source: trunk/sys/libm/s_asinh.c @ 1

Last change on this file since 1 was 1, checked in by alain, 5 years ago

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1
2/* @(#)s_asinh.c 5.1 93/09/24 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14/* asinh(x)
15 * Method :
16 *      Based on
17 *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
18 *      we have
19 *      asinh(x) := x  if  1+x*x=1,
20 *               := sign(x)*(log(x)+ln2)) for large |x|, else
21 *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
22 *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) 
23 */
24
25#include <libm/fdlibm.h>
26
27#ifdef __STDC__
28static const double 
29#else
30static double 
31#endif
32one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
33ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
34huge=  1.00000000000000000000e+300; 
35
36#ifdef __STDC__
37        double asinh(double x)
38#else
39        double asinh(x)
40        double x;
41#endif
42{       
43        double t,w;
44        int n0,hx,ix;
45        n0 = ((*(int*)&one)>>29)^1;
46        hx = *(n0+(int*)&x);
47        ix = hx&0x7fffffff;
48        if(ix>=0x7ff00000) return x+x;  /* x is inf or NaN */
49        if(ix< 0x3e300000) {    /* |x|<2**-28 */
50            if(huge+x>one) return x;    /* return x inexact except 0 */
51        } 
52        if(ix>0x41b00000) {     /* |x| > 2**28 */
53            w = __ieee754_log(fabs(x))+ln2;
54        } else if (ix>0x40000000) {     /* 2**28 > |x| > 2.0 */
55            t = fabs(x);
56            w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t));
57        } else {                /* 2.0 > |x| > 2**-28 */
58            t = x*x;
59            w =log1p(fabs(x)+t/(one+sqrt(one+t)));
60        }
61        if(hx>0) return w; else return -w;
62}
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