>>> getcontext().prec = 6
>>> Decimal(1) / Decimal(7)
- Decimal("0.142857")
+ Decimal('0.142857')
>>> getcontext().prec = 28
>>> Decimal(1) / Decimal(7)
- Decimal("0.1428571428571428571428571429")
+ Decimal('0.1428571428571428571428571429')
* Both binary and decimal floating point are implemented in terms of published
standards. While the built-in float type exposes only a modest portion of its
:const:`Infinity`, and :const:`-0`. ::
>>> Decimal(10)
- Decimal("10")
- >>> Decimal("3.14")
- Decimal("3.14")
+ Decimal('10')
+ >>> Decimal('3.14')
+ Decimal('3.14')
>>> Decimal((0, (3, 1, 4), -2))
- Decimal("3.14")
+ Decimal('3.14')
>>> Decimal(str(2.0 ** 0.5))
- Decimal("1.41421356237")
- >>> Decimal(2) ** Decimal("0.5")
- Decimal("1.414213562373095048801688724")
- >>> Decimal("NaN")
- Decimal("NaN")
- >>> Decimal("-Infinity")
- Decimal("-Infinity")
+ Decimal('1.41421356237')
+ >>> Decimal(2) ** Decimal('0.5')
+ Decimal('1.414213562373095048801688724')
+ >>> Decimal('NaN')
+ Decimal('NaN')
+ >>> Decimal('-Infinity')
+ Decimal('-Infinity')
The significance of a new Decimal is determined solely by the number of digits
input. Context precision and rounding only come into play during arithmetic
>>> getcontext().prec = 6
>>> Decimal('3.0')
- Decimal("3.0")
+ Decimal('3.0')
>>> Decimal('3.1415926535')
- Decimal("3.1415926535")
+ Decimal('3.1415926535')
>>> Decimal('3.1415926535') + Decimal('2.7182818285')
- Decimal("5.85987")
+ Decimal('5.85987')
>>> getcontext().rounding = ROUND_UP
>>> Decimal('3.1415926535') + Decimal('2.7182818285')
- Decimal("5.85988")
+ Decimal('5.85988')
Decimals interact well with much of the rest of Python. Here is a small decimal
floating point flying circus::
>>> data = map(Decimal, '1.34 1.87 3.45 2.35 1.00 0.03 9.25'.split())
>>> max(data)
- Decimal("9.25")
+ Decimal('9.25')
>>> min(data)
- Decimal("0.03")
+ Decimal('0.03')
>>> sorted(data)
- [Decimal("0.03"), Decimal("1.00"), Decimal("1.34"), Decimal("1.87"),
- Decimal("2.35"), Decimal("3.45"), Decimal("9.25")]
+ [Decimal('0.03'), Decimal('1.00'), Decimal('1.34'), Decimal('1.87'),
+ Decimal('2.35'), Decimal('3.45'), Decimal('9.25')]
>>> sum(data)
- Decimal("19.29")
+ Decimal('19.29')
>>> a,b,c = data[:3]
>>> str(a)
'1.34'
>>> int(a)
1
>>> a * 5
- Decimal("6.70")
+ Decimal('6.70')
>>> a * b
- Decimal("2.5058")
+ Decimal('2.5058')
>>> c % a
- Decimal("0.77")
+ Decimal('0.77')
And some mathematical functions are also available to Decimal::
>>> Decimal(2).sqrt()
- Decimal("1.414213562373095048801688724")
+ Decimal('1.414213562373095048801688724')
>>> Decimal(1).exp()
- Decimal("2.718281828459045235360287471")
- >>> Decimal("10").ln()
- Decimal("2.302585092994045684017991455")
- >>> Decimal("10").log10()
- Decimal("1")
+ Decimal('2.718281828459045235360287471')
+ >>> Decimal('10').ln()
+ Decimal('2.302585092994045684017991455')
+ >>> Decimal('10').log10()
+ Decimal('1')
The :meth:`quantize` method rounds a number to a fixed exponent. This method is
useful for monetary applications that often round results to a fixed number of
places::
>>> Decimal('7.325').quantize(Decimal('.01'), rounding=ROUND_DOWN)
- Decimal("7.32")
+ Decimal('7.32')
>>> Decimal('7.325').quantize(Decimal('1.'), rounding=ROUND_UP)
- Decimal("8")
+ Decimal('8')
As shown above, the :func:`getcontext` function accesses the current context and
allows the settings to be changed. This approach meets the needs of most
>>> myothercontext = Context(prec=60, rounding=ROUND_HALF_DOWN)
>>> setcontext(myothercontext)
>>> Decimal(1) / Decimal(7)
- Decimal("0.142857142857142857142857142857142857142857142857142857142857")
+ Decimal('0.142857142857142857142857142857142857142857142857142857142857')
>>> ExtendedContext
Context(prec=9, rounding=ROUND_HALF_EVEN, Emin=-999999999, Emax=999999999,
capitals=1, flags=[], traps=[])
>>> setcontext(ExtendedContext)
>>> Decimal(1) / Decimal(7)
- Decimal("0.142857143")
+ Decimal('0.142857143')
>>> Decimal(42) / Decimal(0)
- Decimal("Infinity")
+ Decimal('Infinity')
>>> setcontext(BasicContext)
>>> Decimal(42) / Decimal(0)
>>> setcontext(ExtendedContext)
>>> getcontext().clear_flags()
>>> Decimal(355) / Decimal(113)
- Decimal("3.14159292")
+ Decimal('3.14159292')
>>> getcontext()
Context(prec=9, rounding=ROUND_HALF_EVEN, Emin=-999999999, Emax=999999999,
capitals=1, flags=[Inexact, Rounded], traps=[])
context::
>>> Decimal(1) / Decimal(0)
- Decimal("Infinity")
+ Decimal('Infinity')
>>> getcontext().traps[DivisionByZero] = 1
>>> Decimal(1) / Decimal(0)
Traceback (most recent call last):
Construct a new :class:`Decimal` object based from *value*.
*value* can be an integer, string, tuple, or another :class:`Decimal`
- object. If no *value* is given, returns ``Decimal("0")``. If *value* is a
+ object. If no *value* is given, returns ``Decimal('0')``. If *value* is a
string, it should conform to the decimal numeric string syntax after leading
and trailing whitespace characters are removed::
If *value* is a :class:`tuple`, it should have three components, a sign
(:const:`0` for positive or :const:`1` for negative), a :class:`tuple` of
digits, and an integer exponent. For example, ``Decimal((0, (1, 4, 1, 4), -3))``
- returns ``Decimal("1.414")``.
+ returns ``Decimal('1.414')``.
The *context* precision does not affect how many digits are stored. That is
determined exclusively by the number of digits in *value*. For example,
- ``Decimal("3.00000")`` records all five zeros even if the context precision is
+ ``Decimal('3.00000')`` records all five zeros even if the context precision is
only three.
The purpose of the *context* argument is determining what to do if *value* is a
.. method:: Decimal.adjusted()
Return the adjusted exponent after shifting out the coefficient's rightmost
- digits until only the lead digit remains: ``Decimal("321e+5").adjusted()``
+ digits until only the lead digit remains: ``Decimal('321e+5').adjusted()``
returns seven. Used for determining the position of the most significant digit
with respect to the decimal point.
instance rather than an integer, and if either operand is a NaN
then the result is a NaN::
- a or b is a NaN ==> Decimal("NaN")
- a < b ==> Decimal("-1")
- a == b ==> Decimal("0")
- a > b ==> Decimal("1")
+ a or b is a NaN ==> Decimal('NaN')
+ a < b ==> Decimal('-1')
+ a == b ==> Decimal('0')
+ a > b ==> Decimal('1')
.. method:: Decimal.compare_signal(other[, context])
value but different representations compare unequal in this
ordering::
- >>> Decimal("12.0").compare_total(Decimal("12"))
- Decimal("-1")
+ >>> Decimal('12.0').compare_total(Decimal('12'))
+ Decimal('-1')
Quiet and signaling NaNs are also included in the total ordering.
- The result of this function is ``Decimal("0")`` if both operands
- have the same representation, ``Decimal("-1")`` if the first
+ The result of this function is ``Decimal('0')`` if both operands
+ have the same representation, ``Decimal('-1')`` if the first
operand is lower in the total order than the second, and
- ``Decimal("1")`` if the first operand is higher in the total order
+ ``Decimal('1')`` if the first operand is higher in the total order
than the second operand. See the specification for details of the
total order.
Return a copy of the first operand with the sign set to be the
same as the sign of the second operand. For example::
- >>> Decimal("2.3").copy_sign(Decimal("-1.5"))
- Decimal("-2.3")
+ >>> Decimal('2.3').copy_sign(Decimal('-1.5'))
+ Decimal('-2.3')
This operation is unaffected by the context and is quiet: no flags
are changed and no rounding is performed.
:const:`ROUND_HALF_EVEN` rounding mode.
>>> Decimal(1).exp()
- Decimal("2.718281828459045235360287471")
+ Decimal('2.718281828459045235360287471')
>>> Decimal(321).exp()
- Decimal("2.561702493119680037517373933E+139")
+ Decimal('2.561702493119680037517373933E+139')
.. method:: Decimal.fma(other, third[, context])
the intermediate product self*other.
>>> Decimal(2).fma(3, 5)
- Decimal("11")
+ Decimal('11')
.. method:: Decimal.is_canonical()
For a nonzero number, return the adjusted exponent of its operand
as a :class:`Decimal` instance. If the operand is a zero then
- ``Decimal("-Infinity")`` is returned and the
+ ``Decimal('-Infinity')`` is returned and the
:const:`DivisionByZero` flag is raised. If the operand is an
- infinity then ``Decimal("Infinity")`` is returned.
+ infinity then ``Decimal('Infinity')`` is returned.
.. method:: Decimal.logical_and(other[, context])
.. method:: Decimal.normalize([context])
Normalize the number by stripping the rightmost trailing zeros and converting
- any result equal to :const:`Decimal("0")` to :const:`Decimal("0e0")`. Used for
+ any result equal to :const:`Decimal('0')` to :const:`Decimal('0e0')`. Used for
producing canonical values for members of an equivalence class. For example,
- ``Decimal("32.100")`` and ``Decimal("0.321000e+2")`` both normalize to the
- equivalent value ``Decimal("32.1")``.
+ ``Decimal('32.100')`` and ``Decimal('0.321000e+2')`` both normalize to the
+ equivalent value ``Decimal('32.1')``.
.. method:: Decimal.number_class([context])
Return a value equal to the first operand after rounding and
having the exponent of the second operand.
- >>> Decimal("1.41421356").quantize(Decimal("1.000"))
- Decimal("1.414")
+ >>> Decimal('1.41421356').quantize(Decimal('1.000'))
+ Decimal('1.414')
Unlike other operations, if the length of the coefficient after the
quantize operation would be greater than precision, then an
Compute the modulo as either a positive or negative value depending on which is
closest to zero. For instance, ``Decimal(10).remainder_near(6)`` returns
- ``Decimal("-2")`` which is closer to zero than ``Decimal("4")``.
