| 1 | /* |
| 2 | * Matt McCutchen's Big Integer Library |
| 3 | * http://mysite.verizon.net/mccutchen/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 numbers |
| 19 | * were written digit by digit in base 256 ^ sizeof(unsigned long). |
| 20 | * |
| 21 | * The memory-management details that used to be in here have |
| 22 | * been moved into NumberlikeArray, which BigUnsigned now derives from. |
| 23 | * `(NlA)' means that member(s) are declared identically in NumberlikeArray. |
| 24 | * Such members are either redeclared here to make them public or are |
| 25 | * here, commented out, for reference. |
| 26 | */ |
| 27 | |
| 28 | class BigUnsigned : protected NumberlikeArray<unsigned long> { |
| 29 | |
| 30 | // TYPES & CONSTANTS |
| 31 | public: |
| 32 | enum CmpRes { less = -1, equal = 0, greater = 1 }; // Enumeration for the result of a comparison |
| 33 | typedef unsigned long Blk; // The number block type that BigUnsigneds are built from |
| 34 | typedef NumberlikeArray<Blk>::Index Index; // (NlA) Type for the index of a block in the array |
| 35 | |
| 36 | /* |
| 37 | // FIELDS |
| 38 | protected: |
| 39 | Index cap; // (NlA) The current allocated capacity of this BigUnsigned (in blocks) |
| 40 | Index len; // (NlA) The actual length of the number stored in this BigUnsigned (in blocks) |
| 41 | Blk *blk; // (NlA) Dynamically allocated array of the number blocks |
| 42 | */ |
| 43 | |
| 44 | // MANAGEMENT |
| 45 | protected: |
| 46 | // These members generally defer to those in NumberlikeArray, possibly with slight changes. |
| 47 | // It might be nice if one could request that constructors be inherited in C++. |
| 48 | |
| 49 | BigUnsigned(int, Index c) : NumberlikeArray<Blk>(0, c) {} // Creates a BigUnsigned with a capacity |
| 50 | |
| 51 | void zapLeadingZeros() { // Decreases len to eliminate leading zeros |
| 52 | while (len > 0 && blk[len - 1] == 0) |
| 53 | len--; |
| 54 | } |
| 55 | |
| 56 | //void allocate(Index c); // (NlA) Ensures the number array has at least the indicated capacity, maybe discarding contents |
| 57 | //void allocateAndCopy(Index c); // (NlA) Ensures the number array has at least the indicated capacity, preserving its contents |
| 58 | |
| 59 | public: |
| 60 | BigUnsigned() : NumberlikeArray<Blk>() {} // Default constructor (value is 0) |
| 61 | BigUnsigned(const BigUnsigned &x) : NumberlikeArray<Blk>(x) {} // Copy constructor |
| 62 | |
| 63 | void operator=(const BigUnsigned &x) { // Assignment operator |
| 64 | NumberlikeArray<Blk>::operator =(x); |
| 65 | } |
| 66 | |
| 67 | BigUnsigned(const Blk *b, Index l) : NumberlikeArray<Blk>(b, l) { // Constructor from an array of blocks |
| 68 | zapLeadingZeros(); |
| 69 | } |
| 70 | |
| 71 | // Constructors from integral types |
| 72 | BigUnsigned(unsigned long x); |
| 73 | BigUnsigned( long x); |
| 74 | BigUnsigned(unsigned int x); |
| 75 | BigUnsigned( int x); |
| 76 | BigUnsigned(unsigned short x); |
| 77 | BigUnsigned( short x); |
| 78 | ~BigUnsigned() {} // Destructor |
| 79 | |
| 80 | // CONVERTERS to integral types |
| 81 | public: |
| 82 | operator unsigned long () const; |
| 83 | operator long () const; |
| 84 | operator unsigned int () const; |
| 85 | operator int () const; |
| 86 | operator unsigned short() const; |
| 87 | operator short() const; |
| 88 | |
| 89 | // PICKING APART |
| 90 | // These accessors can be used to get the pieces of the number |
| 91 | public: |
| 92 | NumberlikeArray<Blk>::getCapacity; |
| 93 | NumberlikeArray<Blk>::getLength; |
| 94 | // Note that getBlock returns 0 if the block index is beyond the length of the number. |
| 95 | // A routine that uses this accessor can safely assume a BigUnsigned has 0s infinitely to the left. |
| 96 | Blk getBlock(Index i) const { return i >= len ? 0 : blk[i]; } |
| 97 | // Note how we replace one level of abstraction with another. Isn't that neat? |
| 98 | bool isZero() const { return NumberlikeArray<Blk>::isEmpty(); } // Often convenient for loops |
| 99 | |
| 100 | // COMPARISONS |
| 101 | public: |
| 102 | // Compares this to x like Perl's <=> |
| 103 | CmpRes compareTo(const BigUnsigned &x) const; |
