| 1 | #include "BigInteger.hh" |
| 2 | |
| 3 | void BigInteger::operator =(const BigInteger &x) { |
| 4 | // Calls like a = a have no effect |
| 5 | if (this == &x) |
| 6 | return; |
| 7 | // Copy sign |
| 8 | sign = x.sign; |
| 9 | // Copy the rest |
| 10 | mag = x.mag; |
| 11 | } |
| 12 | |
| 13 | BigInteger::BigInteger(const Blk *b, Index blen, Sign s) : mag(b, blen) { |
| 14 | switch (s) { |
| 15 | case zero: |
| 16 | if (!mag.isZero()) |
| 17 | throw "BigInteger::BigInteger(const Blk *, Index, Sign): Cannot use a sign of zero with a nonzero magnitude"; |
| 18 | sign = zero; |
| 19 | break; |
| 20 | case positive: |
| 21 | case negative: |
| 22 | // If the magnitude is zero, force the sign to zero. |
| 23 | sign = mag.isZero() ? zero : s; |
| 24 | break; |
| 25 | default: |
| 26 | /* g++ seems to be optimizing out this case on the assumption |
| 27 | * that the sign is a valid member of the enumeration. Oh well. */ |
| 28 | throw "BigInteger::BigInteger(const Blk *, Index, Sign): Invalid sign"; |
| 29 | } |
| 30 | } |
| 31 | |
| 32 | BigInteger::BigInteger(const BigUnsigned &x, Sign s) : mag(x) { |
| 33 | switch (s) { |
| 34 | case zero: |
| 35 | if (!mag.isZero()) |
| 36 | throw "BigInteger::BigInteger(const BigUnsigned &, Sign): Cannot use a sign of zero with a nonzero magnitude"; |
| 37 | sign = zero; |
| 38 | break; |
| 39 | case positive: |
| 40 | case negative: |
| 41 | // If the magnitude is zero, force the sign to zero. |
| 42 | sign = mag.isZero() ? zero : s; |
| 43 | break; |
| 44 | default: |
| 45 | /* g++ seems to be optimizing out this case on the assumption |
| 46 | * that the sign is a valid member of the enumeration. Oh well. */ |
| 47 | throw "BigInteger::BigInteger(const BigUnsigned &, Sign): Invalid sign"; |
| 48 | } |
| 49 | } |
| 50 | |
| 51 | /* CONSTRUCTION FROM PRIMITIVE INTEGERS |
| 52 | * Same idea as in BigUnsigned.cc, except that negative input results in a |
| 53 | * negative BigInteger instead of an exception. */ |
| 54 | |
| 55 | // Done longhand to let us use initialization. |
| 56 | BigInteger::BigInteger(unsigned long x) : mag(x) { sign = mag.isZero() ? zero : positive; } |
| 57 | BigInteger::BigInteger(unsigned int x) : mag(x) { sign = mag.isZero() ? zero : positive; } |
| 58 | BigInteger::BigInteger(unsigned short x) : mag(x) { sign = mag.isZero() ? zero : positive; } |
| 59 | |
| 60 | // For signed input, determine the desired magnitude and sign separately. |
| 61 | |
| 62 | namespace { |
| 63 | template <class X, class UX> |
| 64 | BigInteger::Blk magOf(X x) { |
| 65 | /* UX(...) cast needed to stop short(-2^15), which negates to |
| 66 | * itself, from sign-extending in the conversion to Blk. */ |
| 67 | return BigInteger::Blk(x < 0 ? UX(-x) : x); |
| 68 | } |
| 69 | template <class X> |
| 70 | BigInteger::Sign signOf(X x) { |
| 71 | return (x == 0) ? BigInteger::zero |
| 72 | : (x > 0) ? BigInteger::positive |
| 73 | : BigInteger::negative; |
| 74 | } |
| 75 | } |
| 76 | |
| 77 | BigInteger::BigInteger(long x) : sign(signOf(x)), mag(magOf<long , unsigned long >(x)) {} |
| 78 | BigInteger::BigInteger(int x) : sign(signOf(x)), mag(magOf<int , unsigned int >(x)) {} |
| 79 | BigInteger::BigInteger(short x) : sign(signOf(x)), mag(magOf<short, unsigned short>(x)) {} |
| 80 | |
| 81 | // CONVERSION TO PRIMITIVE INTEGERS |
| 82 | |
| 83 | /* Reuse BigUnsigned's conversion to an unsigned primitive integer. |
| 84 | * The friend is a separate function rather than |
| 85 | * BigInteger::convertToUnsignedPrimitive to avoid requiring BigUnsigned to |
| 86 | * declare BigInteger. */ |
| 87 | template <class X> |
| 88 | inline X convertBigUnsignedToPrimitiveAccess(const BigUnsigned &a) { |
| 89 | return a.convertToPrimitive<X>(); |
