We generate a sequence called Vander Corput's or integer bit reversal which distributes uniformly on the interval (0, 1). Using this sequence and the aid of Sunzi's theorem, we obtain an extended FFT of which length is arbitrary number. And then, we apply this to automatic approximation of function increasing the sample points more gradually than the case of common FFT. For example, we present the automatic Chebyshev expansion of function increasing the sample points as 3×2^l, 4×2^l, 5×2^l, l=0, 1, 2, …. As the automatic quadrature, this technique is efficiently applied to product type integration including typical several singular integrals.
