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annotate libquadmath/math/asinq.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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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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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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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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4 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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5 * Developed at SunPro, a Sun Microsystems, Inc. business.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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6 * Permission to use, copy, modify, and distribute this
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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7 * software is freely granted, provided that this notice
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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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 /*
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13 Long double expansions are
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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14 Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
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15 and are incorporated herein by permission of the author. The author
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16 reserves the right to distribute this material elsewhere under different
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17 copying permissions. These modifications are distributed here under the
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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18 following terms:
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19
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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20 This library is free software; you can redistribute it and/or
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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21 modify it under the terms of the GNU Lesser General Public
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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22 License as published by the Free Software Foundation; either
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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23 version 2.1 of the License, or (at your option) any later version.
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24
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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25 This library is distributed in the hope that it will be useful,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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26 but WITHOUT ANY WARRANTY; without even the implied warranty of
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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27 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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28 Lesser General Public License for more details.
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29
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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30 You should have received a copy of the GNU Lesser General Public
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31 License along with this library; if not, see
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32 <http://www.gnu.org/licenses/>. */
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33
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34 /* __ieee754_asin(x)
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35 * Method :
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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36 * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
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37 * we approximate asin(x) on [0,0.5] by
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38 * asin(x) = x + x*x^2*R(x^2)
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39 * Between .5 and .625 the approximation is
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40 * asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
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41 * For x in [0.625,1]
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42 * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
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43 * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
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44 * then for x>0.98
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45 * asin(x) = pi/2 - 2*(s+s*z*R(z))
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46 * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
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47 * For x<=0.98, let pio4_hi = pio2_hi/2, then
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48 * f = hi part of s;
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49 * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
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50 * and
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51 * asin(x) = pi/2 - 2*(s+s*z*R(z))
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52 * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
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53 * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
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54 *
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55 * Special cases:
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56 * if x is NaN, return x itself;
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57 * if |x|>1, return NaN with invalid signal.
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58 *
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59 */
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60
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61 #include "quadmath-imp.h"
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62
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63 static const __float128
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64 one = 1,
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65 huge = 1.0e+4932Q,
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66 pio2_hi = 1.5707963267948966192313216916397514420986Q,
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67 pio2_lo = 4.3359050650618905123985220130216759843812E-35Q,
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68 pio4_hi = 7.8539816339744830961566084581987569936977E-1Q,
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69
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70 /* coefficient for R(x^2) */
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71
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72 /* asin(x) = x + x^3 pS(x^2) / qS(x^2)
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73 0 <= x <= 0.5
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74 peak relative error 1.9e-35 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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75 pS0 = -8.358099012470680544198472400254596543711E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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76 pS1 = 3.674973957689619490312782828051860366493E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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77 pS2 = -6.730729094812979665807581609853656623219E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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78 pS3 = 6.643843795209060298375552684423454077633E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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79 pS4 = -3.817341990928606692235481812252049415993E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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80 pS5 = 1.284635388402653715636722822195716476156E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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81 pS6 = -2.410736125231549204856567737329112037867E2Q,
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82 pS7 = 2.219191969382402856557594215833622156220E1Q,
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83 pS8 = -7.249056260830627156600112195061001036533E-1Q,
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84 pS9 = 1.055923570937755300061509030361395604448E-3Q,
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85
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86 qS0 = -5.014859407482408326519083440151745519205E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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87 qS1 = 2.430653047950480068881028451580393430537E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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88 qS2 = -4.997904737193653607449250593976069726962E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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89 qS3 = 5.675712336110456923807959930107347511086E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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90 qS4 = -3.881523118339661268482937768522572588022E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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91 qS5 = 1.634202194895541569749717032234510811216E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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92 qS6 = -4.151452662440709301601820849901296953752E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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93 qS7 = 5.956050864057192019085175976175695342168E2Q,
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94 qS8 = -4.175375777334867025769346564600396877176E1Q,
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95 /* 1.000000000000000000000000000000000000000E0 */
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96
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97 /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
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98 -0.0625 <= x <= 0.0625
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99 peak relative error 3.3e-35 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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100 rS0 = -5.619049346208901520945464704848780243887E0Q,
