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 MM |
41 | // Done longhand to let us use initialization. |
42 | BigInteger::BigInteger(unsigned long x) : mag(x) { | |
43 | sign = mag.isZero() ? zero : positive; | |
e67d6049 | 44 | } |
3e132790 MM |
45 | BigInteger::BigInteger(unsigned int x) : mag(x) { |
46 | sign = mag.isZero() ? zero : positive; | |
e67d6049 | 47 | } |
3e132790 MM |
48 | BigInteger::BigInteger(unsigned short x) : mag(x) { |
49 | sign = mag.isZero() ? zero : positive; | |
e67d6049 MM |
50 | } |
51 | ||
3e132790 | 52 | // For signed input, determine the desired magnitude and sign separately. |
e67d6049 | 53 | |
3e132790 MM |
54 | namespace { |
55 | template <class X, class UX> | |
56 | BigInteger::Blk magOf(X x) { | |
57 | /* UX(...) cast needed to stop short(-2^15), which negates to | |
58 | * itself, from sign-extending in the conversion to Blk. */ | |
59 | return BigInteger::Blk(x < 0 ? UX(-x) : x); | |
60 | } | |
61 | template <class X> | |
62 | BigInteger::Sign signOf(X x) { | |
63 | return (x == 0) ? BigInteger::zero | |
64 | : (x > 0) ? BigInteger::positive | |
65 | : BigInteger::negative; | |
e67d6049 MM |
66 | } |
67 | } | |
68 | ||
3e132790 MM |
69 | BigInteger::BigInteger(long x) : sign(signOf(x)), |
70 | mag(magOf<long, unsigned long>(x)) {} | |
71 | BigInteger::BigInteger(int x) : sign(signOf(x)), | |
72 | mag(magOf<int, unsigned int>(x)) {} | |
73 | BigInteger::BigInteger(short x) : sign(signOf(x)), | |
74 | mag(magOf<short, unsigned short>(x)) {} | |
75 | ||
76 | // CONVERSION TO PRIMITIVE INTEGERS | |
77 | ||
78 | /* Reuse BigUnsigned's conversion to an unsigned primitive integer. | |
79 | * The friend is a separate function rather than | |
80 | * BigInteger::convertToUnsignedPrimitive to avoid requiring BigUnsigned to | |
81 | * declare BigInteger. */ | |
82 | template <class X> | |
83 | inline X convertBigUnsignedToPrimitiveAccess(const BigUnsigned &a) { | |
84 | return a.convertToPrimitive<X>(); | |
e67d6049 MM |
85 | } |
86 | ||
3e132790 MM |
87 | template <class X> |
88 | X BigInteger::convertToUnsignedPrimitive() const { | |
89 | if (sign == negative) | |
90 | throw "BigInteger::to<Primitive>: " | |
91 | "Cannot convert a negative integer to an unsigned type"; | |
92 | else | |
93 | return convertBigUnsignedToPrimitiveAccess<X>(mag); | |
e67d6049 MM |
94 | } |
95 | ||
3e132790 MM |
96 | /* Similar to BigUnsigned::convertToPrimitive, but split into two cases for |
97 | * nonnegative and negative numbers. */ | |
98 | template <class X, class UX> | |
99 | X BigInteger::convertToSignedPrimitive() const { | |
100 | if (sign == zero) | |
e67d6049 | 101 | return 0; |
3e132790 MM |
102 | else if (mag.getLength() == 1) { |
103 | // The single block might fit in an X. Try the conversion. | |
104 | Blk b = mag.getBlock(0); | |
105 | if (sign == positive) { | |
106 | X x = X(b); | |
107 | if (x >= 0 && Blk(x) == b) | |
108 | return x; | |
109 | } else { | |
110 | X x = -X(b); | |
111 | /* UX(...) needed to avoid rejecting conversion of | |
112 | * -2^15 to a short. */ | |
113 | if (x < 0 && Blk(UX(-x)) == b) | |
114 | return x; | |
115 | } | |
116 | // Otherwise fall through. | |
e67d6049 | 117 | } |
3e132790 MM |
118 | throw "BigInteger::to<Primitive>: " |
119 | "Value is too big to fit in the requested type"; | |
e67d6049 MM |
120 | } |
121 | ||
3e132790 MM |
122 | unsigned long BigInteger::toUnsignedLong() const { |
123 | return convertToUnsignedPrimitive<unsigned long>(); | |
e67d6049 | 124 | } |
3e132790 MM |
125 | unsigned int BigInteger::toUnsignedInt() const { |
126 | return convertToUnsignedPrimitive<unsigned int>(); | |
e67d6049 | 127 | } |
