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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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Original file line number Diff line number Diff line change
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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7 changes: 5 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 +114,6 @@ function sum_kbn(A)
s - c
end

sum_kbn(f, A) = f.(A)
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This isn't quite correct; f is applied elementwise to A but the result isn't summed. Perhaps you meant sum_kbn(f.(A))?

Even that will make two passes over the array, so we're likely able to do better. I'm not sure this is entirely correct either, but something like this would be a start:

diff --git a/src/KahanSummation.jl b/src/KahanSummation.jl
index fde6700..26a7535 100644
--- a/src/KahanSummation.jl
+++ b/src/KahanSummation.jl
@@ -91,22 +91,23 @@ end
 Return the sum of all elements of `A`, using the Kahan-Babuska-Neumaier compensated
 summation algorithm for additional accuracy.
 """
-function sum_kbn(A)
+function sum_kbn(f, A)
     T = @default_eltype(typeof(A))
-    c = promote_sys_size_add(zero(T)::T)
+    c = f(promote_sys_size_add(zero(T)::T))
     i = start(A)
     if done(A, i)
         return c
     end
     Ai, i = next(A, i)
-    s = Ai - c
+    s = f(Ai) - c
     while !(done(A, i))
         Ai, i = next(A, i)
-        t = s + Ai
-        if abs(s) >= abs(Ai)
-            c -= ((s-t) + Ai)
+        fAi = f(Ai)
+        t = s + fAi
+        if abs(s) >= abs(fAi)
+            c -= ((s-t) + fAi)
         else
-            c -= ((Ai-t) + s)
+            c -= ((fAi-t) + s)
         end
         s = t
     end

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is view applicable?

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Hm, not exactly, I don't think, since the issue is iterating over the input multiple times, whereas view would be useful to avoid making copies.


end # module