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05780f4b MM |
1 | #include "BigUnsigned.hh" |
2 | ||
3e132790 | 3 | // Memory management definitions have moved to the bottom of NumberlikeArray.hh. |
05780f4b | 4 | |
83a639e6 MM |
5 | // The templates used by these constructors and converters are at the bottom of |
6 | // BigUnsigned.hh. | |
05780f4b | 7 | |
3e132790 MM |
8 | BigUnsigned::BigUnsigned(unsigned long x) { initFromPrimitive (x); } |
9 | BigUnsigned::BigUnsigned(unsigned int x) { initFromPrimitive (x); } | |
10 | BigUnsigned::BigUnsigned(unsigned short x) { initFromPrimitive (x); } | |
11 | BigUnsigned::BigUnsigned( long x) { initFromSignedPrimitive(x); } | |
12 | BigUnsigned::BigUnsigned( int x) { initFromSignedPrimitive(x); } | |
13 | BigUnsigned::BigUnsigned( short x) { initFromSignedPrimitive(x); } | |
05780f4b | 14 | |
83a639e6 MM |
15 | unsigned long BigUnsigned::toUnsignedLong () const { return convertToPrimitive <unsigned long >(); } |
16 | unsigned int BigUnsigned::toUnsignedInt () const { return convertToPrimitive <unsigned int >(); } | |
17 | unsigned short BigUnsigned::toUnsignedShort() const { return convertToPrimitive <unsigned short>(); } | |
18 | long BigUnsigned::toLong () const { return convertToSignedPrimitive< long >(); } | |
19 | int BigUnsigned::toInt () const { return convertToSignedPrimitive< int >(); } | |
20 | short BigUnsigned::toShort () const { return convertToSignedPrimitive< short>(); } | |
05780f4b | 21 | |
88dbe518 MM |
22 | // BIT/BLOCK ACCESSORS |
23 | ||
24 | void BigUnsigned::setBlock(Index i, Blk newBlock) { | |
25 | if (newBlock == 0) { | |
26 | if (i < len) { | |
27 | blk[i] = 0; | |
28 | zapLeadingZeros(); | |
29 | } | |
30 | // If i >= len, no effect. | |
31 | } else { | |
32 | if (i >= len) { | |
33 | // The nonzero block extends the number. | |
34 | allocateAndCopy(i+1); | |
35 | // Zero any added blocks that we aren't setting. | |
36 | for (Index j = len; j < i; j++) | |
37 | blk[j] = 0; | |
38 | len = i+1; | |
39 | } | |
40 | blk[i] = newBlock; | |
41 | } | |
42 | } | |
43 | ||
44 | /* Evidently the compiler wants BigUnsigned:: on the return type because, at | |
45 | * that point, it hasn't yet parsed the BigUnsigned:: on the name to get the | |
46 | * proper scope. */ | |
47 | BigUnsigned::Index BigUnsigned::bitLength() const { | |
48 | if (isZero()) | |
49 | return 0; | |
50 | else { | |
51 | Blk leftmostBlock = getBlock(len - 1); | |
52 | Index leftmostBlockLen = 0; | |
53 | while (leftmostBlock != 0) { | |
54 | leftmostBlock >>= 1; | |
55 | leftmostBlockLen++; | |
56 | } | |
57 | return leftmostBlockLen + (len - 1) * N; | |
58 | } | |
59 | } | |
60 | ||
61 | void BigUnsigned::setBit(Index bi, bool newBit) { | |
62 | Index blockI = bi / N; | |
c17afa55 | 63 | Blk block = getBlock(blockI), mask = Blk(1) << (bi % N); |
88dbe518 MM |
64 | block = newBit ? (block | mask) : (block & ~mask); |
65 | setBlock(blockI, block); | |
66 | } | |
67 | ||
05780f4b MM |
68 | // COMPARISON |
69 | BigUnsigned::CmpRes BigUnsigned::compareTo(const BigUnsigned &x) const { | |
70 | // A bigger length implies a bigger number. | |
71 | if (len < x.len) | |
72 | return less; | |
73 | else if (len > x.len) | |
74 | return greater; | |
75 | else { | |
76 | // Compare blocks one by one from left to right. | |
77 | Index i = len; | |
78 | while (i > 0) { | |
79 | i--; | |
80 | if (blk[i] == x.blk[i]) | |
81 | continue; | |
82 | else if (blk[i] > x.blk[i]) | |
83 | return greater; | |
84 | else | |
85 | return less; | |
86 | } | |
87 | // If no blocks differed, the numbers are equal. | |
88 | return equal; | |
89 | } | |
90 | } | |
91 | ||
3e132790 | 92 | // COPY-LESS OPERATIONS |
