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Recursion encodes dependence in the program And finally, it may or may not solve the fairness issue detailed before because the calcula tions required to perform a fair partitioning may end up being a sub stantial amount of work, offsetting any potential gains
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We could dynamically monitor the number of nodes actively being processed, that is, by maintaining an "actively running" counter and then switching between sequential and parallel processing more dynamically Many dynamic work stealing systems do this automat ically This incurs more overhead for runtime checking and is still not perfect because decisions tend to be "greedy," which can lead to depth first parallelization over breadth first (the former usually tends to be more efficient), though we can offset that by combining this approach with the first
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Let's illustrate the hybrid approach mentioned in the previous para graph First, we will use static decomposition to achieve good breadth first parallelization, and then, within each of those partitions, we will use the dynamic "active running" counter to scale up to a factor of the number of processors on the machine
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void P a r a l l e lM i r ro r ( TreeNode nod e ) { int a c t ive nod e , ( i nt ) Math Log ( E nvi ronment P roc e s sorCou nt , 2 ) , ref a c t ive ) j } void P a r a l lelM i r ro r ( T reeNode nod e , int t h re s hold , ref i nt a c t ive ) { if ( node
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{ Interloc ked l n c rement ( ref a c t i ve ) ; int newThreshold = t h reshold == a a DoAl l (
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( ) = > P a r a l lelMi r ro r ( node left , newT h r e s ho l d , ref a c t i ve ) , ( ) = > P a r a l lelMirror ( node right , newThres hold , ref a c t ive ) ); I n t e rlocked Dec rement ( ref a c t i ve ) ; } T reeNode tmp = node left ; node left = node right ; node right = tmp ; } void M i r ro r ( T reeNode nod e , ref int a c t i v e ) { if ( node == n U l l ) ret u r n ; if ( a c t ive < c_s c a l eUpTo ) { P a r a l lelMirror ( nod e , a, ref a c t i ve ) ; } else TreeNode tmp = node left ; node left = node right ; node right = tmp ; } }
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In summary, we begin the computation in P a r a l l e l M i r r o r by forward ing to the more specific overload, initializing threshold to log2 p, where p is the processor count, and passing a byref to a stack local a c t i ve variable that has been initialized to O As before, each recursive parallel call still decre ments the threshold by 1 This is where it gets a more difficult Inside of P a r a l l e l M i r ror, we have modified the threshold detection logic to switch to sequential processing in the M i r r o r method if both the threshold of the current call is 0 and the a c t i ve variable is greater than or equal to c_s c a l e UpTo This deserves some explanation Surrounding each call made to DoAl l, which may introduce parallelism, we increment and decrement the a ct i ve variable (by 1 ) This has the effect of permitting more dynamic par allelism: in our case, roughly twice the number of processors (since c_s c a l eU pTo is defined as E n v i ronment Pro c e s s o rCount * 2) Notice also that the sequential Mi r ro r API also checks the a c t i v e variable! If it ever
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