grthtrhthjhtyjytjytkergtrhtrjytjerhrfh4:24 29/09/2026+ o9zRt.RNRNRNRNRNRNRNRNR NR NR NR NR NRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNR NR!NR"NR#NR$NR%NR&NR'Nt]tR(tR)tR*t^R+It^R+It ^R+I t ^R,I H t ] !RR-R(R.7tRtRtRtRtRtRtRtRtR0tR0t] P4Rx8Xd R1tR1tRytR2tMR3tR3tRztR4t]]^, , t!R5R] 4t!!R6R]!4t"!R7R ]!4t#!R8R]#4t$!R9R ]!]%4t&!R:R]#4t'!R;R]#]%4t(!R<R ]!4t)!R=R]#4t*!R>R ]!4t+!R?R ]!4t,!R@R])]+4t-!RAR])]+],4t.!RBR]!]/4t0]"]&])]-]+].]#],]0. t1]$]#]']#](]#]*]#/t2]]]]]]]]3t3^R+I4t4]4Pj!RC4t6]7!.R{O4t8RDt9REt:A4R|RFlt;RGt<!RHR]=4t>R}RIlt?] PP]>4!RJRK]=4tB!RLR]=4tC!RMRN]=4tDR~ROltE]FPtHRPtIRQtJRRtKRStLRRTltMRUtNRVtO!RWRX]=4tP]P!4PtRRRYltSRZtTR[tUR\^dR]^FR^^5R_^(R`^Ra^Rb^Rc^ Rd^/ 3ReltVRRfltWR}RgltX]C!^]]&]-]#..RhR^^Ri7tY]C!^ ]]&]-]#]"]...Rj7tZ]C!^ ]..Rj7t[^R+I\t\]\P!Rk]\P]\P,4Pta]\P!Rl4Ptb]\P!Rm4Ptc]\P!Rn]\P]\P,4teA\^R+IftgR|RolthRptiRqtjRRrltkRstlRttm]>!Ru4tn]>!Rv4to]>!Rw4tp]>!^4tq]>!^4tr]>!R4ts]n]o3tt] PPtw] PPty] PPt{]|!^ ]w^, ]w4t}A R+# ]dR/tELvi;i ]dLi;i)z Python decimal arithmetic moduleDecimalContext DecimalTupleDefaultContext BasicContextExtendedContextDecimalExceptionClampedInvalidOperationDivisionByZeroInexactRounded SubnormalOverflow UnderflowFloatOperationDivisionImpossibleInvalidContextConversionSyntaxDivisionUndefined ROUND_DOWN ROUND_HALF_UPROUND_HALF_EVEN ROUND_CEILING ROUND_FLOORROUND_UPROUND_HALF_DOWN ROUND_05UP setcontext getcontext localcontext IEEEContextMAX_PRECMAX_EMAXMIN_EMIN MIN_ETINYIEEE_CONTEXT_MAX_BITS HAVE_THREADSHAVE_CONTEXTVARdecimalz1.70z2.4.2N) namedtuplezsign digits exponent)modulecV#N)argss*1/opt/alt/python314/lib64/python3.14/_pydecimal.pyr1CsTlNZoii@Tc*a]tRt^atoRtRtRtVtR#)raBase 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. cR#r-r.selfcontextr/s&&*r0handleDecimalException.handlets r2r.N__name__ __module__ __qualname____firstlineno____doc__r9__static_attributes____classdictcell__ __classdict__s@r0rras$  r2c]tRt^xtRtRtR#)r a Exponent of a 0 changed to fit bounds. This occurs and signals clamped if the exponent of a result has been altered in order to fit the constraints of a specific concrete representation. This may occur when the exponent of a zero result would be outside the bounds of a representation, or when a large normal number would have an encoded exponent that cannot be represented. In this latter case, the exponent is reduced to fit and the corresponding number of zero digits are appended to the coefficient ("fold-down"). r.Nr<r=r>r?r@rAr.r2r0r r x r2c*a]tRt^toRtRtRtVtR#)r aAn invalid operation was performed. Various bad things cause this: Something creates a signaling NaN -INF + INF 0 * (+-)INF (+-)INF / (+-)INF x % 0 (+-)INF % x x._rescale( non-integer ) sqrt(-x) , x > 0 0 ** 0 x ** (non-integer) x ** (+-)INF An operand is invalid The result of the operation after this is a quiet positive NaN, except when the cause is a signaling NaN, in which case the result is also a quiet NaN, but with the original sign, and an optional diagnostic information. cV'dB\V^,PV^,PRR4pVPV4#\#)nT)_dec_from_triple_sign_int_fix_nan_NaN)r7r8r/anss&&* r0r9InvalidOperation.handles9 "47==$q',,TJC<<( ( r2r.Nr;rCs@r0r r s,r2c*a]tRt^toRtRtRtVtR#)rzTrying to convert badly formed string. This occurs and signals invalid-operation if a string is being converted to a number and it does not conform to the numeric string syntax. The result is [0,qNaN]. c\#r-rPr6s&&*r0r9ConversionSyntax.handle r2r.Nr;rCs@r0rrs r2c*a]tRt^toRtRtRtVtR#)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. c\V,#r-)_SignedInfinityr7r8signr/s&&&*r0r9DivisionByZero.handles t$$r2r.Nr;rCs@r0r r s %%r2c*a]tRt^toRtRtRtVtR#)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]. c\#r-rUr6s&&*r0r9DivisionImpossible.handlerWr2r.Nr;rCs@r0rrr2c*a]tRt^toRtRtRtVtR#)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]. c\#r-rUr6s&&*r0r9DivisionUndefined.handlerWr2r.Nr;rCs@r0rrrar2c]tRt^tRtRtR#)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. r.NrFr.r2r0r r rGr2c*a]tRt^toRtRtRtVtR#)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]. c\#r-rUr6s&&*r0r9InvalidContext.handlerWr2r.Nr;rCs@r0rrs r2c]tRt^tRtRtR#)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. r.NrFr.r2r0r r rGr2c]tRt^tRtRtR#)raExponent < 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. r.NrFr.r2r0rrsr2c*a]tRtRtoRtRtRtVtR#)riaNumerical 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. cVP\\\\39d\ V,#V^8XdcVP\ 8Xd\ V,#\VRVP,VPVP, ^,4#V^8XdcVP\8Xd\ V,#\VRVP,VPVP, ^,4#R#)rJ9N) roundingrrrrrZrrLprecEmaxrr[s&&&*r0r9Overflow.handles     / ; ;"4( ( 19=0&t,,#D#gll*:#LL5a79 9 19;.&t,,#D#gll*:$\\',,6q8: : r2r.Nr;rCs@r0rrs* : :r2c]tRtRtRtRtR#)ri)aTNumerical 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. r.NrFr.r2r0rr)s r2c]tRtRtRtRtR#)ri8auEnable 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. r.NrFr.r2r0rr8s r2decimal_contextc\P4# \d%\4p\P T4Tu#i;i)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. )_current_context_varget LookupErrorrsetr8s r0rrcs?#'')) )  )s,AAcV\\\39d!VP4pVP 4\ P V4R#)z%Set this thread's context to context.N)rrrcopy clear_flagsrvryrzs&r0rrqs6><AA,,.W%r2c Vf \4p\V4pVP4F5wr4V\9d\ RV R24h\ VP W44K7 V#)aReturn 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 'z2' is an invalid keyword argument for this function)r_ContextManageritems_context_attributes TypeErrorsetattr new_context)ctxkwargs ctx_managerkeyvalues&, r0r r zscH {l!#&Klln  ) )au$VWX X ''4% r2cV^8:gV\8gV^ ,'d\R\ 24h\4p^ V^ ,,^, Vn^^V^,^,,,Vn^VP, Vn\ Vn^Vn\P\R4Vn V#)z Return a context object initialized to the proper values for one of the IEEE interchange formats. The argument must be a multiple of 32 and less than IEEE_CONTEXT_MAX_BITS. z5argument must be a multiple of 32, with a maximum of F) r& ValueErrorrrorpEminrrnclampdictfromkeys_signalstraps)bitsrs" r0r!r!s  qyD00D2II..C-DFG G )CD"H~!CHA$(Q,'(CH388|CH"CLCI h.CI Jr2c @a]tRtRtoRtR|tR}Rlt]R4t]R4t Rt Rt R~R lt R t R tR tRR ltRRltRRltRRltRRltRRltRtRtRtRtRRltRRltRRltRRltRRltRRlt]t RRlt!RRlt"RRlt#]#t$RR lt%R!t&RR"lt'RR#lt(RR$lt)RR%lt*RR&lt+RR'lt,RR(lt-RR)lt.R*t/R+t0]0t1]2R,4t3]2R-4t4R.t5R/t6R0t7R1t8R2t9R3t:R4t;R5tR8t?R9t@]A!]9]:];]<]=]>]?]@R:7tBRR;ltCR<tDR=tERR>ltFRR?ltGR@tHR~RAltIR~RBltJRRCltKR~RDltLRREltMRFtNRGtOR~RHltPR~RIltQ]QtRRRJltSRRKltTRRLltURMtVRNtWROtXRPtYRRQltZRRRlt[RRSlt\RTt]RUt^RRVlt_RRWlt`RXtaRYtbRZtcR[tdRR\lteR]tfR^tgR_thRR`ltiRatjRbtkRRcltlRdtmRReltnRRfltoRgtpRhtqRRiltrRRjltsRRklttRRlltuRRmltvRRnltwRRoltxRRpltyRRqltzRRrlt{Rst|RRtlt}RRult~RRvltRwtRxtRytR~RzltR{tVtR#)riz,Floating-point class for decimal arithmetic.Nc \PV4p\V\4'Ed\ VP 4P RR44pVf,Vf \4pVP\RV,4#VPR4R8Xd ^Vn M^Vn VPR4pVeVPR4;'gRp\VPR4;'gR 4p\\WV,44Vn V\V4, VnR VnV#VPR 4pVeZ\\T;'gR 44P#R 4Vn VPR 4'd R VnMRVnMR Vn RVnRVnV#\V\4'd@V^8d ^Vn M^Vn ^Vn\\%V44Vn R VnV#\V\&4'dGVPVnVPVn VPVn VP VnV#\V\(4'dOVP*Vn \VP4Vn \VP,4VnR VnV#\V\.\034'Ed\V4^8wd \3R4h\V^,\4'dV^,R9g \3R4hV^,Vn V^,R8XdR Vn V^,VnRVnV#.p V^,FXp \V \4'd7^T u;8:d^ 8:d(MM$V 'gV ^8wdV P5V 4KMKO\3R4h V^,R9d<RP7\9\V 44Vn V^,VnRVnV#\V^,\4'dGRP7\9\T ;'g^.44Vn V^,VnR VnV#\3R4h\V\:4'dVf \4pVP\<R4\&P?V4pVPVnVPVn VPVn VP VnV#\ARV,4h)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') _zInvalid literal for Decimal: %rr\-intfracexp0FdiagsignalNrKFTztInvalid 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.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'.;strict semantics for mixing floats and Decimals are enabledCannot convert %r to DecimalrJrKr)!object__new__ isinstancestr_parserstripreplacer _raise_errorrgrouprMrrNlen_exp _is_speciallstripabsr_WorkRepr\rlisttuplerappendjoinmapfloatr from_floatr) clsrr8r7mintpartfracpartrrdigitsdigits &&& r0rDecimal.__new__se.~~c" eS ! ! --c267Ay?(lG++,< AE IKKwwv#%  ggenG"776?00b!''%.//C0G$4 56 #h-/ #( Kwwv# #C $4 5 < ?? eU # #$,   &&u-EDIDJDI % 1 1D K6>??r2c x\V\\\34'd V!V4#\ RV,4h)aAConverts a real number to a decimal number, exactly. >>> Decimal.from_number(314) # int Decimal('314') >>> Decimal.from_number(0.1) # float Decimal('0.1000000000000000055511151231257827021181583404541015625') >>> Decimal.from_number(Decimal('3.14')) # another decimal instance Decimal('3.14') r)rrrrr)rnumbers&&r0 from_numberDecimal.from_numberbs3 fsGU3 4 4v; 6?@@r2c b\V\4'd#V^8d^M^p^p\\V44pM\V\4'd\ P !V4'g\ P!V4'dV!\V44#\ P!RV4R8Xd^pM^p\V4P4wrVVP4^, p\V^V,,4pM \R4h\W$V)4pV\JdV#V!V4#)aConverts a float to a decimal number, exactly. Note that Decimal.from_float(0.1) is not the same as Decimal('0.1'). Since 0.1 is not exactly representable in binary floating point, the value is stored as the nearest representable value which is 0x1.999999999999ap-4. The exact equivalent of the value in decimal is 0.1000000000000000055511151231257827021181583404541015625. >>> Decimal.from_float(0.1) Decimal('0.1000000000000000055511151231257827021181583404541015625') >>> Decimal.from_float(float('nan')) Decimal('NaN') >>> Decimal.from_float(float('inf')) Decimal('Infinity') >>> Decimal.from_float(-float('inf')) Decimal('-Infinity') >>> Decimal.from_float(-0.0) Decimal('-0') g?zargument must be int or float.)rrrrr_mathisinfisnanreprcopysignas_integer_ratio bit_lengthrrLr)rfr\kcoeffrKdresults&& r0rDecimal.from_floatqs, a  Q1ADAAKE 5 ! !