1 | /* |
2 | * Copyright (C) 2017 Caio Lima <[email protected]> |
3 | * Copyright (C) 2017-2019 Apple Inc. All rights reserved. |
4 | * |
5 | * Redistribution and use in source and binary forms, with or without |
6 | * modification, are permitted provided that the following conditions |
7 | * are met: |
8 | * 1. Redistributions of source code must retain the above copyright |
9 | * notice, this list of conditions and the following disclaimer. |
10 | * 2. Redistributions in binary form must reproduce the above copyright |
11 | * notice, this list of conditions and the following disclaimer in the |
12 | * documentation and/or other materials provided with the distribution. |
13 | * |
14 | * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY |
15 | * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
16 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
17 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR |
18 | * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
19 | * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
20 | * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
21 | * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY |
22 | * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
23 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
24 | * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
25 | * |
26 | * Parts of the implementation below: |
27 | * |
28 | * Copyright 2017 the V8 project authors. All rights reserved. |
29 | * Use of this source code is governed by a BSD-style license that can be |
30 | * found in the LICENSE file. |
31 | * |
32 | * |
33 | * Copyright (c) 2014 the Dart project authors. Please see the AUTHORS file [1] |
34 | * for details. All rights reserved. Use of this source code is governed by a |
35 | * BSD-style license that can be found in the LICENSE file [2]. |
36 | * |
37 | * [1] https://github.com/dart-lang/sdk/blob/master/AUTHORS |
38 | * [2] https://github.com/dart-lang/sdk/blob/master/LICENSE |
39 | * |
40 | * Copyright 2009 The Go Authors. All rights reserved. |
41 | * Use of this source code is governed by a BSD-style |
42 | * license that can be found in the LICENSE file [3]. |
43 | * |
44 | * [3] https://golang.org/LICENSE |
45 | */ |
46 | |
47 | #include "config.h" |
48 | #include "JSBigInt.h" |
49 | |
50 | #include "BigIntObject.h" |
51 | #include "CatchScope.h" |
52 | #include "JSCInlines.h" |
53 | #include "MathCommon.h" |
54 | #include "ParseInt.h" |
55 | #include <algorithm> |
56 | #include <wtf/MathExtras.h> |
57 | |
58 | #define STATIC_ASSERT(cond) static_assert(cond, "JSBigInt assumes " #cond) |
59 | |
60 | namespace JSC { |
61 | |
62 | const ClassInfo JSBigInt::s_info = { "BigInt" , nullptr, nullptr, nullptr, CREATE_METHOD_TABLE(JSBigInt) }; |
63 | |
64 | JSBigInt::JSBigInt(VM& vm, Structure* structure, Digit* data, unsigned length) |
65 | : Base(vm, structure) |
66 | , m_length(length) |
67 | , m_data(data, length) |
68 | { } |
69 | |
70 | void JSBigInt::destroy(JSCell* thisCell) |
71 | { |
72 | static_cast<JSBigInt*>(thisCell)->~JSBigInt(); |
73 | } |
74 | |
75 | void JSBigInt::initialize(InitializationType initType) |
76 | { |
77 | if (initType == InitializationType::WithZero) |
78 | memset(dataStorage(), 0, length() * sizeof(Digit)); |
79 | } |
80 | |
81 | Structure* JSBigInt::createStructure(VM& vm, JSGlobalObject* globalObject, JSValue prototype) |
82 | { |
83 | return Structure::create(vm, globalObject, prototype, TypeInfo(BigIntType, StructureFlags), info()); |
84 | } |
85 | |
86 | JSBigInt* JSBigInt::createZero(VM& vm) |
87 | { |
88 | JSBigInt* zeroBigInt = createWithLengthUnchecked(vm, 0); |
89 | return zeroBigInt; |
90 | } |
91 | |
92 | JSBigInt* JSBigInt::tryCreateWithLength(JSGlobalObject* globalObject, unsigned length) |
93 | { |
94 | VM& vm = globalObject->vm(); |
95 | auto scope = DECLARE_THROW_SCOPE(vm); |
96 | |
97 | if (UNLIKELY(length > maxLength)) { |
98 | throwOutOfMemoryError(globalObject, scope); |
99 | return nullptr; |
100 | } |
101 | |
102 | scope.release(); |
103 | |
104 | return createWithLengthUnchecked(vm, length); |
105 | } |
106 | |
107 | JSBigInt* JSBigInt::createWithLengthUnchecked(VM& vm, unsigned length) |
108 | { |
109 | ASSERT(length <= maxLength); |
110 | void* data = Gigacage::malloc(Gigacage::Primitive, length * sizeof(Digit)); |
111 | JSBigInt* bigInt = new (NotNull, allocateCell<JSBigInt>(vm.heap)) JSBigInt(vm, vm.bigIntStructure.get(), reinterpret_cast<Digit*>(data), length); |
112 | bigInt->finishCreation(vm); |
113 | return bigInt; |
114 | } |
115 | |
116 | JSBigInt* JSBigInt::createFrom(VM& vm, int32_t value) |
117 | { |
118 | if (!value) |
119 | return createZero(vm); |
120 | |
121 | JSBigInt* bigInt = createWithLengthUnchecked(vm, 1); |
122 | if (value < 0) { |
123 | bigInt->setDigit(0, static_cast<Digit>(-1 * static_cast<int64_t>(value))); |
124 | bigInt->setSign(true); |
125 | } else |
126 | bigInt->setDigit(0, static_cast<Digit>(value)); |
127 | |
128 | return bigInt; |
129 | } |
130 | |
131 | JSBigInt* JSBigInt::createFrom(VM& vm, uint32_t value) |
132 | { |
133 | if (!value) |
134 | return createZero(vm); |
135 | |
136 | JSBigInt* bigInt = createWithLengthUnchecked(vm, 1); |
137 | bigInt->setDigit(0, static_cast<Digit>(value)); |
138 | return bigInt; |
139 | } |
140 | |
141 | JSBigInt* JSBigInt::createFrom(VM& vm, int64_t value) |
142 | { |
143 | if (!value) |
144 | return createZero(vm); |
145 | |
146 | if (sizeof(Digit) == 8) { |
147 | JSBigInt* bigInt = createWithLengthUnchecked(vm, 1); |
148 | if (value < 0) { |
149 | bigInt->setDigit(0, static_cast<Digit>(static_cast<uint64_t>(-(value + 1)) + 1)); |
150 | bigInt->setSign(true); |
151 | } else |
152 | bigInt->setDigit(0, static_cast<Digit>(value)); |
153 | |
154 | return bigInt; |
155 | } |
156 | |
157 | JSBigInt* bigInt = createWithLengthUnchecked(vm, 2); |
158 | uint64_t tempValue; |
159 | bool sign = false; |
160 | if (value < 0) { |
161 | tempValue = static_cast<uint64_t>(-(value + 1)) + 1; |
162 | sign = true; |
163 | } else |
164 | tempValue = value; |
165 | |
166 | Digit lowBits = static_cast<Digit>(tempValue & 0xffffffff); |
167 | Digit highBits = static_cast<Digit>((tempValue >> 32) & 0xffffffff); |
168 | |
169 | bigInt->setDigit(0, lowBits); |
170 | bigInt->setDigit(1, highBits); |
171 | bigInt->setSign(sign); |
172 | |
173 | return bigInt; |
174 | } |
175 | |
176 | JSBigInt* JSBigInt::createFrom(VM& vm, bool value) |
177 | { |
178 | if (!value) |
179 | return createZero(vm); |
180 | |
181 | JSBigInt* bigInt = createWithLengthUnchecked(vm, 1); |
182 | bigInt->setDigit(0, static_cast<Digit>(value)); |
183 | return bigInt; |
184 | } |
185 | |
186 | JSValue JSBigInt::toPrimitive(JSGlobalObject*, PreferredPrimitiveType) const |
187 | { |
188 | return const_cast<JSBigInt*>(this); |
189 | } |
190 | |
191 | Optional<uint8_t> JSBigInt::singleDigitValueForString() |
192 | { |
193 | if (isZero()) |
194 | return 0; |
195 | |
196 | if (length() == 1 && !sign()) { |
197 | Digit rDigit = digit(0); |
198 | if (rDigit <= 9) |
199 | return static_cast<uint8_t>(rDigit); |
200 | } |
201 | return { }; |
202 | } |
203 | |
204 | JSBigInt* JSBigInt::parseInt(JSGlobalObject* globalObject, StringView s, ErrorParseMode parserMode) |
205 | { |
206 | if (s.is8Bit()) |
207 | return parseInt(globalObject, s.characters8(), s.length(), parserMode); |
208 | return parseInt(globalObject, s.characters16(), s.length(), parserMode); |
209 | } |
210 | |
211 | JSBigInt* JSBigInt::parseInt(JSGlobalObject* globalObject, VM& vm, StringView s, uint8_t radix, ErrorParseMode parserMode, ParseIntSign sign) |
212 | { |
213 | if (s.is8Bit()) |
214 | return parseInt(globalObject, vm, s.characters8(), s.length(), 0, radix, parserMode, sign, ParseIntMode::DisallowEmptyString); |
215 | return parseInt(globalObject, vm, s.characters16(), s.length(), 0, radix, parserMode, sign, ParseIntMode::DisallowEmptyString); |
216 | } |
217 | |
218 | JSBigInt* JSBigInt::stringToBigInt(JSGlobalObject* globalObject, StringView s) |
219 | { |
220 | return parseInt(globalObject, s, ErrorParseMode::IgnoreExceptions); |
221 | } |
222 | |
223 | String JSBigInt::toString(JSGlobalObject* globalObject, unsigned radix) |
224 | { |
225 | if (this->isZero()) |
226 | return globalObject->vm().smallStrings.singleCharacterStringRep('0'); |
227 | |
228 | if (hasOneBitSet(radix)) |
229 | return toStringBasePowerOfTwo(globalObject->vm(), globalObject, this, radix); |
230 | |
231 | return toStringGeneric(globalObject->vm(), globalObject, this, radix); |
232 | } |
233 | |
234 | String JSBigInt::tryGetString(VM& vm, JSBigInt* bigInt, unsigned radix) |
235 | { |
236 | if (bigInt->isZero()) |
237 | return vm.smallStrings.singleCharacterStringRep('0'); |
238 | |
239 | if (hasOneBitSet(radix)) |
240 | return toStringBasePowerOfTwo(vm, nullptr, bigInt, radix); |
241 | |
242 | return toStringGeneric(vm, nullptr, bigInt, radix); |
243 | } |
244 | |
245 | // Multiplies {this} with {factor} and adds {summand} to the result. |
246 | void JSBigInt::inplaceMultiplyAdd(Digit factor, Digit summand) |
247 | { |
248 | internalMultiplyAdd(this, factor, summand, length(), this); |
249 | } |
250 | |
251 | JSBigInt* JSBigInt::exponentiate(JSGlobalObject* globalObject, JSBigInt* base, JSBigInt* exponent) |
252 | { |
253 | VM& vm = globalObject->vm(); |
254 | auto scope = DECLARE_THROW_SCOPE(vm); |
255 | |
256 | if (exponent->sign()) { |
257 | throwRangeError(globalObject, scope, "Negative exponent is not allowed"_s ); |
258 | return nullptr; |
259 | } |
260 | |
261 | // 2. If base is 0n and exponent is 0n, return 1n. |
262 | if (exponent->isZero()) |
263 | return JSBigInt::createFrom(vm, 1); |
264 | |
265 | // 3. Return a BigInt representing the mathematical value of base raised |
266 | // to the power exponent. |
267 | if (base->isZero()) |
268 | return base; |
269 | |
