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 | 15 | case zero: |
cb2f0c28 MM |
16 | if (!mag.isZero()) |
17 | throw "BigInteger::BigInteger(const Blk *, Index, Sign): Cannot use a sign of zero with a nonzero magnitude"; | |
18 | sign = zero; | |
19 | break; | |
3e132790 MM |
20 | case positive: |
21 | case negative: | |
cb2f0c28 | 22 | // If the magnitude is zero, force the sign to zero. |
3e132790 | 23 | sign = mag.isZero() ? zero : s; |
e67d6049 | 24 | break; |
3e132790 | 25 | default: |
cb2f0c28 MM |
26 | /* g++ seems to be optimizing out this case on the assumption |
27 | * that the sign is a valid member of the enumeration. Oh well. */ | |
3e132790 | 28 | throw "BigInteger::BigInteger(const Blk *, Index, Sign): Invalid sign"; |
e67d6049 MM |
29 | } |
30 | } | |
31 | ||
3e132790 | 32 | BigInteger::BigInteger(const BigUnsigned &x, Sign s) : mag(x) { |
e67d6049 | 33 | switch (s) { |
3e132790 | 34 | case zero: |
cb2f0c28 MM |
35 | if (!mag.isZero()) |
36 | throw "BigInteger::BigInteger(const BigUnsigned &, Sign): Cannot use a sign of zero with a nonzero magnitude"; | |
37 | sign = zero; | |
38 | break; | |
3e132790 MM |
39 | case positive: |
40 | case negative: | |
cb2f0c28 | 41 | // If the magnitude is zero, force the sign to zero. |
3e132790 | 42 | sign = mag.isZero() ? zero : s; |
e67d6049 | 43 | break; |
3e132790 | 44 | default: |
cb2f0c28 MM |
45 | /* g++ seems to be optimizing out this case on the assumption |
46 | * that the sign is a valid member of the enumeration. Oh well. */ | |
47 | throw "BigInteger::BigInteger(const BigUnsigned &, Sign): Invalid sign"; | |
e67d6049 MM |
48 | } |
49 | } | |
50 | ||
3e132790 MM |
51 | /* CONSTRUCTION FROM PRIMITIVE INTEGERS |
52 | * Same idea as in BigUnsigned.cc, except that negative input results in a | |
53 | * negative BigInteger instead of an exception. */ | |
e67d6049 | 54 | |
3e132790 | 55 | // Done longhand to let us use initialization. |
83a639e6 MM |
56 | BigInteger::BigInteger(unsigned long x) : mag(x) { sign = mag.isZero() ? zero : positive; } |
57 | BigInteger::BigInteger(unsigned int x) : mag(x) { sign = mag.isZero() ? zero : positive; } | |
58 | BigInteger::BigInteger(unsigned short x) : mag(x) { sign = mag.isZero() ? zero : positive; } | |
e67d6049 | 59 | |
3e132790 | 60 | // For signed input, determine the desired magnitude and sign separately. |
e67d6049 | 61 | |
3e132790 MM |
62 | namespace { |
63 | template <class X, class UX> | |
64 | BigInteger::Blk magOf(X x) { | |
65 | /* UX(...) cast needed to stop short(-2^15), which negates to | |
66 | * itself, from sign-extending in the conversion to Blk. */ | |
67 | return BigInteger::Blk(x < 0 ? UX(-x) : x); | |
68 | } | |
69 | template <class X> | |
70 | BigInteger::Sign signOf(X x) { | |
71 | return (x == 0) ? BigInteger::zero | |
72 | : (x > 0) ? BigInteger::positive | |
73 | : BigInteger::negative; | |
e67d6049 MM |
74 | } |
75 | } | |
76 | ||
83a639e6 MM |
77 | BigInteger::BigInteger(long x) : sign(signOf(x)), mag(magOf<long , unsigned long >(x)) {} |
78 | BigInteger::BigInteger(int x) : sign(signOf(x)), mag(magOf<int , unsigned int >(x)) {} | |
79 | BigInteger::BigInteger(short x) : sign(signOf(x)), mag(magOf<short, unsigned short>(x)) {} | |
