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g! \ a S r GNGf = f! \ a Nf = f)zz Python decimal arithmetic module)%DecimalContext DecimalTupleDefaultContext BasicContextExtendedContextDecimalExceptionClampedInvalidOperationDivisionByZeroInexactRounded SubnormalOverflow UnderflowFloatOperationDivisionImpossibleInvalidContextConversionSyntaxDivisionUndefined
ROUND_DOWN
ROUND_HALF_UPROUND_HALF_EVEN
ROUND_CEILING ROUND_FLOORROUND_UPROUND_HALF_DOWN
ROUND_05UP
setcontext
getcontext localcontextMAX_PRECMAX_EMAXMIN_EMIN MIN_ETINY HAVE_THREADSHAVE_CONTEXTVARdecimalz1.70z2.4.2 N)
namedtupler zsign digits exponent)modulec U $ N )argss !/usr/lib/python3.13/_pydecimal.pyr0 C s r r r r r r r r Tl l NZolNZoi@Ti c \ rS rSrSrS rSrg)r _ a Base 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.
c g r, r- selfcontextr. s r/ handleDecimalException.handler s r1 r- N__name__
__module__ __qualname____firstlineno____doc__r9 __static_attributes__r- r1 r/ r r _ s $
r1 r c \ rS rSrSrSrg)r v 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@ rA r- r1 r/ r r v r1 r c \ rS rSrSrS rSrg)r
a An invalid operation was performed.
Various bad things cause this:
Something creates a signaling NaN
-INF + INF
0 * (+-)INF
(+-)INF / (+-)INF
x % 0
(+-)INF % x
x._rescale( non-integer )
sqrt(-x) , x > 0
0 ** 0
x ** (non-integer)
x ** (+-)INF
An operand is invalid
The result of the operation after this is a quiet positive NaN,
except when the cause is a signaling NaN, in which case the result is
also a quiet NaN, but with the original sign, and an optional
diagnostic information.
c U( a9 [ US R US R SS5 nUR U5 $ [ $ )Nr( nT)_dec_from_triple_sign_int_fix_nan_NaN)r7 r8 r. anss r/ r9 InvalidOperation.handle s9 "47==$q',,TJC<<( ( r1 r- Nr; r- r1 r/ r
r
s ,r1 r
c \ rS rSrSrS rSrg)r zTrying 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, rN r6 s r/ r9 ConversionSyntax.handle r1 r- Nr; r- r1 r/ r r s r1 r c \ rS rSrSrS rSrg)r a Division 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 [ U $ r, )_SignedInfinityr7 r8 signr. s r/ r9 DivisionByZero.handle s
t$$r1 r- Nr; r- r1 r/ r r s
%r1 r c \ rS rSrSrS rSrg)r zCannot 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, rT r6 s r/ r9 DivisionImpossible.handle rV r1 r- Nr; r- r1 r/ r r r1 r c \ rS rSrSrS rSrg)r zUndefined 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, rT r6 s r/ r9 DivisionUndefined.handle rV r1 r- Nr; r- r1 r/ r r rb r1 r c \ rS rSrSrSrg)r a Had 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- NrD r- r1 r/ r r rE r1 r c \ rS rSrSrS rSrg)r a Invalid 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, rT r6 s r/ r9 InvalidContext.handle rV r1 r- Nr; r- r1 r/ r r s r1 r c \ rS rSrSrSrg)r
a Number 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- NrD r- r1 r/ r
r
rE r1 r
c \ rS rSrSrSrg)r a Exponent < Emin before rounding.
This occurs and signals subnormal whenever the result of a conversion or
operation is subnormal (that is, its adjusted exponent is less than
Emin, before any rounding). The result in all cases is unchanged.
The subnormal signal may be tested (or trapped) to determine if a given
or operation (or sequence of operations) yielded a subnormal result.
r- NrD r- r1 r/ r r s r1 r c \ rS rSrSrS rSrg)r a Numerical 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.
c UR [ [ [ [ 4; a [
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9 19 ;.&t,,#D#gll*: $\\',, 6q 8:
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:r1 r c \ rS rSrSrSrg)r i& aT Numerical 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- NrD r- r1 r/ r r & r1 r c \ rS rSrSrSrg)r i5 at Enable 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- NrD r- r1 r/ r r 5 rz r1 r decimal_context)rv Eminrw capitalsclampru flagstrapsc [ R 5 $ ! [ a$ [ 5 n [ R U 5 U s $ f = f)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 LookupErrorr setr8 s r/ r r _ s? #'')) ) )s +AAc U [ [ [ 4; a U R 5 n U R 5 [
R
U 5 g)z%Set this thread's context to context.N)r r r copy clear_flagsr r r s r/ r r m s6 >< AA,,. W%r1 c U c
[ 5 n [ U 5 nUR 5 H4 u p4U[ ; a [ SU S35 e[ UR X45 M6 U$ )a Return 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 r/ r r v sc H {l!#&K lln
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jrS~S jrS~S jrS~S jrS~S jrS~S jrS rS rS rS rSS jrS~S jrS~S jrS~S jr SS jr S~S jr \ r S~S jr S~S jr!S~S jr"\"r#S~S jr$S! r%S~S" jr&S~S# jr'S~S$ jr(S~S% jr)S~S& jr*S~S' jr+S~S( jr,S~S) jr-S* r.S+ r/\/r0\1S, 5 r2\1S- 5 r3S. r4S/ r5S0 r6S1 r7S2 r8S3 r9S4 r:S5 r;S6 rS9 r?\@" \8\9\:\;\<\=\>\?S:9rAS~S; jrBS< rCS= rDS~S> jrES~S? jrFS@ rGS}SA jrHS~SB jrIS~SC jrJS}SD jrKS~SE jrLSF rMSG rNS}SH jrOS}SI jrP\PrQS~SJ jrRS~SK jrSS~SL jrTSM rUSN rVSO rWSP rXS~SQ jrYS~SR jrZS~SS jr[ST r\SU r]S~SV jr^S~SW jr_SX r`SY raSZ rbS[ rcS~S\ jrdS] reS^ rfS_ rgS~S` jrhSa riSb rjS~Sc jrkSd rlS~Se jrmS~Sf jrnSg roSh rpS~Si jrqS~Sj jrrS~Sk jrsS~Sl jrtS~Sm jruS~Sn jrvS~So jrwS~Sp jrxS~Sq jryS~Sr jrzSs r{S~St jr|S~Su jr}S~Sv jr~Sw rSx rSy rS}Sz jrS{rg)r i z,Floating-point class for decimal arithmetic.)_exprL rK _is_specialNc [ R U 5 n[ U[ 5 ( Ga [ UR 5 R
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[ 5 nUR [ SU- 5 $ UR S5 S:X a SUl OSUl UR S5 nUbt UR S 5 =( d Sn[ UR S
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[ UR, 5 Ul S Ul U$ [ U[. [0 45 ( Gau [ U5 S:w a [3 S5 e[ US [ 5 ( a US S; d [3 S5 eUS Ul US S:X a S Ul
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[ 5 nUR [< S 5 [& R? U5 nUR Ul UR Ul UR Ul
UR Ul U$ [A S U- 5 e) a Create 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')
_ z Invalid literal for Decimal: %rr\ -r2 r( intfracexp0FdiagsignalNrI FT ztInvalid tuple size in creation of Decimal from list or tuple. The list or tuple should have exactly three elements.r( r2 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.rI r 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 enabledz Cannot convert %r to Decimal)!object__new__
isinstancestr_parserstripreplacer _raise_errorr grouprK r rL lenr r lstripabsr _WorkRepr\ r listtuple
ValueErrorappendjoinmapfloatr
from_floatr ) clsr r8 r7 mintpartfracpartr r digitsdigits r/ r Decimal.__new__ sY . ~~c" eS ! !
--c267Ay? (lG ++,< AE IK K wwv#%
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eU # #$,
&&u-E DI DJ DI % 1 1D K6>??r1 c < [ U[ 5 ( a! US: a SOSnSn[ [ U5 5 nO[ U[ 5 ( a [
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R " SU5 S:X a SnOSn[ U5 R 5 u pVUR 5 S-
n[ USU- - 5 nO [ S5 e[ X$U* 5 nU [ L a U$ U " U5 $ )a Converts a float to a decimal number, exactly.
Note that Decimal.from_float(0.1) is not the same as Decimal('0.1').
Since 0.1 is not exactly representable in binary floating point, the
value is stored as the nearest representable value which is
0x1.999999999999ap-4. The exact equivalent of the value in decimal
is 0.1000000000000000055511151231257827021181583404541015625.
>>> Decimal.from_float(0.1)
Decimal('0.1000000000000000055511151231257827021181583404541015625')
>>> Decimal.from_float(float('nan'))
Decimal('NaN')
>>> Decimal.from_float(float('inf'))
Decimal('Infinity')
>>> Decimal.from_float(-float('inf'))
Decimal('-Infinity')
>>> Decimal.from_float(-0.0)
Decimal('-0')
r( r2 g ? z argument must be int or float.)r r r r r _mathisinfisnanreprcopysignas_integer_ratio
bit_lengthr rJ r )r fr\ kcoeffrI dresults r/ r Decimal.from_floatI s , a Q1ADAAKE
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!{{1~~Q 47|#~~c1%,q6**,DA "A!Q$KE <= =!$r2 '>Mv; r1 c Z U R ( a U R nUS:X a gUS:X a gg)zRReturns whether the number is not actually one.
0 if a number
1 if NaN
2 if sNaN
rI r2 r r r( )r r )r7 r s r/ _isnanDecimal._isnanv s- ))Cczr1 c J U R S:X a U R ( a ggg)zYReturns whether the number is infinite
0 if finite or not a number
1 if +INF
-1 if -INF
r r2 r( )r rK r7 s r/ _isinfinityDecimal._isinfinity s 99 zzr1 c L U R 5 nUc SnOUR 5 nU( d U( ap Uc
[ 5 nUS:X a UR [ SU 5 $ US:X a UR [ SU5 $ U( a U R U5 $ UR U5 $ g)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.
Fr sNaNr( )r r r r
rM )r7 otherr8 self_is_nan other_is_nans r/ _check_nansDecimal._check_nans s kkm = L <<>L ,$,a ++,>'* *r1 c Uc
[ 5 nU R ( d UR ( a U R 5 ( a UR [ SU 5 $ UR 5 ( a UR [ SU5 $ U R 5 ( a UR [ SU 5 $ UR 5 ( a UR [ SU5 $ g)a Version of _check_nans used for the signaling comparisons
compare_signal, __le__, __lt__, __ge__, __gt__.
Signal InvalidOperation if either self or other is a (quiet
or signaling) NaN. Signaling NaNs take precedence over quiet
NaNs.
Return 0 if neither operand is a NaN.
zcomparison involving sNaNzcomparison involving NaNr( )r r is_snanr r
is_qnanr7 r r8 s r/ _compare_check_nansDecimal._compare_check_nans s ? lG u 0 0||~~ ++,<,G,02 2 ++,<,G,13 3 ++,<,F,02 2 ++,<,F,13 3 r1 c F U R =( d U R S:g $ )zeReturn True if self is nonzero; otherwise return False.
NaNs and infinities are considered nonzero.
r r rL r s r/ __bool__Decimal.__bool__ s
3499#33r1 c U R ( d UR ( a- U R 5 nUR 5 nX#:X a gX#: a ggU ( d U( d gSUR - * $ U( d SU R - $ UR U R : a gU R UR : a gU R 5 nUR 5 nXE:X a| U R SU R
UR
-
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- - nXg:X a gXg: a SU R - * $ SU R - $ XE: a SU R - $ SU R - * $ )zCompare the two non-NaN decimal instances self and other.
Returns -1 if self < other, 0 if self == other and 1
if self > other. This routine is for internal use only.r( r r2 r )r r rK adjustedrL r )r7 r self_inf other_inf
self_adjustedother_adjusted self_padded other_paddeds r/ _cmp Decimal._cmp sQ u 0 0'')H ))+I$% u{{*++# # ;; # :: #
) * ))c499uzz+A&BBK ::UZZ$))-C(DDL* +djj(((TZZ''
+# #4::%& &r1 c [ XSS9u pU[ L a U$ U R X5 ( a gU R U5 S:H $ )NT) equality_opFr( )_convert_for_comparisonNotImplementedr r r s r/ __eq__Decimal.__eq__ sE -dtL N "L E + +yy 1$$r1 c [ X5 u pU[ L a U$ U R X5 nU( a gU R U5 S: $ NFr( r r r r r7 r r8 rO s r/ __lt__Decimal.__lt__" E -d: N "L&&u6 yy !##r1 c [ X5 u pU[ L a U$ U R X5 nU( a gU R U5 S:* $ r r r s r/ __le__Decimal.__le__+ E -d: N "L&&u6 yy 1$$r1 c [ X5 u pU[ L a U$ U R X5 nU( a gU R U5 S: $ r r r s r/ __gt__Decimal.__gt__4 r r1 c [ X5 u pU[ L a U$ U R X5 nU( a gU R U5 S: $ r r r s r/ __ge__Decimal.__ge__= r r1 c [ USS9nU R ( d U( a+ UR ( a U R X5 nU( a U$ [ U R U5 5 $ )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_otherr r r r r s r/ compareDecimal.compareF sQ ud3
%*;*;""52C
tyy'((r1 c U R ( ah U R 5 ( a [ S5 eU R 5 ( a [ R U 5 $ U R ( a [ * $ [ $ U R S: a [ SU R [ 5 nO [ [ U R * [ 5 n[ U R 5 U- [ - nU S: a UOU* nUS:X a S$ U$ )zx.__hash__() <==> hash(x)z"Cannot hash a signaling NaN value.r(
r )r r r is_nanr __hash__rK _PyHASH_INFr pow_PyHASH_MODULUS
_PyHASH_10INVr rL )r7 exp_hashhash_rO s r/ r Decimal.__hash__X s ||~~ DEE t,,:: '<'&& 99>2tyy/:H=499*oFHDII)O;qyeufBYr'C'r1 c [ U R [ [ [ U R
5 5 U R 5 $ )zURepresents the number as a triple tuple.
