1 /* @(#)s_asinh.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13 #if defined(LIBM_SCCS) && !defined(lint)
14 static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $";
15 #endif
16
17 /* asinh(x)
18 * Method :
19 * Based on
20 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
21 * we have
22 * asinh(x) := x if 1+x*x=1,
23 * := sign(x)*(log(x)+ln2)) for large |x|, else
24 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
25 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
26 */
27
28 #include <float.h>
29 #include <math.h>
30 #include <math_private.h>
31 #include <math-underflow.h>
32 #include <math_ldbl_opt.h>
33
34 static const long double
35 one = 1.00000000000000000000e+00L, /* 0x3ff0000000000000, 0 */
36 ln2 = 0.6931471805599453094172321214581766L, /* 0x3fe62e42fefa39ef, 0x3c7abc9e3b398040 */
37 huge= 1.00000000000000000000e+300L;
38
__asinhl(long double x)39 long double __asinhl(long double x)
40 {
41 long double t,w;
42 int64_t hx,ix;
43 double xhi;
44
45 xhi = ldbl_high (x);
46 EXTRACT_WORDS64 (hx, xhi);
47 ix = hx&0x7fffffffffffffffLL;
48 if(ix>=0x7ff0000000000000LL) return x+x; /* x is inf or NaN */
49 if(ix< 0x3c70000000000000LL) { /* |x|<2**-56 */
50 math_check_force_underflow (x);
51 if(huge+x>one) return x; /* return x inexact except 0 */
52 }
53 if(ix>0x4370000000000000LL) { /* |x| > 2**56 */
54 w = __ieee754_logl(fabsl(x))+ln2;
55 } else if (ix>0x4000000000000000LL) { /* 2**56 >= |x| > 2.0 */
56 t = fabs(x);
57 w = __ieee754_logl(2.0*t+one/(sqrtl(x*x+one)+t));
58 } else { /* 2.0 >= |x| >= 2**-56 */
59 t = x*x;
60 w =__log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
61 }
62 if(hx>0) return w; else return -w;
63 }
64 long_double_symbol (libm, __asinhl, asinhl);
65