1. Chapter 4 (continued): Caching; Testing Memory Modules

2. fig_04_30 Memory organization: Typical “Memory map” For power loss

3. fig_04_31 Memory hierarchy

4. fig_04_32 Paging / Caching Why it typically works: locality of reference (spatial/temporal) “working set” Note: in real-time embedded systems, behavior may be atypical; but caching may still be a useful technique Here we consider caching external to the CPU—the CPU may have one or more levels of caching built in

5. fig_04_33 Typical memory system with cache: hit rate (miss rate) important Remember! Registers here

6. Basic caching strategies: Direct-mapped Associative Block-set associativequestions: what is “associative memory”? what is overhead? what is efficiency (hit rate)? is bigger cache better?

7. Associative memory: storage location related to data stored Example—hashing: --When software program is compiled or assembled, a symbol table must be created to link addresses with symbolic names --table may be large; even binary search of names may be too slow --convert each name to a number associated with the name, this number will be the symbol table index For example, let a = 1, b = 2, c = 3,… Then “cab” has value 1 + 2 + 3 = 6 “ababab” has value 3 *(1 + 2) = 9 And “vvvvv” has value 5*22 = 110 Address will be modulo a prime p, if we expect about 50 unique identifiers, can take p = 101 (make storage about twice as large as number of items to be stored, reduce collisions) Now array of names in symbol table will look like: 0—> 1—> 2---> … 6--->cab … 9--->ababab--->vvvvv … Here there is one collision, at address 9; the two items are stored in a linked list Access time for an identifier <= (time to compute address) + 1 + length of longest linked list ~ constant

8. Caching: the basic process—note OVERHEAD for each task --program needs information M that is not in the CPU --cache is checked for M how do we know if M is in the cache? --hit: M is in cache and can be retrieved and used by CPU --miss: M is not in cache (M in RAM or in secondary memory) where is M? * M must be brought into cache * if there is room, M is copied into cache how do we know if there is room? * if there is no room, must overwrite some info M’ how do we select M’? ++ if M’ has not been modified, overwrite it how do we know if M’ has been modified? ++ if M’ has been modified, must save changes how do we save changes to M’?

9. fig_04_34 Example: direct mapping 32-bit words, cache holds 64K words, in 128 0.5K blocks Memory addresses 32 bits Main memory 128M words; 2K pages, each holds 128 blocks (~ cache) fig_04_35 fig_04_36 2 bits--byte; 9 bits--word address; 7 bits—block address (index); 11 (of 15)—tag (page block is from) Tag table: 128 entries (one for each block in the cache). Contains: Tag: page block came from Valid bit: does this block contain data write-through: any change propagated immediately to main memory delayed write: since this data may change again soon, do not propagate change to main memory immediately— this saves overhead; instead, set the dirty bit Intermediate: use queue, update periodically When a new block is brought in, if the valid bit is true and the dirty bit is true, the old block must first be copied into main memory Replacement algorithm: none; each block only has one valid cache location

10. fig_04_37 Problem with direct mapping: two frequently used parts of code can be in different “Block0’s”—so repeated swapping would be necessary; this can degrade performance unacceptably, especially in realtime systems (similar to “thrashing” in operating system virtual memory system) Another method: associative mapping: put new block anywhere in the cache; now we need an algorithm to decide which block should be removed, if cache is full

11. fig_04_38 Step 1: locate the desired block within the cache; must search tag table, linear search may be too slow; search all entries in parallel or use hashing Step 2: if miss, decide which block to replace. a.Add time accessed to tag table info, use temporal locality: Least recently used (LRU)— a FIFO-type algorithm Most recently used (MRU)— a LIFO-type algorithm b. Choose a block at random Drawbacks: long search times Complexity and cost of supporting logic Advantages: more flexibility in managing cache contents

12. fig_04_39 Intermediate method: block-set associative cache Each index now specifies a set of blocks Main memory: divided into m blocks organized into n groups Group number = m mod n Cache set number ~ main memory group number Block from main memory group j can go into cache set j Search time is less, since search space is smaller How many blocks: simulation  answer (one rule of thumb: doubling associativity ~ doubling cache size, > 4-way probably not efficient) Two-way set-associative scheme

13. Example: 256K memory-64 groups, 512 blocks BlockGroup (m mod 64) 0 64 128... 384 448 0 1 65 129... 385 449 1 2 66 130... 386 450 2... 63 127 192... 447 511 63

14. fig_04_40 Dynamic memory allocation “virtual storage”): --for programs larger than main memory --for multiple processes in main memory --for multiple programs in main memory General strategies may not work well because of hard deadlines for real-time systems in embedded applications— general strategies are nondeterministic Simple setup: Can swap processes/programs And their contexts --Need storage (may be in firmware) --Need small swap time compared to run time --Need determinism Ex: chemical processing, thermal control

15. fig_04_41 Overlays (“pre-virtual storage”): Seqment program into one main section and a set of overlays (kept in ROM?) Swap overlays Choose segmentation carefully to prevent thrashing

16. fig_04_42 Multiprogramming: similar to paging Fixed partition size: Can get memory fragmentation Example: If each partition is 2K and we have 3 jobs: J1 = 1.5K, J2 = 0.5K, J3 = 2.1K Allocate to successive partitions (4) J2 is using only 0.5 K J3 is using 2 partitions, one of size 0.1K If a new job of size 1K enters system, there is no place for it, even though there is actually enough unused memory for it Variable size: Use a scheme like paging Include compaction Choose parameters carefully to prevent thrashing

17. fig_04_43 Memory testing: Components and basic architecture

18. fig_04_45 Faults to test: data and address lines; stuck-at and bridging (if we assume no internal manufacturing defects)

19. fig_04_49 ROM testing: stuck-at faults, bridging faults, correct data stored Method: CRC (cyclic reduncancy check) or signature analysis Use LFSR to compress a data stream into a K-bit pattern, similar to error checking (Q: how is error checking done?) ROM contents modeled as N*M-bit data stream, N= address size, M = word size

20. Error checking: simple examples 1.Detect one bit error: add a parity bit 2.Correct a 1-bit error: Hamming code Example: send m message bits + r parity bits The number of possible error positions is m + r + 1, we need 2 r >= m + r + 1 If m = 8, need r = 4; ri checks parity of bits with i in binary representation Pattern: Bit #: 1 2 3 4 5 6 7 8 9 10 11 12 Info: r0 r1 m1 r2 m2 m3 m4 r3 m5 m6 m7 m8 --- --- 1 --- 1 0 0 --- 0 1 1 1 Set parity = 0 for each group r0: bits 1 + 3 + 5 + 7 + 9 + 11 = r0 + 1 + 1 + 0 + 0 + 1  r0 = 1 r1: bits 2 + 3 + 6 + 7 + 10 + 11 = r1 + 1 + 0 + 0 + 1 + 1  r1 = 1 r2: bits 4 + 5 + 6 + 7 + 12 = r2 + 1 + 0 + 1  r2 = 0 r3: bits 8 + 9 + 10 + 11 + 12 = r3 + 0 + 1 + 1 + 1  r3 = 1 Exercise: suppose message is sent and 1 bit is flipped in received message Compute the parity bits to see which bit is incorrect Addition: add an overall parity bit to end of message to also detect two errors Note: a.this is just one example, a more general formulation of Hamming codes using the finite field arithmetic can also be given b. this is one example of how error correcting codes can be obtained, there are many more complex examples, e.g., Reed-Solomon codes used in CD players