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annotate libquadmath/math/sinhq.c @ 158:494b0b89df80 default tip

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Mon, 25 May 2020 18:13:55 +0900
parents 1830386684a0
children
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1 /* e_sinhl.c -- long double version of e_sinh.c.
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2 * Conversion to long double by Ulrich Drepper,
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3 * Cygnus Support, drepper@cygnus.com.
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4 */
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5
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6 /*
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7 * ====================================================
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8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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9 *
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10 * Developed at SunPro, a Sun Microsystems, Inc. business.
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11 * Permission to use, copy, modify, and distribute this
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12 * software is freely granted, provided that this notice
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13 * is preserved.
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14 * ====================================================
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15 */
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16
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17 /* Changes for 128-bit long double are
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18 Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
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19 and are incorporated herein by permission of the author. The author
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20 reserves the right to distribute this material elsewhere under different
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21 copying permissions. These modifications are distributed here under
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22 the following terms:
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23
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24 This library is free software; you can redistribute it and/or
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25 modify it under the terms of the GNU Lesser General Public
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26 License as published by the Free Software Foundation; either
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27 version 2.1 of the License, or (at your option) any later version.
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28
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29 This library is distributed in the hope that it will be useful,
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30 but WITHOUT ANY WARRANTY; without even the implied warranty of
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31 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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32 Lesser General Public License for more details.
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33
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34 You should have received a copy of the GNU Lesser General Public
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35 License along with this library; if not, see
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36 <http://www.gnu.org/licenses/>. */
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37
111
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38 /* sinhq(x)
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39 * Method :
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40 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
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41 * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
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42 * 2.
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43 * E + E/(E+1)
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44 * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1q(x)
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45 * 2
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46 *
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47 * 25 <= x <= lnovft : sinhl(x) := expq(x)/2
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48 * lnovft <= x <= ln2ovft: sinhl(x) := expq(x/2)/2 * expq(x/2)
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49 * ln2ovft < x : sinhl(x) := x*shuge (overflow)
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50 *
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51 * Special cases:
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52 * sinhl(x) is |x| if x is +INF, -INF, or NaN.
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53 * only sinhl(0)=0 is exact for finite x.
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54 */
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55
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56 #include "quadmath-imp.h"
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57
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58 static const __float128 one = 1.0, shuge = 1.0e4931Q,
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59 ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
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60
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61 __float128
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62 sinhq (__float128 x)
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63 {
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64 __float128 t, w, h;
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65 uint32_t jx, ix;
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66 ieee854_float128 u;
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67
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68 /* Words of |x|. */
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69 u.value = x;
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70 jx = u.words32.w0;
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71 ix = jx & 0x7fffffff;
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72
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73 /* x is INF or NaN */
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74 if (ix >= 0x7fff0000)
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75 return x + x;
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76
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77 h = 0.5;
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78 if (jx & 0x80000000)
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79 h = -h;
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80
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81 /* Absolute value of x. */
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82 u.words32.w0 = ix;
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83
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84 /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
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85 if (ix <= 0x40044000)
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86 {
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87 if (ix < 0x3fc60000) /* |x| < 2^-57 */
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88 {
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89 math_check_force_underflow (x);
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90 if (shuge + x > one)
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91 return x; /* sinh(tiny) = tiny with inexact */
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92 }
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93 t = expm1q (u.value);
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94 if (ix < 0x3fff0000)
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95 return h * (2.0 * t - t * t / (t + one));
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96 return h * (t + t / (t + one));
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97 }
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98
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99 /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
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100 if (ix <= 0x400c62e3) /* 11356.375 */
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101 return h * expq (u.value);
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102
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103 /* |x| in [log(maxdouble), overflowthreshold]
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104 Overflow threshold is log(2 * maxdouble). */
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105 if (u.value <= ovf_thresh)
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106 {
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107 w = expq (0.5 * u.value);
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108 t = h * w;
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109 return t * w;
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110 }
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111
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112 /* |x| > overflowthreshold, sinhl(x) overflow */
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113 return x * shuge;
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114 }