3e132790 MM |
128 | unsigned short BigInteger::toUnsignedShort() const { |
129 | return convertToUnsignedPrimitive<unsigned short>(); | |
e67d6049 | 130 | } |
3e132790 MM |
131 | long BigInteger::toLong() const { |
132 | return convertToSignedPrimitive<long, unsigned long>(); | |
e67d6049 | 133 | } |
3e132790 MM |
134 | int BigInteger::toInt() const { |
135 | return convertToSignedPrimitive<int, unsigned int>(); | |
136 | } | |
137 | short BigInteger::toShort() const { | |
138 | return convertToSignedPrimitive<short, unsigned short>(); | |
e67d6049 MM |
139 | } |
140 | ||
141 | // COMPARISON | |
142 | BigInteger::CmpRes BigInteger::compareTo(const BigInteger &x) const { | |
143 | // A greater sign implies a greater number | |
144 | if (sign < x.sign) | |
145 | return less; | |
146 | else if (sign > x.sign) | |
147 | return greater; | |
148 | else switch (sign) { | |
149 | // If the signs are the same... | |
3e132790 | 150 | case zero: |
e67d6049 | 151 | return equal; // Two zeros are equal |
3e132790 | 152 | case positive: |
e67d6049 | 153 | // Compare the magnitudes |
3e132790 MM |
154 | return mag.compareTo(x.mag); |
155 | case negative: | |
e67d6049 | 156 | // Compare the magnitudes, but return the opposite result |
3e132790 MM |
157 | return CmpRes(-mag.compareTo(x.mag)); |
158 | default: | |
159 | throw "BigInteger internal error"; | |
e67d6049 MM |
160 | } |
161 | } | |
162 | ||
3e132790 MM |
163 | /* COPY-LESS OPERATIONS |
164 | * These do some messing around to determine the sign of the result, | |
165 | * then call one of BigUnsigned's copy-less operations. */ | |
e67d6049 | 166 | |
8c16728a | 167 | // See remarks about aliased calls in BigUnsigned.cc . |
a8e1d2a4 | 168 | #define DTRT_ALIASED(cond, op) \ |
8c16728a MM |
169 | if (cond) { \ |
170 | BigInteger tmpThis; \ | |
171 | tmpThis.op; \ | |
172 | *this = tmpThis; \ | |
173 | return; \ | |
174 | } | |
175 | ||
e67d6049 | 176 | void BigInteger::add(const BigInteger &a, const BigInteger &b) { |
a8e1d2a4 | 177 | DTRT_ALIASED(this == &a || this == &b, add(a, b)); |
e67d6049 MM |
178 | // If one argument is zero, copy the other. |
179 | if (a.sign == zero) | |
180 | operator =(b); | |
181 | else if (b.sign == zero) | |
182 | operator =(a); | |
183 | // If the arguments have the same sign, take the | |
184 | // common sign and add their magnitudes. | |
185 | else if (a.sign == b.sign) { | |
186 | sign = a.sign; | |
3e132790 | 187 | mag.add(a.mag, b.mag); |
e67d6049 MM |
188 | } else { |
189 | // Otherwise, their magnitudes must be compared. | |
3e132790 MM |
190 | switch (a.mag.compareTo(b.mag)) { |
191 | case equal: | |
e67d6049 | 192 | // If their magnitudes are the same, copy zero. |
3e132790 | 193 | mag = 0; |
e67d6049 MM |
194 | sign = zero; |
195 | break; | |
196 | // Otherwise, take the sign of the greater, and subtract | |
197 | // the lesser magnitude from the greater magnitude. | |
3e132790 | 198 | case greater: |
e67d6049 | 199 | sign = a.sign; |
3e132790 | 200 | mag.subtract(a.mag, b.mag); |
e67d6049 | 201 | break; |
3e132790 | 202 | case less: |
e67d6049 | 203 | sign = b.sign; |
3e132790 | 204 | mag.subtract(b.mag, a.mag); |
e67d6049 MM |
205 | break; |
206 | } | |
207 | } | |
208 | } | |
209 | ||
e67d6049 MM |
210 | void BigInteger::subtract(const BigInteger &a, const BigInteger &b) { |
211 | // Notice that this routine is identical to BigInteger::add, | |
212 | // if one replaces b.sign by its opposite. | |
a8e1d2a4 | 213 | DTRT_ALIASED(this == &a || this == &b, subtract(a, b)); |
e67d6049 MM |
214 | // If a is zero, copy b and flip its sign. If b is zero, copy a. |
215 | if (a.sign == zero) { | |
