signet/miner: reduce default interblock interval limit to 30min

[ajtowns]

Reduces the cap on the time between blocks from 60 minutes to 30 minutes, and makes it configurable.

[ajtowns]

signet/miner --poisson attempts to simulate the distribution of times you'd see on mainnet. My original reasoning for the 60 minute cap is that you only expect 0.25% of blocks to take that long, so what does it matter. With a lower cap it seems worthwhile checking what that effects. I think you can work out the expected average with a cap as follows:

def expected_times(tgt, N=100000):
    return [tgt*-math.log(1-i*1.0/N) for i in range(N)]

def capped_average(seq, cap):
    sum, cnt = 0,0
    for v in seq:
        sum += min(v, cap)
        cnt += 1
    return sum/cnt

def bisect(f, want, l=0, h=100000, prec=0.0005):
    while l + prec < h:
        m = (l + h)/2
        if f(m) < want:
            l = m
        else:
            h = m
    return h

for cap in [11, 15, 16, 20, 25, 30, 45, 60]:
    tgt = bisect(lambda t: capped_average(expected_times(t), cap*60), 600)
    print("cap=%dmin, tgt=%.2fmin, average=%ds" % (cap, tgt/60, capped_average(expected_times(tgt), cap*60)))

# results:
# cap=11min, tgt=56.78min, average=600.0s
# cap=15min, tgt=17.16min, average=600.0s
# cap=16min, tgt=15.58min, average=600.0s
# cap=20min, tgt=12.55min, average=600.0s
# cap=25min, tgt=11.20min, average=600.0s
# cap=30min, tgt=10.63min, average=600.0s
# cap=45min, tgt=10.12min, average=600.0s
# cap=60min, tgt=10.03min, average=600.0s

That is, if you have a cap of 30 minutes, you need to be trying to have blocks every 10.63 minutes instead of every ten minutes because after applying the cap, you actual average will be reduced by that much. Effectively, this means the actual difficulty will generally be somewhat above the --nbits target, causing the signet miner to attempt to reduce the difficulty by mining more slowly, but that reduction will be offset in practice by the cap.

It seems to me like 30 minutes is a nice round figure that doesn't cause anything to get too weird; and I've used 16minutes as a lower limit, since below that, you're targetting an average block interval that's higher than your maximum acceptable block interval, so it's probably better to just not use --poisson at all at that point, I think.

[kallewoof]

Looks good to me.