[b478f8] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
---|
| 2 | |
---|
[b52d27] | 3 | /** |
---|
| 4 | * |
---|
[abddbe] | 5 | * @file gengftables-conway.cc |
---|
[b52d27] | 6 | * |
---|
[abddbe] | 7 | * generate addition tables used by Factory |
---|
[b52d27] | 8 | * to calculate in GF(q). |
---|
| 9 | * |
---|
| 10 | * @note This may take quite a while ... |
---|
| 11 | * |
---|
| 12 | **/ |
---|
[b478f8] | 13 | |
---|
[9f7665] | 14 | |
---|
[efce9a] | 15 | #include "config.h" |
---|
[9f7665] | 16 | |
---|
[efce9a] | 17 | |
---|
[19cbad8] | 18 | #ifdef HAVE_IOSTREAM |
---|
[189f83] | 19 | #include <iostream> |
---|
| 20 | #include <fstream> |
---|
[b478f8] | 21 | #include <strstream> |
---|
[e1b374] | 22 | #include <string> |
---|
[19cbad8] | 23 | #else |
---|
[34f6d2] | 24 | #include <iostream> |
---|
| 25 | #include <fstream> |
---|
| 26 | #include <strstream> |
---|
| 27 | #include <string> |
---|
[19cbad8] | 28 | #endif |
---|
| 29 | |
---|
[b478f8] | 30 | |
---|
[189f83] | 31 | #include <stdlib.h> |
---|
| 32 | |
---|
[502f5f6] | 33 | #include "cf_assert.h" |
---|
| 34 | #include "gf_tabutil.h" |
---|
[c44985] | 35 | #include "cf_algorithm.h" |
---|
| 36 | #include "cf_iter.h" |
---|
[b478f8] | 37 | |
---|
| 38 | using namespace std; |
---|
| 39 | |
---|
[34f6d2] | 40 | int gf_tab_numdigits62 ( int q ); |
---|
[b52d27] | 41 | /** |
---|
| 42 | * |
---|
| 43 | * constants. |
---|
| 44 | * |
---|
| 45 | * maxtable: maximal size of a gf_table |
---|
| 46 | * |
---|
| 47 | **/ |
---|
[b478f8] | 48 | const int maxtable = 65536; |
---|
| 49 | |
---|
[b52d27] | 50 | /** |
---|
| 51 | * primes, primes_len: |
---|
| 52 | * used to step through possible extensions |
---|
| 53 | **/ |
---|
[b478f8] | 54 | const int primes_len = 54; |
---|
[b52d27] | 55 | |
---|
| 56 | /** |
---|
| 57 | * primes, primes_len: |
---|
| 58 | * used to step through possible extensions |
---|
| 59 | **/ |
---|
[a3f0fea] | 60 | STATIC_VAR unsigned short primes [] = |
---|
[b478f8] | 61 | { |
---|
| 62 | 2, 3, 5, 7, 11, 13, 17, 19, |
---|
| 63 | 23, 29, 31, 37, 41, 43, 47, 53, |
---|
| 64 | 59, 61, 67, 71, 73, 79, 83, 89, |
---|
| 65 | 97, 101, 103, 107, 109, 113, 127, 131, |
---|
| 66 | 137, 139, 149, 151, 157, 163, 167, 173, |
---|
[806c18] | 67 | 179, 181, 191, 193, 197, 199, 211, 223, |
---|
| 68 | 227, 229, 233, 239, 241, 251 |
---|
[b478f8] | 69 | }; |
---|
[b52d27] | 70 | |
---|
| 71 | /** bool isIrreducible ( const CanonicalForm & f ) |
---|
| 72 | * |
---|
| 73 | * isIrreducible() - return true iff f is irreducible. |
---|
| 74 | * |
---|
| 75 | **/ |
---|
[b478f8] | 76 | bool |
---|
| 77 | isIrreducible ( const CanonicalForm & f ) |
---|
| 78 | { |
---|
| 79 | CFFList F = factorize( f ); |
---|
[b52d27] | 80 | if (F.getFirst().factor().inCoeffDomain()) |
---|
| 81 | F.removeFirst(); |
---|
[b478f8] | 82 | return F.length() == 1 && F.getFirst().exp() == 1; |
