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3//
4// From the double-conversion library. Original license:
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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#include <algorithm>
38#include <cstring>
39
40// ICU PATCH: Customize header file paths for ICU.
41
42#include "double-conversion-bignum.h"
43#include "double-conversion-utils.h"
44
45// ICU PATCH: Wrap in ICU namespace
46U_NAMESPACE_BEGIN
47
48namespace double_conversion {
49
50Bignum::Chunk& Bignum::RawBigit(const int index) {
51 DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);
52 return bigits_buffer_[index];
53}
54
55
56const Bignum::Chunk& Bignum::RawBigit(const int index) const {
57 DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);
58 return bigits_buffer_[index];
59}
60
61
62template<typename S>
63static int BitSize(const S value) {
64 (void) value; // Mark variable as used.
65 return 8 * sizeof(value);
66}
67
68// Guaranteed to lie in one Bigit.
69void Bignum::AssignUInt16(const uint16_t value) {
70 DOUBLE_CONVERSION_ASSERT(kBigitSize >= BitSize(value));
71 Zero();
72 if (value > 0) {
73 RawBigit(0) = value;
74 used_bigits_ = 1;
75 }
76}
77
78
79void Bignum::AssignUInt64(uint64_t value) {
80 Zero();
81 for(int i = 0; value > 0; ++i) {
82 RawBigit(i) = value & kBigitMask;
83 value >>= kBigitSize;
84 ++used_bigits_;
85 }
86}
87
88
89void Bignum::AssignBignum(const Bignum& other) {
90 exponent_ = other.exponent_;
91 for (int i = 0; i < other.used_bigits_; ++i) {
92 RawBigit(i) = other.RawBigit(i);
93 }
94 used_bigits_ = other.used_bigits_;
95}
96
97
98static uint64_t ReadUInt64(const Vector<const char> buffer,
99 const int from,
100 const int digits_to_read) {
101 uint64_t result = 0;
102 for (int i = from; i < from + digits_to_read; ++i) {
103 const int digit = buffer[i] - '0';
104 DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9);
105 result = result * 10 + digit;
106 }
107 return result;
108}
109
110
111void Bignum::AssignDecimalString(const Vector<const char> value) {
112 // 2^64 = 18446744073709551616 > 10^19
113 static const int kMaxUint64DecimalDigits = 19;
114 Zero();
115 int length = value.length();
116 unsigned pos = 0;
117 // Let's just say that each digit needs 4 bits.
118 while (length >= kMaxUint64DecimalDigits) {
119 const uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
120 pos += kMaxUint64DecimalDigits;
121 length -= kMaxUint64DecimalDigits;
122 MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
123 AddUInt64(digits);
124 }
125 const uint64_t digits = ReadUInt64(value, pos, length);
126 MultiplyByPowerOfTen(length);
127 AddUInt64(digits);
128 Clamp();
129}
130
131
132static uint64_t HexCharValue(const int c) {
133 if ('0' <= c && c <= '9') {
134 return c - '0';
135 }
136 if ('a' <= c && c <= 'f') {
137 return 10 + c - 'a';
138 }
139 DOUBLE_CONVERSION_ASSERT('A' <= c && c <= 'F');
140 return 10 + c - 'A';
141}
142
143
144// Unlike AssignDecimalString(), this function is "only" used
145// for unit-tests and therefore not performance critical.
146void Bignum::AssignHexString(Vector<const char> value) {
147 Zero();
148 // Required capacity could be reduced by ignoring leading zeros.
149 EnsureCapacity(((value.length() * 4) + kBigitSize - 1) / kBigitSize);
150 DOUBLE_CONVERSION_ASSERT(sizeof(uint64_t) * 8 >= kBigitSize + 4); // TODO: static_assert
151 // Accumulates converted hex digits until at least kBigitSize bits.
152 // Works with non-factor-of-four kBigitSizes.
