1 // © 2018 and later: Unicode, Inc. and others.
2 // License & terms of use: http://www.unicode.org/copyright.html
3 //
4 // From the double-conversion library. Original license:
5 //
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8 // modification, are permitted provided that the following conditions are
9 // met:
10 //
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20 //
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32
33 // ICU PATCH: ifdef around UCONFIG_NO_FORMATTING
34 #include "unicode/utypes.h"
35 #if !UCONFIG_NO_FORMATTING
36
37 // ICU PATCH: Customize header file paths for ICU.
38
39 #include "double-conversion-bignum.h"
40 #include "double-conversion-utils.h"
41
42 // ICU PATCH: Wrap in ICU namespace
43 U_NAMESPACE_BEGIN
44
45 namespace double_conversion {
46
Bignum()47 Bignum::Bignum()
48 : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
49 for (int i = 0; i < kBigitCapacity; ++i) {
50 bigits_[i] = 0;
51 }
52 }
53
54
55 template<typename S>
BitSize(S value)56 static int BitSize(S value) {
57 (void) value; // Mark variable as used.
58 return 8 * sizeof(value);
59 }
60
61 // Guaranteed to lie in one Bigit.
AssignUInt16(uint16_t value)62 void Bignum::AssignUInt16(uint16_t value) {
63 ASSERT(kBigitSize >= BitSize(value));
64 Zero();
65 if (value == 0) return;
66
67 EnsureCapacity(1);
68 bigits_[0] = value;
69 used_digits_ = 1;
70 }
71
72
AssignUInt64(uint64_t value)73 void Bignum::AssignUInt64(uint64_t value) {
74 const int kUInt64Size = 64;
75
76 Zero();
77 if (value == 0) return;
78
79 int needed_bigits = kUInt64Size / kBigitSize + 1;
80 EnsureCapacity(needed_bigits);
81 for (int i = 0; i < needed_bigits; ++i) {
82 bigits_[i] = value & kBigitMask;
83 value = value >> kBigitSize;
84 }
85 used_digits_ = needed_bigits;
86 Clamp();
87 }
88
89
AssignBignum(const Bignum & other)90 void Bignum::AssignBignum(const Bignum& other) {
91 exponent_ = other.exponent_;
92 for (int i = 0; i < other.used_digits_; ++i) {
93 bigits_[i] = other.bigits_[i];
94 }
95 // Clear the excess digits (if there were any).
96 for (int i = other.used_digits_; i < used_digits_; ++i) {
97 bigits_[i] = 0;
98 }
99 used_digits_ = other.used_digits_;
100 }
101
102
ReadUInt64(Vector<const char> buffer,int from,int digits_to_read)103 static uint64_t ReadUInt64(Vector<const char> buffer,
104 int from,
105 int digits_to_read) {
106 uint64_t result = 0;
107 for (int i = from; i < from + digits_to_read; ++i) {
108 int digit = buffer[i] - '0';
109 ASSERT(0 <= digit && digit <= 9);
110 result = result * 10 + digit;
111 }
112 return result;
113 }
114
115
AssignDecimalString(Vector<const char> value)116 void Bignum::AssignDecimalString(Vector<const char> value) {
117 // 2^64 = 18446744073709551616 > 10^19
118 const int kMaxUint64DecimalDigits = 19;
119 Zero();
120 int length = value.length();
121 unsigned int pos = 0;
122 // Let's just say that each digit needs 4 bits.
123 while (length >= kMaxUint64DecimalDigits) {
124 uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
125 pos += kMaxUint64DecimalDigits;
126 length -= kMaxUint64DecimalDigits;
127 MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
128 AddUInt64(digits);
129 }
130 uint64_t digits = ReadUInt64(value, pos, length);
131 MultiplyByPowerOfTen(length);
132 AddUInt64(digits);
133 Clamp();
134 }
135
136
HexCharValue(char c)137 static int HexCharValue(char c) {
138 if ('0' <= c && c <= '9') return c - '0';
139 if ('a' <= c && c <= 'f') return 10 + c - 'a';
140 ASSERT('A' <= c && c <= 'F');
141 return 10 + c - 'A';
142 }
143
144
AssignHexString(Vector<const char> value)145 void Bignum::AssignHexString(Vector<const char> value) {
146 Zero();
147 int length = value.length();
148
149 int needed_bigits = length * 4 / kBigitSize + 1;
150 EnsureCapacity(needed_bigits);
151 int string_index = length - 1;
152 for (int i = 0; i < needed_bigits - 1; ++i) {
153 // These bigits are guaranteed to be "full".
