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1 // Copyright (c) 1995-2009 Nokia Corporation and/or its subsidiary(-ies). |
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2 // All rights reserved. |
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3 // This component and the accompanying materials are made available |
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4 // under the terms of the License "Eclipse Public License v1.0" |
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5 // which accompanies this distribution, and is available |
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6 // at the URL "http://www.eclipse.org/legal/epl-v10.html". |
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7 // |
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8 // Initial Contributors: |
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9 // Nokia Corporation - initial contribution. |
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10 // |
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11 // Contributors: |
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12 // |
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13 // Description: |
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14 // e32\include\e32math.h |
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15 // |
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16 // |
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17 |
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18 #ifndef __E32MATH_H__ |
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19 #define __E32MATH_H__ |
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20 #include <e32std.h> |
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21 |
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22 |
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23 /** |
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24 @publishedAll |
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25 @released |
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26 */ |
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27 const TInt KMaxPrecision=15; |
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28 |
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29 /** |
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30 @publishedAll |
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31 @released |
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32 |
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33 This constant specifies the maximum number of significant digits available with floating |
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34 point computations. Rounding and string formatting methods will not use more digits than this. |
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35 */ |
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36 const TInt KPrecisionLimit=12; |
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37 |
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38 /** |
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39 @publishedAll |
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40 @released |
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41 |
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42 Let D be the set of real numbers exactly representable by an IEEE-754 'double' |
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43 For any positive integer n let X_n be the set of real numbers with an exact |
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44 decimal representation using n significant digits. |
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45 Let r_n : D -> X_n be defined by r_n(x)=y such that |
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46 |y-x| = inf { |z-x| : z in X_n } |
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47 and (in the case where two such y exist) that the last significant digit in the |
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48 decimal representation of y is even. |
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49 This constant is the least n such that r_n is injective. |
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50 */ |
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51 const TInt KIEEEDoubleInjectivePrecision=17; |
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52 |
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53 /** |
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54 @publishedAll |
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55 @released |
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56 */ |
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57 const TInt KMantissaBits=53; |
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58 /** |
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59 @publishedAll |
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60 @released |
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61 */ |
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62 const TInt KMaxExponent=1023; |
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63 /** |
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64 @publishedAll |
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65 @released |
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66 */ |
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67 const TInt KExponentBias=1022; |
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68 /** |
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69 @publishedAll |
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70 @released |
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71 */ |
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72 const TInt KSpecialExponent=2047; |
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73 // |
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74 |
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75 |
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76 /** |
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77 @publishedAll |
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78 @released |
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79 |
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80 The maximum exponent for a 32-bit floating point number. |
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81 */ |
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82 const TInt KTReal32MaxExponent=128; // changed from 127 |
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83 |
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84 |
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85 /** |
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86 @publishedAll |
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87 @released |
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88 |
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89 The minimum exponent for a 32-bit floating point number. |
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90 */ |
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91 const TInt KTReal32MinExponent=-125; |
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92 /** |
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93 @publishedAll |
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94 @released |
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95 */ |
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96 const TInt KTReal32ExponentBias=126; |
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97 /** |
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98 @publishedAll |
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99 @released |
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100 */ |
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101 const TInt KTReal32SpecialExponent=255; // changed from KTReal32ExponentBad |
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102 |
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103 |
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104 /** |