To show the internals exactly as they are.
)r rK r r r rL r r s r/ as_tupleDecimal.as_tupler s+
DJJc#tyy.A(BDIINNr1 c U R ( a+ U R 5 ( a [ S5 e[ S5 eU ( d g[ U R
5 nU R S: a USU R - - Sp!O{U R * nUS: a$ US- S:X a US- nUS- nUS: a US- S:X a M U R * n[ X* - R 5 S-
U5 nU( a X- nXE- nSU- U- nU R ( a U* nX4$ )aG Express a finite Decimal instance in the form n / d.
Returns a pair (n, d) of integers. When called on an infinity
or NaN, raises OverflowError or ValueError respectively.
>>> Decimal('3.14').as_integer_ratio()
(157, 50)
>>> Decimal('-123e5').as_integer_ratio()
(-12300000, 1)
>>> Decimal('0.00').as_integer_ratio()
(0, 1)
z#cannot convert NaN to integer ratioz(cannot convert Infinity to integer ratior r( r r2 r )
r r r
OverflowErrorr rL r minr rK )r7 rI r d5d2shift2s r/ r Decimal.as_integer_ratioy s {{}} !FGG#$NOO
N 99>r499}$aq ))Bq&QUaZaa q&QUaZ ))B!b&,,.2B7F 2 A ::At r1 c S[ U 5 - $ )z0Represents the number as an instance of Decimal.z
Decimal('%s'))r r s r/ __repr__Decimal.__repr__ s T**r1 c ( SS/U R nU R ( aI U R S:X a US- $ U R S:X a US- U R - $ US- U R - $ U R [ U R 5 - nU R S:: a US : a UnO1U( d S
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[ 5 nSS/UR SXE-
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Captures all of the information in the underlying representation.
r r r InfinityrI NaNr r( r2 r r .NeEz%+d)rK r r rL r r r~ ) r7 engr8 r\
leftdigitsdotplacer r r s r/ __str__Decimal.__str__ s Cy$ yyC j((c!e|dii//f}tyy00 YYTYY /
99>j2o!HH
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'iiXc$))n%< ==GHii *GTYYxy 11H !C$,*W - -.*:M1NNC~(3..r1 c " U R SUS9$ )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)r8 r8 )r; r7 r8 s r/
to_eng_stringDecimal.to_eng_string s ||g|66r1 c U R ( a U R US9nU( a U$ Uc
[ 5 nU ( d% UR [ :w a U R 5 nOU R
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Rounds, if it has reason.
r )r r r ru r copy_abs copy_negate_fixr7 r8 rO s r/ __neg__Decimal.__neg__ sn
""7"3C
? lG((K7 --/C""$Cxx r1 c U R ( a U R US9nU( a U$ Uc
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Rounds the number (if more than precision digits)
r )r r r ru r rB r rD rE s r/ __pos__Decimal.__pos__ sg
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? lG((K7--/C$-Cxx r1 c U( d U R 5 $ U R ( a U R US9nU( a U$ U R ( a U R US9nU$ U R US9nU$ )zReturns the absolute value of self.
If the keyword argument 'round' is false, do not round. The
expression self.__abs__(round=False) is equivalent to
self.copy_abs().
r )rB r r rK rF rI )r7 roundr8 rO s r/ __abs__Decimal.__abs__ sl ==? " ""7"3C
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r1 c [ U5 nU[ L a U$ Uc
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U l UR. U l [ U 5 nUR U5 nU$ )zRReturns self + other.
-INF + INF (or the reverse) cause InvalidOperation errors.
z
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r/ __add__Decimal.__add__. s
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!!::,1B1B1D1D"//0@,OO t}$ "" u~%$))UZZ( { *tzzU[[/H LEtzz5;;/D"4c2C((7#CJc:: 4Q67C..&6&67C((7#CJc99w||3A56C--%5%56C((7#CJtnuo c 5 88sxx ww#''!&|S#>hhw'
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r1 c [ U5 nU[ L a U$ U R ( d UR ( a U R XS9nU( a U$ U R UR 5 US9$ )zReturn self - otherr )r r r r rV rC r s r/ __sub__Decimal.__sub__ sc u% N "L u 0 0""5":C
||E - - /|AAr1 c L [ U5 nU[ L a U$ UR XS9$ )zReturn other - selfr )r r rY r s r/ __rsub__Decimal.__rsub__ s* u% N "L}}T}33r1 c [ U5 nU[ L a U$ Uc
[ 5 nU R UR - nU R ( d UR ( a U R X5 nU( a U$ U R
5 ( a& U( d UR [ S5 $ [ U $ UR
5 ( a& U ( d UR [ S5 $ [ U $ U R UR - nU ( a U( d [ USU5 nUR U5 nU$ U R S:X a) [ X1R U5 nUR U5 nU$ UR S:X a) [ X0R U5 nUR U5 nU$ [ U 5 n[ U5 n[ U[ UR UR - 5 U5 nUR U5 nU$ )zLReturn self * other.
(+-) INF * 0 (or its reverse) raise InvalidOperation.
z (+-)INF * 0z 0 * (+-)INFr 1)r r r rK r r r r r
rZ r rJ rD rL r r r )r7 r r8
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u% N "L ? lGZZ%++-
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r1 c [ U5 nU[ L a [ $ Uc
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zReturn self / other.z(+-)INF/(+-)INFzDivision by infinityr z0 / 0zx / 0r( r2 r r )r r r rK r r r r r
rZ r rJ Etinyr r r r rL rv r divmodr r rD ) r7 r r8 r\ rO r r shiftrT rU remainder ideal_exps r/ __truediv__Decimal.__truediv__ sL u% N "! ! ? lGzzEKK' u 0 0""52C
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X4$ )zReturn (self // other, self % other), to context.prec precision.
Assumes that neither self nor other is a NaN, that self is not
infinite and that other is nonzero.
r r r( r z%quotient too large in //, % or divmod)rK r r r) r rJ rQ ru rv r r r rf r r r ) r7 r r8 r\ ri expdiffrT rU qrrO s r/ _divideDecimal._divide s} zzEKK' IDIIuzz2I--/ENN$44u((**gm$T32MM)-=-=>@
@ ll "4.C5/Cww#''!2#'' 1222#'' 122#''377+DA2w||##(s1vq9(SVYGI I ""#5#JLxr1 c L [ U5 nU[ L a U$ UR XS9$ )z)Swaps self/other and returns __truediv__.r )r r rj r s r/ __rtruediv__Decimal.__rtruediv__1 s- u% N "L 77r1 c j [ U5 nU[ L a U$ Uc
[ 5 nU R X5 nU( a X34$ U R UR - nU R 5 ( aM UR 5 ( a UR
[ S5 nX34$ [ U UR
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zdivmod(INF, INF)INF % xz divmod(0, 0)x // 0x % 0)
r r r r rK r r r
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__divmod__Decimal.__divmod__8 s- u% N "L ? lG u. : zzEKK' "" **+;=OPx'- ,,-=yIK K **+S^#B M1 1S:DII.5#66 6r1 c U $ r, r- r s r/ real Decimal.real s r1 c [ S5 $ )Nr( r r s r/ imag Decimal.imag s qzr1 c U $ r, r- r s r/ conjugateDecimal.conjugate s r1 c * [ [ U 5 5 $ r, )complexr r s r/ __complex__Decimal.__complex__ s uT{##r1 c U R nUR UR -
n[ U5 U: aA U[ U5 U-
S R S5 n[ U R X R S5 $ [ U 5 $ )z2Decapitate the payload of a NaN to fit the contextNr T) rL rv r r r rJ rK r r )r7 r8 payloadmax_payload_lens r/ rM Decimal._fix_nan sm )) ",, 6 w&&x tzzJC ) )J #O G 99w ^dii/'9Fz'
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( a+ U R
5 ( a [ S5 e[ S5 e[ U R S[ 5 5 $ )a Round self to the nearest integer, or to a given precision.
If only one argument is supplied, round a finite Decimal
instance self to the nearest integer. If self is infinite or
a NaN then a Python exception is raised. If self is finite
and lies exactly halfway between two integers then it is
rounded to the integer with even last digit.
>>> round(Decimal('123.456'))
123
>>> round(Decimal('-456.789'))
-457
>>> round(Decimal('-3.0'))
-3
>>> round(Decimal('2.5'))
2
>>> round(Decimal('3.5'))
4
>>> round(Decimal('Inf'))
Traceback (most recent call last):
...
OverflowError: cannot round an infinity
>>> round(Decimal('NaN'))
Traceback (most recent call last):
...
ValueError: cannot round a NaN
If a second argument n is supplied, self is rounded to n
decimal places using the rounding mode for the current
context.
For an integer n, round(self, -n) is exactly equivalent to
self.quantize(Decimal('1En')).
>>> round(Decimal('123.456'), 0)
Decimal('123')
>>> round(Decimal('123.456'), 2)
Decimal('123.46')
>>> round(Decimal('123.456'), -2)
Decimal('1E+2')
>>> round(Decimal('-Infinity'), 37)
Decimal('NaN')
>>> round(Decimal('sNaN123'), 0)
Decimal('NaN123')
z+Second argument to round should be integralr( r_ cannot round a NaNcannot round an infinity) r r r rJ quantizer r r r( rQ r )r7 rI r s r/ __round__Decimal.__round__ s ^
= a%% MNN"1cA2.C==% % {{}} !566#$>??4==O455r1 c U R ( a+ U R 5 ( a [ S5 e[ S5 e[ U R S[ 5 5 $ )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.
r r r( )r r r r( r rQ r r s r/ __floor__Decimal.__floor__
sF {{}} !566#$>??4==K011r1 c U R ( a+ U R 5 ( a [ S5 e[ S5 e[ U R S[ 5 5 $ )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.
r r r( )r r r r( r rQ r r s r/ __ceil__Decimal.__ceil__ sF {{}} !566#$>??4==M233r1 c [ USS9n[ USS9nU R ( d UR ( Ga Uc
[ 5 nU R S:X a UR [
SU 5 $ UR S:X a UR [
SU5 $ U R S:X a U nGO UR S:X a UnGO U R S:X a> U( d UR [
S5 $ [ U R UR - nOUR S:X a= U ( d UR [
S5 $ [ U R UR - nOm[ U R UR - [ [ U R 5 [ UR 5 - 5 U R UR - 5 nWR X#5 $ ) a
Fused multiply-add.
Returns self*other+third with no rounding of the intermediate
product self*other.
self and other are multiplied together, with no rounding of
the result. The third operand is then added to the result,
and a single final rounding is performed.
Tr r r rI r zINF * 0 in fmaz0 * INF in fma)
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SU 5 $ US:X a UR [
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[! US U5 nM [! XR U5 n[' U[) U5 S5 $ )
z!Three argument version of __pow__r r z@pow() 3rd argument not allowed unless all arguments are integersr( zApow() 2nd argument cannot be negative when 3rd argument specifiedz pow() 3rd argument cannot be 0zSinsufficient precision: pow() 3rd argument must not have more than precision digitszXat least one of pow() 1st argument and 2nd argument must be nonzero; 0**0 is not definedr )r r r r r r
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? ==??D::D S[!..01E 3 3 56 6!CDHHf$==Gx||$AtR(D %4 v. c$i33r1 c [ U 5 nUR UR pTUS- S:X a US- nUS-
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- US
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- U- U- nM, UU:X a US:X d gUnUS: a UUS- [ U5 - : a gUU- nUU- nUS: d U 5 eUS- S:w d U 5 e[ U5 n[ U5 U: a gUR 5 ( aC UR
S:X a3 U R [ U5 - n
[ XZ-
U[ U5 -
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5 $ )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.r r( r2 Nr_ r )r ] A r r r d )r r r r\ r rK r r) rJ _nbitsr r _decimal_lshift_exactrf r _log10_lb)r7 r pxxcxeyycyer r zeros
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UR 5 [N [L [& [$ [R 4 H* nURJ U ( d M UR U5 M, U$ URI U5 nU$ )a Return self ** other [ % modulo].
With two arguments, compute self**other.
With three arguments, compute (self**other) % modulo. For the
three argument form, the following restrictions on the
arguments hold:
- all three arguments must be integral
- other must be nonnegative
- either self or other (or both) must be nonzero
- modulo must be nonzero and must have at most p digits,
where p is the context precision.
If any of these restrictions is violated the InvalidOperation
flag is raised.
The result of pow(self, other, modulo) is identical to the
result that would be obtained by computing (self**other) %
modulo with unbounded precision, but is computed more
efficiently. It is always exact.
