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1 // Copyright 2010 the V8 project authors. All rights reserved. | 1 // Copyright 2010 the V8 project authors. All rights reserved. |
2 // Redistribution and use in source and binary forms, with or without | 2 // Redistribution and use in source and binary forms, with or without |
3 // modification, are permitted provided that the following conditions are | 3 // modification, are permitted provided that the following conditions are |
4 // met: | 4 // met: |
5 // | 5 // |
6 // * Redistributions of source code must retain the above copyright | 6 // * Redistributions of source code must retain the above copyright |
7 // notice, this list of conditions and the following disclaimer. | 7 // notice, this list of conditions and the following disclaimer. |
8 // * Redistributions in binary form must reproduce the above | 8 // * Redistributions in binary form must reproduce the above |
9 // copyright notice, this list of conditions and the following | 9 // copyright notice, this list of conditions and the following |
10 // disclaimer in the documentation and/or other materials provided | 10 // disclaimer in the documentation and/or other materials provided |
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26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | 26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
27 | 27 |
28 #include "bignum.h" | 28 #include "bignum.h" |
29 | 29 |
30 #include "utils.h" | 30 #include "utils.h" |
31 | 31 |
32 namespace WTF { | 32 namespace WTF { |
33 | 33 |
34 namespace double_conversion { | 34 namespace double_conversion { |
35 | 35 |
36 Bignum::Bignum() | 36 Bignum::Bignum() |
37 : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) { | 37 : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) { |
38 for (int i = 0; i < kBigitCapacity; ++i) { | 38 for (int i = 0; i < kBigitCapacity; ++i) { |
39 bigits_[i] = 0; | 39 bigits_[i] = 0; |
40 } | 40 } |
41 } | 41 } |
42 | 42 |
43 | 43 template <typename S> |
44 template<typename S> | 44 static int BitSize(S value) { |
45 static int BitSize(S value) { | 45 return 8 * sizeof(value); |
46 return 8 * sizeof(value); | 46 } |
47 } | 47 |
48 | 48 // Guaranteed to lie in one Bigit. |
49 // Guaranteed to lie in one Bigit. | 49 void Bignum::AssignUInt16(uint16_t value) { |
50 void Bignum::AssignUInt16(uint16_t value) { | 50 ASSERT(kBigitSize >= BitSize(value)); |
51 ASSERT(kBigitSize >= BitSize(value)); | 51 Zero(); |
52 Zero(); | 52 if (value == 0) |
53 if (value == 0) return; | 53 return; |
54 | 54 |
55 EnsureCapacity(1); | 55 EnsureCapacity(1); |
56 bigits_[0] = value; | 56 bigits_[0] = value; |
57 used_digits_ = 1; | 57 used_digits_ = 1; |
58 } | 58 } |
59 | 59 |
60 | 60 void Bignum::AssignUInt64(uint64_t value) { |
61 void Bignum::AssignUInt64(uint64_t value) { | 61 const int kUInt64Size = 64; |
62 const int kUInt64Size = 64; | 62 |
63 | 63 Zero(); |
64 Zero(); | 64 if (value == 0) |
65 if (value == 0) return; | 65 return; |
66 | 66 |
67 int needed_bigits = kUInt64Size / kBigitSize + 1; | 67 int needed_bigits = kUInt64Size / kBigitSize + 1; |
68 EnsureCapacity(needed_bigits); | 68 EnsureCapacity(needed_bigits); |
69 for (int i = 0; i < needed_bigits; ++i) { | 69 for (int i = 0; i < needed_bigits; ++i) { |
70 bigits_[i] = (uint32_t)value & kBigitMask; | 70 bigits_[i] = (uint32_t)value & kBigitMask; |
71 value = value >> kBigitSize; | 71 value = value >> kBigitSize; |
72 } | 72 } |
73 used_digits_ = needed_bigits; | 73 used_digits_ = needed_bigits; |
74 Clamp(); | 74 Clamp(); |
75 } | 75 } |
76 | 76 |
77 | 77 void Bignum::AssignBignum(const Bignum& other) { |
78 void Bignum::AssignBignum(const Bignum& other) { | 78 exponent_ = other.exponent_; |
79 exponent_ = other.exponent_; | 79 for (int i = 0; i < other.used_digits_; ++i) { |
80 for (int i = 0; i < other.used_digits_; ++i) { | 80 bigits_[i] = other.bigits_[i]; |
81 bigits_[i] = other.bigits_[i]; | 81 } |
82 } | 82 // Clear the excess digits (if there were any). |
83 // Clear the excess digits (if there were any). | 83 for (int i = other.used_digits_; i < used_digits_; ++i) { |
84 for (int i = other.used_digits_; i < used_digits_; ++i) { | 84 bigits_[i] = 0; |
85 bigits_[i] = 0; | 85 } |
86 } | 86 used_digits_ = other.used_digits_; |
87 used_digits_ = other.used_digits_; | 87 } |
88 } | 88 |
89 | 89 static uint64_t ReadUInt64(Vector<const char> buffer, |
90 | 90 int from, |
91 static uint64_t ReadUInt64(Vector<const char> buffer, | 91 int digits_to_read) { |
92 int from, | 92 uint64_t result = 0; |
93 int digits_to_read) { | 93 for (int i = from; i < from + digits_to_read; ++i) { |
94 uint64_t result = 0; | 94 int digit = buffer[i] - '0'; |
95 for (int i = from; i < from + digits_to_read; ++i) { | 95 ASSERT(0 <= digit && digit <= 9); |
96 int digit = buffer[i] - '0'; | 96 result = result * 10 + digit; |
97 ASSERT(0 <= digit && digit <= 9); | 97 } |
98 result = result * 10 + digit; | 98 return result; |
99 } | 99 } |
100 return result; | 100 |
101 } | 101 void Bignum::AssignDecimalString(Vector<const char> value) { |
102 | 102 // 2^64 = 18446744073709551616 > 10^19 |
103 | 103 const int kMaxUint64DecimalDigits = 19; |
104 void Bignum::AssignDecimalString(Vector<const char> value) { | 104 Zero(); |
105 // 2^64 = 18446744073709551616 > 10^19 | 105 int length = value.length(); |
106 const int kMaxUint64DecimalDigits = 19; | 106 int pos = 0; |
107 Zero(); | 107 // Let's just say that each digit needs 4 bits. |
108 int length = value.length(); | 108 while (length >= kMaxUint64DecimalDigits) { |
109 int pos = 0; | 109 uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); |
110 // Let's just say that each digit needs 4 bits. | 110 pos += kMaxUint64DecimalDigits; |
111 while (length >= kMaxUint64DecimalDigits) { | 111 length -= kMaxUint64DecimalDigits; |
112 uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); | 112 MultiplyByPowerOfTen(kMaxUint64DecimalDigits); |
113 pos += kMaxUint64DecimalDigits; | 113 AddUInt64(digits); |
114 length -= kMaxUint64DecimalDigits; | 114 } |
