Commit | Line | Data |
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05780f4b | 1 | #include "BigInteger.hh" |
e67d6049 | 2 | |
e67d6049 MM |
3 | void BigInteger::operator =(const BigInteger &x) { |
4 | // Calls like a = a have no effect | |
5 | if (this == &x) | |
6 | return; | |
7 | // Copy sign | |
8 | sign = x.sign; | |
9 | // Copy the rest | |
3e132790 | 10 | mag = x.mag; |
e67d6049 MM |
11 | } |
12 | ||
3e132790 | 13 | BigInteger::BigInteger(const Blk *b, Index blen, Sign s) : mag(b, blen) { |
e67d6049 | 14 | switch (s) { |
3e132790 MM |
15 | case zero: |
16 | case positive: | |
17 | case negative: | |
18 | sign = mag.isZero() ? zero : s; | |
e67d6049 | 19 | break; |
3e132790 MM |
20 | default: |
21 | throw "BigInteger::BigInteger(const Blk *, Index, Sign): Invalid sign"; | |
e67d6049 MM |
22 | } |
23 | } | |
24 | ||
3e132790 | 25 | BigInteger::BigInteger(const BigUnsigned &x, Sign s) : mag(x) { |
e67d6049 | 26 | switch (s) { |
3e132790 MM |
27 | case zero: |
28 | case positive: | |
29 | case negative: | |
30 | sign = mag.isZero() ? zero : s; | |
e67d6049 | 31 | break; |
3e132790 | 32 | default: |
05780f4b | 33 | throw "BigInteger::BigInteger(Blk *, Index, Sign): Invalid sign"; |
e67d6049 MM |
34 | } |
35 | } | |
36 | ||
3e132790 MM |
37 | /* CONSTRUCTION FROM PRIMITIVE INTEGERS |
38 | * Same idea as in BigUnsigned.cc, except that negative input results in a | |
39 | * negative BigInteger instead of an exception. */ | |
e67d6049 | 40 | |
3e132790 | 41 | // Done longhand to let us use initialization. |
83a639e6 MM |
42 | BigInteger::BigInteger(unsigned long x) : mag(x) { sign = mag.isZero() ? zero : positive; } |
43 | BigInteger::BigInteger(unsigned int x) : mag(x) { sign = mag.isZero() ? zero : positive; } | |
44 | BigInteger::BigInteger(unsigned short x) : mag(x) { sign = mag.isZero() ? zero : positive; } | |
e67d6049 | 45 | |
3e132790 | 46 | // For signed input, determine the desired magnitude and sign separately. |
e67d6049 | 47 | |
3e132790 MM |
48 | namespace { |
49 | template <class X, class UX> | |
50 | BigInteger::Blk magOf(X x) { | |
51 | /* UX(...) cast needed to stop short(-2^15), which negates to | |
52 | * itself, from sign-extending in the conversion to Blk. */ | |
53 | return BigInteger::Blk(x < 0 ? UX(-x) : x); | |
54 | } | |
55 | template <class X> | |
56 | BigInteger::Sign signOf(X x) { | |
57 | return (x == 0) ? BigInteger::zero | |
58 | : (x > 0) ? BigInteger::positive | |
59 | : BigInteger::negative; | |
e67d6049 MM |
60 | } |
61 | } | |
62 | ||
83a639e6 MM |
63 | BigInteger::BigInteger(long x) : sign(signOf(x)), mag(magOf<long , unsigned long >(x)) {} |
64 | BigInteger::BigInteger(int x) : sign(signOf(x)), mag(magOf<int , unsigned int >(x)) {} | |
65 | BigInteger::BigInteger(short x) : sign(signOf(x)), mag(magOf<short, unsigned short>(x)) {} | |
3e132790 MM |
66 | |
67 | // CONVERSION TO PRIMITIVE INTEGERS | |
68 | ||
69 | /* Reuse BigUnsigned's conversion to an unsigned primitive integer. | |
70 | * The friend is a separate function rather than | |
71 | * BigInteger::convertToUnsignedPrimitive to avoid requiring BigUnsigned to | |
72 | * declare BigInteger. */ | |