Nz0 ** 0r( r2 z+x ** y with x negative and y not an integerr r_ FTr r r r )*r r r r r r r
_OnerK r r rC rJ rZ r rv r r r
r r _log10_exp_boundr r rw re r
rL r r r\ _dpowerr r _signalsr rD r r r r r )r7 r r r8 rO result_sign
multiplierr self_adjexactboundre r r r r r r r extrar rm
newcontext exceptions r/ __pow__Decimal.__pow__ sI 0 %%eW= = u% N "L ? lG u. J ++,3??r1 c [ USS9nUc
[ 5 nUc UR nU R ( d UR ( a U R X5 nU( a U$ UR 5 ( d U R 5 ( aK UR 5 ( a U R 5 ( a [
U 5 $ UR [ S5 $ UR 5 UR s=:: a UR :: d O UR [ S5 $ U ( d2 [ U R SUR 5 nUR U5 $ U R 5 nXSR : a UR [ S5 $ XQR -
S- UR : a UR [ S5 $ U R# UR U5 nUR 5 UR : a UR [ S5 $ [% UR& 5 UR : a UR [ S5 $ U( a3 UR 5 UR( : a UR [* 5 UR U R : a/ X@:w a UR [, 5 UR [. 5 UR U5 nU$ ) zwQuantize self so its exponent is the same as that of exp.
Similar to self._rescale(exp._exp) but with error checking.
Tr zquantize with one INFz)target exponent out of bounds in quantizer z9exponent of quantize result too large for current contextr2 z7quantize result has too many digits for current context)r r ru r r r r r r
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)r7 r ru r8 rO r s r/ r Decimal.quantize sP
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Return True if self and other have the same exponent; otherwise
return False.
If either operand is a special value, the following rules are used:
* return True if both operands are infinities
* return True if both operands are NaNs
* otherwise, return False.
Tr )r r r is_infiniter r s r/ same_quantumDecimal.same_quantum sm ud3 u 0 0KKM4elln ?$$&>5+<+<+>
@yyEJJ&&r1 c P U R ( a [ U 5 $ U ( d [ U R SU5 $ U R U: a4 [ U R U R
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SU =( d SnUS:X a [ [ U5 S- 5 n[ U R Xa5 $ )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
r r( r_ r2 N)
r r rJ rK r rL r r r r )r7 r ru r
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U5 nUR 5 U R 5 :w a& UR UR 5 S- U-
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significant figures, using the given rounding mode.
Infinities, NaNs and zeros are returned unaltered.
This operation is quiet: it raises no flags, and uses no
information from the context.
r( z'argument should be at least 1 in _roundr2 )r r r rQ r )r7 placesru rO s r/ _roundDecimal._round
s Q; FG G 44= mmDMMOA -f 4h?
<<>T]]_ ,,,s||~a / 6AC
r1 c U R ( a# U R US9nU( a U$ [ U 5 $ U R S: a [ U 5 $ U ( d [ U R
SS5 $ Uc
[
5 nUc UR nU R SU5 nX0:w a UR [ 5 UR [ 5 U$ )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.
r r( r ) r r r r rJ rK r ru rQ r r r
r7 ru r8 rO s r/ to_integral_exactDecimal.to_integral_exact!
s ""7"3C
4= 99>4= #DJJQ7 7 ? lG ''HmmAx( ; ) W%
r1 c Uc
[ 5 nUc UR nU R ( a# U R US9nU( a U$ [ U 5 $ U R
S: a [ U 5 $ U R
SU5 $ )z@Rounds to the nearest integer, without raising inexact, rounded.r r( )r ru r r r r rQ r4 s r/ r Decimal.to_integral_value>
ss ? lG ''H ""7"3C
4= 99>4= ==H- -r1 c r Uc
[ 5 nU R ( aH U R US9nU( a U$ U R 5 ( a U R S:X a [ U 5 $ U ( d5 [
U R SU R S- 5 nUR U5 $ U R S:X a UR [ S5 $ UR S- n[ U 5 nUR S- nUR S- ( a+ UR S- n[ U R 5 S- S- nO'UR n[ U R 5 S- S- nX7-
nUS: a USU- - nS n O[# USU* - 5 u pjU
( + n XX- nSU- n Xk- n X:: a O X- S- n M U =( a X- U:H n U ( a US: a U SU- - n O U SU* - - n XX-
nOU S
- S:X a U S-
n [
S[% U 5 U5 nUR' 5 nUR) [* 5 n
UR U5 nXl U$ ) z Return the square root of self.r r( r r r2 zsqrt(-x), x > 0r r Tr )r r r r rK r rJ r rD r r
rv r r r r rL rf r
_shallow_copy
_set_roundingr ru )r7 r8 rO rv opr6 clrg r rh rI rn ru s r/ sqrt Decimal.sqrtQ
s( ? lG ""7"3C
!!djjAo t}$"4::sDIINCC88G$ $ ::?''(8:KL L, ||A~ d^ FFaK
66A: ATYY 1$)AADIIq A%A A:
eOAE!!S5&[1LA!ME
HAvEQJ "!#( zb%iR%Z
JA 1uzQ q#a&!, '')(( 9hhw #
r1 c [ USS9nUc
[ 5 nU R ( d UR ( ay U R 5 nUR 5 nU( d U( aK US:X a US:X a U R U5 $ US:X a US:X a UR U5 $ U R X5 $ U R
U5 nUS:X a U R U5 nUS:X a UnOU nUR U5 $ )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.
Tr r2 r( r r r r r rD r r
compare_totalr7 r r8 snonr= rO s r/ rP Decimal.max
s ud3 ? lG u 0 0 B BR7rQw 99W--7rQw ::g..''77 IIe 6 ""5)A 7CCxx r1 c [ USS9nUc
[ 5 nU R ( d UR ( ay U R 5 nUR 5 nU( d U( aK US:X a US:X a U R U5 $ US:X a US:X a UR U5 $ U R X5 $ U R
U5 nUS:X a U R U5 nUS:X a U nOUnUR U5 $ )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.
Tr r2 r( r rB rD s r/ r) Decimal.min
s ud3 ? lG u 0 0 B BR7rQw 99W--7rQw ::g..''77 IIe 6""5)A 7CCxx r1 c U R ( a gU R S: a gU R U R S nUS[ U5 - :H $ )z"Returns whether self is an integerFr( TNr )r r rL r )r7 rests r/ r Decimal._isinteger sC 99>yy$s3t9}$$r1 c p U ( a U R S: a gU R SU R - S; $ )z:Returns True if self is even. Assumes self is an integer.r( Tr r )r rL r s r/ r Decimal._iseven s. tyy1}yyDII &'11r1 c n U R [ U R 5 - S-
$ ! [ a gf = f)z$Return the adjusted exponent of selfr2 r( )r r rL r r s r/ r Decimal.adjusted s5 99s499~-1 1 s $'
44c U $ )zReturns the same Decimal object.
As we do not have different encodings for the same number, the
received object already is in its canonical form.
r- r s r/ canonicalDecimal.canonical s r1 c h [ USS9nU R X5 nU( a U$ U R XS9$ )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.
Tr r )r r r r s r/ compare_signalDecimal.compare_signal s9 u5&&u6 J||E|33r1 c [ USS9nU R ( a UR ( d [ $ U R ( d UR ( a [ $ U R nU R 5 nUR 5 nU( d U( a XE:X ax [ U R 5 U R 4n[ UR 5 UR 4nXg: a U( a [ $ [ $ Xg: a U( a [ $ [ $ [ $ U( a1 US:X a [ $ US:X a [ $ US:X a [ $ US:X a [ $ O0US:X a [ $ US:X a [ $ US:X a [ $ US:X a [ $ X: a [ $ X: a [ $ U R UR : a U( a [ $ [ $ U R UR : a U( a [ $ [ $ [ $ )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 r2 r ) r rK _NegativeOner r r rL _Zeror )r7 r r8 r\ self_nan other_nanself_key other_keys r/ rC Decimal.compare_total+ s ud3 ::ekk zzekkKzz ;;=LLN y$ tyy>4994
OUZZ 7 ' # ++' ++ # q='' > Kq='' > K " q= K >''q= K >'' < <K 99uzz ! ## 99uzz !## r1 c x [ USS9nU R 5 nUR 5 nUR U5 $ )zCompares self to other using abstract repr., ignoring sign.
Like compare_total, but with operand's sign ignored and assumed to be 0.
Tr )r rB rC )r7 r r8 r os r/ compare_total_magDecimal.compare_total_magt s6
ud3 MMO NN q!!r1 c Z [ SU R U R U R 5 $ )z'Returns a copy with the sign set to 0. r( )rJ rL r r r s r/ rB Decimal.copy_abs s! 499dii9I9IJJr1 c U R ( a, [ SU R U R U R 5 $ [ SU R U R U R 5 $ )z&Returns a copy with the sign inverted.r( r2 )rK rJ rL r r r s r/ rC Decimal.copy_negate sG ::#Atyy$))T=M=MN N#Atyy$))T=M=MN Nr1 c [ USS9n[ UR U R U R U R
5 $ )z$Returns self with the sign of other.Tr )r rJ rK rL r r r s r/ copy_signDecimal.copy_sign s6 ud3 TYY $ 4+;+;= =r1 c Uc
[ 5 nU R US9nU( a U$ U R 5 S:X a [ $ U ( d [ $ U R 5 S:X a [ U 5 $ UR nU R 5 nU R S:X aD U[ [ UR S- S- 5 5 : a [ SSUR S- 5 nGOLU R S:X aL U[ [ UR 5 * S- S- 5 5 : a [ SSUR 5 S-
5 nOU R S:X a! XC* : a [ SSSUS-
- - S- U* 5 nOU R S:X a! XC* S-
: a [ SSUS- - U* S-
5 nO[ U 5 nUR UR pvUR" S:X a U* nSn [% XgX8- 5 u pU S S
[ [ U 5 5 U-
S-
- - - ( a OUS-
nM@ [ S[ U 5 U
5 nUR' 5 nUR) [* 5 n UR- U5 nXl U$ ) zReturns e ** self.r r r2 r( r r_ r rt r r )r r r rY r r rv r rK r r rw rJ re r r r r\ _dexpr: r; r rD ru ) r7 r8 rO r adjr< r= r6 r r r ru s r/ r Decimal.exp s6 ? lG w / J #L K "4=
LLmmo ::?sSgll1na-?)@%A A"1c7<<>:C
ZZ1_s3 0@0BA/E+F'G!G"1c7==?1+<=C
ZZ1_r"1cC1Io&;aR@C
ZZ1_r!t"1c1Q3i!A6C $ B66266qww!|B
E "1 1
Ab3s5z?1#4Q#6 7 78
#1c%j#6C '')(( 9hhw #
r1 c g)zReturn True if self is canonical; otherwise return False.
Currently, the encoding of a Decimal instance is always
canonical, so this method returns True for any Decimal.
Tr- r s r/ is_canonicalDecimal.is_canonical s r1 c $ U R ( + $ )zReturn True if self is finite; otherwise return False.
A Decimal instance is considered finite if it is neither
infinite nor a NaN.
)r r s r/ is_finiteDecimal.is_finite s ####r1 c U R S:H $ )z8Return True if self is infinite; otherwise return False.r r r s r/ r) Decimal.is_infinite yyC r1 c U R S; $ )z>Return True if self is a qNaN or sNaN; otherwise return False.r ru r s r/ r Decimal.is_nan s yyJ&&r1 c U R ( d U ( d gUc
[ 5 nUR U R 5 :* $ )z?Return True if self is a normal number; otherwise return False.F)r r r} r r> s r/ is_normalDecimal.is_normal s1 4 ? lG||t}}..r1 c U R S:H $ )z;Return True if self is a quiet NaN; otherwise return False.rI ru r s r/ r Decimal.is_qnan rw r1 c U R S:H $ )z8Return True if self is negative; otherwise return False.r2 )rK r s r/ is_signedDecimal.is_signed s zzQ r1 c U R S:H $ )z?Return True if self is a signaling NaN; otherwise return False.r ru r s r/ r Decimal.is_snan rw r1 c U R ( d U ( d gUc
[ 5 nU R 5 UR : $ )z9Return True if self is subnormal; otherwise return False.F)r r r r} r> s r/ is_subnormalDecimal.is_subnormal s1 4 ? lG}} --r1 c P U R ( + =( a U R S:H $ )z6Return True if self is a zero; otherwise return False.r r r s r/ is_zeroDecimal.is_zero s ###8 S(88r1 c U R [ U R 5 - S-
nUS: a [ [ US- S- 5 5 S-
$ US:: a [ [ SU-
S- S- 5 5 S-
$ [ U 5 nUR
UR pCUS:X a9 [ USU* - -
5 n[ U5 n[ U5 [ U5 -
XV: -
$ U[ [ SU* - U-
5 5 - S-
$ )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.