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105 @publishedAll |
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106 @released |
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107 |
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108 A zero exponent value for a 32-bit floating point number. |
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109 */ |
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110 const TInt KTReal32ZeroExponent=0; |
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111 // |
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112 |
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113 |
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114 /** |
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115 @publishedAll |
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116 @released |
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117 |
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118 The maximum exponent for a 64-bit floating point number. |
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119 */ |
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120 const TInt KTReal64MaxExponent=1024; // changed from 1023 |
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121 |
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122 |
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123 /** |
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124 @publishedAll |
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125 @released |
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126 |
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127 The minimum exponent for a 64-bit floating point number. |
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128 */ |
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129 const TInt KTReal64MinExponent=-1021; |
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130 |
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131 |
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132 /** |
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133 @publishedAll |
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134 @released |
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135 */ |
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136 const TInt KTReal64ExponentBias=1022; |
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137 |
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138 |
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139 /** |
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140 @publishedAll |
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141 @released |
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142 */ |
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143 const TInt KTReal64SpecialExponent=2047; // changed from KTReal64BadExponent |
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144 |
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145 |
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146 /** |
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147 @publishedAll |
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148 @released |
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149 |
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150 A zero exponent value for a 64-bit floating point number. |
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151 */ |
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152 const TInt KTReal64ZeroExponent=0; |
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153 // |
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154 |
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155 |
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156 /** |
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157 @publishedAll |
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158 @released |
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159 |
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160 The minimum value of a 64-bit floating point number. |
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161 */ |
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162 const TReal KMinTReal=2.2250738585072015E-308; // changed from TReal64 |
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163 |
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164 |
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165 /** |
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166 @publishedAll |
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167 @released |
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168 |
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169 The maximum value of a 64-bit floating point number. |
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170 */ |
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171 const TReal KMaxTReal=1.7976931348623157E+308; // |
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172 // |
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173 |
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174 |
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175 /** |
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176 @publishedAll |
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177 @released |
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178 |
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179 The minimum value of a 32-bit floating point number. |
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180 */ |
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181 const TReal32 KMinTReal32=1.17549435E-38f; |
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182 |
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183 |
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184 /** |
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185 @publishedAll |
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186 @released |
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187 |
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188 The maximum value of a 32-bit floating point number. |
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189 */ |
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190 const TReal32 KMaxTReal32=3.4028234663852885981170418348452e+38f; |
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191 // |
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192 |
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193 |
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194 /** |
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195 @publishedAll |
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196 @released |
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197 |
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198 The minimum value of a 64-bit floating point number. |
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199 */ |
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200 const TReal64 KMinTReal64=2.2250738585072015E-308; |
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201 |
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202 |
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203 /** |
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204 @publishedAll |
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205 @released |
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206 |
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207 The maximum value of a 64-bit floating point number. |
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208 */ |
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209 const TReal64 KMaxTReal64=1.7976931348623157E+308; |
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210 // |
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211 |
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212 |
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213 /** |
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214 @publishedAll |
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215 @released |