270 | if (base->length() == 1 && base->digit(0) == 1) { |
271 | // (-1) ** even_number == 1. |
272 | if (base->sign() && !(exponent->digit(0) & 1)) |
273 | return JSBigInt::unaryMinus(vm, base); |
274 | |
275 | // (-1) ** odd_number == -1; 1 ** anything == 1. |
276 | return base; |
277 | } |
278 | |
279 | // For all bases >= 2, very large exponents would lead to unrepresentable |
280 | // results. |
281 | static_assert(maxLengthBits < std::numeric_limits<Digit>::max(), "maxLengthBits needs to be less than digit::max()" ); |
282 | if (exponent->length() > 1) { |
283 | throwRangeError(globalObject, scope, "BigInt generated from this operation is too big"_s ); |
284 | return nullptr; |
285 | } |
286 | |
287 | Digit expValue = exponent->digit(0); |
288 | if (expValue == 1) |
289 | return base; |
290 | if (expValue >= maxLengthBits) { |
291 | throwRangeError(globalObject, scope, "BigInt generated from this operation is too big"_s ); |
292 | return nullptr; |
293 | } |
294 | |
295 | static_assert(maxLengthBits <= maxInt, "maxLengthBits needs to be <= maxInt" ); |
296 | int n = static_cast<int>(expValue); |
297 | if (base->length() == 1 && base->digit(0) == 2) { |
298 | // Fast path for 2^n. |
299 | int neededDigits = 1 + (n / digitBits); |
300 | JSBigInt* result = JSBigInt::tryCreateWithLength(globalObject, neededDigits); |
301 | RETURN_IF_EXCEPTION(scope, nullptr); |
302 | |
303 | result->initialize(InitializationType::WithZero); |
304 | // All bits are zero. Now set the n-th bit. |
305 | Digit msd = static_cast<Digit>(1) << (n % digitBits); |
306 | result->setDigit(neededDigits - 1, msd); |
307 | // Result is negative for odd powers of -2n. |
308 | if (base->sign()) |
309 | result->setSign(static_cast<bool>(n & 1)); |
310 | |
311 | return result; |
312 | } |
313 | |
314 | JSBigInt* result = nullptr; |
315 | JSBigInt* runningSquare = base; |
316 | |
317 | // This implicitly sets the result's sign correctly. |
318 | if (n & 1) |
319 | result = base; |
320 | |
321 | n >>= 1; |
322 | for (; n; n >>= 1) { |
323 | JSBigInt* maybeResult = JSBigInt::multiply(globalObject, runningSquare, runningSquare); |
324 | RETURN_IF_EXCEPTION(scope, nullptr); |
325 | runningSquare = maybeResult; |
326 | if (n & 1) { |
327 | if (!result) |
328 | result = runningSquare; |
329 | else { |
330 | maybeResult = JSBigInt::multiply(globalObject, result, runningSquare); |
331 | RETURN_IF_EXCEPTION(scope, nullptr); |
332 | result = maybeResult; |
333 | } |
334 | } |
335 | } |
336 | |
337 | return result; |
338 | } |
339 | |
340 | JSBigInt* JSBigInt::multiply(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
341 | { |
342 | VM& vm = globalObject->vm(); |
343 | auto scope = DECLARE_THROW_SCOPE(vm); |
344 | |
345 | if (x->isZero()) |
346 | return x; |
347 | if (y->isZero()) |
348 | return y; |
349 | |
350 | unsigned resultLength = x->length() + y->length(); |
351 | JSBigInt* result = JSBigInt::tryCreateWithLength(globalObject, resultLength); |
352 | RETURN_IF_EXCEPTION(scope, nullptr); |
353 | result->initialize(InitializationType::WithZero); |
354 | |
355 | for (unsigned i = 0; i < x->length(); i++) |
356 | multiplyAccumulate(y, x->digit(i), result, i); |
357 | |
358 | result->setSign(x->sign() != y->sign()); |
359 | return result->rightTrim(vm); |
360 | } |
361 | |
362 | JSBigInt* JSBigInt::divide(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
363 | { |
364 | // 1. If y is 0n, throw a RangeError exception. |
365 | VM& vm = globalObject->vm(); |
366 | auto scope = DECLARE_THROW_SCOPE(vm); |
367 | |
368 | if (y->isZero()) { |
369 | throwRangeError(globalObject, scope, "0 is an invalid divisor value."_s ); |
370 | return nullptr; |
371 | } |
372 | |
373 | // 2. Let quotient be the mathematical value of x divided by y. |
374 | // 3. Return a BigInt representing quotient rounded towards 0 to the next |
375 | // integral value. |
376 | if (absoluteCompare(x, y) == ComparisonResult::LessThan) |
377 | return createZero(vm); |
378 | |
379 | JSBigInt* quotient = nullptr; |
380 | bool resultSign = x->sign() != y->sign(); |
381 | if (y->length() == 1) { |
382 | Digit divisor = y->digit(0); |
383 | if (divisor == 1) |
384 | return resultSign == x->sign() ? x : unaryMinus(vm, x); |
385 | |
386 | Digit remainder; |
387 | absoluteDivWithDigitDivisor(vm, x, divisor, "ient, remainder); |
388 | } else { |
389 | absoluteDivWithBigIntDivisor(globalObject, x, y, "ient, nullptr); |
390 | RETURN_IF_EXCEPTION(scope, nullptr); |
391 | } |
392 | |
393 | quotient->setSign(resultSign); |
394 | return quotient->rightTrim(vm); |
395 | } |
396 | |
397 | JSBigInt* JSBigInt::copy(VM& vm, JSBigInt* x) |
398 | { |
399 | ASSERT(!x->isZero()); |
400 | |
401 | JSBigInt* result = JSBigInt::createWithLengthUnchecked(vm, x->length()); |
402 | std::copy(x->dataStorage(), x->dataStorage() + x->length(), result->dataStorage()); |
403 | result->setSign(x->sign()); |
404 | return result; |
405 | } |
406 | |
407 | JSBigInt* JSBigInt::unaryMinus(VM& vm, JSBigInt* x) |
408 | { |
409 | if (x->isZero()) |
410 | return x; |
411 | |
412 | JSBigInt* result = copy(vm, x); |
413 | result->setSign(!x->sign()); |
414 | return result; |
415 | } |
416 | |
417 | JSBigInt* JSBigInt::remainder(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
418 | { |
419 | // 1. If y is 0n, throw a RangeError exception. |
420 | VM& vm = globalObject->vm(); |
421 | auto scope = DECLARE_THROW_SCOPE(vm); |
422 | |
423 | if (y->isZero()) { |
424 | throwRangeError(globalObject, scope, "0 is an invalid divisor value."_s ); |
425 | return nullptr; |
426 | } |
427 | |
428 | // 2. Return the JSBigInt representing x modulo y. |
429 | // See https://github.com/tc39/proposal-bigint/issues/84 though. |
430 | if (absoluteCompare(x, y) == ComparisonResult::LessThan) |
431 | return x; |
432 | |
433 | JSBigInt* remainder; |
434 | if (y->length() == 1) { |
435 | Digit divisor = y->digit(0); |
436 | if (divisor == 1) |
437 | return createZero(vm); |
438 | |
439 | Digit remainderDigit; |
440 | absoluteDivWithDigitDivisor(vm, x, divisor, nullptr, remainderDigit); |
441 | if (!remainderDigit) |
442 | return createZero(vm); |
443 | |
444 | remainder = createWithLengthUnchecked(vm, 1); |
445 | remainder->setDigit(0, remainderDigit); |
446 | } else { |
447 | absoluteDivWithBigIntDivisor(globalObject, x, y, nullptr, &remainder); |
448 | RETURN_IF_EXCEPTION(scope, nullptr); |
449 | } |
450 | |
451 | remainder->setSign(x->sign()); |
452 | return remainder->rightTrim(vm); |
453 | } |
454 | |
455 | JSBigInt* JSBigInt::inc(JSGlobalObject* globalObject, JSBigInt* x) |
456 | { |
457 | // FIXME: we can probably do something a fair bit more efficient here |
458 | VM& vm = globalObject->vm(); |
459 | return add(globalObject, x, vm.bigIntConstantOne.get()); |
460 | } |
461 | |
462 | JSBigInt* JSBigInt::dec(JSGlobalObject* globalObject, JSBigInt* x) |
463 | { |
464 | // FIXME: we can probably do something a fair bit more efficient here |
465 | VM& vm = globalObject->vm(); |
466 | return sub(globalObject, x, vm.bigIntConstantOne.get()); |
467 | } |
468 | |
469 | JSBigInt* JSBigInt::add(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
470 | { |
471 | VM& vm = globalObject->vm(); |
472 | bool xSign = x->sign(); |
473 | |
474 | // x + y == x + y |
475 | // -x + -y == -(x + y) |
476 | if (xSign == y->sign()) |
477 | return absoluteAdd(globalObject, x, y, xSign); |
478 | |
479 | // x + -y == x - y == -(y - x) |
480 | // -x + y == y - x == -(x - y) |
481 | ComparisonResult comparisonResult = absoluteCompare(x, y); |
482 | if (comparisonResult == ComparisonResult::GreaterThan || comparisonResult == ComparisonResult::Equal) |
483 | return absoluteSub(vm, x, y, xSign); |
484 | |
485 | return absoluteSub(vm, y, x, !xSign); |
486 | } |
487 | |
488 | JSBigInt* JSBigInt::sub(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
489 | { |
490 | VM& vm = globalObject->vm(); |
491 | bool xSign = x->sign(); |
492 | if (xSign != y->sign()) { |
493 | // x - (-y) == x + y |
494 | // (-x) - y == -(x + y) |
495 | return absoluteAdd(globalObject, x, y, xSign); |
496 | } |
497 | // x - y == -(y - x) |
498 | // (-x) - (-y) == y - x == -(x - y) |
499 | ComparisonResult comparisonResult = absoluteCompare(x, y); |
500 | if (comparisonResult == ComparisonResult::GreaterThan || comparisonResult == ComparisonResult::Equal) |
501 | return absoluteSub(vm, x, y, xSign); |
502 | |
503 | return absoluteSub(vm, y, x, !xSign); |
504 | } |
505 | |
506 | JSBigInt* JSBigInt::bitwiseAnd(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
507 | { |
508 | VM& vm = globalObject->vm(); |
509 | auto scope = DECLARE_THROW_SCOPE(vm); |
510 | |
511 | if (!x->sign() && !y->sign()) { |
512 | scope.release(); |
513 | return absoluteAnd(vm, x, y); |
514 | } |
515 | |
516 | if (x->sign() && y->sign()) { |
517 | int resultLength = std::max(x->length(), y->length()) + 1; |
518 | // (-x) & (-y) == ~(x-1) & ~(y-1) == ~((x-1) | (y-1)) |
519 | // == -(((x-1) | (y-1)) + 1) |
520 | JSBigInt* result = absoluteSubOne(globalObject, x, resultLength); |
521 | RETURN_IF_EXCEPTION(scope, nullptr); |
522 | |
523 | JSBigInt* y1 = absoluteSubOne(globalObject, y, y->length()); |
524 | RETURN_IF_EXCEPTION(scope, nullptr); |
525 | result = absoluteOr(vm, result, y1); |
526 | scope.release(); |
527 | return absoluteAddOne(globalObject, result, SignOption::Signed); |
528 | } |
529 | |
530 | ASSERT(x->sign() != y->sign()); |
531 | // Assume that x is the positive BigInt. |
532 | if (x->sign()) |
533 | std::swap(x, y); |
534 | |
535 | // x & (-y) == x & ~(y-1) == x & ~(y-1) |
536 | JSBigInt* y1 = absoluteSubOne(globalObject, y, y->length()); |
537 | RETURN_IF_EXCEPTION(scope, nullptr); |
538 | return absoluteAndNot(vm, x, y1); |
539 | } |
540 | |
541 | JSBigInt* JSBigInt::bitwiseOr(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
542 | { |
543 | VM& vm = globalObject->vm(); |
544 | auto scope = DECLARE_THROW_SCOPE(vm); |
