11448 - Who said crisis/bigint-2007.07.07/BigInteger.hh

   1 /*
   2 * Matt McCutchen's Big Integer Library
   3 */
   4
   5 #ifndef BIGINTEGER
   6 #define BIGINTEGER
   7
   8 #include "BigUnsigned.hh"
   9
  10 /*
  11 * A BigInteger object represents a signed integer of size
  12 * limited only by available memory.  A BigInteger can be
  13 * created from and converted back to most integral types,
  14 * and many math operations are defined on BigIntegers.
  15 *
  16 * The number is stored as a series of blocks in a
  17 * dynamically allocated array.  It is as if the number
  18 * were written digit by digit in base 2 ^ N, **where N is the
  19 * number of bits in an unsigned long.**
  20 *
  21 * This class is derived from BigUnsigned, which represents
  22 * a large nonnegative integer.  BigUnsigned should be studied
  23 * first, as only new or different things are declared here.
  24 * Some things are redeclared so that they use the BigInteger
  25 * versions of methods, rather than the BigUnsigned versions.
  26 */
  27
  28 class BigInteger : public BigUnsigned {
  29
  30         // TYPES & CONSTANTS
  31         public:
  32         enum Sign { negative = -1, zero = 0, positive = 1 }; // Enumeration for the sign of a BigInteger
  33
  34         // FIELDS
  35         protected:
  36         Sign sign; // The sign of this BigInteger
  37
  38         // MANAGEMENT
  39         protected:
  40         BigInteger(Sign s, Index c) : BigUnsigned(0, c), sign(s) {}; // Creates a BigInteger with a sign and capacity
  41         public:
  42
  43         BigInteger() : BigUnsigned(), sign(zero) {} // Default constructor (value is 0)
  44         BigInteger(const BigInteger &x) : BigUnsigned(x), sign(x.sign) {}; // Copy constructor
  45         void operator=(const BigInteger &x); // Assignment operator
  46         BigInteger(const Blk *b, Index l) : BigUnsigned(b, l) { // Constructor from an array of blocks
  47                 sign = (len == 0) ? zero : positive;
  48         }
  49         BigInteger(const Blk *b, Index l, Sign s); // Constructor from an array of blocks and a sign
  50         BigInteger(const BigUnsigned &x) : BigUnsigned(x) { // Constructor from a BigUnsigned
  51                 sign = (len == 0) ? zero : positive;
  52         }
  53         BigInteger(const BigUnsigned &x, Sign s); // Constructor from a BigUnsigned and a sign
  54         // Constructors from integral types
  55         BigInteger(unsigned long  x);
  56         BigInteger(         long  x);
  57         BigInteger(unsigned int   x);
  58         BigInteger(         int   x);
  59         BigInteger(unsigned short x);
  60         BigInteger(         short x);
  61         // Note that a BigInteger can be converted to a BigUnsigned
  62         // automatically; this takes its absolute value.
  63
  64         // CONVERTERS to integral types
  65         public:
  66         operator unsigned long () const;
  67         operator          long () const;
  68         operator unsigned int  () const;
  69         operator          int  () const;
  70         operator unsigned short() const;
  71         operator          short() const;
  72
  73         // PICKING APART
  74         // These accessors can be used to get the pieces of the number
  75         public:
  76         Sign getSign() const;
  77
  78         // COMPARISONS
  79         public:
  80         // Compares this to x like Perl's <=>
  81         CmpRes compareTo(const BigInteger &x) const;
  82         // Normal comparison operators
  83         bool operator ==(const BigInteger &x) const {
  84                 return sign == x.sign && BigUnsigned::operator ==(x);
  85         }
  86         bool operator !=(const BigInteger &x) const { return !operator ==(x); };
  87         bool operator < (const BigInteger &x) const { return compareTo(x) == less   ; }
  88         bool operator <=(const BigInteger &x) const { return compareTo(x) != greater; }
  89         bool operator >=(const BigInteger &x) const { return compareTo(x) != less   ; }
  90         bool operator > (const BigInteger &x) const { return compareTo(x) == greater; }
  91
  92         // PUT-HERE OPERATIONS
  93         /* These store the result of the operation on the arguments into this.
  94         * a.add(b, c) is equivalent to, but faster than, a = b + c.
  95         * See explanation of "put-here operations" in BigUnsigned.cc . */
  96         public:
  97         void add     (const BigInteger &a, const BigInteger &b); // Addition
  98         void subtract(const BigInteger &a, const BigInteger &b); // Subtraction
  99         void multiply(const BigInteger &a, const BigInteger &b); // Multiplication
 100         /* Divisive stuff
 101         * `a.divideWithRemainder(b, q)' is like `q = a / b, a %= b'.
 102         * Semantics similar to Donald E. Knuth's are used for / and %,
 103         * and these usually differ from the semantics of primitive-type
 104         * / and % when negatives and/or zeroes are involved.
 105         * Look in `BigInteger.cc' for details.
 106         * `a.divideWithRemainder(b, a)' causes an exception: it doesn't make
 107         * sense to write quotient and remainder into the same variable.
