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Dependency Test in Loops

Dependency Test in Loops. By Amala Gandhi. Data Dependence. Three types of data dependence: Flow (True) dependence : read-after-write int a, b, c; a = c * 10; b = 2 * a + c ; Anti Dependency: write-after-read int a, b, c; a = b* 4+ c; c = b + 40;

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Dependency Test in Loops

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  1. Dependency Test in Loops By Amala Gandhi

  2. Data Dependence • Three types of data dependence: • Flow (True) dependence : read-after-write int a, b, c; a = c * 10; b = 2 * a + c; • Anti Dependency: write-after-read inta, b, c; a = b* 4+ c; c = b + 40; • Output Dependence: write-after-write inta, b, c; a = b *c ; a = b + c + 10;

  3. Dependency in Loops • Two main types of dependency in loops Loop Independent : Dependence in same iteration for (i= 2; i<= 4; i++){ a[i] = b[i] + c[i]; d[i] = a[i]; } Loop Carried : Dependence over the iteration for (i= 2 ; i< = 4; i++) { a[i] = b[i] + c[i]; d[i] = a[i-1]; }

  4. Loop Dependency Analysis • With automatic parallelization, the compiler detects loops that can be safely and efficiently executed in parallel • Automatic parallelization, kind of optimization • Shorter execution time • Adds the parallel compiler directives • To know whether two usages of an array access the same memory location, compiler needs to perform certain dependency tests

  5. Greatest Common Divisor Test • A Linear Diophantine equation a1*x1 + a2*x2 +...+ an*xn = c • Above equation has a solution if , the greatest common divisor of a1,a2,..an can divide the c i.e. the result of the division is an integer. • Example: 15*x +6*y -9*z = 12 gcdof 15, 6 and 9 is 3 3can divide 12 Hence the equation has a solution. • If equation has a solution , means has dependency ,else no dependency

  6. GCD Test contd. Code Snippet: for (i= 1; i< N; i++) { a[2* i] = .. ; .. = a[3* i- 5]; } Equation formation: 2x = 3y - 5 i.e. 2x – 3y = -5 GCD(2,3) = 1, divides 5 Has a dependency • If there was no dependency, then compiler can directly go forward for applying the parallelization technique.

  7. GCD Test Limitation • GCD ignores bounds for (i= 1; i< 10; i++) { a[i] = b[i] + c[i]; d[i] = a[i-100]; } • For above example, GCD test shows that there is dependence, but actually it has ignored bounds. • GCD test also does not provide distance or direction information • To overcome this limitation, GCD test is combined with Banerjee test • Many such tests are present, different compilers may use different loop dependency test

  8. Take Aways • Terminologies used in Data Dependence and Loop Dependence Analysis • Concept of tests used in Loop Dependence Analysis with the help of GCD test

  9. Thank You

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