clenshaw_timing.m

% All lengths up to 16, plus an additional 8 random sizes for each power of two larger than that.
coeff_lengths = [
          1        2        3        4        5        6        7        8, ...
          9       10       11       12       13       14       15       16, ...
         17       20       23       25       26       29       30       32, ...
         34       37       42       43       49       52       59       64, ...
         65       66       67       71       76       89       97      128, ...
        129      146      165      171      176      203      233      256, ...
        267      276      292      331      378      413      482      512, ...
        522      536      709      754      784      909      921     1024, ...
       1072     1212     1239     1322     1441     1618     1817     2048, ...
       2635     2724     3180     3587     3613     3678     3805     4096, ...
       4330     4695     4872     5279     5836     6684     8001     8192, ...
       8996     9671     9891    11605    14842    15163    15462    16384, ...
      16782    16901    22253    23013    26012    26284    29845    32768, ...
      34395    42716    49348    49523    51202    51930    54064    65536, ...
      67493    71754    88355    91746    92591   105175   118693   131072, ...
     136391   142212   173703   191971   195330   212553   238650   262144, ...
     274693   283853   302696   319160   344417   422508   487256   524288, ...
     536242   585221   792789   823736   879391   891382   971502  1048576, ...
    1154356  1208740  1320692  1355786  1429313  1531966  2003366  2097152, ...
    2547794  2624121  2728230  3428732  3534134  3587105  4104074  4194304, ...
    4294541  5046120  5310993  6712438  7168361  7808795  8084967  8388608, ...
    8800612  9598079 10124236 10759037 11363198 12834330 16125319 16777216];


rand_coeffs = 2 .* rand(16777216, 1) - 1;

ptslen = 4;
rand_pts = 2 .* rand(ptslen, 1) - 1;

tests_per_run = 20;
timings_clenshaw_jrus = zeros(tests_per_run, numel(coeff_lengths));

for li=1:112
    len = coeff_lengths(li);
    rand_coeffs_l = rand_coeffs(1:len);
    
    inner_loop_size = max(floor(50000/ptslen/len), 1);
    
    for testi=1:tests_per_run
        tstart = tic;
        for innerrep=1:inner_loop_size
            y = clenshaw_jrus(rand_pts, rand_coeffs_l);
        end
        timings_clenshaw_jrus(testi, li) = toc(tstart) / inner_loop_size;
    end
end

colen = coeff_lengths(1:112);
timings_jrus =  min(timings_clenshaw_jrus(:,1:112));

plot(log2(colen), log2(ptslen * colen ./ timings_jrus))