---|
| 83 | } |
---|
[b52d27] | 84 | |
---|
| 85 | /** int exponent ( const CanonicalForm & f, int q ) |
---|
| 86 | * |
---|
| 87 | * exponent() - return e > 0 such that x^e == 1 mod f. |
---|
| 88 | * |
---|
| 89 | * q: upper limit for e (?) |
---|
| 90 | * |
---|
| 91 | **/ |
---|
[b478f8] | 92 | int |
---|
| 93 | exponent ( const CanonicalForm & f, int q ) |
---|
| 94 | { |
---|
| 95 | Variable x = f.mvar(); |
---|
| 96 | int e = 1; |
---|
| 97 | CanonicalForm prod = x; |
---|
| 98 | while ( e <= q && ! prod.isOne() ) { |
---|
[806c18] | 99 | e++; |
---|
| 100 | prod = ( prod * x ) % f; |
---|
[b478f8] | 101 | } |
---|
| 102 | return e; |
---|
| 103 | } |
---|
[b52d27] | 104 | |
---|
| 105 | /** bool findGenRec ( int d, int n, int q, const CanonicalForm & m, const Variable & x, CanonicalForm & result ) |
---|
| 106 | * |
---|
| 107 | * findGenRec() - find a generator of GF(q). |
---|
| 108 | * |
---|
| 109 | * Returns true iff result is a valid generator. |
---|
| 110 | * |
---|
| 111 | * d: degree of extension |
---|
| 112 | * q: the q in GF(q) (q == p^d) |
---|
| 113 | * x: generator should be a poly in x |
---|
| 114 | * n, m: used to step recursively through all polys in FF(p) |
---|
| 115 | * Initially, n == d and m == 0. If 0 <= n <= d we are |
---|
| 116 | * in the process of building m, if n < 0 we built m and |
---|
| 117 | * may test whether it generates GF(q). |
---|
| 118 | * result: generator found |
---|
| 119 | * |
---|
| 120 | * i: used to step through GF(p) |
---|
| 121 | * p: current characteristic |
---|
| 122 | * |
---|
| 123 | **/ |
---|
[b478f8] | 124 | bool |
---|
| 125 | findGenRec ( int d, int n, int q, |
---|
[806c18] | 126 | const CanonicalForm & m, const Variable & x, |
---|
| 127 | CanonicalForm & result ) |
---|
[b478f8] | 128 | { |
---|
| 129 | int i, p = getCharacteristic(); |
---|
| 130 | if ( n < 0 ) { |
---|
[806c18] | 131 | cerr << "."; cerr.flush(); |
---|
| 132 | // check whether m is irreducible |
---|
| 133 | if ( isIrreducible( m ) ) { |
---|
| 134 | cerr << "*"; cerr.flush(); |
---|
| 135 | // check whether m generates multiplicative group |
---|
| 136 | if ( exponent( m, q ) == q - 1 ) { |
---|
| 137 | result = m; |
---|
| 138 | return true; |
---|
| 139 | } |
---|
| 140 | else |
---|
| 141 | return false; |
---|
| 142 | } |
---|
| 143 | else |
---|
| 144 | return false; |
---|
[b478f8] | 145 | } |
---|
| 146 | // for each monomial x^0, ..., x^n, ..., x^d, try all possible coefficients |
---|
| 147 | else if ( n == d || n == 0 ) { |
---|
[806c18] | 148 | // we want to have a leading coefficient and a constant term, |
---|
| 149 | // so start with coefficient >= 1 |
---|
| 150 | for ( i = 1; i < p; i++ ) |
---|
| 151 | if ( findGenRec( d, n-1, q, m + i * power( x, n ), x, result ) ) |
---|
| 152 | return true; |
---|
[b478f8] | 153 | } |
---|
| 154 | else { |
