Cache CPI and DFAs and NFAs. CS230 Tutorial 10

Transcription

1 Cche CPI nd DFAs nd NFAs CS230 Tutoril 10

2 Multi-Level Cche: Clculting CPI When memory ccess is ttempted, wht re the possible results? ccess miss miss CPU L1 Cche L2 Cche Memory L1 cche hit L2 cche hit L2 cche miss 2

3 Multi-Level Cche: Clculting CPI We hve three possibilities, find the formul for ech: L1 Cche Hit Cost This is considered prt of norml execution. CPI cost is zero. L2 Cche Hit Cost We missed L1 cche but found the dt in the L2 cche This is L1-miss-penlty L1-miss-chnce L2 Cche Miss Cost We missed L1 nd L2 cche, hve to go ll the wy to memory This is min-memory-ccess-time globl-cche-miss-chnce globl-cche-miss-chnce could be clculted s L1-miss-chnce L2-miss-chnce CPI Formul is: bse-cpi + L2-cche-hit-CPI + L2-cche-miss-CPI 3

4 Multi-Level Cche: CPI Exmple Consider processor running t 5GHz with Bse-CPI of 2.4. It hs two-level cche. The L1 miss penlty is 2ns. The min memory ccess time is 60ns. The L1 cche hit rte is 85%. The L2 cche hit rte is 90%. Clculte the totl CPI of this processor with nd without n L2 cche. Wht is the speedup gined by hving n L2 cche? 4

5 Multi-Level Cche: CPI Exmple Solution A 5GHz processor hs cycle time of 0.2ns. L2 cche hit CPI = 2ns * 0.15 = 0.3ns = 1.5 CPI L2 cche miss CPI = 60ns * 0.15 * 0.10 = 0.9ns = 4.5 CPI So the effective CPI of this processor is: = 8.4 CPI If there ws no L2 cche this would be: L1 cche miss = 60ns * 0.15 = 9ns = 45 CPI So the effective CPI of this processor would hve been: = 47.4 CPI The speedup is therefore: 47.4/8.4 = ~5.6 times fster! 5

6 Multi-Level Cche: CPI Prctice Consider processor running t 2GHz with Bse-CPI of 1.4. It hs two-level cche. The L1 miss penlty is 10ns. The min memory ccess time is 40ns. The L1 cche hit rte is 90%. The globl cche miss rte with n L2 cche is 2%. Clculte the totl CPI of this processor with nd without n L2 cche. Wht is the speedup gined by hving n L2 cche? 6

7 Multi-Level Cche: CPI Prctice Solution A 2GHz processor hs cycle time of 500ps. L2 cche hit CPI = 10ns * 0.1 = 1ns = 1000ps = 2 CPI L2 cche miss CPI = 40ns * 0.02 = 0.8ns = 800ps = 1.6 CPI So the effective CPI of this processor is: = 5 CPI If there ws no L2 cche this would be: L1 cche miss = 40ns * 0.1 = 4ns = 4000ps = 8 CPI So the effective CPI of this processor would hve been: = 9.4 CPI The speedup is therefore: 9.4/5 = 1.88 times fster! 7

8 Regulr Lnguges There re vrious types of Forml Lnguges. Right now we cre bout Regulr Lnguges subset the of forml lnguges. Regulr lnguges cn be represented in vrious wys: DFAs NFAs Regulr Expressions (not covered yet) 8

9 Deterministic Finite Automt (DFAs) DFAs re grph (in the discrete mth sense) where there is set of sttes nd trnsitions between those sttes tht occur upon consuming chrcter from the input. The ide is tht you cn tke string (i.e. list of chrcters) nd check if it is ccepted by (i.e. fits in) the lnguge by seeing if you cn follow long the flow of the DFA nd rech the ccept stte (denoted by double circle) t the end of the string. If you mke it to n ccept stte t the end of the string, then the string is in the regulr lnguge defined by tht DFA. If you re not in n ccept stte t the end of the string, then the the string is not in the regulr lnguge defined by tht DFA. It is possible to enter n ccept stte nd then leve it gin. The string must end in n ccept stte to be ccepted. 9

