24
Recommendation H.261
(03/93)
Annex A
Inverse transform accuracy specification
(This annex forms an integral part of this Recommendation)
A.1
Generate random integer pel data values in the range
−L to +H according to the random number generator given
below (“C” version). Arrange into 8 by 8 blocks. Data set of 10 000 blocks should each be generated for (L
= 256, H = 255),
(L
= H = 5) and (L = H = 300).
A.2
For each 8 by 8 block, perform a separable, orthonormal, matrix multiply, forward discrete cosine transform using
at least 64-bit floating point accuracy.
F u v
C u C v
f x y
x
u
y
v
x
y
( , ) =
( ) ( )
( , ) cos[ (
)
] cos[ (
)
]
1
4
0
7
0
7
2
1
16
2
1
16
=
=
∑ ∑
+
+
π
π
/
/
with
u, v, x, y
= 0, 1, 2, . . .,7
where
x,y
= spatial coordinates in the pel domain,
u,v
= coordinates in the transform domain,
C(u)
= 1/ 2 for u = 0; otherwise 1,
C(v)
= 1/ 2 for v = 0; otherwise 1.
A.3
For each block, round the 64 resulting transformed coefficients to the nearest integer values. Then clip them to the
range –2048 to
+2047. This is the 12-bit input data to the inverse transform.
A.4
For each 8 by 8 block of 12-bit data produced by A.3, perform a separable, orthonormal, matrix multiply, inverse
discrete transform (IDCT) using at least 64-bit floating point accuracy. Round the resulting pels to the nearest integer and clip
to the range
−256 to +255. These blocks of 8 × 8 pels are the reference IDCT input data.
A.5
For each 8 by 8 block produced by A.3, apply the IDCT under test and clip the output to the range –256 to
+255.
These blocks of 8
× 8 pels are the test IDCT output data.
A.6
For each of the 64 IDCT output pels, and for each of the 10,000 block data sets generated above, measure the peak,
mean and mean square error between the reference and the test data.
A.7
For any pel, the peak error should not exceed 1 in magnitude.
For any pel, the mean square error should not exceed 0.06.
Overall, the mean square error should not exceed 0.02.
For any pel, the mean error should not exceed 0.015 in magnitude.
Overall, the mean error should not exceed 0.0015 in magnitude.
A.8
All zeros in must produce all zeros out.
A.9
Re-run the measurements using exactly the same data values of A 1, but change the sign on each pel.
“C” program for random number generation
/* L and H must be long, that is 32 bits */
long rand
(L,H)
long
L,H;
{
static long randx
= 1;
/* long is 32 bits */
static double z
= (double) 0x7fffffff;
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