+ ``Decimal('-2')`` which is closer to zero than ``Decimal('4')``.
If both are equally close, the one chosen will have the same sign as *self*.
Engineering notation has an exponent which is a multiple of 3, so there are up
to 3 digits left of the decimal place. For example, converts
- ``Decimal('123E+1')`` to ``Decimal("1.23E+3")``
+ ``Decimal('123E+1')`` to ``Decimal('1.23E+3')``
.. method:: Decimal.to_integral([rounding[, context]])
change the result::
>>> getcontext().prec = 3
- >>> Decimal("3.4445") + Decimal("1.0023")
- Decimal("4.45")
- >>> Decimal("3.4445") + Decimal(0) + Decimal("1.0023")
- Decimal("4.44")
+ >>> Decimal('3.4445') + Decimal('1.0023')
+ Decimal('4.45')
+ >>> Decimal('3.4445') + Decimal(0) + Decimal('1.0023')
+ Decimal('4.44')
This method implements the to-number operation of the IBM
specification. If the argument is a string, no leading or trailing
>>> u, v, w = Decimal(11111113), Decimal(-11111111), Decimal('7.51111111')
>>> (u + v) + w
- Decimal("9.5111111")
+ Decimal('9.5111111')
>>> u + (v + w)
- Decimal("10")
+ Decimal('10')
>>> u, v, w = Decimal(20000), Decimal(-6), Decimal('6.0000003')
>>> (u*v) + (u*w)
- Decimal("0.01")
+ Decimal('0.01')
>>> u * (v+w)
- Decimal("0.0060000")
+ Decimal('0.0060000')
The :mod:`decimal` module makes it possible to restore the identities by
expanding the precision sufficiently to avoid loss of significance::
>>> getcontext().prec = 20
>>> u, v, w = Decimal(11111113), Decimal(-11111111), Decimal('7.51111111')
>>> (u + v) + w
- Decimal("9.51111111")
+ Decimal('9.51111111')
>>> u + (v + w)
- Decimal("9.51111111")
+ Decimal('9.51111111')
>>>
>>> u, v, w = Decimal(20000), Decimal(-6), Decimal('6.0000003')
>>> (u*v) + (u*w)
- Decimal("0.0060000")
+ Decimal('0.0060000')
>>> u * (v+w)
- Decimal("0.0060000")
+ Decimal('0.0060000')
Special values
the following calculation returns a value equal to zero::
>>> 1 / Decimal('Infinity')
- Decimal("0E-1000000026")
+ Decimal('0E-1000000026')
.. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>>> D = decimal.Decimal
>>> D('1.23') + D('3.45')
- Decimal("4.68")
+ Decimal('4.68')
Q. In a fixed-point application with two decimal places, some inputs have many
places and need to be rounded. Others are not supposed to have excess digits
>>> TWOPLACES = Decimal(10) ** -2 # same as Decimal('0.01')
>>> # Round to two places
- >>> Decimal("3.214").quantize(TWOPLACES)
- Decimal("3.21")
+ >>> Decimal('3.214').quantize(TWOPLACES)
+ Decimal('3.21')
>>> # Validate that a number does not exceed two places
- >>> Decimal("3.21").quantize(TWOPLACES, context=Context(traps=[Inexact]))
- Decimal("3.21")
+ >>> Decimal('3.21').quantize(TWOPLACES, context=Context(traps=[Inexact]))
+ Decimal('3.21')
- >>> Decimal("3.214").quantize(TWOPLACES, context=Context(traps=[Inexact]))
+ >>> Decimal('3.214').quantize(TWOPLACES, context=Context(traps=[Inexact]))
Traceback (most recent call last):
...
Inexact: Changed in rounding
>>> values = map(Decimal, '200 200.000 2E2 .02E+4'.split())
>>> [v.normalize() for v in values]
- [Decimal("2E+2"), Decimal("2E+2"), Decimal("2E+2"), Decimal("2E+2")]
+ [Decimal('2E+2'), Decimal('2E+2'), Decimal('2E+2'), Decimal('2E+2')]
Q. Some decimal values always print with exponential notation. Is there a way
to get a non-exponential representation?
ctx.prec += 1
>>> float_to_decimal(math.pi)
- Decimal("3.141592653589793115997963468544185161590576171875")
+ Decimal('3.141592653589793115997963468544185161590576171875')
Q. Why isn't the :func:`float_to_decimal` routine included in the module?
representation issues associated with binary floating point::
>>> float_to_decimal(1.1)
- Decimal("1.100000000000000088817841970012523233890533447265625")
+ Decimal('1.100000000000000088817841970012523233890533447265625')
Q. Within a complex calculation, how can I make sure that I haven't gotten a
spurious result because of insufficient precision or rounding anomalies.
>>> getcontext().prec = 3
>>> Decimal('3.104') + D('2.104')
- Decimal("5.21")
+ Decimal('5.21')
>>> Decimal('3.104') + D('0.000') + D('2.104')
- Decimal("5.20")
+ Decimal('5.20')
The solution is either to increase precision or to force rounding of inputs
using the unary plus operation::
>>> getcontext().prec = 3
>>> +Decimal('1.23456789') # unary plus triggers rounding
- Decimal("1.23")
+ Decimal('1.23')
Alternatively, inputs can be rounded upon creation using the
:meth:`Context.create_decimal` method::
>>> Context(prec=5, rounding=ROUND_DOWN).create_decimal('1.2345678')
- Decimal("1.2345")
+ Decimal('1.2345')
:class:`decimal.Decimal`.
+.. method:: Fraction.limit_denominator(max_denominator=1000000)
+
+ Finds and returns the closest :class:`Fraction` to ``self`` that
+ has denominator at most max_denominator. This method is useful for
+ finding rational approximations to a given floating-point number::
+
+ >>> Fraction('3.1415926535897932').limit_denominator(1000)
+ Fraction(355, 113)
+
+ or for recovering a rational number that's represented as a float::
+
+ >>> from math import pi, cos
+ >>> Fraction.from_float(cos(pi/3))
+ Fraction(4503599627370497L, 9007199254740992L)
+ >>> Fraction.from_float(cos(pi/3)).limit_denominator()
+ Fraction(1, 2)
+
+
.. method:: Fraction.__floor__()
Returns the greatest :class:`int` ``<= self``. Will be accessible
user time, children's system time, and elapsed real time since a fixed point in
the past, in that order. See the Unix manual page :manpage:`times(2)` or the
corresponding Windows Platform API documentation. Availability: Macintosh, Unix,
- Windows.
+ Windows. On Windows, only the first two items are filled, the others are zero.
.. function:: wait()
def __instancecheck__(cls, instance):
"""Override for isinstance(instance, cls)."""
- return any(cls.__subclasscheck__(c)
- for c in {instance.__class__, type(instance)})
+ # Inline the cache checking
+ subclass = instance.__class__
+ if subclass in cls._abc_cache:
+ return True
+ subtype = type(instance)
+ if subtype is subclass:
+ if (cls._abc_negative_cache_version ==
+ ABCMeta._abc_invalidation_counter and
+ subclass in cls._abc_negative_cache):
+ return False
+ # Fall back to the subclass check.
+ return cls.__subclasscheck__(subclass)
+ return any(cls.__subclasscheck__(c) for c in {subclass, subtype})
def __subclasscheck__(cls, subclass):
"""Override for issubclass(subclass, cls)."""
useful for financial applications or for contexts where users have
expectations that are at odds with binary floating point (for instance,
in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead
-of the expected Decimal("0.00") returned by decimal floating point).
+of the expected Decimal('0.00') returned by decimal floating point).
Here are some examples of using the decimal module:
>>> from decimal import *
>>> setcontext(ExtendedContext)
>>> Decimal(0)
-Decimal("0")
->>> Decimal("1")
-Decimal("1")
->>> Decimal("-.0123")
-Decimal("-0.0123")
+Decimal('0')
+>>> Decimal('1')
+Decimal('1')
+>>> Decimal('-.0123')
+Decimal('-0.0123')
>>> Decimal(123456)
-Decimal("123456")
->>> Decimal("123.45e12345678901234567890")
-Decimal("1.2345E+12345678901234567892")
->>> Decimal("1.33") + Decimal("1.27")
-Decimal("2.60")
->>> Decimal("12.34") + Decimal("3.87") - Decimal("18.41")
-Decimal("-2.20")
+Decimal('123456')
+>>> Decimal('123.45e12345678901234567890')
+Decimal('1.2345E+12345678901234567892')
+>>> Decimal('1.33') + Decimal('1.27')
+Decimal('2.60')
+>>> Decimal('12.34') + Decimal('3.87') - Decimal('18.41')
+Decimal('-2.20')
>>> dig = Decimal(1)
>>> print(dig / Decimal(3))
0.333333333
>>> print(c.flags[InvalidOperation])
0
>>> c.divide(Decimal(0), Decimal(0))
-Decimal("NaN")
+Decimal('NaN')
>>> c.traps[InvalidOperation] = 1
>>> print(c.flags[InvalidOperation])
1
"""Create a decimal point instance.
>>> Decimal('3.14') # string input
- Decimal("3.14")
+ Decimal('3.14')
>>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent)
- Decimal("3.14")
+ Decimal('3.14')
>>> Decimal(314) # int
- Decimal("314")
+ Decimal('314')
>>> Decimal(Decimal(314)) # another decimal instance
- Decimal("314")
+ Decimal('314')
>>> Decimal(' 3.14 \\n') # leading and trailing whitespace okay
- Decimal("3.14")
+ Decimal('3.14')
"""
# Note that the coefficient, self._int, is actually stored as
#
# The hash of a nonspecial noninteger Decimal must depend only
# on the value of that Decimal, and not on its representation.
- # For example: hash(Decimal("100E-1")) == hash(Decimal("10")).
+ # For example: hash(Decimal('100E-1')) == hash(Decimal('10')).
if self._is_special:
if self._isnan():
raise TypeError('Cannot hash a NaN value.')
def __repr__(self):
"""Represents the number as an instance of Decimal."""
# Invariant: eval(repr(d)) == d
- return 'Decimal("%s")' % str(self)
+ return "Decimal('%s')" % str(self)
def __str__(self, eng=False, context=None):
"""Return string representation of the number in scientific notation.
the plus operation on the operand.
>>> ExtendedContext.abs(Decimal('2.1'))
- Decimal("2.1")
+ Decimal('2.1')
>>> ExtendedContext.abs(Decimal('-100'))
- Decimal("100")
+ Decimal('100')
>>> ExtendedContext.abs(Decimal('101.5'))
- Decimal("101.5")
+ Decimal('101.5')
>>> ExtendedContext.abs(Decimal('-101.5'))
- Decimal("101.5")
+ Decimal('101.5')
"""
return a.__abs__(context=self)
"""Return the sum of the two operands.
