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e67d6049 MM |
1 | #ifndef BIGUNSIGNED |
2 | #define BIGUNSIGNED | |
3 | ||
05780f4b MM |
4 | #include "NumberlikeArray.hh" |
5 | ||
e67d6049 | 6 | /* |
6e1e0f2f MM |
7 | * A BigUnsigned object represents a nonnegative integer of size |
8 | * limited only by available memory. A BigUnsigned can be | |
9 | * created from and converted back to most integral types, | |
10 | * and many math operations are defined on BigUnsigneds. | |
11 | * | |
12 | * The number is stored as a series of blocks in a | |
13 | * dynamically allocated array. It is as if the number | |
14 | * were written digit by digit in base 2 ^ N, **where N is the | |
15 | * number of bits in an unsigned long.** | |
16 | * | |
17 | * The memory-management details that used to be in here have | |
18 | * been moved into NumberlikeArray, which BigUnsigned now derives from. | |
19 | * `(NlA)' means that member(s) are declared identically in NumberlikeArray. | |
20 | * Such members are either redeclared here to make them public or are | |
21 | * here, commented out, for reference. | |
22 | */ | |
e67d6049 | 23 | |
05780f4b | 24 | class BigUnsigned : protected NumberlikeArray<unsigned long> { |
5ff40cf5 | 25 | |
e67d6049 MM |
26 | // TYPES & CONSTANTS |
27 | public: | |
28 | enum CmpRes { less = -1, equal = 0, greater = 1 }; // Enumeration for the result of a comparison | |
29 | typedef unsigned long Blk; // The number block type that BigUnsigneds are built from | |
05780f4b | 30 | typedef NumberlikeArray<Blk>::Index Index; // (NlA) Type for the index of a block in the array |
4efbb076 | 31 | NumberlikeArray<Blk>::N; // Number of bits in a Blk |
5ff40cf5 | 32 | |
05780f4b | 33 | /* |
e67d6049 MM |
34 | // FIELDS |
35 | protected: | |
05780f4b MM |
36 | Index cap; // (NlA) The current allocated capacity of this BigUnsigned (in blocks) |
37 | Index len; // (NlA) The actual length of the number stored in this BigUnsigned (in blocks) | |
38 | Blk *blk; // (NlA) Dynamically allocated array of the number blocks | |
39 | */ | |
5ff40cf5 | 40 | |
e67d6049 MM |
41 | // MANAGEMENT |
42 | protected: | |
05780f4b MM |
43 | // These members generally defer to those in NumberlikeArray, possibly with slight changes. |
44 | // It might be nice if one could request that constructors be inherited in C++. | |
5ff40cf5 | 45 | |
05780f4b | 46 | BigUnsigned(int, Index c) : NumberlikeArray<Blk>(0, c) {} // Creates a BigUnsigned with a capacity |
5ff40cf5 | 47 | |
05780f4b MM |
48 | void zapLeadingZeros() { // Decreases len to eliminate leading zeros |
49 | while (len > 0 && blk[len - 1] == 0) | |
50 | len--; | |
51 | } | |
5ff40cf5 | 52 | |
05780f4b MM |
53 | //void allocate(Index c); // (NlA) Ensures the number array has at least the indicated capacity, maybe discarding contents |
54 | //void allocateAndCopy(Index c); // (NlA) Ensures the number array has at least the indicated capacity, preserving its contents | |
5ff40cf5 | 55 | |
e67d6049 | 56 | public: |
05780f4b MM |
57 | BigUnsigned() : NumberlikeArray<Blk>() {} // Default constructor (value is 0) |
58 | BigUnsigned(const BigUnsigned &x) : NumberlikeArray<Blk>(x) {} // Copy constructor | |
5ff40cf5 | 59 | |
05780f4b MM |
60 | void operator=(const BigUnsigned &x) { // Assignment operator |
61 | NumberlikeArray<Blk>::operator =(x); | |
62 | } | |
5ff40cf5 | 63 | |
05780f4b MM |
64 | BigUnsigned(const Blk *b, Index l) : NumberlikeArray<Blk>(b, l) { // Constructor from an array of blocks |
65 | zapLeadingZeros(); | |
66 | } | |
5ff40cf5 | 67 | |
e67d6049 MM |
68 | // Constructors from integral types |
69 | BigUnsigned(unsigned long x); | |
