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........
  r60752 | mark.dickinson | 2008-02-12 22:31:59 +0100 (Tue, 12 Feb 2008) | 5 lines

  Implementation of Fraction.limit_denominator.

  Remove Fraction.to_continued_fraction and
  Fraction.from_continued_fraction
........
  r60754 | mark.dickinson | 2008-02-12 22:40:53 +0100 (Tue, 12 Feb 2008) | 3 lines

  Revert change in r60712:  turn alternate constructors back into
  classmethods instead of staticmethods.
........
  r60755 | mark.dickinson | 2008-02-12 22:46:54 +0100 (Tue, 12 Feb 2008) | 4 lines

  Replace R=fractions.Fraction with F=fractions.Fraction in
  test_fractions.py.  This should have been part of the name
  change from Rational to Fraction.
........
  r60758 | georg.brandl | 2008-02-13 08:20:22 +0100 (Wed, 13 Feb 2008) | 3 lines

  #2063: correct order of utime and stime in os.times()
  result on Windows.
........
  r60762 | jeffrey.yasskin | 2008-02-13 18:58:04 +0100 (Wed, 13 Feb 2008) | 7 lines

  Working on issue #1762: Brought
    ./python.exe -m timeit -s 'from fractions import Fraction; f = Fraction(3, 2)' 'isinstance(3, Fraction); isinstance(f, Fraction)'
  from 12.3 usec/loop to 3.44 usec/loop and
    ./python.exe -m timeit -s 'from fractions import Fraction' 'Fraction(3, 2)'
  from 48.8 usec to 23.6 usec by avoiding genexps and sets in __instancecheck__
  and inlining the common case from __subclasscheck__.
........
  r60765 | brett.cannon | 2008-02-13 20:15:44 +0100 (Wed, 13 Feb 2008) | 5 lines

  Fix --enable-universalsdk and its comment line so that zsh's flag completion
  works.

  Thanks to Jeroen Ruigrok van der Werven for the fix.
........
  r60771 | kurt.kaiser | 2008-02-14 01:08:55 +0100 (Thu, 14 Feb 2008) | 2 lines

  Bring NEWS.txt up to date from check-in msgs.
........
  r60772 | raymond.hettinger | 2008-02-14 02:08:02 +0100 (Thu, 14 Feb 2008) | 3 lines

  Update notes on Decimal.
........
  r60773 | raymond.hettinger | 2008-02-14 03:41:22 +0100 (Thu, 14 Feb 2008) | 1 line

  Fix decimal repr which should have used single quotes like other reprs.
........
  r60785 | jeffrey.yasskin | 2008-02-14 07:12:24 +0100 (Thu, 14 Feb 2008) | 11 lines

  Performance optimizations on Fraction's constructor.

    ./python.exe -m timeit -s 'from fractions import Fraction' 'Fraction(3)`
  31.7 usec/loop -> 9.2 usec/loop

    ./python.exe -m timeit -s 'from fractions import Fraction' 'Fraction(3, 2)'`
  27.7 usec/loop -> 9.32 usec/loop

    ./python.exe -m timeit -s 'from fractions import Fraction; f = Fraction(3, 2)' 'Fraction(f)'
  31.9 usec/loop -> 14.3 usec/loop
........
  r60786 | jeffrey.yasskin | 2008-02-14 08:49:25 +0100 (Thu, 14 Feb 2008) | 5 lines

  Change simple instances (in Fraction) of self.numerator and self.denominator to
  self._numerator and self._denominator. This speeds abs() up from 12.2us to
  10.8us and trunc() from 2.07us to 1.11us. This doesn't change _add and friends
  because they're more complicated.
........
This commit is contained in:
Christian Heimes 2008-02-14 08:27:37 +00:00
parent 9d0d616c3b
commit 68f5fbe944
14 changed files with 675 additions and 627 deletions
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182
Doc/library/decimal.rst
View file

@ -46,10 +46,10 @@ arithmetic. It offers several advantages over the :class:`float` datatype:
>>> 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
@ -128,19 +128,19 @@ representation error). Decimal numbers include special values such as
: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
@ -148,28 +148,28 @@ operations. ::
>>> 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'
@ -180,31 +180,31 @@ floating point flying circus::
>>> 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
@ -222,16 +222,16 @@ enabled::
>>> 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)
@ -248,7 +248,7 @@ using the :meth:`clear_flags` method. ::
>>> 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=[])
@ -261,7 +261,7 @@ Individual traps are set using the dictionary in the :attr:`traps` field of a
context::
>>> Decimal(1) / Decimal(0)
Decimal("Infinity")
Decimal('Infinity')
>>> getcontext().traps[DivisionByZero] = 1
>>> Decimal(1) / Decimal(0)
Traceback (most recent call last):
@ -289,7 +289,7 @@ Decimal objects
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::
@ -307,11 +307,11 @@ Decimal objects
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
@ -338,7 +338,7 @@ also have a number of specialized methods:
.. 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.
@ -367,10 +367,10 @@ also have a number of specialized methods:
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])
@ -389,14 +389,14 @@ also have a number of specialized methods:
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.
@ -428,8 +428,8 @@ also have a number of specialized methods:
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.
@ -442,9 +442,9 @@ also have a number of specialized methods:
: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])
@ -453,7 +453,7 @@ also have a number of specialized methods:
the intermediate product self*other.
>>> Decimal(2).fma(3, 5)
Decimal("11")
Decimal('11')
.. method:: Decimal.is_canonical()
@ -537,9 +537,9 @@ also have a number of specialized methods:
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])
@ -620,10 +620,10 @@ also have a number of specialized methods:
.. 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])
@ -648,8 +648,8 @@ also have a number of specialized methods:
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
@ -680,7 +680,7 @@ also have a number of specialized methods:
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*.
@ -732,7 +732,7 @@ also have a number of specialized methods:
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]])
@ -937,10 +937,10 @@ method. For example, ``C.exp(x)`` is equivalent to
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
@ -1195,15 +1195,15 @@ properties of addition::
>>> 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::
@ -1211,15 +1211,15 @@ 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
@ -1275,7 +1275,7 @@ normalized floating point representations, it is not immediately obvious that
the following calculation returns a value equal to zero::
>>> 1 / Decimal('Infinity')
Decimal("0E-1000000026")
Decimal('0E-1000000026')
.. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -1486,7 +1486,7 @@ minimize typing when using the interactive interpreter?
>>> 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
@ -1498,14 +1498,14 @@ the :const:`Inexact` trap is set, it is also useful for validation::
>>> 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
@ -1527,7 +1527,7 @@ representative::
>>> 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?
@ -1555,7 +1555,7 @@ suggest, so we trap :const:`Inexact` to signal a need for more precision::
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?
@ -1564,7 +1564,7 @@ decimal floating point. Also, its use requires some care to avoid the
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.
@ -1585,20 +1585,20 @@ results can look odd if you forget that the inputs haven't been rounded::
>>> 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')

18
Doc/library/fractions.rst
View file

@ -46,6 +46,24 @@ Rational number class.
: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

2
Doc/library/os.rst
View file

@ -1584,7 +1584,7 @@ written in Python, such as a mail server's external command delivery program.
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()