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216 */ |
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217 const TReal KSqhf=0.70710678118654752440; |
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218 |
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219 |
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220 /** |
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221 @publishedAll |
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222 @released |
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223 |
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224 Log 2 to the base "e". |
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225 */ |
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226 const TReal KRln2=1.4426950408889634; |
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227 |
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228 |
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229 /** |
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230 @publishedAll |
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231 @released |
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232 |
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233 Log 10 to the base "e". |
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234 */ |
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235 const TReal KRln10=0.4342944819032518; |
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236 |
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237 |
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238 /** |
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239 @publishedAll |
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240 @released |
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241 |
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242 Log 2 to the base 10. |
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243 */ |
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244 const TReal KRlg2=0.3010299956639812; |
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245 |
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246 |
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247 /** |
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248 @publishedAll |
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249 @released |
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250 |
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251 The mathematical constant Pi. |
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252 */ |
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253 const TReal KPi=3.1415926535897932; |
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254 |
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255 |
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256 /** |
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257 @publishedAll |
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258 @released |
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259 |
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260 The reciprocal of the mathematical constant Pi. |
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261 */ |
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262 const TReal KPiInv=0.3183098861837907; |
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263 |
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264 |
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265 /** |
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266 @publishedAll |
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267 @released |
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268 |
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269 The mathematical constant Pi divided by 2. |
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270 */ |
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271 const TReal KPiBy2=1.5707963267948966; |
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272 |
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273 |
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274 /** |
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275 @publishedAll |
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276 @released |
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277 |
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278 Not used. |
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279 */ |
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280 const TReal KDrpi=0.6366197723675813; |
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281 |
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282 |
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283 /** |
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284 @publishedAll |
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285 @released |
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286 |
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287 The square root of 3. |
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288 */ |
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289 const TReal KSqt3=1.7320508075688773; |
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290 |
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291 |
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292 /** |
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293 @publishedAll |
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294 @released |
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295 */ |
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296 const TReal KMsq3=0.2679491924311227; |
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297 |
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298 |
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299 /** |
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300 @publishedAll |
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301 @released |
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302 |
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303 The multiplying factor to convert radians to degrees. |
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304 */ |
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305 const TReal KRadToDeg=57.29577951308232; |
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306 |
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307 |
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308 /** |
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309 @publishedAll |
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310 @released |
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311 |
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312 The multiplying factor to convert degrees to radians. |
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313 */ |
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314 const TReal KDegToRad=0.017453292519943296; |
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315 |
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316 |
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317 |
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318 |
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319 class TRealX |
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320 /** |
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321 @publishedAll |
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322 @released |
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323 |
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324 A class encapsulating an extended precision real value. |
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325 |
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326 This class provides 64 bit precision and a dynamic range of approximately |
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327 1E-9863 to 1E+9863. All member functions are optimized for speed. |
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328 */ |
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329 { |
