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authorFred Drake <fdrake@acm.org>1998-05-07 01:49:07 (GMT)
committerFred Drake <fdrake@acm.org>1998-05-07 01:49:07 (GMT)
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-\section{Built-in Module \module{mpz}}
-\label{module-mpz}
-\bimodindex{mpz}
-
-This is an optional module. It is only available when Python is
-configured to include it, which requires that the GNU MP software is
-installed.
-\index{MP, GNU library}
-\index{arbitrary precision integers}
-\index{integer!arbitrary precision}
-
-This module implements the interface to part of the GNU MP library,
-which defines arbitrary precision integer and rational number
-arithmetic routines. Only the interfaces to the \emph{integer}
-(\function{mpz_*()}) routines are provided. If not stated
-otherwise, the description in the GNU MP documentation can be applied.
-
-In general, \dfn{mpz}-numbers can be used just like other standard
-Python numbers, e.g.\ you can use the built-in operators like \code{+},
-\code{*}, etc., as well as the standard built-in functions like
-\function{abs()}, \function{int()}, \ldots, \function{divmod()},
-\function{pow()}. \strong{Please note:} the \emph{bitwise-xor}
-operation has been implemented as a bunch of \emph{and}s,
-\emph{invert}s and \emph{or}s, because the library lacks an
-\cfunction{mpz_xor()} function, and I didn't need one.
-
-You create an mpz-number by calling the function \function{mpz()} (see
-below for an exact description). An mpz-number is printed like this:
-\code{mpz(\var{value})}.
-
-
-\begin{funcdesc}{mpz}{value}
- Create a new mpz-number. \var{value} can be an integer, a long,
- another mpz-number, or even a string. If it is a string, it is
- interpreted as an array of radix-256 digits, least significant digit
- first, resulting in a positive number. See also the \method{binary()}
- method, described below.
-\end{funcdesc}
-
-\begin{datadesc}{MPZType}
- The type of the objects returned by \function{mpz()} and most other
- functions in this module.
-\end{datadesc}
-
-
-A number of \emph{extra} functions are defined in this module. Non
-mpz-arguments are converted to mpz-values first, and the functions
-return mpz-numbers.
-
-\begin{funcdesc}{powm}{base, exponent, modulus}
- Return \code{pow(\var{base}, \var{exponent}) \%{} \var{modulus}}. If
- \code{\var{exponent} == 0}, return \code{mpz(1)}. In contrast to the
- \C{} library function, this version can handle negative exponents.
-\end{funcdesc}
-
-\begin{funcdesc}{gcd}{op1, op2}
- Return the greatest common divisor of \var{op1} and \var{op2}.
-\end{funcdesc}
-
-\begin{funcdesc}{gcdext}{a, b}
- Return a tuple \code{(\var{g}, \var{s}, \var{t})}, such that
- \code{\var{a}*\var{s} + \var{b}*\var{t} == \var{g} == gcd(\var{a}, \var{b})}.
-\end{funcdesc}
-
-\begin{funcdesc}{sqrt}{op}
- Return the square root of \var{op}. The result is rounded towards zero.
-\end{funcdesc}
-
-\begin{funcdesc}{sqrtrem}{op}
- Return a tuple \code{(\var{root}, \var{remainder})}, such that
- \code{\var{root}*\var{root} + \var{remainder} == \var{op}}.
-\end{funcdesc}
-
-\begin{funcdesc}{divm}{numerator, denominator, modulus}
- Returns a number \var{q} such that
- \code{\var{q} * \var{denominator} \%{} \var{modulus} ==
- \var{numerator}}. One could also implement this function in Python,
- using \function{gcdext()}.
-\end{funcdesc}
-
-An mpz-number has one method:
-
-\begin{methoddesc}[mpz]{binary}{}
- Convert this mpz-number to a binary string, where the number has been
- stored as an array of radix-256 digits, least significant digit first.
-
- The mpz-number must have a value greater than or equal to zero,
- otherwise \exception{ValueError} will be raised.
-\end{methoddesc}