115 MultiplyByPowerOfTen(kMaxUint64DecimalDigits); | 115 uint64_t digits = ReadUInt64(value, pos, length); |
116 AddUInt64(digits); | 116 MultiplyByPowerOfTen(length); |
117 } | 117 AddUInt64(digits); |
118 uint64_t digits = ReadUInt64(value, pos, length); | 118 Clamp(); |
119 MultiplyByPowerOfTen(length); | 119 } |
120 AddUInt64(digits); | 120 |
121 Clamp(); | 121 static int HexCharValue(char c) { |
122 } | 122 if ('0' <= c && c <= '9') |
123 | 123 return c - '0'; |
124 | 124 if ('a' <= c && c <= 'f') |
125 static int HexCharValue(char c) { | 125 return 10 + c - 'a'; |
126 if ('0' <= c && c <= '9') return c - '0'; | 126 if ('A' <= c && c <= 'F') |
127 if ('a' <= c && c <= 'f') return 10 + c - 'a'; | 127 return 10 + c - 'A'; |
128 if ('A' <= c && c <= 'F') return 10 + c - 'A'; | 128 UNREACHABLE(); |
129 UNREACHABLE(); | 129 return 0; // To make compiler happy. |
130 return 0; // To make compiler happy. | 130 } |
131 } | 131 |
132 | 132 void Bignum::AssignHexString(Vector<const char> value) { |
133 | 133 Zero(); |
134 void Bignum::AssignHexString(Vector<const char> value) { | 134 int length = value.length(); |
135 Zero(); | 135 |
136 int length = value.length(); | 136 int needed_bigits = length * 4 / kBigitSize + 1; |
137 | 137 EnsureCapacity(needed_bigits); |
138 int needed_bigits = length * 4 / kBigitSize + 1; | 138 int string_index = length - 1; |
139 EnsureCapacity(needed_bigits); | 139 for (int i = 0; i < needed_bigits - 1; ++i) { |
140 int string_index = length - 1; | 140 // These bigits are guaranteed to be "full". |
141 for (int i = 0; i < needed_bigits - 1; ++i) { | 141 Chunk current_bigit = 0; |
142 // These bigits are guaranteed to be "full". | 142 for (int j = 0; j < kBigitSize / 4; j++) { |
143 Chunk current_bigit = 0; | 143 current_bigit += HexCharValue(value[string_index--]) << (j * 4); |
144 for (int j = 0; j < kBigitSize / 4; j++) { | 144 } |
145 current_bigit += HexCharValue(value[string_index--]) << (j * 4); | 145 bigits_[i] = current_bigit; |
146 } | 146 } |
147 bigits_[i] = current_bigit; | 147 used_digits_ = needed_bigits - 1; |
148 } | 148 |
149 used_digits_ = needed_bigits - 1; | 149 Chunk most_significant_bigit = 0; // Could be = 0; |
150 | 150 for (int j = 0; j <= string_index; ++j) { |
151 Chunk most_significant_bigit = 0; // Could be = 0; | 151 most_significant_bigit <<= 4; |
152 for (int j = 0; j <= string_index; ++j) { | 152 most_significant_bigit += HexCharValue(value[j]); |
153 most_significant_bigit <<= 4; | 153 } |
154 most_significant_bigit += HexCharValue(value[j]); | 154 if (most_significant_bigit != 0) { |
155 } | 155 bigits_[used_digits_] = most_significant_bigit; |
156 if (most_significant_bigit != 0) { | 156 used_digits_++; |
157 bigits_[used_digits_] = most_significant_bigit; | 157 } |
158 used_digits_++; | 158 Clamp(); |
159 } | 159 } |
160 Clamp(); | 160 |
161 } | 161 void Bignum::AddUInt64(uint64_t operand) { |
162 | 162 if (operand == 0) |
163 | 163 return; |
164 void Bignum::AddUInt64(uint64_t operand) { | 164 Bignum other; |
165 if (operand == 0) return; | 165 other.AssignUInt64(operand); |
166 Bignum other; | 166 AddBignum(other); |
167 other.AssignUInt64(operand); | 167 } |
168 AddBignum(other); | 168 |
169 } | 169 void Bignum::AddBignum(const Bignum& other) { |
170 | 170 ASSERT(IsClamped()); |
171 | 171 ASSERT(other.IsClamped()); |
172 void Bignum::AddBignum(const Bignum& other) { | 172 |
173 ASSERT(IsClamped()); | 173 // If this has a greater exponent than other append zero-bigits to this. |
174 ASSERT(other.IsClamped()); | 174 // After this call exponent_ <= other.exponent_. |
175 | 175 Align(other); |
176 // If this has a greater exponent than other append zero-bigits to this. | 176 |
177 // After this call exponent_ <= other.exponent_. | 177 // There are two possibilities: |
178 Align(other); | 178 // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) |
179 | 179 // bbbbb 00000000 |
180 // There are two possibilities: | 180 // ---------------- |
181 // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) | 181 // ccccccccccc 0000 |
182 // bbbbb 00000000 | 182 // or |
183 // ---------------- | 183 // aaaaaaaaaa 0000 |
184 // ccccccccccc 0000 | 184 // bbbbbbbbb 0000000 |
185 // or | 185 // ----------------- |
186 // aaaaaaaaaa 0000 | 186 // cccccccccccc 0000 |
187 // bbbbbbbbb 0000000 | 187 // In both cases we might need a carry bigit. |
188 // ----------------- | 188 |
189 // cccccccccccc 0000 | 189 EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); |
190 // In both cases we might need a carry bigit. | 190 Chunk carry = 0; |
191 | 191 int bigit_pos = other.exponent_ - exponent_; |
192 EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); | 192 ASSERT(bigit_pos >= 0); |
193 Chunk carry = 0; | 193 for (int i = 0; i < other.used_digits_; ++i) { |
194 int bigit_pos = other.exponent_ - exponent_; | 194 Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; |
195 ASSERT(bigit_pos >= 0); | 195 bigits_[bigit_pos] = sum & kBigitMask; |
196 for (int i = 0; i < other.used_digits_; ++i) { | 196 carry = sum >> kBigitSize; |
197 Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; | 197 bigit_pos++; |
198 bigits_[bigit_pos] = sum & kBigitMask; | 198 } |
199 carry = sum >> kBigitSize; | 199 |
200 bigit_pos++; | 200 while (carry != 0) { |
201 } | 201 Chunk sum = bigits_[bigit_pos] + carry; |
202 | 202 bigits_[bigit_pos] = sum & kBigitMask; |
203 while (carry != 0) { | 203 carry = sum >> kBigitSize; |
204 Chunk sum = bigits_[bigit_pos] + carry; | 204 bigit_pos++; |
205 bigits_[bigit_pos] = sum & kBigitMask; | 205 } |
206 carry = sum >> kBigitSize; | 206 used_digits_ = Max(bigit_pos, used_digits_); |
207 bigit_pos++; | 207 ASSERT(IsClamped()); |
208 } | 208 } |
209 used_digits_ = Max(bigit_pos, used_digits_); | 209 |
210 ASSERT(IsClamped()); | 210 void Bignum::SubtractBignum(const Bignum& other) { |
211 } | 211 ASSERT(IsClamped()); |
212 | 212 ASSERT(other.IsClamped()); |
213 | 213 // We require this to be bigger than other. |
214 void Bignum::SubtractBignum(const Bignum& other) { | 214 ASSERT(LessEqual(other, *this)); |
215 ASSERT(IsClamped()); | 215 |
