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annotate libquadmath/math/powq.c @ 111:04ced10e8804

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gcc 7
author kono
date Fri, 27 Oct 2017 22:46:09 +0900
parents 561a7518be6b
children 1830386684a0
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rev   line source
68
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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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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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12 /* Expansions and modifications for 128-bit long double are
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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13 Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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14 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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15 reserves the right to distribute this material elsewhere under different
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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16 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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17 the following terms:
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18
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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19 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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20 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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21 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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22 version 2.1 of the License, or (at your option) any later version.
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23
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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24 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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25 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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26 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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27 Lesser General Public License for more details.
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28
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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29 You should have received a copy of the GNU Lesser General Public
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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30 License along with this library; if not, write to the Free Software
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31 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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32
111
kono
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33 /* powq(x,y) return x**y
68
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34 *
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35 * n
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36 * Method: Let x = 2 * (1+f)
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37 * 1. Compute and return log2(x) in two pieces:
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38 * log2(x) = w1 + w2,
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39 * where w1 has 113-53 = 60 bit trailing zeros.
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40 * 2. Perform y*log2(x) = n+y' by simulating muti-precision
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41 * arithmetic, where |y'|<=0.5.
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42 * 3. Return x**y = 2**n*exp(y'*log2)
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43 *
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44 * Special cases:
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45 * 1. (anything) ** 0 is 1
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46 * 2. (anything) ** 1 is itself
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47 * 3. (anything) ** NAN is NAN
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48 * 4. NAN ** (anything except 0) is NAN
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49 * 5. +-(|x| > 1) ** +INF is +INF
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50 * 6. +-(|x| > 1) ** -INF is +0
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51 * 7. +-(|x| < 1) ** +INF is +0
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52 * 8. +-(|x| < 1) ** -INF is +INF
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53 * 9. +-1 ** +-INF is NAN
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54 * 10. +0 ** (+anything except 0, NAN) is +0
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55 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
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56 * 12. +0 ** (-anything except 0, NAN) is +INF
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57 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
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58 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
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59 * 15. +INF ** (+anything except 0,NAN) is +INF
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60 * 16. +INF ** (-anything except 0,NAN) is +0
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61 * 17. -INF ** (anything) = -0 ** (-anything)
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62 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
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63 * 19. (-anything except 0 and inf) ** (non-integer) is NAN
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64 *
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65 */
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66
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67 #include "quadmath-imp.h"
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68
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69 static const __float128 bp[] = {
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70 1.0Q,
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71 1.5Q,
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72 };
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73
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74 /* log_2(1.5) */
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75 static const __float128 dp_h[] = {
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76 0.0,
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77 5.8496250072115607565592654282227158546448E-1Q
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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78 };
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79
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80 /* Low part of log_2(1.5) */
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81 static const __float128 dp_l[] = {
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82 0.0,
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83 1.0579781240112554492329533686862998106046E-16Q
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84 };
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85
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86 static const __float128 zero = 0.0Q,
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87 one = 1.0Q,
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88 two = 2.0Q,
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89 two113 = 1.0384593717069655257060992658440192E34Q,
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90 huge = 1.0e3000Q,
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91 tiny = 1.0e-3000Q;
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92
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93 /* 3/2 log x = 3 z + z^3 + z^3 (z^2 R(z^2))
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94 z = (x-1)/(x+1)
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95 1 <= x <= 1.25
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96 Peak relative error 2.3e-37 */
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97 static const __float128 LN[] =
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98 {
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99 -3.0779177200290054398792536829702930623200E1Q,
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100 6.5135778082209159921251824580292116201640E1Q,
