--- rest25/library/math.rst	2008-12-19 16:58:08.000000000 +0900
+++ rest262/library/math.rst	2009-04-05 05:02:09.000000000 +0900
@@ -12,122 +12,209 @@
 These functions cannot be used with complex numbers; use the functions of the
 same name from the :mod:`cmath` module if you require support for complex
 numbers.  The distinction between functions which support complex numbers and
 those which don't is made since most users do not want to learn quite as much
 mathematics as required to understand complex numbers.  Receiving an exception
 instead of a complex result allows earlier detection of the unexpected complex
 number used as a parameter, so that the programmer can determine how and why it
 was generated in the first place.
 
 The following functions are provided by this module.  Except when explicitly
 noted otherwise, all return values are floats.
 
-Number-theoretic and representation functions:
 
+Number-theoretic and representation functions
+---------------------------------------------
 
 .. function:: ceil(x)
 
    Return the ceiling of *x* as a float, the smallest integer value greater than or
    equal to *x*.
 
 
+.. 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*.
+
+   .. versionadded:: 2.6
+
+
 .. function:: fabs(x)
 
    Return the absolute value of *x*.
 
 
+.. function:: factorial(x)
+
+   Return *x* factorial.  Raises :exc:`ValueError` if *x* is not integral or
+   is negative.
+
+   .. versionadded:: 2.6
+
+
 .. function:: floor(x)
 
    Return the floor of *x* as a float, the largest integer value less than or equal
    to *x*.
 
+   .. versionchanged:: 2.6
+      Added :meth:`__floor__` delegation.
+
 
 .. function:: fmod(x, y)
 
    Return ``fmod(x, y)``, as defined by the platform C library. Note that the
    Python expression ``x % y`` may not return the same result.  The intent of the C
    standard is that ``fmod(x, y)`` be exactly (mathematically; to infinite
    precision) equal to ``x - n*y`` for some integer *n* such that the result has
    the same sign as *x* and magnitude less than ``abs(y)``.  Python's ``x % y``
    returns a result with the sign of *y* instead, and may not be exactly computable
    for float arguments. For example, ``fmod(-1e-100, 1e100)`` is ``-1e-100``, but
    the result of Python's ``-1e-100 % 1e100`` is ``1e100-1e-100``, which cannot be
    represented exactly as a float, and rounds to the surprising ``1e100``.  For
    this reason, function :func:`fmod` is generally preferred when working with
    floats, while Python's ``x % y`` is preferred when working with integers.
 
 
 .. function:: frexp(x)
 
    Return the mantissa and exponent of *x* as the pair ``(m, e)``.  *m* is a float
    and *e* is an integer such that ``x == m * 2**e`` exactly. If *x* is zero,
    returns ``(0.0, 0)``, otherwise ``0.5 <= abs(m) < 1``.  This is used to "pick
    apart" the internal representation of a float in a portable way.
 
 
+.. function:: fsum(iterable)
+
+   Return an accurate floating point sum of values in the iterable.  Avoids
+   loss of precision by tracking multiple intermediate partial sums::
+
+        >>> sum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
+        0.99999999999999989
+        >>> fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
+        1.0
+
+   The algorithm's accuracy depends on IEEE-754 arithmetic guarantees and the
+   typical case where the rounding mode is half-even.  On some non-Windows
+   builds, the underlying C library uses extended precision addition and may
+   occasionally double-round an intermediate sum causing it to be off in its
+   least significant bit.
+
+   For further discussion and two alternative approaches, see the `ASPN cookbook
+   recipes for accurate floating point summation
+   <http://code.activestate.com/recipes/393090/>`_\.
+
+   .. versionadded:: 2.6
+
+
+.. function:: isinf(x)
+
+   Checks if the float *x* is positive or negative infinite.
+
+   .. 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.
+
+   .. versionadded:: 2.6
+
+
 .. function:: ldexp(x, i)
 
    Return ``x * (2**i)``.  This is essentially the inverse of function
    :func:`frexp`.
 
