Examples for some multithreaded algorithms.
- parallel before a loop means each iteration of the loop are independant from each other and can be run in parallel.
- spawn is to indicate creation of a new thread.
- sync is to synchronize all created threads.
- Arrays/matrix are indexed 1 to n in examples.
A is an array and p and q indexes of the array such as you gonna sort the sub-array A[p..r]. B is a sub-array which will be populated by the sort.
A call to p-merge-sort(A,p,r,B,s) sorts elements from A[p..r] and put them in B[s..s+r-p].
p-merge-sort(A,p,r,B,s) n = r-p+1 if n==1 B[s] = A[p] else T = new Array(n) //create a new array T of size n q = floor((p+r)/2)) q_prime = q-p+1 spawn p-merge-sort(A,p,q,T,1) p-merge-sort(A,q+1,r,T,q_prime+1) sync p-merge(T,1,q_prime,q_prime+1,n,B,s)
Here is the auxiliary function that performs the merge in parallel.
p-merge assumes that the two sub-arrays to merge are in the same array but doesn't assume they are adjacent in the array. That's why we need p1,r1,p2,r2.
p-merge(T,p1,r1,p2,r2,A,p3) n1 = r1-p1+1 n2 = r2-p2+1 if n1<n2 //check if n1>=n2 permute p1 and p2 permute r1 and r2 permute n1 and n2 if n1==0 //both empty? return else q1 = floor((p1+r1)/2) q2 = dichotomic-search(T[q1],T,p2,r2) q3 = p3 + (q1-p1) + (q2-p2) A[q3] = T[q1] spawn p-merge(T,p1,q1-1,p2,q2-1,A,p3) p-merge(T,q1+1,r1,q2,r2,A,q3+1) sync
And here is the auxiliary function dichotomic-search.
x is the key to look for in the sub-array T[p..r].
dichotomic-search(x,T,p,r) inf = p sup = max(p,r+1) while inf<sup half = floor((inf+sup)/2) if x<=T[half] sup = half else inf = half+1 return sup
Multiplication matrix vector multithread
matrix-vector(A,x) n = A.lines y = Vector(n) //create a new vector of length n parallel for i = 1 to n y[i] = 0 parallel for i = 1 to n for j = 1 to n y[i] = y[i] + A[i][j]*x[j] return y
Square matrix multiplication multithread
multiply-square-matrix-parallel(A, B) n = A.lines C = Matrix(n,n) //create a new matrix n*n parallel for i = 1 to n parallel for j = 1 to n C[i][j] = 0 pour k = 1 to n C[i][j] = C[i][j] + A[i][k]*B[k][j] return C