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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 | ||
f964490f RM |
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 | ||
f964490f | 30 | static const long double |
f964490f RM |
31 | one = 1.0L, |
32 | ln2 = 6.93147180559945286227e-01L; /* 0x3FE62E42, 0xFEFA39EF */ | |
33 | ||
0ac5ae23 UD |
34 | long double |
35 | __ieee754_acoshl(long double x) | |
f964490f RM |
36 | { |
37 | long double t; | |
38 | int64_t hx; | |
39 | u_int64_t lx; | |
40 | GET_LDOUBLE_WORDS64(hx,lx,x); | |
41 | if(hx<0x3ff0000000000000LL) { /* x < 1 */ | |
42 | return (x-x)/(x-x); | |
43 | } else if(hx >=0x41b0000000000000LL) { /* x > 2**28 */ | |
44 | if(hx >=0x7ff0000000000000LL) { /* x is inf of NaN */ | |
0ac5ae23 | 45 | return x+x; |
f964490f RM |
46 | } else |
47 | return __ieee754_logl(x)+ln2; /* acosh(huge)=log(2x) */ | |
48 | } else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) { | |
49 | return 0.0; /* acosh(1) = 0 */ | |
50 | } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */ | |
51 | t=x*x; | |
52 | return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one))); | |
53 | } else { /* 1<x<2 */ | |
54 | t = x-one; | |
55 | return __log1p(t+__sqrtl(2.0*t+t*t)); | |
56 | } | |
57 | } | |
0ac5ae23 | 58 | strong_alias (__ieee754_acoshl, __acoshl_finite) |