70 | BigUnsigned( long x); | |
71 | BigUnsigned(unsigned int x); | |
72 | BigUnsigned( int x); | |
73 | BigUnsigned(unsigned short x); | |
74 | BigUnsigned( short x); | |
05780f4b | 75 | ~BigUnsigned() {} // Destructor |
5ff40cf5 | 76 | |
e67d6049 MM |
77 | // CONVERTERS to integral types |
78 | public: | |
79 | operator unsigned long () const; | |
80 | operator long () const; | |
81 | operator unsigned int () const; | |
82 | operator int () const; | |
83 | operator unsigned short() const; | |
84 | operator short() const; | |
5ff40cf5 | 85 | |
e67d6049 MM |
86 | // PICKING APART |
87 | // These accessors can be used to get the pieces of the number | |
88 | public: | |
05780f4b MM |
89 | NumberlikeArray<Blk>::getCapacity; |
90 | NumberlikeArray<Blk>::getLength; | |
91 | // Note that getBlock returns 0 if the block index is beyond the length of the number. | |
92 | // A routine that uses this accessor can safely assume a BigUnsigned has 0s infinitely to the left. | |
93 | Blk getBlock(Index i) const { return i >= len ? 0 : blk[i]; } | |
94 | // Note how we replace one level of abstraction with another. Isn't that neat? | |
95 | bool isZero() const { return NumberlikeArray<Blk>::isEmpty(); } // Often convenient for loops | |
5ff40cf5 | 96 | |
e67d6049 MM |
97 | // COMPARISONS |
98 | public: | |
99 | // Compares this to x like Perl's <=> | |
100 | CmpRes compareTo(const BigUnsigned &x) const; | |
101 | // Normal comparison operators | |
918d66f2 MM |
102 | // Bug fixed 2006.04.24: Only we, not the user, can pass a BigUnsigned off as a |
103 | // NumberlikeArray, so we have to wrap == and !=. | |
104 | bool operator ==(const BigUnsigned &x) const { | |
105 | return NumberlikeArray<Blk>::operator ==(x); | |
106 | } | |
107 | bool operator !=(const BigUnsigned &x) const { | |
108 | return NumberlikeArray<Blk>::operator !=(x); | |
109 | } | |
05780f4b MM |
110 | bool operator < (const BigUnsigned &x) const { return compareTo(x) == less ; } |
111 | bool operator <=(const BigUnsigned &x) const { return compareTo(x) != greater; } | |
112 | bool operator >=(const BigUnsigned &x) const { return compareTo(x) != less ; } | |
113 | bool operator > (const BigUnsigned &x) const { return compareTo(x) == greater; } | |
a8b42b68 MM |
114 | |
115 | /* | |
6e1e0f2f MM |
116 | * BigUnsigned and BigInteger both provide three kinds of operators. |
117 | * Here ``big-integer'' refers to BigInteger or BigUnsigned. | |
118 | * | |
119 | * (1) Overloaded ``return-by-value'' operators: | |
120 | * +, -, *, /, %, unary -. | |
121 | * Big-integer code using these operators looks identical to | |
122 | * code using the primitive integer types. These operators take | |
123 | * one or two big-integer inputs and return a big-integer result, | |
124 | * which can then be assigned to a BigInteger variable or used | |
125 | * in an expression. Example: | |
126 | * BigInteger a(1), b = 1; | |
127 | * BigInteger c = a + b; | |
128 | * | |
129 | * (2) Overloaded assignment operators: | |
130 | * +=, -=, *=, /=, %=, &=, |=, ^=, ++, --, flipSign. | |
131 | * Again, these are used on big integers just like on ints. | |
132 | * They take one writable big integer that both provides an | |
133 | * operand and receives a result. The first eight also take | |
134 | * a second read-only operand. Example: | |
135 | * BigInteger a(1), b(1); | |
136 | * a += b; | |
137 | * | |
138 | * (3) ``Put-here'' operations: `add', `subtract', etc. | |
139 | * Using a return-by-value or assignment operator generally involves | |
140 | * copy constructions and/or assignments. The ``put-here'' operations | |
141 | * require none, but they are more of a hassle to use. Most take two | |
