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647 | cejka | 1 | /* |
2 | * Copyright (C) 2005 Josef Cejka |
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3 | * All rights reserved. |
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4 | * |
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5 | * Redistribution and use in source and binary forms, with or without |
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6 | * modification, are permitted provided that the following conditions |
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7 | * are met: |
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8 | * |
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9 | * - Redistributions of source code must retain the above copyright |
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10 | * notice, this list of conditions and the following disclaimer. |
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11 | * - Redistributions in binary form must reproduce the above copyright |
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12 | * notice, this list of conditions and the following disclaimer in the |
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13 | * documentation and/or other materials provided with the distribution. |
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14 | * - The name of the author may not be used to endorse or promote products |
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15 | * derived from this software without specific prior written permission. |
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16 | * |
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17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR |
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18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
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19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
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20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
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21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
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22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
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23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
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24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
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25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
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26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
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27 | */ |
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28 | |||
29 | #include<sftypes.h> |
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30 | #include<arithmetic.h> |
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660 | cejka | 31 | #include<comparison.h> |
647 | cejka | 32 | |
33 | /** Add two Float32 numbers with same signs |
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34 | */ |
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35 | float32 addFloat32(float32 a, float32 b) |
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36 | { |
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37 | int expdiff; |
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38 | __u32 exp1,exp2,mant1,mant2; |
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39 | |||
40 | expdiff=a.parts.exp - b.parts.exp; |
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41 | if (expdiff<0) { |
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42 | if (isFloat32NaN(b)) { |
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43 | //TODO: fix SigNaN |
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44 | if (isFloat32SigNaN(b)) { |
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45 | }; |
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688 | cejka | 46 | |
647 | cejka | 47 | return b; |
48 | }; |
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49 | |||
50 | if (b.parts.exp==0xFF) { |
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51 | return b; |
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52 | } |
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53 | |||
54 | mant1=b.parts.mantisa; |
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55 | exp1=b.parts.exp; |
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56 | mant2=a.parts.mantisa; |
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57 | exp2=a.parts.exp; |
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58 | expdiff*=-1; |
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59 | } else { |
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60 | if (isFloat32NaN(a)) { |
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61 | //TODO: fix SigNaN |
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62 | if ((isFloat32SigNaN(a))||(isFloat32SigNaN(b))) { |
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63 | }; |
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64 | return a; |
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65 | }; |
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66 | |||
67 | if (a.parts.exp==0xFF) { |
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68 | return a; |
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69 | } |
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70 | |||
71 | mant1=a.parts.mantisa; |
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72 | exp1=a.parts.exp; |
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73 | mant2=b.parts.mantisa; |
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74 | exp2=b.parts.exp; |
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75 | }; |
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76 | |||
77 | if (exp1==0) { |
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78 | //both are denormalized |
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79 | mant1+=mant2; |
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80 | if (mant1&0xF00000) { |
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81 | a.parts.exp=1; |
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82 | }; |
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83 | a.parts.mantisa=mant1; |
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84 | return a; |
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85 | }; |
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86 | |||
87 | // create some space for rounding |
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88 | mant1<<=6; |
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89 | mant2<<=6; |
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90 | |||
91 | mant1|=0x20000000; //add hidden bit |
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92 | |||
93 | |||
94 | if (exp2==0) { |
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95 | --expdiff; |
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96 | } else { |
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97 | mant2|=0x20000000; //hidden bit |
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98 | }; |
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99 | |||
100 | if (expdiff>24) { |
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101 | goto done; |
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102 | }; |
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103 | |||
104 | mant2>>=expdiff; |
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105 | mant1+=mant2; |
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106 | done: |
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107 | if (mant1&0x40000000) { |
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108 | ++exp1; |
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109 | mant1>>=1; |
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110 | }; |
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111 | |||
112 | //rounding - if first bit after mantisa is set then round up |
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113 | mant1+=0x20; |
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114 | |||
661 | cejka | 115 | if (mant1&0x40000000) { |
116 | ++exp1; |
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117 | mant1>>=1; |
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118 | }; |
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119 | |||
647 | cejka | 120 | a.parts.exp=exp1; |
661 | cejka | 121 | a.parts.mantisa = ((mant1&(~0x20000000))>>6); /*Clear hidden bit and shift */ |
