// Tencent is pleased to support the open source community by making RapidJSON available. // // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved. // // Licensed under the MIT License (the "License"); you may not use this file except // in compliance with the License. You may obtain a copy of the License at // // http://opensource.org/licenses/MIT // // Unless required by applicable law or agreed to in writing, software distributed // under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR // CONDITIONS OF ANY KIND, either express or implied. See the License for the // specific language governing permissions and limitations under the License. #ifndef RAPIDJSON_BIGINTEGER_H_ #define RAPIDJSON_BIGINTEGER_H_ #include "../rapidjson.h" #if defined(_MSC_VER) && defined(_M_AMD64) #include <intrin.h> // for _umul128 #pragma intrinsic(_umul128) #endif RAPIDJSON_NAMESPACE_BEGIN namespace internal { class BigInteger { public: typedef uint64_t Type; BigInteger(const BigInteger& rhs) : count_(rhs.count_) { std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type)); } explicit BigInteger(uint64_t u) : count_(1) { digits_[0] = u; } BigInteger(const char* decimals, size_t length) : count_(1) { RAPIDJSON_ASSERT(length > 0); digits_[0] = 0; size_t i = 0; const size_t kMaxDigitPerIteration = 19; // 2^64 = 18446744073709551616 > 10^19 while (length >= kMaxDigitPerIteration) { AppendDecimal64(decimals + i, decimals + i + kMaxDigitPerIteration); length -= kMaxDigitPerIteration; i += kMaxDigitPerIteration; } if (length > 0) AppendDecimal64(decimals + i, decimals + i + length); } BigInteger& operator=(const BigInteger &rhs) { if (this != &rhs) { count_ = rhs.count_; std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type)); } return *this; } BigInteger& operator=(uint64_t u) { digits_[0] = u; count_ = 1; return *this; } BigInteger& operator+=(uint64_t u) { Type backup = digits_[0]; digits_[0] += u; for (size_t i = 0; i < count_ - 1; i++) { if (digits_[i] >= backup) return *this; // no carry backup = digits_[i + 1]; digits_[i + 1] += 1; } // Last carry if (digits_[count_ - 1] < backup) PushBack(1); return *this; } BigInteger& operator*=(uint64_t u) { if (u == 0) return *this = 0; if (u == 1) return *this; if (*this == 1) return *this = u; uint64_t k = 0; for (size_t i = 0; i < count_; i++) { uint64_t hi; digits_[i] = MulAdd64(digits_[i], u, k, &hi); k = hi; } if (k > 0) PushBack(k); return *this; } BigInteger& operator*=(uint32_t u) { if (u == 0) return *this = 0; if (u == 1) return *this; if (*this == 1) return *this = u; uint64_t k = 0; for (size_t i = 0; i < count_; i++) { const uint64_t c = digits_[i] >> 32; const uint64_t d = digits_[i] & 0xFFFFFFFF; const uint64_t uc = u * c; const uint64_t ud = u * d; const uint64_t p0 = ud + k; const uint64_t p1 = uc + (p0 >> 32); digits_[i] = (p0 & 0xFFFFFFFF) | (p1 << 32); k = p1 >> 32; } if (k > 0) PushBack(k); return *this; } BigInteger& operator<<=(size_t shift) { if (IsZero() || shift == 0) return *this; size_t offset = shift / kTypeBit; size_t interShift = shift % kTypeBit; RAPIDJSON_ASSERT(count_ + offset <= kCapacity); if (interShift == 0) { std::memmove(&digits_[count_ - 1 + offset], &digits_[count_ - 1], count_ * sizeof(Type)); count_ += offset; } else { digits_[count_] = 0; for (size_t i = count_; i > 0; i--) digits_[i + offset] = (digits_[i] << interShift) | (digits_[i - 1] >> (kTypeBit - interShift)); digits_[offset] = digits_[0] << interShift; count_ += offset; if (digits_[count_]) count_++; } std::memset(digits_, 0, offset * sizeof(Type)); return *this; } bool operator==(const BigInteger& rhs) const { return count_ == rhs.count_ && std::memcmp(digits_, rhs.digits_, count_ * sizeof(Type)) == 0; } bool operator==(const Type rhs) const { return count_ == 1 && digits_[0] == rhs; } BigInteger& MultiplyPow5(unsigned exp) { static const uint32_t kPow5[12] = { 5, 5 * 5, 5 * 5 * 5, 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 }; if (exp == 0) return *this; for (; exp >= 27; exp -= 27) *this *= RAPIDJSON_UINT64_C2(0X6765C793, 0XFA10079D); // 5^27 for (; exp >= 13; exp -= 13) *this *= static_cast<uint32_t>(1220703125u); // 5^13 if (exp > 0) *this *= kPow5[exp - 1]; return *this; } // Compute absolute difference of this and rhs. // Assume this != rhs bool Difference(const BigInteger& rhs, BigInteger* out) const { int cmp = Compare(rhs); RAPIDJSON_ASSERT(cmp != 0); const BigInteger *a, *b; // Makes a > b bool ret; if (cmp < 0) { a = &rhs; b = this; ret = true; } else { a = this; b = &rhs; ret = false; } Type borrow = 0; for (size_t i = 0; i < a->count_; i++) { Type d = a->digits_[i] - borrow; if (i < b->count_) d -= b->digits_[i]; borrow = (d > a->digits_[i]) ? 1 : 0; out->digits_[i] = d; if (d != 0) out->count_ = i + 1; } return ret; } int Compare(const BigInteger& rhs) const { if (count_ != rhs.count_) return count_ < rhs.count_ ? -1 : 1; for (size_t i = count_; i-- > 0;) if (digits_[i] != rhs.digits_[i]) return digits_[i] < rhs.digits_[i] ? -1 : 1; return 0; } size_t GetCount() const { return count_; } Type GetDigit(size_t index) const { RAPIDJSON_ASSERT(index < count_); return digits_[index]; } bool IsZero() const { return count_ == 1 && digits_[0] == 0; } private: void AppendDecimal64(const char* begin, const char* end) { uint64_t u = ParseUint64(begin, end); if (IsZero()) *this = u; else { unsigned exp = static_cast<unsigned>(end - begin); (MultiplyPow5(exp) <<= exp) += u; // *this = *this * 10^exp + u } } void PushBack(Type digit) { RAPIDJSON_ASSERT(count_ < kCapacity); digits_[count_++] = digit; } static uint64_t ParseUint64(const char* begin, const char* end) { uint64_t r = 0; for (const char* p = begin; p != end; ++p) { RAPIDJSON_ASSERT(*p >= '0' && *p <= '9'); r = r * 10u + static_cast<unsigned>(*p - '0'); } return r; } // Assume a * b + k < 2^128 static uint64_t MulAdd64(uint64_t a, uint64_t b, uint64_t k, uint64_t* outHigh) { #if defined(_MSC_VER) && defined(_M_AMD64) uint64_t low = _umul128(a, b, outHigh) + k; if (low < k) (*outHigh)++; return low; #elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__) __extension__ typedef unsigned __int128 uint128; uint128 p = static_cast<uint128>(a) * static_cast<uint128>(b); p += k; *outHigh = static_cast<uint64_t>(p >> 64); return static_cast<uint64_t>(p); #else const uint64_t a0 = a & 0xFFFFFFFF, a1 = a >> 32, b0 = b & 0xFFFFFFFF, b1 = b >> 32; uint64_t x0 = a0 * b0, x1 = a0 * b1, x2 = a1 * b0, x3 = a1 * b1; x1 += (x0 >> 32); // can't give carry x1 += x2; if (x1 < x2) x3 += (static_cast<uint64_t>(1) << 32); uint64_t lo = (x1 << 32) + (x0 & 0xFFFFFFFF); uint64_t hi = x3 + (x1 >> 32); lo += k; if (lo < k) hi++; *outHigh = hi; return lo; #endif } static const size_t kBitCount = 3328; // 64bit * 54 > 10^1000 static const size_t kCapacity = kBitCount / sizeof(Type); static const size_t kTypeBit = sizeof(Type) * 8; Type digits_[kCapacity]; size_t count_; }; } // namespace internal RAPIDJSON_NAMESPACE_END #endif // RAPIDJSON_BIGINTEGER_H_