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152
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1 /* Implementation of the degree trignometric functions COSD, SIND, TAND.
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2 Copyright (C) 2020 Free Software Foundation, Inc.
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3 Contributed by Steven G. Kargl <kargl@gcc.gnu.org>
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4
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5 This file is part of the GNU Fortran runtime library (libgfortran).
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6
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7 Libgfortran is free software; you can redistribute it and/or
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8 modify it under the terms of the GNU General Public
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9 License as published by the Free Software Foundation; either
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10 version 3 of the License, or (at your option) any later version.
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11
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12 Libgfortran is distributed in the hope that it will be useful,
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13 but WITHOUT ANY WARRANTY; without even the implied warranty of
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14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 GNU General Public License for more details.
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16
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17 Under Section 7 of GPL version 3, you are granted additional
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18 permissions described in the GCC Runtime Library Exception, version
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19 3.1, as published by the Free Software Foundation.
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20
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21 You should have received a copy of the GNU General Public License and
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22 a copy of the GCC Runtime Library Exception along with this program;
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23 see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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24 <http://www.gnu.org/licenses/>. */
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25
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26 #include "libgfortran.h"
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27
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28 #include <math.h>
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29
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30 /* Body of library functions which are cannot be implemented on the current
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31 * platform because it lacks a capability, such as an underlying trigonometric
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32 * function (sin, cos, tan) or C99 floating-point function (fabs, fmod). */
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33 #define STRINGIFY_EXPAND(x) #x
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34 #define ERROR_RETURN(f, k, x) runtime_error (#f " is unavailable for" \
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35 " REAL(KIND=" STRINGIFY_EXPAND(k) ") because the system math library" \
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36 " lacks support for it"); \
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37 RETURN(x)
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38
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39 /*
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40 For real x, let {x}_P or x_P be the closest representible number in the
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41 floating point representation which uses P binary bits of fractional
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42 precision (with IEEE rounding semantics).
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43
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44 Similarly, let f_P(x) be shorthand for {f(x)}_P.
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45
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46 Let ulp_P(x) be the unit of least precision for x: in other words the
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47 maximal value of |a_P - b_P| where a_P <= x <= b_P and a_P != b_P.
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48
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49 Let x ~= y <-> | x - y | < ulp_P(x - y).
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50
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51 Let deg(x) be the value of x radians in degrees.
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52
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53 Values for each precision P were selected as follows.
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54
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55
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56 COSD_SMALL = 2**{-N} such that for all x <= COSD_SMALL:
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57
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58 * cos(deg(x)) ~= 1, or equivalently:
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59
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60 | 1 - cos(deg(x)) | < ulp_P(1).
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61
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62 Unfortunately for SIND (and therefore TAND) a similar relation is only
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63 possible for REAL(4) and REAL(8). With REAL(10) and REAL(16), enough
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64 precision is available such that sin_P(x) != x_P for some x less than any
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65 value. (There are values where this equality holds, but the distance has
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66 inflection points.)
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67
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68 For REAL(4) and REAL(8), we can select SIND_SMALL such that:
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69
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70 * sin(deg(x)) ~= deg(x), or equivalently:
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71
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72 | deg(x) - sin(deg(x)) | < ulp_P(deg(x)).
