grthtrhthjhtyjytjytkergtrhtrjytjerhrfh4:24 29/09/2026  fP}+@sfdZddddddddd d d d d ddddddddddddddddddd d!d"d#d$g$Zd%Zd&Zd'd(lZd'd(lZd'd(lZy#d'd)l m Z e dd*Z Wne k rd+d,Z YnXdZdZdZdZdZdZdZdZd-Zejd.d/d0krOd1Zd1Zd1 Znd2Zd2Zd2 Zeed0ZGd3ddeZGd4ddeZGd5d d eZGd6ddeZ Gd7d d ee!Z"Gd8ddeZ#Gd9ddee!Z$Gd:d d eZ%Gd;ddeZ&Gd<d d eZ'Gd=d d eZ(Gd>dde%e'Z)Gd?dde%e'e(Z*Gd@ddee+Z,ee"e%e)e'e*ee(e,g Z-iee 6ee#6ee$6ee&6Z.eeeeeeeefZ/yd'd(l0Z0Wn4e k r]GdAdBdBe1Z2e2Z0[2YnXy e0j3WnNe4k re5e0j6dCre0j6`7ndDdZ8dEdZ9YnIXe0j3Z3e5e3dCre3`7ne3dFdZ9e3dGdZ8[0[3d(dHdZ:GdIdde1Z;dJdKdLZ<ej=j>e;GdMdNdNe1Z?GdOdde1Z@GdPdQdQe1ZAd'dRdSZBeCjDZEdTdUZFdVdWZGdXdYZHdZd[ZId\d]d^ZJd_d`ZKdadbZLGdcdddde1ZMeMjNZOd\dedfZPdgdhZQdidjZRi dkdl6dmdn6dodp6dqdr6dsdt6dudv6dwdx6dydz6d{d|6d}d~ZSdJdJddZTdJddZUe@dddede"e)egdgdddd dd0dd'ZVe@dddede"e)eee*gdgZWe@dddedgdgZXd'd(lYZYeYjZdeYj[eYj\Bj]Z^eYjZdj]Z_eYjZdj]Z`eYjZdeYj[eYjaBZb[Yyd'd(lcZdWne k rYnXd(ddZeddZfddZgd0ddZhddZiddZje;dZke;dZle;dZme;d'Zne;d0Zoe;d0 ZpekelfZqejrjsZtejrjuZvejrjwZxeydyetd.etZz[yd'd(l{Z{Wne k rYnTXe|e}Z~e|e}e{Zxe~eD]Zee=qW[~[[d'dl{Tedkrbd'd(lZd'd(lZejend(S)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 >>> DecimalContext DecimalTupleDefaultContext BasicContextExtendedContextDecimalExceptionClampedInvalidOperationDivisionByZeroInexactRounded SubnormalOverflow UnderflowFloatOperationDivisionImpossibleInvalidContextConversionSyntaxDivisionUndefined ROUND_DOWN ROUND_HALF_UPROUND_HALF_EVEN ROUND_CEILING ROUND_FLOORROUND_UPROUND_HALF_DOWN ROUND_05UP setcontext getcontext localcontextMAX_PRECMAX_EMAXMIN_EMIN MIN_ETINY HAVE_THREADSz1.70z2.4.1N) namedtuplezsign digits exponentcGs|S)N)argsr'r',/opt/alt/python34/lib64/python3.4/decimal.pysr*T?lNZoi@Tc@s"eZdZdZddZdS)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. cGsdS)Nr')selfcontextr(r'r'r)handleszDecimalException.handleN)__name__ __module__ __qualname____doc__r0r'r'r'r)rs c@seZdZdZdS)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)r1r2r3r4r'r'r'r)rs c@s"eZdZdZddZdS)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:|r6t|dj|djdd}|j|StS)Nr%nT)_dec_from_triple_sign_int_fix_nan_NaN)r.r/r(ansr'r'r)r0s# zInvalidOperation.handleN)r1r2r3r4r0r'r'r'r)r s c@s"eZdZdZddZdS)rzTrying to convert badly formed string. This occurs and signals invalid-operation if an string is being converted to a number and it does not conform to the numeric string syntax. The result is [0,qNaN]. cGstS)N)r:)r.r/r(r'r'r)r0szConversionSyntax.handleN)r1r2r3r4r0r'r'r'r)rs c@s"eZdZdZddZdS)r aDivision 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|S)N)_SignedInfinity)r.r/signr(r'r'r)r0szDivisionByZero.handleN)r1r2r3r4r0r'r'r'r)r s c@s"eZdZdZddZdS)rzCannot 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]. cGstS)N)r:)r.r/r(r'r'r)r0szDivisionImpossible.handleN)r1r2r3r4r0r'r'r'r)rs c@s"eZdZdZddZdS)rzUndefined 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]. cGstS)N)r:)r.r/r(r'r'r)r0'szDivisionUndefined.handleN)r1r2r3r4r0r'r'r'r)rs c@seZdZdZdS)r aHad 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. N)r1r2r3r4r'r'r'r)r *s c@s"eZdZdZddZdS)raInvalid 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]. cGstS)N)r:)r.r/r(r'r'r)r0AszInvalidContext.handleN)r1r2r3r4r0r'r'r'r)r6s c@seZdZdZdS)r aNumber 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. N)r1r2r3r4r'r'r'r)r Ds c@seZdZdZdS)r aExponent < 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. N)r1r2r3r4r'r'r'r)r Ps c@s"eZdZdZddZdS)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. cGs|jttttfkr#t|S|dkrk|jtkrFt|St|d|j|j |jdS|dkr|jt krt|St|d|j|j |jdSdS)Nr%9r-) roundingrrrrr<rr6precEmaxr)r.r/r=r(r'r'r)r0qs   zOverflow.handleN)r1r2r3r4r0r'r'r'r)r[s c@seZdZdZdS)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. N)r1r2r3r4r'r'r'r)rs c@seZdZdZdS)raEnable 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. N)r1r2r3r4r'r'r'r)rs c@seZdZeddZdS) MockThreadingcCs |jtS)N)modulesr1)r.sysr'r'r)localszMockThreading.localN)r1r2r3rDrEr'r'r'r)rBs rB__decimal_context__cCsA|tttfkr.|j}|jn|tj_dS)z%Set this thread's context to context.N)rrrcopy clear_flags threadingcurrent_threadrF)r/r'r'r)rs  c CsFytjjSWn.tk rAt}|tj_|SYnXdS)zReturns 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. N)rIrJrFAttributeErrorr)r/r'r'r)rs   c Cs:y |jSWn(tk r5t}||_|SYnXdS)zReturns 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. N)rFrKr)_localr/r'r'r)rs     cCs;|tttfkr.|j}|jn||_dS)z%Set this thread's context to context.N)rrrrGrHrF)r/rLr'r'r)rs  cCs"|dkrt}nt|S)abReturn a context manager for a copy of the supplied context Uses a copy of the current context if no context is specified The returned context manager creates a local decimal context in a with statement: def sin(x): with localcontext() as ctx: ctx.prec += 2 # Rest of sin calculation algorithm # uses a precision 2 greater than normal return +s # Convert result to normal precision def sin(x): with localcontext(ExtendedContext): # Rest of sin calculation algorithm # uses the Extended Context from the # General Decimal Arithmetic Specification return +s # Convert result to normal context >>> setcontext(DefaultContext) >>> print(getcontext().prec) 28 >>> with localcontext(): ... ctx = getcontext() ... ctx.prec += 2 ... print(ctx.prec) ... 30 >>> with localcontext(ExtendedContext): ... print(getcontext().prec) ... 9 >>> print(getcontext().prec) 28 N)r_ContextManager)Zctxr'r'r)rs$ c@seZdZdZdZdddd Zed d Zd d ZddZ ddddZ ddZ ddZ ddZ dddZdddZdddZdddZdd d!Zdd"d#Zdd$d%Zd&d'Zd(d)Zd*d+Zd,dd-d.Zdd/d0Zdd1d2Zdd3d4Zd5dd6d7Zdd8d9ZeZdd:d;Zdd<d=Z dd>d?Z!e!Z"dd@dAZ#dBdCZ$ddDdEZ%ddFdGZ&ddHdIZ'ddJdKZ(ddLdMZ)ddNdOZ*ddPdQZ+ddRdSZ,dTdUZ-dVdWZ.e.Z/dXdYZ0e1e0Z0dZd[Z2e1e2Z2d\d]Z3d^d_Z4d`daZ5dbdcZ6dddeZ7dfdgZ8dhdiZ9djdkZ:dldmZ;dndoZ<dpdqZ=drdsZ>e?dte7due8dve9dwe:dxe;dye<dze=d{e>Z@dd|d}ZAd~dZBddZCdddZDdddZEddZFddddZGdddZHdddZIddd5ddZJdddZKddZLddZMddddZNddddZOeOZPdddZQdddZRdddZSddZTddZUddZVddZWdddZXdddZYdddZZddZ[ddZ\dddZ]dddZ^ddZ_ddZ`ddZaddZbdddZcddZdddZeddZfdddZgddZhddZidddZjddZkdddZldddZmddZnddZodddZpdddZqdddZrdddZsdddZtdddZudddZvdddZwdddZxdddZyddZzdddZ{dddZ|dddZ}ddZ~ddZddZddddZdS)rz,Floating point class for decimal arithmetic._expr8r7 _is_special0Nc Cstj|}t|trt|j}|dkrh|dkrTt}n|jtd|S|j ddkrd|_ n d|_ |j d}|dk r|j dpd }t |j d pd }tt |||_ |t ||_d |_n|j d }|dk r{tt |p?d jd |_ |j drod|_qd|_nd |_ d|_d|_|St|t r|dkrd|_ n d|_ d|_tt||_ d |_|St|tr8|j|_|j |_ |j |_ |j|_|St|tr|j|_ t|j |_ t |j|_d |_|St|ttfrFt |dkrtdnt|dt o|ddkstdn|d|_ |ddkr+d |_ |d|_d|_ng} xn|dD]b} t| t rd| kohdknr| s| dkr| j| qq<tdq<W|ddkrd jtt| |_ |d|_d|_n\t|dt r6d jtt| pdg|_ |d|_d |_n td|St|tr|dkrmt}n|jtdtj|}|j|_|j |_ |j |_ |j|_|Std|dS)aCreate 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') NzInvalid literal for Decimal: %rr=-r-r%intZfracexprPFdiagsignalNr5FTztInvalid tuple size in creation of Decimal from list or tuple. The list or tuple should have exactly three elements.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.r+ zTThe second value in the tuple must be composed of integers in the range 0 through 9.zUThe third value in the tuple must be an integer, or one of the strings 'F', 'n', 'N'.z;strict semantics for mixing floats and Decimals are enabledzCannot convert %r to Decimal)r%r-)r5rW) object__new__ isinstancestr_parserstripr _raise_errorrgroupr7rRr8lenrNrOlstripabsr_WorkRepr=rTlisttuple ValueErrorappendjoinmapfloatr from_float TypeError) clsvaluer/r.mintpartfracpartrTrUdigitsdigitr'r'r)r\2s          $                #    +  $          zDecimal.