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1 // Copyright 2011 the V8 project authors. All rights reserved.
2 // Use of this source code is governed by a BSD-style license that can be
3 // found in the LICENSE file.
4 
5 #include "src/bignum.h"
6 #include "src/utils.h"
7 
8 namespace v8 {
9 namespace internal {
10 
Bignum()11 Bignum::Bignum()
12     : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
13   for (int i = 0; i < kBigitCapacity; ++i) {
14     bigits_[i] = 0;
15   }
16 }
17 
18 
19 template<typename S>
BitSize(S value)20 static int BitSize(S value) {
21   return 8 * sizeof(value);
22 }
23 
24 
25 // Guaranteed to lie in one Bigit.
AssignUInt16(uint16_t value)26 void Bignum::AssignUInt16(uint16_t value) {
27   DCHECK(kBigitSize >= BitSize(value));
28   Zero();
29   if (value == 0) return;
30 
31   EnsureCapacity(1);
32   bigits_[0] = value;
33   used_digits_ = 1;
34 }
35 
36 
AssignUInt64(uint64_t value)37 void Bignum::AssignUInt64(uint64_t value) {
38   const int kUInt64Size = 64;
39 
40   Zero();
41   if (value == 0) return;
42 
43   int needed_bigits = kUInt64Size / kBigitSize + 1;
44   EnsureCapacity(needed_bigits);
45   for (int i = 0; i < needed_bigits; ++i) {
46     bigits_[i] = static_cast<Chunk>(value & kBigitMask);
47     value = value >> kBigitSize;
48   }
49   used_digits_ = needed_bigits;
50   Clamp();
51 }
52 
53 
AssignBignum(const Bignum & other)54 void Bignum::AssignBignum(const Bignum& other) {
55   exponent_ = other.exponent_;
56   for (int i = 0; i < other.used_digits_; ++i) {
57     bigits_[i] = other.bigits_[i];
58   }
59   // Clear the excess digits (if there were any).
60   for (int i = other.used_digits_; i < used_digits_; ++i) {
61     bigits_[i] = 0;
62   }
63   used_digits_ = other.used_digits_;
64 }
65 
66 
ReadUInt64(Vector<const char> buffer,int from,int digits_to_read)67 static uint64_t ReadUInt64(Vector<const char> buffer,
68                            int from,
69                            int digits_to_read) {
70   uint64_t result = 0;
71   int to = from + digits_to_read;
72 
73   for (int i = from; i < to; ++i) {
74     int digit = buffer[i] - '0';
75     DCHECK(0 <= digit && digit <= 9);
76     result = result * 10 + digit;
77   }
78   return result;
79 }
80 
81 
AssignDecimalString(Vector<const char> value)82 void Bignum::AssignDecimalString(Vector<const char> value) {
83   // 2^64 = 18446744073709551616 > 10^19
84   const int kMaxUint64DecimalDigits = 19;
85   Zero();
86   int length = value.length();
87   int pos = 0;
88   // Let's just say that each digit needs 4 bits.
89   while (length >= kMaxUint64DecimalDigits) {
90     uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
91     pos += kMaxUint64DecimalDigits;
92     length -= kMaxUint64DecimalDigits;
93     MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
94     AddUInt64(digits);
95   }
96   uint64_t digits = ReadUInt64(value, pos, length);
97   MultiplyByPowerOfTen(length);
98   AddUInt64(digits);
99   Clamp();
100 }
101 
102 
HexCharValue(char c)103 static int HexCharValue(char c) {
104   if ('0' <= c && c <= '9') return c - '0';
105   if ('a' <= c && c <= 'f') return 10 + c - 'a';
106   if ('A' <= c && c <= 'F') return 10 + c - 'A';
107   UNREACHABLE();
108   return 0;  // To make compiler happy.
109 }
110 
111 
AssignHexString(Vector<const char> value)112 void Bignum::AssignHexString(Vector<const char> value) {
113   Zero();
114   int length = value.length();
115 
116   int needed_bigits = length * 4 / kBigitSize + 1;
117   EnsureCapacity(needed_bigits);
118   int string_index = length - 1;
119   for (int i = 0; i < needed_bigits - 1; ++i) {
120     // These bigits are guaranteed to be "full".
