Move description of math module changes; various edits to description of cmath changes

Doc/whatsnew/2.6.rst

@@ -1292,11 +1292,42 @@ Here are all of the changes that Python 2.6 makes to the core Python language.
   :func:`isnan`, return true if their floating-point argument is
   infinite or Not A Number.  (:issue:`1640`)
 
-  The ``math.copysign(x, y)`` function
-  copies the sign bit of an IEEE 754 number, returning the absolute
-  value of *x* combined with the sign bit of *y*.  For example,
-  ``math.copysign(1, -0.0)`` returns -1.0.  (Contributed by Christian
-  Heimes.)
+* The :mod:`math` module has seven new functions, and the existing
+  functions have been improved to give more consistent behaviour
+  across platforms, especially with respect to handling of
+  floating-point exceptions and IEEE 754 special values.
+  The new functions are: 
+
+  * :func:`isinf` and :func:`isnan` determine whether a given float is
+    a (positive or negative) infinity or a NaN (Not a Number),
+    respectively. 
+
+  * ``copysign(x, y)`` copies the sign bit of an IEEE 754 number,
+    returning the absolute value of *x* combined with the sign bit of
+    *y*.  For example, ``math.copysign(1, -0.0)`` returns -1.0.
+    (Contributed by Christian Heimes.)
+
+  * The inverse hyperbolic functions :func:`acosh`, :func:`asinh` and
+    :func:`atanh`.
+
+  * The function :func:`log1p`, returning the natural logarithm of
+    *1+x* (base *e*).
+
+  There's also a new :func:`trunc` function as a result of the
+  backport of `PEP 3141's type hierarchy for numbers <#pep-3141>`__.
+
+  The existing math functions have been modified to follow the
+  recommendations of the C99 standard with respect to special values
+  whenever possible.  For example, ``sqrt(-1.)`` should now give a
+  :exc:`ValueError` across (nearly) all platforms, while
+  ``sqrt(float('NaN'))`` should return a NaN on all IEEE 754
+  platforms.  Where Annex 'F' of the C99 standard recommends signaling
+  'divide-by-zero' or 'invalid', Python will raise :exc:`ValueError`.
+  Where Annex 'F' of the C99 standard recommends signaling 'overflow',
+  Python will raise :exc:`OverflowError`.  (See :issue:`711019`,
+  :issue:`1640`.)
+
+  (Contributed by Christian Heimes and Mark Dickinson.)
 
 * Changes to the :class:`Exception` interface
   as dictated by :pep:`352` continue to be made.  For 2.6, 
@@ -1415,33 +1446,40 @@ complete list of changes, or look through the CVS logs for all the details.
   available, instead of restricting itself to protocol 1.
   (Contributed by W. Barnes; :issue:`1551443`.)
 
-* The :mod:`cmath` module has gained five new functions: :func:`polar`
-  converts a complex number to polar form, returning the modulus and
-  argument of that complex number. :func:`rect` does the opposite,
-  turning a (modulus, argument) pair back into the corresponding
-  complex number. :func:`phase` returns the phase or argument of a
-  complex number.  :func:`isnan` returns True if either the real or
-  imaginary part of its argument is a NaN.  :func:`isinf` returns True
-  if either the real or imaginary part of its argument is infinite.
+* The :mod:`cmath` module underwent an extensive set of revisions,
+  thanks to Mark Dickinson and Christian Heimes, that added some new
+  features and greatly improved the accuracy of the computations.
 
-  The :mod:`cmath` module is no longer numerically unsound. (See
-  :issue:`1381`): for all functions, the real and imaginary parts of
-  the results are accurate to within a few ulps, whenever possible.
+  Five new functions were added: 
 
-  The branch cuts for :func:`asinh`, :func:`atanh`: and :func:`atan`
-  have been corrected.
+  * :func:`polar` converts a complex number to polar form, returning
+    the modulus and argument of that complex number. 
 
-  The tests for the :mod:`cmath` module have been greatly expanded.  A
-  set of nearly 2000 new testcases provides tests for the algebraic
-  functions.
+  * :func:`rect` does the opposite, turning a (modulus, argument) pair
+    back into the corresponding complex number.
+
+  * :func:`phase` returns the phase or argument of a complex number.  
+
+  * :func:`isnan` returns True if either
+    the real or imaginary part of its argument is a NaN.  
+
+  * :func:`isinf` returns True if either the real or imaginary part of
+    its argument is infinite.
+
+  The revisions also improved the numerical soundness of the
+  :mod:`cmath` module.  For all functions, the real and imaginary
+  parts of the results are accurate to within a few units of least
+  precision (ulps) whenever possible.  See :issue:`1381` for the
+  details.  The branch cuts for :func:`asinh`, :func:`atanh`: and
+  :func:`atan` have also been corrected.
+
+  The tests for the module have been greatly expanded; nearly 2000 new
+  test cases exercise the algebraic functions.
 
   On IEEE 754 platforms, the :mod:`cmath` module now handles IEEE 754
   special values and floating-point exceptions in a manner consistent
   with Annex 'G' of the C99 standard.
 
-  (Updates to :mod:`cmath` contributed by Mark Dickinson and Christian
-  Heimes.)
-
 * A new data type in the :mod:`collections` module: :class:`namedtuple(typename,
   fieldnames)` is a factory function that creates subclasses of the standard tuple
   whose fields are accessible by name as well as index.  For example::
@@ -1678,30 +1716,6 @@ complete list of changes, or look through the CVS logs for all the details.
   :func:`macostools.touched` function to be removed because it depended on the
   :mod:`macfs` module.  (:issue:`1490190`)
 
-* The :mod:`math` module has seven new functions, and the existing
-  functions have been improved to give more consistent behaviour
-  across platforms, especially with respect to handling of
-  floating-point exceptions and IEEE 754 special values.
-
-  The new functions are: :func:`isinf` and :func:`isnan`, which
-  determine whether a given float is a (positive or negative) infinity
-  or a NaN (Not a Number), respectively; :func:`copysign`; the inverse
-  hyperbolic functions :func:`acosh`, :func:`asinh` and :func:`atanh`;
-  and the function :func:`log1p`.  (There's also a new function
-  :func:`trunc` as a result of the backport of PEP 3141; see above.)
-
-  The existing math functions have been modified to follow the
-  recommendations of the C99 standard with respect to special values
-  whenever possible.  For example, sqrt(-1.) should now give a
-  ValueError across (nearly) all platforms, while sqrt(float('NaN'))
-  should return a NaN on all IEEE 754 platforms.  Where Annex 'F' of
-  the C99 standard recommends signaling 'divide-by-zero' or 'invalid',
-  Python will raise ValueError.  Where Annex 'F' of the C99 standard
-  recommends signaling 'overflow', Python will raise OverflowError.
-  (See :issue:`711019`, :issue:`1640`.)
-
-  (Contributed by Christian Heimes and Mark Dickinson.)
-
 * :class:`mmap` objects now have a :meth:`rfind` method that finds
   a substring, beginning at the end of the string and searching
   backwards.  The :meth:`find` method