Range Equivalent Circuit Construction

1. Range Equivalent Circuit Construction Yung-Chih Chen

2. Approach overview Combinational circuit • Simplifying operations • Split fanout PIs • Remove PIs • Merge PIs • Range equivalent checking • Preprocess • ATPG-based approach Range equivalent circuit

3. Split fanout PIs • Split fanout PIsto construct tree structures • Splitting fanout PIs may produce extra images • These extra images will imply two different values at the splitting PIs

4. Remove PIs • Remove PIs: set PIs to be constant values • Removing PIs may eliminate images • These images will imply an opposite value at the removed PI 1

5. Merge PIs • Merge two PIs into a single PI • Merging PIs may eliminate images • These images will imply two different values at the merged two PIs

6. Approach overview Combinational circuit • Simplifying operations • Split fanout PIs • Remove PIs • Merge PIs • Range equivalent checking • Preprocess • ATPG-based approach Range equivalent circuit

7. Preprocess • Calculate mandatory assignments and then perform logic implication • Conflict occurs → no such images→ perform simplifying operations

8. Mandatory assignments for a image test • Side input of dominators must be non-controlling value of its corresponding dominator 0 0 O1 0 Conflict a1 1 a 1 O2 a2 0 1

9. ATPG-based approach • How to check if an image implies two different values at the merged two PIs • (f, g)=(0, 0) implies a1≠a2 • How to check if an image implies an opposite value at the removed PI • (f, g)=(0, 0) implies a1= 0 a1 a2 a1 s-a-0 ? s-a-0 ? s a1 s f f a2 g g

10. Images generation • Branch and bound approach • Branch • Which PO?; 0 or 1? • Bound • Objectives cannot be achieved anymore 0 a 1 b b 0 1 1 0 c c c c 1 0 1 1 0 0 1 0 Depth First Search

11. Branch • Decision order • First, POs which are in the transitive fanout cone of objective node • Then, remaining POs a1=1

12. Bound H • Objective: (a1, a2) = (0, 1) • Bounding occurs when • Implication conflict • a1 = 1 or a2 = 0 • PNODE is empty G a1=1 PNODE a1=1 a1 is a PI

13. Algorithm OPG( ) begin if (Objective_Achieve()) return SUCCESS; if (Bound()) return FAILURE; n = Select_A_PO(); if (Implication(n, 0)==SUCCESS) if (OPG()==SUCCESS) return SUCCESS; if (Implication(n, 1)==SUCCESS) if (OPG()==SUCCESS) return SUCCESS; return FAILURE end

14. Flow Split fanout PIs Remove PIs Remove PIs Remove PIs Merge PIs Merge PIs

15. Experimental results

16. Conclusion • We still cannot handle large circuits • Future work • Improve preprocess • Circuit partition • Recursive learning