/src/icu/source/i18n/double-conversion-bignum.cpp
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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  |  | //  | 
6  |  | // Copyright 2010 the V8 project authors. All rights reserved.  | 
7  |  | // Redistribution and use in source and binary forms, with or without  | 
8  |  | // modification, are permitted provided that the following conditions are  | 
9  |  | // met:  | 
10  |  | //  | 
11  |  | //     * Redistributions of source code must retain the above copyright  | 
12  |  | //       notice, this list of conditions and the following disclaimer.  | 
13  |  | //     * Redistributions in binary form must reproduce the above  | 
14  |  | //       copyright notice, this list of conditions and the following  | 
15  |  | //       disclaimer in the documentation and/or other materials provided  | 
16  |  | //       with the distribution.  | 
17  |  | //     * Neither the name of Google Inc. nor the names of its  | 
18  |  | //       contributors may be used to endorse or promote products derived  | 
19  |  | //       from this software without specific prior written permission.  | 
20  |  | //  | 
21  |  | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS  | 
22  |  | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT  | 
23  |  | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR  | 
24  |  | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT  | 
25  |  | // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,  | 
26  |  | // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT  | 
27  |  | // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,  | 
28  |  | // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY  | 
29  |  | // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT  | 
30  |  | // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE  | 
31  |  | // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.  | 
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  | 
46  |  | U_NAMESPACE_BEGIN  | 
47  |  |  | 
48  |  | namespace double_conversion { | 
49  |  |  | 
50  | 0  | Bignum::Chunk& Bignum::RawBigit(const int index) { | 
51  | 0  |   DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);  | 
52  | 0  |   return bigits_buffer_[index];  | 
53  | 0  | }  | 
54  |  |  | 
55  |  |  | 
56  | 0  | const Bignum::Chunk& Bignum::RawBigit(const int index) const { | 
57  | 0  |   DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);  | 
58  | 0  |   return bigits_buffer_[index];  | 
59  | 0  | }  | 
60  |  |  | 
61  |  |  | 
62  |  | template<typename S>  | 
63  |  | static 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.  | 
69  | 0  | void Bignum::AssignUInt16(const uint16_t value) { | 
70  | 0  |   DOUBLE_CONVERSION_ASSERT(kBigitSize >= BitSize(value));  | 
71  | 0  |   Zero();  | 
72  | 0  |   if (value > 0) { | 
73  | 0  |     RawBigit(0) = value;  | 
74  | 0  |     used_bigits_ = 1;  | 
75  | 0  |   }  | 
76  | 0  | }  | 
77  |  |  | 
78  |  |  | 
79  | 0  | void Bignum::AssignUInt64(uint64_t value) { | 
80  | 0  |   Zero();  | 
81  | 0  |   for(int i = 0; value > 0; ++i) { | 
82  | 0  |     RawBigit(i) = value & kBigitMask;  | 
83  | 0  |     value >>= kBigitSize;  | 
84  | 0  |     ++used_bigits_;  | 
85  | 0  |   }  | 
86  | 0  | }  | 
87  |  |  | 
88  |  |  | 
89  | 0  | void Bignum::AssignBignum(const Bignum& other) { | 
90  | 0  |   exponent_ = other.exponent_;  | 
91  | 0  |   for (int i = 0; i < other.used_bigits_; ++i) { | 
92  | 0  |     RawBigit(i) = other.RawBigit(i);  | 
93  | 0  |   }  | 
94  | 0  |   used_bigits_ = other.used_bigits_;  | 
95  | 0  | }  | 
96  |  |  | 
97  |  |  | 
98  |  | static uint64_t ReadUInt64(const Vector<const char> buffer,  | 
99  |  |                            const int from,  | 
100  | 0  |                            const int digits_to_read) { | 
101  | 0  |   uint64_t result = 0;  | 
102  | 0  |   for (int i = from; i < from + digits_to_read; ++i) { | 
103  | 0  |     const int digit = buffer[i] - '0';  | 
104  | 0  |     DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9);  | 