3e132790 MM |
80 | |
81 | // CONVERSION TO PRIMITIVE INTEGERS | |
82 | ||
83 | /* Reuse BigUnsigned's conversion to an unsigned primitive integer. | |
84 | * The friend is a separate function rather than | |
85 | * BigInteger::convertToUnsignedPrimitive to avoid requiring BigUnsigned to | |
86 | * declare BigInteger. */ | |
87 | template <class X> | |
88 | inline X convertBigUnsignedToPrimitiveAccess(const BigUnsigned &a) { | |
89 | return a.convertToPrimitive<X>(); | |
e67d6049 MM |
90 | } |
91 | ||
3e132790 MM |
92 | template <class X> |
93 | X BigInteger::convertToUnsignedPrimitive() const { | |
94 | if (sign == negative) | |
95 | throw "BigInteger::to<Primitive>: " | |
96 | "Cannot convert a negative integer to an unsigned type"; | |
97 | else | |
98 | return convertBigUnsignedToPrimitiveAccess<X>(mag); | |
e67d6049 MM |
99 | } |
100 | ||
3e132790 MM |
101 | /* Similar to BigUnsigned::convertToPrimitive, but split into two cases for |
102 | * nonnegative and negative numbers. */ | |
103 | template <class X, class UX> | |
104 | X BigInteger::convertToSignedPrimitive() const { | |
105 | if (sign == zero) | |
e67d6049 | 106 | return 0; |
3e132790 MM |
107 | else if (mag.getLength() == 1) { |
108 | // The single block might fit in an X. Try the conversion. | |
109 | Blk b = mag.getBlock(0); | |
110 | if (sign == positive) { | |
111 | X x = X(b); | |
112 | if (x >= 0 && Blk(x) == b) | |
113 | return x; | |
114 | } else { | |
115 | X x = -X(b); | |
116 | /* UX(...) needed to avoid rejecting conversion of | |
117 | * -2^15 to a short. */ | |
118 | if (x < 0 && Blk(UX(-x)) == b) | |
119 | return x; | |
120 | } | |
121 | // Otherwise fall through. | |
e67d6049 | 122 | } |
3e132790 MM |
123 | throw "BigInteger::to<Primitive>: " |
124 | "Value is too big to fit in the requested type"; | |
e67d6049 MM |
125 | } |
126 | ||
83a639e6 MM |
127 | unsigned long BigInteger::toUnsignedLong () const { return convertToUnsignedPrimitive<unsigned long > (); } |
128 | unsigned int BigInteger::toUnsignedInt () const { return convertToUnsignedPrimitive<unsigned int > (); } | |
129 | unsigned short BigInteger::toUnsignedShort() const { return convertToUnsignedPrimitive<unsigned short> (); } | |
130 | long BigInteger::toLong () const { return convertToSignedPrimitive <long , unsigned long> (); } | |
131 | int BigInteger::toInt () const { return convertToSignedPrimitive <int , unsigned int> (); } | |
132 | short BigInteger::toShort () const { return convertToSignedPrimitive <short, unsigned short>(); } | |
e67d6049 MM |
133 | |
134 | // COMPARISON | |
135 | BigInteger::CmpRes BigInteger::compareTo(const BigInteger &x) const { | |
136 | // A greater sign implies a greater number | |
137 | if (sign < x.sign) | |
138 | return less; | |
139 | else if (sign > x.sign) | |
140 | return greater; | |
141 | else switch (sign) { | |
142 | // If the signs are the same... | |
3e132790 | 143 | case zero: |
e67d6049 | 144 | return equal; // Two zeros are equal |
3e132790 | 145 | case positive: |
e67d6049 | 146 | // Compare the magnitudes |
3e132790 MM |
147 | return mag.compareTo(x.mag); |
148 | case negative: | |
e67d6049 | 149 | // Compare the magnitudes, but return the opposite result |
3e132790 MM |
