text: // Copyright (c) 2009-2010 Satoshi Nakamoto
  // Copyright (c) 2009-2018 The Bitcoin Core developers
  // Distributed under the MIT software license, see the accompanying
  // file COPYING or http://www.opensource.org/licenses/mit-license.php.
  
  #include <arith_uint256.h>
  
  #include <uint256.h>
  #include <crypto/common.h>
  
  #include <stdio.h>
  #include <string.h>
  
  template <unsigned int BITS>
  base_uint<BITS>::base_uint(const std::string& str)
  {
      static_assert(BITS/32 > 0 && BITS%32 == 0, "Template parameter BITS must be a positive multiple of 32.");
  
      SetHex(str);
  }
  
  template <unsigned int BITS>
  base_uint<BITS>& base_uint<BITS>::operator<<=(unsigned int shift)
  {
      base_uint<BITS> a(*this);
      for (int i = 0; i < WIDTH; i++)
          pn[i] = 0;
      int k = shift / 32;
      shift = shift % 32;
      for (int i = 0; i < WIDTH; i++) {
          if (i + k + 1 < WIDTH && shift != 0)
              pn[i + k + 1] |= (a.pn[i] >> (32 - shift));
          if (i + k < WIDTH)
              pn[i + k] |= (a.pn[i] << shift);
      }
      return *this;
  }
  
  template <unsigned int BITS>
  base_uint<BITS>& base_uint<BITS>::operator>>=(unsigned int shift)
  {
      base_uint<BITS> a(*this);
      for (int i = 0; i < WIDTH; i++)
          pn[i] = 0;
      int k = shift / 32;
      shift = shift % 32;
      for (int i = 0; i < WIDTH; i++) {
          if (i - k - 1 >= 0 && shift != 0)
              pn[i - k - 1] |= (a.pn[i] << (32 - shift));
          if (i - k >= 0)
              pn[i - k] |= (a.pn[i] >> shift);
      }
      return *this;
  }
  
  template <unsigned int BITS>
  base_uint<BITS>& base_uint<BITS>::operator*=(uint32_t b32)
  {
      uint64_t carry = 0;
      for (int i = 0; i < WIDTH; i++) {
          uint64_t n = carry + (uint64_t)b32 * pn[i];
          pn[i] = n & 0xffffffff;
          carry = n >> 32;
      }
      return *this;
  }
  
  template <unsigned int BITS>
  base_uint<BITS>& base_uint<BITS>::operator*=(const base_uint& b)
  {
      base_uint<BITS> a;
      for (int j = 0; j < WIDTH; j++) {
          uint64_t carry = 0;
          for (int i = 0; i + j < WIDTH; i++) {
              uint64_t n = carry + a.pn[i + j] + (uint64_t)pn[j] * b.pn[i];
              a.pn[i + j] = n & 0xffffffff;
              carry = n >> 32;
          }
      }
      *this = a;
      return *this;
  }
  
  template <unsigned int BITS>
  base_uint<BITS>& base_uint<BITS>::operator/=(const base_uint& b)
  {
      base_uint<BITS> div = b;     // make a copy, so we can shift.
      base_uint<BITS> num = *this; // make a copy, so we can subtract.
      *this = 0;                   // the quotient.
      int num_bits = num.bits();
      int div_bits = div.bits();
      if (div_bits == 0)
          throw uint_error("Division by zero");
      if (div_bits > num_bits) // the result is certainly 0.
          return *this;
      int shift = num_bits - div_bits;
      div <<= shift; // shift so that div and num align.
      while (shift >= 0) {
          if (num >= div) {
              num -= div;
              pn[shift / 32] |= (1 << (shift & 31)); // set a bit of the result.
          }
          div >>= 1; // shift back.
          shift--;
      }
      // num now contains the remainder of the division.
      return *this;
  }
  
  template <unsigned int BITS>
  int base_uint<BITS>::CompareTo(const base_uint<BITS>& b) const
  {
      for (int i = WIDTH - 1; i >= 0; i--) {
          if (pn[i] < b.pn[i])
              return -1;
          if (pn[i] > b.pn[i])
              return 1;
      }
      return 0;
  }
  
  template <unsigned int BITS>
  bool base_uint<BITS>::EqualTo(uint64_t b) const
  {
      for (int i = WIDTH - 1; i >= 2; i--) {
          if (pn[i])
              return false;
      }
      if (pn[1] != (b >> 32))
          return false;
      if (pn[0] != (b & 0xfffffffful))
          return false;
      return true;
  }
  