216 ASSERT(other.IsClamped()); | 216 Align(other); |
217 // We require this to be bigger than other. | 217 |
218 ASSERT(LessEqual(other, *this)); | 218 int offset = other.exponent_ - exponent_; |
219 | 219 Chunk borrow = 0; |
220 Align(other); | 220 int i; |
221 | 221 for (i = 0; i < other.used_digits_; ++i) { |
222 int offset = other.exponent_ - exponent_; | 222 ASSERT((borrow == 0) || (borrow == 1)); |
223 Chunk borrow = 0; | 223 Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; |
224 int i; | 224 bigits_[i + offset] = difference & kBigitMask; |
225 for (i = 0; i < other.used_digits_; ++i) { | 225 borrow = difference >> (kChunkSize - 1); |
226 ASSERT((borrow == 0) || (borrow == 1)); | 226 } |
227 Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; | 227 while (borrow != 0) { |
228 bigits_[i + offset] = difference & kBigitMask; | 228 Chunk difference = bigits_[i + offset] - borrow; |
229 borrow = difference >> (kChunkSize - 1); | 229 bigits_[i + offset] = difference & kBigitMask; |
230 } | 230 borrow = difference >> (kChunkSize - 1); |
231 while (borrow != 0) { | 231 ++i; |
232 Chunk difference = bigits_[i + offset] - borrow; | 232 } |
233 bigits_[i + offset] = difference & kBigitMask; | 233 Clamp(); |
234 borrow = difference >> (kChunkSize - 1); | 234 } |
235 ++i; | 235 |
236 } | 236 void Bignum::ShiftLeft(int shift_amount) { |
237 Clamp(); | 237 if (used_digits_ == 0) |
238 } | 238 return; |
239 | 239 exponent_ += shift_amount / kBigitSize; |
240 | 240 int local_shift = shift_amount % kBigitSize; |
241 void Bignum::ShiftLeft(int shift_amount) { | 241 EnsureCapacity(used_digits_ + 1); |
242 if (used_digits_ == 0) return; | 242 BigitsShiftLeft(local_shift); |
243 exponent_ += shift_amount / kBigitSize; | 243 } |
244 int local_shift = shift_amount % kBigitSize; | 244 |
245 EnsureCapacity(used_digits_ + 1); | 245 void Bignum::MultiplyByUInt32(uint32_t factor) { |
246 BigitsShiftLeft(local_shift); | 246 if (factor == 1) |
247 } | 247 return; |
248 | 248 if (factor == 0) { |
249 | 249 Zero(); |
250 void Bignum::MultiplyByUInt32(uint32_t factor) { | 250 return; |
251 if (factor == 1) return; | 251 } |
252 if (factor == 0) { | 252 if (used_digits_ == 0) |
253 Zero(); | 253 return; |
254 return; | 254 |
255 } | 255 // The product of a bigit with the factor is of size kBigitSize + 32. |
256 if (used_digits_ == 0) return; | 256 // Assert that this number + 1 (for the carry) fits into double chunk. |
257 | 257 ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); |
258 // The product of a bigit with the factor is of size kBigitSize + 32. | 258 DoubleChunk carry = 0; |
259 // Assert that this number + 1 (for the carry) fits into double chunk. | 259 for (int i = 0; i < used_digits_; ++i) { |
260 ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); | 260 DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry; |
261 DoubleChunk carry = 0; | 261 bigits_[i] = static_cast<Chunk>(product & kBigitMask); |
262 for (int i = 0; i < used_digits_; ++i) { | 262 carry = (product >> kBigitSize); |
263 DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i]
+ carry; | 263 } |
264 bigits_[i] = static_cast<Chunk>(product & kBigitMask); | 264 while (carry != 0) { |
265 carry = (product >> kBigitSize); | 265 EnsureCapacity(used_digits_ + 1); |
266 } | 266 bigits_[used_digits_] = (uint32_t)carry & kBigitMask; |
267 while (carry != 0) { | 267 used_digits_++; |
268 EnsureCapacity(used_digits_ + 1); | 268 carry >>= kBigitSize; |
269 bigits_[used_digits_] = (uint32_t)carry & kBigitMask; | 269 } |
270 used_digits_++; | 270 } |
271 carry >>= kBigitSize; | 271 |
272 } | 272 void Bignum::MultiplyByUInt64(uint64_t factor) { |
273 } | 273 if (factor == 1) |
274 | 274 return; |
275 | 275 if (factor == 0) { |
276 void Bignum::MultiplyByUInt64(uint64_t factor) { | 276 Zero(); |
277 if (factor == 1) return; | 277 return; |
278 if (factor == 0) { | 278 } |
279 Zero(); | 279 ASSERT(kBigitSize < 32); |
280 return; | 280 uint64_t carry = 0; |
281 } | 281 uint64_t low = factor & 0xFFFFFFFF; |
282 ASSERT(kBigitSize < 32); | 282 uint64_t high = factor >> 32; |
283 uint64_t carry = 0; | 283 for (int i = 0; i < used_digits_; ++i) { |
284 uint64_t low = factor & 0xFFFFFFFF; | 284 uint64_t product_low = low * bigits_[i]; |
285 uint64_t high = factor >> 32; | 285 uint64_t product_high = high * bigits_[i]; |
286 for (int i = 0; i < used_digits_; ++i) { | 286 uint64_t tmp = (carry & kBigitMask) + product_low; |
287 uint64_t product_low = low * bigits_[i]; | 287 bigits_[i] = (uint32_t)tmp & kBigitMask; |
288 uint64_t product_high = high * bigits_[i]; | 288 carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + |
289 uint64_t tmp = (carry & kBigitMask) + product_low; | |
290 bigits_[i] = (uint32_t)tmp & kBigitMask; | |
291 carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + | |
292 (product_high << (32 - kBigitSize)); | 289 (product_high << (32 - kBigitSize)); |
293 } | 290 } |
294 while (carry != 0) { | 291 while (carry != 0) { |
295 EnsureCapacity(used_digits_ + 1); | 292 EnsureCapacity(used_digits_ + 1); |
296 bigits_[used_digits_] = (uint32_t)carry & kBigitMask; | 293 bigits_[used_digits_] = (uint32_t)carry & kBigitMask; |
297 used_digits_++; | 294 used_digits_++; |
298 carry >>= kBigitSize; | 295 carry >>= kBigitSize; |
299 } | 296 } |
300 } | 297 } |
301 | 298 |
302 | 299 void Bignum::MultiplyByPowerOfTen(int exponent) { |
303 void Bignum::MultiplyByPowerOfTen(int exponent) { | 300 const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d); |
304 const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d); | 301 const uint16_t kFive1 = 5; |
305 const uint16_t kFive1 = 5; | 302 const uint16_t kFive2 = kFive1 * 5; |
306 const uint16_t kFive2 = kFive1 * 5; | 303 const uint16_t kFive3 = kFive2 * 5; |
307 const uint16_t kFive3 = kFive2 * 5; | 304 const uint16_t kFive4 = kFive3 * 5; |
308 const uint16_t kFive4 = kFive3 * 5; | 305 const uint16_t kFive5 = kFive4 * 5; |
309 const uint16_t kFive5 = kFive4 * 5; | 306 const uint16_t kFive6 = kFive5 * 5; |
310 const uint16_t kFive6 = kFive5 * 5; | 307 const uint32_t kFive7 = kFive6 * 5; |
