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e67d6049 MM |
1 | /* |
2 | * Matt McCutchen's Big Integer Library | |
3 | * http://mysite.verizon.net/mccutchen/bigint/ | |
4 | */ | |
5 | ||
6 | #ifndef BIGUNSIGNED | |
7 | #define BIGUNSIGNED | |
8 | ||
05780f4b MM |
9 | #include "NumberlikeArray.hh" |
10 | ||
e67d6049 MM |
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, | |
05780f4b | 15 | * and many math operations are defined on BigUnsigneds. |
e67d6049 MM |
16 | * |
17 | * The number is stored as a series of blocks in a | |
4efbb076 MM |
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.** | |
05780f4b MM |
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. | |
e67d6049 MM |
27 | */ |
28 | ||
05780f4b | 29 | class BigUnsigned : protected NumberlikeArray<unsigned long> { |
e67d6049 MM |
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 | |
05780f4b | 35 | typedef NumberlikeArray<Blk>::Index Index; // (NlA) Type for the index of a block in the array |
4efbb076 | 36 | NumberlikeArray<Blk>::N; // Number of bits in a Blk |
e67d6049 | 37 | |
05780f4b | 38 | /* |
e67d6049 MM |
39 | // FIELDS |
40 | protected: | |
05780f4b MM |
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 | */ | |
e67d6049 MM |
45 | |
46 | // MANAGEMENT | |
47 | protected: | |
05780f4b MM |
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 | ||
e67d6049 | 61 | public: |
05780f4b MM |
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 | ||
e67d6049 MM |
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); | |
05780f4b | 80 | ~BigUnsigned() {} // Destructor |
e67d6049 MM |
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: | |
05780f4b MM |
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 | |
e67d6049 MM |
101 | |
102 | // COMPARISONS | |
103 | public: | |
104 | // Compares this to x like Perl's <=> | |
105 | CmpRes compareTo(const BigUnsigned &x) const; | |
106 | // Normal comparison operators | |
05780f4b MM |
107 | 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 |
108 | NumberlikeArray<Blk>::operator !=; // (NlA) Ditto. | |
109 | bool operator < (const BigUnsigned &x) const { return compareTo(x) == less ; } | |
110 | bool operator <=(const BigUnsigned &x) const { return compareTo(x) != greater; } | |
111 | bool operator >=(const BigUnsigned &x) const { return compareTo(x) != less ; } | |
112 | bool operator > (const BigUnsigned &x) const { return compareTo(x) == greater; } | |
e67d6049 MM |
113 | |
114 | // PUT-HERE OPERATIONS | |
115 | /* These store the result of the operation on the arguments into this. | |
116 | * a.add(b, c) is equivalent to, but faster than, a = b + c. | |
117 | * Calls like a.operation(a, b) are unsafe and not allowed. */ | |
118 | public: | |
05780f4b | 119 | // Easy 3 |
e67d6049 MM |
120 | void add (const BigUnsigned &a, const BigUnsigned &b); // Addition |
121 | void subtract (const BigUnsigned &a, const BigUnsigned &b); // Subtraction | |
122 | void multiply (const BigUnsigned &a, const BigUnsigned &b); // Multiplication | |
05780f4b MM |
123 | /* Divisive stuff |
124 | * `a.divideWithRemainder(b, q)' is like `q = a / b, a %= b'. | |
125 | * Semantics similar to Donald E. Knuth's are used for / and %, | |
126 | * and these differ from the semantics of primitive-type | |
127 | * / and % under division by zero. | |
128 | * Look in `BigUnsigned.cc' for details. | |
129 | */ | |
130 | void divideWithRemainder(const BigUnsigned &b, BigUnsigned &q); | |
