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

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gcc 7
author kono
date Fri, 27 Oct 2017 22:46:09 +0900
parents 561a7518be6b
children 1830386684a0
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
68
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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1 /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
111
kono
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2 Copyright (C) 1999-2017 Free Software Foundation, Inc.
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3 This file is part of the GNU C Library.
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4 Contributed by Jakub Jelinek <jj@ultra.linux.cz>
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5
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6 The GNU C Library is free software; you can redistribute it and/or
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7 modify it under the terms of the GNU Lesser General Public
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8 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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9 version 2.1 of the License, or (at your option) any later version.
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10
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11 The GNU C Library is distributed in the hope that it will be useful,
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12 but WITHOUT ANY WARRANTY; without even the implied warranty of
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13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 Lesser General Public License for more details.
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15
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16 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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17 License along with the GNU C Library; if not, write to the Free
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18 Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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19 02111-1307 USA. */
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20
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21 #include "quadmath-imp.h"
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22
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23 static const __float128 c[] = {
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24 #define ONE c[0]
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25 1.00000000000000000000000000000000000E+00Q, /* 3fff0000000000000000000000000000 */
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26
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27 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
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28 x in <0,1/256> */
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29 #define SCOS1 c[1]
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30 #define SCOS2 c[2]
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31 #define SCOS3 c[3]
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32 #define SCOS4 c[4]
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33 #define SCOS5 c[5]
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34 -5.00000000000000000000000000000000000E-01Q, /* bffe0000000000000000000000000000 */
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35 4.16666666666666666666666666556146073E-02Q, /* 3ffa5555555555555555555555395023 */
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36 -1.38888888888888888888309442601939728E-03Q, /* bff56c16c16c16c16c16a566e42c0375 */
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37 2.48015873015862382987049502531095061E-05Q, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
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38 -2.75573112601362126593516899592158083E-07Q, /* bfe927e4f5dce637cb0b54908754bde0 */
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39
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40 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
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41 x in <0,0.1484375> */
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42 #define COS1 c[6]
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43 #define COS2 c[7]
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44 #define COS3 c[8]
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45 #define COS4 c[9]
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46 #define COS5 c[10]
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47 #define COS6 c[11]
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48 #define COS7 c[12]
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49 #define COS8 c[13]
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50 -4.99999999999999999999999999999999759E-01Q, /* bffdfffffffffffffffffffffffffffb */
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51 4.16666666666666666666666666651287795E-02Q, /* 3ffa5555555555555555555555516f30 */
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52 -1.38888888888888888888888742314300284E-03Q, /* bff56c16c16c16c16c16c16a463dfd0d */
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53 2.48015873015873015867694002851118210E-05Q, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
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54 -2.75573192239858811636614709689300351E-07Q, /* bfe927e4fb7789f5aa8142a22044b51f */
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55 2.08767569877762248667431926878073669E-09Q, /* 3fe21eed8eff881d1e9262d7adff4373 */
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56 -1.14707451049343817400420280514614892E-11Q, /* bfda9397496922a9601ed3d4ca48944b */
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57 4.77810092804389587579843296923533297E-14Q, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
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58
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59 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
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60 x in <0,1/256> */
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61 #define SSIN1 c[14]
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62 #define SSIN2 c[15]
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63 #define SSIN3 c[16]
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64 #define SSIN4 c[17]
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65 #define SSIN5 c[18]
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66 -1.66666666666666666666666666666666659E-01Q, /* bffc5555555555555555555555555555 */
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67 8.33333333333333333333333333146298442E-03Q, /* 3ff81111111111111111111110fe195d */
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68 -1.98412698412698412697726277416810661E-04Q, /* bff2a01a01a01a01a019e7121e080d88 */
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69 2.75573192239848624174178393552189149E-06Q, /* 3fec71de3a556c640c6aaa51aa02ab41 */
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70 -2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */
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71
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72 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
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73 x in <0,0.1484375> */
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74 #define SIN1 c[19]