__new__cCst|tr||St|ts7tdntj|sUtj|re|t|Stjd|dkrd}nd}t |j \}}|j d}t |t |d|| }|tkr|S||SdS)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') zargument must be int or float.g?r%r-N)r]rRrmro_mathZisinfZisnanreprZcopysignreas_integer_ratio bit_lengthr6r^r)rpfr=r5dkresultr'r'r)rns  ! zDecimal.from_floatcCs9|jr5|j}|dkr"dS|dkr5dSndS)zrReturns whether the number is not actually one. 0 if a number 1 if NaN 2 if sNaN r5r-rWr+r%)rOrN)r.rTr'r'r)_isnans    zDecimal._isnancCs$|jdkr |jrdSdSdS)zyReturns whether the number is infinite 0 if finite or not a number 1 if +INF -1 if -INF rXr-r%)rNr7)r.r'r'r) _isinfinitys  zDecimal._isinfinitycCs|j}|dkr!d}n |j}|s9|r|dkrQt}n|dkrp|jtd|S|dkr|jtd|S|r|j|S|j|SdS)zReturns whether the number is not actually one. if self, other are sNaN, signal if self, other are NaN return nan return 0 Done before operations. NFr+sNaNr%)rrrar r9)r.otherr/ self_is_nan other_is_nanr'r'r) _check_nans s"             zDecimal._check_nanscCs|dkrt}n|js*|jr|jrI|jtd|S|jrh|jtd|S|jr|jtd|S|jr|jtd|SndS)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%)rrOis_snanrar is_qnan)r.rr/r'r'r)_compare_check_nans,s(           zDecimal._compare_check_nanscCs|jp|jdkS)zuReturn True if self is nonzero; otherwise return False. NaNs and infinities are considered nonzero. rP)rOr8)r.r'r'r)__bool__MszDecimal.__bool__cCsd|js|jrQ|j}|j}||kr:dS||krJdSdSn|sp|sadSd|j Sn|sd|jS|j|jkrdS|j|jkrdS|j}|j}||kr=|jd|j|j}|jd|j|j}||krdS||kr/d |j Sd |jSn#||krTd |jSd |j SdS) zCompare 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%r-rPNrrrrrrrr)rOrr7adjustedr8rN)r.rZself_infZ other_inf self_adjustedZother_adjusted self_paddedZ other_paddedr'r'r)_cmpTs>             z Decimal._cmpcCsTt||dd\}}|tkr+|S|j||rAdS|j|dkS)N equality_opTFr%)_convert_for_comparisonNotImplementedrr)r.rr/r'r'r)__eq__s  zDecimal.__eq__cCsTt||dd\}}|tkr+|S|j||rAdS|j|dkS)NrTr%)rrrr)r.rr/r'r'r)__ne__s  zDecimal.__ne__cCsTt||\}}|tkr%|S|j||}|rAdS|j|dkS)NFr%)rrrr)r.rr/r;r'r'r)__lt__s zDecimal.__lt__cCsTt||\}}|tkr%|S|j||}|rAdS|j|dkS)NFr%)rrrr)r.rr/r;r'r'r)__le__s zDecimal.__le__cCsTt||\}}|tkr%|S|j||}|rAdS|j|dkS)NFr%)rrrr)r.rr/r;r'r'r)__gt__s zDecimal.__gt__cCsTt||\}}|tkr%|S|j||}|rAdS|j|dkS)NFr%)rrrr)r.rr/r;r'r'r)__ge__s zDecimal.__ge__cCs\t|dd}|js*|rI|jrI|j||}|rI|Snt|j|S)zCompare 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') raiseitT)_convert_otherrOrrr)r.rr/r;r'r'r)compares zDecimal.comparecCs|jrI|jr$tdqI|jr4tS|jrBt StSn|jdkrptd|jt }ntt |j t }t |j |t }|dkr|n| }|dkrdS|S)zx.__hash__() <==> hash(x)z"Cannot hash a signaling NaN value.r% r-r+r) rOrrois_nan _PyHASH_NANr7 _PyHASH_INFrNpow_PyHASH_MODULUS _PyHASH_10INVrRr8)r.Zexp_hashZhash_r;r'r'r)__hash__s    zDecimal.__hash__cCs(t|jttt|j|jS)zeRepresents the number as a triple tuple. To show the internals exactly as they are. )rr7rhrlrRr8rN)r.r'r'r)as_tupleszDecimal.as_tuplecCsdt|S)z0Represents the number as an instance of Decimal.z Decimal('%s'))r^)r.r'r'r)__repr__szDecimal.__repr__Fc Csddg|j}|jrc|jdkr3|dS|jdkrQ|d|jS|d|jSn|jt|j}|jdkr|dkr|}nE|sd }n6|jd kr|d d d }n|d d d }|dkr d }d d | |j}nf|t|jkrI|jd |t|j}d}n*|jd|}d |j|d}||krd}n7|dkrt}nddg|jd||}||||S)zReturn string representation of the number in scientific notation. Captures all of the information in the underlying representation. rSrQrXZInfinityr5NaNrr%r-rPrY.NeEz%+di)r7rOrNr8rcrcapitals) r.engr/r= leftdigitsdotplacersrtrTr'r'r)__str__s:         zDecimal.__str__cCs|jddd|S)aConvert to engineering-type string. Engineering notation has an exponent which is a multiple of 3, so there are up to 3 digits left of the decimal place. Same rules for when in exponential and when as a value as in __str__. rTr/)r)r.r/r'r'r) to_eng_string5szDecimal.to_eng_stringcCs~|jr(|jd|}|r(|Sn|dkr@t}n| re|jtkre|j}n |j}|j|S)zRReturns a copy with the sign switched. Rounds, if it has reason. r/N)rOrrr?rcopy_abs copy_negate_fix)r.r/r;r'r'r)__neg__?s    zDecimal.__neg__cCs~|jr(|jd|}|r(|Sn|dkr@t}n| re|jtkre|j}n t|}|j|S)zhReturns a copy, unless it is a sNaN. Rounds the number (if more then precision digits) r/N)rOrrr?rrrr)r.r/r;r'r'r)__pos__Us    zDecimal.__pos__TcCsl|s|jS|jr8|jd|}|r8|Sn|jrV|jd|}n|jd|}|S)zReturns 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(). r/)rrOrr7rr)r.roundr/r;r'r'r)__abs__js   zDecimal.__abs__c Csqt|}|tkr|S|dkr4t}n|jsF|jr|j||}|rb|S|jr|j|jkr|jr|jtdSt |S|jrt |Snt |j |j }d}|j t kr|j|jkrd}n| r[| r[t |j|j}|r6d}nt|d|}|j|}|S|st||j |jd}|j||j }|j|}|S|st||j |jd}|j||j }|j|}|St|}t|}t|||j\}}t} |j|jkr|j|jkrvt|d|}|j|}|S|j|jkr||}}n|jdkrd| _|j|j|_|_qd| _n6|jdkrd| _d\|_|_n d| _|jdkr3|j|j| _n|j|j| _|j| _t | }|j|}|S)zbReturns self + other. -INF + INF (or the reverse) cause InvalidOperation errors. Nz -INF + INFr%r-rP)r%r%)rrrrOrrr7rar rminrNr?rr6rmaxr@_rescalerf _normalizer=rRrT) r.rr/r;rTZ negativezeror=op1op2rr'r'r)__add__s|        !           zDecimal.__add__cCsit|}|tkr|S|js.|jrP|j|d|}|rP|Sn|j|jd|S)zReturn self - otherr/)rrrOrrr)r.rr/r;r'r'r)__sub__s  zDecimal.__sub__cCs/t|}|tkr|S|j|d|S)zReturn other - selfr/)rrr)r.rr/r'r'r)__rsub__s  zDecimal.__rsub__cCst|}|tkr|S|dkr4t}n|j|jA}|jsV|jr|j||}|rr|S|jr|s|jtdSt |S|jr|s|jtdSt |Sn|j |j }| s| r t |d|}|j |}|S|j dkrCt ||j |}|j |}|S|j dkrzt ||j |}|j |}|St|}t|}t |t|j|j|}|j |}|S)z\Return self * other. (+-) INF * 0 (or its reverse) raise InvalidOperation. Nz (+-)INF * 0z 0 * (+-)INFrP1)rrrr7rOrrrar r<rNr6rr8rfr^rR)r.rr/Z resultsignr;Z resultexprrr'r'r)__mul__sH         "zDecimal.__mul__c Cslt|}|tkrtS|dkr4t}n|j|jA}|jsV|jr|j||}|rr|S|jr|jr|jtdS|jrt |S|jr|jt dt |d|j Sn|s|s|jt dS|jtd|S|s1|j|j}d}nt|jt|j|jd}|j|j|}t|}t|} |dkrt|jd || j\}} n$t|j| jd | \}} | r|d dkrG|d7}qGnG|j|j} x4|| krF|d dkrF|d }|d7}qWt |t||}|j|S) zReturn self / other.Nz(+-)INF/(+-)INFzDivision by infinityrPz0 / 0zx / 0r%r-rrw)rrrr7rOrrrar r<rr6Etinyrr rNrcr8r@rfdivmodrRr^r) r.rr/r=r;rTcoeffshiftrr remainder ideal_expr'r'r) __truediv__'sP       '   &$ zDecimal.__truediv__c Cs|j|jA}|jr(|j}nt|j|j}|j|j}| sr|jsr|dkrt|dd|j||jfS||jkrot |}t |}|j |j kr|j d|j |j 9_ n|j d|j |j 9_ t |j |j \}} |d|jkrot|t |dt|jt | |fSn|jtd} | | fS)zReturn (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. r+rPr%rz%quotient too large in //, % or divmodr)r7rrNrrr6rr?r@rfrTrRrr^rar) r.rr/r=rexpdiffrrqrr;r'r'r)_dividebs*       zDecimal._dividecCs/t|}|tkr|S|j|d|S)z)Swaps self/other and returns __truediv__.r/)rrr)r.rr/r'r'r) __rtruediv__s  zDecimal.__rtruediv__cCs8t|}|tkr|S|dkr4t}n|j||}|rV||fS|j|jA}|jr|jr|jtd}||fSt||jtdfSn|s|s|jt d}||fS|jt d||jtdfSn|j ||\}}|j |}||fS)z6 Return (self // other, self % other) Nzdivmod(INF, INF)zINF % xz divmod(0, 0)zx // 0zx % 0) rrrrr7rrar r<rr rr)r.rr/r;r=Zquotientrr'r'r) __divmod__s0         zDecimal.__divmod__cCs/t|}|tkr|S|j|d|S)z(Swaps self/other and returns __divmod__.r/)rrr)r.rr/r'r'r) __rdivmod__s  zDecimal.__rdivmod__cCst|}|tkr|S|dkr4t}n|j||}|rP|S|jrl|jtdS|s|r|jtdS|jtdSn|j||d}|j |}|S)z self % other NzINF % xzx % 0z0 % 0r-) rrrrrrar rrr)r.rr/r;rr'r'r)__mod__s"     zDecimal.__mod__cCs/t|}|tkr|S|j|d|S)z%Swaps self/other and returns __mod__.r/)rrr)r.rr/r'r'r)__rmod__s  zDecimal.__rmod__c Cs||dkrt}nt|dd}|j||}|rF|S|jrb|jtdS|s|r~|jtdS|jtdSn|jrt|}|j|St |j |j }|st |j d|}|j|S|j |j }||jdkr)|jtS|d krW|j||j}|j|St|}t|}|j|jkr|jd |j|j9_n|jd |j|j9_t|j|j\}} d | |d@|jkr| |j8} |d7}n|d |jkr.