154 Chunk current_bigit = 0;
155 for (int j = 0; j < kBigitSize / 4; j++) {
156 current_bigit += HexCharValue(value[string_index--]) << (j * 4);
157 }
158 bigits_[i] = current_bigit;
159 }
160 used_digits_ = needed_bigits - 1;
161
162 Chunk most_significant_bigit = 0; // Could be = 0;
163 for (int j = 0; j <= string_index; ++j) {
164 most_significant_bigit <<= 4;
165 most_significant_bigit += HexCharValue(value[j]);
166 }
167 if (most_significant_bigit != 0) {
168 bigits_[used_digits_] = most_significant_bigit;
169 used_digits_++;
170 }
171 Clamp();
172 }
173
174
AddUInt64(uint64_t operand)175 void Bignum::AddUInt64(uint64_t operand) {
176 if (operand == 0) return;
177 Bignum other;
178 other.AssignUInt64(operand);
179 AddBignum(other);
180 }
181
182
AddBignum(const Bignum & other)183 void Bignum::AddBignum(const Bignum& other) {
184 ASSERT(IsClamped());
185 ASSERT(other.IsClamped());
186
187 // If this has a greater exponent than other append zero-bigits to this.
188 // After this call exponent_ <= other.exponent_.
189 Align(other);
190
191 // There are two possibilities:
192 // aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
193 // bbbbb 00000000
194 // ----------------
195 // ccccccccccc 0000
196 // or
197 // aaaaaaaaaa 0000
198 // bbbbbbbbb 0000000
199 // -----------------
200 // cccccccccccc 0000
201 // In both cases we might need a carry bigit.
202
203 EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
204 Chunk carry = 0;
205 int bigit_pos = other.exponent_ - exponent_;
206 ASSERT(bigit_pos >= 0);
207 for (int i = 0; i < other.used_digits_; ++i) {
208 Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
209 bigits_[bigit_pos] = sum & kBigitMask;
210 carry = sum >> kBigitSize;
211 bigit_pos++;
212 }
213
214 while (carry != 0) {
215 Chunk sum = bigits_[bigit_pos] + carry;
216 bigits_[bigit_pos] = sum & kBigitMask;
217 carry = sum >> kBigitSize;
218 bigit_pos++;
219 }
220 used_digits_ = Max(bigit_pos, used_digits_);
221 ASSERT(IsClamped());
222 }
223
224
SubtractBignum(const Bignum & other)225 void Bignum::SubtractBignum(const Bignum& other) {
226 ASSERT(IsClamped());
227 ASSERT(other.IsClamped());
228 // We require this to be bigger than other.
229 ASSERT(LessEqual(other, *this));
230
231 Align(other);
232
233 int offset = other.exponent_ - exponent_;
234 Chunk borrow = 0;
235 int i;
236 for (i = 0; i < other.used_digits_; ++i) {
237 ASSERT((borrow == 0) || (borrow == 1));
238 Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
239 bigits_[i + offset] = difference & kBigitMask;
240 borrow = difference >> (kChunkSize - 1);
241 }
242 while (borrow != 0) {
243 Chunk difference = bigits_[i + offset] - borrow;
244 bigits_[i + offset] = difference & kBigitMask;
245 borrow = difference >> (kChunkSize - 1);
246 ++i;
247 }
248 Clamp();
249 }
250
251
ShiftLeft(int shift_amount)252 void Bignum::ShiftLeft(int shift_amount) {
253 if (used_digits_ == 0) return;
254 exponent_ += shift_amount / kBigitSize;
255 int local_shift = shift_amount % kBigitSize;
256 EnsureCapacity(used_digits_ + 1);
257 BigitsShiftLeft(local_shift);
258 }
259
260
MultiplyByUInt32(uint32_t factor)261 void Bignum::MultiplyByUInt32(uint32_t factor) {
262 if (factor == 1) return;
263 if (factor == 0) {
264 Zero();
265 return;
266 }
267 if (used_digits_ == 0) return;
268
269 // The product of a bigit with the factor is of size kBigitSize + 32.
270 // Assert that this number + 1 (for the carry) fits into double chunk.
