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Comment by codefreakxff | Hacker News Reader

Not being snarky, at the simplest level by knowing x ahead of time you can change your code from y = n/2 into y = n * 0.5. Not wildly important by itself, but in a loop - maybe… I suspect compilers optimize for that already.

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I still don't get it. How do you know that 1/x = 0.abc... without performing the division? I mean in general case, not in something matching binary tricks. Such as 1/3 for example. Unless you mean you somehow know the value of 1/x ahead of time. But where does it come from?

If you know the divisor x ahead of time you can pre-compute 1/x at compile time, so that your actual compiled code never does the division--only your compiler does. Your actual compiled code just does the multiplication by a pre-computed constant (and the compiled code doesn't have to know that that constant was pre-computed as the reciprocal of x).

Ah, thanks for clarifying.

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.)

so basically just precompute all the answers you will need and then just look up the values later?

There’s no lookup needed if the value is constant

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