11. Common Sub expression elimination Common Sub expression elimination is a optimization that searches for instances of identical expressions (i.e they all evaluate the same value), and analyses whether it is worthwhile replacing with a single variable holding the computed value. a=b * c + g d=b * c * d temp=b * c a=temp + g d=temp * d
12. Dead Code elimination is a compiler optimization that removes code that does not affect a program. Removing such code has two benefits It shrinks program size, an important consideration in some contexts. It lets the running program avoid executing irrelevant operations, which reduces its running time. Dead Code elimination is of two types Unreachable Code Redundant statement Dead code Optimization:
13. Unreachable Code In Computer Programming, Unreachable Code or dead code is code that exists in the source code of a program but can never be executed. Program Code If (a>b) m=a elseif (a<b) m=b elseif (a==b) m=0 else m=-1 Optimized Code If (a>b) m=a elseif (a<b) m=b else m=0
14. Redundant Code Redundant Code is code that is executed but has no effect on the output from a program main(){ int a,b,c,r; a=5; b=6; c=a + b; r=2; r++; printf(“%d”,c); } Adding time & space complexity
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16. Loop Invariant i = 1 s= 0 do{ s= s + i a =5 i = i + 1 { while (i < =n) i = 1 s= 0 a =5 do{ s= s + i i = i + 1 { while (i < =n) Bringing a=5 outside the do while loop, is called code motion.
17. Induction variables i = 1 s= 0 S1=0 S2=0 while (i < =n) { s= s + a[ i ] t1 = i * 4 s= s + b[ t1 ] t2 = t1 +2 s2= s2 + c[ t2 ] i = i + 1 } i = 1 s= 0 S1=0 S2=0 t2=0 while (i < =n) { s= s + a[ i ] t1 = t1+ 4 s= s + b[ t1 ] s2= s2 + c[t1 +2 ] i = i + 1 } t1,t2 are induction variables. i is inducing t1 and t1 is inducing t2 “ +” replaced “ * ”, t1 was made independent of i
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29. Three Address Code of Quick Sort i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto (5) j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto (9) if i >= j goto (23) t 6 = 4 * i x = a[t 6 ] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 t 7 = 4 * I t 8 = 4 * j t 9 = a[t 8 ] a[t 7 ] = t 9 t 10 = 4 * j a[t 10 ] = x goto (5) t 11 = 4 * I x = a[t 11 ] t 12 = 4 * i t 13 = 4 * n t 14 = a[t 13 ] a[t 12 ] = t 14 t 15 = 4 * n a[t 15 ] = x 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
30. Find The Basic Block i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto (5) j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto (9) if i >= j goto (23) t 6 = 4 * i x = a[t 6 ] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 t 7 = 4 * I t 8 = 4 * j t 9 = a[t 8 ] a[t 7 ] = t 9 t 10 = 4 * j a[t 10 ] = x goto (5) t 11 = 4 * i x = a[t 11 ] t 12 = 4 * i t 13 = 4 * n t 14 = a[t 13 ] a[t 12 ] = t 14 t 15 = 4 * n a[t 15 ] = x 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
31. Flow Graph if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 t 6 = 4 * i x = a[t 6 ] t 7 = 4 * i t 8 = 4 * j t 9 = a[t 8 ] a[t 7 ] = t 9 t 10 = 4 * j a[t 10 ] = x goto B 2 t 11 = 4 * i x = a[t 11 ] t 12 = 4 * i t 13 = 4 * n t 14 = a[t 13 ] a[t 12 ] = t 14 t 15 = 4 * n a[t 15 ] = x B 1 B 2 B 3 B 4 B 5 B 6
32. Common Subexpression Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 t 6 = 4 * i x = a[t 6 ] t 7 = 4 * i t 8 = 4 * j t 9 = a[t 8 ] a[t 7 ] = t 9 t 10 = 4 * j a[t 10 ] = x goto B 2 t 11 = 4 * i x = a[t 11 ] t 12 = 4 * i t 13 = 4 * n t 14 = a[t 13 ] a[t 12 ] = t 14 t 15 = 4 * n a[t 15 ] = x B 1 B 2 B 3 B 4 B 5 B 6
