Also if k is known in advance, you could precompute the signs and map to
the sample.
# clumsy computation of all vectors of length k with 1/-1 as entries using
powerset.
signs(k) = [[(-1)^(i in s) for i = 1:k] for s=powerset(1:k)]
# now return a closure
sdifsums(k) = let s=signs(k) ; a->map(x-> sum(x.*a), s) ; end
# test with arrays of length 6
sdifsums6 = sdifsums(6)
# this gives X10 speedup on my computer
julia> @time
sdifsums6([-0.160767,-1.48275,-0.384419,-1.3541,1.03842,-1.16268])
elapsed time: 0.001349613 seconds (97904 bytes allocated)
64-element Array{Float64,1}:
...