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73
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74 */
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75
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76 #ifdef HAVE_GFC_REAL_4
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77
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78 /* Build _gfortran_sind_r4, _gfortran_cosd_r4, and _gfortran_tand_r4 */
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79
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80 #define KIND 4
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81 #define TINY 0x1.p-100 /* ~= 7.889e-31 */
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82 #define COSD_SMALL 0x1.p-7 /* = 7.8125e-3 */
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83 #define SIND_SMALL 0x1.p-5 /* = 3.125e-2 */
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84 #define COSD30 8.66025388e-01
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85 #define PIO180H 1.74560547e-02 /* high 12 bits. */
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86 #define PIO180L -2.76216747e-06 /* Next 24 bits. */
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87
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88 #if defined(HAVE_FABSF) && defined(HAVE_FMODF) && defined(HAVE_COPYSIGNF)
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89
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90 #ifdef HAVE_SINF
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91 #define ENABLE_SIND
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92 #endif
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93
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94 #ifdef HAVE_COSF
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95 #define ENABLE_COSD
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96 #endif
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97
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98 #ifdef HAVE_TANF
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99 #define ENABLE_TAND
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100 #endif
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101
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102 #endif /* HAVE_FABSF && HAVE_FMODF && HAVE_COPYSIGNF */
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103
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104 #ifdef GFC_REAL_4_INFINITY
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105 #define HAVE_INFINITY_KIND
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106 #endif
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107
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108 #include "trigd_lib.inc"
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109
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110 #undef KIND
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111 #undef TINY
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112 #undef COSD_SMALL
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113 #undef SIND_SMALL
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114 #undef COSD30
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115 #undef PIO180H
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116 #undef PIO180L
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117 #undef ENABLE_SIND
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118 #undef ENABLE_COSD
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119 #undef ENABLE_TAND
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120 #undef HAVE_INFINITY_KIND
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121
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122 #endif /* HAVE_GFC_REAL_4... */
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123
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124
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125 #ifdef HAVE_GFC_REAL_8
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126
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127 /* Build _gfortran_sind_r8, _gfortran_cosd_r8, and _gfortran_tand_r8 */
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128
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129 #define KIND 8
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130 #define TINY 0x1.p-1000 /* ~= 9.33e-302 (min exp -1074) */
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131 #define COSD_SMALL 0x1.p-21 /* ~= 4.768e-7 */
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132 #define SIND_SMALL 0x1.p-19 /* ~= 9.537e-7 */
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133 #define COSD30 8.6602540378443860e-01
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134 #define PIO180H 1.7453283071517944e-02 /* high 21 bits. */
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135 #define PIO180L 9.4484253514332993e-09 /* Next 53 bits. */
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136
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137 #if defined(HAVE_FABS) && defined(HAVE_FMOD) && defined(HAVE_COPYSIGN)
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138
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139 #ifdef HAVE_SIN
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140 #define ENABLE_SIND
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141 #endif
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142
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143 #ifdef HAVE_COS
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144 #define ENABLE_COSD
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145 #endif
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146
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147 #ifdef HAVE_TAN
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148 #define ENABLE_TAND
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149 #endif
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150
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151 #endif /* HAVE_FABS && HAVE_FMOD && HAVE_COPYSIGN */
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152
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153 #ifdef GFC_REAL_8_INFINITY
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154 #define HAVE_INFINITY_KIND
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155 #endif
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156
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157 #include "trigd_lib.inc"
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158
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159 #undef KIND
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160 #undef TINY
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161 #undef COSD_SMALL
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162 #undef SIND_SMALL
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163 #undef COSD30
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164 #undef PIO180H
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165 #undef PIO180L
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166 #undef ENABLE_SIND
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167 #undef ENABLE_COSD
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168 #undef ENABLE_TAND
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169 #undef HAVE_INFINITY_KIND
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170
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171 #endif /* HAVE_GFC_REAL_8... */
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172
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173
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174 #ifdef HAVE_GFC_REAL_10
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175
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176 /* Build _gfortran_sind_r10, _gfortran_cosd_r10, and _gfortran_tand_r10 */
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177
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178 #define KIND 10
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179 #define TINY 0x1.p-16400 /* ~= 1.28e-4937 (min exp -16494) */
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180 #define COSD_SMALL 0x1.p-26 /* ~= 1.490e-8 */
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181 #undef SIND_SMALL /* not precise */
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182 #define COSD30 8.66025403784438646787e-01
