[orlp]

> It just makes it O(n) where n := 64

That's O(1).

> The LZCNT operation itself is a loop over all bits

That's not how circuits work. You can easily make a circuit of O(log n) depth that returns base-2 encoded index of the first 1 bit in a n-bit register.

But since n is just 64 here, you're looking at a circuit of AND/OR depth ~8, so it's no surprise that modern CPUs can compute the LZCNT / TZCNT of a 64-bit integer in a single CPU cycle.

[sapiogram]

Note that rustc will not emit this instruction by default, to support older CPUs. Without `target-cpu=haswell` or similar, the operation will be quite slow, but still O(1) of course.

[jsheard]

It's not that bad, all x86 processors have the BSR instruction which can be mapped to LZCNT semantics with just a few extra instructions.

Left to right - modern x86-64, baseline x86-64, baseline i686:

https://rust.godbolt.org/z/nGsM35TEo

Maybe you're thinking of POPCNT, which hurts a lot more if it doesn't compile down to the native instruction:

https://rust.godbolt.org/z/xcxG3v4Mn

[SkiFire13]

> That's O(1).

A loop over 2^64 elements is also O(1), but I don't think people are ok to label every program that can run on a 64 bit pc as O(1).

[xboxnolifes]

You should really refresh yourself on Big-O notation.