---|
[806c18] | 155 | for ( i = 0; i < p; i++ ) |
---|
| 156 | if ( findGenRec( d, n-1, q, m + i * power( x, n ), x, result ) ) |
---|
| 157 | return true; |
---|
[b478f8] | 158 | } |
---|
| 159 | return false; |
---|
| 160 | } |
---|
[b52d27] | 161 | |
---|
| 162 | /** CanonicalForm findGen ( int d, int q ) |
---|
| 163 | * |
---|
| 164 | * findGen() - find and return a generator of GF(q). |
---|
| 165 | * |
---|
| 166 | * d: degree of extension |
---|
| 167 | * q: the q in GF(q) |
---|
| 168 | * |
---|
| 169 | **/ |
---|
[b478f8] | 170 | CanonicalForm |
---|
| 171 | findGen ( int d, int q ) |
---|
| 172 | { |
---|
| 173 | Variable x( 1 ); |
---|
| 174 | CanonicalForm result; |
---|
| 175 | cerr << "testing p = " << getCharacteristic() << ", d = " << d << " ... "; |
---|
| 176 | cerr.flush(); |
---|
| 177 | bool ok = findGenRec( d, d, q, 0, x, result ); |
---|
| 178 | cerr << endl; |
---|
| 179 | if ( ! ok ) |
---|
[806c18] | 180 | return 0; |
---|
[b478f8] | 181 | else |
---|
[806c18] | 182 | return result; |
---|
[b478f8] | 183 | } |
---|
[b52d27] | 184 | |
---|
| 185 | /** void printTable ( int d, int q, CanonicalForm mipo ) |
---|
| 186 | * |
---|
| 187 | * printTable - print +1 table of field GF(q). |
---|
| 188 | * |
---|
| 189 | * d: degree of extension |
---|
| 190 | * q: the q in GF(q) |
---|
| 191 | * mipo: the minimal polynomial of the extension |
---|
| 192 | * |
---|
| 193 | * p: current characteristic |
---|
| 194 | * |
---|
| 195 | **/ |
---|
[b478f8] | 196 | void |
---|
| 197 | printTable ( int d, int q, CanonicalForm mipo ) |
---|
| 198 | { |
---|
| 199 | int i, p = getCharacteristic(); |
---|
| 200 | |
---|
| 201 | // open file to write to |
---|
[806c18] | 202 | ostrstream fname; |
---|
[7f807d] | 203 | fname << "gftables/" << q << '\0'; |
---|
[b478f8] | 204 | char * fn = fname.str(); |
---|
| 205 | ofstream outfile; |
---|
| 206 | outfile.open( fn, ios::out ); |
---|
| 207 | STICKYASSERT1( outfile, "can not open GF(q) table %s for writing", fn ); |
---|
| 208 | delete fn; |
---|
| 209 | |
---|
| 210 | cerr << "mipo = " << mipo << ": "; |
---|
| 211 | cerr << "generating multiplicative group ... "; |
---|
| 212 | cerr.flush(); |
---|
| 213 | |
---|
| 214 | CanonicalForm * T = new CanonicalForm[maxtable]; |
---|
| 215 | Variable x( 1 ); |
---|
| 216 | |
---|
| 217 | // fill T with powers of x |
---|
| 218 | T[0] = 1; |
---|
| 219 | for ( i = 1; i < q; i++ ) |
---|
[806c18] | 220 | T[i] = ( T[i-1] * x ) % mipo; |
---|
[b478f8] | 221 | |
---|
| 222 | cerr << "generating addition table ... "; |
---|
| 223 | cerr.flush(); |
---|
| 224 | |
---|
| 225 | // brute force method |
---|
| 226 | int * table = new int[maxtable]; |
---|
| 227 | CanonicalForm f; |
---|
| 228 | |
---|
| 229 | for ( i = 0; i < q; i++ ) { |
---|
[806c18] | 230 | f = T[i] + 1; |
---|
| 231 | int j = 0; |
---|
| 232 | while ( j < q && T[j] != f ) j++; |
