1 #include "FEATURE/uwin"
2
3 #if !_UWIN || _lib_asinh
4
_STUB_asinh()5 void _STUB_asinh(){}
6
7 #else
8
9 /*
10 * Copyright (c) 1985, 1993
11 * The Regents of the University of California. All rights reserved.
12 *
13 * Redistribution and use in source and binary forms, with or without
14 * modification, are permitted provided that the following conditions
15 * are met:
16 * 1. Redistributions of source code must retain the above copyright
17 * notice, this list of conditions and the following disclaimer.
18 * 2. Redistributions in binary form must reproduce the above copyright
19 * notice, this list of conditions and the following disclaimer in the
20 * documentation and/or other materials provided with the distribution.
21 * 3. Neither the name of the University nor the names of its contributors
22 * may be used to endorse or promote products derived from this software
23 * without specific prior written permission.
24 *
25 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
26 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
28 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
29 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
30 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
31 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
32 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
33 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
34 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
35 * SUCH DAMAGE.
36 */
37
38 #ifndef lint
39 static char sccsid[] = "@(#)asinh.c 8.1 (Berkeley) 6/4/93";
40 #endif /* not lint */
41
42 /* ASINH(X)
43 * RETURN THE INVERSE HYPERBOLIC SINE OF X
44 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
45 * CODED IN C BY K.C. NG, 2/16/85;
46 * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85.
47 *
48 * Required system supported functions :
49 * copysign(x,y)
50 * sqrt(x)
51 *
52 * Required kernel function:
53 * log1p(x) ...return log(1+x)
54 *
55 * Method :
56 * Based on
57 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
58 * we have
59 * asinh(x) := x if 1+x*x=1,
60 * := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else
61 * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
62 *
63 * Accuracy:
64 * asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
65 * In a test run with 52,000 random arguments on a VAX, the maximum
66 * observed error was 1.58 ulps (units in the last place).
67 *
68 * Constants:
69 * The hexadecimal values are the intended ones for the following constants.
70 * The decimal values may be used, provided that the compiler will convert
71 * from decimal to binary accurately enough to produce the hexadecimal values
72 * shown.
73 */
74 #include "mathimpl.h"
75
76 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
77 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
78
79 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
80 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
81
82 #ifdef vccast
83 #define ln2hi vccast(ln2hi)
84 #define ln2lo vccast(ln2lo)
85 #endif
86
87 extern double asinh(x)
88 double x;
89 {
90 double t,s;
91 const static double small=1.0E-10, /* fl(1+small*small) == 1 */
92 big =1.0E20, /* fl(1+big) == big */
93 one =1.0 ;
94
95 #if !defined(vax)&&!defined(tahoe)
96 if(x!=x) return(x); /* x is NaN */
97 #endif /* !defined(vax)&&!defined(tahoe) */
98 if((t=copysign(x,one))>small)
99 if(t<big) {
100 s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
101 else /* if |x| > big */
102 {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
103 else /* if |x| < small */
104 return(x);
105 }
106
107 #endif
108