Sticker. CS 241 Fall 2009 Final Exam. Draft of 6 December 01:43 hrs

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1 Date: Weds, 16 December 2009 Time: 16:00-18:30 hours Permitted Aids: Provided reference booklet only. Closed book. CS 241 Fall 2009 Final Exam Cheating is an academic offense. Your signature below indicates that you understand you are bound by the University s policies regarding cheating on exams; unsigned exams will not be marked. Sticker Draft of 6 December 01:43 hrs Signature: Instructors: John Beatty, Gord Cormack, Troy Vasiga Instructions read carefully before the exam begins. E 1. This is a closed book examination. No aids are permitted other than the reference booklet provided. 2. Place answers in this booklet. Use the back of the previous page if additional space is required, and indicate clearly when an answer continues there to ensure your entire answer is marked. 3. Before you begin, make certain that you have 17 pages in this booklet and the 6-page reference booklet containing the MIPS reference sheet, the WL grammar and WLPP language specification. 4. Do not attempt to deduce anything about the content of an answer from the number of marks available for it. (Spreadsheets are good at arithmetic.) 5. To ensure that no student is unfairly disadvantaged, questions will not be interpreted or explained. Proctors may only confirm or deny the presence of an error. If you consider the wording of a question to be ambiguous, state your assumption(s) clearly, then answer the question to the best of your ability. Q# Marks Available 1 4 Scanning 2 11 CompPhases 3 7 WLPP 4 5 Trees&Der 5 6 guarded 6 14 CodeGen 7 5 LL-Predict 8 6 LL(1) 9 8 SLR(1) HeapMgmt Total 80 Marks Earned Marker s Initials page 2 page 3 page 4 page 6 page 7 page 8 page 11 page 12 page 13 page 15

2 Question 1: [4 marks] Suppose that the DFA shown to the right defines the valid tokens for some mythical language. Part a) Assume that the simplified maximal munch algorithm is executed using this DFA on the two input strings listed below. List the names of the tokens returned (which correspond to the relevant state names), in the order returned; if no ID a-z token can be returned at some point, write the pseudo-token name ERROR and assume that the lexical analyzer exits immediately thereafter. 0-9 a-z INT S * PLUS + STAR MINUS AINC ADEC * SS * COM alpha* beta alpha01*****beta02 ID STAR MINUS ID ID INT COM ERROR Part b) The DFA shown to the right accepts strings comprising a valid MIPS assembly language token. Observe that this DFA has transitions for the space character only from the COMMENT state, and recognizes an end-of-line character '\n' as an instance of the token EOL. LPAREN REG In pseudocode, provide a detailed description DOLLAR RPAREN of how this DFA could be used as part of a COMMENT lexical scanner for MIPS assembly language DOT DOTW DOTWO DOTWOR programs that reads the characters in a source file, generating a stream of MIPS assembly language tokens in which successive assembly language statements are separated by an EOL token. Your lexical scanner should return a special EOF token (not present in the above DFA) after processing the entire input file and may exit immediately if an error is detected. You may assume that the last character of any input file is the end-of-line character '\n'. I'll refer below to the DFA as the machine M. 1 mark for Place M in its START state and feed it characters from the source file until it blocks (cannot read the next character of input). If M is in a non-accepting state, declare an error and quit. If M is in an accepting state, return the token corresponding to that state. 1 mark for Then throw away whitespace characters (space, tab, or end-of-line), if any, until you encounter (c) the end-of-file or (d) a non-whitespace character. If (c), you return the special EOF token. if (d), you set M to the START state and continue scanning characters from the source file as described above. It s fine if they say modify the DFA so it has a transition from START under all space and tab to a WHITESPACE token that has transitions under both whitespace characters to itself, and explain that, as a special case, you DON T return/output a WHITESPACE token but instead reset the DFA to START and continue scanning as described above. \n START EOL a-za-z ; 0 - ( ), w $ MINUS 1-9 ZERO COMMA ID a-za-z x 0-9 : INT ZEROX LABEL o r a-f 0-9 all but \n d HEXINT a-f DOTWORD CS 241 Fall 2009 Page 2 of 17

