1 /* e_acoshl.c -- long double version of e_acosh.c.
2 */
3
4 /*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunPro, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15 /* __ieee754_acoshl(x)
16 * Method :
17 * Based on
18 * acoshl(x) = logl [ x + sqrtl(x*x-1) ]
19 * we have
20 * acoshl(x) := logl(x)+ln2, if x is large; else
21 * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
22 * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
23 *
24 * Special cases:
25 * acoshl(x) is NaN with signal if x<1.
26 * acoshl(NaN) is NaN without signal.
27 */
28
29 #include <math.h>
30 #include <math_private.h>
31 #include <libm-alias-finite.h>
32
33 static const _Float128
34 one = 1.0,
35 ln2 = L(0.6931471805599453094172321214581766);
36
37 _Float128
__ieee754_acoshl(_Float128 x)38 __ieee754_acoshl(_Float128 x)
39 {
40 _Float128 t;
41 uint64_t lx;
42 int64_t hx;
43 GET_LDOUBLE_WORDS64(hx,lx,x);
44 if(hx<0x3fff000000000000LL) { /* x < 1 */
45 return (x-x)/(x-x);
46 } else if(hx >=0x4035000000000000LL) { /* x > 2**54 */
47 if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */
48 return x+x;
49 } else
50 return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */
51 } else if(((hx-0x3fff000000000000LL)|lx)==0) {
52 return 0; /* acosh(1) = 0 */
53 } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
54 t=x*x;
55 return __ieee754_logl(2*x-one/(x+sqrtl(t-one)));
56 } else { /* 1<x<2 */
57 t = x-one;
58 return __log1pl(t+sqrtl(2*t+t*t));
59 }
60 }
61 libm_alias_finite (__ieee754_acoshl, __acoshl)
62