Question about terbulence of Perlin noise (book 2)

[ttzytt]

The code for turbulence is on following:

double turb(const point3& p, int depth=7) const {
    auto accum = 0.0;
    auto temp_p = p;
    auto weight = 1.0;

    for (int i = 0; i < depth; i++) {
        accum += weight*noise(temp_p);
        weight *= 0.5;
        temp_p *= 2;
    }

    return fabs(accum);
}

weight started with 1.0, but the maximum value for noise(temp_p) is also 1.0. Then would it be possible that the returned fabs(accum) exceed 1.0?

[ttzytt]

However, if I try to make sure that the returned value does not exceed 1 by dividing the returned value by the maximum possible value (1 + 0.5 + 0.25 + 0.125 ...), the output image will be dimmer, and I personally think that's worse then the original version.