1. CSE 522 WCET Analysis Computer Science & Engineering Department Arizona State University Tempe, AZ 85287 Dr. Yann-Hang Lee yhlee@asu.edu (480) 727-7507 Some of the slides were based on the lecture by G. Fainekos (ASU)

2. Execution Time – WCET & BCET (Figure from R.Wilhelm et al., ACM Trans. Embed. Comput. Sys, 2007.) 2

3. The WCET Problem  Given  the code for a software task  the platform (OS + hardware) that it will run on  Determine the WCET of the task.  Why is this problem important?  The WCET is central in the design of real-time computing  Can the WCET always be found?  In general, not a decidability problem, but a complexity problem  Compute bounds for the execution times of instructions and basic blocks and determine a longest path in the basic- block graph of the program.  3

4. Components of Execution Time Analysis  Program path (Control flow) analysis  Want to find longest path through the program  Identify feasible paths through the program  Find loop bounds  Identify dependencies amongst different code fragments  Processor behavior analysis  For small code fragments (basic blocks), generate bounds on run-times on the platform  Model details of architecture, including cache behavior, pipeline stalls, branch prediction, etc.  Outputs of both analyses feed into each other 4

5. Program Path Analysis: Overall Approach (1)  Construct Control-Flow Graph (CFG) for the task  Nodes represent Basic Blocks of the task  Basic block: a sequence of consecutive program statements where there is no possibility of branching  We have a single entry and a single exit node  Edges represent flow of control (jumps, branches, calls, …)  The problem is to identify the longest path in the CFG  Note: CFG can have loops, so need to infer loop bounds and unroll them  This gives us a directed acyclic graph (DAG). How do we find the longest path in this DAG? 5

6. Program Path Analysis: Overall Approach (2)  In a CFG  B i = basic block i  x i = number of times the block B i is executed  d j = number of times edge is executed  c i = worst case running time of block B i  Objective: find  How to get x i ?  Structural constraints  Functionality constraints  Loop bounds -- need to be known 6

7. CFG Example N = 10; q = 0; while(q < N) q++; q = r; Example due to Y.T. Li and S. Malik B1: N = 10; q = 0; B2: while(q<N) B4: q = r; B3: q++; 1 0 x1x1 x2x2 x4x4 x3x3 d1 d2 d3 d4 d5 d6 Want to maximize  i c i x i subject to constraints x 1 = d 1 = d 2 d 1 = 1 x 2 = d 2 +d 4 = d 3 +d 5 x 3 = d 3 = d 4 = 10 x 4 = d 5 = d 6 7

8. CFG – Another example 8 /* k >=0 */ s = k; while (k < 10){ if (ok) j++; else { j = 0; ok = true; } k++; } r = j; d1d1 d5d5 d4d4 d3d3 d2d2 d8d8 d 10 d9d9 d6d6 d7d7 B1B1 s = k; B2B2 while (k < 10){ B3B3 if (ok) B4B4 j++; B6B6 k++; B7B7 r = j; B5B5 j = 0; ok = true; x7x7 x2x2 x3x3 x4x4 x5x5 x6x6 x1x1

9. check_data() { x 1 int i, morecheck, wrongone; x 2 morecheck = 1; i = 0; wrongone = -1; x 3 while (morecheck) { x 4 if (data[i] < 0) { x 5 wrongone = i; morecheck = 0; } else x 6 if (++i >= 10) x 7 morecheck = 0; } x 8 if (wrongone >= 0) x 9 return 0; else x 10 return 1; } Functionality Constraints 9 x 2  x 4 x 4  10x 2 Constraints (x 5 = 0 & x 7 = 1) | (x 5 = 1 & x 7 = 0) x 5 = x 9

10. Micro-architectural Modeling -- Cache  Modify cost function (cache hit and miss have different costs)  Add linear constraints to describe relationship between cache hits and misses  Basic idea  Basic blocks assumed to be smaller than entire cache  Subdivide instruction counts (x i ) into counts of cache hits (x i hit ) and misses (x i miss )  Line-block (or l-block) is a contiguous sequence of code within the same basic block that is mapped to the same cache line in the instruction cache  Either all hit or all miss in a l-block 10

11. Basic Blocks to Line Blocks (Direct- mapped cache) Color Cache Set 0 1 2 3 B1B1 B2B2 B3B3 B 1.1 B 1.2 B 1.3 B 2.1 B 2.2 B 3.1 B 3.2 No conflicting l-blocks: (only the first execution has a miss) Two nonconflicting l-blocks are mapped to same cache line Conflicting blocks: affected by the sequence Cache Constraints: 11

12. Cache Conflict Graph  For every cache set containing two or more conflicting l- blocks  start node, end node, and node B k.l for every l-block in the cache set  Edge from B k.l to B m.n : control can pass between them without passing through any other l-blocks of the same cache set.  p (i. j,u.v) : the number of times that the control passes through that edge. 12 start B m.n end B k.l p (k.l,k.l) p (m.n,m.n) p (s,k.l) p (s,m.n) p (k.l,m.n ) p (m.n,k.l ) p (k.l,e) p (m.n,e) p (s,e)

13. Cache Cache Constraints Example (1) d1d1 d5d5 d4d4 d3d3 d2d2 d8d8 d 10 d9d9 d6d6 d7d7 B 1.1 s = k; B 2.1 while (k < 10){ B 3.1 if (ok) B 4.1 j++; B 6.1 k++; B 7.1 r = j; B 5.1 j = 0; ok = true; x7x7 x2x2 x3x3 x4x4 x5x5 x6x6 x1x1 13

14. Cache Constraints Example (2) S E B 5.1 B 4.1 p (s,4.1) p (s,5.1) p (s,e) p (4.1,4.1) p (5.1,4.1) p (4.1,5.1) p (5.1,5.1) p (5.1,e) p (4.1,e) S E B 6.1 B 1.1 p (s,1.1) p (1.1,6.1) p (1.1,e) p (6.1,e) p (6.1,6.1) 14

15. 1995 20022005 over-estimation 20-30% 15% 30-50% 4 25 60 200 cache-miss penalty Lim et al. Thesing et al.Souyris et al. The explosion of penalties has been compensated by a reduction of uncertainties! 10% 25% Progress During the Past 10 Years 15

16. Open Problems  Architectures are getting much more complex.  Can we create processor behavior models without the pain?  Can we change the architecture to make timing analysis easier?  Small changes to code and/or architecture require completely re-doing the WCET computation  Use robust techniques that learn about processor/platform behavior  Need more reliable ways to measure execution time  References:  Li, Malik, and Wolfe, “Cache Modeling for Real-Time Software: Beyond Direct Mapped Instruction Caches”  Wilhelm, “Determining bounds on execution times,” Handbook on Embedded Systems, CRC Press, 2005 16