| 1 | /* |
| 2 | * Matt McCutchen's Big Integer Library |
| 3 | * http://hashproduct.metaesthetics.net/bigint/ |
| 4 | */ |
| 5 | |
| 6 | #ifndef BIGUNSIGNED |
| 7 | #define BIGUNSIGNED |
| 8 | |
| 9 | #include "NumberlikeArray.hh" |
| 10 | |
| 11 | /* |
| 12 | * A BigUnsigned object represents a nonnegative integer of size |
| 13 | * limited only by available memory. A BigUnsigned can be |
| 14 | * created from and converted back to most integral types, |
| 15 | * and many math operations are defined on BigUnsigneds. |
| 16 | * |
| 17 | * The number is stored as a series of blocks in a |
| 18 | * dynamically allocated array. It is as if the number |
| 19 | * were written digit by digit in base 2 ^ N, **where N is the |
| 20 | * number of bits in an unsigned long.** |
| 21 | * |
| 22 | * The memory-management details that used to be in here have |
| 23 | * been moved into NumberlikeArray, which BigUnsigned now derives from. |
| 24 | * `(NlA)' means that member(s) are declared identically in NumberlikeArray. |
| 25 | * Such members are either redeclared here to make them public or are |
| 26 | * here, commented out, for reference. |
| 27 | */ |
| 28 | |
| 29 | class BigUnsigned : protected NumberlikeArray<unsigned long> { |
| 30 | |
| 31 | // TYPES & CONSTANTS |
| 32 | public: |
| 33 | enum CmpRes { less = -1, equal = 0, greater = 1 }; // Enumeration for the result of a comparison |
| 34 | typedef unsigned long Blk; // The number block type that BigUnsigneds are built from |
| 35 | typedef NumberlikeArray<Blk>::Index Index; // (NlA) Type for the index of a block in the array |
| 36 | NumberlikeArray<Blk>::N; // Number of bits in a Blk |
| 37 | |
| 38 | /* |
| 39 | // FIELDS |
| 40 | protected: |
| 41 | Index cap; // (NlA) The current allocated capacity of this BigUnsigned (in blocks) |
| 42 | Index len; // (NlA) The actual length of the number stored in this BigUnsigned (in blocks) |
| 43 | Blk *blk; // (NlA) Dynamically allocated array of the number blocks |
| 44 | */ |
| 45 | |
| 46 | // MANAGEMENT |
| 47 | protected: |
| 48 | // These members generally defer to those in NumberlikeArray, possibly with slight changes. |
| 49 | // It might be nice if one could request that constructors be inherited in C++. |
| 50 | |
| 51 | BigUnsigned(int, Index c) : NumberlikeArray<Blk>(0, c) {} // Creates a BigUnsigned with a capacity |
| 52 | |
| 53 | void zapLeadingZeros() { // Decreases len to eliminate leading zeros |
| 54 | while (len > 0 && blk[len - 1] == 0) |
| 55 | len--; |
| 56 | } |
| 57 | |
| 58 | //void allocate(Index c); // (NlA) Ensures the number array has at least the indicated capacity, maybe discarding contents |
| 59 | //void allocateAndCopy(Index c); // (NlA) Ensures the number array has at least the indicated capacity, preserving its contents |
| 60 | |
| 61 | public: |
| 62 | BigUnsigned() : NumberlikeArray<Blk>() {} // Default constructor (value is 0) |
| 63 | BigUnsigned(const BigUnsigned &x) : NumberlikeArray<Blk>(x) {} // Copy constructor |
| 64 | |
| 65 | void operator=(const BigUnsigned &x) { // Assignment operator |
| 66 | NumberlikeArray<Blk>::operator =(x); |
| 67 | } |
| 68 | |
| 69 | BigUnsigned(const Blk *b, Index l) : NumberlikeArray<Blk>(b, l) { // Constructor from an array of blocks |
| 70 | zapLeadingZeros(); |
| 71 | } |
| 72 | |
| 73 | // Constructors from integral types |
| 74 | BigUnsigned(unsigned long x); |
| 75 | BigUnsigned( long x); |
| 76 | BigUnsigned(unsigned int x); |
| 77 | BigUnsigned( int x); |
| 78 | BigUnsigned(unsigned short x); |
| 79 | BigUnsigned( short x); |
| 80 | ~BigUnsigned() {} // Destructor |
| 81 | |
| 82 | // CONVERTERS to integral types |
| 83 | public: |
| 84 | operator unsigned long () const; |
| 85 | operator long () const; |
| 86 | operator unsigned int () const; |
| 87 | operator int () const; |
