1 | /*
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2 | * vdtcore_common.h
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3 | * Common functions for the vdt routines.
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4 | * The basic idea is to exploit Pade polynomials.
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5 | * A lot of ideas were inspired by the cephes math library (by Stephen L. Moshier
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6 | * moshier@na-net.ornl.gov) as well as actual code for the exp, log, sin, cos,
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7 | * tan, asin, acos and atan functions. The Cephes library can be found here:
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8 | * http://www.netlib.org/cephes/
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9 | *
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10 | * Created on: Jun 23, 2012
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11 | * Author: Danilo Piparo, Thomas Hauth, Vincenzo Innocente
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12 | */
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13 |
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14 | /*
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15 | * VDT is free software: you can redistribute it and/or modify
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16 | * it under the terms of the GNU Lesser Public License as published by
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17 | * the Free Software Foundation, either version 3 of the License, or
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18 | * (at your option) any later version.
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19 | *
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20 | * This program is distributed in the hope that it will be useful,
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21 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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22 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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23 | * GNU Lesser Public License for more details.
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24 | *
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25 | * You should have received a copy of the GNU Lesser Public License
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26 | * along with this program. If not, see <http://www.gnu.org/licenses/>.
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27 | */
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28 |
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29 | #ifndef VDTCOMMON_H_
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30 | #define VDTCOMMON_H_
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31 |
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32 | #include <cinttypes>
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33 | #include <cmath>
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34 |
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35 | namespace vdt{
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36 |
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37 | namespace details{
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38 |
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39 | // Constants
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40 | const double TWOPI = 2.*M_PI;
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41 | const double PI = M_PI;
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42 | const double PIO2 = M_PI_2;
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43 | const double PIO4 = M_PI_4;
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44 | const double ONEOPIO4 = 4./M_PI;
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45 |
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46 | const float TWOPIF = 2.*M_PI;
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47 | const float PIF = M_PI;
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48 | const float PIO2F = M_PI_2;
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49 | const float PIO4F = M_PI_4;
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50 | const float ONEOPIO4F = 4./M_PI;
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51 |
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52 | const double MOREBITS = 6.123233995736765886130E-17;
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53 |
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54 |
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55 | const float MAXNUMF = 3.4028234663852885981170418348451692544e38f;
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56 |
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57 | //------------------------------------------------------------------------------
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58 |
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59 | /// Used to switch between different type of interpretations of the data (64 bits)
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60 | union ieee754{
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61 | inline ieee754 () {};
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62 | inline ieee754 (double thed) {d=thed;};
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63 | inline ieee754 (uint64_t thell) {ll=thell;};
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64 | inline ieee754 (float thef) {f[0]=thef;};
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65 | inline ieee754 (uint32_t thei) {i[0]=thei;};
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66 | double d;
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67 | float f[2];
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68 | uint32_t i[2];
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69 | uint64_t ll;
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70 | uint16_t s[4];
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71 | };
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72 |
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73 | //------------------------------------------------------------------------------
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74 |
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75 | /// Converts an unsigned long long to a double
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76 | inline double uint642dp(uint64_t ll) {
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77 | ieee754 tmp;
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78 | tmp.ll=ll;
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79 | return tmp.d;
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80 | }
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81 |
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82 | //------------------------------------------------------------------------------
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83 |
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84 | /// Converts a double to an unsigned long long
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85 | inline uint64_t dp2uint64(double x) {
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86 | ieee754 tmp;
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87 | tmp.d=x;
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88 | return tmp.ll;
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89 | }
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90 |
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91 | //------------------------------------------------------------------------------
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92 | /// Makes an AND of a double and a unsigned long long
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93 | inline double dpANDuint64(const double x, const uint64_t i ){
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94 | return uint642dp(dp2uint64(x) & i);
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95 | }
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96 | //------------------------------------------------------------------------------
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97 | /// Makes an OR of a double and a unsigned long long
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98 | inline double dpORuint64(const double x, const uint64_t i ){
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99 | return uint642dp(dp2uint64(x) | i);
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100 | }
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101 |
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102 | /// Makes a XOR of a double and a unsigned long long
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103 | inline double dpXORuint64(const double x, const uint64_t i ){
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104 | return uint642dp(dp2uint64(x) ^ i);
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105 | }
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106 |
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107 | //------------------------------------------------------------------------------
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108 | inline uint64_t getSignMask(const double x){
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109 | const uint64_t mask=0x8000000000000000ULL;
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110 | return dp2uint64(x) & mask;
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111 | }
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112 |
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113 | //------------------------------------------------------------------------------
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114 | /// Converts an int to a float
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115 | inline float uint322sp(int x) {
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116 | ieee754 tmp;
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117 | tmp.i[0]=x;
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118 | return tmp.f[0];
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119 | }
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120 |
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121 | //------------------------------------------------------------------------------
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122 | /// Converts a float to an int
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123 | inline uint32_t sp2uint32(float x) {
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124 | ieee754 tmp;
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125 | tmp.f[0]=x;
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126 | return tmp.i[0];
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127 | }
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128 |
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129 | //------------------------------------------------------------------------------
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130 | /// Makes an AND of a float and a unsigned long
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131 | inline float spANDuint32(const float x, const uint32_t i ){
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132 | return uint322sp(sp2uint32(x) & i);
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133 | }
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134 | //------------------------------------------------------------------------------
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135 | /// Makes an OR of a float and a unsigned long
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136 | inline float spORuint32(const float x, const uint32_t i ){
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137 | return uint322sp(sp2uint32(x) | i);
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138 | }
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139 |
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140 | //------------------------------------------------------------------------------
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141 | /// Makes an OR of a float and a unsigned long
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142 | inline float spXORuint32(const float x, const uint32_t i ){
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143 | return uint322sp(sp2uint32(x) ^ i);
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144 | }
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145 | //------------------------------------------------------------------------------
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146 | /// Get the sign mask
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147 | inline uint32_t getSignMask(const float x){
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148 | const uint32_t mask=0x80000000;
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149 | return sp2uint32(x) & mask;
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150 | }
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151 |
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152 | //------------------------------------------------------------------------------
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153 | /// Like frexp but vectorising and the exponent is a double.