r2 r r r r( r r rL r r r r r7 rl r< r= r6 numdens r/
_ln_exp_boundDecimal._ln_exp_bound s ii#dii.(1, !8s3r62:'!+ + "9sBsFB;?+,q0 0
d^vvrvv1 !8aQBh-Ca&Cs8c#h&#)4 43s2r6A:''!++r1 c
Uc
[ 5 nU R US9nU( a U$ U ( d [ $ U R 5 S:X a [ $ U [
:X a [ $ U R S:X a UR [ S5 $ [ U 5 nUR UR pTUR nX`R 5 -
S- n [ XEU5 nUSS[! [# [% U5 5 5 U-
S-
- - - ( a OUS-
nME [' [ US: 5 [# [% U5 5 U* 5 nUR) 5 nUR+ [, 5 n UR/ U5 nXl U$ ) z/Returns the natural (base e) logarithm of self.r r2 zln of a negative valuer r r r r( )r r _NegativeInfinityr _Infinityr rY rK r r
r r r rv r _dlogr r r rJ r: r; r rD ru
r7 r8 rO r< r= r6 r r0 r ru s
r/ ln
Decimal.ln, sd ? lG w / J $ $ " 4<L ::?''(8(@B
B d^vvrvv1 LL ''))A-!'E"s3s5z? 3A 5a 7889 aKF s57|SU_vgF'')(( 9hhw #
r1 c U R [ U R 5 - S-
nUS: a [ [ U5 5 S-
$ US:: a [ [ SU-
5 5 S-
$ [ U 5 nUR
UR pCUS:X a? [ USU* - -
5 n[ SU- 5 n[ U5 [ U5 -
XV: -
S- $ [ SU* - U-
5 n[ U5 U- US: -
S-
$ ) 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.
r2 r r r( r r 231r r s r/ r Decimal._log10_exp_bound^ s ii#dii.(1, !8s3x=? " "9s2c6{#A% %
d^vvrvv1 !8aQBh-Cc!e*Cs8c#h&#)4q8 8"qb&(m3x!|sU{+a//r1 c
Uc
[ 5 nU R US9nU( a U$ U ( d [ $ U R 5 S:X a [ $ U R
S:X a UR
[ S5 $ U R S S:X a[ U R SS S[ U R 5 S-
- :X a/ [ U R [ U R 5 - S-
5 nO[ U 5 nUR UR pTUR nX`R! 5 -
S- n [# XEU5 nUS S
[ [% [' U5 5 5 U-
S-
- - - ( a OUS -
nME [) [ US: 5 [% [' U5 5 U* 5 nUR+ 5 nUR- [. 5 n UR1 U5 nXl U$ ) z&Returns the base 10 logarithm of self.Nr r2 zlog10 of a negative valuer( r_ r r r r r )r r r r r rK r r
rL r r r r r r rv r _dlog10r r rJ r: r; r rD ru r s
r/ log10
Decimal.log10| s ? lG w / J $ $ " ::?''(8(CE
E 99Q<3 499QR=CTYY !9K4L#L$))c$))n4q89C $ B66266q A ,,..q0F f-Ab3s3u:#7#9!#; < <=! #3uQw<SZ 6'JC'')(( 9hhw #
r1 c U R US9nU( a U$ Uc
[ 5 nU R 5 ( a [ $ U ( d UR [
SS5 $ [
U R 5 5 nUR U5 $ )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).
r zlogb(0)r2 ) r r r r r r r r rD rE s r/ logb Decimal.logb s} w / J ? lG '' 1E E
dmmo&xx r1 c | U R S:w d U R S:w a gU R H nUS; d M g g)zReturn True if self is a logical operand.
For being logical, it must be a finite number with a sign of 0,
an exponent of 0, and a coefficient whose digits must all be
either 0 or 1.
r( F01T)rK r rL )r7 digs r/
_islogicalDecimal._islogical s9 ::?dii1n99C$ r1 c UR [ U5 -
nUS: a SU- U- nOUS: a X!R * S nUR [ U5 -
nUS: a SU- U- nX#4$ US: a X1R * S nX#4$ )Nr( r )rv r )r7 r8 opaopbdifs r/
_fill_logicalDecimal._fill_logical s llSX% 7c'C-C
1W||mn%CllSX% 7c'C-C x 1W||mn%Cxr1 c Uc
[ 5 n[ USS9nU R 5 ( a UR 5 ( d UR [ 5 $ U R X R UR 5 u p4SR [ X45 VVs/ s H% u pV[ [ U5 [ U5 - 5 PM' snn5 n[ SUR S5 =( d SS5 $ s snnf )z;Applies an 'and' operation between self and other's digits.Tr r r( r
r r r r r
r rL r zipr r rJ r r7 r r8 r r r br s r/ logical_andDecimal.logical_and ? lG ud3 (8(8(:(:''(89 9 ''EJJG
C E #c!fSVm, EF 6==#5#<a@@ F ,C1
c p Uc
[ 5 nU R [ SSUR - S5 U5 $ )zInvert all its digits.r( r_ )r logical_xorrJ rv r> s r/ logical_invertDecimal.logical_invert s9 ? lG 03w||3CA F ') )r1 c Uc
[ 5 n[ USS9nU R 5 ( a UR 5 ( d UR [ 5 $ U R X R UR 5 u p4SR [ X45 VVs/ s H% u pV[ [ U5 [ U5 - 5 PM' snn5 n[ SUR S5 =( d SS5 $ s snnf )z:Applies an 'or' operation between self and other's digits.Tr r r( r r r s r/
logical_orDecimal.logical_or
r r c Uc
[ 5 n[ USS9nU R 5 ( a UR 5 ( d UR [ 5 $ U R X R UR 5 u p4SR [ X45 VVs/ s H% u pV[ [ U5 [ U5 - 5 PM' snn5 n[ SUR S5 =( d SS5 $ s snnf )z;Applies an 'xor' operation between self and other's digits.Tr r r( r r r s r/ r Decimal.logical_xor
r r c & [ USS9nUc
[ 5 nU R ( d UR ( ay U R 5 nUR 5 nU( d U( aK US:X a US:X a U R U5 $ US:X a US:X a UR U5 $ U R X5 $ U R
5 R UR
5 5 nUS:X a U R U5 nUS:X a UnOU nUR U5 $ z8Compares the values numerically with their sign ignored.Tr r2 r( r r r r r rD r rB r rC rD s r/ max_magDecimal.max_mag"
s ud3 ? lG u 0 0 B BR7rQw 99W--7rQw ::g..''77 MMO !1 2 6""5)A 7CCxx r1 c & [ USS9nUc
[ 5 nU R ( d UR ( ay U R 5 nUR 5 nU( d U( aK US:X a US:X a U R U5 $ US:X a US:X a UR U5 $ U R X5 $ U R
5 R UR
5 5 nUS:X a U R U5 nUS:X a U nOUnUR U5 $ r r rD s r/ min_magDecimal.min_mag@
s ud3 ? lG u 0 0 B BR7rQw 99W--7rQw ::g..''77 MMO !1 2 6""5)A 7CCxx r1 c Uc
[ 5 nU R US9nU( a U$ U R 5 S:X a [ $ U R 5 S:X a( [ SSUR
- UR
5 5 $ UR 5 nUR [ 5 UR 5 U R U5 nX0:w a U$ U R [ SSUR 5 S-
5 U5 $ )z=Returns the largest representable number smaller than itself.r r r2 r( rt r_ )r r r r rJ rv r r r; r _ignore_all_flagsrD rY re r7 r8 rO new_selfs r/
next_minusDecimal.next_minus^
s ? lG w / J #$ $ "#As7<<'7 H H,,. k*!!#99W% O|| ,QW]]_Q5F G #% %r1 c Uc
[ 5 nU R US9nU( a U$ U R 5 S:X a [ $ U R 5 S:X a( [ SSUR
- UR
5 5 $ UR 5 nUR [ 5 UR 5 U R U5 nX0:w a U$ U R [ SSUR 5 S-
5 U5 $ )z=Returns the smallest representable number larger than itself.r r2 r rt r( r_ )r r r r rJ rv r r r; r r rD rV re r s r/ next_plusDecimal.next_plusu
s ? lG w / J " ##As7<<'7 H H,,. m,!!#99W% O|| ,QW]]_Q5F G #% %r1 c [ USS9nUc
[ 5 nU R X5 nU( a U$ U R U5 nUS:X a U R U5 $ US:X a U R U5 nOU R
U5 nUR 5 ( aM UR [ SUR 5 UR [ 5 UR [ 5 U$ UR 5 UR : ap UR [ 5 UR [ 5 UR [ 5 UR [ 5 U( d UR [" 5 U$ )a[ Returns the number closest to self, in the direction towards other.
The result is the closest representable number to self
(excluding self) that is in the direction towards other,
unless both have the same value. If the two operands are
numerically equal, then the result is a copy of self with the
sign set to be the same as the sign of other.
Tr r( r z Infinite result from next_toward)r r r r rh r r r r r rK r r
r r} r r r )r7 r r8 rO
comparisons r/ next_towardDecimal.next_toward
s. ud3 ? lG u. JYYu%
?>>%( ( ..)C//'*C ?? !C!$
,
) )
\\^gll
* + + ) ) $$W-
r1 c t U R 5 ( a gU R 5 ( a gU R 5 nUS:X a gUS:X a gU R 5 ( a U R ( a ggUc
[ 5 nU R
US 9( a U R ( a g
g U R ( a g g
)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
r r3 r2 z +Infinityr z -Infinityz-Zeroz+Zeror z
-Subnormalz
+Subnormalz-Normalz+Normal)r r r r rK r r )r7 r8 infs r/ number_classDecimal.number_class
s <<>> <<>> !8 "9 <<>>zz ? lG W -zz## :: r1 c [ S5 $ )z'Just returns 10, as this is Decimal, :)r r r s r/ radix
Decimal.radix
s r{r1 c Uc
[ 5 n[ USS9nU R X5 nU( a U$ UR S:w a UR [
5 $ UR * [ U5 s=:: a UR :: d O UR [
5 $ U R 5 ( a [ U 5 $ [ U5 nU R nUR [ U5 -
nUS: a SU- U- nO US: a XV* S nXTS USU - n[ U R UR S5 =( d SU R 5 $ )z5Returns a rotated copy of self, value-of-other times.NTr r( r r r r r r r
rv r r r rL r rJ rK r )r7 r r8 rO torotrotdigtopadrotateds r/ rotateDecimal.rotate
s$ ? lG ud3 u. J ::?''(89 9
U;w||;''(89 9 4= E
s6{* 19Y'F
QYFG_F .6&5>1
's 3 :sDIIG Gr1 c L Uc
[ 5 n[ USS9nU R X5 nU( a U$ UR S:w a UR [
5 $ SUR UR - - nSUR UR - - nU[ U5 s=:: a U:: d O UR [
5 $ U R 5 ( a [ U 5 $ [ U R U R U R [ U5 - 5 nUR U5 nU$ )z>Returns self operand after adding the second value to its exp.Tr r( r r )r r r r r r
rw rv r r r rJ rK rL rD )r7 r r8 rO liminflimsupr s r/ scalebDecimal.scaleb s ? lG ud3 u. J ::?''(89 9w||gll23w||gll23#e*..''(89 9 4= TZZDIIE
4J K
FF7Or1 c Uc
[ 5 n[ USS9nU R X5 nU( a U$ UR S:w a UR [
5 $ UR * [ U5 s=:: a UR :: d O UR [
5 $ U R 5 ( a [ U 5 $ [ U5 nU R nUR [ U5 -
nUS: a SU- U- nO US: a XV* S nUS: a USU nOUSU- - nXrR * S n[ U R UR S5 =( d SU R 5 $ )z5Returns a shifted copy of self, value-of-other times.NTr r( r r )r7 r r8 rO r r r shifteds r/ rg
Decimal.shift" s@ ? lG ud3 u. J ::?''(89 9
U;w||;''(89 9 4= E
s6{* 19Y'F
QYFG_F 19 VenG s5y(G ||mn-G
$+NN3$7$>3 K Kr1 c 2 U R [ U 5 44$ r, ) __class__r r s r/
__reduce__Decimal.__reduce__I s T --r1 c ^ [ U 5 [ L a U $ U R [ U 5 5 $ r, typer r r r s r/ __copy__Decimal.__copy__L & : K~~c$i((r1 c ^ [ U 5 [ L a U $ U R [ U 5 5 $ r, r )r7 memos r/ __deepcopy__Decimal.__deepcopy__Q r r1 c \ Uc
[ 5 n[ XS9nU R ( aI [ U R U5 n[ U R
5 5 nUS S:X a US-
n[ XVU5 $ US c SS/UR US' US S:X a. [ U R U R U R S- 5 n UR nUS nUbo US S ; a U R US
- U5 n OPUS S ; a U R U* U5 n O3US S ; a* [ U R 5 U: a U R X5 n U ( d+ U R S
: a US S ; a U R S
U5 n U ( d US ( a U R ( a S
n O U R n U R [ U R 5 - n
US S ; a U ( d Ub S
U-
n O3S
n O0US S ; a U
n O$US S ; a U R S
:: a U
S: a U
n OS
n W S
: a Sn SU * - U R - n
OkU [ U R 5 : a+ U R SU [ U R 5 -
- - n Sn
O'U R SU =( d Sn U R U S n
X-
n[! XXU5 $ )aL Format a Decimal instance according to the given specifier.
The specifier should be a standard format specifier, with the
form described in PEP 3101. Formatting types 'e', 'E', 'f',
'F', 'g', 'G', 'n' and '%' are supported. If the formatting
type is omitted it defaults to 'g' or 'G', depending on the
value of context.capitals.
