theora dev - Mar 2011 - DCT-coefficients in

Why for white-pixel image, oc_enc_fdct8x8_c() returns
the matrix with non-zero AC-coefficients?

_x[64]:

* 107 107 107 107 107 107 107 107
* 107 107 107 107 107 107 107 107
* 107 107 107 107 107 107 107 107
* 107 107 107 107 107 107 107 107
* 107 107 107 107 107 107 107 107
* 107 107 107 107 107 107 107 107
* 107 107 107 107 107 107 107 107
* 107 107 107 107 107 107 107 107

_y[64]:

*   3426      1      1      1      0      0      0      0
*      1      2      1      1      0      0      0      0
*      1      1      1      1      0      0      0      0
*      1      2      1      1      0      0      0      0
*      1      1      1      1      0      0      0      0
*      0      1      1      1      0      0      0      0
*      1      1      1      1      1      0      1      0
*      0      0      0      0      0      0      0      0

This is - error of butterfly-method?

P.S. My program dct.py returns:
   1016      0     -0      0      0      0     -0     -0
      0     -0      0      0      0      0      0     -0
      0     -0      0      0      0     -0      0      0
      0      0     -0      0      0      0     -0      0
      0     -0      0     -0      0      0     -0     -0
      0      0      0      0      0      0      0      0
     -0      0     -0     -0      0      0     -0     -0
     -0     -0      0      0     -0     -0      0      0

> Why for white-pixel image, oc_enc_fdct8x8_c() returns
> the matrix with non-zero AC-coefficients?
Theora defines an exact-integer inverse DCT in the specification, that 
only approximately corresponds to the "real" DCT, and includes some 
scaling. See section 7.9.3 of the specification for details.

An encoder is allowed to use any forward DCT it wants, but a poor choice 
can have a substantial impact on quality, especially at high rates. A 
naive implementation (e.g., like VP3 used, which is the one currently 
referenced in the specification) or a direct matrix multiply will 
introduce significant round-trip error. The forward DCT used in 
libtheora is designed to minimize this round-trip error, and as such has 
a small amount of DC leakage (nothing that would exceed the minimum 
quantization threshold, however). See 
http://people.xiph.org/~xiphmont/demo/theora/demo7.html for some 
additional discussion.

I should probably update the (non-normative) description of the forward 
DCT in the spcification to match libtheora's, but for the moment the C 
code should be fairly straightforward.