311 const uint32_t kFive7 = kFive6 * 5; | 308 const uint32_t kFive8 = kFive7 * 5; |
312 const uint32_t kFive8 = kFive7 * 5; | 309 const uint32_t kFive9 = kFive8 * 5; |
313 const uint32_t kFive9 = kFive8 * 5; | 310 const uint32_t kFive10 = kFive9 * 5; |
314 const uint32_t kFive10 = kFive9 * 5; | 311 const uint32_t kFive11 = kFive10 * 5; |
315 const uint32_t kFive11 = kFive10 * 5; | 312 const uint32_t kFive12 = kFive11 * 5; |
316 const uint32_t kFive12 = kFive11 * 5; | 313 const uint32_t kFive13 = kFive12 * 5; |
317 const uint32_t kFive13 = kFive12 * 5; | 314 const uint32_t kFive1_to_12[] = {kFive1, kFive2, kFive3, kFive4, |
318 const uint32_t kFive1_to_12[] = | 315 kFive5, kFive6, kFive7, kFive8, |
319 { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, | 316 kFive9, kFive10, kFive11, kFive12}; |
320 kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; | 317 |
321 | 318 ASSERT(exponent >= 0); |
322 ASSERT(exponent >= 0); | 319 if (exponent == 0) |
323 if (exponent == 0) return; | 320 return; |
324 if (used_digits_ == 0) return; | 321 if (used_digits_ == 0) |
325 | 322 return; |
326 // We shift by exponent at the end just before returning. | 323 |
327 int remaining_exponent = exponent; | 324 // We shift by exponent at the end just before returning. |
328 while (remaining_exponent >= 27) { | 325 int remaining_exponent = exponent; |
329 MultiplyByUInt64(kFive27); | 326 while (remaining_exponent >= 27) { |
330 remaining_exponent -= 27; | 327 MultiplyByUInt64(kFive27); |
331 } | 328 remaining_exponent -= 27; |
332 while (remaining_exponent >= 13) { | 329 } |
333 MultiplyByUInt32(kFive13); | 330 while (remaining_exponent >= 13) { |
334 remaining_exponent -= 13; | 331 MultiplyByUInt32(kFive13); |
335 } | 332 remaining_exponent -= 13; |
336 if (remaining_exponent > 0) { | 333 } |
337 MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); | 334 if (remaining_exponent > 0) { |
338 } | 335 MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); |
339 ShiftLeft(exponent); | 336 } |
340 } | 337 ShiftLeft(exponent); |
341 | 338 } |
342 | 339 |
343 void Bignum::Square() { | 340 void Bignum::Square() { |
344 ASSERT(IsClamped()); | 341 ASSERT(IsClamped()); |
345 int product_length = 2 * used_digits_; | 342 int product_length = 2 * used_digits_; |
346 EnsureCapacity(product_length); | 343 EnsureCapacity(product_length); |
347 | 344 |
348 // Comba multiplication: compute each column separately. | 345 // Comba multiplication: compute each column separately. |
349 // Example: r = a2a1a0 * b2b1b0. | 346 // Example: r = a2a1a0 * b2b1b0. |
350 // r = 1 * a0b0 + | 347 // r = 1 * a0b0 + |
351 // 10 * (a1b0 + a0b1) + | 348 // 10 * (a1b0 + a0b1) + |
352 // 100 * (a2b0 + a1b1 + a0b2) + | 349 // 100 * (a2b0 + a1b1 + a0b2) + |
353 // 1000 * (a2b1 + a1b2) + | 350 // 1000 * (a2b1 + a1b2) + |
354 // 10000 * a2b2 | 351 // 10000 * a2b2 |
355 // | 352 // |
356 // In the worst case we have to accumulate nb-digits products of digit*d
igit. | 353 // In the worst case we have to accumulate nb-digits products of digit*digit. |
357 // | 354 // |
358 // Assert that the additional number of bits in a DoubleChunk are enough
to | 355 // Assert that the additional number of bits in a DoubleChunk are enough to |
359 // sum up used_digits of Bigit*Bigit. | 356 // sum up used_digits of Bigit*Bigit. |
360 if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { | 357 if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { |
361 UNIMPLEMENTED(); | 358 UNIMPLEMENTED(); |
362 } | 359 } |
363 DoubleChunk accumulator = 0; | 360 DoubleChunk accumulator = 0; |
364 // First shift the digits so we don't overwrite them. | 361 // First shift the digits so we don't overwrite them. |
365 int copy_offset = used_digits_; | 362 int copy_offset = used_digits_; |
366 for (int i = 0; i < used_digits_; ++i) { | 363 for (int i = 0; i < used_digits_; ++i) { |
367 bigits_[copy_offset + i] = bigits_[i]; | 364 bigits_[copy_offset + i] = bigits_[i]; |
368 } | 365 } |
369 // We have two loops to avoid some 'if's in the loop. | 366 // We have two loops to avoid some 'if's in the loop. |
370 for (int i = 0; i < used_digits_; ++i) { | 367 for (int i = 0; i < used_digits_; ++i) { |
371 // Process temporary digit i with power i. | 368 // Process temporary digit i with power i. |
372 // The sum of the two indices must be equal to i. | 369 // The sum of the two indices must be equal to i. |
373 int bigit_index1 = i; | 370 int bigit_index1 = i; |
374 int bigit_index2 = 0; | 371 int bigit_index2 = 0; |
375 // Sum all of the sub-products. | 372 // Sum all of the sub-products. |
376 while (bigit_index1 >= 0) { | 373 while (bigit_index1 >= 0) { |
377 Chunk chunk1 = bigits_[copy_offset + bigit_index1]; | 374 Chunk chunk1 = bigits_[copy_offset + bigit_index1]; |
378 Chunk chunk2 = bigits_[copy_offset + bigit_index2]; | 375 Chunk chunk2 = bigits_[copy_offset + bigit_index2]; |
379 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; | 376 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
380 bigit_index1--; | 377 bigit_index1--; |
381 bigit_index2++; | 378 bigit_index2++; |
382 } | 379 } |
383 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; | 380 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; |
384 accumulator >>= kBigitSize; | 381 accumulator >>= kBigitSize; |
385 } | 382 } |
386 for (int i = used_digits_; i < product_length; ++i) { | 383 for (int i = used_digits_; i < product_length; ++i) { |
387 int bigit_index1 = used_digits_ - 1; | 384 int bigit_index1 = used_digits_ - 1; |
388 int bigit_index2 = i - bigit_index1; | 385 int bigit_index2 = i - bigit_index1; |
389 // Invariant: sum of both indices is again equal to i. | 386 // Invariant: sum of both indices is again equal to i. |
390 // Inner loop runs 0 times on last iteration, emptying accumulator. | 387 // Inner loop runs 0 times on last iteration, emptying accumulator. |
391 while (bigit_index2 < used_digits_) { | 388 while (bigit_index2 < used_digits_) { |
392 Chunk chunk1 = bigits_[copy_offset + bigit_index1]; | 389 Chunk chunk1 = bigits_[copy_offset + bigit_index1]; |