153 uint64_t tmp = 0; // Accumulates converted hex digits until at least
154 for (int cnt = 0; !value.is_empty(); value.pop_back()) {
155 tmp |= (HexCharValue(value.last()) << cnt);
156 if ((cnt += 4) >= kBigitSize) {
157 RawBigit(used_bigits_++) = (tmp & kBigitMask);
158 cnt -= kBigitSize;
159 tmp >>= kBigitSize;
160 }
161 }
162 if (tmp > 0) {
163 RawBigit(used_bigits_++) = tmp;
164 }
165 Clamp();
166}
167
168
169void Bignum::AddUInt64(const uint64_t operand) {
170 if (operand == 0) {
171 return;
172 }
173 Bignum other;
174 other.AssignUInt64(operand);
175 AddBignum(other);
176}
177
178
179void Bignum::AddBignum(const Bignum& other) {
180 DOUBLE_CONVERSION_ASSERT(IsClamped());
181 DOUBLE_CONVERSION_ASSERT(other.IsClamped());
182
183 // If this has a greater exponent than other append zero-bigits to this.
184 // After this call exponent_ <= other.exponent_.
185 Align(other);
186
187 // There are two possibilities:
188 // aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
189 // bbbbb 00000000
190 // ----------------
191 // ccccccccccc 0000
192 // or
193 // aaaaaaaaaa 0000
194 // bbbbbbbbb 0000000
195 // -----------------
196 // cccccccccccc 0000
197 // In both cases we might need a carry bigit.
198
199 EnsureCapacity(1 + (std::max)(BigitLength(), other.BigitLength()) - exponent_);
200 Chunk carry = 0;
201 int bigit_pos = other.exponent_ - exponent_;
202 DOUBLE_CONVERSION_ASSERT(bigit_pos >= 0);
203 for (int i = used_bigits_; i < bigit_pos; ++i) {
204 RawBigit(i) = 0;
205 }
206 for (int i = 0; i < other.used_bigits_; ++i) {
207 const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;
208 const Chunk sum = my + other.RawBigit(i) + carry;
209 RawBigit(bigit_pos) = sum & kBigitMask;
210 carry = sum >> kBigitSize;
211 ++bigit_pos;
212 }
213 while (carry != 0) {
214 const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;
215 const Chunk sum = my + carry;
216 RawBigit(bigit_pos) = sum & kBigitMask;
217 carry = sum >> kBigitSize;
218 ++bigit_pos;
219 }
220 used_bigits_ = (std::max)(bigit_pos, static_cast<int>(used_bigits_));
221 DOUBLE_CONVERSION_ASSERT(IsClamped());
222}
223
224
225void Bignum::SubtractBignum(const Bignum& other) {
226 DOUBLE_CONVERSION_ASSERT(IsClamped());
227 DOUBLE_CONVERSION_ASSERT(other.IsClamped());
228 // We require this to be bigger than other.
229 DOUBLE_CONVERSION_ASSERT(LessEqual(other, *this));
230
231 Align(other);
232
233 const int offset = other.exponent_ - exponent_;
234 Chunk borrow = 0;
235 int i;
236 for (i = 0; i < other.used_bigits_; ++i) {
237 DOUBLE_CONVERSION_ASSERT((borrow == 0) || (borrow == 1));
238 const Chunk difference = RawBigit(i + offset) - other.RawBigit(i) - borrow;
239 RawBigit(i + offset) = difference & kBigitMask;
240 borrow = difference >> (kChunkSize - 1);
241 }
242 while (borrow != 0) {
243 const Chunk difference = RawBigit(i + offset) - borrow;
244 RawBigit(i + offset) = difference & kBigitMask;
245 borrow = difference >> (kChunkSize - 1);
246 ++i;
247 }
248 Clamp();
249}
250
251
252void Bignum::ShiftLeft(const int shift_amount) {
253 if (used_bigits_ == 0) {
254 return;
255 }
256 exponent_ += (shift_amount / kBigitSize);
257 const int local_shift = shift_amount % kBigitSize;
258 EnsureCapacity(used_bigits_ + 1);
259 BigitsShiftLeft(local_shift);
260}
261
262
263void Bignum::MultiplyByUInt32(const uint32_t factor) {
264 if (factor == 1) {
265 return;
266 }
267 if (factor == 0) {
268 Zero();
269 return;
270 }
271 if (used_bigits_ == 0) {
272 return;
273 }
274 // The product of a bigit with the factor is of size kBigitSize + 32.
