calc/cal/mod.cal

/*
 * mod - routines to handle numbers modulo a specified number
 *
 * Copyright (C) 1999  David I. Bell
 *
 * Calc is open software; you can redistribute it and/or modify it under
 * the terms of the version 2.1 of the GNU Lesser General Public License
 * as published by the Free Software Foundation.
 *
 * Calc is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 * or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
 * Public License for more details.
 *
 * A copy of version 2.1 of the GNU Lesser General Public License is
 * distributed with calc under the filename COPYING-LGPL.  You should have
 * received a copy with calc; if not, write to Free Software Foundation, Inc.
 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 *
 * Under source code control:	1990/02/15 01:50:34
 * File existed as early as:	before 1990
 *
 * Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
 */


obj mod {a};			/* definition of the object */

global mod_value = 100;		/* modulus value (value of N) */


define lmod(a)
{
	local obj mod	x;

	if (!isreal(a) || !isint(a))
		quit "Bad argument for lmod function";
	x.a = a % mod_value;
	return x;
}


define mod_print(a)
{
	if (digits(mod_value) <= 20)
		print a.a, "(mod", mod_value : ")" :;
	else
		print a.a, "(mod N)" :;
}


define mod_one()
{
	return lmod(1);
}


define mod_cmp(a, b)
{
	if (isnum(a))
		return (a % mod_value) != b.a;
	if (isnum(b))
		return (b % mod_value) != a.a;
	return a.a != b.a;
}


define mod_rel(a, b)
{
	if (isnum(a))
		a = lmod(a);
	if (isnum(b))
		b = lmod(b);
	if (a.a < b.a)
		return -1;
	return a.a != b.a;
}


define mod_add(a, b)
{
	local obj mod	x;

	if (isnum(b)) {
		if (!isint(b))
			quit "Adding non-integer";
		x.a = (a.a + b) % mod_value;
		return x;
	}
	if (isnum(a)) {
		if (!isint(a))
			quit "Adding non-integer";
		x.a = (a + b.a) % mod_value;
		return x;
	}
	x.a = (a.a + b.a) % mod_value;
	return x;
}


define mod_sub(a, b)
{
	return a + (-b);
}


define mod_neg(a)
{
	local obj mod	x;

	x.a = mod_value - a.a;
	return x;
}


define mod_mul(a, b)
{
	local obj mod	x;

	if (isnum(b)) {
		if (!isint(b))
			quit "Multiplying by non-integer";
		x.a = (a.a * b) % mod_value;
		return x;
	}
	if (isnum(a)) {
		if (!isint(a))
			quit "Multiplying by non-integer";
		x.a = (a * b.a) % mod_value;
		return x;
	}
	x.a = (a.a * b.a) % mod_value;
	return x;
}


define mod_square(a)
{
	local obj mod	x;

	x.a = a.a^2 % mod_value;
	return x;
}


define mod_inc(a)
{
	local x;

	x = a;
	if (++x.a == mod_value)
		x.a = 0;
	return x;
}


define mod_dec(a)
{
	local x;

	x = a;
	if (--x.a < 0)
		x.a = mod_value - 1;
	return x;
}


define mod_inv(a)
{
	local obj mod	x;

	x.a = minv(a.a, mod_value);
	return x;
}


define mod_div(a, b)
{
	local c;
	local obj mod x;
	local obj mod y;
	if (isnum(a))
		a = lmod(a);
	if (isnum(b))
		b = lmod(b);
	c = gcd(a.a, b.a);
	x.a = a.a / c;
	y.a = b.a / c;
	return x * inverse(y);
}


define mod_pow(a, b)
{
	local x, y, z;

	obj mod x;
	y = a;
	z = b;
	if (b < 0) {
		y = inverse(a);
		z = -b;
	}
	x.a = pmod(y.a, z, mod_value);
	return x;
}


if (config("resource_debug") & 3) {
    print "obj mod {a} defined";
    print "mod_value defined";
    print "set mod_value as needed";
}