1 | /* |
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2 | * CRC32 implementation. |
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3 | * |
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4 | * The basic concept of a CRC is that you treat your bit-string |
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5 | * abcdefg... as a ludicrously long polynomial M=a+bx+cx^2+dx^3+... |
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6 | * over Z[2]. You then take a modulus polynomial P, and compute the |
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7 | * remainder of M on division by P. Thus, an erroneous message N |
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8 | * will only have the same CRC if the difference E = M-N is an |
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9 | * exact multiple of P. (Note that as we are working over Z[2], M-N |
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10 | * = N-M = M+N; but that's not very important.) |
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11 | * |
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12 | * What makes the CRC good is choosing P to have good properties: |
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13 | * |
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14 | * - If its first and last terms are both nonzero then it cannot |
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15 | * be a factor of any single term x^i. Therefore if M and N |
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16 | * differ by exactly one bit their CRCs will guaranteeably |
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17 | * be distinct. |
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18 | * |
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19 | * - If it has a prime (irreducible) factor with three terms then |
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20 | * it cannot divide a polynomial of the form x^i(1+x^j). |
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21 | * Therefore if M and N differ by exactly _two_ bits they will |
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22 | * have different CRCs. |
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23 | * |
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24 | * - If it has a factor (x+1) then it cannot divide a polynomial |
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25 | * with an odd number of terms. Therefore if M and N differ by |
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26 | * _any odd_ number of bits they will have different CRCs. |
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27 | * |
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28 | * - If the error term E is of the form x^i*B(x) where B(x) has |
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29 | * order less than P (i.e. a short _burst_ of errors) then P |
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30 | * cannot divide E (since no polynomial can divide a shorter |
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31 | * one), so any such error burst will be spotted. |
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32 | * |
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33 | * The CRC32 standard polynomial is |
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34 | * x^32+x^26+x^23+x^22+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x^1+x^0 |
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35 | * |
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36 | * In fact, we don't compute M mod P; we compute M*x^32 mod P. |
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37 | * |
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38 | * The concrete implementation of the CRC is this: we maintain at |
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39 | * all times a 32-bit word which is the current remainder of the |
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40 | * polynomial mod P. Whenever we receive an extra bit, we multiply |
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41 | * the existing remainder by x, add (XOR) the x^32 term thus |
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42 | * generated to the new x^32 term caused by the incoming bit, and |
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43 | * remove the resulting combined x^32 term if present by replacing |
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44 | * it with (P-x^32). |
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45 | * |
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46 | * Bit 0 of the word is the x^31 term and bit 31 is the x^0 term. |
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47 | * Thus, multiplying by x means shifting right. So the actual |
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48 | * algorithm goes like this: |
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49 | * |
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50 | * x32term = (crcword & 1) ^ newbit; |
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51 | * crcword = (crcword >> 1) ^ (x32term * 0xEDB88320); |
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52 | * |
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53 | * In practice, we pre-compute what will happen to crcword on any |
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54 | * given sequence of eight incoming bits, and store that in a table |
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55 | * which we then use at run-time to do the job: |
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56 | * |
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57 | * outgoingplusnew = (crcword & 0xFF) ^ newbyte; |
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58 | * crcword = (crcword >> 8) ^ table[outgoingplusnew]; |
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59 | * |
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60 | * where table[outgoingplusnew] is computed by setting crcword=0 |
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61 | * and then iterating the first code fragment eight times (taking |
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62 | * the incoming byte low bit first). |
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63 | * |
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64 | * Note that all shifts are rightward and thus no assumption is |
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65 | * made about exact word length! (Although word length must be at |
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66 | * _least_ 32 bits, but ANSI C guarantees this for `unsigned long' |
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67 | * anyway.) |
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68 | */ |
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69 | |
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70 | #include <stdlib.h> |
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71 | |
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72 | #include "ssh.h" |
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73 | |
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74 | /* ---------------------------------------------------------------------- |