647 | cejka | 122 | return a; |
123 | }; |
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124 | |||
661 | cejka | 125 | /** Subtract two float32 numbers with same signs |
647 | cejka | 126 | */ |
127 | float32 subFloat32(float32 a, float32 b) |
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128 | { |
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661 | cejka | 129 | int expdiff; |
130 | __u32 exp1,exp2,mant1,mant2; |
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131 | float32 result; |
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132 | |||
133 | result.f = 0; |
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647 | cejka | 134 | |
661 | cejka | 135 | expdiff=a.parts.exp - b.parts.exp; |
136 | if ((expdiff<0)||((expdiff==0)&&(a.parts.mantisa<b.parts.mantisa))) { |
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137 | if (isFloat32NaN(b)) { |
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138 | //TODO: fix SigNaN |
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139 | if (isFloat32SigNaN(b)) { |
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140 | }; |
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141 | return b; |
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142 | }; |
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143 | |||
144 | if (b.parts.exp==0xFF) { |
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145 | b.parts.sign=!b.parts.sign; /* num -(+-inf) = -+inf */ |
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146 | return b; |
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147 | } |
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148 | |||
149 | result.parts.sign = !a.parts.sign; |
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150 | |||
151 | mant1=b.parts.mantisa; |
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152 | exp1=b.parts.exp; |
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153 | mant2=a.parts.mantisa; |
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154 | exp2=a.parts.exp; |
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155 | expdiff*=-1; |
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156 | } else { |
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157 | if (isFloat32NaN(a)) { |
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158 | //TODO: fix SigNaN |
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159 | if ((isFloat32SigNaN(a))||(isFloat32SigNaN(b))) { |
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160 | }; |
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161 | return a; |
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162 | }; |
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163 | |||
164 | if (a.parts.exp==0xFF) { |
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165 | if (b.parts.exp==0xFF) { |
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166 | /* inf - inf => nan */ |
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167 | //TODO: fix exception |
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168 | result.binary = FLOAT32_NAN; |
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169 | return result; |
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170 | }; |
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171 | return a; |
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172 | } |
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173 | |||
174 | result.parts.sign = a.parts.sign; |
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175 | |||
176 | mant1=a.parts.mantisa; |
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177 | exp1=a.parts.exp; |
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178 | mant2=b.parts.mantisa; |
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179 | exp2=b.parts.exp; |
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180 | |||
181 | |||
182 | |||
183 | }; |
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647 | cejka | 184 | |
661 | cejka | 185 | if (exp1==0) { |
186 | //both are denormalized |
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187 | result.parts.mantisa=mant1-mant2; |
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188 | if (result.parts.mantisa>mant1) { |
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189 | //TODO: underflow exception |
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190 | return result; |
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191 | }; |
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192 | result.parts.exp=0; |
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193 | return result; |
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194 | }; |
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195 | |||
196 | // create some space for rounding |
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197 | mant1<<=6; |
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198 | mant2<<=6; |
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199 | |||
200 | mant1|=0x20000000; //add hidden bit |
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201 | |||
202 | |||
203 | if (exp2==0) { |
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204 | --expdiff; |
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205 | } else { |
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206 | mant2|=0x20000000; //hidden bit |
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207 | }; |
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208 | |||
209 | if (expdiff>24) { |
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210 | goto done; |
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211 | }; |
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212 | |||
213 | mant1 = mant1-(mant2>>expdiff); |
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214 | done: |
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215 | |||
216 | //TODO: find first nonzero digit and shift result and detect possibly underflow |
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217 | while ((exp1>0)&&(!(mant1&0x20000000))) { |
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218 | exp1--; |
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219 | mant1 <<= 1; |
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220 | if(mant1 == 0) { |
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221 | /* Realy is it an underflow? ... */ |
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688 | cejka | 222 | /* TODO: fix underflow */ |
661 | cejka | 223 | }; |
224 | }; |
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225 | |||
226 | //rounding - if first bit after mantisa is set then round up |
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227 | mant1 += 0x20; |
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228 | |||
229 | if (mant1&0x40000000) { |
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230 | ++exp1; |
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231 | mant1>>=1; |
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232 | }; |
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233 | |||
234 | result.parts.mantisa = ((mant1&(~0x20000000))>>6); /*Clear hidden bit and shift */ |
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235 | result.parts.exp = exp1; |
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236 | |||
237 | return result; |
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647 | cejka | 238 | }; |
239 | |||
688 | cejka | 240 | /** Multiply two 32 bit float numbers |
241 | * |
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242 | */ |
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243 | float32 mulFloat32(float32 a, float32 b) |
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244 | { |
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245 | float32 result; |
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246 | __u64 mant1, mant2; |
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247 | __s32 exp; |
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248 | |||
249 | result.parts.sign = a.parts.sign ^ b.parts.sign; |
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250 | |||
251 | if ((isFloat32NaN(a))||(isFloat32NaN(b))) { |
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252 | /* TODO: fix SigNaNs */ |
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253 | if (isFloat32SigNaN(a)) { |
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254 | result.parts.mantisa = a.parts.mantisa; |
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255 | result.parts.exp = a.parts.exp; |
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256 | return result; |
