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WIP: Fast implementation of reduction along dims #5294

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merged 12 commits into from
Jan 5, 2014
Merged

WIP: Fast implementation of reduction along dims #5294

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d5339ea
move reducedim related stuff to a separate file
lindahua Jan 2, 2014
994bbce
move reducedim codes from array.jl to reducedim.jl
lindahua Jan 2, 2014
4060391
more efficient implementation of reduced_dims
lindahua Jan 3, 2014
579ab44
Fast sum along dimensions over contiguous arrays
lindahua Jan 4, 2014
2ffdbfa
specialized for cases with region being an integer
lindahua Jan 4, 2014
01dfa4a
some tuning of the vector kernels
lindahua Jan 4, 2014
c3771fe
allow specify the result type of sum.
lindahua Jan 4, 2014
483e13f
allow minimum and maximum over a subvector
lindahua Jan 4, 2014
54ba470
apply the new reduction framework to maximum & minimum
lindahua Jan 4, 2014
3b1a8ea
apply new reduction framework to prod
lindahua Jan 4, 2014
9ecc321
updates to the maximum & minimum codes
lindahua Jan 4, 2014
da2d02c
more flexible code generation functions
lindahua Jan 4, 2014
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94 changes: 24 additions & 70 deletions base/abstractarray.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -1409,34 +1409,9 @@ function nnz{T}(a::AbstractArray{T})
return n
end

# for reductions that expand 0 dims to 1
reduced_dims(A, region) = ntuple(ndims(A), i->(in(i, region) ? 1 :
size(A,i)))

# keep 0 dims in place
reduced_dims0(A, region) = ntuple(ndims(A), i->(size(A,i)==0 ? 0 :
in(i, region) ? 1 :
size(A,i)))

reducedim(f::Function, A, region, v0) =
reducedim(f, A, region, v0, similar(A, reduced_dims(A, region)))

maximum{T}(A::AbstractArray{T}, region) =
isempty(A) ? similar(A,reduced_dims0(A,region)) : reducedim(scalarmax,A,region,typemin(T))
minimum{T}(A::AbstractArray{T}, region) =
isempty(A) ? similar(A,reduced_dims0(A,region)) : reducedim(scalarmin,A,region,typemax(T))
sum{T}(A::AbstractArray{T}, region) = reducedim(+,A,region,zero(T))
prod{T}(A::AbstractArray{T}, region) = reducedim(*,A,region,one(T))

all(A::AbstractArray{Bool}, region) = reducedim(&,A,region,true)
any(A::AbstractArray{Bool}, region) = reducedim(|,A,region,false)
sum(A::AbstractArray{Bool}, region) = reducedim(+,A,region,0,similar(A,Int,reduced_dims(A,region)))
sum(A::AbstractArray{Bool}) = nnz(A)
prod(A::AbstractArray{Bool}) =
error("use all() instead of prod() for boolean arrays")
prod(A::AbstractArray{Bool}, region) =
error("use all() instead of prod() for boolean arrays")


# a fast implementation of sum in sequential order (from left to right)
function sum_seq{T}(a::AbstractArray{T}, ifirst::Int, ilast::Int)
Expand Down Expand Up @@ -1594,56 +1569,33 @@ function cumsum_kbn{T<:FloatingPoint}(A::AbstractArray{T}, axis::Integer)
return B + C
end

function prod{T}(A::AbstractArray{T})
if isempty(A)
return one(T)
end
v = A[1]
for i=2:length(A)
@inbounds v *= A[i]
end
v
end

function minimum{T<:Real}(A::AbstractArray{T})
if isempty(A); error("argument must not be empty"); end
v = A[1]
for i=2:length(A)
@inbounds x = A[i]
if x < v
v = x
end
function prod_rgn{T}(A::AbstractArray{T}, first::Int, last::Int)
if first > last
return one(T)
end
v
end

function maximum{T<:Real}(A::AbstractArray{T})
if isempty(A); error("argument must not be empty"); end
v = A[1]
for i=2:length(A)
@inbounds x = A[i]
if x > v
v = x
end
i = first
v = A[i]
while i < last
@inbounds v *= A[i+=1]
end
v
return v
end
prod{T}(A::AbstractArray{T}) = prod_rgn(A, 1, length(A))