|jtS|j } | d krWd| } | } nt | t| |}|j|S) zI Remainder nearest to 0- abs(remainder-near) <= other/2 NrTzremainder_near(infinity, x)zremainder_near(x, 0)zremainder_near(0, 0)rPr-r+rr%r)rrrrrar rrrrrNr6r7rr@rrr?rfrTrRrr^) r.rr/r;ideal_exponentrrrrrr=r'r'r)remainder_nearsZ                        zDecimal.remainder_nearcCst|}|tkr|S|dkr4t}n|j||}|rP|S|jr|jrx|jtdSt|j|jASn|s|r|jt d|j|jAS|jt dSn|j ||dS)z self // otherNz INF // INFzx // 0z0 // 0r%) rrrrrrar r<r7r rr)r.rr/r;r'r'r) __floordiv__"s$       zDecimal.__floordiv__cCs/t|}|tkr|S|j|d|S)z*Swaps self/other and returns __floordiv__.r/)rrr)r.rr/r'r'r) __rfloordiv__>s  zDecimal.__rfloordiv__cCsU|jr?|jr'tdn|jr6dnd}n t|}t|S)zFloat representation.z%Cannot convert signaling NaN to floatz-nannan)rrrir7r^rm)r.sr'r'r) __float__Es    zDecimal.__float__cCs|jrB|jr$tdqB|jrBtdqBnd|j}|jdkrz|t|jd|jS|t|jd|jpdSdS) z1Converts self to an int, truncating if necessary.zCannot convert NaN to integerz"Cannot convert infinity to integerr-r%rNrPr) rOrrir OverflowErrorr7rNrRr8)r.rr'r'r)__int__Os    zDecimal.__int__cCs|S)Nr')r.r'r'r)real^sz Decimal.realcCs tdS)Nr%)r)r.r'r'r)imagbsz Decimal.imagcCs|S)Nr')r.r'r'r) conjugatefszDecimal.conjugatecCstt|S)N)complexrm)r.r'r'r) __complex__iszDecimal.__complex__cCsq|j}|j|j}t||krg|t||djd}t|j||jdSt|S)z2Decapitate the payload of a NaN to fit the contextNrPT) r8r@clamprcrdr6r7rNr)r.r/ZpayloadZmax_payload_lenr'r'r)r9ls  #zDecimal._fix_nancCs;|jr/|jr"|j|St|Sn|j}|j}|s|j|g|j}tt |j ||}||j kr|j t t |jd|St|Snt|j|j |j}||kr|j td|j}|j t|j t|S||k}|r4|}n|j |krt|j|j |} | dkrt |jd|d}d} n|j|j} | || } |jd| pd} | dkrtt| d} t| |jkr| dd} |d7}qn||krA|j td|j}nt |j| |}| rr|rr|j tn|r|j tn| r|j tn|j t|s|j t n|S|r|j tn|jdkr1|j |kr1|j t |jd|j |} t |j| |St|S)zRound 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. rPz above Emaxr%rr-Nr)rOrr9rrEtoprArrrrNrarr6r7rcr8r@rr r _pick_rounding_functionr?r^rRrr )r.r/rrexp_maxZnew_expZexp_minr;Zself_is_subnormalruZrounding_methodchangedrrr'r'r)rxsn                    z Decimal._fixcCst|j|rdSdSdS)z(Also known as round-towards-0, truncate.r%r-Nr) _all_zerosr8)r.r@r'r'r) _round_downszDecimal._round_downcCs|j| S)zRounds away from 0.)r)r.r@r'r'r) _round_upszDecimal._round_upcCs5|j|dkrdSt|j|r-dSdSdS)zRounds 5 up (away from 0)Z56789r-r%Nr)r8r)r.r@r'r'r)_round_half_ups zDecimal._round_half_upcCs't|j|rdS|j|SdS)z Round 5 downr-Nr) _exact_halfr8r)r.r@r'r'r)_round_half_downszDecimal._round_half_downcCsJt|j|r9|dks5|j|ddkr9dS|j|SdS)z!Round 5 to even, rest to nearest.r%r-02468Nr)rr8r)r.r@r'r'r)_round_half_evens#zDecimal._round_half_evencCs(|jr|j|S|j| SdS)z(Rounds up (not away from 0 if negative.)N)r7r)r.r@r'r'r)_round_ceilings  zDecimal._round_ceilingcCs(|js|j|S|j| SdS)z'Rounds down (not towards 0 if negative)N)r7r)r.r@r'r'r) _round_floors  zDecimal._round_floorcCs<|r*|j|ddkr*|j|S|j| SdS)z)Round down unless digit prec-1 is 0 or 5.r-Z05N)r8r)r.r@r'r'r) _round_05ups zDecimal._round_05uprrrrrrrrcCs|dk rJt|ts*tdntdd| }|j|S|jr}|jrntdq}tdnt|j dt S)aRound 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%rzcannot round a NaNzcannot round an infinity) r]rRror6quantizerOrrirrr)r.r5rTr'r'r) __round__!s/    zDecimal.__round__cCsI|jr3|jr$tdq3tdnt|jdtS)zReturn 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. zcannot round a NaNzcannot round an infinityr%)rOrrirrRrr)r.r'r'r) __floor___s   zDecimal.__floor__cCsI|jr3|jr$tdq3tdnt|jdtS)zReturn 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. zcannot round a NaNzcannot round an infinityr%)rOrrirrRrr)r.r'r'r)__ceil__ns   zDecimal.__ceil__cCst|dd}t|dd}|js6|jr=|dkrNt}n|jdkrp|jtd|S|jdkr|jtd|S|jdkr|}q|jdkr|}q|jdkr|s|jtdSt|j|jA}q|jdkr|s#|jtd St|j|jA}qnBt|j|jAt t |j t |j |j|j}|j ||S) a:Fused multiply-add. Returns self*other+third with no rounding of the intermediate product self*other. self and other are multiplied together, with no rounding of the result. The third operand is then added to the result, and a single final rounding is performed. rTNrWrr5rXzINF * 0 in fmaz0 * INF in fma) rrOrrNrar r<r7r6r^rRr8r)r.rZthirdr/productr'r'r)fma}s6       z Decimal.fmac Cst|}|tkr|St|}|tkr8|S|dkrPt}n|j}|j}|j}|s|s|r|dkr|jtd|S|dkr|jtd|S|dkr|jtd|S|r|j|S|r |j|S|j|S|jo7|jo7|jsJ|jtdS|dkrf|jtdS|s||jtdS|j|j kr|jtdS| r| r|jtd S|j rd}n |j }t t |}t|j}t|j} |j |td |j||}x)t| jD]} t|d |}qGWt|| j |}t|t|dS) z!Three argument version of __pow__Nr+rz@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 definedr)rrrrrar r9 _isintegerrr@_isevenr7rerRrfto_integral_valuerrTranger6r^) r.rmodulor/rrZ modulo_is_nanr=baseexponentir'r'r) _power_modulosl                              $zDecimal._power_modulocCs?t|}|j|j}}x(|ddkrI|d}|d7}q"Wt|}|j|j}}x(|ddkr|d}|d7}qlW|dkrv||9}x(|ddkr|d}|d7}qW|dkrdS|d|} |jdkr | } n|jrT|jdkrT|jt|} t| | |d} nd} tddd| | | S|jdkry|d} | dkrI|| @|krdSt |d} |d d }|t t |krdSt | ||} t |||}| dks(|dkr,dS| |kr<dSd | }n| d kr@t |dd } t d | |\}}|rdSx(|d dkr|d }| d8} qW|dd}|t t |krdSt | ||} t |||}| dks|dkr#dS| |kr3dSd| }ndS|d|krXdS| |}tdt ||S|dkr|d|d}}n|dkrt t t||| krdSt |}|dkrt t t||| krdS|d| }}x<|d|dkoCdknr_|d}|d}q$Wx<|d |d kodknr|d }|d }qcW|dkrq|dkr||krdSt ||\}}|dkrdSdt | | >}xGt |||d\}}||kr2Pq||d||}qW||koa|dkshdS|}n|dkr||dt|krdS||}||9}|d|krdSt |}|jr|jdkr|jt|} t|| |t |} nd} td|d| || S)ahAttempt to compute self**other exactly. Given Decimals self and other and an integer p, attempt to compute an exact result for the power self**other, with p digits of precision. Return None if self**other is not exactly representable in p digits. Assumes that elimination of special cases has already been performed: self and other must both be nonspecial; self must be positive and not numerically equal to 1; other must be nonzero. For efficiency, other._exp should not be too large, so that 10**abs(other._exp) is a feasible calculation.rr%r-NrrPr+r]ArwrYd)r+rrr)rfrRrTr=rr7rNrr6_nbitsrcr^_decimal_lshift_exactrre _log10_lb)r.rpxxcxeyycyerrZzerosZ last_digitrZemaxrrrr5Zxc_bitsremarrZstr_xcr'r'r) _power_exacts:                   / /' '     &    zDecimal._power_exactcCs|dk r|j|||St|}|tkr;|S|dkrSt}n|j||}|ro|S|s|s|jtdStSnd}|jdkr|j r|j sd}qn|r|jtdS|j }n|s |jdkrt |ddSt |Sn|jrV|jdkrCt |St |ddSn|tkr-|j r|jdkrd}n'||jkr|j}n t|}|j|}|d|jkrd|j}|jtqn'|jt|jtd|j}t |dd| |S|j}|jr{|jdk|dkkrpt |ddSt |Snd}d} |j|j} |dk|jdkkr| tt|jkr0t |d|jd}q0n>|j} | tt| kr0t |d| d}n|dkr|j||jd}|dk r|dkrt d|j|j}nd } qn|dkr~|j} t|} | j| j}}t|}|j|j}}|jdkr| }nd }xZt||||| |\}}|d d tt|| drUPn|d 7}q Wt |t||}n| r|j rt|j|jkr|jdt|j}t |j|jd||j|}n|j }|j!xt"D]}d|j#| 0rrTrw)rrOrrr7rr6rNrrar r@rfrTrRrcr8rr^ _shallow_copy _set_roundingrr?)r.r/r;r@oprclrrrr5rr?r'r'r)sqrt s`                       z Decimal.sqrtcCst|dd}|dkr*t}n|js<|jr|j}|j}|s`|r|dkr|dkr|j|S|dkr|dkr|j|S|j||Sn|j|}|dkr|j|}n|dkr|}n|}|j|S)zReturns the larger value. Like max(self, other) except if one is not a number, returns NaN (and signals if one is sNaN). Also rounds. rTNr-r%r)rrrOrrrr compare_total)r.rr/snonr*r;r'r'r)r s&          z Decimal.maxcCst|dd}|dkr*t}n|js<|jr|j}|j}|s`|r|dkr|dkr|j|S|dkr|dkr|j|S|j||Sn|j|}|dkr|j|}n|dkr|}n|}|j|S)zReturns the smaller value. Like min(self, other) except if one is not a number, returns NaN (and signals if one is sNaN). Also rounds. rTNr-r%r)rrrOrrrrr-)r.rr/r.r/r*r;r'r'r)r/ s&          z Decimal.mincCsJ|jr dS|jdkr dS|j|jd}|dt|kS)z"Returns whether self is an integerFr%TNrP)rOrNr8rc)r.restr'r'r)rQ s  zDecimal._isintegercCs2| s|jdkrdS|jd|jdkS)z:Returns True if self is even. Assumes self is an integer.r%Tr-rr)rNr8)r.r'r'r)rZ szDecimal._isevenc Cs9y|jt|jdSWntk r4dSYnXdS)z$Return the adjusted exponent of selfr-r%N)rNrcr8ro)r.r'r'r)r` s zDecimal.adjustedcCs|S)zReturns the same Decimal object. As we do not have different encodings for the same number, the received object already is in its canonical form. r')r.r'r'r) canonicalh szDecimal.canonicalcCsAt|dd}|j||}|r.