131 | void divide(const BigUnsigned &a, const BigUnsigned &b) { | |
132 | // Division, deprecated and provided for compatibility | |
133 | BigUnsigned a2(a); | |
134 | a2.divideWithRemainder(b, *this); | |
135 | // quotient now in *this | |
136 | // don't care about remainder left in a2 | |
137 | } | |
138 | void modulo(const BigUnsigned &a, const BigUnsigned &b) { | |
139 | // Modular reduction, deprecated and provided for compatibility | |
140 | *this = a; | |
141 | BigUnsigned q; | |
142 | divideWithRemainder(b, q); | |
143 | // remainder now in *this | |
144 | // don't care about quotient left in q | |
145 | } | |
146 | // Bitwise | |
e67d6049 MM |
147 | void bitAnd (const BigUnsigned &a, const BigUnsigned &b); // Bitwise AND |
148 | void bitOr (const BigUnsigned &a, const BigUnsigned &b); // Bitwise OR | |
149 | void bitXor (const BigUnsigned &a, const BigUnsigned &b); // Bitwise XOR | |
05780f4b MM |
150 | |
151 | // These functions are declared but not defined. (Sorry.) | |
152 | // Trying to call either will result in a link-time error. | |
153 | void bitShiftLeft (const BigUnsigned &a, unsigned int b); // Bitwise left shift | |
154 | void bitShiftRight(const BigUnsigned &a, unsigned int b); // Bitwise right shift | |
e67d6049 MM |
155 | |
156 | // NORMAL OPERATORS | |
157 | // These perform the operation on this (to the left of the operator) | |
158 | // and x (to the right of the operator) and return a new BigUnsigned with the result. | |
159 | public: | |
160 | BigUnsigned operator +(const BigUnsigned &x) const; // Addition | |
161 | BigUnsigned operator -(const BigUnsigned &x) const; // Subtraction | |
162 | BigUnsigned operator *(const BigUnsigned &x) const; // Multiplication | |
163 | BigUnsigned operator /(const BigUnsigned &x) const; // Division | |
164 | BigUnsigned operator %(const BigUnsigned &x) const; // Modular reduction | |
165 | BigUnsigned operator &(const BigUnsigned &x) const; // Bitwise AND | |
166 | BigUnsigned operator |(const BigUnsigned &x) const; // Bitwise OR | |
167 | BigUnsigned operator ^(const BigUnsigned &x) const; // Bitwise XOR | |
168 | ||
169 | // ASSIGNMENT OPERATORS | |
170 | // These perform the operation on this and x, storing the result into this. | |
171 | public: | |
172 | void operator +=(const BigUnsigned &x); // Addition | |
173 | void operator -=(const BigUnsigned &x); // Subtraction | |
174 | void operator *=(const BigUnsigned &x); // Multiplication | |
175 | void operator /=(const BigUnsigned &x); // Division | |
176 | void operator %=(const BigUnsigned &x); // Modular reduction | |
177 | void operator &=(const BigUnsigned &x); // Bitwise AND | |
178 | void operator |=(const BigUnsigned &x); // Bitwise OR | |
179 | void operator ^=(const BigUnsigned &x); // Bitwise XOR | |
180 | ||
181 | // INCREMENT/DECREMENT OPERATORS | |
182 | // These increase or decrease the number by 1. To discourage side effects, | |
183 | // these do not return *this, so prefix and postfix behave the same. | |
184 | public: | |
185 | void operator ++( ); // Prefix increment | |
186 | void operator ++(int); // Postfix decrement | |
187 | void operator --( ); // Prefix increment | |
188 | void operator --(int); // Postfix decrement | |
189 | ||
4efbb076 MM |
190 | // Helper function that needs access to BigUnsigned internals |
191 | friend Blk getShiftedBlock(const BigUnsigned &num, Index x, unsigned int y); | |
e67d6049 MM |
192 | }; |
193 | ||
e67d6049 MM |