 108         */
 109         void divideWithRemainder(const BigInteger &b, BigInteger &q);
 110         void divide(const BigInteger &a, const BigInteger &b) {
 111                 BigInteger a2(a);
 112                 a2.divideWithRemainder(b, *this);
 113                 // quotient now in *this
 114                 // don't care about remainder left in a2
 115         }
 116         void modulo(const BigInteger &a, const BigInteger &b) {
 117                 *this = a;
 118                 BigInteger q;
 119                 divideWithRemainder(b, q);
 120                 // remainder now in *this
 121                 // don't care about quotient left in q
 122         }
 123         void negate(const BigInteger &a); // Negative
 124         // Some operations are inherently unsigned and are not
 125         // redefined for BigIntegers.  Calling one of these on
 126         // a BigInteger will convert it to a BigUnsigned,
 127         // which takes its absolute value.
 128
 129         // NORMAL OPERATORS
 130         // These perform the operation on this (to the left of the operator)
 131         // and x (to the right of the operator) and return a new BigInteger with the result.
 132         public:
 133         BigInteger operator +(const BigInteger &x) const; // Addition
 134         BigInteger operator -(const BigInteger &x) const; // Subtraction
 135         BigInteger operator *(const BigInteger &x) const; // Multiplication
 136         BigInteger operator /(const BigInteger &x) const; // Division
 137         BigInteger operator %(const BigInteger &x) const; // Modular reduction
 138         BigInteger operator -(                   ) const; // Negative
 139
 140         // ASSIGNMENT OPERATORS
 141         // These perform the operation on this and x, storing the result into this.
 142         public:
 143         void operator +=(const BigInteger &x); // Addition
 144         void operator -=(const BigInteger &x); // Subtraction
 145         void operator *=(const BigInteger &x); // Multiplication
 146         void operator /=(const BigInteger &x); // Division
 147         void operator %=(const BigInteger &x); // Modular reduction
 148         void flipSign();                       // Negative
 149
 150         // INCREMENT/DECREMENT OPERATORS
 151         // These increase or decrease the number by 1.  To discourage side effects,
 152         // these do not return *this, so prefix and postfix behave the same.
 153         public:
 154         void operator ++(   ); // Prefix  increment
 155         void operator ++(int); // Postfix decrement
 156         void operator --(   ); // Prefix  increment
 157         void operator --(int); // Postfix decrement
 158
 159 };
 160
 161 // PICKING APART
 162 inline BigInteger::Sign BigInteger::getSign() const { return sign; }
 163
 164 // NORMAL OPERATORS
 165 /* These create an object to hold the result and invoke
 166 * the appropriate put-here operation on it, passing
 167 * this and x.  The new object is then returned. */
 168 inline BigInteger BigInteger::operator +(const BigInteger &x) const {
 169         BigInteger ans;
 170         ans.add(*this, x);
 171         return ans;
 172 }
 173 inline BigInteger BigInteger::operator -(const BigInteger &x) const {
 174         BigInteger ans;
 175         ans.subtract(*this, x);
 176         return ans;
 177 }
 178 inline BigInteger BigInteger::operator *(const BigInteger &x) const {
 179         BigInteger ans;
 180         ans.multiply(*this, x);
 181         return ans;
 182 }
 183 inline BigInteger BigInteger::operator /(const BigInteger &x) const {
 184         BigInteger ans;
 185         ans.divide(*this, x);
 186         return ans;
 187 }
 188 inline BigInteger BigInteger::operator %(const BigInteger &x) const {
 189         BigInteger ans;
 190         ans.modulo(*this, x);
 191         return ans;
 192 }
 193 inline BigInteger BigInteger::operator -() const {
 194         BigInteger ans;
 195         ans.negate(*this);
 196         return ans;
 197 }
 198
 199 /*
 200  * ASSIGNMENT OPERATORS
 201  *
 202  * Now the responsibility for making a temporary copy if necessary
 203  * belongs to the put-here operations.  See Assignment Operators in
 204  * BigUnsigned.hh.
 205  */
 206 inline void BigInteger::operator +=(const BigInteger &x) {
 207         add(*this, x);
 208 }
 209 inline void BigInteger::operator -=(const BigInteger &x) {
 210         subtract(*this, x);
 211 }
 212 inline void BigInteger::operator *=(const BigInteger &x) {
 213         multiply(*this, x);
 214 }
 215 inline void BigInteger::operator /=(const BigInteger &x) {
 216         // Updated for divideWithRemainder
 217         BigInteger thisCopy(*this);
 218         thisCopy.divideWithRemainder(x, *this);
 219         // quotient left in *this
 220         // don't care about remainder left in thisCopy
 221 }
 222 inline void BigInteger::operator %=(const BigInteger &x) {
 223         // Shortcut (woohoo!)
 224         BigInteger q;
 225         divideWithRemainder(x, q);
 226         // remainder left in *this
 227         // don't care about quotient left in q
 228 }
 229 // This one is trivial
 230 inline void BigInteger::flipSign() {
 231         sign = Sign(-sign);
 232 }
 233
 234 #endif