{{1~~Q47|#~~c1%,q6**,DA "A!Q$KE<= =!$r2 '>Mv; r2c fVP'dVPpVR8Xd^#VR8Xd^#^#)zRReturns whether the number is not actually one. 0 if a number 1 if NaN 2 if sNaN rKr)rr)r7rs& r0_isnanDecimal._isnans0    ))Cczr2c TVPR8XdVP'dR#^#^#)zYReturns whether the number is infinite 0 if finite or not a number 1 if +INF -1 if -INF r)rrMr7s&r0 _isinfinityDecimal._isinfinitys$ 99 zzz r2c \VP4pVfRpMVP4pV'g V'duVf \4pV^8XdVP\RV4#V^8XdVP\RV4#V'dVP V4#VP V4#^#)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. FsNaN)rrrr rO)r7otherr8 self_is_nan other_is_nans&&& r0 _check_nansDecimal._check_nansskkm = L <<>L ,$,a++,>'* *r2c Vf \4pVP'gVP'dVP4'dVP\RV4#VP4'dVP\RV4#VP 4'dVP\RV4#VP 4'dVP\RV4#^#)aVersion of _check_nans used for the signaling comparisons compare_signal, __le__, __lt__, __ge__, __gt__. Signal InvalidOperation if either self or other is a (quiet or signaling) NaN. Signaling NaNs take precedence over quiet NaNs. Return 0 if neither operand is a NaN. zcomparison involving sNaNzcomparison involving NaN)rris_snanrr is_qnanr7rr8s&&&r0_compare_check_nansDecimal._compare_check_nanss ? lG    u000||~~++,<,G,022++,<,G,133++,<,F,022++,<,F,133r2c HVP;'gVPR8g#)zeReturn True if self is nonzero; otherwise return False. NaNs and infinities are considered nonzero. rrrNrs&r0__bool__Decimal.__bool__s! 33499#33r2c VP'gVP'd3VP4pVP4pW#8Xd^#W#8dR#^#V'gV'g^#RVP,)#V'gRVP,#VPVP8dR#VPVP8d^#VP4pVP4pWE8XdVPRVP VP , ,,pVPRVP VP , ,,pWg8Xd^#Wg8dRVP,)#RVP,#WE8dRVP,#RVP,)#)zCompare the two non-NaN decimal instances self and other. Returns -1 if self < other, 0 if self == other and 1 if self > other. This routine is for internal use only.rr)rrrMadjustedrNr)r7rself_inf other_inf self_adjustedother_adjusted self_padded other_paddeds&& r0_cmp Decimal._cmps[    u000'')H))+I$% u{{*++# # ;; #I :: #  )  *))c499uzz+A&BBK ::UZZ$))-C(DDL*+djj(((TZZ''  +# #4::%& &r2c\WRR7wrV\JdV#VPW4'dR#VPV4^8H#)T) equality_opF)_convert_for_comparisonNotImplementedrrrs&&&r0__eq__Decimal.__eq__BsE-dtL  N "L   E + +yy1$$r2c\W4wrV\JdV#VPW4pV'dR#VPV4^8#Frrrrr7rr8rQs&&& r0__lt__Decimal.__lt__JE-d:  N "L&&u6 yy!##r2c\W4wrV\JdV#VPW4pV'dR#VPV4^8*#rrrs&&& r0__le__Decimal.__le__SE-d:  N "L&&u6 yy1$$r2c\W4wrV\JdV#VPW4pV'dR#VPV4^8#rrrs&&& r0__gt__Decimal.__gt__\rr2c\W4wrV\JdV#VPW4pV'dR#VPV4^8#rrrs&&& r0__ge__Decimal.__ge__err2c \VRR7pVP'gV'd.VP'dVPW4pV'dV#\VP V44#)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') Traiseit)_convert_otherrrrrrs&&& r0compareDecimal.comparensWud3    %*;*;*;""52C tyy'((r2c VP'dlVP4'd \R4hVP4'd\P V4#VP 'd\)#\#VP^8d\^ VP\4pM \\VP)\4p\VP4V,\,pV^8dTMV)pVR8XdR#T#)zx.__hash__() <==> hash(x)z"Cannot hash a signaling NaN value.r)rrris_nanr__hash__rM _PyHASH_INFrpow_PyHASH_MODULUS _PyHASH_10INVrrN)r7exp_hashhash_rQs& r0rDecimal.__hash__s    ||~~ DEEt,,:::'<'&& 99>2tyy/:H=499*oFHDII)O;qyeufBYr'C'r2c  \VP\\\VP 44VP 4#)zURepresents the number as a triple tuple. To show the internals exactly as they are. )rrMrrrrNrrs&r0as_tupleDecimal.as_tuples+ DJJc#tyy.A(BDIINNr2c lVP'd-VP4'd \R4h\R4hV'gR#\ VP 4pVP ^8dV^ VP ,,^r!MVP )pV^8d#V^,^8XdV^,pV^,pK)VP )p\W),P4^, V4pV'dW,pWE,p^V,V,pVP'dV)pW3#)aGExpress a finite Decimal instance in the form n / d. Returns a pair (n, d) of integers. When called on an infinity or NaN, raises OverflowError or ValueError respectively. >>> Decimal('3.14').as_integer_ratio() (157, 50) >>> Decimal('-123e5').as_integer_ratio() (-12300000, 1) >>> Decimal('0.00').as_integer_ratio() (0, 1) z#cannot convert NaN to integer ratioz(cannot convert Infinity to integer ratior) rrr OverflowErrorrrNrminrrM)r7rKrd5d2shift2s& r0rDecimal.as_integer_ratios    {{}} !FGG#$NOOK  N 99>r499}$aq))Bq&QUaZaa))B!b&,,.2B7F  2 A :::At r2c &R\V4,#)z0Represents the number as an instance of Decimal.z Decimal('%s'))rrs&r0__repr__Decimal.__repr__sT**r2c RR.VP,pVP'd`VPR8Xd VR,#VPR8XdVR,VP,#VR,VP,#VP\ VP4,pVP^8:d VR8dTpMKV'g^pM@VPR8XdV^,^,^, pMV^, ^,^,pV^8:d&RpR RV),,VP,pMvV\ VP48d8VPRV\ VP4, ,,pRpM%VPR VpR VPVR ,pWE8XdRpM7Vf \ 4pR R .VP ,R WE, ,,pW6,V,V,#)zReturn string representation of the number in scientific notation. Captures all of the information in the underlying representation. rrrInfinityrKNaNrr.NeEz%+d)rMrrrNrrcapitals) r7engr8r\ leftdigitsdotplacerrrs &&& r0__str__Decimal.__str__s Cy$    yyCj((c!e|dii//f}tyy00YYTYY/ 99>j2o!HH YY# "Q!+a/H#Q!+a/H q=GS8)_,tyy8H TYY 'iiXc$))n%< ==GHii *GTYYxy11H  !C$,*W--.*:M1NNC~(3..r2c (VPRVR7#)a Convert to a string, using engineering notation if an exponent is needed. Engineering notation has an exponent which is a multiple of 3. This can leave up to 3 digits to the left of the decimal place and may require the addition of either one or two trailing zeros. T)r5r8)r8r7r8s&&r0 to_eng_stringDecimal.to_eng_string s||g|66r2c VP'dVPVR7pV'dV#Vf \4pV'g'VP\8wdVP 4pMVP 4pVPV4#)zBReturns a copy with the sign switched. Rounds, if it has reason. rz)rrrrnrcopy_abs copy_negate_fixr7r8rQs&& r0__neg__Decimal.__neg__sq    ""7"3C ? lG((K7--/C""$Cxx  r2c VP'dVPVR7pV'dV#Vf \4pV'g'VP\8wdVP 4pM \ V4pVPV4#)zXReturns a copy, unless it is a sNaN. Rounds the number (if more than precision digits) rz)rrrrnrr?rrArBs&& r0__pos__Decimal.__pos__+sj    ""7"3C ? lG((K7--/C$-Cxx  r2c V'gVP4#VP'dVPVR7pV'dV#VP'dVP VR7pV#VP VR7pV#)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(). rz)r?rrrMrCrF)r7roundr8rQs&&& r0__abs__Decimal.__abs__@sq==? "    ""7"3C :::,,w,/C ,,w,/C r2c \V4pV\JdV#Vf \4pVP'gVP'dVP W4pV'dV#VP 4'dSVP VP 8wd-VP 4'dVP\R4#\V4#VP 4'd \V4#\VPVP4p^pVP\8XdVP VP 8wd^pV'gSV'gK\VP VP 4pV'd^p\VRV4pVPV4pV#V'g\\!WAPVP", ^, 4pVP%WBP4pVPV4pV#V'g\\!W@PVP", ^, 4pVP%WBP4pVPV4pV#\'V4p\'V4p\)WxVP"4wrx\'4p VP*VP*8wdVP,VP,8Xd!\VRV4pVPV4pV#VP,VP,8dYrVP*^8Xd,^V nVP*VP*uVnVnM7^V nM/VP*^8Xd^V n^^uVnVnM^V nVP*^8Xd$VP,VP,,V nM"VP,VP,, V nVP.V n\V 4pVPV4pV#)zRReturns self + other. -INF + INF (or the reverse) cause InvalidOperation errors. z -INF + INFr)rrrrrrrMrr rr%rrnrrLrAmaxro_rescaler _normalizer\rr) r7rr8rQr negativezeror\op1op2rs &&& r0__add__Decimal.__add__Vs u% N "L ? lG    u000""52C !!::,1B1B1D1D"//0@,OOt}$  ""u~%$))UZZ(   { *tzzU[[/HLEtzz5;;/D"4c2C((7#CJc:: 4Q67C..&6&67C((7#CJc99w||3A56C--%5%56C((7#CJtnuoc 5 88sxx ww#''!&|S#>hhw' ww Sxx1} %(XXsxx"#( XX]FK"#Q CHchFK 88q=377*FJ377*FJWW fohhw r2c \V4pV\JdV#VP'gVP'dVPWR7pV'dV#VP VP 4VR7#)zReturn self - otherrz)rrrrrSr@rs&&& r0__sub__Decimal.__sub__siu% N "L    u000""5":C ||E--/|AAr2c T\V4pV\JdV#VPWR7#)zReturn other - selfrz)rrrVrs&&&r0__rsub__Decimal.__rsub__s*u% N "L}}T}33r2c >\V4pV\JdV#Vf \4pVPVP, pVP'gVP'dVP W4pV'dV#VP 4'd,V'gVP\R4#\V,#VP 4'd,V'gVP\R4#\V,#VPVP,pV'd V'g!\VRV4pVPV4pV#VPR8Xd*\W1PV4pVPV4pV#VPR8Xd*\W0PV4pVPV4pV#\V4p\V4p\V\VP VP ,4V4pVPV4pV#)zLReturn self * other. (+-) INF * 0 (or its reverse) raise InvalidOperation. z (+-)INF * 0z 0 * (+-)INFr1)rrrrMrrrrr rZrrLrArNrrr)r7rr8 resultsignrQ resultexprQrRs&&& r0__mul__Decimal.__mul__s u% N "L ? lGZZ%++-    u000""52C !!"//0@-PP&z22  """//0@-PP&z22II * 5":sI>C((7#CJ 99 ":zz9EC((7#CJ :: ":yy)DC((7#CJtnuoz3sww/@+A9Mhhw r2c \V4pV\Jd\#Vf \4pVPVP, pVP'gVP'dVP W4pV'dV#VP 4'd-VP 4'dVP\R4#VP 4'd\V,#VP 4'd2VP\R4\VRVP44#V'g6V'gVP\R4#VP\RV4#V'g"VPVP, p^pEMO\!VP"4\!VP"4, VP$,^,pVPVP, V, p\'V4p\'V4p V^8d2\)VP*^ V,,V P*4wrjM1\)VP*V P*^ V),,4wrjV 'dV^,^8Xd V^, pMEVPVP, p W[8d#V^ ,^8XdV^ ,pV^, pK(\V\-V4V4pVP/V4#)zReturn self / other.z(+-)INF/(+-)INFzDivision by infinityrz0 / 0zx / 0)rrrrMrrrrr rZr rLEtinyrr rrrNrordivmodrrrA) r7rr8r\rQrrshiftrQrR remainder ideal_exps &&& r0 __truediv__Decimal.__truediv__s?u% N "! ! ? lGzzEKK'    u000""52C !!e&7&7&9&9++,<>OPP!!&t,,  ""$$W.DE'c7==?CC++,=wGG''F F))ejj(CE Oc$))n4w||CaGE))ejj(50C4.C5/Cz#)#''BI*=sww#G y#)#''377R%Z3G#H 19>QJE!II 2 o%"*/bLE1HCtSZ5xx  r2c *VPVP, pVP4'dVPpM \VPVP4pVP 4VP 4, pV'dVP4'gVR8:d)\ VR^4VP WBP43#WRP8:Ed\V4p\V4pVPVP8d=V;P^ VPVP, ,,un M;V;P^ VPVP, ,,un \VPVP4wrV^ VP,8d7\ V\V4^4\ VP\V 4V43#VP\R4p W3#)zReturn (self // other, self % other), to context.prec precision. Assumes that neither self nor other is a NaN, that self is not infinite and that other is nonzero. rz%quotient too large in //, % or divmodr)rMrrr%rrLrNrnrorrrrcrrr) r7rr8r\rfexpdiffrQrRqrrQs &&& r0_divideDecimal._divide8s} zzEKK'      IDIIuzz2I--/ENN$44u((**gm$T32MM)-=-=>@ @ ll "4.C5/Cww#''!2#'' 1222#'' 122#''377+DA2w||##(s1vq9(SVYGII""#5#JLxr2c T\V4pV\JdV#VPWR7#)z)Swaps self/other and returns __truediv__.rz)rrrgrs&&&r0 __rtruediv__Decimal.