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Merge pull request #7106 from JuliaLang/dh/reducedim3
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Refactoring reducedim and related functions
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@lindahua
lindahua committed Jun 5, 2014
2 parents a1e9890 + 99193d9 commit 74a41d2
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3 changes: 1 addition & 2 deletions base/bitarray.jl
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Expand Up @@ -1385,8 +1385,7 @@ end

## Reductions ##

sum(A::BitArray, region) = reducedim(+, A, region, 0, Array(Int,reduced_dims(A,region)))

sum(A::BitArray, region) = reducedim(AddFun(), A, region)
sum(B::BitArray) = countnz(B)

function all(B::BitArray)
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299 changes: 155 additions & 144 deletions base/reducedim.jl
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Expand Up @@ -5,14 +5,11 @@ reduced_dims(a::AbstractArray, region) = reduced_dims(size(a), region)

# for reductions that keep 0 dims as 0
reduced_dims0(a::AbstractArray, region) = reduced_dims0(size(a), region)

reduced_dims{N}(siz::NTuple{N,Int}, d::Int, rd::Int) = (d == 1 ? tuple(rd, siz[d+1:N]...) :
d == N ? tuple(siz[1:N-1]..., rd) :
1 < d < N ? tuple(siz[1:d-1]..., rd, siz[d+1:N]...) :
siz)::typeof(siz)

reduced_dims{N}(siz::NTuple{N,Int}, d::Int) = reduced_dims(siz, d, 1)

reduced_dims0{N}(siz::NTuple{N,Int}, d::Int) = 1 <= d <= N ? reduced_dims(siz, d, (siz[d] == 0 ? 0 : 1)) : siz

function reduced_dims{N}(siz::NTuple{N,Int}, region)
Expand Down Expand Up @@ -46,184 +43,196 @@ end

###### Generic reduction functions #####

reducedim(f::Function, A, region, initial) = reducedim!(f, reduction_init(A, region, initial), A)
## initialization

reducedim(f::Function, A, region, initial, R) = reducedim!(f, fill!(R, initial), A)
for (Op, initfun) in ((:AddFun, :zero), (:MulFun, :one), (:MaxFun, :typemin), (:MinFun, :typemax))
@eval initarray!{T}(a::AbstractArray{T}, ::$(Op), init::Bool) = (init && fill!(a, $(initfun)(T)); a)
end

function reducedim!_function(N::Int, f::Function)
body = gen_reduction_body(N, f)
@eval begin
local _F_
function _F_(R, A)
$body
end
_F_
end
for (Op, initval) in ((:AndFun, true), (:OrFun, false))
@eval initarray!(a::AbstractArray, ::$(Op), init::Bool) = (init && fill!(a, $initval); a)
end

let reducedim_cache = Dict()
# reducedim! assumes that R has already been initialized with a seed value
global reducedim!
function reducedim!(f::Function, R, A)
if isempty(R)
return R
end
ndimsA = ndims(A)
key = (ndimsA, f)
if !haskey(reducedim_cache,key)
func = reducedim!_function(ndimsA, f)
reducedim_cache[key] = func
reducedim_initarray{R}(A::AbstractArray, region, v0, ::Type{R}) = fill!(similar(A,R,reduced_dims(A,region)), v0)
reducedim_initarray{T}(A::AbstractArray, region, v0::T) = reducedim_initarray(A, region, v0, T)

reducedim_initarray0{R}(A::AbstractArray, region, v0, ::Type{R}) = fill!(similar(A,R,reduced_dims0(A,region)), v0)
reducedim_initarray0{T}(A::AbstractArray, region, v0::T) = reducedim_initarray0(A, region, v0, T)

# TODO: better way to handle reducedim initialization
#
# The current scheme is basically following Steven G. Johnson's original implementation
#
function reducedim_init{T}(f, op::AddFun, A::AbstractArray{T}, region)
if method_exists(zero, (Type{T},))
x = evaluate(f, zero(T))
z = zero(x) + zero(x)
Tr = typeof(z) == typeof(x) && !isbits(T) ? T : typeof(z)
else
func = reducedim_cache[key]
z = zero(sum(f, A))
Tr = typeof(z)
end
func(R, A)::typeof(R)
return reducedim_initarray(A, region, z, Tr)
end
end # let reducedim_cache

