fatbase

portable OpenBSD tools
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bc.library (5125B)


      1 /*      $OpenBSD: bc.library,v 1.4 2012/03/14 07:35:53 otto Exp $	*/
      2 
      3 /*
      4  * Copyright (C) Caldera International Inc.  2001-2002.
      5  * All rights reserved.
      6  *
      7  * Redistribution and use in source and binary forms, with or without
      8  * modification, are permitted provided that the following conditions
      9  * are met:
     10  * 1. Redistributions of source code and documentation must retain the above
     11  *    copyright notice, this list of conditions and the following disclaimer.
     12  * 2. Redistributions in binary form must reproduce the above copyright
     13  *    notice, this list of conditions and the following disclaimer in the
     14  *    documentation and/or other materials provided with the distribution.
     15  * 3. All advertising materials mentioning features or use of this software
     16  *    must display the following acknowledgement:
     17  *      This product includes software developed or owned by Caldera
     18  *      International, Inc.
     19  * 4. Neither the name of Caldera International, Inc. nor the names of other
     20  *    contributors may be used to endorse or promote products derived from
     21  *    this software without specific prior written permission.
     22  *
     23  * USE OF THE SOFTWARE PROVIDED FOR UNDER THIS LICENSE BY CALDERA
     24  * INTERNATIONAL, INC. AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR
     25  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
     26  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
     27  * IN NO EVENT SHALL CALDERA INTERNATIONAL, INC. BE LIABLE FOR ANY DIRECT,
     28  * INDIRECT INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
     29  * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
     30  * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     31  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
     32  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
     33  * IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
     34  * POSSIBILITY OF SUCH DAMAGE.
     35  */
     36 
     37 /*
     38  *	@(#)bc.library	5.1 (Berkeley) 4/17/91
     39  */
     40 
     41 scale = 20
     42 define e(x) {
     43 	auto a, b, c, d, e, g, t, w, y, r
     44 
     45 	r = ibase
     46 	ibase = A
     47 	t = scale
     48 	scale = 0
     49 	if (x > 0) scale = (0.435*x)/1
     50 	scale = scale + t + length(scale + t) + 1
     51 
     52 	w = 0
     53 	if (x < 0) {
     54 		x = -x
     55 		w = 1
     56 	}
     57 	y = 0
     58 	while (x > 2) {
     59 		x = x/2
     60 		y = y + 1
     61 	}
     62 
     63 	a = 1
     64 	b = 1
     65 	c = b
     66 	d = 1
     67 	e = 1
     68 	for (a = 1; 1 == 1; a++) {
     69 		b = b*x
     70 		c = c*a + b
     71 		d = d*a
     72 		g = c/d
     73 		if (g == e) {
     74 			g = g/1
     75 			while (y--) {
     76 				g = g*g
     77 			}
     78 			scale = t
     79 			ibase = r
     80 			if (w == 1) return (1/g)
     81 			return (g/1)
     82 		}
     83 		e = g
     84 	}
     85 }
     86 
     87 define l(x) {
     88 	auto a, b, c, d, e, f, g, u, s, t, r
     89 	r = ibase
     90 	ibase = A
     91 	if (x <= 0) {
     92 		a = (1 - 10^scale)
     93 		ibase = r
     94 		return (a)
     95 	}
     96 	t = scale
     97 
     98 	f = 1
     99 	if (x < 1) {
    100 		s = scale(x)
    101 	} else {
    102 		s = length(x)-scale(x)
    103 	}
    104 	scale = 0
    105 	a = (2.31*s)/1 /* estimated integer part of the answer */