545 | |
546 | unsigned resultLength = std::max(x->length(), y->length()); |
547 | |
548 | if (!x->sign() && !y->sign()) { |
549 | scope.release(); |
550 | return absoluteOr(vm, x, y); |
551 | } |
552 | |
553 | if (x->sign() && y->sign()) { |
554 | // (-x) | (-y) == ~(x-1) | ~(y-1) == ~((x-1) & (y-1)) |
555 | // == -(((x-1) & (y-1)) + 1) |
556 | JSBigInt* result = absoluteSubOne(globalObject, x, resultLength); |
557 | RETURN_IF_EXCEPTION(scope, nullptr); |
558 | JSBigInt* y1 = absoluteSubOne(globalObject, y, y->length()); |
559 | RETURN_IF_EXCEPTION(scope, nullptr); |
560 | result = absoluteAnd(vm, result, y1); |
561 | RETURN_IF_EXCEPTION(scope, nullptr); |
562 | |
563 | scope.release(); |
564 | return absoluteAddOne(globalObject, result, SignOption::Signed); |
565 | } |
566 | |
567 | ASSERT(x->sign() != y->sign()); |
568 | |
569 | // Assume that x is the positive BigInt. |
570 | if (x->sign()) |
571 | std::swap(x, y); |
572 | |
573 | // x | (-y) == x | ~(y-1) == ~((y-1) &~ x) == -(((y-1) &~ x) + 1) |
574 | JSBigInt* result = absoluteSubOne(globalObject, y, resultLength); |
575 | RETURN_IF_EXCEPTION(scope, nullptr); |
576 | result = absoluteAndNot(vm, result, x); |
577 | |
578 | scope.release(); |
579 | return absoluteAddOne(globalObject, result, SignOption::Signed); |
580 | } |
581 | |
582 | JSBigInt* JSBigInt::bitwiseXor(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
583 | { |
584 | VM& vm = globalObject->vm(); |
585 | auto scope = DECLARE_THROW_SCOPE(vm); |
586 | |
587 | if (!x->sign() && !y->sign()) { |
588 | scope.release(); |
589 | return absoluteXor(vm, x, y); |
590 | } |
591 | |
592 | if (x->sign() && y->sign()) { |
593 | int resultLength = std::max(x->length(), y->length()); |
594 | |
595 | // (-x) ^ (-y) == ~(x-1) ^ ~(y-1) == (x-1) ^ (y-1) |
596 | JSBigInt* result = absoluteSubOne(globalObject, x, resultLength); |
597 | RETURN_IF_EXCEPTION(scope, nullptr); |
598 | JSBigInt* y1 = absoluteSubOne(globalObject, y, y->length()); |
599 | RETURN_IF_EXCEPTION(scope, nullptr); |
600 | |
601 | scope.release(); |
602 | return absoluteXor(vm, result, y1); |
603 | } |
604 | ASSERT(x->sign() != y->sign()); |
605 | int resultLength = std::max(x->length(), y->length()) + 1; |
606 | |
607 | // Assume that x is the positive BigInt. |
608 | if (x->sign()) |
609 | std::swap(x, y); |
610 | |
611 | // x ^ (-y) == x ^ ~(y-1) == ~(x ^ (y-1)) == -((x ^ (y-1)) + 1) |
612 | JSBigInt* result = absoluteSubOne(globalObject, y, resultLength); |
613 | RETURN_IF_EXCEPTION(scope, nullptr); |
614 | |
615 | result = absoluteXor(vm, result, x); |
616 | scope.release(); |
617 | return absoluteAddOne(globalObject, result, SignOption::Signed); |
618 | } |
619 | |
620 | JSBigInt* JSBigInt::leftShift(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
621 | { |
622 | if (y->isZero() || x->isZero()) |
623 | return x; |
624 | |
625 | if (y->sign()) |
626 | return rightShiftByAbsolute(globalObject, x, y); |
627 | |
628 | return leftShiftByAbsolute(globalObject, x, y); |
629 | } |
630 | |
631 | JSBigInt* JSBigInt::signedRightShift(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
632 | { |
633 | if (y->isZero() || x->isZero()) |
634 | return x; |
635 | |
636 | if (y->sign()) |
637 | return leftShiftByAbsolute(globalObject, x, y); |
638 | |
639 | return rightShiftByAbsolute(globalObject, x, y); |
640 | } |
641 | |
642 | JSBigInt* JSBigInt::bitwiseNot(JSGlobalObject* globalObject, JSBigInt* x) |
643 | { |
644 | if (x->sign()) { |
645 | // ~(-x) == ~(~(x-1)) == x-1 |
646 | return absoluteSubOne(globalObject, x, x->length()); |
647 | } |
648 | // ~x == -x-1 == -(x+1) |
649 | return absoluteAddOne(globalObject, x, SignOption::Signed); |
650 | } |
651 | |
652 | #if USE(JSVALUE32_64) |
653 | #define HAVE_TWO_DIGIT 1 |
654 | typedef uint64_t TwoDigit; |
655 | #elif HAVE(INT128_T) |
656 | #define HAVE_TWO_DIGIT 1 |
657 | typedef __uint128_t TwoDigit; |
658 | #else |
659 | #define HAVE_TWO_DIGIT 0 |
660 | #endif |
661 | |
662 | // {carry} must point to an initialized Digit and will either be incremented |
663 | // by one or left alone. |
664 | inline JSBigInt::Digit JSBigInt::digitAdd(Digit a, Digit b, Digit& carry) |
665 | { |
666 | Digit result = a + b; |
667 | carry += static_cast<bool>(result < a); |
668 | return result; |
669 | } |
670 | |
671 | // {borrow} must point to an initialized Digit and will either be incremented |
672 | // by one or left alone. |
673 | inline JSBigInt::Digit JSBigInt::digitSub(Digit a, Digit b, Digit& borrow) |
674 | { |
675 | Digit result = a - b; |
676 | borrow += static_cast<bool>(result > a); |
677 | return result; |
678 | } |
679 | |
680 | // Returns the low half of the result. High half is in {high}. |
681 | inline JSBigInt::Digit JSBigInt::digitMul(Digit a, Digit b, Digit& high) |
682 | { |
683 | #if HAVE(TWO_DIGIT) |
684 | TwoDigit result = static_cast<TwoDigit>(a) * static_cast<TwoDigit>(b); |
685 | high = result >> digitBits; |
686 | |
687 | return static_cast<Digit>(result); |
688 | #else |
689 | // Multiply in half-pointer-sized chunks. |
690 | // For inputs [AH AL]*[BH BL], the result is: |
691 | // |
692 | // [AL*BL] // rLow |
693 | // + [AL*BH] // rMid1 |
694 | // + [AH*BL] // rMid2 |
695 | // + [AH*BH] // rHigh |
696 | // = [R4 R3 R2 R1] // high = [R4 R3], low = [R2 R1] |
697 | // |
698 | // Where of course we must be careful with carries between the columns. |
699 | Digit aLow = a & halfDigitMask; |
700 | Digit aHigh = a >> halfDigitBits; |
701 | Digit bLow = b & halfDigitMask; |
702 | Digit bHigh = b >> halfDigitBits; |
703 | |
704 | Digit rLow = aLow * bLow; |
705 | Digit rMid1 = aLow * bHigh; |
706 | Digit rMid2 = aHigh * bLow; |
707 | Digit rHigh = aHigh * bHigh; |
708 | |
709 | Digit carry = 0; |
710 | Digit low = digitAdd(rLow, rMid1 << halfDigitBits, carry); |
711 | low = digitAdd(low, rMid2 << halfDigitBits, carry); |
712 | |
713 | high = (rMid1 >> halfDigitBits) + (rMid2 >> halfDigitBits) + rHigh + carry; |
714 | |
715 | return low; |
716 | #endif |
717 | } |
718 | |
719 | // Raises {base} to the power of {exponent}. Does not check for overflow. |
720 | inline JSBigInt::Digit JSBigInt::digitPow(Digit base, Digit exponent) |
721 | { |
722 | Digit result = 1ull; |
723 | while (exponent > 0) { |
724 | if (exponent & 1) |
725 | result *= base; |
726 | |
727 | exponent >>= 1; |
728 | base *= base; |
729 | } |
730 | |
731 | return result; |
732 | } |
733 | |
734 | // Returns the quotient. |
735 | // quotient = (high << digitBits + low - remainder) / divisor |
736 | inline JSBigInt::Digit JSBigInt::digitDiv(Digit high, Digit low, Digit divisor, Digit& remainder) |
737 | { |
738 | ASSERT(high < divisor); |
739 | #if CPU(X86_64) && COMPILER(GCC_COMPATIBLE) |
740 | Digit quotient; |
741 | Digit rem; |
742 | __asm__("divq %[divisor]" |
743 | // Outputs: {quotient} will be in rax, {rem} in rdx. |
744 | : "=a" (quotient), "=d" (rem) |
745 | // Inputs: put {high} into rdx, {low} into rax, and {divisor} into |
746 | // any register or stack slot. |
747 | : "d" (high), "a" (low), [divisor] "rm" (divisor)); |
748 | remainder = rem; |
749 | return quotient; |
750 | #elif CPU(X86) && COMPILER(GCC_COMPATIBLE) |
751 | Digit quotient; |
752 | Digit rem; |
753 | __asm__("divl %[divisor]" |
754 | // Outputs: {quotient} will be in eax, {rem} in edx. |
755 | : "=a" (quotient), "=d" (rem) |
756 | // Inputs: put {high} into edx, {low} into eax, and {divisor} into |
757 | // any register or stack slot. |
758 | : "d" (high), "a" (low), [divisor] "rm" (divisor)); |
759 | remainder = rem; |
760 | return quotient; |
761 | #else |
762 | static constexpr Digit halfDigitBase = 1ull << halfDigitBits; |
763 | // Adapted from Warren, Hacker's Delight, p. 152. |
764 | unsigned s = clz(divisor); |
765 | // If {s} is digitBits here, it causes an undefined behavior. |
766 | // But {s} is never digitBits since {divisor} is never zero here. |
767 | ASSERT(s != digitBits); |
768 | divisor <<= s; |
769 | |
770 | Digit vn1 = divisor >> halfDigitBits; |
771 | Digit vn0 = divisor & halfDigitMask; |
772 | |
773 | // {sZeroMask} which is 0 if s == 0 and all 1-bits otherwise. |
774 | // {s} can be 0. If {s} is 0, performing "low >> (digitBits - s)" must not be done since it causes an undefined behavior |
775 | // since `>> digitBits` is undefied in C++. Quoted from C++ spec, "The type of the result is that of the promoted left operand. |
776 | // The behavior is undefined if the right operand is negative, or greater than or equal to the length in bits of the promoted |
777 | // left operand". We mask the right operand of the shift by {shiftMask} (`digitBits - 1`), which makes `digitBits - 0` zero. |
778 | // This shifting produces a value which covers 0 < {s} <= (digitBits - 1) cases. {s} == digitBits never happen as we asserted. |
779 | // Since {sZeroMask} clears the value in the case of {s} == 0, {s} == 0 case is also covered. |
780 | STATIC_ASSERT(sizeof(CPURegister) == sizeof(Digit)); |
781 | Digit sZeroMask = static_cast<Digit>((-static_cast<CPURegister>(s)) >> (digitBits - 1)); |
782 | static constexpr unsigned shiftMask = digitBits - 1; |
783 | Digit un32 = (high << s) | ((low >> ((digitBits - s) & shiftMask)) & sZeroMask); |
784 | |
785 | Digit un10 = low << s; |
786 | Digit un1 = un10 >> halfDigitBits; |
787 | Digit un0 = un10 & halfDigitMask; |
788 | Digit q1 = un32 / vn1; |
789 | Digit rhat = un32 - q1 * vn1; |
790 | |
791 | while (q1 >= halfDigitBase || q1 * vn0 > rhat * halfDigitBase + un1) { |
792 | q1--; |
793 | rhat += vn1; |
794 | if (rhat >= halfDigitBase) |
795 | break; |
796 | } |
797 | |
798 | Digit un21 = un32 * halfDigitBase + un1 - q1 * divisor; |
799 | Digit q0 = un21 / vn1; |
800 | rhat = un21 - q0 * vn1; |
801 | |
802 | while (q0 >= halfDigitBase || q0 * vn0 > rhat * halfDigitBase + un0) { |
803 | q0--; |
804 | rhat += vn1; |
805 | if (rhat >= halfDigitBase) |
806 | break; |