>>> ExtendedContext.add(Decimal('12'), Decimal('7.00'))
- Decimal("19.00")
+ Decimal('19.00')
>>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4'))
- Decimal("1.02E+4")
+ Decimal('1.02E+4')
"""
return a.__add__(b, context=self)
received object already is in its canonical form.
>>> ExtendedContext.canonical(Decimal('2.50'))
- Decimal("2.50")
+ Decimal('2.50')
"""
return a.canonical(context=self)
zero or negative zero, or '1' if the result is greater than zero.
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('3'))
- Decimal("-1")
+ Decimal('-1')
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.compare(Decimal('3'), Decimal('2.1'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1'))
- Decimal("-1")
+ Decimal('-1')
"""
return a.compare(b, context=self)
>>> c = ExtendedContext
>>> c.compare_signal(Decimal('2.1'), Decimal('3'))
- Decimal("-1")
+ Decimal('-1')
>>> c.compare_signal(Decimal('2.1'), Decimal('2.1'))
- Decimal("0")
+ Decimal('0')
>>> c.flags[InvalidOperation] = 0
>>> print(c.flags[InvalidOperation])
0
>>> c.compare_signal(Decimal('NaN'), Decimal('2.1'))
- Decimal("NaN")
+ 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")
+ Decimal('NaN')
>>> print(c.flags[InvalidOperation])
1
"""
representations.
>>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9'))
- Decimal("-1")
+ Decimal('-1')
>>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12'))
- Decimal("-1")
+ Decimal('-1')
>>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3'))
- Decimal("-1")
+ Decimal('-1')
>>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN'))
- Decimal("-1")
+ Decimal('-1')
"""
return a.compare_total(b)
"""Returns a copy of the operand with the sign set to 0.
>>> ExtendedContext.copy_abs(Decimal('2.1'))
- Decimal("2.1")
+ Decimal('2.1')
>>> ExtendedContext.copy_abs(Decimal('-100'))
- Decimal("100")
+ Decimal('100')
"""
return a.copy_abs()
"""Returns a copy of the decimal objet.
>>> ExtendedContext.copy_decimal(Decimal('2.1'))
- Decimal("2.1")
+ Decimal('2.1')
>>> ExtendedContext.copy_decimal(Decimal('-1.00'))
- Decimal("-1.00")
+ Decimal('-1.00')
"""
return Decimal(a)
"""Returns a copy of the operand with the sign inverted.
>>> ExtendedContext.copy_negate(Decimal('101.5'))
- Decimal("-101.5")
+ Decimal('-101.5')
>>> ExtendedContext.copy_negate(Decimal('-101.5'))
- Decimal("101.5")
+ Decimal('101.5')
"""
return a.copy_negate()
equal to the sign of the second operand.
>>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33'))
- Decimal("1.50")
+ Decimal('1.50')
>>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33'))
- Decimal("1.50")
+ Decimal('1.50')
>>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33'))
- Decimal("-1.50")
+ Decimal('-1.50')
>>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33'))
- Decimal("-1.50")
+ Decimal('-1.50')
"""
return a.copy_sign(b)
"""Decimal division in a specified context.
>>> ExtendedContext.divide(Decimal('1'), Decimal('3'))
- Decimal("0.333333333")
+ Decimal('0.333333333')
>>> ExtendedContext.divide(Decimal('2'), Decimal('3'))
- Decimal("0.666666667")
+ Decimal('0.666666667')
>>> ExtendedContext.divide(Decimal('5'), Decimal('2'))
- Decimal("2.5")
+ Decimal('2.5')
>>> ExtendedContext.divide(Decimal('1'), Decimal('10'))
- Decimal("0.1")
+ Decimal('0.1')
>>> ExtendedContext.divide(Decimal('12'), Decimal('12'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.divide(Decimal('8.00'), Decimal('2'))
- Decimal("4.00")
+ Decimal('4.00')
>>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0'))
- Decimal("1.20")
+ Decimal('1.20')
>>> ExtendedContext.divide(Decimal('1000'), Decimal('100'))
- Decimal("10")
+ Decimal('10')
>>> ExtendedContext.divide(Decimal('1000'), Decimal('1'))
- Decimal("1000")
+ Decimal('1000')
>>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2'))
- Decimal("1.20E+6")
+ Decimal('1.20E+6')
"""
return a.__truediv__(b, context=self)
"""Divides two numbers and returns the integer part of the result.
>>> ExtendedContext.divide_int(Decimal('2'), Decimal('3'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.divide_int(Decimal('10'), Decimal('3'))
- Decimal("3")
+ Decimal('3')
>>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3'))
- Decimal("3")
+ Decimal('3')
"""
return a.__floordiv__(b, context=self)
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.exp(Decimal('-Infinity'))
- Decimal("0")
+ Decimal('0')
>>> c.exp(Decimal('-1'))
- Decimal("0.367879441")
+ Decimal('0.367879441')
>>> c.exp(Decimal('0'))
- Decimal("1")
+ Decimal('1')
>>> c.exp(Decimal('1'))
- Decimal("2.71828183")
+ Decimal('2.71828183')
>>> c.exp(Decimal('0.693147181'))
- Decimal("2.00000000")
+ Decimal('2.00000000')
>>> c.exp(Decimal('+Infinity'))
- Decimal("Infinity")
+ Decimal('Infinity')
"""
return a.exp(context=self)
multiplication, using add, all with only one final rounding.
>>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7'))
- Decimal("22")
+ Decimal('22')
>>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7'))
- Decimal("-8")
+ Decimal('-8')
>>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578'))
- Decimal("1.38435736E+12")
+ Decimal('1.38435736E+12')
"""
return a.fma(b, c, context=self)
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.ln(Decimal('0'))
- Decimal("-Infinity")
+ Decimal('-Infinity')
>>> c.ln(Decimal('1.000'))
- Decimal("0")
+ Decimal('0')
>>> c.ln(Decimal('2.71828183'))
- Decimal("1.00000000")
+ Decimal('1.00000000')
>>> c.ln(Decimal('10'))
- Decimal("2.30258509")
+ Decimal('2.30258509')
>>> c.ln(Decimal('+Infinity'))
- Decimal("Infinity")
+ Decimal('Infinity')
"""
return a.ln(context=self)
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.log10(Decimal('0'))
- Decimal("-Infinity")
+ Decimal('-Infinity')
>>> c.log10(Decimal('0.001'))
- Decimal("-3")
+ Decimal('-3')
>>> c.log10(Decimal('1.000'))
- Decimal("0")
+ Decimal('0')
>>> c.log10(Decimal('2'))
- Decimal("0.301029996")
+ Decimal('0.301029996')
>>> c.log10(Decimal('10'))
- Decimal("1")
+ Decimal('1')
>>> c.log10(Decimal('70'))
- Decimal("1.84509804")
+ Decimal('1.84509804')
>>> c.log10(Decimal('+Infinity'))
- Decimal("Infinity")
+ Decimal('Infinity')
"""
return a.log10(context=self)
value of that digit and without limiting the resulting exponent).
>>> ExtendedContext.logb(Decimal('250'))
- Decimal("2")
+ Decimal('2')
>>> ExtendedContext.logb(Decimal('2.50'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.logb(Decimal('0.03'))
- Decimal("-2")
+ Decimal('-2')
>>> ExtendedContext.logb(Decimal('0'))
- Decimal("-Infinity")
+ Decimal('-Infinity')
"""
return a.logb(context=self)
The operands must be both logical numbers.
>>> ExtendedContext.logical_and(Decimal('0'), Decimal('0'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.logical_and(Decimal('0'), Decimal('1'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.logical_and(Decimal('1'), Decimal('0'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.logical_and(Decimal('1'), Decimal('1'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010'))
- Decimal("1000")
+ Decimal('1000')
>>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10'))
- Decimal("10")
+ Decimal('10')
"""
return a.logical_and(b, context=self)
The operand must be a logical number.
>>> ExtendedContext.logical_invert(Decimal('0'))
- Decimal("111111111")
+ Decimal('111111111')
>>> ExtendedContext.logical_invert(Decimal('1'))
- Decimal("111111110")
+ Decimal('111111110')
>>> ExtendedContext.logical_invert(Decimal('111111111'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.logical_invert(Decimal('101010101'))
- Decimal("10101010")
+ Decimal('10101010')
"""
return a.logical_invert(context=self)
The operands must be both logical numbers.
>>> ExtendedContext.logical_or(Decimal('0'), Decimal('0'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.logical_or(Decimal('0'), Decimal('1'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.logical_or(Decimal('1'), Decimal('0'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.logical_or(Decimal('1'), Decimal('1'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010'))
- Decimal("1110")
+ Decimal('1110')
>>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10'))
- Decimal("1110")
+ Decimal('1110')
"""
return a.logical_or(b, context=self)
The operands must be both logical numbers.
>>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010'))
- Decimal("110")
+ Decimal('110')
>>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10'))
- Decimal("1101")
+ Decimal('1101')
"""
return a.logical_xor(b, context=self)
infinity) of the two operands is chosen as the result.
>>> ExtendedContext.max(Decimal('3'), Decimal('2'))
- Decimal("3")
+ Decimal('3')
>>> ExtendedContext.max(Decimal('-10'), Decimal('3'))
- Decimal("3")
+ Decimal('3')
>>> ExtendedContext.max(Decimal('1.0'), Decimal('1'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.max(Decimal('7'), Decimal('NaN'))
- Decimal("7")
+ Decimal('7')
"""
return a.max(b, context=self)
infinity) of the two operands is chosen as the result.
>>> ExtendedContext.min(Decimal('3'), Decimal('2'))
- Decimal("2")
+ Decimal('2')
>>> ExtendedContext.min(Decimal('-10'), Decimal('3'))
- Decimal("-10")
+ Decimal('-10')
>>> ExtendedContext.min(Decimal('1.0'), Decimal('1'))
- Decimal("1.0")
+ Decimal('1.0')
>>> ExtendedContext.min(Decimal('7'), Decimal('NaN'))
- Decimal("7")
+ Decimal('7')
"""
return a.min(b, context=self)
has the same exponent as the operand.
>>> ExtendedContext.minus(Decimal('1.3'))
- Decimal("-1.3")
+ Decimal('-1.3')
>>> ExtendedContext.minus(Decimal('-1.3'))
- Decimal("1.3")
+ Decimal('1.3')
"""
return a.__neg__(context=self)
of the two operands.
