Often, you can amortize a division or reciprocal by calculating it once and then reusing it. Frequently the divisor is dynamic, but reused locally.
For example, if you want to normalize a 3D vector you could do:
mag = sqrt(x*x + y*y + z*z)
x /= mag
y /= mag
z /= mag
That's three divisions with the same divisor. But you could instead do:
invMag = 1.0 / sqrt(x*x + y*y + z*z)
x *= invMag
y *= invMag
z *= invMag
There's still a single division (or reciprocal) done here. But you've eliminated at least the other two. (And it's even better if you have an rsqrt function.)
Comments
Often, you can amortize a division or reciprocal by calculating it once and then reusing it. Frequently the divisor is dynamic, but reused locally.
For example, if you want to normalize a 3D vector you could do:
That's three divisions with the same divisor. But you could instead do: There's still a single division (or reciprocal) done here. But you've eliminated at least the other two. (And it's even better if you have an rsqrt function.)