105  | 0  |     result = result * 10 + digit;  | 
106  | 0  |   }  | 
107  | 0  |   return result;  | 
108  | 0  | }  | 
109  |  |  | 
110  |  |  | 
111  | 0  | void Bignum::AssignDecimalString(const Vector<const char> value) { | 
112  |  |   // 2^64 = 18446744073709551616 > 10^19  | 
113  | 0  |   static const int kMaxUint64DecimalDigits = 19;  | 
114  | 0  |   Zero();  | 
115  | 0  |   int length = value.length();  | 
116  | 0  |   unsigned pos = 0;  | 
117  |  |   // Let's just say that each digit needs 4 bits.  | 
118  | 0  |   while (length >= kMaxUint64DecimalDigits) { | 
119  | 0  |     const uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);  | 
120  | 0  |     pos += kMaxUint64DecimalDigits;  | 
121  | 0  |     length -= kMaxUint64DecimalDigits;  | 
122  | 0  |     MultiplyByPowerOfTen(kMaxUint64DecimalDigits);  | 
123  | 0  |     AddUInt64(digits);  | 
124  | 0  |   }  | 
125  | 0  |   const uint64_t digits = ReadUInt64(value, pos, length);  | 
126  | 0  |   MultiplyByPowerOfTen(length);  | 
127  | 0  |   AddUInt64(digits);  | 
128  | 0  |   Clamp();  | 
129  | 0  | }  | 
130  |  |  | 
131  |  |  | 
132  | 0  | static uint64_t HexCharValue(const int c) { | 
133  | 0  |   if ('0' <= c && c <= '9') { | 
134  | 0  |     return c - '0';  | 
135  | 0  |   }  | 
136  | 0  |   if ('a' <= c && c <= 'f') { | 
137  | 0  |     return 10 + c - 'a';  | 
138  | 0  |   }  | 
139  | 0  |   DOUBLE_CONVERSION_ASSERT('A' <= c && c <= 'F'); | 
140  | 0  |   return 10 + c - 'A';  | 
141  | 0  | }  | 
142  |  |  | 
143  |  |  | 
144  |  | // Unlike AssignDecimalString(), this function is "only" used  | 
145  |  | // for unit-tests and therefore not performance critical.  | 
146  | 0  | void Bignum::AssignHexString(Vector<const char> value) { | 
147  | 0  |   Zero();  | 
148  |  |   // Required capacity could be reduced by ignoring leading zeros.  | 
149  | 0  |   EnsureCapacity(((value.length() * 4) + kBigitSize - 1) / kBigitSize);  | 
150  | 0  |   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  | 0  |   uint64_t tmp = 0;  // Accumulates converted hex digits until at least  | 
154  | 0  |   for (int cnt = 0; !value.is_empty(); value.pop_back()) { | 
155  | 0  |     tmp |= (HexCharValue(value.last()) << cnt);  | 
156  | 0  |     if ((cnt += 4) >= kBigitSize) { | 
157  | 0  |       RawBigit(used_bigits_++) = (tmp & kBigitMask);  | 
158  | 0  |       cnt -= kBigitSize;  | 
159  | 0  |       tmp >>= kBigitSize;  | 
160  | 0  |     }  | 
161  | 0  |   }  | 
162  | 0  |   if (tmp > 0) { | 
163  | 0  |     RawBigit(used_bigits_++) = tmp;  | 
164  | 0  |   }  | 
165  | 0  |   Clamp();  | 
166  | 0  | }  | 
167  |  |  | 
168  |  |  | 
169  | 0  | void Bignum::AddUInt64(const uint64_t operand) { | 
170  | 0  |   if (operand == 0) { | 
171  | 0  |     return;  | 
172  | 0  |   }  | 
173  | 0  |   Bignum other;  | 
174  | 0  |   other.AssignUInt64(operand);  | 
175  | 0  |   AddBignum(other);  | 
176  | 0  | }  | 
177  |  |  | 
178  |  |  | 
179  | 0  | void Bignum::AddBignum(const Bignum& other) { | 
180  | 0  |   DOUBLE_CONVERSION_ASSERT(IsClamped());  | 
181  | 0  |   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  | 0  |   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  | 0  |   EnsureCapacity(1 + (std::max)(BigitLength(), other.BigitLength()) - exponent_);  | 
200  | 0  |   Chunk carry = 0;  | 
201  | 0  |   int bigit_pos = other.exponent_ - exponent_;  | 
202  | 0  |   DOUBLE_CONVERSION_ASSERT(bigit_pos >= 0);  | 
203  | 0  |   for (int i = used_bigits_; i < bigit_pos; ++i) { | 
204  | 0  |     RawBigit(i) = 0;  | 
205  | 0  |   }  | 
206  | 0  |   for (int i = 0; i < other.used_bigits_; ++i) { | 
207  | 0  |     const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;  | 
208  | 0  |     const Chunk sum = my + other.RawBigit(i) + carry;  | 
209  | 0  |     RawBigit(bigit_pos) = sum & kBigitMask;  | 
210  | 0  |     carry = sum >> kBigitSize;  | 
211  | 0  |     ++bigit_pos;  | 
212  | 0  |   }  | 
213  | 0  |   while (carry != 0) { | 