>>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3'))
- Decimal("3.60")
+ Decimal('3.60')
>>> ExtendedContext.multiply(Decimal('7'), Decimal('3'))
- Decimal("21")
+ Decimal('21')
>>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8'))
- Decimal("0.72")
+ Decimal('0.72')
>>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0'))
- Decimal("-0.0")
+ Decimal('-0.0')
>>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321'))
- Decimal("4.28135971E+11")
+ Decimal('4.28135971E+11')
"""
return a.__mul__(b, context=self)
>>> c.Emin = -999
>>> c.Emax = 999
>>> ExtendedContext.next_minus(Decimal('1'))
- Decimal("0.999999999")
+ Decimal('0.999999999')
>>> c.next_minus(Decimal('1E-1007'))
- Decimal("0E-1007")
+ Decimal('0E-1007')
>>> ExtendedContext.next_minus(Decimal('-1.00000003'))
- Decimal("-1.00000004")
+ Decimal('-1.00000004')
>>> c.next_minus(Decimal('Infinity'))
- Decimal("9.99999999E+999")
+ Decimal('9.99999999E+999')
"""
return a.next_minus(context=self)
>>> c.Emin = -999
>>> c.Emax = 999
>>> ExtendedContext.next_plus(Decimal('1'))
- Decimal("1.00000001")
+ Decimal('1.00000001')
>>> c.next_plus(Decimal('-1E-1007'))
- Decimal("-0E-1007")
+ Decimal('-0E-1007')
>>> ExtendedContext.next_plus(Decimal('-1.00000003'))
- Decimal("-1.00000002")
+ Decimal('-1.00000002')
>>> c.next_plus(Decimal('-Infinity'))
- Decimal("-9.99999999E+999")
+ Decimal('-9.99999999E+999')
"""
return a.next_plus(context=self)
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.next_toward(Decimal('1'), Decimal('2'))
- Decimal("1.00000001")
+ Decimal('1.00000001')
>>> c.next_toward(Decimal('-1E-1007'), Decimal('1'))
- Decimal("-0E-1007")
+ Decimal('-0E-1007')
>>> c.next_toward(Decimal('-1.00000003'), Decimal('0'))
- Decimal("-1.00000002")
+ Decimal('-1.00000002')
>>> c.next_toward(Decimal('1'), Decimal('0'))
- Decimal("0.999999999")
+ Decimal('0.999999999')
>>> c.next_toward(Decimal('1E-1007'), Decimal('-100'))
- Decimal("0E-1007")
+ Decimal('0E-1007')
>>> c.next_toward(Decimal('-1.00000003'), Decimal('-10'))
- Decimal("-1.00000004")
+ Decimal('-1.00000004')
>>> c.next_toward(Decimal('0.00'), Decimal('-0.0000'))
- Decimal("-0.00")
+ Decimal('-0.00')
"""
return a.next_toward(b, context=self)
result.
>>> ExtendedContext.normalize(Decimal('2.1'))
- Decimal("2.1")
+ Decimal('2.1')
>>> ExtendedContext.normalize(Decimal('-2.0'))
- Decimal("-2")
+ Decimal('-2')
>>> ExtendedContext.normalize(Decimal('1.200'))
- Decimal("1.2")
+ Decimal('1.2')
>>> ExtendedContext.normalize(Decimal('-120'))
- Decimal("-1.2E+2")
+ Decimal('-1.2E+2')
>>> ExtendedContext.normalize(Decimal('120.00'))
- Decimal("1.2E+2")
+ Decimal('1.2E+2')
>>> ExtendedContext.normalize(Decimal('0.00'))
- Decimal("0")
+ Decimal('0')
"""
return a.normalize(context=self)
has the same exponent as the operand.
>>> ExtendedContext.plus(Decimal('1.3'))
- Decimal("1.3")
+ Decimal('1.3')
>>> ExtendedContext.plus(Decimal('-1.3'))
- Decimal("-1.3")
+ Decimal('-1.3')
"""
return a.__pos__(context=self)
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.power(Decimal('2'), Decimal('3'))
- Decimal("8")
+ Decimal('8')
>>> c.power(Decimal('-2'), Decimal('3'))
- Decimal("-8")
+ Decimal('-8')
>>> c.power(Decimal('2'), Decimal('-3'))
- Decimal("0.125")
+ Decimal('0.125')
>>> c.power(Decimal('1.7'), Decimal('8'))
- Decimal("69.7575744")
+ Decimal('69.7575744')
>>> c.power(Decimal('10'), Decimal('0.301029996'))
- Decimal("2.00000000")
+ Decimal('2.00000000')
>>> c.power(Decimal('Infinity'), Decimal('-1'))
- Decimal("0")
+ Decimal('0')
>>> c.power(Decimal('Infinity'), Decimal('0'))
- Decimal("1")
+ Decimal('1')
>>> c.power(Decimal('Infinity'), Decimal('1'))
- Decimal("Infinity")
+ Decimal('Infinity')
>>> c.power(Decimal('-Infinity'), Decimal('-1'))
- Decimal("-0")
+ Decimal('-0')
>>> c.power(Decimal('-Infinity'), Decimal('0'))
- Decimal("1")
+ Decimal('1')
>>> c.power(Decimal('-Infinity'), Decimal('1'))
- Decimal("-Infinity")
+ Decimal('-Infinity')
>>> c.power(Decimal('-Infinity'), Decimal('2'))
- Decimal("Infinity")
+ Decimal('Infinity')
>>> c.power(Decimal('0'), Decimal('0'))
- Decimal("NaN")
+ Decimal('NaN')
>>> c.power(Decimal('3'), Decimal('7'), Decimal('16'))
- Decimal("11")
+ Decimal('11')
>>> c.power(Decimal('-3'), Decimal('7'), Decimal('16'))
- Decimal("-11")
+ Decimal('-11')
>>> c.power(Decimal('-3'), Decimal('8'), Decimal('16'))
- Decimal("1")
+ Decimal('1')
>>> c.power(Decimal('3'), Decimal('7'), Decimal('-16'))
- Decimal("11")
+ Decimal('11')
>>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789'))
- Decimal("11729830")
+ Decimal('11729830')
>>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729'))
- Decimal("-0")
+ Decimal('-0')
>>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537'))
- Decimal("1")
+ Decimal('1')
"""
return a.__pow__(b, modulo, context=self)
if the result is subnormal and inexact.
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001'))
- Decimal("2.170")
+ Decimal('2.170')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01'))
- Decimal("2.17")
+ Decimal('2.17')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1'))
- Decimal("2.2")
+ Decimal('2.2')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0'))
- Decimal("2")
+ Decimal('2')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1'))
- Decimal("0E+1")
+ Decimal('0E+1')
>>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity'))
- Decimal("-Infinity")
+ Decimal('-Infinity')
>>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity'))
- Decimal("NaN")
+ Decimal('NaN')
>>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1'))
- Decimal("-0")
+ Decimal('-0')
>>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5'))
- Decimal("-0E+5")
+ Decimal('-0E+5')
>>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2'))
- Decimal("NaN")
+ Decimal('NaN')
>>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2'))
- Decimal("NaN")
+ Decimal('NaN')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1'))
- Decimal("217.0")
+ Decimal('217.0')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0'))
- Decimal("217")
+ Decimal('217')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1'))
- Decimal("2.2E+2")
+ Decimal('2.2E+2')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2'))
- Decimal("2E+2")
+ Decimal('2E+2')
"""
return a.quantize(b, context=self)
"""Just returns 10, as this is Decimal, :)
>>> ExtendedContext.radix()
- Decimal("10")
+ Decimal('10')
"""
return Decimal(10)
remainder cannot be calculated).
>>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3'))
- Decimal("2.1")
+ Decimal('2.1')
>>> ExtendedContext.remainder(Decimal('10'), Decimal('3'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.remainder(Decimal('-10'), Decimal('3'))
- Decimal("-1")
+ Decimal('-1')
>>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1'))
- Decimal("0.2")
+ Decimal('0.2')
>>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3'))
- Decimal("0.1")
+ Decimal('0.1')
>>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3'))
- Decimal("1.0")
+ Decimal('1.0')
"""
return a.__mod__(b, context=self)
remainder cannot be calculated).
>>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3'))
- Decimal("-0.9")
+ Decimal('-0.9')
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6'))
- Decimal("-2")
+ Decimal('-2')
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3'))
- Decimal("-1")
+ Decimal('-1')
>>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1'))
- Decimal("0.2")
+ Decimal('0.2')
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3'))
- Decimal("0.1")
+ Decimal('0.1')
>>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3'))
- Decimal("-0.3")
+ Decimal('-0.3')
"""
return a.remainder_near(b, context=self)
positive or to the right otherwise.
>>> ExtendedContext.rotate(Decimal('34'), Decimal('8'))
- Decimal("400000003")
+ Decimal('400000003')
>>> ExtendedContext.rotate(Decimal('12'), Decimal('9'))
- Decimal("12")
+ Decimal('12')
>>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2'))
- Decimal("891234567")
+ Decimal('891234567')
>>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0'))
- Decimal("123456789")
+ Decimal('123456789')
>>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2'))
- Decimal("345678912")
+ Decimal('345678912')
"""
return a.rotate(b, context=self)
"""Returns the first operand after adding the second value its exp.
>>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2'))
- Decimal("0.0750")
+ Decimal('0.0750')
>>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0'))
- Decimal("7.50")
+ Decimal('7.50')
>>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3'))
- Decimal("7.50E+3")
+ Decimal('7.50E+3')
"""
return a.scaleb (b, context=self)
coefficient are zeros.
>>> ExtendedContext.shift(Decimal('34'), Decimal('8'))
- Decimal("400000000")
+ Decimal('400000000')
>>> ExtendedContext.shift(Decimal('12'), Decimal('9'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2'))
- Decimal("1234567")
+ Decimal('1234567')
>>> ExtendedContext.shift(Decimal('123456789'), Decimal('0'))
- Decimal("123456789")
+ Decimal('123456789')
>>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2'))
- Decimal("345678900")
+ Decimal('345678900')
"""
return a.shift(b, context=self)
algorithm.
>>> ExtendedContext.sqrt(Decimal('0'))
- Decimal("0")
+ Decimal('0')
>>> ExtendedContext.sqrt(Decimal('-0'))
- Decimal("-0")
+ Decimal('-0')
>>> ExtendedContext.sqrt(Decimal('0.39'))
- Decimal("0.624499800")
+ Decimal('0.624499800')
>>> ExtendedContext.sqrt(Decimal('100'))
- Decimal("10")
+ Decimal('10')
>>> ExtendedContext.sqrt(Decimal('1'))
- Decimal("1")
+ Decimal('1')
>>> ExtendedContext.sqrt(Decimal('1.0'))
- Decimal("1.0")
+ Decimal('1.0')
>>> ExtendedContext.sqrt(Decimal('1.00'))
- Decimal("1.0")
+ Decimal('1.0')
>>> ExtendedContext.sqrt(Decimal('7'))
- Decimal("2.64575131")
+ Decimal('2.64575131')
>>> ExtendedContext.sqrt(Decimal('10'))
- Decimal("3.16227766")
+ Decimal('3.16227766')
>>> ExtendedContext.prec
9
"""
"""Return the difference between the two operands.
