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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 |
| (...skipping 15 matching lines...) Expand all Loading... |
| 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 |
| OLD | NEW |