3 Question 2: [11 marks] Listed below are several kinds of errors typically encountered during compilation and/or linking. For each of them, indicate the phase of the compilation and linking process in which the error would most likely be reported. Your answer in each case should be one of the following: scanning parsing semantic analysis optimization code generation linking a) Illegal character " " encountered. scanning b) Missing semicolon. parsing c) Attempt to assign a pointer to an int. semantic analysis d) String literal missing an end quotation mark. scanning e) Numeric literal out of range. code generation (or scanning, or semantic analysis) f) Multiple definitions encountered for the external symbol "Camelot". linking g) Attempt to use the undeclared variable "foo". semantic analysis h) Unmatched right parenthesis encountered. parsing i) Fill in the blank to produce a program that violates the WL lexical syntax rules. int wain( int foo, int bar ) { return ; } j) Fill in the blank to produce a program that satisfies the WL lexical syntax rules but violates the WL context-free syntax rules. int wain( int foo, int bar ) { return ; } k) Fill in the blank to produce a program that satisfies the WL lexical syntax and context-free syntax rules but violates the WL context-sensitive syntax rules. int wain( int foo, int bar ) { return ; } CS 241 Fall 2009 Page 3 of 17

4 Question 3: [7 marks] On the next page, write a WLPP program that takes as input an integer n+1 and an array containing n+1 numbers. The first number in the array is k (you can assume 0 k n-1), followed by n elements which form array A. Your program should print the elements of array A in the following order: A[k] A[k+1] A[k+2]... A[n-1] A[0] A[1]... A[k-2] A[k-1] and should return the value k. That is, begin printing at index k, increasing the index, and eventually wrapping around the array and end by printing the value at index k-1. For example if the input is: the output should be: and the returned value should be: 2 Please write your answer on the next page. (You will find the WLPP Language Specification in the Reference Booklet.) CS 241 Fall 2009 Page 4 of 17

5 Write below your answer to the question on the preceding page. CS 241 Fall 2009 Page 5 of 17

6 Question 4: [5 marks] Consider the following context-free grammar G S X C S A Y X a X b X ε Y b Y c Y ε A a A A ε C c C C ε and the following derivation of a word in L(G). S AY AbYc AbbYcc AbbbYccc Abbbccc aabbbccc abbbccc Part a) Circle each of the following phrases that correctly describes the above derivation. leftmost rightmost neither leftmost nor rightmost both leftmost & rightmost Part b) Draw the parse tree corresponding to the above derivation. Part c) Give a leftmost derivation of the string abc. S L XC L axbc L abc L abcc L abc S L AY L aay L ay L abyc L abc 1 f or either leftmost derivation if done perfectly, else 0. It s OK if there s no subscript L on the arrows. Part d) Is this grammar ambiguous? Justify your answer briefly. Yes. There are two distinct derivation trees for any non-null string having an equal number of a s, b s & c s. EG 1 for Yes. 1 for the justification. Anything they say that conveys an understanding that a grammar is ambiguous iff it generates at least one string for which there are at least two distinct derivation trees or canonical derivations is sufficient. And they must produce example derivations or trees illustrating this. CS 241 Fall 2009 Page 6 of 17

7 Question 5: [6 marks] Suppose that we wish to add to the WL language generalized conditional statements like the following guarded case test { } case test { } case test { } default { } endguarded that may appear wherever any other WL statement may appear, and in which: each test is an instance of a WL test such as may appear in a WL if statement; there must be at least one case clause; there may be an arbitrarily large number of case clauses; { } represents a sequence of zero or more WL statements (exactly as may appear in the body of a WL loop); the default clause may be absent. What changes are needed to the WL grammar to implement this additional statement type? You may add new vocabulary and productions as needed, but may not change existing vocabulary and productions. Four additional terminals are needed: guarded, case, default and endguarded. [1] mark. [1] mark for adding a non-terminal with which to define a list of one or more cases, distinct from whether the rules are correct. They need not expiicitly say it's a new non-terminal, provided that it appears on the LHS of at least one production. They need not define the non-terminals I've named defaultclause, since these can be directly included and there's a mark for each of these listed below, which they should get regardless of how they (correctly) get cases and the default clause into the statement. The following additional rules are needed: statement GUARDED caselist defaultclause ENDGUARDED caselist casestmt caselist caselist casestmt casestmt case test LBRACE statements RBRACE defaultclause DEFAULT LBRACE statements RBRACE defaultclause ε [1] mark. [1] mark. May be either L- or R-recursive. Marking: it's OK if they add two alternatives for statement, one with a default stmt and one w/o. It's also OK if they include the [1] mark. [1] mark. CS 241 Fall 2009 Page 7 of 17

