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@fastmath support for sum, prod, extrema and extrema! #49910

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@fastmath support for sum, prod, extrema and extrema! #49910

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f8f236b
`@fastmath` support for `sum`, `prod`, `extrema` and `extrema!`
matthias314 May 21, 2023
13e1a62
Merge branch 'master' into m3/fast-reductions
fingolfin Feb 13, 2024
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43 changes: 34 additions & 9 deletions base/fastmath.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -86,10 +86,14 @@ const fast_op =
:tan => :tan_fast,
:tanh => :tanh_fast,
# reductions
:sum => :sum_fast,
:prod => :prod_fast,
:maximum => :maximum_fast,
:minimum => :minimum_fast,
:maximum! => :maximum!_fast,
:minimum! => :minimum!_fast)
:minimum! => :minimum!_fast,
:extrema => :extrema_fast,
:extrema! => :extrema!_fast)

const rewrite_op =
Dict(:+= => :+,
Expand Down Expand Up @@ -368,16 +372,23 @@ end

# Reductions

maximum_fast(a; kw...) = Base.reduce(max_fast, a; kw...)
minimum_fast(a; kw...) = Base.reduce(min_fast, a; kw...)
add_sum_fast(x, y) = Base.add_sum(x, y)
add_sum_fast(x::T, y::T) where {T<:FloatTypes} = @fastmath x+y

maximum_fast(f, a; kw...) = Base.mapreduce(f, max_fast, a; kw...)
minimum_fast(f, a; kw...) = Base.mapreduce(f, min_fast, a; kw...)
mul_prod_fast(x, y) = Base.mul_prod(x, y)
mul_prod_fast(x::T, y::T) where {T<:FloatTypes} = @fastmath x*y

Base.reducedim_init(f, ::typeof(max_fast), A::AbstractArray, region) =
Base.reducedim_init(f, max, A::AbstractArray, region)
Base.reducedim_init(f, ::typeof(min_fast), A::AbstractArray, region) =
Base.reducedim_init(f, min, A::AbstractArray, region)
for (fred_fast, f, f_fast) in ((:sum_fast, :add_sum, :add_sum_fast),
(:prod_fast, :mul_prod, :mul_prod_fast),
(:maximum_fast, :max, :max_fast),
(:minimum_fast, :min, :min_fast))
@eval begin
Base.reducedim_init(f, ::typeof($f_fast), A::AbstractArray, region) =
Base.reducedim_init(f, Base.$f, A, region)
$fred_fast(a; kw...) = Base.reduce($f_fast, a; kw...)
$fred_fast(f, a; kw...) = Base.mapreduce(f, $f_fast, a; kw...)
end
end

maximum!_fast(r::AbstractArray, A::AbstractArray; kw...) =
maximum!_fast(identity, r, A; kw...)
Expand All @@ -389,4 +400,18 @@ maximum!_fast(f::Function, r::AbstractArray, A::AbstractArray; init::Bool=true)
minimum!_fast(f::Function, r::AbstractArray, A::AbstractArray; init::Bool=true) =
Base.mapreducedim!(f, min_fast, Base.initarray!(r, f, min, init, A), A)

_extrema_rf_fast((min1, max1), (min2, max2)) = (min_fast(min1, min2), max_fast(max1, max2))

Base.reducedim_init(f, ::typeof(_extrema_rf_fast), A::AbstractArray, region) =
Base.reducedim_init(f, Base._extrema_rf, A, region)

extrema_fast(a; kw...) = extrema_fast(identity, a; kw...)
extrema_fast(f, a; kw...) = Base.mapreduce(Base.ExtremaMap(f), _extrema_rf_fast, a; kw...)

extrema!_fast(r::AbstractArray, A::AbstractArray; kw...) =
extrema!_fast(identity, r, A; kw...)
extrema!_fast(f::Function, r::AbstractArray, A::AbstractArray; init::Bool=true) =
Base.mapreducedim!(Base.ExtremaMap(f), _extrema_rf_fast,
Base.initarray!(r, Base.ExtremaMap(f), Base._extrema_rf, init, A), A)

end
103 changes: 82 additions & 21 deletions test/fastmath.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -209,27 +209,88 @@ end
end

@testset "reductions" begin
@test @fastmath(maximum([1,2,3])) == 3
@test @fastmath(minimum([1,2,3])) == 1
@test @fastmath(maximum(abs2, [1,2,3+0im])) == 9
@test @fastmath(minimum(sqrt, [1,2,3])) == 1
@test @fastmath(maximum(Float32[4 5 6; 7 8 9])) == 9.0f0
@test @fastmath(minimum(Float32[4 5 6; 7 8 9])) == 4.0f0

