Chapter 5

1. Chapter 5 Large and Fast: Exploiting Memory Hierarchy

2. Memory Technology §5.1 Introduction • Static RAM (SRAM) • 0.5ns – 2.5ns, $2000 – $5000 per GB • Dynamic RAM (DRAM) • 50ns – 70ns, $20 – $75 per GB • Magnetic disk • 5ms – 20ms, $0.20 – $2 per GB • Ideal memory • Access time of SRAM • Capacity and cost/GB of disk Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 2

3. Principle of Locality • Programs access a small proportion of their address space at any time • Temporal locality (in time) • Items accessed recently are likely to be accessed again soon • e.g., instructions in a loop, induction variables • Spatial locality (in space) • Items near those accessed recently are likely to be accessed soon • E.g., sequential instruction access, array data Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 3

4. Taking Advantage of Locality • Memory hierarchy • Store everything on disk • Copy recently accessed (and nearby) items from disk to smaller DRAM memory • Main memory • Copy more recently accessed (and nearby) items from DRAM to smaller SRAM memory • Cache memory attached to CPU Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 4

5. Memory Hierarchy Levels • Block (aka line): unit of copying • May be multiple words • If accessed data is present in upper level • Hit: access satisfied by upper level • Hit ratio: hits/accesses • If accessed data is absent • Miss: block copied from lower level • Time taken: miss penalty • Miss ratio: misses/accesses= 1 – hit ratio • Then accessed data supplied from upper level Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 5

6. The Memory Hierarchy: Terminology • Hit Rate: the fraction of memory accesses found in a level of the memory hierarchy • Hit Time: Time to access that level which consists of Time to access the block + Time to determine hit/miss • Miss Rate: the fraction of memory accesses not found in a level of the memory hierarchy  1 - (Hit Rate) • Miss Penalty: Time to replace a block in that level with the corresponding block from a lower level which consists of Time to access the block in the lower level + Time to transmit that block to the level that experienced the miss + Time to insert the block in that level + Time to pass the block to the requestor Hit Time << Miss Penalty

7. Cache Memory • Cache memory • The level of the memory hierarchy closest to the CPU • Given accesses X1, …, Xn–1, Xn §5.2 The Basics of Caches • How do we know if the data is present? • Where do we look? Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 7

8. Direct Mapped Cache • Location determined by address • Direct mapped: only one choice • (Block address) modulo (#Blocks in cache) • #Blocks is a power of 2 • Use low-order address bits Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 8

9. Tags and Valid Bits • How do we know which particular block is stored in a cache location? • Store block address as well as the data • Actually, only need the high-order bits • Called the tag • What if there is no data in a location? • Valid bit: 1 = present, 0 = not present • Initially 0 Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 9

10. Cache Example • 8-blocks, 1 word/block, direct mapped • Initial state Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 10

11. Cache Example Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 11

12. Cache Example Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 12

13. Cache Example Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 13

14. Cache Example Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 14

15. Cache Example Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 15

16. Address Subdivision Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 16

17. Caching: A Simple First Example Main Memory 0000xx 0001xx 0010xx 0011xx 0100xx 0101xx 0110xx 0111xx 1000xx 1001xx 1010xx 1011xx 1100xx 1101xx 1110xx 1111xx One word blocks Two low order bits define the byte in the word (32b words) Cache Index Valid Tag Data 00 01 10 11 Q2: How do we find it? Use next 2 low order memory address bits – the index – to determine which cache block (i.e., modulo the number of blocks in the cache) Q1: Is it there? Compare the cache tag to the high order 2 memory address bits to tell if the memory block is in the cache (block address) modulo (# of blocks in the cache)

18. 01 4 11 15 Direct Mapped Cache • Consider the main memory word reference string 0 1 2 3 4 3 4 15 Start with an empty cache - all blocks initially marked as not valid 0 miss 1 miss 2 miss 3 miss 00 Mem(0) 00 Mem(1) 00 Mem(0) 00 Mem(0) 00 Mem(1) 00 Mem(2) 00 Mem(0) 00 Mem(1) 00 Mem(2) 00 Mem(3) miss 3 hit 4 hit 15 miss 4 00 Mem(0) 00 Mem(1) 00 Mem(2) 00 Mem(3) 01 Mem(4) 00 Mem(1) 00 Mem(2) 00 Mem(3) 01 Mem(4) 00 Mem(1) 00 Mem(2) 00 Mem(3) 01 Mem(4) 00 Mem(1) 00 Mem(2) 00 Mem(3) • 8 requests, 6 misses

19. Byte offset 31 30 . . . 13 12 11 . . . 2 1 0 Tag 20 Data 10 Hit Index Index Valid Tag Data 0 1 2 . . . 1021 1022 1023 20 32 MIPS Direct Mapped Cache Example • One word blocks, cache size = 1K words (or 4KB) What kind of locality are we taking advantage of?