8 Question 6: [14 marks] You are to extend WL to include the ability to declare and call functions of one or two parameters that return an integer as part of a WL expression. If a program calls one or more functions, it will be linked with a library of available functions as the program is loaded for execution. To accomplish this extension, the terminal keyword function (represented by the token FUNCTION) and the productions Rule 1: dcl Rule 2: dcl FUNCTION INT ID LPAREN INT RPAREN FUNCTION INT ID LPAREN INT COMMA INT RPAREN Rule 3: factor ID LPAREN expr RPAREN Rule 4: factor ID LPAREN expr COMMA expr RPAREN are added to WL s grammar and the WL specification is modified to require that any function called must have appeared in exactly one function declaration, be called with the number of parameters appearing in its declaration, not have appeared in a variable declaration, and the first (left) parameter is evaluated before the second (right) when there are two parameters. You should use our standard MIPS parameter passing conventions: $1 contains the first parameter, $2 contains the second parameter (when there is a second parameter), and the function called will return its value in $3. You may assume that the following helper methods/functions already exist: exprcode( node ), which takes a node of the parse tree as a parameter and returns MIPS assembly language code that evaluates the expression represented by the subtree rooted at that node and places its value in register $3; pushregister( number ), which returns MIPS assembly language code that pushes the contents of the register specified as a parameter onto the stack and decrements the stack pointer appropriately; popregister( number ), which returns MIPS assembly language code that pops the topmost value off the stack into the register whose number is specified as a parameter. Part a) On the next page you are to write pseudo code for helper methods/functions oneparametercall( node ) and twoparametercall( node ) that take a node of the parse tree as a parameter and return MIPS assembly code appropriate for rules 3 and 4, respectively. You may assume that the node passed to oneparametercall(...) does, indeed, correspond to an instance in the parse tree of rule 3, and similarly for twoparametercall(...) you do not need to do any error-checking. Neither do you need to implement any of the other rules already present in the WL language. Please answer on the next page. (You will find the WL grammar in the Reference Booklet, should you wish to refer to it.) CS 241 Fall 2009 Page 8 of 17

9 (Space in which to answer part a of Question 6 on the preceding page.) oneparametercall( node ) { fcnname = lexeme( child 0 of node ) // factor ID LPAREN expr RPAREN [1] for obtaining the id (here or inline below) ans = exprcode( child 2 of node ) [1] for call & order. ans += " add $1, $0,$3" + "\n" [1] for moving the returned value to $1 ans += " lis $JR " + "\n" [1] for setup and call ans += ".word" + fcnname + "\n" ans += " jalr $JR " + "\n" ans += " jr $31 " + "\n" [1] for return return ans [1] for returning the accumulated assembly code. $JR can be any register except $1, $30, or $31. It's ok if they forget to surround things with quotes, and it's ok if they forget to append the "\n"s. Full credit in each case only if the same (or equivalent) code is present in the implementation of twoparameter(...), too, and full credit if one of the instances has a trivial error; otherwise 1/2 point. Mainly the intent is to give a 1/2 point for each of the above if they have no answerr whatsoever for twoparameter(...), and of course 0 if neither answer is present, with the expectation that if they get it right here, they ll get it right below, and to give additional credit below for things that aren t relevant here. That s 6 marks for oneparameter(...) (if the corresponding assembly is in twoparameter(...), too). } twoparametercall( node ) { // factor ID LPAREN expr COMMA expr RPAREN fcnname = lexeme( child 0 of node ) ans = exprcode( child 2 of node ) ans += " pushregister( $3 )" + "\n" ans = exprcode( child 4 of node ) ans += " popregister( $1 ) " + "\n" ans += " add $2, $0,$3" + "\n" ans += " lis $JR " + "\n" ans += ".word" + fcnname + "\n" ans += " jalr $JR " + "\n" ans += " jr $31 " + "\n" return ans [1] for evaluating the left expression (child 2) before the right expression (child 4 of node). [1] for saving the left expression on the stack while the right expression is computed, then restoring it to $1 [1] for moving the returned value of the right expression from $3 to $2 before the jalr. That s an additional 3 marks for the things in twoparametercall(...) that aren t in oneparametercall(...), for a total of 9 marks for part a. } CS 241 Fall 2009 Page 9 of 17