4efbb076 | 93 | |
8c16728a | 94 | /* |
3e132790 | 95 | * On most calls to copy-less operations, it's safe to read the inputs little by |
8c16728a MM |
96 | * little and write the outputs little by little. However, if one of the |
97 | * inputs is coming from the same variable into which the output is to be | |
98 | * stored (an "aliased" call), we risk overwriting the input before we read it. | |
99 | * In this case, we first compute the result into a temporary BigUnsigned | |
100 | * variable and then copy it into the requested output variable *this. | |
ef2b7c59 | 101 | * Each put-here operation uses the DTRT_ALIASED macro (Do The Right Thing on |
8c16728a MM |
102 | * aliased calls) to generate code for this check. |
103 | * | |
104 | * I adopted this approach on 2007.02.13 (see Assignment Operators in | |
105 | * BigUnsigned.hh). Before then, put-here operations rejected aliased calls | |
106 | * with an exception. I think doing the right thing is better. | |
107 | * | |
108 | * Some of the put-here operations can probably handle aliased calls safely | |
109 | * without the extra copy because (for example) they process blocks strictly | |
110 | * right-to-left. At some point I might determine which ones don't need the | |
111 | * copy, but my reasoning would need to be verified very carefully. For now | |
112 | * I'll leave in the copy. | |
113 | */ | |
ef2b7c59 | 114 | #define DTRT_ALIASED(cond, op) \ |
8c16728a MM |
115 | if (cond) { \ |
116 | BigUnsigned tmpThis; \ | |
117 | tmpThis.op; \ | |
118 | *this = tmpThis; \ | |
119 | return; \ | |
120 | } | |
121 | ||
3e132790 MM |
122 | |
123 | ||
05780f4b | 124 | void BigUnsigned::add(const BigUnsigned &a, const BigUnsigned &b) { |
ef2b7c59 | 125 | DTRT_ALIASED(this == &a || this == &b, add(a, b)); |
05780f4b MM |
126 | // If one argument is zero, copy the other. |
127 | if (a.len == 0) { | |
128 | operator =(b); | |
129 | return; | |
130 | } else if (b.len == 0) { | |
131 | operator =(a); | |
132 | return; | |
133 | } | |
4efbb076 | 134 | // Some variables... |
05780f4b MM |
135 | // Carries in and out of an addition stage |
136 | bool carryIn, carryOut; | |
137 | Blk temp; | |
138 | Index i; | |
139 | // a2 points to the longer input, b2 points to the shorter | |
140 | const BigUnsigned *a2, *b2; | |
141 | if (a.len >= b.len) { | |
142 | a2 = &a; | |
143 | b2 = &b; | |
144 | } else { | |
145 | a2 = &b; | |
146 | b2 = &a; | |
147 | } | |
148 | // Set prelimiary length and make room in this BigUnsigned | |
149 | len = a2->len + 1; | |
150 | allocate(len); | |
151 | // For each block index that is present in both inputs... | |
152 | for (i = 0, carryIn = false; i < b2->len; i++) { | |
153 | // Add input blocks | |
154 | temp = a2->blk[i] + b2->blk[i]; | |
155 | // If a rollover occurred, the result is less than either input. | |
156 | // This test is used many times in the BigUnsigned code. | |
157 | carryOut = (temp < a2->blk[i]); | |
158 | // If a carry was input, handle it | |
159 | if (carryIn) { | |
160 | temp++; | |
161 | carryOut |= (temp == 0); | |
162 | } | |
163 | blk[i] = temp; // Save the addition result | |
164 | carryIn = carryOut; // Pass the carry along | |
165 | } | |
166 | // If there is a carry left over, increase blocks until | |
167 | // one does not roll over. | |
168 | for (; i < a2->len && carryIn; i++) { | |
169 | temp = a2->blk[i] + 1; | |
170 | carryIn = (temp == 0); | |
171 | blk[i] = temp; | |
172 | } | |
173 | // If the carry was resolved but the larger number | |
174 | // still has blocks, copy them over. | |
175 | for (; i < a2->len; i++) | |
176 | blk[i] = a2->blk[i]; | |
177 | // Set the extra block if there's still a carry, decrease length otherwise | |
