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 /*
14 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
15 *
16 * Permission to use, copy, modify, and distribute this software for any
17 * purpose with or without fee is hereby granted, provided that the above
18 * copyright notice and this permission notice appear in all copies.
19 *
20 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
21 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
22 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
23 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
24 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
25 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
26 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
27 */
28
29 /* sinhl(x)
30 * Method :
31 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
32 * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
33 * 2.
34 * E + E/(E+1)
35 * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
36 * 2
37 *
38 * 25 <= x <= lnovft : sinhl(x) := expl(x)/2
39 * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
40 * ln2ovft < x : sinhl(x) := x*shuge (overflow)
41 *
42 * Special cases:
43 * sinhl(x) is |x| if x is +INF, -INF, or NaN.
44 * only sinhl(0)=0 is exact for finite x.
45 */
46
47
48
49 static const long double one = 1.0L, shuge = 1.0e4931L,
50 ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
51
52 long double
sinhl(long double x)53 sinhl(long double x)
54 {
55 long double t, w, h;
56 int32_t jx;
57 u_int32_t ix;
58 ieee_quad_shape_type u;
59
60 /* Words of |x|. */
61 u.value = x;
62 jx = u.parts32.mswhi;
63 ix = jx & 0x7fffffff;
64
65 /* x is INF or NaN */
66 if (ix >= 0x7fff0000)
67 return x + x;
68
69 h = 0.5L;
70 if (jx < 0)
71 h = -h;
72
73 /* Absolute value of x. */
74 u.parts32.mswhi = ix;
75
76 /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
77 if (ix <= 0x40044000)
78 {
79 if (ix < 0x3fc60000) /* |x| < 2^-57 */
80 if (shuge + x > one)
81 return x; /* sinh(tiny) = tiny with inexact */
82 t = expm1l (u.value);
83 if (ix < 0x3fff0000)
84 return h * (2.0L * t - t * t / (t + one));
85 return h * (t + t / (t + one));
86 }
87
88 /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
89 if (ix <= 0x400c62e3) /* 11356.375 */
90 return h * expl (u.value);
91
92 /* |x| in [log(maxdouble), overflowthreshold]
93 Overflow threshold is log(2 * maxdouble). */
94 if (u.value <= ovf_thresh)
95 {
96 w = expl (0.5L * u.value);
97 t = h * w;
98 return t * w;
99 }
100
101 /* |x| > overflowthreshold, sinhl(x) overflow */
102 return __math_oflowl(jx < 0);
103 }
104