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07'))
- Decimal("0.23")
+ Decimal('0.23')
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30'))
- Decimal("0.00")
+ Decimal('0.00')
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07'))
- Decimal("-0.77")
+ Decimal('-0.77')
"""
return a.__sub__(b, context=self)
context.
>>> ExtendedContext.to_integral_exact(Decimal('2.1'))
- Decimal("2")
+ Decimal('2')
>>> ExtendedContext.to_integral_exact(Decimal('100'))
- Decimal("100")
+ Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('100.0'))
- Decimal("100")
+ Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('101.5'))
- Decimal("102")
+ Decimal('102')
>>> ExtendedContext.to_integral_exact(Decimal('-101.5'))
- Decimal("-102")
+ Decimal('-102')
>>> ExtendedContext.to_integral_exact(Decimal('10E+5'))
- Decimal("1.0E+6")
+ Decimal('1.0E+6')
>>> ExtendedContext.to_integral_exact(Decimal('7.89E+77'))
- Decimal("7.89E+77")
+ Decimal('7.89E+77')
>>> ExtendedContext.to_integral_exact(Decimal('-Inf'))
- Decimal("-Infinity")
+ Decimal('-Infinity')
"""
return a.to_integral_exact(context=self)
be set. The rounding mode is taken from the context.
>>> ExtendedContext.to_integral_value(Decimal('2.1'))
- Decimal("2")
+ Decimal('2')
>>> ExtendedContext.to_integral_value(Decimal('100'))
- Decimal("100")
+ Decimal('100')
>>> ExtendedContext.to_integral_value(Decimal('100.0'))
- Decimal("100")
+ Decimal('100')
>>> ExtendedContext.to_integral_value(Decimal('101.5'))
- Decimal("102")
+ Decimal('102')
>>> ExtendedContext.to_integral_value(Decimal('-101.5'))
- Decimal("-102")
+ Decimal('-102')
>>> ExtendedContext.to_integral_value(Decimal('10E+5'))
- Decimal("1.0E+6")
+ Decimal('1.0E+6')
>>> ExtendedContext.to_integral_value(Decimal('7.89E+77'))
- Decimal("7.89E+77")
+ Decimal('7.89E+77')
>>> ExtendedContext.to_integral_value(Decimal('-Inf'))
- Decimal("-Infinity")
+ Decimal('-Infinity')
"""
return a.to_integral_value(context=self)
"""
self = super(Fraction, cls).__new__(cls)
- if denominator == 1:
+ if not isinstance(numerator, int) and denominator == 1:
if isinstance(numerator, str):
# Handle construction from strings.
input = numerator
if m.group('sign') == '-':
numerator = -numerator
- elif (not isinstance(numerator, numbers.Integral) and
- isinstance(numerator, numbers.Rational)):
- # Handle copies from other rationals.
+ elif isinstance(numerator, numbers.Rational):
+ # Handle copies from other rationals. Integrals get
+ # caught here too, but it doesn't matter because
+ # denominator is already 1.
other_rational = numerator
numerator = other_rational.numerator
denominator = other_rational.denominator
- if (not isinstance(numerator, numbers.Integral) or
- not isinstance(denominator, numbers.Integral)):
- raise TypeError("Fraction(%(numerator)s, %(denominator)s):"
- " Both arguments must be integral." % locals())
-
if denominator == 0:
raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
+ numerator = numerator.__index__()
+ denominator = denominator.__index__()
g = gcd(numerator, denominator)
- self._numerator = int(numerator // g)
- self._denominator = int(denominator // g)
+ self._numerator = numerator // g
+ self._denominator = denominator // g
return self
@classmethod
else:
return cls(digits, 10 ** -exp)
- @classmethod
- def from_continued_fraction(cls, seq):
- 'Build a Fraction from a continued fraction expessed as a sequence'
- n, d = 1, 0
- for e in reversed(seq):
- n, d = d, n
- n += e * d
- return cls(n, d) if seq else cls(0)
-
- def as_continued_fraction(self):
- 'Return continued fraction expressed as a list'
- n = self.numerator
- d = self.denominator
- cf = []
- while d:
- e = int(n // d)
- cf.append(e)
- n -= e * d
- n, d = d, n
- return cf
-
- def approximate(self, max_denominator):
- 'Best rational approximation with a denominator <= max_denominator'
- # XXX First cut at algorithm
- # Still needs rounding rules as specified at
- # http://en.wikipedia.org/wiki/Continued_fraction
- if self.denominator <= max_denominator:
- return self
- cf = self.as_continued_fraction()
- result = Fraction(0)
- for i in range(1, len(cf)):
- new = self.from_continued_fraction(cf[:i])
- if new.denominator > max_denominator:
+ def limit_denominator(self, max_denominator=1000000):
+ """Closest Fraction to self with denominator at most max_denominator.
+
+ >>> Fraction('3.141592653589793').limit_denominator(10)
+ Fraction(22, 7)
+ >>> Fraction('3.141592653589793').limit_denominator(100)
+ Fraction(311, 99)
+ >>> Fraction(1234, 5678).limit_denominator(10000)
+ Fraction(1234, 5678)
+
+ """
+ # Algorithm notes: For any real number x, define a *best upper
+ # approximation* to x to be a rational number p/q such that:
+ #
+ # (1) p/q >= x, and
+ # (2) if p/q > r/s >= x then s > q, for any rational r/s.
+ #
+ # Define *best lower approximation* similarly. Then it can be
+ # proved that a rational number is a best upper or lower
+ # approximation to x if, and only if, it is a convergent or
+ # semiconvergent of the (unique shortest) continued fraction
+ # associated to x.
+ #
+ # To find a best rational approximation with denominator <= M,
+ # we find the best upper and lower approximations with
+ # denominator <= M and take whichever of these is closer to x.
+ # In the event of a tie, the bound with smaller denominator is
+ # chosen. If both denominators are equal (which can happen
+ # only when max_denominator == 1 and self is midway between
+ # two integers) the lower bound---i.e., the floor of self, is
+ # taken.
+
+ if max_denominator < 1:
+ raise ValueError("max_denominator should be at least 1")
+ if self._denominator <= max_denominator:
+ return Fraction(self)
+
+ p0, q0, p1, q1 = 0, 1, 1, 0
+ n, d = self._numerator, self._denominator
+ while True:
+ a = n//d
+ q2 = q0+a*q1
+ if q2 > max_denominator:
break
- result = new
- return result
+ p0, q0, p1, q1 = p1, q1, p0+a*p1, q2
+ n, d = d, n-a*d
+
+ k = (max_denominator-q0)//q1
+ bound1 = Fraction(p0+k*p1, q0+k*q1)
+ bound2 = Fraction(p1, q1)
+ if abs(bound2 - self) <= abs(bound1-self):
+ return bound2
+ else:
+ return bound1
@property
def numerator(a):
def __repr__(self):
"""repr(self)"""
- return ('Fraction(%r,%r)' % (self.numerator, self.denominator))
+ return ('Fraction(%r, %r)' % (self._numerator, self._denominator))
def __str__(self):
"""str(self)"""
- if self.denominator == 1:
- return str(self.numerator)
+ if self._denominator == 1:
+ return str(self._numerator)
else:
- return '%s/%s' % (self.numerator, self.denominator)
+ return '%s/%s' % (self._numerator, self._denominator)
def _operator_fallbacks(monomorphic_operator, fallback_operator):
"""Generates forward and reverse operators given a purely-rational
if b.denominator == 1:
power = b.numerator
if power >= 0:
- return Fraction(a.numerator ** power,
- a.denominator ** power)
+ return Fraction(a._numerator ** power,
+ a._denominator ** power)
else:
- return Fraction(a.denominator ** -power,
- a.numerator ** -power)
+ return Fraction(a._denominator ** -power,
+ a._numerator ** -power)
else:
# A fractional power will generally produce an
# irrational number.
def __rpow__(b, a):
"""a ** b"""
- if b.denominator == 1 and b.numerator >= 0:
+ if b._denominator == 1 and b._numerator >= 0:
# If a is an int, keep it that way if possible.
- return a ** b.numerator
+ return a ** b._numerator
if isinstance(a, numbers.Rational):
return Fraction(a.numerator, a.denominator) ** b
- if b.denominator == 1:
- return a ** b.numerator
+ if b._denominator == 1:
+ return a ** b._numerator
return a ** float(b)
def __pos__(a):
"""+a: Coerces a subclass instance to Fraction"""
- return Fraction(a.numerator, a.denominator)
+ return Fraction(a._numerator, a._denominator)
def __neg__(a):
"""-a"""
- return Fraction(-a.numerator, a.denominator)
+ return Fraction(-a._numerator, a._denominator)
def __abs__(a):
"""abs(a)"""
- return Fraction(abs(a.numerator), a.denominator)
+ return Fraction(abs(a._numerator), a._denominator)
def __trunc__(a):
"""trunc(a)"""
- if a.numerator < 0:
- return -(-a.numerator // a.denominator)
+ if a._numerator < 0:
+ return -(-a._numerator // a._denominator)
else:
- return a.numerator // a.denominator
+ return a._numerator // a._denominator
def __floor__(a):
"""Will be math.floor(a) in 3.0."""
"""
# XXX since this method is expensive, consider caching the result
- if self.denominator == 1:
+ if self._denominator == 1:
# Get integers right.
- return hash(self.numerator)
+ return hash(self._numerator)
# Expensive check, but definitely correct.
if self == float(self):
return hash(float(self))
else:
# Use tuple's hash to avoid a high collision rate on
# simple fractions.
- return hash((self.numerator, self.denominator))
+ return hash((self._numerator, self._denominator))
def __eq__(a, b):
"""a == b"""
if isinstance(b, numbers.Rational):
- return (a.numerator == b.numerator and
- a.denominator == b.denominator)
+ return (a._numerator == b.numerator and
+ a._denominator == b.denominator)
if isinstance(b, numbers.Complex) and b.imag == 0:
b = b.real
if isinstance(b, float):
def __bool__(a):
"""a != 0"""
- return a.numerator != 0
+ return a._numerator != 0
# support for pickling, copy, and deepcopy
def __copy__(self):
if type(self) == Fraction:
return self # I'm immutable; therefore I am my own clone
- return self.__class__(self.numerator, self.denominator)
+ return self.__class__(self._numerator, self._denominator)
def __deepcopy__(self, memo):
if type(self) == Fraction:
return self # My components are also immutable
- return self.__class__(self.numerator, self.denominator)
+ return self.__class__(self._numerator, self._denominator)
- Clean up EditorWindow close.
+- Patch 1693258: Fix for duplicate "preferences" menu-OS X. Backport of r56204.