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75 | * Multi-function module. Can be compiled three ways. |
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76 | * |
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77 | * - Compile with no special #defines. Will generate a table |
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78 | * that's already initialised at compile time, and one function |
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79 | * crc32_compute(buf,len) that uses it. Normal usage. |
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80 | * |
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81 | * - Compile with INITFUNC defined. Will generate an uninitialised |
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82 | * array as the table, and as well as crc32_compute(buf,len) it |
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83 | * will also generate void crc32_init(void) which sets up the |
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84 | * table at run time. Useful if binary size is important. |
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85 | * |
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86 | * - Compile with GENPROGRAM defined. Will create a standalone |
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87 | * program that does the initialisation and outputs the table as |
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88 | * C code. |
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89 | */ |
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90 | |
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91 | #define POLY (0xEDB88320L) |
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92 | |
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93 | #ifdef GENPROGRAM |
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94 | #define INITFUNC /* the gen program needs the init func :-) */ |
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95 | #endif |
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96 | |
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97 | #ifdef INITFUNC |
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98 | |
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99 | /* |
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100 | * This variant of the code generates the table at run-time from an |
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101 | * init function. |
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102 | */ |
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103 | static unsigned long crc32_table[256]; |
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104 | |
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105 | void crc32_init(void) |
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106 | { |
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107 | unsigned long crcword; |
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108 | int i; |
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109 | |
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110 | for (i = 0; i < 256; i++) { |
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111 | unsigned long newbyte, x32term; |
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112 | int j; |
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113 | crcword = 0; |
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114 | newbyte = i; |
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115 | for (j = 0; j < 8; j++) { |
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116 | x32term = (crcword ^ newbyte) & 1; |
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117 | crcword = (crcword >> 1) ^ (x32term * POLY); |
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118 | newbyte >>= 1; |
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119 | } |
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120 | crc32_table[i] = crcword; |
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121 | } |
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122 | } |
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123 | |
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124 | #else |
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125 | |
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126 | /* |
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127 | * This variant of the code has the data already prepared. |
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128 | */ |
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129 | static const unsigned long crc32_table[256] = { |
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130 | 0x00000000L, 0x77073096L, 0xEE0E612CL, 0x990951BAL, |
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131 | 0x076DC419L, 0x706AF48FL, 0xE963A535L, 0x9E6495A3L, |
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132 | 0x0EDB8832L, 0x79DCB8A4L, 0xE0D5E91EL, 0x97D2D988L, |
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133 | 0x09B64C2BL, 0x7EB17CBDL, 0xE7B82D07L, 0x90BF1D91L, |
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134 | 0x1DB71064L, 0x6AB020F2L, 0xF3B97148L, 0x84BE41DEL, |
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135 | 0x1ADAD47DL, 0x6DDDE4EBL, 0xF4D4B551L, 0x83D385C7L, |
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136 | 0x136C9856L, 0x646BA8C0L, 0xFD62F97AL, 0x8A65C9ECL, |
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137 | 0x14015C4FL, 0x63066CD9L, 0xFA0F3D63L, 0x8D080DF5L, |
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138 | 0x3B6E20C8L, 0x4C69105EL, 0xD56041E4L, 0xA2677172L, |
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139 | 0x3C03E4D1L, 0x4B04D447L, 0xD20D85FDL, 0xA50AB56BL, |
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140 | 0x35B5A8FAL, 0x42B2986CL, 0xDBBBC9D6L, 0xACBCF940L, |
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141 | 0x32D86CE3L, 0x45DF5C75L, 0xDCD60DCFL, 0xABD13D59L, |
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142 | 0x26D930ACL, 0x51DE003AL, 0xC8D75180L, 0xBFD06116L, |
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143 | 0x21B4F4B5L, 0x56B3C423L, 0xCFBA9599L, 0xB8BDA50FL, |
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144 | 0x2802B89EL, 0x5F058808L, 0xC60CD9B2L, 0xB10BE924L, |
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145 | 0x2F6F7C87L, 0x58684C11L, 0xC1611DABL, 0xB6662D3DL, |
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146 | 0x76DC4190L, 0x01DB7106L, 0x98D220BCL, 0xEFD5102AL, |
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147 | 0x71B18589L, 0x06B6B51FL, 0x9FBFE4A5L, 0xE8B8D433L, |
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148 | 0x7807C9A2L, 0x0F00F934L, 0x9609A88EL, 0xE10E9818L, |
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149 | 0x7F6A0DBBL, 0x086D3D2DL, 0x91646C97L, 0xE6635C01L, |
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150 | 0x6B6B51F4L, 0x1C6C6162L, 0x856530D8L, 0xF262004EL, |
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151 | 0x6C0695EDL, 0x1B01A57BL, 0x8208F4C1L, 0xF50FC457L, |
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152 | 0x65B0D9C6L, 0x12B7E950L, 0x8BBEB8EAL, 0xFCB9887CL, |
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153 | 0x62DD1DDFL, 0x15DA2D49L, 0x8CD37CF3L, 0xFBD44C65L, |
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154 | 0x4DB26158L, 0x3AB551CEL, 0xA3BC0074L, 0xD4BB30E2L, |