| 88 | operator unsigned short() const; |
| 89 | operator short() const; |
| 90 | |
| 91 | // PICKING APART |
| 92 | // These accessors can be used to get the pieces of the number |
| 93 | public: |
| 94 | NumberlikeArray<Blk>::getCapacity; |
| 95 | NumberlikeArray<Blk>::getLength; |
| 96 | // Note that getBlock returns 0 if the block index is beyond the length of the number. |
| 97 | // A routine that uses this accessor can safely assume a BigUnsigned has 0s infinitely to the left. |
| 98 | Blk getBlock(Index i) const { return i >= len ? 0 : blk[i]; } |
| 99 | // Note how we replace one level of abstraction with another. Isn't that neat? |
| 100 | bool isZero() const { return NumberlikeArray<Blk>::isEmpty(); } // Often convenient for loops |
| 101 | |
| 102 | // COMPARISONS |
| 103 | public: |
| 104 | // Compares this to x like Perl's <=> |
| 105 | CmpRes compareTo(const BigUnsigned &x) const; |
| 106 | // Normal comparison operators |
| 107 | // Bug fixed 2006.04.24: Only we, not the user, can pass a BigUnsigned off as a |
| 108 | // NumberlikeArray, so we have to wrap == and !=. |
| 109 | bool operator ==(const BigUnsigned &x) const { |
| 110 | return NumberlikeArray<Blk>::operator ==(x); |
| 111 | } |
| 112 | bool operator !=(const BigUnsigned &x) const { |
| 113 | return NumberlikeArray<Blk>::operator !=(x); |
| 114 | } |
| 115 | bool operator < (const BigUnsigned &x) const { return compareTo(x) == less ; } |
| 116 | bool operator <=(const BigUnsigned &x) const { return compareTo(x) != greater; } |
| 117 | bool operator >=(const BigUnsigned &x) const { return compareTo(x) != less ; } |
| 118 | bool operator > (const BigUnsigned &x) const { return compareTo(x) == greater; } |
| 119 | |
| 120 | /* |
| 121 | * BigUnsigned and BigInteger both provide three kinds of operators. |
| 122 | * Here ``big-integer'' refers to BigInteger or BigUnsigned. |
| 123 | * |
| 124 | * (1) Overloaded ``return-by-value'' operators: |
| 125 | * +, -, *, /, %, unary -. |
| 126 | * Big-integer code using these operators looks identical to |
| 127 | * code using the primitive integer types. These operators take |
| 128 | * one or two big-integer inputs and return a big-integer result, |
| 129 | * which can then be assigned to a BigInteger variable or used |
| 130 | * in an expression. Example: |
| 131 | * BigInteger a(1), b = 1; |
| 132 | * BigInteger c = a + b; |
| 133 | * |
| 134 | * (2) Overloaded assignment operators: |
| 135 | * +=, -=, *=, /=, %=, &=, |=, ^=, ++, --, flipSign. |
| 136 | * Again, these are used on big integers just like on ints. |
| 137 | * They take one writable big integer that both provides an |
| 138 | * operand and receives a result. The first eight also take |
| 139 | * a second read-only operand. Example: |
| 140 | * BigInteger a(1), b(1); |
| 141 | * a += b; |
| 142 | * |
| 143 | * (3) ``Put-here'' operations: `add', `subtract', etc. |
| 144 | * Using a return-by-value or assignment operator generally involves |
| 145 | * copy constructions and/or assignments. The ``put-here'' operations |
| 146 | * require none, but they are more of a hassle to use. Most take two |
| 147 | * read-only operands and save the result in the calling object `*this', |
| 148 | * whose previous value is ignored. `divideWithRemainder' is an exception. |
| 149 | * <<< NOTE >>>: Put-here operations do not return a value: they don't need to!! |
| 150 | * Examples: |
| 151 | * BigInteger a(43), b(7), c, d; |
| 152 | * c = a + b; // Now c == 50. |
| 153 | * c.add(a, b); // Same effect but without the two bulk-copies. |
| 154 | * c.divideWithRemainder(b, d); // 50 / 7; now d == 7 (quotient) and c == 1 (remainder). |
| 155 | * a.add(a, b); // Unsafe ``aliased'' call; causes a runtime error. |
| 156 | */ |
| 157 | |
| 158 | // PUT-HERE OPERATIONS |
| 159 | public: |
| 160 | /* These 3: Two read-only operands as arguments. Result left in *this. */ |
