Optimizing a floating point division and conversion operation

Question

I have the following formula

float mean = (r+b+g)/3/255.0f;

I want to speed it up. There are the following preconditions

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Answer 1

Pre-convert your divisions into a multiplicable constant:

a / 3 / 255

is the same as

a * (1 / (3 * 255))

so pre-compute:

const float AVERAGE_SCALE_FACTOR = 1.f / (3.f * 255.f)

then just do

float mean = (r + g + b) * AVERAGE_SCALE_FACTOR;

since multiplying is generally a lot faster than dividing.