271 ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
272 DoubleChunk carry = 0;
273 for (int i = 0; i < used_digits_; ++i) {
274 DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
275 bigits_[i] = static_cast<Chunk>(product & kBigitMask);
276 carry = (product >> kBigitSize);
277 }
278 while (carry != 0) {
279 EnsureCapacity(used_digits_ + 1);
280 bigits_[used_digits_] = carry & kBigitMask;
281 used_digits_++;
282 carry >>= kBigitSize;
283 }
284 }
285
286
MultiplyByUInt64(uint64_t factor)287 void Bignum::MultiplyByUInt64(uint64_t factor) {
288 if (factor == 1) return;
289 if (factor == 0) {
290 Zero();
291 return;
292 }
293 ASSERT(kBigitSize < 32);
294 uint64_t carry = 0;
295 uint64_t low = factor & 0xFFFFFFFF;
296 uint64_t high = factor >> 32;
297 for (int i = 0; i < used_digits_; ++i) {
298 uint64_t product_low = low * bigits_[i];
299 uint64_t product_high = high * bigits_[i];
300 uint64_t tmp = (carry & kBigitMask) + product_low;
301 bigits_[i] = tmp & kBigitMask;
302 carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
303 (product_high << (32 - kBigitSize));
304 }
305 while (carry != 0) {
306 EnsureCapacity(used_digits_ + 1);
307 bigits_[used_digits_] = carry & kBigitMask;
308 used_digits_++;
309 carry >>= kBigitSize;
310 }
311 }
312
313
MultiplyByPowerOfTen(int exponent)314 void Bignum::MultiplyByPowerOfTen(int exponent) {
315 const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d);
316 const uint16_t kFive1 = 5;
317 const uint16_t kFive2 = kFive1 * 5;
318 const uint16_t kFive3 = kFive2 * 5;
319 const uint16_t kFive4 = kFive3 * 5;
320 const uint16_t kFive5 = kFive4 * 5;
321 const uint16_t kFive6 = kFive5 * 5;
322 const uint32_t kFive7 = kFive6 * 5;
323 const uint32_t kFive8 = kFive7 * 5;
324 const uint32_t kFive9 = kFive8 * 5;
325 const uint32_t kFive10 = kFive9 * 5;
326 const uint32_t kFive11 = kFive10 * 5;
327 const uint32_t kFive12 = kFive11 * 5;
328 const uint32_t kFive13 = kFive12 * 5;
329 const uint32_t kFive1_to_12[] =
330 { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
331 kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
332
333 ASSERT(exponent >= 0);
334 if (exponent == 0) return;
335 if (used_digits_ == 0) return;
336
337 // We shift by exponent at the end just before returning.
338 int remaining_exponent = exponent;
339 while (remaining_exponent >= 27) {
340 MultiplyByUInt64(kFive27);
341 remaining_exponent -= 27;
342 }
343 while (remaining_exponent >= 13) {
344 MultiplyByUInt32(kFive13);
345 remaining_exponent -= 13;
346 }
347 if (remaining_exponent > 0) {
348 MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
349 }
350 ShiftLeft(exponent);
351 }
352
353
Square()354 void Bignum::Square() {
355 ASSERT(IsClamped());
356 int product_length = 2 * used_digits_;
357 EnsureCapacity(product_length);
358
359 // Comba multiplication: compute each column separately.
360 // Example: r = a2a1a0 * b2b1b0.
361 // r = 1 * a0b0 +
362 // 10 * (a1b0 + a0b1) +
363 // 100 * (a2b0 + a1b1 + a0b2) +
364 // 1000 * (a2b1 + a1b2) +
365 // 10000 * a2b2
366 //
367 // In the worst case we have to accumulate nb-digits products of digit*digit.
368 //
369 // Assert that the additional number of bits in a DoubleChunk are enough to
370 // sum up used_digits of Bigit*Bigit.
371 if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
372 UNIMPLEMENTED();
373 }
374 DoubleChunk accumulator = 0;
375 // First shift the digits so we don't overwrite them.
376 int copy_offset = used_digits_;
377 for (int i = 0; i < used_digits_; ++i) {
378 bigits_[copy_offset + i] = bigits_[i];
379 }
380 // We have two loops to avoid some 'if's in the loop.
381 for (int i = 0; i < used_digits_; ++i) {
382 // Process temporary digit i with power i.
383 // The sum of the two indices must be equal to i.
384 int bigit_index1 = i;
385 int bigit_index2 = 0;
386 // Sum all of the sub-products.
