import numpy as np
from numba import jit

@jit(nopython=True)
def kahan_harmonic_sum(n):
    s = 0
    c = 0
    for i in range(1, n + 1):
        y = 1 / i - c
        t = s + y
        c = (t - s) - y
        s = t
    return s

@jit
def euler(precision=1e-10):
    max_iter = int(1/precision)
    return kahan_harmonic_sum(max_iter) - np.log(max_iter, dtype=np.float128)