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Lazy Spilling for a Time-Predictable Stack Cache: Implementation and Analysis Sahar Abbaspour, Alexander Jordan Florian Brandner Embedded Systems Engineering Sect. Unit e dInformatique et dIng. des Syst` emes Technical University of

  1. Lazy Spilling for a Time-Predictable Stack Cache: Implementation and Analysis Sahar Abbaspour, Alexander Jordan Florian Brandner Embedded Systems Engineering Sect. Unit´ e d’Informatique et d’Ing. des Syst` emes Technical University of Denmark ENSTA-ParisTech This work is partially supported by the EC project T-CREST. 1/25

  2. Real-Time Systems Strict timing guarantees • Critical tasks have to be completed in time 2/25

  3. Real-Time Systems Strict timing guarantees • Critical tasks have to be completed in time • Bound Worst-Case Execution Time (WCET) Worst-Case Execution Time Bound Worst-Case Execution Time # Executions Best-Case Execution Time Average Execution Time Overestimation Execution Time 2/25

  4. WCET Analysis Bound longest possible execution time of a program • Covering all potential execution paths • Covering all potential program inputs • Covering all potential hardware states 3/25

  5. WCET Analysis Bound longest possible execution time of a program • Covering all potential execution paths • Covering all potential program inputs • Covering all potential hardware states • Processor pipeline • Branch predictors • Data and instruction caches • Main memory 3/25

  6. Example: Miss/Hit Classification Initial cache state ∗ 0x100 0x200 0x101 0x103 ∗ Cache configuration 2-way set-associative, 1 word blocks, 2 cache lines, LRU replacement 4/25

  7. Example: Miss/Hit Classification Initial cache state ∗ 0x100 0x200 0x101 0x103 0x100 0x200 Classified as hit lw [0x100] 0x101 0x103 ∗ Cache configuration 2-way set-associative, 1 word blocks, 2 cache lines, LRU replacement 4/25

  8. Example: Miss/Hit Classification Initial cache state ∗ 0x100 0x200 0x101 0x103 0x100 0x200 Classified as hit lw [0x100] 0x101 0x103 0x100 0x200 lw [0x105] Classified as miss 0x105 0x101 ∗ Cache configuration 2-way set-associative, 1 word blocks, 2 cache lines, LRU replacement 4/25

  9. Example: Miss/Hit Classification Initial cache state ∗ 0x100 0x200 0x101 0x103 0x100 0x200 Classified as hit lw [0x100] 0x101 0x103 0x100 0x200 lw [0x105] Classified as miss 0x105 0x101 ?? ?? lw [??] Classification unclear ?? ?? ∗ Cache configuration 2-way set-associative, 1 word blocks, 2 cache lines, LRU replacement 4/25

  10. Example: Miss/Hit Classification Initial cache state ∗ 0x100 0x200 0x101 0x103 0x100 0x200 Classified as hit lw [0x100] 0x101 0x103 0x100 0x200 lw [0x105] Classified as miss 0x105 0x101 ?? ?? lw [??] Classification unclear ?? ?? Main challenge The abstract cache state of the analysis depends on the precise address and order of the executed memory accesses. ∗ Cache configuration 2-way set-associative, 1 word blocks, 2 cache lines, LRU replacement 4/25

  11. Context-Sensitivity Miss/hit classification requires • Precise information to disambiguate addresses • High levels of context-sensitivity • High levels of virtual loop unrolling • Analysis effort is multiplied accordingly 5/25

  12. Context-Sensitivity Miss/hit classification requires • Precise information to disambiguate addresses • High levels of context-sensitivity • High levels of virtual loop unrolling • Analysis effort is multiplied accordingly Main problem Subsequent phases of WCET analysis suffer from high complexity due to this virtual code duplication. 5/25

  13. Alternative Solution Predictable caching • Dedicated caches designed for analyzability/predictability • Easy to analyze • Simple hardware design • Requiring no/little information on accesses addresses 6/25

  14. Alternative Solution Predictable caching • Dedicated caches designed for analyzability/predictability • Easy to analyze • Simple hardware design • Requiring no/little information on accesses addresses In this work Time-predictable caching of stack data using a stack cache . 6/25

  15. What is a Stack Cache? Dedicated cache for stack data • Simple ring buffer ( FIFO replacement ) • All stack accesses are guaranteed hits (no need to analyze them) • Dedicated stack control instructions (need to be analyzed) sres x : reserve x blocks on the stack • • sfree x : free x blocks on the stack sens x : ensure that at least x blocks are cached • • Intuitively: a cache window following the stack top • Implemented as two pointers • MT : Memory-Top • ST : Stack-Top 7/25