178 | if (carryIn) | |
179 | blk[i] = 1; | |
180 | else | |
181 | len--; | |
182 | } | |
183 | ||
05780f4b | 184 | void BigUnsigned::subtract(const BigUnsigned &a, const BigUnsigned &b) { |
ef2b7c59 | 185 | DTRT_ALIASED(this == &a || this == &b, subtract(a, b)); |
05780f4b | 186 | if (b.len == 0) { |
3e132790 | 187 | // If b is zero, copy a. |
05780f4b MM |
188 | operator =(a); |
189 | return; | |
190 | } else if (a.len < b.len) | |
3e132790 MM |
191 | // If a is shorter than b, the result is negative. |
192 | throw "BigUnsigned::subtract: " | |
193 | "Negative result in unsigned calculation"; | |
4efbb076 | 194 | // Some variables... |
05780f4b MM |
195 | bool borrowIn, borrowOut; |
196 | Blk temp; | |
197 | Index i; | |
198 | // Set preliminary length and make room | |
199 | len = a.len; | |
200 | allocate(len); | |
201 | // For each block index that is present in both inputs... | |
202 | for (i = 0, borrowIn = false; i < b.len; i++) { | |
203 | temp = a.blk[i] - b.blk[i]; | |
3e132790 MM |
204 | // If a reverse rollover occurred, |
205 | // the result is greater than the block from a. | |
05780f4b MM |
206 | borrowOut = (temp > a.blk[i]); |
207 | // Handle an incoming borrow | |
208 | if (borrowIn) { | |
209 | borrowOut |= (temp == 0); | |
210 | temp--; | |
211 | } | |
212 | blk[i] = temp; // Save the subtraction result | |
213 | borrowIn = borrowOut; // Pass the borrow along | |
214 | } | |
215 | // If there is a borrow left over, decrease blocks until | |
216 | // one does not reverse rollover. | |
217 | for (; i < a.len && borrowIn; i++) { | |
218 | borrowIn = (a.blk[i] == 0); | |
219 | blk[i] = a.blk[i] - 1; | |
220 | } | |
3e132790 MM |
221 | /* If there's still a borrow, the result is negative. |
222 | * Throw an exception, but zero out this object so as to leave it in a | |
223 | * predictable state. */ | |
05780f4b MM |
224 | if (borrowIn) { |
225 | len = 0; | |
226 | throw "BigUnsigned::subtract: Negative result in unsigned calculation"; | |
3e132790 MM |
227 | } else |
228 | // Copy over the rest of the blocks | |
229 | for (; i < a.len; i++) | |
230 | blk[i] = a.blk[i]; | |
05780f4b MM |
231 | // Zap leading zeros |
232 | zapLeadingZeros(); | |
233 | } | |
234 | ||
4efbb076 | 235 | /* |
6e1e0f2f MM |
236 | * About the multiplication and division algorithms: |
237 | * | |
3e132790 | 238 | * I searched unsucessfully for fast C++ built-in operations like the `b_0' |
6e1e0f2f MM |
239 | * and `c_0' Knuth describes in Section 4.3.1 of ``The Art of Computer |
240 | * Programming'' (replace `place' by `Blk'): | |
241 | * | |
242 | * ``b_0[:] multiplication of a one-place integer by another one-place | |
243 | * integer, giving a two-place answer; | |
244 | * | |
245 | * ``c_0[:] division of a two-place integer by a one-place integer, | |
246 | * provided that the quotient is a one-place integer, and yielding | |
247 | * also a one-place remainder.'' | |
248 | * | |
249 | * I also missed his note that ``[b]y adjusting the word size, if | |
250 | * necessary, nearly all computers will have these three operations | |
251 | * available'', so I gave up on trying to use algorithms similar to his. | |
252 | * A future version of the library might include such algorithms; I | |
253 | * would welcome contributions from others for this. | |
254 | * | |
255 | * I eventually decided to use bit-shifting algorithms. To multiply `a' | |
256 | * and `b', we zero out the result. Then, for each `1' bit in `a', we | |
257 | * shift `b' left the appropriate amount and add it to the result. | |
258 | * Similarly, to divide `a' by `b', we shift `b' left varying amounts, | |
259 | * repeatedly trying to subtract it from `a'. When we succeed, we note | |
