import math

# fdlibm's split of ln 2: the high part has trailing zero bits, so e * LN2_HI
# is exact for any exponent a double can have.
LN2_HI = 6.93147180369123816490e-01
LN2_LO = 1.90821492927058770002e-10
SQRT2 = 1.4142135623730951


def ln(x: float) -> float:
    """Natural logarithm using only +, -, * and /.

    math.log comes from the platform's C library, whose last bit may differ
    from JavaScript's and Rust's. This follows the same steps in the same
    order as the TypeScript and Rust versions, so all three return the same
    double. See the README for the method.
    """
    if isinstance(x, bool) or not isinstance(x, (int, float)) or not math.isfinite(x) or x <= 0:
        raise ValueError("ln is only defined for finite numbers greater than zero, received %r" % (x,))
    m = float(x)
    e = 0
    while m >= 2:
        m /= 2
        e += 1
    while m < 1:
        m *= 2
        e -= 1
    if m > SQRT2:
        m /= 2
        e += 1
    f = m - 1
    s = f / (2 + f)
    z = s * s
    p = 1 / 25
    p = 1 / 23 + z * p
    p = 1 / 21 + z * p
    p = 1 / 19 + z * p
    p = 1 / 17 + z * p
    p = 1 / 15 + z * p
    p = 1 / 13 + z * p
    p = 1 / 11 + z * p
    p = 1 / 9 + z * p
    p = 1 / 7 + z * p
    p = 1 / 5 + z * p
    p = 1 / 3 + z * p
    lnm = 2 * s + 2 * s * (z * p)
    return e * LN2_HI + (e * LN2_LO + lnm)