Target adjustment simulation

simul.cpp

#include <math.h>
#include <stdio.h>
#include <random>

#define RETARGET_INTERVAL 2016
#define INTERBLOCK_TIME 600

#define PERIODS 10000

static std::random_device rng;
static std::mt19937 gen(rng());

static inline long double time_for_next_block(long double rate) {
    std::exponential_distribution<long double> dist(rate);
    return dist(gen);
}

int main(void) {
    //! The timestamps of the past 2016 blocks
    int64_t blocktimes[RETARGET_INTERVAL];

    //! The current timestamp
    long double ts = 0;

    //! The current difficulty (the hashrate is held constant at 1 H/s)
    // It doesn't matter what value we start at (it'll converge), but
    // we expect a target that corresponds to a rate of one block per
    // INTERBLOCK_TIME.
    long double target = powl(2.0, 256) / INTERBLOCK_TIME;

    for (int j = 0; j < PERIODS; ++j) {
        // Adjust difficulty (except in the first period)
        if (j > 0) {
            int64_t timediff = blocktimes[RETARGET_INTERVAL-1] - blocktimes[0];
            target *= timediff;
            target /= (INTERBLOCK_TIME*RETARGET_INTERVAL);
        }

        // Simulate the creation of blocks in that interval
        for (int i = 0; i < RETARGET_INTERVAL; ++i) {
            ts += time_for_next_block(target / powl(2.0, 256));

            // Blocks use the current timestamp
            blocktimes[i] = int64_t(ts);
        }
    }
    printf("Average block time %.15Lg\n", ts / (RETARGET_INTERVAL*PERIODS));
    return(0);
}