text: // Copyright (c) 2014-2018, The Monero Project
  // Copyright (c)      2018, The Loki Project
  // Copyright (c)      2018, The Kredits Project
  //
  // All rights reserved.
  //
  // Redistribution and use in source and binary forms, with or without modification, are
  // permitted provided that the following conditions are met:
  //
  // 1. Redistributions of source code must retain the above copyright notice, this list of
  //    conditions and the following disclaimer.
  //
  // 2. Redistributions in binary form must reproduce the above copyright notice, this list
  //    of conditions and the following disclaimer in the documentation and/or other
  //    materials provided with the distribution.
  //
  // 3. Neither the name of the copyright holder nor the names of its contributors may be
  //    used to endorse or promote products derived from this software without specific
  //    prior written permission.
  //
  // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
  // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
  // MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
  // THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
  // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  // STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
  // THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  //
  // Parts of this file are originally copyright (c) 2012-2013 The Cryptonote developers
  
  #include <algorithm>
  #include <cassert>
  #include <cstddef>
  #include <cstdint>
  #include <vector>
  
  #include "common/kredits.h"
  #include "int-util.h"
  #include "crypto/hash.h"
  #include "cryptonote_config.h"
  #include "difficulty.h"
  
  #undef KREDITS_DEFAULT_LOG_CATEGORY
  #define KREDITS_DEFAULT_LOG_CATEGORY "difficulty"
  
  namespace cryptonote {
  
    using std::size_t;
    using std::uint64_t;
    using std::vector;
  
  #if defined(__x86_64__)
    static inline void mul(uint64_t a, uint64_t b, uint64_t &low, uint64_t &high) {
      low = mul128(a, b, &high);
    }
  
  #else
  
    static inline void mul(uint64_t a, uint64_t b, uint64_t &low, uint64_t &high) {
      // __int128 isn't part of the standard, so the previous function wasn't portable. mul128() in Windows is fine,
      // but this portable function should be used elsewhere. Credit for this function goes to latexi95.
  
      uint64_t aLow = a & 0xFFFFFFFF;
      uint64_t aHigh = a >> 32;
      uint64_t bLow = b & 0xFFFFFFFF;
      uint64_t bHigh = b >> 32;
  
      uint64_t res = aLow * bLow;
      uint64_t lowRes1 = res & 0xFFFFFFFF;
      uint64_t carry = res >> 32;
  
      res = aHigh * bLow + carry;
      uint64_t highResHigh1 = res >> 32;
      uint64_t highResLow1 = res & 0xFFFFFFFF;
  
      res = aLow * bHigh;
      uint64_t lowRes2 = res & 0xFFFFFFFF;
      carry = res >> 32;
  
      res = aHigh * bHigh + carry;
      uint64_t highResHigh2 = res >> 32;
      uint64_t highResLow2 = res & 0xFFFFFFFF;
  
      //Addition
  
      uint64_t r = highResLow1 + lowRes2;
      carry = r >> 32;
      low = (r << 32) | lowRes1;
      r = highResHigh1 + highResLow2 + carry;
      uint64_t d3 = r & 0xFFFFFFFF;
      carry = r >> 32;
      r = highResHigh2 + carry;
      high = d3 | (r << 32);
    }
  
  #endif
  
    static inline bool cadd(uint64_t a, uint64_t b) {
      return a + b < a;
    }
  
    static inline bool cadc(uint64_t a, uint64_t b, bool c) {
      return a + b < a || (c && a + b == (uint64_t) -1);
    }
  
    bool check_hash(const crypto::hash &hash, difficulty_type difficulty) {
      uint64_t low, high, top, cur;
      // First check the highest word, this will most likely fail for a random hash.
      mul(swap64le(((const uint64_t *) &hash)[3]), difficulty, top, high);
      if (high != 0) {
        return false;
      }
      mul(swap64le(((const uint64_t *) &hash)[0]), difficulty, low, cur);
      mul(swap64le(((const uint64_t *) &hash)[1]), difficulty, low, high);
      bool carry = cadd(cur, low);
      cur = high;
      mul(swap64le(((const uint64_t *) &hash)[2]), difficulty, low, high);
      carry = cadc(cur, low, carry);
      carry = cadc(high, top, carry);
      return !carry;
    }
  
    // LWMA difficulty algorithm
    // Background:  https://github.com/zawy12/difficulty-algorithms/issues/3
    // Copyright (c) 2017-2018 Zawy (pseudocode)
    // MIT license http://www.opensource.org/licenses/mit-license.php
    // Copyright (c) 2018 Wownero Inc., a Monero Enterprise Alliance partner company
    // Copyright (c) 2018 The Karbowanec developers (initial code)
    // Copyright (c) 2018 Haven Protocol (refinements)
    // Degnr8, Karbowanec, Masari, Bitcoin Gold, Bitcoin Candy, and Haven have contributed.
  