N) _localeconvr %gGr precisioneEr2 zfF%gGr( no_neg_0r4 r r )r _parse_format_specifierr _format_signrK r rB
_format_alignr~ rJ rL r ru r1 rQ r _format_number)r7 specifierr8 r specr\ bodyru r
adjusted_signr9 r: r r r s r/
__format__Decimal.__format__X s ? lG&yJ
D1Dt}}'DF|s" T2 2 < :g&6&67DL <3 #DJJ 499Q;GD ##% F|t#{{9Q;9f &}}iZ:f %#dii.9*D{{97 A
$v,%*?==H-DZ(TZZ M JJM YYTYY /
<4 I 1 y=
&\U
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)TKr1 r c h [ R [ 5 nXl Xl X$l X4l U$ )zCreate a decimal instance directly, without any validation,
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conversion.
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)r r r rK rL r r )r\ coefficientr specialr7 s r/ rJ rJ s, >>' "DJII Kr1 c * \ rS rSrSrS rS rS rSrg)r i zContext manager class to support localcontext().
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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)
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r r r r rv ru r} rw r~ r )r7 sigr# r r s r/ r Context.__reduce__B s #'::#3#3#5;#5#5;#'::#3#3#5;#5#5;DMM499dii
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U R U R U R U R 5 nU$ )z!Returns a shallow copy from self.)
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U R U R R 5 U R R 5 U R 5 nU$ )z Returns a deep copy from self.) r rv ru r} rw r~ r r r r r2 r\ s r/ r Context.copyg s\
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(9((* r1 c [ R X5 nX@R ; a U" 5 R " U /UQ76 $ SU R U' U R
U ( d U" 5 R " U /UQ76 $ U" U5 e)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.
r2 )_condition_mapr r2 r9 r r )r7 condition explanationr. errors r/ r Context._raise_errorp su ""98 '' '7>>$.. .
5zz% ;%%d2T2 2 K r1 c ( U R " [ 6 $ )z$Ignore all flags, if they are raised)
_ignore_flagsr r s r/ r Context._ignore_all_flags s !!8,,r1 c R U R [ U5 - U l [ U5 $ )z$Ignore the flags, if they are raised)r2 r )r7 r s r/ rh Context._ignore_flags s% $ 2 2T%[ @E{r1 c U( a# [ US [ [ 45 ( a US nU H nU R R U5 M g)z+Stop ignoring the flags, if they are raisedr( N)r r r r2 remove)r7 r rU s r/
_regard_flagsContext._regard_flags s@ Za5,77!HED & &t , r1 c L [ U R U R -
S- 5 $ )z!Returns Etiny (= Emin - prec + 1)r2 )r r} rv r s r/ re
Context.Etiny 499tyy(1,--r1 c L [ U R U R -
S- 5 $ )z,Returns maximum exponent (= Emax - prec + 1)r2 )r rw rv r s r/ r Context.Etop rr r1 c * U R nXl U$ )a Sets 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.
)ru )r7 r ru s r/ r; Context._set_rounding s ==
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: a U R [ S5 $ UR U 5 $ )zCreates a new Decimal instance but using self as context.
This method implements the to-number operation of the
IBM Decimal specification.r zAtrailing or leading whitespace and underscores are not permitted.r z diagnostic info too long in NaN) r r r r r r r r rL rv r rD )r7 r r s r/ create_decimalContext.create_decimal s c3 SIIK%73#:$$%5&FG
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Hvvd|r1 c N [ R U5 nUR U 5 $ )a Creates 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
)r r rD )r7 r r s r/ create_decimal_from_float!Context.create_decimal_from_float s"
q !vvd|r1 c 4 [ USS9nUR U S9$ )a Returns the absolute value of the operand.
If the operand is negative, the result is the same as using the minus
operation on the operand. Otherwise, the result is the same as using
the plus operation on the operand.
>>> ExtendedContext.abs(Decimal('2.1'))
Decimal('2.1')
>>> ExtendedContext.abs(Decimal('-100'))
Decimal('100')
>>> ExtendedContext.abs(Decimal('101.5'))
Decimal('101.5')
>>> ExtendedContext.abs(Decimal('-101.5'))
Decimal('101.5')
>>> ExtendedContext.abs(-1)
Decimal('1')
Tr r )r rM r7 r s r/ r Context.abs s! $
1d +yyy&&r1 c f [ USS9nUR X S9nU[ L a [ SU- 5 eU$ )aS Return the sum of the two operands.
>>> ExtendedContext.add(Decimal('12'), Decimal('7.00'))
Decimal('19.00')
>>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4'))
Decimal('1.02E+4')
>>> ExtendedContext.add(1, Decimal(2))
Decimal('3')
>>> ExtendedContext.add(Decimal(8), 5)
Decimal('13')
>>> ExtendedContext.add(5, 5)
Decimal('10')
Tr r Unable to convert %s to Decimal)r rV r r r7 r r ro s r/ add Context.add s>
1d +
IIaI & = AB BHr1 c 6 [ UR U 5 5 $ r, )r rD r~ s r/ _applyContext._apply s 166$< r1 c b [ U[ 5 ( d [ S5 eUR 5 $ )zReturns the same Decimal object.
As we do not have different encodings for the same number, the
received object already is in its canonical form.
>>> ExtendedContext.canonical(Decimal('2.50'))
Decimal('2.50')
z,canonical requires a Decimal as an argument.)r r r rR r~ s r/ rR Context.canonical s) !W%% JK K{{} r1 c 4 [ USS9nUR X S9$ )a Compares values numerically.
If the signs of the operands differ, a value representing each operand
('-1' if the operand is less than zero, '0' if the operand is zero or
negative zero, or '1' if the operand is greater than zero) is used in
place of that operand for the comparison instead of the actual
operand.
The comparison is then effected by subtracting the second operand from
the first and then returning a value according to the result of the
subtraction: '-1' if the result is less than zero, '0' if the result is
zero or negative zero, or '1' if the result is greater than zero.
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('3'))
Decimal('-1')
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1'))
Decimal('0')
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10'))
Decimal('0')
>>> ExtendedContext.compare(Decimal('3'), Decimal('2.1'))
Decimal('1')
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3'))
Decimal('1')
>>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1'))
Decimal('-1')
>>> ExtendedContext.compare(1, 2)
Decimal('-1')
>>> ExtendedContext.compare(Decimal(1), 2)
Decimal('-1')
>>> ExtendedContext.compare(1, Decimal(2))
Decimal('-1')
Tr r )r r r7 r r s r/ r Context.compare s" B
1d +yyy))r1 c 4 [ USS9nUR X S9$ )a8 Compares the values of the two operands numerically.
It's pretty much like compare(), but all NaNs signal, with signaling
NaNs taking precedence over quiet NaNs.
>>> c = ExtendedContext
>>> c.compare_signal(Decimal('2.1'), Decimal('3'))
Decimal('-1')
>>> c.compare_signal(Decimal('2.1'), Decimal('2.1'))
Decimal('0')
>>> c.flags[InvalidOperation] = 0
>>> print(c.flags[InvalidOperation])
0
>>> c.compare_signal(Decimal('NaN'), Decimal('2.1'))
Decimal('NaN')
>>> print(c.flags[InvalidOperation])
1
>>> c.flags[InvalidOperation] = 0
>>> print(c.flags[InvalidOperation])
0
>>> c.compare_signal(Decimal('sNaN'), Decimal('2.1'))
Decimal('NaN')
>>> print(c.flags[InvalidOperation])
1
>>> c.compare_signal(-1, 2)
Decimal('-1')
>>> c.compare_signal(Decimal(-1), 2)
Decimal('-1')
>>> c.compare_signal(-1, Decimal(2))
Decimal('-1')
Tr r )r rU r s r/ rU Context.compare_signal7 s% @
1d + 00r1 c 8 [ USS9nUR U5 $ )a{ Compares two operands using their abstract representation.
This is not like the standard compare, which use their numerical
value. Note that a total ordering is defined for all possible abstract
representations.
>>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9'))
Decimal('-1')
>>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12'))
Decimal('-1')
>>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3'))
Decimal('-1')
>>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30'))
Decimal('0')
>>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300'))
Decimal('1')
>>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN'))
Decimal('-1')
>>> ExtendedContext.compare_total(1, 2)
Decimal('-1')
>>> ExtendedContext.compare_total(Decimal(1), 2)
Decimal('-1')
>>> ExtendedContext.compare_total(1, Decimal(2))
Decimal('-1')
Tr )r rC r s r/ rC Context.compare_totalZ s 4
1d +q!!r1 c 8 [ USS9nUR U5 $ )zCompares two operands using their abstract representation ignoring sign.
Like compare_total, but with operand's sign ignored and assumed to be 0.
Tr )r ra r s r/ ra Context.compare_total_magw s!
1d +""1%%r1 c 6 [ USS9nUR 5 $ )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 )r rB r~ s r/ rB Context.copy_abs s
1d +zz|r1 c , [ USS9n[ U5 $ )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 )r r r~ s r/ copy_decimalContext.copy_decimal s
1d +qzr1 c 6 [ USS9nUR 5 $ )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 )r rC r~ s r/ rC Context.copy_negate s
1d +}} r1 c 8 [ USS9nUR U5 $ )a Copies the second operand's sign to the first one.
In detail, it returns a copy of the first operand with the sign
equal to the sign of the second operand.
>>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33'))
Decimal('1.50')
>>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33'))
Decimal('1.50')
>>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33'))
Decimal('-1.50')
>>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33'))
Decimal('-1.50')
>>> ExtendedContext.copy_sign(1, -2)
Decimal('-1')
>>> ExtendedContext.copy_sign(Decimal(1), -2)
Decimal('-1')
>>> ExtendedContext.copy_sign(1, Decimal(-2))
Decimal('-1')
Tr )r rh r s r/ rh Context.copy_sign s *
1d +{{1~ r1 c f [ USS9nUR X S9nU[ L a [ SU- 5 eU$ )a Decimal division in a specified context.
>>> ExtendedContext.divide(Decimal('1'), Decimal('3'))
Decimal('0.333333333')
>>> ExtendedContext.divide(Decimal('2'), Decimal('3'))
Decimal('0.666666667')
>>> ExtendedContext.divide(Decimal('5'), Decimal('2'))
Decimal('2.5')
>>> ExtendedContext.divide(Decimal('1'), Decimal('10'))
Decimal('0.1')
>>> ExtendedContext.divide(Decimal('12'), Decimal('12'))
Decimal('1')
>>> ExtendedContext.divide(Decimal('8.00'), Decimal('2'))
Decimal('4.00')
>>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0'))
Decimal('1.20')
>>> ExtendedContext.divide(Decimal('1000'), Decimal('100'))
Decimal('10')
>>> ExtendedContext.divide(Decimal('1000'), Decimal('1'))
Decimal('1000')
>>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2'))
Decimal('1.20E+6')
>>> ExtendedContext.divide(5, 5)
Decimal('1')
>>> ExtendedContext.divide(Decimal(5), 5)
Decimal('1')
>>> ExtendedContext.divide(5, Decimal(5))
Decimal('1')
Tr r r )r rj r r r s r/ divideContext.divide s> <
1d +
MM!M * = AB BHr1 c f [ USS9nUR X S9nU[ L a [ SU- 5 eU$ )a Divides two numbers and returns the integer part of the result.
>>> ExtendedContext.divide_int(Decimal('2'), Decimal('3'))
Decimal('0')
>>> ExtendedContext.divide_int(Decimal('10'), Decimal('3'))
Decimal('3')
>>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3'))
Decimal('3')
>>> ExtendedContext.divide_int(10, 3)
Decimal('3')
>>> ExtendedContext.divide_int(Decimal(10), 3)
Decimal('3')
>>> ExtendedContext.divide_int(10, Decimal(3))
Decimal('3')
Tr r r )r r r r r s r/
divide_intContext.divide_int s>
1d +
NN1N + = AB BHr1 c f [ USS9nUR X S9nU[ L a [ SU- 5 eU$ )a Return (a // b, a % b).
>>> ExtendedContext.divmod(Decimal(8), Decimal(3))
(Decimal('2'), Decimal('2'))
>>> ExtendedContext.divmod(Decimal(8), Decimal(4))
(Decimal('2'), Decimal('0'))
>>> ExtendedContext.divmod(8, 4)
(Decimal('2'), Decimal('0'))
>>> ExtendedContext.divmod(Decimal(8), 4)
(Decimal('2'), Decimal('0'))
>>> ExtendedContext.divmod(8, Decimal(4))
(Decimal('2'), Decimal('0'))
Tr r r )r rz r r r s r/ rf Context.divmod s>
1d +
LLL ) = AB BHr1 c 4 [ USS9nUR U S9$ )a Returns e ** a.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.exp(Decimal('-Infinity'))
Decimal('0')
>>> c.exp(Decimal('-1'))
Decimal('0.367879441')
>>> c.exp(Decimal('0'))
Decimal('1')
>>> c.exp(Decimal('1'))
Decimal('2.71828183')
>>> c.exp(Decimal('0.693147181'))
Decimal('2.00000000')
>>> c.exp(Decimal('+Infinity'))
Decimal('Infinity')
>>> c.exp(10)
Decimal('22026.4658')
Tr r )r r r~ s r/ r Context.exp s! * !T *uuTu""r1 c 6 [ USS9nUR X#U S9$ )a Returns a multiplied by b, plus c.
The first two operands are multiplied together, using multiply,
the third operand is then added to the result of that
multiplication, using add, all with only one final rounding.