3e132790 | 216 | mag = b.mag; |
f316def7 MM |
217 | // Take the negative of _b_'s, sign, not ours. |
218 | // Bug pointed out by Sam Larkin on 2005.03.30. | |
219 | sign = Sign(-b.sign); | |
e67d6049 | 220 | } else if (b.sign == zero) |
f316def7 | 221 | operator =(a); |
e67d6049 MM |
222 | // If their signs differ, take a.sign and add the magnitudes. |
223 | else if (a.sign != b.sign) { | |
224 | sign = a.sign; | |
3e132790 | 225 | mag.add(a.mag, b.mag); |
e67d6049 MM |
226 | } else { |
227 | // Otherwise, their magnitudes must be compared. | |
3e132790 | 228 | switch (a.mag.compareTo(b.mag)) { |
e67d6049 | 229 | // If their magnitudes are the same, copy zero. |
3e132790 MM |
230 | case equal: |
231 | mag = 0; | |
e67d6049 MM |
232 | sign = zero; |
233 | break; | |
234 | // If a's magnitude is greater, take a.sign and | |
235 | // subtract a from b. | |
3e132790 | 236 | case greater: |
e67d6049 | 237 | sign = a.sign; |
3e132790 | 238 | mag.subtract(a.mag, b.mag); |
e67d6049 MM |
239 | break; |
240 | // If b's magnitude is greater, take the opposite | |
241 | // of b.sign and subtract b from a. | |
3e132790 | 242 | case less: |
e67d6049 | 243 | sign = Sign(-b.sign); |
3e132790 | 244 | mag.subtract(b.mag, a.mag); |
e67d6049 MM |
245 | break; |
246 | } | |
247 | } | |
248 | } | |
249 | ||
e67d6049 | 250 | void BigInteger::multiply(const BigInteger &a, const BigInteger &b) { |
a8e1d2a4 | 251 | DTRT_ALIASED(this == &a || this == &b, multiply(a, b)); |
e67d6049 MM |
252 | // If one object is zero, copy zero and return. |
253 | if (a.sign == zero || b.sign == zero) { | |
254 | sign = zero; | |
3e132790 | 255 | mag = 0; |
e67d6049 MM |
256 | return; |
257 | } | |
258 | // If the signs of the arguments are the same, the result | |
259 | // is positive, otherwise it is negative. | |
260 | sign = (a.sign == b.sign) ? positive : negative; | |
261 | // Multiply the magnitudes. | |
3e132790 | 262 | mag.multiply(a.mag, b.mag); |
e67d6049 MM |
263 | } |
264 | ||
05780f4b | 265 | /* |
6e1e0f2f MM |
266 | * DIVISION WITH REMAINDER |
267 | * Please read the comments before the definition of | |
268 | * `BigUnsigned::divideWithRemainder' in `BigUnsigned.cc' for lots of | |
269 | * information you should know before reading this function. | |
270 | * | |
271 | * Following Knuth, I decree that x / y is to be | |
272 | * 0 if y==0 and floor(real-number x / y) if y!=0. | |
273 | * Then x % y shall be x - y*(integer x / y). | |
274 | * | |
275 | * Note that x = y * (x / y) + (x % y) always holds. | |
276 | * In addition, (x % y) is from 0 to y - 1 if y > 0, | |
277 | * and from -(|y| - 1) to 0 if y < 0. (x % y) = x if y = 0. | |
278 | * | |
279 | * Examples: (q = a / b, r = a % b) | |
280 | * a b q r | |
281 | * === === === === | |
282 | * 4 3 1 1 | |
283 | * -4 3 -2 2 | |
284 | * 4 -3 -2 -2 | |
285 | * -4 -3 1 -1 | |
286 | */ | |
05780f4b | 287 | void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) { |
8c16728a MM |
288 | // Defend against aliased calls; |
289 | // same idea as in BigUnsigned::divideWithRemainder . | |
290 | if (this == &q) | |
291 | throw "BigInteger::divideWithRemainder: Cannot write quotient and remainder into the same variable"; | |
292 | if (this == &b || &q == &b) { | |
293 | BigInteger tmpB(b); | |
294 | divideWithRemainder(tmpB, q); | |
295 | return; | |
296 | } | |
5ff40cf5 | 297 | |
05780f4b MM |
298 | // Division by zero gives quotient 0 and remainder *this |
299 | if (b.sign == zero) { | |
3e132790 | 300 | q.mag = 0; |
05780f4b | 301 | q.sign = zero; |
e67d6049 MM |
302 | return; |
303 | } | |
05780f4b MM |
304 | // 0 / b gives quotient 0 and remainder 0 |
305 | if (sign == zero) { | |