__rtruediv__Ys-u% N "L   77r2c \V4pV\JdV#Vf \4pVPW4pV'dW33#VPVP, pVP 4'dSVP 4'dVP \R4pW33#\V,VP \R43#V'gOV'gVP \R4pW33#VP \RV4VP \R43#VPW4wrVVPV4pWV3#)z& Return (self // other, self % other) zdivmod(INF, INF)INF % xz divmod(0, 0)x // 0x % 0) rrrrrMrrr rZrr rmrA)r7rr8rQr\quotientres&&& r0 __divmod__Decimal.__divmod__`s-u% N "L ? lGu. : zzEKK'       ""**+;=OPx'-,,-=yIKK**+S^#B M1 1S:DII.55#66 6r2cV#r-r.rs&r0real Decimal.real4s r2c\^4#rJrrs&r0imag Decimal.imag8s qzr2cV#r-r.rs&r0 conjugateDecimal.conjugate<s r2c*\\V44#r-)complexrrs&r0 __complex__Decimal.__complex__?suT{##r2c VPpVPVP, p\V4V8dFV\V4V, RP R4p\ VP W PR4#\V4#)z2Decapitate the payload of a NaN to fit the contextNrT) rNrorrrrLrMrr)r7r8payloadmax_payload_lens&& r0rODecimal._fix_nanBsm))",,6 w&&xtzzJC   )   )J#O G 99w ^dii/'9Fz' CC"::7;K;KLO%d3GIIgv&--#E{CJqL)u: ,!#2JEqLG~**8\4::N&tzz5B,$$Y/ $$Y/$$W-   )$$W-J    + ==A $))d"2   )))c499t+;&< DIId1f%T1##D) )$$T** *r2)rrrrrrrrc DVeA\V\4'g \R4h\^RV)4pVP V4#VP 'd-VP 4'd \R4h\R4h\VP^\44#)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') z+Second argument to round should be integralr\cannot round a NaNcannot round an infinity) rrrrLquantizerrrr$rNr)r7rKrs&& r0 __round__Decimal.__round__s^ =a%% MNN"1cA2.C==% %    {{}} !566#$>??4==O455r2c VP'd-VP4'd \R4h\R4h\ VP ^\ 44#)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. rr)rrrr$rrNrrs&r0 __floor__Decimal.__floor__5sI    {{}} !566#$>??4==K011r2c VP'd-VP4'd \R4h\R4h\ VP ^\ 44#)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. rr)rrrr$rrNrrs&r0__ceil__Decimal.__ceil__DsI    {{}} !566#$>??4==M233r2c  \VRR7p\VRR7pVP'gVP'Ed9Vf \4pVPR8XdVP \ RV4#VPR8XdVP \ RV4#VPR8XdTpEM>VPR8XdTpEM)VPR8XdHV'gVP \ R4#\ VPVP, ,pMVPR8XdGV'gVP \ R4#\ VPVP, ,pMy\VPVP, \\VP4\VP4,4VPVP,4pXPW#4#) 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. TrrrrKrzINF * 0 in fmaz0 * INF in fma) rrrrrr rZrMrLrrrNrS)r7rthirdr8products&&&& r0fma Decimal.fmaSsud3ud3    u000$,yyC++,C O+K'L'+yy5::'=?Gu..r2c \V4pV\JdV#\V4pV\JdV#Vf \4pVP4pVP4pVP4pV'gV'g V'dV^8XdVP \ RV4#V^8XdVP \ RV4#V^8XdVP \ RV4#V'dVP V4#V'dVP V4#VP V4#VP4'd-VP4'dVP4'gVP \ R4#V^8dVP \ R4#V'gVP \ R4#VP4VP8dVP \ R4#V'gV'gVP \ R4#VP4'd^pM VPp\\V44p\VP44p\VP44p VPV,\!^ VP"V4,V,p\%V P"4Fp \!V^ V4pK \!WPV4p\'V\)V4^4#)z!Three argument version of __pow__rz@pow() 3rd argument not allowed unless all arguments are integerszApow() 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 defined)rrrrrr rO _isintegerrro_isevenrMrrrto_integral_valuerrrangerLr) r7rmodulor8rr modulo_is_nanr\baseexponentis &&&& r0 _power_moduloDecimal._power_modulosu% N "L' ^ #M ? lGkkm ||~   ,-a++,? ? ==??D::DS[!..01E33566!CDHHf$==Gx||$AtR(D%4v.c$i33r2c \V4pVPVPrTV^ ,^8XdV^ ,pV^, pK"\V4pVPVPrV^ ,^8XdV^ ,pV^, pK"V^8XdWW,pV^ ,^8XdV^ ,pV^, pK"V^8dR#V^ V,,p VP^8XdV )p VP 4'dHVP ^8Xd7VP \V4,p \W, V^, 4p M^p \^RRV ,,W, 4#VP^8XEdV^ ,p V R9dWD),V8wdR#\V4^, p V^],^A,pV\\V448dR#\W,V4p \WW,V4pV eVfR#W8dR#^V ,pMV ^8Xd\V4^,^A,p \^V ,V4wrOV'dR#V^,^8XdV^,pV ^,p K"V^ ,^,pV\\V448dR#\W,V4p \WW,V4pV eVfR#W8dR#^V ,pMR#V^8gQV4hV^ ,^8wgQV4h\V4p\V4V8dR#V )V, p\^VV4#V^8dV^ V,,^ppMV^8wd,\\\Wu,444V)8:dR#\V4p\\\V4V,44V)8:dR#T^ V),ppV^,V^,u;8Xd^8XdMMV^,pV^,pK4V^,V^,u;8Xd^8XdMMV^,pV^,pK4V^8dXV8:dR#\VV4wppV^8wdR#^\V4)V,),p\VVV^, ,4wppVV8:dM VV^, ,V,V,pKFVV8XdV^8XgR#TpV^8d!VV^d,\V4,8dR#VV,pVV,pV^8gQV4hV^ ,^8wgQV4h\V4p\V4V8dR#VP 4'dQVP ^8Xd@VP \V4,p \WZ, V\V4, 4p M^p \^VRV ,,W[, 4#)a Attempt 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.Nr\r))rrrr\rrMrr%rL_nbitsrr_decimal_lshift_exactrcr _log10_lb)r7rpxxcxeyycyerrzeros last_digitr1emaxrestrxcrrKxc_bitsremarkrlstr_xcs&&& r0 _power_exactDecimal._power_exactst TNB2gl 2IB !GB UOB2gl 2IB !GB 7 HBr'Q,r aAvBF{Hvv{$9!!ekkQ&6!%3u:!5H3QqS9#AsSYG G 66Q;bJY&8r>2JqL6tRxSY'*!&"5*27B79 8Tq2JrM2% &q!tR 0 1fk1HBFA tQwSY')!&"5*27B79 8T 6 4 67a< % %<GE5zA~BB#Aub1 1 7b"f9aqAqQw3s3ru:/B36RjG3s2ww'(RC/rRCyqAa%1q5%A%aaa%1q5%A%aa q5!|RmGBaxr {A~&&Ab!ac(+16AaC1q(AFqAvB 6a!C%2.. U aAvtvBw!|!T!|R v;?     %++"2!YYs5z1N)1S[=9EE6#e)#3RX>>r2c L VeVPWV4#\V4pV\JdV#Vf \4pVP W4pV'dV#V'g%V'gVP \ R4#\#^pVP^8Xd^VP4'dVP4'g^pMV'dVP \ R4#VP4pV'g,VP^8Xd\VR^4#\V,#VP4'd,VP^8Xd\V,#\VR^4#V\8XEdVP4'dVP^8Xd^pM(WP8dVPpM \!V4pVP"V,pV^VP, 8d)^VP, pVP \$4M=VP \&4VP \$4^VP, p\VRRV),,V4#VP)4pVP4'd2VP^8HV^88Xd\VR^4#\V,#RpRp VP+4VP)4,p V^8VP^8H8XdCV \-\/VP0448d\VRVP0^,4pM>VP34p V \-\/V )448d\VRV ^, 4pVfQVP5WP^,4pVe+V^8Xd"\^VP6VP"4pRp VfVPp \9V4p V P V P:r\9V4pVP VP:ppVP<^8XdV)p^p\?WVVV V,4wppV^^ \-\/V44V , ^, ,,,'dM V^, pKb\V\/V4V4pV 'EdVP4'Eg\-VP64VP8:dnVP^,\-VP64, p\VPVP6RV,,VP"V, 4pVPA4pVPC4\DFp^VPFV&K VPIV4pVP \&4VPJ\L,'dVP \N4VPJ\P,'d"VP \PRVP4\N\L\&\$\R3F/pVPJV,'gKVP V4K1 V#VPIV4pV#) aReturn self ** other [ % modulo]. With two arguments, compute self**other. With three arguments, compute (self**other) % modulo. For the three argument form, the following restrictions on the arguments hold: - all three arguments must be integral - other must be nonnegative - either self or other (or both) must be nonzero - modulo must be nonzero and must have at most p digits, where p is the context precision. If any of these restrictions is violated the InvalidOperation flag is raised. The result of pow(self, other, modulo) is identical to the result that would be obtained by computing (self**other) % modulo with unbounded precision, but is computed more efficiently. It is always exact. Nz0 ** 0z+x ** y with x negative and y not an integerrr\FTr)*rrrrrrr _OnerMrrr@rLrZrrorrr r r_log10_exp_boundrrrprbrrNrrr\_dpowerr|r}rrrAflagsrrrr )r7rrr8rQ result_sign multiplierrself_adjexactboundrbrrrrrrrextrarrj newcontext exceptions&&&& r0__pow__Decimal.__pow__sM0  %%eW= =u% N "L ? lGu. J++,3??r2c \VRR7pVf \4pVf VPpVP'gVP'dVP W4pV'dV#VP 4'gVP 4'dNVP 4'd"VP 4'd \ V4#VP\R4#VP4VPu;8:dVP8:gMVP\R4#V'g3\VPRVP4pVPV4#VP4pWSP8dVP\R4#WQP, ^,VP 8dVP\R4#VP#VPV4pVP4VP8dVP\R4#\%VP&4VP 8dVP\R4#V'd5VP4VP(8dVP\*4VPVP8d1W@8wdVP\,4VP\.4VPV4pV#)zwQuantize self so its exponent is the same as that of exp. Similar to self._rescale(exp._exp) but with error checking. Trzquantize with one INFz)target exponent out of bounds in quantizerz9exponent of quantize result too large for current contextz7quantize result has too many digits for current context)rrrnrrrrrr rbrrprLrMrArrorNrrNrrr r )r7rrnr8rQrs&&&& r0rDecimal.quantize sU S$/ ? lG  ''H    s""30C   D$4$4$6$6??$$)9)9););"4=(++,<(?AA 388;w||;''(8>@ @"4::sCHH=C88G$ $  << '''(8(ce e 88 #a '',, 6''(8(ac cmmCHHh/ <<>GLL (''(8(ce e sxx=7<< '''(8(ac c 3<<>GLL0   + 88dii {$$W-   )hhw r2c F\VRR7pVP'gVP'dYVP4;'dVP4;'g)VP4;'dVP4#VPVP8H#)a Return True if self and other have the same exponent; otherwise return False. If either operand is a special value, the following rules are used: * return True if both operands are infinities * return True if both operands are NaNs * otherwise, return False. Tr)rrr is_infiniterrs&&&r0 same_quantumDecimal.same_quantum s~ud3    u000KKM44elln??$$&>>5+<+<+> @yyEJJ&&r2c VP'd \V4#V'g\VPRV4#VPV8dA\VPVP RVPV, ,,V4#\ VP 4VP,V, pV^8d!\VPRV^, 4p^pVPV,pV!W4pVP RV;'gRpV^8Xd\\V4^,4p\VPWa4#)a;Rescale self so that the exponent is exp, either by padding with zeros or by truncating digits, using the given rounding mode. Specials are returned without change. This operation is quiet: it raises no flags, and uses no information from the context. exp = exp to scale to (an integer) rounding = rounding mode rr\N) rrrLrMrrNrrrr)r7rrnr this_functionrrs&&& r0rNDecimal._rescale s    4= #DJJS9 9 99 #DJJ(, CS4I(I3P P TYY$))+c1 A:#DJJSU;DF44X> - '6"))c a<E 1 %E E77r2c rV^8:d \R4hVP'g V'g \V4#VPVP 4^,V, V4pVP 4VP 48wd/VPVP 4^,V, V4pV#)zRound a nonzero, nonspecial Decimal to a fixed number of significant figures, using the given rounding mode. Infinities, NaNs and zeros are returned unaltered. This operation is quiet: it raises no flags, and uses no information from the context. z'argument should be at least 1 in _round)rrrrNr)r7placesrnrQs&&& r0_roundDecimal._round2 s Q;FG G    44= mmDMMOA-f4h? <<>T]]_ ,,,s||~a/6AC r2c VP'd(VPVR7pV'dV#\V4#VP^8d \V4#V'g\ VP R^4#Vf \ 4pVf VPpVP^V4pW08wdVP\4VP\4V#)a&Rounds to a nearby integer. If no rounding mode is specified, take the rounding mode from the context. This method raises the Rounded and Inexact flags when appropriate. See also: to_integral_value, which does exactly the same as this method except that it doesn't raise Inexact or Rounded. rzr) rrrrrLrMrrnrNrr r r7rnr8rQs&&& r0to_integral_exactDecimal.to_integral_exactI s    ""7"3C 4= 99>4= #DJJQ7 7 ? lG  ''HmmAx( ;   )W% r2c Vf \4pVf VPpVP'd(VPVR7pV'dV#\ V4#VP ^8d \ V4#VP ^V4#)z@Rounds to the nearest integer, without raising inexact, rounded.rz)rrnrrrrrNr.s&&& r0rDecimal.to_integral_valuef sv ? lG  ''H    ""7"3C 4= 99>4= ==H- -r2c dVf \4pVP'dOVPVR7pV'dV#VP4'dVP^8Xd \ V4#V'g:\ VPRVP^,4pVPV4#VP^8XdVP\R4#VP^,p\V4pVP^, pVP^,'d8VP^ ,p\VP 4^, ^,pM/VPp\VP 4^,^, pW7, pV^8dV^dV,,pRp M\#V^dV),4wrjV '*p WX,p^ V,p Wk,p W8:dMW,^, p K!T ;'d W,V8Hp V 'd3V^8dV ^ V,,p MV ^ V),,p WX, pMV ^,^8Xd V ^, p \ ^\%V 4V4pVP'4pVP)\*4p VPV4pWnV#)zReturn the square root of self.rzrzsqrt(-x), x > 0T)rrrrrMrrLrrArr rorrrrrNrcr _shallow_copy _set_roundingrrn)r7r8rQroopr1clrdrrerKrkrns&& r0sqrt Decimal.sqrty s) ? lG    ""7"3C !!djjAot}$"4::sDIINCC88G$ $ ::?''