---|
| 233 | table[i] = j; |
---|
[b478f8] | 234 | } |
---|
| 235 | |
---|
| 236 | cerr << "writing table ... "; |
---|
| 237 | cerr.flush(); |
---|
| 238 | |
---|
| 239 | outfile << "@@ factory GF(q) table @@" << endl; |
---|
| 240 | outfile << p << " " << d << " " << mipo << "; "; |
---|
| 241 | |
---|
| 242 | // print simple reprenstation of mipo |
---|
| 243 | outfile << d; |
---|
| 244 | CFIterator MiPo = mipo; |
---|
| 245 | for ( i = d; MiPo.hasTerms(); i--, MiPo++ ) { |
---|
[806c18] | 246 | int exp; |
---|
| 247 | for ( exp = MiPo.exp(); exp < i; i-- ) |
---|
| 248 | outfile << " 0"; |
---|
| 249 | outfile << " " << MiPo.coeff(); |
---|
[b478f8] | 250 | } |
---|
| 251 | // since mipo is irreducible, it has a constant term, |
---|
| 252 | // so i == 0 at this point |
---|
| 253 | outfile << endl; |
---|
| 254 | |
---|
| 255 | int m = gf_tab_numdigits62( q ); |
---|
| 256 | char * outstr = new char[30*m+1]; |
---|
| 257 | outstr[30*m] = '\0'; |
---|
| 258 | i = 1; |
---|
| 259 | while ( i < q ) { |
---|
[806c18] | 260 | int k = 0; |
---|
| 261 | char * sptr = outstr; |
---|
| 262 | while ( i < q && k < 30 ) { |
---|
| 263 | convert62( table[i], m, sptr ); |
---|
| 264 | sptr += m; |
---|
| 265 | k++; i++; |
---|
| 266 | } |
---|
| 267 | while ( k < 30 ) { |
---|
| 268 | convert62( 0, m, sptr ); |
---|
| 269 | sptr += m; |
---|
| 270 | k++; |
---|
| 271 | } |
---|
| 272 | outfile << outstr << endl; |
---|
[b478f8] | 273 | } |
---|
| 274 | outfile.close(); |
---|
| 275 | |
---|
| 276 | delete [] outstr; |
---|
| 277 | delete [] T; |
---|
| 278 | delete [] table; |
---|
| 279 | |
---|
| 280 | cerr << endl; |
---|
| 281 | } |
---|
[b52d27] | 282 | |
---|
| 283 | /** |
---|
| 284 | * The new function for getting the minimal polynomials. |
---|
| 285 | * It uses the Conway polynomials. |
---|
| 286 | * It reads the polynomials from a file. |
---|
[3e8b64] | 287 | * The file contains all polynomials with p^k <= 2^16 |
---|
[b52d27] | 288 | * but currently only polynomials with p^k <= 2^14 are used. |
---|
| 289 | **/ |
---|
| 290 | static CanonicalForm findGenNew(int n, ///< n is the exponent |
---|
| 291 | int q ///< parameter q is not used. It is added to respect the old version |
---|
| 292 | ) |
---|
[b478f8] | 293 | { |
---|
[806c18] | 294 | CanonicalForm conway = 0; |
---|
| 295 | Variable x( 1 ); |
---|
| 296 | int p = getCharacteristic(); |
---|
| 297 | int ntmp,ptmp,pos1,pos2,ii; |
---|
| 298 | string ns, ps; |
---|
| 299 | string LineSe,coef,PC; |
---|
| 300 | int flag=1; |
---|
| 301 | ifstream in("./ConwayList.txt"); |
---|
| 302 | getline(in,LineSe); // For the first line |
---|
| 303 | |
---|
| 304 | string err="END"; //to check if we are at the end of the file |
---|
| 305 | while((flag) && (err != LineSe)) |
---|
| 306 | { |
---|
| 307 | getline(in,LineSe); //for the line: allConwayPolynomials := [ |
