1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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2 | /* $Id: gengftables.cc,v 1.2 1997-10-23 13:25:52 schmidt Exp $ */ |
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3 | |
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4 | //{{{ docu |
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5 | // |
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6 | // gengftables.cc - generate addition tables used by Factory |
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7 | // to calculate in GF(q). |
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8 | // |
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9 | // Note: This may take quite a while ... |
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10 | // |
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11 | //}}} |
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12 | |
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13 | #include <iostream.h> |
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14 | #include <fstream.h> |
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15 | #include <strstream.h> |
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16 | |
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17 | #include <factory.h> |
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18 | |
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19 | #include <assert.h> |
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20 | #include <gf_tabutil.h> |
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21 | |
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22 | //{{{ constants |
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23 | //{{{ docu |
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24 | // |
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25 | // - constants. |
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26 | // |
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27 | // maxtable: maximal size of a gf_table |
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28 | // primes, primes_len: |
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29 | // used to step through possible extensions |
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30 | // |
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31 | //}}} |
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32 | const int maxtable = 32767; |
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33 | |
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34 | const int primes_len = 42; |
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35 | static unsigned short primes [] = |
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36 | { |
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37 | 2, 3, 5, 7, 11, 13, 17, 19, |
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38 | 23, 29, 31, 37, 41, 43, 47, 53, |
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39 | 59, 61, 67, 71, 73, 79, 83, 89, |
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40 | 97, 101, 103, 107, 109, 113, 127, 131, |
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41 | 137, 139, 149, 151, 157, 163, 167, 173, |
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42 | 179, 181 |
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43 | }; |
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44 | //}}} |
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45 | |
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46 | //{{{ bool isIrreducible ( const CanonicalForm & f ) |
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47 | //{{{ docu |
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48 | // |
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49 | // isIrreducible() - return true iff f is irreducible. |
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50 | // |
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51 | //}}} |
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52 | bool |
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53 | isIrreducible ( const CanonicalForm & f ) |
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54 | { |
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55 | CFFList F = factorize( f ); |
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56 | return F.length() == 1 && F.getFirst().exp() == 1; |
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57 | } |
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58 | //}}} |
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59 | |
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60 | //{{{ int exponent ( const CanonicalForm & f, int q ) |
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61 | //{{{ docu |
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62 | // |
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63 | // exponent() - return e > 0 such that x^e == 1 mod f. |
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64 | // |
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65 | // q: upper limit for e (?) |
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66 | // |
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67 | //}}} |
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68 | int |
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69 | exponent ( const CanonicalForm & f, int q ) |
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70 | { |
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71 | Variable x = f.mvar(); |
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72 | int e = 1; |
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73 | CanonicalForm prod = x; |
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74 | while ( e <= q && ! prod.isOne() ) { |
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75 | e++; |
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76 | prod = ( prod * x ) % f; |
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77 | } |
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78 | return e; |
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79 | } |
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80 | //}}} |
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81 | |
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82 | //{{{ bool findGenRec ( int d, int n, int q, const CanonicalForm & m, const Variable & x, CanonicalForm & result ) |
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83 | //{{{ docu |
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84 | // |
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85 | // findGenRec() - find a generator of GF(q). |
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86 | // |
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87 | // Returns true iff result is a valid generator. |
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88 | // |
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89 | // d: degree of extension |
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90 | // q: the q in GF(q) (q == p^d) |
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91 | // x: generator should be a poly in x |
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92 | // n, m: used to step recursively through all polys in FF(p) |
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93 | // Initially, n == d and m == 0. If 0 <= n <= d we are |
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94 | // in the process of building m, if n < 0 we built m and |
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95 | // may test whether it generates GF(q). |
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96 | // result: generator found |
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97 | // |
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98 | // i: used to step through GF(p) |
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99 | // p: current characteristic |
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100 | // |
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101 | //}}} |
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102 | bool |
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103 | findGenRec ( int d, int n, int q, |
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104 | const CanonicalForm & m, const Variable & x, |
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105 | CanonicalForm & result ) |
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106 | { |
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107 | int i, p = getCharacteristic(); |
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108 | if ( n < 0 ) { |
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109 | cerr << "."; cerr.flush(); |
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110 | // check whether m is irreducible |
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111 | if ( isIrreducible( m ) ) { |
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112 | cerr << "*"; cerr.flush(); |
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113 | // check whether m generates multiplicative group |
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114 | if ( exponent( m, q ) == q - 1 ) { |
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115 | result = m; |
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116 | return true; |
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117 | } |
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118 | else |
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119 | return false; |
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120 | } |
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121 | else |
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122 | return false; |
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123 | } |
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124 | // for each monomial x^0, ..., x^n, ..., x^d, try all possible coefficients |
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125 | else if ( n == d || n == 0 ) { |
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126 | // we want to have a leading coefficient and a constant term, |
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127 | // so start with coefficient >= 1 |
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128 | for ( i = 1; i < p; i++ ) |
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129 | if ( findGenRec( d, n-1, q, m + i * power( x, n ), x, result ) ) |
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130 | return true; |
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131 | } |
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132 | else { |
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133 | for ( i = 0; i < p; i++ ) |
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134 | if ( findGenRec( d, n-1, q, m + i * power( x, n ), x, result ) ) |
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135 | return true; |
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136 | } |
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137 | return false; |
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138 | } |
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139 | //}}} |
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140 | |
