GCD test
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A |GCD Test is the test used in study of loop optimization to test the dependency between loop statements. Whenever a sequential loop like for loop is made to be paralle so that it can be executed on more than one machine like in case of grid computing or cluster computing then certain dependencies are checked to know whether this loop can be parallalized or not.One of which is to test flow dependence of statement.According to this test by comapring the indexes of two array presenmt in two or more statements it can be calculated that whether it is legal to split the loop or not.
Process
Loop code in general:
for (int i=0;i<n;i++)
{
s1 a[x*i+k] = b[i];
s2 c[i] = a[y*i+m];
}
If GCD(x,y) divides (m-k) then there may exist some dependency in the loop statement s1 and s2. If GCD(x,y) does not divisible by (m-k) then both statements are independent and can be executed parrelley.Similarly this test is conducted for all statements present in a given loop. An example source code in C would appear as:
for(int i=0;i<100;i++)
{
s1 a[2*i]=b[i];
s2 c[i]=a[4*i+1];
}
The GCD of(2,4) is 2 and dividend is 1. As 2 can not divide 1 properly(leaving remainder zero),there is no dependency between s1 and s2 and varoous other loop transformation methods can be applied.
References
- Advanced Compiler Design and Implementation by Steven S Muchnick