20. Byte offset Hit 31 30 . . . 13 12 11 . . . 4 3 2 1 0 Data 20 Block offset Tag 8 Index Data Index Valid Tag 0 1 2 . . . 253 254 255 20 32 Multiword Block Direct Mapped Cache • Four words/block, cache size = 1K words What kind of locality are we taking advantage of?

21. 0 1 2 3 4 3 11 01 5 15 14 4 4 15 Taking Advantage of Spatial Locality • Let cache block hold more than one word 0 1 2 3 4 3 4 15 Start with an empty cache - all blocks initially marked as not valid miss hit miss 00 Mem(1) Mem(0) 00 Mem(1) Mem(0) 00 Mem(1) Mem(0) 00 Mem(3) Mem(2) hit miss hit 00 Mem(1) Mem(0) 00 Mem(1) Mem(0) 01 Mem(5) Mem(4) 00 Mem(3) Mem(2) 00 Mem(3) Mem(2) 00 Mem(3) Mem(2) hit miss 01 Mem(5) Mem(4) 01 Mem(5) Mem(4) 00 Mem(3) Mem(2) 00 Mem(3) Mem(2) • 8 requests, 4 misses

22. Total # of bit needed for a cache • function of the cache size and the address size. • For the following • 32-bit byte addresses • A direct-mapped cache • The cache size is 2n blocks • n bits for the index • The block size is 2m words (2m+2 bytes) • m bits for the word within the block • tag size = 32 – (n+m+2). • Total # of bits = 2n *(block size+tag size+valid field size) Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 25

23. Example Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 26

24. 31 10 9 4 3 0 Tag Index Offset 22 bits 6 bits 4 bits Example: Larger Block Size • 64 blocks, 16 bytes/block • To what block number does address 1200 map? • Block address = 1200/16 = 75 • Block number = 75 modulo 64 = 11 Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 27

25. Sources of Cache Misses • Compulsory (cold start or process migration, first reference): • First access to a block, “cold” fact of life, not a whole lot you can do about it. If you are going to run “millions” of instruction, compulsory misses are insignificant • Solution: increase block size (increases miss penalty; very large blocks could increase miss rate) • Capacity: • Cache cannot contain all blocks accessed by the program • Solution: increase cache size (may increase access time) • Conflict (collision): • Multiple memory locations mapped to the same cache location • Solution 1: increase cache size • Solution 2: increase associativity (stay tuned) (may increase access time)

26. Block Size Considerations • Larger blocks should reduce miss rate • Due to spatial locality • But in a fixed-sized cache • Larger blocks  fewer of them • More competition  increased miss rate • Larger blocks  pollution • Larger miss penalty • Can override benefit of reduced miss rate • Early restart • Resume exe. as soon as the requested word of the block is returned • critical-word-first Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 29

27. Miss Rate Versus Block Size Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 30

28. Cache Misses • On cache hit, CPU proceeds normally • On cache miss • Stall the CPU pipeline • Fetch block from next level of hierarchy • Instruction cache miss • Restart instruction fetch • Data cache miss • Complete data access Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 31

29. Write-Through • On data-write hit, could just update the block in cache • But then cache and memory would be inconsistent • Write through: All writes go to main memory as well as cache • Lots of traffic • Slows down writes • But makes writes take longer • e.g., if base CPI = 1 without misses, 10% of instructions are stores, write to memory takes 100 cycles • Effective CPI = 1 + 0.1×100 = 11 Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 32

30. Write-Through • Solution: write buffer • Holds data waiting to be written to memory • CPU continues immediately • Only stalls on write if write buffer is already full Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 33

31. Write-Back • Alternative: On data-write hit (block is already in cache but needs to be updated) just update the block in cache • Keep track of whether each block is dirty • When a dirty block is replaced • Write it back to memory • Can use a write buffer to allow replacing block to be read first Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 34

32. Write Allocation • What should happen on a write miss? • Alternatives for write-through • Allocate on miss: fetch the block • Write around: don’t fetch the block • Since programs often write a whole block before reading it (e.g., initialization) • For write-back • Usually fetch the block Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 35