387 while (bigit_index1 >= 0) {
388 Chunk chunk1 = bigits_[copy_offset + bigit_index1];
389 Chunk chunk2 = bigits_[copy_offset + bigit_index2];
390 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
391 bigit_index1--;
392 bigit_index2++;
393 }
394 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
395 accumulator >>= kBigitSize;
396 }
397 for (int i = used_digits_; i < product_length; ++i) {
398 int bigit_index1 = used_digits_ - 1;
399 int bigit_index2 = i - bigit_index1;
400 // Invariant: sum of both indices is again equal to i.
401 // Inner loop runs 0 times on last iteration, emptying accumulator.
402 while (bigit_index2 < used_digits_) {
403 Chunk chunk1 = bigits_[copy_offset + bigit_index1];
404 Chunk chunk2 = bigits_[copy_offset + bigit_index2];
405 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
406 bigit_index1--;
407 bigit_index2++;
408 }
409 // The overwritten bigits_[i] will never be read in further loop iterations,
410 // because bigit_index1 and bigit_index2 are always greater
411 // than i - used_digits_.
412 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
413 accumulator >>= kBigitSize;
414 }
415 // Since the result was guaranteed to lie inside the number the
416 // accumulator must be 0 now.
417 ASSERT(accumulator == 0);
418
419 // Don't forget to update the used_digits and the exponent.
420 used_digits_ = product_length;
421 exponent_ *= 2;
422 Clamp();
423 }
424
425
AssignPowerUInt16(uint16_t base,int power_exponent)426 void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
427 ASSERT(base != 0);
428 ASSERT(power_exponent >= 0);
429 if (power_exponent == 0) {
430 AssignUInt16(1);
431 return;
432 }
433 Zero();
434 int shifts = 0;
435 // We expect base to be in range 2-32, and most often to be 10.
436 // It does not make much sense to implement different algorithms for counting
437 // the bits.
438 while ((base & 1) == 0) {
439 base >>= 1;
440 shifts++;
441 }
442 int bit_size = 0;
443 int tmp_base = base;
444 while (tmp_base != 0) {
445 tmp_base >>= 1;
446 bit_size++;
447 }
448 int final_size = bit_size * power_exponent;
449 // 1 extra bigit for the shifting, and one for rounded final_size.
450 EnsureCapacity(final_size / kBigitSize + 2);
451
452 // Left to Right exponentiation.
453 int mask = 1;
454 while (power_exponent >= mask) mask <<= 1;
455
456 // The mask is now pointing to the bit above the most significant 1-bit of
457 // power_exponent.
458 // Get rid of first 1-bit;
459 mask >>= 2;
460 uint64_t this_value = base;
461
462 bool delayed_multipliciation = false;
463 const uint64_t max_32bits = 0xFFFFFFFF;
464 while (mask != 0 && this_value <= max_32bits) {
465 this_value = this_value * this_value;
466 // Verify that there is enough space in this_value to perform the
467 // multiplication. The first bit_size bits must be 0.
468 if ((power_exponent & mask) != 0) {
469 uint64_t base_bits_mask =
470 ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
471 bool high_bits_zero = (this_value & base_bits_mask) == 0;
472 if (high_bits_zero) {
473 this_value *= base;
474 } else {
475 delayed_multipliciation = true;
476 }
477 }
478 mask >>= 1;
479 }
480 AssignUInt64(this_value);
481 if (delayed_multipliciation) {
482 MultiplyByUInt32(base);
483 }
484
485 // Now do the same thing as a bignum.
486 while (mask != 0) {
487 Square();
488 if ((power_exponent & mask) != 0) {
489 MultiplyByUInt32(base);
490 }
491 mask >>= 1;
492 }
493
494 // And finally add the saved shifts.
495 ShiftLeft(shifts * power_exponent);
496 }
497
498
499 // Precondition: this/other < 16bit.
DivideModuloIntBignum(const Bignum & other)500 uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
501 ASSERT(IsClamped());
502 ASSERT(other.IsClamped());
503 ASSERT(other.used_digits_ > 0);
504
505 // Easy case: if we have less digits than the divisor than the result is 0.
506 // Note: this handles the case where this == 0, too.
507 if (BigitLength() < other.BigitLength()) {
508 return 0;
509 }
510
511 Align(other);
512
513 uint16_t result = 0;
514
515 // Start by removing multiples of 'other' until both numbers have the same
516 // number of digits.
517 while (BigitLength() > other.BigitLength()) {
518 // This naive approach is extremely inefficient if `this` divided by other
519 // is big. This function is implemented for doubleToString where
520 // the result should be small (less than 10).
521 ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
522 ASSERT(bigits_[used_digits_ - 1] < 0x10000);
523 // Remove the multiples of the first digit.