214  | 0  |     const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;  | 
215  | 0  |     const Chunk sum = my + carry;  | 
216  | 0  |     RawBigit(bigit_pos) = sum & kBigitMask;  | 
217  | 0  |     carry = sum >> kBigitSize;  | 
218  | 0  |     ++bigit_pos;  | 
219  | 0  |   }  | 
220  | 0  |   used_bigits_ = (std::max)(bigit_pos, static_cast<int>(used_bigits_));  | 
221  | 0  |   DOUBLE_CONVERSION_ASSERT(IsClamped());  | 
222  | 0  | }  | 
223  |  |  | 
224  |  |  | 
225  | 0  | void Bignum::SubtractBignum(const Bignum& other) { | 
226  | 0  |   DOUBLE_CONVERSION_ASSERT(IsClamped());  | 
227  | 0  |   DOUBLE_CONVERSION_ASSERT(other.IsClamped());  | 
228  |  |   // We require this to be bigger than other.  | 
229  | 0  |   DOUBLE_CONVERSION_ASSERT(LessEqual(other, *this));  | 
230  |  | 
  | 
231  | 0  |   Align(other);  | 
232  |  | 
  | 
233  | 0  |   const int offset = other.exponent_ - exponent_;  | 
234  | 0  |   Chunk borrow = 0;  | 
235  | 0  |   int i;  | 
236  | 0  |   for (i = 0; i < other.used_bigits_; ++i) { | 
237  | 0  |     DOUBLE_CONVERSION_ASSERT((borrow == 0) || (borrow == 1));  | 
238  | 0  |     const Chunk difference = RawBigit(i + offset) - other.RawBigit(i) - borrow;  | 
239  | 0  |     RawBigit(i + offset) = difference & kBigitMask;  | 
240  | 0  |     borrow = difference >> (kChunkSize - 1);  | 
241  | 0  |   }  | 
242  | 0  |   while (borrow != 0) { | 
243  | 0  |     const Chunk difference = RawBigit(i + offset) - borrow;  | 
244  | 0  |     RawBigit(i + offset) = difference & kBigitMask;  | 
245  | 0  |     borrow = difference >> (kChunkSize - 1);  | 
246  | 0  |     ++i;  | 
247  | 0  |   }  | 
248  | 0  |   Clamp();  | 
249  | 0  | }  | 
250  |  |  | 
251  |  |  | 
252  | 0  | void Bignum::ShiftLeft(const int shift_amount) { | 
253  | 0  |   if (used_bigits_ == 0) { | 
254  | 0  |     return;  | 
255  | 0  |   }  | 
256  | 0  |   exponent_ += (shift_amount / kBigitSize);  | 
257  | 0  |   const int local_shift = shift_amount % kBigitSize;  | 
258  | 0  |   EnsureCapacity(used_bigits_ + 1);  | 
259  | 0  |   BigitsShiftLeft(local_shift);  | 
260  | 0  | }  | 
261  |  |  | 
262  |  |  | 
263  | 0  | void Bignum::MultiplyByUInt32(const uint32_t factor) { | 
264  | 0  |   if (factor == 1) { | 
265  | 0  |     return;  | 
266  | 0  |   }  | 
267  | 0  |   if (factor == 0) { | 
268  | 0  |     Zero();  | 
269  | 0  |     return;  | 
270  | 0  |   }  | 
271  | 0  |   if (used_bigits_ == 0) { | 
272  | 0  |     return;  | 
273  | 0  |   }  | 
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  | 0  |   DOUBLE_CONVERSION_ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);  | 
277  | 0  |   DoubleChunk carry = 0;  | 
278  | 0  |   for (int i = 0; i < used_bigits_; ++i) { | 
279  | 0  |     const DoubleChunk product = static_cast<DoubleChunk>(factor) * RawBigit(i) + carry;  | 
280  | 0  |     RawBigit(i) = static_cast<Chunk>(product & kBigitMask);  | 
281  | 0  |     carry = (product >> kBigitSize);  | 
282  | 0  |   }  | 
283  | 0  |   while (carry != 0) { | 
284  | 0  |     EnsureCapacity(used_bigits_ + 1);  | 
285  | 0  |     RawBigit(used_bigits_) = carry & kBigitMask;  | 
286  | 0  |     used_bigits_++;  | 
287  | 0  |     carry >>= kBigitSize;  | 
288  | 0  |   }  | 
289  | 0  | }  | 
290  |  |  | 
291  |  |  | 
292  | 0  | void Bignum::MultiplyByUInt64(const uint64_t factor) { | 
293  | 0  |   if (factor == 1) { | 
294  | 0  |     return;  | 
295  | 0  |   }  | 
296  | 0  |   if (factor == 0) { | 
297  | 0  |     Zero();  | 
298  | 0  |     return;  | 
299  | 0  |   }  | 
300  | 0  |   if (used_bigits_ == 0) { | 
301  | 0  |     return;  | 
302  | 0  |   }  | 
303  | 0  |   DOUBLE_CONVERSION_ASSERT(kBigitSize < 32);  | 
304  | 0  |   uint64_t carry = 0;  | 
305  | 0  |   const uint64_t low = factor & 0xFFFFFFFF;  | 
306  | 0  |   const uint64_t high = factor >> 32;  | 
307  | 0  |   for (int i = 0; i < used_bigits_; ++i) { | 
308  | 0  |     const uint64_t product_low = low * RawBigit(i);  | 
309  | 0  |     const uint64_t product_high = high * RawBigit(i);  | 