|S|j|d|S)zCompares self to the other operand numerically. It's pretty much like compare(), but all NaNs signal, with signaling NaNs taking precedence over quiet NaNs. rTr/)rrr)r.rr/r;r'r'r)compare_signalp s zDecimal.compare_signalcCst|dd}|jr)|j r)tS|j r@|jr@tS|j}|j}|j}|sm|rs||krt|j|jf}t|j|jf}||kr|rtStSn||kr|rtStSntS|r0|dkrtS|dkr tS|dkrtS|dkrptSqs|dkr@tS|dkrPtS|dkr`tS|dkrstSn||krtS||krtS|j|jkr|rtStSn|j|jkr|rtStSntS)zCompares self to other using the abstract representations. This is not like the standard compare, which use their numerical value. Note that a total ordering is defined for all possible abstract representations. rTr-r+) rr7 _NegativeOnerrrcr8_ZerorN)r.rr/r=Zself_nanZ other_nanZself_keyZ other_keyr'r'r)r-| sf                 zDecimal.compare_totalcCs7t|dd}|j}|j}|j|S)zCompares self to other using abstract repr., ignoring sign. Like compare_total, but with operand's sign ignored and assumed to be 0. rT)rrr-)r.rr/ror'r'r)compare_total_mag s  zDecimal.compare_total_magcCstd|j|j|jS)z'Returns a copy with the sign set to 0. r%)r6r8rNrO)r.r'r'r)r szDecimal.copy_abscCsE|jr%td|j|j|jStd|j|j|jSdS)z&Returns a copy with the sign inverted.r%r-N)r7r6r8rNrO)r.r'r'r)r s zDecimal.copy_negatecCs1t|dd}t|j|j|j|jS)z$Returns self with the sign of other.rT)rr6r7r8rNrO)r.rr/r'r'r) copy_sign szDecimal.copy_signc Cs|dkrt}n|jd|}|r4|S|jd krJtS|sTtS|jdkrpt|S|j}|j}|jdkr|t t |j ddkrt dd|j d}n|jdkr(|t t |j ddkr(t dd|j d}n1|jdkrj|| krjt ddd|dd| }n|jdkr|| dkrt dd|d| d}nt|}|j|j}}|jdkr| }nd}xTt||||\} } | d d t t | |dr3Pn|d7}qWt dt | | }|j}|jt} |j|}| |_|S) zReturns e ** self.Nr/r-r%rYrrPr>rwrr)rrrr4rrr@rr7rcr^rAr6rrfrRrTr=_dexpr'r(rrr?) r.r/r;r adjr)r*rrrrTr?r'r'r)rT sJ     26& "  &  z Decimal.expcCsdS)zReturn 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) is_canonical, szDecimal.is_canonicalcCs|j S)zReturn True if self is finite; otherwise return False. A Decimal instance is considered finite if it is neither infinite nor a NaN. )rO)r.r'r'r) is_finite4 szDecimal.is_finitecCs |jdkS)z8Return True if self is infinite; otherwise return False.rX)rN)r.r'r'r)r"< szDecimal.is_infinitecCs |jdkS)z>Return True if self is a qNaN or sNaN; otherwise return False.r5rW)r5rW)rN)r.r'r'r)r@ szDecimal.is_nancCs?|js| rdS|dkr,t}n|j|jkS)z?Return True if self is a normal number; otherwise return False.FN)rOrr!r)r.r/r'r'r) is_normalD s   zDecimal.is_normalcCs |jdkS)z;Return True if self is a quiet NaN; otherwise return False.r5)rN)r.r'r'r)rL szDecimal.is_qnancCs |jdkS)z8Return True if self is negative; otherwise return False.r-)r7)r.r'r'r) is_signedP szDecimal.is_signedcCs |jdkS)z?Return True if self is a signaling NaN; otherwise return False.rW)rN)r.r'r'r)rT szDecimal.is_snancCs?|js| rdS|dkr,t}n|j|jkS)z9Return True if self is subnormal; otherwise return False.FN)rOrrr!)r.r/r'r'r) is_subnormalX s   zDecimal.is_subnormalcCs|j o|jdkS)z6Return True if self is a zero; otherwise return False.rP)rOr8)r.r'r'r)is_zero` szDecimal.is_zerocCs|jt|jd}|dkrBtt|dddS|dkrnttd|dddSt|}|j|j}}|dkrt|d| }t|}t|t|||kS|ttd| |dS)zCompute 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-rr+r%rr)rNrcr8r^rfrRrT)r.r9r)r*rnumdenr'r'r) _ln_exp_boundd s      zDecimal._ln_exp_boundc Cst|dkrt}n|jd|}|r4|S|s>tS|jdkrTtS|tkrdtS|jdkr|jt dSt |}|j |j }}|j }||jd}xPt|||}|ddttt||drPn|d7}qWtt |d ktt|| }|j}|jt} |j|}| |_|S) z/Returns the natural (base e) logarithm of self.Nr/r-zln of a negative valuer+rwrrYr%)rr_NegativeInfinityr _Infinityrr4r7rar rfrRrTr@rC_dlogrcr^rer6r'r(rrr?) r.r/r;r)r*rr r$rr?r'r'r)ln} s:      ,+  z Decimal.lncCs|jt|jd}|dkr:tt|dS|dkr^ttd|dSt|}|j|j}}|dkrt|d| }td|}t|t|||kdStd| |}t|||dkdS) zCompute a lower bound for the adjusted exponent of self.log10(). In other words, find r such that self.log10() >= 10**r. Assumes that self is finite and positive and that self != 1. r-r+r%rZ231rr)rNrcr8r^rfrRrT)r.r9r)r*rrArBr'r'r)r s     "zDecimal._log10_exp_boundc Cs|dkrt}n|jd|}|r4|S|s>tS|jdkrTtS|jdkrs|jtdS|jddkr|jdddt |jdkrt |j t |jd}nt |}|j |j}}|j}||jd}xPt|||}|d d t tt||drTPn|d 7}qWtt |dktt|| }|j}|jt} |j|}| |_|S) z&Returns the base 10 logarithm of self.Nr/r-zlog10 of a negative valuer%rrPr+rwrrY)rrrDrrEr7rar r8rcrrNrfrRrTr@r_dlog10r^rer6r'r(rrr?) r.r/r;r)r*rr r$rr?r'r'r)log10 s:   =#  ,+  z Decimal.log10cCs||jd|}|r|S|dkr4t}n|jrDtS|s]|jtddSt|j}|j|S)aM Returns the exponent of the magnitude of self's MSD. The result is the integer which is the exponent of the magnitude of the most significant digit of self (as though it were truncated to a single digit while maintaining the value of that digit and without limiting the resulting exponent). r/Nzlogb(0)r-) rrrrErar rrr)r.r/r;r'r'r)logb s    z Decimal.logbcCsJ|jdks|jdkr"dSx!|jD]}|dkr,dSq,WdS)zReturn 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)r7rNr8)r.digr'r'r) _islogical s  zDecimal._islogicalcCs|jt|}|dkr0d||}n#|dkrS||j d}n|jt|}|dkrd||}n#|dkr||j d}n||fS)Nr%rP)r@rc)r.r/opaopbZdifr'r'r) _fill_logical, s    zDecimal._fill_logicalcCs|dkrt}nt|dd}|j sD|j rQ|jtS|j||j|j\}}djddt||D}t d|j dpddS) z;Applies an 'and' operation between self and other's digits.NrTrScSs2g|](\}}tt|t|@qSr')r^rR).0rbr'r'r) G s z'Decimal.logical_and..r%rP) rrrMrar rPr8rkzipr6rd)r.rr/rNrOrr'r'r) logical_and9 s   !%zDecimal.logical_andcCs;|dkrt}n|jtdd|jd|S)zInvert all its digits.Nr%r)r logical_xorr6r@)r.r/r'r'r)logical_invertJ s  zDecimal.logical_invertcCs|dkrt}nt|dd}|j sD|j rQ|jtS|j||j|j\}}djddt||D}t d|j dpddS) z:Applies an 'or' operation between self and other's digits.NrTrScSs2g|](\}}tt|t|BqSr')r^rR)rQrrRr'r'r)rS_ s z&Decimal.logical_or..r%rP) rrrMrar rPr8rkrTr6rd)r.rr/rNrOrr'r'r) logical_orQ s   !%zDecimal.logical_orcCs|dkrt}nt|dd}|j sD|j rQ|jtS|j||j|j\}}djddt||D}t d|j dpddS) z;Applies an 'xor' operation between self and other's digits.NrTrScSs2g|](\}}tt|t|AqSr')r^rR)rQrrRr'r'r)rSp s z'Decimal.logical_xor..r%rP) rrrMrar rPr8rkrTr6rd)r.rr/rNrOrr'r'r)rVb s   !%zDecimal.logical_xorcCst|dd}|dkr*t}n|js<|jr|j}|j}|s`|r|dkr|dkr|j|S|dkr|dkr|j|S|j||Sn|jj|j}|dkr|j|}n|dkr |}n|}|j|S)z8Compares the values numerically with their sign ignored.rTNr-r%r) rrrOrrrrrr-)r.rr/r.r/r*r;r'r'r)max_mags s&          zDecimal.max_magcCst|dd}|dkr*t}n|js<|jr|j}|j}|s`|r|dkr|dkr|j|S|dkr|dkr|j|S|j||Sn|jj|j}|dkr|j|}n|dkr |}n|}|j|S)z8Compares the values numerically with their sign ignored.rTNr-r%r) rrrOrrrrrr-)r.rr/r.r/r*r;r'r'r)min_mag s&          zDecimal.min_magcCs|dkrt}n|jd|}|r4|S|jdkrJtS|jdkrytdd|j|jS|j}|jt |j |j |}||kr|S|j tdd|j d|S)z=Returns the largest representable number smaller than itself.Nr/r-r%r>rr)rrrrDr6r@rrGr(r_ignore_all_flagsrrr)r.r/r;new_selfr'r'r) next_minus s"      zDecimal.next_minuscCs|dkrt}n|jd|}|r4|S|jdkrJtS|jdkrytdd|j|jS|j}|jt |j |j |}||kr|S|j tdd|j d|S)z=Returns the smallest representable number larger than itself.Nr/r-r>r%rr)rrrrEr6r@rrGr(rr[rrr)r.r/r;r\r'r'r) next_plus s"      zDecimal.next_pluscCs@t|dd}|dkr*t}n|j||}|rF|S|j|}|dkrn|j|S|dkr|j|}n|j|}|jr|jt d|j |jt |jt nb|j |jkr<|jt|jt|jt |jt |s<|jtq<n|S)aReturns 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. rTNr%r-z Infinite result from next_towardr)rrrrr7r^r]rrarr7r r rr!rr r)r.rr/r;Z comparisonr'r'r) next_toward s4              