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101 rS1 = 4.460504162777731472539175700169871920352E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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102 rS2 = -1.317669505315409261479577040530751477488E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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103 rS3 = 1.626532582423661989632442410808596009227E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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104 rS4 = -3.144806644195158614904369445440583873264E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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105 rS5 = -9.806674443470740708765165604769099559553E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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106 rS6 = 5.708468492052010816555762842394927806920E1Q,
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107 rS7 = 1.396540499232262112248553357962639431922E1Q,
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108 rS8 = -1.126243289311910363001762058295832610344E1Q,
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109 rS9 = -4.956179821329901954211277873774472383512E-1Q,
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110 rS10 = 3.313227657082367169241333738391762525780E-1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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111
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112 sS0 = -4.645814742084009935700221277307007679325E0Q,
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113 sS1 = 3.879074822457694323970438316317961918430E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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114 sS2 = -1.221986588013474694623973554726201001066E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
115 sS3 = 1.658821150347718105012079876756201905822E2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
116 sS4 = -4.804379630977558197953176474426239748977E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
117 sS5 = -1.004296417397316948114344573811562952793E2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
118 sS6 = 7.530281592861320234941101403870010111138E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
119 sS7 = 1.270735595411673647119592092304357226607E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
120 sS8 = -1.815144839646376500705105967064792930282E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
121 sS9 = -7.821597334910963922204235247786840828217E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
122 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
123
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
124 asinr5625 = 5.9740641664535021430381036628424864397707E-1Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
125
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
126
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
127
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
128 __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
129 asinq (__float128 x)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
130 {
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
131 __float128 t, w, p, q, c, r, s;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
132 int32_t ix, sign, flag;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
133 ieee854_float128 u;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
134
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
135 flag = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
136 u.value = x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
137 sign = u.words32.w0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
138 ix = sign & 0x7fffffff;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
139 u.words32.w0 = ix; /* |x| */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
140 if (ix >= 0x3fff0000) /* |x|>= 1 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
141 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
142 if (ix == 0x3fff0000
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
143 && (u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
144 /* asin(1)=+-pi/2 with inexact */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
145 return x * pio2_hi + x * pio2_lo;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
146 return (x - x) / (x - x); /* asin(|x|>1) is NaN */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
147 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
148 else if (ix < 0x3ffe0000) /* |x| < 0.5 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
149 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
150 if (ix < 0x3fc60000) /* |x| < 2**-57 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
151 {
111
kono
parents: 68
diff changeset
152 math_check_force_underflow (x);
kono
parents: 68
diff changeset
153 __float128 force_inexact = huge + x;
kono
parents: 68
diff changeset
154 math_force_eval (force_inexact);
kono
parents: 68
diff changeset
155 return x; /* return x with inexact if x!=0 */
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
156 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
157 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
158 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
159 t = x * x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
160 /* Mark to use pS, qS later on. */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
161 flag = 1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
162 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
163 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
164 else if (ix < 0x3ffe4000) /* 0.625 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
165 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
166 t = u.value - 0.5625;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
167 p = ((((((((((rS10 * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
168 + rS9) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
169 + rS8) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
170 + rS7) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
171 + rS6) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
172 + rS5) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
173 + rS4) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
174 + rS3) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
175 + rS2) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
176 + rS1) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
177 + rS0) * t;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
178
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
179 q = ((((((((( t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
180 + sS9) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
181 + sS8) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
182 + sS7) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
183 + sS6) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
184 + sS5) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
185 + sS4) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
186 + sS3) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
187 + sS2) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
188 + sS1) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
189 + sS0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
190 t = asinr5625 + p / q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
191 if ((sign & 0x80000000) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
192 return t;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
193 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
194 return -t;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
195 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
196 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
197 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
198 /* 1 > |x| >= 0.625 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
199 w = one - u.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
200 t = w * 0.5;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
201 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
202
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
203 p = (((((((((pS9 * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
204 + pS8) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
205 + pS7) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
206 + pS6) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
207 + pS5) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
208 + pS4) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
209 + pS3) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
210 + pS2) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
211 + pS1) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
212 + pS0) * t;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
213
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
214 q = (((((((( t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
215 + qS8) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
216 + qS7) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
217 + qS6) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
218 + qS5) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
219 + qS4) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
220 + qS3) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
221 + qS2) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
222 + qS1) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
223 + qS0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
224
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
225 if (flag) /* 2^-57 < |x| < 0.5 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
226 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
227 w = p / q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
228 return x + x * w;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
229 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
230
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
231 s = sqrtq (t);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
232 if (ix >= 0x3ffef333) /* |x| > 0.975 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
233 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
234 w = p / q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
235 t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
236 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
237 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
238 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
239 u.value = s;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
240 u.words32.w3 = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
241 u.words32.w2 = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
242 w = u.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
243 c = (t - w * w) / (s + w);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
244 r = p / q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
245 p = 2.0 * s * r - (pio2_lo - 2.0 * c);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
246 q = pio4_hi - 2.0 * w;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
247 t = pio4_hi - (p - q);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
248 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
249
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
250 if ((sign & 0x80000000) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
251 return t;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
252 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
253 return -t;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
254 }