im*Matrix is much slower than real scalar*Matrix

[ViralBShah]

Multiplying a matrix with im is 10x slower than multiplying it by a real number.

julia> @time im*ones(2000,2000);
elapsed time: 1.40052605 seconds

julia> @time 2*ones(2000,2000);
elapsed time: 0.13868904 seconds

[ViralBShah]

Does this have anything to do with global variables in the REPL or something? Since I am not creating a matrix and using it, It seems that the type inference on globals is not an issue here, especially since the real scalar*Matrix does work fast.

[JeffBezanson]

Not that it changes this issue, but as a side note we should always use complex(r,i) and not r+im*i, and encourage others to do the same.

[JeffBezanson]

Adding this definition speeds it up by more than 2x:

*(z::ImaginaryUnit, w::Real) = complex(0, w)

So that much of the time is taken just by the extra operations in complex *.

[JeffBezanson]

Ok, and all the rest of the time is taken by the integer manipulations in the complex constructor:

function complex128(r::Float64, i::Float64)
    box(Complex128,
        or_int(shl_int(zext_int(Complex128,unbox64(i)),unbox32(64)),
               zext_int(Complex128,unbox64(r))))
end

[ViralBShah]

We are now down to 5x slower.

julia> @time im*ones(2000,2000);
elapsed time: 0.59639478 seconds

[JeffBezanson]

Subsumed by #323.