# specialized versions for floating-point, which deal with NaNs

function minimum{T<:FloatingPoint}(A::AbstractArray{T})
if isempty(A); error("argument must not be empty"); end
n = length(A)
function minimum_rgn{T<:Real}(A::AbstractArray{T}, first::Int, last::Int)
if first > last; error("argument range must not be empty"); end

# locate the first non NaN number
v = A[1]
i = 2
while v != v && i <= n
v = A[first]
i = first + 1
while v != v && i <= last
@inbounds v = A[i]
i += 1
end

while i <= n
while i <= last
@inbounds x = A[i]
if x < v
v = x
Expand All @@ -1653,19 +1605,18 @@ function minimum{T<:FloatingPoint}(A::AbstractArray{T})
v
end

function maximum{T<:FloatingPoint}(A::AbstractArray{T})
if isempty(A); error("argument must not be empty"); end
n = length(A)
function maximum_rgn{T<:Real}(A::AbstractArray{T}, first::Int, last::Int)
if first > last; error("argument range must not be empty"); end

# locate the first non NaN number
v = A[1]
i = 2
while v != v && i <= n
v = A[first]
i = first + 1
while v != v && i <= last
@inbounds v = A[i]
i += 1
end

while i <= n
while i <= last
@inbounds x = A[i]
if x > v
v = x
Expand All @@ -1675,6 +1626,9 @@ function maximum{T<:FloatingPoint}(A::AbstractArray{T})
v
end

minimum{T<:Real}(A::AbstractArray{T}) = minimum_rgn(A, 1, length(A))
maximum{T<:Real}(A::AbstractArray{T}) = maximum_rgn(A, 1, length(A))

# extrema

function extrema{T<:Real}(A::AbstractArray{T})
Expand Down
76 changes: 0 additions & 76 deletions base/array.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -1401,82 +1401,6 @@ function indcopy(sz::Dims, I::(RangeIndex...))
end


## Reductions ##

# TODO:
# - find out why inner loop with dimsA[i] instead of size(A,i) is way too slow

let reducedim_cache = nothing
# generate the body of the N-d loop to compute a reduction
function gen_reducedim_func(n, f)
ivars = { symbol(string("i",i)) for i=1:n }
# limits and vars for reduction loop
lo = { symbol(string("lo",i)) for i=1:n }
hi = { symbol(string("hi",i)) for i=1:n }
rvars = { symbol(string("r",i)) for i=1:n }
setlims = { quote
# each dim of reduction is either 1:sizeA or ivar:ivar
if in($i,region)
$(lo[i]) = 1
$(hi[i]) = size(A,$i)
else
$(lo[i]) = $(hi[i]) = $(ivars[i])
end
end for i=1:n }
rranges = { :( $(lo[i]):$(hi[i]) ) for i=1:n } # lo:hi for all dims
body =
quote
_tot = v0
$(setlims...)
$(make_loop_nest(rvars, rranges,
:(_tot = ($f)(_tot, A[$(rvars...)]))))
R[_ind] = _tot
_ind += 1
end
quote
local _F_
function _F_(f, A, region, R, v0)
_ind = 1
$(make_loop_nest(ivars, { :(1:size(R,$i)) for i=1:n }, body))
end
_F_
end
end

global reducedim
function reducedim(f::Function, A, region, v0, R)
ndimsA = ndims(A)

if is(reducedim_cache,nothing)
reducedim_cache = Dict()
end

key = ndimsA
fname = :f

if (is(f,+) && (fname=:+;true)) ||
(is(f,*) && (fname=:*;true)) ||
(is(f,scalarmax) && (fname=:scalarmax;true)) ||
(is(f,scalarmin) && (fname=:scalarmin;true)) ||
(is(f,&) && (fname=:&;true)) ||
(is(f,|) && (fname=:|;true))
key = (fname, ndimsA)
end

if !haskey(reducedim_cache,key)
fexpr = gen_reducedim_func(ndimsA, fname)
func = eval(fexpr)
reducedim_cache[key] = func
else
func = reducedim_cache[key]
end

func(f, A, region, R, v0)

return R
end
end

## Filter ##

# given a function returning a boolean and an array, return matching elements
Expand Down
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