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annotate libquadmath/math/acosq.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
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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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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8 * is preserved.
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9 * ====================================================
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10 */
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11
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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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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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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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
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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18 the 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>
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28 Lesser General Public License for more details.
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29
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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
111
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34 /* acosq(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 * acos(x) = pi/2 - asin(x)
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37 * acos(-x) = pi/2 + asin(x)
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38 * For |x| <= 0.375
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39 * acos(x) = pi/2 - asin(x)
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40 * Between .375 and .5 the approximation is
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41 * acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x)
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42 * Between .5 and .625 the approximation is
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43 * acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
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44 * For x > 0.625,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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45 * acos(x) = 2 asin(sqrt((1-x)/2))
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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46 * computed with an extended precision square root in the leading term.
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47 * For x < -0.625
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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48 * acos(x) = pi - 2 asin(sqrt((1-|x|)/2))
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49 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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50 * Special cases:
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51 * if x is NaN, return x itself;
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52 * if |x|>1, return NaN with invalid signal.
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53 *
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54 * Functions needed: sqrtq.
68
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55 */
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56
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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57 #include "quadmath-imp.h"
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58
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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59 static const __float128
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60 one = 1,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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61 pio2_hi = 1.5707963267948966192313216916397514420986Q,
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62 pio2_lo = 4.3359050650618905123985220130216759843812E-35Q,
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63
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64 /* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
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65 -0.0625 <= x <= 0.0625
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66 peak relative error 3.3e-35 */
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67
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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68 rS0 = 5.619049346208901520945464704848780243887E0Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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69 rS1 = -4.460504162777731472539175700169871920352E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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70 rS2 = 1.317669505315409261479577040530751477488E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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71 rS3 = -1.626532582423661989632442410808596009227E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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72 rS4 = 3.144806644195158614904369445440583873264E1Q,
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73 rS5 = 9.806674443470740708765165604769099559553E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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74 rS6 = -5.708468492052010816555762842394927806920E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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75 rS7 = -1.396540499232262112248553357962639431922E1Q,
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76 rS8 = 1.126243289311910363001762058295832610344E1Q,
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77 rS9 = 4.956179821329901954211277873774472383512E-1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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78 rS10 = -3.313227657082367169241333738391762525780E-1Q,
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79
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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80 sS0 = -4.645814742084009935700221277307007679325E0Q,
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81 sS1 = 3.879074822457694323970438316317961918430E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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82 sS2 = -1.221986588013474694623973554726201001066E2Q,
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83 sS3 = 1.658821150347718105012079876756201905822E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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84 sS4 = -4.804379630977558197953176474426239748977E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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85 sS5 = -1.004296417397316948114344573811562952793E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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86 sS6 = 7.530281592861320234941101403870010111138E1Q,
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87 sS7 = 1.270735595411673647119592092304357226607E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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88 sS8 = -1.815144839646376500705105967064792930282E1Q,
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89 sS9 = -7.821597334910963922204235247786840828217E-2Q,
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90 /* 1.000000000000000000000000000000000000000E0 */
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91
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92 acosr5625 = 9.7338991014954640492751132535550279812151E-1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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93 pimacosr5625 = 2.1682027434402468335351320579240000860757E0Q,
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94
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95 /* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x)
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96 -0.0625 <= x <= 0.0625
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97 peak relative error 2.1e-35 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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98
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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99 P0 = 2.177690192235413635229046633751390484892E0Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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100 P1 = -2.848698225706605746657192566166142909573E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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101 P2 = 1.040076477655245590871244795403659880304E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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102 P3 = -1.400087608918906358323551402881238180553E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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103 P4 = 2.221047917671449176051896400503615543757E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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104 P5 = 9.643714856395587663736110523917499638702E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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105 P6 = -5.158406639829833829027457284942389079196E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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106 P7 = -1.578651828337585944715290382181219741813E1Q,
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107 P8 = 1.093632715903802870546857764647931045906E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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108 P9 = 5.448925479898460003048760932274085300103E-1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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109 P10 = -3.315886001095605268470690485170092986337E-1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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110 Q0 = -1.958219113487162405143608843774587557016E0Q,
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111 Q1 = 2.614577866876185080678907676023269360520E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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112 Q2 = -9.990858606464150981009763389881793660938E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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113 Q3 = 1.443958741356995763628660823395334281596E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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114 Q4 = -3.206441012484232867657763518369723873129E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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115 Q5 = -1.048560885341833443564920145642588991492E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
116 Q6 = 6.745883931909770880159915641984874746358E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
117 Q7 = 1.806809656342804436118449982647641392951E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
118 Q8 = -1.770150690652438294290020775359580915464E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
119 Q9 = -5.659156469628629327045433069052560211164E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
120 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
121
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
122 acosr4375 = 1.1179797320499710475919903296900511518755E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
123 pimacosr4375 = 2.0236129215398221908706530535894517323217E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
124
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
125 /* asin(x) = x + x^3 pS(x^2) / qS(x^2)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
126 0 <= x <= 0.5
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
127 peak relative error 1.9e-35 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
128 pS0 = -8.358099012470680544198472400254596543711E2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
129 pS1 = 3.674973957689619490312782828051860366493E3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
130 pS2 = -6.730729094812979665807581609853656623219E3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
131 pS3 = 6.643843795209060298375552684423454077633E3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
132 pS4 = -3.817341990928606692235481812252049415993E3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
133 pS5 = 1.284635388402653715636722822195716476156E3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
134 pS6 = -2.410736125231549204856567737329112037867E2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