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101 -4.6312921812152436921591152809994014413540E1Q,
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102 1.2510208195629420304615674658258363295208E1Q,
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103 -9.9266909031921425609179910128531667336670E-1Q
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104 };
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105 static const __float128 LD[] =
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106 {
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107 -5.129862866715009066465422805058933131960E1Q,
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108 1.452015077564081884387441590064272782044E2Q,
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109 -1.524043275549860505277434040464085593165E2Q,
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110 7.236063513651544224319663428634139768808E1Q,
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111 -1.494198912340228235853027849917095580053E1Q
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112 /* 1.0E0 */
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113 };
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114
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115 /* exp(x) = 1 + x - x / (1 - 2 / (x - x^2 R(x^2)))
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116 0 <= x <= 0.5
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117 Peak relative error 5.7e-38 */
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118 static const __float128 PN[] =
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119 {
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120 5.081801691915377692446852383385968225675E8Q,
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121 9.360895299872484512023336636427675327355E6Q,
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diff changeset
122 4.213701282274196030811629773097579432957E4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
123 5.201006511142748908655720086041570288182E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
124 9.088368420359444263703202925095675982530E-3Q,
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 static const __float128 PD[] =
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 3.049081015149226615468111430031590411682E9Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
129 1.069833887183886839966085436512368982758E8Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
130 8.259257717868875207333991924545445705394E5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
131 1.872583833284143212651746812884298360922E3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
132 /* 1.0E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
133 };
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 static const __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
136 /* ln 2 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
137 lg2 = 6.9314718055994530941723212145817656807550E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
138 lg2_h = 6.9314718055994528622676398299518041312695E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
139 lg2_l = 2.3190468138462996154948554638754786504121E-17Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
140 ovt = 8.0085662595372944372e-0017Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
141 /* 2/(3*log(2)) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
142 cp = 9.6179669392597560490661645400126142495110E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
143 cp_h = 9.6179669392597555432899980587535537779331E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
144 cp_l = 5.0577616648125906047157785230014751039424E-17Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
145
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
146 __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
147 powq (__float128 x, __float128 y)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
148 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
149 __float128 z, ax, z_h, z_l, p_h, p_l;
111
kono
parents: 68
diff changeset
150 __float128 y1, t1, t2, r, s, sgn, t, u, v, w;
kono
parents: 68
diff changeset
151 __float128 s2, s_h, s_l, t_h, t_l, ay;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
152 int32_t i, j, k, yisint, n;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
153 uint32_t ix, iy;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
154 int32_t hx, hy;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
155 ieee854_float128 o, p, q;
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 p.value = x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
158 hx = p.words32.w0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
159 ix = hx & 0x7fffffff;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
160
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
161 q.value = y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
162 hy = q.words32.w0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
163 iy = hy & 0x7fffffff;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
164
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 /* y==zero: x**0 = 1 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
167 if ((iy | q.words32.w1 | q.words32.w2 | q.words32.w3) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
168 return one;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
169
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
170 /* 1.0**y = 1; -1.0**+-Inf = 1 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
171 if (x == one)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
172 return one;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
173 if (x == -1.0Q && iy == 0x7fff0000
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
174 && (q.words32.w1 | q.words32.w2 | q.words32.w3) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
175 return one;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
176
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
177 /* +-NaN return x+y */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
178 if ((ix > 0x7fff0000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
179 || ((ix == 0x7fff0000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
180 && ((p.words32.w1 | p.words32.w2 | p.words32.w3) != 0))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
181 || (iy > 0x7fff0000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
182 || ((iy == 0x7fff0000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
183 && ((q.words32.w1 | q.words32.w2 | q.words32.w3) != 0)))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
184 return x + y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
185
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
186 /* determine if y is an odd int when x < 0
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
187 * yisint = 0 ... y is not an integer
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
188 * yisint = 1 ... y is an odd int
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
189 * yisint = 2 ... y is an even int
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
190 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
191 yisint = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
192 if (hx < 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
193 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
194 if (iy >= 0x40700000) /* 2^113 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
195 yisint = 2; /* even integer y */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
196 else if (iy >= 0x3fff0000) /* 1.0 */
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 if (floorq (y) == y)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
199 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
200 z = 0.5 * y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
201 if (floorq (z) == z)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
202 yisint = 2;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
203 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
204 yisint = 1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
205 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
206 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
207 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
208
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
209 /* special value of y */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
210 if ((q.words32.w1 | q.words32.w2 | q.words32.w3) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