807 | } |
808 | |
809 | remainder = (un21 * halfDigitBase + un0 - q0 * divisor) >> s; |
810 | return q1 * halfDigitBase + q0; |
811 | #endif |
812 | } |
813 | |
814 | // Multiplies {source} with {factor} and adds {summand} to the result. |
815 | // {result} and {source} may be the same BigInt for inplace modification. |
816 | void JSBigInt::internalMultiplyAdd(JSBigInt* source, Digit factor, Digit summand, unsigned n, JSBigInt* result) |
817 | { |
818 | ASSERT(source->length() >= n); |
819 | ASSERT(result->length() >= n); |
820 | |
821 | Digit carry = summand; |
822 | Digit high = 0; |
823 | for (unsigned i = 0; i < n; i++) { |
824 | Digit current = source->digit(i); |
825 | Digit newCarry = 0; |
826 | |
827 | // Compute this round's multiplication. |
828 | Digit newHigh = 0; |
829 | current = digitMul(current, factor, newHigh); |
830 | |
831 | // Add last round's carryovers. |
832 | current = digitAdd(current, high, newCarry); |
833 | current = digitAdd(current, carry, newCarry); |
834 | |
835 | // Store result and prepare for next round. |
836 | result->setDigit(i, current); |
837 | carry = newCarry; |
838 | high = newHigh; |
839 | } |
840 | |
841 | if (result->length() > n) { |
842 | result->setDigit(n++, carry + high); |
843 | |
844 | // Current callers don't pass in such large results, but let's be robust. |
845 | while (n < result->length()) |
846 | result->setDigit(n++, 0); |
847 | } else |
848 | ASSERT(!(carry + high)); |
849 | } |
850 | |
851 | // Multiplies {multiplicand} with {multiplier} and adds the result to |
852 | // {accumulator}, starting at {accumulatorIndex} for the least-significant |
853 | // digit. |
854 | // Callers must ensure that {accumulator} is big enough to hold the result. |
855 | void JSBigInt::multiplyAccumulate(JSBigInt* multiplicand, Digit multiplier, JSBigInt* accumulator, unsigned accumulatorIndex) |
856 | { |
857 | ASSERT(accumulator->length() > multiplicand->length() + accumulatorIndex); |
858 | if (!multiplier) |
859 | return; |
860 | |
861 | Digit carry = 0; |
862 | Digit high = 0; |
863 | for (unsigned i = 0; i < multiplicand->length(); i++, accumulatorIndex++) { |
864 | Digit acc = accumulator->digit(accumulatorIndex); |
865 | Digit newCarry = 0; |
866 | |
867 | // Add last round's carryovers. |
868 | acc = digitAdd(acc, high, newCarry); |
869 | acc = digitAdd(acc, carry, newCarry); |
870 | |
871 | // Compute this round's multiplication. |
872 | Digit multiplicandDigit = multiplicand->digit(i); |
873 | Digit low = digitMul(multiplier, multiplicandDigit, high); |
874 | acc = digitAdd(acc, low, newCarry); |
875 | |
876 | // Store result and prepare for next round. |
877 | accumulator->setDigit(accumulatorIndex, acc); |
878 | carry = newCarry; |
879 | } |
880 | |
881 | while (carry || high) { |
882 | ASSERT(accumulatorIndex < accumulator->length()); |
883 | Digit acc = accumulator->digit(accumulatorIndex); |
884 | Digit newCarry = 0; |
885 | acc = digitAdd(acc, high, newCarry); |
886 | high = 0; |
887 | acc = digitAdd(acc, carry, newCarry); |
888 | accumulator->setDigit(accumulatorIndex, acc); |
889 | carry = newCarry; |
890 | accumulatorIndex++; |
891 | } |
892 | } |
893 | |
894 | bool JSBigInt::equals(JSBigInt* x, JSBigInt* y) |
895 | { |
896 | if (x->sign() != y->sign()) |
897 | return false; |
898 | |
899 | if (x->length() != y->length()) |
900 | return false; |
901 | |
902 | for (unsigned i = 0; i < x->length(); i++) { |
903 | if (x->digit(i) != y->digit(i)) |
904 | return false; |
905 | } |
906 | |
907 | return true; |
908 | } |
909 | |
910 | JSBigInt::ComparisonResult JSBigInt::compare(JSBigInt* x, JSBigInt* y) |
911 | { |
912 | bool xSign = x->sign(); |
913 | |
914 | if (xSign != y->sign()) |
915 | return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan; |
916 | |
917 | ComparisonResult result = absoluteCompare(x, y); |
918 | if (result == ComparisonResult::GreaterThan) |
919 | return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan; |
920 | if (result == ComparisonResult::LessThan) |
921 | return xSign ? ComparisonResult::GreaterThan : ComparisonResult::LessThan; |
922 | |
923 | return ComparisonResult::Equal; |
924 | } |
925 | |
926 | inline JSBigInt::ComparisonResult JSBigInt::absoluteCompare(JSBigInt* x, JSBigInt* y) |
927 | { |
928 | ASSERT(!x->length() || x->digit(x->length() - 1)); |
929 | ASSERT(!y->length() || y->digit(y->length() - 1)); |
930 | |
931 | int diff = x->length() - y->length(); |
932 | if (diff) |
933 | return diff < 0 ? ComparisonResult::LessThan : ComparisonResult::GreaterThan; |
934 | |
935 | int i = x->length() - 1; |
936 | while (i >= 0 && x->digit(i) == y->digit(i)) |
937 | i--; |
938 | |
939 | if (i < 0) |
940 | return ComparisonResult::Equal; |
941 | |
942 | return x->digit(i) > y->digit(i) ? ComparisonResult::GreaterThan : ComparisonResult::LessThan; |
943 | } |
944 | |
945 | JSBigInt* JSBigInt::absoluteAdd(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y, bool resultSign) |
946 | { |
947 | VM& vm = globalObject->vm(); |
948 | |
949 | if (x->length() < y->length()) |
950 | return absoluteAdd(globalObject, y, x, resultSign); |
951 | |
952 | if (x->isZero()) { |
953 | ASSERT(y->isZero()); |
954 | return x; |
955 | } |
956 | |
957 | if (y->isZero()) |
958 | return resultSign == x->sign() ? x : unaryMinus(vm, x); |
959 | |
960 | JSBigInt* result = JSBigInt::tryCreateWithLength(globalObject, x->length() + 1); |
961 | if (!result) |
962 | return nullptr; |
963 | Digit carry = 0; |
964 | unsigned i = 0; |
965 | for (; i < y->length(); i++) { |
966 | Digit newCarry = 0; |
967 | Digit sum = digitAdd(x->digit(i), y->digit(i), newCarry); |
968 | sum = digitAdd(sum, carry, newCarry); |
969 | result->setDigit(i, sum); |
970 | carry = newCarry; |
971 | } |
972 | |
973 | for (; i < x->length(); i++) { |
974 | Digit newCarry = 0; |
975 | Digit sum = digitAdd(x->digit(i), carry, newCarry); |
976 | result->setDigit(i, sum); |
977 | carry = newCarry; |
978 | } |
979 | |
980 | result->setDigit(i, carry); |
981 | result->setSign(resultSign); |
982 | |
983 | return result->rightTrim(vm); |
984 | } |
985 | |
986 | JSBigInt* JSBigInt::absoluteSub(VM& vm, JSBigInt* x, JSBigInt* y, bool resultSign) |
987 | { |
988 | ComparisonResult comparisonResult = absoluteCompare(x, y); |
989 | ASSERT(x->length() >= y->length()); |
990 | ASSERT(comparisonResult == ComparisonResult::GreaterThan || comparisonResult == ComparisonResult::Equal); |
991 | |
992 | if (x->isZero()) { |
993 | ASSERT(y->isZero()); |
994 | return x; |
995 | } |
996 | |
997 | if (y->isZero()) |
998 | return resultSign == x->sign() ? x : unaryMinus(vm, x); |
999 | |
1000 | if (comparisonResult == ComparisonResult::Equal) |
1001 | return JSBigInt::createZero(vm); |
1002 | |
1003 | JSBigInt* result = JSBigInt::createWithLengthUnchecked(vm, x->length()); |
1004 | |
1005 | Digit borrow = 0; |
1006 | unsigned i = 0; |
1007 | for (; i < y->length(); i++) { |
1008 | Digit newBorrow = 0; |
1009 | Digit difference = digitSub(x->digit(i), y->digit(i), newBorrow); |
1010 | difference = digitSub(difference, borrow, newBorrow); |
1011 | result->setDigit(i, difference); |
1012 | borrow = newBorrow; |
1013 | } |
1014 | |
1015 | for (; i < x->length(); i++) { |
1016 | Digit newBorrow = 0; |
1017 | Digit difference = digitSub(x->digit(i), borrow, newBorrow); |
1018 | result->setDigit(i, difference); |
1019 | borrow = newBorrow; |
1020 | } |
1021 | |
1022 | ASSERT(!borrow); |
1023 | result->setSign(resultSign); |
1024 | return result->rightTrim(vm); |
1025 | } |
1026 | |
1027 | // Divides {x} by {divisor}, returning the result in {quotient} and {remainder}. |
1028 | // Mathematically, the contract is: |
1029 | // quotient = (x - remainder) / divisor, with 0 <= remainder < divisor. |
1030 | // If {quotient} is an empty handle, an appropriately sized BigInt will be |
1031 | // allocated for it; otherwise the caller must ensure that it is big enough. |
1032 | // {quotient} can be the same as {x} for an in-place division. {quotient} can |
1033 | // also be nullptr if the caller is only interested in the remainder. |
1034 | void JSBigInt::absoluteDivWithDigitDivisor(VM& vm, JSBigInt* x, Digit divisor, JSBigInt** quotient, Digit& remainder) |
1035 | { |
1036 | ASSERT(divisor); |
1037 | |
1038 | ASSERT(!x->isZero()); |
1039 | remainder = 0; |
1040 | if (divisor == 1) { |
1041 | if (quotient != nullptr) |
1042 | *quotient = x; |
1043 | return; |
1044 | } |
1045 | |
1046 | unsigned length = x->length(); |
1047 | if (quotient != nullptr) { |
1048 | if (*quotient == nullptr) |
1049 | *quotient = JSBigInt::createWithLengthUnchecked(vm, length); |
1050 | |
1051 | for (int i = length - 1; i >= 0; i--) { |
1052 | Digit q = digitDiv(remainder, x->digit(i), divisor, remainder); |
1053 | (*quotient)->setDigit(i, q); |
1054 | } |
1055 | } else { |
1056 | for (int i = length - 1; i >= 0; i--) |
1057 | digitDiv(remainder, x->digit(i), divisor, remainder); |
1058 | } |
1059 | } |
1060 | |
1061 | // Divides {dividend} by {divisor}, returning the result in {quotient} and |
1062 | // {remainder}. Mathematically, the contract is: |
1063 | // quotient = (dividend - remainder) / divisor, with 0 <= remainder < divisor. |
1064 | // Both {quotient} and {remainder} are optional, for callers that are only |
1065 | // interested in one of them. |
1066 | // See Knuth, Volume 2, section 4.3.1, Algorithm D. |
1067 | void JSBigInt::absoluteDivWithBigIntDivisor(JSGlobalObject* globalObject, JSBigInt* dividend, JSBigInt* divisor, JSBigInt** quotient, JSBigInt** remainder) |
1068 | { |
1069 | ASSERT(divisor->length() >= 2); |
1070 | ASSERT(dividend->length() >= divisor->length()); |
1071 | VM& vm = globalObject->vm(); |
1072 | auto scope = DECLARE_THROW_SCOPE(vm); |
1073 | |
1074 | // The unusual variable names inside this function are consistent with |
1075 | // Knuth's book, as well as with Go's implementation of this algorithm. |