 
 .. function:: modf(x)
 
-   Return the fractional and integer parts of *x*.  Both results carry the sign of
-   *x*, and both are floats.
+   Return the fractional and integer parts of *x*.  Both results carry the sign
+   of *x* and are floats.
+
+
+.. function:: trunc(x)
+
+   Return the :class:`Real` value *x* truncated to an :class:`Integral` (usually
+   a long integer). Delegates to ``x.__trunc__()``.
+
+   .. versionadded:: 2.6
+
 
 Note that :func:`frexp` and :func:`modf` have a different call/return pattern
 than their C equivalents: they take a single argument and return a pair of
 values, rather than returning their second return value through an 'output
 parameter' (there is no such thing in Python).
 
 For the :func:`ceil`, :func:`floor`, and :func:`modf` functions, note that *all*
 floating-point numbers of sufficiently large magnitude are exact integers.
 Python floats typically carry no more than 53 bits of precision (the same as the
 platform C double type), in which case any float *x* with ``abs(x) >= 2**52``
 necessarily has no fractional bits.
 
-Power and logarithmic functions:
 
+Power and logarithmic functions
+-------------------------------
 
 .. function:: exp(x)
 
    Return ``e**x``.
 
 
 .. function:: log(x[, base])
 
    Return the logarithm of *x* to the given *base*. If the *base* is not specified,
    return the natural logarithm of *x* (that is, the logarithm to base *e*).
 
    .. versionchanged:: 2.3
       *base* argument added.
 
 
+.. function:: log1p(x)
+
+   Return the natural logarithm of *1+x* (base *e*). The
+   result is calculated in a way which is accurate for *x* near zero.
+
+   .. versionadded:: 2.6
+
+
 .. function:: log10(x)
 
    Return the base-10 logarithm of *x*.
 
 
 .. function:: pow(x, y)
 
-   Return ``x**y``.
+   Return ``x`` raised to the power ``y``.  Exceptional cases follow
+   Annex 'F' of the C99 standard as far as possible.  In particular,
+   ``pow(1.0, x)`` and ``pow(x, 0.0)`` always return ``1.0``, even
+   when ``x`` is a zero or a NaN.  If both ``x`` and ``y`` are finite,
+   ``x`` is negative, and ``y`` is not an integer then ``pow(x, y)``
+   is undefined, and raises :exc:`ValueError`.
+
+   .. versionchanged:: 2.6
+      The outcome of ``1**nan`` and ``nan**0`` was undefined.
 
 
 .. function:: sqrt(x)
 
    Return the square root of *x*.
 
-Trigonometric functions:
 
+Trigonometric functions
+-----------------------
 
 .. function:: acos(x)
 
    Return the arc cosine of *x*, in radians.
 
 
 .. function:: asin(x)
 
    Return the arc sine of *x*, in radians.
 
 
 .. function:: atan(x)
@@ -156,72 +243,105 @@
    from the origin to point ``(x, y)``.
 
 
 .. function:: sin(x)
 
    Return the sine of *x* radians.
 
 
 .. function:: tan(x)
 
    Return the tangent of *x* radians.
 
-Angular conversion:
 
+Angular conversion
+------------------
 
 .. function:: degrees(x)
 
    Converts angle *x* from radians to degrees.
 
 
 .. function:: radians(x)
 
    Converts angle *x* from degrees to radians.
 
-Hyperbolic functions:
+
+Hyperbolic functions
+--------------------
+
+.. function:: acosh(x)
+
+   Return the inverse hyperbolic cosine of *x*.
+
+   .. versionadded:: 2.6
+
+
+.. function:: asinh(x)
+
+   Return the inverse hyperbolic sine of *x*.
+
+   .. versionadded:: 2.6
+
+
+.. function:: atanh(x)
+
+   Return the inverse hyperbolic tangent of *x*.
+
+   .. versionadded:: 2.6
 
 
 .. function:: cosh(x)
 
    Return the hyperbolic cosine of *x*.
 
 
 .. function:: sinh(x)
 
    Return the hyperbolic sine of *x*.
 
 
 .. function:: tanh(x)
 
    Return the hyperbolic tangent of *x*.
 
-The module also defines two mathematical constants:
 
+Constants
+---------
 
 .. data:: pi
 
    The mathematical constant *pi*.
 
 
 .. data:: e
 
    The mathematical constant *e*.
 
+
 .. note::
 
    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 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.
+
+   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*.
+
+   .. versionchanged:: 2.6
+      In earlier versions of Python the outcome of an operation with NaN as
+      input depended on platform and libm implementation.
 
 
 .. seealso::
 
    Module :mod:`cmath`
       Complex number versions of many of these functions.
-
