2. Exam 2 Review Two’s Complement Arithmetic Ripple carry ALU logic and performance Look-ahead techniques, performance and equations Basic multiplication and division ( non- restoring) algorithms IEEE 754 floating point standard (definition provided) Write a sequence of register transfers to implement a given instruction for MIPS Given a set of Register Transfers, design the control needed for some component

3. Cache Design Issues 1.Where can a word or block of words be placed in the cache?

4. Cache Design Issues 1.Where can a word or block of words be placed in the cache? 2. How can a word be found if it is in the cache?

5. Cache Design Issues 1.Where can a word or block of words be placed in the cache? 2.How can a word be found if it is in the cache? 3.Which word or block of words should be replaced on a cache miss?

6. Cache Design Issues 1.Where can a word or block of words be placed in the cache? 2.How can a word be found if it is in the cache? 3.Which word or block of words should be replaced on a cache miss? 4. When do we write the main memory?

7. Cache Design Issues 1.Where can a word or block of words be placed in the cache? 2.How can a word be found if it is in the cache? 3.Which word or block of words should be replaced on a cache miss? 4.When do we write the main memory? Remember READS dominate WRITES

8. 10 bit Address 10 bit Addr Main 1K words 10 bit words 4 bit Addr Cache 16 Entries

9. 10 bit Address 10 bit Addr Main 1K words 10 bit words 4 bit Addr Cache 16 Entries 1.Where can a word be placed in the cache?

10. 10 bit Address 10 bit Addr Main 1K words 10 bit words 4 bit Addr Cache 16 Entries 1.Where can a word be placed in the cache? Use the last 4 bits of the address.

11. Index 10 bit Addr Main 1K words 10 bit words Index 4 bit Addr Cache 16 Entries 1.Where can a word be placed in the cache? Use the last 4 bits of the address. Address

12. Index 10 bit Addr Main 1K words 10 bit words Index 4 bit Addr Cache 16 Entries Address..... 9 8 7 6 5 4 3 2 1 0

13. Index 10 bit Addr Main 1K words 10 bit words Index 4 bit Addr Cache 16 Entries Address How can a word be found if it is in the cache? 2 6 = 64 possibilities Need to know the rest of the address !..... 9 8 7 6 5 4 3 2 1 0

14. Index 10 bit Addr Main 1K words 10 bit words Index 4 bit Addr Cache 16 Entries Address How can a word be found if it is in the cache? 2 6 = 64 possibilities Need to know the rest of the address ! Save it in the Cache..... 9 8 7 6 5 4 3 2 1 0

15. Tag Index 10 bit Addr Main 1K words 10 bit words Index 4 bit Addr Cache Address..... 9 8 7 6 5 4 3 2 1 0 Data -10 bitTag – 6 bits

16. Tag Index 10 bit Addr Main 1K words 10 bit words Index 4 bit Addr Cache Address..... 9 8 7 6 5 4 3 2 1 0 Data -10 bit 1 Tag – 6 bits Also need a Valid bit to indicate that the cache has valid data

17. Tag Index 10 bit Addr Main 1K words 10 bit words Index 4 bit Addr Cache Address..... 9 8 7 6 5 4 3 2 1 0 Data -10 bit 1 Tag – 6 bits Valid Which word should be replaced on a cache miss?

18. Tag Index 10 bit Addr Main 1K words 10 bit words Index 4 bit Addr Cache Address..... 9 8 7 6 5 4 3 2 1 0 Data -10 bit 1 Tag – 6 bits Valid Which word should be replaced on a cache miss? The one with the same Index.

19. Hit if: the location has been accessed and there has not been a location accessed with the same index since then.

20. Hit if: the location has been accessed and there has not been a location accessed with the same index since then. Temporal locality: most recently accessed Spatial locality: will not be replaced until an access occurs beyond the size of the cache

21. Hit if: the location has been accessed and there has not been a location accessed with the same tag since then. Temporal locality: most recently accessed Spatial locality: will not be replaced until an access occurs beyond the size of the cache The larger the cache the lower the miss rate and the lower the average access time (approaches Hit time)

22. Tag Index 10 bit Addr Main 1K words 10 bit words Index 4 bit Addr Cache Address..... 9 8 7 6 5 4 3 2 1 0 Data -10 bit 1 Tag – 6 bits Valid When do we write the main memory?

