƒ‚|d|_|ddkrd|_ |d|_d|_|Sg} |dD]+} t| tƒrLd| kr8dkrLntdƒ‚| sE| dkrJ| | ¡q$tdƒ‚|ddvrjd tt| ƒ¡|_ |d|_d|_|St|dtƒr‰d tt| p{dgƒ¡|_ |d|_d |_|Stdƒ‚t|tƒr¸|dur›tƒ}| td¡t |¡}|j|_|j|_|j |_ |j|_|St d|ƒ‚)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: %rrHú-r.r&ÚintZfracÚexprYFÚdiagÚsignalÚNr=ÚFTéztInvalid tuple size in creation of Decimal from list or tuple. The list or tuple should have exactly three elements.©r&r.z|Invalid sign. The first value in the tuple should be an integer; either 0 for a positive number or 1 for a negative number.éé zTThe second value in the tuple must be composed of integers in the range 0 through 9.©r=razUThe 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_errorrÚgroupr?r]r@ÚlenrWrXÚlstripÚabsrÚ_WorkReprHr^ÚlistÚtupleÚ ValueErrorÚappendÚjoinÚmapÚfloatrÚ from_floatÚ TypeError)ÚclsÚvaluer2r1ÚmÚintpartÚfracpartr^r_ÚdigitsZdigitr*r*r,rj sº ÿ ó è&ý € ÷ ý ÿ zDecimal.__new__cCsÈt|tƒr|dkrdnd}d}tt|ƒƒ}n=t|tƒrOt |¡s%t |¡r+|t|ƒƒSt d|¡dkr6d}nd}t|ƒ ¡\}}| ¡d}t|d|ƒ}ntdƒ‚t |||ƒ}|tur`|S||ƒS)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&r.gð?ézargument must be int or float.)rkr]rlrtr|Ú_mathZisinfZisnanÚreprZcopysignÚas_integer_ratioÚ bit_lengthr~r>r)rÚfrHÚkÚcoeffr=ÚdÚresultr*r*r,r} s$ zDecimal.from_floatcCs(|jr|j}|dkrdS|dkrdSdS)zrReturns whether the number is not actually one. 0 if a number 1 if NaN 2 if sNaN r=r.rarer&)rXrW)r1r^r*r*r,Ú_isnanÍszDecimal._isnancCs|jdkr|jr dSdSdS)zyReturns whether the number is infinite 0 if finite or not a number 1 if +INF -1 if -INF rbéÿÿÿÿr.r&)rWr?©r1r*r*r,Ú_isinfinityÜs zDecimal._isinfinitycCs|| ¡}|durd}n| ¡}|s|r<|durtƒ}|dkr%| td|¡S|dkr0| td|¡S|r7| |¡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. NFreÚsNaNr&)rrrpr rA)r1Úotherr2Úself_is_nanÚother_is_nanr*r*r,Ú_check_nansés& ÿÿ zDecimal._check_nanscCsv|durtƒ}|js |jr9| ¡r| td|¡S| ¡r#| td|¡S| ¡r.| td|¡S| ¡r9| 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&)rrXÚis_snanrpr Úis_qnan©r1r”r2r*r*r,Ú_compare_check_nans s0þþþþzDecimal._compare_check_nanscCs|jp|jdkS)zuReturn True if self is nonzero; otherwise return False. NaNs and infinities are considered nonzero. rY©rXr@r‘r*r*r,Ú__bool__*szDecimal.__bool__cCs |js|jr| ¡}| ¡}||krdS||krdSdS|s(|s"dSd|jS|s/d|jS|j|jkr7dS|j|jkr?dS| ¡}| ¡}||krv|jd|j|j}|jd|j|j}||krgdS||krqd|jSd|jS||krd|jSd|jS)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&rr.rY)rXr’r?Úadjustedr@rW)r1r”Zself_infZ other_infÚ self_adjustedZother_adjustedÚself_paddedZother_paddedr*r*r,Ú_cmp1s> zDecimal._cmpcCs<t||dd\}}|tur|S| ||¡rdS| |¡dkS)NT)Úequality_opFr&)Ú_convert_for_comparisonÚNotImplementedr—r¡ršr*r*r,Ú__eq__qszDecimal.__eq__cCs<t||ƒ\}}|tur |S| ||¡}|rdS| |¡dkS©NFr&©r£r¤r›r¡©r1r”r2rCr*r*r,Ú__lt__yózDecimal.__lt__cCs<t||ƒ\}}|tur |S| ||¡}|rdS| |¡dkSr¦r§r¨r*r*r,Ú__le__‚rªzDecimal.__le__cCs<t||ƒ\}}|tur |S| ||¡}|rdS| |¡dkSr¦r§r¨r*r*r,Ú__gt__‹rªzDecimal.__gt__cCs<t||ƒ\}}|tur |S| ||¡}|rdS| |¡dkSr¦r§r¨r*r*r,Ú__ge__”rªzDecimal.__ge__cCs>t|dd}|js|r|jr| ||¡}|r|St| |¡ƒS)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_otherrXr—rr¡r¨r*r*r,ÚcompareszDecimal.comparecCs–|jr| ¡rtdƒ‚| ¡rt |¡S|jrtStS|jdkr)t d|jt ƒ}nt t|jt ƒ}t|j ƒ|t }|dkr@|n|}|dkrIdS|S)zx.__hash__() <==> hash(x)z"Cannot hash a signaling NaN value.r&é réþÿÿÿ)rXr˜r~Úis_nanriÚ__hash__r?Ú_PyHASH_INFrWÚpowÚ_PyHASH_MODULUSÚ _PyHASH_10INVr]r@)r1Zexp_hashZhash_rCr*r*r,rµ¯s zDecimal.__hash__cCst|jttt|jƒƒ|jƒS)zeRepresents the number as a triple tuple. To show the internals exactly as they are. )rr?rwr{r]r@rWr‘r*r*r,Úas_tupleÉszDecimal.as_tuplecCsä|jr| ¡rtdƒ‚tdƒ‚|sdSt|jƒ}|jdkr(|d|jd}}n@|j}|dkrH|ddkrH|d}|d8}|dkrH|ddks6|j}t||@ ¡d|ƒ}|rb||L}||8}d||>}|j rn|}||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 ratiordr&r²r.r…) rXr´rxÚ OverflowErrorr]r@rWÚminr‰r?)r1r=rZd5Zd2Zshift2r*r*r,rˆÐs. þzDecimal.as_integer_ratiocCsdt|ƒS)z0Represents the number as an instance of Decimal.z Decimal('%s'))rlr‘r*r*r,Ú__repr__szDecimal.__repr__Fc Cs^ddg|j}|jr&|jdkr|dS|jdkr|d|jS|d|jS|jt|jƒ}|jdkr:|d kr:|}n|s?d }n|jdkrM|d dd }n|d dd }|dkrfd}d d||j}n&|t|jƒkr||jd|t|jƒ}d}n|jd|…}d |j|d…}||kr“d}n|durštƒ}ddg|jd||}||||S)z–Return string representation of the number in scientific notation. Captures all of the information in the underlying representation. r[r\rbZInfinityr=ÚNaNr“r&éúÿÿÿr.rYrcÚ.NÚeÚEz%+d)r?rXrWr@rrrÚcapitals) r1Úengr2rHÚ leftdigitsÚdotplacer‚rƒr^r*r*r,Ú__str__s: zDecimal.__str__cCs|jd|dS)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)rÄr2)rÇ©r1r2r*r*r,Ú to_eng_string;szDecimal.to_eng_stringcCsR|jr |j|d}|r |S|durtƒ}|s |jtkr | ¡}n| ¡}| |¡S)zRReturns a copy with the sign switched. Rounds, if it has reason. rRN)rXr—rrKrÚcopy_absÚcopy_negateÚ_fix©r1r2rCr*r*r,Ú__neg__Ds zDecimal.__neg__cCsR|jr |j|d}|r |S|durtƒ}|s |jtkr | ¡}nt|ƒ}| |¡S)zhReturns a copy, unless it is a sNaN. Rounds the number (if more than precision digits) rRN)rXr—rrKrrÊrrÌrÍr*r*r,Ú__pos__Zs zDecimal.__pos__TcCsL|s| ¡S|jr|j|d}|r|S|jr|j|d}|S|j|d}|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(). rR)rÊrXr—r?rÎrÏ)r1Úroundr2rCr*r*r,Ú__abs__osþzDecimal.__abs__c Cs\t|ƒ}|tur |S|durtƒ}|js|jrA| ||¡}|r!|S| ¡r9|j|jkr5| ¡r5| td¡St |ƒS| ¡rAt |ƒSt |j|jƒ}d}|jt krW|j|jkrWd}|ss|sst |j|jƒ}|rfd}t|d|ƒ}| |¡}|S|sŽt||j|jdƒ}| ||j¡}| |¡}|S|s©t||j|jdƒ}| ||j¡}| |¡}|St|ƒ}t|ƒ}t|||jƒ\}}tƒ} |j|jkr÷|j|jkrÖt|d|ƒ}| |¡}|S|j|jkrá||}}|jdkród| _|j|j|_|_nd| _n|jdkrd| _d\|_|_nd| _|jdkr|j|j| _n|j|j| _|j| _t | ƒ}| |¡}|S)zbReturns self + other. -INF + INF (or the reverse) cause InvalidOperation errors. Nz -INF + INFr&r.rY)r&r&)r°r¤rrXr—r’r?rpr rr¼rWrKrr>rÌÚmaxrLÚ_rescaleruÚ _normalizerHr]r^) r1r”r2rCr^ZnegativezerorHÚop1Úop2rŽr*r*r,Ú__add__…s| zDecimal.__add__cCsHt|ƒ}|tur |S|js|jr|j||d}|r|S|j| ¡|dS)zReturn self - otherrR)r°r¤rXr—r×rËr¨r*r*r,Ú__sub__ÝszDecimal.__sub__cCó"t|ƒ}|tur |S|j||dS)zReturn other - selfrR)r°r¤rØršr*r*r,Ú__rsub__ëszDecimal.