| 104 | // Normal comparison operators |
| 105 | NumberlikeArray<Blk>::operator ==; // (NlA) The body used to be `{ return compareTo(x) == equal; }'. For performance reasons we use NumberlikeArray code that only worries about (in)equality and doesn't waste time determining which is bigger |
| 106 | NumberlikeArray<Blk>::operator !=; // (NlA) Ditto. |
| 107 | bool operator < (const BigUnsigned &x) const { return compareTo(x) == less ; } |
| 108 | bool operator <=(const BigUnsigned &x) const { return compareTo(x) != greater; } |
| 109 | bool operator >=(const BigUnsigned &x) const { return compareTo(x) != less ; } |
| 110 | bool operator > (const BigUnsigned &x) const { return compareTo(x) == greater; } |
| 111 | |
| 112 | // PUT-HERE OPERATIONS |
| 113 | /* These store the result of the operation on the arguments into this. |
| 114 | * a.add(b, c) is equivalent to, but faster than, a = b + c. |
| 115 | * Calls like a.operation(a, b) are unsafe and not allowed. */ |
| 116 | public: |
| 117 | // Easy 3 |
| 118 | void add (const BigUnsigned &a, const BigUnsigned &b); // Addition |
| 119 | void subtract (const BigUnsigned &a, const BigUnsigned &b); // Subtraction |
| 120 | void multiply (const BigUnsigned &a, const BigUnsigned &b); // Multiplication |
| 121 | /* Divisive stuff |
| 122 | * `a.divideWithRemainder(b, q)' is like `q = a / b, a %= b'. |
| 123 | * Semantics similar to Donald E. Knuth's are used for / and %, |
| 124 | * and these differ from the semantics of primitive-type |
| 125 | * / and % under division by zero. |
| 126 | * Look in `BigUnsigned.cc' for details. |
| 127 | */ |
| 128 | void divideWithRemainder(const BigUnsigned &b, BigUnsigned &q); |
| 129 | void divide(const BigUnsigned &a, const BigUnsigned &b) { |
| 130 | // Division, deprecated and provided for compatibility |
| 131 | BigUnsigned a2(a); |
| 132 | a2.divideWithRemainder(b, *this); |
| 133 | // quotient now in *this |
| 134 | // don't care about remainder left in a2 |
| 135 | } |
| 136 | void modulo(const BigUnsigned &a, const BigUnsigned &b) { |
| 137 | // Modular reduction, deprecated and provided for compatibility |
| 138 | *this = a; |
| 139 | BigUnsigned q; |
| 140 | divideWithRemainder(b, q); |
| 141 | // remainder now in *this |
| 142 | // don't care about quotient left in q |
| 143 | } |
| 144 | // Bitwise |
| 145 | void bitAnd (const BigUnsigned &a, const BigUnsigned &b); // Bitwise AND |
| 146 | void bitOr (const BigUnsigned &a, const BigUnsigned &b); // Bitwise OR |
| 147 | void bitXor (const BigUnsigned &a, const BigUnsigned &b); // Bitwise XOR |
| 148 | |
| 149 | // These functions are declared but not defined. (Sorry.) |
| 150 | // Trying to call either will result in a link-time error. |
| 151 | void bitShiftLeft (const BigUnsigned &a, unsigned int b); // Bitwise left shift |
| 152 | void bitShiftRight(const BigUnsigned &a, unsigned int b); // Bitwise right shift |
| 153 | |
| 154 | // NORMAL OPERATORS |
| 155 | // These perform the operation on this (to the left of the operator) |
| 156 | // and x (to the right of the operator) and return a new BigUnsigned with the result. |
| 157 | public: |
| 158 | BigUnsigned operator +(const BigUnsigned &x) const; // Addition |
| 159 | BigUnsigned operator -(const BigUnsigned &x) const; // Subtraction |
| 160 | BigUnsigned operator *(const BigUnsigned &x) const; // Multiplication |
| 161 | BigUnsigned operator /(const BigUnsigned &x) const; // Division |
| 162 | BigUnsigned operator %(const BigUnsigned &x) const; // Modular reduction |
| 163 | BigUnsigned operator &(const BigUnsigned &x) const; // Bitwise AND |
| 164 | BigUnsigned operator |(const BigUnsigned &x) const; // Bitwise OR |
| 165 | BigUnsigned operator ^(const BigUnsigned &x) const; // Bitwise XOR |
| 166 | |
| 167 | // ASSIGNMENT OPERATORS |
| 168 | // These perform the operation on this and x, storing the result into this. |
| 169 | public: |
| 170 | void operator +=(const BigUnsigned &x); // Addition |
| 171 | void operator -=(const BigUnsigned &x); // Subtraction |
| 172 | void operator *=(const BigUnsigned &x); // Multiplication |
| 173 | void operator /=(const BigUnsigned &x); // Division |
