In practice, we use Euler's Formula to express the complex exponentials of eqn. (16) in terms of sine and cosine vectors, avoiding complex and imaginary numbers entirely in the implementation. This will likely be the rate limiting step and, while we have made no attempts to optimize the pilot codes at this stage, many options exist to achieve performant code. The trigonometric functions need to be evaluated at each cubature point; this involves many completely independent, but identical, operations: an ideal scenario for avoiding "warp divergence" on GPUs and for "embarassingly parallel" implementation in general. Many libraries such as CUDA provide a combined sincos function that can compute both values at reduced cost, compared to individual sin and cos calls, further boosting performance. Even on a CPU, there are vector libraries available for trigonometric function evaluation, such as the Short Vector Math Library (SVML) and (oneAPI) libraries provided by Intel; these utilities will allow the algorithm to take full advantage of the long SIMD vector lengths supported by modern CPUs. Distinct S vectors are required at each scale, and can be constructed recursively from those for the lowest required scale by recursion, using the double-angle formulas sin(2x) = 2 sin(x) cos(x) cos(2x) = 2 cos 2 (x) -1 = 1 -2 sin 2 (x), (19) whose evaluation over large point sets is well suited to modern vector hardware.