    106 	s = t + length(a) + 2 /* estimated length of the answer */
    107 	while (x > 2) {
    108 		scale = 0
    109 		scale = (length(x) + scale(x))/2 + 1
    110 		if (scale < s) scale = s
    111 		x = sqrt(x)
    112 		f = f*2
    113 	}
    114 	while (x < .5) {
    115 		scale = 0
    116 		scale = scale(x)/2 + 1
    117 		if (scale < s) scale = s
    118 		x = sqrt(x)
    119 		f = f*2
    120 	}
    121 
    122 	scale = 0
    123 	scale = t + length(f) + length((1.05*(t+length(f))/1)) + 1
    124 	u = (x - 1)/(x + 1)
    125 	s = u*u
    126 	scale = t + 2
    127 	b = 2*f
    128 	c = b
    129 	d = 1
    130 	e = 1
    131 	for (a = 3; 1 == 1 ; a = a + 2) {
    132 		b = b*s
    133 		c = c*a + d*b
    134 		d = d*a
    135 		g = c/d
    136 		if (g == e) {
    137 			scale = t
    138 			ibase = r
    139 			return (u*c/d)
    140 		}
    141 		e = g
    142 	}
    143 }
    144 
    145 define s(x) {
    146 	auto a, b, c, s, t, y, p, n, i, r
    147 	r = ibase
    148 	ibase = A
    149 	t = scale
    150 	y = x/.7853
    151 	s = t + length(y) - scale(y)
    152 	if (s < t) s = t
    153 	scale = s
    154 	p = a(1)
    155 
    156 	scale = 0
    157 	if (x >= 0) n = (x/(2*p) + 1)/2
    158 	if (x < 0) n = (x/(2*p) - 1)/2
    159 	x = x - 4*n*p
    160 	if (n % 2 != 0) x = -x
    161 
    162 	scale = t + length(1.2*t) - scale(1.2*t)
    163 	y = -x*x
    164 	a = x
    165 	b = 1
    166 	s = x
    167 	for (i =3 ; 1 == 1; i = i + 2) {
    168 		a = a*y
    169 		b = b*i*(i - 1)
    170 		c = a/b
    171 		if (c == 0) {
    172 			scale = t
    173 			ibase = r
    174 			return (s/1)
    175 		}
    176 		s = s + c
    177 	}
    178 }
    179 
    180 define c(x) {
    181 	auto t, r
    182 	r = ibase
    183 	ibase = A
    184 	t = scale
    185 	scale = scale + 1
    186 	x = s(x + 2*a(1))
    187 	scale = t
    188 	ibase = r
    189 	return (x/1)
    190 }
    191 
    192 define a(x) {
    193 	auto a, b, c, d, e, f, g, s, t, r
    194 	if (x == 0) return(0)
    195 
    196 	r = ibase
    197 	ibase = A
    198 	if (x == 1) {
    199 		if (scale < 52) {
    200 			 a = .7853981633974483096156608458198757210492923498437764/1
    201 			 ibase = r
    202 			 return (a)
    203 		}
    204 	}
    205 	t = scale
    206 	f = 1
    207 	while (x > .5) {
    208 		scale = scale + 1
    209 		x = -(1 - sqrt(1. + x*x))/x
    210 		f = f*2
    211 	}
    212 	while (x < -.5) {
    213 		scale = scale + 1
    214 		x = -(1 - sqrt(1. + x*x))/x
    215 		f = f*2
    216 	}
    217 	s = -x*x
    218 	b = f
    219 	c = f
    220 	d = 1
    221 	e = 1
    222 	for (a = 3; 1 == 1; a = a + 2) {
    223 		b = b*s
    224 		c = c*a + d*b
    225 		d = d*a
    226 		g = c/d
    227 		if (g == e) {
    228 			ibase = r
    229 			scale = t
    230 			return (x*c/d)
    231 		}
    232 		e = g
    233 	}
    234 }
    235 
    236 define j(n,x) {
    237 	auto a, b, c, d, e, g, i, s, k, t, r
    238 
    239 	r = ibase
    240 	ibase = A
    241 	t = scale
    242 	k = 1.36*x + 1.16*t - n
    243 	k = length(k) - scale(k)
    244 	if (k > 0) scale = scale + k
    245 
    246 	s = -x*x/4
    247 	if (n < 0) {
    248 		n = -n
    249 		x = -x
    250 	}
    251 	a = 1
    252 	c = 1
    253 	for (i = 1; i <= n; i++) {
    254 		a = a*x
    255 		c = c*2*i
    256 	}
    257 	b = a
    258 	d = 1
    259 	e = 1
    260 	for (i = 1; 1; i++) {
    261 		a = a*s
    262 		b = b*i*(n + i) + a
    263 		c = c*i*(n + i)
    264 		g = b/c
    265 		if (g == e) {
    266 			ibase = r
    267 			scale = t
    268 			return (g/1)
    269 		}
    270 		e = g
    271 	}
    272 }