__rsub__cCs>t|ƒ}|tur |S|durtƒ}|j|jA}|js|jrG| ||¡}|r'|S| ¡r7|s3| td¡St |S| ¡rG|sC| td¡St |S|j |j }|rQ|s^t|d|ƒ}| |¡}|S|j dkrqt||j |ƒ}| |¡}|S|j dkr„t||j |ƒ}| |¡}|St|ƒ}t|ƒ}t|t|j|jƒ|ƒ}| |¡}|S)z\Return self * other. (+-) INF * 0 (or its reverse) raise InvalidOperation. Nz(+-)INF * 0z0 * (+-)INFrYÚ1)r°r¤rr?rXr—r’rpr rFrWr>rÌr@rurlr])r1r”r2Z resultsignrCZ resultexprÕrÖr*r*r,Ú__mul__ósH zDecimal.__mul__cCsÌt|ƒ}|tur tS|durtƒ}|j|jA}|js|jrO| ||¡}|r'|S| ¡r5| ¡r5| td¡S| ¡r=t |S| ¡rO| t d¡t|d| ¡ƒS|s`|sY| t d¡S| td|¡S|sk|j|j}d}nnt|jƒt|jƒ|jd}|j|j|}t|ƒ}t|ƒ} |dkrœt|jd || jƒ\}} nt|j| jd |ƒ\}} | r·|d dkr¶|d7}n"|j|j}||krÙ|d dkrÙ|d }|d7}||krÙ|d dksÇt|t|ƒ|ƒ}| |¡S)zReturn self / other.Nz(+-)INF/(+-)INFzDivision by infinityrYz0 / 0zx / 0r&r.r²r…)r°r¤rr?rXr—r’rpr rFrr>ÚEtinyrr rWrrr@rLruÚdivmodr]rlrÌ)r1r”r2rHrCr^rŒÚshiftrÕrÖÚ remainderÚ ideal_expr*r*r,Ú__truediv__,sT€þ zDecimal.__truediv__cCs|j|jA}| ¡r|j}nt|j|jƒ}| ¡| ¡}|r'| ¡s'|dkr4t|ddƒ| ||j¡fS||jkrƒt |ƒ}t |ƒ}|j |j krU|jd|j |j 9_n |jd|j |j 9_t|j|jƒ\}} |d|jkrƒt|t |ƒdƒt|jt | ƒ|ƒfS| 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. r³rYr&r²z%quotient too large in //, % or divmod)r?r’rWr¼ržr>rÓrKrLrur^r]rÞrlrpr)r1r”r2rHráÚexpdiffrÕrÖÚqÚrrCr*r*r,Ú_dividegs0 ÿ ÿÿzDecimal._dividecCrÙ)z)Swaps self/other and returns __truediv__.rR)r°r¤râršr*r*r,Ú__rtruediv__ˆózDecimal.__rtruediv__cCsÖt|ƒ}|tur |S|durtƒ}| ||¡}|r||fS|j|jA}| ¡r?| ¡r5| td¡}||fSt|| td¡fS|sZ|sM| t d¡}||fS| t d|¡| td¡fS| ||¡\}}| |¡}||fS)z6 Return (self // other, self % other) Nzdivmod(INF, INF)úINF % xzdivmod(0, 0)úx // 0úx % 0) r°r¤rr—r?r’rpr rFrr rærÌ)r1r”r2rCrHZquotientràr*r*r,Ú __divmod__s4 ÿ ÿ zDecimal.__divmod__cCrÙ)z(Swaps self/other and returns __divmod__.rR)r°r¤rìršr*r*r,Ú__rdivmod__³rèzDecimal.__rdivmod__cCsˆt|ƒ}|tur |S|durtƒ}| ||¡}|r|S| ¡r%| td¡S|s5|r/| td¡S| td¡S| ||¡d}| |¡}|S)z self % other Nrérëz0 % 0r.) r°r¤rr—r’rpr rrærÌ)r1r”r2rCràr*r*r,Ú__mod__ºs" zDecimal.__mod__cCrÙ)z%Swaps self/other and returns __mod__.rR)r°r¤rîršr*r*r,Ú__rmod__ÕrèzDecimal.__rmod__cCsÈ|durtƒ}t|dd}| ||¡}|r|S| ¡r!| td¡S|s1|r+| td¡S| td¡S| ¡r>t|ƒ}| |¡St |j |j ƒ}|sSt|jd|ƒ}| |¡S| ¡| ¡}||jdkrg| t¡S|d krw| ||j¡}| |¡St|ƒ}t|ƒ}|j|jkr“|jd |j|j9_n |jd |j|j9_t|j|jƒ\}} d| |d@|jkr½| |j8} |d7}|d |jkrÉ| t¡S|j} | dkr×d| } | } t| t| ƒ|ƒ}| |¡S) zI Remainder nearest to 0- abs(remainder-near) <= other/2 NTr®zremainder_near(infinity, x)zremainder_near(x, 0)zremainder_near(0, 0)rYr.r³r²rer&)rr°r—r’rpr rrrÌr¼rWr>r?ržrLrrÓrKrur^r]rÞrl)r1r”r2rCÚideal_exponentrãrÕrÖrärårHr*r*r,Úremainder_nearÜs`ÿÿÿ zDecimal.remainder_nearcCsœt|ƒ}|tur |S|durtƒ}| ||¡}|r|S| ¡r1| ¡r)| td¡St|j|jAS|sF|r@| t d|j|jA¡S| t d¡S| ||¡dS)z self // otherNz INF // INFrêz0 // 0r&)r°r¤rr—r’rpr rFr?r rrær¨r*r*r,Ú__floordiv__'s& ÿzDecimal.__floordiv__cCrÙ)z*Swaps self/other and returns __floordiv__.rR)r°r¤ròršr*r*r,Ú __rfloordiv__CrèzDecimal.__rfloordiv__cCs>| ¡r| ¡rtdƒ‚|jrdnd}t|ƒSt|ƒ}t|ƒS)zFloat representation.z%Cannot convert signaling NaN to floatz-nanÚnan)rr˜rxr?rlr|©r1Úsr*r*r,Ú __float__JsÿzDecimal.__float__cCsn|jr| ¡rtdƒ‚| ¡rtdƒ‚d|j}|jdkr)|t|jƒd|jS|t|jd|j…p4dƒS)z1Converts self to an int, truncating if necessary.zCannot convert NaN to integerz"Cannot convert infinity to integerrr&r²NrY) rXrrxr’r»r?rWr]r@rõr*r*r,Ú__int__Ts zDecimal.__int__cCr(r)r*r‘r*r*r,ÚrealcszDecimal.realcCótdƒS)Nr&©rr‘r*r*r,ÚimaggózDecimal.imagcCr(r)r*r‘r*r*r,Ú conjugatekr4zDecimal.conjugatecCstt|ƒƒSr))Úcomplexr|r‘r*r*r,Ú__complex__nózDecimal.__complex__cCsR|j}|j|j}t|ƒ|kr%|t|ƒ|d… d¡}t|j||jdƒSt|ƒS)z2Decapitate the payload of a NaN to fit the contextNrYT) r@rLÚclamprrrsr>r?rWr)r1r2ZpayloadZmax_payload_lenr*r*r,rAqszDecimal._fix_nancCs@|jr| ¡r| |¡St|ƒS| ¡}| ¡}|s@|j|g|j}tt |j |ƒ|ƒ}||j kr<| t¡t |jd|ƒSt|ƒSt|jƒ|j |j}||krc| td|j¡}| t¡| t¡|S||k}|rk|}|j |krót|jƒ|j |} | dkr‰t |jd|dƒ}d} |j|j} | || ƒ}|jd| …pœd}|dkrºtt|ƒdƒ}t|ƒ|jkrº|dd…}|d7}||krÇ| td|j¡}nt |j||ƒ}|r×|r×| t¡|rÞ| t¡|rå| t¡| t¡|sñ| t¡|S|rú| t¡|jdkr|j |kr| t¡|jd|j |} t |j| |ƒSt|ƒS)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. rYú above Emaxr&rÛr.Nr)rXrrArrÝÚEtoprMrr¼rÒrWrprr>r?rrr@rLrrrÚ_pick_rounding_functionrKrlr]rr )r1r2rÝrÚexp_maxZnew_expZexp_minrCZself_is_subnormalr„Zrounding_methodÚchangedrŒr r*r*r,rÌ}sn zDecimal._fixcCst|j|ƒrdSdS)z(Also known as round-towards-0, truncate.r&r)Ú _all_zerosr@©r1rLr*r*r,Ú_round_downãszDecimal._round_downcCs| |¡S)zRounds away from 0.)r r r*r*r,Ú _round_upêszDecimal._round_upcCs&|j|dvr dSt|j|ƒrdSdS)zRounds 5 up (away from 0)Z56789r.r&r)r@rr r*r*r,Ú_round_half_upîs zDecimal._round_half_upcCst|j|ƒrdS| |¡S)zRound 5 downr©Ú_exact_halfr@rr r*r*r,Ú_round_half_down÷s zDecimal._round_half_downcCs4t|j|ƒr|dks|j|ddvrdS| |¡S)z!Round 5 to even, rest to nearest.r&r.Ú02468rr r r*r*r,Ú_round_half_evenþs zDecimal._round_half_evencCs|jr| |¡S| |¡S)z(Rounds up (not away from 0 if negative.)©r?r r r*r*r,Ú_round_ceilingó zDecimal._round_ceilingcCs|js| |¡S| |¡S)z'Rounds down (not towards 0 if negative)rr r*r*r,Ú_round_floor rzDecimal._round_floorcCs,|r|j|ddvr| |¡S| |¡S)z)Round down unless digit prec-1 is 0 or 5.r.Z05)r@r r r*r*r,Ú_round_05ups zDecimal._round_05up)rrrrrrrrcCs`|durt|tƒs tdƒ‚tdd|ƒ}| |¡S|jr(| ¡r$tdƒ‚tdƒ‚t| dt ¡ƒS)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&rÛúcannot round a NaNúcannot round an infinity)rkr]r~r>ÚquantizerXr´rxr»rÓr)r1r=r^r*r*r,Ú __round__&s/ zDecimal.__round__cCó.|jr| ¡rtdƒ‚tdƒ‚t| dt¡ƒS)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. rrr&)rXr´rxr»r]rÓrr‘r*r*r,Ú __floor__dó zDecimal.__floor__cCr)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. rrr&)rXr´rxr»r]rÓrr‘r*r*r,Ú__ceil__srzDecimal.__ceil__cCst|dd}t|dd}|js|jrm|durtƒ}|jdkr%| td|¡S|jdkr1| td|¡S|jdkr9|}nL|jdkrA|}nD|jdkrW|sN| td¡St|j|jA}n.