121     Chunk current_bigit = 0;
122     for (int j = 0; j < kBigitSize / 4; j++) {
123       current_bigit += HexCharValue(value[string_index--]) << (j * 4);
124     }
125     bigits_[i] = current_bigit;
126   }
127   used_digits_ = needed_bigits - 1;
128 
129   Chunk most_significant_bigit = 0;  // Could be = 0;
130   for (int j = 0; j <= string_index; ++j) {
131     most_significant_bigit <<= 4;
132     most_significant_bigit += HexCharValue(value[j]);
133   }
134   if (most_significant_bigit != 0) {
135     bigits_[used_digits_] = most_significant_bigit;
136     used_digits_++;
137   }
138   Clamp();
139 }
140 
141 
AddUInt64(uint64_t operand)142 void Bignum::AddUInt64(uint64_t operand) {
143   if (operand == 0) return;
144   Bignum other;
145   other.AssignUInt64(operand);
146   AddBignum(other);
147 }
148 
149 
AddBignum(const Bignum & other)150 void Bignum::AddBignum(const Bignum& other) {
151   DCHECK(IsClamped());
152   DCHECK(other.IsClamped());
153 
154   // If this has a greater exponent than other append zero-bigits to this.
155   // After this call exponent_ <= other.exponent_.
156   Align(other);
157 
158   // There are two possibilities:
159   //   aaaaaaaaaaa 0000  (where the 0s represent a's exponent)
160   //     bbbbb 00000000
161   //   ----------------
162   //   ccccccccccc 0000
163   // or
164   //    aaaaaaaaaa 0000
165   //  bbbbbbbbb 0000000
166   //  -----------------
167   //  cccccccccccc 0000
168   // In both cases we might need a carry bigit.
169 
170   EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
171   Chunk carry = 0;
172   int bigit_pos = other.exponent_ - exponent_;
173   DCHECK(bigit_pos >= 0);
174   for (int i = 0; i < other.used_digits_; ++i) {
175     Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
176     bigits_[bigit_pos] = sum & kBigitMask;
177     carry = sum >> kBigitSize;
178     bigit_pos++;
179   }
180 
181   while (carry != 0) {
182     Chunk sum = bigits_[bigit_pos] + carry;
183     bigits_[bigit_pos] = sum & kBigitMask;
184     carry = sum >> kBigitSize;
185     bigit_pos++;
186   }
187   used_digits_ = Max(bigit_pos, used_digits_);
188   DCHECK(IsClamped());
189 }
190 
191 
SubtractBignum(const Bignum & other)192 void Bignum::SubtractBignum(const Bignum& other) {
193   DCHECK(IsClamped());
194   DCHECK(other.IsClamped());
195   // We require this to be bigger than other.
196   DCHECK(LessEqual(other, *this));
197 
198   Align(other);
199 
200   int offset = other.exponent_ - exponent_;
201   Chunk borrow = 0;
202   int i;
203   for (i = 0; i < other.used_digits_; ++i) {
204     DCHECK((borrow == 0) || (borrow == 1));
205     Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
206     bigits_[i + offset] = difference & kBigitMask;
207     borrow = difference >> (kChunkSize - 1);
208   }
209   while (borrow != 0) {
210     Chunk difference = bigits_[i + offset] - borrow;
211     bigits_[i + offset] = difference & kBigitMask;
212     borrow = difference >> (kChunkSize - 1);
213     ++i;
214   }
215   Clamp();
216 }
217 
218 
ShiftLeft(int shift_amount)219 void Bignum::ShiftLeft(int shift_amount) {
220   if (used_digits_ == 0) return;
221   exponent_ += shift_amount / kBigitSize;
222   int local_shift = shift_amount % kBigitSize;
223   EnsureCapacity(used_digits_ + 1);
224   BigitsShiftLeft(local_shift);
225 }
226 
227 
MultiplyByUInt32(uint32_t factor)228 void Bignum::MultiplyByUInt32(uint32_t factor) {
229   if (factor == 1) return;
230   if (factor == 0) {
231     Zero();
232     return;
233   }
234   if (used_digits_ == 0) return;
235 
236   // The product of a bigit with the factor is of size kBigitSize + 32.
237   // Assert that this number + 1 (for the carry) fits into double chunk.
