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
13 /* acoshl(x)
14 * Method :
15 * Based on
16 * acoshl(x) = logl [ x + sqrtl(x*x-1) ]
17 * we have
18 * acoshl(x) := logl(x)+ln2, if x is large; else
19 * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
20 * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
21 *
22 * Special cases:
23 * acoshl(x) is NaN with signal if x<1.
24 * acoshl(NaN) is NaN without signal.
25 */
26
27
28
29 static const long double
30 one = 1.0L,
31 ln2 = 0.6931471805599453094172321214581766L;
32
33 long double
acoshl(long double x)34 acoshl(long double x)
35 {
36 long double t;
37 u_int64_t lx;
38 int64_t hx;
39 GET_LDOUBLE_WORDS64(hx,lx,x);
40 if(hx<0x3fff000000000000LL) { /* x < 1 */
41 return __math_invalidl(x);
42 } else if(hx >=0x4035000000000000LL) { /* x > 2**54 */
43 if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */
44 return x+x;
45 } else
46 return logl(x)+ln2; /* acoshl(huge)=logl(2x) */
47 } else if(((hx-0x3fff000000000000LL)|lx)==0) {
48 return 0.0L; /* acosh(1) = 0 */
49 } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
50 t=x*x;
51 return logl(2.0L*x-one/(x+sqrtl(t-one)));
52 } else { /* 1<x<2 */
53 t = x-one;
54 return log1pl(t+sqrtl(2.0L*t+t*t));
55 }
56 }
57