23. Tag Index 10 bit Addr Main 1K words 10 bit words Index 4 bit Addr Cache Address..... 9 8 7 6 5 4 3 2 1 0 Data -10 bit 1 Tag – 6 bits Valid When do we write the main memory? As soon as the cache is written. Called Write-Through

24. Direct Mapped General Structure Tag Index Address - n bits 2 k Cache Words 1 Tag (n-k-2 bits) Computer Word (n bits) Valid Byte Offset n-k-2 k 2

25. Direct Mapped General Structure Tag Index Address - n bits 2 k Cache Words 1 Tag (n-k-2 bits) Computer Word (n bits) Valid Byte Offset n-k-2 k 2 Ex: 32 bit address and 2 14 words of data cache, k = 14

26. Direct Mapped General Structure Tag Index Address - n bits 2 k Cache Words 1 Tag (n-k-2 bits) Computer Word (n bits) Valid Byte Offset n-k-2 k 2 Ex: 32 bit address and 2 14 words of data cache, k = 14 Cache width is 32 +32-14-2+1 = 49 bits 49 / 32 = 1.53 bits more than just data

27. Tag Index Address – 32 bits 16 14 2 Byte Offset 16K entries Valid Tag Data 16 32

28. Tag Index Address – 32 bits 16 14 2 Byte Offset 16K entries Valid Tag Data 16 32

29. Tag Index Address – 32 bits 16 14 2 Byte Offset 16K entries Valid Tag Data 16 32 = Hit

30. Tag Index Address – 32 bits 16 14 2 Byte Offset 16K entries Valid Tag Data 16 32 = Hit Data

31. Cache Control for MIPS Lite Tag Index Byte Offset 31 30... 17 16 15... 3 2 1 0 Address Cache 48 47 46... 33 32 31 30... 3 2 1 0 Valid Tag Data Notation: Cache Memory ( Field) [Address] Data field addressed by PC Index CM(31 –0)[PC(15-2)] Tag Field Addressed by PC Index CM(47-32)[PC(15-2]

32. Cache Control for MIPS Lite Tag Index Byte Offset 31 30... 17 16 15... 3 2 1 0 Address Cache 48 47 46... 33 32 31 30... 3 2 1 0 Valid Tag Data Instruction Fetch - Assume Main Memory access is 5 clock cycles Was: S0 M[PC] IR, PC+4 PC,S1 S

33. Cache Control for MIPS Lite Tag Index Byte Offset 31 30... 17 16 15... 3 2 1 0 Address Cache 48 47 46... 33 32 31 30... 3 2 1 0 Valid Tag Data Instruction Fetch - Assume Main Memory access is 5 clock cycles Was: S0 M[PC] IR, PC+4 PC,S1 S S0 CM(31-0)[ PC(15-2)] IR, PC+4 PC, HitS1+HitS10 S

34. Cache Control for MIPS Lite Tag Index Byte Offset 31 30... 17 16 15... 3 2 1 0 Address Cache 48 47 46... 33 32 31 30... 3 2 1 0 Valid Tag Data Instruction Fetch - Assume Main Memory access is 5 clock cycles Was: S0 M[PC] IR, PC+4 PC,S1 S S0 CM(31-0)[ PC(15-2)] IR, PC+4 PC, HitS1+HitS10 S S10 PC – 4 PCS11 S S11 MM[PC] MMOutS12 S S12 S13 S S13S14 S S14S15 S S15S16 S

35. Cache Control for MIPS Lite Tag Index Byte Offset 31 30... 17 16 15... 3 2 1 0 Address Cache 48 47 46... 33 32 31 30... 3 2 1 0 Valid Tag Data Instruction Fetch - Assume Main Memory access is 5 clock cycles Was: S0 M[PC] IR, PC+4 PC,S1 S S0 CM(31-0)[ PC(15-2)] IR, PC+4 PC, HitS1+HitS10 S S10 PC – 4 PCS11 S S11 MM[PC] MMOutS12 S S12 S13 S S13S14 S S14S15 S S15S16 S S16 MMOut CM(31-0)[PC(15-2)], PC(31-16) CM(47-32)[PC(15-2)] 1 CM(48)[PC(15-2)]S0 S

36. Cache Control for MIPS Lite Tag Index Byte Offset 31 30... 17 16 15... 3 2 1 0 Address Cache 48 47 46... 33 32 31 30... 3 2 1 0 Valid Tag Data Instruction Fetch - Assume Main Memory access is 5 clock cycles Hit = Valid[Index] { Cache Tag[Index] = Addr Tag} For CM addressed by PC(15-2)

37. Tag Index Address – 32 bits 16 14 2 Byte Offset 16K entries Valid Tag Data 16 32 = Hit Data WRITE Write Cache Write Main