310  | 0  |     const uint64_t tmp = (carry & kBigitMask) + product_low;  | 
311  | 0  |     RawBigit(i) = tmp & kBigitMask;  | 
312  | 0  |     carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +  | 
313  | 0  |         (product_high << (32 - kBigitSize));  | 
314  | 0  |   }  | 
315  | 0  |   while (carry != 0) { | 
316  | 0  |     EnsureCapacity(used_bigits_ + 1);  | 
317  | 0  |     RawBigit(used_bigits_) = carry & kBigitMask;  | 
318  | 0  |     used_bigits_++;  | 
319  | 0  |     carry >>= kBigitSize;  | 
320  | 0  |   }  | 
321  | 0  | }  | 
322  |  |  | 
323  |  |  | 
324  | 0  | void Bignum::MultiplyByPowerOfTen(const int exponent) { | 
325  | 0  |   static const uint64_t kFive27 = DOUBLE_CONVERSION_UINT64_2PART_C(0x6765c793, fa10079d);  | 
326  | 0  |   static const uint16_t kFive1 = 5;  | 
327  | 0  |   static const uint16_t kFive2 = kFive1 * 5;  | 
328  | 0  |   static const uint16_t kFive3 = kFive2 * 5;  | 
329  | 0  |   static const uint16_t kFive4 = kFive3 * 5;  | 
330  | 0  |   static const uint16_t kFive5 = kFive4 * 5;  | 
331  | 0  |   static const uint16_t kFive6 = kFive5 * 5;  | 
332  | 0  |   static const uint32_t kFive7 = kFive6 * 5;  | 
333  | 0  |   static const uint32_t kFive8 = kFive7 * 5;  | 
334  | 0  |   static const uint32_t kFive9 = kFive8 * 5;  | 
335  | 0  |   static const uint32_t kFive10 = kFive9 * 5;  | 
336  | 0  |   static const uint32_t kFive11 = kFive10 * 5;  | 
337  | 0  |   static const uint32_t kFive12 = kFive11 * 5;  | 
338  | 0  |   static const uint32_t kFive13 = kFive12 * 5;  | 
339  | 0  |   static const uint32_t kFive1_to_12[] =  | 
340  | 0  |       { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, | 
341  | 0  |         kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };  | 
342  |  | 
  | 
343  | 0  |   DOUBLE_CONVERSION_ASSERT(exponent >= 0);  | 
344  |  | 
  | 
345  | 0  |   if (exponent == 0) { | 
346  | 0  |     return;  | 
347  | 0  |   }  | 
348  | 0  |   if (used_bigits_ == 0) { | 
349  | 0  |     return;  | 
350  | 0  |   }  | 
351  |  |   // We shift by exponent at the end just before returning.  | 
352  | 0  |   int remaining_exponent = exponent;  | 
353  | 0  |   while (remaining_exponent >= 27) { | 
354  | 0  |     MultiplyByUInt64(kFive27);  | 
355  | 0  |     remaining_exponent -= 27;  | 
356  | 0  |   }  | 
357  | 0  |   while (remaining_exponent >= 13) { | 
358  | 0  |     MultiplyByUInt32(kFive13);  | 
359  | 0  |     remaining_exponent -= 13;  | 
360  | 0  |   }  | 
361  | 0  |   if (remaining_exponent > 0) { | 
362  | 0  |     MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);  | 
363  | 0  |   }  | 
364  | 0  |   ShiftLeft(exponent);  | 
365  | 0  | }  | 
366  |  |  | 
367  |  |  | 
368  | 0  | void Bignum::Square() { | 
369  | 0  |   DOUBLE_CONVERSION_ASSERT(IsClamped());  | 
370  | 0  |   const int product_length = 2 * used_bigits_;  | 
371  | 0  |   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  | 0  |   if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_bigits_) { | 
386  | 0  |     DOUBLE_CONVERSION_UNIMPLEMENTED();  | 
387  | 0  |   }  | 
388  | 0  |   DoubleChunk accumulator = 0;  | 
389  |  |   // First shift the digits so we don't overwrite them.  | 
390  | 0  |   const int copy_offset = used_bigits_;  | 
391  | 0  |   for (int i = 0; i < used_bigits_; ++i) { | 
392  | 0  |     RawBigit(copy_offset + i) = RawBigit(i);  | 
393  | 0  |   }  | 
394  |  |   // We have two loops to avoid some 'if's in the loop.  | 
395  | 0  |   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  | 0  |     int bigit_index1 = i;  | 
399  | 0  |     int bigit_index2 = 0;  | 
400  |  |     // Sum all of the sub-products.  | 
401  | 0  |     while (bigit_index1 >= 0) { | 
402  | 0  |       const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);  | 
403  | 0  |       const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);  | 
404  | 0  |       accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;  | 
405  | 0  |       bigit_index1--;  | 
406  | 0  |       bigit_index2++;  | 
