Andrew login ID Full Name CS 15 213 Fall 2006 Final Exam Thursday Dec 14 2006 Make sure that your exam is not missing any sheets then write your full name and Andrew login ID on the front Write your answers in the space provided below the problem If you make a mess clearly indicate your final answer The exam has a maximum score of 92 points This exam is OPEN BOOK You may use any books or notes you like You may use a calculator but no other electronic devices Good luck 01 06 02 09 03 06 04 12 05 12 06 06 07 15 08 06 09 04 10 08 11 08 TOTAL 92 Page 1 of 17 Problem 1 6 points Floating point encoding Consider the following 5 bit floating point representation based on the IEEE floating point format This format does not have a sign bit it can only represent nonnegative numbers There are k 3 exponent bits The exponent bias is 3 There are n 2 fraction bits Numeric values are encoded as a value of the form V M 2E where E is exponent after biasing and M is the significand value The fraction bits encode the significand value M using either a denormalized exponent field 0 or a normalized representation exponent field nonzero Any rounding of the significand is based on round to even Below you are given some decimal values and your task it to encode them in floating point format In addition you should give the rounded value of the encoded floating point number Give these as whole numbers e g 17 or as fractions in reduced form e g 3 4 Value Floating Point Bits Rounded value 9 32 001 00 1 4 1 32 1 16 3 32 1 11 12 Page 2 of 17 Problem 2 9 points Structs and arrays The next two problems require understanding how C code accessing structures and arrays is compiled Assume the x86 64 conventions for data sizes and alignments You are given the following C code include decls h typedef struct int x CNT2 int y int z CNT3 struct a typedef struct struct a data CNT1 int idx struct b Unknown constant Unknown constant Unknown constant void set y struct b bp int val int idx bp idx bp data idx y val You do not have a copy of the file decls h in which constants CNT1 CNT2 and CNT3 are defined but you have the following x86 64 code for the function set y set y bp in rdi val in esi movslq leaq movl ret 168 rdi rax rax rax 2 rax esi 12 rdi rax 8 Based on this code determine the values of the three constants A CNT1 B CNT2 C CNT3 Page 3 of 17 Problem 3 6 points Structs and arrays As in the previous problem assume the x86 64 conventions for data sizes and alignments You are given the following C code include decls h typedef struct type t x int y 3 struct a typedef struct int low struct a val N int high struct b Unknown type Unknown constant int get high struct b bp return bp high You do not have a copy of the file decls h in which constant N and data type type t are declared but you have the following x86 64 code for the function get high get high bp in rdi movl ret 104 rdi eax Provide some valid combination of these two parameters for which the assembly code would be generated A type t B N Page 4 of 17 Problem 4 12 points Loops Consider the following x86 64 assembly function called looped looped a in rdi n in esi movl 0 edx testl esi esi jle L4 movl 0 ecx L5 movslq movl cmpl cmovl incl cmpl jg ecx rax rdi rax 4 eax eax edx eax edx ecx edx esi L5 movl ret edx eax L4 Fill in the blanks of the corresponding C code You may only use the C variable names n a i and x not register names Use array notation in showing accesses or updates to elements of a int looped int a int n int i int x for i i if x return x Page 5 of 17 Problem 5 12 points Stack discipline Below is a segment of code you will remember from your buffer lab the section that reads a string from standard input int getbuf char buf 8 Gets buf return 1 The function Gets is similar to the library function gets It reads a string from standard input terminated by n or end of file and stores it along with a null terminator at the specified destination Gets has no way of determining whether buf is large enough to store the whole input It simply copies the entire input string possibly overrunning the bounds of the storage allocated at the destination Below is the object dump of the getbuf function 08048c4b getbuf 8048c4b 55 8048c4c 89 e5 8048c4e 83 ec 38 8048c51 8d 45 d8 8048c54 89 04 24 8048c57 e8 f2 00 00 00 8048c5c b8 01 00 00 00 8048c61 c9 8048c62 c3 push mov sub lea mov call mov leave ret ebp esp ebp 0x20 esp 0xfffffff0 ebp eax eax esp 8048d4e Gets 0x1 eax over Page 6 of 17 Suppose that we set a breakpoint in function getbuf and then use gdb to run the program with an input file redirected to standard input The program stops at the breakpoint when it has completed the sub instruction at 0x08048c4e and is poised to execute the lea instruction at 0x08048c51 At this point we run the following gdb command that lists the 12 4 byte words on the stack starting at the address in esp 0x08048c51 in getbuf gdb x 12w esp 0x55683a58 0x003164f8 0x55683a68 0x003166a4 0x55683a78 0x55683ab0 0x00000001 0x555832e8 0x08048bf9 0x55683a98 0x00000001 0x55683ab0 0x0030bab6 0x00000001 0x0035b690 A What is the address of buf 0x B When the program reaches the breakpoint what is the value of ebp 0x C To which address will getbuf return after executing 0x D When the program reaches the breakpoint what is the value of esp 0x E Instead of having getbuf return to its calling function suppose we want it to return to a function smoke that has the address 0x8048b20 Below is an incomplete sequence of the hex values of each byte in the file that was input to the program we have given you the first 8 padding values Fill in the remaining blank hex values so that the call to Gets will return to smoke Note that smoke does not depend on the value stored in ebp 0x01 0x02 0x03 0x04 0x05 0x06 0x07 0x08 0x 0x 0x 0x 0x 0x 0x 0x 0x 0x 0x 0x 0x 0x 0x 0x Page 7 of 17 Problem 6 6 points Consider the following function for computing the dot product of two arrays of n integers each We have unrolled the loop by a factor of 3 int dotprod int a int b int n int i …
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