260 | * the fact by setting a bit in the quotient. While these algorithms | |
261 | * have the same O(n^2) time complexity as Knuth's, the ``constant factor'' | |
262 | * is likely to be larger. | |
263 | * | |
264 | * Because I used these algorithms, which require single-block addition | |
265 | * and subtraction rather than single-block multiplication and division, | |
266 | * the innermost loops of all four routines are very similar. Study one | |
267 | * of them and all will become clear. | |
268 | */ | |
4efbb076 MM |
269 | |
270 | /* | |
6e1e0f2f MM |
271 | * This is a little inline function used by both the multiplication |
272 | * routine and the division routine. | |
273 | * | |
274 | * `getShiftedBlock' returns the `x'th block of `num << y'. | |
275 | * `y' may be anything from 0 to N - 1, and `x' may be anything from | |
276 | * 0 to `num.len'. | |
277 | * | |
278 | * Two things contribute to this block: | |
279 | * | |
280 | * (1) The `N - y' low bits of `num.blk[x]', shifted `y' bits left. | |
281 | * | |
282 | * (2) The `y' high bits of `num.blk[x-1]', shifted `N - y' bits right. | |
283 | * | |
284 | * But we must be careful if `x == 0' or `x == num.len', in | |
285 | * which case we should use 0 instead of (2) or (1), respectively. | |
286 | * | |
287 | * If `y == 0', then (2) contributes 0, as it should. However, | |
288 | * in some computer environments, for a reason I cannot understand, | |
289 | * `a >> b' means `a >> (b % N)'. This means `num.blk[x-1] >> (N - y)' | |
290 | * will return `num.blk[x-1]' instead of the desired 0 when `y == 0'; | |
291 | * the test `y == 0' handles this case specially. | |
292 | */ | |
4efbb076 MM |
293 | inline BigUnsigned::Blk getShiftedBlock(const BigUnsigned &num, |
294 | BigUnsigned::Index x, unsigned int y) { | |
295 | BigUnsigned::Blk part1 = (x == 0 || y == 0) ? 0 : (num.blk[x - 1] >> (BigUnsigned::N - y)); | |
296 | BigUnsigned::Blk part2 = (x == num.len) ? 0 : (num.blk[x] << y); | |
297 | return part1 | part2; | |
298 | } | |
299 | ||
05780f4b | 300 | void BigUnsigned::multiply(const BigUnsigned &a, const BigUnsigned &b) { |
ef2b7c59 | 301 | DTRT_ALIASED(this == &a || this == &b, multiply(a, b)); |
05780f4b MM |
302 | // If either a or b is zero, set to zero. |
303 | if (a.len == 0 || b.len == 0) { | |
304 | len = 0; | |
305 | return; | |
306 | } | |
4efbb076 | 307 | /* |
6e1e0f2f MM |
308 | * Overall method: |
309 | * | |
310 | * Set this = 0. | |
311 | * For each 1-bit of `a' (say the `i2'th bit of block `i'): | |
312 | * Add `b << (i blocks and i2 bits)' to *this. | |
313 | */ | |
05780f4b MM |
314 | // Variables for the calculation |
315 | Index i, j, k; | |
316 | unsigned int i2; | |
4efbb076 | 317 | Blk temp; |
05780f4b MM |
318 | bool carryIn, carryOut; |
319 | // Set preliminary length and make room | |
320 | len = a.len + b.len; | |
321 | allocate(len); | |
322 | // Zero out this object | |
323 | for (i = 0; i < len; i++) | |
324 | blk[i] = 0; | |
325 | // For each block of the first number... | |
326 | for (i = 0; i < a.len; i++) { | |
327 | // For each 1-bit of that block... | |
4efbb076 | 328 | for (i2 = 0; i2 < N; i2++) { |
26a5f52b | 329 | if ((a.blk[i] & (Blk(1) << i2)) == 0) |
05780f4b | 330 | continue; |
4efbb076 | 331 | /* |
6e1e0f2f MM |
332 | * Add b to this, shifted left i blocks and i2 bits. |
333 | * j is the index in b, and k = i + j is the index in this. | |
334 | * | |
335 | * `getShiftedBlock', a short inline function defined above, | |
336 | * is now used for the bit handling. It replaces the more | |
337 | * complex `bHigh' code, in which each run of the loop dealt | |
338 | * immediately with the low bits and saved the high bits to | |