38. Cache Control for MIPS Lite Tag Index Byte Offset 31 30... 17 16 15... 3 2 1 0 Address Cache 48 47 46... 33 32 31 30... 3 2 1 0 Valid Tag Data Memory Write - Assume Main Memory access is 5 clock cycles WAS: S5 B M[ALUOut]S0 S

39. Cache Control for MIPS Lite Tag Index Byte Offset 31 30... 17 16 15... 3 2 1 0 Address Cache 48 47 46... 33 32 31 30... 3 2 1 0 Valid Tag Data Memory Write - Assume Main Memory access is 5 clock cycles WAS: S5 B M[ALUOut]S0 S S5 B CM(31-0)[ALUOut(15-2)],

40. Cache Control for MIPS Lite Tag Index Byte Offset 31 30... 17 16 15... 3 2 1 0 Address Cache 48 47 46... 33 32 31 30... 3 2 1 0 Valid Tag Data Memory Write - Assume Main Memory access is 5 clock cycles WAS: S5 B M[ALUOut]S0 S S5 B CM(31-0)[ALUOut(15-2)], ALUOut(31-16) CM(47-32)[ALUOut(15-2)] 1 CM(48)[ALUOut(15-2)]

41. Cache Control for MIPS Lite Tag Index Byte Offset 31 30... 17 16 15... 3 2 1 0 Address Cache 48 47 46... 33 32 31 30... 3 2 1 0 Valid Tag Data Memory Write - Assume Main Memory access is 5 clock cycles WAS: S5 B M[ALUOut]S0 S S5 B CM(31-0)[ALUOut(15-2)], ALUOut(31-16) CM(47-32)[ALUOut(15-2)] 1 CM(48)[ALUOut(15-2)] B MM[ALUOut]S17 S S17S18 S S18S19 S S19S20 S S20S0 S

42. DECStation 3100 Processor Instruction Cache Data Cache 14 bit Index 32 bit Data Word 16K Entries 64 KB Data Main Memory

43. DECStation 3100 Instruction DataEffective ProgramMiss RateMiss Rate Miss Rate gcc 6.1% 2.1% 5.4% spice 1.2% 1.3% 1.2% Only Read Misses Effective is weighted average of accesses Instruction Miss Rate not always less than Data Miss Rates clearly depend on the program Direct Mapped 1 word cache is effective

44. DECStation 3100 Instruction DataEffective ProgramMiss RateMiss Rate Miss Rate gcc 6.1% 2.1% 5.4% spice 1.2% 1.3% 1.2% Direct Mapped 1 word cache is effective Average Memory Access Time = Hit Time + Miss Rate * Miss Penalty

45. DECStation 3100 Instruction DataEffective ProgramMiss RateMiss Rate Miss Rate gcc 6.1% 2.1% 5.4% spice 1.2% 1.3% 1.2% What if combined into one large cache?

46. DECStation 3100 Instruction DataEffective Combined ProgramMiss RateMiss Rate Miss Rate Miss Rate gcc 6.1% 2.1% 5.4% 4.8% spice 1.2% 1.3% 1.2% What if combined into one large cache? One large cache has lower miss rate than two half caches Split caches can double the bandwidth by simultaneous access ( pipelining)

47. Write – Through Performance Improvement Every Write : Write Cache and Write Main Memory Can be 10% to 15% of instructions

48. Write – Through Performance Improvement Consider a Write Buffer Processor Write Buffer Cache Main Memory

49. Write – Through Performance Improvement Consider a Write Buffer Processor Write Buffer Cache Main Memory Valid Address Data

50. Write – Through Performance Improvement Consider a Write Buffer Processor Write Buffer Cache Main Memory Memory Controller Writes Data from Buffer to Main and Releases Buffer

51. Write – Through Performance Improvement Consider a Write Buffer Processor Write Buffer Cache Main Memory Write Cache and Buffer Continue until? Memory Controller Writes Data from Buffer to Main and Releases Buffer

52. Write – Through Performance Improvement Consider a Write Buffer Processor Write Buffer Cache Main Memory Write Cache and Buffer Continue until? 1.Write Buffer Full (Write Miss – HOLD)

53. Write – Through Performance Improvement Consider a Write Buffer Processor Write Buffer Cache Main Memory Write Cache and Buffer Continue until? 1.Write Buffer Full (Write Miss – HOLD) 2. Read Miss

54. Write – Through Performance Improvement Consider a Write Buffer Processor Write Buffer Cache Main Memory Write Cache and Buffer Continue until? 1.Write Buffer Full (Write Miss – HOLD) 2.Read Miss Wait until Write Buffer is empty.