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 | |
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: x))+ln2; |
55 | } else if (ix>0x4000000000000000LL) { /* 2**56 >= |x| > 2.0 */ |
56 | t = fabs(x: 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(x: fabsl(x: 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 | |