Graphics Reference
In-Depth Information
a
b
Fig. 10.8
4 matrix multiplication in Eq. (
10.1
) without and with unique operations. (
a
) Generic
implementation. (
b
) Exploiting unique operations
4
Table 10.2
Area reduction by exploiting unique operations
Area for generic
implementation
(kgates)
Area exploiting
unique operations
(kgates)
Matrix
multiplication
Area
savings
4
4
10.7
7.3
32 %
8
8
23.2
13.5
42 %
16
16
46.7
34.4
26 %
case, only two of these inputs are available per cycle. So, it is enough to perform
a partial 2
16 matrix multiplication every cycle and accumulate the outputs over
eight cycles. In general, this would require 32 full multipliers and 32 lookup tables to
store the matrix. However, knowing that the matrix has only 15 unique numbers, we
can simply instantiate 15 constant multipliers with some negators and multiplexers
to implement the matrix multiplication. This is shown for the 4
4 odd matrix
multiplication (Eq. (
10.1
)) of the 8-pt IDCT in Fig.
10.8
b. The area savings are
shown in Table
10.2
.
2
4
3
5
89 75 50 18
75
18
89
50
50
89
y
0
y
1
y
2
y
3
D
u
0
u
1
u
2
u
3
(10.1)
18
75
18
50
75
89
