Use sincos

[giordano]

In Julia master, where an efficient sincos function is defined, this change should provide a 5-10% speed-up.

Note that TimeIt.jl package doesn't work on Julia master, most probably due to this Julia issue: JuliaLang/julia#23221.

[giordano]

This is the script I'm using for benchmark (the simple @benchmark macro doesn't currently work on Julia master for the same reason why @timeit is broken):

#!/usr/bin/env julia
using SkyCoords
using BenchmarkTools

io = open("julia_times.csv", "w")
println(io, "n,system,time")
for n in [1, 10, 100, 1000, 10_000, 100_000, 1_000_000]
    println("$n coordinates: ")
    if n == 1
        c = ICRSCoords(2pi*rand(), pi*(rand() - 0.5))
        t1 = minimum(run(tune!(@benchmarkable( convert(GalCoords, $c) ))).times) / 1e9
        println(io, "$n,galactic,$t1")
        t2 = minimum(run(tune!(@benchmarkable( convert(FK5Coords{2000}, $c) ))).times) / 1e9
        println(io, "$n,fk5j2000,$t2")
        t3 = minimum(run(tune!(@benchmarkable( convert(FK5Coords{1975}, $c) ))).times) / 1e9
        println(io, "$n,fk5j1975,$t3")
    else
        c = [ICRSCoords(2pi*rand(), pi*(rand() - 0.5)) for i=1:n]
        t1 = minimum(run(tune!(@benchmarkable( convert(Vector{GalCoords{Float64}}, $c) ))).times) / 1e9
        println(io, "$n,galactic,$t1")
        t2 = minimum(run(tune!(@benchmarkable( convert(Vector{FK5Coords{2000, Float64}}, $c) ))).times) / 1e9
        println(io, "$n,fk5j2000,$t2")
        t3 = minimum(run(tune!(@benchmarkable( convert(Vector{FK5Coords{1975, Float64}}, $c) ))).times) / 1e9
        println(io, "$n,fk5j1975,$t3")
    end
end
close(io)

Result on current master of SkyCoords:

n,system,time
1,galactic,1.0194373673036093e-7
1,fk5j2000,1.7845755395683453e-7
1,fk5j1975,1.8471951219512196e-7
10,galactic,9.211923076923078e-7
10,fk5j2000,9.809333333333332e-7
10,fk5j1975,9.872307692307692e-7
100,galactic,8.904e-6
100,fk5j2000,8.94e-6
100,fk5j1975,8.959666666666667e-6
1000,galactic,0.000111156
1000,fk5j2000,0.000112682
1000,fk5j1975,0.000112151
10000,galactic,0.001142591
10000,fk5j2000,0.00115665
10000,fk5j1975,0.001141865
100000,galactic,0.011440471
100000,fk5j2000,0.011608919
100000,fk5j1975,0.011480269
1000000,galactic,0.115397807
1000000,fk5j2000,0.116892337
1000000,fk5j1975,0.115666098

Result with this PR:

n,system,time
1,galactic,8.347925311203319e-8
1,fk5j2000,1.5674120603015074e-7
1,fk5j1975,1.6583355176933158e-7
10,galactic,8.52828125e-7
10,fk5j2000,9.316551724137931e-7
10,fk5j1975,9.428076923076923e-7
100,galactic,8.383e-6
100,fk5j2000,8.541333333333334e-6
100,fk5j1975,8.529e-6
1000,galactic,0.00010513
1000,fk5j2000,0.00010537
1000,fk5j1975,0.000105959
10000,galactic,0.001079322
10000,fk5j2000,0.001080466
10000,fk5j1975,0.001084719
100000,galactic,0.010842601
100000,fk5j2000,0.010863911
100000,fk5j1975,0.010902358
1000000,galactic,0.10911997
1000000,fk5j2000,0.109268721
1000000,fk5j1975,0.110885803

I ran the benchmarks with Julia master, where the fast sincos is defined. There are performance improvements in the range 4-18%, with the largest improvement for the single element conversion.

[kbarbary]

Looks good!