Issue #7947: Clarify math module behaviour for IEEE 754 special cases, along

with a number of additional minor edits and typo corrections.

Doc/library/math.rst

@@ -33,8 +33,8 @@ Number-theoretic and representation functions
 
 .. function:: copysign(x, y)
 
-   Return *x* with the sign of *y*. ``copysign`` copies the sign bit of an IEEE
-   754 float, ``copysign(1, -0.0)`` returns *-1.0*.
+   Return *x* with the sign of *y*.  On a platform that supports
+   signed zeros, ``copysign(1.0, -0.0)`` returns *-1.0*.
 
    .. versionadded:: 2.6
 
@@ -109,17 +109,15 @@ Number-theoretic and representation functions
 
 .. function:: isinf(x)
 
-   Checks if the float *x* is positive or negative infinite.
+   Check if the float *x* is positive or negative infinity.
 
    .. versionadded:: 2.6
 
 
 .. function:: isnan(x)
 
-   Checks if the float *x* is a NaN (not a number). NaNs are part of the
-   IEEE 754 standards. Operation like but not limited to ``inf * 0``,
-   ``inf / inf`` or any operation involving a NaN, e.g. ``nan * 1``, return
-   a NaN.
+   Check if the float *x* is a NaN (not a number).  For more information
+   on NaNs, see the IEEE 754 standards.
 
    .. versionadded:: 2.6
 
@@ -247,7 +245,7 @@ Trigonometric functions
    The vector in the plane from the origin to point ``(x, y)`` makes this angle
    with the positive X axis. The point of :func:`atan2` is that the signs of both
    inputs are known to it, so it can compute the correct quadrant for the angle.
-   For example, ``atan(1``) and ``atan2(1, 1)`` are both ``pi/4``, but ``atan2(-1,
+   For example, ``atan(1)`` and ``atan2(1, 1)`` are both ``pi/4``, but ``atan2(-1,
    -1)`` is ``-3*pi/4``.
 
 
@@ -361,35 +359,35 @@ Constants
 
 .. data:: pi
 
-   The mathematical constant *pi*.
+   The mathematical constant π = 3.141592..., to available precision.
 
 
 .. data:: e
 
-   The mathematical constant *e*.
+   The mathematical constant e = 2.718281..., to available precision.
 
 
 .. impl-detail::
 
    The :mod:`math` module consists mostly of thin wrappers around the platform C
-   math library functions.  Behavior in exceptional cases is loosely specified
-   by the C standards, and Python inherits much of its math-function
-   error-reporting behavior from the platform C implementation.  As a result,
-   the specific exceptions raised in error cases (and even whether some
-   arguments are considered to be exceptional at all) are not defined in any
-   useful cross-platform or cross-release way.  For example, whether
-   ``math.log(0)`` returns ``-Inf`` or raises :exc:`ValueError` or
-   :exc:`OverflowError` isn't defined, and in cases where ``math.log(0)`` raises
-   :exc:`OverflowError`, ``math.log(0L)`` may raise :exc:`ValueError` instead.
+   math library functions.  Behavior in exceptional cases follows Annex F of
+   the C99 standard where appropriate.  The current implementation will raise
+   :exc:`ValueError` for invalid operations like ``sqrt(-1.0)`` or ``log(0.0)``
+   (where C99 Annex F recommends signaling invalid operation or divide-by-zero),
+   and :exc:`OverflowError` for results that overflow (for example,
+   ``exp(1000.0)``).  A *NaN* will not be returned from any of the functions
+   above unless one or more of the input arguments was a *NaN*; in that case,
+   most functions will return a *NaN*, but (again following C99 Annex F) there
+   are some exceptions to this rule, for example ``pow(float('nan'), 0.0)`` or
+   ``hypot(float('nan'), float('inf'))``.
 
-   All functions return a quiet *NaN* if at least one of the args is *NaN*.
-   Signaling *NaN*\s raise an exception. The exception type still depends on the
-   platform and libm implementation. It's usually :exc:`ValueError` for *EDOM*
-   and :exc:`OverflowError` for errno *ERANGE*.
+   Note that Python makes no effort to distinguish signaling nans from
+   quiet nans, and behavior for signaling nans remains unspecified.
+   Typical behavior is to treat all nans as though they were quiet.
 
    .. versionchanged:: 2.6
-      In earlier versions of Python the outcome of an operation with NaN as
-      input depended on platform and libm implementation.
+      Behavior in special cases now aims to follow C99 Annex F.  In earlier
+      versions of Python the behavior in special cases was loosely specified.
 
 
 .. seealso::