1/* e_acoshl.c -- long double version of e_acosh.c.
2 */
3
4/*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunPro, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15/* __ieee754_acoshl(x)
16 * Method :
17 * Based on
18 * acoshl(x) = logl [ x + sqrtl(x*x-1) ]
19 * we have
20 * acoshl(x) := logl(x)+ln2, if x is large; else
21 * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
22 * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
23 *
24 * Special cases:
25 * acoshl(x) is NaN with signal if x<1.
26 * acoshl(NaN) is NaN without signal.
27 */
28
29#include <math.h>
30#include <math_private.h>
31#include <libm-alias-finite.h>
32
33static const long double
34one = 1.0,
35ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
36
37long double
38__ieee754_acoshl(long double x)
39{
40 long double t;
41 uint32_t se,i0,i1;
42 GET_LDOUBLE_WORDS(se,i0,i1,x);
43 if(se<0x3fff || se & 0x8000) { /* x < 1 */
44 return (x-x)/(x-x);
45 } else if(se >=0x401d) { /* x > 2**30 */
46 if(se >=0x7fff) { /* x is inf of NaN */
47 return x+x;
48 } else
49 return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */
50 } else if(((se-0x3fff)|(i0^0x80000000)|i1)==0) {
51 return 0.0; /* acosh(1) = 0 */
52 } else if (se > 0x4000) { /* 2**28 > x > 2 */
53 t=x*x;
54 return __ieee754_logl(2.0*x-one/(x+sqrtl(t-one)));
55 } else { /* 1<x<2 */
56 t = x-one;
57 return __log1pl(t+sqrtl(2.0*t+t*t));
58 }
59}
60libm_alias_finite (__ieee754_acoshl, __acoshl)
61