speed up Float16 conversions a bit

[JeffBezanson]

For me this speeds up the first benchmark in #29889 by about 20%, by removing all the unnecessary error checks. Hardly game-changing, but might as well.

[JeffBezanson]

Before:

julia> @time value_16 .*= mult;
  2.315576 seconds (6 allocations: 208 bytes)

After:

julia> @time value_16 .*= mult;
  1.801816 seconds (6 allocations: 208 bytes)

[JeffBezanson]

The tables are quite small, and can be made immutable and inlined, leading to

julia> @time value_16 .*= mult;
  1.206085 seconds (6 allocations: 208 bytes)

Almost 2x speedup. Now we're cooking!

[PeterJacko]

The tables are quite small, and can be made immutable and inlined, leading to

julia> @time value_16 .*= mult;
  1.206085 seconds (6 allocations: 208 bytes)

Almost 2x speedup. Now we're cooking!

Many thanks! Are you achieving the same speed-up also for mult = 1.0 rather then mult = 1? (See the second benchmark in #29889.) It seems that it might make sense to convert an integer multiplier to float to perform the multiplication.

[StefanKarpinski]

It seems that it might make sense to convert an integer multiplier to float to perform the multiplication.

This has to happen internally anyway—there's no way to directly multiply an int and a float (except for special cases with constants like 2x which can get implemented as x+x instead of a multiplication). The thing to avoid is converting the integer to a Float16 first via promotion and then back to Float32 for the multiplication. It will be really nice when LLVM supports Float16 directly.

[JeffBezanson]

There should also be some speedup for mult = 1.0 since it also requires Float16 conversions. But it needs fewer (which is why it's faster than the integer case), since:

The thing to avoid is converting the integer to a Float16 first via promotion and then back to Float32 for the multiplication.

Indeed we seem to be doing that. I guess we'll need a bunch of special methods to handle it better.