1 // Tencent is pleased to support the open source community by making RapidJSON available. 2 // 3 // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved. 4 // 5 // Licensed under the MIT License (the "License"); you may not use this file except 6 // in compliance with the License. You may obtain a copy of the License at 7 // 8 // http://opensource.org/licenses/MIT 9 // 10 // Unless required by applicable law or agreed to in writing, software distributed 11 // under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR 12 // CONDITIONS OF ANY KIND, either express or implied. See the License for the 13 // specific language governing permissions and limitations under the License. 14 15 #ifndef RAPIDJSON_BIGINTEGER_H_ 16 #define RAPIDJSON_BIGINTEGER_H_ 17 18 #include "../rapidjson.h" 19 20 #if defined(_MSC_VER) && defined(_M_AMD64) 21 #include <intrin.h> // for _umul128 22 #pragma intrinsic(_umul128) 23 #endif 24 25 RAPIDJSON_NAMESPACE_BEGIN 26 namespace internal { 27 28 class BigInteger { 29 public: 30 typedef uint64_t Type; 31 32 BigInteger(const BigInteger& rhs) : count_(rhs.count_) { 33 std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type)); 34 } 35 36 explicit BigInteger(uint64_t u) : count_(1) { 37 digits_[0] = u; 38 } 39 40 BigInteger(const char* decimals, size_t length) : count_(1) { 41 RAPIDJSON_ASSERT(length > 0); 42 digits_[0] = 0; 43 size_t i = 0; 44 const size_t kMaxDigitPerIteration = 19; // 2^64 = 18446744073709551616 > 10^19 45 while (length >= kMaxDigitPerIteration) { 46 AppendDecimal64(decimals + i, decimals + i + kMaxDigitPerIteration); 47 length -= kMaxDigitPerIteration; 48 i += kMaxDigitPerIteration; 49 } 50 51 if (length > 0) 52 AppendDecimal64(decimals + i, decimals + i + length); 53 } 54 55 BigInteger& operator=(const BigInteger &rhs) 56 { 57 if (this != &rhs) { 58 count_ = rhs.count_; 59 std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type)); 60 } 61 return *this; 62 } 63 64 BigInteger& operator=(uint64_t u) { 65 digits_[0] = u; 66 count_ = 1; 67 return *this; 68 } 69 70 BigInteger& operator+=(uint64_t u) { 71 Type backup = digits_[0]; 72 digits_[0] += u; 73 for (size_t i = 0; i < count_ - 1; i++) { 74 if (digits_[i] >= backup) 75 return *this; // no carry 76 backup = digits_[i + 1]; 77 digits_[i + 1] += 1; 78 } 79 80 // Last carry 81 if (digits_[count_ - 1] < backup) 82 PushBack(1); 83 84 return *this; 85 } 86 87 BigInteger& operator*=(uint64_t u) { 88 if (u == 0) return *this = 0; 89 if (u == 1) return *this; 90 if (*this == 1) return *this = u; 91 92 uint64_t k = 0; 93 for (size_t i = 0; i < count_; i++) { 94 uint64_t hi; 95 digits_[i] = MulAdd64(digits_[i], u, k, &hi); 96 k = hi; 97 } 98 99 if (k > 0) 100 PushBack(k); 101 102 return *this; 103 } 104 105 BigInteger& operator*=(uint32_t u) { 106 if (u == 0) return *this = 0; 107 if (u == 1) return *this; 108 if (*this == 1) return *this = u; 109 110 uint64_t k = 0; 111 for (size_t i = 0; i < count_; i++) { 112 const uint64_t c = digits_[i] >> 32; 113 const uint64_t d = digits_[i] & 0xFFFFFFFF; 114 const uint64_t uc = u * c; 115 const uint64_t ud = u * d; 116 const uint64_t p0 = ud + k; 117 const uint64_t p1 = uc + (p0 >> 32); 118 digits_[i] = (p0 & 0xFFFFFFFF) | (p1 << 32); 119 k = p1 >> 32; 120 } 121 122 if (k > 0) 123 PushBack(k); 124 125 return *this; 126 } 127 128 BigInteger& operator<<=(size_t shift) { 129 if (IsZero() || shift == 0) return *this; 130 131 size_t offset = shift / kTypeBit; 132 size_t interShift = shift % kTypeBit; 133 RAPIDJSON_ASSERT(count_ + offset <= kCapacity); 134 135 if (interShift == 0) { 136 std::memmove(&digits_[count_ - 1 + offset], &digits_[count_ - 1], count_ * sizeof(Type)); 137 count_ += offset; 138 } 139 else { 140 digits_[count_] = 0; 141 for (size_t i = count_; i > 0; i--) 142 digits_[i + offset] = (digits_[i] << interShift) | (digits_[i - 1] >> (kTypeBit - interShift)); 143 digits_[offset] = digits_[0] << interShift; 144 count_ += offset; 145 if (digits_[count_]) 146 count_++; 147 } 148 149 std::memset(digits_, 0, offset * sizeof(Type)); 150 151 return *this; 152 } 153 154 bool operator==(const BigInteger& rhs) const { 155 return count_ == rhs.count_ && std::memcmp(digits_, rhs.digits_, count_ * sizeof(Type)) == 0; 156 } 157 158 bool operator==(const Type rhs) const { 159 return count_ == 1 && digits_[0] == rhs; 160 } 161 162 BigInteger& MultiplyPow5(unsigned exp) { 163 static const uint32_t kPow5[12] = { 164 5, 165 5 * 5, 166 5 * 5 * 5, 167 5 * 5 * 5 * 5, 168 5 * 5 * 5 * 5 * 5, 169 5 * 5 * 5 * 5 * 5 * 5, 170 5 * 5 * 5 * 5 * 5 * 5 * 5, 171 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 172 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 173 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 174 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 175 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 176 }; 177 if (exp == 0) return *this; 178 for (; exp >= 27; exp -= 27) *this *= RAPIDJSON_UINT64_C2(0X6765C793, 0XFA10079D); // 5^27 179 for (; exp >= 13; exp -= 13) *this *= static_cast<uint32_t>(1220703125u); // 5^13 180 if (exp > 0) *this *= kPow5[exp - 1]; 181 return *this; 182 } 183 184 // Compute absolute difference of this and rhs. 185 // Assume this != rhs 186 bool Difference(const BigInteger& rhs, BigInteger* out) const { 187 int cmp = Compare(rhs); 188 RAPIDJSON_ASSERT(cmp != 0); 189 const BigInteger *a, *b; // Makes a > b 190 bool ret; 191 if (cmp < 0) { a = &rhs; b = this; ret = true; } 192 else { a = this; b = &rhs; ret = false; } 193 194 Type borrow = 0; 195 for (size_t i = 0; i < a->count_; i++) { 196 Type d = a->digits_[i] - borrow; 197 if (i < b->count_) 198 d -= b->digits_[i]; 199 borrow = (d > a->digits_[i]) ? 1 : 0; 200 out->digits_[i] = d; 201 if (d != 0) 202 out->count_ = i + 1; 203 } 204 205 return ret; 206 } 207 208 int Compare(const BigInteger& rhs) const { 209 if (count_ != rhs.count_) 210 return count_ < rhs.count_ ? -1 : 1; 211 212 for (size_t i = count_; i-- > 0;) 213 if (digits_[i] != rhs.digits_[i]) 214 return digits_[i] < rhs.digits_[i] ? -1 : 1; 215 216 return 0; 217 } 218 219 size_t GetCount() const { return count_; } 220 Type GetDigit(size_t index) const { RAPIDJSON_ASSERT(index < count_); return digits_[index]; } 221 bool IsZero() const { return count_ == 1 && digits_[0] == 0; } 222 223 private: 224 void AppendDecimal64(const char* begin, const char* end) { 225 uint64_t u = ParseUint64(begin, end); 226 if (IsZero()) 227 *this = u; 228 else { 229 unsigned exp = static_cast<unsigned>(end - begin); 230 (MultiplyPow5(exp) <<= exp) += u; // *this = *this * 10^exp + u 231 } 232 } 233 234 void PushBack(Type digit) { 235 RAPIDJSON_ASSERT(count_ < kCapacity); 236 digits_[count_++] = digit; 237 } 238 239 static uint64_t ParseUint64(const char* begin, const char* end) { 240 uint64_t r = 0; 241 for (const char* p = begin; p != end; ++p) { 242 RAPIDJSON_ASSERT(*p >= '0' && *p <= '9'); 243 r = r * 10u + (unsigned)(*p - '0'); 244 } 245 return r; 246 } 247 248 // Assume a * b + k < 2^128 249 static uint64_t MulAdd64(uint64_t a, uint64_t b, uint64_t k, uint64_t* outHigh) { 250 #if defined(_MSC_VER) && defined(_M_AMD64) 251 uint64_t low = _umul128(a, b, outHigh) + k; 252 if (low < k) 253 (*outHigh)++; 254 return low; 255 #elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__) 256 __extension__ typedef unsigned __int128 uint128; 257 uint128 p = static_cast<uint128>(a) * static_cast<uint128>(b); 258 p += k; 259 *outHigh = static_cast<uint64_t>(p >> 64); 260 return static_cast<uint64_t>(p); 261 #else 262 const uint64_t a0 = a & 0xFFFFFFFF, a1 = a >> 32, b0 = b & 0xFFFFFFFF, b1 = b >> 32; 263 uint64_t x0 = a0 * b0, x1 = a0 * b1, x2 = a1 * b0, x3 = a1 * b1; 264 x1 += (x0 >> 32); // can't give carry 265 x1 += x2; 266 if (x1 < x2) 267 x3 += (static_cast<uint64_t>(1) << 32); 268 uint64_t lo = (x1 << 32) + (x0 & 0xFFFFFFFF); 269 uint64_t hi = x3 + (x1 >> 32); 270 271 lo += k; 272 if (lo < k) 273 hi++; 274 *outHigh = hi; 275 return lo; 276 #endif 277 } 278 279 static const size_t kBitCount = 3328; // 64bit * 54 > 10^1000 280 static const size_t kCapacity = kBitCount / sizeof(Type); 281 static const size_t kTypeBit = sizeof(Type) * 8; 282 283 Type digits_[kCapacity]; 284 size_t count_; 285 }; 286 287 } // namespace internal 288 RAPIDJSON_NAMESPACE_END 289 290 #endif // RAPIDJSON_BIGINTEGER_H_ 291
