1*49393c00Smartynas /* @(#)e_acosh.c 5.1 93/09/24 */
2*49393c00Smartynas /*
3*49393c00Smartynas * ====================================================
4*49393c00Smartynas * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*49393c00Smartynas *
6*49393c00Smartynas * Developed at SunPro, a Sun Microsystems, Inc. business.
7*49393c00Smartynas * Permission to use, copy, modify, and distribute this
8*49393c00Smartynas * software is freely granted, provided that this notice
9*49393c00Smartynas * is preserved.
10*49393c00Smartynas * ====================================================
11*49393c00Smartynas */
12*49393c00Smartynas
13*49393c00Smartynas /* acoshl(x)
14*49393c00Smartynas * Method :
15*49393c00Smartynas * Based on
16*49393c00Smartynas * acoshl(x) = logl [ x + sqrtl(x*x-1) ]
17*49393c00Smartynas * we have
18*49393c00Smartynas * acoshl(x) := logl(x)+ln2, if x is large; else
19*49393c00Smartynas * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
20*49393c00Smartynas * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
21*49393c00Smartynas *
22*49393c00Smartynas * Special cases:
23*49393c00Smartynas * acoshl(x) is NaN with signal if x<1.
24*49393c00Smartynas * acoshl(NaN) is NaN without signal.
25*49393c00Smartynas */
26*49393c00Smartynas
27*49393c00Smartynas #include <math.h>
28*49393c00Smartynas
29*49393c00Smartynas #include "math_private.h"
30*49393c00Smartynas
31*49393c00Smartynas static const long double
32*49393c00Smartynas one = 1.0,
33*49393c00Smartynas ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
34*49393c00Smartynas
35*49393c00Smartynas long double
acoshl(long double x)36*49393c00Smartynas acoshl(long double x)
37*49393c00Smartynas {
38*49393c00Smartynas long double t;
39*49393c00Smartynas u_int32_t se,i0,i1;
40*49393c00Smartynas GET_LDOUBLE_WORDS(se,i0,i1,x);
41*49393c00Smartynas if(se<0x3fff || se & 0x8000) { /* x < 1 */
42*49393c00Smartynas return (x-x)/(x-x);
43*49393c00Smartynas } else if(se >=0x401d) { /* x > 2**30 */
44*49393c00Smartynas if(se >=0x7fff) { /* x is inf of NaN */
45*49393c00Smartynas return x+x;
46*49393c00Smartynas } else
47*49393c00Smartynas return logl(x)+ln2; /* acoshl(huge)=logl(2x) */
48*49393c00Smartynas } else if(((se-0x3fff)|i0|i1)==0) {
49*49393c00Smartynas return 0.0; /* acosh(1) = 0 */
50*49393c00Smartynas } else if (se > 0x4000) { /* 2**28 > x > 2 */
51*49393c00Smartynas t=x*x;
52*49393c00Smartynas return logl(2.0*x-one/(x+sqrtl(t-one)));
53*49393c00Smartynas } else { /* 1<x<2 */
54*49393c00Smartynas t = x-one;
55*49393c00Smartynas return log1pl(t+sqrtl(2.0*t+t*t));
56*49393c00Smartynas }
57*49393c00Smartynas }
58