FFT inaccuracy

[Dirk Laurie]

>> ifft(fft([1 1 0 0 1]))
ans =
    1.0000e+00    1.0000e+00   -1.4682e-08   -1.4682e-08    1.0000e+00

This seems to indicate a lack of accuracy.  And indeed, comparison with
the exact value shows

>> fft([1 1 0 0 1])-[3, sin(3*(1:4)*pi/5)./sin((1:4)*pi/5)]
ans =
    0.0000e+00    1.6415e-08   -1.6415e-08   -1.6415e-08    1.6415e-08

This suggests some single-precision constant in the radix-5 special case.
The error does not occur with n=7:

>> ifft(fft([1 1 0 0 0 0 1]))
ans =
 Columns 1 through 5:
    1.0000e-00    1.0000e+00   -7.8064e-16    1.2067e-16    1.2067e-16
 Columns 6 and 7:
   -7.8064e-16    1.0000e+00

Dirk Laurie