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141 | //{{{ CanonicalForm findGen ( int d, int q ) |
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142 | //{{{ docu |
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143 | // |
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144 | // findGen() - find and return a generator of GF(q). |
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145 | // |
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146 | // d: degree of extension |
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147 | // q: the q in GF(q) |
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148 | // |
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149 | //}}} |
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150 | CanonicalForm |
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151 | findGen ( int d, int q ) |
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152 | { |
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153 | Variable x( 1 ); |
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154 | CanonicalForm result; |
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155 | cerr << "testing p = " << getCharacteristic() << ", d = " << d << " ... "; |
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156 | cerr.flush(); |
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157 | bool ok = findGenRec( d, d, q, 0, x, result ); |
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158 | cerr << endl; |
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159 | if ( ! ok ) |
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160 | return 0; |
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161 | else |
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162 | return result; |
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163 | } |
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164 | //}}} |
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165 | |
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166 | //{{{ void printTable ( int d, int q, CanonicalForm mipo ) |
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167 | //{{{ docu |
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168 | // |
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169 | // printTable - print +1 table of field GF(q). |
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170 | // |
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171 | // d: degree of extension |
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172 | // q: the q in GF(q) |
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173 | // mipo: the minimal polynomial of the extension |
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174 | // |
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175 | // p: current characteristic |
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176 | // |
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177 | //}}} |
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178 | void |
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179 | printTable ( int d, int q, CanonicalForm mipo ) |
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180 | { |
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181 | int i, p = getCharacteristic(); |
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182 | |
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183 | // open file to write to |
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184 | ostrstream fname; |
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185 | fname << "gftables/gftable." << p << "." << d << '\0'; |
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186 | char * fn = fname.str(); |
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187 | ofstream outfile; |
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188 | outfile.open( fn, ios::out ); |
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189 | STICKYASSERT1( outfile, "can not open GF(q) table %s for writing", fn ); |
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190 | delete fn; |
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191 | |
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192 | cerr << "mipo = " << mipo << ": "; |
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193 | cerr << "generating multiplicative group ... "; |
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194 | cerr.flush(); |
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195 | |
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196 | CanonicalForm * T = new CanonicalForm[maxtable]; |
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197 | Variable x( 1 ); |
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198 | |
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199 | // fill T with powers of x |
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200 | T[0] = 1; |
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201 | for ( i = 1; i < q; i++ ) |
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202 | T[i] = ( T[i-1] * x ) % mipo; |
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203 | |
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204 | cerr << "generating addition table ... "; |
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205 | cerr.flush(); |
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206 | |
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207 | // brute force method |
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208 | int * table = new int[maxtable]; |
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209 | CanonicalForm f; |
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210 | |
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211 | for ( i = 0; i < q; i++ ) { |
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212 | f = T[i] + 1; |
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213 | int j = 0; |
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214 | while ( j < q && T[j] != f ) j++; |
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215 | table[i] = j; |
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216 | } |
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217 | |
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218 | cerr << "writing table ... "; |
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219 | cerr.flush(); |
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220 | |
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221 | outfile << "@@ factory GF(q) table @@" << endl; |
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222 | outfile << p << " " << d << " " << mipo << "; "; |
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223 | |
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224 | // print simple reprenstation of mipo |
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225 | outfile << d; |
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226 | CFIterator MiPo = mipo; |
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227 | for ( i = d; MiPo.hasTerms(); i--, MiPo++ ) { |
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228 | int exp; |
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229 | for ( exp = MiPo.exp(); exp < i; i-- ) |
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230 | outfile << " 0"; |
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231 | outfile << " " << MiPo.coeff(); |
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232 | } |
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233 | // since mipo is irreducible, it has a constant term, |
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234 | // so i == 0 at this point |
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235 | outfile << endl; |
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236 | |
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237 | int m = gf_tab_numdigits62( q ); |
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238 | char * outstr = new char[30*m+1]; |
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239 | outstr[30*m] = '\0'; |
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240 | i = 1; |
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241 | while ( i < q ) { |
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242 | int k = 0; |
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243 | char * sptr = outstr; |
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244 | while ( i < q && k < 30 ) { |
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245 | convert62( table[i], m, sptr ); |
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246 | sptr += m; |
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247 | k++; i++; |
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248 | } |
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249 | while ( k < 30 ) { |
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250 | convert62( 0, m, sptr ); |
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251 | sptr += m; |
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252 | k++; |
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253 | } |
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254 | outfile << outstr << endl; |
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255 | } |
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256 | outfile.close(); |
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257 | |
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258 | delete [] outstr; |
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259 | delete [] T; |
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260 | delete [] table; |
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261 | |
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262 | cerr << endl; |
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263 | } |
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264 | //}}} |
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265 | |
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266 | int |
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267 | main() |
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268 | { |
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269 | int i, p, q, n; |
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270 | for ( i = 0; i < primes_len; i++ ) { |
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271 | p = primes[i]; |
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272 | q = p*p; |
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273 | n = 2; |
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274 | setCharacteristic( p ); |
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275 | while ( q < maxtable ) { |
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276 | CanonicalForm f = findGen( n, q ); |
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277 | ASSERT( f != 0, "no generator found" ); |
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278 | printTable( n, q, f ); |
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279 | n++; q *= p; |
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280 | } |
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281 | } |
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282 | } |
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