| 90 | } |
| 91 | |
| 92 | template <class X> |
| 93 | X BigInteger::convertToUnsignedPrimitive() const { |
| 94 | if (sign == negative) |
| 95 | throw "BigInteger::to<Primitive>: " |
| 96 | "Cannot convert a negative integer to an unsigned type"; |
| 97 | else |
| 98 | return convertBigUnsignedToPrimitiveAccess<X>(mag); |
| 99 | } |
| 100 | |
| 101 | /* Similar to BigUnsigned::convertToPrimitive, but split into two cases for |
| 102 | * nonnegative and negative numbers. */ |
| 103 | template <class X, class UX> |
| 104 | X BigInteger::convertToSignedPrimitive() const { |
| 105 | if (sign == zero) |
| 106 | return 0; |
| 107 | else if (mag.getLength() == 1) { |
| 108 | // The single block might fit in an X. Try the conversion. |
| 109 | Blk b = mag.getBlock(0); |
| 110 | if (sign == positive) { |
| 111 | X x = X(b); |
| 112 | if (x >= 0 && Blk(x) == b) |
| 113 | return x; |
| 114 | } else { |
| 115 | X x = -X(b); |
| 116 | /* UX(...) needed to avoid rejecting conversion of |
| 117 | * -2^15 to a short. */ |
| 118 | if (x < 0 && Blk(UX(-x)) == b) |
| 119 | return x; |
| 120 | } |
| 121 | // Otherwise fall through. |
| 122 | } |
| 123 | throw "BigInteger::to<Primitive>: " |
| 124 | "Value is too big to fit in the requested type"; |
| 125 | } |
| 126 | |
| 127 | unsigned long BigInteger::toUnsignedLong () const { return convertToUnsignedPrimitive<unsigned long > (); } |
| 128 | unsigned int BigInteger::toUnsignedInt () const { return convertToUnsignedPrimitive<unsigned int > (); } |
| 129 | unsigned short BigInteger::toUnsignedShort() const { return convertToUnsignedPrimitive<unsigned short> (); } |
| 130 | long BigInteger::toLong () const { return convertToSignedPrimitive <long , unsigned long> (); } |
| 131 | int BigInteger::toInt () const { return convertToSignedPrimitive <int , unsigned int> (); } |
| 132 | short BigInteger::toShort () const { return convertToSignedPrimitive <short, unsigned short>(); } |
| 133 | |
| 134 | // COMPARISON |
| 135 | BigInteger::CmpRes BigInteger::compareTo(const BigInteger &x) const { |
| 136 | // A greater sign implies a greater number |
| 137 | if (sign < x.sign) |
| 138 | return less; |
| 139 | else if (sign > x.sign) |
| 140 | return greater; |
| 141 | else switch (sign) { |
| 142 | // If the signs are the same... |
| 143 | case zero: |
| 144 | return equal; // Two zeros are equal |
| 145 | case positive: |
| 146 | // Compare the magnitudes |
| 147 | return mag.compareTo(x.mag); |
| 148 | case negative: |
| 149 | // Compare the magnitudes, but return the opposite result |
| 150 | return CmpRes(-mag.compareTo(x.mag)); |
| 151 | default: |
| 152 | throw "BigInteger internal error"; |
| 153 | } |
| 154 | } |
| 155 | |
| 156 | /* COPY-LESS OPERATIONS |
| 157 | * These do some messing around to determine the sign of the result, |
| 158 | * then call one of BigUnsigned's copy-less operations. */ |
| 159 | |
| 160 | // See remarks about aliased calls in BigUnsigned.cc . |
| 161 | #define DTRT_ALIASED(cond, op) \ |
| 162 | if (cond) { \ |
| 163 | BigInteger tmpThis; \ |
| 164 | tmpThis.op; \ |
| 165 | *this = tmpThis; \ |
| 166 | return; \ |
| 167 | } |
| 168 | |
| 169 | void BigInteger::add(const BigInteger &a, const BigInteger &b) { |
| 170 | DTRT_ALIASED(this == &a || this == &b, add(a, b)); |
| 171 | // If one argument is zero, copy the other. |
| 172 | if (a.sign == zero) |
| 173 | operator =(b); |
| 174 | else if (b.sign == zero) |
| 175 | operator =(a); |
| 176 | // If the arguments have the same sign, take the |
| 177 | // common sign and add their magnitudes. |
| 178 | else if (a.sign == b.sign) { |
| 179 | sign = a.sign; |
| 180 | mag.add(a.mag, b.mag); |
| 181 | } else { |
| 182 | // Otherwise, their magnitudes must be compared. |