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330 public: |
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331 enum TRealXOrder {ELessThan=1,EEqual=2,EGreaterThan=4,EUnordered=8}; |
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332 public: |
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333 IMPORT_C TRealX(); |
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334 IMPORT_C TRealX(TInt aInt); |
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335 IMPORT_C TRealX(TUint aInt); |
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336 IMPORT_C TRealX(TUint aExp, TUint aMantHi, TUint aMantLo); |
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337 IMPORT_C TRealX(const TInt64 &aInt); |
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338 IMPORT_C TRealX(TReal32 aReal) __SOFTFP; |
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339 IMPORT_C TRealX(TReal64 aReal) __SOFTFP; |
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340 IMPORT_C TRealX &operator=(TInt aInt); |
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341 IMPORT_C TRealX &operator=(TUint aInt); |
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342 IMPORT_C TRealX &operator=(const TInt64& aInt); |
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343 IMPORT_C TRealX &operator=(TReal32 aReal) __SOFTFP; |
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344 IMPORT_C TRealX &operator=(TReal64 aReal) __SOFTFP; |
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345 IMPORT_C TInt Set(TInt aInt); |
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346 IMPORT_C TInt Set(TUint aInt); |
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347 IMPORT_C TInt Set(const TInt64& aInt); |
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348 IMPORT_C TInt Set(TReal32 aReal) __SOFTFP; |
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349 IMPORT_C TInt Set(TReal64 aReal) __SOFTFP; |
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350 IMPORT_C operator TInt() const; |
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351 IMPORT_C operator TUint() const; |
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352 IMPORT_C operator TInt64() const; |
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353 IMPORT_C operator TReal32() const __SOFTFP; |
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354 IMPORT_C operator TReal64() const __SOFTFP; |
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355 IMPORT_C TInt GetTReal(TReal32 &aVal) const; |
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356 IMPORT_C TInt GetTReal(TReal64 &aVal) const; |
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357 IMPORT_C void SetZero(TBool aNegative=EFalse); |
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358 IMPORT_C void SetNaN(); |
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359 IMPORT_C void SetInfinite(TBool aNegative); |
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360 IMPORT_C TBool IsZero() const; |
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361 IMPORT_C TBool IsNaN() const; |
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362 IMPORT_C TBool IsInfinite() const; |
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363 IMPORT_C TBool IsFinite() const; |
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364 IMPORT_C const TRealX &operator+=(const TRealX &aVal); |
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365 IMPORT_C const TRealX &operator-=(const TRealX &aVal); |
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366 IMPORT_C const TRealX &operator*=(const TRealX &aVal); |
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367 IMPORT_C const TRealX &operator/=(const TRealX &aVal); |
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368 IMPORT_C const TRealX &operator%=(const TRealX &aVal); |
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369 IMPORT_C TInt AddEq(const TRealX &aVal); |
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370 IMPORT_C TInt SubEq(const TRealX &aVal); |
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371 IMPORT_C TInt MultEq(const TRealX &aVal); |
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372 IMPORT_C TInt DivEq(const TRealX &aVal); |
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373 IMPORT_C TInt ModEq(const TRealX &aVal); |
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374 IMPORT_C TRealX operator+() const; |
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375 IMPORT_C TRealX operator-() const; |
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376 IMPORT_C TRealX &operator++(); |
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377 IMPORT_C TRealX operator++(TInt); |
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378 IMPORT_C TRealX &operator--(); |
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379 IMPORT_C TRealX operator--(TInt); |
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380 IMPORT_C TRealX operator+(const TRealX &aVal) const; |
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381 IMPORT_C TRealX operator-(const TRealX &aVal) const; |
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382 IMPORT_C TRealX operator*(const TRealX &aVal) const; |
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383 IMPORT_C TRealX operator/(const TRealX &aVal) const; |
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384 IMPORT_C TRealX operator%(const TRealX &aVal) const; |
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385 IMPORT_C TInt Add(TRealX& aResult,const TRealX &aVal) const; |
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386 IMPORT_C TInt Sub(TRealX& aResult,const TRealX &aVal) const; |
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387 IMPORT_C TInt Mult(TRealX& aResult,const TRealX &aVal) const; |
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388 IMPORT_C TInt Div(TRealX& aResult,const TRealX &aVal) const; |
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389 IMPORT_C TInt Mod(TRealX& aResult,const TRealX &aVal) const; |
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390 IMPORT_C TRealXOrder Compare(const TRealX& aVal) const; |
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391 inline TBool operator==(const TRealX &aVal) const; |
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392 inline TBool operator!=(const TRealX &aVal) const; |
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393 inline TBool operator>=(const TRealX &aVal) const; |
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394 inline TBool operator<=(const TRealX &aVal) const; |
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395 inline TBool operator>(const TRealX &aVal) const; |
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396 inline TBool operator<(const TRealX &aVal) const; |
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397 public: |
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398 /** |
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399 The mantissa. |
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400 */ |
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401 // Represented as two adjacent 32 bit values, rather than one 64 value. |
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402 // This is to avoid EABI introduced padding overheads and BC breakages. |
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403 // This representation works because the mantissa is always accessed from |
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404 // assembler code as two 32 bit quantities. The C++ code that accesses it |
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405 // now constructs an automatic TInt64 with the two components. |
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406 TUint32 iMantLo; |
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407 TUint32 iMantHi; |
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408 |
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409 /** |
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410 The sign: 0 for +, 1 for - |