393 Chunk chunk2 = bigits_[copy_offset + bigit_index2]; | 390 Chunk chunk2 = bigits_[copy_offset + bigit_index2]; |
394 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; | 391 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
395 bigit_index1--; | 392 bigit_index1--; |
396 bigit_index2++; | 393 bigit_index2++; |
397 } | 394 } |
398 // The overwritten bigits_[i] will never be read in further loop ite
rations, | 395 // The overwritten bigits_[i] will never be read in further loop iterations, |
399 // because bigit_index1 and bigit_index2 are always greater | 396 // because bigit_index1 and bigit_index2 are always greater |
400 // than i - used_digits_. | 397 // than i - used_digits_. |
401 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; | 398 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; |
402 accumulator >>= kBigitSize; | 399 accumulator >>= kBigitSize; |
403 } | 400 } |
404 // Since the result was guaranteed to lie inside the number the | 401 // Since the result was guaranteed to lie inside the number the |
405 // accumulator must be 0 now. | 402 // accumulator must be 0 now. |
406 ASSERT(accumulator == 0); | 403 ASSERT(accumulator == 0); |
407 | 404 |
408 // Don't forget to update the used_digits and the exponent. | 405 // Don't forget to update the used_digits and the exponent. |
409 used_digits_ = product_length; | 406 used_digits_ = product_length; |
410 exponent_ *= 2; | 407 exponent_ *= 2; |
411 Clamp(); | 408 Clamp(); |
412 } | 409 } |
413 | 410 |
414 | 411 void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { |
415 void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { | 412 ASSERT(base != 0); |
416 ASSERT(base != 0); | 413 ASSERT(power_exponent >= 0); |
417 ASSERT(power_exponent >= 0); | 414 if (power_exponent == 0) { |
418 if (power_exponent == 0) { | 415 AssignUInt16(1); |
419 AssignUInt16(1); | 416 return; |
420 return; | 417 } |
421 } | 418 Zero(); |
422 Zero(); | 419 int shifts = 0; |
423 int shifts = 0; | 420 // We expect base to be in range 2-32, and most often to be 10. |
424 // We expect base to be in range 2-32, and most often to be 10. | 421 // It does not make much sense to implement different algorithms for counting |
425 // It does not make much sense to implement different algorithms for cou
nting | 422 // the bits. |
426 // the bits. | 423 while ((base & 1) == 0) { |
427 while ((base & 1) == 0) { | 424 base >>= 1; |
428 base >>= 1; | 425 shifts++; |
429 shifts++; | 426 } |
430 } | 427 int bit_size = 0; |
431 int bit_size = 0; | 428 int tmp_base = base; |
432 int tmp_base = base; | 429 while (tmp_base != 0) { |
433 while (tmp_base != 0) { | 430 tmp_base >>= 1; |
434 tmp_base >>= 1; | 431 bit_size++; |
435 bit_size++; | 432 } |
436 } | 433 int final_size = bit_size * power_exponent; |
437 int final_size = bit_size * power_exponent; | 434 // 1 extra bigit for the shifting, and one for rounded final_size. |
438 // 1 extra bigit for the shifting, and one for rounded final_size. | 435 EnsureCapacity(final_size / kBigitSize + 2); |
439 EnsureCapacity(final_size / kBigitSize + 2); | 436 |
440 | 437 // Left to Right exponentiation. |
441 // Left to Right exponentiation. | 438 int mask = 1; |
442 int mask = 1; | 439 while (power_exponent >= mask) |
443 while (power_exponent >= mask) mask <<= 1; | 440 mask <<= 1; |
444 | 441 |
445 // The mask is now pointing to the bit above the most significant 1-bit
of | 442 // The mask is now pointing to the bit above the most significant 1-bit of |
446 // power_exponent. | 443 // power_exponent. |
447 // Get rid of first 1-bit; | 444 // Get rid of first 1-bit; |
448 mask >>= 2; | 445 mask >>= 2; |
449 uint64_t this_value = base; | 446 uint64_t this_value = base; |
450 | 447 |
451 bool delayed_multipliciation = false; | 448 bool delayed_multipliciation = false; |
452 const uint64_t max_32bits = 0xFFFFFFFF; | 449 const uint64_t max_32bits = 0xFFFFFFFF; |
453 while (mask != 0 && this_value <= max_32bits) { | 450 while (mask != 0 && this_value <= max_32bits) { |
454 this_value = this_value * this_value; | 451 this_value = this_value * this_value; |
455 // Verify that there is enough space in this_value to perform the | 452 // Verify that there is enough space in this_value to perform the |
456 // multiplication. The first bit_size bits must be 0. | 453 // multiplication. The first bit_size bits must be 0. |
457 if ((power_exponent & mask) != 0) { | 454 if ((power_exponent & mask) != 0) { |
458 uint64_t base_bits_mask = | 455 uint64_t base_bits_mask = |
459 ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); | 456 ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); |
460 bool high_bits_zero = (this_value & base_bits_mask) == 0; | 457 bool high_bits_zero = (this_value & base_bits_mask) == 0; |
461 if (high_bits_zero) { | 458 if (high_bits_zero) { |
462 this_value *= base; | 459 this_value *= base; |
463 } else { | 460 } else { |
464 delayed_multipliciation = true; | 461 delayed_multipliciation = true; |
465 } | 462 } |
466 } | 463 } |
467 mask >>= 1; | 464 mask >>= 1; |
468 } | 465 } |
469 AssignUInt64(this_value); | 466 AssignUInt64(this_value); |
470 if (delayed_multipliciation) { | 467 if (delayed_multipliciation) { |
471 MultiplyByUInt32(base); | 468 MultiplyByUInt32(base); |
472 } | 469 } |
473 | 470 |
474 // Now do the same thing as a bignum. | 471 // Now do the same thing as a bignum. |
475 while (mask != 0) { | 472 while (mask != 0) { |
476 Square(); | 473 Square(); |
477 if ((power_exponent & mask) != 0) { | 474 if ((power_exponent & mask) != 0) { |
478 MultiplyByUInt32(base); | 475 MultiplyByUInt32(base); |
479 } | 476 } |
480 mask >>= 1; | 477 mask >>= 1; |
481 } | 478 } |
482 | 479 |
483 // And finally add the saved shifts. | 480 // And finally add the saved shifts. |
484 ShiftLeft(shifts * power_exponent); | 481 ShiftLeft(shifts * power_exponent); |
485 } | 482 } |
486 | 483 |
487 | 484 // Precondition: this/other < 16bit. |
488 // Precondition: this/other < 16bit. | 485 uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { |
489 uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { | 486 ASSERT(IsClamped()); |
490 ASSERT(IsClamped()); | 487 ASSERT(other.IsClamped()); |
491 ASSERT(other.IsClamped()); | 488 ASSERT(other.used_digits_ > 0); |
492 ASSERT(other.used_digits_ > 0); | 489 |
493 | 490 // Easy case: if we have less digits than the divisor than the result is 0. |
494 // Easy case: if we have less digits than the divisor than the result is
0. | 491 // Note: this handles the case where this == 0, too. |
495 // Note: this handles the case where this == 0, too. | 492 if (BigitLength() < other.BigitLength()) { |
496 if (BigitLength() < other.BigitLength()) { | 493 return 0; |
497 return 0; | 494 } |
498 } | 495 |
499 | 496 Align(other); |
500 Align(other); | 497 |
501 | 498 uint16_t result = 0; |
502 uint16_t result = 0; | 499 |
503 | 500 // Start by removing multiples of 'other' until both numbers have the same |
504 // Start by removing multiples of 'other' until both numbers have the sa
me | 501 // number of digits. |
505 // number of digits. | 502 while (BigitLength() > other.BigitLength()) { |
506 while (BigitLength() > other.BigitLength()) { | 503 // This naive approach is extremely inefficient if the this divided other |
507 // This naive approach is extremely inefficient if the this divided
other | 504 // might be big. This function is implemented for doubleToString where |
508 // might be big. This function is implemented for doubleToString whe
re | 505 // the result should be small (less than 10). |
509 // the result should be small (less than 10). | 506 ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16)); |
510 ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) /
16)); | 507 // Remove the multiples of the first digit. |
511 // Remove the multiples of the first digit. | 508 // Example this = 23 and other equals 9. -> Remove 2 multiples. |
512 // Example this = 23 and other equals 9. -> Remove 2 multiples. | 509 result += static_cast<uint16_t>(bigits_[used_digits_ - 1]); |
513 result += static_cast<uint16_t>(bigits_[used_digits_ - 1]); | 510 SubtractTimes(other, bigits_[used_digits_ - 1]); |
514 SubtractTimes(other, bigits_[used_digits_ - 1]); | 511 } |
515 } | 512 |
516 | 513 ASSERT(BigitLength() == other.BigitLength()); |
517 ASSERT(BigitLength() == other.BigitLength()); | 514 |
518 | 515 // Both bignums are at the same length now. |
519 // Both bignums are at the same length now. | 516 // Since other has more than 0 digits we know that the access to |
520 // Since other has more than 0 digits we know that the access to | 517 // bigits_[used_digits_ - 1] is safe. |
521 // bigits_[used_digits_ - 1] is safe. | 518 Chunk this_bigit = bigits_[used_digits_ - 1]; |
522 Chunk this_bigit = bigits_[used_digits_ - 1]; | 519 Chunk other_bigit = other.bigits_[other.used_digits_ - 1]; |
523 Chunk other_bigit = other.bigits_[other.used_digits_ - 1]; | 520 |
524 | 521 if (other.used_digits_ == 1) { |
525 if (other.used_digits_ == 1) { | 522 // Shortcut for easy (and common) case. |
526 // Shortcut for easy (and common) case. | 523 uint16_t quotient = static_cast<uint16_t>(this_bigit / other_bigit); |
527 uint16_t quotient = static_cast<uint16_t>(this_bigit / other_bigit); | 524 bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; |
528 bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; | 525 result += quotient; |
529 result += quotient; | 526 Clamp(); |
530 Clamp(); | 527 return result; |
531 return result; | 528 } |
532 } | 529 |
533 | 530 uint16_t division_estimate = |
534 uint16_t division_estimate = static_cast<uint16_t>(this_bigit / (other_b
igit + 1)); | 531 static_cast<uint16_t>(this_bigit / (other_bigit + 1)); |
535 result += division_estimate; | 532 result += division_estimate; |
536 SubtractTimes(other, division_estimate); | 533 SubtractTimes(other, division_estimate); |
537 | 534 |
538 if (other_bigit * (division_estimate + 1) > this_bigit) { | 535 if (other_bigit * (division_estimate + 1) > this_bigit) { |
539 // No need to even try to subtract. Even if other's remaining digits
were 0 | 536 // No need to even try to subtract. Even if other's remaining digits were 0 |
540 // another subtraction would be too much. | 537 // another subtraction would be too much. |
541 return result; | 538 return result; |
542 } | 539 } |
543 | 540 |
544 while (LessEqual(other, *this)) { | 541 while (LessEqual(other, *this)) { |
545 SubtractBignum(other); | 542 SubtractBignum(other); |
546 result++; | 543 result++; |
547 } | 544 } |
548 return result; | 545 return result; |
549 } | 546 } |
550 | 547 |
551 | 548 template <typename S> |
552 template<typename S> | 549 static int SizeInHexChars(S number) { |
553 static int SizeInHexChars(S number) { | 550 ASSERT(number > 0); |
554 ASSERT(number > 0); | 551 int result = 0; |
555 int result = 0; | 552 while (number != 0) { |
556 while (number != 0) { | 553 number >>= 4; |
557 number >>= 4; | 554 result++; |
558 result++; | 555 } |
559 } | 556 return result; |
560 return result; | 557 } |
561 } | 558 |
562 | 559 static char HexCharOfValue(uint8_t value) { |
563 | 560 ASSERT(0 <= value && value <= 16); |
564 static char HexCharOfValue(uint8_t value) { | 561 if (value < 10) |
565 ASSERT(0 <= value && value <= 16); | 562 return value + '0'; |
566 if (value < 10) return value + '0'; | 563 return value - 10 + 'A'; |
567 return value - 10 + 'A'; | 564 } |
568 } | 565 |
569 | 566 bool Bignum::ToHexString(char* buffer, int buffer_size) const { |
570 | 567 ASSERT(IsClamped()); |
571 bool Bignum::ToHexString(char* buffer, int buffer_size) const { | 568 // Each bigit must be printable as separate hex-character. |
572 ASSERT(IsClamped()); | 569 ASSERT(kBigitSize % 4 == 0); |
573 // Each bigit must be printable as separate hex-character. | 570 const int kHexCharsPerBigit = kBigitSize / 4; |
574 ASSERT(kBigitSize % 4 == 0); | 571 |
575 const int kHexCharsPerBigit = kBigitSize / 4; | 572 if (used_digits_ == 0) { |
576 | 573 if (buffer_size < 2) |
577 if (used_digits_ == 0) { | 574 return false; |
578 if (buffer_size < 2) return false; | 575 buffer[0] = '0'; |