73 | template <class X> | |
74 | inline X convertBigUnsignedToPrimitiveAccess(const BigUnsigned &a) { | |
75 | return a.convertToPrimitive<X>(); | |
e67d6049 MM |
76 | } |
77 | ||
3e132790 MM |
78 | template <class X> |
79 | X BigInteger::convertToUnsignedPrimitive() const { | |
80 | if (sign == negative) | |
81 | throw "BigInteger::to<Primitive>: " | |
82 | "Cannot convert a negative integer to an unsigned type"; | |
83 | else | |
84 | return convertBigUnsignedToPrimitiveAccess<X>(mag); | |
e67d6049 MM |
85 | } |
86 | ||
3e132790 MM |
87 | /* Similar to BigUnsigned::convertToPrimitive, but split into two cases for |
88 | * nonnegative and negative numbers. */ | |
89 | template <class X, class UX> | |
90 | X BigInteger::convertToSignedPrimitive() const { | |
91 | if (sign == zero) | |
e67d6049 | 92 | return 0; |
3e132790 MM |
93 | else if (mag.getLength() == 1) { |
94 | // The single block might fit in an X. Try the conversion. | |
95 | Blk b = mag.getBlock(0); | |
96 | if (sign == positive) { | |
97 | X x = X(b); | |
98 | if (x >= 0 && Blk(x) == b) | |
99 | return x; | |
100 | } else { | |
101 | X x = -X(b); | |
102 | /* UX(...) needed to avoid rejecting conversion of | |
103 | * -2^15 to a short. */ | |
104 | if (x < 0 && Blk(UX(-x)) == b) | |
105 | return x; | |
106 | } | |
107 | // Otherwise fall through. | |
e67d6049 | 108 | } |
3e132790 MM |
109 | throw "BigInteger::to<Primitive>: " |
110 | "Value is too big to fit in the requested type"; | |
e67d6049 MM |
111 | } |
112 | ||
83a639e6 MM |
113 | unsigned long BigInteger::toUnsignedLong () const { return convertToUnsignedPrimitive<unsigned long > (); } |
114 | unsigned int BigInteger::toUnsignedInt () const { return convertToUnsignedPrimitive<unsigned int > (); } | |
115 | unsigned short BigInteger::toUnsignedShort() const { return convertToUnsignedPrimitive<unsigned short> (); } | |
116 | long BigInteger::toLong () const { return convertToSignedPrimitive <long , unsigned long> (); } | |
117 | int BigInteger::toInt () const { return convertToSignedPrimitive <int , unsigned int> (); } | |
118 | short BigInteger::toShort () const { return convertToSignedPrimitive <short, unsigned short>(); } | |
e67d6049 MM |
119 | |
120 | // COMPARISON | |
121 | BigInteger::CmpRes BigInteger::compareTo(const BigInteger &x) const { | |
122 | // A greater sign implies a greater number | |
123 | if (sign < x.sign) | |
124 | return less; | |
125 | else if (sign > x.sign) | |
126 | return greater; | |
127 | else switch (sign) { | |
128 | // If the signs are the same... | |
3e132790 | 129 | case zero: |
e67d6049 | 130 | return equal; // Two zeros are equal |
3e132790 | 131 | case positive: |
e67d6049 | 132 | // Compare the magnitudes |
3e132790 MM |
133 | return mag.compareTo(x.mag); |
134 | case negative: | |
e67d6049 | 135 | // Compare the magnitudes, but return the opposite result |
3e132790 MM |
136 | return CmpRes(-mag.compareTo(x.mag)); |
137 | default: | |
138 | throw "BigInteger internal error"; | |
e67d6049 MM |
139 | } |
140 | } | |
141 | ||
3e132790 MM |
142 | /* COPY-LESS OPERATIONS |
143 | * These do some messing around to determine the sign of the result, | |
