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
32 static const __float128
33 one = 1.0,
34 ln2 = 0.6931471805599453094172321214581766Q;
35
36 __float128
acoshq(__float128 x)37 acoshq(__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