zDecimal.next_towardcCs|jrdS|jr dS|j}|dkr<dS|dkrLdS|jrl|jredSdSn|dkrt}n|jd |r|jrd Sd Sn|jrd Sd 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 rrr-z +Infinityz -Infinityz-Zeroz+ZeroNr/z -Subnormalz +Subnormalz-Normalz+Normalr)rrrr?r7rr>)r.r/infr'r'r) number_class s,           zDecimal.number_classcCs tdS)z'Just returns 10, as this is Decimal, :)r)r)r.r'r'r)radix5sz Decimal.radixcCsV|dkrt}nt|dd}|j||}|rF|S|jdkrb|jtS|j t|ko|jkns|jtS|jrt |St|}|j }|jt |}|dkrd||}n |dkr|| d}n||d|d|}t |j |jdpLd|jS)z5Returns a rotated copy of self, value-of-other times.NrTr%rP)rrrrNrar r@rRrrr8rcr6r7rd)r.rr/r;torotrotdigtopadZrotatedr'r'r)rotate9s,   )        zDecimal.rotatecCs|dkrt}nt|dd}|j||}|rF|S|jdkrb|jtSd|j|j}d|j|j}|t|ko|kns|jtS|j rt |St |j |j |jt|}|j|}|S)z>Returns self operand after adding the second value to its exp.NrTr%r+r)rrrrNrar rAr@rRrrr6r7r8r)r.rr/r;ZliminfZlimsupr}r'r'r)scalebZs"   "   %zDecimal.scalebcCsy|dkrt}nt|dd}|j||}|rF|S|jdkrb|jtS|j t|ko|jkns|jtS|jrt |St|}|j }|jt |}|dkrd||}n |dkr|| d}n|dkr2|d|}n"|d|}||j d}t |j |jdpod|jS)z5Returns a shifted copy of self, value-of-other times.NrTr%rP)rrrrNrar r@rRrrr8rcr6r7rd)r.rr/r;rcrdreZshiftedr'r'r)rss2   )         z Decimal.shiftcCs|jt|ffS)N) __class__r^)r.r'r'r) __reduce__szDecimal.__reduce__cCs)t|tkr|S|jt|S)N)typerrhr^)r.r'r'r)__copy__szDecimal.__copy__cCs)t|tkr|S|jt|S)N)rjrrhr^)r.memor'r'r) __deepcopy__szDecimal.__deepcopy__cCs|dkrt}nt|d|}|jrt|j|}t|j}|ddkrt|d7}nt|||S|ddkrddg|j|dr?rCrGrrJrKrMrPrUrWrXrVrYrZr]r^r_rarbrfrgrrirkrmrzr'r'r'r)r)s  (   !  @        4 V7; !$K        f        >  ,U G " c*"    I  K         2 3  .* !'   FcCs7tjt}||_||_||_||_|S)zCreate a decimal instance directly, without any validation, normalization (e.g. removal of leading zeros) or argument conversion. This function is for *internal use only*. )r[r\rr7r8rNrO)r=Z coefficientrZspecialr.r'r'r)r6s     r6c@s:eZdZdZddZddZddZdS) rMzContext manager class to support localcontext(). Sets a copy of the supplied context in __enter__() and restores the previous decimal context in __exit__() cCs|j|_dS)N)rG new_context)r.rr'r'r)__init__sz_ContextManager.__init__cCs t|_t|j|jS)N)r saved_contextrr)r.r'r'r) __enter__s  z_ContextManager.__enter__cCst|jdS)N)rr)r.tvtbr'r'r)__exit__sz_ContextManager.__exit__N)r1r2r3r4rrrr'r'r'r)rMs   rMc @seZdZdZddddddddddd ZddZddZd d Zd d Zd dZ ddZ ddZ ddZ ddZ ddZeZdddZddZddZdd ZdZd!d"Zd#d$Zd%d&Zd'd(d)Zd*d+Zd,d-Zd.d/Zd0d1Zd2d3Zd4d5Zd6d7Zd8d9Z d:d;Z!d<d=Z"d>d?Z#d@dAZ$dBdCZ%dDdEZ&dFdGZ'dHdIZ(dJdKZ)dLdMZ*dNdOZ+dPdQZ,dRdSZ-dTdUZ.dVdWZ/dXdYZ0dZd[Z1d\d]Z2d^d_Z3d`daZ4dbdcZ5dddeZ6dfdgZ7dhdiZ8djdkZ9dldmZ:dndoZ;dpdqZ<drdsZ=dtduZ>dvdwZ?dxdyZ@dzd{ZAd|d}ZBd~dZCddZDddZEddZFddZGdddZHddZIddZJddZKddZLddZMddZNddZOddZPddZQddZRddZSddZTddZUddZVeVZWdS)raContains 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 sy t} Wntk rYnX|dk r1|n| j|_|dk rO|n| j|_|dk rm|n| j|_|dk r|n| j|_|dk r|n| j|_|dk r|n| j|_| dkrg|_n | |_dkr| j j |_ nAt t sMt fddt D|_ n |_ dkrzt jt d|_nAt t st fddt D|_n |_dS)Nc3s'|]}|t|kfVqdS)N)rR)rQr)rr'r) Nsz#Context.__init__..r%c3s'|]}|t|kfVqdS)N)rR)rQr)rr'r)rUs)r NameErrorr@r?r!rArr_ignored_flagsrrGr]rrfromkeysr) r.r@r?r!rArrrrrZdcr')rrr)r5s.      )  )zContext.__init__cCst|ts"td|n|dkr\||krtd||||fqnq|dkr||krtd||||fqn7||ks||krtd||||fntj|||S)Nz%s must be an integerz-infz%s must be in [%s, %d]. got: %sr`z%s must be in [%d, %s]. got: %sz%s must be in [%d, %d]. got %s)r]rRrorir[ __setattr__)r.namerqZvminZvmaxr'r'r)_set_integer_checkYs  "  "zContext._set_integer_checkcCst|ts"td|nx-|D]%}|tkr)td|q)q)Wx-tD]%}||krYtd|qYqYWtj|||S)Nz%s must be a signal dictz%s is not a valid signal dict)r]rrorKeyErrorr[r)r.rr}keyr'r'r)_set_signal_dictgs    zContext._set_signal_dictcCsC|dkr"|j||ddS|dkrD|j||ddS|dkrf|j||ddS|dkr|j||ddS|d kr|j||ddS|d kr|tkrtd |ntj|||S|d ks|d kr|j||S|dkr/tj|||Std|dS)Nr@r-r`r!z-infr%rArrr?z%s: invalid rounding moderrrz.'decimal.Context' object has no attribute '%s')r_rounding_modesror[rrrK)r.rrqr'r'r)rrs(        zContext.__setattr__cCstd|dS)Nz%s cannot be deleted)rK)r.rr'r'r) __delattr__szContext.__delattr__c Csodd|jjD}dd|jjD}|j|j|j|j|j|j|j ||ffS)NcSs"g|]\}}|r|qSr'r')rQsigrr'r'r)rSs z&Context.__reduce__..cSs"g|]\}}|r|qSr'r')rQrrr'r'r)rSs ) ritemsrrhr@r?r!rArr)r.rrr'r'r)ris zContext.__reduce__cCsg}|jdt|dd|jjD}|jddj|ddd|jjD}|jddj|ddj|d S) zShow the current context.zrContext(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, clamp=%(clamp)dcSs%g|]\}}|r|jqSr')r1)rQr|rr'r'r)rSs z$Context.__repr__..zflags=[z, ]cSs%g|]\}}|r|jqSr')r1)rQrrr'r'r)rSs ztraps=[))rjvarsrrrkr)r.rnamesr'r'r)rs zContext.__repr__cCs%x|jD]}d|j|>> 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 )rrnr)r.r|r}r'r'r)create_decimal_from_floatsz!Context.create_decimal_from_floatcCs"t|dd}|jd|S)a[Returns the absolute value of the operand. If the operand is negative, the result is the same as using the minus operation on the operand. Otherwise, the result is the same as using the plus operation on the operand. >>> ExtendedContext.abs(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.abs(Decimal('-100')) Decimal('100') >>> ExtendedContext.abs(Decimal('101.5')) Decimal('101.5') >>> ExtendedContext.abs(Decimal('-101.5')) Decimal('101.5') >>> ExtendedContext.abs(-1) Decimal('1') rTr/)rr)r.rr'r'r)re&sz Context.abscCsNt|dd}|j|d|}|tkrFtd|n|SdS)aReturn 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') rTr/zUnable to convert %s to DecimalN)rrrro)r.rrRrr'r'r)add;s  z Context.addcCst|j|S)N)r^r)r.rr'r'r)_applyPszContext._applycCs(t|tstdn|jS)zReturns the same Decimal object. As we do not have different encodings for the same number, the received object already is in its canonical form. >>> ExtendedContext.canonical(Decimal('2.50')) Decimal('2.50') z,canonical requires a Decimal as an argument.)r]rror1)r.rr'r'r)r1Ss zContext.canonicalcCs%t|dd}|j|d|S)aCompares 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') rTr/)rr)r.rrRr'r'r)r`s!zContext.comparecCs%t|dd}|j|d|S)aCompares the values of the two operands numerically. It's pretty much like compare(), but all NaNs signal, with signaling NaNs taking precedence over quiet NaNs. >>> c = ExtendedContext >>> c.compare_signal(Decimal('2.1'), Decimal('3')) Decimal('-1') >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) Decimal('0') >>> c.flags[InvalidOperation] = 0 >>> print(c.flags[InvalidOperation]) 0 >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) Decimal('NaN') >>> print(c.flags[InvalidOperation]) 1 >>> c.flags[InvalidOperation] = 0 >>> print(c.flags[InvalidOperation]) 0 >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) Decimal('NaN') >>> print(c.flags[InvalidOperation]) 1 >>> c.compare_signal(-1, 2) Decimal('-1') >>> c.compare_signal(Decimal(-1), 2) Decimal('-1') >>> c.compare_signal(-1, Decimal(2)) Decimal('-1') rTr/)rr2)r.rrRr'r'r)r2s zContext.compare_signalcCst|dd}|j|S)a+Compares two operands using their abstract representation. This is not like the standard compare, which use their numerical value. Note that a total ordering is defined for all possible abstract representations. >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) Decimal('0') >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) Decimal('1') >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) Decimal('-1') >>> ExtendedContext.compare_total(1, 2) Decimal('-1') >>> ExtendedContext.compare_total(Decimal(1), 