1076 | // Maintaining this consistency is probably more useful than trying to |
1077 | // come up with more descriptive names for them. |
1078 | unsigned n = divisor->length(); |
1079 | unsigned m = dividend->length() - n; |
1080 | |
1081 | // The quotient to be computed. |
1082 | JSBigInt* q = nullptr; |
1083 | if (quotient != nullptr) |
1084 | q = createWithLengthUnchecked(globalObject->vm(), m + 1); |
1085 | |
1086 | // In each iteration, {qhatv} holds {divisor} * {current quotient digit}. |
1087 | // "v" is the book's name for {divisor}, "qhat" the current quotient digit. |
1088 | JSBigInt* qhatv = tryCreateWithLength(globalObject, n + 1); |
1089 | RETURN_IF_EXCEPTION(scope, void()); |
1090 | |
1091 | // D1. |
1092 | // Left-shift inputs so that the divisor's MSB is set. This is necessary |
1093 | // to prevent the digit-wise divisions (see digit_div call below) from |
1094 | // overflowing (they take a two digits wide input, and return a one digit |
1095 | // result). |
1096 | Digit lastDigit = divisor->digit(n - 1); |
1097 | unsigned shift = clz(lastDigit); |
1098 | |
1099 | if (shift > 0) { |
1100 | divisor = absoluteLeftShiftAlwaysCopy(globalObject, divisor, shift, LeftShiftMode::SameSizeResult); |
1101 | RETURN_IF_EXCEPTION(scope, void()); |
1102 | } |
1103 | |
1104 | // Holds the (continuously updated) remaining part of the dividend, which |
1105 | // eventually becomes the remainder. |
1106 | JSBigInt* u = absoluteLeftShiftAlwaysCopy(globalObject, dividend, shift, LeftShiftMode::AlwaysAddOneDigit); |
1107 | RETURN_IF_EXCEPTION(scope, void()); |
1108 | |
1109 | // D2. |
1110 | // Iterate over the dividend's digit (like the "grad school" algorithm). |
1111 | // {vn1} is the divisor's most significant digit. |
1112 | Digit vn1 = divisor->digit(n - 1); |
1113 | for (int j = m; j >= 0; j--) { |
1114 | // D3. |
1115 | // Estimate the current iteration's quotient digit (see Knuth for details). |
1116 | // {qhat} is the current quotient digit. |
1117 | Digit qhat = std::numeric_limits<Digit>::max(); |
1118 | |
1119 | // {ujn} is the dividend's most significant remaining digit. |
1120 | Digit ujn = u->digit(j + n); |
1121 | if (ujn != vn1) { |
1122 | // {rhat} is the current iteration's remainder. |
1123 | Digit rhat = 0; |
1124 | // Estimate the current quotient digit by dividing the most significant |
1125 | // digits of dividend and divisor. The result will not be too small, |
1126 | // but could be a bit too large. |
1127 | qhat = digitDiv(ujn, u->digit(j + n - 1), vn1, rhat); |
1128 | |
1129 | // Decrement the quotient estimate as needed by looking at the next |
1130 | // digit, i.e. by testing whether |
1131 | // qhat * v_{n-2} > (rhat << digitBits) + u_{j+n-2}. |
1132 | Digit vn2 = divisor->digit(n - 2); |
1133 | Digit ujn2 = u->digit(j + n - 2); |
1134 | while (productGreaterThan(qhat, vn2, rhat, ujn2)) { |
1135 | qhat--; |
1136 | Digit prevRhat = rhat; |
1137 | rhat += vn1; |
1138 | // v[n-1] >= 0, so this tests for overflow. |
1139 | if (rhat < prevRhat) |
1140 | break; |
1141 | } |
1142 | } |
1143 | |
1144 | // D4. |
1145 | // Multiply the divisor with the current quotient digit, and subtract |
1146 | // it from the dividend. If there was "borrow", then the quotient digit |
1147 | // was one too high, so we must correct it and undo one subtraction of |
1148 | // the (shifted) divisor. |
1149 | internalMultiplyAdd(divisor, qhat, 0, n, qhatv); |
1150 | Digit c = u->absoluteInplaceSub(qhatv, j); |
1151 | if (c) { |
1152 | c = u->absoluteInplaceAdd(divisor, j); |
1153 | u->setDigit(j + n, u->digit(j + n) + c); |
1154 | qhat--; |
1155 | } |
1156 | |
1157 | if (quotient != nullptr) |
1158 | q->setDigit(j, qhat); |
1159 | } |
1160 | |
1161 | if (quotient != nullptr) { |
1162 | // Caller will right-trim. |
1163 | *quotient = q; |
1164 | } |
1165 | |
1166 | if (remainder != nullptr) { |
1167 | u->inplaceRightShift(shift); |
1168 | *remainder = u; |
1169 | } |
1170 | } |
1171 | |
1172 | // Returns whether (factor1 * factor2) > (high << digitBits) + low. |
1173 | inline bool JSBigInt::productGreaterThan(Digit factor1, Digit factor2, Digit high, Digit low) |
1174 | { |
1175 | Digit resultHigh; |
1176 | Digit resultLow = digitMul(factor1, factor2, resultHigh); |
1177 | return resultHigh > high || (resultHigh == high && resultLow > low); |
1178 | } |
1179 | |
1180 | // Adds {summand} onto {this}, starting with {summand}'s 0th digit |
1181 | // at {this}'s {startIndex}'th digit. Returns the "carry" (0 or 1). |
1182 | JSBigInt::Digit JSBigInt::absoluteInplaceAdd(JSBigInt* summand, unsigned startIndex) |
1183 | { |
1184 | Digit carry = 0; |
1185 | unsigned n = summand->length(); |
1186 | ASSERT(length() >= startIndex + n); |
1187 | for (unsigned i = 0; i < n; i++) { |
1188 | Digit newCarry = 0; |
1189 | Digit sum = digitAdd(digit(startIndex + i), summand->digit(i), newCarry); |
1190 | sum = digitAdd(sum, carry, newCarry); |
1191 | setDigit(startIndex + i, sum); |
1192 | carry = newCarry; |
1193 | } |
1194 | |
1195 | return carry; |
1196 | } |
1197 | |
1198 | // Subtracts {subtrahend} from {this}, starting with {subtrahend}'s 0th digit |
1199 | // at {this}'s {startIndex}-th digit. Returns the "borrow" (0 or 1). |
1200 | JSBigInt::Digit JSBigInt::absoluteInplaceSub(JSBigInt* subtrahend, unsigned startIndex) |
1201 | { |
1202 | Digit borrow = 0; |
1203 | unsigned n = subtrahend->length(); |
1204 | ASSERT(length() >= startIndex + n); |
1205 | for (unsigned i = 0; i < n; i++) { |
1206 | Digit newBorrow = 0; |
1207 | Digit difference = digitSub(digit(startIndex + i), subtrahend->digit(i), newBorrow); |
1208 | difference = digitSub(difference, borrow, newBorrow); |
1209 | setDigit(startIndex + i, difference); |
1210 | borrow = newBorrow; |
1211 | } |
1212 | |
1213 | return borrow; |
1214 | } |
1215 | |
1216 | void JSBigInt::inplaceRightShift(unsigned shift) |
1217 | { |
1218 | ASSERT(shift < digitBits); |
1219 | ASSERT(!(digit(0) & ((static_cast<Digit>(1) << shift) - 1))); |
1220 | |
1221 | if (!shift) |
1222 | return; |
1223 | |
1224 | Digit carry = digit(0) >> shift; |
1225 | unsigned last = length() - 1; |
1226 | for (unsigned i = 0; i < last; i++) { |
1227 | Digit d = digit(i + 1); |
1228 | setDigit(i, (d << (digitBits - shift)) | carry); |
1229 | carry = d >> shift; |
1230 | } |
1231 | setDigit(last, carry); |
1232 | } |
1233 | |
1234 | // Always copies the input, even when {shift} == 0. |
1235 | JSBigInt* JSBigInt::absoluteLeftShiftAlwaysCopy(JSGlobalObject* globalObject, JSBigInt* x, unsigned shift, LeftShiftMode mode) |
1236 | { |
1237 | ASSERT(shift < digitBits); |
1238 | ASSERT(!x->isZero()); |
1239 | |
1240 | unsigned n = x->length(); |
1241 | unsigned resultLength = mode == LeftShiftMode::AlwaysAddOneDigit ? n + 1 : n; |
1242 | JSBigInt* result = tryCreateWithLength(globalObject, resultLength); |
1243 | if (!result) |
1244 | return nullptr; |
1245 | |
1246 | if (!shift) { |
1247 | for (unsigned i = 0; i < n; i++) |
1248 | result->setDigit(i, x->digit(i)); |
1249 | if (mode == LeftShiftMode::AlwaysAddOneDigit) |
1250 | result->setDigit(n, 0); |
1251 | |
1252 | return result; |
1253 | } |
1254 | |
1255 | Digit carry = 0; |
1256 | for (unsigned i = 0; i < n; i++) { |
1257 | Digit d = x->digit(i); |
1258 | result->setDigit(i, (d << shift) | carry); |
1259 | carry = d >> (digitBits - shift); |
1260 | } |
1261 | |
1262 | if (mode == LeftShiftMode::AlwaysAddOneDigit) |
1263 | result->setDigit(n, carry); |
1264 | else { |
1265 | ASSERT(mode == LeftShiftMode::SameSizeResult); |
1266 | ASSERT(!carry); |
1267 | } |
1268 | |
1269 | return result; |
1270 | } |
1271 | |
1272 | // Helper for Absolute{And,AndNot,Or,Xor}. |
1273 | // Performs the given binary {op} on digit pairs of {x} and {y}; when the |
1274 | // end of the shorter of the two is reached, {extraDigits} configures how |
1275 | // remaining digits in the longer input (if {symmetric} == Symmetric, in |
1276 | // {x} otherwise) are handled: copied to the result or ignored. |
1277 | // Example: |
1278 | // y: [ y2 ][ y1 ][ y0 ] |
1279 | // x: [ x3 ][ x2 ][ x1 ][ x0 ] |
1280 | // | | | | |
1281 | // (Copy) (op) (op) (op) |
1282 | // | | | | |
1283 | // v v v v |
1284 | // result: [ 0 ][ x3 ][ r2 ][ r1 ][ r0 ] |
1285 | template<typename BitwiseOp> |
1286 | inline JSBigInt* JSBigInt::absoluteBitwiseOp(VM& vm, JSBigInt* x, JSBigInt* y, ExtraDigitsHandling , SymmetricOp symmetric, BitwiseOp&& op) |
1287 | { |
1288 | unsigned xLength = x->length(); |
1289 | unsigned yLength = y->length(); |
1290 | unsigned numPairs = yLength; |
1291 | if (xLength < yLength) { |
1292 | numPairs = xLength; |
1293 | if (symmetric == SymmetricOp::Symmetric) { |
1294 | std::swap(x, y); |
1295 | std::swap(xLength, yLength); |
1296 | } |
1297 | } |
1298 | |
1299 | ASSERT(numPairs == std::min(xLength, yLength)); |
1300 | unsigned resultLength = extraDigits == ExtraDigitsHandling::Copy ? xLength : numPairs; |
1301 | JSBigInt* result = createWithLengthUnchecked(vm, resultLength); |
1302 | unsigned i = 0; |
1303 | for (; i < numPairs; i++) |
1304 | result->setDigit(i, op(x->digit(i), y->digit(i))); |
1305 | |
1306 | if (extraDigits == ExtraDigitsHandling::Copy) { |
1307 | for (; i < xLength; i++) |
1308 | result->setDigit(i, x->digit(i)); |
1309 | } |
1310 | |
1311 | for (; i < resultLength; i++) |
1312 | result->setDigit(i, 0); |
1313 | |
1314 | return result->rightTrim(vm); |
1315 | } |
1316 | |
1317 | JSBigInt* JSBigInt::absoluteAnd(VM& vm, JSBigInt* x, JSBigInt* y) |
1318 | { |
1319 | auto digitOperation = [](Digit a, Digit b) { |
1320 | return a & b; |
1321 | }; |
1322 | return absoluteBitwiseOp(vm, x, y, ExtraDigitsHandling::Skip, SymmetricOp::Symmetric, digitOperation); |
1323 | } |
1324 | |
1325 | JSBigInt* JSBigInt::absoluteOr(VM& vm, JSBigInt* x, JSBigInt* y) |
1326 | { |
1327 | auto digitOperation = [](Digit a, Digit b) { |
1328 | return a | b; |