+
+- OSX: Avoid crash for those versions of Tcl/Tk which don't have a console
+
+- Bug in idlelib.MultiCall: Options dialog was crashing IDLE if there was an
+ option in config-extensions w/o a value. Patch #1672481, Tal Einat
+
- Corrected some bugs in AutoComplete. Also, Page Up/Down in ACW implemented;
mouse and cursor selection in ACWindow implemented; double Tab inserts
current selection and closes ACW (similar to double-click and Return); scroll
# Inexact.register(decimal.Decimal)
-## Notes on Decimal and it how relates to the numeric tower
-## --------------------------------------------------------
-## Decimal is Real except that it does not support rich comparisons.
+## Notes on Decimal
+## ----------------
+## Decimal has all of the methods specified by the Real abc, but it should
+## not be registered as a Real because decimals do not interoperate with
+## binary floats.
##
## Decimal has some of the characteristics of Integrals. It provides
## logical operations but not as operators. The logical operations only apply
return +self
Real.register(float)
-# Real.register(decimal.Decimal)
class Rational(Real, Exact):
self.assertEqual(issubclass(C, A), True)
self.assertEqual(isinstance(c, A), True)
+ def test_isinstance_invalidation(self):
+ class A(metaclass=abc.ABCMeta):
+ pass
+ class B:
+ pass
+ b = B()
+ self.assertEqual(isinstance(b, A), False)
+ A.register(B)
+ self.assertEqual(isinstance(b, A), True)
+
def test_registration_builtins(self):
class A(metaclass=abc.ABCMeta):
pass
d = Decimal('15.32')
self.assertEqual(str(d), '15.32') # str
- self.assertEqual(repr(d), 'Decimal("15.32")') # repr
+ self.assertEqual(repr(d), "Decimal('15.32')") # repr
def test_tonum_methods(self):
#Test float, int and long methods.
import unittest
from copy import copy, deepcopy
from pickle import dumps, loads
-R = fractions.Fraction
+F = fractions.Fraction
gcd = fractions.gcd
self.fail("%s not raised" % exc_type.__name__)
def testInit(self):
- self.assertEquals((0, 1), _components(R()))
- self.assertEquals((7, 1), _components(R(7)))
- self.assertEquals((7, 3), _components(R(R(7, 3))))
+ self.assertEquals((0, 1), _components(F()))
+ self.assertEquals((7, 1), _components(F(7)))
+ self.assertEquals((7, 3), _components(F(F(7, 3))))
- self.assertEquals((-1, 1), _components(R(-1, 1)))
- self.assertEquals((-1, 1), _components(R(1, -1)))
- self.assertEquals((1, 1), _components(R(-2, -2)))
- self.assertEquals((1, 2), _components(R(5, 10)))
- self.assertEquals((7, 15), _components(R(7, 15)))
- self.assertEquals((10**23, 1), _components(R(10**23)))
+ self.assertEquals((-1, 1), _components(F(-1, 1)))
+ self.assertEquals((-1, 1), _components(F(1, -1)))
+ self.assertEquals((1, 1), _components(F(-2, -2)))
+ self.assertEquals((1, 2), _components(F(5, 10)))
+ self.assertEquals((7, 15), _components(F(7, 15)))
+ self.assertEquals((10**23, 1), _components(F(10**23)))
self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)",
- R, 12, 0)
- self.assertRaises(TypeError, R, 1.5)
- self.assertRaises(TypeError, R, 1.5 + 3j)
+ F, 12, 0)
+ self.assertRaises(AttributeError, F, 1.5)
+ self.assertRaises(AttributeError, F, 1.5 + 3j)
- self.assertRaises(TypeError, R, R(1, 2), 3)
- self.assertRaises(TypeError, R, "3/2", 3)
+ self.assertRaises(AttributeError, F, F(1, 2), 3)
+ self.assertRaises(AttributeError, F, "3/2", 3)
def testFromString(self):
- self.assertEquals((5, 1), _components(R("5")))
- self.assertEquals((3, 2), _components(R("3/2")))
- self.assertEquals((3, 2), _components(R(" \n +3/2")))
- self.assertEquals((-3, 2), _components(R("-3/2 ")))
- self.assertEquals((3, 2), _components(R(" 03/02 \n ")))
- self.assertEquals((3, 2), _components(R(" 03/02 \n ")))
- self.assertEquals((16, 5), _components(R(" 3.2 ")))
- self.assertEquals((-16, 5), _components(R(" -3.2 ")))
- self.assertEquals((-3, 1), _components(R(" -3. ")))
- self.assertEquals((3, 5), _components(R(" .6 ")))
+ self.assertEquals((5, 1), _components(F("5")))
+ self.assertEquals((3, 2), _components(F("3/2")))
+ self.assertEquals((3, 2), _components(F(" \n +3/2")))
+ self.assertEquals((-3, 2), _components(F("-3/2 ")))
+ self.assertEquals((13, 2), _components(F(" 013/02 \n ")))
+ self.assertEquals((16, 5), _components(F(" 3.2 ")))
+ self.assertEquals((-16, 5), _components(F(" -3.2 ")))
+ self.assertEquals((-3, 1), _components(F(" -3. ")))
+ self.assertEquals((3, 5), _components(F(" .6 ")))
self.assertRaisesMessage(
ZeroDivisionError, "Fraction(3, 0)",
- R, "3/0")
+ F, "3/0")
self.assertRaisesMessage(
ValueError, "Invalid literal for Fraction: 3/",
- R, "3/")
+ F, "3/")
self.assertRaisesMessage(
ValueError, "Invalid literal for Fraction: 3 /2",
- R, "3 /2")
+ F, "3 /2")
self.assertRaisesMessage(
# Denominators don't need a sign.
ValueError, "Invalid literal for Fraction: 3/+2",
- R, "3/+2")
+ F, "3/+2")
self.assertRaisesMessage(
# Imitate float's parsing.
ValueError, "Invalid literal for Fraction: + 3/2",
- R, "+ 3/2")
+ F, "+ 3/2")
self.assertRaisesMessage(
# Avoid treating '.' as a regex special character.
ValueError, "Invalid literal for Fraction: 3a2",
- R, "3a2")
+ F, "3a2")
self.assertRaisesMessage(
# Only parse ordinary decimals, not scientific form.
ValueError, "Invalid literal for Fraction: 3.2e4",
- R, "3.2e4")
+ F, "3.2e4")
self.assertRaisesMessage(
# Don't accept combinations of decimals and rationals.
ValueError, "Invalid literal for Fraction: 3/7.2",
- R, "3/7.2")
+ F, "3/7.2")
self.assertRaisesMessage(
# Don't accept combinations of decimals and rationals.
ValueError, "Invalid literal for Fraction: 3.2/7",
- R, "3.2/7")
+ F, "3.2/7")
self.assertRaisesMessage(
# Allow 3. and .3, but not .
ValueError, "Invalid literal for Fraction: .",
- R, ".")
+ F, ".")
def testImmutable(self):
- r = R(7, 3)
+ r = F(7, 3)
r.__init__(2, 15)
self.assertEquals((7, 3), _components(r))
r._denominator = 2
self.assertEquals((4, 2), _components(r))
# Which breaks some important operations:
- self.assertNotEquals(R(4, 2), r)
+ self.assertNotEquals(F(4, 2), r)
def testFromFloat(self):
self.assertRaisesMessage(
TypeError, "Fraction.from_float() only takes floats, not 3 (int)",
- R.from_float, 3)
+ F.from_float, 3)
- self.assertEquals((0, 1), _components(R.from_float(-0.0)))
- self.assertEquals((10, 1), _components(R.from_float(10.0)))
- self.assertEquals((-5, 2), _components(R.from_float(-2.5)))
+ self.assertEquals((0, 1), _components(F.from_float(-0.0)))
+ self.assertEquals((10, 1), _components(F.from_float(10.0)))
+ self.assertEquals((-5, 2), _components(F.from_float(-2.5)))
self.assertEquals((99999999999999991611392, 1),
- _components(R.from_float(1e23)))
- self.assertEquals(float(10**23), float(R.from_float(1e23)))
+ _components(F.from_float(1e23)))
+ self.assertEquals(float(10**23), float(F.from_float(1e23)))
self.assertEquals((3602879701896397, 1125899906842624),
- _components(R.from_float(3.2)))
- self.assertEquals(3.2, float(R.from_float(3.2)))
+ _components(F.from_float(3.2)))
+ self.assertEquals(3.2, float(F.from_float(3.2)))
inf = 1e1000
nan = inf - inf
self.assertRaisesMessage(
TypeError, "Cannot convert inf to Fraction.",
- R.from_float, inf)
+ F.from_float, inf)
self.assertRaisesMessage(
TypeError, "Cannot convert -inf to Fraction.",
- R.from_float, -inf)
+ F.from_float, -inf)
self.assertRaisesMessage(
TypeError, "Cannot convert nan to Fraction.",
- R.from_float, nan)
+ F.from_float, nan)
def testFromDecimal(self):
self.assertRaisesMessage(
TypeError,
"Fraction.from_decimal() only takes Decimals, not 3 (int)",
- R.from_decimal, 3)
- self.assertEquals(R(0), R.from_decimal(Decimal("-0")))
- self.assertEquals(R(5, 10), R.from_decimal(Decimal("0.5")))
- self.assertEquals(R(5, 1000), R.from_decimal(Decimal("5e-3")))
- self.assertEquals(R(5000), R.from_decimal(Decimal("5e3")))
- self.assertEquals(1 - R(1, 10**30),
- R.from_decimal(Decimal("0." + "9" * 30)))
+ F.from_decimal, 3)
+ self.assertEquals(F(0), F.from_decimal(Decimal("-0")))
+ self.assertEquals(F(5, 10), F.from_decimal(Decimal("0.5")))
+ self.assertEquals(F(5, 1000), F.from_decimal(Decimal("5e-3")))
+ self.assertEquals(F(5000), F.from_decimal(Decimal("5e3")))
+ self.assertEquals(1 - F(1, 10**30),
+ F.from_decimal(Decimal("0." + "9" * 30)))
self.assertRaisesMessage(
TypeError, "Cannot convert Infinity to Fraction.",
- R.from_decimal, Decimal("inf"))
+ F.from_decimal, Decimal("inf"))
self.assertRaisesMessage(
TypeError, "Cannot convert -Infinity to Fraction.",
- R.from_decimal, Decimal("-inf"))
+ F.from_decimal, Decimal("-inf"))
self.assertRaisesMessage(
TypeError, "Cannot convert NaN to Fraction.",