238   DCHECK(kDoubleChunkSize >= kBigitSize + 32 + 1);
239   DoubleChunk carry = 0;
240   for (int i = 0; i < used_digits_; ++i) {
241     DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
242     bigits_[i] = static_cast<Chunk>(product & kBigitMask);
243     carry = (product >> kBigitSize);
244   }
245   while (carry != 0) {
246     EnsureCapacity(used_digits_ + 1);
247     bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask);
248     used_digits_++;
249     carry >>= kBigitSize;
250   }
251 }
252 
253 
MultiplyByUInt64(uint64_t factor)254 void Bignum::MultiplyByUInt64(uint64_t factor) {
255   if (factor == 1) return;
256   if (factor == 0) {
257     Zero();
258     return;
259   }
260   DCHECK(kBigitSize < 32);
261   uint64_t carry = 0;
262   uint64_t low = factor & 0xFFFFFFFF;
263   uint64_t high = factor >> 32;
264   for (int i = 0; i < used_digits_; ++i) {
265     uint64_t product_low = low * bigits_[i];
266     uint64_t product_high = high * bigits_[i];
267     uint64_t tmp = (carry & kBigitMask) + product_low;
268     bigits_[i] = static_cast<Chunk>(tmp & kBigitMask);
269     carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
270         (product_high << (32 - kBigitSize));
271   }
272   while (carry != 0) {
273     EnsureCapacity(used_digits_ + 1);
274     bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask);
275     used_digits_++;
276     carry >>= kBigitSize;
277   }
278 }
279 
280 
MultiplyByPowerOfTen(int exponent)281 void Bignum::MultiplyByPowerOfTen(int exponent) {
282   const uint64_t kFive27 = V8_2PART_UINT64_C(0x6765c793, fa10079d);
283   const uint16_t kFive1 = 5;
284   const uint16_t kFive2 = kFive1 * 5;
285   const uint16_t kFive3 = kFive2 * 5;
286   const uint16_t kFive4 = kFive3 * 5;
287   const uint16_t kFive5 = kFive4 * 5;
288   const uint16_t kFive6 = kFive5 * 5;
289   const uint32_t kFive7 = kFive6 * 5;
290   const uint32_t kFive8 = kFive7 * 5;
291   const uint32_t kFive9 = kFive8 * 5;
292   const uint32_t kFive10 = kFive9 * 5;
293   const uint32_t kFive11 = kFive10 * 5;
294   const uint32_t kFive12 = kFive11 * 5;
295   const uint32_t kFive13 = kFive12 * 5;
296   const uint32_t kFive1_to_12[] =
297       { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
298         kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
299 
300   DCHECK(exponent >= 0);
301   if (exponent == 0) return;
302   if (used_digits_ == 0) return;
303 
304   // We shift by exponent at the end just before returning.
305   int remaining_exponent = exponent;
306   while (remaining_exponent >= 27) {
307     MultiplyByUInt64(kFive27);
308     remaining_exponent -= 27;
309   }
310   while (remaining_exponent >= 13) {
311     MultiplyByUInt32(kFive13);
312     remaining_exponent -= 13;
313   }
314   if (remaining_exponent > 0) {
315     MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
316   }
317   ShiftLeft(exponent);
318 }
319 
320 
Square()321 void Bignum::Square() {
322   DCHECK(IsClamped());
323   int product_length = 2 * used_digits_;
324   EnsureCapacity(product_length);
325 
326   // Comba multiplication: compute each column separately.
327   // Example: r = a2a1a0 * b2b1b0.
328   //    r =  1    * a0b0 +
329   //        10    * (a1b0 + a0b1) +
330   //        100   * (a2b0 + a1b1 + a0b2) +
331   //        1000  * (a2b1 + a1b2) +
332   //        10000 * a2b2
333   //
334   // In the worst case we have to accumulate nb-digits products of digit*digit.
335   //
336   // Assert that the additional number of bits in a DoubleChunk are enough to
337   // sum up used_digits of Bigit*Bigit.
338   if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
339     UNIMPLEMENTED();
340   }
341   DoubleChunk accumulator = 0;
342   // First shift the digits so we don't overwrite them.
343   int copy_offset = used_digits_;
344   for (int i = 0; i < used_digits_; ++i) {
345     bigits_[copy_offset + i] = bigits_[i];
346   }
347   // We have two loops to avoid some 'if's in the loop.
348   for (int i = 0; i < used_digits_; ++i) {
349     // Process temporary digit i with power i.
350     // The sum of the two indices must be equal to i.
351     int bigit_index1 = i;
352     int bigit_index2 = 0;
353     // Sum all of the sub-products.
354     while (bigit_index1 >= 0) {
355       Chunk chunk1 = bigits_[copy_offset + bigit_index1];
356       Chunk chunk2 = bigits_[copy_offset + bigit_index2];
357       accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
358       bigit_index1--;
359       bigit_index2++;
360     }
361     bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
362     accumulator >>= kBigitSize;
363   }
364   for (int i = used_digits_; i < product_length; ++i) {
365     int bigit_index1 = used_digits_ - 1;
366     int bigit_index2 = i - bigit_index1;
367     // Invariant: sum of both indices is again equal to i.
