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 // 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.
 //
 // 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(__INTEL_COMPILER) && defined(_M_AMD64)
 #include <intrin.h> // for _umul128
 #if !defined(_ARM64EC_)
 #pragma intrinsic(_umul128)
 #else
 #pragma comment(lib, "softintrin")
 #endif
 #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; }
  
     template <typename Ch>
     BigInteger(const Ch* 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:
     template <typename Ch>
     void AppendDecimal64(const Ch* begin, const Ch* 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;
     }
  
     template <typename Ch>
     static uint64_t ParseUint64(const Ch* begin, const Ch* end)
     {
         uint64_t r = 0;
         for(const Ch* p = begin; p != end; ++p)
         {
             RAPIDJSON_ASSERT(*p >= Ch('0') && *p <= Ch('9'));
             r = r * 10u + static_cast<unsigned>(*p - Ch('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 defined(__GNUC__) && (__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_