What is the fastest way to count elements in an array?

Question

In my models, one of the most repeated tasks to be done is counting the number of each element within an array. The counting is from a closed set, so I know there are

Answer 1

We know that that the input vector always contains integers, so why not use this to "squeeze" a bit more performance out of the algorithm?

I've been experimenting with some optimizations of the the two best binning methods suggested by the OP, and this is what I came up with:

• The number of unique values (X in the question, or n in the example) should be explicitly converted to an (unsigned) integer type.
• It's faster to compute an extra bin and then discard it, than to "only process" valid values (see the accumi_new function below).

This function takes about 30sec to run on my machine. I'm using MATLAB R2016a.

---

function q38941694
datestr(now)
N = 25;
func_times = zeros(N,4);
for n = 1:N
    func_times(n,:) = timing_hist(2^n,500);
end
% Plotting:
figure('Position',[572 362 758 608]);
hP = plot(1:n,log10(func_times.*1000),'-o','MarkerEdgeColor','k','LineWidth',2);
xlabel('Log_2(Array size)'); ylabel('Log_{10}(Execution time) (ms)')
legend({'histcounts (double)','histcounts (uint)','accumarray (old)',...
  'accumarray (new)'},'FontSize',12,'Location','NorthWest')
grid on; grid minor;
set(hP([2,4]),'Marker','s'); set(gca,'Fontsize',16);
datestr(now)
end

function out = timing_hist(N,n)
% Convert n into an appropriate integer class:
if n < intmax('uint8')
  classname = 'uint8';
  n = uint8(n);
elseif n < intmax('uint16')
  classname = 'uint16';
  n = uint16(n);
elseif n < intmax('uint32')
  classname = 'uint32';
  n = uint32(n);
else % n < intmax('uint64')  
  classname = 'uint64';
  n = uint64(n);
end
% Generate an input:
M = randi([0 n],N,1,classname);
% Time different options:
warning off 'MATLAB:timeit:HighOverhead'
func_times = {'histcounts (double)','histcounts (uint)','accumarray (old)',...
  'accumarray (new)';
    timeit(@() histci(double(M),double(n))),...
    timeit(@() histci(M,n)),...
    timeit(@() accumi(M)),...
    timeit(@() accumi_new(M))
    };
out = cell2mat(func_times(2,:));
end

function spp = histci(M,n)
  spp = histcounts(M,1:n+1);
end

function spp = accumi(M)
  spp = accumarray(M(M>0),1);
end

function spp = accumi_new(M)
  spp = accumarray(M+1,1);
  spp = spp(2:end);
end