Simple Test

Simplest test when a single loop (2 unknowns) and a single dimension with linear subscript expression.

Definition Use

And assume same coefficient

• This has integer solution if gcd of coefficients divides rhs
• In this case gcd(a, a) = a
  Therefore, if a divides then there is a dependence

Example

For I = 2 to 10 do

Endfor

Using normalized loop,

Therefore,
Therefore,

• Now determine actual dependence solution
  • Either a flow dependence with distance Therefore,
  • Or, anti-dependence with distance Therefore,
    Therefore, or