10 Part b) Briefly explain the other significant changes to the WL compiler that would be needed to implement the added capability described on page 8. The entry in the symbol table for a function must have an additional field that records whether the ID corresponds to a variable or a function name [1] and an additional field that records whether the function takes one or two parameters [1]. It's ok, though unaesthetic, if they add ONE field to the symbol table that has the value 0 for variables and 1 or 2 for functions. The compiler must verify that every function call made invokes an ID that was declared to be of type function [1], and passes the correct number of arguements [1]. At the beginning of the code generation phase the compiler must generate a.export statement for each function declared [1]. That's a total of 5. If they cover a point listed here in their answer to part a, give them credit for it. CS 241 Fall 2009 Page 10 of 17

11 Question 7: [5 marks] Consider the following context-free grammar G S A A a B c A B B b B ε Fill in the following LL(1) parsing table [aka Predict( non-terminal, terminal)] for this grammar. a b c S S A A A B A a B c A B B B ε B b B ε Marking: 1 for each completely correct cell, then divide by 3 and round to the nearest integer. It's fine if they enter ERROR in the cells I ve left empty. CS 241 Fall 2009 Page 11 of 17

12 Question 8: [6 marks] Consider the following augmented LL(1) grammar G, whose start symbol is S, whose non-terminals are { S, P, L, B, E, T } and whose remaining symbols { if, then, else, print,... } are terminals. Here is the LL(1) parsing table for this grammar. r0 represents the rule S P, r1 represents the rule P if B then P else P, etc. S if then else { } print ; = # + r0 P r1 r2 r3 L r5 r4 B E r0: S P r1: P if B then P else P r2: P { P L } r3: P print E r4: L ; P L r5: L ε r6: B E = E r7: E # T r8: T + # T r9: T ε T r9 r9 r9 r9 r9 r9 r8 In the table below, write the next six steps of an LL(1) parse for the input shown, supplying information as is done in the first three rows. Action Stack Input yet to be read Initialization S if # = # then print # Expand r0 P if # = # then print # Read P if # = # then print # r6 r7 P if B then P else P [r1] if B then P else P if # = # then print # Read if B then P else P # = # then print # B E = E [r6] E = E then P else P # = # then print # E # T [r7] # T = E then P else P # = # then print # Read # T = E then S else P = # then print # T ε [r9] = E then S else P = # then print # 1 for each correct cell (total of 18), then divide by 3 and round up to get the marks awarded (max of 6). CS 241 Fall 2009 Page 12 of 17

13 Question 9: [8 marks] Consider the augmented cfg G S P P ( L ) P x L P L P, L whose start symbol is S, whose non-terminals are S, P and L, and whose terminal symbols are ( ) x, The LR(1) parsing table for this grammar appears below. snn means shift and move to state NN; A γ means reduce using the rule A γ. On the next page, you are to use this parsing table to parse the input shown there until you have filled the table or the parse is complete. DFA State ( ) x, S P L 00 s01 01 s02 s03 s09 02 s02 s03 s04 s07 03 P x P x P x 04 L P s05 05 s02 s03 s04 s06 06 L P, L 07 s08 08 P ( L ) P ( L ) P ( L ) 09 Accept CS 241 Fall 2009 Page 13 of 17