144 | * then call one of BigUnsigned's copy-less operations. */ | |
e67d6049 | 145 | |
8c16728a | 146 | // See remarks about aliased calls in BigUnsigned.cc . |
a8e1d2a4 | 147 | #define DTRT_ALIASED(cond, op) \ |
8c16728a MM |
148 | if (cond) { \ |
149 | BigInteger tmpThis; \ | |
150 | tmpThis.op; \ | |
151 | *this = tmpThis; \ | |
152 | return; \ | |
153 | } | |
154 | ||
e67d6049 | 155 | void BigInteger::add(const BigInteger &a, const BigInteger &b) { |
a8e1d2a4 | 156 | DTRT_ALIASED(this == &a || this == &b, add(a, b)); |
e67d6049 MM |
157 | // If one argument is zero, copy the other. |
158 | if (a.sign == zero) | |
159 | operator =(b); | |
160 | else if (b.sign == zero) | |
161 | operator =(a); | |
162 | // If the arguments have the same sign, take the | |
163 | // common sign and add their magnitudes. | |
164 | else if (a.sign == b.sign) { | |
165 | sign = a.sign; | |
3e132790 | 166 | mag.add(a.mag, b.mag); |
e67d6049 MM |
167 | } else { |
168 | // Otherwise, their magnitudes must be compared. | |
3e132790 MM |
169 | switch (a.mag.compareTo(b.mag)) { |
170 | case equal: | |
e67d6049 | 171 | // If their magnitudes are the same, copy zero. |
3e132790 | 172 | mag = 0; |
e67d6049 MM |
173 | sign = zero; |
174 | break; | |
175 | // Otherwise, take the sign of the greater, and subtract | |
176 | // the lesser magnitude from the greater magnitude. | |
3e132790 | 177 | case greater: |
e67d6049 | 178 | sign = a.sign; |
3e132790 | 179 | mag.subtract(a.mag, b.mag); |
e67d6049 | 180 | break; |
3e132790 | 181 | case less: |
e67d6049 | 182 | sign = b.sign; |
3e132790 | 183 | mag.subtract(b.mag, a.mag); |
e67d6049 MM |
184 | break; |
185 | } | |
186 | } | |
187 | } | |
188 | ||
e67d6049 MM |
189 | void BigInteger::subtract(const BigInteger &a, const BigInteger &b) { |
190 | // Notice that this routine is identical to BigInteger::add, | |
191 | // if one replaces b.sign by its opposite. | |
a8e1d2a4 | 192 | DTRT_ALIASED(this == &a || this == &b, subtract(a, b)); |
e67d6049 MM |
193 | // If a is zero, copy b and flip its sign. If b is zero, copy a. |
194 | if (a.sign == zero) { | |
3e132790 | 195 | mag = b.mag; |
f316def7 MM |
196 | // Take the negative of _b_'s, sign, not ours. |
197 | // Bug pointed out by Sam Larkin on 2005.03.30. | |
198 | sign = Sign(-b.sign); | |
e67d6049 | 199 | } else if (b.sign == zero) |
f316def7 | 200 | operator =(a); |
e67d6049 MM |
201 | // If their signs differ, take a.sign and add the magnitudes. |
202 | else if (a.sign != b.sign) { | |
203 | sign = a.sign; | |
3e132790 | 204 | mag.add(a.mag, b.mag); |
e67d6049 MM |
205 | } else { |
206 | // Otherwise, their magnitudes must be compared. | |
3e132790 | 207 | switch (a.mag.compareTo(b.mag)) { |
e67d6049 | 208 | // If their magnitudes are the same, copy zero. |
3e132790 MM |
209 | case equal: |
210 | mag = 0; | |
e67d6049 MM |
211 | sign = zero; |
212 | break; | |
213 | // If a's magnitude is greater, take a.sign and | |
214 | // subtract a from b. | |
3e132790 | 215 | case greater: |
e67d6049 | 216 | sign = a.sign; |
3e132790 | 217 | mag.subtract(a.mag, b.mag); |
e67d6049 MM |
218 | break; |
