Mercurial > hg > CbC > CbC_gcc

comparison libquadmath/math/sinhq.c @ 145:1830386684a0

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
gcc-9.2.0
author anatofuz
date Thu, 13 Feb 2020 11:34:05 +0900
parents 04ced10e8804
children
comparison
equal deleted inserted replaced
131:84e7813d76e9 145:1830386684a0
1 /* sinhq.c -- __float128 version of e_sinh.c. 1 /* e_sinhl.c -- long double version of e_sinh.c.
2 * Conversion to __float128 by Ulrich Drepper, 2 * Conversion to long double by Ulrich Drepper,
3 * Cygnus Support, drepper@cygnus.com. 3 * Cygnus Support, drepper@cygnus.com.
4 */ 4 */
5 5
6 /* 6 /*
7 * ==================================================== 7 * ====================================================
12 * software is freely granted, provided that this notice 12 * software is freely granted, provided that this notice
13 * is preserved. 13 * is preserved.
14 * ==================================================== 14 * ====================================================
15 */ 15 */
16 16
17 /* Changes for 128-bit __float128 are 17 /* Changes for 128-bit long double are
18 Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> 18 Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
19 and are incorporated herein by permission of the author. The author 19 and are incorporated herein by permission of the author. The author
20 reserves the right to distribute this material elsewhere under different 20 reserves the right to distribute this material elsewhere under different
21 copying permissions. These modifications are distributed here under 21 copying permissions. These modifications are distributed here under
22 the following terms: 22 the following terms:
23 23
24 This library is free software; you can redistribute it and/or 24 This library is free software; you can redistribute it and/or
25 modify it under the terms of the GNU Lesser General Public 25 modify it under the terms of the GNU Lesser General Public
26 License as published by the Free Software Foundation; either 26 License as published by the Free Software Foundation; either
30 but WITHOUT ANY WARRANTY; without even the implied warranty of 30 but WITHOUT ANY WARRANTY; without even the implied warranty of
31 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 31 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
32 Lesser General Public License for more details. 32 Lesser General Public License for more details.
33 33
34 You should have received a copy of the GNU Lesser General Public 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 35 License along with this library; if not, see
36 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ 36 <http://www.gnu.org/licenses/>. */
37 37
38 /* sinhq(x) 38 /* sinhq(x)
39 * Method : 39 * Method :
40 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 40 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
41 * 1. Replace x by |x| (sinhq(-x) = -sinhq(x)). 41 * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
42 * 2. 42 * 2.
43 * E + E/(E+1) 43 * E + E/(E+1)
44 * 0 <= x <= 25 : sinhq(x) := --------------, E=expm1q(x) 44 * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1q(x)
45 * 2 45 * 2
46 * 46 *
47 * 25 <= x <= lnovft : sinhq(x) := expq(x)/2 47 * 25 <= x <= lnovft : sinhl(x) := expq(x)/2
48 * lnovft <= x <= ln2ovft: sinhq(x) := expq(x/2)/2 * expq(x/2) 48 * lnovft <= x <= ln2ovft: sinhl(x) := expq(x/2)/2 * expq(x/2)
49 * ln2ovft < x : sinhq(x) := x*shuge (overflow) 49 * ln2ovft < x : sinhl(x) := x*shuge (overflow)
50 * 50 *
51 * Special cases: 51 * Special cases:
52 * sinhq(x) is |x| if x is +INF, -INF, or NaN. 52 * sinhl(x) is |x| if x is +INF, -INF, or NaN.
53 * only sinhq(0)=0 is exact for finite x. 53 * only sinhl(0)=0 is exact for finite x.
54 */ 54 */
55 55
56 #include "quadmath-imp.h" 56 #include "quadmath-imp.h"
57 57
58 static const __float128 one = 1.0, shuge = 1.0e4931Q, 58 static const __float128 one = 1.0, shuge = 1.0e4931Q,
59 ovf_thresh = 1.1357216553474703894801348310092223067821E4Q; 59 ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
60 60
61 __float128 61 __float128
62 sinhq (__float128 x) 62 sinhq (__float128 x)
63 { 63 {
64 __float128 t, w, h; 64 __float128 t, w, h;
72 72
73 /* x is INF or NaN */ 73 /* x is INF or NaN */
74 if (ix >= 0x7fff0000) 74 if (ix >= 0x7fff0000)
75 return x + x; 75 return x + x;
76 76
77 h = 0.5Q; 77 h = 0.5;
78 if (jx & 0x80000000) 78 if (jx & 0x80000000)
79 h = -h; 79 h = -h;
80 80
81 /* Absolute value of x. */ 81 /* Absolute value of x. */
82 u.words32.w0 = ix; 82 u.words32.w0 = ix;
90 if (shuge + x > one) 90 if (shuge + x > one)
91 return x; /* sinh(tiny) = tiny with inexact */ 91 return x; /* sinh(tiny) = tiny with inexact */
92 } 92 }
93 t = expm1q (u.value); 93 t = expm1q (u.value);
94 if (ix < 0x3fff0000) 94 if (ix < 0x3fff0000)
95 return h * (2.0Q * t - t * t / (t + one)); 95 return h * (2.0 * t - t * t / (t + one));
96 return h * (t + t / (t + one)); 96 return h * (t + t / (t + one));
97 } 97 }
98 98
99 /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */ 99 /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
100 if (ix <= 0x400c62e3) /* 11356.375 */ 100 if (ix <= 0x400c62e3) /* 11356.375 */
102 102
103 /* |x| in [log(maxdouble), overflowthreshold] 103 /* |x| in [log(maxdouble), overflowthreshold]
104 Overflow threshold is log(2 * maxdouble). */ 104 Overflow threshold is log(2 * maxdouble). */
105 if (u.value <= ovf_thresh) 105 if (u.value <= ovf_thresh)
106 { 106 {
107 w = expq (0.5Q * u.value); 107 w = expq (0.5 * u.value);
108 t = h * w; 108 t = h * w;
109 return t * w; 109 return t * w;
110 } 110 }
111 111
112 /* |x| > overflowthreshold, sinhq(x) overflow */ 112 /* |x| > overflowthreshold, sinhl(x) overflow */
113 return x * shuge; 113 return x * shuge;
114 } 114 }