407  | 0  |     }  | 
408  | 0  |     RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;  | 
409  | 0  |     accumulator >>= kBigitSize;  | 
410  | 0  |   }  | 
411  | 0  |   for (int i = used_bigits_; i < product_length; ++i) { | 
412  | 0  |     int bigit_index1 = used_bigits_ - 1;  | 
413  | 0  |     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  | 0  |     while (bigit_index2 < used_bigits_) { | 
417  | 0  |       const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);  | 
418  | 0  |       const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);  | 
419  | 0  |       accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;  | 
420  | 0  |       bigit_index1--;  | 
421  | 0  |       bigit_index2++;  | 
422  | 0  |     }  | 
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  | 0  |     RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;  | 
427  | 0  |     accumulator >>= kBigitSize;  | 
428  | 0  |   }  | 
429  |  |   // Since the result was guaranteed to lie inside the number the  | 
430  |  |   // accumulator must be 0 now.  | 
431  | 0  |   DOUBLE_CONVERSION_ASSERT(accumulator == 0);  | 
432  |  |  | 
433  |  |   // Don't forget to update the used_digits and the exponent.  | 
434  | 0  |   used_bigits_ = product_length;  | 
435  | 0  |   exponent_ *= 2;  | 
436  | 0  |   Clamp();  | 
437  | 0  | }  | 
438  |  |  | 
439  |  |  | 
440  | 0  | void Bignum::AssignPowerUInt16(uint16_t base, const int power_exponent) { | 
441  | 0  |   DOUBLE_CONVERSION_ASSERT(base != 0);  | 
442  | 0  |   DOUBLE_CONVERSION_ASSERT(power_exponent >= 0);  | 
443  | 0  |   if (power_exponent == 0) { | 
444  | 0  |     AssignUInt16(1);  | 
445  | 0  |     return;  | 
446  | 0  |   }  | 
447  | 0  |   Zero();  | 
448  | 0  |   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  | 0  |   while ((base & 1) == 0) { | 
453  | 0  |     base >>= 1;  | 
454  | 0  |     shifts++;  | 
455  | 0  |   }  | 
456  | 0  |   int bit_size = 0;  | 
457  | 0  |   int tmp_base = base;  | 
458  | 0  |   while (tmp_base != 0) { | 
459  | 0  |     tmp_base >>= 1;  | 
460  | 0  |     bit_size++;  | 
461  | 0  |   }  | 
462  | 0  |   const int final_size = bit_size * power_exponent;  | 
463  |  |   // 1 extra bigit for the shifting, and one for rounded final_size.  | 
464  | 0  |   EnsureCapacity(final_size / kBigitSize + 2);  | 
465  |  |  | 
466  |  |   // Left to Right exponentiation.  | 
467  | 0  |   int mask = 1;  | 
468  | 0  |   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  | 0  |   mask >>= 2;  | 
474  | 0  |   uint64_t this_value = base;  | 
475  |  | 
  | 
476  | 0  |   bool delayed_multiplication = false;  | 
477  | 0  |   const uint64_t max_32bits = 0xFFFFFFFF;  | 
478  | 0  |   while (mask != 0 && this_value <= max_32bits) { | 
479  | 0  |     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  | 0  |     if ((power_exponent & mask) != 0) { | 
483  | 0  |       DOUBLE_CONVERSION_ASSERT(bit_size > 0);  | 
484  | 0  |       const uint64_t base_bits_mask =  | 
485  | 0  |         ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);  | 
486  | 0  |       const bool high_bits_zero = (this_value & base_bits_mask) == 0;  | 
487  | 0  |       if (high_bits_zero) { | 
488  | 0  |         this_value *= base;  | 
489  | 0  |       } else { | 
490  | 0  |         delayed_multiplication = true;  | 
491  | 0  |       }  | 
492  | 0  |     }  | 
493  | 0  |     mask >>= 1;  | 
494  | 0  |   }  | 
495  | 0  |   AssignUInt64(this_value);  | 
496  | 0  |   if (delayed_multiplication) { | 
497  | 0  |     MultiplyByUInt32(base);  | 
498  | 0  |   }  | 
499  |  |  | 
500  |  |   // Now do the same thing as a bignum.  | 
501  | 0  |   while (mask != 0) { | 
502  | 0  |     Square();  | 
503  | 0  |     if ((power_exponent & mask) != 0) { | 
504  | 0  |       MultiplyByUInt32(base);  | 
505  | 0  |     }  | 
506  | 0  |     mask >>= 1;  | 
507  | 0  |   }  | 
508  |  |  | 
509  |  |   // And finally add the saved shifts.  | 
510  | 0  |   ShiftLeft(shifts * power_exponent);  | 
511  | 0  | }  | 
