Optimize clamp

[kimikage]

This adds a specialized method for clamp with all arguments in the same FixedPoint type. This also supports the new clamp(x, T) method (cf. JuliaLang/julia#34426).

This partially solves #179, but this is not helpful in cases where promotions occur.
cc: @johnnychen94

[codecov]

Codecov Report

Merging #194 into master will increase coverage by 0.04%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #194      +/-   ##
==========================================
+ Coverage   89.11%   89.15%   +0.04%     
==========================================
  Files           6        6              
  Lines         450      452       +2     
==========================================
+ Hits          401      403       +2     
  Misses         49       49              

Impacted Files	Coverage Δ
src/FixedPointNumbers.jl	86.66% <100.00%> (+0.25%)	⬆️

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[kimikage]

julia> @btime clamp.(x, 0.1N0f8, 0.9N0f8) setup=(x=collect(rand(N0f8, 512, 512)));
  460.800 μs (2 allocations: 256.14 KiB) # before (Julia ｖ1.4.2)
  11.801 μs (2 allocations: 256.14 KiB) # after (Julia ｖ1.4.2)

It seems to be faster on Julia v1.6.0-DEV for large arrays.

[timholy]

At least on Julia 1.5, doesn't this give the same codegen?

julia> @code_typed clamp(0.5N0f8, 0N0f8, 1N0f8)
CodeInfo(
1 ─ %1 = Base.getfield(hi, :i)::UInt8
│   %2 = Base.getfield(x, :i)::UInt8
│   %3 = Base.ult_int(%1, %2)::Bool
│   %4 = Base.getfield(x, :i)::UInt8
│   %5 = Base.getfield(lo, :i)::UInt8
│   %6 = Base.ult_int(%4, %5)::Bool
│   %7 = Base.Math.ifelse(%6, lo, x)::Normed{UInt8,8}
│   %8 = Base.Math.ifelse(%3, hi, %7)::Normed{UInt8,8}
└──      return %8
) => Normed{UInt8,8}

julia> newclamp(x::X, lo::X, hi::X) where {X <: FixedPoint} = X(clamp(x.i, lo.i, hi.i), 0)
newclamp (generic function with 1 method)

julia> @code_typed newclamp(0.5N0f8, 0N0f8, 1N0f8)
CodeInfo(
1 ─ %1 = Base.getfield(x, :i)::UInt8
│   %2 = Base.getfield(lo, :i)::UInt8
│   %3 = Base.getfield(hi, :i)::UInt8
│   %4 = Base.ult_int(%3, %1)::Bool
│   %5 = Base.ult_int(%1, %2)::Bool
│   %6 = Base.Math.ifelse(%5, %2, %1)::UInt8
│   %7 = Base.Math.ifelse(%4, %3, %6)::UInt8
│   %8 = %new(Normed{UInt8,8}, %7)::Normed{UInt8,8}
└──      return %8
) => Normed{UInt8,8}

[kimikage]

I believed that too (#179 (comment)), and I don't know the cause, but the actual results are different (in v1.0.5, v1.4.2, v1.5.0-rc1 and v1.6.0-DEV). 😕

julia> @btime clamp(x,y,z) setup=(x=rand(N0f8); y=rand(N0f8); z=rand(N0f8)); # non-vectorized version is OK
  1.099 ns (0 allocations: 0 bytes) # before (Julia v1.5.0-rc1)
  1.099 ns (0 allocations: 0 bytes) # after (Julia v1.5.0-rc1)

julia> @btime clamp.(x, 0.1N0f8, 0.9N0f8) setup=(x=collect(rand(N0f8, 512, 512)));
  160.399 μs (2 allocations: 256.14 KiB) # before (Julia v1.5.0-rc1)
  15.300 μs (2 allocations: 256.14 KiB) # after (Julia v1.5.0-rc1)

[timholy]

That is pretty crazy. I don't understand either, but this is fine. Since it is surprising, perhaps add a code-comment linking to this PR? Then fine to merge.

[kimikage]

I think it's a common thing on Julia's auto-vectorization. 😅

Edit:
I added the comment. I will merge this after a while. Done.