xref: /freebsd/usr.bin/bc/bc.library (revision bdcbfde3)

/*      $OpenBSD: bc.library,v 1.4 2012/03/14 07:35:53 otto Exp $	*/

/*
 * Copyright (C) Caldera International Inc.  2001-2002.
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code and documentation must retain the above
 *    copyright notice, this list of conditions and the following disclaimer.
 * 2. 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.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *      This product includes software developed or owned by Caldera
 *      International, Inc.
 * 4. Neither the name of Caldera International, Inc. nor the names of other
 *    contributors may be used to endorse or promote products derived from
 *    this software without specific prior written permission.
 *
 * USE OF THE SOFTWARE PROVIDED FOR UNDER THIS LICENSE BY CALDERA
 * INTERNATIONAL, INC. 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 CALDERA INTERNATIONAL, INC. 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 THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
 * IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 */

/*
 */

scale = 20
define e(x) {
	auto a, b, c, d, e, g, t, w, y, r

	r = ibase
	ibase = A
	t = scale
	scale = 0
	if (x > 0) scale = (0.435*x)/1
	scale = scale + t + length(scale + t) + 1

	w = 0
	if (x < 0) {
		x = -x
		w = 1
	}
	y = 0
	while (x > 2) {
		x = x/2
		y = y + 1
	}

	a = 1
	b = 1
	c = b
	d = 1
	e = 1
	for (a = 1; 1 == 1; a++) {
		b = b*x
		c = c*a + b
		d = d*a
		g = c/d
		if (g == e) {
			g = g/1
			while (y--) {
				g = g*g
			}
			scale = t
			ibase = r
			if (w == 1) return (1/g)
			return (g/1)
		}
		e = g
	}
}

define l(x) {
	auto a, b, c, d, e, f, g, u, s, t, r
	r = ibase
	ibase = A
	if (x <= 0) {
		a = (1 - 10^scale)
		ibase = r
		return (a)
	}
	t = scale

	f = 1
	if (x < 1) {
		s = scale(x)
	} else {
		s = length(x)-scale(x)
	}
	scale = 0
	a = (2.31*s)/1 /* estimated integer part of the answer */
	s = t + length(a) + 2 /* estimated length of the answer */
	while (x > 2) {
		scale = 0
		scale = (length(x) + scale(x))/2 + 1
		if (scale < s) scale = s
		x = sqrt(x)
		f = f*2
	}
	while (x < .5) {
		scale = 0
		scale = scale(x)/2 + 1
		if (scale < s) scale = s
		x = sqrt(x)
		f = f*2
	}

	scale = 0
	scale = t + length(f) + length((1.05*(t+length(f))/1)) + 1
	u = (x - 1)/(x + 1)
	s = u*u
	scale = t + 2
	b = 2*f
	c = b
	d = 1
	e = 1
	for (a = 3; 1 == 1 ; a = a + 2) {
		b = b*s
		c = c*a + d*b
		d = d*a
		g = c/d
		if (g == e) {
			scale = t
			ibase = r
			return (u*c/d)
		}
		e = g
	}
}

define s(x) {
	auto a, b, c, s, t, y, p, n, i, r
	r = ibase
	ibase = A
	t = scale
	y = x/.7853
	s = t + length(y) - scale(y)
	if (s < t) s = t
	scale = s
	p = a(1)

	scale = 0
	if (x >= 0) n = (x/(2*p) + 1)/2
	if (x < 0) n = (x/(2*p) - 1)/2
	x = x - 4*n*p
	if (n % 2 != 0) x = -x

	scale = t + length(1.2*t) - scale(1.2*t)
	y = -x*x
	a = x
	b = 1
	s = x
	for (i =3 ; 1 == 1; i = i + 2) {
		a = a*y
		b = b*i*(i - 1)
		c = a/b
		if (c == 0) {
			scale = t
			ibase = r
			return (s/1)
		}
		s = s + c
	}
}

define c(x) {
	auto t, r
	r = ibase
	ibase = A
	t = scale
	scale = scale + 1
	x = s(x + 2*a(1))
	scale = t
	ibase = r
	return (x/1)
}

define a(x) {
	auto a, b, c, d, e, f, g, s, t, r
	if (x == 0) return(0)

	r = ibase
	ibase = A
	if (x == 1) {
		if (scale < 52) {
			 a = .7853981633974483096156608458198757210492923498437764/1
			 ibase = r
			 return (a)
		}
	}
	t = scale
	f = 1
	while (x > .5) {
		scale = scale + 1
		x = -(1 - sqrt(1. + x*x))/x
		f = f*2
	}
	while (x < -.5) {
		scale = scale + 1
		x = -(1 - sqrt(1. + x*x))/x
		f = f*2
	}
	s = -x*x
	b = f
	c = f
	d = 1
	e = 1
	for (a = 3; 1 == 1; a = a + 2) {
		b = b*s
		c = c*a + d*b
		d = d*a
		g = c/d
		if (g == e) {
			ibase = r
			scale = t
			return (x*c/d)
		}
		e = g
	}
}

define j(n,x) {
	auto a, b, c, d, e, g, i, s, k, t, r

	r = ibase
	ibase = A
	t = scale
	k = 1.36*x + 1.16*t - n
	k = length(k) - scale(k)
	if (k > 0) scale = scale + k

	s = -x*x/4
	if (n < 0) {
		n = -n
		x = -x
	}
	a = 1
	c = 1
	for (i = 1; i <= n; i++) {
		a = a*x
		c = c*2*i
	}
	b = a
	d = 1
	e = 1
	for (i = 1; 1; i++) {
		a = a*s
		b = b*i*(n + i) + a
		c = c*i*(n + i)
		g = b/c
		if (g == e) {
			ibase = r
			scale = t
			return (g/1)
		}
		e = g
	}
}
/* vim: set filetype=bc shiftwidth=8 noexpandtab: */