512  |  |  | 
513  |  |  | 
514  |  | // Precondition: this/other < 16bit.  | 
515  | 0  | uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { | 
516  | 0  |   DOUBLE_CONVERSION_ASSERT(IsClamped());  | 
517  | 0  |   DOUBLE_CONVERSION_ASSERT(other.IsClamped());  | 
518  | 0  |   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  | 0  |   if (BigitLength() < other.BigitLength()) { | 
523  | 0  |     return 0;  | 
524  | 0  |   }  | 
525  |  |  | 
526  | 0  |   Align(other);  | 
527  |  | 
  | 
528  | 0  |   uint16_t result = 0;  | 
529  |  |  | 
530  |  |   // Start by removing multiples of 'other' until both numbers have the same  | 
531  |  |   // number of digits.  | 
532  | 0  |   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  | 0  |     DOUBLE_CONVERSION_ASSERT(other.RawBigit(other.used_bigits_ - 1) >= ((1 << kBigitSize) / 16));  | 
537  | 0  |     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  | 0  |     result += static_cast<uint16_t>(RawBigit(used_bigits_ - 1));  | 
541  | 0  |     SubtractTimes(other, RawBigit(used_bigits_ - 1));  | 
542  | 0  |   }  | 
543  |  | 
  | 
544  | 0  |   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  | 0  |   const Chunk this_bigit = RawBigit(used_bigits_ - 1);  | 
550  | 0  |   const Chunk other_bigit = other.RawBigit(other.used_bigits_ - 1);  | 
551  |  | 
  | 
552  | 0  |   if (other.used_bigits_ == 1) { | 
553  |  |     // Shortcut for easy (and common) case.  | 
554  | 0  |     int quotient = this_bigit / other_bigit;  | 
555  | 0  |     RawBigit(used_bigits_ - 1) = this_bigit - other_bigit * quotient;  | 
556  | 0  |     DOUBLE_CONVERSION_ASSERT(quotient < 0x10000);  | 
557  | 0  |     result += static_cast<uint16_t>(quotient);  | 
558  | 0  |     Clamp();  | 
559  | 0  |     return result;  | 
560  | 0  |   }  | 
561  |  |  | 
562  | 0  |   const int division_estimate = this_bigit / (other_bigit + 1);  | 
563  | 0  |   DOUBLE_CONVERSION_ASSERT(division_estimate < 0x10000);  | 
564  | 0  |   result += static_cast<uint16_t>(division_estimate);  | 
565  | 0  |   SubtractTimes(other, division_estimate);  | 
566  |  | 
  | 
567  | 0  |   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  | 0  |     return result;  | 
571  | 0  |   }  | 
572  |  |  | 
573  | 0  |   while (LessEqual(other, *this)) { | 
574  | 0  |     SubtractBignum(other);  | 
575  | 0  |     result++;  | 
576  | 0  |   }  | 
577  | 0  |   return result;  | 
578  | 0  | }  | 
579  |  |  | 
580  |  |  | 
581  |  | template<typename S>  | 
582  | 0  | static int SizeInHexChars(S number) { | 
583  | 0  |   DOUBLE_CONVERSION_ASSERT(number > 0);  | 
584  | 0  |   int result = 0;  | 
585  | 0  |   while (number != 0) { | 
586  | 0  |     number >>= 4;  | 
587  | 0  |     result++;  | 
588  | 0  |   }  | 
589  | 0  |   return result;  | 
590  | 0  | }  | 
591  |  |  | 
592  |  |  | 
593  | 0  | static char HexCharOfValue(const int value) { | 
594  | 0  |   DOUBLE_CONVERSION_ASSERT(0 <= value && value <= 16);  | 
595  | 0  |   if (value < 10) { | 
596  | 0  |     return static_cast<char>(value + '0');  | 
597  | 0  |   }  | 
598  | 0  |   return static_cast<char>(value - 10 + 'A');  | 
599  | 0  | }  | 
600  |  |  | 
601  |  |  | 
602  | 0  | bool Bignum::ToHexString(char* buffer, const int buffer_size) const { | 
603  | 0  |   DOUBLE_CONVERSION_ASSERT(IsClamped());  | 
604  |  |   // Each bigit must be printable as separate hex-character.  | 
605  | 0  |   DOUBLE_CONVERSION_ASSERT(kBigitSize % 4 == 0);  | 
606  | 0  |   static const int kHexCharsPerBigit = kBigitSize / 4;  | 
607  |  | 
  | 
608  | 0  |   if (used_bigits_ == 0) { | 
609  | 0  |     if (buffer_size < 2) { | 
610  | 0  |       return false;  | 
611  | 0  |     }  | 
612  | 0  |     buffer[0] = '0';  | 
613  | 0  |     buffer[1] = '\0';  | 
614  | 0  |     return true;  | 
615  | 0  |   }  | 
616  |  |   // We add 1 for the terminating '\0' character.  | 
617  | 0  |   const int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +  | 
618  | 0  |     SizeInHexChars(RawBigit(used_bigits_ - 1)) + 1;  | 
