NEXTFASTFFT - Next higher number with a fast FFT

function [nfft,tableout]=nextfastfft(n)
%NEXTFASTFFT  Next higher number with a fast FFT
%   Usage: nfft=nextfastfft(n);
%
%   NEXTFASTFFT(n) returns the next number greater than or equal to n,
%   for which the computation of a FFT is fast. Such a number is solely
%   comprised of small prime-factors of 2, 3, 5 and 7.
%
%   NEXTFASTFFT is intended as a replacement of nextpow2, which is often
%   used for the same purpose. However, a modern FFT implementation (like
%   FFTW) usually performs well for sizes which are powers or 2,3,5 and 7,
%   and not only just for powers of 2.
%
%   The algorithm will look up the best size in a table, which is computed
%   the first time the function is run. If the input size is larger than the
%   largest value in the table, the input size will be reduced by factors of
%   2, until it is in range.
%
%   [n,nfft]=NEXTFASTFFT(n) additionally returns the table used for
%   lookup.
%
%   See also: ceil23, ceil235
%
%   Demos: demo_nextfastfft
%
%   References:
%     J. Cooley and J. Tukey. An algorithm for the machine calculation of
%     complex Fourier series. Math. Comput, 19(90):297--301, 1965.
%     
%     M. Frigo and S. G. Johnson. The design and implementation of FFTW3.
%     Proceedings of the IEEE, 93(2):216--231, 2005. Special issue on
%     "Program Generation, Optimization, and Platform Adaptation".
%     
%     P. L. Søndergaard. LTFAT-note 17: Next fast FFT size. Technical report,
%     Technical University of Denmark, 2011.
%     
%
%   Url: http://ltfat.github.io/doc/fourier/nextfastfft.html

% Copyright (C) 2005-2023 Peter L. Soendergaard <peter@sonderport.dk> and others.
% This file is part of LTFAT version 2.6.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program.  If not, see <http://www.gnu.org/licenses/>.
  
%   AUTHOR: Peter L. Søndergaard and Johan Sebastian Rosenkilde Nielsen
  
  
persistent table;
  
maxval=2^20;

if isempty(table)
  % Compute the table for the first time, it is empty.
  l2=log(2);
  l3=log(3);
  l5=log(5);
  l7=log(7);
  lmaxval=log(maxval);
  table=zeros(1286,1);
  ii=1;
  prod2=1;
  for i2=0:floor(lmaxval/l2)
    prod3=prod2;
    for i3=0:floor((lmaxval-i2*l2)/l3)               
      prod5=prod3;
      for i5=0:floor((lmaxval-i2*l2-i3*l3)/l5)
        prod7=prod5;
        for i7=0:floor((lmaxval-i2*l2-i3*l3-i5*l5)/l7)
          table(ii)=prod7; 
          prod7=prod7*7;
          ii=ii+1;
        end;
        prod5=prod5*5;                    
      end;
      prod3=prod3*3;
    end;
    prod2=prod2*2;            
  end;
  table=sort(table);
end;

% Copy input to output. This allows us to efficiently work in-place.
nfft=n;

% Handle input of any shape by Fortran indexing.
for ii=1:numel(n)
  n2reduce=0;
  
  if n(ii)>maxval
    % Reduce by factors of 2 to get below maxval
    n2reduce=ceil(log2(nfft(ii)/maxval));
    nfft(ii)=nfft(ii)/2^n2reduce;
  end;
  
  % Use a simple bisection method to find the answer in the table.
  from=1;
  to=numel(table);
  while from<=to
    mid = round((from + to)/2);    
    diff = table(mid)-nfft(ii);
    if diff<0
      from=mid+1;
    else
      to=mid-1;                       
    end
  end
  nfft(ii)=table(from);
  
  % Add back the missing factors of 2 (if any)
  nfft(ii)=nfft(ii)*2^n2reduce;
  
end;

tableout=table;