142 | * read-only operands and save the result in the calling object `*this', | |
143 | * whose previous value is ignored. `divideWithRemainder' is an exception. | |
144 | * <<< NOTE >>>: Put-here operations do not return a value: they don't need to!! | |
145 | * Examples: | |
146 | * BigInteger a(43), b(7), c, d; | |
147 | * c = a + b; // Now c == 50. | |
148 | * c.add(a, b); // Same effect but without the two bulk-copies. | |
149 | * c.divideWithRemainder(b, d); // 50 / 7; now d == 7 (quotient) and c == 1 (remainder). | |
150 | * a.add(a, b); // ``Aliased'' calls now do the right thing using a | |
151 | * // temporary copy, but see note on divideWithRemainder. | |
152 | */ | |
5ff40cf5 | 153 | |
e67d6049 | 154 | // PUT-HERE OPERATIONS |
e67d6049 | 155 | public: |
a8b42b68 MM |
156 | /* These 3: Two read-only operands as arguments. Result left in *this. */ |
157 | void add(const BigUnsigned &a, const BigUnsigned &b); // Addition | |
158 | void subtract(const BigUnsigned &a, const BigUnsigned &b); // Subtraction | |
159 | void multiply(const BigUnsigned &a, const BigUnsigned &b); // Multiplication | |
05780f4b | 160 | /* Divisive stuff |
6e1e0f2f MM |
161 | * `a.divideWithRemainder(b, q)' is like `q = a / b, a %= b'. |
162 | * Semantics similar to Donald E. Knuth's are used for / and %, | |
163 | * and these differ from the semantics of primitive-type | |
164 | * / and % under division by zero. | |
165 | * Look in `BigUnsigned.cc' for details. | |
166 | * `a.divideWithRemainder(b, a)' causes an exception: it doesn't make | |
167 | * sense to write quotient and remainder into the same variable. | |
168 | */ | |
05780f4b MM |
169 | void divideWithRemainder(const BigUnsigned &b, BigUnsigned &q); |
170 | void divide(const BigUnsigned &a, const BigUnsigned &b) { | |
05780f4b MM |
171 | BigUnsigned a2(a); |
172 | a2.divideWithRemainder(b, *this); | |
173 | // quotient now in *this | |
174 | // don't care about remainder left in a2 | |
175 | } | |
176 | void modulo(const BigUnsigned &a, const BigUnsigned &b) { | |
05780f4b MM |
177 | *this = a; |
178 | BigUnsigned q; | |
179 | divideWithRemainder(b, q); | |
180 | // remainder now in *this | |
181 | // don't care about quotient left in q | |
182 | } | |
ef2b7c59 | 183 | // Bitwise operations. Result left in *this. |
a8b42b68 MM |
184 | // These are not provided for BigIntegers; I think that using them on BigIntegers |
185 | // will discard the sign first. | |
186 | void bitAnd(const BigUnsigned &a, const BigUnsigned &b); // Bitwise AND | |
187 | void bitOr(const BigUnsigned &a, const BigUnsigned &b); // Bitwise OR | |
188 | void bitXor(const BigUnsigned &a, const BigUnsigned &b); // Bitwise XOR | |
ef2b7c59 MM |
189 | void bitShiftLeft(const BigUnsigned &a, unsigned int b); // Bitwise left shift |
190 | void bitShiftRight(const BigUnsigned &a, unsigned int b); // Bitwise right shift | |
5ff40cf5 | 191 | |
e67d6049 MM |
192 | // NORMAL OPERATORS |
193 | // These perform the operation on this (to the left of the operator) | |
194 | // and x (to the right of the operator) and return a new BigUnsigned with the result. | |
195 | public: | |
196 | BigUnsigned operator +(const BigUnsigned &x) const; // Addition | |
197 | BigUnsigned operator -(const BigUnsigned &x) const; // Subtraction | |
198 | BigUnsigned operator *(const BigUnsigned &x) const; // Multiplication | |
199 | BigUnsigned operator /(const BigUnsigned &x) const; // Division | |
200 | BigUnsigned operator %(const BigUnsigned &x) const; // Modular reduction | |
201 | BigUnsigned operator &(const BigUnsigned &x) const; // Bitwise AND | |
