1/* e_asinhl.c -- long double version of e_asinh.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#if defined(LIBM_SCCS) && !defined(lint)
16static char rcsid[] = "$NetBSD: $";
17#endif
18
19/* __ieee754_sinhl(x)
20 * Method :
21 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
22 * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
23 * 2.
24 * E + E/(E+1)
25 * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
26 * 2
27 *
28 * 25 <= x <= lnovft : sinhl(x) := expl(x)/2
29 * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
30 * ln2ovft < x : sinhl(x) := x*shuge (overflow)
31 *
32 * Special cases:
33 * sinhl(x) is |x| if x is +INF, -INF, or NaN.
34 * only sinhl(0)=0 is exact for finite x.
35 */
36
37#include <float.h>
38#include <math.h>
39#include <math_private.h>
40#include <math-underflow.h>
41#include <libm-alias-finite.h>
42
43static const long double one = 1.0, shuge = 1.0e4931L;
44
45long double
46__ieee754_sinhl(long double x)
47{
48 long double t,w,h;
49 uint32_t jx,ix,i0,i1;
50
51 /* Words of |x|. */
52 GET_LDOUBLE_WORDS(jx,i0,i1,x);
53 ix = jx&0x7fff;
54
55 /* x is INF or NaN */
56 if(__builtin_expect(ix==0x7fff, 0)) return x+x;
57
58 h = 0.5;
59 if (jx & 0x8000) h = -h;
60 /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
61 if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */
62 if (ix<0x3fdf) { /* |x|<2**-32 */
63 math_check_force_underflow (x);
64 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
65 }
66 t = __expm1l(fabsl(x));
67 if(ix<0x3fff) return h*(2.0*t-t*t/(t+one));
68 return h*(t+t/(t+one));
69 }
70
71 /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
72 if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
73 return h*__ieee754_expl(fabsl(x));
74
75 /* |x| in [log(maxdouble), overflowthreshold] */
76 if (ix<0x400c || (ix == 0x400c && (i0 < 0xb174ddc0
77 || (i0 == 0xb174ddc0
78 && i1 <= 0x31aec0ea)))) {
79 w = __ieee754_expl(0.5*fabsl(x));
80 t = h*w;
81 return t*w;
82 }
83
84 /* |x| > overflowthreshold, sinhl(x) overflow */
85 return x*shuge;
86}
87libm_alias_finite (__ieee754_sinhl, __sinhl)
88