275 // Assert that this number + 1 (for the carry) fits into double chunk.
276 DOUBLE_CONVERSION_ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
277 DoubleChunk carry = 0;
278 for (int i = 0; i < used_bigits_; ++i) {
279 const DoubleChunk product = static_cast<DoubleChunk>(factor) * RawBigit(i) + carry;
280 RawBigit(i) = static_cast<Chunk>(product & kBigitMask);
281 carry = (product >> kBigitSize);
282 }
283 while (carry != 0) {
284 EnsureCapacity(used_bigits_ + 1);
285 RawBigit(used_bigits_) = carry & kBigitMask;
286 used_bigits_++;
287 carry >>= kBigitSize;
288 }
289}
290
291
292void Bignum::MultiplyByUInt64(const uint64_t factor) {
293 if (factor == 1) {
294 return;
295 }
296 if (factor == 0) {
297 Zero();
298 return;
299 }
300 if (used_bigits_ == 0) {
301 return;
302 }
303 DOUBLE_CONVERSION_ASSERT(kBigitSize < 32);
304 uint64_t carry = 0;
305 const uint64_t low = factor & 0xFFFFFFFF;
306 const uint64_t high = factor >> 32;
307 for (int i = 0; i < used_bigits_; ++i) {
308 const uint64_t product_low = low * RawBigit(i);
309 const uint64_t product_high = high * RawBigit(i);
310 const uint64_t tmp = (carry & kBigitMask) + product_low;
311 RawBigit(i) = tmp & kBigitMask;
312 carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
313 (product_high << (32 - kBigitSize));
314 }
315 while (carry != 0) {
316 EnsureCapacity(used_bigits_ + 1);
317 RawBigit(used_bigits_) = carry & kBigitMask;
318 used_bigits_++;
319 carry >>= kBigitSize;
320 }
321}
322
323
324void Bignum::MultiplyByPowerOfTen(const int exponent) {
325 static const uint64_t kFive27 = DOUBLE_CONVERSION_UINT64_2PART_C(0x6765c793, fa10079d);
326 static const uint16_t kFive1 = 5;
327 static const uint16_t kFive2 = kFive1 * 5;
328 static const uint16_t kFive3 = kFive2 * 5;
329 static const uint16_t kFive4 = kFive3 * 5;
330 static const uint16_t kFive5 = kFive4 * 5;
331 static const uint16_t kFive6 = kFive5 * 5;
332 static const uint32_t kFive7 = kFive6 * 5;
333 static const uint32_t kFive8 = kFive7 * 5;
334 static const uint32_t kFive9 = kFive8 * 5;
335 static const uint32_t kFive10 = kFive9 * 5;
336 static const uint32_t kFive11 = kFive10 * 5;
337 static const uint32_t kFive12 = kFive11 * 5;
338 static const uint32_t kFive13 = kFive12 * 5;
339 static const uint32_t kFive1_to_12[] =
340 { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
341 kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
342
343 DOUBLE_CONVERSION_ASSERT(exponent >= 0);
344
345 if (exponent == 0) {
346 return;
347 }
348 if (used_bigits_ == 0) {
349 return;
350 }
351 // We shift by exponent at the end just before returning.
352 int remaining_exponent = exponent;
353 while (remaining_exponent >= 27) {
354 MultiplyByUInt64(kFive27);
355 remaining_exponent -= 27;
356 }
357 while (remaining_exponent >= 13) {
358 MultiplyByUInt32(kFive13);
359 remaining_exponent -= 13;
360 }
361 if (remaining_exponent > 0) {
362 MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
363 }
364 ShiftLeft(exponent);
365}
366
367
368void Bignum::Square() {
369 DOUBLE_CONVERSION_ASSERT(IsClamped());
370 const int product_length = 2 * used_bigits_;
371 EnsureCapacity(product_length);
372
373 // Comba multiplication: compute each column separately.