  16. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 sres 3 sres 2 (3) call B() call C() sfree 2 (4) sens 2 sens 3 (5) call C() call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack MT ↿ MT ↿ ↾ ST Stack cache ∗ MT ↿ ∗ Cache configuration: 4 blocks 8/25

  17. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 ← sres 3 sres 2 (3) call B() call C() sfree 2 (4) sens 2 sens 3 (5) call C() call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A MT ↿ MT ↿ ↾ ST Stack cache ∗ A A MT ↿ ∗ Cache configuration: 4 blocks 8/25

  18. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 sres 3 sres 2 (3) call B() ← call C() sfree 2 (4) sens 2 sens 3 (5) call C() call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A MT ↿ MT ↿ ↾ ST Stack cache ∗ A A MT ↿ ∗ Cache configuration: 4 blocks 8/25

  19. Example: Stack Cache (1) function A() function B() function C() sres 3 ← (2) sres 2 sres 2 (3) call B() call C() sfree 2 (4) sens 2 sens 3 (5) call C() call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A B B B MT ↿ MT ↿ ↾ ST Stack cache ∗ A B B B MT ↿ spill 1 block ∗ Cache configuration: 4 blocks 8/25

  20. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 sres 3 sres 2 call C() ← (3) call B() sfree 2 (4) sens 2 sens 3 (5) call C() call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A B B B MT ↿ MT ↿ ↾ ST Stack cache ∗ A B B B MT ↿ ∗ Cache configuration: 4 blocks 8/25

  21. Example: Stack Cache (1) function A() function B() function C() sres 2 ← (2) sres 2 sres 3 (3) call B() call C() sfree 2 (4) sens 2 sens 3 (5) call C() call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A B B B C C MT ↿ MT ↿ ↾ ST Stack cache ∗ B B C C MT ↿ spill 2 blocks ∗ Cache configuration: 4 blocks 8/25

  22. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 sres 3 sres 2 sfree 2 ← (3) call B() call C() (4) sens 2 sens 3 (5) call C() call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A B B B MT ↿ MT ↿ ↾ ST Stack cache ∗ B B MT ↿ ∗ Cache configuration: 4 blocks 8/25

  23. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 sres 3 sres 2 (3) call B() call C() sfree 2 sens 3 ← (4) sens 2 (5) call C() call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A B B B MT ↿ MT ↿ ↾ ST Stack cache ∗ B B B MT ↿ fill 1 block ∗ Cache configuration: 4 blocks 8/25

  24. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 sres 3 sres 2 (3) call B() call C() sfree 2 (4) sens 2 sens 3 call C() ← (5) call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A B B B MT ↿ MT ↿ ↾ ST Stack cache ∗ B B B MT ↿ ∗ Cache configuration: 4 blocks 8/25

  25. Example: Stack Cache (1) function A() function B() function C() sres 2 ← (2) sres 2 sres 3 (3) call B() call C() sfree 2 (4) sens 2 sens 3 (5) call C() call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A B B B C C MT ↿ MT ↿ ↾ ST Stack cache ∗ B B C C MT ↿ spill 1 block ∗ Cache configuration: 4 blocks 8/25

  26. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 sres 3 sres 2 sfree 2 ← (3) call B() call C() (4) sens 2 sens 3 (5) call C() call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A B B B MT ↿ MT ↿ ↾ ST Stack cache ∗ B B MT ↿ ∗ Cache configuration: 4 blocks 8/25

  27. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 sres 3 sres 2 (3) call B() call C() sfree 2 (4) sens 2 sens 3 (5) call C() call C() sens 3 ← (6) sens 2 (7) sfree 2 sfree 3 Logical stack A A B B B MT ↿ MT ↿ ↾ ST Stack cache ∗ B B B MT ↿ fill 1 block ∗ Cache configuration: 4 blocks 8/25

  28. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 sres 3 sres 2 (3) call B() call C() sfree 2 (4) sens 2 sens 3 (5) call C() call C() (6) sens 2 sens 3 sfree 3 ← (7) sfree 2 Logical stack A A MT ↿ MT ↿ ↾ ST Stack cache ∗ MT ↿ ∗ Cache configuration: 4 blocks 8/25

  29. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 sres 3 sres 2 (3) call B() call C() sfree 2 (4) sens 2 ← sens 3 (5) call C() call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A MT ↿ MT ↿ ↾ ST Stack cache ∗ A A MT ↿ fill 2 blocks ∗ Cache configuration: 4 blocks 8/25

  30. Example: Stack Cache (1) function A() function B() function C() (2) sres 2 sres 3 sres 2 (3) call B() call C() sfree 2 (4) sens 2 sens 3 (5) call C() ← call C() (6) sens 2 sens 3 (7) sfree 2 sfree 3 Logical stack A A MT ↿ MT ↿ ↾ ST Stack cache ∗ A A MT ↿ ∗ Cache configuration: 4 blocks 8/25

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