1 /* e_acoshl.c -- long double version of e_acosh.c.
2 * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
13 * ====================================================
16 /* __ieee754_acoshl(x)
19 * acoshl(x) = logl [ x + sqrtl(x*x-1) ]
21 * acoshl(x) := logl(x)+ln2, if x is large; else
22 * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
23 * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
26 * acoshl(x) is NaN with signal if x<1.
27 * acoshl(NaN) is NaN without signal.
31 #include "math_private.h"
34 static const long double
39 ln2 = 0.6931471805599453094172321214581766L;
42 long double __ieee754_acoshl(long double x)
44 long double __ieee754_acoshl(x)
51 GET_LDOUBLE_WORDS64(hx,lx,x);
52 if(hx<0x3fff000000000000LL) { /* x < 1 */
54 } else if(hx >=0x4035000000000000LL) { /* x > 2**54 */
55 if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */
58 return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */
59 } else if(((hx-0x3fff000000000000LL)|lx)==0) {
60 return 0.0L; /* acosh(1) = 0 */
61 } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
63 return __ieee754_logl(2.0L*x-one/(x+__ieee754_sqrtl(t-one)));
66 return __log1pl(t+__sqrtl(2.0L*t+t*t));