tuna = [2,3,4,6,10,12,14,17,19,20];

treats = [4,3,5,0,5,4,5,6,1,7,6,3,7,1,3,6,3,5,1,2];

sum(treats[tuna])

sum(treats) - sum(treats[tuna])

binomial(20,10)

using StatsBase
sum(sample(treats,10))

@time tunasamp = [sum(sample(treats,10)) for i in 1:100000];

using Gadfly, DataFrames
set_default_plot_size(15cm,9cm)
plot(DataFrame(samp=tunasamp), x=:samp, Geom.histogram, Guide.XLabel("Samples from reference distribution"))

for c in combinations(1:4,2)
    show(c)
    println()
end

combsums(v::Vector, sz) = [sum(c) for c in combinations(v,sz)]
ss = combsums(treats,10);
length(ss)             # should be 184756

countnz(ss .<= 29)

countnz(ss .<= 29)/length(ss)

countmap(combsums(treats,10))

function dfsums(v::Vector,sz)
    mm = countmap([sum(c) for c in combinations(v,sz)])
    sums = sort([k for k in keys(mm)])
    DataFrame(sum=sums, count=[mm[s] for s in sums])
end

dd = dfsums(treats,10)

dd[:le29] = [s .<= 29 ? "≤ 29" : "> 29" for s in dd[:sum]]
plot(dd, x=:sum, y=:count, Geom.bar, color=:le29)

@time dfsums(treats,10);

function dfsums1(v::Vector, sz)
    mm = (eltype(v)=>Int)[]
    for c in combinations(v,sz)
        key = sum(c)
        mm[key] = get(mm,key,0) + 1
    end
    sums = sort([k for k in keys(mm)])
    DataFrame(sums=sums, counts=[mm[k] for k in sums])
end

dfsums1(treats,10);   # one call to force compilation
@time dfsums1(treats,10);

countnz(ss .< 29) + div(countnz(ss .== 29), 2)

3950/184756

function signedsum(v::Vector, j::Integer)
    s = zero(eltype(v))
    for i in 1:length(v)
        if bool(j & 1)
            s += v[i]
        else 
            s -= v[i]
        end
        j >>= 1
    end
    s
end

ssums(v::Vector) = [signedsum(v,j) for j in 0:2^length(v)-1]

diffs = [1.56, -0.07, 0.75, 0.71, 0.34, 0.39, 1, 0.46, 0.56, 1.13, 0.1, 
    -0.03, 0.45, 0.23, 0.66, 0.55, 0.96, 0.24, 0.75, 0.5, -0.1, -0.2];
ss = ssums(diffs);
length(ss)              # should be 2^22

plot(DataFrame(signedSums=ss), x=:signedSums, Geom.density)

function signedsum1(v::Vector, j::Integer)
    s = zero(eltype(v))
    @inbounds for i in 1:length(v)
        s += bool(j & 1) ? v[i] : -v[i]
        j >>= 1
    end
    s
end

ssums1(v::Vector) = [signedsum1(v,j) for j in 0:2^length(v) - 1]

code_native(signedsum1,(Vector{Float64},Int))

ssums1(diffs);  # force compilation
@time ssums1(diffs);