| 183 | switch (a.mag.compareTo(b.mag)) { |
| 184 | case equal: |
| 185 | // If their magnitudes are the same, copy zero. |
| 186 | mag = 0; |
| 187 | sign = zero; |
| 188 | break; |
| 189 | // Otherwise, take the sign of the greater, and subtract |
| 190 | // the lesser magnitude from the greater magnitude. |
| 191 | case greater: |
| 192 | sign = a.sign; |
| 193 | mag.subtract(a.mag, b.mag); |
| 194 | break; |
| 195 | case less: |
| 196 | sign = b.sign; |
| 197 | mag.subtract(b.mag, a.mag); |
| 198 | break; |
| 199 | } |
| 200 | } |
| 201 | } |
| 202 | |
| 203 | void BigInteger::subtract(const BigInteger &a, const BigInteger &b) { |
| 204 | // Notice that this routine is identical to BigInteger::add, |
| 205 | // if one replaces b.sign by its opposite. |
| 206 | DTRT_ALIASED(this == &a || this == &b, subtract(a, b)); |
| 207 | // If a is zero, copy b and flip its sign. If b is zero, copy a. |
| 208 | if (a.sign == zero) { |
| 209 | mag = b.mag; |
| 210 | // Take the negative of _b_'s, sign, not ours. |
| 211 | // Bug pointed out by Sam Larkin on 2005.03.30. |
| 212 | sign = Sign(-b.sign); |
| 213 | } else if (b.sign == zero) |
| 214 | operator =(a); |
| 215 | // If their signs differ, take a.sign and add the magnitudes. |
| 216 | else if (a.sign != b.sign) { |
| 217 | sign = a.sign; |
| 218 | mag.add(a.mag, b.mag); |
| 219 | } else { |
| 220 | // Otherwise, their magnitudes must be compared. |
| 221 | switch (a.mag.compareTo(b.mag)) { |
| 222 | // If their magnitudes are the same, copy zero. |
| 223 | case equal: |
| 224 | mag = 0; |
| 225 | sign = zero; |
| 226 | break; |
| 227 | // If a's magnitude is greater, take a.sign and |
| 228 | // subtract a from b. |
| 229 | case greater: |
| 230 | sign = a.sign; |
| 231 | mag.subtract(a.mag, b.mag); |
| 232 | break; |
| 233 | // If b's magnitude is greater, take the opposite |
| 234 | // of b.sign and subtract b from a. |
| 235 | case less: |
| 236 | sign = Sign(-b.sign); |
| 237 | mag.subtract(b.mag, a.mag); |
| 238 | break; |
| 239 | } |
| 240 | } |
| 241 | } |
| 242 | |
| 243 | void BigInteger::multiply(const BigInteger &a, const BigInteger &b) { |
| 244 | DTRT_ALIASED(this == &a || this == &b, multiply(a, b)); |
| 245 | // If one object is zero, copy zero and return. |
| 246 | if (a.sign == zero || b.sign == zero) { |
| 247 | sign = zero; |
| 248 | mag = 0; |
| 249 | return; |
| 250 | } |
| 251 | // If the signs of the arguments are the same, the result |
| 252 | // is positive, otherwise it is negative. |
| 253 | sign = (a.sign == b.sign) ? positive : negative; |
| 254 | // Multiply the magnitudes. |
| 255 | mag.multiply(a.mag, b.mag); |
| 256 | } |
| 257 | |
| 258 | /* |
| 259 | * DIVISION WITH REMAINDER |
| 260 | * Please read the comments before the definition of |
| 261 | * `BigUnsigned::divideWithRemainder' in `BigUnsigned.cc' for lots of |
| 262 | * information you should know before reading this function. |
| 263 | * |
| 264 | * Following Knuth, I decree that x / y is to be |
| 265 | * 0 if y==0 and floor(real-number x / y) if y!=0. |
| 266 | * Then x % y shall be x - y*(integer x / y). |
| 267 | * |
| 268 | * Note that x = y * (x / y) + (x % y) always holds. |
| 269 | * In addition, (x % y) is from 0 to y - 1 if y > 0, |
| 270 | * and from -(|y| - 1) to 0 if y < 0. (x % y) = x if y = 0. |
| 271 | * |
| 272 | * Examples: (q = a / b, r = a % b) |
| 273 | * a b q r |
| 274 | * === === === === |
| 275 | * 4 3 1 1 |
| 276 | * -4 3 -2 2 |
| 277 | * 4 -3 -2 -2 |
| 278 | * -4 -3 1 -1 |
| 279 | */ |
| 280 | void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) { |
| 281 | // Defend against aliased calls; |
| 282 | // same idea as in BigUnsigned::divideWithRemainder . |
| 283 | if (this == &q) |
