Performance-tuning a simple 2D Table construct

Question

I've recently been playing with some performance tuning over a seemingly simple construction where I build a 2D array of Sin[x*y] for {x, y}∈Interval[{0, 2π}, {0, 2π}].

I think it's also a good example of how vastly different results one can get depending on how efficiently the operation is performed.

Here's the operation in the simplest/least efficient way I could think up:

Table[N@Sin[x*y], 
    {x, 0, 2π, π/250},  
    {y, 0, 2π, π/250}
    ]; // RepeatedTiming // First

2.01

Now, how can we speed this up? (or slow it down in non-intuitive ways)

For reference, the best I managed to get was 0.0011 but all answers are good answers, especially if they provide analysis of how they speed up/slow down the problem.

Also feel free to cut down on the number of points 250 was simply most evocative.

Answer 1

Use packed arrays, and vector operations. Here are 2 possibilities:

Table[N@Sin[x*y],{x,0,2π,π/12},{y,0,2π,π/12}]; //RepeatedTiming//First

With[{pa=Developer`ToPackedArray @ N @ Range[0,2π,π/12]},
    Sin @ Outer[Times, pa, pa]
]; //RepeatedTiming//First

With[{pa=Developer`ToPackedArray @ N @ Range[0,2π,π/12]},
    Sin @ KroneckerProduct[pa, pa]
]; //RepeatedTiming//First

0.0025

0.0000322

0.0000314

Update

It seems that converting to a packed array takes the most time, so here is a version that avoids packing:

With[{pa = Range[0, 24] N[Pi/12]},
    Sin @ KroneckerProduct[pa, pa]
]; //RepeatedTiming //First

8.3*10^-6

Answer 2

With[{r = Range[0., 2Pi, Pi/12.] }, Sin @ Outer[Times, r, r]];// RepeatedTiming// First

0.000014