What is this algorithm for computation of the convolution integral in continuous wavelet transform?

Looking into demo of continous wavelet transform by waveletAnalyzer (Wavelet toolbox) I came across an unknown numerical method for computation of the convolution integral. It is specifed as numALG = 1 in the file cw1dmnr.m lines 537-576:

switch numALG
case 1
  [psi,psi_xval] = intwave(wav_Name,precis);
  psi_xval = psi_xval-psi_xval(1);
  dxval = psi_xval(2);
  xmax  = psi_xval(length(psi_xval));
  ind   = 1;
  for a = scales
      msg = {' ',getWavMSG('Wavelet:divGUIRF:Str_CompSca',num2str(a,'%5.3f'))};
      set(txt_msg,'String',msg);
      drawnow
      j = 1+floor((0:a*xmax)/(a*dxval));
      if length(j)==1 , j = [1 1]; end
      f = fliplr(psi(j));
      varargout{1}(ind,:) = -sqrt(a)*wkeep1(diff(conv(sig_Anal,f)),len);
      ind = ind+1;
  end
case 2        
  switch wtype
    case {1,3} , [~,psi,psi_xval] = wavefun(wav_Name,precis);
    case 2     , [~,psi,~,~,psi_xval] = wavefun(wav_Name,precis);
    case {4,5} , [psi,psi_xval] = wavefun(wav_Name,precis);
  end
  % if wtype==5 , psi = conj(psi); end
  psi_xval = psi_xval-psi_xval(1);
  dxval = psi_xval(2);
  xmax  = psi_xval(end);
  ind   = 1;
  for a = scales
      msg = {' ',getWavMSG('Wavelet:divGUIRF:Str_CompSca',num2str(a,'%5.3f'))};
      set(txt_msg,'String',msg);
      drawnow
      j = 1 + floor((0:a*xmax)/(a*dxval));
      if length(j)==1 , j = [1 1]; end
      f = fliplr(psi(j));
      varargout{1}(ind,:) = wkeep1(conv(sig_Anal,f),len);
      ind = ind+1;
  end
end

The second algorithm (case numALG == 2) straightforwardly computes the inner products between signal and translated wavelets by usual convolution:

psi = wavefun(wav_Name, precis)
out = conv(signal, fliplr(psi), 'same')

But I struggle to understand the first one, where signal is convolved with the integral of the wavelet and the result is differentiated:

integ_psi = intwave(wav_Name, precis)
out = diff(conv(signal,fliplr(integ_psi)))

Any insights into what is this method based on?