| 161 | void add(const BigUnsigned &a, const BigUnsigned &b); // Addition |
| 162 | void subtract(const BigUnsigned &a, const BigUnsigned &b); // Subtraction |
| 163 | void multiply(const BigUnsigned &a, const BigUnsigned &b); // Multiplication |
| 164 | /* Divisive stuff |
| 165 | * `a.divideWithRemainder(b, q)' is like `q = a / b, a %= b'. |
| 166 | * Semantics similar to Donald E. Knuth's are used for / and %, |
| 167 | * and these differ from the semantics of primitive-type |
| 168 | * / and % under division by zero. |
| 169 | * Look in `BigUnsigned.cc' for details. |
| 170 | */ |
| 171 | void divideWithRemainder(const BigUnsigned &b, BigUnsigned &q); |
| 172 | void divide(const BigUnsigned &a, const BigUnsigned &b) { |
| 173 | // Division, deprecated and provided for backward compatibility |
| 174 | BigUnsigned a2(a); |
| 175 | a2.divideWithRemainder(b, *this); |
| 176 | // quotient now in *this |
| 177 | // don't care about remainder left in a2 |
| 178 | } |
| 179 | void modulo(const BigUnsigned &a, const BigUnsigned &b) { |
| 180 | // Modular reduction, deprecated and provided for backward compatibility |
| 181 | *this = a; |
| 182 | BigUnsigned q; |
| 183 | divideWithRemainder(b, q); |
| 184 | // remainder now in *this |
| 185 | // don't care about quotient left in q |
| 186 | } |
| 187 | // Bitwise operations. Two read-only operands as arguments. Result left in *this. |
| 188 | // These are not provided for BigIntegers; I think that using them on BigIntegers |
| 189 | // will discard the sign first. |
| 190 | void bitAnd(const BigUnsigned &a, const BigUnsigned &b); // Bitwise AND |
| 191 | void bitOr(const BigUnsigned &a, const BigUnsigned &b); // Bitwise OR |
| 192 | void bitXor(const BigUnsigned &a, const BigUnsigned &b); // Bitwise XOR |
| 193 | |
| 194 | // These functions are declared but not defined. (Sorry.) |
| 195 | // Trying to call either will result in a link-time error. |
| 196 | void bitShiftLeft(const BigUnsigned &a, unsigned int b); // Bitwise left shift |
| 197 | void bitShiftRight(const BigUnsigned &a, unsigned int b); // Bitwise right shift |
| 198 | |
| 199 | // NORMAL OPERATORS |
| 200 | // These perform the operation on this (to the left of the operator) |
| 201 | // and x (to the right of the operator) and return a new BigUnsigned with the result. |
| 202 | public: |
| 203 | BigUnsigned operator +(const BigUnsigned &x) const; // Addition |
| 204 | BigUnsigned operator -(const BigUnsigned &x) const; // Subtraction |
| 205 | BigUnsigned operator *(const BigUnsigned &x) const; // Multiplication |
| 206 | BigUnsigned operator /(const BigUnsigned &x) const; // Division |
| 207 | BigUnsigned operator %(const BigUnsigned &x) const; // Modular reduction |
| 208 | BigUnsigned operator &(const BigUnsigned &x) const; // Bitwise AND |
| 209 | BigUnsigned operator |(const BigUnsigned &x) const; // Bitwise OR |
| 210 | BigUnsigned operator ^(const BigUnsigned &x) const; // Bitwise XOR |
| 211 | |
| 212 | // ASSIGNMENT OPERATORS |
| 213 | // These perform the operation on this and x, storing the result into this. |
| 214 | public: |
| 215 | void operator +=(const BigUnsigned &x); // Addition |
| 216 | void operator -=(const BigUnsigned &x); // Subtraction |
| 217 | void operator *=(const BigUnsigned &x); // Multiplication |
| 218 | void operator /=(const BigUnsigned &x); // Division |
| 219 | void operator %=(const BigUnsigned &x); // Modular reduction |
| 220 | void operator &=(const BigUnsigned &x); // Bitwise AND |
| 221 | void operator |=(const BigUnsigned &x); // Bitwise OR |
| 222 | void operator ^=(const BigUnsigned &x); // Bitwise XOR |
| 223 | |
| 224 | // INCREMENT/DECREMENT OPERATORS |
| 225 | // These increase or decrease the number by 1. To discourage side effects, |
| 226 | // these do not return *this, so prefix and postfix behave the same. |
