Removed Exact/Inexact after discussion with Yasskin.

Unlike Scheme where exactness is implemented as taints, the Python
implementation associated exactness with data types.  This created
inheritance issues (making an exact subclass of floats would result
in the subclass having both an explicit Exact registration and an
inherited Inexact registration).  This was a problem for the
decimal module which was designed to span both exact and inexact
arithmetic.  There was also a question of use cases and no examples
were found where ABCs for exactness could be used to improve code.
One other issue was having separate tags for both the affirmative
and negative cases.  This is at odds with the approach taken
elsewhere in the Python (i.e. we don't have an ABC both Hashable
and Unhashable).

diff --git a/Lib/numbers.py b/Lib/numbers.py
index b6de8acf0eb54d05941f4dcf3c1eb3c0d54ab036..7fb61b04e769b275c3a856094363cb617e02d8cc 100644 (file)
--- a/Lib/numbers.py
+++ b/Lib/numbers.py
@@ -8,10 +8,7 @@ TODO: Fill out more detailed documentation on the operators."""
 from __future__ import division
 from abc import ABCMeta, abstractmethod, abstractproperty
 
-__all__ = ["Number", "Exact", "Inexact",
-           "Complex", "Real", "Rational", "Integral",
-           ]
-
+__all__ = ["Number", "Complex", "Real", "Rational", "Integral"]
 
 class Number(object):
     """All numbers inherit from this class.
@@ -22,60 +19,13 @@ class Number(object):
     __metaclass__ = ABCMeta
 
 
-class Exact(Number):
-    """Operations on instances of this type are exact.
-
-    As long as the result of a homogenous operation is of the same
-    type, you can assume that it was computed exactly, and there are
-    no round-off errors. Laws like commutativity and associativity
-    hold.
-    """
-
-Exact.register(int)
-Exact.register(long)
-
-
-class Inexact(Number):
-    """Operations on instances of this type are inexact.
-
-    Given X, an instance of Inexact, it is possible that (X + -X) + 3
-    == 3, but X + (-X + 3) == 0. The exact form this error takes will
-    vary by type, but it's generally unsafe to compare this type for
-    equality.
-    """
-
-Inexact.register(complex)
-Inexact.register(float)
-# Inexact.register(decimal.Decimal)
-
-
 ## 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
-## to a subset of decimals (those that are non-negative, have a zero exponent,
-## and have digits that are only 0 or 1).  It does provide __long__() and
-## a three argument form of __pow__ that includes exactness guarantees.
-## It does not provide an __index__() method.
-##
-## Depending on context, decimal operations may be exact or inexact.
-##
-## When decimal is run in a context with small precision and automatic rounding,
-## it is Inexact.  See the "Floating point notes" section of the decimal docs
-## for an example of losing the associative and distributive properties of
-## addition.
-##
-## When decimal is used for high precision integer arithmetic, it is Exact.
-## When the decimal used as fixed-point, it is Exact.
-## When it is run with sufficient precision, it is Exact.
-## When the decimal.Inexact trap is set, decimal operations are Exact.
-## For an example, see the float_to_decimal() recipe in the "Decimal FAQ"
-## section of the docs -- it shows an how traps are used in conjunction
-## with variable precision to reliably achieve exact results.
+## binary floats (i.e.  Decimal('3.14') + 2.71828 is undefined).  But,
+## abstract reals are expected to interoperate (i.e. R1 + R2 should be
+## expected to work if R1 and R2 are both Reals).
 
 class Complex(Number):
     """Complex defines the operations that work on the builtin complex type.

diff --git a/Lib/test/test_abstract_numbers.py b/Lib/test/test_abstract_numbers.py
index 0c1f28db05ec20c7d6f05cc211f1713b52dcc91e..034fb52a43aa501a8e5a7a6c1766475824fe3ddb 100644 (file)
--- a/Lib/test/test_abstract_numbers.py
+++ b/Lib/test/test_abstract_numbers.py
@@ -4,7 +4,6 @@ import math
 import operator
 import unittest
 from numbers import Complex, Real, Rational, Integral
-from numbers import Exact, Inexact
 from numbers import Number
 from test import test_support
 
@@ -12,8 +11,6 @@ class TestNumbers(unittest.TestCase):
     def test_int(self):
         self.failUnless(issubclass(int, Integral))
         self.failUnless(issubclass(int, Complex))
-        self.failUnless(issubclass(int, Exact))
-        self.failIf(issubclass(int, Inexact))
 
         self.assertEqual(7, int(7).real)
         self.assertEqual(0, int(7).imag)
@@ -24,8 +21,6 @@ class TestNumbers(unittest.TestCase):
     def test_long(self):
         self.failUnless(issubclass(long, Integral))
         self.failUnless(issubclass(long, Complex))
-        self.failUnless(issubclass(long, Exact))
-        self.failIf(issubclass(long, Inexact))
 
         self.assertEqual(7, long(7).real)
         self.assertEqual(0, long(7).imag)
@@ -36,8 +31,6 @@ class TestNumbers(unittest.TestCase):
     def test_float(self):
         self.failIf(issubclass(float, Rational))
         self.failUnless(issubclass(float, Real))
-        self.failIf(issubclass(float, Exact))
-        self.failUnless(issubclass(float, Inexact))
 
         self.assertEqual(7.3, float(7.3).real)
         self.assertEqual(0, float(7.3).imag)
@@ -46,8 +39,6 @@ class TestNumbers(unittest.TestCase):
     def test_complex(self):
         self.failIf(issubclass(complex, Real))
         self.failUnless(issubclass(complex, Complex))
-        self.failIf(issubclass(complex, Exact))
-        self.failUnless(issubclass(complex, Inexact))
 
         c1, c2 = complex(3, 2), complex(4,1)
         # XXX: This is not ideal, but see the comment in math_trunc().