1/* e_asinhl.c -- long double version of e_asinh.c.
2 * Conversion to long double by Ulrich Drepper,
3 * Cygnus Support, drepper@cygnus.com.
4 */
5
6/*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
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 * ====================================================
15 */
16
17#if defined(LIBM_SCCS) && !defined(lint)
18static char rcsid[] = "$NetBSD: $";
19#endif
20
21/* __ieee754_sinhl(x)
22 * Method :
23 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
24 * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
25 * 2.
26 * E + E/(E+1)
27 * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
28 * 2
29 *
30 * 25 <= x <= lnovft : sinhl(x) := expl(x)/2
31 * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
32 * ln2ovft < x : sinhl(x) := x*shuge (overflow)
33 *
34 * Special cases:
35 * sinhl(x) is |x| if x is +INF, -INF, or NaN.
36 * only sinhl(0)=0 is exact for finite x.
37 */
38
39#include <float.h>
40#include <math.h>
41#include <math_private.h>
42#include <math-underflow.h>
43#include <libm-alias-finite.h>
44
45static const long double one = 1.0, shuge = 1.0e4931L;
46
47long double
48__ieee754_sinhl(long double x)
49{
50 long double t,w,h;
51 uint32_t jx,ix,i0,i1;
52
53 /* Words of |x|. */
54 GET_LDOUBLE_WORDS(jx,i0,i1,x);
55 ix = jx&0x7fff;
56
57 /* x is INF or NaN */
58 if(__builtin_expect(ix==0x7fff, 0)) return x+x;
59
60 h = 0.5;
61 if (jx & 0x8000) h = -h;
62 /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
63 if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */
64 if (ix<0x3fdf) { /* |x|<2**-32 */
65 math_check_force_underflow (x);
66 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
67 }
68 t = __expm1l(fabsl(x));
69 if(ix<0x3fff) return h*(2.0*t-t*t/(t+one));
70 return h*(t+t/(t+one));
71 }
72
73 /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
74 if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
75 return h*__ieee754_expl(fabsl(x));
76
77 /* |x| in [log(maxdouble), overflowthreshold] */
78 if (ix<0x400c || (ix == 0x400c && (i0 < 0xb174ddc0
79 || (i0 == 0xb174ddc0
80 && i1 <= 0x31aec0ea)))) {
81 w = __ieee754_expl(0.5*fabsl(x));
82 t = h*w;
83 return t*w;
84 }
85
86 /* |x| > overflowthreshold, sinhl(x) overflow */
87 return x*shuge;
88}
89libm_alias_finite (__ieee754_sinhl, __sinhl)
90