|jdkrl|sd| td ¡St|j|jA}nt|j|jAt t |jƒt |jƒƒ|j|jƒ}| ||¡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. Tr®Nrar“r=rbzINF * 0 in fmaz0 * INF in fma) r°rXrrWrpr rFr?r>rlr]r@r×)r1r”Zthirdr2Úproductr*r*r,Úfma‚s> ÿ ÿ€ þzDecimal.fmacCsÆt|ƒ}|tur |St|ƒ}|tur|S|durtƒ}| ¡}| ¡}| ¡}|s-|s-|ra|dkr8| td|¡S|dkrC| td|¡S|dkrN| td|¡S|rU| |¡S|r\| |¡S| |¡S| ¡rm| ¡rm| ¡ss| td¡S|dkr}| td¡S|s…| td¡S| ¡|j kr’| td¡S|sœ|sœ| td ¡S| ¡r£d}n|j}tt |ƒƒ}t| ¡ƒ}t| ¡ƒ} |j |td |j|ƒ|}t| jƒD]} t|d |ƒ}qËt|| j |ƒ}t|t|ƒdƒS)z!Three argument version of __pow__Nrer“z@pow() 3rd argument not allowed unless all arguments are integersr&zApow() 2nd argument cannot be negative when 3rd argument specifiedzpow() 3rd argument cannot be 0zSinsufficient precision: pow() 3rd argument must not have more than precision digitszXat least one of pow() 1st argument and 2nd argument must be nonzero; 0**0 is not definedr²)r°r¤rrrpr rAÚ _isintegerržrLÚ_isevenr?rtr]ruÚto_integral_valuer·r^Úranger>rl)r1r”Úmodulor2r•r–Z modulo_is_nanrHÚbaseÚexponentÚir*r*r,Ú _power_modulo®s€ÿÿÿ ÿþÿÿÿÿÿzDecimal._power_modulocCsRt|ƒ}|j|j}}|ddkr|d}|d7}|ddkst|ƒ}|j|j}}|ddkr>|d}|d7}|ddks0|dkr–||9}|ddkrZ|d}|d7}|ddksL|dkr`dS|d|} |jdkrn| } | ¡rˆ|jdkrˆ|jt|ƒ} t| | |dƒ}nd}tddd|| |ƒS|jdkrf|d}|dvræ||@|krdSt |ƒd} |dd }|t t|ƒƒkrÃdSt| ||ƒ} t|||ƒ}| dusÙ|durÛdS| |krádSd | }nj|d krNt |ƒdd } t d | |ƒ\}}|rdS|d dkr|d }| d8} |d dks|dd}|t t|ƒƒkr(dSt| ||ƒ} t|||ƒ}| dus@|durBdS| |krIdSd | }ndS|d|krYdS| |}tdt|ƒ|ƒS|dkru|d|d}}nŒ|dkrŠt tt||ƒƒƒ|krŠdSt |ƒ}|dkr£t tt|ƒ|ƒƒ|kr£dS|d|}}|d |d kr»dkrÖnn|d }|d }|d |d krÕdks½n|d |d krædkrnn|d }|d }|d |d krdksèn|dkrV|dkr||krdSt ||ƒ\}}|dkr dSdt |ƒ|>} t |||dƒ\}}||krÚ_nbitsrrrlÚ_decimal_lshift_exactrÞrtÚ _log10_lb)r1r”ÚpÚxÚxcÚxeÚyÚycÚyer'rðZzerosZ last_digitrÁZemaxràrr=Zxc_bitsÚremÚaräråZstr_xcr*r*r,Ú_power_exactsà:þþþ þ &&$"þ$"þ û zDecimal._power_exactcCs(|dur| |||¡St|ƒ}|tur|S|durtƒ}| ||¡}|r&|S|s2|s0| td¡StSd}|jdkrP| ¡rD| ¡sCd}n|rL| td¡S| ¡}|sa|jdkr]t|ddƒSt |S| ¡rt|jdkrnt |St|ddƒS|tkrÂ| ¡r¨|jdkr„d}n ||jkr|j}nt|ƒ}|j|}|d|jkr§d|j}| t¡n| t¡| t¡d|j}t|dd||ƒS| ¡}| ¡rÝ|jdk|dkkrÙt|ddƒSt |Sd}d} | ¡| ¡} |dk|jdkkr| tt|jƒƒkrt|d|jdƒ}n| ¡}| tt|ƒƒkrt|d|dƒ}|dur?| ||jd¡}|dur?|dkr=td|j|jƒ}d } |dur•|j}t|ƒ} | j| j}}t|ƒ}|j|j}}|jdkrf|}d } t||||||ƒ\}}|ddtt|ƒƒ|dr‡n|d 7}qit|t|ƒ|ƒ}| r | ¡s t|jƒ|jkr¿|jdt|jƒ}t|j|jd||j|ƒ}| ¡}| !¡t"D]}d|j#|<qÉ| $|¡}| t¡|j%t&rç| t'¡|j%t(rõ| t(d |j¡t't&ttt)fD]}|j%|r | |¡qü|S| $|¡}|S)aHReturn self ** other [ % modulo]. With two arguments, compute self**other. With three arguments, compute (self**other) % modulo. For the three argument form, the following restrictions on the arguments hold: - all three arguments must be integral - other must be nonnegative - either self or other (or both) must be nonzero - modulo must be nonzero and must have at most p digits, where p is the context precision. If any of these restrictions is violated the InvalidOperation flag is raised. The result of pow(self, other, modulo) is identical to the result that would be obtained by computing (self**other) % modulo with unbounded precision, but is computed more efficiently. It is always exact. Nz0 ** 0r&r.z+x ** y with x negative and y not an integerrYrÛFTrcr…r²r)*r)r°r¤rr—rpr Ú_Oner?r!r"rËr>rFr’rLr]rWrrržÚ_log10_exp_boundrrrlrMrÝr=r@rur^rHÚ_dpowerrSrTÚ_signalsÚtrapsrÌÚflagsr rrr)r1r”r%r2rCZresult_signZ multiplierr^Zself_adjÚexactZboundrÝr4r5r6r7r8r9r:ÚextrarŒrãZ newcontextZ exceptionr*r*r,Ú__pow__ðsÚ €ÿ € € "üÿ € þzDecimal.__pow__cCrÙ)z%Swaps self/other and returns __pow__.rR)r°r¤rFršr*r*r,Ú__rpow__È rèzDecimal.__rpow__cCsÐ|durtƒ}|jr|j|d}|r|S| |¡}| ¡r|S|s(t|jddƒS|j| ¡g|j }t |jƒ}|j}|j|ddkr\||kr\|d7}|d8}|j|ddkr\||ksGt|j|jd|…|ƒS)z?Normalize- strip trailing 0s, change anything equal to 0 to 0e0NrRrYr&r.) rrXr—rÌr’r>r?rMrrrrr@rW)r1r2rCÚduprÚendr^r*r*r,Ú normalizeÏ s& þzDecimal.normalizecCs˜t|dd}|dur tƒ}|dur|j}|js|jr>| ||¡}|r$|S| ¡s,| ¡r>| ¡r8| ¡r8t|ƒS| td¡S| ¡|j krL|jksSn| td¡S|sbt|j d|j ƒ}| |¡S| ¡}||jkrq| td¡S||j d|jkr| td ¡S| |j |¡}| ¡|jkr•| td¡St|jƒ|jkr£| td ¡S|r±| ¡|jkr±| t¡|j |j krÅ||krÀ| 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. Tr®Nzquantize with one INFz)target exponent out of bounds in quantizerYz9exponent of quantize result too large for current contextr.z7quantize result has too many digits for current context)r°rrKrXr—r’rrpr rÝrWrMr>r?rÌržrLrÓrrr@ÚEminr rr)r1r^rKr2rCrŸr*r*r,rè s`ÿÿ ÿÿÿÿ zDecimal.quantizecCsDt|dd}|js|jr| ¡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. Tr®)r°rXr´Úis_infiniterWršr*r*r,Úsame_quantum% s ÿzDecimal.same_quantumcCsÆ|jrt|ƒS|st|jd|ƒS|j|kr$t|j|jd|j||ƒSt|jƒ|j|}|dkr=t|jd|dƒ}d}|j|}|||ƒ}|jd|…pOd}|dkr\tt |ƒdƒ}t|j||ƒS)asRescale self so that the exponent is exp, either by padding with zeros or by truncating digits, using the given rounding mode. Specials are returned without change. This operation is quiet: it raises no flags, and uses no information from the context. exp = exp to scale to (an integer) rounding = rounding mode rYr&rÛr.N) rXrr>r?rWr@rrrrlr])r1r^rKr„Z this_functionrrŒr*r*r,rÓ4 s$ ÿ zDecimal._rescalecCsf|dkrtdƒ‚|js |st|ƒS| | ¡d||¡}| ¡| ¡kr1| | ¡d||¡}|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 _roundr.)rxrXrrÓrž)r1ÚplacesrKrCr*r*r,Ú_roundV s zDecimal._roundcCsŽ|jr|j|d}|r |St|ƒS|jdkrt|ƒS|s#t|jddƒS|dur*tƒ}|dur1|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. rRr&rYN)rXr—rrWr>r?rrKrÓrprr©r1rKr2rCr*r*r,Úto_integral_exactm s$ zDecimal.to_integral_exactcCs\|durtƒ}|dur|j}|jr|j|d}|r|St|ƒS|jdkr(t|ƒS| d|¡S)z@Rounds to the nearest integer, without raising inexact, rounded.NrRr&)rrKrXr—rrWrÓrPr*r*r,r#Š s zDecimal.to_integral_valuecCsÐ|durtƒ}|jr!|j|d}|r|S| ¡r!|jdkr!t|ƒS|s2t|jd|jdƒ}| |¡S|jdkr=| t d¡S|jd}t|ƒ}|j d?}|j d@r_|jd}t|jƒd?d}n|j}t|jƒdd?}||}|dkr||d |9}d } n t|d |ƒ\}} | } ||8}d|} ||}||kr›n||d?}q’| o©|||k} | rÃ|dkr·|d|}n|d|9}||7}n |ddkrÍ|d7}tdt|ƒ|ƒ}| ¡}| t¡} | |¡}| |_|S)zReturn the square root of self.NrRr&rYrer.zsqrt(-x), x > 0r²r0Tr…)rrXr—r’r?rr>rWrÌrpr rLrur^r]rrr@rÞrlÚ _shallow_copyÚ _set_roundingrrK)r1r2rCrLÚoprÁÚcÚlrßrDràr=rärKr*r*r,Úsqrt sb û zDecimal.sqrtcCs¶t|dd}|dur tƒ}|js|jr?| ¡}| ¡}|s|r?|dkr,|dkr,| |¡S|dkr9|dkr9| |¡S| ||¡S| |¡}|dkrM| |¡}|dkrT|}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. Tr®Nr.r&r©r°rrXrrÌr—r¡Ú compare_total©r1r”r2ZsnZonrUrCr*r*r,rÒs& zDecimal.maxcCs¶t|dd}|dur tƒ}|js|jr?