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183 #define PIO180H 1.74532925229868851602e-02 /* high 32 bits */
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184 #define PIO180L -3.04358939097084072823e-12 /* Next 64 bits */
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185
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186 #if defined(HAVE_FABSL) && defined(HAVE_FMODL) && defined(HAVE_COPYSIGNL)
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187
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188 #ifdef HAVE_SINL
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189 #define ENABLE_SIND
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190 #endif
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191
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192 #ifdef HAVE_COSL
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193 #define ENABLE_COSD
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194 #endif
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195
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196 #ifdef HAVE_TANL
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197 #define ENABLE_TAND
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198 #endif
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199
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200 #endif /* HAVE_FABSL && HAVE_FMODL && HAVE_COPYSIGNL */
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201
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202 #ifdef GFC_REAL_10_INFINITY
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203 #define HAVE_INFINITY_KIND
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204 #endif
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205
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206 #include "trigd_lib.inc"
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207
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208 #undef KIND
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209 #undef TINY
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210 #undef COSD_SMALL
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211 #undef SIND_SMALL
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212 #undef COSD30
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213 #undef PIO180H
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214 #undef PIO180L
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215 #undef ENABLE_SIND
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216 #undef ENABLE_COSD
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217 #undef ENABLE_TAND
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218 #undef HAVE_INFINITY_KIND
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219
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220 #endif /* HAVE_GFC_REAL_10 */
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221
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222
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223 #ifdef HAVE_GFC_REAL_16
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224
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225 /* Build _gfortran_sind_r16, _gfortran_cosd_r16, and _gfortran_tand_r16 */
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226
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227 #define KIND 16
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228 #define TINY 0x1.p-16400 /* ~= 1.28e-4937 */
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229 #undef SIND_SMALL /* not precise */
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230
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231 #if GFC_REAL_16_DIGITS == 64
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232 /* 80 bit precision, use constants from REAL(10). */
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233 #define COSD_SMALL 0x1.p-26 /* ~= 1.490e-8 */
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234 #define COSD30 8.66025403784438646787e-01
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235 #define PIO180H 1.74532925229868851602e-02 /* high 32 bits */
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236 #define PIO180L -3.04358939097084072823e-12 /* Next 64 bits */
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237
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238 #else
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239 /* Proper float128 precision. */
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240 #define COSD_SMALL 0x1.p-51 /* ~= 4.441e-16 */
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241 #define COSD30 8.66025403784438646763723170752936183e-01
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242 #define PIO180H 1.74532925199433197605003442731685936e-02
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243 #define PIO180L -2.39912634365882824665106671063098954e-17
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244 #endif
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245
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246 #ifdef GFC_REAL_16_IS_LONG_DOUBLE
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247
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248 #if defined(HAVE_FABSL) && defined(HAVE_FMODL) && defined(HAVE_COPYSIGNL)
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249
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250 #ifdef HAVE_SINL
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251 #define ENABLE_SIND
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252 #endif
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253
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254 #ifdef HAVE_COSL
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255 #define ENABLE_COSD
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256 #endif
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257
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258 #ifdef HAVE_TANL
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259 #define ENABLE_TAND
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260 #endif
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261
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262 #endif /* HAVE_FABSL && HAVE_FMODL && HAVE_COPYSIGNL */
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263
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264 #else
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265
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266 /* libquadmath: HAVE_*Q are never defined. They must be available. */
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267 #define ENABLE_SIND
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268 #define ENABLE_COSD
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269 #define ENABLE_TAND
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270
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271 #endif /* GFC_REAL_16_IS_LONG_DOUBLE */
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272
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273 #ifdef GFC_REAL_16_INFINITY
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274 #define HAVE_INFINITY_KIND
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275 #endif
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276
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277 #include "trigd_lib.inc"
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278
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279 #undef KIND
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280 #undef TINY
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281 #undef COSD_SMALL
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282 #undef SIND_SMALL
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283 #undef COSD30
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284 #undef PIO180H
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285 #undef PIO180L
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286 #undef ENABLE_SIND
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287 #undef ENABLE_COSD
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288 #undef ENABLE_TAND
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289 #undef HAVE_INFINITY_KIND
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290
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291 #endif /* HAVE_GFC_REAL_16 */
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