1/* @(#)e_sinh.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
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
9 * is preserved.
10 * ====================================================
11 */
12
13#if defined(LIBM_SCCS) && !defined(lint)
14static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $";
15#endif
16
17/* __ieee754_sinh(x)
18 * Method :
19 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
20 * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
21 * 2.
22 * E + E/(E+1)
23 * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
24 * 2
25 *
26 * 22 <= x <= lnovft : sinh(x) := exp(x)/2
27 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
28 * ln2ovft < x : sinh(x) := x*shuge (overflow)
29 *
30 * Special cases:
31 * sinh(x) is |x| if x is +INF, -INF, or NaN.
32 * only sinh(0)=0 is exact for finite x.
33 */
34
35#include <float.h>
36#include <math.h>
37#include <math_private.h>
38
39static const double one = 1.0, shuge = 1.0e307;
40
41double
42__ieee754_sinh (double x)
43{
44 double t, w, h;
45 int32_t ix, jx;
46 uint32_t lx;
47
48 /* High word of |x|. */
49 GET_HIGH_WORD (jx, x);
50 ix = jx & 0x7fffffff;
51
52 /* x is INF or NaN */
53 if (__glibc_unlikely (ix >= 0x7ff00000))
54 return x + x;
55
56 h = 0.5;
57 if (jx < 0)
58 h = -h;
59 /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
60 if (ix < 0x40360000) /* |x|<22 */
61 {
62 if (__glibc_unlikely (ix < 0x3e300000)) { /* |x|<2**-28 */
63 math_check_force_underflow (x);
64 if (shuge + x > one)
65 return x;
66 /* sinh(tiny) = tiny with inexact */
67 }
68 t = __expm1 (fabs (x));
69 if (ix < 0x3ff00000)
70 return h * (2.0 * t - t * t / (t + one));
71 return h * (t + t / (t + one));
72 }
73
74 /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
75 if (ix < 0x40862e42)
76 return h * __ieee754_exp (fabs (x));
77
78 /* |x| in [log(maxdouble), overflowthresold] */
79 GET_LOW_WORD (lx, x);
80 if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (uint32_t) 0x8fb9f87d)))
81 {
82 w = __ieee754_exp (0.5 * fabs (x));
83 t = h * w;
84 return t * w;
85 }
86
87 /* |x| > overflowthresold, sinh(x) overflow */
88 return math_narrow_eval (x * shuge);
89}
90strong_alias (__ieee754_sinh, __sinh_finite)
91