Embedded Software for SoC - Grupo de Mecatrônica EESC/USP

Dynamic Functional Unit Assignment for Low Power 489
4.2. Approximating the hamming distance computation
To reduce the overhead of the above strategy, full Hamming distance computations
must be avoided. We achieve this by exploiting certain properties
of numerical data to represent an operand by a single information bit.
Integer bit patterns. It is known [3], that most integer operands are small. As
a consequence, most of the bits in a 2’s complement representation are
constant and represent the sign. It is likely that the Hamming distance between
any two consecutive operand values will be dominated by the difference in
their sign bits. Thus we can replace the operands by just their top bits, for
the purposes of Figure 35-2.
Table 35-1 validates this technique. This table records the operand bit
Table 35-1. Bit patterns in data. The values in the first three columns are used to separate the
results into 8 rows. Columns 1 and 2 show the information bits of both operands; (for integers,
the top bit; for floating points, the OR-ing of the bottom four bits of the mantissa). Columns 4
and 7 are the occurrence frequencies for the given operand bits and commutativity pattern, as
a percentage of all executions of the FU type. Columns 5, 6, 8, and 9 display, for the specified
operand, the probability of any single bit being high.
OP1
OP 2
Commutative
()
IALU
Frequency
(%)
Operand
1 bit
prob.
Operand
2 bit
prob.
FPAU
Frequency
(%)
Operand
1 bit
prob.
Operand
2 bit
prob.
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
Yes
No
Yes
No
Yes
No
Yes
No
40.11
29.38
9.56
0.58
17.07
1.51
1.52
0.27
0.123
0.078
0.175
0.109
0.608
0.643
0.703
0.663
0.068
0.040
0.594
0.820
0.089
0.048
0.822
0.719
16.79
10.28
15.64
4.90
5.92
4.22
31.00
11.25
0.099
0.107
0.188
0.132
0.513
0.500
0.508
0.507
0.094
0.158
0.522
0.514
0.190
0.188
0.502
0.506