- R.from_decimal, Decimal("nan"))
+ F.from_decimal, Decimal("nan"))
self.assertRaisesMessage(
TypeError, "Cannot convert sNaN to Fraction.",
- R.from_decimal, Decimal("snan"))
-
- def testFromContinuedFraction(self):
- self.assertRaises(TypeError, R.from_continued_fraction, None)
- phi = R.from_continued_fraction([1]*100)
- self.assertEquals(round(phi - (1 + 5 ** 0.5) / 2, 10), 0.0)
-
- minusphi = R.from_continued_fraction([-1]*100)
- self.assertEquals(round(minusphi + (1 + 5 ** 0.5) / 2, 10), 0.0)
-
- self.assertEquals(R.from_continued_fraction([0]), R(0))
- self.assertEquals(R.from_continued_fraction([]), R(0))
-
- def testAsContinuedFraction(self):
- self.assertEqual(R.from_float(math.pi).as_continued_fraction()[:15],
- [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 3, 3])
- self.assertEqual(R.from_float(-math.pi).as_continued_fraction()[:16],
- [-4, 1, 6, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 3, 3])
- self.assertEqual(R(0).as_continued_fraction(), [0])
-
- def testApproximateFrom(self):
- self.assertEqual(R.from_float(math.pi).approximate(10000), R(355, 113))
- self.assertEqual(R.from_float(-math.pi).approximate(10000), R(-355, 113))
- self.assertEqual(R.from_float(0.0).approximate(10000), R(0))
+ F.from_decimal, Decimal("snan"))
+
+ def testLimitDenominator(self):
+ rpi = F('3.1415926535897932')
+ self.assertEqual(rpi.limit_denominator(10000), F(355, 113))
+ self.assertEqual(-rpi.limit_denominator(10000), F(-355, 113))
+ self.assertEqual(rpi.limit_denominator(113), F(355, 113))
+ self.assertEqual(rpi.limit_denominator(112), F(333, 106))
+ self.assertEqual(F(201, 200).limit_denominator(100), F(1))
+ self.assertEqual(F(201, 200).limit_denominator(101), F(102, 101))
+ self.assertEqual(F(0).limit_denominator(10000), F(0))
def testConversions(self):
- self.assertTypedEquals(-1, math.trunc(R(-11, 10)))
- self.assertTypedEquals(-2, math.floor(R(-11, 10)))
- self.assertTypedEquals(-1, math.ceil(R(-11, 10)))
- self.assertTypedEquals(-1, math.ceil(R(-10, 10)))
- self.assertTypedEquals(-1, int(R(-11, 10)))
-
- self.assertTypedEquals(0, round(R(-1, 10)))
- self.assertTypedEquals(0, round(R(-5, 10)))
- self.assertTypedEquals(-2, round(R(-15, 10)))
- self.assertTypedEquals(-1, round(R(-7, 10)))
-
- self.assertEquals(False, bool(R(0, 1)))
- self.assertEquals(True, bool(R(3, 2)))
- self.assertTypedEquals(0.1, float(R(1, 10)))
+ self.assertTypedEquals(-1, math.trunc(F(-11, 10)))
+ self.assertTypedEquals(-2, math.floor(F(-11, 10)))
+ self.assertTypedEquals(-1, math.ceil(F(-11, 10)))
+ self.assertTypedEquals(-1, math.ceil(F(-10, 10)))
+ self.assertTypedEquals(-1, int(F(-11, 10)))
+ self.assertTypedEquals(0, round(F(-1, 10)))
+ self.assertTypedEquals(0, round(F(-5, 10)))
+ self.assertTypedEquals(-2, round(F(-15, 10)))
+ self.assertTypedEquals(-1, round(F(-7, 10)))
+
+ self.assertEquals(False, bool(F(0, 1)))
+ self.assertEquals(True, bool(F(3, 2)))
+ self.assertTypedEquals(0.1, float(F(1, 10)))
# Check that __float__ isn't implemented by converting the
# numerator and denominator to float before dividing.
self.assertRaises(OverflowError, float, int('2'*400+'7'))
self.assertAlmostEquals(2.0/3,
- float(R(int('2'*400+'7'), int('3'*400+'1'))))
+ float(F(int('2'*400+'7'), int('3'*400+'1'))))
- self.assertTypedEquals(0.1+0j, complex(R(1,10)))
+ self.assertTypedEquals(0.1+0j, complex(F(1,10)))
def testRound(self):
- self.assertTypedEquals(R(-200), round(R(-150), -2))
- self.assertTypedEquals(R(-200), round(R(-250), -2))
- self.assertTypedEquals(R(30), round(R(26), -1))
- self.assertTypedEquals(R(-2, 10), round(R(-15, 100), 1))
- self.assertTypedEquals(R(-2, 10), round(R(-25, 100), 1))
+ self.assertTypedEquals(F(-200), round(F(-150), -2))
+ self.assertTypedEquals(F(-200), round(F(-250), -2))
+ self.assertTypedEquals(F(30), round(F(26), -1))
+ self.assertTypedEquals(F(-2, 10), round(F(-15, 100), 1))
+ self.assertTypedEquals(F(-2, 10), round(F(-25, 100), 1))
def testArithmetic(self):
- self.assertEquals(R(1, 2), R(1, 10) + R(2, 5))
- self.assertEquals(R(-3, 10), R(1, 10) - R(2, 5))
- self.assertEquals(R(1, 25), R(1, 10) * R(2, 5))
- self.assertEquals(R(1, 4), R(1, 10) / R(2, 5))
- self.assertTypedEquals(2, R(9, 10) // R(2, 5))
- self.assertTypedEquals(10**23, R(10**23, 1) // R(1))
- self.assertEquals(R(2, 3), R(-7, 3) % R(3, 2))
- self.assertEquals(R(8, 27), R(2, 3) ** R(3))
- self.assertEquals(R(27, 8), R(2, 3) ** R(-3))
- self.assertTypedEquals(2.0, R(4) ** R(1, 2))
- z = pow(R(-1), R(1, 2))
+ self.assertEquals(F(1, 2), F(1, 10) + F(2, 5))
+ self.assertEquals(F(-3, 10), F(1, 10) - F(2, 5))
+ self.assertEquals(F(1, 25), F(1, 10) * F(2, 5))
+ self.assertEquals(F(1, 4), F(1, 10) / F(2, 5))
+ self.assertTypedEquals(2, F(9, 10) // F(2, 5))
+ self.assertTypedEquals(10**23, F(10**23, 1) // F(1))
+ self.assertEquals(F(2, 3), F(-7, 3) % F(3, 2))
+ self.assertEquals(F(8, 27), F(2, 3) ** F(3))
+ self.assertEquals(F(27, 8), F(2, 3) ** F(-3))
+ self.assertTypedEquals(2.0, F(4) ** F(1, 2))
+ z = pow(F(-1), F(1, 2))
self.assertAlmostEquals(z.real, 0)
self.assertEquals(z.imag, 1)
def testMixedArithmetic(self):
- self.assertTypedEquals(R(11, 10), R(1, 10) + 1)
- self.assertTypedEquals(1.1, R(1, 10) + 1.0)
- self.assertTypedEquals(1.1 + 0j, R(1, 10) + (1.0 + 0j))
- self.assertTypedEquals(R(11, 10), 1 + R(1, 10))
- self.assertTypedEquals(1.1, 1.0 + R(1, 10))
- self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + R(1, 10))
-
- self.assertTypedEquals(R(-9, 10), R(1, 10) - 1)
- self.assertTypedEquals(-0.9, R(1, 10) - 1.0)
- self.assertTypedEquals(-0.9 + 0j, R(1, 10) - (1.0 + 0j))
- self.assertTypedEquals(R(9, 10), 1 - R(1, 10))
- self.assertTypedEquals(0.9, 1.0 - R(1, 10))
- self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - R(1, 10))
-
- self.assertTypedEquals(R(1, 10), R(1, 10) * 1)
- self.assertTypedEquals(0.1, R(1, 10) * 1.0)
- self.assertTypedEquals(0.1 + 0j, R(1, 10) * (1.0 + 0j))
- self.assertTypedEquals(R(1, 10), 1 * R(1, 10))
- self.assertTypedEquals(0.1, 1.0 * R(1, 10))
- self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * R(1, 10))
-
- self.assertTypedEquals(R(1, 10), R(1, 10) / 1)
- self.assertTypedEquals(0.1, R(1, 10) / 1.0)
- self.assertTypedEquals(0.1 + 0j, R(1, 10) / (1.0 + 0j))
- self.assertTypedEquals(R(10, 1), 1 / R(1, 10))
- self.assertTypedEquals(10.0, 1.0 / R(1, 10))
- self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / R(1, 10))
-
- self.assertTypedEquals(0, R(1, 10) // 1)
- self.assertTypedEquals(0, R(1, 10) // 1.0)
- self.assertTypedEquals(10, 1 // R(1, 10))
- self.assertTypedEquals(10**23, 10**22 // R(1, 10))
- self.assertTypedEquals(10, 1.0 // R(1, 10))
-
- self.assertTypedEquals(R(1, 10), R(1, 10) % 1)
- self.assertTypedEquals(0.1, R(1, 10) % 1.0)
- self.assertTypedEquals(R(0, 1), 1 % R(1, 10))
- self.assertTypedEquals(0.0, 1.0 % R(1, 10))
+ self.assertTypedEquals(F(11, 10), F(1, 10) + 1)
+ self.assertTypedEquals(1.1, F(1, 10) + 1.0)
+ self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j))
+ self.assertTypedEquals(F(11, 10), 1 + F(1, 10))
+ self.assertTypedEquals(1.1, 1.0 + F(1, 10))
+ self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10))
+
+ self.assertTypedEquals(F(-9, 10), F(1, 10) - 1)
+ self.assertTypedEquals(-0.9, F(1, 10) - 1.0)
+ self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j))
+ self.assertTypedEquals(F(9, 10), 1 - F(1, 10))
+ self.assertTypedEquals(0.9, 1.0 - F(1, 10))
+ self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10))
+
+ self.assertTypedEquals(F(1, 10), F(1, 10) * 1)
+ self.assertTypedEquals(0.1, F(1, 10) * 1.0)
+ self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j))
+ self.assertTypedEquals(F(1, 10), 1 * F(1, 10))
+ self.assertTypedEquals(0.1, 1.0 * F(1, 10))
+ self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10))
+
+ self.assertTypedEquals(F(1, 10), F(1, 10) / 1)
+ self.assertTypedEquals(0.1, F(1, 10) / 1.0)
+ self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j))
+ self.assertTypedEquals(F(10, 1), 1 / F(1, 10))
+ self.assertTypedEquals(10.0, 1.0 / F(1, 10))
+ self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10))
+
+ self.assertTypedEquals(0, F(1, 10) // 1)
+ self.assertTypedEquals(0, F(1, 10) // 1.0)
+ self.assertTypedEquals(10, 1 // F(1, 10))
+ self.assertTypedEquals(10**23, 10**22 // F(1, 10))
+ self.assertTypedEquals(10, 1.0 // F(1, 10))
+
+ self.assertTypedEquals(F(1, 10), F(1, 10) % 1)
+ self.assertTypedEquals(0.1, F(1, 10) % 1.0)
+ self.assertTypedEquals(F(0, 1), 1 % F(1, 10))
+ self.assertTypedEquals(0.0, 1.0 % F(1, 10))
