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1 | /* |
2 | * Matt McCutchen's Big Integer Library | |
b1f5f69e | 3 | * http://hashproduct.metaesthetics.net/bigint/ |
e67d6049 MM |
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. |
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16 | * |
17 | * The number is stored as a series of blocks in a | |
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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.** | |
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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. | |
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27 | */ |
28 | ||
05780f4b | 29 | class BigUnsigned : protected NumberlikeArray<unsigned long> { |
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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 | /* |
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39 | // FIELDS |
40 | protected: | |
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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 | */ | |
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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 |
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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 | |
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101 | |
102 | // COMPARISONS | |
103 | public: | |
104 | // Compares this to x like Perl's <=> | |
105 | CmpRes compareTo(const BigUnsigned &x) const; | |
106 | // Normal comparison operators | |
918d66f2 MM |
107 | // Bug fixed 2006.04.24: Only we, not the user, can pass a BigUnsigned off as a |
108 | // NumberlikeArray, so we have to wrap == and !=. | |
109 | bool operator ==(const BigUnsigned &x) const { | |
110 | return NumberlikeArray<Blk>::operator ==(x); | |
111 | } | |
112 | bool operator !=(const BigUnsigned &x) const { | |
113 | return NumberlikeArray<Blk>::operator !=(x); | |
114 | } | |
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115 | bool operator < (const BigUnsigned &x) const { return compareTo(x) == less ; } |
116 | bool operator <=(const BigUnsigned &x) const { return compareTo(x) != greater; } | |
117 | bool operator >=(const BigUnsigned &x) const { return compareTo(x) != less ; } | |
118 | bool operator > (const BigUnsigned &x) const { return compareTo(x) == greater; } | |
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119 | |
120 | /* | |
121 | * BigUnsigned and BigInteger both provide three kinds of operators. | |
122 | * Here ``big-integer'' refers to BigInteger or BigUnsigned. | |
123 | * | |
124 | * (1) Overloaded ``return-by-value'' operators: | |
125 | * +, -, *, /, %, unary -. | |
126 | * Big-integer code using these operators looks identical to | |
127 | * code using the primitive integer types. These operators take | |
128 | * one or two big-integer inputs and return a big-integer result, | |
129 | * which can then be assigned to a BigInteger variable or used | |
130 | * in an expression. Example: | |
131 | * BigInteger a(1), b = 1; | |
132 | * BigInteger c = a + b; | |
133 | * | |
134 | * (2) Overloaded assignment operators: | |
135 | * +=, -=, *=, /=, %=, &=, |=, ^=, ++, --, flipSign. | |
136 | * Again, these are used on big integers just like on ints. | |
137 | * They take one writable big integer that both provides an | |
138 | * operand and receives a result. The first eight also take | |
139 | * a second read-only operand. Example: | |
140 | * BigInteger a(1), b(1); | |
141 | * a += b; | |
142 | * | |
143 | * (3) ``Put-here'' operations: `add', `subtract', etc. | |
144 | * Using a return-by-value or assignment operator generally involves | |
145 | * copy constructions and/or assignments. The ``put-here'' operations | |
146 | * require none, but they are more of a hassle to use. Most take two | |
147 | * read-only operands and save the result in the calling object `*this', | |
148 | * whose previous value is ignored. `divideWithRemainder' is an exception. | |
149 | * <<< NOTE >>>: Put-here operations do not return a value: they don't need to!! | |
150 | * Examples: | |
151 | * BigInteger a(43), b(7), c, d; | |
152 | * c = a + b; // Now c == 50. | |
