Notes. Performance of the ENP5KE routine for different values of the eccentricity e, when the accuracy is set to the best value 10⁻¹⁵ rad that can be obtained for M ∈ [0, 2π] using double precision. The number n of grid intervals j needed for computing the coefficients, breakpoints, and k-vector at this accuracy level, and the average CPU time t^init (in milliseconds) required for this task, are given in the second and sixth columns, respectively. The third column shows the average number of iterations (only involving precomputed values) required for finding the relevant intervals for the piecewise polynomial when generating the solution of KE for a large and homogeneous set of values M_a. The average CPU time per solution (in ns in the lastcolumn), t^gen∕N, has been obtained by dividing the time for computing N = 10⁸ solutions of KE by N, running the ENP5KE_evaluate routine in parallel. The values in the parentheses correspond to the routine with the control sentence for the switch, which is not necessary for e ≤ 0.99. The fourth and fifth columns show the average and the maximum number of bisection root searching iterations, which are only applied for e > 0.99 and for M < 0.0045 rad or M > 2π − 0.0045 rad. While the results of the first five columns are characteristic of the algorithm, the speed performances shown in the last two columns correspond to the hardware specified in the text.