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INSTRUCTION SET DESCRIPTIONS
MOTOROLA
INSTRUCTION SET DETAILS
A - 259
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
;round A accumulator into A1, zero A0
:
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.
RND
Round Accumulator
RND
Before Execution
After Execution
Case I: A
$00:123456:789AB
Case II: A
A
$00:123456:800000
$00:123456:000000
$00:123456:000000
A
Case III: A
$
00:123456:800000
$00:123456:000000
A
Summary of Contents for DSP56K
Page 12: ...xii LIST of TABLES MOTOROLA List of Tables Continued Table Page Number Title Number ...
Page 13: ...MOTOROLA DSP56K FAMILY INTRODUCTION 1 1 SECTION 1 DSP56K FAMILY INTRODUCTION ...
Page 31: ...MOTOROLA DATA ARITHMETIC LOGIC UNIT 3 1 SECTION 3 DATA ARITHMETIC LOGIC UNIT ...
Page 50: ...DATA ALU SUMMARY 3 20 DATA ARITHMETIC LOGIC UNIT MOTOROLA ...
Page 51: ...MOTOROLA ADDRESS GENERATION UNIT 4 1 SECTION 4 ADDRESS GENERATION UNIT ...
Page 77: ...MOTOROLA PROGRAM CONTROL UNIT 5 1 SECTION 5 PROGRAM CONTROL UNIT ...
Page 124: ...INSTRUCTION GROUPS 6 30 INSTRUCTION SET INTRODUCTION MOTOROLA ...
Page 125: ...MOTOROLA PROCESSING STATES 7 1 SECTION 7 PROCESSING STATES STOP WAIT EXCEPTION NORMAL RESET ...
Page 167: ...STOP PROCESSING STATE MOTOROLA PROCESSING STATES 7 43 ...
Page 168: ...STOP PROCESSING STATE 7 44 PROCESSING STATES MOTOROLA ...
Page 169: ...MOTOROLA PORT A 8 1 SECTION 8 PORT A ...
Page 176: ...PORT A INTERFACE 8 8 PORT A MOTOROLA ...
Page 177: ...MOTOROLA PLL CLOCK OSCILLATOR 9 1 SECTION 9 PLL CLOCK OSCILLATOR x x d Φ VCO ...
Page 191: ...10 2 ON CHIP EMULATION OnCE MOTOROLA SECTION 10 ON CHIP EMULATION OnCE ...
Page 218: ...USING THE OnCE MOTOROLA ON CHIP EMULATION OnCE 10 29 ...
Page 604: ...INSTRUCTION ENCODING A 338 INSTRUCTION SET DETAILS MOTOROLA ...
Page 605: ...MOTOROLA BENCHMARK PROGRAMS B 1 APPENDIX B BENCHMARK PROGRAMS T T T T T P1 P3 P2 P4 T T T ...
Page 609: ...BENCHMARK PROGRAMS MOTOROLA BENCHMARK PROGRAMS B 5 ...
Page 611: ...BENCHMARK PROGRAMS MOTOROLA BENCHMARK PROGRAMS B 7 ...
Page 613: ...BENCHMARK PROGRAMS MOTOROLA BENCHMARK PROGRAMS B 9 ...
Page 615: ...BENCHMARK PROGRAMS MOTOROLA BENCHMARK PROGRAMS B 11 ...