150 | return CmpRes(-mag.compareTo(x.mag)); |
151 | default: | |
152 | throw "BigInteger internal error"; | |
e67d6049 MM |
153 | } |
154 | } | |
155 | ||
3e132790 MM |
156 | /* COPY-LESS OPERATIONS |
157 | * These do some messing around to determine the sign of the result, | |
158 | * then call one of BigUnsigned's copy-less operations. */ | |
e67d6049 | 159 | |
8c16728a | 160 | // See remarks about aliased calls in BigUnsigned.cc . |
a8e1d2a4 | 161 | #define DTRT_ALIASED(cond, op) \ |
8c16728a MM |
162 | if (cond) { \ |
163 | BigInteger tmpThis; \ | |
164 | tmpThis.op; \ | |
165 | *this = tmpThis; \ | |
166 | return; \ | |
167 | } | |
168 | ||
e67d6049 | 169 | void BigInteger::add(const BigInteger &a, const BigInteger &b) { |
a8e1d2a4 | 170 | DTRT_ALIASED(this == &a || this == &b, add(a, b)); |
e67d6049 MM |
171 | // If one argument is zero, copy the other. |
172 | if (a.sign == zero) | |
173 | operator =(b); | |
174 | else if (b.sign == zero) | |
175 | operator =(a); | |
176 | // If the arguments have the same sign, take the | |
177 | // common sign and add their magnitudes. | |
178 | else if (a.sign == b.sign) { | |
179 | sign = a.sign; | |
3e132790 | 180 | mag.add(a.mag, b.mag); |
e67d6049 MM |
181 | } else { |
182 | // Otherwise, their magnitudes must be compared. | |
3e132790 MM |
183 | switch (a.mag.compareTo(b.mag)) { |
184 | case equal: | |
e67d6049 | 185 | // If their magnitudes are the same, copy zero. |
3e132790 | 186 | mag = 0; |
e67d6049 MM |
187 | sign = zero; |
188 | break; | |
189 | // Otherwise, take the sign of the greater, and subtract | |
190 | // the lesser magnitude from the greater magnitude. | |
3e132790 | 191 | case greater: |
e67d6049 | 192 | sign = a.sign; |
3e132790 | 193 | mag.subtract(a.mag, b.mag); |
e67d6049 | 194 | break; |
3e132790 | 195 | case less: |
e67d6049 | 196 | sign = b.sign; |
3e132790 | 197 | mag.subtract(b.mag, a.mag); |
e67d6049 MM |
198 | break; |
199 | } | |
200 | } | |
201 | } | |
202 | ||
e67d6049 MM |
203 | void BigInteger::subtract(const BigInteger &a, const BigInteger &b) { |
204 | // Notice that this routine is identical to BigInteger::add, | |
205 | // if one replaces b.sign by its opposite. | |
a8e1d2a4 | 206 | DTRT_ALIASED(this == &a || this == &b, subtract(a, b)); |
e67d6049 MM |
207 | // If a is zero, copy b and flip its sign. If b is zero, copy a. |
208 | if (a.sign == zero) { | |
3e132790 | 209 | mag = b.mag; |
f316def7 MM |
210 | // Take the negative of _b_'s, sign, not ours. |
211 | // Bug pointed out by Sam Larkin on 2005.03.30. | |
212 | sign = Sign(-b.sign); | |
e67d6049 | 213 | } else if (b.sign == zero) |
f316def7 | 214 | operator =(a); |
e67d6049 MM |
215 | // If their signs differ, take a.sign and add the magnitudes. |
216 | else if (a.sign != b.sign) { | |
217 | sign = a.sign; | |
3e132790 | 218 | mag.add(a.mag, b.mag); |
e67d6049 MM |
219 | } else { |
220 | // Otherwise, their magnitudes must be compared. | |
3e132790 | 221 | switch (a.mag.compareTo(b.mag)) { |
e67d6049 | 222 | // If their magnitudes are the same, copy zero. |
3e132790 MM |
223 | case equal: |
224 | mag = 0; | |
e67d6049 MM |
225 | sign = zero; |
226 | break; | |
227 | // If a's magnitude is greater, take a.sign and | |
228 | // subtract a from b. | |
