1 /* e_acoshl.c -- long double version of e_acosh.c.
2 * Conversion to long double by Ulrich Drepper,
3 * Cygnus Support, drepper@cygnus.com.
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
14 * ====================================================
17 #if defined(LIBM_SCCS) && !defined(lint)
18 static char rcsid[] = "$NetBSD: $";
21 /* __ieee754_acoshl(x)
24 * acoshl(x) = logl [ x + sqrtl(x*x-1) ]
26 * acoshl(x) := logl(x)+ln2, if x is large; else
27 * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
28 * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
31 * acoshl(x) is NaN with signal if x<1.
32 * acoshl(NaN) is NaN without signal.
36 #include "math_private.h"
39 static const long double
44 ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
47 long double __ieee754_acoshl(long double x)
49 long double __ieee754_acoshl(x)
55 GET_LDOUBLE_WORDS(se,i0,i1,x);
56 if(se<0x3fff) { /* x < 1 */
58 } else if(se >=0x401b) { /* x > 2**28 */
59 if(se >=0x7fff) { /* x is inf of NaN */
62 return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */
63 } else if(((se-0x3fff)|i0|i1)==0) {
64 return 0.0; /* acosh(1) = 0 */
65 } else if (se > 0x4000) { /* 2**28 > x > 2 */
67 return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one)));
70 return __log1pl(t+__sqrtl(2.0*t+t*t));