368     // Inner loop runs 0 times on last iteration, emptying accumulator.
369     while (bigit_index2 < used_digits_) {
370       Chunk chunk1 = bigits_[copy_offset + bigit_index1];
371       Chunk chunk2 = bigits_[copy_offset + bigit_index2];
372       accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
373       bigit_index1--;
374       bigit_index2++;
375     }
376     // The overwritten bigits_[i] will never be read in further loop iterations,
377     // because bigit_index1 and bigit_index2 are always greater
378     // than i - used_digits_.
379     bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
380     accumulator >>= kBigitSize;
381   }
382   // Since the result was guaranteed to lie inside the number the
383   // accumulator must be 0 now.
384   DCHECK(accumulator == 0);
385 
386   // Don't forget to update the used_digits and the exponent.
387   used_digits_ = product_length;
388   exponent_ *= 2;
389   Clamp();
390 }
391 
392 
AssignPowerUInt16(uint16_t base,int power_exponent)393 void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
394   DCHECK(base != 0);
395   DCHECK(power_exponent >= 0);
396   if (power_exponent == 0) {
397     AssignUInt16(1);
398     return;
399   }
400   Zero();
401   int shifts = 0;
402   // We expect base to be in range 2-32, and most often to be 10.
403   // It does not make much sense to implement different algorithms for counting
404   // the bits.
405   while ((base & 1) == 0) {
406     base >>= 1;
407     shifts++;
408   }
409   int bit_size = 0;
410   int tmp_base = base;
411   while (tmp_base != 0) {
412     tmp_base >>= 1;
413     bit_size++;
414   }
415   int final_size = bit_size * power_exponent;
416   // 1 extra bigit for the shifting, and one for rounded final_size.
417   EnsureCapacity(final_size / kBigitSize + 2);
418 
419   // Left to Right exponentiation.
420   int mask = 1;
421   while (power_exponent >= mask) mask <<= 1;
422 
423   // The mask is now pointing to the bit above the most significant 1-bit of
424   // power_exponent.
425   // Get rid of first 1-bit;
426   mask >>= 2;
427   uint64_t this_value = base;
428 
429   bool delayed_multipliciation = false;
430   const uint64_t max_32bits = 0xFFFFFFFF;
431   while (mask != 0 && this_value <= max_32bits) {
432     this_value = this_value * this_value;
433     // Verify that there is enough space in this_value to perform the
434     // multiplication.  The first bit_size bits must be 0.
435     if ((power_exponent & mask) != 0) {
436       uint64_t base_bits_mask =
437           ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
438       bool high_bits_zero = (this_value & base_bits_mask) == 0;
439       if (high_bits_zero) {
440         this_value *= base;
441       } else {
442         delayed_multipliciation = true;
443       }
444     }
445     mask >>= 1;
446   }
447   AssignUInt64(this_value);
448   if (delayed_multipliciation) {
449     MultiplyByUInt32(base);
450   }
451 
452   // Now do the same thing as a bignum.
453   while (mask != 0) {
454     Square();
455     if ((power_exponent & mask) != 0) {
456       MultiplyByUInt32(base);
457     }
458     mask >>= 1;
459   }
460 
461   // And finally add the saved shifts.
462   ShiftLeft(shifts * power_exponent);
463 }
464 
465 
466 // Precondition: this/other < 16bit.
DivideModuloIntBignum(const Bignum & other)467 uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
468   DCHECK(IsClamped());
469   DCHECK(other.IsClamped());
470   DCHECK(other.used_digits_ > 0);
471 
472   // Easy case: if we have less digits than the divisor than the result is 0.
473   // Note: this handles the case where this == 0, too.
474   if (BigitLength() < other.BigitLength()) {
475     return 0;
476   }
477 
478   Align(other);
479 
480   uint16_t result = 0;
481 
482   // Start by removing multiples of 'other' until both numbers have the same
483   // number of digits.
484   while (BigitLength() > other.BigitLength()) {
485     // This naive approach is extremely inefficient if the this divided other
486     // might be big. This function is implemented for doubleToString where
487     // the result should be small (less than 10).
488     DCHECK(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
489     // Remove the multiples of the first digit.
490     // Example this = 23 and other equals 9. -> Remove 2 multiples.
