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diff --git a/Doc/libmpz.tex b/Doc/libmpz.tex new file mode 100644 index 0000000..ea0d1b7 --- /dev/null +++ b/Doc/libmpz.tex @@ -0,0 +1,74 @@ +\section{Built-in module \sectcode{mpz}} +\bimodindex{mpz} + +This module implements the interface to part of the GNU MP library. +This library contains arbitrary precision integer and rational number +arithmetic routines. Only the interfaces to the \emph{integer} +(\samp{mpz_{\rm \ldots}}) 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 +\code{abs}, \code{int}, \ldots, \code{divmod}, \code{pow}. +\strong{Please note:} the {\it bitwise-xor} operation has been implemented as +a bunch of {\it and}s, {\it invert}s and {\it or}s, because the library +lacks an \code{mpz_xor} function, and I didn't need one. + +You create an mpz-number, by calling the function called \code{mpz} (see +below for an excact description). An mpz-number is printed like this: +\code{mpz(\var{value})}. + +\renewcommand{\indexsubitem}{(in module mpz)} +\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 \code{binary} + method, described below. +\end{funcdesc} + +A number of {\em 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 \code{gcdext}. +\end{funcdesc} + +An mpz-number has one method: + +\renewcommand{\indexsubitem}{(mpz method)} +\begin{funcdesc}{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 a \code{ValueError}-exception will be raised. +\end{funcdesc} |