33. Common Subexpression Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 t 6 = 4 * i x = a[t 6 ] t 8 = 4 * j t 9 = a[t 8 ] a[ t 6 ] = t 9 t 10 = 4 * j a[t 10 ] = x goto B 2 t 11 = 4 * i x = a[t 11 ] t 12 = 4 * i t 13 = 4 * n t 14 = a[t 13 ] a[t 12 ] = t 14 t 15 = 4 * n a[t 15 ] = x B 1 B 2 B 3 B 4 B 5 B 6
34. Common Subexpression Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 t 6 = 4 * i x = a[t 6 ] t 8 = 4 * j t 9 = a[t 8 ] a[ t 6 ] = t 9 a[ t 8 ] = x goto B 2 t 11 = 4 *i x = a[t 11 ] t 12 = 4 * i t 13 = 4 * n t 14 = a[t 13 ] a[t 12 ] = t 14 t 15 = 4 * n a[t 15 ] = x B 1 B 2 B 3 B 4 B 5 B 6
35. Common Subexpression Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 t 6 = 4 * i x = a[t 6 ] t 8 = 4 * j t 9 = a[t 8 ] a[ t 6 ] = t 9 a[ t 8 ] = x goto B 2 t 11 = 4 * i x = a[t 11 ] t 12 = 4 * i t 13 = 4 * n t 14 = a[t 13 ] a[t 12 ] = t 14 t 15 = 4 * n a[t 15 ] = x B 1 B 2 B 3 B 4 B 5 B 6
36. Common Subexpression Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 t 6 = 4 * i x = a[t 6 ] t 8 = 4 * j t 9 = a[t 8 ] a[ t 6 ] = t 9 a[ t 8 ] = x goto B 2 t 11 = 4 * i x = a[t 11 ] t 13 = 4 * n t 14 = a[t 13 ] a[ t 11 ] = t 14 t 15 = 4 * n a[t 15 ] = x B 1 B 2 B 3 B 4 B 5 B 6
37. Common Subexpression Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 t 6 = 4 * i x = a[t 6 ] t 8 = 4 * j t 9 = a[t 8 ] a[ t 6 ] = t 9 a[ t 8 ] = x goto B 2 t 11 = 4 * i x = a[t 11 ] t 13 = 4 * n t 14 = a[t 13 ] a[ t 11 ] = t 14 a[ t 13 ] = x B 1 B 2 B 3 B 4 B 5 B 6
38. Common Subexpression Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 t 6 = 4 * i x = a[t 6 ] t 8 = 4 * j t 9 = a[t 8 ] a[ t 6 ] = t 9 a[ t 8 ] = x goto B 2 t 11 = 4 * i x = a[t 11 ] t 13 = 4 * n t 14 = a[t 13 ] a[ t 11 ] = t 14 a[ t 13 ] = x B 1 B 2 B 3 B 4 B 5 B 6
39. Common Subexpression Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 x = a[ t 2 ] t 8 = 4 * j t 9 = a[t 8 ] a[ t 2 ] = t 9 a[ t 8 ] = x goto B 2 t 11 = 4 * i x = a[t 11 ] t 13 = 4 * n t 14 = a[t 13 ] a[ t 11 ] = t 14 a[ t 13 ] = x B 1 B 2 B 3 B 4 B 5 B 6
40. Common Subexpression Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 x = t 3 t 8 = 4 * j t 9 = a[t 8 ] a[ t 2 ] = t 9 a[ t 8 ] = x goto B 2 t 11 = 4 * i x = a[t 11 ] t 13 = 4 * n t 14 = a[t 13 ] a[ t 11 ] = t 14 a[ t 13 ] = x B 1 B 2 B 3 B 4 B 5 B 6
41. Common Subexpression Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 x = t 3 a[ t 2 ] = t 5 a[ t 4 ] = x goto B 2 t 11 = 4 * i x = a[t 11 ] t 13 = 4 * n t 14 = a[t 13 ] a[ t 11 ] = t 14 a[ t 13 ] = x B 1 B 2 B 3 B 4 B 5 B 6
42. Common Subexpression Elimination if i >= j goto B 6 Similarly for B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 x = t 3 a[ t 2 ] = t 5 a[ t 4 ] = x goto B 2 x = t 3 t 14 = a[t 1 ] a[ t 2 ] = t 14 a[ t 1 ] = x B 1 B 2 B 3 B 4 B 5 B 6
43. Dead Code Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 x = t 3 a[ t 2 ] = t 5 a[ t 4 ] = x goto B 2 x = t 3 t 14 = a[t 1 ] a[ t 2 ] = t 14 a[ t 1 ] = x B 1 B 2 B 3 B 4 B 5 B 6
44. Dead Code Elimination if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 a[ t 2 ] = t 5 a[ t 4 ] = t 3 goto B 2 t 14 = a[t 1 ] a[ t 2 ] = t 14 a[ t 1 ] = t 3 B 1 B 2 B 3 B 4 B 5 B 6
45. Reduction in Strength if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] i = i + 1 t 2 = 4 * i t 3 = a[t 2 ] if t 3 < v goto B 2 j = j – 1 t 4 = 4 * j t 5 = a[t 4 ] if t 5 > v goto B 3 a[ t 2 ] = t 5 a[ t 4 ] = t 3 goto B 2 t 14 = a[t 1 ] a[ t 2 ] = t 14 a[ t 1 ] = t 3 B 1 B 2 B 3 B 4 B 5 B 6
46. Reduction in Strength if i >= j goto B 6 i = m - 1 j = n t 1 =4 * n v = a[t 1 ] t 2 = 4 * i t 4 = 4 * j t 2 = t 2 + 4 t 3 = a[t 2 ] if t 3 < v goto B 2 t 4 = t 4 - 4 t 5 = a[t 4 ] if t 5 > v goto B 3 a[ t 2 ] = t 5 a[ t 4 ] = t 3 goto B 2 t 14 = a[t 1 ] a[ t 2 ] = t 14 a[ t 1 ] = t 3 B 1 B 2 B 3 B 4 B 5 B 6