>>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7'))
Decimal('22')
>>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7'))
Decimal('-8')
>>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578'))
Decimal('1.38435736E+12')
>>> ExtendedContext.fma(1, 3, 4)
Decimal('7')
>>> ExtendedContext.fma(1, Decimal(3), 4)
Decimal('7')
>>> ExtendedContext.fma(1, 3, Decimal(4))
Decimal('7')
Tr r )r r )r7 r r r= s r/ r Context.fma' s# (
1d +uuQ4u((r1 c b [ U[ 5 ( d [ S5 eUR 5 $ )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.)r r r ro r~ s r/ ro Context.is_canonical> s* !W%% MN N~~ r1 c 6 [ USS9nUR 5 $ )a Return True if the operand is finite; otherwise return False.
A Decimal instance is considered finite if it is neither
infinite nor a NaN.
>>> ExtendedContext.is_finite(Decimal('2.50'))
True
>>> ExtendedContext.is_finite(Decimal('-0.3'))
True
>>> ExtendedContext.is_finite(Decimal('0'))
True
>>> ExtendedContext.is_finite(Decimal('Inf'))
False
>>> ExtendedContext.is_finite(Decimal('NaN'))
False
>>> ExtendedContext.is_finite(1)
True
Tr )r rr r~ s r/ rr Context.is_finiteK s &
1d +{{} r1 c 6 [ USS9nUR 5 $ )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 )r r) r~ s r/ r) Context.is_infinitea s
1d +}} r1 c 6 [ USS9nUR 5 $ )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 )r r r~ s r/ r Context.is_nanp s
1d +xxzr1 c 4 [ USS9nUR U S9$ )ag Return True if the operand is a normal number;
otherwise return False.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.is_normal(Decimal('2.50'))
True
>>> c.is_normal(Decimal('0.1E-999'))
False
>>> c.is_normal(Decimal('0.00'))
False
>>> c.is_normal(Decimal('-Inf'))
False
>>> c.is_normal(Decimal('NaN'))
False
>>> c.is_normal(1)
True
Tr r )r r{ r~ s r/ r{ Context.is_normal s! (
1d +{{4{((r1 c 6 [ USS9nUR 5 $ )a Return True if the operand is a quiet NaN; otherwise return False.
>>> ExtendedContext.is_qnan(Decimal('2.50'))
False
>>> ExtendedContext.is_qnan(Decimal('NaN'))
True
>>> ExtendedContext.is_qnan(Decimal('sNaN'))
False
>>> ExtendedContext.is_qnan(1)
False
Tr )r r r~ s r/ r Context.is_qnan s
1d +yy{r1 c 6 [ USS9nUR 5 $ )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 )r r r~ s r/ r Context.is_signed s
1d +{{} r1 c 6 [ USS9nUR 5 $ )a Return True if the operand is a signaling NaN;
otherwise return False.
>>> ExtendedContext.is_snan(Decimal('2.50'))
False
>>> ExtendedContext.is_snan(Decimal('NaN'))
False
>>> ExtendedContext.is_snan(Decimal('sNaN'))
True
>>> ExtendedContext.is_snan(1)
False
Tr )r r r~ s r/ r Context.is_snan s
1d +yy{r1 c 4 [ USS9nUR U S9$ )at Return True if the operand is subnormal; otherwise return False.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.is_subnormal(Decimal('2.50'))
False
>>> c.is_subnormal(Decimal('0.1E-999'))
True
>>> c.is_subnormal(Decimal('0.00'))
False
>>> c.is_subnormal(Decimal('-Inf'))
False
>>> c.is_subnormal(Decimal('NaN'))
False
>>> c.is_subnormal(1)
False
Tr r )r r r~ s r/ r Context.is_subnormal s! &
1d +~~d~++r1 c 6 [ USS9nUR 5 $ )a Return True if the operand is a zero; otherwise return False.
>>> ExtendedContext.is_zero(Decimal('0'))
True
>>> ExtendedContext.is_zero(Decimal('2.50'))
False
>>> ExtendedContext.is_zero(Decimal('-0E+2'))
True
>>> ExtendedContext.is_zero(1)
False
>>> ExtendedContext.is_zero(0)
True
Tr )r r r~ s r/ r Context.is_zero s
1d +yy{r1 c 4 [ USS9nUR U S9$ )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')
Tr r )r r r~ s r/ r
Context.ln s! &
1d +ttDt!!r1 c 4 [ USS9nUR U S9$ )a Returns the base 10 logarithm of the operand.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.log10(Decimal('0'))
Decimal('-Infinity')
>>> c.log10(Decimal('0.001'))
Decimal('-3')
>>> c.log10(Decimal('1.000'))
Decimal('0')
>>> c.log10(Decimal('2'))
Decimal('0.301029996')
>>> c.log10(Decimal('10'))
Decimal('1')
>>> c.log10(Decimal('70'))
Decimal('1.84509804')
>>> c.log10(Decimal('+Infinity'))
Decimal('Infinity')
>>> c.log10(0)
Decimal('-Infinity')
>>> c.log10(1)
Decimal('0')
Tr r )r r r~ s r/ r
Context.log10 s! 2
1d +wwtw$$r1 c 4 [ USS9nUR U S9$ )a Returns the exponent of the magnitude of the operand's MSD.
The result is the integer which is the exponent of the magnitude
of the most significant digit of the operand (as though the
operand were truncated to a single digit while maintaining the
value of that digit and without limiting the resulting exponent).
>>> ExtendedContext.logb(Decimal('250'))
Decimal('2')
>>> ExtendedContext.logb(Decimal('2.50'))
Decimal('0')
>>> ExtendedContext.logb(Decimal('0.03'))
Decimal('-2')
>>> ExtendedContext.logb(Decimal('0'))
Decimal('-Infinity')
>>> ExtendedContext.logb(1)
Decimal('0')
>>> ExtendedContext.logb(10)
Decimal('1')
>>> ExtendedContext.logb(100)
Decimal('2')
Tr r )r r r~ s r/ r Context.logb s! .
1d +vvdv##r1 c 4 [ USS9nUR X S9$ )a Applies the logical operation 'and' between each operand's digits.
The operands must be both logical numbers.
>>> ExtendedContext.logical_and(Decimal('0'), Decimal('0'))
Decimal('0')
>>> ExtendedContext.logical_and(Decimal('0'), Decimal('1'))
Decimal('0')
>>> ExtendedContext.logical_and(Decimal('1'), Decimal('0'))
Decimal('0')
>>> ExtendedContext.logical_and(Decimal('1'), Decimal('1'))
Decimal('1')
>>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010'))
Decimal('1000')
>>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10'))
Decimal('10')
>>> ExtendedContext.logical_and(110, 1101)
Decimal('100')
>>> ExtendedContext.logical_and(Decimal(110), 1101)
Decimal('100')
>>> ExtendedContext.logical_and(110, Decimal(1101))
Decimal('100')
Tr r )r r r s r/ r Context.logical_and: ! 0
1d +}}Q}--r1 c 4 [ USS9nUR U S9$ )a Invert all the digits in the operand.
The operand must be a logical number.
>>> ExtendedContext.logical_invert(Decimal('0'))
Decimal('111111111')
>>> ExtendedContext.logical_invert(Decimal('1'))
Decimal('111111110')
>>> ExtendedContext.logical_invert(Decimal('111111111'))
Decimal('0')
>>> ExtendedContext.logical_invert(Decimal('101010101'))
Decimal('10101010')
>>> ExtendedContext.logical_invert(1101)
Decimal('111110010')
Tr r )r r r~ s r/ r Context.logical_invertU s$
1d + --r1 c 4 [ USS9nUR X S9$ )a Applies the logical operation 'or' between each operand's digits.
The operands must be both logical numbers.
>>> ExtendedContext.logical_or(Decimal('0'), Decimal('0'))
Decimal('0')
>>> ExtendedContext.logical_or(Decimal('0'), Decimal('1'))
Decimal('1')
>>> ExtendedContext.logical_or(Decimal('1'), Decimal('0'))
Decimal('1')
>>> ExtendedContext.logical_or(Decimal('1'), Decimal('1'))
Decimal('1')
>>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010'))
Decimal('1110')
>>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10'))
Decimal('1110')
>>> ExtendedContext.logical_or(110, 1101)
Decimal('1111')
>>> ExtendedContext.logical_or(Decimal(110), 1101)
Decimal('1111')
>>> ExtendedContext.logical_or(110, Decimal(1101))
Decimal('1111')
Tr r )r r r s r/ r Context.logical_orh s! 0
1d +||A|,,r1 c 4 [ USS9nUR X S9$ )a Applies the logical operation 'xor' between each operand's digits.
The operands must be both logical numbers.
>>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0'))
Decimal('0')
>>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1'))
Decimal('1')
>>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0'))
Decimal('1')
>>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1'))
Decimal('0')
>>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010'))
Decimal('110')
>>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10'))
Decimal('1101')
>>> ExtendedContext.logical_xor(110, 1101)
Decimal('1011')
>>> ExtendedContext.logical_xor(Decimal(110), 1101)
Decimal('1011')
>>> ExtendedContext.logical_xor(110, Decimal(1101))
Decimal('1011')
Tr r )r r r s r/ r Context.logical_xor r r1 c 4 [ USS9nUR X S9$ )a max compares two values numerically and returns the maximum.
If either operand is a NaN then the general rules apply.
Otherwise, the operands are compared as though by the compare
operation. If they are numerically equal then the left-hand operand
is chosen as the result. Otherwise the maximum (closer to positive
infinity) of the two operands is chosen as the result.
>>> ExtendedContext.max(Decimal('3'), Decimal('2'))
Decimal('3')
>>> ExtendedContext.max(Decimal('-10'), Decimal('3'))
Decimal('3')
>>> ExtendedContext.max(Decimal('1.0'), Decimal('1'))
Decimal('1')
>>> ExtendedContext.max(Decimal('7'), Decimal('NaN'))
Decimal('7')
>>> ExtendedContext.max(1, 2)
Decimal('2')
>>> ExtendedContext.max(Decimal(1), 2)
Decimal('2')
>>> ExtendedContext.max(1, Decimal(2))
Decimal('2')
Tr r )r rP r s r/ rP Context.max ! 0
1d +uuQu%%r1 c 4 [ USS9nUR X S9$ )ao Compares the values numerically with their sign ignored.
>>> ExtendedContext.max_mag(Decimal('7'), Decimal('NaN'))
Decimal('7')
>>> ExtendedContext.max_mag(Decimal('7'), Decimal('-10'))
Decimal('-10')
>>> ExtendedContext.max_mag(1, -2)
Decimal('-2')
>>> ExtendedContext.max_mag(Decimal(1), -2)
Decimal('-2')
>>> ExtendedContext.max_mag(1, Decimal(-2))
Decimal('-2')
Tr r )r r r s r/ r Context.max_mag !
1d +yyy))r1 c 4 [ USS9nUR X S9$ )a min compares two values numerically and returns the minimum.
If either operand is a NaN then the general rules apply.
Otherwise, the operands are compared as though by the compare
operation. If they are numerically equal then the left-hand operand
is chosen as the result. Otherwise the minimum (closer to negative
infinity) of the two operands is chosen as the result.
>>> ExtendedContext.min(Decimal('3'), Decimal('2'))
Decimal('2')
>>> ExtendedContext.min(Decimal('-10'), Decimal('3'))
Decimal('-10')
>>> ExtendedContext.min(Decimal('1.0'), Decimal('1'))
Decimal('1.0')
>>> ExtendedContext.min(Decimal('7'), Decimal('NaN'))
Decimal('7')
>>> ExtendedContext.min(1, 2)
Decimal('1')
>>> ExtendedContext.min(Decimal(1), 2)
Decimal('1')
>>> ExtendedContext.min(1, Decimal(29))
Decimal('1')
Tr r )r r) r s r/ r) Context.min r r1 c 4 [ USS9nUR X S9$ )al Compares the values numerically with their sign ignored.
>>> ExtendedContext.min_mag(Decimal('3'), Decimal('-2'))
Decimal('-2')
>>> ExtendedContext.min_mag(Decimal('-3'), Decimal('NaN'))
Decimal('-3')
>>> ExtendedContext.min_mag(1, -2)
Decimal('1')
>>> ExtendedContext.min_mag(Decimal(1), -2)
Decimal('1')
>>> ExtendedContext.min_mag(1, Decimal(-2))
Decimal('1')
Tr r )r r r s r/ r Context.min_mag r r1 c 4 [ USS9nUR U S9$ )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')
Tr r )r rF r~ s r/ minus
Context.minus !
1d +yyy&&r1 c f [ USS9nUR X S9nU[ L a [ SU- 5 eU$ )a8 multiply multiplies two operands.
If either operand is a special value then the general rules apply.
Otherwise, the operands are multiplied together
('long multiplication'), resulting in a number which may be as long as
the sum of the lengths of the two operands.