| 284 | throw "BigInteger::divideWithRemainder: Cannot write quotient and remainder into the same variable"; |
| 285 | if (this == &b || &q == &b) { |
| 286 | BigInteger tmpB(b); |
| 287 | divideWithRemainder(tmpB, q); |
| 288 | return; |
| 289 | } |
| 290 | |
| 291 | // Division by zero gives quotient 0 and remainder *this |
| 292 | if (b.sign == zero) { |
| 293 | q.mag = 0; |
| 294 | q.sign = zero; |
| 295 | return; |
| 296 | } |
| 297 | // 0 / b gives quotient 0 and remainder 0 |
| 298 | if (sign == zero) { |
| 299 | q.mag = 0; |
| 300 | q.sign = zero; |
| 301 | return; |
| 302 | } |
| 303 | |
| 304 | // Here *this != 0, b != 0. |
| 305 | |
| 306 | // Do the operands have the same sign? |
| 307 | if (sign == b.sign) { |
| 308 | // Yes: easy case. Quotient is zero or positive. |
| 309 | q.sign = positive; |
| 310 | } else { |
| 311 | // No: harder case. Quotient is negative. |
| 312 | q.sign = negative; |
| 313 | // Decrease the magnitude of the dividend by one. |
| 314 | mag--; |
| 315 | /* |
| 316 | * We tinker with the dividend before and with the |
| 317 | * quotient and remainder after so that the result |
| 318 | * comes out right. To see why it works, consider the following |
| 319 | * list of examples, where A is the magnitude-decreased |
| 320 | * a, Q and R are the results of BigUnsigned division |
| 321 | * with remainder on A and |b|, and q and r are the |
| 322 | * final results we want: |
| 323 | * |
| 324 | * a A b Q R q r |
| 325 | * -3 -2 3 0 2 -1 0 |
| 326 | * -4 -3 3 1 0 -2 2 |
| 327 | * -5 -4 3 1 1 -2 1 |
| 328 | * -6 -5 3 1 2 -2 0 |
| 329 | * |
| 330 | * It appears that we need a total of 3 corrections: |
| 331 | * Decrease the magnitude of a to get A. Increase the |
| 332 | * magnitude of Q to get q (and make it negative). |
| 333 | * Find r = (b - 1) - R and give it the desired sign. |
| 334 | */ |
| 335 | } |
| 336 | |
| 337 | // Divide the magnitudes. |
| 338 | mag.divideWithRemainder(b.mag, q.mag); |
| 339 | |
| 340 | if (sign != b.sign) { |
| 341 | // More for the harder case (as described): |
| 342 | // Increase the magnitude of the quotient by one. |
| 343 | q.mag++; |
| 344 | // Modify the remainder. |
| 345 | mag.subtract(b.mag, mag); |
| 346 | mag--; |
| 347 | } |
| 348 | |
| 349 | // Sign of the remainder is always the sign of the divisor b. |
| 350 | sign = b.sign; |
| 351 | |
| 352 | // Set signs to zero as necessary. (Thanks David Allen!) |
| 353 | if (mag.isZero()) |
| 354 | sign = zero; |
| 355 | if (q.mag.isZero()) |
| 356 | q.sign = zero; |
| 357 | |
| 358 | // WHEW!!! |
| 359 | } |
| 360 | |
| 361 | // Negation |
| 362 | void BigInteger::negate(const BigInteger &a) { |
| 363 | DTRT_ALIASED(this == &a, negate(a)); |
| 364 | // Copy a's magnitude |
| 365 | mag = a.mag; |
| 366 | // Copy the opposite of a.sign |
| 367 | sign = Sign(-a.sign); |
| 368 | } |
| 369 | |
| 370 | // INCREMENT/DECREMENT OPERATORS |
| 371 | |
| 372 | // Prefix increment |
| 373 | void BigInteger::operator ++() { |
| 374 | if (sign == negative) { |
| 375 | mag--; |
| 376 | if (mag == 0) |
| 377 | sign = zero; |
| 378 | } else { |
| 379 | mag++; |
| 380 | sign = positive; // if not already |
| 381 | } |
| 382 | } |
| 383 | |
| 384 | // Postfix increment: same as prefix |
| 385 | void BigInteger::operator ++(int) { |
| 386 | operator ++(); |
| 387 | } |
| 388 | |
| 389 | // Prefix decrement |
| 390 | void BigInteger::operator --() { |
| 391 | if (sign == positive) { |
| 392 | mag--; |
| 393 | if (mag == 0) |
| 394 | sign = zero; |
| 395 | } else { |
| 396 | mag++; |
| 397 | sign = negative; |
| 398 | } |
| 399 | } |
| 400 | |
| 401 | // Postfix decrement: same as prefix |
| 402 | void BigInteger::operator --(int) { |
| 403 | operator --(); |
| 404 | } |
| 405 | |