1 | /* @(#)e_acosh.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 | /* __ieee754_acosh(x) |
14 | * Method : |
15 | * Based on |
16 | * acosh(x) = log [ x + sqrt(x*x-1) ] |
17 | * we have |
18 | * acosh(x) := log(x)+ln2, if x is large; else |
19 | * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else |
20 | * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. |
21 | * |
22 | * Special cases: |
23 | * acosh(x) is NaN with signal if x<1. |
24 | * acosh(NaN) is NaN without signal. |
25 | */ |
26 | |
27 | #include <math.h> |
28 | #include <math_private.h> |
29 | #include <libm-alias-finite.h> |
30 | |
31 | static const long double |
32 | one = 1.0L, |
33 | ln2 = M_LN2l; |
34 | |
35 | long double |
36 | __ieee754_acoshl(long double x) |
37 | { |
38 | long double t; |
39 | int64_t hx; |
40 | uint64_t lx; |
41 | double xhi, xlo; |
42 | |
43 | ldbl_unpack (x, &xhi, &xlo); |
44 | EXTRACT_WORDS64 (hx, xhi); |
45 | EXTRACT_WORDS64 (lx, xlo); |
46 | if(hx<0x3ff0000000000000LL) { /* x < 1 */ |
47 | return (x-x)/(x-x); |
48 | } else if(hx >=0x4370000000000000LL) { /* x >= 2**56 */ |
49 | if(hx >=0x7ff0000000000000LL) { /* x is inf of NaN */ |
50 | return x+x; |
51 | } else |
52 | return __ieee754_logl(x)+ln2; /* acosh(huge)=log(2x) */ |
53 | } else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) { |
54 | return 0.0; /* acosh(1) = 0 */ |
55 | } else if (hx > 0x4000000000000000LL) { /* 2**56 > x > 2 */ |
56 | t=x*x; |
57 | return __ieee754_logl(2.0*x-one/(x+sqrtl(t-one))); |
58 | } else { /* 1<x<2 */ |
59 | t = x-one; |
60 | return __log1pl(x: t+sqrtl(2.0*t+t*t)); |
61 | } |
62 | } |
63 | libm_alias_finite (__ieee754_acoshl, __acoshl) |
64 | |