491     result += bigits_[used_digits_ - 1];
492     SubtractTimes(other, bigits_[used_digits_ - 1]);
493   }
494 
495   DCHECK(BigitLength() == other.BigitLength());
496 
497   // Both bignums are at the same length now.
498   // Since other has more than 0 digits we know that the access to
499   // bigits_[used_digits_ - 1] is safe.
500   Chunk this_bigit = bigits_[used_digits_ - 1];
501   Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
502 
503   if (other.used_digits_ == 1) {
504     // Shortcut for easy (and common) case.
505     int quotient = this_bigit / other_bigit;
506     bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
507     result += quotient;
508     Clamp();
509     return result;
510   }
511 
512   int division_estimate = this_bigit / (other_bigit + 1);
513   result += division_estimate;
514   SubtractTimes(other, division_estimate);
515 
516   if (other_bigit * (division_estimate + 1) > this_bigit) {
517     // No need to even try to subtract. Even if other's remaining digits were 0
518     // another subtraction would be too much.
519     return result;
520   }
521 
522   while (LessEqual(other, *this)) {
523     SubtractBignum(other);
524     result++;
525   }
526   return result;
527 }
528 
529 
530 template<typename S>
SizeInHexChars(S number)531 static int SizeInHexChars(S number) {
532   DCHECK(number > 0);
533   int result = 0;
534   while (number != 0) {
535     number >>= 4;
536     result++;
537   }
538   return result;
539 }
540 
541 
HexCharOfValue(int value)542 static char HexCharOfValue(int value) {
543   DCHECK(0 <= value && value <= 16);
544   if (value < 10) return value + '0';
545   return value - 10 + 'A';
546 }
547 
548 
ToHexString(char * buffer,int buffer_size) const549 bool Bignum::ToHexString(char* buffer, int buffer_size) const {
550   DCHECK(IsClamped());
551   // Each bigit must be printable as separate hex-character.
552   DCHECK(kBigitSize % 4 == 0);
553   const int kHexCharsPerBigit = kBigitSize / 4;
554 
555   if (used_digits_ == 0) {
556     if (buffer_size < 2) return false;
557     buffer[0] = '0';
558     buffer[1] = '\0';
559     return true;
560   }
561   // We add 1 for the terminating '\0' character.
562   int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
563       SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
564   if (needed_chars > buffer_size) return false;
565   int string_index = needed_chars - 1;
566   buffer[string_index--] = '\0';
567   for (int i = 0; i < exponent_; ++i) {
568     for (int j = 0; j < kHexCharsPerBigit; ++j) {
569       buffer[string_index--] = '0';
570     }
571   }
572   for (int i = 0; i < used_digits_ - 1; ++i) {
573     Chunk current_bigit = bigits_[i];
574     for (int j = 0; j < kHexCharsPerBigit; ++j) {
575       buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
576       current_bigit >>= 4;
577     }
578   }
579   // And finally the last bigit.
580   Chunk most_significant_bigit = bigits_[used_digits_ - 1];
581   while (most_significant_bigit != 0) {
582     buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
583     most_significant_bigit >>= 4;
584   }
585   return true;
586 }
587 
588 
BigitAt(int index) const589 Bignum::Chunk Bignum::BigitAt(int index) const {
590   if (index >= BigitLength()) return 0;
591   if (index < exponent_) return 0;
592   return bigits_[index - exponent_];
593 }
594 
595 
Compare(const Bignum & a,const Bignum & b)596 int Bignum::Compare(const Bignum& a, const Bignum& b) {
597   DCHECK(a.IsClamped());
598   DCHECK(b.IsClamped());
599   int bigit_length_a = a.BigitLength();
600   int bigit_length_b = b.BigitLength();
601   if (bigit_length_a < bigit_length_b) return -1;
602   if (bigit_length_a > bigit_length_b) return +1;
603   for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
604     Chunk bigit_a = a.BigitAt(i);
605     Chunk bigit_b = b.BigitAt(i);
606     if (bigit_a < bigit_b) return -1;
607     if (bigit_a > bigit_b) return +1;
608     // Otherwise they are equal up to this digit. Try the next digit.
609   }
610   return 0;
611 }
612 
613 
PlusCompare(const Bignum & a,const Bignum & b,const Bignum & c)614 int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
615   DCHECK(a.IsClamped());
616   DCHECK(b.IsClamped());
617   DCHECK(c.IsClamped());
618   if (a.BigitLength() < b.BigitLength()) {
619     return PlusCompare(b, a, c);
620   }
621   if (a.BigitLength() + 1 < c.BigitLength()) return -1;
622   if (a.BigitLength() > c.BigitLength()) return +1;
623   // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
624   // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
625   // of 'a'.
