src/fdlibm/e_asin.c

/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 *
 * ***** BEGIN LICENSE BLOCK *****
 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
 *
 * The contents of this file are subject to the Mozilla Public License Version
 * 1.1 (the "License"); you may not use this file except in compliance with
 * the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * Software distributed under the License is distributed on an "AS IS" basis,
 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
 * for the specific language governing rights and limitations under the
 * License.
 *
 * The Original Code is Mozilla Communicator client code, released
 * March 31, 1998.
 *
 * The Initial Developer of the Original Code is
 * Sun Microsystems, Inc.
 * Portions created by the Initial Developer are Copyright (C) 1998
 * the Initial Developer. All Rights Reserved.
 *
 * Contributor(s):
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either of the GNU General Public License Version 2 or later (the "GPL"),
 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
 * in which case the provisions of the GPL or the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of either the GPL or the LGPL, and not to allow others to
 * use your version of this file under the terms of the MPL, indicate your
 * decision by deleting the provisions above and replace them with the notice
 * and other provisions required by the GPL or the LGPL. If you do not delete
 * the provisions above, a recipient may use your version of this file under
 * the terms of any one of the MPL, the GPL or the LGPL.
 *
 * ***** END LICENSE BLOCK ***** */

/* @(#)e_asin.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/* __ieee754_asin(x)
 * Method :                  
 *      Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
 *      we approximate asin(x) on [0,0.5] by
 *              asin(x) = x + x*x^2*R(x^2)
 *      where
 *              R(x^2) is a rational approximation of (asin(x)-x)/x^3 
 *      and its remez error is bounded by
 *              |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
 *
 *      For x in [0.5,1]
 *              asin(x) = pi/2-2*asin(sqrt((1-x)/2))
 *      Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
 *      then for x>0.98
 *              asin(x) = pi/2 - 2*(s+s*z*R(z))
 *                      = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
 *      For x<=0.98, let pio4_hi = pio2_hi/2, then
 *              f = hi part of s;
 *              c = sqrt(z) - f = (z-f*f)/(s+f)         ...f+c=sqrt(z)
 *      and
 *              asin(x) = pi/2 - 2*(s+s*z*R(z))
 *                      = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
 *                      = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
 *
 * Special cases:
 *      if x is NaN, return x itself;
 *      if |x|>1, return NaN with invalid signal.
 *
 */


#include "fdlibm.h"

#ifdef __STDC__
static const double 
#else
static double 
#endif
one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
really_big =  1.000e+300,
pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pio4_hi =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
        /* coefficient for R(x^2) */
pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */

#ifdef __STDC__
        double __ieee754_asin(double x)
#else
        double __ieee754_asin(x)
        double x;
#endif
{
        fd_twoints u;
        double w,t,p,q,c,r,s;
        int hx,ix;
        u.d = x;
        hx = __HI(u);
        x = u.d;
        ix = hx&0x7fffffff;
        if(ix>= 0x3ff00000) {           /* |x|>= 1 */
            if(((ix-0x3ff00000)|__LO(u))==0)
                    /* asin(1)=+-pi/2 with inexact */
                return x*pio2_hi+x*pio2_lo;     
            return (x-x)/(x-x);         /* asin(|x|>1) is NaN */   
        } else if (ix<0x3fe00000) {     /* |x|<0.5 */
            if(ix<0x3e400000) {         /* if |x| < 2**-27 */
                if(really_big+x>one) return x;/* return x with inexact if x!=0*/
            } else 
                t = x*x;
                p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
                q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
                w = p/q;
                return x+x*w;
        }
        /* 1> |x|>= 0.5 */
        w = one-fd_fabs(x);
        t = w*0.5;
        p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
        q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
        s = fd_sqrt(t);
        if(ix>=0x3FEF3333) {    /* if |x| > 0.975 */
            w = p/q;
            t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
        } else {
            u.d  = s;
            __LO(u) = 0;
            w = u.d;
            c  = (t-w*w)/(s+w);
            r  = p/q;
            p  = 2.0*s*r-(pio2_lo-2.0*c);
            q  = pio4_hi-2.0*w;
            t  = pio4_hi-(p-q);
        }    
        if(hx>0) return t; else return -t;    
}
1	siliconforks	2	/* -- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 --
2			*
3			* *** BEGIN LICENSE BLOCK ***
4			* Version: MPL 1.1/GPL 2.0/LGPL 2.1
5			*
6			* The contents of this file are subject to the Mozilla Public License Version
7			* 1.1 (the "License"); you may not use this file except in compliance with
8			* the License. You may obtain a copy of the License at
9			* http://www.mozilla.org/MPL/
10			*
11			* Software distributed under the License is distributed on an "AS IS" basis,
12			* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13			* for the specific language governing rights and limitations under the
14			* License.
15			*
16			* The Original Code is Mozilla Communicator client code, released
17			* March 31, 1998.
18			*
19			* The Initial Developer of the Original Code is
20			* Sun Microsystems, Inc.
21			* Portions created by the Initial Developer are Copyright (C) 1998
22			* the Initial Developer. All Rights Reserved.
23			*
24			* Contributor(s):
25			*
26			* Alternatively, the contents of this file may be used under the terms of
27			* either of the GNU General Public License Version 2 or later (the "GPL"),
28			* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29			* in which case the provisions of the GPL or the LGPL are applicable instead
30			* of those above. If you wish to allow use of your version of this file only
31			* under the terms of either the GPL or the LGPL, and not to allow others to
32			* use your version of this file under the terms of the MPL, indicate your
33			* decision by deleting the provisions above and replace them with the notice
34			* and other provisions required by the GPL or the LGPL. If you do not delete
35			* the provisions above, a recipient may use your version of this file under
36			* the terms of any one of the MPL, the GPL or the LGPL.
37			*
38			* *** END LICENSE BLOCK *** */
39
40			/* @(#)e_asin.c 1.3 95/01/18 */
41			/*
42			* ====================================================
43			* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
44			*
45			* Developed at SunSoft, a Sun Microsystems, Inc. business.
46			* Permission to use, copy, modify, and distribute this
47			* software is freely granted, provided that this notice
48			* is preserved.
49			* ====================================================
50			*/
51
52			/* __ieee754_asin(x)
53			* Method :
54			* Since asin(x) = x + x^3/6 + x^53/40 + x^715/336 + ...
55			* we approximate asin(x) on [0,0.5] by
56			* asin(x) = x + xx^2R(x^2)
57			* where
58			* R(x^2) is a rational approximation of (asin(x)-x)/x^3
59			* and its remez error is bounded by
60			* \|(asin(x)-x)/x^3 - R(x^2)\| < 2^(-58.75)
61			*
62			* For x in [0.5,1]
63			* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
64			* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
65			* then for x>0.98
66			* asin(x) = pi/2 - 2(s+sz*R(z))
67			* = pio2_hi - (2(s+sz*R(z)) - pio2_lo)
68			* For x<=0.98, let pio4_hi = pio2_hi/2, then
69			* f = hi part of s;
70			* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
71			* and
72			* asin(x) = pi/2 - 2(s+sz*R(z))
73			* = pio4_hi+(pio4-2s)-(2szR(z)-pio2_lo)
74			* = pio4_hi+(pio4-2f)-(2szR(z)-(pio2_lo+2c))
75			*
76			* Special cases:
77			* if x is NaN, return x itself;
78			* if \|x\|>1, return NaN with invalid signal.
79			*
80			*/
81
82
83			#include "fdlibm.h"
84
85			#ifdef __STDC__
86			static const double
87			#else
88			static double
89			#endif
90			one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
91			really_big = 1.000e+300,
92			pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
93			pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
94			pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
95			/* coefficient for R(x^2) */
96			pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
97			pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
98			pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
99			pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
100			pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
101			pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
102			qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
103			qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
104			qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
105			qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
106
107			#ifdef __STDC__
108			double __ieee754_asin(double x)
109			#else
110			double __ieee754_asin(x)
111			double x;
112			#endif
113			{
114			fd_twoints u;
115			double w,t,p,q,c,r,s;
116			int hx,ix;
117			u.d = x;
118			hx = __HI(u);
119			x = u.d;
120			ix = hx&0x7fffffff;
121			if(ix>= 0x3ff00000) { /* \|x\|>= 1 */
122			if(((ix-0x3ff00000)\|__LO(u))==0)
123			/* asin(1)=+-pi/2 with inexact */
124			return xpio2_hi+xpio2_lo;
125			return (x-x)/(x-x); /* asin(\|x\|>1) is NaN */
126			} else if (ix<0x3fe00000) { /* \|x\|<0.5 */
127			if(ix<0x3e400000) { /* if \|x\| < 2*-27 /
128			if(really_big+x>one) return x;/* return x with inexact if x!=0*/
129			} else
130			t = x*x;
131			p = t(pS0+t(pS1+t(pS2+t(pS3+t(pS4+tpS5)))));
132			q = one+t(qS1+t(qS2+t(qS3+tqS4)));
133			w = p/q;
134			return x+x*w;
135			}
136			/* 1> \|x\|>= 0.5 */
137			w = one-fd_fabs(x);
138			t = w*0.5;
139			p = t(pS0+t(pS1+t(pS2+t(pS3+t(pS4+tpS5)))));
140			q = one+t(qS1+t(qS2+t(qS3+tqS4)));
141			s = fd_sqrt(t);
142			if(ix>=0x3FEF3333) { /* if \|x\| > 0.975 */
143			w = p/q;
144			t = pio2_hi-(2.0(s+sw)-pio2_lo);
145			} else {
146			u.d = s;
147			__LO(u) = 0;
148			w = u.d;
149			c = (t-w*w)/(s+w);
150			r = p/q;
151			p = 2.0sr-(pio2_lo-2.0*c);
152			q = pio4_hi-2.0*w;
153			t = pio4_hi-(p-q);
154			}
155			if(hx>0) return t; else return -t;
156			}