    // This algorithm is: next_difficulty = harmonic_mean(Difficulties) * T / LWMA(Solvetimes)
    // The harmonic_mean(Difficulties) = 1/average(Targets) so it is also:
    // next_target = avg(Targets) * LWMA(Solvetimes) / T.
    // This is "the best algorithm" because it has lowest root-mean-square error between 
    // needed & actual difficulty during hash attacks while having the lowest standard 
    // deviation during stable hashrate. That is, it's the fastest for a given stability and vice versa.
    // Do not use "if solvetime < 1 then solvetime = 1" which allows a catastrophic exploit.
    // Do not sort timestamps.  "Solvetimes" and "LWMA" variables must allow negatives.
    // Do not use MTP as most recent block.  Do not use (POW)Limits, filtering, or tempering.
    // Do not forget to set N (aka DIFFICULTY_WINDOW in Cryptonote) to recommendation below.
    // The nodes' future time limit (FTL) aka CRYPTONOTE_BLOCK_FUTURE_TIME_LIMIT needs to
    // be reduced from 60*60*2 to 500 seconds to prevent timestamp manipulation from miner's with 
    //  > 50% hash power.  If this is too small, it can be increased to 1000 at a cost in protection.
  
    // Cryptonote clones:  #define DIFFICULTY_BLOCKS_COUNT_V2 DIFFICULTY_WINDOW_V2 + 1
  
  
    difficulty_type next_difficulty_v2(std::vector<std::uint64_t> timestamps, std::vector<difficulty_type> cumulative_difficulties, size_t target_seconds, bool use_old_lwma) {
  
      const int64_t T = static_cast<int64_t>(target_seconds);
  
      size_t N = DIFFICULTY_WINDOW_V2 - 1;
  
      // Return a difficulty of 1 for first 4 blocks if it's the start of the chain.
      if (timestamps.size() < 4) {
        return 1;
      }
      // Otherwise, use a smaller N if the start of the chain is less than N+1.
      else if ( timestamps.size()-1 < N ) {
        N = timestamps.size() - 1;
      }
      // Otherwise make sure timestamps and cumulative_difficulties are correct size.
      else {
        // TODO: put asserts here, so that the difficulty algorithm is never called with an oversized window
        //       OR make this use the last N+1 timestamps and cum_diff, not the first.
        timestamps.resize(N+1);
        cumulative_difficulties.resize(N+1);
      }
      // To get an average solvetime to within +/- ~0.1%, use an adjustment factor.
      // adjust=0.999 for 80 < N < 120(?)
      const double adjust = 0.998;
      // The divisor k normalizes the LWMA sum to a standard LWMA.
      const double k = N * (N + 1) / 2;
  
      double LWMA(0), sum_inverse_D(0), harmonic_mean_D(0), nextDifficulty(0);
      int64_t solveTime(0);
      uint64_t difficulty(0), next_difficulty(0);
  
      // Loop through N most recent blocks. N is most recently solved block.
      for (int64_t i = 1; i <= (int64_t)N; i++) {
        solveTime = static_cast<int64_t>(timestamps[i]) - static_cast<int64_t>(timestamps[i - 1]);
  
        if (use_old_lwma) solveTime = std::max<int64_t>(solveTime, (-7 * T));
        solveTime = std::min<int64_t>(solveTime, (T * 7));
  
        difficulty = cumulative_difficulties[i] - cumulative_difficulties[i - 1];
        LWMA += (solveTime * i) / k;
        sum_inverse_D += 1 / static_cast<double>(difficulty);
      }
  
      harmonic_mean_D = N / sum_inverse_D;
  
      // Keep LWMA sane in case something unforeseen occurs.
      if (static_cast<int64_t>(kredits::round(LWMA)) < T / 20)
        LWMA = static_cast<double>(T / 20);
  
      nextDifficulty = harmonic_mean_D * T / LWMA * adjust;
  
      // No limits should be employed, but this is correct way to employ a 20% symmetrical limit:
      // nextDifficulty=max(previous_Difficulty*0.8,min(previous_Difficulty/0.8, next_Difficulty));
      next_difficulty = static_cast<uint64_t>(nextDifficulty);
  
      if (next_difficulty == 0)
          next_difficulty = 1;
  
      return next_difficulty;
    }
  }
  