chickadee » modular-arithmetic

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modular-arithmetic

Author

Thomas Chust

Requirements

Description

This library allows you to perform modular arithmetic on finite fields with arbitrarily large integer moduli.

API

xgcd a bprocedure

Computes the "extended greatest common divisor" of a and b, ie. it returns the two values x and y that constitute the solution of the equation

 x*a + y*b = gcd(a, b)
modulus n ...procedure

Computes the sum of all n parameters just like the standard procedure + does, but operating on the finite field with the given modulus.

modulus a n ...procedure

Computes the difference of a and all n parameters or the additive inverse of a just like the standard procedure - does, but operating on the finite field with the given modulus.

modulus n ...procedure

Computes the product of all n parameters just like the standard procedure * does, but operating on the finite field with the given modulus.

modulus a n ...procedure

Computes the quotient of a and all n parameters or the multiplicative inverse of a just like the standard procedure / does, but operating on the finite field with the given modulus.

Note that a unique multiplicative inverse of an element in a finite field only exists if the element and the modulus are coprime. This procedure only works in that case.

modulus a bprocedure

Computes a raised to the power of b modulo the given modulus, but does so far more efficiently than using

 (modulo (* a b) modulus).

If b is negative, the multiplicative inverse of a is raised to the power of (abs b).

(with-modulus modulus body ...)syntax

Overloads the symbols +, add1, -, sub1, *, / and expt inside body with the modular versions operating on the finite field with the given modulus instead of the standard arithmetic procedures.

License

 Copyright (c) 2010, Thomas Chust
 All rights reserved.
 
 Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following
 conditions are met:
 
 * Redistributions of source code must retain the above copyright notice, this list of conditions and the following
     disclaimer.
 * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following
     disclaimer in the documentation and/or other materials provided with the distribution.
 * Neither the name of the author nor the names of its contributors may be used to endorse or promote
     products derived from this software without specific prior written permission.
 
 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS
 OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
 AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR
 CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
 SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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Version history

1.0.1
Fixed borked setup script
1.0.0
Initial release

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