374 // Example: r = a2a1a0 * b2b1b0.
375 // r = 1 * a0b0 +
376 // 10 * (a1b0 + a0b1) +
377 // 100 * (a2b0 + a1b1 + a0b2) +
378 // 1000 * (a2b1 + a1b2) +
379 // 10000 * a2b2
380 //
381 // In the worst case we have to accumulate nb-digits products of digit*digit.
382 //
383 // Assert that the additional number of bits in a DoubleChunk are enough to
384 // sum up used_digits of Bigit*Bigit.
385 if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_bigits_) {
386 DOUBLE_CONVERSION_UNIMPLEMENTED();
387 }
388 DoubleChunk accumulator = 0;
389 // First shift the digits so we don't overwrite them.
390 const int copy_offset = used_bigits_;
391 for (int i = 0; i < used_bigits_; ++i) {
392 RawBigit(copy_offset + i) = RawBigit(i);
393 }
394 // We have two loops to avoid some 'if's in the loop.
395 for (int i = 0; i < used_bigits_; ++i) {
396 // Process temporary digit i with power i.
397 // The sum of the two indices must be equal to i.
398 int bigit_index1 = i;
399 int bigit_index2 = 0;
400 // Sum all of the sub-products.
401 while (bigit_index1 >= 0) {
402 const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);
403 const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);
404 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
405 bigit_index1--;
406 bigit_index2++;
407 }
408 RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;
409 accumulator >>= kBigitSize;
410 }
411 for (int i = used_bigits_; i < product_length; ++i) {
412 int bigit_index1 = used_bigits_ - 1;
413 int bigit_index2 = i - bigit_index1;
414 // Invariant: sum of both indices is again equal to i.
415 // Inner loop runs 0 times on last iteration, emptying accumulator.
416 while (bigit_index2 < used_bigits_) {
417 const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);
418 const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);
419 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
420 bigit_index1--;
421 bigit_index2++;
422 }
423 // The overwritten RawBigit(i) will never be read in further loop iterations,
424 // because bigit_index1 and bigit_index2 are always greater
425 // than i - used_bigits_.
426 RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;
427 accumulator >>= kBigitSize;
428 }
429 // Since the result was guaranteed to lie inside the number the
430 // accumulator must be 0 now.
431 DOUBLE_CONVERSION_ASSERT(accumulator == 0);
432
433 // Don't forget to update the used_digits and the exponent.
434 used_bigits_ = product_length;
435 exponent_ *= 2;
436 Clamp();
437}
438
439
440void Bignum::AssignPowerUInt16(uint16_t base, const int power_exponent) {
441 DOUBLE_CONVERSION_ASSERT(base != 0);
442 DOUBLE_CONVERSION_ASSERT(power_exponent >= 0);
443 if (power_exponent == 0) {
444 AssignUInt16(1);
445 return;
446 }
447 Zero();
448 int shifts = 0;
449 // We expect base to be in range 2-32, and most often to be 10.
450 // It does not make much sense to implement different algorithms for counting
451 // the bits.
452 while ((base & 1) == 0) {
453 base >>= 1;
454 shifts++;
455 }
456 int bit_size = 0;
457 int tmp_base = base;
458 while (tmp_base != 0) {
459 tmp_base >>= 1;
460 bit_size++;
461 }
462 const int final_size = bit_size * power_exponent;
463 // 1 extra bigit for the shifting, and one for rounded final_size.
464 EnsureCapacity(final_size / kBigitSize + 2);
465
466 // Left to Right exponentiation.
467 int mask = 1;
468 while (power_exponent >= mask) mask <<= 1;
469
470 // The mask is now pointing to the bit above the most significant 1-bit of
471 // power_exponent.
472 // Get rid of first 1-bit;
473 mask >>= 2;
474 uint64_t this_value = base;
475
476 bool delayed_multiplication = false;
477 const uint64_t max_32bits = 0xFFFFFFFF;
478 while (mask != 0 && this_value <= max_32bits) {
479 this_value = this_value * this_value;
480 // Verify that there is enough space in this_value to perform the
481 // multiplication. The first bit_size bits must be 0.