3e132790 | 229 | case greater: |
e67d6049 | 230 | sign = a.sign; |
3e132790 | 231 | mag.subtract(a.mag, b.mag); |
e67d6049 MM |
232 | break; |
233 | // If b's magnitude is greater, take the opposite | |
234 | // of b.sign and subtract b from a. | |
3e132790 | 235 | case less: |
e67d6049 | 236 | sign = Sign(-b.sign); |
3e132790 | 237 | mag.subtract(b.mag, a.mag); |
e67d6049 MM |
238 | break; |
239 | } | |
240 | } | |
241 | } | |
242 | ||
e67d6049 | 243 | void BigInteger::multiply(const BigInteger &a, const BigInteger &b) { |
a8e1d2a4 | 244 | DTRT_ALIASED(this == &a || this == &b, multiply(a, b)); |
e67d6049 MM |
245 | // If one object is zero, copy zero and return. |
246 | if (a.sign == zero || b.sign == zero) { | |
247 | sign = zero; | |
3e132790 | 248 | mag = 0; |
e67d6049 MM |
249 | return; |
250 | } | |
251 | // If the signs of the arguments are the same, the result | |
252 | // is positive, otherwise it is negative. | |
253 | sign = (a.sign == b.sign) ? positive : negative; | |
254 | // Multiply the magnitudes. | |
3e132790 | 255 | mag.multiply(a.mag, b.mag); |
e67d6049 MM |
256 | } |
257 | ||
05780f4b | 258 | /* |
6e1e0f2f MM |
259 | * DIVISION WITH REMAINDER |
260 | * Please read the comments before the definition of | |
261 | * `BigUnsigned::divideWithRemainder' in `BigUnsigned.cc' for lots of | |
262 | * information you should know before reading this function. | |
263 | * | |
264 | * Following Knuth, I decree that x / y is to be | |
265 | * 0 if y==0 and floor(real-number x / y) if y!=0. | |
266 | * Then x % y shall be x - y*(integer x / y). | |
267 | * | |
268 | * Note that x = y * (x / y) + (x % y) always holds. | |
269 | * In addition, (x % y) is from 0 to y - 1 if y > 0, | |
270 | * and from -(|y| - 1) to 0 if y < 0. (x % y) = x if y = 0. | |
271 | * | |
272 | * Examples: (q = a / b, r = a % b) | |
273 | * a b q r | |
274 | * === === === === | |
275 | * 4 3 1 1 | |
276 | * -4 3 -2 2 | |
277 | * 4 -3 -2 -2 | |
278 | * -4 -3 1 -1 | |
279 | */ | |
05780f4b | 280 | void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) { |
8c16728a MM |
281 | // Defend against aliased calls; |
282 | // same idea as in BigUnsigned::divideWithRemainder . | |
283 | if (this == &q) | |
284 | throw "BigInteger::divideWithRemainder: Cannot write quotient and remainder into the same variable"; | |
285 | if (this == &b || &q == &b) { | |
286 | BigInteger tmpB(b); | |
287 | divideWithRemainder(tmpB, q); | |
288 | return; | |
289 | } | |
5ff40cf5 | 290 | |
05780f4b MM |
291 | // Division by zero gives quotient 0 and remainder *this |
292 | if (b.sign == zero) { | |
3e132790 | 293 | q.mag = 0; |
05780f4b | 294 | q.sign = zero; |
e67d6049 MM |
295 | return; |
296 | } | |
05780f4b MM |
297 | // 0 / b gives quotient 0 and remainder 0 |
298 | if (sign == zero) { | |
3e132790 | 299 | q.mag = 0; |
05780f4b | 300 | q.sign = zero; |
e67d6049 MM |
301 | return; |
302 | } | |
5ff40cf5 | 303 | |
05780f4b | 304 | // Here *this != 0, b != 0. |
5ff40cf5 | 305 | |
05780f4b MM |
306 | // Do the operands have the same sign? |
307 | if (sign == b.sign) { | |
308 | // Yes: easy case. Quotient is zero or positive. | |
309 | q.sign = positive; | |
310 | } else { | |
