1 /* @(#)e_acosh.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
16 * acosh(x) = log [ x + sqrt(x*x-1) ]
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.
23 * acosh(x) is NaN with signal if x<1.
24 * acosh(NaN) is NaN without signal.
28 #include <math_private.h>
29 #include <libm-alias-finite.h>
31 static const long double
36 __ieee754_acoshl(long double x
)
43 ldbl_unpack (x
, &xhi
, &xlo
);
44 EXTRACT_WORDS64 (hx
, xhi
);
45 EXTRACT_WORDS64 (lx
, xlo
);
46 if(hx
<0x3ff0000000000000LL
) { /* x < 1 */
48 } else if(hx
>=0x4370000000000000LL
) { /* x >= 2**56 */
49 if(hx
>=0x7ff0000000000000LL
) { /* x is inf of NaN */
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 */
57 return __ieee754_logl(2.0*x
-one
/(x
+sqrtl(t
-one
)));
60 return __log1pl(t
+sqrtl(2.0*t
+t
*t
));
63 libm_alias_finite (__ieee754_acoshl
, __acoshl
)