1/* e_acoshl.c -- long double version of e_acosh.c.
2 * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
3 */
4
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16/* acoshq(x)
17 * Method :
18 *	Based on
19 *		acoshl(x) = logq [ x + sqrtq(x*x-1) ]
20 *	we have
21 *		acoshl(x) := logq(x)+ln2,	if x is large; else
22 *		acoshl(x) := logq(2x-1/(sqrtq(x*x-1)+x)) if x>2; else
23 *		acoshl(x) := log1pq(t+sqrtq(2.0*t+t*t)); where t=x-1.
24 *
25 * Special cases:
26 *	acoshl(x) is NaN with signal if x<1.
27 *	acoshl(NaN) is NaN without signal.
28 */
29
30#include "quadmath-imp.h"
31
32static const __float128
33one	= 1.0,
34ln2	= 0.6931471805599453094172321214581766Q;
35
36__float128
37acoshq(__float128 x)
38{
39	__float128 t;
40	uint64_t lx;
41	int64_t hx;
42	GET_FLT128_WORDS64(hx,lx,x);
43	if(hx<0x3fff000000000000LL) {		/* x < 1 */
44	    return (x-x)/(x-x);
45	} else if(hx >=0x4035000000000000LL) {	/* x > 2**54 */
46	    if(hx >=0x7fff000000000000LL) {	/* x is inf of NaN */
47		return x+x;
48	    } else
49		return logq(x)+ln2;	/* acoshl(huge)=logq(2x) */
50	} else if(((hx-0x3fff000000000000LL)|lx)==0) {
51	    return 0;			/* acosh(1) = 0 */
52	} else if (hx > 0x4000000000000000LL) {	/* 2**28 > x > 2 */
53	    t=x*x;
54	    return logq(2*x-one/(x+sqrtq(t-one)));
55	} else {			/* 1<x<2 */
56	    t = x-one;
57	    return log1pq(t+sqrtq(2*t+t*t));
58	}
59}
60