194 | // NORMAL OPERATORS |
195 | /* These create an object to hold the result and invoke | |
196 | * the appropriate put-here operation on it, passing | |
197 | * this and x. The new object is then returned. */ | |
198 | inline BigUnsigned BigUnsigned::operator +(const BigUnsigned &x) const { | |
199 | BigUnsigned ans; | |
200 | ans.add(*this, x); | |
201 | return ans; | |
202 | } | |
203 | inline BigUnsigned BigUnsigned::operator -(const BigUnsigned &x) const { | |
204 | BigUnsigned ans; | |
205 | ans.subtract(*this, x); | |
206 | return ans; | |
207 | } | |
208 | inline BigUnsigned BigUnsigned::operator *(const BigUnsigned &x) const { | |
209 | BigUnsigned ans; | |
210 | ans.multiply(*this, x); | |
211 | return ans; | |
212 | } | |
213 | inline BigUnsigned BigUnsigned::operator /(const BigUnsigned &x) const { | |
214 | BigUnsigned ans; | |
215 | ans.divide(*this, x); | |
216 | return ans; | |
217 | } | |
218 | inline BigUnsigned BigUnsigned::operator %(const BigUnsigned &x) const { | |
219 | BigUnsigned ans; | |
220 | ans.modulo(*this, x); | |
221 | return ans; | |
222 | } | |
223 | inline BigUnsigned BigUnsigned::operator &(const BigUnsigned &x) const { | |
224 | BigUnsigned ans; | |
225 | ans.bitAnd(*this, x); | |
226 | return ans; | |
227 | } | |
228 | inline BigUnsigned BigUnsigned::operator |(const BigUnsigned &x) const { | |
229 | BigUnsigned ans; | |
230 | ans.bitOr(*this, x); | |
231 | return ans; | |
232 | } | |
233 | inline BigUnsigned BigUnsigned::operator ^(const BigUnsigned &x) const { | |
234 | BigUnsigned ans; | |
235 | ans.bitXor(*this, x); | |
236 | return ans; | |
237 | } | |
238 | ||
239 | // ASSIGNMENT OPERATORS | |
240 | // These create a copy of this, then invoke the appropriate | |
241 | // put-here operation on this, passing the copy and x. | |
05780f4b | 242 | // Exception: those updated for divideWithRemainder. |
e67d6049 MM |
243 | inline void BigUnsigned::operator +=(const BigUnsigned &x) { |
244 | BigUnsigned thisCopy(*this); | |
245 | add(thisCopy, x); | |
246 | } | |
247 | inline void BigUnsigned::operator -=(const BigUnsigned &x) { | |
248 | BigUnsigned thisCopy(*this); | |
249 | subtract(thisCopy, x); | |
250 | } | |
251 | inline void BigUnsigned::operator *=(const BigUnsigned &x) { | |
252 | BigUnsigned thisCopy(*this); | |
253 | multiply(thisCopy, x); | |
254 | } | |
255 | inline void BigUnsigned::operator /=(const BigUnsigned &x) { | |
05780f4b | 256 | // Updated for divideWithRemainder |
e67d6049 | 257 | BigUnsigned thisCopy(*this); |
05780f4b MM |
258 | thisCopy.divideWithRemainder(x, *this); |
259 | // quotient left in *this | |
260 | // don't care about remainder left in thisCopy | |
e67d6049 MM |
261 | } |
262 | inline void BigUnsigned::operator %=(const BigUnsigned &x) { | |
05780f4b MM |
263 | // Shortcut (woohoo!) |
264 | BigUnsigned q; | |
265 | divideWithRemainder(x, q); | |
266 | // remainder left in *this | |
267 | // don't care about quotient left in q | |
e67d6049 MM |
268 | } |
269 | inline void BigUnsigned::operator &=(const BigUnsigned &x) { | |
270 | BigUnsigned thisCopy(*this); | |
271 | bitAnd(thisCopy, x); | |
272 | } | |
273 | inline void BigUnsigned::operator |=(const BigUnsigned &x) { | |
274 | BigUnsigned thisCopy(*this); | |
275 | bitOr(thisCopy, x); | |
276 | } | |
277 | inline void BigUnsigned::operator ^=(const BigUnsigned &x) { | |
278 | BigUnsigned thisCopy(*this); | |
279 | bitXor(thisCopy, x); | |
280 | } | |
281 | ||
282 | #endif |