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 /* __ieee754_acosh(x)
14 * Method :
15 * Based on
16 * acosh(x) = log [ x + sqrt(x*x-1) ]
17 * we have
18 * acosh(x) := log(x)+ln2, if x is large; else
19 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
20 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
21 *
22 * Special cases:
23 * acosh(x) is NaN with signal if x<1.
24 * acosh(NaN) is NaN without signal.
25 */
26
27 #include <math.h>
28 #include <math_private.h>
29 #include <libm-alias-finite.h>
30
31 static const long double
32 one = 1.0L,
33 ln2 = M_LN2l;
34
35 long double
__ieee754_acoshl(long double x)36 __ieee754_acoshl(long double x)
37 {
38 long double t;
39 int64_t hx;
40 uint64_t lx;
41 double xhi, xlo;
42
43 ldbl_unpack (x, &xhi, &xlo);
44 EXTRACT_WORDS64 (hx, xhi);
45 EXTRACT_WORDS64 (lx, xlo);
46 if(hx<0x3ff0000000000000LL) { /* x < 1 */
47 return (x-x)/(x-x);
48 } else if(hx >=0x4370000000000000LL) { /* x >= 2**56 */
49 if(hx >=0x7ff0000000000000LL) { /* x is inf of NaN */
50 return x+x;
51 } else
52 return __ieee754_logl(x)+ln2; /* acosh(huge)=log(2x) */
53 } else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) {
54 return 0.0; /* acosh(1) = 0 */
55 } else if (hx > 0x4000000000000000LL) { /* 2**56 > x > 2 */
56 t=x*x;
57 return __ieee754_logl(2.0*x-one/(x+sqrtl(t-one)));
58 } else { /* 1<x<2 */
59 t = x-one;
60 return __log1pl(t+sqrtl(2.0*t+t*t));
61 }
62 }
63 libm_alias_finite (__ieee754_acoshl, __acoshl)
64