482 if ((power_exponent & mask) != 0) {
483 DOUBLE_CONVERSION_ASSERT(bit_size > 0);
484 const uint64_t base_bits_mask =
485 ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
486 const bool high_bits_zero = (this_value & base_bits_mask) == 0;
487 if (high_bits_zero) {
488 this_value *= base;
489 } else {
490 delayed_multiplication = true;
491 }
492 }
493 mask >>= 1;
494 }
495 AssignUInt64(this_value);
496 if (delayed_multiplication) {
497 MultiplyByUInt32(base);
498 }
499
500 // Now do the same thing as a bignum.
501 while (mask != 0) {
502 Square();
503 if ((power_exponent & mask) != 0) {
504 MultiplyByUInt32(base);
505 }
506 mask >>= 1;
507 }
508
509 // And finally add the saved shifts.
510 ShiftLeft(shifts * power_exponent);
511}
512
513
514// Precondition: this/other < 16bit.
515uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
516 DOUBLE_CONVERSION_ASSERT(IsClamped());
517 DOUBLE_CONVERSION_ASSERT(other.IsClamped());
518 DOUBLE_CONVERSION_ASSERT(other.used_bigits_ > 0);
519
520 // Easy case: if we have less digits than the divisor than the result is 0.
521 // Note: this handles the case where this == 0, too.
522 if (BigitLength() < other.BigitLength()) {
523 return 0;
524 }
525
526 Align(other);
527
528 uint16_t result = 0;
529
530 // Start by removing multiples of 'other' until both numbers have the same
531 // number of digits.
532 while (BigitLength() > other.BigitLength()) {
533 // This naive approach is extremely inefficient if `this` divided by other
534 // is big. This function is implemented for doubleToString where
535 // the result should be small (less than 10).
536 DOUBLE_CONVERSION_ASSERT(other.RawBigit(other.used_bigits_ - 1) >= ((1 << kBigitSize) / 16));
537 DOUBLE_CONVERSION_ASSERT(RawBigit(used_bigits_ - 1) < 0x10000);
538 // Remove the multiples of the first digit.
539 // Example this = 23 and other equals 9. -> Remove 2 multiples.
540 result += static_cast<uint16_t>(RawBigit(used_bigits_ - 1));
541 SubtractTimes(other, RawBigit(used_bigits_ - 1));
542 }
543
544 DOUBLE_CONVERSION_ASSERT(BigitLength() == other.BigitLength());
545
546 // Both bignums are at the same length now.
547 // Since other has more than 0 digits we know that the access to
548 // RawBigit(used_bigits_ - 1) is safe.
549 const Chunk this_bigit = RawBigit(used_bigits_ - 1);
550 const Chunk other_bigit = other.RawBigit(other.used_bigits_ - 1);
551
552 if (other.used_bigits_ == 1) {
553 // Shortcut for easy (and common) case.
554 int quotient = this_bigit / other_bigit;
555 RawBigit(used_bigits_ - 1) = this_bigit - other_bigit * quotient;
556 DOUBLE_CONVERSION_ASSERT(quotient < 0x10000);
557 result += static_cast<uint16_t>(quotient);
558 Clamp();
559 return result;
560 }
561
562 const int division_estimate = this_bigit / (other_bigit + 1);
563 DOUBLE_CONVERSION_ASSERT(division_estimate < 0x10000);
564 result += static_cast<uint16_t>(division_estimate);
565 SubtractTimes(other, division_estimate);
566
567 if (other_bigit * (division_estimate + 1) > this_bigit) {
568 // No need to even try to subtract. Even if other's remaining digits were 0
569 // another subtraction would be too much.
