On-Chip Logic Minimization

1. On-Chip Logic Minimization Roman Lysecky & Frank Vahid* Department of Computer Science and Engineering University of California, Riverside *Also with the Center for Embedded Computer Systems, UC Irvine This work was supported in part by the National Science Foundation, the Semiconductor Research Corporation, and a Department of Education GAANN fellowship

2. Introduction • Boolean logic minimization typically used during logic synthesis • Two-level logic minimization can be considered as a general optimization technique • Many applications can benefit from using logic minimization dynamically • IP routing table reduction • Access control list (ACL) reduction

3. Incoming IP packet 138.23.16.9 138.23.16.9 Destination IP address Prefix Next hop 138.23.16.x Port 7 Lookup Destination IP in Routing Table 138.23.x.x Port 5 125.x.x.x Port 3 Port 7 Choose Longest Prefix Match On-Chip Minimization Applications (IP Routing Table Reduction)

4. On-Chip Minimization Applications (IP Routing Table Reduction) • Longest Prefix Match • Ternary CAM (McAuley & Francis, 1993) • Store 0,1,* • Store IP address as TCAM entry • Store prefix length using the TCAM entries mask • Fast • Smaller hardware resources than binary CAM • Very large power consumption • How can we reduce hardware resources and power consumption?

5. Logic Minimization TCAM Entries after Mask Extension # IP Addr. Mask Next Hop P1&P2 10001100 11101100 7 On-Chip Minimization Applications (IP Routing Table Reduction) • Mask Extension (Liu, 2002) • Uses two-level logic minimization • Performing minimization for each update too slow • Incremental update • Existing minimized set becomes don’t care set • New route becomes single entry in on set • Achieves an average of 50 updates/second • Not considering communication, though Original TCAM Entries

6. Type Protocol In IP In Port Out IP Out Port Action On-Chip Minimization Applications (Access Control List Reduction) • Access Control List (ACL) • Used to restrict IP traffic through network routers • ACL size can range anywhere from from 300 (UCR CS&E Dept.) to 10,000 (AOL) • Common use is to block a particular protocol or port number to avoid attacks such as Denial of Service attacks • ACL Minimization • Similar approach as used for IP routing table reduction • However, order of the list must be preserved ACL Input Format

7. Transmit Data to Server Transmit Data to Server MEM Proc. MEM MEM MEM I$ Execute Minimizer Execute Minimizer D$ Server Network Router Chip Transmit Result to Router Introduction(Off-chip Logic Minimization) • Slow due to communication • Sensitive to server failures • Security issues Router

8. MEM Proc. I$ Initialize Minimizer D$ Execute Minimizer ARM7 ARM7 ARM7 DMA ARM7 Indicate Completion Mem. Mem. Mem. Network Router Chip On-chip Minimizer On-chip Minimizer Introduction(On-chip Logic Minimization) Router

9. On-Chip Logic MinimizationRequirements • On-chip Logic Minimization Requirements • Data Memory Resources • On-chip minimization algorithms must be very memory conscious • Instruction Memory Resources • On-chip minimization algorithm must incorporate simplified approaches that result in acceptable designs • Execution time • Limited data and instruction memory will likely lead to longer execution times • Must still remain reasonable • Quality of results • Must be capable of producing solution relatively close to optimal Focus on developing an on-chip logic minimization tool that produces acceptable results with reasonable increases in execution time while using limited memory resources.

10. ROCM • ROCM – Riverside On-Chip Minimizer • Two-level minimization tool • Utilized a combination of approaches from Espresso-II (Brayton, et al. 1984) and Presto (Svoboda & White, 1979) IterativeExpand(F,D,c) { W = {} c' = c for i=1 to |c| { c' = Expand(c',i) (val,W') = ValidExpansion(F,D,c') if val = true W = W  W' else Revert(c',i) }  return (c',W) } Optimize(F,D) { OrderCubes(F) for i=1 to |F| { c = Fi (c',W) = IterativeExpand(F,D,c) F = (F  c') - W } }

11. Only 2% larger than optimal on average ROCM Results – Quality (Full Routing Table Reduction)

12. ROCM executing on a 40MHz ARM7 requires less than 1 second ROCM Results – Performance (Incremental Update Execution Time) On a 40 MHz ARM 7 On a 500 MHz Sun Ultra60

13. Small code size of only 22 kilobytes Average data memory usage of only 1 megabyte ROCM Results – Memory (Code Size and Data Memory Usage) Data Memory Usage Code Size

14. Only 2% larger than optimal on average ROCM Results – Quality(Access Control List Reduction)

15. Customizing ROCM • ROCM Customization • Beneficial to optimize an algorithm for a particular application • Customize ROCM’s data structures and algorithms for a particular input size • Require less memory • Reduce dynamic memory allocation • Improve performance • Created ROCM-32 customized for IP routing table reduction

16. 11% reduction in data memory usage vs. ROCM 37% reduction in execution time vs. ROCM Customized ROCM-32 Results(IP Routing Table Reduction)

17. Conclusions • Presented Riverside On-Chip Minimizer (ROCM) • Feasible to execute logic minimization on chip • Can be executed on an embedded 40 MHz ARM7 in seconds for real networking problem sizes • Requires small code size (22 kilobytes) • Requires small data memory (1 megabyte) • Produces good results • On average only 2% larger than exact minimization • Shown usefulness for networking applications

18. Future Work • More Applications • May appear now that on-chip minimization is feasible • Dynamic HW/SW Partitioning • Dynamically partition executing binary to on-chip configurable logic • Logic minimization is used during the logic synthesis stage • Initial work on dynamic HW/SW partitioning presented at DAC 2003 yesterday in session 15