DCT Scalings

Hello All,

I am trying to implement forward and inverse DCT based on Y. Arai, T.
Agui, and M. Nakajima, "A Fast DCT-SQ Scheme for Images," Trans. of the
IEICE, vol. E-71, no. 11, pp. 1095-1097, Nov. 1988 paper.

Both flow graphs for the forward and inverse DCT are given in the paper.
When I tried to implement the forward DCT I got a different result from
the DCT given in MATLAB.

I know that my problem is in scaling.
When I used the scalings in W. B. Pennebaker and J. L. Mitchell. JPEG
Still Image Data Compression Standard book the forward DCT output was
similar to the MATLAB's dct (they differ by 10^-13). But then the inverse
DCT output deviated so much.

According to ARAI's paper the scaling is done accoridng:
s(n) = 2*C(n)/cos(n*pi/16) where C(0) = 1/sqrt(2) & 1 for n>0

Accroding to Pennebaker's book the scaling is done accroding:
s(n) = 1/[4*cos(n*pi/16)] & s(0) = 1/[2*sqrt(2)]

Furthermore, In ARAI they divided the s(n)'s by 8 or 16 and these are the
outputs of the real DFT algorithm. Because the idea is to get the real DFT
and then do the scaling to have the DCT.

If some can know the problem or knows the correct scalings of the inverse
DCT please let me know, I would be grateful!