219 | // If b's magnitude is greater, take the opposite | |
220 | // of b.sign and subtract b from a. | |
3e132790 | 221 | case less: |
e67d6049 | 222 | sign = Sign(-b.sign); |
3e132790 | 223 | mag.subtract(b.mag, a.mag); |
e67d6049 MM |
224 | break; |
225 | } | |
226 | } | |
227 | } | |
228 | ||
e67d6049 | 229 | void BigInteger::multiply(const BigInteger &a, const BigInteger &b) { |
a8e1d2a4 | 230 | DTRT_ALIASED(this == &a || this == &b, multiply(a, b)); |
e67d6049 MM |
231 | // If one object is zero, copy zero and return. |
232 | if (a.sign == zero || b.sign == zero) { | |
233 | sign = zero; | |
3e132790 | 234 | mag = 0; |
e67d6049 MM |
235 | return; |
236 | } | |
237 | // If the signs of the arguments are the same, the result | |
238 | // is positive, otherwise it is negative. | |
239 | sign = (a.sign == b.sign) ? positive : negative; | |
240 | // Multiply the magnitudes. | |
3e132790 | 241 | mag.multiply(a.mag, b.mag); |
e67d6049 MM |
242 | } |
243 | ||
05780f4b | 244 | /* |
6e1e0f2f MM |
245 | * DIVISION WITH REMAINDER |
246 | * Please read the comments before the definition of | |
247 | * `BigUnsigned::divideWithRemainder' in `BigUnsigned.cc' for lots of | |
248 | * information you should know before reading this function. | |
249 | * | |
250 | * Following Knuth, I decree that x / y is to be | |
251 | * 0 if y==0 and floor(real-number x / y) if y!=0. | |
252 | * Then x % y shall be x - y*(integer x / y). | |
253 | * | |
254 | * Note that x = y * (x / y) + (x % y) always holds. | |
255 | * In addition, (x % y) is from 0 to y - 1 if y > 0, | |
256 | * and from -(|y| - 1) to 0 if y < 0. (x % y) = x if y = 0. | |
257 | * | |
258 | * Examples: (q = a / b, r = a % b) | |
259 | * a b q r | |
260 | * === === === === | |
261 | * 4 3 1 1 | |
262 | * -4 3 -2 2 | |
263 | * 4 -3 -2 -2 | |
264 | * -4 -3 1 -1 | |
265 | */ | |
05780f4b | 266 | void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) { |
8c16728a MM |
267 | // Defend against aliased calls; |
268 | // same idea as in BigUnsigned::divideWithRemainder . | |
269 | if (this == &q) | |
270 | throw "BigInteger::divideWithRemainder: Cannot write quotient and remainder into the same variable"; | |
271 | if (this == &b || &q == &b) { | |
272 | BigInteger tmpB(b); | |
273 | divideWithRemainder(tmpB, q); | |
274 | return; | |
275 | } | |
5ff40cf5 | 276 | |
05780f4b MM |
277 | // Division by zero gives quotient 0 and remainder *this |
278 | if (b.sign == zero) { | |
3e132790 | 279 | q.mag = 0; |
05780f4b | 280 | q.sign = zero; |
e67d6049 MM |
281 | return; |
282 | } | |
05780f4b MM |
283 | // 0 / b gives quotient 0 and remainder 0 |
284 | if (sign == zero) { | |
3e132790 | 285 | q.mag = 0; |
05780f4b | 286 | q.sign = zero; |
e67d6049 MM |
287 | return; |
288 | } | |
5ff40cf5 | 289 | |
05780f4b | 290 | // Here *this != 0, b != 0. |
5ff40cf5 | 291 | |
05780f4b MM |
292 | // Do the operands have the same sign? |
293 | if (sign == b.sign) { | |
294 | // Yes: easy case. Quotient is zero or positive. | |
295 | q.sign = positive; | |
296 | } else { | |
297 | // No: harder case. Quotient is negative. | |
298 | q.sign = negative; | |