  template <unsigned int BITS>
  double base_uint<BITS>::getdouble() const
  {
      double ret = 0.0;
      double fact = 1.0;
      for (int i = 0; i < WIDTH; i++) {
          ret += fact * pn[i];
          fact *= 4294967296.0;
      }
      return ret;
  }
  
  template <unsigned int BITS>
  std::string base_uint<BITS>::GetHex() const
  {
      return ArithToUint256(*this).GetHex();
  }
  
  template <unsigned int BITS>
  void base_uint<BITS>::SetHex(const char* psz)
  {
      *this = UintToArith256(uint256S(psz));
  }
  
  template <unsigned int BITS>
  void base_uint<BITS>::SetHex(const std::string& str)
  {
      SetHex(str.c_str());
  }
  
  template <unsigned int BITS>
  std::string base_uint<BITS>::ToString() const
  {
      return (GetHex());
  }
  
  template <unsigned int BITS>
  unsigned int base_uint<BITS>::bits() const
  {
      for (int pos = WIDTH - 1; pos >= 0; pos--) {
          if (pn[pos]) {
              for (int nbits = 31; nbits > 0; nbits--) {
                  if (pn[pos] & 1U << nbits)
                      return 32 * pos + nbits + 1;
              }
              return 32 * pos + 1;
          }
      }
      return 0;
  }
  
  // Explicit instantiations for base_uint<256>
  template base_uint<256>::base_uint(const std::string&);
  template base_uint<256>& base_uint<256>::operator<<=(unsigned int);
  template base_uint<256>& base_uint<256>::operator>>=(unsigned int);
  template base_uint<256>& base_uint<256>::operator*=(uint32_t b32);
  template base_uint<256>& base_uint<256>::operator*=(const base_uint<256>& b);
  template base_uint<256>& base_uint<256>::operator/=(const base_uint<256>& b);
  template int base_uint<256>::CompareTo(const base_uint<256>&) const;
  template bool base_uint<256>::EqualTo(uint64_t) const;
  template double base_uint<256>::getdouble() const;
  template std::string base_uint<256>::GetHex() const;
  template std::string base_uint<256>::ToString() const;
  template void base_uint<256>::SetHex(const char*);
  template void base_uint<256>::SetHex(const std::string&);
  template unsigned int base_uint<256>::bits() const;
  
  // This implementation directly uses shifts instead of going
  // through an intermediate MPI representation.
  arith_uint256& arith_uint256::SetCompact(uint32_t nCompact, bool* pfNegative, bool* pfOverflow)
  {
      int nSize = nCompact >> 24;
      uint32_t nWord = nCompact & 0x007fffff;
      if (nSize <= 3) {
          nWord >>= 8 * (3 - nSize);
          *this = nWord;
      } else {
          *this = nWord;
          *this <<= 8 * (nSize - 3);
      }
      if (pfNegative)
          *pfNegative = nWord != 0 && (nCompact & 0x00800000) != 0;
      if (pfOverflow)
          *pfOverflow = nWord != 0 && ((nSize > 34) ||
                                       (nWord > 0xff && nSize > 33) ||
                                       (nWord > 0xffff && nSize > 32));
      return *this;
  }
  
  uint32_t arith_uint256::GetCompact(bool fNegative) const
  {
      int nSize = (bits() + 7) / 8;
      uint32_t nCompact = 0;
      if (nSize <= 3) {
          nCompact = GetLow64() << 8 * (3 - nSize);
      } else {
          arith_uint256 bn = *this >> 8 * (nSize - 3);
          nCompact = bn.GetLow64();
      }
      // The 0x00800000 bit denotes the sign.
      // Thus, if it is already set, divide the mantissa by 256 and increase the exponent.
      if (nCompact & 0x00800000) {
          nCompact >>= 8;
          nSize++;
      }
      assert((nCompact & ~0x007fffff) == 0);
      assert(nSize < 256);
      nCompact |= nSize << 24;
      nCompact |= (fNegative && (nCompact & 0x007fffff) ? 0x00800000 : 0);
      return nCompact;
  }
  
  uint256 ArithToUint256(const arith_uint256 &a)
  {
      uint256 b;
      for(int x=0; x<a.WIDTH; ++x)
          WriteLE32(b.begin() + x*4, a.pn[x]);
      return b;
  }
  arith_uint256 UintToArith256(const uint256 &a)
  {
      arith_uint256 b;
      for(int x=0; x<b.WIDTH; ++x)
          b.pn[x] = ReadLE32(a.begin() + x*4);
      return b;
  }
  