---|
| 308 | if(LineSe == err){ |
---|
| 309 | break; |
---|
| 310 | } |
---|
| 311 | pos1 = LineSe.find( ",", 0 ); |
---|
| 312 | pos2 = LineSe.find( ",", pos1 + 1); // we check where are the "," to now p and n of this line |
---|
| 313 | ps = LineSe.substr(0, pos1); |
---|
| 314 | ns = LineSe.substr(pos1 + 1,pos2 - pos1); |
---|
[189f83] | 315 | ptmp = atoi(ps.c_str()); //we have the value of p and n of these line |
---|
| 316 | ntmp = atoi(ns.c_str()); |
---|
[806c18] | 317 | |
---|
| 318 | if((ntmp==n)&&(ptmp==p)){flag=0;} // we check if they are our p and n to stop the search |
---|
| 319 | |
---|
| 320 | } |
---|
| 321 | |
---|
| 322 | if (err==LineSe) // If the Conway Polynomial is not in the list, there is an error. |
---|
| 323 | { |
---|
| 324 | //cout << "Error: This Conway polinomial is not in the list" << endl; |
---|
| 325 | return(0); |
---|
| 326 | } |
---|
| 327 | |
---|
| 328 | // Read the polynomial from the file |
---|
| 329 | pos1 = pos2 + 1; |
---|
| 330 | pos2 = LineSe.find(",", pos1 + 1); |
---|
[189f83] | 331 | conway = atoi(LineSe.substr(pos1, pos2 - pos1).c_str()); // value of the constant term in PC=Conway Polynomial |
---|
[b478f8] | 332 | pos1 = pos2; |
---|
[806c18] | 333 | pos2 = LineSe.find(",", pos1 + 1); |
---|
[b478f8] | 334 | |
---|
[806c18] | 335 | for(ii = 2; ii <= n; ii++) |
---|
| 336 | { |
---|
| 337 | coef = LineSe.substr(pos1 + 1,pos2 - pos1 - 1); //Coefficient of the monomial of degree ii-1 |
---|
[b478f8] | 338 | if(coef != "0") |
---|
[806c18] | 339 | { |
---|
[189f83] | 340 | conway = conway + atoi(coef.c_str()) * power(x, ii - 1) ; //We add this monomial to the Conway Polynomial |
---|
[806c18] | 341 | } |
---|
| 342 | pos1 = pos2; |
---|
| 343 | pos2 = LineSe.find( ",", pos1+1); |
---|
| 344 | } |
---|
| 345 | |
---|
| 346 | pos2 = LineSe.find( ",END", pos1 + 1); // To obtain the last coefficient we search "END" instead of "," |
---|
| 347 | coef = LineSe.substr(pos1 + 1,pos2 - pos1 - 1); |
---|
[189f83] | 348 | conway = conway + atoi(coef.c_str()) * power(x, ii - 1) ; //We add the last monomial to the Conway Polynomial |
---|
[806c18] | 349 | |
---|
| 350 | in.close(); |
---|
| 351 | |
---|
| 352 | return(conway); |
---|
| 353 | |
---|
[b478f8] | 354 | } |
---|
| 355 | |
---|
| 356 | |
---|
| 357 | int |
---|
| 358 | main() |
---|
| 359 | { |
---|
| 360 | int i, p, q, n; |
---|
| 361 | for ( i = 0; i < primes_len; i++ ) { |
---|
[806c18] | 362 | p = primes[i]; |
---|
[3e8b64] | 363 | q = p; |
---|
| 364 | n = 1; |
---|
[806c18] | 365 | setCharacteristic( p ); |
---|
| 366 | while ( q < maxtable ) { |
---|
| 367 | CanonicalForm f = findGenNew( n, q ); |
---|
| 368 | ASSERT( f != 0, "no generator found" ); |
---|
[f38e34] | 369 | printTable( n, q, f ); |
---|
[806c18] | 370 | n++; q *= p; |
---|
| 371 | } |
---|
[b478f8] | 372 | } |
---|
| 373 | } |
---|
| 374 | |
---|