calc/cal/surd.cal

/*
 * surd - calculate using quadratic surds of the form: a + b * sqrt(D).
 *
 * 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 01:50:38
 * File existed as early as:	before 1990
 *
 * Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
 */


obj surd {a, b};		/* definition of the surd object */

global surd_type = -1;		/* type of surd (value of D) */
static obj surd surd__;		/* example surd for testing against */


define surd(a,b)
{
	local x;

	obj surd x;
	x.a = a;
	x.b = b;
	return x;
}


define surd_print(a)
{
	print "surd(" : a.a : ", " : a.b : ")" :;
}


define surd_conj(a)
{
	local	x;

	obj surd x;
	x.a = a.a;
	x.b = -a.b;
	return x;
}


define surd_norm(a)
{
	return a.a^2 + abs(surd_type) * a.b^2;
}


define surd_value(a, xepsilon)
{
	local	epsilon;

	epsilon = xepsilon;
	if (isnull(epsilon))
		epsilon = epsilon();
	return a.a + a.b * sqrt(surd_type, epsilon);
}

define surd_add(a, b)
{
	local obj surd	x;

	if (!istype(b, x)) {
		x.a = a.a + b;
		x.b = a.b;
		return x;
	}
	if (!istype(a, x)) {
		x.a = a + b.a;
		x.b = b.b;
		return x;
	}
	x.a = a.a + b.a;
	x.b = a.b + b.b;
	if (x.b)
		return x;
	return x.a;
}


define surd_sub(a, b)
{
	local obj surd	x;

	if (!istype(b, x)) {
		x.a = a.a - b;
		x.b = a.b;
		return x;
	}
	if (!istype(a, x)) {
		x.a = a - b.a;
		x.b = -b.b;
		return x;
	}
	x.a = a.a - b.a;
	x.b = a.b - b.b;
	if (x.b)
		return x;
	return x.a;
}


define surd_inc(a)
{
	local	x;

	x = a;
	x.a++;
	return x;
}


define surd_dec(a)
{
	local	x;

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


define surd_neg(a)
{
	local obj surd	x;

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


define surd_mul(a, b)
{
	local obj surd	x;

	if (!istype(b, x)) {
		x.a = a.a * b;
		x.b = a.b * b;
	} else if (!istype(a, x)) {
		x.a = b.a * a;
		x.b = b.b * a;
	} else {
		x.a = a.a * b.a + surd_type * a.b * b.b;
		x.b = a.a * b.b + a.b * b.a;
	}
	if (x.b)
		return x;
	return x.a;
}


define surd_square(a)
{
	local obj surd	x;

	x.a = a.a^2 + a.b^2 * surd_type;
	x.b = a.a * a.b * 2;
	if (x.b)
		return x;
	return x.a;
}


define surd_scale(a, b)
{
	local obj surd	x;

	x.a = scale(a.a, b);
	x.b = scale(a.b, b);
	return x;
}


define surd_shift(a, b)
{
	local obj surd	x;

	x.a = a.a << b;
	x.b = a.b << b;
	if (x.b)
		return x;
	return x.a;
}


define surd_div(a, b)
{
	local x, y;

	if ((a == 0) && b)
		return 0;
	obj surd x;
	if (!istype(b, x)) {
		x.a = a.a / b;
		x.b = a.b / b;
		return x;
	}
	y = b;
	y.b = -b.b;
	return (a * y) / (b.a^2 - surd_type * b.b^2);
}


define surd_inv(a)
{
	return 1 / a;
}


define surd_sgn(a)
{
	if (surd_type < 0)
		quit "Taking sign of complex surd";
	if (a.a == 0)
		return sgn(a.b);
	if (a.b == 0)
		return sgn(a.a);
	if ((a.a > 0) && (a.b > 0))
		return 1;
	if ((a.a < 0) && (a.b < 0))
		return -1;
	return sgn(a.a^2 - a.b^2 * surd_type) * sgn(a.a);
}


define surd_cmp(a, b)
{
	if (!istype(a, surd__))
		return ((b.b != 0) || (a != b.a));
	if (!istype(b, surd__))
		return ((a.b != 0) || (b != a.a));
	return ((a.a != b.a) || (a.b != b.b));
}


define surd_rel(a, b)
{
	local x, y;

	if (surd_type < 0)
		quit "Relative comparison of complex surds";
	if (!istype(a, surd__)) {
		x = a - b.a;
		y = -b.b;
	} else if (!istype(b, surd__)) {
		x = a.a - b;
		y = a.b;
	} else {
		x = a.a - b.a;
		y = a.b - b.b;
	}
	if (y == 0)
		return sgn(x);
	if (x == 0)
		return sgn(y);
	if ((x < 0) && (y < 0))
		return -1;
	if ((x > 0) && (y > 0))
		return 1;
	return sgn(x^2 - y^2 * surd_type) * sgn(x);
}

if (config("resource_debug") & 3) {
    print "obj surd {a, b} defined";
    print "surd_type defined";
    print "set surd_type as needed";
}