# Generate the body for a reduction function reduce!(f, R, A), using binary operation f,
# where R is the output and A is the input.
# R must have already been set to the appropriate size and initialized with the seed value
function gen_reduction_body(N, f::Function)
F = Expr(:quote, f)
quote
(isempty(R) || isempty(A)) && return R
for i = 1:$N
(size(R, i) == size(A, i) || size(R, i) == 1) || throw(DimensionMismatch("Reduction on array of size $(size(A)) with output of size $(size(R))"))
end
@nextract $N sizeR d->size(R,d)
# If we're reducing along dimension 1, for efficiency we can make use of a temporary.
# Otherwise, keep the result in R so that we traverse A in storage order.
if size(R, 1) < size(A, 1)
@nloops $N i d->(d>1? (1:size(A,d)) : (1:1)) d->(j_d = sizeR_d==1 ? 1 : i_d) begin
@inbounds tmp = (@nref $N R j)
for i_1 = 1:size(A,1)
@inbounds tmp = ($F)(tmp, (@nref $N A i))
end
@inbounds (@nref $N R j) = tmp
end
else
@nloops $N i A d->(j_d = sizeR_d==1 ? 1 : i_d) begin
@inbounds (@nref $N R j) = ($F)((@nref $N R j), (@nref $N A i))
end
end
R
function reducedim_init{T}(f, op::MulFun, A::AbstractArray{T}, region)
if method_exists(zero, (Type{T},))
x = evaluate(f, zero(T))
z = one(x) * one(x)
Tr = typeof(z) == typeof(x) && !isbits(T) ? T : typeof(z)
else
z = one(prod(f, A))
Tr = typeof(z)
end
return reducedim_initarray(A, region, z, Tr)
end

reduction_init{T}(A::AbstractArray, region, initial::T, Tr=T) = fill!(similar(A,Tr,reduced_dims(A,region)), initial)

function initarray!{T}(a::AbstractArray{T}, v::T, init::Bool)
if init
fill!(a, v)
end
return a
end
reducedim_init{T}(f, op::MaxFun, A::AbstractArray{T}, region) = reducedim_initarray0(A, region, typemin(evaluate(f, zero(T))))
reducedim_init{T}(f, op::MinFun, A::AbstractArray{T}, region) = reducedim_initarray0(A, region, typemax(evaluate(f, zero(T))))
reducedim_init{T}(f::Union(AbsFun,Abs2Fun), op::MaxFun, A::AbstractArray{T}, region) =
reducedim_initarray(A, region, zero(evaluate(f, zero(T))))

reducedim_init(f, op::AndFun, A::AbstractArray, region) = reducedim_initarray(A, region, true)
reducedim_init(f, op::OrFun, A::AbstractArray, region) = reducedim_initarray(A, region, false)

##### Specific reduction functions #####
# specialize to make initialization more efficient for common cases

## sum
typealias CommonReduceResult Union(Uint64,Uint128,Int64,Int128,Float32,Float64,Complex64,Complex128)

@ngenerate N typeof(R) function _sum!{T,N}(f, R::AbstractArray, A::AbstractArray{T,N})
(isempty(R) || isempty(A)) && return R
rdims = 0
for i = 1:N
if size(R, i) == size(A, i)
elseif size(R, i) == 1
rdims += 1
for (IT, RT) in ((:CommonReduceResult, :T), (:SmallSigned, :Int), (:SmallUnsigned, :Uint))
@eval begin
reducedim_init{T<:$IT}(f::Union(IdFun,AbsFun,Abs2Fun), op::AddFun, A::AbstractArray{T}, region) =
reducedim_initarray(A, region, zero($RT))
reducedim_init{T<:$IT}(f::Union(IdFun,AbsFun,Abs2Fun), op::MulFun, A::AbstractArray{T}, region) =
reducedim_initarray(A, region, one($RT))
end
end
reducedim_init(f::Union(IdFun,AbsFun,Abs2Fun), op::AddFun, A::AbstractArray{Bool}, region) =
reducedim_initarray(A, region, 0)


