from math import log, log1p

def n_naive(p,H):
    return max(2,(2 * H * log(1/(1-p)))**.5)

def n_clever(p,H):
    return max(2,(2 * H * -log1p(-p))**.5)

def dotable(f):
    bb = (16, 32, 64, 128, 256, 384, 512)
    pp = (1e-18, 1e-15, 1e-12, 1e-9, 1e-6, .001)
    pt = "1e-18 1e-15 1e-12 1e-9 1e-6 .1%".split()

    print("    " + " ".join(f"{p:>8}" for p in pt))
    for b in bb:
        print(end=f"{b:>3}")
        for p in pp:
            print(end=f" {f(p,2**b):8.3g}")
        print()

print("Naive")
dotable(n_naive)
print()

print("With log1p")
dotable(n_clever)