10 DFA Exmples Drw DFA for the lnguge of ny combintion of the letters nd b. Drw DFA for the lnguge of t lest one, following by zero or more numeric digits followed by nd x nd then n optionl y. 10

11 DFA Exmple Solution 1 Drw DFA for the lnguge of ny combintion of the letters nd b. Solution:, b strt q 0 11

12 DFA Exmple Solution 2 Drw DFA for the lnguge represented by t lest one, following by zero or more numeric digits followed by nd x nd then n optionl y. 0-9 Solution: q 3 strt q 0 q x x y q 4 q 5 12

13 DFA Prctice Drw DFA for the lnguge of ny number of s, followed by n even number of c s. Drw DFA for the lnguge of two or three b s followed by zero or more c s followed by n or d. Drw DFA for the lnguge of t lest two s followed by n odd number of d s followed by two s or one c. 13

14 DFA Prctice Solution 1 Drw DFA for the lnguge of ny number of s, followed by n even number of c s. Solution: strt c q 0 c q 1 c q 2 14

15 DFA Prctice Solution 2 Drw DFA for the lnguge of two or three b s followed by zero or more c s followed by n or d. Solution: c strt b b b,c,d q 0 q 1 q 2 q 3 q 4,d 15

16 DFA Prctice Solution 3 Drw DFA for the lnguge of t lest two s followed by n odd number of d s followed by two s or one c. Solution: strt d d q 0 q 1 q 2 q 3 c d q 4 q 5 q 6 16

17 Non-Deterministic Finite Automt (NFAs) With DFAs, there is no mbiguity t ll, nd only one possible pth between sttes for given string. With NFAs, there re situtions where there could be more thn one choice for move from stte to stte while prsing string. NFAs cn hve (which DFAs do not hve): epsilon trnsitions (stte trnsitions on the empty chrcter) multiple trnsitions on the sme stte for prticulr chrcter (for exmple, on one stte, there could be 2 rrows out on the sme chrcter) NFAs cn lwys be trnslted to n equivlent DFA. 17

18 NFA Exmple Let s look t one of the exmples we ve been looking t so fr: Drw NFA for the lnguge of t lest one, following by zero or more numeric digits followed by nd x nd then n optionl y. 0-9 Recll tht the DFA is s follows: q 3 strt q 0 q x x y q 4 q 5 18

19 NFA Exmple Solution Exmple: Drw NFA for the lnguge of t lest one, following by zero or more numeric digits followed by nd x nd then n optionl y. Solution: Note: there re more thn one possible NFA for this problem, nd I m purposely showing mny NFA fetures strt nd not going for optiml NFA construction. q 3 ε x q 0 q 1 x 0-9 ε, y q 4 q 5 19

20 NFA Prctice Drw n NFA for the lnguge of ny number of s, followed by ny number of repetitions of bb. Drw n NFA for the lnguge of two or three b s followed by ny number of c s followed by n or d. Drw n NFA for the lnguge of one or more d s followed by ny number of c s followed by cd, or c, or nothing. 20

21 NFA Prctice Solution 1 Drw n NFA for the lnguge of ny number of s, followed by ny number of repetitions of bb. Solution: q 3 b strt q 0 b q 2 q 1 21

22 NFA Prctice Solution 2 Drw n NFA for the lnguge of two or three b s followed by zero or more c s followed by n or d. Solution: c strt b b b,ε,d q 0 q 1 q 2 q 3 q 4 22

23 NFA Prctice Solution 3 Drw n NFA for the lnguge of one or more d s followed by ny number of c s followed by cd, or c, or nothing. Solution: d c ε strt d ε c d q 0 q 1 q 2 q 3 q 5 c q 4 23

24 Assignment reminders Submit.txt XOR.pdf for ech question Do not submit both for the sme question! You my submit.pdf for one question nd.txt for different question Mke sure your digrms nd tbles re cler nd esy to red Mke sure to leve enough spce 24