339 | * be picked up next time. The last run of the loop used to | |
340 | * leave leftover high bits, which were handled separately. | |
341 | * Instead, this loop runs an additional time with j == b.len. | |
342 | * These changes were made on 2005.01.11. | |
343 | */ | |
4efbb076 MM |
344 | for (j = 0, k = i, carryIn = false; j <= b.len; j++, k++) { |
345 | /* | |
6e1e0f2f MM |
346 | * The body of this loop is very similar to the body of the first loop |
347 | * in `add', except that this loop does a `+=' instead of a `+'. | |
348 | */ | |
4efbb076 | 349 | temp = blk[k] + getShiftedBlock(b, j, i2); |
05780f4b MM |
350 | carryOut = (temp < blk[k]); |
351 | if (carryIn) { | |
352 | temp++; | |
353 | carryOut |= (temp == 0); | |
354 | } | |
355 | blk[k] = temp; | |
356 | carryIn = carryOut; | |
05780f4b | 357 | } |
4efbb076 MM |
358 | // No more extra iteration to deal with `bHigh'. |
359 | // Roll-over a carry as necessary. | |
05780f4b MM |
360 | for (; carryIn; k++) { |
361 | blk[k]++; | |
362 | carryIn = (blk[k] == 0); | |
363 | } | |
364 | } | |
365 | } | |
366 | // Zap possible leading zero | |
367 | if (blk[len - 1] == 0) | |
368 | len--; | |
369 | } | |
370 | ||
371 | /* | |
6e1e0f2f | 372 | * DIVISION WITH REMAINDER |
3e132790 MM |
373 | * This monstrous function mods *this by the given divisor b while storing the |
374 | * quotient in the given object q; at the end, *this contains the remainder. | |
375 | * The seemingly bizarre pattern of inputs and outputs was chosen so that the | |
376 | * function copies as little as possible (since it is implemented by repeated | |
377 | * subtraction of multiples of b from *this). | |
378 | * | |
379 | * "modWithQuotient" might be a better name for this function, but I would | |
380 | * rather not change the name now. | |
6e1e0f2f | 381 | */ |
05780f4b | 382 | void BigUnsigned::divideWithRemainder(const BigUnsigned &b, BigUnsigned &q) { |
3e132790 MM |
383 | /* Defending against aliased calls is more complex than usual because we |
384 | * are writing to both *this and q. | |
8c16728a MM |
385 | * |
386 | * It would be silly to try to write quotient and remainder to the | |
3e132790 | 387 | * same variable. Rule that out right away. */ |
8c16728a MM |
388 | if (this == &q) |
389 | throw "BigUnsigned::divideWithRemainder: Cannot write quotient and remainder into the same variable"; | |
3e132790 MM |
390 | /* Now *this and q are separate, so the only concern is that b might be |
391 | * aliased to one of them. If so, use a temporary copy of b. */ | |
8c16728a MM |
392 | if (this == &b || &q == &b) { |
393 | BigUnsigned tmpB(b); | |
394 | divideWithRemainder(tmpB, q); | |
395 | return; | |
396 | } | |
5ff40cf5 | 397 | |
05780f4b | 398 | /* |
3e132790 MM |
399 | * Knuth's definition of mod (which this function uses) is somewhat |
400 | * different from the C++ definition of % in case of division by 0. | |
6e1e0f2f | 401 | * |
3e132790 MM |
402 | * We let a / 0 == 0 (it doesn't matter much) and a % 0 == a, no |
403 | * exceptions thrown. This allows us to preserve both Knuth's demand | |
404 | * that a mod 0 == a and the useful property that | |
405 | * (a / b) * b + (a % b) == a. | |
6e1e0f2f | 406 | */ |
05780f4b MM |
407 | if (b.len == 0) { |
408 | q.len = 0; | |
409 | return; | |
410 | } | |
5ff40cf5 | 411 | |
05780f4b | 412 | /* |
6e1e0f2f MM |
413 | * If *this.len < b.len, then *this < b, and we can be sure that b doesn't go into |
414 | * *this at all. The quotient is 0 and *this is already the remainder (so leave it alone). | |
415 | */ | |
05780f4b MM |
416 | if (len < b.len) { |
417 | q.len = 0; | |
418 | return; | |
419 | } | |