(8:KL L,||A~ d^ FFaK 66A:: ATYY1$)AADIIq A%A A: eOAE!!S5&[1LA!ME  HAvEQJ""!#( zb%iR%Z JA1uzQq#a&!,'')((9hhw# r2c \VRR7pVf \4pVP'gVP'dVP4pVP4pV'g V'dPV^8XdV^8XdVP V4#V^8XdV^8XdVP V4#VP W4#VP V4pV^8XdVPV4pVR8XdTpMTpVP V4#)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. TrrrrrrrArr compare_totalr7rr8snonr7rQs&&& r0rM Decimal.max s ud3 ? lG    u000BBR7rQw99W--7rQw ::g..''77 IIe  6""5)A 7CCxx  r2c \VRR7pVf \4pVP'gVP'dVP4pVP4pV'g V'dPV^8XdV^8XdVP V4#V^8XdV^8XdVP V4#VP W4#VP V4pV^8XdVPV4pVR8XdTpMTpVP V4#)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. Trrr<r>s&&& r0r% Decimal.min s ud3 ? lG    u000BBR7rQw99W--7rQw ::g..''77 IIe  6""5)A 7CCxx  r2c VP'dR#VP^8dR#VPVPRpVR\V4,8H#)z"Returns whether self is an integerFTNr)rrrNr)r7rests& r0rDecimal._isinteger( sF     99>yy$s3t9}$$r2c V'dVP^8dR#VPRVP,,R9#)z:Returns True if self is even. Assumes self is an integer.Trr)rrNrs&r0rDecimal._iseven1 s.tyy1}yyDII&'11r2c VP\VP4,^, # \d^#i;i)z$Return the adjusted exponent of self)rrrNrrs&r0rDecimal.adjusted7 s5 99s499~-1 1  s ,/ >>c V#)zReturns the same Decimal object. As we do not have different encodings for the same number, the received object already is in its canonical form. r.rs&r0 canonicalDecimal.canonical? s  r2c v\VRR7pVPW4pV'dV#VPWR7#)zCompares self to the other operand numerically. It's pretty much like compare(), but all NaNs signal, with signaling NaNs taking precedence over quiet NaNs. Trrz)rrrrs&&& r0compare_signalDecimal.compare_signalG s9 u5&&u6 J||E|33r2c \VRR7pVP'dVP'g\#VP'gVP'd\#VPpVP 4pVP 4pV'g V'dWE8Xd}\ VP 4VP 3p\ VP 4VP 3pWg8dV'd\#\#Wg8dV'd\#\#\#V'd6V^8Xd\#V^8Xd\#V^8Xd\#V^8Xd\#M4V^8Xd\#V^8Xd\#V^8Xd\#V^8Xd\#W8d\#W8d\#VPVP8dV'd\#\#VPVP8dV'd\#\#\#)zCompares self to other using the abstract representations. This is not like the standard compare, which use their numerical value. Note that a total ordering is defined for all possible abstract representations. Tr) rrM _NegativeOner rrrN_Zeror)r7rr8r\self_nan other_nanself_key other_keys&&& r0r=Decimal.compare_totalS sud3 :::ekkk zzzekkkKzz;;=LLN y$tyy>4994 OUZZ7 '# ++'++#  q=''>Kq=''>K"q=K>''q=K>'' <  <K 99uzz ! ## 99uzz !##  r2c ~\VRR7pVP4pVP4pVPV4#)zCompares self to other using abstract repr., ignoring sign. Like compare_total, but with operand's sign ignored and assumed to be 0. Tr)rr?r=)r7rr8ros&&& r0compare_total_magDecimal.compare_total_mag s6 ud3 MMO NN q!!r2c Z\^VPVPVP4#)z'Returns a copy with the sign set to 0. )rLrNrrrs&r0r?Decimal.copy_abs s!499dii9I9IJJr2c VP'd-\^VPVPVP4#\^VPVPVP4#)z&Returns a copy with the sign inverted.)rMrLrNrrrs&r0r@Decimal.copy_negate sI :::#Atyy$))T=M=MN N#Atyy$))T=M=MN Nr2c \VRR7p\VPVPVPVP 4#)z$Returns self with the sign of other.Tr)rrLrMrNrrrs&&&r0 copy_signDecimal.copy_sign s6ud3 TYY $ 4+;+;= =r2c Vf \4pVPVR7pV'dV#VP4R8Xd\#V'g\#VP4^8Xd \ V4#VP pVP4pVP^8XdRV\\VP^,^,448d!\^RVP^,4pEMVP^8Xd[V\\VP4)^,^,448d%\^RVP4^, 4pEM2VP^8Xd3WC)8d,\^RRV^, ,,R,V)4pMVP^8Xd3WC)^, 8d%\^RV^,,V)^, 4pM\V4pVPVP rvVP"^8XdV)p^p\%WgW8,4wrV ^^ \\V 44V, ^, ,,,'dM V^, pK^\^\V 4V 4pVP'4pVP)\*4p VP-V4pWnV#)zReturns e ** self.rzr\rrmr)rrrrSr rrorrMrrrprLrbrrrr\_dexpr4r5rrArn) r7r8rQradjr6r7r1rrrrns && r0r Decimal.exp s2 ? lGw/ J     #LK     "4= LLmmo ::?sSgll1na-?)@%AA"1c7<<>:C ZZ1_s30@0BA/E+F'G!G"1c7==?1+<=C ZZ1_r"1cC1Io&;aR@C ZZ1_r!t"1c1Q3i!A6C$B66266qww!|B E"11 Ab3s5z?1#4Q#67788 "1c%j#6C'')((9hhw# r2c R#)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.rs&r0 is_canonicalDecimal.is_canonical s r2c $VP'*#)zReturn True if self is finite; otherwise return False. A Decimal instance is considered finite if it is neither infinite nor a NaN. )rrs&r0 is_finiteDecimal.is_finite s ####r2c VPR8H#)z8Return True if self is infinite; otherwise return False.rrrs&r0r#Decimal.is_infinite yyCr2c VPR9#)z>Return True if self is a qNaN or sNaN; otherwise return False.rrors&r0rDecimal.is_nan syyJ&&r2c VP'g V'gR#Vf \4pVPVP48*#)z?Return True if self is a normal number; otherwise return False.F)rrrrr;s&&r0 is_normalDecimal.is_normal s4    4 ? lG||t}}..r2c VPR8H#)z;Return True if self is a quiet NaN; otherwise return False.rKrors&r0rDecimal.is_qnan$ rqr2c VP^8H#)z8Return True if self is negative; otherwise return False.)rMrs&r0 is_signedDecimal.is_signed( szzQr2c VPR8H#)z?Return True if self is a signaling NaN; otherwise return False.rrors&r0rDecimal.is_snan, rqr2c VP'g V'gR#Vf \4pVP4VP8#)z9Return True if self is subnormal; otherwise return False.F)rrrrr;s&&r0 is_subnormalDecimal.is_subnormal0 s4    4 ? lG}}--r2c RVP'*;'dVPR8H#)z6Return True if self is a zero; otherwise return False.rrrs&r0is_zeroDecimal.is_zero8 s"###88 S(88r2c pVP\VP4,^, pV^8d*\\V^,^ ,44^, #VR8:d1\\RV, ^,^ ,44^, #\ V4pVP VP rCV^8XdJ\V^ V),, 4p\V4p\V4\V4, WV8, #V\\^ V),V, 44,^, #)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. rrrrrNrrrrr7rfr6r7r1numdens& r0 _ln_exp_boundDecimal._ln_exp_bound< sii#dii.(1, !8s3r62:'!+ + "9sBsFB;?+,q0 0 d^vvrvv1 !8aQBh-Ca&Cs8c#h&#)4 43s2r6A:''!++r2c  @Vf \4pVPVR7pV'dV#V'g\#VP4^8Xd\#V\ 8Xd\ #VP^8XdVP\R4#\V4pVPVPrTVPpW`P4, ^,p\WEV4pV^^ \!\#\%V444V, ^, ,,,'dM V^, pK_\'\V^84\#\%V44V)4pVP)4pVP+\,4p VP/V4pWnV#)z/Returns the natural (base e) logarithm of self.rzzln of a negative value)rr_NegativeInfinityr _Infinityr rSrMrr rrrror_dlogrrrrLr4r5rrArn r7r8rQr6r7r1rr*rrns && r0ln Decimal.lnU s` ? lGw/ J$ $     "  4<L ::?''(8(@B Bd^vvrvv1 LL''))A-!'E"s3s5z?3A5a78899 aKFs57|SU_vgF'')((9hhw# r2c lVP\VP4,^, pV^8d\\V44^, #VR8:d#\\RV, 44^, #\ V4pVP VP rCV^8XdX\V^ V),, 4p\^V,4p\V4\V4, WV8, ^,#\^ V),V, 4p\V4V,VR8, ^, #)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. 231rrrrs& r0r Decimal._log10_exp_bound sii#dii.(1, !8s3x=? " "9s2c6{#A% % d^vvrvv1 !8aQBh-Cc!e*Cs8c#h&#)4q8 8"qb&(m3x!|sU{+a//r2c  .Vf \4pVPVR7pV'dV#V'g\#VP4^8Xd\#VP ^8XdVP \R4#VP^,R8XdqVPR,R\VP4^, ,8Xd8\VP\VP4,^, 4pM\V4pVPVPrTVPpW`P!4, ^,p\#WEV4pV^^ \\%\'V444V, ^, ,,,'dM V^, pK_\)\V^84\%\'V44V)4pVP+4pVP-\.4p VP1V4pWnV#)z&Returns the base 10 logarithm of self.rzzlog10 of a negative valuer\:rNNr)rrrrrrMrr rNrrrrrrror _dlog10rrrLr4r5rrArnrs && r0log10 Decimal.log10 s ? lGw/ J$ $     "  ::?''(8(CE E 99Q<3 499R=CTYY!9K4L#L$))c$))n4q89C$B66266q A,,..q0Ff-Ab3s3u:#7#9!#;<<==! "3uQw<SZ6'JC'')((9hhw# r2c VPVR7pV'dV#Vf \4pVP4'd\#V'gVP \ R^4#\ VP44pVPV4#)a$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). rzzlogb(0)) rrrrrr rrrArBs&& r0logb Decimal.logb s}w/ J ? lG      '' 1E E dmmo&xx  r2c VP^8wgVP^8wdR#VPF pVR9gK R# R#)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. F01T)rMrrN)r7digs& r0 _islogicalDecimal._islogical s9 ::?dii1n99C$r2c4VP\V4, pV^8dRV,V,pMV^8dW!P)RpVP\V4, pV^8dRV,V,pW#3#V^8dW1P)RpW#3#)rJrN)ror)r7r8opaopbdifs&&&& r0 _fill_logicalDecimal._fill_logical sllSX% 7c'C-C 1W||mn%CllSX% 7c'C-Cx1W||mn%Cxr2c  Vf \4p\VRR7pVP4'dVP4'gVP\4#VP W P VP 4wr4RP\W44UUu.uF)wrV\\V4\V4,4NK+ upp4p\^VPR4;'gR^4#uuppi)zjApplies an 'and' operation between self and other's digits. Both self and other must be logical numbers. Trrr rrrrr rrNrziprrrLrr7rr8rrrbrs&&& r0 logical_andDecimal.logical_and ? lGud3  (8(8(:(:''(89 9''EJJG C E #c!fSVm, EF6==#5#<#<a@@F/C; c zVf \4pVP\^RVP,^4V4#)z9Invert all its digits. The self must be logical number. r\)r logical_xorrLror;s&&r0logical_invertDecimal.logical_invert% s; ? lG 03w||3CA F ') )r2c  Vf \4p\VRR7pVP4'dVP4'gVP\4#VP W P VP 4wr4RP\W44UUu.uF)wrV\\V4\V4,4NK+ upp4p\^VPR4;'gR^4#uuppi)ziApplies an 'or' operation between self and other's digits. Both self and other must be logical numbers. Trrrrrs&&& r0 logical_orDecimal.logical_or/ rrc  Vf \4p\VRR7pVP4'dVP4'gVP\4#VP W P VP 4wr4RP\W44UUu.uF)wrV\\V4\V4, 4NK+ upp4p\^VPR4;'gR^4#uuppi)zjApplies an 'xor' operation between self and other's digits. Both self and other must be logical numbers. Trrrrrs&&& r0rDecimal.logical_xorC rrc B\VRR7pVf \4pVP'gVP'dVP4pVP4pV'g V'dPV^8XdV^8XdVP V4#V^8XdV^8XdVP V4#VP W4#VP 4PVP 44pV^8XdVPV4pVR8XdTpMTpVP V4#z8Compares the values numerically with their sign ignored.Trr rrrrrArr?rr=r>s&&& r0max_magDecimal.max_magW sud3 ? lG    u000BBR7rQw99W--7rQw ::g..''77 MMO !1 2 6""5)A 7CCxx  r2c B\VRR7pVf \4pVP'gVP'dVP4pVP4pV'g V'dPV^8XdV^8XdVP V4#V^8XdV^8XdVP V4#VP W4#VP 4PVP 44pV^8XdVPV4pVR8XdTpMTpVP V4#rrr>s&&& r0min_magDecimal.min_magu sud3 ? lG    u000BBR7rQw99W--7rQw ::g..''77 MMO !1 2 6""5)A 7CCxx  r2c Vf \4pVPVR7pV'dV#VP4R8Xd\#VP4^8Xd-\ ^RVP ,VP 44#VP4pVP\4VP4VPV4pW08wdV#VP\ ^RVP4^, 4V4#)z=Returns the largest representable number smaller than itself.rzrmr\r)rrrrrLrorr|r5r_ignore_all_flagsrArVrbr7r8rQnew_selfs&& r0 next_minusDecimal.next_minus s ? lGw/ J     #$ $     "#As7<<'7H H,,.k*!!