mith College Computer Science CSC231 Assembly Week #13 Fall 2017 Dominique Thiébaut

Transcription

1 mith College Computer Science CSC21 Assembly Week #1 Fall 2017 Dominique Thiébaut

2 for n in ; do echo "n =$n"./hw7b $n echo "" done Pascal Triangle n =0 n =1 1 n = n =

3 Short/Long Jumps if ( x < y ) { f1(x); } else { f2(y); } if ( x >= y ) { f2(y); } else { f1(x); }

4 Short/Long Jumps if: cmp eax, ebx jge else then: jmp endif else: endif:

5 Short/Long Jumps if: cmp eax, ebx jge else then: jmp endif else: endif: same if: cmp eax, ebx jl then jmp else then: jmp endif else: endif:

6 RURSION

7 Python.5.0b1 (v.5.0b1:071fefbb5ed, May , 18:22:54) [G (Apple Inc. build 5666) (dot )] on darwin Type "copyright", "credits" or "license()" for more information. >>> def fact( n ): if n <= 1: return 1 return n * fact( n - 1 ) >>> fact( ) 6 >>> fact( 5 ) 120 >>> fact( 20 ) >>> fact( 100 ) >>> { 1 if n<=1 n! = n * (n-1)! otherwise

8 Class Exercise: Act out the Play "Compute Fact(5)"

9 Class Exercise 2: Write a Python Program with a main() function and a fact() function

10 Using Python as example, write fact(n) in Assembly

11

12 Question 1 What is the largest value of n the assembly and recursive version of fact can compute? Note: there are several possible good answers

13 We stopped here last time

14 Single-Stepping the Assembly Code Computing Fact()

15 eax 100 F8 E8 D8

16 eax 100 F8 E8 D8

17 eax 100 F8 E8 D8 ret addr _printint

18 eax 100 F8 E8 D8 ret addr _printint old ebp

19 eax 100 ebp F8 E8 D8 red addr _printint old ebp

20 eax 100 ebp F8 E8 D8 red addr _printint old ebp

21 eax 100 ebp F8 E8 D8 red addr _printint old ebp

22 eax 100 ebp F8 E8 D8 red addr _printint old ebp

23 eax: 100 ebp F8 E8 D8 red addr _printint old ebp

24 eax: ebp F8 E8 D8 red addr _printint old ebp

25 eax: ebp F8 E8 D8 red addr _printint old ebp 2

26 eax: ebp F8 E8 D8 red addr _printint old ebp 2 ret addr mul

27 eax: ebp F8 E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8)

28 eax: F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8)

29 eax: F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8)

30 eax: F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8)

31 eax: F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8)

32 eax: F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8)

33 eax: F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8)

34 eax: F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8) 1

35 eax: F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8) 1 ret addr mul

36 eax: F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8) 1 ret addr mul old ebp (E8)

37 eax: F8 E8 ebp D8 red addr _printint old ebp 2 ret addr mul old ebp (F8) 1 ret addr mul old ebp (E8)

38 eax: F8 E8 ebp D8 red addr _printint old ebp 2 ret addr mul old ebp (F8) 1 ret addr mul old ebp (E8)

39 eax: F8 E8 ebp D8 red addr _printint old ebp 2 ret addr mul old ebp (F8) 1 ret addr mul old ebp (E8)

40 eax: F8 E8 ebp D8 red addr _printint old ebp 2 ret addr mul old ebp (F8) 1 ret addr mul old ebp (E8)

41 eax: F8 E8 ebp D8 red addr _printint old ebp 2 ret addr mul old ebp (F8) 1 ret addr mul old ebp (E8)

42 eax: F8 E8 ebp D8 red addr _printint old ebp 2 ret addr mul old ebp (F8) 1 ret addr mul old ebp (E8)

43 eax: F8 E8 ebp D8 red addr _printint old ebp 2 ret addr mul old ebp (F8) 1 ret addr mul old ebp (E8)

44 eax: F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8) 1 ret addr mul

45 eax: F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8)

46 eax: edx: 0 F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8)

47 eax: edx: xxxx F8 ebp E8 D8 red addr _printint old ebp 2 ret addr mul old ebp (F8)

48 eax: edx: xxxx ebpf8 E8 D8 red addr _printint old ebp 2 ret addr mul

49 eax: edx: xxxx ebpf8 E8 D8 red addr _printint old ebp

50 eax: edx: 0 ebpf8 E8 D8 red addr _printint old ebp

51 eax: edx: XXX ebpf8 E8 D8 red addr _printint old ebp

52 eax: edx: XXX F8 E8 ebp D8 ret addr _printint

53 eax: edx: XXX F8 E8 ebp D8

54 Following the path of the Execution for fact()

55

56

57 Java Version Does it break down at some point? getcopy Factorial.java

58 java Factorial java Factorial > javaerrors.log less javaerrors.log cat javaerrors.log wc -l

59 Compare to Non-Recursive Version getcopy factorialnonrecursive.asm

60 Question 2 Compare the execution time of the recursive version of factorial() to its non-recursive version. (Use the assembly versions to answer this question)

61 count the number of cycles for each for N!, non-recursive # steps= k1 + 2(N) for N! recursive # steps = k2 + 1(N)

62 Question If the maximum stack size given to a program is 8 GBytes, how many terms could the assembly fact() function compute, at most, if we didn't care about multiplication overflow? Note: We can get the default stack size linux uses with ulimit -a

63 Question 4 What are the space complexities for the recursive and non-recursive versions of Factorial?

64 For the recursive version, we have n stack frames in the stack when computing n! Each stack frame contains 1) n, 2) the return address, ) old ebp, 4), or 4x4 bytes = 16 bytes. Total stack space= 16n bytes = O(n) For the non-recursive version, we have dwords in the stack: 1) return address, 2), and ) old ecx. Total stack space = x = 9 bytes = O(1)

65 Towers of Hanoi in Assembly In Python first In Assembly next

66 main program calling hanoi User provides N, # of disks

67

68 Version 1

69 Version 2