570 return result;
571 }
572
573 while (LessEqual(other, *this)) {
574 SubtractBignum(other);
575 result++;
576 }
577 return result;
578}
579
580
581template<typename S>
582static int SizeInHexChars(S number) {
583 DOUBLE_CONVERSION_ASSERT(number > 0);
584 int result = 0;
585 while (number != 0) {
586 number >>= 4;
587 result++;
588 }
589 return result;
590}
591
592
593static char HexCharOfValue(const int value) {
594 DOUBLE_CONVERSION_ASSERT(0 <= value && value <= 16);
595 if (value < 10) {
596 return static_cast<char>(value + '0');
597 }
598 return static_cast<char>(value - 10 + 'A');
599}
600
601
602bool Bignum::ToHexString(char* buffer, const int buffer_size) const {
603 DOUBLE_CONVERSION_ASSERT(IsClamped());
604 // Each bigit must be printable as separate hex-character.
605 DOUBLE_CONVERSION_ASSERT(kBigitSize % 4 == 0);
606 static const int kHexCharsPerBigit = kBigitSize / 4;
607
608 if (used_bigits_ == 0) {
609 if (buffer_size < 2) {
610 return false;
611 }
612 buffer[0] = '0';
613 buffer[1] = '\0';
614 return true;
615 }
616 // We add 1 for the terminating '\0' character.
617 const int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
618 SizeInHexChars(RawBigit(used_bigits_ - 1)) + 1;
619 if (needed_chars > buffer_size) {
620 return false;
621 }
622 int string_index = needed_chars - 1;
623 buffer[string_index--] = '\0';
624 for (int i = 0; i < exponent_; ++i) {
625 for (int j = 0; j < kHexCharsPerBigit; ++j) {
626 buffer[string_index--] = '0';
627 }
628 }
629 for (int i = 0; i < used_bigits_ - 1; ++i) {
630 Chunk current_bigit = RawBigit(i);
631 for (int j = 0; j < kHexCharsPerBigit; ++j) {
632 buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
633 current_bigit >>= 4;
634 }
635 }
636 // And finally the last bigit.
637 Chunk most_significant_bigit = RawBigit(used_bigits_ - 1);
638 while (most_significant_bigit != 0) {
639 buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
640 most_significant_bigit >>= 4;
641 }
642 return true;
643}
644
645
646Bignum::Chunk Bignum::BigitOrZero(const int index) const {
647 if (index >= BigitLength()) {
648 return 0;
649 }
650 if (index < exponent_) {
651 return 0;
652 }
653 return RawBigit(index - exponent_);
654}
655
656
657int Bignum::Compare(const Bignum& a, const Bignum& b) {
658 DOUBLE_CONVERSION_ASSERT(a.IsClamped());
659 DOUBLE_CONVERSION_ASSERT(b.IsClamped());
660 const int bigit_length_a = a.BigitLength();
661 const int bigit_length_b = b.BigitLength();
662 if (bigit_length_a < bigit_length_b) {
663 return -1;
664 }
665 if (bigit_length_a > bigit_length_b) {
666 return +1;
667 }
668 for (int i = bigit_length_a - 1; i >= (std::min)(a.exponent_, b.exponent_); --i) {
669 const Chunk bigit_a = a.BigitOrZero(i);
670 const Chunk bigit_b = b.BigitOrZero(i);
671 if (bigit_a < bigit_b) {
672 return -1;
673 }
674 if (bigit_a > bigit_b) {
675 return +1;
676 }
677 // Otherwise they are equal up to this digit. Try the next digit.
678 }
679 return 0;
680}
681
682
683int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
684 DOUBLE_CONVERSION_ASSERT(a.IsClamped());
685 DOUBLE_CONVERSION_ASSERT(b.IsClamped());
686 DOUBLE_CONVERSION_ASSERT(c.IsClamped());
687 if (a.BigitLength() < b.BigitLength()) {
688 return PlusCompare(b, a, c);
689 }
690 if (a.BigitLength() + 1 < c.BigitLength()) {
691 return -1;
692 }
693 if (a.BigitLength() > c.BigitLength()) {
694 return +1;
695 }
696 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
697 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
698 // of 'a'.
699 if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
700 return -1;
701 }
702
703 Chunk borrow = 0;
704 // Starting at min_exponent all digits are == 0. So no need to compare them.
