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annotate libquadmath/math/coshq.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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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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1 /*
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2 * ====================================================
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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4 *
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5 * Developed at SunPro, a Sun Microsystems, Inc. business.
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6 * Permission to use, copy, modify, and distribute this
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7 * software is freely granted, provided that this notice
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8 * is preserved.
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9 * ====================================================
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10 */
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11
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12 /* Changes for 128-bit long double are
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13 Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
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14 and are incorporated herein by permission of the author. The author
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15 reserves the right to distribute this material elsewhere under different
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16 copying permissions. These modifications are distributed here under
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17 the following terms:
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18
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19 This library is free software; you can redistribute it and/or
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20 modify it under the terms of the GNU Lesser General Public
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21 License as published by the Free Software Foundation; either
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22 version 2.1 of the License, or (at your option) any later version.
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23
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24 This library is distributed in the hope that it will be useful,
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25 but WITHOUT ANY WARRANTY; without even the implied warranty of
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26 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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27 Lesser General Public License for more details.
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28
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29 You should have received a copy of the GNU Lesser General Public
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30 License along with this library; if not, see
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31 <http://www.gnu.org/licenses/>. */
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32
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33 /* coshq(x)
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34 * Method :
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35 * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
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36 * 1. Replace x by |x| (coshl(x) = coshl(-x)).
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37 * 2.
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38 * [ exp(x) - 1 ]^2
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39 * 0 <= x <= ln2/2 : coshl(x) := 1 + -------------------
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40 * 2*exp(x)
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41 *
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42 * exp(x) + 1/exp(x)
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43 * ln2/2 <= x <= 22 : coshl(x) := -------------------
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44 * 2
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45 * 22 <= x <= lnovft : coshl(x) := expq(x)/2
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46 * lnovft <= x <= ln2ovft: coshl(x) := expq(x/2)/2 * expq(x/2)
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47 * ln2ovft < x : coshl(x) := huge*huge (overflow)
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48 *
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49 * Special cases:
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50 * coshl(x) is |x| if x is +INF, -INF, or NaN.
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51 * only coshl(0)=1 is exact for finite x.
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52 */
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53
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54 #include "quadmath-imp.h"
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55
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56 static const __float128 one = 1.0, half = 0.5, huge = 1.0e4900Q,
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57 ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
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58
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59 __float128
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60 coshq (__float128 x)
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61 {
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62 __float128 t, w;
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63 int32_t ex;
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64 ieee854_float128 u;
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65
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66 u.value = x;
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67 ex = u.words32.w0 & 0x7fffffff;
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68
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69 /* Absolute value of x. */
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70 u.words32.w0 = ex;
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71
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72 /* x is INF or NaN */
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73 if (ex >= 0x7fff0000)
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74 return x * x;
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75
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76 /* |x| in [0,0.5*ln2], return 1+expm1q(|x|)^2/(2*expq(|x|)) */
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77 if (ex < 0x3ffd62e4) /* 0.3465728759765625 */
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78 {
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79 if (ex < 0x3fb80000) /* |x| < 2^-116 */
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80 return one; /* cosh(tiny) = 1 */
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81 t = expm1q (u.value);
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82 w = one + t;
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83
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84 return one + (t * t) / (w + w);
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85 }
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86
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87 /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */
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88 if (ex < 0x40044000)
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89 {
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90 t = expq (u.value);
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91 return half * t + half / t;
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92 }
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93
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94 /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
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95 if (ex <= 0x400c62e3) /* 11356.375 */
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96 return half * expq (u.value);
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97
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98 /* |x| in [log(maxdouble), overflowthresold] */
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99 if (u.value <= ovf_thresh)
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100 {
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101 w = expq (half * u.value);
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102 t = half * w;
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103 return t * w;
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104 }
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105
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106 /* |x| > overflowthresold, cosh(x) overflow */
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107 return huge * huge;
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108 }