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 static const long double
28 one = 1.0l,
29 ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
30
31 long double
acoshl(long double x)32 acoshl(long double x)
33 {
34 long double t;
35 u_int32_t se,i0,i1;
36 GET_LDOUBLE_WORDS(se,i0,i1,x);
37 if(se<0x3fff || se & 0x8000) { /* x < 1 */
38 return __math_invalidl(x);
39 } else if(se >=0x401d) { /* x > 2**30 */
40 if(se >=0x7fff) { /* x is inf of NaN */
41 return x+x;
42 } else
43 return logl(x)+ln2; /* acoshl(huge)=logl(2x) */
44 } else if(((se-0x3fff)|i0|i1)==0) {
45 return 0.0l; /* acosh(1) = 0 */
46 } else if (se > 0x4000) { /* 2**28 > x > 2 */
47 t=x*x;
48 return logl(2.0l*x-one/(x+sqrtl(t-one)));
49 } else { /* 1<x<2 */
50 t = x-one;
51 return log1pl(t+sqrtl(2.0l*t+t*t));
52 }
53 }
54
