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Comment by jvickers | Hacker News Reader

In JavaScript (specifically node / V8) if dividing multiple values by the same divisor, is it fastest to calculate the reciprocal and then multiply it?

How about other languages (and compiler systems)?

Are there binary tricks worth knowing about to quickly calculate reciprocals?

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It's typically faster to calculate a reciprocal (especially at compile time) and then multiply it, but this is often at the expense of precision. In C++, for example, the -O3 flag on gcc will still emit a division (divss) to preserve compliant floating point precision in this example: https://godbolt.org/z/PY3Wjno4P

However, when we enable `-ffast-math`, we permit the compiler to do a bit more aggressive optimization in this domain (trading off precision), and we see multiplication (mulss) is emitted: https://godbolt.org/z/KEb1nc43z

> Are there binary tricks worth knowing about to quickly calculate reciprocals?

Yes! You can calculate an approximate reciprocal with a single subtraction and some type-casting or bit manipulation.

The accuracy isn’t great (relative error of up to ~5%), but it might be good enough for many applications. The method is famous for being used to normalize 3d vectors in Quake https://en.wikipedia.org/wiki/Fast_inverse_square_root

This same method for calculating 1/x^2 can also be used to calculate 1/x by using a different magic constant and skipping the shift-right by one bit.

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