biginteger.h

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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. 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_