#ifndef BIGINTEGER_H #define BIGINTEGER_H #include "BigUnsigned.hh" /* A BigInteger object represents a signed integer of size limited only by * available memory. BigUnsigneds support most mathematical operators and can * be converted to and from most primitive integer types. * * A BigInteger is just an aggregate of a BigUnsigned and a sign. (It is no * longer derived from BigUnsigned because that led to harmful implicit * conversions.) */ class BigInteger { public: typedef BigUnsigned::Blk Blk; typedef BigUnsigned::Index Index; typedef BigUnsigned::CmpRes CmpRes; static const CmpRes less = BigUnsigned::less , equal = BigUnsigned::equal , greater = BigUnsigned::greater; // Enumeration for the sign of a BigInteger. enum Sign { negative = -1, zero = 0, positive = 1 }; protected: Sign sign; BigUnsigned mag; public: // Constructs zero. BigInteger() : sign(zero), mag() {} // Copy constructor BigInteger(const BigInteger &x) : sign(x.sign), mag(x.mag) {}; // Assignment operator void operator=(const BigInteger &x); // Constructor that copies from a given array of blocks with a sign. BigInteger(const Blk *b, Index blen, Sign s); // Nonnegative constructor that copies from a given array of blocks. BigInteger(const Blk *b, Index blen) : mag(b, blen) { sign = mag.isZero() ? zero : positive; } // Constructor from a BigUnsigned and a sign BigInteger(const BigUnsigned &x, Sign s); // Nonnegative constructor from a BigUnsigned BigInteger(const BigUnsigned &x) : mag(x) { sign = mag.isZero() ? zero : positive; } // Constructors from primitive integer types BigInteger(unsigned long x); BigInteger( long x); BigInteger(unsigned int x); BigInteger( int x); BigInteger(unsigned short x); BigInteger( short x); /* Converters to primitive integer types * The implicit conversion operators caused trouble, so these are now * named. */ unsigned long toUnsignedLong () const; long toLong () const; unsigned int toUnsignedInt () const; int toInt () const; unsigned short toUnsignedShort() const; short toShort () const; protected: // Helper template X convertToUnsignedPrimitive() const; template X convertToSignedPrimitive() const; public: // ACCESSORS Sign getSign() const { return sign; } /* The client can't do any harm by holding a read-only reference to the * magnitude. */ const BigUnsigned &getMagnitude() const { return mag; } // Some accessors that go through to the magnitude Index getLength() const { return mag.getLength(); } Index getCapacity() const { return mag.getCapacity(); } Blk getBlock(Index i) const { return mag.getBlock(i); } bool isZero() const { return sign == zero; } // A bit special // COMPARISONS // Compares this to x like Perl's <=> CmpRes compareTo(const BigInteger &x) const; // Ordinary comparison operators bool operator ==(const BigInteger &x) const { return sign == x.sign && mag == x.mag; } bool operator !=(const BigInteger &x) const { return !operator ==(x); }; bool operator < (const BigInteger &x) const { return compareTo(x) == less ; } bool operator <=(const BigInteger &x) const { return compareTo(x) != greater; } bool operator >=(const BigInteger &x) const { return compareTo(x) != less ; } bool operator > (const BigInteger &x) const { return compareTo(x) == greater; } // OPERATORS -- See the discussion in BigUnsigned.hh. void add (const BigInteger &a, const BigInteger &b); void subtract(const BigInteger &a, const BigInteger &b); void multiply(const BigInteger &a, const BigInteger &b); /* See the comment on BigUnsigned::divideWithRemainder. Semantics * differ from those of primitive integers when negatives and/or zeros * are involved. */ void divideWithRemainder(const BigInteger &b, BigInteger &q); void negate(const BigInteger &a); /* Bitwise operators are not provided for BigIntegers. Use * getMagnitude to get the magnitude and operate on that instead. */ BigInteger operator +(const BigInteger &x) const; BigInteger operator -(const BigInteger &x) const; BigInteger operator *(const BigInteger &x) const; BigInteger operator /(const BigInteger &x) const; BigInteger operator %(const BigInteger &x) const; BigInteger operator -() const; void operator +=(const BigInteger &x); void operator -=(const BigInteger &x); void operator *=(const BigInteger &x); void operator /=(const BigInteger &x); void operator %=(const BigInteger &x); void flipSign(); // INCREMENT/DECREMENT OPERATORS void operator ++( ); void operator ++(int); void operator --( ); void operator --(int); }; // NORMAL OPERATORS /* These create an object to hold the result and invoke * the appropriate put-here operation on it, passing * this and x. The new object is then returned. */ inline BigInteger BigInteger::operator +(const BigInteger &x) const { BigInteger ans; ans.add(*this, x); return ans; } inline BigInteger BigInteger::operator -(const BigInteger &x) const { BigInteger ans; ans.subtract(*this, x); return ans; } inline BigInteger BigInteger::operator *(const BigInteger &x) const { BigInteger ans; ans.multiply(*this, x); return ans; } inline BigInteger BigInteger::operator /(const BigInteger &x) const { if (x.isZero()) throw "BigInteger::operator /: division by zero"; BigInteger q, r; r = *this; r.divideWithRemainder(x, q); return q; } inline BigInteger BigInteger::operator %(const BigInteger &x) const { if (x.isZero()) throw "BigInteger::operator %: division by zero"; BigInteger q, r; r = *this; r.divideWithRemainder(x, q); return r; } inline BigInteger BigInteger::operator -() const { BigInteger ans; ans.negate(*this); return ans; } /* * ASSIGNMENT OPERATORS * * Now the responsibility for making a temporary copy if necessary * belongs to the put-here operations. See Assignment Operators in * BigUnsigned.hh. */ inline void BigInteger::operator +=(const BigInteger &x) { add(*this, x); } inline void BigInteger::operator -=(const BigInteger &x) { subtract(*this, x); } inline void BigInteger::operator *=(const BigInteger &x) { multiply(*this, x); } inline void BigInteger::operator /=(const BigInteger &x) { if (x.isZero()) throw "BigInteger::operator /=: division by zero"; /* The following technique is slightly faster than copying *this first * when x is large. */ BigInteger q; divideWithRemainder(x, q); // *this contains the remainder, but we overwrite it with the quotient. *this = q; } inline void BigInteger::operator %=(const BigInteger &x) { if (x.isZero()) throw "BigInteger::operator %=: division by zero"; BigInteger q; // Mods *this by x. Don't care about quotient left in q. divideWithRemainder(x, q); } // This one is trivial inline void BigInteger::flipSign() { sign = Sign(-sign); } #endif 1 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466