211 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
212 if (iy == 0x7fff0000) /* y is +-inf */
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 if (((ix - 0x3fff0000) | p.words32.w1 | p.words32.w2 | p.words32.w3)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
215 == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
216 return y - y; /* +-1**inf is NaN */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
217 else if (ix >= 0x3fff0000) /* (|x|>1)**+-inf = inf,0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
218 return (hy >= 0) ? y : zero;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
219 else /* (|x|<1)**-,+inf = inf,0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
220 return (hy < 0) ? -y : zero;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
221 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
222 if (iy == 0x3fff0000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
223 { /* y is +-1 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
224 if (hy < 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
225 return one / x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
226 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
227 return x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
228 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
229 if (hy == 0x40000000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
230 return x * x; /* y is 2 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
231 if (hy == 0x3ffe0000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
232 { /* y is 0.5 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
233 if (hx >= 0) /* x >= +0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
234 return sqrtq (x);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
235 }
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
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
238 ax = fabsq (x);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
239 /* special value of x */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
240 if ((p.words32.w1 | p.words32.w2 | p.words32.w3) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
241 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
242 if (ix == 0x7fff0000 || ix == 0 || ix == 0x3fff0000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
243 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
244 z = ax; /*x is +-0,+-inf,+-1 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
245 if (hy < 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
246 z = one / z; /* z = (1/|x|) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
247 if (hx < 0)
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 if (((ix - 0x3fff0000) | yisint) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
250 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
251 z = (z - z) / (z - z); /* (-1)**non-int is NaN */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
252 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
253 else if (yisint == 1)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
254 z = -z; /* (x<0)**odd = -(|x|**odd) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
255 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
256 return z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
257 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
258 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
259
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
260 /* (x<0)**(non-int) is NaN */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
261 if (((((uint32_t) hx >> 31) - 1) | yisint) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
262 return (x - x) / (x - x);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
263
111
kono
parents: 68
diff changeset
264 /* sgn (sign of result -ve**odd) = -1 else = 1 */
kono
parents: 68
diff changeset
265 sgn = one;
kono
parents: 68
diff changeset
266 if (((((uint32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
kono
parents: 68
diff changeset
267 sgn = -one; /* (-ve)**(odd int) */
kono
parents: 68
diff changeset
268
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
269 /* |y| is huge.
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
270 2^-16495 = 1/2 of smallest representable value.
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
271 If (1 - 1/131072)^y underflows, y > 1.4986e9 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
272 if (iy > 0x401d654b)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
273 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
274 /* if (1 - 2^-113)^y underflows, y > 1.1873e38 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
275 if (iy > 0x407d654b)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
276 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
277 if (ix <= 0x3ffeffff)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
278 return (hy < 0) ? huge * huge : tiny * tiny;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
279 if (ix >= 0x3fff0000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
280 return (hy > 0) ? huge * huge : tiny * tiny;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
281 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
282 /* over/underflow if x is not close to one */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
283 if (ix < 0x3ffeffff)
111
kono
parents: 68
diff changeset
284 return (hy < 0) ? sgn * huge * huge : sgn * tiny * tiny;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
285 if (ix > 0x3fff0000)
111
kono
parents: 68
diff changeset
286 return (hy > 0) ? sgn * huge * huge : sgn * tiny * tiny;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
287 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
288
111
kono
parents: 68
diff changeset
289 ay = y > 0 ? y : -y;
kono
parents: 68
diff changeset
290 if (ay < 0x1p-128)
kono
parents: 68
diff changeset
291 y = y < 0 ? -0x1p-128 : 0x1p-128;
kono
parents: 68
diff changeset
292
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
293 n = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
294 /* take care subnormal number */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
295 if (ix < 0x00010000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
296 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
297 ax *= two113;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
298 n -= 113;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
299 o.value = ax;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
300 ix = o.words32.w0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
301 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
302 n += ((ix) >> 16) - 0x3fff;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
303 j = ix & 0x0000ffff;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
304 /* determine interval */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
305 ix = j | 0x3fff0000; /* normalize ix */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
306 if (j <= 0x3988)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
307 k = 0; /* |x|<sqrt(3/2) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
308 else if (j < 0xbb67)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
309 k = 1; /* |x|<sqrt(3) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
310 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
311 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
312 k = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
313 n += 1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
314 ix -= 0x00010000;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
315 }
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 o.value = ax;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
318 o.words32.w0 = ix;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
319 ax = o.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
320
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
321 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
322 u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
323 v = one / (ax + bp[k]);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
324 s = u * v;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
325 s_h = s;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
326
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
327 o.value = s_h;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
328 o.words32.w3 = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
329 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
330 s_h = o.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
