Variable Precision Integer Arithmetic
19 Jan 2009
31 Jul 2013)
Arithmetic with integers of fully arbitrary size. Arrays and vectors of vpi numbers are supported.
function [Q,R] = quotient(numerator,denominator)
% quotient: divides two integers, computing a quotient and remainder
% usage: [Q,R] = quotient(numerator,denominator);
% quotient is used by the rdivide and rem functions.
% When numerator and/or demonimator represent negative
% numbers, then the quotient and remainders will be
% consistent with the signs that / and rem would return.
% Specifically, when numerator and denominator have
% signs as given below, then Q and R will behave as
% given by this table:
% num, den, Q, R
% >0 >0 >0 >0
% >0 <0 <0 >0
% <0 >0 <0 <0
% <0 <0 >0 <0
% Quotient supports vector or array inputs, although
% the vpi version does not do so at this time.
% arguments: (input)
% numerator,denominator - integer scalar numeric variables
% arguments: (output)
% Q,R - integers such that numerator = Q*denominator + R
% R has the property that it will be smaller
% in magnitude than numerator.
% See also: vpi/quotient, rem, mod, rdivide
% Author: John D'Errico
% e-mail: firstname.lastname@example.org
% Release: 1.0
% Release date: 2/25/09
if nargin ~= 2
error('Both a numerator and denominator must be supplied')
maxint = 2^53 - 1;
% can we represent numerator as a double?
if any(abs(numerator(:))>maxint) || any(abs(denominator(:))>maxint)
error('Numbers too large, exact computation impossible. Convert to vpi form first')
% is the denominator zero?
if denominator == 0
error('Divide by zero')
% use matlab's divide operator.
Q = fix(numerator./denominator);
R = numerator - Q.*denominator;