# No need for divmod since we don't override it.
# ** has more interesting conversion rules.
- self.assertTypedEquals(R(100, 1), R(1, 10) ** -2)
- self.assertTypedEquals(R(100, 1), R(10, 1) ** 2)
- self.assertTypedEquals(0.1, R(1, 10) ** 1.0)
- self.assertTypedEquals(0.1 + 0j, R(1, 10) ** (1.0 + 0j))
- self.assertTypedEquals(4 , 2 ** R(2, 1))
- z = pow(-1, R(1, 2))
+ self.assertTypedEquals(F(100, 1), F(1, 10) ** -2)
+ self.assertTypedEquals(F(100, 1), F(10, 1) ** 2)
+ self.assertTypedEquals(0.1, F(1, 10) ** 1.0)
+ self.assertTypedEquals(0.1 + 0j, F(1, 10) ** (1.0 + 0j))
+ self.assertTypedEquals(4 , 2 ** F(2, 1))
+ z = pow(-1, F(1, 2))
self.assertAlmostEquals(0, z.real)
self.assertEquals(1, z.imag)
- self.assertTypedEquals(R(1, 4) , 2 ** R(-2, 1))
- self.assertTypedEquals(2.0 , 4 ** R(1, 2))
- self.assertTypedEquals(0.25, 2.0 ** R(-2, 1))
- self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** R(1, 10))
+ self.assertTypedEquals(F(1, 4) , 2 ** F(-2, 1))
+ self.assertTypedEquals(2.0 , 4 ** F(1, 2))
+ self.assertTypedEquals(0.25, 2.0 ** F(-2, 1))
+ self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10))
def testMixingWithDecimal(self):
# Decimal refuses mixed comparisons.
self.assertRaisesMessage(
TypeError,
"unsupported operand type(s) for +: 'Fraction' and 'Decimal'",
- operator.add, R(3,11), Decimal('3.1415926'))
- self.assertNotEquals(R(5, 2), Decimal('2.5'))
+ operator.add, F(3,11), Decimal('3.1415926'))
+ self.assertNotEquals(F(5, 2), Decimal('2.5'))
def testComparisons(self):
- self.assertTrue(R(1, 2) < R(2, 3))
- self.assertFalse(R(1, 2) < R(1, 2))
- self.assertTrue(R(1, 2) <= R(2, 3))
- self.assertTrue(R(1, 2) <= R(1, 2))
- self.assertFalse(R(2, 3) <= R(1, 2))
- self.assertTrue(R(1, 2) == R(1, 2))
- self.assertFalse(R(1, 2) == R(1, 3))
- self.assertFalse(R(1, 2) != R(1, 2))
- self.assertTrue(R(1, 2) != R(1, 3))
+ self.assertTrue(F(1, 2) < F(2, 3))
+ self.assertFalse(F(1, 2) < F(1, 2))
+ self.assertTrue(F(1, 2) <= F(2, 3))
+ self.assertTrue(F(1, 2) <= F(1, 2))
+ self.assertFalse(F(2, 3) <= F(1, 2))
+ self.assertTrue(F(1, 2) == F(1, 2))
+ self.assertFalse(F(1, 2) == F(1, 3))
+ self.assertFalse(F(1, 2) != F(1, 2))
+ self.assertTrue(F(1, 2) != F(1, 3))
def testMixedLess(self):
- self.assertTrue(2 < R(5, 2))
- self.assertFalse(2 < R(4, 2))
- self.assertTrue(R(5, 2) < 3)
- self.assertFalse(R(4, 2) < 2)
+ self.assertTrue(2 < F(5, 2))
+ self.assertFalse(2 < F(4, 2))
+ self.assertTrue(F(5, 2) < 3)
+ self.assertFalse(F(4, 2) < 2)
- self.assertTrue(R(1, 2) < 0.6)
- self.assertFalse(R(1, 2) < 0.4)
- self.assertTrue(0.4 < R(1, 2))
- self.assertFalse(0.5 < R(1, 2))
+ self.assertTrue(F(1, 2) < 0.6)
+ self.assertFalse(F(1, 2) < 0.4)
+ self.assertTrue(0.4 < F(1, 2))
+ self.assertFalse(0.5 < F(1, 2))
def testMixedLessEqual(self):
- self.assertTrue(0.5 <= R(1, 2))
- self.assertFalse(0.6 <= R(1, 2))
- self.assertTrue(R(1, 2) <= 0.5)
- self.assertFalse(R(1, 2) <= 0.4)
- self.assertTrue(2 <= R(4, 2))
- self.assertFalse(2 <= R(3, 2))
- self.assertTrue(R(4, 2) <= 2)
- self.assertFalse(R(5, 2) <= 2)
+ self.assertTrue(0.5 <= F(1, 2))
+ self.assertFalse(0.6 <= F(1, 2))
+ self.assertTrue(F(1, 2) <= 0.5)
+ self.assertFalse(F(1, 2) <= 0.4)
+ self.assertTrue(2 <= F(4, 2))
+ self.assertFalse(2 <= F(3, 2))
+ self.assertTrue(F(4, 2) <= 2)
+ self.assertFalse(F(5, 2) <= 2)
def testBigFloatComparisons(self):
# Because 10**23 can't be represented exactly as a float:
- self.assertFalse(R(10**23) == float(10**23))
+ self.assertFalse(F(10**23) == float(10**23))
# The first test demonstrates why these are important.
- self.assertFalse(1e23 < float(R(math.trunc(1e23) + 1)))
- self.assertTrue(1e23 < R(math.trunc(1e23) + 1))
- self.assertFalse(1e23 <= R(math.trunc(1e23) - 1))
- self.assertTrue(1e23 > R(math.trunc(1e23) - 1))
- self.assertFalse(1e23 >= R(math.trunc(1e23) + 1))
+ self.assertFalse(1e23 < float(F(math.trunc(1e23) + 1)))
+ self.assertTrue(1e23 < F(math.trunc(1e23) + 1))
+ self.assertFalse(1e23 <= F(math.trunc(1e23) - 1))
+ self.assertTrue(1e23 > F(math.trunc(1e23) - 1))
+ self.assertFalse(1e23 >= F(math.trunc(1e23) + 1))
def testBigComplexComparisons(self):
- self.assertFalse(R(10**23) == complex(10**23))
- self.assertTrue(R(10**23) > complex(10**23))
- self.assertFalse(R(10**23) <= complex(10**23))
+ self.assertFalse(F(10**23) == complex(10**23))
+ self.assertTrue(F(10**23) > complex(10**23))
+ self.assertFalse(F(10**23) <= complex(10**23))
def testMixedEqual(self):
- self.assertTrue(0.5 == R(1, 2))
- self.assertFalse(0.6 == R(1, 2))
- self.assertTrue(R(1, 2) == 0.5)
- self.assertFalse(R(1, 2) == 0.4)
- self.assertTrue(2 == R(4, 2))
- self.assertFalse(2 == R(3, 2))
- self.assertTrue(R(4, 2) == 2)
- self.assertFalse(R(5, 2) == 2)
+ self.assertTrue(0.5 == F(1, 2))
+ self.assertFalse(0.6 == F(1, 2))
+ self.assertTrue(F(1, 2) == 0.5)
+ self.assertFalse(F(1, 2) == 0.4)
+ self.assertTrue(2 == F(4, 2))
+ self.assertFalse(2 == F(3, 2))
+ self.assertTrue(F(4, 2) == 2)
+ self.assertFalse(F(5, 2) == 2)
def testStringification(self):
- self.assertEquals("Fraction(7,3)", repr(R(7, 3)))
- self.assertEquals("7/3", str(R(7, 3)))
- self.assertEquals("7", str(R(7, 1)))
+ self.assertEquals("Fraction(7, 3)", repr(F(7, 3)))
+ self.assertEquals("7/3", str(F(7, 3)))
+ self.assertEquals("7", str(F(7, 1)))
def testHash(self):
- self.assertEquals(hash(2.5), hash(R(5, 2)))
- self.assertEquals(hash(10**50), hash(R(10**50)))
- self.assertNotEquals(hash(float(10**23)), hash(R(10**23)))
+ self.assertEquals(hash(2.5), hash(F(5, 2)))
+ self.assertEquals(hash(10**50), hash(F(10**50)))
+ self.assertNotEquals(hash(float(10**23)), hash(F(10**23)))
def testApproximatePi(self):
# Algorithm borrowed from
# http://docs.python.org/lib/decimal-recipes.html
- three = R(3)
+ three = F(3)
lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24
- while abs(s - lasts) > R(1, 10**9):
+ while abs(s - lasts) > F(1, 10**9):
lasts = s
n, na = n+na, na+8
d, da = d+da, da+32
def testApproximateCos1(self):
# Algorithm borrowed from
# http://docs.python.org/lib/decimal-recipes.html
- x = R(1)
- i, lasts, s, fact, num, sign = 0, 0, R(1), 1, 1, 1
- while abs(s - lasts) > R(1, 10**9):
+ x = F(1)
+ i, lasts, s, fact, num, sign = 0, 0, F(1), 1, 1, 1
+ while abs(s - lasts) > F(1, 10**9):
lasts = s
i += 2
fact *= i * (i-1)
self.assertAlmostEquals(math.cos(1), s)
def test_copy_deepcopy_pickle(self):
- r = R(13, 7)
+ r = F(13, 7)
self.assertEqual(r, loads(dumps(r)))
self.assertEqual(id(r), id(copy(r)))
self.assertEqual(id(r), id(deepcopy(r)))
*/
return Py_BuildValue(
"ddddd",
- (double)(kernel.dwHighDateTime*429.4967296 +
- kernel.dwLowDateTime*1e-7),
(double)(user.dwHighDateTime*429.4967296 +
user.dwLowDateTime*1e-7),
+ (double)(kernel.dwHighDateTime*429.4967296 +
+ kernel.dwLowDateTime*1e-7),
(double)0,
(double)0,
(double)0);
#! /bin/sh
-# From configure.in Revision: 60489 .
+# From configure.in Revision: 60552 .
# Guess values for system-dependent variables and create Makefiles.
# Generated by GNU Autoconf 2.61 for python 3.0.
#
Optional Features:
--disable-FEATURE do not include FEATURE (same as --enable-FEATURE=no)
--enable-FEATURE[=ARG] include FEATURE [ARG=yes]
- --enable-universalsdk[SDKDIR]
+ --enable-universalsdk[=SDKDIR]
Build against Mac OS X 10.4u SDK (ppc/i386)
--enable-framework[=INSTALLDIR]
Build (MacOSX|Darwin) framework
CONFIG_ARGS="$ac_configure_args"
AC_ARG_ENABLE(universalsdk,
- AC_HELP_STRING(--enable-universalsdk@<:@SDKDIR@:>@, Build against Mac OS X 10.4u SDK (ppc/i386)),
+ AC_HELP_STRING(--enable-universalsdk@<:@=SDKDIR@:>@, Build against Mac OS X 10.4u SDK (ppc/i386)),
[
case $enableval in
yes)
projects / python / commitdiff