Analog Devices ADSP-BF535 Blackfin, Hardware Reference Manual

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Data Types
2-20 ADSP-BF535 Blackfin Processor Hardware Reference
In Figure 2-7 ,
A0
bit 16 is forced to zero. This algorithm is employed on
every rounding operation, but is evident only when the bit patterns shown
in the lower 16 bits of the next example are present.
Biased Rounding
The round-to-nearest method also returns the number closest to the origi-
nal. However, by convention, an original number lying exactly halfway
between two numbers always rounds up to the larger of the two. 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, this method
returns 0.5 (binary 0.1). The original fraction lies exactly midway between
0.5 and 0.0 (binary 0.0), so this method rounds up. Because it always
rounds up, this method is called
biased rounding .
The
RND_MOD
bit in the
ASTAT
register enables biased rounding. When the
RND_MOD
bit is cleared, the
RND
option in multiplier instructions uses the
normal, unbiased rounding operation, as discussed in “Unbiased Round-
ing” on page 2-18 .
When the
RND_MOD
bit is set (=1), the processor uses biased rounding
instead of unbiased rounding. When operating in biased rounding mode,
all rounding operations with
A0.L/A1.L
set to 0x8000 round up, rather
than only rounding odd values up. For an example of biased rounding, see
Figure 2-8 .
Figure 2-7. Avoiding Net Bias in Unbiased Multiplier Rounding
........|................|................
xxxxxxxx|xxxxxxxx01100110|1000000000000000
........|................|1...............
xxxxxxxx|xxxxxxxx01100111|0000000000000000
Unrounded value:
Add 1 and carry:
A0 bit 16=1:
xxxxxxxx|xxxxxxxx01100110|0000000000000000
Rounded value:
A0.X A0.W