Save an instruction in EntityHasher

[scottmcm]

Objective

Keep essentially the same structure of EntityHasher from #9903, but rephrase the multiplication slightly to save an instruction.

cc @superdump
Discord thread: https://discord.com/channels/691052431525675048/1172033156845674507/1174969772522356756

Solution

Today, the hash is

        self.hash = i | (i.wrapping_mul(FRAC_U64MAX_PI) << 32);

with i being (generation << 32) | index.

Expanding things out, we get

i | ( (i * CONST) << 32 )
= (generation << 32) | index | ((((generation << 32) | index) * CONST) << 32)
= (generation << 32) | index | ((index * CONST) << 32)  // because the generation overflowed
= (index * CONST | generation) << 32 | index

What if we do the same thing, but with + instead of |? That's almost the same thing, except that it has carries, which are actually often better in a hash function anyway, since it doesn't saturate. (| can be dangerous, since once something becomes -1 it'll stay that, and there's no mixing available.)

(index * CONST + generation) << 32 + index
= (CONST << 32 + 1) * index + generation << 32
= (CONST << 32 + 1) * index + (WHATEVER << 32 + generation) << 32 // because the extra overflows and thus can be anything
= (CONST << 32 + 1) * index + ((CONST * generation) << 32 + generation) << 32 // pick "whatever" to be something convenient
= (CONST << 32 + 1) * index + ((CONST << 32 + 1) * generation) << 32
= (CONST << 32 + 1) * index +((CONST << 32 + 1) * (generation << 32)
= (CONST << 32 + 1) * (index + generation << 32)
= (CONST << 32 + 1) * (generation << 32 | index)
= (CONST << 32 + 1) * i

So we can do essentially the same thing using a single multiplication instead of doing multiply-shift-or.

LLVM was already smart enough to merge the shifting into a multiplication, but this saves the extra or:

https://rust.godbolt.org/z/MEvbz4eo4

It's a very small change, and often will disappear in load latency anyway, but it's a couple percent faster in lookups:

(There was more of an improvement here before #10558, but with to_bits being a single qword load now, keeping things mostly as it is turned out to be better than the bigger changes I'd tried in #10605.)

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Changelog

(Probably skip it)

Migration Guide

(none needed)

[james7132]

This looks good, with the appropriate tests and documentation all the way through. One thing that did bother me about #10605 was that the stress tests seemed to show improvements that were potentially within the margin of error. I know this is asking more from an already thorough PR, but could you rerun those stress tests to see if the improvements are still there?

[mockersf]

(and also rebase or merge main in to get the latest change in CI)

[alice-i-cecile]

Can you please rebase / merge in main to get the latest CI check running on your PR?