src/fdlibm/s_asinh.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 ***** */

/* @(#)s_asinh.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.
 * ====================================================
 */

/* asinh(x)
 * Method :
 *      Based on 
 *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
 *      we have
 *      asinh(x) := x  if  1+x*x=1,
 *               := sign(x)*(log(x)+ln2)) for large |x|, else
 *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
 *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))  
 */

#include "fdlibm.h"

#ifdef __STDC__
static const double 
#else
static double 
#endif
one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
really_big=  1.00000000000000000000e+300; 

#ifdef __STDC__
        double fd_asinh(double x)
#else
        double fd_asinh(x)
        double x;
#endif
{       
        fd_twoints u;
        double t,w;
        int hx,ix;
        u.d = x;
        hx = __HI(u);
        ix = hx&0x7fffffff;
        if(ix>=0x7ff00000) return x+x;  /* x is inf or NaN */
        if(ix< 0x3e300000) {    /* |x|<2**-28 */
            if(really_big+x>one) return x;      /* return x inexact except 0 */
        } 
        if(ix>0x41b00000) {     /* |x| > 2**28 */
            w = __ieee754_log(fd_fabs(x))+ln2;
        } else if (ix>0x40000000) {     /* 2**28 > |x| > 2.0 */
            t = fd_fabs(x);
            w = __ieee754_log(2.0*t+one/(fd_sqrt(x*x+one)+t));
        } else {                /* 2.0 > |x| > 2**-28 */
            t = x*x;
            w =fd_log1p(fd_fabs(x)+t/(one+fd_sqrt(one+t)));
        }
        if(hx>0) return w; else return -w;
}
1	/* -- 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	/* @(#)s_asinh.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	/* asinh(x)
53	* Method :
54	* Based on
55	* asinh(x) = sign(x) * log [ \|x\| + sqrt(x*x+1) ]
56	* we have
57	* asinh(x) := x if 1+x*x=1,
58	* := sign(x)*(log(x)+ln2)) for large \|x\|, else
59	* := sign(x)log(2\|x\|+1/(\|x\|+sqrt(xx+1))) if\|x\|>2, else
60	* := sign(x)*log1p(\|x\| + x^2/(1 + sqrt(1+x^2)))
61	*/
62
63	#include "fdlibm.h"
64
65	#ifdef __STDC__
66	static const double
67	#else
68	static double
69	#endif
70	one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
71	ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
72	really_big= 1.00000000000000000000e+300;
73
74	#ifdef __STDC__
75	double fd_asinh(double x)
76	#else
77	double fd_asinh(x)
78	double x;
79	#endif
80	{
81	fd_twoints u;
82	double t,w;
83	int hx,ix;
84	u.d = x;
85	hx = __HI(u);
86	ix = hx&0x7fffffff;
87	if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
88	if(ix< 0x3e300000) { /* \|x\|<2*-28 /
89	if(really_big+x>one) return x; /* return x inexact except 0 */
90	}
91	if(ix>0x41b00000) { /* \|x\| > 2*28 /
92	w = __ieee754_log(fd_fabs(x))+ln2;
93	} else if (ix>0x40000000) { /* 2*28 > \|x\| > 2.0 /
94	t = fd_fabs(x);
95	w = __ieee754_log(2.0t+one/(fd_sqrt(xx+one)+t));
96	} else { /* 2.0 > \|x\| > 2*-28 /
97	t = x*x;
98	w =fd_log1p(fd_fabs(x)+t/(one+fd_sqrt(one+t)));
99	}
100	if(hx>0) return w; else return -w;
101	}