5ff40cf5 | 420 | |
3e132790 | 421 | // At this point we know (*this).len >= b.len > 0. (Whew!) |
5ff40cf5 | 422 | |
05780f4b | 423 | /* |
6e1e0f2f MM |
424 | * Overall method: |
425 | * | |
426 | * For each appropriate i and i2, decreasing: | |
3e132790 MM |
427 | * Subtract (b << (i blocks and i2 bits)) from *this, storing the |
428 | * result in subtractBuf. | |
429 | * If the subtraction succeeds with a nonnegative result: | |
6e1e0f2f | 430 | * Turn on bit i2 of block i of the quotient q. |
3e132790 MM |
431 | * Copy subtractBuf back into *this. |
432 | * Otherwise bit i2 of block i remains off, and *this is unchanged. | |
6e1e0f2f MM |
433 | * |
434 | * Eventually q will contain the entire quotient, and *this will | |
435 | * be left with the remainder. | |
436 | * | |
3e132790 MM |
437 | * subtractBuf[x] corresponds to blk[x], not blk[x+i], since 2005.01.11. |
438 | * But on a single iteration, we don't touch the i lowest blocks of blk | |
439 | * (and don't use those of subtractBuf) because these blocks are | |
440 | * unaffected by the subtraction: we are subtracting | |
441 | * (b << (i blocks and i2 bits)), which ends in at least `i' zero | |
442 | * blocks. */ | |
05780f4b MM |
443 | // Variables for the calculation |
444 | Index i, j, k; | |
445 | unsigned int i2; | |
4efbb076 | 446 | Blk temp; |
05780f4b | 447 | bool borrowIn, borrowOut; |
5ff40cf5 | 448 | |
2f145f11 | 449 | /* |
6e1e0f2f MM |
450 | * Make sure we have an extra zero block just past the value. |
451 | * | |
452 | * When we attempt a subtraction, we might shift `b' so | |
453 | * its first block begins a few bits left of the dividend, | |
454 | * and then we'll try to compare these extra bits with | |
455 | * a nonexistent block to the left of the dividend. The | |
456 | * extra zero block ensures sensible behavior; we need | |
3e132790 | 457 | * an extra block in `subtractBuf' for exactly the same reason. |
6e1e0f2f | 458 | */ |
4efbb076 | 459 | Index origLen = len; // Save real length. |
3e132790 MM |
460 | /* To avoid an out-of-bounds access in case of reallocation, allocate |
461 | * first and then increment the logical length. */ | |
462 | allocateAndCopy(len + 1); | |
463 | len++; | |
464 | blk[origLen] = 0; // Zero the added block. | |
5ff40cf5 | 465 | |
3e132790 MM |
466 | // subtractBuf holds part of the result of a subtraction; see above. |
467 | Blk *subtractBuf = new Blk[len]; | |
5ff40cf5 | 468 | |
05780f4b | 469 | // Set preliminary length for quotient and make room |
2f145f11 | 470 | q.len = origLen - b.len + 1; |
05780f4b MM |
471 | q.allocate(q.len); |
472 | // Zero out the quotient | |
473 | for (i = 0; i < q.len; i++) | |
474 | q.blk[i] = 0; | |
5ff40cf5 | 475 | |
05780f4b MM |
476 | // For each possible left-shift of b in blocks... |
477 | i = q.len; | |
478 | while (i > 0) { | |
479 | i--; | |
480 | // For each possible left-shift of b in bits... | |
4efbb076 | 481 | // (Remember, N is the number of bits in a Blk.) |
05780f4b | 482 | q.blk[i] = 0; |
4efbb076 | 483 | i2 = N; |
05780f4b MM |
484 | while (i2 > 0) { |
485 | i2--; | |
486 | /* | |
6e1e0f2f | 487 | * Subtract b, shifted left i blocks and i2 bits, from *this, |
3e132790 | 488 | * and store the answer in subtractBuf. In the for loop, `k == i + j'. |
6e1e0f2f MM |
489 | * |
490 | * Compare this to the middle section of `multiply'. They | |
491 | * are in many ways analogous. See especially the discussion | |
492 | * of `getShiftedBlock'. | |
493 | */ | |
4efbb076 MM |
494 | for (j = 0, k = i, borrowIn = false; j <= b.len; j++, k++) { |
495 | temp = blk[k] - getShiftedBlock(b, j, i2); | |
05780f4b MM |
496 | borrowOut = (temp > blk[k]); |
497 | if (borrowIn) { | |
