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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 | |
18 | * dynamically allocated array. It is as if the numbers | |
05780f4b MM |
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. | |
e67d6049 MM |
26 | */ |
27 | ||
05780f4b | 28 | class BigUnsigned : protected NumberlikeArray<unsigned long> { |
e67d6049 MM |
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 | |
05780f4b | 34 | typedef NumberlikeArray<Blk>::Index Index; // (NlA) Type for the index of a block in the array |
e67d6049 | 35 | |
05780f4b | 36 | /* |
e67d6049 MM |
37 | // FIELDS |
38 | protected: | |
05780f4b MM |
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 | */ | |
e67d6049 MM |
43 | |
44 | // MANAGEMENT | |
45 | protected: | |
05780f4b MM |
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 | ||
e67d6049 | 59 | public: |
05780f4b MM |
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 | ||
e67d6049 MM |
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); | |
05780f4b | 78 | ~BigUnsigned() {} // Destructor |
e67d6049 MM |
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: | |
05780f4b MM |
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 | |
e67d6049 MM |
99 | |
100 | // COMPARISONS | |
101 | public: | |
102 | // Compares this to x like Perl's <=> | |
103 | CmpRes compareTo(const BigUnsigned &x) const; | |
104 | // Normal comparison operators | |
05780f4b MM |
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; } | |
e67d6049 MM |
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: | |
05780f4b | 117 | // Easy 3 |
e67d6049 MM |
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 | |
05780f4b MM |
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 | |
e67d6049 MM |
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 | |
05780f4b MM |
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 | |
e67d6049 MM |
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 | ||
e67d6049 MM |
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. | |
05780f4b | 238 | // Exception: those updated for divideWithRemainder. |
e67d6049 MM |
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) { | |
05780f4b | 252 | // Updated for divideWithRemainder |
e67d6049 | 253 | BigUnsigned thisCopy(*this); |
05780f4b MM |
254 | thisCopy.divideWithRemainder(x, *this); |
255 | // quotient left in *this | |
256 | // don't care about remainder left in thisCopy | |
e67d6049 MM |
257 | } |
258 | inline void BigUnsigned::operator %=(const BigUnsigned &x) { | |
05780f4b MM |
259 | // Shortcut (woohoo!) |
260 | BigUnsigned q; | |
261 | divideWithRemainder(x, q); | |
262 | // remainder left in *this | |
263 | // don't care about quotient left in q | |
e67d6049 MM |
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 |