[AlotOfReading]

A better value is 0x7eb504f3. You can follow that up with Newton-raphson to refine the approximation, or approximate the Newton-raphson too by multiplying 1.385356f*x.

I did this a few days ago in the approximate division thread: https://news.ycombinator.com/item?id=42481612#42489596

In some cases, it can be faster than hardware division.

[dahart]

Not sure I understand your number 0x7eb504f3 - does it require using the 1.385 factor? Is it possible there is a typo in the number? That value doesn’t make sense to me. I’m measuring error here as the absolute value of relative error, e.g., | (v - v_approx) / v |. With that constant alone plugged into the poster’s code, I get a much less accurate approximation, with a minimum error of at least ~0.27 (meaning it’s always far away from the target) and worst case error of ~0.293 over the input range [1/1000…1000]. For comparison, the original 0x7effffff error is min:0 max:0.125. With 0x7eeeebb3, the error I get is min:0 max:0.0667. With 0x7ef311bc, error is min:0 max:0.0505. It’s important that the min error over a large interval is zero, because it means the approximation actually touches the target at least once.