153 | * c.add(a, b); // Same effect but without the two bulk-copies. | |
154 | * c.divideWithRemainder(b, d); // 50 / 7; now d == 7 (quotient) and c == 1 (remainder). | |
155 | * a.add(a, b); // Unsafe ``aliased'' call; causes a runtime error. | |
156 | */ | |
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157 | |
158 | // PUT-HERE OPERATIONS | |
e67d6049 | 159 | public: |
a8b42b68 MM |
160 | /* These 3: Two read-only operands as arguments. Result left in *this. */ |
161 | void add(const BigUnsigned &a, const BigUnsigned &b); // Addition | |
162 | void subtract(const BigUnsigned &a, const BigUnsigned &b); // Subtraction | |
163 | void multiply(const BigUnsigned &a, const BigUnsigned &b); // Multiplication | |
05780f4b MM |
164 | /* Divisive stuff |
165 | * `a.divideWithRemainder(b, q)' is like `q = a / b, a %= b'. | |
166 | * Semantics similar to Donald E. Knuth's are used for / and %, | |
167 | * and these differ from the semantics of primitive-type | |
168 | * / and % under division by zero. | |
169 | * Look in `BigUnsigned.cc' for details. | |
170 | */ | |
171 | void divideWithRemainder(const BigUnsigned &b, BigUnsigned &q); | |
172 | void divide(const BigUnsigned &a, const BigUnsigned &b) { | |
a8b42b68 | 173 | // Division, deprecated and provided for backward compatibility |
05780f4b MM |
174 | BigUnsigned a2(a); |
175 | a2.divideWithRemainder(b, *this); | |
176 | // quotient now in *this | |
177 | // don't care about remainder left in a2 | |
178 | } | |
179 | void modulo(const BigUnsigned &a, const BigUnsigned &b) { | |
a8b42b68 | 180 | // Modular reduction, deprecated and provided for backward compatibility |
05780f4b MM |
181 | *this = a; |
182 | BigUnsigned q; | |
183 | divideWithRemainder(b, q); | |
184 | // remainder now in *this | |
185 | // don't care about quotient left in q | |
186 | } | |
a8b42b68 MM |
187 | // Bitwise operations. Two read-only operands as arguments. Result left in *this. |
188 | // These are not provided for BigIntegers; I think that using them on BigIntegers | |
189 | // will discard the sign first. | |
190 | void bitAnd(const BigUnsigned &a, const BigUnsigned &b); // Bitwise AND | |
191 | void bitOr(const BigUnsigned &a, const BigUnsigned &b); // Bitwise OR | |
192 | void bitXor(const BigUnsigned &a, const BigUnsigned &b); // Bitwise XOR | |
05780f4b MM |
193 | |
194 | // These functions are declared but not defined. (Sorry.) | |
195 | // Trying to call either will result in a link-time error. | |
a8b42b68 | 196 | void bitShiftLeft(const BigUnsigned &a, unsigned int b); // Bitwise left shift |
05780f4b | 197 | void bitShiftRight(const BigUnsigned &a, unsigned int b); // Bitwise right shift |
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198 | |
199 | // NORMAL OPERATORS | |
200 | // These perform the operation on this (to the left of the operator) | |
201 | // and x (to the right of the operator) and return a new BigUnsigned with the result. | |
202 | public: | |
203 | BigUnsigned operator +(const BigUnsigned &x) const; // Addition | |
204 | BigUnsigned operator -(const BigUnsigned &x) const; // Subtraction | |
205 | BigUnsigned operator *(const BigUnsigned &x) const; // Multiplication | |
206 | BigUnsigned operator /(const BigUnsigned &x) const; // Division | |
207 | BigUnsigned operator %(const BigUnsigned &x) const; // Modular reduction | |
208 | BigUnsigned operator &(const BigUnsigned &x) const; // Bitwise AND | |
209 | BigUnsigned operator |(const BigUnsigned &x) const; // Bitwise OR | |
210 | BigUnsigned operator ^(const BigUnsigned &x) const; // Bitwise XOR | |
211 | ||
212 | // ASSIGNMENT OPERATORS | |
213 | // These perform the operation on this and x, storing the result into this. | |
214 | public: | |
215 | void operator +=(const BigUnsigned &x); // Addition | |
216 | void operator -=(const BigUnsigned &x); // Subtraction | |
217 | void operator *=(const BigUnsigned &x); // Multiplication | |
218 | void operator /=(const BigUnsigned &x); // Division | |
219 | void operator %=(const BigUnsigned &x); // Modular reduction | |
220 | void operator &=(const BigUnsigned &x); // Bitwise AND | |
221 | void operator |=(const BigUnsigned &x); // Bitwise OR | |
