# 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
```rust
self.hash = i | (i.wrapping_mul(FRAC_U64MAX_PI) << 32);
```
with `i` being `(generation << 32) | index`.
Expanding things out, we get
```rust
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.)
```rust
(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.)
---
## Changelog
(Probably skip it)
## Migration Guide
(none needed)
a902ea6f85