311 | // No: harder case. Quotient is negative. | |
312 | q.sign = negative; | |
313 | // Decrease the magnitude of the dividend by one. | |
3e132790 | 314 | mag--; |
05780f4b | 315 | /* |
6e1e0f2f MM |
316 | * We tinker with the dividend before and with the |
317 | * quotient and remainder after so that the result | |
318 | * comes out right. To see why it works, consider the following | |
319 | * list of examples, where A is the magnitude-decreased | |
320 | * a, Q and R are the results of BigUnsigned division | |
321 | * with remainder on A and |b|, and q and r are the | |
322 | * final results we want: | |
323 | * | |
324 | * a A b Q R q r | |
325 | * -3 -2 3 0 2 -1 0 | |
326 | * -4 -3 3 1 0 -2 2 | |
327 | * -5 -4 3 1 1 -2 1 | |
328 | * -6 -5 3 1 2 -2 0 | |
329 | * | |
330 | * It appears that we need a total of 3 corrections: | |
331 | * Decrease the magnitude of a to get A. Increase the | |
332 | * magnitude of Q to get q (and make it negative). | |
333 | * Find r = (b - 1) - R and give it the desired sign. | |
334 | */ | |
05780f4b | 335 | } |
5ff40cf5 | 336 | |
05780f4b | 337 | // Divide the magnitudes. |
3e132790 | 338 | mag.divideWithRemainder(b.mag, q.mag); |
5ff40cf5 | 339 | |
05780f4b MM |
340 | if (sign != b.sign) { |
341 | // More for the harder case (as described): | |
342 | // Increase the magnitude of the quotient by one. | |
3e132790 | 343 | q.mag++; |
05780f4b | 344 | // Modify the remainder. |
3e132790 MM |
345 | mag.subtract(b.mag, mag); |
346 | mag--; | |
05780f4b | 347 | } |
5ff40cf5 | 348 | |
05780f4b MM |
349 | // Sign of the remainder is always the sign of the divisor b. |
350 | sign = b.sign; | |
5ff40cf5 | 351 | |
05780f4b | 352 | // Set signs to zero as necessary. (Thanks David Allen!) |
3e132790 | 353 | if (mag.isZero()) |
e67d6049 | 354 | sign = zero; |
3e132790 | 355 | if (q.mag.isZero()) |
05780f4b | 356 | q.sign = zero; |
5ff40cf5 | 357 | |
05780f4b | 358 | // WHEW!!! |
e67d6049 MM |
359 | } |
360 | ||
361 | // Negation | |
362 | void BigInteger::negate(const BigInteger &a) { | |
a8e1d2a4 | 363 | DTRT_ALIASED(this == &a, negate(a)); |
e67d6049 | 364 | // Copy a's magnitude |
3e132790 | 365 | mag = a.mag; |
e67d6049 MM |
366 | // Copy the opposite of a.sign |
367 | sign = Sign(-a.sign); | |
368 | } | |
369 | ||
370 | // INCREMENT/DECREMENT OPERATORS | |
371 | ||
372 | // Prefix increment | |
373 | void BigInteger::operator ++() { | |
3e132790 MM |
374 | if (sign == negative) { |
375 | mag--; | |
376 | if (mag == 0) | |
e67d6049 | 377 | sign = zero; |
3e132790 MM |
378 | } else { |
379 | mag++; | |
380 | sign = positive; // if not already | |
e67d6049 MM |
381 | } |
382 | } | |
383 | ||
384 | // Postfix increment: same as prefix | |
385 | void BigInteger::operator ++(int) { | |
386 | operator ++(); | |
387 | } | |
388 | ||
389 | // Prefix decrement | |
390 | void BigInteger::operator --() { | |
3e132790 MM |
391 | if (sign == positive) { |
392 | mag--; | |
393 | if (mag == 0) | |
e67d6049 | 394 | sign = zero; |
3e132790 MM |
395 | } else { |
396 | mag++; | |
397 | sign = negative; | |
e67d6049 MM |
398 | } |
399 | } | |
400 | ||
401 | // Postfix decrement: same as prefix | |
402 | void BigInteger::operator --(int) { | |
403 | operator --(); | |
404 | } | |
405 |