## generic (map)reduction

has_fast_linear_indexing(a::AbstractArray) = false
has_fast_linear_indexing(a::Array) = true

function check_reducdims(R, A)
# Check whether R has compatible dimensions w.r.t. A for reduction
#
# It returns an integer value value (useful for choosing implementation)
# - If it reduces only along leading dimensions, e.g. sum(A, 1) or sum(A, (1, 2)),
# it returns the length of the leading slice. For the two examples above,
# it will be size(A, 1) or size(A, 1) * size(A, 2).
# - Otherwise, e.g. sum(A, 2) or sum(A, (1, 3)), it returns 0.
#
lsiz = 1
had_nonreduc = false
for i = 1:ndims(A)
sRi = size(R, i)
sAi = size(A, i)
if sRi == 1
if sAi > 1
if had_nonreduc
lsiz = 0 # to reduce along i, but some previous dimensions were non-reducing
else
lsiz *= sAi # if lsiz was set to zero, it will stay to be zero
end
end
else
throw(DimensionMismatch("sum of array of size $(size(A)) with output of size $(size(R))"))
sRi == sAi ||
throw(DimensionMismatch("Reduction on array of size $(size(A)) with output of size $(size(R))"))
had_nonreduc = true
end
end
return lsiz
end

@ngenerate N typeof(R) function _mapreducedim!{T,N}(f, op, R::AbstractArray, A::AbstractArray{T,N})
lsiz = check_reducdims(R, A)
isempty(A) && return R
@nextract N sizeR d->size(R,d)
# If we're reducing along dimension 1 and dimension 1 is
# sufficiently large, use the pairwise implementation. Otherwise,
# keep the result in R so that we traverse A in storage order.
sz1 = size(A, 1)
if size(R, 1) < sz1 && sz1 >= 16 && rdims == 1
for i = 1:div(length(A), sz1)
@inbounds R[i] = mapreduce_impl(f, AddFun(), A, (i-1)*sz1+1, i*sz1)
sizA1 = size(A, 1)

if has_fast_linear_indexing(A) && lsiz > 16
# use mapreduce_impl, which is probably better tuned to achieve higher performance
nslices = div(length(A), lsiz)
ibase = 0
for i = 1:nslices
@inbounds R[i] = mapreduce_impl(f, op, A, ibase+1, ibase+lsiz)
ibase += lsiz
end
elseif size(R, 1) == 1 && sizA1 > 1
# keep the accumulator as a local variable when reducing along the first dimension
@nloops N i d->(d>1? (1:size(A,d)) : (1:1)) d->(j_d = sizeR_d==1 ? 1 : i_d) begin
@inbounds r = (@nref N R j)
for i_1 = 1:sizA1
@inbounds v = evaluate(f, (@nref N A i))
r = evaluate(op, r, v)
end
@inbounds (@nref N R j) = r
end
else
# general implementation
@nloops N i A d->(j_d = sizeR_d==1 ? 1 : i_d) begin
@inbounds (@nref N R j) += evaluate(f, @nref N A i)
@inbounds v = evaluate(f, (@nref N A i))
@inbounds (@nref N R j) = evaluate(op, (@nref N R j), v)
end
end
R
end

function sum{T}(f::Union(Function,Func{1}), A::AbstractArray{T}, region)
if method_exists(zero, (Type{T},))
fz = evaluate(f, zero(T))
z = fz + fz
Tr = typeof(z) == typeof(fz) && !isbits(T) ? T : typeof(z)
else
# TODO: handle more heterogeneous sums. e.g. sum(A, 1) where
# A is a Matrix{Any} with one column of numbers and one of vectors
z = zero(sum(f, A))
Tr = typeof(z)
end
_sum!(f, reduction_init(A, region, z, Tr), A)
end

sum!{R}(f::Union(Function,Func{1}), r::AbstractArray{R}, A::AbstractArray; init::Bool=true) =
_sum!(f, initarray!(r, zero(R), init), A)

for (fname, func) in ((:sum, :IdFun), (:sumabs, :AbsFun), (:sumabs2, :Abs2Fun))
@eval begin
$fname(A::AbstractArray, region) = sum($func(), A, region)
$(symbol("$(fname)!")){R}(r::AbstractArray{R}, A::AbstractArray; init::Bool=true) =
sum!($func(), r, A; init=init)
end
return R
end

mapreducedim!(f, op, R::AbstractArray, A::AbstractArray) = _mapreducedim!(f, op, R, A)