619  | 0  |   if (needed_chars > buffer_size) { | 
620  | 0  |     return false;  | 
621  | 0  |   }  | 
622  | 0  |   int string_index = needed_chars - 1;  | 
623  | 0  |   buffer[string_index--] = '\0';  | 
624  | 0  |   for (int i = 0; i < exponent_; ++i) { | 
625  | 0  |     for (int j = 0; j < kHexCharsPerBigit; ++j) { | 
626  | 0  |       buffer[string_index--] = '0';  | 
627  | 0  |     }  | 
628  | 0  |   }  | 
629  | 0  |   for (int i = 0; i < used_bigits_ - 1; ++i) { | 
630  | 0  |     Chunk current_bigit = RawBigit(i);  | 
631  | 0  |     for (int j = 0; j < kHexCharsPerBigit; ++j) { | 
632  | 0  |       buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);  | 
633  | 0  |       current_bigit >>= 4;  | 
634  | 0  |     }  | 
635  | 0  |   }  | 
636  |  |   // And finally the last bigit.  | 
637  | 0  |   Chunk most_significant_bigit = RawBigit(used_bigits_ - 1);  | 
638  | 0  |   while (most_significant_bigit != 0) { | 
639  | 0  |     buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);  | 
640  | 0  |     most_significant_bigit >>= 4;  | 
641  | 0  |   }  | 
642  | 0  |   return true;  | 
643  | 0  | }  | 
644  |  |  | 
645  |  |  | 
646  | 0  | Bignum::Chunk Bignum::BigitOrZero(const int index) const { | 
647  | 0  |   if (index >= BigitLength()) { | 
648  | 0  |     return 0;  | 
649  | 0  |   }  | 
650  | 0  |   if (index < exponent_) { | 
651  | 0  |     return 0;  | 
652  | 0  |   }  | 
653  | 0  |   return RawBigit(index - exponent_);  | 
654  | 0  | }  | 
655  |  |  | 
656  |  |  | 
657  | 0  | int Bignum::Compare(const Bignum& a, const Bignum& b) { | 
658  | 0  |   DOUBLE_CONVERSION_ASSERT(a.IsClamped());  | 
659  | 0  |   DOUBLE_CONVERSION_ASSERT(b.IsClamped());  | 
660  | 0  |   const int bigit_length_a = a.BigitLength();  | 
661  | 0  |   const int bigit_length_b = b.BigitLength();  | 
662  | 0  |   if (bigit_length_a < bigit_length_b) { | 
663  | 0  |     return -1;  | 
664  | 0  |   }  | 
665  | 0  |   if (bigit_length_a > bigit_length_b) { | 
666  | 0  |     return +1;  | 
667  | 0  |   }  | 
668  | 0  |   for (int i = bigit_length_a - 1; i >= (std::min)(a.exponent_, b.exponent_); --i) { | 
669  | 0  |     const Chunk bigit_a = a.BigitOrZero(i);  | 
670  | 0  |     const Chunk bigit_b = b.BigitOrZero(i);  | 
671  | 0  |     if (bigit_a < bigit_b) { | 
672  | 0  |       return -1;  | 
673  | 0  |     }  | 
674  | 0  |     if (bigit_a > bigit_b) { | 
675  | 0  |       return +1;  | 
676  | 0  |     }  | 
677  |  |     // Otherwise they are equal up to this digit. Try the next digit.  | 
678  | 0  |   }  | 
679  | 0  |   return 0;  | 
680  | 0  | }  | 
681  |  |  | 
682  |  |  | 
683  | 0  | int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { | 
684  | 0  |   DOUBLE_CONVERSION_ASSERT(a.IsClamped());  | 
685  | 0  |   DOUBLE_CONVERSION_ASSERT(b.IsClamped());  | 
686  | 0  |   DOUBLE_CONVERSION_ASSERT(c.IsClamped());  | 
687  | 0  |   if (a.BigitLength() < b.BigitLength()) { | 
688  | 0  |     return PlusCompare(b, a, c);  | 
689  | 0  |   }  | 
690  | 0  |   if (a.BigitLength() + 1 < c.BigitLength()) { | 
691  | 0  |     return -1;  | 
692  | 0  |   }  | 
693  | 0  |   if (a.BigitLength() > c.BigitLength()) { | 
694  | 0  |     return +1;  | 
695  | 0  |   }  | 
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  | 0  |   if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { | 
700  | 0  |     return -1;  | 
701  | 0  |   }  | 
702  |  |  | 
703  | 0  |   Chunk borrow = 0;  | 
704  |  |   // Starting at min_exponent all digits are == 0. So no need to compare them.  | 
705  | 0  |   const int min_exponent = (std::min)((std::min)(a.exponent_, b.exponent_), c.exponent_);  | 
706  | 0  |   for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { | 
707  | 0  |     const Chunk chunk_a = a.BigitOrZero(i);  | 
708  | 0  |     const Chunk chunk_b = b.BigitOrZero(i);  | 
709  | 0  |     const Chunk chunk_c = c.BigitOrZero(i);  | 
710  | 0  |     const Chunk sum = chunk_a + chunk_b;  | 
711  | 0  |     if (sum > chunk_c + borrow) { | 