| ¡}| ¡}|s|r?|dkr,|dkr,| |¡S|dkr9|dkr9| |¡S| ||¡S| |¡}|dkrM| |¡}|dkrT|}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. Tr®Nr.r&rrXrZr*r*r,r¼*s& zDecimal.mincCs8|jrdS|jdkrdS|j|jd…}|dt|ƒkS)z"Returns whether self is an integerFr&TNrY)rXrWr@rr)r1Úrestr*r*r,r!Ls zDecimal._isintegercCs&|r|jdkr dS|jd|jdvS)z:Returns True if self is even. Assumes self is an integer.r&Trr)rWr@r‘r*r*r,r"UszDecimal._isevencCs,z|jt|jƒdWStyYdSw)z$Return the adjusted exponent of selfr.r&)rWrrr@r~r‘r*r*r,rž[s ÿzDecimal.adjustedcCr()z«Returns the same Decimal object. As we do not have different encodings for the same number, the received object already is in its canonical form. r*r‘r*r*r,Ú canonicalcózDecimal.canonicalcCs.t|dd}| ||¡}|r|S|j||dS)z¶Compares self to the other operand numerically. It's pretty much like compare(), but all NaNs signal, with signaling NaNs taking precedence over quiet NaNs. Tr®rR)r°r›r±r¨r*r*r,Úcompare_signalks zDecimal.compare_signalcCsPt|dd}|jr|jstS|js|jrtS|j}| ¡}| ¡}|s%|r‚||krOt|jƒ|jf}t|jƒ|jf}||krC|rAtStS||krM|rKtStStS|rj|dkrWtS|dkr]tS|dkrctS|dkritSn|dkrptS|dkrvtS|dkr|tS|dkr‚tS||krˆtS||krŽtS|j|jkrš|r˜tStS|j|jkr¦|r¤tStStS)zõCompares self to other using the abstract representations. This is not like the standard compare, which use their numerical value. Note that a total ordering is defined for all possible abstract representations. Tr®r.re) r°r?Ú_NegativeOner>rrrr@Ú_ZerorW)r1r”r2rHZself_nanZ other_nanZself_keyZ other_keyr*r*r,rYwshÿzDecimal.compare_totalcCs&t|dd}| ¡}| ¡}| |¡S)z–Compares self to other using abstract repr., ignoring sign. Like compare_total, but with operand's sign ignored and assumed to be 0. Tr®)r°rÊrY)r1r”r2röÚor*r*r,Úcompare_total_magÀs zDecimal.compare_total_magcCstd|j|j|jƒS)z'Returns a copy with the sign set to 0. r&)r>r@rWrXr‘r*r*r,rÊËózDecimal.copy_abscCs.|jr td|j|j|jƒStd|j|j|jƒS)z&Returns a copy with the sign inverted.r&r.)r?r>r@rWrXr‘r*r*r,rËÏszDecimal.copy_negatecCs"t|dd}t|j|j|j|jƒS)z$Returns self with the sign of other.Tr®)r°r>r?r@rWrXršr*r*r,Ú copy_signÖs ÿzDecimal.copy_signcCsÜ|durtƒ}|j|d}|r|S| ¡dkrtS|stS| ¡dkr't|ƒS|j}| ¡}|jdkrJ|t t |jddƒƒkrJtdd|jdƒ}n‘|jdkri|t t | ¡ddƒƒkritdd| ¡dƒ}nr|jdkrƒ||krƒtddd|dd|ƒ}nX|jdkr||dkrtdd |d|dƒ}n>t|ƒ}|j|j}}|jdkr°|}d} t||||ƒ\} } | ddt t | ƒƒ|drÎn|d7}q³tdt | ƒ| ƒ}| ¡}| t¡}| |¡}||_|S) zReturns e ** self.NrRrr.r&rcrÛrYrJTr…r²)rr—r’r`r>rrLržr?rrrlrMr>rÝrur]r^rHÚ_dexprRrSrrÌrK)r1r2rCr4ÚadjrTrUrÁrErŒr^rKr*r*r,r^ÜsL$( ü zDecimal.expcCsdS)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*r‘r*r*r,Úis_canonical'r]zDecimal.is_canonicalcCs|jS)zReturn True if self is finite; otherwise return False. A Decimal instance is considered finite if it is neither infinite nor a NaN. )rXr‘r*r*r,Ú is_finite/ózDecimal.is_finitecCó |jdkS)z8Return True if self is infinite; otherwise return False.rb©rWr‘r*r*r,rL7ó zDecimal.is_infinitecCs |jdvS)z>Return True if self is a qNaN or sNaN; otherwise return False.rgrkr‘r*r*r,r´;rlzDecimal.is_nancCs*|js|sdS|durtƒ}|j| ¡kS)z?Return True if self is a normal number; otherwise return False.FN)rXrrKržrÈr*r*r,Ú is_normal?ó zDecimal.is_normalcCrj)z;Return True if self is a quiet NaN; otherwise return False.r=rkr‘r*r*r,r™GrlzDecimal.is_qnancCrj)z8Return True if self is negative; otherwise return False.r.)r?r‘r*r*r,Ú is_signedKrlzDecimal.is_signedcCrj)z?Return True if self is a signaling NaN; otherwise return False.rarkr‘r*r*r,r˜OrlzDecimal.is_snancCs*|js|sdS|durtƒ}| ¡|jkS)z9Return True if self is subnormal; otherwise return False.FN)rXrržrKrÈr*r*r,Úis_subnormalSrnzDecimal.is_subnormalcCs|jo|jdkS)z6Return True if self is a zero; otherwise return False.rYrœr‘r*r*r,Úis_zero[szDecimal.is_zerocCsÆ|jt|jƒd}|dkrtt|ddƒƒdS|dkr,ttd|ddƒƒdSt|ƒ}|j|j}}|dkrTt|d|ƒ}t|ƒ}t|ƒt|ƒ||kS|ttd||ƒƒdS)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. r.ér²r³rr&©rWrrr@rlrur]r^©r1rfrTrUrÁÚnumZdenr*r*r,Ú _ln_exp_bound_szDecimal._ln_exp_boundc Cs |durtƒ}|j|d}|r|S|stS| ¡dkrtS|tkr#tS|jdkr.| t d¡St |ƒ}|j|j}}|j }|| ¡d} t|||ƒ}|ddttt|ƒƒƒ|dr^n|d 7}qEtt|d kƒtt|ƒƒ|ƒ}| ¡}| t¡} | |¡}| |_|S)z/Returns the natural (base e) logarithm of self.NrRr.zln of a negative valuereTr…r²rcr&)rr—Ú_NegativeInfinityr’Ú _Infinityr>r`r?rpr rur]r^rLrvÚ_dlogrrrlrtr>rRrSrrÌrK© r1r2rCrTrUrÁr4rNrŒrKr*r*r,Úlnxs> ÿ$û z Decimal.lncCsÊ|jt|jƒd}|dkrtt|ƒƒdS|dkr$ttd|ƒƒdSt|ƒ}|j|j}}|dkrPt|d|ƒ}td|ƒ}t|ƒt|ƒ||kdStd||ƒ}t|ƒ||dkdS) zÎCompute a lower bound for the adjusted exponent of self.log10(). In other words, find r such that self.log10() >= 10**r. Assumes that self is finite and positive and that self != 1. r.r³rr&r²éçreZ231rsrtr*r*r,r?ªszDecimal._log10_exp_boundc CsF|durtƒ}|j|d}|r|S|stS| ¡dkrtS|jdkr(| td¡S|jddkrL|jdd…dt |jƒdkrLt |jt |jƒdƒ}nDt|ƒ}|j |j}}|j}|| ¡d} t|||ƒ}|d dt tt|ƒƒƒ|dr|n|d7}qctt |dkƒtt|ƒƒ|ƒ}| ¡}| t¡} | |¡}| |_|S) z&Returns the base 10 logarithm of self.NrRr.zlog10 of a negative valuer&rÛrYreTr…r²rc)rr—rwr’rxr?rpr r@rrrrWrur]r^rLr?Ú_dlog10rlrtr>rRrSrrÌrKrzr*r*r,Úlog10Ès> ÿ.$û z Decimal.log10cCsV|j|d}|r |S|durtƒ}| ¡rtS|s | tdd¡St| ¡ƒ}| |¡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). rRNzlogb(0)r.) r—rr’rxrpr rržrÌrÍr*r*r,Úlogbûs zDecimal.logbcCs6|jdks |jdkrdS|jD] }|dvrdSqdS)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&FZ01T)r?rWr@)r1Údigr*r*r,Ú _islogical s ÿzDecimal._islogicalcCs†|jt|ƒ}|dkrd||}n|dkr||jd…}|jt|ƒ}|dkr3d||}||fS|dkr?||jd…}||fS)Nr&rY)rLrr)r1r2ÚopaÚopbZdifr*r*r,Ú _fill_logical' sþzDecimal._fill_logicalcCóz|durtƒ}t|dd}| ¡r| ¡s| t¡S| ||j|j¡\}}d dd„t||ƒDƒ¡}t d| d¡p:ddƒS) z;Applies an 'and' operation between self and other's digits.NTr®r[cSs$g|]\}}tt|ƒt|ƒ@ƒ‘qSr*©rlr]©Ú.0r<Úbr*r*r,Ú B ó$z'Decimal.logical_and..r&rY©rr°rrpr r„r@rzÚzipr>rs©r1r”r2r‚rƒrŽr*r*r,Úlogical_and4 ó zDecimal.logical_andcCs(|durtƒ}| tdd|jdƒ|¡S)zInvert all its digits.Nr&rÛ)rÚlogical_xorr>rLrÈr*r*r,Úlogical_invertE s ÿzDecimal.logical_invertcCr…) z:Applies an 'or' operation between self and other's digits.NTr®r[cSs$g|]\}}tt|ƒt|ƒBƒ‘qSr*r†r‡r*r*r,rŠZ r‹z&Decimal.logical_or..r&rYrŒrŽr*r*r,Ú logical_orL rzDecimal.logical_orcCr…) z;Applies an 'xor' operation between self and other's digits.NTr®r[cSs$g|]\}}tt|ƒt|ƒAƒ‘qSr*r†r‡r*r*r,rŠk r‹z'Decimal.logical_xor..r&rYrŒrŽr*r*r,r‘] rzDecimal.logical_xorcCs¾t|dd}|dur tƒ}|js|jr?