1/* e_acoshl.c -- long double version of e_acosh.c.
2 * Conversion to long double by Ulrich Drepper,
3 * Cygnus Support, drepper@cygnus.com.
4 */
5
6/*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
13 * is preserved.
14 * ====================================================
15 */
16
17/* __ieee754_acoshl(x)
18 * Method :
19 * Based on
20 * acoshl(x) = logl [ x + sqrtl(x*x-1) ]
21 * we have
22 * acoshl(x) := logl(x)+ln2, if x is large; else
23 * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
24 * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
25 *
26 * Special cases:
27 * acoshl(x) is NaN with signal if x<1.
28 * acoshl(NaN) is NaN without signal.
29 */
30
31#include <math.h>
32#include <math_private.h>
33#include <libm-alias-finite.h>
34
35static const long double
36one = 1.0,
37ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
38
39long double
40__ieee754_acoshl(long double x)
41{
42 long double t;
43 uint32_t se,i0,i1;
44 GET_LDOUBLE_WORDS(se,i0,i1,x);
45 if(se<0x3fff || se & 0x8000) { /* x < 1 */
46 return (x-x)/(x-x);
47 } else if(se >=0x401d) { /* x > 2**30 */
48 if(se >=0x7fff) { /* x is inf of NaN */
49 return x+x;
50 } else
51 return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */
52 } else if(((se-0x3fff)|(i0^0x80000000)|i1)==0) {
53 return 0.0; /* acosh(1) = 0 */
54 } else if (se > 0x4000) { /* 2**28 > x > 2 */
55 t=x*x;
56 return __ieee754_logl(2.0*x-one/(x+sqrtl(t-one)));
57 } else { /* 1<x<2 */
58 t = x-one;
59 return __log1pl(t+sqrtl(2.0*t+t*t));
60 }
61}
62libm_alias_finite (__ieee754_acoshl, __acoshl)
63