| 174 | void operator %=(const BigUnsigned &x); // Modular reduction |
| 175 | void operator &=(const BigUnsigned &x); // Bitwise AND |
| 176 | void operator |=(const BigUnsigned &x); // Bitwise OR |
| 177 | void operator ^=(const BigUnsigned &x); // Bitwise XOR |
| 178 | |
| 179 | // INCREMENT/DECREMENT OPERATORS |
| 180 | // These increase or decrease the number by 1. To discourage side effects, |
| 181 | // these do not return *this, so prefix and postfix behave the same. |
| 182 | public: |
| 183 | void operator ++( ); // Prefix increment |
| 184 | void operator ++(int); // Postfix decrement |
| 185 | void operator --( ); // Prefix increment |
| 186 | void operator --(int); // Postfix decrement |
| 187 | |
| 188 | }; |
| 189 | |
| 190 | // NORMAL OPERATORS |
| 191 | /* These create an object to hold the result and invoke |
| 192 | * the appropriate put-here operation on it, passing |
| 193 | * this and x. The new object is then returned. */ |
| 194 | inline BigUnsigned BigUnsigned::operator +(const BigUnsigned &x) const { |
| 195 | BigUnsigned ans; |
| 196 | ans.add(*this, x); |
| 197 | return ans; |
| 198 | } |
| 199 | inline BigUnsigned BigUnsigned::operator -(const BigUnsigned &x) const { |
| 200 | BigUnsigned ans; |
| 201 | ans.subtract(*this, x); |
| 202 | return ans; |
| 203 | } |
| 204 | inline BigUnsigned BigUnsigned::operator *(const BigUnsigned &x) const { |
| 205 | BigUnsigned ans; |
| 206 | ans.multiply(*this, x); |
| 207 | return ans; |
| 208 | } |
| 209 | inline BigUnsigned BigUnsigned::operator /(const BigUnsigned &x) const { |
| 210 | BigUnsigned ans; |
| 211 | ans.divide(*this, x); |
| 212 | return ans; |
| 213 | } |
| 214 | inline BigUnsigned BigUnsigned::operator %(const BigUnsigned &x) const { |
| 215 | BigUnsigned ans; |
| 216 | ans.modulo(*this, x); |
| 217 | return ans; |
| 218 | } |
| 219 | inline BigUnsigned BigUnsigned::operator &(const BigUnsigned &x) const { |
| 220 | BigUnsigned ans; |
| 221 | ans.bitAnd(*this, x); |
| 222 | return ans; |
| 223 | } |
| 224 | inline BigUnsigned BigUnsigned::operator |(const BigUnsigned &x) const { |
| 225 | BigUnsigned ans; |
| 226 | ans.bitOr(*this, x); |
| 227 | return ans; |
| 228 | } |
| 229 | inline BigUnsigned BigUnsigned::operator ^(const BigUnsigned &x) const { |
| 230 | BigUnsigned ans; |
| 231 | ans.bitXor(*this, x); |
| 232 | return ans; |
| 233 | } |
| 234 | |
| 235 | // ASSIGNMENT OPERATORS |
| 236 | // These create a copy of this, then invoke the appropriate |
| 237 | // put-here operation on this, passing the copy and x. |
| 238 | // Exception: those updated for divideWithRemainder. |
| 239 | inline void BigUnsigned::operator +=(const BigUnsigned &x) { |
| 240 | BigUnsigned thisCopy(*this); |
| 241 | add(thisCopy, x); |
| 242 | } |
| 243 | inline void BigUnsigned::operator -=(const BigUnsigned &x) { |
| 244 | BigUnsigned thisCopy(*this); |
| 245 | subtract(thisCopy, x); |
| 246 | } |
| 247 | inline void BigUnsigned::operator *=(const BigUnsigned &x) { |
| 248 | BigUnsigned thisCopy(*this); |
| 249 | multiply(thisCopy, x); |
| 250 | } |
| 251 | inline void BigUnsigned::operator /=(const BigUnsigned &x) { |
| 252 | // Updated for divideWithRemainder |
| 253 | BigUnsigned thisCopy(*this); |
| 254 | thisCopy.divideWithRemainder(x, *this); |
| 255 | // quotient left in *this |
| 256 | // don't care about remainder left in thisCopy |
| 257 | } |
| 258 | inline void BigUnsigned::operator %=(const BigUnsigned &x) { |
| 259 | // Shortcut (woohoo!) |
| 260 | BigUnsigned q; |
| 261 | divideWithRemainder(x, q); |
| 262 | // remainder left in *this |
| 263 | // don't care about quotient left in q |
| 264 | } |
| 265 | inline void BigUnsigned::operator &=(const BigUnsigned &x) { |
| 266 | BigUnsigned thisCopy(*this); |
| 267 | bitAnd(thisCopy, x); |
| 268 | } |
| 269 | inline void BigUnsigned::operator |=(const BigUnsigned &x) { |
| 270 | BigUnsigned thisCopy(*this); |
| 271 | bitOr(thisCopy, x); |
| 272 | } |
| 273 | inline void BigUnsigned::operator ^=(const BigUnsigned &x) { |
| 274 | BigUnsigned thisCopy(*this); |
| 275 | bitXor(thisCopy, x); |
| 276 | } |
| 277 | |
| 278 | #endif |