626   if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
627     return -1;
628   }
629 
630   Chunk borrow = 0;
631   // Starting at min_exponent all digits are == 0. So no need to compare them.
632   int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
633   for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
634     Chunk chunk_a = a.BigitAt(i);
635     Chunk chunk_b = b.BigitAt(i);
636     Chunk chunk_c = c.BigitAt(i);
637     Chunk sum = chunk_a + chunk_b;
638     if (sum > chunk_c + borrow) {
639       return +1;
640     } else {
641       borrow = chunk_c + borrow - sum;
642       if (borrow > 1) return -1;
643       borrow <<= kBigitSize;
644     }
645   }
646   if (borrow == 0) return 0;
647   return -1;
648 }
649 
650 
Clamp()651 void Bignum::Clamp() {
652   while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
653     used_digits_--;
654   }
655   if (used_digits_ == 0) {
656     // Zero.
657     exponent_ = 0;
658   }
659 }
660 
661 
IsClamped() const662 bool Bignum::IsClamped() const {
663   return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
664 }
665 
666 
Zero()667 void Bignum::Zero() {
668   for (int i = 0; i < used_digits_; ++i) {
669     bigits_[i] = 0;
670   }
671   used_digits_ = 0;
672   exponent_ = 0;
673 }
674 
675 
Align(const Bignum & other)676 void Bignum::Align(const Bignum& other) {
677   if (exponent_ > other.exponent_) {
678     // If "X" represents a "hidden" digit (by the exponent) then we are in the
679     // following case (a == this, b == other):
680     // a:  aaaaaaXXXX   or a:   aaaaaXXX
681     // b:     bbbbbbX      b: bbbbbbbbXX
682     // We replace some of the hidden digits (X) of a with 0 digits.
683     // a:  aaaaaa000X   or a:   aaaaa0XX
684     int zero_digits = exponent_ - other.exponent_;
685     EnsureCapacity(used_digits_ + zero_digits);
686     for (int i = used_digits_ - 1; i >= 0; --i) {
687       bigits_[i + zero_digits] = bigits_[i];
688     }
689     for (int i = 0; i < zero_digits; ++i) {
690       bigits_[i] = 0;
691     }
692     used_digits_ += zero_digits;
693     exponent_ -= zero_digits;
694     DCHECK(used_digits_ >= 0);
695     DCHECK(exponent_ >= 0);
696   }
697 }
698 
699 
BigitsShiftLeft(int shift_amount)700 void Bignum::BigitsShiftLeft(int shift_amount) {
701   DCHECK(shift_amount < kBigitSize);
702   DCHECK(shift_amount >= 0);
703   Chunk carry = 0;
704   for (int i = 0; i < used_digits_; ++i) {
705     Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
706     bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
707     carry = new_carry;
708   }
709   if (carry != 0) {
710     bigits_[used_digits_] = carry;
711     used_digits_++;
712   }
713 }
714 
715 
SubtractTimes(const Bignum & other,int factor)716 void Bignum::SubtractTimes(const Bignum& other, int factor) {
717 #ifdef DEBUG
718   Bignum a, b;
719   a.AssignBignum(*this);
720   b.AssignBignum(other);
721   b.MultiplyByUInt32(factor);
722   a.SubtractBignum(b);
723 #endif
724   DCHECK(exponent_ <= other.exponent_);
725   if (factor < 3) {
726     for (int i = 0; i < factor; ++i) {
727       SubtractBignum(other);
728     }
729     return;
730   }
731   Chunk borrow = 0;
732   int exponent_diff = other.exponent_ - exponent_;
733   for (int i = 0; i < other.used_digits_; ++i) {
734     DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
735     DoubleChunk remove = borrow + product;
736     Chunk difference =
737         bigits_[i + exponent_diff] - static_cast<Chunk>(remove & kBigitMask);
738     bigits_[i + exponent_diff] = difference & kBigitMask;
739     borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
740                                 (remove >> kBigitSize));
741   }
742   for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
743     if (borrow == 0) return;
744     Chunk difference = bigits_[i] - borrow;
745     bigits_[i] = difference & kBigitMask;
746     borrow = difference >> (kChunkSize - 1);
747   }
748   Clamp();
749   DCHECK(Bignum::Equal(a, *this));
750 }
751 
752 
753 }  // namespace internal
754 }  // namespace v8
755