| ¡}| ¡}|s|r?|dkr,|dkr,| |¡S|dkr9|dkr9| |¡S| ||¡S| ¡ | ¡¡}|dkrQ| |¡}|dkrX|}n|}| |¡S©z8Compares the values numerically with their sign ignored.Tr®Nr.r&r© r°rrXrrÌr—rÊr¡rYrZr*r*r,Úmax_magn ó& zDecimal.max_magcCs¾t|dd}|dur tƒ}|js|jr?| ¡}| ¡}|s|r?|dkr,|dkr,| |¡S|dkr9|dkr9| |¡S| ||¡S| ¡ | ¡¡}|dkrQ| |¡}|dkrX|}n|}| |¡Sr”r•rZr*r*r,Úmin_magŒ r—zDecimal.min_magcCs |durtƒ}|j|d}|r|S| ¡dkrtS| ¡dkr*tdd|j| ¡ƒS| ¡}| t ¡| ¡| |¡}||krB|S| tdd| ¡dƒ|¡S)z=Returns the largest representable number smaller than itself.NrRrr.r&rJrÛ)rr—r’rwr>rLrrSrSrÚ_ignore_all_flagsrÌrØrÝ©r1r2rCZnew_selfr*r*r,Ú next_minusª ó$ ÿzDecimal.next_minuscCs |durtƒ}|j|d}|r|S| ¡dkrtS| ¡dkr*tdd|j| ¡ƒS| ¡}| t ¡| ¡| |¡}||krB|S| tdd| ¡dƒ|¡S)z=Returns the smallest representable number larger than itself.NrRr.rrJr&rÛ)rr—r’rxr>rLrrSrSrr™rÌr×rÝršr*r*r,Ú next_plusÁ rœzDecimal.next_pluscCsàt|dd}|dur tƒ}| ||¡}|r|S| |¡}|dkr%| |¡S|dkr/| |¡}n| |¡}| ¡rL| t d|j ¡| t¡| t¡|S| ¡|jkrn| t¡| t¡| t¡| t¡|sn| 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. Tr®Nr&rz Infinite result from next_toward)r°rr—r¡rdrr›r’rprr?rrržrKrr r)r1r”r2rCZ comparisonr*r*r,Únext_towardØ s8 þ ö zDecimal.next_towardcCs„| ¡rdS| ¡rdS| ¡}|dkrdS|dkrdS| ¡r'|jr%dSdS|d ur.tƒ}|j|d r;|jr9dSdS|jr@d 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 r“r¾r.z +Infinityrz -Infinityz-Zeroz+ZeroNrRz -Subnormalz +Subnormalz-Normalz+Normal)r˜r™r’rqr?rrp)r1r2Úinfr*r*r,Únumber_classs,zDecimal.number_classcCrú)z'Just returns 10, as this is Decimal, :)r²rûr‘r*r*r,Úradix0rýz Decimal.radixcCsö|durtƒ}t|dd}| ||¡}|r|S|jdkr!| t¡S|jt|ƒkr0|jks6n| t¡S| ¡r>t |ƒSt|ƒ}|j }|jt|ƒ}|dkrWd||}n|dkrb||d…}||d…|d|…}t|j | d¡pwd|jƒS)z5Returns a rotated copy of self, value-of-other times.NTr®r&rY©rr°r—rWrpr rLr]r’rr@rrr>r?rs)r1r”r2rCÚtorotÚrotdigÚtopadZrotatedr*r*r,Úrotate4s. ÿzDecimal.rotatecCs¾|durtƒ}t|dd}| ||¡}|r|S|jdkr!| t¡Sd|j|j}d|j|j}|t|ƒkr=|ksCn| t¡S| ¡rKt |ƒSt|j|j |jt|ƒƒ}| |¡}|S)z>Returns self operand after adding the second value to its exp.NTr®r&r³re)rr°r—rWrpr rMrLr]r’rr>r?r@rÌ)r1r”r2rCZliminfZlimsuprr*r*r,ÚscalebUs" zDecimal.scalebcCs|durtƒ}t|dd}| ||¡}|r|S|jdkr!| t¡S|jt|ƒkr0|jks6n| t¡S| ¡r>t |ƒSt|ƒ}|j }|jt|ƒ}|dkrWd||}n|dkrb||d…}|dkrm|d|…}n|d|}||jd…}t|j | d¡p„d|jƒS)z5Returns a shifted copy of self, value-of-other times.NTr®r&rYr¢)r1r”r2rCr£r¤r¥Zshiftedr*r*r,rßns4 ÿz Decimal.shiftcCs|jt|ƒffSr))Ú __class__rlr‘r*r*r,Ú __reduce__•szDecimal.__reduce__cCót|ƒtur|S| t|ƒ¡Sr)©Útyperr¨rlr‘r*r*r,Ú__copy__˜ózDecimal.__copy__cCrªr)r«)r1Zmemor*r*r,Ú__deepcopy__r®zDecimal.__deepcopy__cCs,|durtƒ}t||d}|jr,t|j|ƒ}t| ¡ƒ}|ddkr&|d7}t|||ƒS|ddur;ddg|j|d<|ddkrLt |j|j |jdƒ}|j}|d}|dur‡|dd vrf| |d |¡}n!|ddvrt| ||¡}n|ddvr‡t|j ƒ|kr‡| ||¡}|sš|jd krš|ddvrš| d |¡}|jt|j ƒ} |dd vr¶|s³|dur³d |} n d } n|ddvr¿| } n|ddvrÓ|jd krÑ| dkrÑ| } nd } | d krâd}d| |j }n'| t|j ƒkrø|j d| t|j ƒ}d}n|j d| …pd}|j | d…}| | } t|j||| |ƒS)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_localeconvr¬ú%ÚgÚGreÚ precisionÚeEr.zfF%ZgGr&r¿rYr[)rÚ_parse_format_specifierrXÚ_format_signr?rlrÊÚ _format_alignrÃr>r@rWrKrOrÓrrÚ_format_number)r1Z specifierr2r°ÚspecrHÚbodyrKr´rÅrÆr‚rƒr^r*r*r,Ú __format__¤sZ zDecimal.__format__)rYN)NNr))FN)TN)‚r6r7r8r9Ú __slots__rjÚclassmethodr}rr’r—r›rr¡r¥r©r«r¬rr±rµrºrˆr½rÇrÉrÎrÏrÑr×Ú__radd__rØrÚrÜÚ__rmul__rârærçrìrírîrïrñròrór÷røÚ __trunc__ÚpropertyrùrürþrrArÌr rrrrrrrÚdictrrrrr r)r=rFrGrJrrMrÓrOrQr#Úto_integralrWrÒr¼r!r"ržr\r^rYrbrÊrËrdr^rgrhrLr´rmr™ror˜rprqrvr{r?r~rrr„rr’r“r‘r–r˜r›rržr r¡r¦r§rßr©rr¯r¼r*r*r*r,rs , ! @ 2 4 V 7 ; ! $ K f ø > ,U n Y =" c *" I K 2 3 .* ! 'rFcCs&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*. )rirjrr?r@rWrX)rHZcoefficientr'Zspecialr1r*r*r,r>ös r>c@s(eZdZdZdd„Zdd„Zdd„ZdS) rUzContext manager class to support localcontext(). Sets a copy of the supplied context in __enter__() and restores the previous decimal context in __exit__() cCs| ¡|_dSr))rSÚnew_context)r1rÅr*r*r,Ú__init__óz_ContextManager.__init__cCstƒ|_t|jƒ|jSr))rÚ saved_contextrrÅr‘r*r*r,Ú __enter__s z_ContextManager.__enter__cCst|jƒdSr))rrÈ)r1ÚtÚvÚtbr*r*r,Ú__exit__rÇz_ContextManager.__exit__N)r6r7r8r9rÆrÉrÍr*r*r*r,rUs rUc@s²eZdZdZ d¦dd„Zdd„Zdd„Zd d „Zdd„Zd d„Z dd„Z dd„Zdd„Zdd„Z dd„ZeZd§dd„Zdd„Zdd„Zdd „ZdZd!d"„Zd#d$„Zd%d&„Zd¨d(d)„Zd*d+„Zd,d-„Zd.d/„Zd0d1„Zd2d3„Zd4d5„Zd6d7„Zd8d9„Z d:d;„Z!dd?„Z#d@dA„Z$dBdC„Z%dDdE„Z&dFdG„Z'dHdI„Z(dJdK„Z)dLdM„Z*dNdO„Z+dPdQ„Z,dRdS„Z-dTdU„Z.dVdW„Z/dXdY„Z0dZd[„Z1d\d]„Z2d^d_„Z3d`da„Z4dbdc„Z5ddde„Z6dfdg„Z7dhdi„Z8djdk„Z9dldm„Z:dndo„Z;dpdq„Zdvdw„Z?dxdy„Z@dzd{„ZAd|d}„ZBd~d„ZCd€d„ZDd‚dƒ„ZEd„d…„ZFd†d‡„ZGd§dˆd‰„ZHdŠd‹„ZIdŒd„ZJdŽd„ZKdd‘„ZLd’d“„ZMd”d•„ZNd–d—„ZOd˜d™„ZPdšd›„ZQdœd„ZRdždŸ„ZSd d¡„ZTd¢d£„ZUd¤d¥„ZVeVZWdS)©raßContains 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 s<zt} Wn ty Ynw|dur|n| j|_|dur|n| j|_|dur(|n| j|_|dur2|n| j|_|dur<|n| j|_|durF|n| j|_| durRg|_n| |_ˆdur`| j ¡|_ ntˆtƒstt‡fdd„t ˆDƒƒ|_ nˆ|_ ˆdur„t t d¡|_dStˆtƒs™t‡fdd„t ˆDƒƒ|_dSˆ|_dS)Nc3ó |]}|t|ˆvƒfVqdSr)©r]©rˆrö©rBr*r,Ú Ió€z#Context.__init__..r&c3rÎr)rÏrÐ©rCr*r,rÒPrÓ)rÚ NameErrorrLrKrKrMrÃrÚ_ignored_flagsrBrSrkrÃrAÚfromkeysrC)r1rLrKrKrMrÃrrCrBrÖZdcr*)rCrBr,rÆ0s0ÿ zContext.__init__cCs”t|tƒstd|ƒ‚|dkr||krtd||||fƒ‚n%|dkr1||kr0td||||fƒ‚n||ks9||krCtd||||fƒ‚t |||¡S)Nz%s must be an integerú-infz%s must be in [%s, %d]. got: %srŸz%s must be in [%d, %s]. got: %sz%s must be in [%d, %d]. got %s)rkr]r~rxriÚ__setattr__)r1Únamer€ZvminZvmaxr*r*r,Ú_set_integer_checkTs ÿÿzContext._set_integer_checkcCs`t|tƒstd|ƒ‚|D]}|tvrtd|ƒ‚q tD]}||vr(td|ƒ‚qt |||¡S)Nz%s must be a signal dictz%s is not a valid signal dict)rkrÃr~rAÚKeyErrorrirÙ)r1rÚrÚkeyr*r*r,Ú_set_signal_dictbs ÿÿzContext._set_signal_dictcCsà|dkr| ||dd¡S|dkr| ||dd¡S|dkr$| ||dd¡S|dkr0| ||dd¡S|d kr<| ||dd¡S|d krQ|tvrJtd|ƒ‚t |||¡S|dksY|d kr_| ||¡S|dkrjt |||¡Std|ƒ‚)NrLr.rŸrKrØr&rMrÃrrKz%s: invalid rounding moderCrBrÖz.'decimal.Context' object has no attribute '%s')rÛÚ_rounding_modesr~rirÙrÞÚAttributeError)r1rÚr€r*r*r,rÙms*ÿzContext.