202 | BigUnsigned operator |(const BigUnsigned &x) const; // Bitwise OR | |
203 | BigUnsigned operator ^(const BigUnsigned &x) const; // Bitwise XOR | |
ef2b7c59 MM |
204 | BigUnsigned operator <<(unsigned int b) const; // Bitwise left shift |
205 | BigUnsigned operator >>(unsigned int b) const; // Bitwise right shift | |
206 | // Additional operators in an attempt to avoid overloading tangles. | |
207 | BigUnsigned operator <<(int b) const; | |
208 | BigUnsigned operator >>(int b) const; | |
5ff40cf5 | 209 | |
e67d6049 MM |
210 | // ASSIGNMENT OPERATORS |
211 | // These perform the operation on this and x, storing the result into this. | |
212 | public: | |
213 | void operator +=(const BigUnsigned &x); // Addition | |
214 | void operator -=(const BigUnsigned &x); // Subtraction | |
215 | void operator *=(const BigUnsigned &x); // Multiplication | |
216 | void operator /=(const BigUnsigned &x); // Division | |
217 | void operator %=(const BigUnsigned &x); // Modular reduction | |
218 | void operator &=(const BigUnsigned &x); // Bitwise AND | |
219 | void operator |=(const BigUnsigned &x); // Bitwise OR | |
220 | void operator ^=(const BigUnsigned &x); // Bitwise XOR | |
ef2b7c59 MM |
221 | void operator <<=(unsigned int b); // Bitwise left shift |
222 | void operator >>=(unsigned int b); // Bitwise right shift | |
223 | // Additional operators in an attempt to avoid overloading tangles. | |
224 | void operator <<=(int b); | |
225 | void operator >>=(int b); | |
5ff40cf5 | 226 | |
e67d6049 MM |
227 | // INCREMENT/DECREMENT OPERATORS |
228 | // These increase or decrease the number by 1. To discourage side effects, | |
229 | // these do not return *this, so prefix and postfix behave the same. | |
230 | public: | |
231 | void operator ++( ); // Prefix increment | |
232 | void operator ++(int); // Postfix decrement | |
233 | void operator --( ); // Prefix increment | |
234 | void operator --(int); // Postfix decrement | |
5ff40cf5 | 235 | |
4efbb076 MM |
236 | // Helper function that needs access to BigUnsigned internals |
237 | friend Blk getShiftedBlock(const BigUnsigned &num, Index x, unsigned int y); | |
e67d6049 MM |
238 | }; |
239 | ||
e67d6049 MM |
240 | // NORMAL OPERATORS |
241 | /* These create an object to hold the result and invoke | |
6e1e0f2f MM |
242 | * the appropriate put-here operation on it, passing |
243 | * this and x. The new object is then returned. */ | |
e67d6049 MM |
244 | inline BigUnsigned BigUnsigned::operator +(const BigUnsigned &x) const { |
245 | BigUnsigned ans; | |
246 | ans.add(*this, x); | |
247 | return ans; | |
248 | } | |
249 | inline BigUnsigned BigUnsigned::operator -(const BigUnsigned &x) const { | |
250 | BigUnsigned ans; | |
251 | ans.subtract(*this, x); | |
252 | return ans; | |
253 | } | |
254 | inline BigUnsigned BigUnsigned::operator *(const BigUnsigned &x) const { | |
255 | BigUnsigned ans; | |
256 | ans.multiply(*this, x); | |
257 | return ans; | |
258 | } | |
259 | inline BigUnsigned BigUnsigned::operator /(const BigUnsigned &x) const { | |
260 | BigUnsigned ans; | |
261 | ans.divide(*this, x); | |
262 | return ans; | |
263 | } | |
264 | inline BigUnsigned BigUnsigned::operator %(const BigUnsigned &x) const { | |
265 | BigUnsigned ans; | |
266 | ans.modulo(*this, x); | |
267 | return ans; | |
268 | } | |
269 | inline BigUnsigned BigUnsigned::operator &(const BigUnsigned &x) const { | |
270 | BigUnsigned ans; | |
271 | ans.bitAnd(*this, x); | |
272 | return ans; | |
273 | } | |
274 | inline BigUnsigned BigUnsigned::operator |(const BigUnsigned &x) const { | |
275 | BigUnsigned ans; | |
276 | ans.bitOr(*this, x); | |
277 | return ans; | |
278 | } | |