| 227 | public: |
| 228 | void operator ++( ); // Prefix increment |
| 229 | void operator ++(int); // Postfix decrement |
| 230 | void operator --( ); // Prefix increment |
| 231 | void operator --(int); // Postfix decrement |
| 232 | |
| 233 | // Helper function that needs access to BigUnsigned internals |
| 234 | friend Blk getShiftedBlock(const BigUnsigned &num, Index x, unsigned int y); |
| 235 | }; |
| 236 | |
| 237 | // NORMAL OPERATORS |
| 238 | /* These create an object to hold the result and invoke |
| 239 | * the appropriate put-here operation on it, passing |
| 240 | * this and x. The new object is then returned. */ |
| 241 | inline BigUnsigned BigUnsigned::operator +(const BigUnsigned &x) const { |
| 242 | BigUnsigned ans; |
| 243 | ans.add(*this, x); |
| 244 | return ans; |
| 245 | } |
| 246 | inline BigUnsigned BigUnsigned::operator -(const BigUnsigned &x) const { |
| 247 | BigUnsigned ans; |
| 248 | ans.subtract(*this, x); |
| 249 | return ans; |
| 250 | } |
| 251 | inline BigUnsigned BigUnsigned::operator *(const BigUnsigned &x) const { |
| 252 | BigUnsigned ans; |
| 253 | ans.multiply(*this, x); |
| 254 | return ans; |
| 255 | } |
| 256 | inline BigUnsigned BigUnsigned::operator /(const BigUnsigned &x) const { |
| 257 | BigUnsigned ans; |
| 258 | ans.divide(*this, x); |
| 259 | return ans; |
| 260 | } |
| 261 | inline BigUnsigned BigUnsigned::operator %(const BigUnsigned &x) const { |
| 262 | BigUnsigned ans; |
| 263 | ans.modulo(*this, x); |
| 264 | return ans; |
| 265 | } |
| 266 | inline BigUnsigned BigUnsigned::operator &(const BigUnsigned &x) const { |
| 267 | BigUnsigned ans; |
| 268 | ans.bitAnd(*this, x); |
| 269 | return ans; |
| 270 | } |
| 271 | inline BigUnsigned BigUnsigned::operator |(const BigUnsigned &x) const { |
| 272 | BigUnsigned ans; |
| 273 | ans.bitOr(*this, x); |
| 274 | return ans; |
| 275 | } |
| 276 | inline BigUnsigned BigUnsigned::operator ^(const BigUnsigned &x) const { |
| 277 | BigUnsigned ans; |
| 278 | ans.bitXor(*this, x); |
| 279 | return ans; |
| 280 | } |
| 281 | |
| 282 | // ASSIGNMENT OPERATORS |
| 283 | // These create a copy of this, then invoke the appropriate |
| 284 | // put-here operation on this, passing the copy and x. |
| 285 | // Exception: those updated for divideWithRemainder. |
| 286 | inline void BigUnsigned::operator +=(const BigUnsigned &x) { |
| 287 | BigUnsigned thisCopy(*this); |
| 288 | add(thisCopy, x); |
| 289 | } |
| 290 | inline void BigUnsigned::operator -=(const BigUnsigned &x) { |
| 291 | BigUnsigned thisCopy(*this); |
| 292 | subtract(thisCopy, x); |
| 293 | } |
| 294 | inline void BigUnsigned::operator *=(const BigUnsigned &x) { |
| 295 | BigUnsigned thisCopy(*this); |
| 296 | multiply(thisCopy, x); |
| 297 | } |
| 298 | inline void BigUnsigned::operator /=(const BigUnsigned &x) { |
| 299 | // Updated for divideWithRemainder |
| 300 | BigUnsigned thisCopy(*this); |
| 301 | thisCopy.divideWithRemainder(x, *this); |
| 302 | // quotient left in *this |
| 303 | // don't care about remainder left in thisCopy |
| 304 | } |
| 305 | inline void BigUnsigned::operator %=(const BigUnsigned &x) { |
| 306 | // Shortcut (woohoo!) |
| 307 | BigUnsigned q; |
| 308 | divideWithRemainder(x, q); |
| 309 | // remainder left in *this |
| 310 | // don't care about quotient left in q |
| 311 | } |
| 312 | inline void BigUnsigned::operator &=(const BigUnsigned &x) { |
| 313 | BigUnsigned thisCopy(*this); |
| 314 | bitAnd(thisCopy, x); |
| 315 | } |
| 316 | inline void BigUnsigned::operator |=(const BigUnsigned &x) { |
| 317 | BigUnsigned thisCopy(*this); |
| 318 | bitOr(thisCopy, x); |
| 319 | } |
| 320 | inline void BigUnsigned::operator ^=(const BigUnsigned &x) { |
| 321 | BigUnsigned thisCopy(*this); |
| 322 | bitXor(thisCopy, x); |
| 323 | } |
| 324 | |
| 325 | #endif |