__setattr__cCstd|ƒ‚)Nz%s cannot be deleted)rà)r1rÚr*r*r,Ú__delattr__†rzContext.__delattr__c CsNdd„|j ¡Dƒ}dd„|j ¡Dƒ}|j|j|j|j|j|j|j ||ffS)NcSóg|]\}}|r|‘qSr*r*©rˆZsigrËr*r*r,rŠ‹óz&Context.__reduce__..cSrâr*r*rãr*r*r,rŠŒrä) rCÚitemsrBr¨rLrKrKrMrÃr)r1rCrBr*r*r,r©ŠsÿÿzContext.__reduce__cCs|g}| dt|ƒ¡dd„|j ¡Dƒ}| dd |¡d¡dd„|j ¡Dƒ}| dd |¡d¡d |¡d S) zShow the current context.zrContext(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, clamp=%(clamp)dcSóg|] \}}|r|j‘qSr*©r6)rˆrŠrËr*r*r,rŠ˜óz$Context.__repr__..zflags=[z, ú]cSrær*rç)rˆrÊrËr*r*r,rŠšrèztraps=[ú))ryÚvarsrCrårzrB)r1röÚnamesr*r*r,r½‘sýzContext.__repr__cCó|jD]}d|j|<qdS)zReset all flags to zeror&NrÔ©r1Úflagr*r*r,rTžó ÿzContext.clear_flagscCrí)zReset all traps to zeror&NrÑrîr*r*r,Úclear_traps£rðzContext.clear_trapsc Cs.t|j|j|j|j|j|j|j|j|j ƒ }|S)z!Returns a shallow copy from self.) rrLrKrKrMrÃrrCrBrÖ©r1Zncr*r*r,rR¨s þzContext._shallow_copyc Cs6t|j|j|j|j|j|j|j ¡|j ¡|j ƒ }|S)zReturns a deep copy from self.)rrLrKrKrMrÃrrCrSrBrÖròr*r*r,rS¯sýzContext.copycGsZt ||¡}||jvr|ƒj|g|¢RŽSd|j|<|j|s)|ƒj|g|¢RŽS||ƒ‚)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. r.)Ú_condition_maprOrÖr3rCrB)r1Z conditionZexplanationr+Úerrorr*r*r,rp¸s zContext._raise_errorcCs |jtŽS)z$Ignore all flags, if they are raised)Ú _ignore_flagsrAr‘r*r*r,r™ÎrlzContext._ignore_all_flagscGs|jt|ƒ|_t|ƒS)z$Ignore the flags, if they are raised)rÖrv)r1rCr*r*r,rõÒszContext._ignore_flagscGs8|rt|dttfƒr|d}|D]}|j |¡qdS)z+Stop ignoring the flags, if they are raisedr&N)rkrwrvrÖÚremove)r1rCrïr*r*r,Ú _regard_flagsÙs ÿzContext._regard_flagscCót|j|jdƒS)z!Returns Etiny (= Emin - prec + 1)r.)r]rKrLr‘r*r*r,rÝãrcz Context.EtinycCrø)z,Returns maximum exponent (= Emax - prec + 1)r.)r]rMrLr‘r*r*r,rçrczContext.EtopcCs|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. )rK)r1r¬rKr*r*r,rSëszContext._set_roundingrYcCsjt|tƒr|| ¡ksd|vr| td¡St||d}| ¡r0t|jƒ|j |j kr0| 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.rZzAtrailing or leading whitespace and underscores are not permitted.rRzdiagnostic info too long in NaN)rkrlrnrprrrrrr@rLrrÌ)r1rurr*r*r,Úcreate_decimalþsÿÿ zContext.create_decimalcCst |¡}| |¡S)aÏCreates a new Decimal instance from a float but rounding using self as the context. >>> context = Context(prec=5, rounding=ROUND_DOWN) >>> context.create_decimal_from_float(3.1415926535897932) Decimal('3.1415') >>> context = Context(prec=5, traps=[Inexact]) >>> context.create_decimal_from_float(3.1415926535897932) Traceback (most recent call last): ... decimal.Inexact: None )rr}rÌ)r1rŠrr*r*r,Úcreate_decimal_from_floats z!Context.create_decimal_from_floatcCót|dd}|j|dS)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') Tr®rR)r°rÑ©r1r<r*r*r,rt!szContext.abscCó2t|dd}|j||d}|turtd|ƒ‚|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') Tr®rRúUnable to convert %s to Decimal)r°r×r¤r~©r1r<r‰rår*r*r,Úadd6ó zContext.addcCst| |¡ƒSr))rlrÌrür*r*r,Ú_applyKrÇzContext._applycCót|tƒs tdƒ‚| ¡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.)rkrr~r\rür*r*r,r\Nó zContext.canonicalcCót|dd}|j||dS)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') Tr®rR)r°r±©r1r<r‰r*r*r,r±[s!zContext.comparecCr)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') Tr®rR)r°r^rr*r*r,r^ó zContext.compare_signalcCót|dd}| |¡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') Tr®)r°rYrr*r*r,rY¢s zContext.compare_totalcCr)z£Compares two operands using their abstract representation ignoring sign. Like compare_total, but with operand's sign ignored and assumed to be 0. Tr®)r°rbrr*r*r,rb¿s zContext.compare_total_magcCót|dd}| ¡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') Tr®)r°rÊrür*r*r,rÊÇó zContext.copy_abscCst|dd}t|ƒS)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') Tr®)r°rrür*r*r,Úcopy_decimalÔr zContext.copy_decimalcCr )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') Tr®)r°rËrür*r*r,rËár zContext.copy_negatecCr)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') Tr®)r°rdrr*r*r,rdîó zContext.copy_signcCrý)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') Tr®rRrþ)r°râr¤r~rÿr*r*r,Údivides zContext.dividecCrý)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') Tr®rRrþ)r°ròr¤r~rÿr*r*r,Ú divide_int+ó zContext.divide_intcCrý)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')) Tr®rRrþ)r°rìr¤r~rÿr*r*r,rÞBrzContext.divmodcCrû)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') Tr®rR)r°r^rür*r*r,r^WózContext.expcCst|dd}|j|||dS)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') Tr®rR)r°r )r1r<r‰rUr*r*r,r oszContext.fmacCr)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.)rkrr~rgrür*r*r,rg†rzContext.is_canonicalcCr )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 Tr®)r°rhrür*r*r,rh“szContext.is_finitecCr )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 Tr®)r°rLrür*r*r,rL©ózContext.is_infinitecCr )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 Tr®)r°r´rür*r*r,r´¸ó zContext.is_nancCrû)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 Tr®rR)r°rmrür*r*r,rmÈszContext.is_normalcCr )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 Tr®)r°r™rür*r*r,r™ßrzContext.is_qnancCr )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 Tr®)r°rorür*r*r,roîózContext.is_signedcCr )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 Tr®)r°r˜rür*r*r,r˜ÿrzContext.is_snancCrû)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 Tr®rR)r°rprür*r*r,rpózContext.is_subnormalcCr )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 