Integer log2 with 14-bit fractional part in Python

log2.py

def polyval_fixed(coeffs, x, scale):
    res = 0
    for c in coeffs:
        res = (((x * res) >> scale) + c)
    return res

def log2_approx(x):
    if x < 1:
        return 0

    # Return the integer logarithm
    log2_int = 0
    x_tmp = x
    while x_tmp > 1:
        log2_int += 1
        x_tmp >>= 1

    # Normalize the fractional part to 31 bits
    x -= (1 << log2_int)
    if x <= 0:
        return log2_int << 14
    x = x << (31 - log2_int)

    # Divide by 2^17, resulting in 14 bit dynamic range
    x >>= 17

    # Evaluate an order-three polynomial evaluating the logarithm on the
    # fractional part
    return polyval_fixed([2529, -9324, 23174, 0], x, 14) + (log2_int << 14)