498 | borrowOut |= (temp == 0); | |
499 | temp--; | |
500 | } | |
3e132790 MM |
501 | // Since 2005.01.11, indices of `subtractBuf' directly match those of `blk', so use `k'. |
502 | subtractBuf[k] = temp; | |
05780f4b | 503 | borrowIn = borrowOut; |
05780f4b | 504 | } |
4efbb076 MM |
505 | // No more extra iteration to deal with `bHigh'. |
506 | // Roll-over a borrow as necessary. | |
507 | for (; k < origLen && borrowIn; k++) { | |
05780f4b | 508 | borrowIn = (blk[k] == 0); |
3e132790 | 509 | subtractBuf[k] = blk[k] - 1; |
05780f4b | 510 | } |
4efbb076 | 511 | /* |
6e1e0f2f MM |
512 | * If the subtraction was performed successfully (!borrowIn), |
513 | * set bit i2 in block i of the quotient. | |
514 | * | |
3e132790 | 515 | * Then, copy the portion of subtractBuf filled by the subtraction |
6e1e0f2f MM |
516 | * back to *this. This portion starts with block i and ends-- |
517 | * where? Not necessarily at block `i + b.len'! Well, we | |
3e132790 MM |
518 | * increased k every time we saved a block into subtractBuf, so |
519 | * the region of subtractBuf we copy is just [i, k). | |
6e1e0f2f | 520 | */ |
05780f4b | 521 | if (!borrowIn) { |
26a5f52b | 522 | q.blk[i] |= (Blk(1) << i2); |
4efbb076 | 523 | while (k > i) { |
05780f4b | 524 | k--; |
3e132790 | 525 | blk[k] = subtractBuf[k]; |
05780f4b MM |
526 | } |
527 | } | |
528 | } | |
529 | } | |
530 | // Zap possible leading zero in quotient | |
531 | if (q.blk[q.len - 1] == 0) | |
532 | q.len--; | |
533 | // Zap any/all leading zeros in remainder | |
534 | zapLeadingZeros(); | |
3e132790 | 535 | // Deallocate subtractBuf. |
05780f4b | 536 | // (Thanks to Brad Spencer for noticing my accidental omission of this!) |
3e132790 | 537 | delete [] subtractBuf; |
05780f4b MM |
538 | } |
539 | ||
3e132790 MM |
540 | /* BITWISE OPERATORS |
541 | * These are straightforward blockwise operations except that they differ in | |
542 | * the output length and the necessity of zapLeadingZeros. */ | |
543 | ||
05780f4b | 544 | void BigUnsigned::bitAnd(const BigUnsigned &a, const BigUnsigned &b) { |
ef2b7c59 | 545 | DTRT_ALIASED(this == &a || this == &b, bitAnd(a, b)); |
3e132790 | 546 | // The bitwise & can't be longer than either operand. |
05780f4b MM |
547 | len = (a.len >= b.len) ? b.len : a.len; |
548 | allocate(len); | |
549 | Index i; | |
550 | for (i = 0; i < len; i++) | |
551 | blk[i] = a.blk[i] & b.blk[i]; | |
552 | zapLeadingZeros(); | |
553 | } | |
554 | ||
05780f4b | 555 | void BigUnsigned::bitOr(const BigUnsigned &a, const BigUnsigned &b) { |
ef2b7c59 | 556 | DTRT_ALIASED(this == &a || this == &b, bitOr(a, b)); |
05780f4b MM |
557 | Index i; |
558 | const BigUnsigned *a2, *b2; | |
559 | if (a.len >= b.len) { | |
560 | a2 = &a; | |
561 | b2 = &b; | |
562 | } else { | |
563 | a2 = &b; | |
564 | b2 = &a; | |
565 | } | |
566 | allocate(a2->len); | |
567 | for (i = 0; i < b2->len; i++) | |
568 | blk[i] = a2->blk[i] | b2->blk[i]; | |
569 | for (; i < a2->len; i++) | |
570 | blk[i] = a2->blk[i]; | |
571 | len = a2->len; | |
3e132790 | 572 | // Doesn't need zapLeadingZeros. |
05780f4b MM |
573 | } |
574 | ||
05780f4b | 575 | void BigUnsigned::bitXor(const BigUnsigned &a, const BigUnsigned &b) { |
ef2b7c59 | 576 | DTRT_ALIASED(this == &a || this == &b, bitXor(a, b)); |
05780f4b MM |
577 | Index i; |
578 | const BigUnsigned *a2, *b2; | |
579 | if (a.len >= b.len) { | |
580 | a2 = &a; | |
581 | b2 = &b; | |
582 | } else { | |
583 | a2 = &b; | |
584 | b2 = &a; | |
585 | } | |
3aaa5ce6 | 586 | allocate(a2->len); |
05780f4b MM |
587 | for (i = 0; i < b2->len; i++) |
588 | blk[i] = a2->blk[i] ^ b2->blk[i]; | |
589 | for (; i < a2->len; i++) | |
590 | blk[i] = a2->blk[i]; | |
591 | len = a2->len; | |
