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sum_kbn(fn, A) (issue 3, in part) #6

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ef5aef4
vec -> avec (vec is a function)
JeffreySarnoff Dec 11, 2017
4876eb7
https://github.com/JuliaMath/KahanSummation.jl/issues/3 (in part)
JeffreySarnoff Dec 11, 2017
32b1e76
Update KahanSummation.jl
JeffreySarnoff Dec 11, 2017
863d46c
test sum_kbn(f, A)
JeffreySarnoff Dec 11, 2017
d345164
respond to comment
JeffreySarnoff Dec 11, 2017
ee5abb3
fixup
JeffreySarnoff Dec 11, 2017
423929c
correct for Method definition sum_kbn(Any, Any) overwrite
JeffreySarnoff Dec 11, 2017
3d93013
change name of testset
JeffreySarnoff Dec 11, 2017
733f0ea
combine test sets
JeffreySarnoff Dec 11, 2017
f8915eb
test identity
JeffreySarnoff Dec 11, 2017
39bc274
try to make coveralls happy
JeffreySarnoff Dec 11, 2017
ad48228
fold special case for identity into sum_kbn
JeffreySarnoff Dec 11, 2017
03c5bc2
Update KahanSummation.jl
JeffreySarnoff Dec 12, 2017
cbbcbcc
maybe ok
JeffreySarnoff Dec 12, 2017
5cbd33a
add more cumsum_kbr(A, dim) tests
JeffreySarnoff Dec 12, 2017
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8 changes: 4 additions & 4 deletions README.md
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Expand Up @@ -14,14 +14,14 @@ These functions were formerly part of Julia's Base library.
```julia
julia> using KahanSummation

julia> vec = [1.0, 1.0e16, -1.0e16, -0.5];
julia> avec = [1.0, 1.0e16, -1.0e16, -0.5];

julia> sum(vec), sum_kbn(vec)
julia> sum(avec), sum_kbn(avec)
(-0.5, 0.5)

julia> vec = [1.0, 1.0e16, 1.0, -1.0e16];
julia> avec = [1.0, 1.0e16, 1.0, -1.0e16];

julia> cumsum_kbn(vec) .- cumsum(vec)
julia> cumsum_kbn(avec) .- cumsum(avec)
4-element Array{Float64,1}:
0.0
0.0
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28 changes: 26 additions & 2 deletions src/KahanSummation.jl
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Expand Up @@ -86,10 +86,11 @@ function cumsum_kbn(v::AbstractVector{T}) where T<:AbstractFloat
end

"""
sum_kbn(A)
sum_kbn([f,] A)

Return the sum of all elements of `A`, using the Kahan-Babuska-Neumaier compensated
summation algorithm for additional accuracy.
summation algorithm for additional accuracy. When a function `f` is supplied, the
result of calling f on each element of `A` is summed.
"""
function sum_kbn(A)
T = @default_eltype(typeof(A))
Expand All @@ -113,4 +114,27 @@ function sum_kbn(A)
s - c
end

function sum_kbn(f::Function, A)
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This needn't be a function; for example, one could also pass a type.

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I know -- I do not know how to annotate Function or TypeConstructor. When I had it as sum_kbn(f, A) things got murky with sum_kbn(identity, A) and there was no clean dispatch resolution. What is the correct way to approach this while following the guide that sum_kbn(A) should be defined in terms of sum_kbn(identity, A)?

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I think the issue there is that the definition with identity was backwards. It should be sum_kbn(A) = sub_kbn(identity, A), with sum_kbn(f, A) as the only long-form definition of the function. That should remove any ambiguities.

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does the application of identity disappear always?

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e.g. map(identity, [....])

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Yes, the function call should get optimized out

f === identity && return sum_kbn(A)
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This is backwards. sum_kbn(A) should be implemented in terms of sum_kbn(identity, A), not the other way around. This way there will be only one implementation of the sum.

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Do you mean that I should follow this pattern?

function sum_kbn(f, A)
     ...
end
sum_kbn(a) = sum_kbn(identity, A)

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later comment says "yes" -- I will do that

T = @default_eltype(typeof(A))
c = promote_sys_size_add(zero(T)::T)
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You'll need to apply the function here as well

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This is the wrong type. The output of f might not match the eltype of A.

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how does one obtain the f mapped eltype from eltype(A)?

i = start(A)
if done(A, i)
return c
end
Ai, i = next(A, i)
s = f(Ai) - c
while !(done(A, i))
Ai, i = next(A, i)
fAi = f(Ai); t = s + fAi
if abs(s) >= abs(fAi)
c -= ((s-t) + fAi)
else
c -= ((fAi-t) + s)
end
s = t
end
s - c
end

end # module
22 changes: 21 additions & 1 deletion test/runtests.jl
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Expand Up @@ -44,5 +44,25 @@ end
@test sum_kbn([7 8 9]) === sum_kbn([8 9 7])
@test sum_kbn(i for i=1:1:10) === sum_kbn(i for i=10:-1:1)
@test sum_kbn([-0.0]) === -0.0
@test sum_kbn([-0.0,-0.0]) === -0.0

@test sum_kbn(identity, [1,1e100,1,-1e100]) === 2.0
@test sum_kbn(identity, Float64[]) === 0.0
@test sum_kbn(identity, i for i=1.0:1.0:10.0) === 55.0
@test sum_kbn(identity, i for i=1:1:10) === 55
@test sum_kbn(identity, [1 2 3]) === 6
@test sum_kbn(identity, [2+im 3-im]) === 5+0im
@test sum_kbn(identity, [1+im 2+3im]) === 3+4im
@test sum_kbn(identity, [7 8 9]) === sum_kbn([8 9 7])
@test sum_kbn(identity, i for i=1:1:10) === sum_kbn(i for i=10:-1:1)
@test sum_kbn(identity, [-0.0]) === -0.0

@test sum_kbn([-0.0]) === -0.0
@test sum_kbn(x->x*x, [1.0]) === 1.0
@test sum_kbn(x->x*x, [2.0]) === 4.0
@test sum_kbn(x->x+1, Float64[]) === 0.0
@test sum_kbn(x->x+1, [6 7 8]) === sum_kbn([8 9 7])
@test sum_kbn(sqrt, i for i=1.0:1.0:10.0) === 22.4682781862041
@test sum_kbn(x->x*im,[1+im 2+3im]) === -4+3im
@test sum_kbn(sqrt, [i for i in 1.0:1.0:10.0]) === sum_kbn(sqrt, [i for i in 10.0:-1.0:1.0])
@test sum_kbn([1.0, 1.0e16, 1.0, -1.0e16]) === sum_kbn(x->x+1, [1.0, 1.0e16, 1.0, -1.0e16] - 1.0)
end