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## Arbitrary precision integer arithmetic

 From: Etienne Grossmann Subject: Arbitrary precision integer arithmetic Date: Mon, 03 Sep 2018 17:21:35 -0700 User-agent: Internet Messaging Program (IMP) H3 (4.3.10)

Hi all,

I couldn't find arbitrary-precision integer arithmetic for Octave the other day (I didn't look that hard, though), and I thought it would be fun to write a few functions myself.

I made them available (GPL'd) at https://sourceforge.net/p/octave-intinf/code/ci/master/tree/

Cheers,

Etienne

```The supported operations are:

>> s = a = intinf (126)               % Creation of intinf-class object from integer or string
s = 126
>> b = intinf ('-792716404922304611755050042308687')
b = -792716404922304611755050042308687
>> c = a + b                          % Addition
c = -792716404922304611755050042308561
>> d = a - b                          % Subtraction
d = 792716404922304611755050042308813
>> e = c * d                          % Multiplication
e = -628399298632943207296804593622614025887290777301864028724995648093
>> f = (e - a^2) / b                  % Exponentiation, division
f = 792716404922304611755050042308687
>> f == -b                            % Logical operators
ans =  1
>> [q, r] = intinf_divide (b^2, a)    % Divsion and remainder
q = 4987296020896374661085750743036619253073736327792571656547584634
r = 85
>> r < a
ans =  1
>> x = intinf_rand (100)              % Random number (here, with 100 digits)
x = 5957920324041182863967505832677200714276564790135557044108872634353981714576255029666518574621376764
>> tic, a^a, toc                      % Don't be in a big hurry
ans = 4432907660220782149197257457170010056248664733961715006433455717789043517106373872170818953941792055669609014893218047089803712563472169065833738899530142657476809234058293370126853817068631046152741967763913240019546541793769190722594113575550312228000452759781376
Elapsed time is 2.70419 seconds.

Code organization:

* This directory contains non-class m-files, e.g. intinf_div().
* The sub-directory @intinf contains the class m-files, e.g. intinf(), times().
* The sub-sub-directory @intinf/private contains the back-end functions that
actually perform the calculations, e.g. apia_add(), app_mul(). "apia" stands
for "arbitrary-precision integer arithmetic". The integers are represented as
strings. These functions take double or string arguments.

TODO:

* Don't use a gimmick in intinf() to put the apia_X() functions in the Octave
path.
* Better errors.
* Make a package loadable by octave's pkg function.```

--

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