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75 #define SIN2 c[20]
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76 #define SIN3 c[21]
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77 #define SIN4 c[22]
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78 #define SIN5 c[23]
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79 #define SIN6 c[24]
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80 #define SIN7 c[25]
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81 #define SIN8 c[26]
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82 -1.66666666666666666666666666666666538e-01Q, /* bffc5555555555555555555555555550 */
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83 8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */
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84 -1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */
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85 2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */
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86 -2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */
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87 1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */
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88 -7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
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89 2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */
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90 };
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91
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92 #define SINCOSQ_COS_HI 0
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93 #define SINCOSQ_COS_LO 1
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94 #define SINCOSQ_SIN_HI 2
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95 #define SINCOSQ_SIN_LO 3
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96 extern const __float128 __sincosq_table[];
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97
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98 void
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99 __quadmath_kernel_sincosq(__float128 x, __float128 y, __float128 *sinx,
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100 __float128 *cosx, int iy)
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101 {
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102 __float128 h, l, z, sin_l, cos_l_m1;
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103 int64_t ix;
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104 uint32_t tix, hix, index;
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105 GET_FLT128_MSW64 (ix, x);
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106 tix = ((uint64_t)ix) >> 32;
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107 tix &= ~0x80000000; /* tix = |x|'s high 32 bits */
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108 if (tix < 0x3ffc3000) /* |x| < 0.1484375 */
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109 {
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110 /* Argument is small enough to approximate it by a Chebyshev
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111 polynomial of degree 16(17). */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
112 if (tix < 0x3fc60000) /* |x| < 2^-57 */
111
kono
parents: 68
diff changeset
113 {
kono
parents: 68
diff changeset
114 math_check_force_underflow (x);
kono
parents: 68
diff changeset
115 if (!((int)x)) /* generate inexact */
kono
parents: 68
diff changeset
116 {
kono
parents: 68
diff changeset
117 *sinx = x;
kono
parents: 68
diff changeset
118 *cosx = ONE;
kono
parents: 68
diff changeset
119 return;
kono
parents: 68
diff changeset
120 }
kono
parents: 68
diff changeset
121 }
68
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
122 z = x * x;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
123 *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
124 z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
125 *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
126 z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
127 }
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
128 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
129 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
130 /* So that we don't have to use too large polynomial, we find
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
131 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
111
kono
parents: 68
diff changeset
132 possible values for h. We look up cosq(h) and sinq(h) in
kono
parents: 68
diff changeset
133 pre-computed tables, compute cosq(l) and sinq(l) using a
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
134 Chebyshev polynomial of degree 10(11) and compute
111
kono
parents: 68
diff changeset
135 sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l) and
kono
parents: 68
diff changeset
136 cosq(h+l) = cosq(h)cosq(l) - sinq(h)sinq(l). */
68
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
137 index = 0x3ffe - (tix >> 16);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
138 hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
111
kono
parents: 68
diff changeset
139 if (signbitq (x))
kono
parents: 68
diff changeset
140 {
kono
parents: 68
diff changeset
141 x = -x;
kono
parents: 68
diff changeset
142 y = -y;
kono
parents: 68
diff changeset
143 }
68
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
144 switch (index)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
145 {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
146 case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
147 case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
148 default:
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
149 case 2: index = (hix - 0x3ffc3000) >> 10; break;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
150 }
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
151
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
152 SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0);
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
153 if (iy)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
154 l = y - (h - x);
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
155 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
156 l = x - h;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
157 z = l * l;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
158 sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
159 cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
160 z = __sincosq_table [index + SINCOSQ_SIN_HI]
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
161 + (__sincosq_table [index + SINCOSQ_SIN_LO]
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
162 + (__sincosq_table [index + SINCOSQ_SIN_HI] * cos_l_m1)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
163 + (__sincosq_table [index + SINCOSQ_COS_HI] * sin_l));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
164 *sinx = (ix < 0) ? -z : z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
165 *cosx = __sincosq_table [index + SINCOSQ_COS_HI]
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
166 + (__sincosq_table [index + SINCOSQ_COS_LO]
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
167 - (__sincosq_table [index + SINCOSQ_SIN_HI] * sin_l
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
168 - __sincosq_table [index + SINCOSQ_COS_HI] * cos_l_m1));
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 }