Analog Devices ADSP-BF535 Blackfin, Hardware Reference Manual

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ADSP-BF535 Blackfin Processor Hardware Reference 2-19
Computational Units
The accumulator uses an unbiased rounding scheme. The conventional
method of biased rounding adds a 1 into bit position 15 of the adder
chain. This method causes a net positive bias because the midway value
(when
A0.L/A1.L = 0x8000
) is always rounded upward.
The accumulator eliminates this bias by forcing bit 16 in the result output
to zero when it detects this midway point. Forcing bit 16 to zero has the
effect of rounding odd
A0.L/A1.L
values upward and even values down-
ward, yielding a zero large sample bias, assuming uniformly distributed
values.
The following examples use x to represent any bit pattern (not all zeros).
The example in Figure 2-6 shows a typical rounding operation for
A0
; the
example also applies for
A1
.
The compensation to avoid net bias becomes visible when all lower 15 bits
are zero and bit 15 is one (the midpoint value) as shown in
Figure 2-7 .
Figure 2-6. Typical Unbiased Multiplier Rounding
.........|................|................
xxxxxxxx|xxxxxxxx00100101|1xxxxxxxxxxxxxxx
........|................|1...............
xxxxxxxx|xxxxxxxx00100110|0xxxxxxxxxxxxxxx
Unrounded value:
Add 1 and carry:
Rounded value:
A0.X A0
.
W