712  | 0  |       return +1;  | 
713  | 0  |     } else { | 
714  | 0  |       borrow = chunk_c + borrow - sum;  | 
715  | 0  |       if (borrow > 1) { | 
716  | 0  |         return -1;  | 
717  | 0  |       }  | 
718  | 0  |       borrow <<= kBigitSize;  | 
719  | 0  |     }  | 
720  | 0  |   }  | 
721  | 0  |   if (borrow == 0) { | 
722  | 0  |     return 0;  | 
723  | 0  |   }  | 
724  | 0  |   return -1;  | 
725  | 0  | }  | 
726  |  |  | 
727  |  |  | 
728  | 0  | void Bignum::Clamp() { | 
729  | 0  |   while (used_bigits_ > 0 && RawBigit(used_bigits_ - 1) == 0) { | 
730  | 0  |     used_bigits_--;  | 
731  | 0  |   }  | 
732  | 0  |   if (used_bigits_ == 0) { | 
733  |  |     // Zero.  | 
734  | 0  |     exponent_ = 0;  | 
735  | 0  |   }  | 
736  | 0  | }  | 
737  |  |  | 
738  |  |  | 
739  | 0  | void Bignum::Align(const Bignum& other) { | 
740  | 0  |   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  | 0  |     const int zero_bigits = exponent_ - other.exponent_;  | 
748  | 0  |     EnsureCapacity(used_bigits_ + zero_bigits);  | 
749  | 0  |     for (int i = used_bigits_ - 1; i >= 0; --i) { | 
750  | 0  |       RawBigit(i + zero_bigits) = RawBigit(i);  | 
751  | 0  |     }  | 
752  | 0  |     for (int i = 0; i < zero_bigits; ++i) { | 
753  | 0  |       RawBigit(i) = 0;  | 
754  | 0  |     }  | 
755  | 0  |     used_bigits_ += zero_bigits;  | 
756  | 0  |     exponent_ -= zero_bigits;  | 
757  |  | 
  | 
758  | 0  |     DOUBLE_CONVERSION_ASSERT(used_bigits_ >= 0);  | 
759  | 0  |     DOUBLE_CONVERSION_ASSERT(exponent_ >= 0);  | 
760  | 0  |   }  | 
761  | 0  | }  | 
762  |  |  | 
763  |  |  | 
764  | 0  | void Bignum::BigitsShiftLeft(const int shift_amount) { | 
765  | 0  |   DOUBLE_CONVERSION_ASSERT(shift_amount < kBigitSize);  | 
766  | 0  |   DOUBLE_CONVERSION_ASSERT(shift_amount >= 0);  | 
767  | 0  |   Chunk carry = 0;  | 
768  | 0  |   for (int i = 0; i < used_bigits_; ++i) { | 
769  | 0  |     const Chunk new_carry = RawBigit(i) >> (kBigitSize - shift_amount);  | 
770  | 0  |     RawBigit(i) = ((RawBigit(i) << shift_amount) + carry) & kBigitMask;  | 
771  | 0  |     carry = new_carry;  | 
772  | 0  |   }  | 
773  | 0  |   if (carry != 0) { | 
774  | 0  |     RawBigit(used_bigits_) = carry;  | 
775  | 0  |     used_bigits_++;  | 
776  | 0  |   }  | 
777  | 0  | }  | 
778  |  |  | 
779  |  |  | 
780  | 0  | void Bignum::SubtractTimes(const Bignum& other, const int factor) { | 
781  | 0  |   DOUBLE_CONVERSION_ASSERT(exponent_ <= other.exponent_);  | 
782  | 0  |   if (factor < 3) { | 
783  | 0  |     for (int i = 0; i < factor; ++i) { | 
784  | 0  |       SubtractBignum(other);  | 
785  | 0  |     }  | 
786  | 0  |     return;  | 
787  | 0  |   }  | 
788  | 0  |   Chunk borrow = 0;  | 
789  | 0  |   const int exponent_diff = other.exponent_ - exponent_;  | 
790  | 0  |   for (int i = 0; i < other.used_bigits_; ++i) { | 
791  | 0  |     const DoubleChunk product = static_cast<DoubleChunk>(factor) * other.RawBigit(i);  | 
792  | 0  |     const DoubleChunk remove = borrow + product;  | 
793  | 0  |     const Chunk difference = RawBigit(i + exponent_diff) - (remove & kBigitMask);  | 
794  | 0  |     RawBigit(i + exponent_diff) = difference & kBigitMask;  | 
795  | 0  |     borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +  | 
796  | 0  |                                 (remove >> kBigitSize));  | 
797  | 0  |   }  | 
798  | 0  |   for (int i = other.used_bigits_ + exponent_diff; i < used_bigits_; ++i) { | 
799  | 0  |     if (borrow == 0) { | 
800  | 0  |       return;  | 
801  | 0  |     }  | 
802  | 0  |     const Chunk difference = RawBigit(i) - borrow;  | 
803  | 0  |     RawBigit(i) = difference & kBigitMask;  | 
804  | 0  |     borrow = difference >> (kChunkSize - 1);  | 
805  | 0  |   }  | 
806  | 0  |   Clamp();  | 
807  | 0  | }  | 
808  |  |  | 
809  |  |  | 
810  |  | }  // namespace double_conversion  | 
811  |  |  | 
812  |  | // ICU PATCH: Close ICU namespace  | 
813  |  | U_NAMESPACE_END  | 
814  |  | #endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING  |