>>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3'))
Decimal('3.60')
>>> ExtendedContext.multiply(Decimal('7'), Decimal('3'))
Decimal('21')
>>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8'))
Decimal('0.72')
>>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0'))
Decimal('-0.0')
>>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321'))
Decimal('4.28135971E+11')
>>> ExtendedContext.multiply(7, 7)
Decimal('49')
>>> ExtendedContext.multiply(Decimal(7), 7)
Decimal('49')
>>> ExtendedContext.multiply(7, Decimal(7))
Decimal('49')
Tr r r )r rb r r r s r/ multiplyContext.multiply s> 2
1d +
IIaI & = AB BHr1 c 4 [ USS9nUR U S9$ )a Returns the largest representable number smaller than a.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> ExtendedContext.next_minus(Decimal('1'))
Decimal('0.999999999')
>>> c.next_minus(Decimal('1E-1007'))
Decimal('0E-1007')
>>> ExtendedContext.next_minus(Decimal('-1.00000003'))
Decimal('-1.00000004')
>>> c.next_minus(Decimal('Infinity'))
Decimal('9.99999999E+999')
>>> c.next_minus(1)
Decimal('0.999999999')
Tr r )r r r~ s r/ r Context.next_minus' s! "
1d +||D|))r1 c 4 [ USS9nUR U S9$ )a Returns the smallest representable number larger than a.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> ExtendedContext.next_plus(Decimal('1'))
Decimal('1.00000001')
>>> c.next_plus(Decimal('-1E-1007'))
Decimal('-0E-1007')
>>> ExtendedContext.next_plus(Decimal('-1.00000003'))
Decimal('-1.00000002')
>>> c.next_plus(Decimal('-Infinity'))
Decimal('-9.99999999E+999')
>>> c.next_plus(1)
Decimal('1.00000001')
Tr r )r r r~ s r/ r Context.next_plus; s! "
1d +{{4{((r1 c 4 [ USS9nUR X S9$ )a Returns the number closest to a, in direction towards b.
The result is the closest representable number from the first
operand (but not the first operand) that is in the direction
towards the second operand, unless the operands have the same
value.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.next_toward(Decimal('1'), Decimal('2'))
Decimal('1.00000001')
>>> c.next_toward(Decimal('-1E-1007'), Decimal('1'))
Decimal('-0E-1007')
>>> c.next_toward(Decimal('-1.00000003'), Decimal('0'))
Decimal('-1.00000002')
>>> c.next_toward(Decimal('1'), Decimal('0'))
Decimal('0.999999999')
>>> c.next_toward(Decimal('1E-1007'), Decimal('-100'))
Decimal('0E-1007')
>>> c.next_toward(Decimal('-1.00000003'), Decimal('-10'))
Decimal('-1.00000004')
>>> c.next_toward(Decimal('0.00'), Decimal('-0.0000'))
Decimal('-0.00')
>>> c.next_toward(0, 1)
Decimal('1E-1007')
>>> c.next_toward(Decimal(0), 1)
Decimal('1E-1007')
>>> c.next_toward(0, Decimal(1))
Decimal('1E-1007')
Tr r )r r r s r/ r Context.next_towardO s" @
1d +}}Q}--r1 c 4 [ USS9nUR U S9$ )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')
Tr r )r r$ r~ s r/ r$ Context.normalizer s! *
1d +{{4{((r1 c 4 [ USS9nUR U S9$ )a Returns an indication of the class of the operand.
The class is one of the following strings:
-sNaN
-NaN
-Infinity
-Normal
-Subnormal
-Zero
+Zero
+Subnormal
+Normal
+Infinity
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.number_class(Decimal('Infinity'))
'+Infinity'
>>> c.number_class(Decimal('1E-10'))
'+Normal'
>>> c.number_class(Decimal('2.50'))
'+Normal'
>>> c.number_class(Decimal('0.1E-999'))
'+Subnormal'
>>> c.number_class(Decimal('0'))
'+Zero'
>>> c.number_class(Decimal('-0'))
'-Zero'
>>> c.number_class(Decimal('-0.1E-999'))
'-Subnormal'
>>> c.number_class(Decimal('-1E-10'))
'-Normal'
>>> c.number_class(Decimal('-2.50'))
'-Normal'
>>> c.number_class(Decimal('-Infinity'))
'-Infinity'
>>> c.number_class(Decimal('NaN'))
'NaN'
>>> c.number_class(Decimal('-NaN'))
'NaN'
>>> c.number_class(Decimal('sNaN'))
'sNaN'
>>> c.number_class(123)
'+Normal'
Tr r )r r r~ s r/ r Context.number_class s" ^
1d +~~d~++r1 c 4 [ USS9nUR U S9$ )ao Plus corresponds to unary prefix plus in Python.
The operation is evaluated using the same rules as add; the
operation plus(a) is calculated as add('0', a) where the '0'
has the same exponent as the operand.
>>> ExtendedContext.plus(Decimal('1.3'))
Decimal('1.3')
>>> ExtendedContext.plus(Decimal('-1.3'))
Decimal('-1.3')
>>> ExtendedContext.plus(-1)
Decimal('-1')
Tr r )r rI r~ s r/ plus Context.plus r r1 c h [ USS9nUR X#U S9nU[ L a [ SU- 5 eU$ )a Raises a to the power of b, to modulo if given.
With two arguments, compute a**b. If a is negative then b
must be integral. The result will be inexact unless b is
integral and the result is finite and can be expressed exactly
in 'precision' digits.
With three arguments, compute (a**b) % modulo. For the
three argument form, the following restrictions on the
arguments hold:
- all three arguments must be integral
- b must be nonnegative
- at least one of a or b must be nonzero
- modulo must be nonzero and have at most 'precision' digits
The result of pow(a, b, modulo) is identical to the result
that would be obtained by computing (a**b) % modulo with
unbounded precision, but is computed more efficiently. It is
always exact.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.power(Decimal('2'), Decimal('3'))
Decimal('8')
>>> c.power(Decimal('-2'), Decimal('3'))
Decimal('-8')
>>> c.power(Decimal('2'), Decimal('-3'))
Decimal('0.125')
>>> c.power(Decimal('1.7'), Decimal('8'))
Decimal('69.7575744')
>>> c.power(Decimal('10'), Decimal('0.301029996'))
Decimal('2.00000000')
>>> c.power(Decimal('Infinity'), Decimal('-1'))
Decimal('0')
>>> c.power(Decimal('Infinity'), Decimal('0'))
Decimal('1')
>>> c.power(Decimal('Infinity'), Decimal('1'))
Decimal('Infinity')
>>> c.power(Decimal('-Infinity'), Decimal('-1'))
Decimal('-0')
>>> c.power(Decimal('-Infinity'), Decimal('0'))
Decimal('1')
>>> c.power(Decimal('-Infinity'), Decimal('1'))
Decimal('-Infinity')
>>> c.power(Decimal('-Infinity'), Decimal('2'))
Decimal('Infinity')
>>> c.power(Decimal('0'), Decimal('0'))
Decimal('NaN')
>>> c.power(Decimal('3'), Decimal('7'), Decimal('16'))
Decimal('11')
>>> c.power(Decimal('-3'), Decimal('7'), Decimal('16'))
Decimal('-11')
>>> c.power(Decimal('-3'), Decimal('8'), Decimal('16'))
Decimal('1')
>>> c.power(Decimal('3'), Decimal('7'), Decimal('-16'))
Decimal('11')
>>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789'))
Decimal('11729830')
>>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729'))
Decimal('-0')
>>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537'))
Decimal('1')
>>> ExtendedContext.power(7, 7)
Decimal('823543')
>>> ExtendedContext.power(Decimal(7), 7)
Decimal('823543')
>>> ExtendedContext.power(7, Decimal(7), 2)
Decimal('1')
Tr r r )r r r r )r7 r r r ro s r/ power
Context.power sA R
1d +
IIaI . = AB BHr1 c 4 [ USS9nUR X S9$ )a Returns a value equal to 'a' (rounded), having the exponent of 'b'.
The coefficient of the result is derived from that of the left-hand
operand. It may be rounded using the current rounding setting (if the
exponent is being increased), multiplied by a positive power of ten (if
the exponent is being decreased), or is unchanged (if the exponent is
already equal to that of the right-hand operand).
Unlike other operations, if the length of the coefficient after the
quantize operation would be greater than precision then an Invalid
operation condition is raised. This guarantees that, unless there is
an error condition, the exponent of the result of a quantize is always
equal to that of the right-hand operand.
Also unlike other operations, quantize will never raise Underflow, even
if the result is subnormal and inexact.
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001'))
Decimal('2.170')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01'))
Decimal('2.17')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1'))
Decimal('2.2')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0'))
Decimal('2')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1'))
Decimal('0E+1')
>>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity'))
Decimal('-Infinity')
>>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity'))
Decimal('NaN')
>>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1'))
Decimal('-0')
>>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5'))
Decimal('-0E+5')
>>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2'))
Decimal('NaN')
>>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2'))
Decimal('NaN')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1'))
Decimal('217.0')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0'))
Decimal('217')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1'))
Decimal('2.2E+2')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2'))
Decimal('2E+2')
>>> ExtendedContext.quantize(1, 2)
Decimal('1')
>>> ExtendedContext.quantize(Decimal(1), 2)
Decimal('1')
>>> ExtendedContext.quantize(1, Decimal(2))
Decimal('1')
Tr r )r r r s r/ r Context.quantize s" n
1d +zz!z**r1 c [ S5 $ )zSJust returns 10, as this is Decimal, :)
>>> ExtendedContext.radix()
Decimal('10')
r r r s r/ r
Context.radixW s r{r1 c f [ USS9nUR X S9nU[ L a [ SU- 5 eU$ )aF Returns the remainder from integer division.
The result is the residue of the dividend after the operation of
calculating integer division as described for divide-integer, rounded
to precision digits if necessary. The sign of the result, if
non-zero, is the same as that of the original dividend.
This operation will fail under the same conditions as integer division
(that is, if integer division on the same two operands would fail, the
remainder cannot be calculated).
>>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3'))
Decimal('2.1')
>>> ExtendedContext.remainder(Decimal('10'), Decimal('3'))
Decimal('1')
>>> ExtendedContext.remainder(Decimal('-10'), Decimal('3'))
Decimal('-1')
>>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1'))
Decimal('0.2')
>>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3'))
Decimal('0.1')
>>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3'))
Decimal('1.0')
>>> ExtendedContext.remainder(22, 6)
Decimal('4')
>>> ExtendedContext.remainder(Decimal(22), 6)
Decimal('4')
>>> ExtendedContext.remainder(22, Decimal(6))
Decimal('4')
Tr r r )r r r r r s r/ rh Context.remainder_ s> >
1d +
IIaI & = AB BHr1 c 4 [ USS9nUR X S9$ )ao Returns to be "a - b * n", where n is the integer nearest the exact
value of "x / b" (if two integers are equally near then the even one
is chosen). If the result is equal to 0 then its sign will be the
sign of a.
This operation will fail under the same conditions as integer division
(that is, if integer division on the same two operands would fail, the
remainder cannot be calculated).
>>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3'))
Decimal('-0.9')
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6'))
Decimal('-2')
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3'))
Decimal('1')
>>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3'))
Decimal('-1')
>>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1'))
Decimal('0.2')
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3'))
Decimal('0.1')
>>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3'))
Decimal('-0.3')
>>> ExtendedContext.remainder_near(3, 11)
Decimal('3')
>>> ExtendedContext.remainder_near(Decimal(3), 11)
Decimal('3')
>>> ExtendedContext.remainder_near(3, Decimal(11))
Decimal('3')
Tr r )r r r s r/ r Context.remainder_near s$ >
1d + 00r1 c 4 [ USS9nUR X S9$ )a Returns a rotated copy of a, b times.
The coefficient of the result is a rotated copy of the digits in
the coefficient of the first operand. The number of places of
rotation is taken from the absolute value of the second operand,
with the rotation being to the left if the second operand is
positive or to the right otherwise.
>>> ExtendedContext.rotate(Decimal('34'), Decimal('8'))
Decimal('400000003')
>>> ExtendedContext.rotate(Decimal('12'), Decimal('9'))
Decimal('12')
>>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2'))
Decimal('891234567')
>>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0'))
Decimal('123456789')
>>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2'))
Decimal('345678912')
>>> ExtendedContext.rotate(1333333, 1)
Decimal('13333330')
>>> ExtendedContext.rotate(Decimal(1333333), 1)
Decimal('13333330')
>>> ExtendedContext.rotate(1333333, Decimal(1))
Decimal('13333330')
Tr r )r r r s r/ r Context.rotate s! 4
1d +xxx((r1 c 8 [ USS9nUR U5 $ )aU Returns True if the two operands have the same exponent.
The result is never affected by either the sign or the coefficient of
either operand.
>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001'))
False
>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01'))
True
>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1'))
False
>>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf'))
True
>>> ExtendedContext.same_quantum(10000, -1)
True
>>> ExtendedContext.same_quantum(Decimal(10000), -1)
True
>>> ExtendedContext.same_quantum(10000, Decimal(-1))
True
Tr )r r* r s r/ r* Context.same_quantum s *
1d +~~a r1 c 4 [ USS9nUR X S9$ )a Returns the first operand after adding the second value its exp.
>>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2'))
Decimal('0.0750')
>>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0'))
Decimal('7.50')
>>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3'))
Decimal('7.50E+3')
>>> ExtendedContext.scaleb(1, 4)
Decimal('1E+4')
>>> ExtendedContext.scaleb(Decimal(1), 4)
Decimal('1E+4')
>>> ExtendedContext.scaleb(1, Decimal(4))
Decimal('1E+4')
Tr r )r r r s r/ r Context.scaleb s!
1d +xxx((r1 c 4 [ USS9nUR X S9$ )a Returns a shifted copy of a, b times.
The coefficient of the result is a shifted copy of the digits
in the coefficient of the first operand. The number of places
to shift is taken from the absolute value of the second operand,
with the shift being to the left if the second operand is
positive or to the right otherwise. Digits shifted into the
coefficient are zeros.