## prod

eval(ngenerate(:N, :(typeof(R)), :(_prod!{T,N}(R::AbstractArray, A::AbstractArray{T,N})), N->gen_reduction_body(N, *)))
prod!{R}(r::AbstractArray{R}, A::AbstractArray; init::Bool=true) = _prod!(initarray!(r, one(R), init), A)

function prod{T}(A::AbstractArray{T}, region)
if method_exists(one, (Type{T},))
z = one(T) * one(T)
Tr = typeof(z) == typeof(one(T)) ? T : typeof(z)
else
# TODO: handle more heterogeneous products. e.g. prod(A, 1) where
# A is a Matrix{Any} with one column of numbers and one of vectors
z = one(prod(A))
Tr = typeof(z)
end
_prod!(reduction_init(A, region, z, Tr), A)
function mapreducedim!(f::Function, op, R::AbstractArray, A::AbstractArray)
is(op, +) ? _mapreducedim!(f, AddFun(), R, A) :
is(op, *) ? _mapreducedim!(f, MulFun(), R, A) :
is(op, &) ? _mapreducedim!(f, AndFun(), R, A) :
is(op, |) ? _mapreducedim!(f, OrFun(), R, A) :
_mapreducedim!(f, op, R, A)
end

prod(A::AbstractArray{Bool}, region) = error("use all() instead of prod() for boolean arrays")
reducedim!{RT}(op, R::AbstractArray{RT}, A::AbstractArray) = mapreducedim!(IdFun(), op, R, A, zero(RT))

mapreducedim(f, op, A::AbstractArray, region, v0) = mapreducedim!(f, op, reducedim_initarray(A, region, v0), A)
mapreducedim{T}(f, op, A::AbstractArray{T}, region) = mapreducedim!(f, op, reducedim_init(f, op, A, region), A)

## maximum & minimum
reducedim(op, A::AbstractArray, region, v0) = mapreducedim(IdFun(), op, A, region, v0)
reducedim(op, A::AbstractArray, region) = mapreducedim(IdFun(), op, A, region)

eval(ngenerate(:N, :(typeof(R)), :(_maximum!{T,N}(R::AbstractArray, A::AbstractArray{T,N})), N->gen_reduction_body(N, scalarmax)))
maximum!{R}(r::AbstractArray{R}, A::AbstractArray; init::Bool=true) = _maximum!(initarray!(r, typemin(R), init), A)
maximum{T}(A::AbstractArray{T}, region) =
isempty(A) ? similar(A,reduced_dims0(A,region)) : _maximum!(reduction_init(A, region, typemin(T)), A)

eval(ngenerate(:N, :(typeof(R)), :(_minimum!{T,N}(R::AbstractArray, A::AbstractArray{T,N})), N->gen_reduction_body(N, scalarmin)))
minimum!{R}(r::AbstractArray{R}, A::AbstractArray; init::Bool=true) = _minimum!(initarray!(r, typemax(R), init), A)
minimum{T}(A::AbstractArray{T}, region) =
isempty(A) ? similar(A, reduced_dims0(A, region)) : _minimum!(reduction_init(A, region, typemax(T)), A)
##### Specific reduction functions #####

for (fname, Op) in [(:sum, :AddFun), (:prod, :MulFun),
(:maximum, :MaxFun), (:minimum, :MinFun),
(:all, :AndFun), (:any, :OrFun)]