222 | void operator ^=(const BigUnsigned &x); // Bitwise XOR | |
223 | ||
224 | // INCREMENT/DECREMENT OPERATORS | |
225 | // These increase or decrease the number by 1. To discourage side effects, | |
226 | // these do not return *this, so prefix and postfix behave the same. | |
227 | public: | |
228 | void operator ++( ); // Prefix increment | |
229 | void operator ++(int); // Postfix decrement | |
230 | void operator --( ); // Prefix increment | |
231 | void operator --(int); // Postfix decrement | |
232 | ||
4efbb076 MM |
233 | // Helper function that needs access to BigUnsigned internals |
234 | friend Blk getShiftedBlock(const BigUnsigned &num, Index x, unsigned int y); | |
e67d6049 MM |
235 | }; |
236 | ||
e67d6049 MM |
237 | // NORMAL OPERATORS |
238 | /* These create an object to hold the result and invoke | |
239 | * the appropriate put-here operation on it, passing | |
240 | * this and x. The new object is then returned. */ | |
241 | inline BigUnsigned BigUnsigned::operator +(const BigUnsigned &x) const { | |
242 | BigUnsigned ans; | |
243 | ans.add(*this, x); | |
244 | return ans; | |
245 | } | |
246 | inline BigUnsigned BigUnsigned::operator -(const BigUnsigned &x) const { | |
247 | BigUnsigned ans; | |
248 | ans.subtract(*this, x); | |
249 | return ans; | |
250 | } | |
251 | inline BigUnsigned BigUnsigned::operator *(const BigUnsigned &x) const { | |
252 | BigUnsigned ans; | |
253 | ans.multiply(*this, x); | |
254 | return ans; | |
255 | } | |
256 | inline BigUnsigned BigUnsigned::operator /(const BigUnsigned &x) const { | |
257 | BigUnsigned ans; | |
258 | ans.divide(*this, x); | |
259 | return ans; | |
260 | } | |
261 | inline BigUnsigned BigUnsigned::operator %(const BigUnsigned &x) const { | |
262 | BigUnsigned ans; | |
263 | ans.modulo(*this, x); | |
264 | return ans; | |
265 | } | |
266 | inline BigUnsigned BigUnsigned::operator &(const BigUnsigned &x) const { | |
267 | BigUnsigned ans; | |
268 | ans.bitAnd(*this, x); | |
269 | return ans; | |
270 | } | |
271 | inline BigUnsigned BigUnsigned::operator |(const BigUnsigned &x) const { | |
272 | BigUnsigned ans; | |
273 | ans.bitOr(*this, x); | |
274 | return ans; | |
275 | } | |
276 | inline BigUnsigned BigUnsigned::operator ^(const BigUnsigned &x) const { | |
277 | BigUnsigned ans; | |
278 | ans.bitXor(*this, x); | |
279 | return ans; | |
280 | } | |
281 | ||
282 | // ASSIGNMENT OPERATORS | |
283 | // These create a copy of this, then invoke the appropriate | |
284 | // put-here operation on this, passing the copy and x. | |
05780f4b | 285 | // Exception: those updated for divideWithRemainder. |
e67d6049 MM |
286 | inline void BigUnsigned::operator +=(const BigUnsigned &x) { |
287 | BigUnsigned thisCopy(*this); | |
288 | add(thisCopy, x); | |
289 | } | |
290 | inline void BigUnsigned::operator -=(const BigUnsigned &x) { | |
291 | BigUnsigned thisCopy(*this); | |
292 | subtract(thisCopy, x); | |
293 | } | |
294 | inline void BigUnsigned::operator *=(const BigUnsigned &x) { | |
295 | BigUnsigned thisCopy(*this); | |
296 | multiply(thisCopy, x); | |
297 | } | |
298 | inline void BigUnsigned::operator /=(const BigUnsigned &x) { | |
05780f4b | 299 | // Updated for divideWithRemainder |
e67d6049 | 300 | BigUnsigned thisCopy(*this); |
05780f4b MM |
301 | thisCopy.divideWithRemainder(x, *this); |
302 | // quotient left in *this | |
303 | // don't care about remainder left in thisCopy | |
e67d6049 MM |
304 | } |
305 | inline void BigUnsigned::operator %=(const BigUnsigned &x) { | |
05780f4b MM |
306 | // Shortcut (woohoo!) |
307 | BigUnsigned q; | |
308 | divideWithRemainder(x, q); | |
309 | // remainder left in *this | |
310 | // don't care about quotient left in q | |
e67d6049 MM |
311 | } |
312 | inline void BigUnsigned::operator &=(const BigUnsigned &x) { | |
313 | BigUnsigned thisCopy(*this); | |
314 | bitAnd(thisCopy, x); | |
315 | } | |
316 | inline void BigUnsigned::operator |=(const BigUnsigned &x) { | |
317 | BigUnsigned thisCopy(*this); | |
318 | bitOr(thisCopy, x); | |
319 | } | |
320 | inline void BigUnsigned::operator ^=(const BigUnsigned &x) { | |
321 | BigUnsigned thisCopy(*this); | |
322 | bitXor(thisCopy, x); | |
323 | } | |
324 | ||
325 | #endif |