#99W%  O||,QW]]_Q5FG#% %r2c Vf \4pVPVR7pV'dV#VP4^8Xd\#VP4R8Xd-\ ^RVP ,VP 44#VP4pVP\4VP4VPV4pW08wdV#VP\ ^RVP4^, 4V4#)z=Returns the smallest representable number larger than itself.rzrmr\r)rrrrrLrorr|r5rrrArSrbrs&& r0 next_plusDecimal.next_plus s ? lGw/ J     "      ##As7<<'7H H,,.m,!!#99W%  O||,QW]]_Q5FG#% %r2c \VRR7pVf \4pVPW4pV'dV#VPV4pV^8XdVP V4#VR8XdVP V4pMVP V4pVP4'dNVP\RVP4VP\4VP\4V#VP4VP8drVP\4VP\ 4VP\4VP\4V'gVP\"4V#)a[Returns the number closest to self, in the direction towards other. The result is the closest representable number to self (excluding self) that is in the direction towards other, unless both have the same value. If the two operands are numerically equal, then the result is a copy of self with the sign set to be the same as the sign of other. Trz Infinite result from next_towardr)rrrrrbrrrrrrMr r rrrrr )r7rr8rQ comparisons&&& r0 next_towardDecimal.next_toward s.ud3 ? lGu. JYYu% ?>>%( (  ..)C//'*C ??    !C!$ ,   )   ) \\^gll *   +   +   )   )$$W- r2c VP4'dR#VP4'dR#VP4pV^8XdR#VR 8XdR#VP4'dVP'dR#R#Vf \ 4pVP VR7'dVP'dR#R #VP'dR #R #) zReturns 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 rr/z +Infinityz -Infinityz-Zeroz+Zerorzz -Subnormalz +Subnormalz-Normalz+Normalr)rrrrrMrr)r7r8infs&& r0 number_classDecimal.number_class s <<>> <<>>  !8 "9 <<>>zzz ? lG   W  - -zzz## :::r2c \^ 4#)z'Just returns 10, as this is Decimal, :)rrs&r0radix Decimal.radixs r{r2c Vf \4p\VRR7pVPW4pV'dV#VP^8wdVP \ 4#VP )\V4u;8:dVP 8:gMVP \ 4#VP4'd \V4#\V4pVPpVP \V4, pV^8dRV,V,pM V^8dWV)RpWTRVRV,p\VPVPR4;'gRVP4#)z5Returns a rotated copy of self, value-of-other times.NTrrrrrrrr rorrrrNrrLrMr)r7rr8rQtorotrotdigtopadrotateds&&& r0rotateDecimal.rotates' ? lGud3u. J ::?''(89 9 U;w||;''(89 9     4= E  s6{* 19Y'F QYFG_F.6&5>1 's 3 : :sDIIG Gr2c Vf \4p\VRR7pVPW4pV'dV#VP^8wdVP \ 4#RVP VP,,p^VP VP,,pV\V4u;8:dV8:gMVP \ 4#VP4'd \V4#\VPVPVP\V4,4pVPV4pV#)z>Returns self operand after adding the second value to its exp.Trr)rrrrrr rprorrrrLrMrNrA)r7rr8rQliminflimsuprs&&& r0scalebDecimal.scaleb>s ? lGud3u. J ::?''(89 9w||gll23w||gll23#e*..''(89 9     4= TZZDIIE 4J K FF7Or2c Vf \4p\VRR7pVPW4pV'dV#VP^8wdVP \ 4#VP )\V4u;8:dVP 8:gMVP \ 4#VP4'd \V4#\V4pVPpVP \V4, pV^8dRV,V,pM V^8dWV)RpV^8dVRVpMVRV,,pWrP )Rp\VPVPR4;'gRVP4#)z5Returns a shifted copy of self, value-of-other times.NTrrr)r7rr8rQrrrshifteds&&& r0rd Decimal.shiftWsC ? lGud3u. J ::?''(89 9 U;w||;''(89 9     4= E  s6{* 19Y'F QYFG_F 19VenGs5y(G||mn-G $+NN3$7$>$>3 K Kr2c2VP\V433#r-) __class__rrs&r0 __reduce__Decimal.__reduce__~sT --r2c`\V4\JdV#VP\V44#r-typerrrrs&r0__copy__Decimal.__copy__& : K~~c$i((r2c`\V4\JdV#VP\V44#r-r)r7memos&&r0 __deepcopy__Decimal.__deepcopy__rr2c VVf \4p\WR7pVP'dS\VPV4p\ VP 44pVR,R8Xd VR, p\WVV4#VR,fRR.VP,VR&VR,R8Xd3\VPVPVP^,4pVPpVR,pVeVR,R9dVPV^,V4pM[VR,R 9dVPV)V4pM9VR,R 9d,\VP4V8dVPW4pV'g2VP^8d!VR,R 9dVP^V4pV'g%VR ,'dVP'd^p M VPp VP\VP4,p VR,R9dV'gVe ^V, p M?^p M"??GHii *11cGyy+H!mhTJJr2)rrNrrM)rrNrMr)rN)NNr-)FN)TN)r<r=r>r?r@ __slots__r classmethodrrrrrrrrrrrr r rrr!rr+r8r<rCrFrJrS__radd__rVrYr___rmul__rgrmrprwrzr}rrrrrr __trunc__propertyrrrrrOrArrrrrrrrrrrrrrrrrrrrr$rNr+r/r to_integralr9rMr%rrrrLrOr=r[r?r@rbrrirlr#rrurrzrrrrrr rrrrrrrrrrrrrrrrrrdrrrrrArBrCs@r0rrs66I T@l A A**X  @B4-'@%$%$%)$(4O0d+ 2/h7!,!*,TlH B46nH9!vB8"#H764I!V/89 7I $ ZL'--+++# &**&"  <6| 2 4*/XS4jv?pVp<@2;z ' 8D.:."$KaF(!T !D%2  4FR "KO= IV$ '/  .9,20d0<1f!<  A()A(A(!<!<%.%.,\(TGB2$KN.) )TKTKr2ch\P\4pWnWnW$nW4nV#)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*. )rrrrMrNrr)r\ coefficientrspecialr7s&&&& r0rLrLs, >>' "DJII Kr2c6a]tRtRtoRtRtRtRtRtVt R#)rizContext manager class to support localcontext(). Sets a copy of the supplied context in __enter__() and restores the previous decimal context in __exit__() c0VP4VnR#r-)r|r)r7rs&&r0__init___ContextManager.__init__s&++-r2cb\4Vn\VP4VP#r-)r saved_contextrrrs&r0 __enter___ContextManager.__enter__s&'\4##$r2c0\VP4R#r-)rr)r7tvtbs&&&&r0__exit___ContextManager.__exit__s4%%&r2)rrN) r<r=r>r?r@rrrrArBrCs@r0rrs . ''r2rc&a]tRtRtoRtRVRltRtRtRtRt R t R t R t R t R tRt]tRWRltRtRtRtRtRtRtRtRXRltRtRtRtRtRtRtRt Rt!Rt"R t#R!t$R"t%R#t&R$t'R%t(R&t)R't*R(t+R)t,R*t-R+t.R,t/R-t0R.t1R/t2R0t3R1t4R2t5R3t6R4t7R5t8R6t9R7t:R8t;R9tR<t?R=t@R>tAR?tBR@tCRAtDRBtERCtFRDtGREtHRWRFltIRGtJRHtKRItLRJtMRKtNRLtORMtPRNtQROtRRPtSRQtTRRtURStVRTtW]WtXRUtYVtZR#)Yri aContains the context for a Decimal instance. Contains: prec - precision (for use in rounding, division, square roots..) rounding - rounding type (how you round) traps - If traps[exception] = 1, then the exception is raised when it is caused. Otherwise, a value is substituted in. flags - When an exception is caused, flags[exception] is set. (Whether or not the trap_enabler is set) Should be reset by user of Decimal instance. Emin - Minimum exponent Emax - Maximum exponent capitals - If 1, 1*10^1 is printed as 1E+1. If 0, printed as 1e1 clamp - If 1, change exponents if too high (Default 0) Nc aa\p VeTM X PVnVeTM X PVnVeTM X PVnVeTM X P VnVeTM X P VnVeTM X PVnV f .VnMWnSf!X PP4Vn MC\S\4'g'\V3Rl\S,44Vn MSVn Sf"\P\^4VnR#\S\4'g(\V3Rl\S,44VnR#SVnR# \dEL|i;i)Nc3B<"TFq\VS943xK R#5ir-r).0rrs& r0 #Context.__init__..6M| !BdRVE^!^__ U]| !BdRVE^!^__|u| !ATQUD]!]^^!!$e44r2c\V\4'g\RV,4hVF pV\9dK\ RV,4h \FpW29dK \ RV,4h \ P WV4#)z%s must be a signal dictz%s is not a valid signal dict)rrrrKeyErrorrr.)r7r/rrs&&& r0_set_signal_dictContext._set_signal_dictOsy!T""6:; ;C(?>BCCC8>BCC!!$a00r2cVR8XdVPW^R4#VR8XdVPWR^4#VR8XdVPW^R4#VR8XdVPW^^4#VR8XdVPW^^4#VR8Xd4V\9g\RV,4h\P WV4#VR 8XgVR 8XdVP W4#VR 8Xd\P WV4#\ R V,4h) rorrr-rpr4rrnz%s: invalid rounding moder rr)z.'decimal.Context' object has no attribute '%s')r2_rounding_modesrrr.r6AttributeError)r7r/rs&&&r0r.Context.__setattr__Zs 6>**45A A V^**4B B V^**45A A Z **41= = W_**41= = Z O+ ;e CDD%%d%8 8 W_((5 5 % %%%d%8 8 @4GI Ir2c&\RV,4h)z%s cannot be deleted)r:)r7r/s&&r0 __delattr__Context.__delattr__ss3d:;;r2c VPP4UUu.uFwrV'gKVNK pppVPP4UUu.uFwrV'gKVNK pppVPVPVP VP VPVPVPW433#uuppiuuppir-) r rrrrornrrpr4r)r7sigrr rs& r0rContext.__reduce__ws#'::#3#3#5;#5#5;#'::#3#3#5;#5#5;DMM499dii E:; ;<;s CC C&Cc L.pVPR\V4,4VPP4UUu.uFwr#V'gKVPNK pppVPRRP V4,R,4VP P4UUu.uFwrSV'gKVPNK pppVPRRP V4,R,4RP V4R,#uuppiuuppi)zShow the current context.zrContext(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, clamp=%(clamp)dzflags=[, ]ztraps=[))rvarsr rr<rr)r7rrrnamesrs& r0r+Context.__repr__~s  #: )- (8(8(:@(:a(:@ TYYu--34(, (8(8(:@(:a(:@ TYYu--34yy|c!! A@s DD0 D D c JVPFp^VPV&K R#)zReset all flags to zeroN)r r7flags& r0r}Context.clear_flagsJJD DJJt r2c JVPFp^VPV&K R#)zReset all traps to zeroN)rrJs& r0 clear_trapsContext.clear_trapsrMr2c  \VPVPVPVPVP VP VPVPVP4 pV#)z!Returns a shallow copy from self.) rrornrrpr4rr rr)r7ncs& r0r4Context._shallow_copysM TYY tyy$))]]DJJ DJJ((* r2c  \VPVPVPVPVP VP VPP4VPP4VP4 pV#)zReturns a deep copy from self.) rrornrrpr4rr r|rr)rRs& r0r| Context.copys\ TYY tyy$))]]DJJZZ__& (9((* r2c \PW4pW@P9dV!4P!V.VO5!#^VPV&VP V,'gV!4P!V.VO5!#V!V4h)zHandles an error If the flag is in _ignored_flags, returns the default response. Otherwise, it sets the flag, then, if the corresponding trap_enabler is set, it reraises the exception. Otherwise, it returns the default value after setting the flag. )_condition_maprwr)r9r r)r7 condition explanationr/errors&&&* r0rContext._raise_errorsx""98 '' '7>>$.. . 5zz%  ;%%d2T2 2K  r2c (VP!\#)z$Ignore all flags, if they are raised) _ignore_flagsrrs&r0rContext._ignore_all_flagss!!8,,r2c ZVP\V4,Vn\V4#)z$Ignore the flags, if they are raised)r)r)r7r s&*r0r^Context._ignore_flagss% $22T%[@E{r2c V'd-\V^,\\34'd V^,pVFpVPP V4K R#)z+Stop ignoring the flags, if they are raisedN)rrrr)remove)r7r rKs&* r0 _regard_flagsContext._regard_flagss@ Za5,77!HED    & &t ,r2c \\VPVP, ^,4#)z!Returns Etiny (= Emin - prec + 1))rrrors&r0rb Context.Etiny499tyy(1,--r2c \\VPVP, ^,4#)z,Returns maximum exponent (= Emax - prec + 1))rrprors&r0r Context.Etoprhr2c *VPpWnV#)aSets the rounding type. Sets the rounding type, and returns the current (previous) rounding type. Often used like: context = context.copy() # so you don't change the calling context # if an error occurs in the middle. rounding = context._set_rounding(ROUND_UP) val = self.