705 const int min_exponent = (std::min)((std::min)(a.exponent_, b.exponent_), c.exponent_);
706 for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
707 const Chunk chunk_a = a.BigitOrZero(i);
708 const Chunk chunk_b = b.BigitOrZero(i);
709 const Chunk chunk_c = c.BigitOrZero(i);
710 const Chunk sum = chunk_a + chunk_b;
711 if (sum > chunk_c + borrow) {
712 return +1;
713 } else {
714 borrow = chunk_c + borrow - sum;
715 if (borrow > 1) {
716 return -1;
717 }
718 borrow <<= kBigitSize;
719 }
720 }
721 if (borrow == 0) {
722 return 0;
723 }
724 return -1;
725}
726
727
728void Bignum::Clamp() {
729 while (used_bigits_ > 0 && RawBigit(used_bigits_ - 1) == 0) {
730 used_bigits_--;
731 }
732 if (used_bigits_ == 0) {
733 // Zero.
734 exponent_ = 0;
735 }
736}
737
738
739void Bignum::Align(const Bignum& other) {
740 if (exponent_ > other.exponent_) {
741 // If "X" represents a "hidden" bigit (by the exponent) then we are in the
742 // following case (a == this, b == other):
743 // a: aaaaaaXXXX or a: aaaaaXXX
744 // b: bbbbbbX b: bbbbbbbbXX
745 // We replace some of the hidden digits (X) of a with 0 digits.
746 // a: aaaaaa000X or a: aaaaa0XX
747 const int zero_bigits = exponent_ - other.exponent_;
748 EnsureCapacity(used_bigits_ + zero_bigits);
749 for (int i = used_bigits_ - 1; i >= 0; --i) {
750 RawBigit(i + zero_bigits) = RawBigit(i);
751 }
752 for (int i = 0; i < zero_bigits; ++i) {
753 RawBigit(i) = 0;
754 }
755 used_bigits_ += zero_bigits;
756 exponent_ -= zero_bigits;
757
758 DOUBLE_CONVERSION_ASSERT(used_bigits_ >= 0);
759 DOUBLE_CONVERSION_ASSERT(exponent_ >= 0);
760 }
761}
762
763
764void Bignum::BigitsShiftLeft(const int shift_amount) {
765 DOUBLE_CONVERSION_ASSERT(shift_amount < kBigitSize);
766 DOUBLE_CONVERSION_ASSERT(shift_amount >= 0);
767 Chunk carry = 0;
768 for (int i = 0; i < used_bigits_; ++i) {
769 const Chunk new_carry = RawBigit(i) >> (kBigitSize - shift_amount);
770 RawBigit(i) = ((RawBigit(i) << shift_amount) + carry) & kBigitMask;
771 carry = new_carry;
772 }
773 if (carry != 0) {
774 RawBigit(used_bigits_) = carry;
775 used_bigits_++;
776 }
777}
778
779
780void Bignum::SubtractTimes(const Bignum& other, const int factor) {
781 DOUBLE_CONVERSION_ASSERT(exponent_ <= other.exponent_);
782 if (factor < 3) {
783 for (int i = 0; i < factor; ++i) {
784 SubtractBignum(other);
785 }
786 return;
787 }
788 Chunk borrow = 0;
789 const int exponent_diff = other.exponent_ - exponent_;
790 for (int i = 0; i < other.used_bigits_; ++i) {
791 const DoubleChunk product = static_cast<DoubleChunk>(factor) * other.RawBigit(i);
792 const DoubleChunk remove = borrow + product;
793 const Chunk difference = RawBigit(i + exponent_diff) - (remove & kBigitMask);
794 RawBigit(i + exponent_diff) = difference & kBigitMask;
795 borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
796 (remove >> kBigitSize));
797 }
798 for (int i = other.used_bigits_ + exponent_diff; i < used_bigits_; ++i) {
799 if (borrow == 0) {
800 return;
801 }
802 const Chunk difference = RawBigit(i) - borrow;
803 RawBigit(i) = difference & kBigitMask;
804 borrow = difference >> (kChunkSize - 1);
805 }
806 Clamp();
807}
808
809
810} // namespace double_conversion
811
812// ICU PATCH: Close ICU namespace
813U_NAMESPACE_END
814#endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING
815