Tr®)r°rqrür*r*r,rq%rzContext.is_zerocCrû)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') Tr®rR)r°r{rür*r*r,r{6rz Context.lncCrû)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') Tr®rR)r°r~rür*r*r,r~Lóz Context.log10cCrû)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') Tr®rR)r°rrür*r*r,rhszContext.logbcCr)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') Tr®rR)r°rrr*r*r,r‚ózContext.logical_andcCrû)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') Tr®rR)r°r’rür*r*r,r’szContext.logical_invertcCr)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') Tr®rR)r°r“rr*r*r,r“°rzContext.logical_orcCr)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') Tr®rR)r°r‘rr*r*r,r‘ËrzContext.logical_xorcCr)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') Tr®rR)r°rÒrr*r*r,rÒærzContext.maxcCr)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') Tr®rR)r°r–rr*r*r,r–ózContext.max_magcCr)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') Tr®rR)r°r¼rr*r*r,r¼rzContext.mincCr)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') Tr®rR)r°r˜rr*r*r,r˜-rzContext.min_magcCrû)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') Tr®rR)r°rÎrür*r*r,Úminus>óz Context.minuscCrý)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') Tr®rRrþ)r°rÜr¤r~rÿr*r*r,ÚmultiplyOs zContext.multiplycCrû)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') Tr®rR)r°r›rür*r*r,r›oózContext.next_minuscCrû)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') Tr®rR)r°rrür*r*r,rƒrzContext.next_pluscCr)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') Tr®rR)r°ržrr*r*r,rž—rzContext.next_towardcCrû)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') Tr®rR)r°rJrür*r*r,rJºrzContext.normalizecCrû)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' Tr®rR)r°r rür*r*r,r Òs/zContext.number_classcCrû)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') Tr®rR)r°rÏrür*r*r,ÚplusrzContext.pluscCs4t|dd}|j|||d}|turtd|ƒ‚|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') Tr®rRrþ)r°rFr¤r~)r1r<r‰r%rår*r*r,Úpowers Iz Context.powercCr)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') Tr®rR)r°rrr*r*r,res7zContext.quantizecCrú)zkJust returns 10, as this is Decimal, :) >>> ExtendedContext.radix() Decimal('10') r²rûr‘r*r*r,r¡Ÿriz Context.radixcCrý)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') Tr®rRrþ)r°rîr¤r~rÿr*r*r,rà§s zContext.remaindercCr)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') Tr®rR)r°rñrr*r*r,rñÍszContext.remainder_nearcCr)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') Tr®rR)r°r¦rr*r*r,r¦ïszContext.rotatecCr)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 Tr®)r°rMrr*r*r,rMrzContext.same_quantumcCr)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') Tr®rR)r°r§rr*r*r,r§$szContext.scalebcCr)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') Tr®rR)r°rßrr*r*r,rß7sz Context.shiftcCrû)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 Tr®rR)r°rWrür*r*r,rWUszContext.sqrtcCrý)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') Tr®rRrþ)r°rØr¤r~rÿr*r*r,ÚsubtracturzContext.subtractcCrû)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' Tr®rR)r°rÉrür*r*r,rÉŒrzContext.to_eng_stringcCrû)zyConverts a number to a string, using scientific notation. The operation is not affected by the context. Tr®rR)r°rÇrür*r*r,Ú to_sci_string¨szContext.to_sci_stringcCrû)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') Tr®rR)r°rQrür*r*r,rQ°szContext.to_integral_exactcCrû)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') Tr®rR)r°r#rür*r*r,r#ÎszContext.to_integral_value) NNNNNNNNNr))rY)Xr6r7r8r9rÆrÛrÞrÙrár©r½rTrñrRrSrrpr™rõr÷rµrÝrrSrùrúrtrrr\r±r^rYrbrÊrrËrdr rrÞr^r rgrhrLr´rmr™ror˜rprqr{r~rrr’r“r‘rÒr–r¼r˜rrr›rržrJr rrrr¡ràrñr¦rMr§rßrWrrÉrrQr#rÄr*r*r*r,rs² þ$ $# % #2 P:&" rc@s"eZdZdZddd„Zdd„ZdS)ru©rHr]r^NcCsj|durd|_d|_d|_dSt|tƒr$|j|_t|jƒ|_|j|_dS|d|_|d|_|d|_dS)Nr&r.re)rHr]r^rkrr?r@rW)r1r€r*r*r,rÆôs z_WorkRep.__init__cCsd|j|j|jfS)Nz(%r, %r, %r)r r‘r*r*r,r½sz_WorkRep.__repr__r))r6r7r8r½rÆr½r*r*r*r,ruîs rucCsš|j|jkr|}|}n|}|}tt|jƒƒ}tt|jƒƒ}|jtd||dƒ}||jd|kr8d|_||_|jd|j|j9_|j|_||fS)zcNormalizes op1, op2 to have the same exp and length of coefficient. Done during addition. rrer.r²)r^rrrlr]r¼)rÕrÖrLÚtmpr”Ztmp_lenZ other_lenr^r*r*r,rÔsrÔcCs^|dkrdS|dkr|d|Stt|ƒƒ}t|ƒt| d¡ƒ}||kr(dS|d|S)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&r²rYN)rlrtrrÚrstrip)r=rÁZstr_nZval_nr*r*r,r2(sr2cCsH|dks|dkrtdƒ‚d}||kr"||||d?}}||ks|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.r.)rx)r=r<r‰r*r*r,Ú _sqrt_nearest=sÿr#cCs2d|>||?}}|d||d@|d@|kS)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. r.rer*)r5rßr‰rär*r*r,Ú_rshift_nearestLs r$cCs&t||ƒ\}}|d||d@|kS)zaClosest integer to a/b, a and b positive integers; rounds to even in the case of a tie. rer.)rÞ)r<r‰rärår*r*r,Ú_div_nearestTsr%r,c Cs||}d}||krt|ƒ||>|ks"||krWt|ƒ||?|krWt||d>|t||t||ƒ|ƒƒ}|d7}||krIt|ƒ||>|ks"||krWt|ƒ||?|ks"tdtt|ƒƒd|ƒ}t||ƒ}t||ƒ}t|dddƒD]}t||ƒt|||ƒ}qxt|||ƒS)aÉInteger approximation to M*log(x/M), with absolute error boundable in terms only of x/M. Given positive integers x and M, return an integer approximation to M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference between the approximation and the exact result is at most 22. For L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In both cases these are upper bounds on the error; it will usually be much smaller.r&r.