135 pS7 = 2.219191969382402856557594215833622156220E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
136 pS8 = -7.249056260830627156600112195061001036533E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
137 pS9 = 1.055923570937755300061509030361395604448E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
138
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
139 qS0 = -5.014859407482408326519083440151745519205E3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
140 qS1 = 2.430653047950480068881028451580393430537E4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
141 qS2 = -4.997904737193653607449250593976069726962E4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
142 qS3 = 5.675712336110456923807959930107347511086E4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
143 qS4 = -3.881523118339661268482937768522572588022E4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
144 qS5 = 1.634202194895541569749717032234510811216E4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
145 qS6 = -4.151452662440709301601820849901296953752E3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
146 qS7 = 5.956050864057192019085175976175695342168E2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
147 qS8 = -4.175375777334867025769346564600396877176E1Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
148 /* 1.000000000000000000000000000000000000000E0 */
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 __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
151 acosq (__float128 x)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
152 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
153 __float128 z, r, w, p, q, s, t, f2;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
154 int32_t ix, sign;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
155 ieee854_float128 u;
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 u.value = x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
158 sign = u.words32.w0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
159 ix = sign & 0x7fffffff;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
160 u.words32.w0 = ix; /* |x| */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
161 if (ix >= 0x3fff0000) /* |x| >= 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 if (ix == 0x3fff0000
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
164 && (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
165 { /* |x| == 1 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
166 if ((sign & 0x80000000) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
167 return 0.0; /* acos(1) = 0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
168 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
169 return (2.0 * pio2_hi) + (2.0 * pio2_lo); /* acos(-1)= pi */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
170 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
171 return (x - x) / (x - x); /* acos(|x| > 1) is NaN */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
172 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
173 else if (ix < 0x3ffe0000) /* |x| < 0.5 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
174 {
111
kono
parents: 68
diff changeset
175 if (ix < 0x3f8e0000) /* |x| < 2**-113 */
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
176 return pio2_hi + pio2_lo;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
177 if (ix < 0x3ffde000) /* |x| < .4375 */
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 /* Arcsine of x. */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
180 z = x * x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
181 p = (((((((((pS9 * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
182 + pS8) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
183 + pS7) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
184 + pS6) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
185 + pS5) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
186 + pS4) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
187 + pS3) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
188 + pS2) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
189 + pS1) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
190 + pS0) * z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
191 q = (((((((( z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
192 + qS8) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
193 + qS7) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
194 + qS6) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
195 + qS5) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
196 + qS4) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
197 + qS3) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
198 + qS2) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
199 + qS1) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
200 + qS0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
201 r = x + x * p / q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
202 z = pio2_hi - (r - pio2_lo);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
203 return z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
204 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
205 /* .4375 <= |x| < .5 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
206 t = u.value - 0.4375Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
207 p = ((((((((((P10 * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
208 + P9) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
209 + P8) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
210 + P7) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
211 + P6) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
212 + P5) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
213 + P4) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
214 + P3) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
215 + P2) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
216 + P1) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
217 + P0) * t;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
218
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
219 q = (((((((((t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
220 + Q9) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
221 + Q8) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
222 + Q7) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
223 + Q6) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
224 + Q5) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
225 + Q4) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
226 + Q3) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
227 + Q2) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
228 + Q1) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
229 + Q0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
230 r = p / q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
231 if (sign & 0x80000000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
232 r = pimacosr4375 - r;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
233 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
234 r = acosr4375 + r;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
235 return r;
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 if (ix < 0x3ffe4000) /* |x| < 0.625 */
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 t = u.value - 0.5625Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
240 p = ((((((((((rS10 * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
241 + rS9) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
242 + rS8) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
243 + rS7) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
244 + rS6) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
245 + rS5) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
246 + rS4) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
247 + rS3) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
248 + rS2) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
249 + rS1) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
250 + rS0) * t;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
251
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
252 q = (((((((((t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
253 + sS9) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
254 + sS8) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
255 + sS7) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
256 + sS6) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
257 + sS5) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
258 + sS4) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
259 + sS3) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
260 + sS2) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
261 + sS1) * t
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
262 + sS0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
263 if (sign & 0x80000000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
264 r = pimacosr5625 - p / q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
265 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
266 r = acosr5625 + p / q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
267 return r;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
268 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
269 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
270 { /* |x| >= .625 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
271 z = (one - u.value) * 0.5;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
272 s = sqrtq (z);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
273 /* Compute an extended precision square root from
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
274 the Newton iteration s -> 0.5 * (s + z / s).
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
275 The change w from s to the improved value is
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
276 w = 0.5 * (s + z / s) - s = (s^2 + z)/2s - s = (z - s^2)/2s.
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
277 Express s = f1 + f2 where f1 * f1 is exactly representable.
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
278 w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s .
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
279 s + w has extended precision. */
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
280 u.value = s;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
281 u.words32.w2 = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
282 u.words32.w3 = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
283 f2 = s - u.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
284 w = z - u.value * u.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
285 w = w - 2.0 * u.value * f2;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
286 w = w - f2 * f2;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
287 w = w / (2.0 * s);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
288 /* Arcsine of s. */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
289 p = (((((((((pS9 * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
290 + pS8) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
291 + pS7) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
292 + pS6) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
293 + pS5) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
294 + pS4) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
295 + pS3) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
296 + pS2) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
297 + pS1) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
298 + pS0) * z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
299 q = (((((((( z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
300 + qS8) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
301 + qS7) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
302 + qS6) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
303 + qS5) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
304 + qS4) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
305 + qS3) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
306 + qS2) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
307 + qS1) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
308 + qS0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
309 r = s + (w + s * p / q);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
310
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
311 if (sign & 0x80000000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
312 w = pio2_hi + (pio2_lo - r);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
313 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
314 w = r;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
315 return 2.0 * w;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
316 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
317 }