__sub__(other, context=context) context._set_rounding(rounding) This will make it round up for that operation. )rn)r7rrns&& r0r5Context._set_roundings== r2c \V\4'd2WP48wgRV9dVP\R4#\ WR7pVP 4'dL\VP4VPVP, 8dVP\R4#VPV4#)zCreates a new Decimal instance but using self as context. This method implements the to-number operation of the IBM Decimal specification.rzAtrailing or leading whitespace and underscores are not permitted.rzzdiagnostic info too long in NaN) rrrrrrrrrNrorrA)r7rrs&& r0create_decimalContext.create_decimals c3  SIIK%73#:$$%5&FG G C & 88::#aff+ DJJ(>>$$%5%FH Hvvd|r2c N\PV4pVPV4#)aCreates a new Decimal instance from a float but rounding using self as the context. >>> context = Context(prec=5, rounding=ROUND_DOWN) >>> context.create_decimal_from_float(3.1415926535897932) Decimal('3.1415') >>> context = Context(prec=5, traps=[Inexact]) >>> context.create_decimal_from_float(3.1415926535897932) Traceback (most recent call last): ... decimal.Inexact: None )rrrA)r7rrs&& r0create_decimal_from_float!Context.create_decimal_from_floats"   q !vvd|r2c @\VRR7pVPVR7#)aReturns 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') Trrz)rrJr7rs&&r0r Context.abss!$ 1d +yyy&&r2c |\VRR7pVPW R7pV\Jd\RV,4hV#)aSReturn 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') TrrzUnable to convert %s to Decimal)rrSrrr7rrrls&&& r0add Context.add#s> 1d + IIaI &  =AB BHr2c6\VPV44#r-)rrArts&&r0_applyContext._apply8s166$<  r2c d\V\4'g \R4hVP4#)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.)rrrrLrts&&r0rLContext.canonical;s)!W%%JK K{{}r2c @\VRR7pVPW R7#)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') Trrz)rrr7rrs&&&r0rContext.compareHs"D 1d +yyy))r2c @\VRR7pVPW R7#)a8Compares 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') Trrz)rrOrs&&&r0rOContext.compare_signalms%@ 1d +00r2c >\VRR7pVPV4#)a|Compares two operands using their abstract representation. This is not like the standard compare, which use their numerical value. Note that a total ordering is defined for all possible abstract representations. >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) Decimal('0') >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) Decimal('1') >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) Decimal('-1') >>> ExtendedContext.compare_total(1, 2) Decimal('-1') >>> ExtendedContext.compare_total(Decimal(1), 2) Decimal('-1') >>> ExtendedContext.compare_total(1, Decimal(2)) Decimal('-1') Tr)rr=rs&&&r0r=Context.compare_totals4 1d +q!!r2c >\VRR7pVPV4#)zCompares two operands using their abstract representation ignoring sign. Like compare_total, but with operand's sign ignored and assumed to be 0. Tr)rr[rs&&&r0r[Context.compare_total_mags! 1d +""1%%r2c <\VRR7pVP4#)zReturns a copy of the operand with the sign set to 0. >>> ExtendedContext.copy_abs(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.copy_abs(Decimal('-100')) Decimal('100') >>> ExtendedContext.copy_abs(-1) Decimal('1') Tr)rr?rts&&r0r?Context.copy_abss 1d +zz|r2c 2\VRR7p\V4#)zReturns a copy of the decimal object. >>> ExtendedContext.copy_decimal(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.copy_decimal(Decimal('-1.00')) Decimal('-1.00') >>> ExtendedContext.copy_decimal(1) Decimal('1') Tr)rrrts&&r0 copy_decimalContext.copy_decimals 1d +qzr2c <\VRR7pVP4#)zReturns a copy of the operand with the sign inverted. >>> ExtendedContext.copy_negate(Decimal('101.5')) Decimal('-101.5') >>> ExtendedContext.copy_negate(Decimal('-101.5')) Decimal('101.5') >>> ExtendedContext.copy_negate(1) Decimal('-1') Tr)rr@rts&&r0r@Context.copy_negates 1d +}}r2c >\VRR7pVPV4#)aCopies the second operand's sign to the first one. In detail, it returns a copy of the first operand with the sign equal to the sign of the second operand. >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) Decimal('1.50') >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) Decimal('1.50') >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) Decimal('-1.50') >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) Decimal('-1.50') >>> ExtendedContext.copy_sign(1, -2) Decimal('-1') >>> ExtendedContext.copy_sign(Decimal(1), -2) Decimal('-1') >>> ExtendedContext.copy_sign(1, Decimal(-2)) Decimal('-1') Tr)rrbrs&&&r0rbContext.copy_signs* 1d +{{1~r2c |\VRR7pVPW R7pV\Jd\RV,4hV#)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') Trrzrw)rrgrrrxs&&& r0divideContext.divides>< 1d + MM!M *  =AB BHr2c |\VRR7pVPW R7pV\Jd\RV,4hV#)aDivides 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') Trrzrw)rrrrrxs&&& r0 divide_intContext.divide_ints> 1d + NN1N +  =AB BHr2c |\VRR7pVPW R7pV\Jd\RV,4hV#)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')) Trrzrw)rrwrrrxs&&& r0rcContext.divmod1s> 1d + LLL )  =AB BHr2c @\VRR7pVPVR7#)aReturns 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') Trrz)rrrts&&r0r Context.expFs!* !T *uuTu""r2c B\VRR7pVPW#VR7#)aReturns a multiplied by b, plus c. The first two operands are multiplied together, using multiply, the third operand is then added to the result of that multiplication, using add, all with only one final rounding. >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) Decimal('22') >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) Decimal('-8') >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) Decimal('1.38435736E+12') >>> ExtendedContext.fma(1, 3, 4) Decimal('7') >>> ExtendedContext.fma(1, Decimal(3), 4) Decimal('7') >>> ExtendedContext.fma(1, 3, Decimal(4)) Decimal('7') Trrz)rr)r7rrr7s&&&&r0r Context.fma^s#( 1d +uuQ4u((r2c d\V\4'g \R4hVP4#)zReturn 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.)rrrrirts&&r0riContext.is_canonicalus*!W%%MN N~~r2c <\VRR7pVP4#)aReturn True if the operand is finite; otherwise return False. A Decimal instance is considered finite if it is neither infinite nor a NaN. >>> ExtendedContext.is_finite(Decimal('2.50')) True >>> ExtendedContext.is_finite(Decimal('-0.3')) True >>> ExtendedContext.is_finite(Decimal('0')) True >>> ExtendedContext.is_finite(Decimal('Inf')) False >>> ExtendedContext.is_finite(Decimal('NaN')) False >>> ExtendedContext.is_finite(1) True Tr)rrlrts&&r0rlContext.is_finites& 1d +{{}r2c <\VRR7pVP4#)a Return True if the operand is infinite; otherwise return False. >>> ExtendedContext.is_infinite(Decimal('2.50')) False >>> ExtendedContext.is_infinite(Decimal('-Inf')) True >>> ExtendedContext.is_infinite(Decimal('NaN')) False >>> ExtendedContext.is_infinite(1) False Tr)rr#rts&&r0r#Context.is_infinites 1d +}}r2c <\VRR7pVP4#)zReturn True if the operand is a qNaN or sNaN; otherwise return False. >>> ExtendedContext.is_nan(Decimal('2.50')) False >>> ExtendedContext.is_nan(Decimal('NaN')) True >>> ExtendedContext.is_nan(Decimal('-sNaN')) True >>> ExtendedContext.is_nan(1) False Tr)rrrts&&r0rContext.is_nans 1d +xxzr2c @\VRR7pVPVR7#)agReturn 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 Trrz)rrurts&&r0ruContext.is_normals!( 1d +{{4{((r2c <\VRR7pVP4#)aReturn True if the operand is a quiet NaN; otherwise return False. >>> ExtendedContext.is_qnan(Decimal('2.50')) False >>> ExtendedContext.is_qnan(Decimal('NaN')) True >>> ExtendedContext.is_qnan(Decimal('sNaN')) False >>> ExtendedContext.is_qnan(1) False Tr)rrrts&&r0rContext.is_qnans 1d +yy{r2c <\VRR7pVP4#)a)Return True if the operand is negative; otherwise return False. >>> ExtendedContext.is_signed(Decimal('2.50')) False >>> ExtendedContext.is_signed(Decimal('-12')) True >>> ExtendedContext.is_signed(Decimal('-0')) True >>> ExtendedContext.is_signed(8) False >>> ExtendedContext.is_signed(-8) True Tr)rrzrts&&r0rzContext.is_signeds 1d +{{}r2c <\VRR7pVP4#)aReturn True if the operand is a signaling NaN; otherwise return False. >>> ExtendedContext.is_snan(Decimal('2.50')) False >>> ExtendedContext.is_snan(Decimal('NaN')) False >>> ExtendedContext.is_snan(Decimal('sNaN')) True >>> ExtendedContext.is_snan(1) False Tr)rrrts&&r0rContext.is_snans 1d +yy{r2c @\VRR7pVPVR7#)atReturn 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 Trrz)rrrts&&r0rContext.is_subnormals!& 1d +~~d~++r2c <\VRR7pVP4#)aReturn True if the operand is a zero; otherwise return False. >>> ExtendedContext.is_zero(Decimal('0')) True >>> ExtendedContext.is_zero(Decimal('2.50')) False >>> ExtendedContext.is_zero(Decimal('-0E+2')) True >>> ExtendedContext.is_zero(1) False >>> ExtendedContext.is_zero(0) True Tr)rrrts&&r0rContext.is_zeros 1d +yy{r2c @\VRR7pVPVR7#)a~Returns 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') Trrz)rrrts&&r0r Context.ln%s!& 1d +ttDt!!r2c @\VRR7pVPVR7#)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') Trrz)rrrts&&r0r Context.log10;s!2 1d +wwtw$$r2c @\VRR7pVPVR7#)aReturns 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') Trrz)rrrts&&r0r Context.logbWs!. 