Analog Devices ADSP-BF535 Blackfin, Hardware Reference Manual

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Data Types
2-18 ADSP-BF535 Blackfin Processor Hardware Reference
Rounding Multiplier Results
On many multiplier operations, the processor supports multiplier results
rounding (
RND
option). Rounding is a means of reducing the precision of a
number by removing a lower order range of bits from that number’s repre-
sentation and possibly modifying the remaining portion of the number to
more accurately represent its former value. For example, the original num-
ber will have N bits of precision, whereas the new number will have only
M bits of precision (where N>M). The process of rounding, then, removes
N-M bits of precision from the number.
The
RND_MOD
bit in the
ASTAT
register determines whether the
RND
option
provides biased or unbiased rounding. For unbiased rounding, set
RND_MOD
bit = 0. For biased rounding, set
RND_MOD
bit = 1.

For most algorithms, unbiased rounding is preferred.
Unbiased Rounding
The convergent rounding method returns the number closest to the origi-
nal. In cases where the original number lies exactly halfway between two
numbers, this method returns the nearest even number, the one contain-
ing an LSB of 0. For example, when rounding the 3-bit,
two’s-complement fraction 0.25 (binary 0.01) to the nearest 2-bit,
two’s-complement fraction, the result would be 0.0, because that is the
even-numbered choice of 0.5 and 0.0. Since it rounds up and down based
on the surrounding values, this method is called
unbiased rounding .
Unbiased rounding uses the multiplier’s capability of rounding the 40-bit
result at the boundary between bit 15 and bit 16. Rounding can be speci-
fied as part of the instruction code. When rounding is selected,
A0.H/A1.H
contain the rounded 16-bit result; the rounding effect in
A0.H/A1.H
affects
A0.X/A1.X
as well. The
A0.X/A0.H
and
A1.X/A1.H
registers repre-
sent the rounded 24-bit result, including sign extension and overflow.