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