33. Example: Intrinsity FastMATH • Embedded MIPS processor • 12-stage pipeline • Instruction and data access on each cycle • Split cache: separate I-cache and D-cache • Each 16KB: 256 blocks × 16 words/block • D-cache: write-through or write-back • SPEC2000 miss rates • I-cache: 0.4% • D-cache: 11.4% • Weighted average: 3.2% Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 36

34. Example: Intrinsity FastMATH Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 37

35. Main Memory Supporting Caches • Use DRAMs for main memory • Fixed width (e.g., 1 word) • Connected by fixed-width clocked bus • Bus clock is typically slower than CPU clock • Example cache block read • 1 bus cycle for address transfer • 15 bus cycles per DRAM access • 1 bus cycle per data transfer • For 4-word block, 1-word-wide DRAM • Miss penalty = 1 + 4×15 + 4×1 = 65 bus cycles • The number of bytes transferred per bus cycle for a single miss is • Bandwidth = 16 bytes / 65 cycles = 0.25 B/cycle Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 38

36. Increasing Memory Bandwidth • 4-word wide memory • Miss penalty = 1 + 15 + 1 = 17 bus cycles • Bandwidth = 16 bytes / 17 cycles = 0.94 B/cycle • 4-bank interleaved memory • Miss penalty = 1 + 15 + 4×1 = 20 bus cycles • Bandwidth = 16 bytes / 20 cycles = 0.8 B/cycle Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 39

37. Advanced DRAM Organization • Bits in a DRAM are organized as a rectangular array • DRAM accesses an entire row • Burst mode: supply successive words from a row with reduced latency • Double data rate (DDR) DRAM • Transfer on rising and falling clock edges • Quad data rate (QDR) DRAM • Separate DDR inputs and outputs Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 40

38. DRAM Generations Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 41

39. Measuring Cache Performance • Components of CPU time • Program execution cycles • Includes cache hit time • Memory stall cycles • Mainly from cache misses • With simplifying assumptions: §5.3 Measuring and Improving Cache Performance Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 42

40. Cache Performance Example • Given • I-cache miss rate = 2% • D-cache miss rate = 4% • Miss penalty = 100 cycles • Base CPI (ideal cache) = 2 • Load & stores are 36% of instructions • Miss cycles per instruction • I-cache: 0.02 × 100 = 2 • D-cache: 0.36 × 0.04 × 100 = 1.44 • Actual CPI = 2 + 2 + 1.44 = 5.44 • Ideal CPU is 5.44/2 =2.72 times faster Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 43

41. Average Access Time • Hit time is also important for performance • Average memory access time (AMAT) • AMAT = Hit time + Miss rate × Miss penalty • Example • CPU with 1ns clock, hit time = 1 cycle, miss penalty = 20 cycles, I-cache miss rate = 5% • AMAT = 1 + 0.05 × 20 = 2ns • 2 cycles per instruction Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 44

42. Performance Summary • When CPU performance increased • Miss penalty becomes more significant • Decreasing base CPI • Greater proportion of time spent on memory stalls • Increasing clock rate • Memory stalls account for more CPU cycles • Can’t neglect cache behavior when evaluating system performance Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 45

43. Associative Caches • Fully associative • Allow a given block to go in any cache entry • Requires all entries to be searched at once • Comparator per entry (expensive) • n-way set associative • Each set contains n entries • Block number determines which set • (Block number) modulo (#Sets in cache) • Search all entries in a given set at once • n comparators (less expensive) Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 46

44. Associative Cache Example Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 47

45. Spectrum of Associativity • For a cache with 8 entries Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 48

46. Associativity Example • Compare 4-block caches • Direct mapped, 2-way set associative,fully associative • Block access sequence: 0, 8, 0, 6, 8 • Direct mapped Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 49

47. Associativity Example • 2-way set associative • Fully associative Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 50

48. How Much Associativity • Increased associativity decreases miss rate • But with diminishing returns • Simulation of a system with 64KBD-cache, 16-word blocks, SPEC2000 • 1-way: 10.3% • 2-way: 8.6% • 4-way: 8.3% • 8-way: 8.1% Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 51

49. Set Associative Cache Organization Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 52

50. Replacement Policy • Direct mapped: no choice • Set associative • Prefer non-valid entry, if there is one • Otherwise, choose among entries in the set • Least-recently used (LRU) • Choose the one unused for the longest time • Simple for 2-way, manageable for 4-way, too hard beyond that • Random • Gives approximately the same performance as LRU for high associativity Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 53