text: // 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 "src/json/rapidjson/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_
  