Update.
[glibc.git] / sysdeps / libm-ieee754 / e_acoshl.c
bloba60704aa29afbfc7273cf8eaf8abda772b63e898
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.
4 */
6 /*
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
13 * is preserved.
14 * ====================================================
17 #if defined(LIBM_SCCS) && !defined(lint)
18 static char rcsid[] = "$NetBSD: $";
19 #endif
21 /* __ieee754_acoshl(x)
22 * Method :
23 * Based on
24 * acoshl(x) = logl [ x + sqrtl(x*x-1) ]
25 * we have
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.
30 * Special cases:
31 * acoshl(x) is NaN with signal if x<1.
32 * acoshl(NaN) is NaN without signal.
35 #include "math.h"
36 #include "math_private.h"
38 #ifdef __STDC__
39 static const long double
40 #else
41 static long double
42 #endif
43 one = 1.0,
44 ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
46 #ifdef __STDC__
47 long double __ieee754_acoshl(long double x)
48 #else
49 long double __ieee754_acoshl(x)
50 long double x;
51 #endif
53 long double t;
54 u_int32_t se,i0,i1;
55 GET_LDOUBLE_WORDS(se,i0,i1,x);
56 if(se<0x3fff || se & 0x8000) { /* x < 1 */
57 return (x-x)/(x-x);
58 } else if(se >=0x401b) { /* x > 2**28 */
59 if(se >=0x7fff) { /* x is inf of NaN */
60 return x+x;
61 } else
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 */
66 t=x*x;
67 return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one)));
68 } else { /* 1<x<2 */
69 t = x-one;
70 return __log1pl(t+__sqrtl(2.0*t+t*t));