579 buffer[0] = '0'; | 576 buffer[1] = '\0'; |
580 buffer[1] = '\0'; | 577 return true; |
581 return true; | 578 } |
582 } | 579 // We add 1 for the terminating '\0' character. |
583 // We add 1 for the terminating '\0' character. | 580 int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + |
584 int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + | 581 SizeInHexChars(bigits_[used_digits_ - 1]) + 1; |
585 SizeInHexChars(bigits_[used_digits_ - 1]) + 1; | 582 if (needed_chars > buffer_size) |
586 if (needed_chars > buffer_size) return false; | 583 return false; |
587 int string_index = needed_chars - 1; | 584 int string_index = needed_chars - 1; |
588 buffer[string_index--] = '\0'; | 585 buffer[string_index--] = '\0'; |
589 for (int i = 0; i < exponent_; ++i) { | 586 for (int i = 0; i < exponent_; ++i) { |
590 for (int j = 0; j < kHexCharsPerBigit; ++j) { | 587 for (int j = 0; j < kHexCharsPerBigit; ++j) { |
591 buffer[string_index--] = '0'; | 588 buffer[string_index--] = '0'; |
592 } | 589 } |
593 } | 590 } |
594 for (int i = 0; i < used_digits_ - 1; ++i) { | 591 for (int i = 0; i < used_digits_ - 1; ++i) { |
595 Chunk current_bigit = bigits_[i]; | 592 Chunk current_bigit = bigits_[i]; |
596 for (int j = 0; j < kHexCharsPerBigit; ++j) { | 593 for (int j = 0; j < kHexCharsPerBigit; ++j) { |
597 buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); | 594 buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); |
598 current_bigit >>= 4; | 595 current_bigit >>= 4; |
599 } | 596 } |
600 } | 597 } |
601 // And finally the last bigit. | 598 // And finally the last bigit. |
602 Chunk most_significant_bigit = bigits_[used_digits_ - 1]; | 599 Chunk most_significant_bigit = bigits_[used_digits_ - 1]; |
603 while (most_significant_bigit != 0) { | 600 while (most_significant_bigit != 0) { |
604 buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF
); | 601 buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); |
605 most_significant_bigit >>= 4; | 602 most_significant_bigit >>= 4; |
606 } | 603 } |
607 return true; | 604 return true; |
608 } | 605 } |
609 | 606 |
610 | 607 Bignum::Chunk Bignum::BigitAt(int index) const { |
611 Bignum::Chunk Bignum::BigitAt(int index) const { | 608 if (index >= BigitLength()) |
612 if (index >= BigitLength()) return 0; | 609 return 0; |
613 if (index < exponent_) return 0; | 610 if (index < exponent_) |
614 return bigits_[index - exponent_]; | 611 return 0; |
615 } | 612 return bigits_[index - exponent_]; |
616 | 613 } |
617 | 614 |
618 int Bignum::Compare(const Bignum& a, const Bignum& b) { | 615 int Bignum::Compare(const Bignum& a, const Bignum& b) { |
619 ASSERT(a.IsClamped()); | 616 ASSERT(a.IsClamped()); |
620 ASSERT(b.IsClamped()); | 617 ASSERT(b.IsClamped()); |
621 int bigit_length_a = a.BigitLength(); | 618 int bigit_length_a = a.BigitLength(); |
622 int bigit_length_b = b.BigitLength(); | 619 int bigit_length_b = b.BigitLength(); |
623 if (bigit_length_a < bigit_length_b) return -1; | 620 if (bigit_length_a < bigit_length_b) |
624 if (bigit_length_a > bigit_length_b) return +1; | 621 return -1; |
625 for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i
) { | 622 if (bigit_length_a > bigit_length_b) |
626 Chunk bigit_a = a.BigitAt(i); | 623 return +1; |
627 Chunk bigit_b = b.BigitAt(i); | 624 for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) { |
628 if (bigit_a < bigit_b) return -1; | 625 Chunk bigit_a = a.BigitAt(i); |
629 if (bigit_a > bigit_b) return +1; | 626 Chunk bigit_b = b.BigitAt(i); |
630 // Otherwise they are equal up to this digit. Try the next digit. | 627 if (bigit_a < bigit_b) |
631 } | 628 return -1; |
632 return 0; | 629 if (bigit_a > bigit_b) |
633 } | 630 return +1; |
634 | 631 // Otherwise they are equal up to this digit. Try the next digit. |
635 | 632 } |
636 int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { | 633 return 0; |
637 ASSERT(a.IsClamped()); | 634 } |
638 ASSERT(b.IsClamped()); | 635 |
639 ASSERT(c.IsClamped()); | 636 int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { |
640 if (a.BigitLength() < b.BigitLength()) { | 637 ASSERT(a.IsClamped()); |
641 return PlusCompare(b, a, c); | 638 ASSERT(b.IsClamped()); |
642 } | 639 ASSERT(c.IsClamped()); |
643 if (a.BigitLength() + 1 < c.BigitLength()) return -1; | 640 if (a.BigitLength() < b.BigitLength()) { |
644 if (a.BigitLength() > c.BigitLength()) return +1; | 641 return PlusCompare(b, a, c); |
645 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' t
han | 642 } |
646 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the
one | 643 if (a.BigitLength() + 1 < c.BigitLength()) |
647 // of 'a'. | 644 return -1; |
648 if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength())
{ | 645 if (a.BigitLength() > c.BigitLength()) |
649 return -1; | 646 return +1; |
650 } | 647 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than |
651 | 648 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one |
652 Chunk borrow = 0; | 649 // of 'a'. |
653 // Starting at min_exponent all digits are == 0. So no need to compare t
hem. | 650 if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { |
654 int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); | 651 return -1; |
655 for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { | 652 } |
656 Chunk chunk_a = a.BigitAt(i); | 653 |
657 Chunk chunk_b = b.BigitAt(i); | 654 Chunk borrow = 0; |
658 Chunk chunk_c = c.BigitAt(i); | 655 // Starting at min_exponent all digits are == 0. So no need to compare them. |
659 Chunk sum = chunk_a + chunk_b; | 656 int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); |
660 if (sum > chunk_c + borrow) { | 657 for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { |
661 return +1; | 658 Chunk chunk_a = a.BigitAt(i); |
662 } else { | 659 Chunk chunk_b = b.BigitAt(i); |
663 borrow = chunk_c + borrow - sum; | 660 Chunk chunk_c = c.BigitAt(i); |
664 if (borrow > 1) return -1; | 661 Chunk sum = chunk_a + chunk_b; |
665 borrow <<= kBigitSize; | 662 if (sum > chunk_c + borrow) { |
666 } | 663 return +1; |
667 } | 664 } else { |