331 /* t_h=ax+bp[k] High */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
332 t_h = ax + bp[k];
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
333 o.value = t_h;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
334 o.words32.w3 = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
335 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
336 t_h = o.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
337 t_l = ax - (t_h - bp[k]);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
338 s_l = v * ((u - s_h * t_h) - s_h * t_l);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
339 /* compute log(ax) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
340 s2 = s * s;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
341 u = LN[0] + s2 * (LN[1] + s2 * (LN[2] + s2 * (LN[3] + s2 * LN[4])));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
342 v = LD[0] + s2 * (LD[1] + s2 * (LD[2] + s2 * (LD[3] + s2 * (LD[4] + s2))));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
343 r = s2 * s2 * u / v;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
344 r += s_l * (s_h + s);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
345 s2 = s_h * s_h;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
346 t_h = 3.0 + s2 + r;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
347 o.value = t_h;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
348 o.words32.w3 = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
349 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
350 t_h = o.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
351 t_l = r - ((t_h - 3.0) - s2);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
352 /* u+v = s*(1+...) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
353 u = s_h * t_h;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
354 v = s_l * t_h + t_l * s;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
355 /* 2/(3log2)*(s+...) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
356 p_h = u + v;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
357 o.value = p_h;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
358 o.words32.w3 = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
359 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
360 p_h = o.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
361 p_l = v - (p_h - u);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
362 z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
363 z_l = cp_l * p_h + p_l * cp + dp_l[k];
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
364 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
365 t = (__float128) n;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
366 t1 = (((z_h + z_l) + dp_h[k]) + t);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
367 o.value = t1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
368 o.words32.w3 = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
369 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
370 t1 = o.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
371 t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
372
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
373 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
374 y1 = y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
375 o.value = y1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
376 o.words32.w3 = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
377 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
378 y1 = o.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
379 p_l = (y - y1) * t1 + y * t2;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
380 p_h = y1 * t1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
381 z = p_l + p_h;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
382 o.value = z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
383 j = o.words32.w0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
384 if (j >= 0x400d0000) /* z >= 16384 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
385 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
386 /* if z > 16384 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
387 if (((j - 0x400d0000) | o.words32.w1 | o.words32.w2 | o.words32.w3) != 0)
111
kono
parents: 68
diff changeset
388 return sgn * huge * huge; /* overflow */
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
389 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
390 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
391 if (p_l + ovt > z - p_h)
111
kono
parents: 68
diff changeset
392 return sgn * huge * huge; /* overflow */
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
393 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
394 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
395 else if ((j & 0x7fffffff) >= 0x400d01b9) /* z <= -16495 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
396 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
397 /* z < -16495 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
398 if (((j - 0xc00d01bc) | o.words32.w1 | o.words32.w2 | o.words32.w3)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
399 != 0)
111
kono
parents: 68
diff changeset
400 return sgn * tiny * tiny; /* underflow */
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
401 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
402 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
403 if (p_l <= z - p_h)
111
kono
parents: 68
diff changeset
404 return sgn * tiny * tiny; /* underflow */
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
405 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
406 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
407 /* compute 2**(p_h+p_l) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
408 i = j & 0x7fffffff;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
409 k = (i >> 16) - 0x3fff;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
410 n = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
411 if (i > 0x3ffe0000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
412 { /* if |z| > 0.5, set n = [z+0.5] */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
413 n = floorq (z + 0.5Q);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
414 t = n;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
415 p_h -= t;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
416 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
417 t = p_l + p_h;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
418 o.value = t;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
419 o.words32.w3 = 0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
420 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
421 t = o.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
422 u = t * lg2_h;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
423 v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
424 z = u + v;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
425 w = v - (z - u);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
426 /* exp(z) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
427 t = z * z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
428 u = PN[0] + t * (PN[1] + t * (PN[2] + t * (PN[3] + t * PN[4])));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
429 v = PD[0] + t * (PD[1] + t * (PD[2] + t * (PD[3] + t)));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
430 t1 = z - t * u / v;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
431 r = (z * t1) / (t1 - two) - (w + z * w);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
432 z = one - (r - z);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
433 o.value = z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
434 j = o.words32.w0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
435 j += (n << 16);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
436 if ((j >> 16) <= 0)
111
kono
parents: 68
diff changeset
437 {
kono
parents: 68
diff changeset
438 z = scalbnq (z, n); /* subnormal output */
kono
parents: 68
diff changeset
439 __float128 force_underflow = z * z;
kono
parents: 68
diff changeset
440 math_force_eval (force_underflow);
kono
parents: 68
diff changeset
441 }
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
442 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
443 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
444 o.words32.w0 = j;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
445 z = o.value;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
446 }
111
kono
parents: 68
diff changeset
447 return sgn * z;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
448 }