Index: library/functions.rst
===================================================================
--- library/functions.rst	(revision 86636)
+++ library/functions.rst	(working copy)
@@ -399,27 +399,37 @@
 
 .. function:: float([x])
 
-   Convert a string or a number to floating point.  If the argument is a string,
-   it must contain a possibly signed decimal or floating point number, possibly
-   embedded in whitespace. The argument may also be ``'[+|-]nan'`` or
-   ``'[+|-]inf'``.  Otherwise, the argument may be an integer or a floating
+   .. index::
+      single: NaN
+      single: Infinity
+
+   Convert a string or a number to floating point.
+
+   If the argument is a string, it should contain a decimal number, optionally
+   preceded by a sign, and optionally embedded in whitespace.  The optional
+   sign may be ``'+'`` or ``'-'``; a ``'+'`` sign has no effect on the value
+   produced.  The argument may also be a string representing a NaN
+   (not-a-number), or a positive or negative infinity.  More precisely, the
+   input must conform to the following grammar after leading and trailing
+   whitespace characters are removed:
+
+   .. productionlist::
+      sign: "+" | "-"
+      infinity: "Infinity" | "inf"
+      nan: "nan"
+      numeric-value: `floatnumber` | `infinity` | `nan`
+      numeric-string: [`sign`] `numeric-value`
+
+   Here ``floatnumber`` is the form of a Python floating-point literal,
+   described in :ref:`floating`.  Case is not significant, so, for example,
+   "inf", "Inf", "INFINITY" and "iNfINity" are all acceptable spellings for
+   positive infinity.
+
+   Otherwise, the argument may be an integer or a floating
    point number, and a floating point number with the same value (within
    Python's floating point precision) is returned.  If no argument is given,
    ``0.0`` is returned.
 
-   .. note::
-
-      .. index::
-         single: NaN
-         single: Infinity
-
-      When passing in a string, values for NaN and Infinity may be returned,
-      depending on the underlying C library.  Float accepts the strings
-      ``'nan'``, ``'inf'`` and ``'-inf'`` for NaN and positive or negative
-      infinity.  The case and a leading + are ignored as well as a leading - is
-      ignored for NaN.  Float always represents NaN and infinity as ``nan``,
-      ``inf`` or ``-inf``.
-
    The float type is described in :ref:`typesnumeric`.
 
 .. function:: format(value[, format_spec])