Module 17: Loops
  Lecture 34: Symbolic Analysis
 


Example:

for i = 1 to n-1
for j = 1 to n-i+1
B[i,j] = B[i,n-1]
endfor
endfor

Triangular Lower Limits

  • Compiler may use semi-normalized space
  • Same iteration space shape must be used
  • Existence of integer solution is the same
  • Dependence distance/direction can be different
for i = 2 to n
for j = i+1 to n+i+1
B[i,,j] = B[i-1,,j-1] + C[i]
endfor
endfor

The normalized statement is:

B[2 + i1, 3 + i1 + i2] = B[i1 + 1, i1 + i2 + 2]+ · · ·