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 | /* asinh(x) |
14 | * Method : |
15 | * Based on |
16 | * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
17 | * we have |
18 | * asinh(x) := x if 1+x*x=1, |
19 | * := sign(x)*(log(x)+ln2)) for large |x|, else |
20 | * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else |
21 | * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) |
22 | */ |
23 | |
24 | #include <float.h> |
25 | #include <math.h> |
26 | #include <math_private.h> |
27 | |
28 | static const double |
29 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
30 | ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
31 | huge = 1.00000000000000000000e+300; |
32 | |
33 | double |
34 | __asinh (double x) |
35 | { |
36 | double w; |
37 | int32_t hx, ix; |
38 | GET_HIGH_WORD (hx, x); |
39 | ix = hx & 0x7fffffff; |
40 | if (__glibc_unlikely (ix < 0x3e300000)) /* |x|<2**-28 */ |
41 | { |
42 | math_check_force_underflow (x); |
43 | if (huge + x > one) |
44 | return x; /* return x inexact except 0 */ |
45 | } |
46 | if (__glibc_unlikely (ix > 0x41b00000)) /* |x| > 2**28 */ |
47 | { |
48 | if (ix >= 0x7ff00000) |
49 | return x + x; /* x is inf or NaN */ |
50 | w = __ieee754_log (fabs (x)) + ln2; |
51 | } |
52 | else |
53 | { |
54 | double xa = fabs (x); |
55 | if (ix > 0x40000000) /* 2**28 > |x| > 2.0 */ |
56 | { |
57 | w = __ieee754_log (2.0 * xa + one / (__ieee754_sqrt (xa * xa + one) + |
58 | xa)); |
59 | } |
60 | else /* 2.0 > |x| > 2**-28 */ |
61 | { |
62 | double t = xa * xa; |
63 | w = __log1p (xa + t / (one + __ieee754_sqrt (one + t))); |
64 | } |
65 | } |
66 | return __copysign (w, x); |
67 | } |
68 | weak_alias (__asinh, asinh) |
69 | #ifdef NO_LONG_DOUBLE |
70 | strong_alias (__asinh, __asinhl) |
71 | weak_alias (__asinh, asinhl) |
72 | #endif |
73 | |