1*181254a7Smrg /* e_sinhl.c -- long double version of e_sinh.c.
2*181254a7Smrg * Conversion to long double by Ulrich Drepper,
3*181254a7Smrg * Cygnus Support, drepper@cygnus.com.
4*181254a7Smrg */
5*181254a7Smrg
6*181254a7Smrg /*
7*181254a7Smrg * ====================================================
8*181254a7Smrg * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9*181254a7Smrg *
10*181254a7Smrg * Developed at SunPro, a Sun Microsystems, Inc. business.
11*181254a7Smrg * Permission to use, copy, modify, and distribute this
12*181254a7Smrg * software is freely granted, provided that this notice
13*181254a7Smrg * is preserved.
14*181254a7Smrg * ====================================================
15*181254a7Smrg */
16*181254a7Smrg
17*181254a7Smrg /* Changes for 128-bit long double are
18*181254a7Smrg Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
19*181254a7Smrg and are incorporated herein by permission of the author. The author
20*181254a7Smrg reserves the right to distribute this material elsewhere under different
21*181254a7Smrg copying permissions. These modifications are distributed here under
22*181254a7Smrg the following terms:
23*181254a7Smrg
24*181254a7Smrg This library is free software; you can redistribute it and/or
25*181254a7Smrg modify it under the terms of the GNU Lesser General Public
26*181254a7Smrg License as published by the Free Software Foundation; either
27*181254a7Smrg version 2.1 of the License, or (at your option) any later version.
28*181254a7Smrg
29*181254a7Smrg This library is distributed in the hope that it will be useful,
30*181254a7Smrg but WITHOUT ANY WARRANTY; without even the implied warranty of
31*181254a7Smrg MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
32*181254a7Smrg Lesser General Public License for more details.
33*181254a7Smrg
34*181254a7Smrg You should have received a copy of the GNU Lesser General Public
35*181254a7Smrg License along with this library; if not, see
36*181254a7Smrg <http://www.gnu.org/licenses/>. */
37*181254a7Smrg
38*181254a7Smrg /* sinhq(x)
39*181254a7Smrg * Method :
40*181254a7Smrg * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
41*181254a7Smrg * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
42*181254a7Smrg * 2.
43*181254a7Smrg * E + E/(E+1)
44*181254a7Smrg * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1q(x)
45*181254a7Smrg * 2
46*181254a7Smrg *
47*181254a7Smrg * 25 <= x <= lnovft : sinhl(x) := expq(x)/2
48*181254a7Smrg * lnovft <= x <= ln2ovft: sinhl(x) := expq(x/2)/2 * expq(x/2)
49*181254a7Smrg * ln2ovft < x : sinhl(x) := x*shuge (overflow)
50*181254a7Smrg *
51*181254a7Smrg * Special cases:
52*181254a7Smrg * sinhl(x) is |x| if x is +INF, -INF, or NaN.
53*181254a7Smrg * only sinhl(0)=0 is exact for finite x.
54*181254a7Smrg */
55*181254a7Smrg
56*181254a7Smrg #include "quadmath-imp.h"
57*181254a7Smrg
58*181254a7Smrg static const __float128 one = 1.0, shuge = 1.0e4931Q,
59*181254a7Smrg ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
60*181254a7Smrg
61*181254a7Smrg __float128
sinhq(__float128 x)62*181254a7Smrg sinhq (__float128 x)
63*181254a7Smrg {
64*181254a7Smrg __float128 t, w, h;
65*181254a7Smrg uint32_t jx, ix;
66*181254a7Smrg ieee854_float128 u;
67*181254a7Smrg
68*181254a7Smrg /* Words of |x|. */
69*181254a7Smrg u.value = x;
70*181254a7Smrg jx = u.words32.w0;
71*181254a7Smrg ix = jx & 0x7fffffff;
72*181254a7Smrg
73*181254a7Smrg /* x is INF or NaN */
74*181254a7Smrg if (ix >= 0x7fff0000)
75*181254a7Smrg return x + x;
76*181254a7Smrg
77*181254a7Smrg h = 0.5;
78*181254a7Smrg if (jx & 0x80000000)
79*181254a7Smrg h = -h;
80*181254a7Smrg
81*181254a7Smrg /* Absolute value of x. */
82*181254a7Smrg u.words32.w0 = ix;
83*181254a7Smrg
84*181254a7Smrg /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
85*181254a7Smrg if (ix <= 0x40044000)
86*181254a7Smrg {
87*181254a7Smrg if (ix < 0x3fc60000) /* |x| < 2^-57 */
88*181254a7Smrg {
89*181254a7Smrg math_check_force_underflow (x);
90*181254a7Smrg if (shuge + x > one)
91*181254a7Smrg return x; /* sinh(tiny) = tiny with inexact */
92*181254a7Smrg }
93*181254a7Smrg t = expm1q (u.value);
94*181254a7Smrg if (ix < 0x3fff0000)
95*181254a7Smrg return h * (2.0 * t - t * t / (t + one));
96*181254a7Smrg return h * (t + t / (t + one));
97*181254a7Smrg }
98*181254a7Smrg
99*181254a7Smrg /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
100*181254a7Smrg if (ix <= 0x400c62e3) /* 11356.375 */
101*181254a7Smrg return h * expq (u.value);
102*181254a7Smrg
103*181254a7Smrg /* |x| in [log(maxdouble), overflowthreshold]
104*181254a7Smrg Overflow threshold is log(2 * maxdouble). */
105*181254a7Smrg if (u.value <= ovf_thresh)
106*181254a7Smrg {
107*181254a7Smrg w = expq (0.5 * u.value);
108*181254a7Smrg t = h * w;
109*181254a7Smrg return t * w;
110*181254a7Smrg }
111*181254a7Smrg
112*181254a7Smrg /* |x| > overflowthreshold, sinhl(x) overflow */
113*181254a7Smrg return x * shuge;
114*181254a7Smrg }
115