4 #include "BigUnsigned.hh"
6 /* A BigInteger object represents a signed integer of size limited only by
7 * available memory. BigUnsigneds support most mathematical operators and can
8 * be converted to and from most primitive integer types.
10 * A BigInteger is just an aggregate of a BigUnsigned and a sign. (It is no
11 * longer derived from BigUnsigned because that led to harmful implicit
16 typedef BigUnsigned::Blk Blk;
17 typedef BigUnsigned::Index Index;
18 typedef BigUnsigned::CmpRes CmpRes;
20 less = BigUnsigned::less ,
21 equal = BigUnsigned::equal ,
22 greater = BigUnsigned::greater;
23 // Enumeration for the sign of a BigInteger.
24 enum Sign { negative = -1, zero = 0, positive = 1 };
32 BigInteger() : sign(zero), mag() {}
35 BigInteger(const BigInteger &x) : sign(x.sign), mag(x.mag) {};
37 // Assignment operator
38 void operator=(const BigInteger &x);
40 // Constructor that copies from a given array of blocks with a sign.
41 BigInteger(const Blk *b, Index blen, Sign s);
43 // Nonnegative constructor that copies from a given array of blocks.
44 BigInteger(const Blk *b, Index blen) : mag(b, blen) {
45 sign = mag.isZero() ? zero : positive;
48 // Constructor from a BigUnsigned and a sign
49 BigInteger(const BigUnsigned &x, Sign s);
51 // Nonnegative constructor from a BigUnsigned
52 BigInteger(const BigUnsigned &x) : mag(x) {
53 sign = mag.isZero() ? zero : positive;
56 // Constructors from primitive integer types
57 BigInteger(unsigned long x);
59 BigInteger(unsigned int x);
61 BigInteger(unsigned short x);
64 /* Converters to primitive integer types
65 * The implicit conversion operators caused trouble, so these are now
67 unsigned long toUnsignedLong () const;
69 unsigned int toUnsignedInt () const;
71 unsigned short toUnsignedShort() const;
72 short toShort () const;
75 template <class X> X convertToUnsignedPrimitive() const;
76 template <class X, class UX> X convertToSignedPrimitive() const;
80 Sign getSign() const { return sign; }
81 /* The client can't do any harm by holding a read-only reference to the
83 const BigUnsigned &getMagnitude() const { return mag; }
85 // Some accessors that go through to the magnitude
86 Index getLength() const { return mag.getLength(); }
87 Index getCapacity() const { return mag.getCapacity(); }
88 Blk getBlock(Index i) const { return mag.getBlock(i); }
89 bool isZero() const { return sign == zero; } // A bit special
93 // Compares this to x like Perl's <=>
94 CmpRes compareTo(const BigInteger &x) const;
96 // Ordinary comparison operators
97 bool operator ==(const BigInteger &x) const {
98 return sign == x.sign && mag == x.mag;
100 bool operator !=(const BigInteger &x) const { return !operator ==(x); };
101 bool operator < (const BigInteger &x) const { return compareTo(x) == less ; }
102 bool operator <=(const BigInteger &x) const { return compareTo(x) != greater; }
103 bool operator >=(const BigInteger &x) const { return compareTo(x) != less ; }
104 bool operator > (const BigInteger &x) const { return compareTo(x) == greater; }
106 // OPERATORS -- See the discussion in BigUnsigned.hh.
107 void add (const BigInteger &a, const BigInteger &b);
108 void subtract(const BigInteger &a, const BigInteger &b);
109 void multiply(const BigInteger &a, const BigInteger &b);
110 /* See the comment on BigUnsigned::divideWithRemainder. Semantics
111 * differ from those of primitive integers when negatives and/or zeros
113 void divideWithRemainder(const BigInteger &b, BigInteger &q);
114 void negate(const BigInteger &a);
116 /* Bitwise operators are not provided for BigIntegers. Use
117 * getMagnitude to get the magnitude and operate on that instead. */
119 BigInteger operator +(const BigInteger &x) const;
120 BigInteger operator -(const BigInteger &x) const;
121 BigInteger operator *(const BigInteger &x) const;
122 BigInteger operator /(const BigInteger &x) const;
123 BigInteger operator %(const BigInteger &x) const;
124 BigInteger operator -() const;
126 void operator +=(const BigInteger &x);
127 void operator -=(const BigInteger &x);
128 void operator *=(const BigInteger &x);
129 void operator /=(const BigInteger &x);
130 void operator %=(const BigInteger &x);
133 // INCREMENT/DECREMENT OPERATORS
135 void operator ++(int);
137 void operator --(int);
141 /* These create an object to hold the result and invoke
142 * the appropriate put-here operation on it, passing
143 * this and x. The new object is then returned. */
144 inline BigInteger BigInteger::operator +(const BigInteger &x) const {
149 inline BigInteger BigInteger::operator -(const BigInteger &x) const {
151 ans.subtract(*this, x);
154 inline BigInteger BigInteger::operator *(const BigInteger &x) const {
156 ans.multiply(*this, x);
159 inline BigInteger BigInteger::operator /(const BigInteger &x) const {
160 if (x.isZero()) throw "BigInteger::operator /: division by zero";
163 r.divideWithRemainder(x, q);
166 inline BigInteger BigInteger::operator %(const BigInteger &x) const {
167 if (x.isZero()) throw "BigInteger::operator %: division by zero";
170 r.divideWithRemainder(x, q);
173 inline BigInteger BigInteger::operator -() const {
180 * ASSIGNMENT OPERATORS
182 * Now the responsibility for making a temporary copy if necessary
183 * belongs to the put-here operations. See Assignment Operators in
186 inline void BigInteger::operator +=(const BigInteger &x) {
189 inline void BigInteger::operator -=(const BigInteger &x) {
192 inline void BigInteger::operator *=(const BigInteger &x) {
195 inline void BigInteger::operator /=(const BigInteger &x) {
196 if (x.isZero()) throw "BigInteger::operator /=: division by zero";
197 /* The following technique is slightly faster than copying *this first
198 * when x is large. */
200 divideWithRemainder(x, q);
201 // *this contains the remainder, but we overwrite it with the quotient.
204 inline void BigInteger::operator %=(const BigInteger &x) {
205 if (x.isZero()) throw "BigInteger::operator %=: division by zero";
207 // Mods *this by x. Don't care about quotient left in q.
208 divideWithRemainder(x, q);
210 // This one is trivial
211 inline void BigInteger::flipSign() {