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257 | }; |
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258 | if (isFloat32SigNaN(b)) { /* TODO: fix SigNaN */ |
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259 | result.parts.mantisa = b.parts.mantisa; |
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260 | result.parts.exp = b.parts.exp; |
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261 | return result; |
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262 | }; |
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263 | /* set NaN as result */ |
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264 | result.parts.mantisa = 0x1; |
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265 | result.parts.exp = 0xFF; |
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266 | return result; |
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267 | }; |
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268 | |||
269 | if (isFloat32Infinity(a)) { |
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270 | if (isFloat32Zero(b)) { |
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271 | /* FIXME: zero * infinity */ |
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272 | result.parts.mantisa = 0x1; |
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273 | result.parts.exp = 0xFF; |
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274 | return result; |
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275 | } |
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276 | result.parts.mantisa = a.parts.mantisa; |
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277 | result.parts.exp = a.parts.exp; |
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278 | return result; |
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279 | } |
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280 | |||
281 | if (isFloat32Infinity(b)) { |
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282 | if (isFloat32Zero(a)) { |
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283 | /* FIXME: zero * infinity */ |
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284 | result.parts.mantisa = 0x1; |
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285 | result.parts.exp = 0xFF; |
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286 | return result; |
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287 | } |
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288 | result.parts.mantisa = b.parts.mantisa; |
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289 | result.parts.exp = b.parts.exp; |
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290 | return result; |
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291 | } |
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292 | |||
293 | /* exp is signed so we can easy detect underflow */ |
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294 | exp = a.parts.exp + b.parts.exp; |
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295 | exp -= FLOAT32_BIAS; |
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296 | |||
297 | if (exp >= 0xFF ) { |
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298 | /* FIXME: overflow */ |
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299 | /* set infinity as result */ |
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300 | result.parts.mantisa = 0x0; |
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301 | result.parts.exp = 0xFF; |
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302 | return result; |
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303 | }; |
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304 | |||
305 | if (exp < 0) { |
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306 | /* FIXME: underflow */ |
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307 | /* return signed zero */ |
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308 | result.parts.mantisa = 0x0; |
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309 | result.parts.exp = 0x0; |
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310 | return result; |
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311 | }; |
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312 | |||
313 | mant1 = a.parts.mantisa; |
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314 | if (a.parts.exp>0) { |
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315 | mant1 |= 0x800000; |
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316 | } else { |
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317 | ++exp; |
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318 | }; |
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319 | |||
320 | mant2 = b.parts.mantisa; |
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321 | if (b.parts.exp>0) { |
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322 | mant2 |= 0x800000; |
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323 | } else { |
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324 | ++exp; |
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325 | }; |
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326 | |||
327 | mant1 <<= 1; /* one bit space for rounding */ |
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328 | |||
329 | mant1 = mant1 * mant2; |
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330 | /* round and return */ |
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331 | |||
332 | while ((exp < 0xFF )&&(mant1 > 0x1FFFFFF )) { /* 0xFFFFFF is 23 bits of mantisa + one more for hidden bit (all shifted 1 bit left)*/ |
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333 | ++exp; |
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334 | mant1 >>= 1; |
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335 | }; |
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336 | |||
337 | /* rounding */ |
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338 | //++mant1; /* FIXME: not works - without it is ok */ |
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339 | mant1 >>= 1; /* shift off rounding space */ |
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340 | |||
341 | if ((exp < 0xFF )&&(mant1 > 0xFFFFFF )) { |
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342 | ++exp; |
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343 | mant1 >>= 1; |
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344 | }; |
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345 | |||
346 | if (exp >= 0xFF ) { |
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347 | /* TODO: fix overflow */ |
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348 | /* return infinity*/ |
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349 | result.parts.exp = 0xFF; |
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350 | result.parts.mantisa = 0x0; |
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351 | return result; |
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352 | } |
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353 | |||
354 | exp -= FLOAT32_MANTISA_SIZE; |
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355 | |||
356 | if (exp <= FLOAT32_MANTISA_SIZE) { |
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357 | /* denormalized number */ |
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358 | mant1 >>= 1; /* denormalize */ |
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359 | while ((mant1 > 0) && (exp < 0)) { |
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360 | mant1 >>= 1; |
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361 | ++exp; |
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362 | }; |
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363 | if (mant1 == 0) { |
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364 | /* FIXME : underflow */ |
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365 | result.parts.exp = 0; |
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366 | result.parts.mantisa = 0; |
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367 | return result; |
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368 | }; |
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369 | }; |
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370 | result.parts.exp = exp; |
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371 | result.parts.mantisa = mant1 & 0x7FFFFF; |
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372 | |||
373 | return result; |
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374 | |||
375 | }; |
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376 | |||
377 |