3e132790 | 306 | q.mag = 0; |
05780f4b | 307 | q.sign = zero; |
e67d6049 MM |
308 | return; |
309 | } | |
5ff40cf5 | 310 | |
05780f4b | 311 | // Here *this != 0, b != 0. |
5ff40cf5 | 312 | |
05780f4b MM |
313 | // Do the operands have the same sign? |
314 | if (sign == b.sign) { | |
315 | // Yes: easy case. Quotient is zero or positive. | |
316 | q.sign = positive; | |
317 | } else { | |
318 | // No: harder case. Quotient is negative. | |
319 | q.sign = negative; | |
320 | // Decrease the magnitude of the dividend by one. | |
3e132790 | 321 | mag--; |
05780f4b | 322 | /* |
6e1e0f2f MM |
323 | * We tinker with the dividend before and with the |
324 | * quotient and remainder after so that the result | |
325 | * comes out right. To see why it works, consider the following | |
326 | * list of examples, where A is the magnitude-decreased | |
327 | * a, Q and R are the results of BigUnsigned division | |
328 | * with remainder on A and |b|, and q and r are the | |
329 | * final results we want: | |
330 | * | |
331 | * a A b Q R q r | |
332 | * -3 -2 3 0 2 -1 0 | |
333 | * -4 -3 3 1 0 -2 2 | |
334 | * -5 -4 3 1 1 -2 1 | |
335 | * -6 -5 3 1 2 -2 0 | |
336 | * | |
337 | * It appears that we need a total of 3 corrections: | |
338 | * Decrease the magnitude of a to get A. Increase the | |
339 | * magnitude of Q to get q (and make it negative). | |
340 | * Find r = (b - 1) - R and give it the desired sign. | |
341 | */ | |
05780f4b | 342 | } |
5ff40cf5 | 343 | |
05780f4b | 344 | // Divide the magnitudes. |
3e132790 | 345 | mag.divideWithRemainder(b.mag, q.mag); |
5ff40cf5 | 346 | |
05780f4b MM |
347 | if (sign != b.sign) { |
348 | // More for the harder case (as described): | |
349 | // Increase the magnitude of the quotient by one. | |
3e132790 | 350 | q.mag++; |
05780f4b | 351 | // Modify the remainder. |
3e132790 MM |
352 | mag.subtract(b.mag, mag); |
353 | mag--; | |
05780f4b | 354 | } |
5ff40cf5 | 355 | |
05780f4b MM |
356 | // Sign of the remainder is always the sign of the divisor b. |
357 | sign = b.sign; | |
5ff40cf5 | 358 | |
05780f4b | 359 | // Set signs to zero as necessary. (Thanks David Allen!) |
3e132790 | 360 | if (mag.isZero()) |
e67d6049 | 361 | sign = zero; |
3e132790 | 362 | if (q.mag.isZero()) |
05780f4b | 363 | q.sign = zero; |
5ff40cf5 | 364 | |
05780f4b | 365 | // WHEW!!! |
e67d6049 MM |
366 | } |
367 | ||
368 | // Negation | |
369 | void BigInteger::negate(const BigInteger &a) { | |
a8e1d2a4 | 370 | DTRT_ALIASED(this == &a, negate(a)); |
e67d6049 | 371 | // Copy a's magnitude |
3e132790 | 372 | mag = a.mag; |
e67d6049 MM |
373 | // Copy the opposite of a.sign |
374 | sign = Sign(-a.sign); | |
375 | } | |
376 | ||
377 | // INCREMENT/DECREMENT OPERATORS | |
378 | ||
379 | // Prefix increment | |
380 | void BigInteger::operator ++() { | |
3e132790 MM |
381 | if (sign == negative) { |
382 | mag--; | |
383 | if (mag == 0) | |
e67d6049 | 384 | sign = zero; |
3e132790 MM |
385 | } else { |
386 | mag++; | |
387 | sign = positive; // if not already | |
e67d6049 MM |
388 | } |
389 | } | |
390 | ||
391 | // Postfix increment: same as prefix | |
392 | void BigInteger::operator ++(int) { | |
393 | operator ++(); | |
394 | } | |
395 | ||
396 | // Prefix decrement | |
397 | void BigInteger::operator --() { | |
3e132790 MM |
398 | if (sign == positive) { |
399 | mag--; | |
400 | if (mag == 0) | |
e67d6049 | 401 | sign = zero; |
3e132790 MM |
402 | } else { |
403 | mag++; | |
404 | sign = negative; | |
e67d6049 MM |
405 | } |
406 | } | |
407 | ||
408 | // Postfix decrement: same as prefix | |
409 | void BigInteger::operator --(int) { | |
410 | operator --(); | |
411 | } | |
412 |