Adding more than 3 complex numbers (inlining threshold)

[ivarne]

First reported by @jtravs on the mailinglist. This is similar to #3206, but with complex numbers, and it seems like +(a,b,c,d,e) is performed in a suboptmal way because of varargs.

function sum5(scale, sa1, a1, sa2, a2, sa3, a3, sa4, a4, sa5, a5, out)
    for i=1:length(out)
        out[i] = scale*(sa1*a1[i] + sa2*a2[i] + sa3*a3[i]
                                            + sa4*a4[i] + sa5*a5[i])
    end
end

function sum5b(scale, sa1, a1, sa2, a2, sa3, a3, sa4, a4, sa5, a5, out)
    for i=1:length(out)
        out[i] = scale*(sa1*a1[i] + sa2*a2[i] + sa3*a3[i])
        out[i] += scale*(sa4*a4[i] + sa5*a5[i])
    end
end

function dosums(T)
    scale = rand()
    sa1 = rand()
    a1 = rand(T,200000)
    sa2 = rand()
    a2 = rand(T,200000)
    sa3 = rand()
    a3 = rand(T,200000)
    sa4 = rand()
    a4 = rand(T,200000)
    sa5 = rand()
    a5 = rand(T,200000)
    out = similar(a1)
    sum5(scale,sa1,a1,sa2,a2,sa3,a3,sa4,a4,sa5,a5,out)
    @time sum5(scale,sa1,a1,sa2,a2,sa3,a3,sa4,a4,sa5,a5,out)
    sum5b(scale,sa1,a1,sa2,a2,sa3,a3,sa4,a4,sa5,a5,out)
    @time sum5b(scale,sa1,a1,sa2,a2,sa3,a3,sa4,a4,sa5,a5,out)
end
dosums(Complex{Float64}) 

The result show that there is a huge penalty when we add too many numbers in one invocation of +.

elapsed time: 0.022001424 seconds (28800096 bytes allocated) 
elapsed time: 0.00194736 seconds (96 bytes allocated)

[vtjnash]

this has a rather complex interaction with the inlining threshold, because it is just under the threshold for splitting out the parts of the sum into multiple variables, which puts it just over the threshold after inlining N variables

however, the bigger question is why this is falling back to the julia calling convention for more than three arguments to +:

julia> code_llvm(+,(Complex{Float64},Complex{Float64},Complex{Float64},Complex{Float64},Complex{Float64}))

define %jl_value_t* @"julia_+15722"(%jl_value_t*, %jl_value_t**, i32) {

[JeffBezanson]

fixed by #7075