Evaluation of Logic by Software Using BDDs

1
Evaluation of Logic by Software Using BDDs

• Andrew Mihal
• EE219B Spring 2000
• 5/16/2000

2
Outline

• Problem Statement
• Simple Approach
• Table-based BDD Approach
• Branch-based BDD Approach
• BDD Visualization
• Clumping Algorithms

3
Problem Statement

• Given
• A multilevel combinational network in BLIF format
• Generate
• A software function that evaluates the network
• void eval_network(int PI, int PO)

4
Simple Approach

• Perform topological sort on nodes
• Output each node as a C assignment using boolean
  operators in SOP form

void eval_network(PI, PO) int I6 I0
PI1 PI2 I1 ( ) ( )
... PO0 I4 PO1 I5
return
5
Simple Approach

• Pros
• Very simple to program
• No control flow
• Potential for compiler optimizations
• Cons
• Q(n) in time and space
• Not sophisiticated

6
Benchmarks

• Input BLIF Files (mcnc91)
• 1 to 3500 nodes

9symml apex7 comp i5 sct C1355
b1 cordic i6 small C17 b9
count i7 t C1908 c8 cu
i8 t481 C2670 cc dalu i9
tcon C3540 cht decod k2
term1 C432 cm138a des lal
too_large C499 cm150a example2 majority
ttt2 C5315 cm151a f51m mux
unreg C6288 cm152a frg1 my_adder
vda C7552 cm162a frg2 pair x1 C880
cm163a i1 parity x2 cm42a i10
pcle x3 x4 alu2 cm82a i2
pcler8 z4ml alu4 cm85a i3 pm1
rot apex6 cmb i4
7
Benchmarks

• gcc -O3 -pg
• Pentium-class machine
• Each network tested with 100,000 random input
  vectors (deterministic)
• Measure average time spent in each eval_network
  call
• Scripts used to run tests and gather statistics

8
Simple Approach Performance
9
Table-based BDD Approach

• Instead of statements of the form
• I1 (PI0 PI1) I0
• Use BDDs instead
• I1 eval_bdd(bdd_1, PI, I)
• Assume we have an efficient eval_bdd function
• Statements are still in topological order
• bdd_1 is a constant hardcoded table
• BDD ordering with sift

10
Table-based Approach

• Building a network node into a table

const bddn bdd_1 INT, I0, 1, POS, 3,
POS, INT, PI0, 3, NEG, 2, POS, INT,
PI1, 3, NEG, 3, POS, CONSTANT_1
11
Table-based Approach

• Pros
• BDD may be more efficient than SOP form
• Data hardcoded into program
• All we need to write is eval_bdd function
• Cons
• Compiler doesn't optimize hardcoded data
• eval_bdd function is inefficient
• Function call overhead
• BDD data table indexing

12
Table-based Peformance
13
Branch-based Approach

• Get rid of tables and eval_bdd function calls
• Replace eval_bdd statements with inline code
• Still use topological sort

14
Branch-based Approach
void eval_network(int PI, int PO) int
I6 int complement ...
NODE_1_START complement 1 NODE_1_0
if (I0) goto NODE_1_3 else goto
NODE_1_1 NODE_1_1 if (PI0) goto
NODE_1_2 else complement 1
goto NODE_1_2 NODE_1_2 if
(PI1) goto NODE_1_3 else complement
1 goto NODE_1_3
NODE_1_3 I1 complement ...
15
Branch-based Approach

• Pros
• No table lookups
• No function calls
• goto compiles straight to a simple jump
• Cons
• Performance?

16
Branch-based Performance
17
Branch-based Performance
18
BDD Visualization

• Instead of emitting BDDs as tables or branch
  structures, produce a graph
• Uses DOT, a graph drawing tool from ATT

19
(No Transcript)
20
Clumping Algorithms

• Can we improve performance by making BDDs larger?
• Clumping Collapse a node into its fanouts,
  removing it from the network

F A C D B
A
B
21
Clumping Algorithms

• Two different heuristics
• Input clumping
• Tries to make all BDDs have about N inputs
• Greedy algorithm
• Size clumping
• Tries to make all BDDs have about N nodes
• Greedy algorithm

22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
Performance with Clumping
28
Performance with Clumping
29
Performance with Clumping
30
Performance with Clumping
31
Clumping Issues

• Number of nodes decreases, but BDD size increases
• Average number of BDD nodes we evaluate stays the
  same?
• Synthesis and compile time very long and very
  memory intensive when using clumping
• Flat method synthesizes and compiles quickly, and
  scales to larger networks