14 Row # State Action (Bot) Stack (Top) Remaining Input On even numbered rows, state the next action of the parser. On odd numbered rows, enter the current state of the parser, the contents of the stack, and the input remaining to be read in the appropriately labelled column. The first few entries have already been filled in so that you will know exactly how to supply the information needed. 00: Initialize! 01: 00 ( x, ( x ) ) 02: Shift 03: 01 [,1] 04: Shift ( ( x, ( x ) ) 05: 02 [,1] [(,2] x, ( x ) ) 06: Shift x 07: 03 [,1] [(,2] [x,3], ( x ) ) 08: Reduce P x 09: 04 [,1] [(,2] [P,4], ( x ) ) 10: Shift 11: 05 [,1] [(,2] [P,4] [,,5] ( x ) ) 12: Shift 13: 02 [,1] [(,2] [P,4] [,,5] [(,2] x ) ) 14: Shift x 15: 03 [,1] [(,2] [P,4] [,,5] [(,2] [x,3] ) ) 16: Reduce P x 17: 04 [,1] [(,2] [P,4] [,,5] [(,2] [P,4] ) ) 18: Reduce L P 19: 07 [,1] [(,2] [P,4] [,,5] [(,2] [L,7] ) ) 20: Shift ) 21: 08 [,1] [(,2] [P,4] [,,5] [(,2] [L,7] [),8] ) 22: Reduce P (L) 23: 04 [,1] [(,2] [P,4] [,,5] [P,4] ) (The parse may not be done yet, but if so, you are not asked to trace it further.) CS 241 Fall 2009 Page 14 of 17

15 Question 10: [14 marks] Part a) Consider a system to allocate and deallocate fixed-sized non-relocatable blocks of memory in an arena starting at address S and ending at address E. The operations required are: init() a = allocate() Initialize the arena and any necessary variables. Allocate a two-word block of memory. Return the address of the first word, or null if the allocation fails. deallocate(a) Deallocate the two-word block of memory at address a. Assume that Figure 1 illustrates the result of the sequence of operations shown immediately below. init() a = allocate() b = allocate() c = allocate() deallocate( a ) deallocate( c ) Figure 1 S free b cur E In Figure 2, draw the final result of applying the following four additional operations, starting from Figure 1. Draw on Figure 1 for your rough work, then copy the final result to Figure 2. Please ensure that Figure 2 contains no erasures or crossed-out material. ( *) d = allocate() e = allocate() Figure 2 f = allocate() g = allocate() S free cur E In Figure 3, draw the final result of applying the three following additional operations, starting from Figure 2. Please ensure that Figure 3 contains no erasures or crossed-out material. ( *) deallocate( d ) deallocate( e ) Figure 3 deallocate( f ) S free cur E (*) If you make a mistake in Figure 2 or 3, cross out the entire diagram clearly and redraw your answer on the back of the previous page. CS 241 Fall 2009 Page 15 of 17

16 Part b) Give pseudocode for each of the operations listed below. Assume that S and E contain appropriate values prior to init(); assume that all other memory is uninitialized. init() cur = S free = NULL a = allocate() if free!= NULL tmp = free free = *free else if cur < S tmp = cur cur++ return tmp deallocate( a ) *a = free free = a CS 241 Fall 2009 Page 16 of 17

17 Part c) Suppose that you wish to extend your solution to allocate blocks of variable size; that is, a = allocate( k ) allocates a block of k words, returning its address or null. Please read part (ii) before answering part (i). (i) What structural information must be added to each block? pointers for doubly linked list of blocks size of block whether allocated or free General marking instructions are on the preceding page. (ii) Outline an implementation of deallocate(a), assuming that the other operations correctly maintain the structural information described in (i). Use high level operations such as insert from list or delete from list. You need not give the detailed pointer operations necessary to implement these operations. if next(a) is unallocated combine a, next(a), adjusting length, and list pointers to form one node if prev(a) is unallocated combine prev(a), a, adjusting length and list pointers to form one node set a to point to the one node mark a as unallocated Note: they will give various levels of detail for the pointer threading. Give full marks if they outline a scenario that covers the four cases: alloc, a, alloc alloc, a, free free, a, alloc free, a, free General marking instructions are on the preceding page. CS 241 Fall 2009 Page 17 of 17

RYERSON POLYTECHNIC UNIVERSITY DEPARTMENT OF MATH, PHYSICS, AND COMPUTER SCIENCE CPS 710 FINAL EXAM FALL 96 INSTRUCTIONS

RYERSON POLYTECHNIC UNIVERSITY DEPARTMENT OF MATH, PHYSICS, AND COMPUTER SCIENCE CPS 710 FINAL EXAM FALL 96 STUDENT ID: INSTRUCTIONS Please write your student ID on this page. Do not write it or your name