Motorola DSP56000 Manual page 525

RND
Convergent rounding differs from ''standard'' rounding in that convergent rounding
attempts to remove the aforementioned positive bias by equally distributing the round-off
error. The convergent rounding technique initially performs "standard" rounding as previ-
ously described. Again, the rounding constant depends on the scaling mode being used.
Once "standard" rounding has been done, the convergent rounding method tests the
result to determine if all bits including and to the right of the rounding position are
zero. If, and only if, this special condition is true, the convergent rounding method will
clear the bit immediately to the left of the rounding position. When this special condition
is true, numbers which have a "1" in the bit immediately to the left of the rounding posi-
tion are rounded up; numbers with a "0" in the bit immediately to the left of the rounding
position are rounded down. Thus, these numbers are rounded up half the time and
rounded down the rest of the time. Therefore, the roundoff error averages out to zero.
The LS bits of the convergently rounded result are then cleared so that the rounded
result may be immediately used by the next instruction.
Example:
:
RND A #$123456,X1 B,Y1
:
Before Execution
Case I: A
$00:123456:789AB
Case II: A
$00:123456:800000
Case III: A
00:123456:800000
$
Explanation of Example: Prior to execution, the 56-bit A accumulator contains the
value $00:123456:789ABC for Case I, the value $00:123456:800000 for Case II, and the
value $00:123455:800000 for Case III. The execution of the RND A instruction rounds
the value in the A accumulator into the MSP portion of the A accumulator (A1), using
convergent rounding, and then zeros the LSP portion of the A accumulator (A0). Note
that Case II is the special case that distinguishes convergent rounding from standard or
biased rounding.
MOTOROLA
INSTRUCTION SET DESCRIPTIONS
Round Accumulator
;round A accumulator into A1, zero A0
INSTRUCTION SET DETAILS
After Execution
A
$00:123456:000000
A
$00:123456:000000
A
$00:123456:000000
RND
A - 259