@test @fastmath(maximum(Float32[4 5 6; 7 8 9]; dims=1)) == Float32[7.0 8.0 9.0]
@test @fastmath(minimum(Float32[4 5 6; 7 8 9]; dims=2)) == Float32[4.0; 7.0;;]
@test @fastmath(maximum(abs, [4+im -5 6-im; -7 8 -9]; dims=1)) == [7.0 8.0 9.0]
@test @fastmath(minimum(cbrt, [4 -5 6; -7 8 -9]; dims=2)) == cbrt.([-5; -9;;])

x = randn(3,4,5)
x1 = sum(x; dims=1)
x23 = sum(x; dims=(2,3))
@test @fastmath(maximum!(x1, x)) ≈ maximum(x; dims=1)
@test x1 ≈ maximum(x; dims=1)
@test @fastmath(minimum!(x23, x)) ≈ minimum(x; dims=(2,3))
@test x23 ≈ minimum(x; dims=(2,3))
@test @fastmath(maximum!(abs, x23, x .+ im)) ≈ maximum(abs, x .+ im; dims=(2,3))
@test @fastmath(minimum!(abs2, x1, x .+ im)) ≈ minimum(abs2, x .+ im; dims=1)
for T in (Int, Float16, Float32, Float64)
S = T == Int ? Float64 : T
x = @fastmath(sum(T[1,2,3,4]))
@test x isa T && x == 10
x = @fastmath(prod(T[1,2,3,4]))
@test x isa T && x == 24
x = @fastmath(sum(abs2, T[1,2,3]))
@test x isa T && x == 14
x = @fastmath(prod(sqrt, T[1,4,9]))
@test x isa S && x == 6
x = @fastmath(sum(T[1 2 3; 4 5 6]))
@test x isa T && x == 21
x = @fastmath(prod(T[1 2 3; 4 5 6]))
@test x isa T && x == 720

x = @fastmath(sum(T[4 5 6; 7 8 9]; dims=1))
@test x isa Matrix{T} && x == [11 13 15]
x = @fastmath(prod(T[4 5 6; 7 8 9]; dims=2))
@test x isa Matrix{T} && x == [120; 504;;]
x = @fastmath(sum(abs, Complex{T}[2im -2im 2im; -1 2 -3]; dims=1))
@test x isa Matrix{S} && x == [3 4 5]
x = @fastmath(prod(cbrt, T[1 -8 1; 8 1 -8]; dims=2))
@test x isa Matrix{S} && x == [-2; -4;;]
end

for T in (Int, Float16, Float32, Float64)
if T == Float16 ; continue end # necessary until #49907 is fixed
S = T == Int ? Float64 : T
y = @fastmath(maximum(T[1,2,3]))
@test y isa T && y == 3
y = @fastmath(minimum(T[1,2,3]))
@test y isa T && y == 1
y = @fastmath(extrema(T[1,2,3]))
@test y isa Tuple{T,T} && y == (1,3)
y = @fastmath(maximum(abs2, Complex{T}[1,2,3im]))
@test y isa T && y == 9
y = @fastmath(minimum(sqrt, T[1,2,3]))
@test y isa S && y == 1
y = @fastmath(extrema(abs, T[-1,-2,3]))
@test y isa Tuple{T,T} && y == (1,3)
y = @fastmath(maximum(T[4 5 6; 7 8 9]))
@test y isa T && y == 9
y = @fastmath(minimum(T[4 5 6; 7 8 9]))
@test y isa T && y == 4
y = @fastmath(extrema(T[4 5 6; 7 8 9]))
@test y isa Tuple{T,T} && y == (4,9)

y = @fastmath(maximum(T[4 5 6; 7 8 9]; dims=1))
@test y isa Matrix{T} && y == [7 8 9]
y = @fastmath(minimum(T[4 5 6; 7 8 9]; dims=2))
@test y isa Matrix{T} && y == [4; 7;;]
y = @fastmath(extrema(T[4 5 6; 7 8 9]; dims=2))
@test y isa Matrix{Tuple{T,T}} && y == [(4,6);(7,9);;]
y = @fastmath(maximum(abs, Complex{T}[4+im -5 6-im; -7 8 -9]; dims=1))
@test y isa Matrix{S} && y == T[7 8 9]
y = @fastmath(minimum(cbrt, T[4 -5 6; -7 8 -9]; dims=2))
@test y isa Matrix{S} && y == cbrt.(T[-5; -9;;])
y = @fastmath(extrema(abs, T[-4 5 6; 7 -8 -9]; dims=1))
@test y isa Matrix{Tuple{T,T}} && y == [(4,7) (5,8) (6,9)]

x = rand(T, 3,4,5)
x1 = sum(x; dims=1)
x23 = sum(x; dims=(2,3))
y1 = map(z -> (z,z), x1)
y23 = map(z -> (z,z), x23)
y = @fastmath(maximum!(x1, x))
@test y ≈ maximum(x; dims=1)
@test y === x1
y = @fastmath(minimum!(x23, x))
@test y ≈ minimum(x; dims=(2,3))
@test y === x23
@test @fastmath(maximum!(abs, x23, x .+ im)) ≈ maximum(abs, x .+ im; dims=(2,3))
@test @fastmath(minimum!(abs2, x1, x .+ im)) ≈ minimum(abs2, x .+ im; dims=1)
y = @fastmath(extrema!(y1, x))
@test map(z -> z[1], y) ≈ minimum(x; dims=1)
@test map(z -> z[2], y) ≈ maximum(x; dims=1)
@test y === y1
y = @fastmath(extrema!(y23, x))
@test map(z -> z[1], y) ≈ minimum(x; dims=(2,3))
@test map(z -> z[2], y) ≈ maximum(x; dims=(2,3))
@test y === y23
end
end

@testset "issue #10544" begin
Expand Down