ECE468 Fall 2003, Final Exam

Transcription

1 Name ECE468 Fall 2003, Final Exam This test has 9 pages and 9 questions. When told to begin please check to make sure you have all 9 pages. Let us know immediately if it doesn t. This test is open book and open notes. If a question seems ambiguous, ask a proctor to clarify the question. If the answer doesn t satisfy you, please state your assumptions. 1

2 1: S! A$ A! xc C! Ay C! z (a): Complete the LL(0) Characteristic Finite State Machine (CFSM) for the grammar. Big boxes need to be filled in, little boxes are complete, and blank lines need to be filled in. S ->. A $ x C -> z. A C -> A y. A A -> x C. A S -> A $. (b): Given your CFSM, is the grammar parseable by an LL(0) parser? (c): Is the language defined by the grammar recognizable by a deterministic finite automata? 2

3 2: Given the grammar and CFSM below: S ->. X $ X ->. X X X ->. a X ->. b 1 b S! X$ X! XX X! a X! b X 2 a X -> a. a 3 X -> b. b S -> X. $ S -> X. X X ->. a X ->. b 5 $ X 4 X -> X X. 6 S -> X $. a: Fill in the parse tree for the string a b a b a $accepted by the language. 3

4 3: Given the grammar (the same as on the previous page) and it s CFSM below: S! X$ X! XX X! a X! b S ->. X $ X ->. X X X ->. a X ->. b 1 X -> a. S -> X. $ S -> X. X X ->. a X ->. b 5 What follows is a listing of the parse stack configurations for parsing the string a b a $. Two states are missing from the stack (indicated by. Fill these in. X 2 a a $ X b 3 X -> b. b 4 X -> X X. 6 S -> X $

5 4a: Given the regular expression a(ajb) Λ a, give a non-deterministic finite automaton (NDFA) that recognizes the regular expression. Do not give a deterministic finite automaton (DFA)! You do not have to put in all the transitions that the book algorithm does, however. 4a: Convert the NDFA to a DFA. 5

6 5: Uset the semantic routines and productions for the if-then-else construct on page 429 of your text book in the problem, with the change < elsepart >! else #gen jump #gen realelse label < stmtlist > < elsepart >! #gen realelse label For the else part productions, the semantic routine #gen else label has been changed to #gen realelse label. We want to change the code generated by the production and semantic routine so that after the statements associated with an if or an elseif clause are executed, the statements in the else clause are executed. If no test is true, only the else statements are executed. Show the changed semantic routines. Show any additions you make to the semantic record. Show any changes you make to productions to call new or different semantic routines, and any new semantic routines. 6

7 6: After getting a passing grade in ECE 468, and breathing a sigh of relief that the semester is over, you decide to spend the break enhancing on your project compiler. You decide to implement an is a constant dataflow analysis routine. Note: this is not a constant propagation routine we don t care what the constant values of a variable might be, only that the variable has a constant value. A variable v is a constant at block B if v has a constant value at B for all possible executions of the program. Note: to make life simpler, assume that the assignment a = 4 assigns a constant to a,buta = bdoes not, even if b has a constant value. a: Is this an Any or All paths algorithm? b: Is this a backwards or forwards algorithm? c: Describe the elements in the Gen set your description must be specific to this problem. d: Describe the elements in the Kill set your description must be specific to this problem. d: Give the equation for the In set. d: Give the equation for the Out set. 7

8 7: On the left hand side a program is given using virtual registers. You need to do register assignment to assign these virtual registers to 2 real registers, r0 and r1. On the right hand side is the program with real registers assigned. There is one space on almost every line fill this in with the register assigned. When a spill is needed, the register holding the virtual register value that is used latest is spilled. If there is a tie, i.e. both virtual registers held in a register are used next in the same instruction, spill r0. Virtual registers values that are not used again in the program below do not need to be spilled. Note that the statements generated for a statement on the left are given on the right. The ST instructions in the generated code perform spills. 8

9 LR T1, A LR r0, A LR T2, B LR r1, B LR T3, C ST, TMP1 LR, C LR T4, D ST, TMP2 LR, D ST, TMP3 + T1, T3, H LR, TMP1 + r0, r1, H LR T6, E LR, E ST T6, F ST, F + T5, T2, G LR r1, + r1, r0, G ST T4, I LR ST r0, T4 r0, I 9

10 9: Given the loop: do i = 1, n do j = 1, n a(2*i,j) = b(i,j) b(i+2,j-1) = a(2*i+1,j) end do end do 9a: is there a dependence involving a(2*i,j) and a(2*i+1,j)? If there is, what kind of dependence is it? 9b: is there a dependence involving b(i+2,j-1) and b(i,j)? If there is, what kind of dependence is it, and give the dependence distance and direction vector. 9c: What transformations are legal on this loop without performing other transformations? (Circle those that are legal.) unrolling parallelization vectorization statement reordering followed by vectorization distribtution privatization of a privatization of b 10