éöÿÿÿrcr)rtr%r#r$r]rrrlr$) r5ÚMÚLr8ÚRÚTZyshiftÚwr‹r*r*r,Ú_ilog\s ÿü r,c Cs¶|d7}tt|ƒƒ}||||dk}|dkrJd|}|||}|dkr-|d|9}nt|d|ƒ}t||ƒ}t|ƒ}t|||ƒ}||} n d}t|d|ƒ} t| |dƒS)z¾Given integers c, e and p with c > 0, p >= 0, compute an integer approximation to 10**p * log10(c*10**e), with an absolute error of at most 1. Assumes that c*10**e is not exactly 1.rer.r&r²r0)rrrlr%r,Ú _log10_digits) rUrÁr4rVrŠr'r‹Úlog_dZlog_10Zlog_tenpowerr*r*r,r}Œs r}c CsÎ|d7}tt|ƒƒ}||||dk}|dkr9|||}|dkr)|d|9}nt|d|ƒ}t|d|ƒ}nd}|r^ttt|ƒƒƒd}||dkr[t|t||ƒd|ƒ}nd}nd}t||dƒS)z´Given integers c, e and p with c > 0, compute an integer approximation to 10**p * log(c*10**e), with an absolute error of at most 1. Assumes that c*10**e is not exactly 1.rer.r&r²r0)rrrlr%r,rtr-) rUrÁr4rVrŠr‹r.rEZ f_log_tenr*r*r,ry®s"ryc@s eZdZdZdd„Zdd„ZdS)Ú _Log10Memoizez¾Class to compute, store, and allow retrieval of, digits of the constant log(10) = 2.302585.... This constant is needed by Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.cCs d|_dS)NZ/23025850929940456840179914546843642076011014886)r„r‘r*r*r,rÆÞs z_Log10Memoize.__init__cCs˜|dkrtdƒ‚|t|jƒkrAd} d||d}tttd||ƒdƒƒ}||d…d |kr2n|d7}q| d ¡dd …|_t|jd|d…ƒS)ztGiven an integer p >= 0, return floor(10**p)*log(10). For example, self.getdigits(3) returns 2302. r&zp should be nonnegativercTr²rer0NrYrr.)rxrrr„rlr%r,r"r])r1r4rEr'r„r*r*r,Ú getdigitsás ú z_Log10Memoize.getdigitsN)r6r7r8r9rÆr0r*r*r*r,r/Úsr/c Cs¨t||>|ƒ}tdtt|ƒƒd|ƒ}t||ƒ}||>}t|dddƒD] }t|||||ƒ}q(t|dddƒD]}||d>}t||||ƒ}q>||S)zëGiven integers x and M, M > 0, such that x/M is small in absolute value, compute an integer approximation to M*exp(x/M). For 0 <= x/M <= 2.4, the absolute error in the result is bounded by 60 (and is usually much smaller).r&rcr.r&rre)r1r]rrrlr%r$) r5r'r(r)r*r8ZMshiftr(r‹r*r*r,Ú_iexpÿs r1c Cs–|d7}td|tt|ƒƒdƒ}||}||}|dkr$|d|}n|d|}t|t|ƒƒ\}}t|d|ƒ}tt|d|ƒdƒ||dfS)aÐCompute an approximation to exp(c*10**e), with p decimal places of precision. Returns integers d, f such that: 10**(p-1) <= d <= 10**p, and (d-1)*10**f < exp(c*10**e) < (d+1)*10**f In other words, d*10**f is an approximation to exp(c*10**e) with p digits of precision, and with an error in d of at most 1. This is almost, but not quite, the same as the error being < 1ulp: when d = 10**(p-1) the error could be up to 10 ulp.rer&r.r²ièrc)rÒrrrlrÞr-r%r1) rUrÁr4rErärßZcshiftZquotr;r*r*r,re$s recCsôttt|ƒƒƒ|}t||||dƒ}||}|dkr%||d|}n t||d|ƒ}|dkr`tt|ƒƒ|dk|dkkrRd|ddd|} } | | fSd|d|} } | | fSt||d|dƒ\} } t| dƒ} | d7} | | fS)a5Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: 10**(p-1) <= c <= 10**p, and (c-1)*10**e < x**y < (c+1)*10**e in other words, c*10**e is an approximation to x**y with p digits of precision, and with an error in c of at most 1. (This is almost, but not quite, the same as the error being < 1ulp: when c == 10**(p-1) we can only guarantee error < 10ulp.) We assume that: x is positive and not equal to 1, and y is nonzero. r.r&r²)rrrlrtryr%re)r6r7r9r:r4r‰ZlxcrßZpcrŒr^r*r*r,r@Hs úü r@r0éFé5é(érrér²r…) rÛÚ2Ú3Ú4Ú5Ú6Ú7Ú8rJcCs0|dkrtdƒ‚t|ƒ}dt|ƒ||dS)z@Compute a lower bound for 100*log10(c) for a positive integer c.r&z0The argument to _log10_lb should be nonnegative.r0)rxrlrr)rUZ correctionZstr_cr*r*r,r3rsr3cCsLt|tƒr|St|tƒrt|ƒS|rt|tƒrt |¡S|r$td|ƒ‚tS)zÙConvert other to Decimal. Verifies that it's ok to use in an implicit construction. If allow_float is true, allow conversion from float; this is used in the comparison methods (__eq__ and friends). rþ)rkrr]r|r}r~r¤)r”r¯Zallow_floatr*r*r,r°}s r°cCs´t|tƒr ||fSt|tjƒr)|js"t|jtt|j ƒ|j ƒ|jƒ}|t|jƒfS|r9t|tj ƒr9|jdkr9|j}t|tƒrVtƒ}|rId|jt<n| td¡|t |¡fSttfS)zÔGiven a Decimal instance self and a Python object other, return a pair (s, o) of Decimal instances such that "s op o" is equivalent to "self op other" for any of the 6 comparison operators "op". r&r.rh)rkrÚ_numbersZRationalrXr>r?rlr]r@ÚdenominatorrWÚ numeratorZComplexrürùr|rrCrrpr}r¤)r1r”r¢r2r*r*r,r£s( þ ÿr£r/i?BiÁ½ðÿ)rLrKrBrCrMrKrÃrrf)rLrKrBrCa· # A numeric string consists of: # \s* (?P[-+])? # an optional sign, followed by either... ( (?=\d|\.\d) # ...a number (with at least one digit) (?P\d*) # having a (possibly empty) integer part (\.(?P\d*))? # followed by an optional fractional part (E(?P[-+]?\d+))? # followed by an optional exponent, or... | Inf(inity)? # ...an infinity, or... | (?Ps)? # ...an (optionally signaling) NaN # NaN (?P\d*) # with (possibly empty) diagnostic info. ) # \s* \Z z0*$z50*$zÉ\A (?: (?P.)? (?P[<>=^]) )? (?P[-+ ])? (?P\#)? (?P0)? (?P(?!0)\d+)? (?P,)? (?:\.(?P0|(?!0)\d+))? (?P[eEfFgGn%])? \Z cCsŽt |¡}|durtd|ƒ‚| ¡}|d}|d}|ddu|d<|dr;|dur1td|ƒ‚|dur;td|ƒ‚|p>d|d<|pDd |d<|d durQd|d <t|dpWd ƒ|d<|ddurit|dƒ|d<|ddkr|ddus{|ddvrd|d<|ddkr±d|d<|dur‘t ¡}|ddurtd|ƒ‚|d|d<|d|d<|d|d<|S|ddur»d|d<ddg|d<d|d<|S)aÚParse and validate a format specifier. Turns a standard numeric format specifier into a dict, with the following entries: fill: fill character to pad field to minimum width align: alignment type, either '<', '>', '=' or '^' sign: either '+', '-' or ' ' minimumwidth: nonnegative integer giving minimum width zeropad: boolean, indicating whether to pad with zeros thousands_sep: string to use as thousands separator, or '' grouping: grouping for thousands separators, in format used by localeconv decimal_point: string to use for decimal point precision: nonnegative integer giving precision, or None type: one of the characters 'eEfFgG%', or None NzInvalid format specifier: ÚfillÚalignÚzeropadz7Fill character conflicts with '0' in format specifier: z2Alignment conflicts with '0' in format specifier: ú ú>rHr\ÚminimumwidthrYr´r&r¬ZgGnr.r=r²Ú thousands_sepzJExplicit thousands separator conflicts with 'n' type in format specifier: ÚgroupingÚ decimal_pointr[rcrÀ)Ú_parse_format_specifier_regexÚmatchrxÚ groupdictr]Ú_localeÚ localeconv)Úformat_specr°rZformat_dictrArBr*r*r,r¶sV ÿÿÿûr¶c Cs¸|d}|d}||t|ƒt|ƒ}|d}|dkr$|||}|S|dkr0|||}|S|dkr<|||}|S|dkrXt|ƒd}|d |…||||d …}|Std ƒ‚)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). rFrArBúÚsysÚcollectionsr'Z_namedtuplerÚImportErrorrrrrrrrrr$r%Úmaxsizer r!r"r#ÚArithmeticErrorrrr rÚZeroDivisionErrorr rrrrrr rrr~rrArórßZcontextvarsZ ContextVarrNrrrrirr>ÚNumberÚregisterrUrrurÔr]r‰r1r2r#r$r%r,r}ryr/r0r-r1rer@r3r°r£rrrÚreÚcompileÚVERBOSEÚ IGNORECASErKrmrrÚDOTALLrJÚlocalerMr¶r¸rWr\r·r¹rxrwrBr`r>r_rFÚ hash_infoÚmodulusr¸rŸr¶rôZ_PyHASH_NANr·r¹r*r*r*r,Úslc#ÿ & ÿýÿ . ^ 0",# %$ +þ *ùýý ïï óÿ P % )