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