2) Decimal('-1') >>> ExtendedContext.compare_total(1, Decimal(2)) Decimal('-1') rT)rr-)r.rrRr'r'r)r-szContext.compare_totalcCst|dd}|j|S)zCompares two operands using their abstract representation ignoring sign. Like compare_total, but with operand's sign ignored and assumed to be 0. rT)rr6)r.rrRr'r'r)r6szContext.compare_total_magcCst|dd}|jS)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') rT)rr)r.rr'r'r)rs zContext.copy_abscCst|dd}t|S)aReturns a copy of the decimal object. >>> ExtendedContext.copy_decimal(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.copy_decimal(Decimal('-1.00')) Decimal('-1.00') >>> ExtendedContext.copy_decimal(1) Decimal('1') rT)rr)r.rr'r'r) copy_decimals zContext.copy_decimalcCst|dd}|jS)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') rT)rr)r.rr'r'r)rs zContext.copy_negatecCst|dd}|j|S)aCopies the second operand's sign to the first one. In detail, it returns a copy of the first operand with the sign equal to the sign of the second operand. >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) Decimal('1.50') >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) Decimal('1.50') >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) Decimal('-1.50') >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) Decimal('-1.50') >>> ExtendedContext.copy_sign(1, -2) Decimal('-1') >>> ExtendedContext.copy_sign(Decimal(1), -2) Decimal('-1') >>> ExtendedContext.copy_sign(1, Decimal(-2)) Decimal('-1') rT)rr7)r.rrRr'r'r)r7szContext.copy_signcCsNt|dd}|j|d|}|tkrFtd|n|SdS)aDecimal 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') rTr/zUnable to convert %s to DecimalN)rrrro)r.rrRrr'r'r)divide s  zContext.dividecCsNt|dd}|j|d|}|tkrFtd|n|SdS)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') rTr/zUnable to convert %s to DecimalN)rrrro)r.rrRrr'r'r) divide_int0s  zContext.divide_intcCsNt|dd}|j|d|}|tkrFtd|n|SdS)aReturn (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')) rTr/zUnable to convert %s to DecimalN)rrrro)r.rrRrr'r'r)rGs  zContext.divmodcCs"t|dd}|jd|S)a#Returns e ** a. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.exp(Decimal('-Infinity')) Decimal('0') >>> c.exp(Decimal('-1')) Decimal('0.367879441') >>> c.exp(Decimal('0')) Decimal('1') >>> c.exp(Decimal('1')) Decimal('2.71828183') >>> c.exp(Decimal('0.693147181')) Decimal('2.00000000') >>> c.exp(Decimal('+Infinity')) Decimal('Infinity') >>> c.exp(10) Decimal('22026.4658') rTr/)rrT)r.rr'r'r)rT\sz Context.expcCs(t|dd}|j||d|S)a Returns 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') rTr/)rr)r.rrRr*r'r'r)rtsz Context.fmacCs(t|tstdn|jS)aReturn True if the operand is canonical; otherwise return False. Currently, the encoding of a Decimal instance is always canonical, so this method returns True for any Decimal. >>> ExtendedContext.is_canonical(Decimal('2.50')) True z/is_canonical requires a Decimal as an argument.)r]rror:)r.rr'r'r)r:s zContext.is_canonicalcCst|dd}|jS)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 rT)rr;)r.rr'r'r)r;szContext.is_finitecCst|dd}|jS)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 rT)rr")r.rr'r'r)r"s zContext.is_infinitecCst|dd}|jS)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 rT)rr)r.rr'r'r)rs zContext.is_nancCs"t|dd}|jd|S)aReturn 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 rTr/)rr<)r.rr'r'r)r<szContext.is_normalcCst|dd}|jS)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 rT)rr)r.rr'r'r)rs zContext.is_qnancCst|dd}|jS)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 rT)rr=)r.rr'r'r)r=szContext.is_signedcCst|dd}|jS)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 rT)rr)r.rr'r'r)rs zContext.is_snancCs"t|dd}|jd|S)aReturn 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 rTr/)rr>)r.rr'r'r)r>szContext.is_subnormalcCst|dd}|jS)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 rT)rr?)r.rr'r'r)r?*szContext.is_zerocCs"t|dd}|jd|S)aReturns 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') rTr/)rrG)r.rr'r'r)rG;sz Context.lncCs"t|dd}|jd|S)aReturns 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') rTr/)rrJ)r.rr'r'r)rJQsz Context.log10cCs"t|dd}|jd|S)a4 Returns the exponent of the magnitude of the operand's MSD. The result is the integer which is the exponent of the magnitude of the most significant digit of the operand (as though the operand were truncated to a single digit while maintaining the value of that digit and without limiting the resulting exponent). >>> ExtendedContext.logb(Decimal('250')) Decimal('2') >>> ExtendedContext.logb(Decimal('2.50')) Decimal('0') >>> ExtendedContext.logb(Decimal('0.03')) Decimal('-2') >>> ExtendedContext.logb(Decimal('0')) Decimal('-Infinity') >>> ExtendedContext.logb(1) Decimal('0') >>> ExtendedContext.logb(10) Decimal('1') >>> ExtendedContext.logb(100) Decimal('2') rTr/)rrK)r.rr'r'r)rKmsz Context.logbcCs%t|dd}|j|d|S)aApplies 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') rTr/)rrU)r.rrRr'r'r)rUszContext.logical_andcCs"t|dd}|jd|S)a Invert 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') rTr/)rrW)r.rr'r'r)rWszContext.logical_invertcCs%t|dd}|j|d|S)aApplies the logical operation 'or' between each operand's digits. The operands must be both logical numbers. >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) Decimal('0') >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) Decimal('1') >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) Decimal('1') >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) Decimal('1') >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) Decimal('1110') >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) Decimal('1110') >>> ExtendedContext.logical_or(110, 1101) Decimal('1111') >>> ExtendedContext.logical_or(Decimal(110), 1101) Decimal('1111') >>> ExtendedContext.logical_or(110, Decimal(1101)) Decimal('1111') rTr/)rrX)r.rrRr'r'r)rXszContext.logical_orcCs%t|dd}|j|d|S)aApplies 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') rTr/)rrV)r.rrRr'r'r)rVszContext.logical_xorcCs%t|dd}|j|d|S)amax 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') rTr/)rr)r.rrRr'r'r)rsz Context.maxcCs%t|dd}|j|d|S)aCompares 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') rTr/)rrY)r.rrRr'r'r)rYszContext.max_magcCs%t|dd}|j|d|S)amin 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') rTr/)rr)r.rrRr'r'r)rsz Context.mincCs%t|dd}|j|d|S)aCompares 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') rTr/)rrZ)r.rrRr'r'r)rZ2szContext.min_magcCs"t|dd}|jd|S)aMinus 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') rTr/)rr)r.rr'r'r)minusCsz Context.minuscCsNt|dd}|j|d|}|tkrFtd|n|SdS)amultiply 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') rTr/zUnable to convert %s to DecimalN)rrrro)r.rrRrr'r'r)multiplyTs  zContext.multiplycCs"t|dd}|jd|S)a"Returns the largest representable number smaller than a. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> ExtendedContext.next_minus(Decimal('1')) Decimal('0.999999999') >>> c.next_minus(Decimal('1E-1007')) Decimal('0E-1007') >>> ExtendedContext.next_minus(Decimal('-1.00000003')) Decimal('-1.00000004') >>> c.next_minus(Decimal('Infinity')) Decimal('9.99999999E+999') >>> c.next_minus(1) Decimal('0.999999999') rTr/)rr])r.rr'r'r)r]tszContext.next_minuscCs"t|dd}|jd|S)aReturns the smallest representable number larger than a. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> ExtendedContext.next_plus(Decimal('1')) Decimal('1.00000001') >>> c.next_plus(Decimal('-1E-1007')) Decimal('-0E-1007') >>> ExtendedContext.next_plus(Decimal('-1.00000003')) Decimal('-1.00000002') >>> c.next_plus(Decimal('-Infinity')) Decimal('-9.99999999E+999') >>> c.next_plus(1) Decimal('1.00000001') rTr/)rr^)r.rr'r'r)r^szContext.next_pluscCs%t|dd}|j|d|S)aReturns 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') rTr/)rr_)r.rrRr'r'r)r_s zContext.next_towardcCs"t|dd}|jd|S)anormalize 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') rTr/)rr )r.rr'r'r)r szContext.normalizecCs"t|dd}|jd|S)aReturns 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' rTr/)rra)r.rr'r'r)ras/zContext.number_classcCs"t|dd}|jd|S)aPlus 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') rTr/)rr)r.rr'r'r)plus sz Context.pluscCsQt|dd}|j||d|}|tkrItd|n|SdS)a Raises 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') rTr/zUnable to convert %s to DecimalN)rrrro)r.rrRrrr'r'r)powers I z Context.powercCs%t|dd}|j|d|S)a Returns a value equal to 'a' (rounded), having the exponent of 'b'. The coefficient of the result is derived from that of the left-hand operand. It may be rounded using the current rounding setting (if the exponent is being increased), multiplied by a positive power of ten (if the exponent is being decreased), or is unchanged (if the exponent is already equal to that of the right-hand operand). Unlike other operations, if the length of the coefficient after the quantize operation would be greater than precision then an Invalid operation condition is raised. This guarantees that, unless there is an error condition, the exponent of the result of a quantize is always equal to that of the right-hand operand. Also unlike other operations, quantize will never raise Underflow, even if the result is subnormal and inexact. >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) Decimal('2.170') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) Decimal('2.17') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) Decimal('2.2') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) Decimal('2') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) Decimal('0E+1') >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) Decimal('-Infinity') >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) Decimal('NaN') >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) Decimal('-0') >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) Decimal('-0E+5') >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) Decimal('NaN') >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) Decimal('NaN') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) Decimal('217.0') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) Decimal('217') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) Decimal('2.2E+2') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) Decimal('2E+2') >>> ExtendedContext.quantize(1, 2) Decimal('1') >>> ExtendedContext.quantize(Decimal(1), 2) Decimal('1') >>> ExtendedContext.quantize(1, Decimal(2)) Decimal('1') rTr/)rr)r.rrRr'r'r)rjs7zContext.quantizecCs tdS)zkJust returns 10, as this is Decimal, :) >>> ExtendedContext.radix() Decimal('10') r)r)r.r'r'r)rbsz Context.radixcCsNt|dd}|j|d|}|tkrFtd|n|SdS)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') rTr/zUnable to convert %s to DecimalN)rrrro)r.rrRrr'r'r)rs  zContext.remaindercCs%t|dd}|j|d|S)aGReturns to be "a - b * n", where n is the integer nearest the exact value of "x / b" (if two integers are equally near then the even one is chosen). If the result is equal to 0 then its sign will be the sign of a. This operation will fail under the same conditions as integer division (that is, if integer division on the same two operands would fail, the remainder cannot be calculated). >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) Decimal('-0.9') >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) Decimal('-2') >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) Decimal('1') >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) Decimal('-1') >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) Decimal('0.2') >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) Decimal('0.1') >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) Decimal('-0.3') >>> ExtendedContext.remainder_near(3, 11) Decimal('3') >>> ExtendedContext.remainder_near(Decimal(3), 11) Decimal('3') >>> ExtendedContext.remainder_near(3, Decimal(11)) Decimal('3') rTr/)rr)r.rrRr'r'r)rszContext.remainder_nearcCs%t|dd}|j|d|S)aNReturns a rotated copy of a, b times. The coefficient of the result is a rotated copy of the digits in the coefficient of the first operand. The number of places of rotation is taken from the absolute value of the second operand, with the rotation being to the left if the second operand is positive or to the right otherwise. >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) Decimal('400000003') >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) Decimal('12') >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) Decimal('891234567') >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) Decimal('123456789') >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) Decimal('345678912') >>> ExtendedContext.rotate(1333333, 1) Decimal('13333330') >>> ExtendedContext.rotate(Decimal(1333333), 1) Decimal('13333330') >>> ExtendedContext.rotate(1333333, Decimal(1)) Decimal('13333330') rTr/)rrf)r.rrRr'r'r)rfszContext.rotatecCst|dd}|j|S)aReturns 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 rT)rr#)r.rrRr'r'r)r#szContext.same_quantumcCs%t|dd}|j|d|S)a3Returns the first operand after adding the second value its exp. >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) Decimal('0.0750') >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) Decimal('7.50') >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) Decimal('7.50E+3') >>> ExtendedContext.scaleb(1, 4) Decimal('1E+4') >>> ExtendedContext.scaleb(Decimal(1), 4) Decimal('1E+4') >>> ExtendedContext.scaleb(1, Decimal(4)) Decimal('1E+4') rTr/)rrg)r.rrRr'r'r)rg)szContext.scalebcCs%t|dd}|j|d|S)a{Returns a shifted copy of a, b times. The coefficient of the result is a shifted copy of the digits in the coefficient of the first operand. The number of places to shift is taken from the absolute value of the second operand, with the shift being to the left if the second operand is positive or to the right otherwise. Digits shifted into the coefficient are zeros. >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) Decimal('400000000') >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) Decimal('0') >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) Decimal('1234567') >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) Decimal('123456789') >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) Decimal('345678900') >>> ExtendedContext.shift(88888888, 2) Decimal('888888800') >>> ExtendedContext.shift(Decimal(88888888), 2) Decimal('888888800') >>> ExtendedContext.shift(88888888, Decimal(2)) Decimal('888888800') rTr/)rr)r.rrRr'r'r)r<sz Context.shiftcCs"t|dd}|jd|S)aSquare 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 rTr/)rr,)r.rr'r'r)r,Zsz Context.sqrtcCsNt|dd}|j|d|}|tkrFtd|n|SdS)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') rTr/zUnable to convert %s to DecimalN)rrrro)r.rrRrr'r'r)subtractzs  zContext.subtractcCs"t|dd}|jd|S)zyConverts a number to a string, using scientific notation. The operation is not affected by the context. rTr/)rr)r.rr'r'r)rszContext.to_eng_stringcCs"t|dd}|jd|S)zyConverts a number to a string, using scientific notation. The operation is not affected by the context. rTr/)rr)r.rr'r'r) to_sci_stringszContext.to_sci_stringcCs"t|dd}|jd|S)akRounds to an integer. When the operand has a negative exponent, the result is the same as using the quantize() operation using the given operand as the left-hand-operand, 1E+0 as the right-hand-operand, and the precision of the operand as the precision setting; Inexact and Rounded flags are allowed in this operation. The rounding mode is taken from the context. >>> ExtendedContext.to_integral_exact(Decimal('2.1')) Decimal('2') >>> ExtendedContext.to_integral_exact(Decimal('100')) Decimal('100') >>> ExtendedContext.to_integral_exact(Decimal('100.0')) Decimal('100') >>> ExtendedContext.to_integral_exact(Decimal('101.5')) Decimal('102') >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) Decimal('-102') >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) Decimal('1.0E+6') >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) Decimal('7.89E+77') >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) Decimal('-Infinity') rTr/)rr&)r.rr'r'r)r&szContext.to_integral_exactcCs"t|dd}|jd|S)aLRounds to an integer. When the operand has a negative exponent, the result is the same as using the quantize() operation using the given operand as the left-hand-operand, 1E+0 as the right-hand-operand, and the precision of the operand as the precision setting, except that no flags will be set. The rounding mode is taken from the context. >>> ExtendedContext.to_integral_value(Decimal('2.1')) Decimal('2') >>> ExtendedContext.to_integral_value(Decimal('100')) Decimal('100') >>> ExtendedContext.to_integral_value(Decimal('100.0')) Decimal('100') >>> ExtendedContext.to_integral_value(Decimal('101.5')) Decimal('102') >>> ExtendedContext.to_integral_value(Decimal('-101.5')) Decimal('-102') >>> ExtendedContext.to_integral_value(Decimal('10E+5')) Decimal('1.0E+6') >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) Decimal('7.89E+77') >>> ExtendedContext.to_integral_value(Decimal('-Inf')) Decimal('-Infinity') rTr/)rr)r.rr'r'r)rszContext.to_integral_value)Xr1r2r3r4rrrrrrirrHrr'rGrkrar[rrrrrr(rrrerrr1rr2r-r6rrrr7rrrrTrr:r;r"rr<rr=rr>r?rGrJrKrUrWrXrVrrYrrZrrr]r^r_r rarrrrbrrrfr#rgrr,rrrr&rrr'r'r'r)r"s   "                   $ #    %                            #  2 P :  & "         c@s7eZdZd ZdddZddZeZdS) rfr=rRrTNcCs|dkr*d|_d|_d|_nct|trf|j|_t|j|_|j|_n'|d|_|d|_|d|_dS)Nr%r-r+)r=rRrTr]rr7r8rN)r.rqr'r'r)rs       z_WorkRep.__init__cCsd|j|j|jfS)Nz (%r, %r, %r))r=rRrT)r.r'r'r)rsz_WorkRep.__repr__)zsignzintzexp)r1r2r3r{rrrr'r'r'r)rfs  rfcCs|j|jkr!|}|}n |}|}tt|j}tt|j}|jtd||d}||jd|krd|_||_n|jd|j|j9_|j|_||fS)zcNormalizes op1, op2 to have the same exp and length of coefficient. Done during addition. r-r+rr)rTrcr^rRr)rrr@ZtmprZtmp_lenZ other_lenrTr'r'r)rs    rcCs{|dkrdS|dkr(|d|Stt|}t|t|jd}|| krjdS|d| SdS)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%rrPN)r^rercrstrip)r5rZstr_nZval_nr'r'r)rs   rcCs^|dks|dkr'tdnd}x*||krY||| |d?}}q0W|S)zClosest 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-)ri)r5rrRr'r'r) _sqrt_nearest0s rcCs7d|>||?}}|d||d@|d@|kS)zGiven 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-r+r')r rrRrr'r'r)_rshift_nearest?srcCs/t||\}}|d||d@|kS)zaClosest integer to a/b, a and b positive integers; rounds to even in the case of a tie. r+r-)r)rrRrrr'r'r) _div_nearestGsrrc Cs7||}d}x||kr9t|||>|ks_||krt|||?|krt||d>|t||t|||}|d7}qWtdtt|d| }t||}t||}x>t|dddD]&}t||t|||}qWt|||S)aInteger 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-rrYir)rerrrrRrcr^r) r MLrRTZyshiftwr~r'r'r)_ilogOs )&'%$rc Cs|d7}tt|}||||dk}|dkrd|}|||}|dkru|d|9}nt|d| }t||}t|}t|||}||} nd}t|d| } t| |dS)zGiven integers c, e and p with c > 0, p >= 0, compute an integer approximation to 10**p * log10(c*10**e), with an absolute error of at most 1. Assumes that c*10**e is not exactly 1.r+r-r%rr)rcr^rr _log10_digits) r*rr r+r|rr~log_dZlog_10Z log_tenpowerr'r'r)rIs       rIc Cs|d7}tt|}||||dk}|dkr|||}|dkrk|d|9}nt|d| }t|d|}nd}|rttt|d}||dkrt|t||d|}qd}nd}t||dS)zGiven integers c, e and p with c > 0, compute an integer approximation to 10**p * log(c*10**e), with an absolute error of at most 1. Assumes that c*10**e is not exactly 1.r+r-r%rr)rcr^rrrer) r*rr r+r|r~rrZ f_log_tenr'r'r)rFs"   $ rFc@s.eZdZdZddZddZdS) _Log10MemoizezClass 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)ru)r.r'r'r)rsz_Log10Memoize.__init__cCs|dkrtdn|t|jkrd}xad||d}tttd||d}|| dd|krPn|d7}q9W|jddd |_nt|jd|d S) ztGiven an integer p >= 0, return floor(10**p)*log(10). For example, self.getdigits(3) returns 2302. r%zp should be nonnegativerYrr+rNrPr-r)rircrur^rrrrR)r.r rrrur'r'r) getdigitss "z_Log10Memoize.getdigitsN)r1r2r3r4rrr'r'r'r)rs  rc Cst||>|}tdtt|d| }t||}||>}x9t|dddD]!}t|||||}qiWxCt|ddd D]+}||d>}t||||}qW||S) zGiven 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).rrYr-r%r+irrr)rrRrcr^rr) r rrrrrZMshiftrr~r'r'r)_iexps% rc Cs|d7}td|tt|d}||}||}|dkr^|d|}n|d| }t|t|\}}t|d|}tt|d|d||dfS)aCompute an approximation to exp(c*10**e), with p decimal places of precision. Returns integers d, f such that: 10**(p-1) <= d <= 10**p, and (d-1)*10**f < exp(c*10**e) < (d+1)*10**f In other words, d*10**f is an approximation to exp(c*10**e) with p digits of precision, and with an error in d of at most 1. This is almost, but not quite, the same as the error being < 1ulp: when d = 10**(p-1) the error could be up to 10 ulp.r+r%r-rirY)rrcr^rrrr) r*rr rrrZcshiftZquotrr'r'r)r8s #   r8c Cs*ttt||}t||||d}||}|dkra||d|}nt||d| }|dkrtt||dk|dkkrd|ddd|} } q d|d| } } n:t||d |d\} } t| d} | 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%r)rcr^rerFrr8) r r rrr rRZlxcrZpcrrTr'r'r)r;s   ( ! rrrF253(45r@67r8rwr>cCsA|dkrtdnt|}dt|||dS)z@Compute a lower bound for 100*log10(c) for a positive integer c.r%z0The argument to _log10_lb should be nonnegative.r)rir^rc)r*Z correctionZstr_cr'r'r)r es  r cCskt|tr|St|tr,t|S|rNt|trNtj|S|rgtd|ntS)zConvert 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). zUnable to convert %s to Decimal)r]rrRrmrnror)rrZ allow_floatr'r'r)rps  rcCst|tr||fSt|tjrx|jset|jtt|j |j |j }n|t|j fS|rt|tj r|jdkr|j}nt|trt}|rd|jt[-+])? # 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*$z50*$z\A (?: (?P.)? (?P[<>=^]) )? (?P[-+ ])? (?P\#)? (?P0)? (?P(?!0)\d+)? (?P,)? (?:\.(?P0|(?!0)\d+))? (?P[eEfFgGn%])? \Z cCs+tj|}|dkr.td|n|j}|d}|d}|ddk |d<|dr|dk rtd|n|dk rtd|qn|pd|d<|pd |d<|d dkrd |d ', '=' 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: fillalignzeropadz7Fill character conflicts with '0' in format specifier: z2Alignment conflicts with '0' in format specifier:  >r=rQ minimumwidthrPrrr%rjZgGnr-r5rp thousands_sepzJExplicit thousands separator conflicts with 'n' type in format specifier: grouping decimal_pointrSrYr)_parse_format_specifier_regexmatchri groupdictrR_locale localeconv)Z format_specrnrrZ format_dictrrr'r'r)rtsN               rtc Cs|d}|d}||t|t|}|d}|dkrY|||}n|dkrv|||}nn|dkr|||}nQ|dkrt|d}|d |||||d }n td |S) zGiven 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). rrrqsn                    &           .     0 " ,# % $ *#( *          P  % )