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-\section{\module{math} ---
-         Mathematical functions}
-
-\declaremodule{builtin}{math}
-\modulesynopsis{Mathematical functions (\function{sin()} etc.).}
-
-This module is always available.  It provides access to the
-mathematical functions defined by the C standard.
-
-These functions cannot be used with complex numbers; use the functions
-of the same name from the \refmodule{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:
-
-\begin{funcdesc}{ceil}{x}
-Return the ceiling of \var{x} as a float, the smallest integer value
-greater than or equal to \var{x}.
-\end{funcdesc}
-
-\begin{funcdesc}{fabs}{x}
-Return the absolute value of \var{x}.
-\end{funcdesc}
-
-\begin{funcdesc}{floor}{x}
-Return the floor of \var{x} as a float, the largest integer value
-less than or equal to \var{x}.
-\end{funcdesc}
-
-\begin{funcdesc}{fmod}{x, y}
-Return \code{fmod(\var{x}, \var{y})}, as defined by the platform C library.
-Note that the Python expression \code{\var{x} \%\ \var{y}} may not return
-the same result.  The intent of the C standard is that
-\code{fmod(\var{x}, \var{y})} be exactly (mathematically; to infinite
-precision) equal to \code{\var{x} - \var{n}*\var{y}} for some integer
-\var{n} such that the result has the same sign as \var{x} and
-magnitude less than \code{abs(\var{y})}.  Python's
-\code{\var{x} \%\ \var{y}} returns a result with the sign of
-\var{y} instead, and may not be exactly computable for float arguments.
-For example, \code{fmod(-1e-100, 1e100)} is \code{-1e-100}, but the
-result of Python's \code{-1e-100 \%\ 1e100} is \code{1e100-1e-100}, which
-cannot be represented exactly as a float, and rounds to the surprising
-\code{1e100}.  For this reason, function \function{fmod()} is generally
-preferred when working with floats, while Python's
-\code{\var{x} \%\ \var{y}} is preferred when working with integers.
-\end{funcdesc}
-
-\begin{funcdesc}{frexp}{x}
-Return the mantissa and exponent of \var{x} as the pair
-\code{(\var{m}, \var{e})}.  \var{m} is a float and \var{e} is an
-integer such that \code{\var{x} == \var{m} * 2**\var{e}} exactly.
-If \var{x} is zero, returns \code{(0.0, 0)}, otherwise
-\code{0.5 <= abs(\var{m}) < 1}.  This is used to "pick apart" the
-internal representation of a float in a portable way.
-\end{funcdesc}
-
-\begin{funcdesc}{ldexp}{x, i}
-Return \code{\var{x} * (2**\var{i})}.  This is essentially the inverse of
-function \function{frexp()}.
-\end{funcdesc}
-
-\begin{funcdesc}{modf}{x}
-Return the fractional and integer parts of \var{x}.  Both results
-carry the sign of \var{x}, and both are floats.
-\end{funcdesc}
-
-Note that \function{frexp()} and \function{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 \function{ceil()}, \function{floor()}, and \function{modf()}
-functions, note that \emph{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 \var{x} with \code{abs(\var{x}) >= 2**52}
-necessarily has no fractional bits.
-
-
-Power and logarithmic functions:
-
-\begin{funcdesc}{exp}{x}
-Return \code{e**\var{x}}.
-\end{funcdesc}
-
-\begin{funcdesc}{log}{x\optional{, base}}
-Return the logarithm of \var{x} to the given \var{base}.
-If the \var{base} is not specified, return the natural logarithm of \var{x}
-(that is, the logarithm to base \emph{e}).
-\versionchanged[\var{base} argument added]{2.3}
-\end{funcdesc}
-
-\begin{funcdesc}{log10}{x}
-Return the base-10 logarithm of \var{x}.
-\end{funcdesc}
-
-\begin{funcdesc}{pow}{x, y}
-Return \code{\var{x}**\var{y}}.
-\end{funcdesc}
-
-\begin{funcdesc}{sqrt}{x}
-Return the square root of \var{x}.
-\end{funcdesc}
-
-Trigonometric functions:
-
-\begin{funcdesc}{acos}{x}
-Return the arc cosine of \var{x}, in radians.
-\end{funcdesc}
-
-\begin{funcdesc}{asin}{x}
-Return the arc sine of \var{x}, in radians.
-\end{funcdesc}
-
-\begin{funcdesc}{atan}{x}
-Return the arc tangent of \var{x}, in radians.
-\end{funcdesc}
-
-\begin{funcdesc}{atan2}{y, x}
-Return \code{atan(\var{y} / \var{x})}, in radians.
-The result is between \code{-pi} and \code{pi}.
-The vector in the plane from the origin to point \code{(\var{x}, \var{y})}
-makes this angle with the positive X axis.
-The point of \function{atan2()} is that the signs of both inputs are
-known to it, so it can compute the correct quadrant for the angle.
-For example, \code{atan(1}) and \code{atan2(1, 1)} are both \code{pi/4},
-but \code{atan2(-1, -1)} is \code{-3*pi/4}.
-\end{funcdesc}
-
-\begin{funcdesc}{cos}{x}
-Return the cosine of \var{x} radians.
-\end{funcdesc}
-
-\begin{funcdesc}{hypot}{x, y}
-Return the Euclidean norm, \code{sqrt(\var{x}*\var{x} + \var{y}*\var{y})}.
-This is the length of the vector from the origin to point
-\code{(\var{x}, \var{y})}.
-\end{funcdesc}
-
-\begin{funcdesc}{sin}{x}
-Return the sine of \var{x} radians.
-\end{funcdesc}
-
-\begin{funcdesc}{tan}{x}
-Return the tangent of \var{x} radians.
-\end{funcdesc}
-
-Angular conversion:
-
-\begin{funcdesc}{degrees}{x}
-Converts angle \var{x} from radians to degrees.
-\end{funcdesc}
-
-\begin{funcdesc}{radians}{x}
-Converts angle \var{x} from degrees to radians.
-\end{funcdesc}
-
-Hyperbolic functions:
-
-\begin{funcdesc}{cosh}{x}
-Return the hyperbolic cosine of \var{x}.
-\end{funcdesc}
-
-\begin{funcdesc}{sinh}{x}
-Return the hyperbolic sine of \var{x}.
-\end{funcdesc}
-
-\begin{funcdesc}{tanh}{x}
-Return the hyperbolic tangent of \var{x}.
-\end{funcdesc}
-
-The module also defines two mathematical constants:
-
-\begin{datadesc}{pi}
-The mathematical constant \emph{pi}.
-\end{datadesc}
-
-\begin{datadesc}{e}
-The mathematical constant \emph{e}.
-\end{datadesc}
-
-\begin{notice}
-  The \module{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
-  \code{math.log(0)} returns \code{-Inf} or raises \exception{ValueError} or
-  \exception{OverflowError} isn't defined, and in
-  cases where \code{math.log(0)} raises \exception{OverflowError},
-  \code{math.log(0L)} may raise \exception{ValueError} instead.
-\end{notice}
-
-\begin{seealso}
-  \seemodule{cmath}{Complex number versions of many of these functions.}
-\end{seealso}