668 if (borrow == 0) return 0; | 665 borrow = chunk_c + borrow - sum; |
| 666 if (borrow > 1) |
669 return -1; | 667 return -1; |
670 } | 668 borrow <<= kBigitSize; |
671 | 669 } |
672 | 670 } |
673 void Bignum::Clamp() { | 671 if (borrow == 0) |
674 while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { | 672 return 0; |
675 used_digits_--; | 673 return -1; |
676 } | 674 } |
677 if (used_digits_ == 0) { | 675 |
678 // Zero. | 676 void Bignum::Clamp() { |
679 exponent_ = 0; | 677 while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { |
680 } | 678 used_digits_--; |
681 } | 679 } |
682 | 680 if (used_digits_ == 0) { |
683 | 681 // Zero. |
684 bool Bignum::IsClamped() const { | 682 exponent_ = 0; |
685 return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; | 683 } |
686 } | 684 } |
687 | 685 |
688 | 686 bool Bignum::IsClamped() const { |
689 void Bignum::Zero() { | 687 return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; |
690 for (int i = 0; i < used_digits_; ++i) { | 688 } |
691 bigits_[i] = 0; | 689 |
692 } | 690 void Bignum::Zero() { |
693 used_digits_ = 0; | 691 for (int i = 0; i < used_digits_; ++i) { |
694 exponent_ = 0; | 692 bigits_[i] = 0; |
695 } | 693 } |
696 | 694 used_digits_ = 0; |
697 | 695 exponent_ = 0; |
698 void Bignum::Align(const Bignum& other) { | 696 } |
699 if (exponent_ > other.exponent_) { | 697 |
700 // If "X" represents a "hidden" digit (by the exponent) then we are
in the | 698 void Bignum::Align(const Bignum& other) { |
701 // following case (a == this, b == other): | 699 if (exponent_ > other.exponent_) { |
702 // a: aaaaaaXXXX or a: aaaaaXXX | 700 // If "X" represents a "hidden" digit (by the exponent) then we are in the |
703 // b: bbbbbbX b: bbbbbbbbXX | 701 // following case (a == this, b == other): |
704 // We replace some of the hidden digits (X) of a with 0 digits. | 702 // a: aaaaaaXXXX or a: aaaaaXXX |
705 // a: aaaaaa000X or a: aaaaa0XX | 703 // b: bbbbbbX b: bbbbbbbbXX |
706 int zero_digits = exponent_ - other.exponent_; | 704 // We replace some of the hidden digits (X) of a with 0 digits. |
707 EnsureCapacity(used_digits_ + zero_digits); | 705 // a: aaaaaa000X or a: aaaaa0XX |
708 for (int i = used_digits_ - 1; i >= 0; --i) { | 706 int zero_digits = exponent_ - other.exponent_; |
709 bigits_[i + zero_digits] = bigits_[i]; | 707 EnsureCapacity(used_digits_ + zero_digits); |
710 } | 708 for (int i = used_digits_ - 1; i >= 0; --i) { |
711 for (int i = 0; i < zero_digits; ++i) { | 709 bigits_[i + zero_digits] = bigits_[i]; |
712 bigits_[i] = 0; | 710 } |
713 } | 711 for (int i = 0; i < zero_digits; ++i) { |
714 used_digits_ += zero_digits; | 712 bigits_[i] = 0; |
715 exponent_ -= zero_digits; | 713 } |
716 ASSERT(used_digits_ >= 0); | 714 used_digits_ += zero_digits; |
717 ASSERT(exponent_ >= 0); | 715 exponent_ -= zero_digits; |
718 } | 716 ASSERT(used_digits_ >= 0); |
719 } | 717 ASSERT(exponent_ >= 0); |
720 | 718 } |
721 | 719 } |
722 void Bignum::BigitsShiftLeft(int shift_amount) { | 720 |
723 ASSERT(shift_amount < kBigitSize); | 721 void Bignum::BigitsShiftLeft(int shift_amount) { |
724 ASSERT(shift_amount >= 0); | 722 ASSERT(shift_amount < kBigitSize); |
725 Chunk carry = 0; | 723 ASSERT(shift_amount >= 0); |
726 for (int i = 0; i < used_digits_; ++i) { | 724 Chunk carry = 0; |
727 Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); | 725 for (int i = 0; i < used_digits_; ++i) { |
728 bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; | 726 Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); |
729 carry = new_carry; | 727 bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; |
730 } | 728 carry = new_carry; |
731 if (carry != 0) { | 729 } |
732 bigits_[used_digits_] = carry; | 730 if (carry != 0) { |
733 used_digits_++; | 731 bigits_[used_digits_] = carry; |
734 } | 732 used_digits_++; |
735 } | 733 } |
736 | 734 } |
737 | 735 |
738 void Bignum::SubtractTimes(const Bignum& other, int factor) { | 736 void Bignum::SubtractTimes(const Bignum& other, int factor) { |
739 ASSERT(exponent_ <= other.exponent_); | 737 ASSERT(exponent_ <= other.exponent_); |
740 if (factor < 3) { | 738 if (factor < 3) { |
741 for (int i = 0; i < factor; ++i) { | 739 for (int i = 0; i < factor; ++i) { |
742 SubtractBignum(other); | 740 SubtractBignum(other); |
743 } | 741 } |
744 return; | 742 return; |
745 } | 743 } |
746 Chunk borrow = 0; | 744 Chunk borrow = 0; |
747 int exponent_diff = other.exponent_ - exponent_; | 745 int exponent_diff = other.exponent_ - exponent_; |
748 for (int i = 0; i < other.used_digits_; ++i) { | 746 for (int i = 0; i < other.used_digits_; ++i) { |
749 DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigit
s_[i]; | 747 DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i]; |
750 DoubleChunk remove = borrow + product; | 748 DoubleChunk remove = borrow + product; |
751 Chunk difference = bigits_[i + exponent_diff] - ((uint32_t)remove &
kBigitMask); | 749 Chunk difference = |
752 bigits_[i + exponent_diff] = difference & kBigitMask; | 750 bigits_[i + exponent_diff] - ((uint32_t)remove & kBigitMask); |
753 borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + | 751 bigits_[i + exponent_diff] = difference & kBigitMask; |
754 (remove >> kBigitSize)); | 752 borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + |
755 } | 753 (remove >> kBigitSize)); |
756 for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i)
{ | 754 } |
757 if (borrow == 0) return; | 755 for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) { |
758 Chunk difference = bigits_[i] - borrow; | 756 if (borrow == 0) |
759 bigits_[i] = difference & kBigitMask; | 757 return; |
760 borrow = difference >> (kChunkSize - 1); | 758 Chunk difference = bigits_[i] - borrow; |
761 } | 759 bigits_[i] = difference & kBigitMask; |
762 Clamp(); | 760 borrow = difference >> (kChunkSize - 1); |
763 } | 761 } |
764 | 762 Clamp(); |
| 763 } |
765 | 764 |
766 } // namespace double_conversion | 765 } // namespace double_conversion |
767 | 766 |
768 } // namespace WTF | 767 } // namespace WTF |
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