def log_taylor_cached(x, prec):
    """
    Fixed-point computation of log(x), assuming x in (0.5, 2)
    and prec <= LOG_TAYLOR_PREC.
    """
    n = x >> (prec-LOG_TAYLOR_SHIFT)
    cached_prec = cache_prec_steps[prec]
    dprec = cached_prec - prec
    if (n, cached_prec) in log_taylor_cache:
        a, log_a = log_taylor_cache[n, cached_prec]
    else:
        a = n << (cached_prec - LOG_TAYLOR_SHIFT)
        log_a = log_taylor(a, cached_prec, 8)
        log_taylor_cache[n, cached_prec] = (a, log_a)
    a >>= dprec
    log_a >>= dprec
    u = ((x - a) << prec) // a
    v = (u << prec) // ((MPZ_TWO << prec) + u)
    v2 = (v*v) >> prec
    v4 = (v2*v2) >> prec
    s0 = v
    s1 = v//3
    v = (v*v4) >> prec
    k = 5
    while v:
        s0 += v//k
        k += 2
        s1 += v//k
        v = (v*v4) >> prec
        k += 2
    s1 = (s1*v2) >> prec
    s = (s0+s1) << 1
    return log_a + s
dataset/ETHPy150Open fredrik-johansson/mpmath/mpmath/libmp/libelefun.py/log_taylor_cached/original