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155 | 0x4ADFA541L, 0x3DD895D7L, 0xA4D1C46DL, 0xD3D6F4FBL, |
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156 | 0x4369E96AL, 0x346ED9FCL, 0xAD678846L, 0xDA60B8D0L, |
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157 | 0x44042D73L, 0x33031DE5L, 0xAA0A4C5FL, 0xDD0D7CC9L, |
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158 | 0x5005713CL, 0x270241AAL, 0xBE0B1010L, 0xC90C2086L, |
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159 | 0x5768B525L, 0x206F85B3L, 0xB966D409L, 0xCE61E49FL, |
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160 | 0x5EDEF90EL, 0x29D9C998L, 0xB0D09822L, 0xC7D7A8B4L, |
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161 | 0x59B33D17L, 0x2EB40D81L, 0xB7BD5C3BL, 0xC0BA6CADL, |
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162 | 0xEDB88320L, 0x9ABFB3B6L, 0x03B6E20CL, 0x74B1D29AL, |
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163 | 0xEAD54739L, 0x9DD277AFL, 0x04DB2615L, 0x73DC1683L, |
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164 | 0xE3630B12L, 0x94643B84L, 0x0D6D6A3EL, 0x7A6A5AA8L, |
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165 | 0xE40ECF0BL, 0x9309FF9DL, 0x0A00AE27L, 0x7D079EB1L, |
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166 | 0xF00F9344L, 0x8708A3D2L, 0x1E01F268L, 0x6906C2FEL, |
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167 | 0xF762575DL, 0x806567CBL, 0x196C3671L, 0x6E6B06E7L, |
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168 | 0xFED41B76L, 0x89D32BE0L, 0x10DA7A5AL, 0x67DD4ACCL, |
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169 | 0xF9B9DF6FL, 0x8EBEEFF9L, 0x17B7BE43L, 0x60B08ED5L, |
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170 | 0xD6D6A3E8L, 0xA1D1937EL, 0x38D8C2C4L, 0x4FDFF252L, |
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171 | 0xD1BB67F1L, 0xA6BC5767L, 0x3FB506DDL, 0x48B2364BL, |
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172 | 0xD80D2BDAL, 0xAF0A1B4CL, 0x36034AF6L, 0x41047A60L, |
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173 | 0xDF60EFC3L, 0xA867DF55L, 0x316E8EEFL, 0x4669BE79L, |
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174 | 0xCB61B38CL, 0xBC66831AL, 0x256FD2A0L, 0x5268E236L, |
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175 | 0xCC0C7795L, 0xBB0B4703L, 0x220216B9L, 0x5505262FL, |
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176 | 0xC5BA3BBEL, 0xB2BD0B28L, 0x2BB45A92L, 0x5CB36A04L, |
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177 | 0xC2D7FFA7L, 0xB5D0CF31L, 0x2CD99E8BL, 0x5BDEAE1DL, |
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178 | 0x9B64C2B0L, 0xEC63F226L, 0x756AA39CL, 0x026D930AL, |
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179 | 0x9C0906A9L, 0xEB0E363FL, 0x72076785L, 0x05005713L, |
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180 | 0x95BF4A82L, 0xE2B87A14L, 0x7BB12BAEL, 0x0CB61B38L, |
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181 | 0x92D28E9BL, 0xE5D5BE0DL, 0x7CDCEFB7L, 0x0BDBDF21L, |
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182 | 0x86D3D2D4L, 0xF1D4E242L, 0x68DDB3F8L, 0x1FDA836EL, |
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183 | 0x81BE16CDL, 0xF6B9265BL, 0x6FB077E1L, 0x18B74777L, |
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184 | 0x88085AE6L, 0xFF0F6A70L, 0x66063BCAL, 0x11010B5CL, |
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185 | 0x8F659EFFL, 0xF862AE69L, 0x616BFFD3L, 0x166CCF45L, |
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186 | 0xA00AE278L, 0xD70DD2EEL, 0x4E048354L, 0x3903B3C2L, |
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187 | 0xA7672661L, 0xD06016F7L, 0x4969474DL, 0x3E6E77DBL, |
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188 | 0xAED16A4AL, 0xD9D65ADCL, 0x40DF0B66L, 0x37D83BF0L, |
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189 | 0xA9BCAE53L, 0xDEBB9EC5L, 0x47B2CF7FL, 0x30B5FFE9L, |
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190 | 0xBDBDF21CL, 0xCABAC28AL, 0x53B39330L, 0x24B4A3A6L, |
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191 | 0xBAD03605L, 0xCDD70693L, 0x54DE5729L, 0x23D967BFL, |
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192 | 0xB3667A2EL, 0xC4614AB8L, 0x5D681B02L, 0x2A6F2B94L, |
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193 | 0xB40BBE37L, 0xC30C8EA1L, 0x5A05DF1BL, 0x2D02EF8DL |
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194 | }; |
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195 | |
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196 | #endif |
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197 | |
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198 | #ifdef GENPROGRAM |
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199 | int main(void) |
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200 | { |
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201 | unsigned long crcword; |
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202 | int i; |
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203 | |
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204 | crc32_init(); |
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205 | for (i = 0; i < 256; i++) { |
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206 | printf("%s0x%08XL%s", |
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207 | (i % 4 == 0 ? " " : " "), |
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208 | crc32_table[i], |
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209 | (i % 4 == 3 ? (i == 255 ? "\n" : ",\n") : ",")); |
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210 | } |
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211 | |
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212 | return 0; |
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213 | } |
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214 | #endif |
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215 | |
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216 | unsigned long crc32_update(unsigned long crcword, const void *buf, size_t len) |
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217 | { |
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218 | const unsigned char *p = (const unsigned char *) buf; |
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219 | while (len--) { |
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220 | unsigned long newbyte = *p++; |
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221 | newbyte ^= crcword & 0xFFL; |
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222 | crcword = (crcword >> 8) ^ crc32_table[newbyte]; |
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223 | } |
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224 | return crcword; |
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225 | } |
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226 | |
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227 | unsigned long crc32_compute(const void *buf, size_t len) |
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228 | { |
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229 | return crc32_update(0L, buf, len); |
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230 | } |
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