Acknowledgement 15 213 The Class That Gives CMU Its Zip 1515 213 was developed and finefine tuned by Randal E Bryant and David O Hallaron O Hallaron They wrote The Book Book Introduction to Computer Systems Andreas G Nowatzyk August 26 2003 Topics Theme Five great realities of computer systems How this fits within CS curriculum class01a ppt CS 213 F 03 Course Theme 15 213 F 03 2 Great Reality 1 Abstraction is good but don t forget reality Int s are not Integers Float s are not Reals Courses to date emphasize abstraction Abstract data types Asymptotic analysis Examples Is x2 These abstractions have limits Especially in the presence of bugs Need to understand underlying implementations Is x y z x y z Useful outcomes Unsigned Signed Int s Yes Float s 1e20 1e20 3 14 3 14 1e20 1e20 3 14 Become more effective programmers Able to find and eliminate bugs efficiently Able to tune program performance Prepare for later systems classes in CS ECE 3 Compilers Operating Systems Networks Computer Architecture Embedded Systems 0 Float s Yes Int s 40000 40000 1600000000 50000 50000 15 213 F 03 4 15 213 F 03 Computer Arithmetic Great Reality 2 Does not generate random values You ve got to know assembly Arithmetic operations have important mathematical properties Chances are you ll never write program in assembly Cannot assume usual properties Compilers are much better more patient than you are Due to finiteness of representations Integer operations satisfy ring properties Understanding assembly key to machinemachine level execution model Commutativity associativity distributivity Behavior of programs in presence of bugs Floating point operations satisfy ordering properties High level language model breaks down Monotonicity values of signs Tuning program performance Observation 5 Understanding sources of program inefficiency Need to understand which abstractions apply in which contexts Important issues for compiler writers and serious application programmers 15 213 F 03 Assembly Code Example Implementing system software Compiler has machine code as target Operating systems must manage process state Code to Read Counter Write small amount of assembly code using GCC s asm facility Inserts assembly code into machine code generated by compiler Time Stamp Counter Special 64 bit register in Intel compatible machines Incremented every clock cycle Read with rdtsc instruction static unsigned cyc hi 0 static unsigned cyc lo 0 Application Measure time required by procedure Set hi and lo to the high and low order bits of the cycle counter void access counter unsigned hi unsigned lo asm rdtsc movl edx 0 movl eax 1 r hi r lo edx eax In units of clock cycles double t start counter P t get counter printf P required f clock cycles n t 7 15 213 F 03 6 15 213 F 03 8 15 213 F 03 Code to Read Counter Measuring Time Record the current value of the cycle counter void start counter access counter cyc hi cyc lo Trickier than it Might Look Many sources of variation Example Sum integers from 1 to n Number of cycles since the last call to start counter double get counter unsigned ncyc hi ncyc lo unsigned hi lo borrow Get cycle counter access counter ncyc hi ncyc lo Do double precision subtraction lo ncyc lo cyc lo borrow lo ncyc lo hi ncyc hi cyc hi borrow return double hi 1 30 4 lo 15 213 F 03 9 Great Reality 3 n 100 1 000 1 000 10 000 10 000 1 000 000 1 000 000 1 000 000 000 Cycles n 9 61 8 41 8 43 8 29 8 29 8 42 8 43 8 37 15 213 F 03 10 Memory Referencing Bug Example Memory Matters Random Access Memory is an unun physical abstraction main main long long int int a 2 a 2 double double dd 3 14 3 14 a 2 a 2 1073741824 1073741824 Out Out of of bounds bounds reference reference printf d 15g n d printf d 15g n d exit 0 exit 0 Memory is not unbounded It must be allocated and managed Many applications are memory dominated Memory referencing bugs especially pernicious Effects are distant in both time and space Alpha Memory performance is not uniform Cache and virtual memory effects can greatly affect program performance Adapting program to characteristics of memory system can lead to major speed improvements 11 Cycles 961 8 407 8 426 82 861 82 876 8 419 907 8 425 181 8 371 2305 591 15 213 F 03 MIPS Linux g 5 30498947741318e 315 3 1399998664856 3 14 O 3 14 3 14 3 14 Linux version gives correct result but implementing as separate function gives segmentation fault 12 15 213 F 03 Memory Referencing Errors Memory Performance Example C and C do not provide any memory protection Out of bounds array references Invalid pointer values Abuses of malloc free Implementations of Matrix Multiplication Multiple ways to nest loops Can lead to nasty bugs Whether or not bug has any effect depends on system and compiler Action at a distance Corrupted object logically unrelated to one being accessed Effect of bug may be first observed long after it is generated How can I deal with this 13 Program in Java Lisp or ML Understand what possible interactions may occur Use or develop tools to detect referencing errors 15 213 F 03 Matmult Performance Alpha 21164 Too big for L1 Cache ijk ijk for for i 0 i 0 i n i n i i for for j 0 j 0 j n j n j j sum sum 0 0 0 0 for for k 0 k 0 k n k n k k sum a i k sum a i k b k j b k j c i j c i j sum sum jik jik for for j 0 j 0 j n j n j j for for i 0 i 0 i n i n i i sum sum 0 0 0 0 for for k 0 k 0 k n k n k k sum a i k sum a i k b k j b k j c i j c i j sum sum 15 213 F 03 14 Blocked matmult perf Alpha 21164 Too big for L2 Cache 160 160 140 140 120 120 ijk 100 100 ikj bijk jik 80 bikj 80 jki ijk kij 60 kji ikj 60 40 40 20 20 0 0 50 matrix size n 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 matrix size n 15 15 213 F 03 16 15 213 F 03 Real Memory Performance Great Reality 4 Pointer Chase Results There s more to performance than asymptotic complexity Iteration Time ns 1000 Constant factors matter too 100 Easily see 10 1 performance range depending on how code written Must optimize at multiple levels algorithm data representations procedures and loops 10 Must understand system to optimize performance 1 How programs compiled and executed How to measure program performance and identify bottlenecks How to improve performance without destroying code modularity and generality From Tom Womack s memory …
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