Course Theme 15 213 The Class That Gives CMU Its Zip Abstraction is good but don t forget reality Courses to date emphasize abstraction Introduction to Computer Systems Abstract data types Asymptotic analysis These abstractions have limits Especially in the presence of bugs Need to understand underlying implementations Randal E Bryant August 28 2001 Useful outcomes Become more effective programmers Able to find and eliminate bugs efficiently Able to tune program performance Prepare for later systems classes in CS ECE Compilers Operating Systems Networks Computer Architecture Embedded Systems Topics Theme Five great realities of computer systems How this fits within CS curriculum class01a ppt CS 213 F 01 Great Reality 1 class01a ppt 2 CS 213 F 01 Computer Arithmetic Int s are not Integers Float s are not Reals Does not generate random values Arithmetic operations have important mathematical properties Examples Is x2 0 Float s Yes Int s 40000 40000 50000 50000 Cannot assume usual properties Due to finiteness of representations Integer operations satisfy ring properties Commutativity associativity distributivity Floating point operations satisfy ordering properties Monotonicity values of signs 1600000000 Is x y z x y z Unsigned Signed Int s Yes Float s 1e20 1e20 3 14 3 14 1e20 1e20 3 14 class01a ppt 3 Observation Need to understand which abstractions apply in which contexts Important issues for compiler writers and serious application programmers CS 213 F 01 class01a ppt 4 CS 213 F 01 Great Reality 2 Assembly Code Example You ve got to know assembly Time Stamp Counter Chances are you ll never write program in assembly Compilers are much better patient at this than you are Application Understanding assembly key to machine level execution model Measure time required by procedure In units of clock cycles Behavior of programs in presence of bugs High level language model breaks down Tuning program performance Understanding sources of program inefficiency Implementing system software Compiler has machine code as target Operating systems must manage process state class01a ppt 5 double t start counter P t get counter printf P required f clock cycles n t CS 213 F 01 Code to Read Counter static unsigned cyc hi 0 static unsigned cyc lo 0 6 CS 213 F 01 Record the current value of the cycle counter void start counter access counter cyc hi cyc lo 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 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 7 class01a ppt Code to Read Counter Write small amount of assembly code using GCC s asm facility Inserts assembly code into machine code generated by compiler class01a ppt Special 64 bit register in Intel compatible machines Incremented every clock cycle Read with rdtsc instruction CS 213 F 01 class01a ppt 8 CS 213 F 01 Measuring Time Great Reality 3 Trickier than it Might Look Memory Matters Many sources of variation Example Memory is not unbounded Sum integers from 1 to n n Cycles 100 961 1 000 8 407 1 000 8 426 10 000 82 861 10 000 82 876 1 000 000 8 419 907 1 000 000 8 425 181 1 000 000 000 8 371 2305 591 class01a ppt It must be allocated and managed Many applications are memory dominated Cycles n 9 61 8 41 8 43 8 29 8 29 8 42 8 43 8 37 Memory referencing bugs especially pernicious Effects are distant in both time and space 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 CS 213 F 01 9 Memory Referencing Bug Example class01a ppt 10 CS 213 F 01 Memory Referencing Errors C and C do not provide any memory protection 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 Alpha MIPS Linux g 5 30498947741318e 315 3 1399998664856 3 14 O 3 14 3 14 3 14 Out of bounds array references Invalid pointer values Abuses of malloc free 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 Program in Java Lisp or ML Understand what possible interactions may occur Use or develop tools to detect referencing errors E g Purify Linux version gives correct result but implementing as separate function gives segmentation fault class01a ppt 11 CS 213 F 01 class01a ppt 12 CS 213 F 01 Memory Performance Example Matmult Performance Alpha 21164 Implementations of Matrix Multiplication Too big for L1 Cache Too big for L2 Cache Multiple ways to nest loops 160 140 120 ijk ikj jik jki kij kji 100 ijk ijk for for i 0 i 0 i n i n i i for j 0 j n for j 0 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 class01a ppt jik jik for for j 0 j 0 j n j n j j for i 0 i n for i 0 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 13 CS 213 F 01 80 60 40 20 0 matrix size n class01a ppt 14 CS 213 F 01 Great Reality 4 Blocked matmult perf Alpha 21164 There s more to performance than asymptotic complexity 160 140 Constant factors matter too 120 100 bijk bikj ijk ikj 80 60 Easily see 10 1 performance range depending on how code written Must optimize at multiple levels algorithm data representations procedures and loops Must understand system to optimize performance How programs compiled and executed How to measure program performance and identify bottlenecks How to improve performance without destroying code modularity and generality 40 20 0 50 7 5 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 matrix size n class01a ppt 15 CS 213 F 01 class01a ppt 16 CS 213 F 01 Great Reality 5 Role within Curriculum Computers do more than execute programs CS 441 …
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