>>> ExtendedContext.shift(Decimal('34'), Decimal('8'))
Decimal('400000000')
>>> ExtendedContext.shift(Decimal('12'), Decimal('9'))
Decimal('0')
>>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2'))
Decimal('1234567')
>>> ExtendedContext.shift(Decimal('123456789'), Decimal('0'))
Decimal('123456789')
>>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2'))
Decimal('345678900')
>>> ExtendedContext.shift(88888888, 2)
Decimal('888888800')
>>> ExtendedContext.shift(Decimal(88888888), 2)
Decimal('888888800')
>>> ExtendedContext.shift(88888888, Decimal(2))
Decimal('888888800')
Tr r )r rg r s r/ rg
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1d +wwqw''r1 c 4 [ USS9nUR U S9$ )a Square root of a non-negative number to context precision.
If the result must be inexact, it is rounded using the round-half-even
algorithm.
>>> ExtendedContext.sqrt(Decimal('0'))
Decimal('0')
>>> ExtendedContext.sqrt(Decimal('-0'))
Decimal('-0')
>>> ExtendedContext.sqrt(Decimal('0.39'))
Decimal('0.624499800')
>>> ExtendedContext.sqrt(Decimal('100'))
Decimal('10')
>>> ExtendedContext.sqrt(Decimal('1'))
Decimal('1')
>>> ExtendedContext.sqrt(Decimal('1.0'))
Decimal('1.0')
>>> ExtendedContext.sqrt(Decimal('1.00'))
Decimal('1.0')
>>> ExtendedContext.sqrt(Decimal('7'))
Decimal('2.64575131')
>>> ExtendedContext.sqrt(Decimal('10'))
Decimal('3.16227766')
>>> ExtendedContext.sqrt(2)
Decimal('1.41421356')
>>> ExtendedContext.prec
9
Tr r )r r? r~ s r/ r? Context.sqrt
s! :
1d +vvdv##r1 c f [ USS9nUR X S9nU[ L a [ SU- 5 eU$ )a Return the difference between the two operands.
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07'))
Decimal('0.23')
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30'))
Decimal('0.00')
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07'))
Decimal('-0.77')
>>> ExtendedContext.subtract(8, 5)
Decimal('3')
>>> ExtendedContext.subtract(Decimal(8), 5)
Decimal('3')
>>> ExtendedContext.subtract(8, Decimal(5))
Decimal('3')
Tr r r )r rY r r r s r/ subtractContext.subtract- s>
1d +
IIaI & = AB BHr1 c 4 [ USS9nUR U S9$ )a Convert to a string, using engineering notation if an exponent is needed.
Engineering notation has an exponent which is a multiple of 3. This
can leave up to 3 digits to the left of the decimal place and may
require the addition of either one or two trailing zeros.
The operation is not affected by the context.
>>> ExtendedContext.to_eng_string(Decimal('123E+1'))
'1.23E+3'
>>> ExtendedContext.to_eng_string(Decimal('123E+3'))
'123E+3'
>>> ExtendedContext.to_eng_string(Decimal('123E-10'))
'12.3E-9'
>>> ExtendedContext.to_eng_string(Decimal('-123E-12'))
'-123E-12'
>>> ExtendedContext.to_eng_string(Decimal('7E-7'))
'700E-9'
>>> ExtendedContext.to_eng_string(Decimal('7E+1'))
'70'
>>> ExtendedContext.to_eng_string(Decimal('0E+1'))
'0.00E+3'
Tr r )r r? r~ s r/ r? Context.to_eng_stringD s! 2
1d +t,,r1 c 4 [ USS9nUR U S9$ )ziConverts a number to a string, using scientific notation.
The operation is not affected by the context.
Tr r )r r; r~ s r/
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1d +yyy&&r1 c 4 [ USS9nUR U S9$ )a Rounds to an integer.
When the operand has a negative exponent, the result is the same
as using the quantize() operation using the given operand as the
left-hand-operand, 1E+0 as the right-hand-operand, and the precision
of the operand as the precision setting; Inexact and Rounded flags
are allowed in this operation. The rounding mode is taken from the
context.
>>> ExtendedContext.to_integral_exact(Decimal('2.1'))
Decimal('2')
>>> ExtendedContext.to_integral_exact(Decimal('100'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('100.0'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('101.5'))
Decimal('102')
>>> ExtendedContext.to_integral_exact(Decimal('-101.5'))
Decimal('-102')
>>> ExtendedContext.to_integral_exact(Decimal('10E+5'))
Decimal('1.0E+6')
>>> ExtendedContext.to_integral_exact(Decimal('7.89E+77'))
Decimal('7.89E+77')
>>> ExtendedContext.to_integral_exact(Decimal('-Inf'))
Decimal('-Infinity')
Tr r )r r5 r~ s r/ r5 Context.to_integral_exacth s$ 6
1d +""4"00r1 c 4 [ USS9nUR U S9$ )a Rounds to an integer.
When the operand has a negative exponent, the result is the same
as using the quantize() operation using the given operand as the
left-hand-operand, 1E+0 as the right-hand-operand, and the precision
of the operand as the precision setting, except that no flags will
be set. The rounding mode is taken from the context.
>>> ExtendedContext.to_integral_value(Decimal('2.1'))
Decimal('2')
>>> ExtendedContext.to_integral_value(Decimal('100'))
Decimal('100')
>>> ExtendedContext.to_integral_value(Decimal('100.0'))
Decimal('100')
>>> ExtendedContext.to_integral_value(Decimal('101.5'))
Decimal('102')
>>> ExtendedContext.to_integral_value(Decimal('-101.5'))
Decimal('-102')
>>> ExtendedContext.to_integral_value(Decimal('10E+5'))
Decimal('1.0E+6')
>>> ExtendedContext.to_integral_value(Decimal('7.89E+77'))
Decimal('7.89E+77')
>>> ExtendedContext.to_integral_value(Decimal('-Inf'))
Decimal('-Infinity')
Tr r )r r r~ s r/ r Context.to_integral_value s$ 4
1d +""4"00r1 ) rw r} r2 r~ r r rv ru r ) NNNNNNNNNr, )r )Zr< r= r> r? r@ r r< r@ r8 rG r r/ r rY r: r r r r rh rn r re r r; rx r{ r r r rR r rU rC ra rB r rC rh r r rf r r ro rr r) r r{ r r r r r r r r r r r r rP r r) r r r r r r r$ r r r r r rh r r r* r rg r? r r? r r5 r r rA r- r1 r/ r r s $ BFDH&*" H 5 1I2<; "!
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Done during addition.
r r r2 r )r r r r r) )rT rU rv tmpr tmp_len other_lenr s r/ rR rR s
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nX1* : a S$ U SU* - - $ )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
r( r r N)r r r rstrip)rI r6 str_nval_ns r/ r r si Av
a2q5y CF E
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S- pX:w a M U$ )zClosest integer to the square root of the positive integer n. a is
an initial approximation to the square root. Any positive integer
will do for a, but the closer a is to the square root of n the
faster convergence will be.
r( z3Both arguments to _sqrt_nearest should be positive.r2 )r )rI r r s r/
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integer to x / 2**shift; use round-to-even in case of a tie.
r2 r r- )r rg r rn s r/ _rshift_nearestr s4
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1%) **r1 c > [ X5 u p#USU- US- - U: - $ )zYClosest integer to a/b, a and b positive integers; rounds to even
in the case of a tie.
r r2 )rf )r r rn ro s r/ _div_nearestr s*
! 0, p >= 0, compute an integer
approximation to 10**p * log10(c*10**e), with an absolute error of
at most 1. Assumes that c*10**e is not exactly 1.r r2 r( r r )r r r r'
_log10_digits)
r= r6 r r> r r! r log_dlog_10 log_tenpowers
r/ r r D s FA CF A qsaxA1u E
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nX'- S: a [ U[ X'- 5 - SU- 5 nOSnOSn[ X- S5 $ )zGiven integers c, e and p with c > 0, compute an integer
approximation to 10**p * log(c*10**e), with an absolute error of
at most 1. Assumes that c*10**e is not exactly 1.r r2 r( r r )r r r r' r r) ) r= r6 r r> r r r* r f_log_tens r/ r r f s FA
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_Log10Memoizei zClass 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__.c SU l g )N/23025850929940456840179914546843642076011014886r r s r/ r _Log10Memoize.__init__ s G r1 c D US: a [ S5 eU[ U R 5 : a\ Sn SX- S- - n[ [ [ SU- U5 S5 5 nXB* S SU- :w a OUS-
nM@ UR
S5 SS U l [ U R SUS
- 5 $ ) zdGiven an integer p >= 0, return floor(10**p)*log(10).
For example, self.getdigits(3) returns 2302.
r( zp should be nonnegativer r r r Nr r r2 )r r r r r r' r r )r7 r r r! r s r/ getdigits_Log10Memoize.getdigits s
q5 67 7 DKK EO \%1a.# >?&'?c%i/
!--,Sb1DK4;;t!$%%r1 r3 N)r< r= r> r? r@ r r6 rA r- r1 r/ r0 r0 s CH&r1 r0 c H [ X- U- 5 n[ S[ [ U5 5 - SU- - 5 * n[ X5 nX- n[ US-
SS5 H n[ XU- - Xg- 5 nM [ US-
SS5 H nXS- - n[ XUU- - U5 nM X- $ )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).r r r2 r( r r )r r r r r r ) r r! r" r# r$ r Mshiftr r s r/ _iexpr: s * qyA
SSV_qs
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USU- 5 S5 Xr-
S- 4$ )a Compute an approximation to exp(c*10**e), with p decimal places of
precision.
Returns integers d, f such that:
10**(p-1) <= d <= 10**p, and
(d-1)*10**f < exp(c*10**e) < (d+1)*10**f
In other words, d*10**f is an approximation to exp(c*10**e) with p
digits of precision, and with an error in d of at most 1. This is
almost, but not quite, the same as the error being < 1ulp: when d
= 10**(p-1) the error could be up to 10 ulp.r r( r2 r i r )rP r r rf r) r r: ) r= r6 r r rn rg cshiftquotr
s r/ rk rk s FA
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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.
r2 r( r )r r r r r rk ) r r r r r r lxcrg pcr r s r/ r r s CBLB A A
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correctionstr_cs r/ r r * s: AvKLL FE s5z>JQx 0 00r1 c [ U [ 5 ( a U $ [ U [ 5 ( a [ U 5 $ U( a* [ U [ 5 ( a [ R U 5 $ U( a [ SU - 5 e[ $ )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).
r )r r r r r r r )r r allow_floats r/ r r 5 sg %!! % u~ z%//!!%((9EABB r1 c [ U[ 5 ( a X4$ [ U[ R 5 ( ar U R ( dJ [ U R [ [ U R 5 UR - 5 U R 5 n U [ UR 5 4$ U( a; [ U[ R 5 ( a UR S:X a UR n[ U[ 5 ( aR [# 5 nU( a SUR$ [& ' OUR) [& S5 U [ R+ U5 4$ [, [, 4$ )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( r2 r )r r _numbersRationalr rJ rK r r rL denominatorr numeratorComplexr r r r r r r r r )r7 r r r8 s r/ r r H s %!!{ %**++ #DJJ$'DII9J9J(J$K$(II/D WU__---
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OW''... > ))r1 r i?B i)rv ru r r rw r} r~ r r )rv ru r r a # A numeric string consists of:
# \s*
(?P[-+])? # an optional sign, followed by either...
(
(?=\d|\.\d) # ...a number (with at least one digit)
(?P\d*) # having a (possibly empty) integer part
(\.(?P\d*))? # followed by an optional fractional part
(E(?P[-+]?\d+))? # followed by an optional exponent, or...
|
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)
# \s*
\Z
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(?:
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c [ R U 5 nUc [ SU - 5 eUR 5 nUS nUS nUS SLUS' US ( a" Ub [ SU - 5 eUb [ SU - 5 eU=( d SUS' U=( d S US' US
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R " 5 nUS b [ SU - 5 eUS US' US US' US US' U$ US c SUS' SS/US' SUS' U$ ) a Parse 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 minimumwidthr r r( r gGnr2 rI r
thousands_sepzJExplicit thousands separator conflicts with 'n' type in format specifier: grouping
decimal_pointr r r5 ) _parse_format_specifier_regexmatchr groupdictr _locale
localeconv) format_specr r format_dictrY rZ s r/ r r s
& &++K8Ay5 CDD ++-K v D E )) 4D @K 9 68C D E
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string 'sign', add padding and alignment conforming to the given
format specifier dictionary 'spec' (as produced by
parse_format_specifier).
r^ rY rZ M 788r1 c SSK JnJn U ( d / $ U S S:X a$ [ U 5 S: a U" U SS U" U S 5 5 $ U S [ R
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iterable of integers representing group lengths.
r( )chainrepeatr r Nr z unrecognised format for grouping) itertoolsrq rr r rf CHAR_MAXr )ra rq rr s r/ _group_lengthsru A sl ( " s8} 1Xcr]F8B<$899 " )) )} ;< s r/ _insert_thousands_sepr{ X s "
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c1s6{?+fRSk9: 88HV$ %%r1 c 0 U ( a gUS S; a US $ g)zDetermine sign character.r r\ z +r r- ) is_negativer s r/ r r } s#
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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
altrb r( r r r7 r6 )r7 r6 r r z{0}{1:+}r r[ r^ )r formatr r{ r )r} r r r r r\ echarrx s r/ r r s $ *D4;(83
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