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411 */ |
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412 TInt8 iSign; |
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413 |
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414 /** |
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415 Flags: 0 for exact, 1 for rounded down, 2 for rounded up |
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416 */ |
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417 TUint8 iFlag; |
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418 |
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419 /** |
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420 Exponent: biased by 32767, iExp=0 => zero, +65535 => infinity or NaN |
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421 */ |
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422 TUint16 iExp; |
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423 }; |
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424 |
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425 |
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426 |
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427 |
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428 struct SPoly |
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429 /** |
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430 @publishedAll |
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431 @released |
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432 |
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433 A structure containing the set of coefficients for a polynomial. |
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434 |
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435 @see Math::Poly |
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436 */ |
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437 { |
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438 TInt num; |
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439 TReal c[1]; |
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440 }; |
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441 |
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442 |
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443 |
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444 |
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445 class Math |
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446 /** |
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447 @publishedAll |
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448 @released |
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449 |
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450 A collection of mathematical functions. |
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451 */ |
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452 { |
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453 public: |
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454 IMPORT_C static TInt ACos(TReal &aTrg,const TReal &aSrc); |
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455 IMPORT_C static TInt ASin(TReal &aTrg,const TReal &aSrc); |
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456 IMPORT_C static TInt ATan(TReal &aTrg,const TReal &aSrc); |
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457 IMPORT_C static TInt ATan(TReal &aTrg,const TReal &aSrcY,const TReal &aSrcX); |
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458 IMPORT_C static TInt Cos(TReal &aTrg,const TReal &aSrc); |
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459 |
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460 /** |
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461 This function is not implemented by Symbian OS. |
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462 */ |
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463 IMPORT_C static TInt DtoR(TReal &aTrg,const TDesC &aSrc,TInt &aPos,const TChar aPoint); |
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464 IMPORT_C static TInt Exp(TReal &aTrg,const TReal &aSrc); |
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465 IMPORT_C static TInt Frac(TReal &aTrg,const TReal &aSrc); |
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466 IMPORT_C static TInt Int(TReal &aTrg,const TReal &aSrc); |
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467 IMPORT_C static TInt Int(TInt16 &aTrg,const TReal &aSrc); |
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468 IMPORT_C static TInt Int(TInt32 &aTrg,const TReal &aSrc); |
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469 IMPORT_C static TInt Log(TReal &aTrg,const TReal &aSrc); |
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470 IMPORT_C static TInt Ln(TReal &aTrg,const TReal &aSrc); |
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471 IMPORT_C static TInt Mod(TReal &aTrg,const TReal &aSrc,const TReal &aModulus); |
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472 IMPORT_C static TReal Poly(TReal aVal,const SPoly *aPoly) __SOFTFP; |
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473 IMPORT_C static TInt Pow(TReal &aTrg,const TReal &aSrc,const TReal &aPower); |
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474 IMPORT_C static TInt Pow10(TReal &aTrg,const TInt exp); |
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475 IMPORT_C static TInt Rand(TInt64 &aSeed); |
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476 IMPORT_C static TReal FRand(TInt64 &aSeed) __SOFTFP; |
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477 IMPORT_C static TUint32 Random(); |
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478 IMPORT_C static TInt Round(TReal &aTrg,const TReal &aSrc,TInt aDecimalPlaces); |
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479 IMPORT_C static TInt Sin(TReal &aTrg,const TReal &aSrc); |
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480 IMPORT_C static TInt Sqrt(TReal &aTrg,const TReal &aSrc); |
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481 IMPORT_C static TInt Tan(TReal &aTrg,const TReal &aSrc); |
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482 IMPORT_C static TBool IsZero(const TReal &aVal); |
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483 IMPORT_C static TBool IsNaN(const TReal &aVal); |
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484 IMPORT_C static TBool IsInfinite(const TReal &aVal); |
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485 IMPORT_C static TBool IsFinite(const TReal &aVal); |
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486 IMPORT_C static void PolyX(TRealX& aY, const TRealX& aX, TInt aDeg, const TRealX *aCoef); |
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487 static TInt MultPow10X(TRealX& aTrg, TInt aPower); |
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488 IMPORT_C static void Mul64(Int64 aX, Int64 aY, Int64& aOutH, Uint64& aOutL); |
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489 IMPORT_C static void UMul64(Uint64 aX, Uint64 aY, Uint64& aOutH, Uint64& aOutL); |
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490 IMPORT_C static Int64 DivMod64(Int64 aDividend, Int64 aDivisor, Int64& aRemainder); |
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491 IMPORT_C static Uint64 UDivMod64(Uint64 aDividend, Uint64 aDivisor, Uint64& aRemainder); |
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492 private: |
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493 IMPORT_C static void SetZero(TReal &aVal,TInt aSign=0); |
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494 IMPORT_C static void SetNaN(TReal &aVal); |
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495 IMPORT_C static void SetInfinite(TReal &aVal,TInt aSign); |
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496 }; |
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497 |
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498 #include <e32math.inl> |
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499 |
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500 #endif // __E32MATH_H__ |