279 | inline BigUnsigned BigUnsigned::operator ^(const BigUnsigned &x) const { | |
280 | BigUnsigned ans; | |
281 | ans.bitXor(*this, x); | |
282 | return ans; | |
283 | } | |
ef2b7c59 MM |
284 | inline BigUnsigned BigUnsigned::operator <<(unsigned int b) const { |
285 | BigUnsigned ans; | |
286 | ans.bitShiftLeft(*this, b); | |
287 | return ans; | |
288 | } | |
289 | inline BigUnsigned BigUnsigned::operator >>(unsigned int b) const { | |
290 | BigUnsigned ans; | |
291 | ans.bitShiftRight(*this, b); | |
292 | return ans; | |
293 | } | |
294 | inline BigUnsigned BigUnsigned::operator <<(int b) const { | |
295 | if (b < 0) | |
296 | throw "BigUnsigned::operator <<(int): Negative shift amounts are not supported"; | |
297 | return *this << (unsigned int)(b); | |
298 | } | |
299 | inline BigUnsigned BigUnsigned::operator >>(int b) const { | |
300 | if (b < 0) | |
301 | throw "BigUnsigned::operator >>(int): Negative shift amounts are not supported"; | |
302 | return *this >> (unsigned int)(b); | |
303 | } | |
e67d6049 | 304 | |
8c16728a MM |
305 | /* |
306 | * ASSIGNMENT OPERATORS | |
307 | * | |
308 | * Now the responsibility for making a temporary copy if necessary | |
309 | * belongs to the put-here operations. I made this change on 2007.02.13 after | |
310 | * Boris Dessy pointed out that the old implementation handled calls like | |
311 | * "a *= a" badly: it translated them to essentially "a.multiply(aCopy, a)", | |
312 | * which threw an exception. | |
313 | */ | |
e67d6049 | 314 | inline void BigUnsigned::operator +=(const BigUnsigned &x) { |
8c16728a | 315 | add(*this, x); |
e67d6049 MM |
316 | } |
317 | inline void BigUnsigned::operator -=(const BigUnsigned &x) { | |
8c16728a | 318 | subtract(*this, x); |
e67d6049 MM |
319 | } |
320 | inline void BigUnsigned::operator *=(const BigUnsigned &x) { | |
8c16728a | 321 | multiply(*this, x); |
e67d6049 MM |
322 | } |
323 | inline void BigUnsigned::operator /=(const BigUnsigned &x) { | |
05780f4b | 324 | // Updated for divideWithRemainder |
e67d6049 | 325 | BigUnsigned thisCopy(*this); |
05780f4b MM |
326 | thisCopy.divideWithRemainder(x, *this); |
327 | // quotient left in *this | |
328 | // don't care about remainder left in thisCopy | |
e67d6049 MM |
329 | } |
330 | inline void BigUnsigned::operator %=(const BigUnsigned &x) { | |
05780f4b MM |
331 | // Shortcut (woohoo!) |
332 | BigUnsigned q; | |
333 | divideWithRemainder(x, q); | |
334 | // remainder left in *this | |
335 | // don't care about quotient left in q | |
e67d6049 MM |
336 | } |
337 | inline void BigUnsigned::operator &=(const BigUnsigned &x) { | |
8c16728a | 338 | bitAnd(*this, x); |
e67d6049 MM |
339 | } |
340 | inline void BigUnsigned::operator |=(const BigUnsigned &x) { | |
8c16728a | 341 | bitOr(*this, x); |
e67d6049 MM |
342 | } |
343 | inline void BigUnsigned::operator ^=(const BigUnsigned &x) { | |
8c16728a | 344 | bitXor(*this, x); |
e67d6049 | 345 | } |
ef2b7c59 MM |
346 | inline void BigUnsigned::operator <<=(unsigned int b) { |
347 | bitShiftLeft(*this, b); | |
348 | } | |
349 | inline void BigUnsigned::operator >>=(unsigned int b) { | |
350 | bitShiftRight(*this, b); | |
351 | } | |
352 | inline void BigUnsigned::operator <<=(int b) { | |
353 | if (b < 0) | |
354 | throw "BigUnsigned::operator <<=(int): Negative shift amounts are not supported"; | |
355 | *this <<= (unsigned int)(b); | |
356 | } | |
357 | inline void BigUnsigned::operator >>=(int b) { | |
358 | if (b < 0) | |
359 | throw "BigUnsigned::operator >>=(int): Negative shift amounts are not supported"; | |
360 | *this >>= (unsigned int)(b); | |
361 | } | |
e67d6049 MM |
362 | |
363 | #endif |