1 /* sinhq.c -- __float128 version of e_sinh.c.
2 * Conversion to __float128 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 /* Changes for 128-bit __float128 are
18 Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
19 and are incorporated herein by permission of the author. The author
20 reserves the right to distribute this material elsewhere under different
21 copying permissions. These modifications are distributed here under
22 the following terms:
23
24 This library is free software; you can redistribute it and/or
25 modify it under the terms of the GNU Lesser General Public
26 License as published by the Free Software Foundation; either
27 version 2.1 of the License, or (at your option) any later version.
28
29 This library is distributed in the hope that it will be useful,
30 but WITHOUT ANY WARRANTY; without even the implied warranty of
31 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
32 Lesser General Public License for more details.
33
34 You should have received a copy of the GNU Lesser General Public
35 License along with this library; if not, write to the Free Software
36 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
37
38 /* sinhq(x)
39 * Method :
40 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
41 * 1. Replace x by |x| (sinhq(-x) = -sinhq(x)).
42 * 2.
43 * E + E/(E+1)
44 * 0 <= x <= 25 : sinhq(x) := --------------, E=expm1q(x)
45 * 2
46 *
47 * 25 <= x <= lnovft : sinhq(x) := expq(x)/2
48 * lnovft <= x <= ln2ovft: sinhq(x) := expq(x/2)/2 * expq(x/2)
49 * ln2ovft < x : sinhq(x) := x*shuge (overflow)
50 *
51 * Special cases:
52 * sinhq(x) is |x| if x is +INF, -INF, or NaN.
53 * only sinhq(0)=0 is exact for finite x.
54 */
55
56 #include "quadmath-imp.h"
57
58 static const __float128 one = 1.0, shuge = 1.0e4931Q,
59 ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
60
61 __float128
sinhq(__float128 x)62 sinhq (__float128 x)
63 {
64 __float128 t, w, h;
65 uint32_t jx, ix;
66 ieee854_float128 u;
67
68 /* Words of |x|. */
69 u.value = x;
70 jx = u.words32.w0;
71 ix = jx & 0x7fffffff;
72
73 /* x is INF or NaN */
74 if (ix >= 0x7fff0000)
75 return x + x;
76
77 h = 0.5Q;
78 if (jx & 0x80000000)
79 h = -h;
80
81 /* Absolute value of x. */
82 u.words32.w0 = ix;
83
84 /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
85 if (ix <= 0x40044000)
86 {
87 if (ix < 0x3fc60000) /* |x| < 2^-57 */
88 if (shuge + x > one)
89 return x; /* sinh(tiny) = tiny with inexact */
90 t = expm1q (u.value);
91 if (ix < 0x3fff0000)
92 return h * (2.0Q * t - t * t / (t + one));
93 return h * (t + t / (t + one));
94 }
95
96 /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
97 if (ix <= 0x400c62e3) /* 11356.375 */
98 return h * expq (u.value);
99
100 /* |x| in [log(maxdouble), overflowthreshold]
101 Overflow threshold is log(2 * maxdouble). */
102 if (u.value <= ovf_thresh)
103 {
104 w = expq (0.5Q * u.value);
105 t = h * w;
106 return t * w;
107 }
108
109 /* |x| > overflowthreshold, sinhq(x) overflow */
110 return x * shuge;
111 }
112