## all & any
fname! = symbol(string(fname, '!'))
@eval begin
$(fname!)(f::Union(Function,Func{1}), r::AbstractArray, A::AbstractArray; init::Bool=true) =
mapreducedim!(f, $(Op)(), initarray!(r, $(Op)(), init), A)
$(fname!)(r::AbstractArray, A::AbstractArray; init::Bool=true) = $(fname!)(IdFun(), r, A; init=init)

eval(ngenerate(:N, :(typeof(R)), :(_all!{N}(R::AbstractArray, A::AbstractArray{Bool,N})), N->gen_reduction_body(N, &)))
all!(r::AbstractArray, A::AbstractArray{Bool}; init::Bool=true) = _all!(initarray!(r, true, init), A)
all(A::AbstractArray{Bool}, region) = _all!(reduction_init(A, region, true), A)
$(fname)(f::Union(Function,Func{1}), A::AbstractArray, region) =
mapreducedim(f, $(Op)(), A, region)
$(fname)(A::AbstractArray, region) = $(fname)(IdFun(), A, region)
end
end

eval(ngenerate(:N, :(typeof(R)), :(_any!{N}(R::AbstractArray, A::AbstractArray{Bool,N})), N->gen_reduction_body(N, |)))
any!(r::AbstractArray, A::AbstractArray{Bool}; init::Bool=true) = _any!(initarray!(r, false, init), A)
any(A::AbstractArray{Bool}, region) = _any!(reduction_init(A, region, false), A)
for (fname, fbase, Fun) in [(:sumabs, :sum, :AbsFun),
(:sumabs2, :sum, :Abs2Fun),
(:maxabs, :maximum, :AbsFun),
(:minabs, :minimum, :AbsFun)]
fname! = symbol(string(fname, '!'))
fbase! = symbol(string(fbase, '!'))
@eval begin
$(fname!)(r::AbstractArray, A::AbstractArray; init::Bool=true) =
$(fbase!)($(Fun)(), r, A; init=init)
$(fname)(A::AbstractArray, region) = $(fbase)($(Fun)(), A, region)
end
end


## findmin & findmax
##### findmin & findmax #####

# Generate the body for a reduction function reduce!(f, Rval, Rind, A), using a comparison operator f
# Rind contains the index of A from which Rval was taken
Expand Down Expand Up @@ -272,10 +281,12 @@ eval(ngenerate(:N, :(typeof((Rval,Rind))), :(_findmin!{T,N}(Rval::AbstractArray,
findmin!{R}(rval::AbstractArray{R}, rind::AbstractArray, A::AbstractArray; init::Bool=true) = _findmin!(initarray!(rval, typemax(R), init), rind, A)
findmin{T}(A::AbstractArray{T}, region) =
isempty(A) ? (similar(A,reduced_dims0(A,region)), zeros(Int,reduced_dims0(A,region))) :
_findmin!(reduction_init(A, region, typemax(T)), zeros(Int,reduced_dims0(A,region)), A)
_findmin!(reducedim_initarray0(A, region, typemax(T)), zeros(Int,reduced_dims0(A,region)), A)

eval(ngenerate(:N, :(typeof((Rval,Rind))), :(_findmax!{T,N}(Rval::AbstractArray, Rind::AbstractArray, A::AbstractArray{T,N})), N->gen_findreduction_body(N, >)))
findmax!{R}(rval::AbstractArray{R}, rind::AbstractArray, A::AbstractArray; init::Bool=true) = _findmax!(initarray!(rval, typemin(R), init), rind, A)
findmax{T}(A::AbstractArray{T}, region) =
isempty(A) ? (similar(A,reduced_dims0(A,region)), zeros(Int,reduced_dims0(A,region))) :
_findmax!(reduction_init(A, region, typemin(T)), zeros(Int,reduced_dims0(A,region)), A)
_findmax!(reducedim_initarray0(A, region, typemin(T)), zeros(Int,reduced_dims0(A,region)), A)


4 changes: 2 additions & 2 deletions test/reducedim.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -13,9 +13,9 @@ safe_sumabs2{T}(A::Array{T}, region) = safe_mapslices(sum, abs2(A), region)

Areduc = rand(3, 4, 5, 6)
for region in {
1, 2, 3, 4, 5, (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4),
1, 2, 3, 4, 5, (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4),
(1, 2, 3), (1, 3, 4), (2, 3, 4), (1, 2, 3, 4)}

# println("region = $region")
r = fill(NaN, Base.reduced_dims(size(Areduc), region))
@test_approx_eq sum!(r, Areduc) safe_sum(Areduc, region)
@test_approx_eq prod!(r, Areduc) safe_prod(Areduc, region)
Expand Down

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