592 | zapLeadingZeros(); | |
593 | } | |
594 | ||
0afe80d5 | 595 | void BigUnsigned::bitShiftLeft(const BigUnsigned &a, int b) { |
ef2b7c59 | 596 | DTRT_ALIASED(this == &a, bitShiftLeft(a, b)); |
0afe80d5 MM |
597 | if (b < 0) { |
598 | if (b << 1 == 0) | |
599 | throw "BigUnsigned::bitShiftLeft: " | |
600 | "Pathological shift amount not implemented"; | |
601 | else { | |
602 | bitShiftRight(a, -b); | |
603 | return; | |
604 | } | |
605 | } | |
ef2b7c59 MM |
606 | Index shiftBlocks = b / N; |
607 | unsigned int shiftBits = b % N; | |
608 | // + 1: room for high bits nudged left into another block | |
609 | len = a.len + shiftBlocks + 1; | |
610 | allocate(len); | |
611 | Index i, j; | |
612 | for (i = 0; i < shiftBlocks; i++) | |
613 | blk[i] = 0; | |
614 | for (j = 0, i = shiftBlocks; j <= a.len; j++, i++) | |
615 | blk[i] = getShiftedBlock(a, j, shiftBits); | |
616 | // Zap possible leading zero | |
617 | if (blk[len - 1] == 0) | |
618 | len--; | |
619 | } | |
620 | ||
0afe80d5 | 621 | void BigUnsigned::bitShiftRight(const BigUnsigned &a, int b) { |
ef2b7c59 | 622 | DTRT_ALIASED(this == &a, bitShiftRight(a, b)); |
0afe80d5 MM |
623 | if (b < 0) { |
624 | if (b << 1 == 0) | |
625 | throw "BigUnsigned::bitShiftRight: " | |
626 | "Pathological shift amount not implemented"; | |
627 | else { | |
628 | bitShiftLeft(a, -b); | |
629 | return; | |
630 | } | |
631 | } | |
ef2b7c59 MM |
632 | // This calculation is wacky, but expressing the shift as a left bit shift |
633 | // within each block lets us use getShiftedBlock. | |
634 | Index rightShiftBlocks = (b + N - 1) / N; | |
635 | unsigned int leftShiftBits = N * rightShiftBlocks - b; | |
636 | // Now (N * rightShiftBlocks - leftShiftBits) == b | |
637 | // and 0 <= leftShiftBits < N. | |
638 | if (rightShiftBlocks >= a.len + 1) { | |
639 | // All of a is guaranteed to be shifted off, even considering the left | |
640 | // bit shift. | |
641 | len = 0; | |
642 | return; | |
643 | } | |
644 | // Now we're allocating a positive amount. | |
645 | // + 1: room for high bits nudged left into another block | |
646 | len = a.len + 1 - rightShiftBlocks; | |
647 | allocate(len); | |
648 | Index i, j; | |
649 | for (j = rightShiftBlocks, i = 0; j <= a.len; j++, i++) | |
650 | blk[i] = getShiftedBlock(a, j, leftShiftBits); | |
651 | // Zap possible leading zero | |
652 | if (blk[len - 1] == 0) | |
653 | len--; | |
654 | } | |
655 | ||
05780f4b MM |
656 | // INCREMENT/DECREMENT OPERATORS |
657 | ||
658 | // Prefix increment | |
659 | void BigUnsigned::operator ++() { | |
660 | Index i; | |
661 | bool carry = true; | |
662 | for (i = 0; i < len && carry; i++) { | |
663 | blk[i]++; | |
664 | carry = (blk[i] == 0); | |
665 | } | |
666 | if (carry) { | |
3e132790 | 667 | // Allocate and then increase length, as in divideWithRemainder |
918d66f2 | 668 | allocateAndCopy(len + 1); |
05780f4b | 669 | len++; |
05780f4b MM |
670 | blk[i] = 1; |
671 | } | |
672 | } | |
673 | ||
674 | // Postfix increment: same as prefix | |
675 | void BigUnsigned::operator ++(int) { | |
676 | operator ++(); | |
677 | } | |
678 | ||
679 | // Prefix decrement | |
680 | void BigUnsigned::operator --() { | |
681 | if (len == 0) | |
682 | throw "BigUnsigned::operator --(): Cannot decrement an unsigned zero"; | |
683 | Index i; | |
684 | bool borrow = true; | |
685 | for (i = 0; borrow; i++) { | |
686 | borrow = (blk[i] == 0); | |
687 | blk[i]--; | |
688 | } | |
689 | // Zap possible leading zero (there can only be one) | |
690 | if (blk[len - 1] == 0) | |
691 | len--; | |
692 | } | |
693 | ||
694 | // Postfix decrement: same as prefix | |
695 | void BigUnsigned::operator --(int) { | |
696 | operator --(); | |
697 | } |