524 // Example this = 23 and other equals 9. -> Remove 2 multiples.
525 result += static_cast<uint16_t>(bigits_[used_digits_ - 1]);
526 SubtractTimes(other, bigits_[used_digits_ - 1]);
527 }
528
529 ASSERT(BigitLength() == other.BigitLength());
530
531 // Both bignums are at the same length now.
532 // Since other has more than 0 digits we know that the access to
533 // bigits_[used_digits_ - 1] is safe.
534 Chunk this_bigit = bigits_[used_digits_ - 1];
535 Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
536
537 if (other.used_digits_ == 1) {
538 // Shortcut for easy (and common) case.
539 int quotient = this_bigit / other_bigit;
540 bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
541 ASSERT(quotient < 0x10000);
542 result += static_cast<uint16_t>(quotient);
543 Clamp();
544 return result;
545 }
546
547 int division_estimate = this_bigit / (other_bigit + 1);
548 ASSERT(division_estimate < 0x10000);
549 result += static_cast<uint16_t>(division_estimate);
550 SubtractTimes(other, division_estimate);
551
552 if (other_bigit * (division_estimate + 1) > this_bigit) {
553 // No need to even try to subtract. Even if other's remaining digits were 0
554 // another subtraction would be too much.
555 return result;
556 }
557
558 while (LessEqual(other, *this)) {
559 SubtractBignum(other);
560 result++;
561 }
562 return result;
563 }
564
565
566 template<typename S>
SizeInHexChars(S number)567 static int SizeInHexChars(S number) {
568 ASSERT(number > 0);
569 int result = 0;
570 while (number != 0) {
571 number >>= 4;
572 result++;
573 }
574 return result;
575 }
576
577
HexCharOfValue(int value)578 static char HexCharOfValue(int value) {
579 ASSERT(0 <= value && value <= 16);
580 if (value < 10) return static_cast<char>(value + '0');
581 return static_cast<char>(value - 10 + 'A');
582 }
583
584
ToHexString(char * buffer,int buffer_size) const585 bool Bignum::ToHexString(char* buffer, int buffer_size) const {
586 ASSERT(IsClamped());
587 // Each bigit must be printable as separate hex-character.
588 ASSERT(kBigitSize % 4 == 0);
589 const int kHexCharsPerBigit = kBigitSize / 4;
590
591 if (used_digits_ == 0) {
592 if (buffer_size < 2) return false;
593 buffer[0] = '0';
594 buffer[1] = '\0';
595 return true;
596 }
597 // We add 1 for the terminating '\0' character.
598 int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
599 SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
600 if (needed_chars > buffer_size) return false;
601 int string_index = needed_chars - 1;
602 buffer[string_index--] = '\0';
603 for (int i = 0; i < exponent_; ++i) {
604 for (int j = 0; j < kHexCharsPerBigit; ++j) {
605 buffer[string_index--] = '0';
606 }
607 }
608 for (int i = 0; i < used_digits_ - 1; ++i) {
609 Chunk current_bigit = bigits_[i];
610 for (int j = 0; j < kHexCharsPerBigit; ++j) {
611 buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
612 current_bigit >>= 4;
613 }
614 }
615 // And finally the last bigit.
616 Chunk most_significant_bigit = bigits_[used_digits_ - 1];
617 while (most_significant_bigit != 0) {
618 buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
619 most_significant_bigit >>= 4;
620 }
621 return true;
622 }
623
624
BigitAt(int index) const625 Bignum::Chunk Bignum::BigitAt(int index) const {
626 if (index >= BigitLength()) return 0;
627 if (index < exponent_) return 0;
628 return bigits_[index - exponent_];
629 }
630
631
Compare(const Bignum & a,const Bignum & b)632 int Bignum::Compare(const Bignum& a, const Bignum& b) {
633 ASSERT(a.IsClamped());
634 ASSERT(b.IsClamped());
635 int bigit_length_a = a.BigitLength();
636 int bigit_length_b = b.BigitLength();
637 if (bigit_length_a < bigit_length_b) return -1;
638 if (bigit_length_a > bigit_length_b) return +1;
639 for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
640 Chunk bigit_a = a.BigitAt(i);
641 Chunk bigit_b = b.BigitAt(i);
642 if (bigit_a < bigit_b) return -1;
643 if (bigit_a > bigit_b) return +1;
644 // Otherwise they are equal up to this digit. Try the next digit.