1d +vvdv##r2c @\VRR7pVPW R7#)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') Trrz)rrrs&&&r0rContext.logical_andq!0 1d +}}Q}--r2c @\VRR7pVPVR7#)aInvert all the digits in the operand. The operand must be a logical number. >>> ExtendedContext.logical_invert(Decimal('0')) Decimal('111111111') >>> ExtendedContext.logical_invert(Decimal('1')) Decimal('111111110') >>> ExtendedContext.logical_invert(Decimal('111111111')) Decimal('0') >>> ExtendedContext.logical_invert(Decimal('101010101')) Decimal('10101010') >>> ExtendedContext.logical_invert(1101) Decimal('111110010') Trrz)rrrts&&r0rContext.logical_inverts$ 1d +--r2c @\VRR7pVPW R7#)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') Trrz)rrrs&&&r0rContext.logical_ors!0 1d +||A|,,r2c @\VRR7pVPW R7#)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') Trrz)rrrs&&&r0rContext.logical_xorrr2c @\VRR7pVPW R7#)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') Trrz)rrMrs&&&r0rM Context.max!0 1d +uuQu%%r2c @\VRR7pVPW R7#)aoCompares 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') Trrz)rrrs&&&r0rContext.max_mag! 1d +yyy))r2c @\VRR7pVPW R7#)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') Trrz)rr%rs&&&r0r% Context.minrr2c @\VRR7pVPW R7#)alCompares 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') Trrz)rrrs&&&r0rContext.min_magrr2c @\VRR7pVPVR7#)a~Minus 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') Trrz)rrCrts&&r0minus Context.minus-! 1d +yyy&&r2c |\VRR7pVPW R7pV\Jd\RV,4hV#)a8multiply 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') Trrzrw)rr_rrrxs&&& r0multiplyContext.multiply>s>2 1d + IIaI &  =AB BHr2c @\VRR7pVPVR7#)aReturns 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') Trrz)rrrts&&r0rContext.next_minus^s!" 1d +||D|))r2c @\VRR7pVPVR7#)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') Trrz)rrrts&&r0rContext.next_plusrs!" 1d +{{4{((r2c @\VRR7pVPW R7#)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') Trrz)rrrs&&&r0rContext.next_towards"@ 1d +}}Q}--r2c @\VRR7pVPVR7#)a+normalize 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') Trrz)rrrts&&r0rContext.normalizes!* 1d +{{4{((r2c @\VRR7pVPVR7#)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' Trrz)rrrts&&r0rContext.number_classs"^ 1d +~~d~++r2c @\VRR7pVPVR7#)aoPlus 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') Trrz)rrFrts&&r0plus Context.plusrr2c ~\VRR7pVPW#VR7pV\Jd\RV,4hV#)aRaises a to the power of b, to modulo if given. With two arguments, compute a**b. If a is negative then b must be integral. The result will be inexact unless b is integral and the result is finite and can be expressed exactly in 'precision' digits. With three arguments, compute (a**b) % modulo. For the three argument form, the following restrictions on the arguments hold: - all three arguments must be integral - b must be nonnegative - at least one of a or b must be nonzero - modulo must be nonzero and have at most 'precision' digits The result of pow(a, b, modulo) is identical to the result that would be obtained by computing (a**b) % modulo with unbounded precision, but is computed more efficiently. It is always exact. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.power(Decimal('2'), Decimal('3')) Decimal('8') >>> c.power(Decimal('-2'), Decimal('3')) Decimal('-8') >>> c.power(Decimal('2'), Decimal('-3')) Decimal('0.125') >>> c.power(Decimal('1.7'), Decimal('8')) Decimal('69.7575744') >>> c.power(Decimal('10'), Decimal('0.301029996')) Decimal('2.00000000') >>> c.power(Decimal('Infinity'), Decimal('-1')) Decimal('0') >>> c.power(Decimal('Infinity'), Decimal('0')) Decimal('1') >>> c.power(Decimal('Infinity'), Decimal('1')) Decimal('Infinity') >>> c.power(Decimal('-Infinity'), Decimal('-1')) Decimal('-0') >>> c.power(Decimal('-Infinity'), Decimal('0')) Decimal('1') >>> c.power(Decimal('-Infinity'), Decimal('1')) Decimal('-Infinity') >>> c.power(Decimal('-Infinity'), Decimal('2')) Decimal('Infinity') >>> c.power(Decimal('0'), Decimal('0')) Decimal('NaN') >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) Decimal('11') >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) Decimal('-11') >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) Decimal('1') >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) Decimal('11') >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) Decimal('11729830') >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) Decimal('-0') >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) Decimal('1') >>> ExtendedContext.power(7, 7) Decimal('823543') >>> ExtendedContext.power(Decimal(7), 7) Decimal('823543') >>> ExtendedContext.power(7, Decimal(7), 2) Decimal('1') Trrzrw)rrrr)r7rrrrls&&&& r0power Context.powersAR 1d + IIaI .  =AB BHr2c @\VRR7pVPW R7#)aReturns 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') Trrz)rrrs&&&r0rContext.quantizeTs"n 1d +zz!z**r2c \^ 4#)zSJust returns 10, as this is Decimal, :) >>> ExtendedContext.radix() Decimal('10') rrs&r0r Context.radixs r{r2c |\VRR7pVPW R7pV\Jd\RV,4hV#)aFReturns 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') Trrzrw)rr}rrrxs&&& r0reContext.remainders>> 1d + IIaI &  =AB BHr2c @\VRR7pVPW R7#)aoReturns 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') Trrz)rrrs&&&r0rContext.remainder_nears$> 1d +00r2c @\VRR7pVPW R7#)aReturns 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') Trrz)rrrs&&&r0rContext.rotates!4 1d +xxx((r2c >\VRR7pVPV4#)aUReturns True if the two operands have the same exponent. The result is never affected by either the sign or the coefficient of either operand. >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) False >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) True >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) False >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) True >>> ExtendedContext.same_quantum(10000, -1) True >>> ExtendedContext.same_quantum(Decimal(10000), -1) True >>> ExtendedContext.same_quantum(10000, Decimal(-1)) True Tr)rr$rs&&&r0r$Context.same_quantums* 1d +~~a  r2c @\VRR7pVPW R7#)aReturns 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') Trrz)rrrs&&&r0rContext.scalebs! 1d +xxx((r2c @\VRR7pVPW R7#)aReturns 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') Trrz)rrdrs&&&r0rd Context.shift&s!6 1d +wwqw''r2c @\VRR7pVPVR7#)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 Trrz)rr9rts&&r0r9 Context.sqrtDs!: 1d +vvdv##r2c |\VRR7pVPW R7pV\Jd\RV,4hV#)aReturn 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') Trrzrw)rrVrrrxs&&& r0subtractContext.subtractds> 1d + IIaI &  =AB BHr2c @\VRR7pVPVR7#)aConvert to a string, using engineering notation if an exponent is needed. Engineering notation has an exponent which is a multiple of 3. This can leave up to 3 digits to the left of the decimal place and may require the addition of either one or two trailing zeros. The operation is not affected by the context. >>> ExtendedContext.to_eng_string(Decimal('123E+1')) '1.23E+3' >>> ExtendedContext.to_eng_string(Decimal('123E+3')) '123E+3' >>> ExtendedContext.to_eng_string(Decimal('123E-10')) '12.3E-9' >>> ExtendedContext.to_eng_string(Decimal('-123E-12')) '-123E-12' >>> ExtendedContext.to_eng_string(Decimal('7E-7')) '700E-9' >>> ExtendedContext.to_eng_string(Decimal('7E+1')) '70' >>> ExtendedContext.to_eng_string(Decimal('0E+1')) '0.00E+3' Trrz)rr<rts&&r0r<Context.to_eng_string{s!2 1d +t,,r2c @\VRR7pVPVR7#)ziConverts a number to a string, using scientific notation. The operation is not affected by the context. Trrz)rr8rts&&r0 to_sci_stringContext.to_sci_strings! 1d +yyy&&r2c @\VRR7pVPVR7#)aRounds 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') Trrz)rr/rts&&r0r/Context.to_integral_exacts$6 1d +""4"00r2c @\VRR7pVPVR7#)aRounds 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') Trrz)rrrts&&r0rContext.to_integral_values$4 1d +""4"00r2) rprr)r4rr rornr) NNNNNNNNNr-)r)[r<r=r>r?r@rr2r6r.r=rr+r}rOr4r|rrrr^rdrrbrr5rnrqrryr|rLrrOr=r[r?rr@rbrrrcrrrirlr#rrurrzrrrrrrrrrrrMrr%rrrrrrrrrrrrrerrr$rrdr9rr<rr/rr rArBrCs@r0rr s$"H 5 1I2<; "! ! H!,--H..&"$'**! #*J!1F":&   0#J.*#0).  ,  ). " ,,"",%8$4.6.&-6.6&6*"&6*"'"@*()(!.F)00,d'"N`8+t$L 1D):!0)&(<$@.-8'1<1<$Kr2c4a]tRtRtoRtRRltRtRtVtR#)riNc8VfRVn^VnRVnR#\V\4'd?VP Vn\VP 4VnVPVnR#V^,VnV^,VnV^,VnR#r-)r\rrrrrMrNr)r7rs&&r0r_WorkRep.__init__sq =DIDHDH w ' ' DI5::DHzzDHaDIQxDHQxDHr2c\RVP: RVP: RVP: R2#)(rCrEr\rrrs&r0r+_WorkRep.__repr__s!