1329 | }; |
1330 | return absoluteBitwiseOp(vm, x, y, ExtraDigitsHandling::Copy, SymmetricOp::Symmetric, digitOperation); |
1331 | } |
1332 | |
1333 | JSBigInt* JSBigInt::absoluteAndNot(VM& vm, JSBigInt* x, JSBigInt* y) |
1334 | { |
1335 | auto digitOperation = [](Digit a, Digit b) { |
1336 | return a & ~b; |
1337 | }; |
1338 | return absoluteBitwiseOp(vm, x, y, ExtraDigitsHandling::Copy, SymmetricOp::NotSymmetric, digitOperation); |
1339 | } |
1340 | |
1341 | JSBigInt* JSBigInt::absoluteXor(VM& vm, JSBigInt* x, JSBigInt* y) |
1342 | { |
1343 | auto digitOperation = [](Digit a, Digit b) { |
1344 | return a ^ b; |
1345 | }; |
1346 | return absoluteBitwiseOp(vm, x, y, ExtraDigitsHandling::Copy, SymmetricOp::Symmetric, digitOperation); |
1347 | } |
1348 | |
1349 | JSBigInt* JSBigInt::absoluteAddOne(JSGlobalObject* globalObject, JSBigInt* x, SignOption signOption) |
1350 | { |
1351 | unsigned inputLength = x->length(); |
1352 | // The addition will overflow into a new digit if all existing digits are |
1353 | // at maximum. |
1354 | bool willOverflow = true; |
1355 | for (unsigned i = 0; i < inputLength; i++) { |
1356 | if (std::numeric_limits<Digit>::max() != x->digit(i)) { |
1357 | willOverflow = false; |
1358 | break; |
1359 | } |
1360 | } |
1361 | |
1362 | unsigned resultLength = inputLength + willOverflow; |
1363 | JSBigInt* result = tryCreateWithLength(globalObject, resultLength); |
1364 | if (!result) |
1365 | return nullptr; |
1366 | |
1367 | Digit carry = 1; |
1368 | for (unsigned i = 0; i < inputLength; i++) { |
1369 | Digit newCarry = 0; |
1370 | result->setDigit(i, digitAdd(x->digit(i), carry, newCarry)); |
1371 | carry = newCarry; |
1372 | } |
1373 | if (resultLength > inputLength) |
1374 | result->setDigit(inputLength, carry); |
1375 | else |
1376 | ASSERT(!carry); |
1377 | |
1378 | result->setSign(signOption == SignOption::Signed); |
1379 | return result->rightTrim(globalObject->vm()); |
1380 | } |
1381 | |
1382 | JSBigInt* JSBigInt::absoluteSubOne(JSGlobalObject* globalObject, JSBigInt* x, unsigned resultLength) |
1383 | { |
1384 | ASSERT(!x->isZero()); |
1385 | ASSERT(resultLength >= x->length()); |
1386 | VM& vm = globalObject->vm(); |
1387 | auto scope = DECLARE_THROW_SCOPE(vm); |
1388 | |
1389 | JSBigInt* result = tryCreateWithLength(globalObject, resultLength); |
1390 | RETURN_IF_EXCEPTION(scope, nullptr); |
1391 | |
1392 | unsigned length = x->length(); |
1393 | Digit borrow = 1; |
1394 | for (unsigned i = 0; i < length; i++) { |
1395 | Digit newBorrow = 0; |
1396 | result->setDigit(i, digitSub(x->digit(i), borrow, newBorrow)); |
1397 | borrow = newBorrow; |
1398 | } |
1399 | ASSERT(!borrow); |
1400 | for (unsigned i = length; i < resultLength; i++) |
1401 | result->setDigit(i, borrow); |
1402 | |
1403 | return result->rightTrim(vm); |
1404 | } |
1405 | |
1406 | JSBigInt* JSBigInt::leftShiftByAbsolute(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
1407 | { |
1408 | VM& vm = globalObject->vm(); |
1409 | auto scope = DECLARE_THROW_SCOPE(vm); |
1410 | |
1411 | auto optionalShift = toShiftAmount(y); |
1412 | if (!optionalShift) { |
1413 | throwRangeError(globalObject, scope, "BigInt generated from this operation is too big"_s ); |
1414 | return nullptr; |
1415 | } |
1416 | |
1417 | Digit shift = *optionalShift; |
1418 | unsigned digitShift = static_cast<unsigned>(shift / digitBits); |
1419 | unsigned bitsShift = static_cast<unsigned>(shift % digitBits); |
1420 | unsigned length = x->length(); |
1421 | bool grow = bitsShift && (x->digit(length - 1) >> (digitBits - bitsShift)); |
1422 | int resultLength = length + digitShift + grow; |
1423 | if (static_cast<unsigned>(resultLength) > maxLength) { |
1424 | throwRangeError(globalObject, scope, "BigInt generated from this operation is too big"_s ); |
1425 | return nullptr; |
1426 | } |
1427 | |
1428 | JSBigInt* result = tryCreateWithLength(globalObject, resultLength); |
1429 | RETURN_IF_EXCEPTION(scope, nullptr); |
1430 | if (!bitsShift) { |
1431 | unsigned i = 0; |
1432 | for (; i < digitShift; i++) |
1433 | result->setDigit(i, 0ul); |
1434 | |
1435 | for (; i < static_cast<unsigned>(resultLength); i++) |
1436 | result->setDigit(i, x->digit(i - digitShift)); |
1437 | } else { |
1438 | Digit carry = 0; |
1439 | for (unsigned i = 0; i < digitShift; i++) |
1440 | result->setDigit(i, 0ul); |
1441 | |
1442 | for (unsigned i = 0; i < length; i++) { |
1443 | Digit d = x->digit(i); |
1444 | result->setDigit(i + digitShift, (d << bitsShift) | carry); |
1445 | carry = d >> (digitBits - bitsShift); |
1446 | } |
1447 | |
1448 | if (grow) |
1449 | result->setDigit(length + digitShift, carry); |
1450 | else |
1451 | ASSERT(!carry); |
1452 | } |
1453 | |
1454 | result->setSign(x->sign()); |
1455 | return result->rightTrim(vm); |
1456 | } |
1457 | |
1458 | JSBigInt* JSBigInt::rightShiftByAbsolute(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y) |
1459 | { |
1460 | VM& vm = globalObject->vm(); |
1461 | unsigned length = x->length(); |
1462 | bool sign = x->sign(); |
1463 | auto optionalShift = toShiftAmount(y); |
1464 | if (!optionalShift) |
1465 | return rightShiftByMaximum(vm, sign); |
1466 | |
1467 | Digit shift = *optionalShift; |
1468 | unsigned digitalShift = static_cast<unsigned>(shift / digitBits); |
1469 | unsigned bitsShift = static_cast<unsigned>(shift % digitBits); |
1470 | int resultLength = length - digitalShift; |
1471 | if (resultLength <= 0) |
1472 | return rightShiftByMaximum(vm, sign); |
1473 | |
1474 | // For negative numbers, round down if any bit was shifted out (so that e.g. |
1475 | // -5n >> 1n == -3n and not -2n). Check now whether this will happen and |
1476 | // whether it can cause overflow into a new digit. If we allocate the result |
1477 | // large enough up front, it avoids having to do a second allocation later. |
1478 | bool mustRoundDown = false; |
1479 | if (sign) { |
1480 | const Digit mask = (static_cast<Digit>(1) << bitsShift) - 1; |
1481 | if (x->digit(digitalShift) & mask) |
1482 | mustRoundDown = true; |
1483 | else { |
1484 | for (unsigned i = 0; i < digitalShift; i++) { |
1485 | if (x->digit(i)) { |
1486 | mustRoundDown = true; |
1487 | break; |
1488 | } |
1489 | } |
1490 | } |
1491 | } |
1492 | |
1493 | // If bitsShift is non-zero, it frees up bits, preventing overflow. |
1494 | if (mustRoundDown && !bitsShift) { |
1495 | // Overflow cannot happen if the most significant digit has unset bits. |
1496 | Digit msd = x->digit(length - 1); |
1497 | bool roundingCanOverflow = !static_cast<Digit>(~msd); |
1498 | if (roundingCanOverflow) |
1499 | resultLength++; |
1500 | } |
1501 | |
1502 | ASSERT(static_cast<unsigned>(resultLength) <= length); |
1503 | JSBigInt* result = createWithLengthUnchecked(vm, static_cast<unsigned>(resultLength)); |
1504 | if (!bitsShift) { |
1505 | for (unsigned i = digitalShift; i < length; i++) |
1506 | result->setDigit(i - digitalShift, x->digit(i)); |
1507 | } else { |
1508 | Digit carry = x->digit(digitalShift) >> bitsShift; |
1509 | unsigned last = length - digitalShift - 1; |
1510 | for (unsigned i = 0; i < last; i++) { |
1511 | Digit d = x->digit(i + digitalShift + 1); |
1512 | result->setDigit(i, (d << (digitBits - bitsShift)) | carry); |
1513 | carry = d >> bitsShift; |
1514 | } |
1515 | result->setDigit(last, carry); |
1516 | } |
1517 | |
1518 | if (sign) { |
1519 | result->setSign(true); |
1520 | if (mustRoundDown) { |
1521 | // Since the result is negative, rounding down means adding one to |
1522 | // its absolute value. This cannot overflow. |
1523 | result = result->rightTrim(vm); |
1524 | return absoluteAddOne(globalObject, result, SignOption::Signed); |
1525 | } |
1526 | } |
1527 | |
1528 | return result->rightTrim(vm); |
1529 | } |
1530 | |
1531 | JSBigInt* JSBigInt::rightShiftByMaximum(VM& vm, bool sign) |
1532 | { |
1533 | if (sign) |
1534 | return createFrom(vm, -1); |
1535 | |
1536 | return createZero(vm); |
1537 | } |
1538 | |
1539 | // Lookup table for the maximum number of bits required per character of a |
1540 | // base-N string representation of a number. To increase accuracy, the array |
1541 | // value is the actual value multiplied by 32. To generate this table: |
1542 | // for (var i = 0; i <= 36; i++) { print(Math.ceil(Math.log2(i) * 32) + ","); } |
1543 | constexpr uint8_t maxBitsPerCharTable[] = { |
1544 | 0, 0, 32, 51, 64, 75, 83, 90, 96, // 0..8 |
1545 | 102, 107, 111, 115, 119, 122, 126, 128, // 9..16 |
1546 | 131, 134, 136, 139, 141, 143, 145, 147, // 17..24 |
1547 | 149, 151, 153, 154, 156, 158, 159, 160, // 25..32 |
1548 | 162, 163, 165, 166, // 33..36 |
1549 | }; |
1550 | |
1551 | static constexpr unsigned bitsPerCharTableShift = 5; |
1552 | static constexpr size_t bitsPerCharTableMultiplier = 1u << bitsPerCharTableShift; |
1553 | |
1554 | // Compute (an overapproximation of) the length of the resulting string: |
1555 | // Divide bit length of the BigInt by bits representable per character. |
1556 | uint64_t JSBigInt::calculateMaximumCharactersRequired(unsigned length, unsigned radix, Digit lastDigit, bool sign) |
1557 | { |
1558 | unsigned leadingZeros = clz(lastDigit); |
1559 | |
1560 | size_t bitLength = length * digitBits - leadingZeros; |
1561 | |
1562 | // Maximum number of bits we can represent with one character. We'll use this |
1563 | // to find an appropriate chunk size below. |
1564 | uint8_t maxBitsPerChar = maxBitsPerCharTable[radix]; |
1565 | |
1566 | // For estimating result length, we have to be pessimistic and work with |
1567 | // the minimum number of bits one character can represent. |
1568 | uint8_t minBitsPerChar = maxBitsPerChar - 1; |
1569 | |
1570 | // Perform the following computation with uint64_t to avoid overflows. |
1571 | uint64_t maximumCharactersRequired = bitLength; |
1572 | maximumCharactersRequired *= bitsPerCharTableMultiplier; |
1573 | |
1574 | // Round up. |