645 }
646 return 0;
647 }
648
649
PlusCompare(const Bignum & a,const Bignum & b,const Bignum & c)650 int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
651 ASSERT(a.IsClamped());
652 ASSERT(b.IsClamped());
653 ASSERT(c.IsClamped());
654 if (a.BigitLength() < b.BigitLength()) {
655 return PlusCompare(b, a, c);
656 }
657 if (a.BigitLength() + 1 < c.BigitLength()) return -1;
658 if (a.BigitLength() > c.BigitLength()) return +1;
659 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
660 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
661 // of 'a'.
662 if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
663 return -1;
664 }
665
666 Chunk borrow = 0;
667 // Starting at min_exponent all digits are == 0. So no need to compare them.
668 int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
669 for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
670 Chunk chunk_a = a.BigitAt(i);
671 Chunk chunk_b = b.BigitAt(i);
672 Chunk chunk_c = c.BigitAt(i);
673 Chunk sum = chunk_a + chunk_b;
674 if (sum > chunk_c + borrow) {
675 return +1;
676 } else {
677 borrow = chunk_c + borrow - sum;
678 if (borrow > 1) return -1;
679 borrow <<= kBigitSize;
680 }
681 }
682 if (borrow == 0) return 0;
683 return -1;
684 }
685
686
Clamp()687 void Bignum::Clamp() {
688 while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
689 used_digits_--;
690 }
691 if (used_digits_ == 0) {
692 // Zero.
693 exponent_ = 0;
694 }
695 }
696
697
IsClamped() const698 bool Bignum::IsClamped() const {
699 return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
700 }
701
702
Zero()703 void Bignum::Zero() {
704 for (int i = 0; i < used_digits_; ++i) {
705 bigits_[i] = 0;
706 }
707 used_digits_ = 0;
708 exponent_ = 0;
709 }
710
711
Align(const Bignum & other)712 void Bignum::Align(const Bignum& other) {
713 if (exponent_ > other.exponent_) {
714 // If "X" represents a "hidden" digit (by the exponent) then we are in the
715 // following case (a == this, b == other):
716 // a: aaaaaaXXXX or a: aaaaaXXX
717 // b: bbbbbbX b: bbbbbbbbXX
718 // We replace some of the hidden digits (X) of a with 0 digits.
719 // a: aaaaaa000X or a: aaaaa0XX
720 int zero_digits = exponent_ - other.exponent_;
721 EnsureCapacity(used_digits_ + zero_digits);
722 for (int i = used_digits_ - 1; i >= 0; --i) {
723 bigits_[i + zero_digits] = bigits_[i];
724 }
725 for (int i = 0; i < zero_digits; ++i) {
726 bigits_[i] = 0;
727 }
728 used_digits_ += zero_digits;
729 exponent_ -= zero_digits;
730 ASSERT(used_digits_ >= 0);
731 ASSERT(exponent_ >= 0);
732 }
733 }
734
735
BigitsShiftLeft(int shift_amount)736 void Bignum::BigitsShiftLeft(int shift_amount) {
737 ASSERT(shift_amount < kBigitSize);
738 ASSERT(shift_amount >= 0);
739 Chunk carry = 0;
740 for (int i = 0; i < used_digits_; ++i) {
741 Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
742 bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
743 carry = new_carry;
744 }
745 if (carry != 0) {
746 bigits_[used_digits_] = carry;
747 used_digits_++;
748 }
749 }
750
751
SubtractTimes(const Bignum & other,int factor)752 void Bignum::SubtractTimes(const Bignum& other, int factor) {
753 ASSERT(exponent_ <= other.exponent_);
754 if (factor < 3) {
755 for (int i = 0; i < factor; ++i) {
756 SubtractBignum(other);
757 }
758 return;
759 }
760 Chunk borrow = 0;
761 int exponent_diff = other.exponent_ - exponent_;
762 for (int i = 0; i < other.used_digits_; ++i) {
763 DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
764 DoubleChunk remove = borrow + product;
765 Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask);
766 bigits_[i + exponent_diff] = difference & kBigitMask;
767 borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
768 (remove >> kBigitSize));
769 }
770 for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
771 if (borrow == 0) return;
772 Chunk difference = bigits_[i] - borrow;
773 bigits_[i] = difference & kBigitMask;
774 borrow = difference >> (kChunkSize - 1);
775 }
776 Clamp();
777 }
778
779
780 } // namespace double_conversion
781
782 // ICU PATCH: Close ICU namespace
783 U_NAMESPACE_END
784 #endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING
785