%DHHdhh??r2)rrr\rr-) r<r=r>r?rrr+rArBrCs@r0rrs$I  @@r2rc VPVP8dTpTpMTpTp\\VP44p\\VP44pVP\ RWR, ^, 4,pWdP,^, V8d^VnWtnV;P^ VPVP, ,,unVPVnW3#)z[Normalizes op1, op2 to have the same exp and length of coefficient. Done during addition. r)rrrrr%)rQrRrotmprtmp_len other_lenrs&&& r0rOrOs  ww#cgg,GC N#I ''CGNQ./ /C99q 3&  GGrcgg )**GiiCG 8Or2cV^8Xd^#V^8dV^ V,,#\\V44p\V4\VPR44, pW1)8dR#V^ V),,#)zGiven 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 rN)rrrrstrip)rKr1str_nval_ns&& r0rrsi Av a2q5yCF E Sc!233rzt2qBF{2r2c|V^8:gV^8:d \R4h^pW8wdYV)V,, ^, rK V#)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. z3Both arguments to _sqrt_nearest should be positive.)r)rKrrs&& r0 _sqrt_nearestr,s? AvaNOOA &QBE'1*1 Hr2c~^V,W, r2V^W^, ,,V^,,V8,#)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.)rrdrrks&& r0_rshift_nearestr;s4 :qzq 1!9 1%) **r2c^\W4wr#V^V,V^,,V8,#)zYClosest integer to a/b, a and b positive integers; rounds to even in the case of a tie. )rc)rrrkrls&& r0 _div_nearestrCs* ! 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.)rrrr _log10_digits) r7r1rr8rrrlog_dlog_10 log_tenpowers &&& r0rr{sFA CF A qsaxA1u E CE 6 QJAQQB'Aa q!UWf-s #ArA2v.  *C 00r2cV^, p\\V44pW,W,^8, pV^8dPW,V, pV^8dV^ V,,pM\V^ V),4p\V^ V,4pM^pV'd_\\\ V444^, pW',^8d+\V\ W',4,^ V,4pM^pM^p\W,^d4#)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.)rrrrrr) r7r1rr8rrr r f_log_tens &&& r0rrsFA CF A qsaxA 1u CE 6 QJAQQB'AaQ CAK " 9>%Q}QW'=%=r5yIII   )3 //r2c0a]tRtRtoRtRtRtRtVtR#) _Log10MemoizeizClass 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__.cRVnR#)/23025850929940456840179914546843642076011014886Nrrs&r0r_Log10Memoize.__init__s G r2c V^8d \R4hV\VP48dv^p^ W,^,,p\\ \ ^ V,V4^d44pWB)RRV,8wdM V^, pKZVP R4RRVn\VPRV^,4#)zdGiven an integer p >= 0, return floor(10**p)*log(10). For example, self.getdigits(3) returns 2302. zp should be nonnegativeNrr)rrrrrrr r)r7rrrrs&& r0 getdigits_Log10Memoize.getdigitss q567 7 DKK EO\%1a.#>?&'?c%i/ !--,Sb1DK4;;t!$%%r2r)N) r<r=r>r?r@rr,rArBrCs@r0r&r&sCH&&r2r&c\W,V,4p\R\\V44,^V,,4)p\ W4pW,p\ V^, ^R4F"p\ WV,,Wg,4pK$ \ V^, RR4F+pW^,,p\ WUV,,V4pK- W,#)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).rr)rrrrrr) rrrrrrMshiftrrs &&& r0_iexpr0s* qyA SSV_qs # $$AQA TF 1Q32  QJ 41Q3B qS fHv .  3Jr2c V^, p\^V\\V44,^, 4pW#,pW,pV^8dV^ V,,pMV^ V),,p\V\ V44wrx\ V^ V,4p\ \ V^ V,4R4Wr, ^,3#)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.i)rMrrrcrrr0) r7r1rrrkrdcshiftquotrs &&& r0reresFA 1s3q6{?Q& 'E A CE z2u9BJv}Q/0ID sBI &C c2q5)4 0$(Q, >>r2c0\\\V444V,p\WWE,^,4pW5, pV^8dWb,^ V,,pM\ Wb,^ V),4pV^8Xd_\\V44V,^8V^88Xd#^ V^, ,^,^V, rW3#^ V,^, V)rW3#\ W^,)V^,4wr\ V ^ 4p V ^, p W3#)aGiven integers xc, xe, yc and ye representing Decimals x = xc*10**xe and y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: 10**(p-1) <= c <= 10**p, and (c-1)*10**e < x**y < (c+1)*10**e in other words, c*10**e is an approximation to x**y with p digits of precision, and with an error in c of at most 1. (This is almost, but not quite, the same as the error being < 1ulp: when c == 10**(p-1) we can only guarantee error < 10ulp.) We assume that: x is positive and not equal to 1, and y is nonzero. )rrrrrre) rrrrrrlxcrdpcrrs &&&&& r0r r 7s CBLBA A C DE z VBI  #&"uf* - QwR\B ! #a 0ac1ac3 : Qq1"3 : 21vqs+ UB' q :r2r\2345678rmcV^8:d \R4h\V4p^d\V4,W^,,, #)z@Compute a lower bound for 100*log10(c) for a positive integer c.z0The argument to _log10_lb should be nonnegative.)rrr)r7 correctionstr_cs&& r0rras: AvKLL FE s5z>JQx0 00r2c\V\4'dV#\V\4'd \V4#V'd,\V\4'd\P V4#V'd\ RV,4h\ #)zConvert other to Decimal. Verifies that it's ok to use in an implicit construction. If allow_float is true, allow conversion from float; this is used in the comparison methods (__eq__ and friends). rw)rrrrrrr)rr allow_floats&&&r0rrlsg%!! %u~z%//!!%((9EABB r2c\V\4'dW3#\V\P4'dxVP'gO\ VP \\VP4VP,4VP4pV\VP43#V'd>\V\P4'dVP^8Xd VPp\V\ 4'dT\#4pV'd^VP$\&&MVP)\&R4V\P+V43#\,\,3#)zGiven a Decimal instance self and a Python object other, return a pair (s, o) of Decimal instances such that "s op o" is equivalent to "self op other" for any of the 6 comparison operators "op". r)rr_numbersRationalrrLrMrrrN denominatorr numeratorComplexrrrrr rrrr)r7rrr8s&&& r0rrs%!!{ %**++#DJJ$'DII9J9J(J$K$(II/DWU__--- z%)9)9::uzzQ %, ,-GMM. )  M OW''... > ))r2i?B)rornrr rprr4r)rornrr a # A numeric string consists of: # \s* (?P[-+])? # an optional sign, followed by either... ( (?=\d|\.\d) # ...a number (with at least one digit) (?P\d*) # having a (possibly empty) integer part (\.(?P\d*))? # followed by an optional fractional part (E(?P[-+]?\d+))? # followed by an optional exponent, or... | Inf(inity)? # ...an infinity, or... | (?Ps)? # ...an (optionally signaling) NaN # NaN (?P\d*) # with (possibly empty) diagnostic info. ) # \s* \z z0*$z50*$a*\A (?: (?P.)? (?P[<>=^]) )? (?P[-+ ])? (?Pz)? (?P\#)? (?P0)? (?P\d+)? (?P[,_])? (?:\. (?=[\d,_]) # lookahead for digit or separator (?P\d+)? (?P[,_])? )? (?P[eEfFgGn%])? \z c\PV4pVf\RV,4hVP4pVR,pVR,pVR,RJVR&VR,'d-Ve\RV,4hVe\RV,4hT;'gRVR&T;'gR VR&VR ,fR VR &\ VR ,;'gR 4VR &VR,e\ VR,4VR&VR,^8XdVR,eVR,R9d^VR&VR,R8XdaRVR&Vf\ P !4pVR,e\RV,4hVR,VR&VR,VR&VR,VR&MVR,fRVR&^^.VR&RVR&VR,fRVR&V#)aParse and validate a format specifier. Turns a standard numeric format specifier into a dict, with the following entries: fill: fill character to pad field to minimum width align: alignment type, either '<', '>', '=' or '^' sign: either '+', '-' or ' ' minimumwidth: nonnegative integer giving minimum width zeropad: boolean, indicating whether to pad with zeros thousands_sep: string to use as thousands separator, or '' grouping: grouping for thousands separators, in format used by localeconv decimal_point: string to use for decimal point precision: nonnegative integer giving precision, or None type: one of the characters 'eEfFgG%', or None NzInvalid format specifier: fillalignzeropadz7Fill character conflicts with '0' in format specifier: z2Alignment conflicts with '0' in format specifier:  >r\r minimumwidthrrrgGnrKr thousands_sepzJExplicit thousands separator conflicts with 'n' type in format specifier: grouping decimal_pointrr0frac_separators)_parse_format_specifier_regexmatchr groupdictr_locale localeconv) format_specrr format_dictrJrKs&& r0rrs$& &++K8Ay5 CDD++-K v D  E))4D@K 9  68CDE E  24?@A A++#K!<@KLM M'2?'C O$"-j"9 J'2?'C O$  ' /+-K (#$a& J'* O$$%-)+ %& r2cVR,pVR,pWC\V4, \V4, ,pVR,pVR8XdW,V,pV#VR8XdWP,V,pV#VR8XdW,V,pV#VR8Xd1\V4^,pVRVV,V,WXR,pV#\R 4h) 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). rOrJrK M788r2c^RIHpHpV'g.#VR,^8Xd*\V4^8dV!VRRV!VR,44#VR,\P 8XdVRR#\ R4h)zqConvert a localeconv-style grouping into a (possibly infinite) iterable of integers representing group lengths. )chainrepeatNz unrecognised format for groupingrr) itertoolsrcrdrrXCHAR_MAXr)rRrcrds& r0_group_lengthsrgsl(  " s8}1Xcr]F8B<$899 ")) )};<? ? CKA. 2 c1s6{?+fRSk9:! )q. SX & F Y * c1s6{?+fRSk9: 88HV$ %%r2cHV'dR#VR,R9d VR,#R#)zDetermine sign character.rr\z +rr.) is_negativers&&r0rrs# f F|r2c da\W4pVR,pS'd8V'd0VPV3Rl\^\S4^444oS'gVR,'dVR,S,oV^8wgVR,R9d1RRRRR RR R/VR,,pSR P Ws4, oVR,R 8Xd SR , oVR ,'d+VR,\S4, \V4, pM^p\ WV4p\ WQS,V4#)a/Format a number, given the following data: is_negative: true if the number is negative, else false intpart: string of digits that must appear before the decimal point fracpart: string of digits that must come after the point exp: exponent, as an integer spec: dictionary resulting from parsing the format specifier This function uses the information in spec to: insert separators (decimal separator and thousands separators) format the sign format the exponent add trailing '%' for the '%' type zero-pad if necessary fill and align if necessary rTc3:<"TFpSW^,xK R#5i)Nr.)r"posrs& r0r#!_format_number..s"!H,FS"*#Ag!6,FsaltrSrrr2r1rrz{0}{1:+}rrLrO)rrrrformatrmr) rorrrrr\frac_sepecharrjs &&f&& r0rrs $  *D%&HH==!H,1!S]A,F!HH4;;(83 ax4<4'c3S#sC8fFJ%%e11 F|sC I(3x=83t9D  #G9=G x/ 66r2Infz-Infr/llNZoi)rorrpr4rrnr rr-rr)r)FFi)rr)~r@__all__r< __xname__ __version____libmpdec_version__mathrnumbersrDsys collectionsr* _namedtupler ImportErrorrrrrrrrrr'r(maxsizer"r#r$r&r%ArithmeticErrorrr r rZeroDivisionErrorr rrr rr rrrrrrrXr9 contextvars ContextVarrv frozensetrrrr r!rrrLNumberregisterrrrrOrrrrrrrrrrr&r,rr0rer rrrrrrrecompileVERBOSE IGNORECASErVrrrDOTALLrUlocalerXrrrgrmrrrrrPrSr rRrZ hash_infomodulusrrrr _PyHASH_NANrrr.r2r0rsr '!  ! !   ! ! %! '8! ! "! $6! 8H! ! ! &! (2! 4?! !  !!  +!!  -?!!  AT!! &'! &"'! &$5'! &7F'! ()! ()! ( 1)! (3?)! ./! ./! .!//! .1>/! 45! 45! 4(5! 4*55! 47N5! :;! @A! F    &5~/EiXL   #  #   ;;'!H!H"HHHH  #   .  ':'%%'8% )  (*;    %     #:w#:L ) %y" ^Wh 'N D##3$%5#$4 !13 }o}/:G"--.?@O &+\6^4Kf^4K@i& ! 'f 'Q$fQ$f6@v@4< 3*  +!. ` 1D*0X!&F!&F)) #J"?H(V S#r3CS" Rb#r3+1&"*T /x)9:   x)97IN  * **"ZZ"--# !""'#&ZZ  $ $ jj && !# ,$ZZ %!(  Qf6=.#&J(7\ EN FOu~ qzr{ /0--''mm mm B!+_= IF&%L&X~  s$(O">O3" O0/O03O=<O=