1575 | maximumCharactersRequired += minBitsPerChar - 1; |
1576 | maximumCharactersRequired /= minBitsPerChar; |
1577 | maximumCharactersRequired += sign; |
1578 | |
1579 | return maximumCharactersRequired; |
1580 | } |
1581 | |
1582 | String JSBigInt::toStringBasePowerOfTwo(VM& vm, JSGlobalObject* globalObject, JSBigInt* x, unsigned radix) |
1583 | { |
1584 | ASSERT(hasOneBitSet(radix)); |
1585 | ASSERT(radix >= 2 && radix <= 32); |
1586 | ASSERT(!x->isZero()); |
1587 | |
1588 | const unsigned length = x->length(); |
1589 | const bool sign = x->sign(); |
1590 | const unsigned bitsPerChar = ctz(radix); |
1591 | const unsigned charMask = radix - 1; |
1592 | // Compute the length of the resulting string: divide the bit length of the |
1593 | // BigInt by the number of bits representable per character (rounding up). |
1594 | const Digit msd = x->digit(length - 1); |
1595 | |
1596 | const unsigned msdLeadingZeros = clz(msd); |
1597 | |
1598 | const size_t bitLength = length * digitBits - msdLeadingZeros; |
1599 | const size_t charsRequired = (bitLength + bitsPerChar - 1) / bitsPerChar + sign; |
1600 | |
1601 | if (charsRequired > JSString::MaxLength) { |
1602 | if (globalObject) { |
1603 | auto scope = DECLARE_THROW_SCOPE(vm); |
1604 | throwOutOfMemoryError(globalObject, scope); |
1605 | } |
1606 | return String(); |
1607 | } |
1608 | |
1609 | Vector<LChar> resultString(charsRequired); |
1610 | Digit digit = 0; |
1611 | // Keeps track of how many unprocessed bits there are in {digit}. |
1612 | unsigned availableBits = 0; |
1613 | int pos = static_cast<int>(charsRequired - 1); |
1614 | for (unsigned i = 0; i < length - 1; i++) { |
1615 | Digit newDigit = x->digit(i); |
1616 | // Take any leftover bits from the last iteration into account. |
1617 | int current = (digit | (newDigit << availableBits)) & charMask; |
1618 | resultString[pos--] = radixDigits[current]; |
1619 | int consumedBits = bitsPerChar - availableBits; |
1620 | digit = newDigit >> consumedBits; |
1621 | availableBits = digitBits - consumedBits; |
1622 | while (availableBits >= bitsPerChar) { |
1623 | resultString[pos--] = radixDigits[digit & charMask]; |
1624 | digit >>= bitsPerChar; |
1625 | availableBits -= bitsPerChar; |
1626 | } |
1627 | } |
1628 | // Take any leftover bits from the last iteration into account. |
1629 | int current = (digit | (msd << availableBits)) & charMask; |
1630 | resultString[pos--] = radixDigits[current]; |
1631 | digit = msd >> (bitsPerChar - availableBits); |
1632 | while (digit) { |
1633 | resultString[pos--] = radixDigits[digit & charMask]; |
1634 | digit >>= bitsPerChar; |
1635 | } |
1636 | |
1637 | if (sign) |
1638 | resultString[pos--] = '-'; |
1639 | |
1640 | ASSERT(pos == -1); |
1641 | return StringImpl::adopt(WTFMove(resultString)); |
1642 | } |
1643 | |
1644 | String JSBigInt::toStringGeneric(VM& vm, JSGlobalObject* globalObject, JSBigInt* x, unsigned radix) |
1645 | { |
1646 | // FIXME: [JSC] Revisit usage of Vector into JSBigInt::toString |
1647 | // https://bugs.webkit.org/show_bug.cgi?id=18067 |
1648 | Vector<LChar> resultString; |
1649 | |
1650 | ASSERT(radix >= 2 && radix <= 36); |
1651 | ASSERT(!x->isZero()); |
1652 | |
1653 | unsigned length = x->length(); |
1654 | bool sign = x->sign(); |
1655 | |
1656 | uint8_t maxBitsPerChar = maxBitsPerCharTable[radix]; |
1657 | uint64_t maximumCharactersRequired = calculateMaximumCharactersRequired(length, radix, x->digit(length - 1), sign); |
1658 | |
1659 | if (maximumCharactersRequired > JSString::MaxLength) { |
1660 | if (globalObject) { |
1661 | auto scope = DECLARE_THROW_SCOPE(vm); |
1662 | throwOutOfMemoryError(globalObject, scope); |
1663 | } |
1664 | return String(); |
1665 | } |
1666 | |
1667 | Digit lastDigit; |
1668 | if (length == 1) |
1669 | lastDigit = x->digit(0); |
1670 | else { |
1671 | unsigned chunkChars = digitBits * bitsPerCharTableMultiplier / maxBitsPerChar; |
1672 | Digit chunkDivisor = digitPow(radix, chunkChars); |
1673 | |
1674 | // By construction of chunkChars, there can't have been overflow. |
1675 | ASSERT(chunkDivisor); |
1676 | unsigned nonZeroDigit = length - 1; |
1677 | ASSERT(x->digit(nonZeroDigit)); |
1678 | |
1679 | // {rest} holds the part of the BigInt that we haven't looked at yet. |
1680 | // Not to be confused with "remainder"! |
1681 | JSBigInt* rest = nullptr; |
1682 | |
1683 | // In the first round, divide the input, allocating a new BigInt for |
1684 | // the result == rest; from then on divide the rest in-place. |
1685 | JSBigInt** dividend = &x; |
1686 | do { |
1687 | Digit chunk; |
1688 | absoluteDivWithDigitDivisor(vm, *dividend, chunkDivisor, &rest, chunk); |
1689 | dividend = &rest; |
1690 | for (unsigned i = 0; i < chunkChars; i++) { |
1691 | resultString.append(radixDigits[chunk % radix]); |
1692 | chunk /= radix; |
1693 | } |
1694 | ASSERT(!chunk); |
1695 | |
1696 | if (!rest->digit(nonZeroDigit)) |
1697 | nonZeroDigit--; |
1698 | |
1699 | // We can never clear more than one digit per iteration, because |
1700 | // chunkDivisor is smaller than max digit value. |
1701 | ASSERT(rest->digit(nonZeroDigit)); |
1702 | } while (nonZeroDigit > 0); |
1703 | |
1704 | lastDigit = rest->digit(0); |
1705 | } |
1706 | |
1707 | do { |
1708 | resultString.append(radixDigits[lastDigit % radix]); |
1709 | lastDigit /= radix; |
1710 | } while (lastDigit > 0); |
1711 | ASSERT(resultString.size()); |
1712 | ASSERT(resultString.size() <= static_cast<size_t>(maximumCharactersRequired)); |
1713 | |
1714 | // Remove leading zeroes. |
1715 | unsigned newSizeNoLeadingZeroes = resultString.size(); |
1716 | while (newSizeNoLeadingZeroes > 1 && resultString[newSizeNoLeadingZeroes - 1] == '0') |
1717 | newSizeNoLeadingZeroes--; |
1718 | |
1719 | resultString.shrink(newSizeNoLeadingZeroes); |
1720 | |
1721 | if (sign) |
1722 | resultString.append('-'); |
1723 | |
1724 | std::reverse(resultString.begin(), resultString.end()); |
1725 | |
1726 | return StringImpl::adopt(WTFMove(resultString)); |
1727 | } |
1728 | |
1729 | JSBigInt* JSBigInt::rightTrim(VM& vm) |
1730 | { |
1731 | if (isZero()) { |
1732 | ASSERT(!sign()); |
1733 | return this; |
1734 | } |
1735 | |
1736 | int nonZeroIndex = m_length - 1; |
1737 | while (nonZeroIndex >= 0 && !digit(nonZeroIndex)) |
1738 | nonZeroIndex--; |
1739 | |
1740 | if (nonZeroIndex < 0) |
1741 | return createZero(vm); |
1742 | |
1743 | if (nonZeroIndex == static_cast<int>(m_length - 1)) |
1744 | return this; |
1745 | |
1746 | unsigned newLength = nonZeroIndex + 1; |
1747 | JSBigInt* trimmedBigInt = createWithLengthUnchecked(vm, newLength); |
1748 | std::copy(dataStorage(), dataStorage() + newLength, trimmedBigInt->dataStorage()); |
1749 | |
1750 | trimmedBigInt->setSign(this->sign()); |
1751 | |
1752 | return trimmedBigInt; |
1753 | } |
1754 | |
1755 | JSBigInt* JSBigInt::allocateFor(JSGlobalObject* globalObject, VM& vm, unsigned radix, unsigned charcount) |
1756 | { |
1757 | ASSERT(2 <= radix && radix <= 36); |
1758 | |
1759 | size_t bitsPerChar = maxBitsPerCharTable[radix]; |
1760 | size_t chars = charcount; |
1761 | const unsigned roundup = bitsPerCharTableMultiplier - 1; |
1762 | if (chars <= (std::numeric_limits<size_t>::max() - roundup) / bitsPerChar) { |
1763 | size_t bitsMin = bitsPerChar * chars; |
1764 | |
1765 | // Divide by 32 (see table), rounding up. |
1766 | bitsMin = (bitsMin + roundup) >> bitsPerCharTableShift; |
1767 | if (bitsMin <= static_cast<size_t>(maxInt)) { |
1768 | // Divide by kDigitsBits, rounding up. |
1769 | unsigned length = (bitsMin + digitBits - 1) / digitBits; |
1770 | if (length <= maxLength) { |
1771 | JSBigInt* result = JSBigInt::createWithLengthUnchecked(vm, length); |
1772 | return result; |
1773 | } |
1774 | } |
1775 | } |
1776 | |
1777 | if (globalObject) { |
1778 | auto scope = DECLARE_THROW_SCOPE(vm); |
1779 | throwOutOfMemoryError(globalObject, scope); |
1780 | } |
1781 | return nullptr; |
1782 | } |
1783 | |
1784 | size_t JSBigInt::estimatedSize(JSCell* cell, VM& vm) |
1785 | { |
1786 | return Base::estimatedSize(cell, vm) + jsCast<JSBigInt*>(cell)->m_length * sizeof(Digit); |
1787 | } |
1788 | |
1789 | double JSBigInt::toNumber(JSGlobalObject* globalObject) const |
1790 | { |
1791 | VM& vm = globalObject->vm(); |
1792 | auto scope = DECLARE_THROW_SCOPE(vm); |
1793 | throwTypeError(globalObject, scope, "Conversion from 'BigInt' to 'number' is not allowed."_s ); |
1794 | return 0.0; |
1795 | } |
1796 | |
1797 | bool JSBigInt::getPrimitiveNumber(JSGlobalObject* globalObject, double& number, JSValue& result) const |
1798 | { |
1799 | result = this; |
1800 | number = toNumber(globalObject); |
1801 | return true; |
1802 | } |
1803 | |
1804 | template <typename CharType> |
1805 | JSBigInt* JSBigInt::parseInt(JSGlobalObject* globalObject, CharType* data, unsigned length, ErrorParseMode errorParseMode) |
1806 | { |
1807 | VM& vm = globalObject->vm(); |
1808 | |
1809 | unsigned p = 0; |
1810 | while (p < length && isStrWhiteSpace(data[p])) |
1811 | ++p; |
1812 | |
1813 | // Check Radix from frist characters |
1814 | if (static_cast<unsigned>(p) + 1 < static_cast<unsigned>(length) && data[p] == '0') { |
1815 | if (isASCIIAlphaCaselessEqual(data[p + 1], 'b')) |
1816 | return parseInt(globalObject, vm, data, length, p + 2, 2, errorParseMode, ParseIntSign::Unsigned, ParseIntMode::DisallowEmptyString); |
1817 | |
1818 | if (isASCIIAlphaCaselessEqual(data[p + 1], 'x')) |
1819 | return parseInt(globalObject, vm, data, length, p + 2, 16, errorParseMode, ParseIntSign::Unsigned, ParseIntMode::DisallowEmptyString); |
1820 | |
1821 | if (isASCIIAlphaCaselessEqual(data[p + 1], 'o')) |
1822 | return parseInt(globalObject, vm, data, length, p + 2, 8, errorParseMode, ParseIntSign::Unsigned, ParseIntMode::DisallowEmptyString); |
1823 | } |
1824 | |
1825 | ParseIntSign sign = ParseIntSign::Unsigned; |
1826 | if (p < length) { |
1827 | if (data[p] == '+') |
1828 | ++p; |
1829 | else if (data[p] == '-') { |