299 | // Decrease the magnitude of the dividend by one. | |
3e132790 | 300 | mag--; |
05780f4b | 301 | /* |
6e1e0f2f MM |
302 | * We tinker with the dividend before and with the |
303 | * quotient and remainder after so that the result | |
304 | * comes out right. To see why it works, consider the following | |
305 | * list of examples, where A is the magnitude-decreased | |
306 | * a, Q and R are the results of BigUnsigned division | |
307 | * with remainder on A and |b|, and q and r are the | |
308 | * final results we want: | |
309 | * | |
310 | * a A b Q R q r | |
311 | * -3 -2 3 0 2 -1 0 | |
312 | * -4 -3 3 1 0 -2 2 | |
313 | * -5 -4 3 1 1 -2 1 | |
314 | * -6 -5 3 1 2 -2 0 | |
315 | * | |
316 | * It appears that we need a total of 3 corrections: | |
317 | * Decrease the magnitude of a to get A. Increase the | |
318 | * magnitude of Q to get q (and make it negative). | |
319 | * Find r = (b - 1) - R and give it the desired sign. | |
320 | */ | |
05780f4b | 321 | } |
5ff40cf5 | 322 | |
05780f4b | 323 | // Divide the magnitudes. |
3e132790 | 324 | mag.divideWithRemainder(b.mag, q.mag); |
5ff40cf5 | 325 | |
05780f4b MM |
326 | if (sign != b.sign) { |
327 | // More for the harder case (as described): | |
328 | // Increase the magnitude of the quotient by one. | |
3e132790 | 329 | q.mag++; |
05780f4b | 330 | // Modify the remainder. |
3e132790 MM |
331 | mag.subtract(b.mag, mag); |
332 | mag--; | |
05780f4b | 333 | } |
5ff40cf5 | 334 | |
05780f4b MM |
335 | // Sign of the remainder is always the sign of the divisor b. |
336 | sign = b.sign; | |
5ff40cf5 | 337 | |
05780f4b | 338 | // Set signs to zero as necessary. (Thanks David Allen!) |
3e132790 | 339 | if (mag.isZero()) |
e67d6049 | 340 | sign = zero; |
3e132790 | 341 | if (q.mag.isZero()) |
05780f4b | 342 | q.sign = zero; |
5ff40cf5 | 343 | |
05780f4b | 344 | // WHEW!!! |
e67d6049 MM |
345 | } |
346 | ||
347 | // Negation | |
348 | void BigInteger::negate(const BigInteger &a) { | |
a8e1d2a4 | 349 | DTRT_ALIASED(this == &a, negate(a)); |
e67d6049 | 350 | // Copy a's magnitude |
3e132790 | 351 | mag = a.mag; |
e67d6049 MM |
352 | // Copy the opposite of a.sign |
353 | sign = Sign(-a.sign); | |
354 | } | |
355 | ||
356 | // INCREMENT/DECREMENT OPERATORS | |
357 | ||
358 | // Prefix increment | |
359 | void BigInteger::operator ++() { | |
3e132790 MM |
360 | if (sign == negative) { |
361 | mag--; | |
362 | if (mag == 0) | |
e67d6049 | 363 | sign = zero; |
3e132790 MM |
364 | } else { |
365 | mag++; | |
366 | sign = positive; // if not already | |
e67d6049 MM |
367 | } |
368 | } | |
369 | ||
370 | // Postfix increment: same as prefix | |
371 | void BigInteger::operator ++(int) { | |
372 | operator ++(); | |
373 | } | |
374 | ||
375 | // Prefix decrement | |
376 | void BigInteger::operator --() { | |
3e132790 MM |
377 | if (sign == positive) { |
378 | mag--; | |
379 | if (mag == 0) | |
e67d6049 | 380 | sign = zero; |
3e132790 MM |
381 | } else { |
382 | mag++; | |
383 | sign = negative; | |
e67d6049 MM |
384 | } |
385 | } | |
386 | ||
387 | // Postfix decrement: same as prefix | |
388 | void BigInteger::operator --(int) { | |
389 | operator --(); | |
390 | } | |
391 |