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154 | inline double getMantExponent(const double x, double & fe){
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155 |
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156 | uint64_t n = dp2uint64(x);
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157 |
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158 | // Shift to the right up to the beginning of the exponent.
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159 | // Then with a mask, cut off the sign bit
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160 | uint64_t le = (n >> 52);
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161 |
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162 | // chop the head of the number: an int contains more than 11 bits (32)
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163 | int32_t e = le; // This is important since sums on uint64_t do not vectorise
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164 | fe = e-1023 ;
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165 |
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166 | // This puts to 11 zeroes the exponent
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167 | n &=0x800FFFFFFFFFFFFFULL;
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168 | // build a mask which is 0.5, i.e. an exponent equal to 1022
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169 | // which means *2, see the above +1.
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170 | const uint64_t p05 = 0x3FE0000000000000ULL; //dp2uint64(0.5);
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171 | n |= p05;
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172 |
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173 | return uint642dp(n);
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174 | }
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175 |
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176 | //------------------------------------------------------------------------------
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177 | /// Like frexp but vectorising and the exponent is a float.
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178 | inline float getMantExponentf(const float x, float & fe){
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179 |
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180 | uint32_t n = sp2uint32(x);
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181 | int32_t e = (n >> 23)-127;
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182 | fe = e;
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183 |
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184 | // fractional part
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185 | const uint32_t p05f = 0x3f000000; // //sp2uint32(0.5);
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186 | n &= 0x807fffff;// ~0x7f800000;
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187 | n |= p05f;
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188 |
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189 | return uint322sp(n);
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190 |
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191 | }
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192 |
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193 | //------------------------------------------------------------------------------
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194 | /// Converts a fp to an int
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195 | inline uint32_t fp2uint(float x) {
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196 | return sp2uint32(x);
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197 | }
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198 | /// Converts a fp to an int
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199 | inline uint64_t fp2uint(double x) {
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200 | return dp2uint64(x);
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201 | }
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202 | /// Converts an int to fp
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203 | inline float int2fp(uint32_t i) {
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204 | return uint322sp(i);
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205 | }
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206 | /// Converts an int to fp
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207 | inline double int2fp(uint64_t i) {
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208 | return uint642dp(i);
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209 | }
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210 |
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211 | //------------------------------------------------------------------------------
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212 | /**
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213 | * A vectorisable floor implementation, not only triggered by fast-math.
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214 | * These functions do not distinguish between -0.0 and 0.0, so are not IEC6509
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215 | * compliant for argument -0.0
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216 | **/
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217 | inline double fpfloor(const double x){
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218 | // no problem since exp is defined between -708 and 708. Int is enough for it!
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219 | int32_t ret = int32_t (x);
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220 | ret-=(sp2uint32(x)>>31);
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221 | return ret;
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222 |
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223 | }
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224 | //------------------------------------------------------------------------------
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225 | /**
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226 | * A vectorisable floor implementation, not only triggered by fast-math.
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227 | * These functions do not distinguish between -0.0 and 0.0, so are not IEC6509
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228 | * compliant for argument -0.0
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229 | **/
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230 | inline float fpfloor(const float x){
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231 | int32_t ret = int32_t (x);
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232 | ret-=(sp2uint32(x)>>31);
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233 | return ret;
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234 |
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235 | }
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236 |
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237 | //------------------------------------------------------------------------------
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238 |
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239 | }
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240 |
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241 | } // end of namespace vdt
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242 |
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243 | #endif /* VDTCOMMON_H_ */
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