| // 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) && !__INTEL_COMPILER && 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_ + offset, digits_, 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_ |