1830 | sign = ParseIntSign::Signed; |
1831 | ++p; |
1832 | } |
1833 | } |
1834 | |
1835 | JSBigInt* result = parseInt(globalObject, vm, data, length, p, 10, errorParseMode, sign); |
1836 | |
1837 | if (result && !result->isZero()) |
1838 | result->setSign(sign == ParseIntSign::Signed); |
1839 | |
1840 | return result; |
1841 | } |
1842 | |
1843 | template <typename CharType> |
1844 | JSBigInt* JSBigInt::parseInt(JSGlobalObject* globalObject, VM& vm, CharType* data, unsigned length, unsigned startIndex, unsigned radix, ErrorParseMode errorParseMode, ParseIntSign sign, ParseIntMode parseMode) |
1845 | { |
1846 | ASSERT(length >= 0); |
1847 | unsigned p = startIndex; |
1848 | |
1849 | auto scope = DECLARE_THROW_SCOPE(vm); |
1850 | |
1851 | if (parseMode != ParseIntMode::AllowEmptyString && startIndex == length) { |
1852 | ASSERT(globalObject); |
1853 | if (errorParseMode == ErrorParseMode::ThrowExceptions) |
1854 | throwVMError(globalObject, scope, createSyntaxError(globalObject, "Failed to parse String to BigInt" )); |
1855 | return nullptr; |
1856 | } |
1857 | |
1858 | // Skipping leading zeros |
1859 | while (p < length && data[p] == '0') |
1860 | ++p; |
1861 | |
1862 | int endIndex = length - 1; |
1863 | // Removing trailing spaces |
1864 | while (endIndex >= static_cast<int>(p) && isStrWhiteSpace(data[endIndex])) |
1865 | --endIndex; |
1866 | |
1867 | length = endIndex + 1; |
1868 | |
1869 | if (p == length) |
1870 | return createZero(vm); |
1871 | |
1872 | unsigned limit0 = '0' + (radix < 10 ? radix : 10); |
1873 | unsigned limita = 'a' + (radix - 10); |
1874 | unsigned limitA = 'A' + (radix - 10); |
1875 | |
1876 | JSBigInt* result = allocateFor(globalObject, vm, radix, length - p); |
1877 | RETURN_IF_EXCEPTION(scope, nullptr); |
1878 | |
1879 | result->initialize(InitializationType::WithZero); |
1880 | |
1881 | for (unsigned i = p; i < length; i++, p++) { |
1882 | uint32_t digit; |
1883 | if (data[i] >= '0' && data[i] < limit0) |
1884 | digit = data[i] - '0'; |
1885 | else if (data[i] >= 'a' && data[i] < limita) |
1886 | digit = data[i] - 'a' + 10; |
1887 | else if (data[i] >= 'A' && data[i] < limitA) |
1888 | digit = data[i] - 'A' + 10; |
1889 | else |
1890 | break; |
1891 | |
1892 | result->inplaceMultiplyAdd(static_cast<Digit>(radix), static_cast<Digit>(digit)); |
1893 | } |
1894 | |
1895 | result->setSign(sign == ParseIntSign::Signed ? true : false); |
1896 | if (p == length) |
1897 | return result->rightTrim(vm); |
1898 | |
1899 | ASSERT(globalObject); |
1900 | if (errorParseMode == ErrorParseMode::ThrowExceptions) |
1901 | throwVMError(globalObject, scope, createSyntaxError(globalObject, "Failed to parse String to BigInt" )); |
1902 | |
1903 | return nullptr; |
1904 | } |
1905 | |
1906 | inline JSBigInt::Digit JSBigInt::digit(unsigned n) |
1907 | { |
1908 | ASSERT(n < length()); |
1909 | return dataStorage()[n]; |
1910 | } |
1911 | |
1912 | inline void JSBigInt::setDigit(unsigned n, Digit value) |
1913 | { |
1914 | ASSERT(n < length()); |
1915 | dataStorage()[n] = value; |
1916 | } |
1917 | |
1918 | JSObject* JSBigInt::toObject(JSGlobalObject* globalObject) const |
1919 | { |
1920 | return BigIntObject::create(globalObject->vm(), globalObject, const_cast<JSBigInt*>(this)); |
1921 | } |
1922 | |
1923 | bool JSBigInt::equalsToNumber(JSValue numValue) |
1924 | { |
1925 | ASSERT(numValue.isNumber()); |
1926 | |
1927 | if (numValue.isInt32()) { |
1928 | int value = numValue.asInt32(); |
1929 | if (!value) |
1930 | return this->isZero(); |
1931 | |
1932 | return (this->length() == 1) && (this->sign() == (value < 0)) && (this->digit(0) == static_cast<Digit>(std::abs(static_cast<int64_t>(value)))); |
1933 | } |
1934 | |
1935 | double value = numValue.asDouble(); |
1936 | return compareToDouble(this, value) == ComparisonResult::Equal; |
1937 | } |
1938 | |
1939 | JSBigInt::ComparisonResult JSBigInt::compareToDouble(JSBigInt* x, double y) |
1940 | { |
1941 | // This algorithm expect that the double format is IEEE 754 |
1942 | |
1943 | uint64_t doubleBits = bitwise_cast<uint64_t>(y); |
1944 | int rawExponent = static_cast<int>(doubleBits >> 52) & 0x7FF; |
1945 | |
1946 | if (rawExponent == 0x7FF) { |
1947 | if (std::isnan(y)) |
1948 | return ComparisonResult::Undefined; |
1949 | |
1950 | return (y == std::numeric_limits<double>::infinity()) ? ComparisonResult::LessThan : ComparisonResult::GreaterThan; |
1951 | } |
1952 | |
1953 | bool xSign = x->sign(); |
1954 | |
1955 | // Note that this is different from the double's sign bit for -0. That's |
1956 | // intentional because -0 must be treated like 0. |
1957 | bool ySign = y < 0; |
1958 | if (xSign != ySign) |
1959 | return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan; |
1960 | |
1961 | if (!y) { |
1962 | ASSERT(!xSign); |
1963 | return x->isZero() ? ComparisonResult::Equal : ComparisonResult::GreaterThan; |
1964 | } |
1965 | |
1966 | if (x->isZero()) |
1967 | return ComparisonResult::LessThan; |
1968 | |
1969 | uint64_t mantissa = doubleBits & 0x000FFFFFFFFFFFFF; |
1970 | |
1971 | // Non-finite doubles are handled above. |
1972 | ASSERT(rawExponent != 0x7FF); |
1973 | int exponent = rawExponent - 0x3FF; |
1974 | if (exponent < 0) { |
1975 | // The absolute value of the double is less than 1. Only 0n has an |
1976 | // absolute value smaller than that, but we've already covered that case. |
1977 | return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan; |
1978 | } |
1979 | |
1980 | int xLength = x->length(); |
1981 | Digit xMSD = x->digit(xLength - 1); |
1982 | int msdLeadingZeros = clz(xMSD); |
1983 | |
1984 | int xBitLength = xLength * digitBits - msdLeadingZeros; |
1985 | int yBitLength = exponent + 1; |
1986 | if (xBitLength < yBitLength) |
1987 | return xSign? ComparisonResult::GreaterThan : ComparisonResult::LessThan; |
1988 | |
1989 | if (xBitLength > yBitLength) |
1990 | return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan; |
1991 | |
1992 | // At this point, we know that signs and bit lengths (i.e. position of |
1993 | // the most significant bit in exponent-free representation) are identical. |
1994 | // {x} is not zero, {y} is finite and not denormal. |
1995 | // Now we virtually convert the double to an integer by shifting its |
1996 | // mantissa according to its exponent, so it will align with the BigInt {x}, |
1997 | // and then we compare them bit for bit until we find a difference or the |
1998 | // least significant bit. |
1999 | // <----- 52 ------> <-- virtual trailing zeroes --> |
2000 | // y / mantissa: 1yyyyyyyyyyyyyyyyy 0000000000000000000000000000000 |
2001 | // x / digits: 0001xxxx xxxxxxxx xxxxxxxx ... |
2002 | // <--> <------> |
2003 | // msdTopBit digitBits |
2004 | // |
2005 | mantissa |= 0x0010000000000000; |
2006 | const int mantissaTopBit = 52; // 0-indexed. |
2007 | |
2008 | // 0-indexed position of {x}'s most significant bit within the {msd}. |
2009 | int msdTopBit = digitBits - 1 - msdLeadingZeros; |
2010 | ASSERT(msdTopBit == static_cast<int>((xBitLength - 1) % digitBits)); |
2011 | |
2012 | // Shifted chunk of {mantissa} for comparing with {digit}. |
2013 | Digit compareMantissa; |
2014 | |
2015 | // Number of unprocessed bits in {mantissa}. We'll keep them shifted to |
2016 | // the left (i.e. most significant part) of the underlying uint64_t. |
2017 | int remainingMantissaBits = 0; |
2018 | |
2019 | // First, compare the most significant digit against the beginning of |
2020 | // the mantissa and then we align them. |
2021 | if (msdTopBit < mantissaTopBit) { |
2022 | remainingMantissaBits = (mantissaTopBit - msdTopBit); |
2023 | compareMantissa = static_cast<Digit>(mantissa >> remainingMantissaBits); |
2024 | mantissa = mantissa << (64 - remainingMantissaBits); |
2025 | } else { |
2026 | compareMantissa = static_cast<Digit>(mantissa << (msdTopBit - mantissaTopBit)); |
2027 | mantissa = 0; |
2028 | } |
2029 | |
2030 | if (xMSD > compareMantissa) |
2031 | return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan; |
2032 | |
2033 | if (xMSD < compareMantissa) |
2034 | return xSign ? ComparisonResult::GreaterThan : ComparisonResult::LessThan; |
2035 | |
2036 | // Then, compare additional digits against any remaining mantissa bits. |
2037 | for (int digitIndex = xLength - 2; digitIndex >= 0; digitIndex--) { |
2038 | if (remainingMantissaBits > 0) { |
2039 | remainingMantissaBits -= digitBits; |
2040 | if (sizeof(mantissa) != sizeof(xMSD)) { |
2041 | compareMantissa = static_cast<Digit>(mantissa >> (64 - digitBits)); |
2042 | // "& 63" to appease compilers. digitBits is 32 here anyway. |
2043 | mantissa = mantissa << (digitBits & 63); |
2044 | } else { |
2045 | compareMantissa = static_cast<Digit>(mantissa); |
2046 | mantissa = 0; |
2047 | } |
2048 | } else |
2049 | compareMantissa = 0; |
2050 | |
2051 | Digit digit = x->digit(digitIndex); |
2052 | if (digit > compareMantissa) |
2053 | return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan; |
2054 | if (digit < compareMantissa) |
2055 | return xSign ? ComparisonResult::GreaterThan : ComparisonResult::LessThan; |
2056 | } |
2057 | |
2058 | // Integer parts are equal; check whether {y} has a fractional part. |
2059 | if (mantissa) { |
2060 | ASSERT(remainingMantissaBits > 0); |
2061 | return xSign ? ComparisonResult::GreaterThan : ComparisonResult::LessThan; |
2062 | } |
2063 | |
2064 | return ComparisonResult::Equal; |
2065 | } |
2066 | |
2067 | Optional<JSBigInt::Digit> JSBigInt::toShiftAmount(JSBigInt* x) |
2068 | { |
2069 | if (x->length() > 1) |
2070 | return WTF::nullopt; |
2071 | |
2072 | Digit value = x->digit(0); |
2073 | static_assert(maxLengthBits < std::numeric_limits<Digit>::max(), "maxLengthBits needs to be less than digit" ); |
2074 | |
2075 | if (value > maxLengthBits) |
2076 | return WTF::nullopt; |
2077 | |
2078 | return value; |
2079 | } |
2080 | |
2081 | } // namespace JSC |
2082 | |