// ************************************************************************** // // // // eses eses // // eses eses // // eses eseses esesese eses Embedded Systems Group // // ese ese ese ese ese // // ese eseseses eseseses ese Department of Computer Science // // eses eses ese eses // // eses eseses eseseses eses University of Kaiserslautern // // eses eses // // // // ************************************************************************** // // Factorial numbers are recursively defined as follows: F(n) := n * F(n-1) // with F(0) := 1. The following algorithm is based on the parallel prefix sum // and computes the first N factorial numbers in time O(log(n)) with O(n) work. // ************************************************************************** // macro M = 4; macro N = exp(2,M); module Factorial([N]nat fac, event rdy) { // initialize array fac fac[0] = 1; for(i=1..N-1) fac[i] = i; // bottom-up traversal requires time log(N) // with N-1 work and N/2 processors for(l=1..M) { for(j=1..N/exp(2,l)) { let(s = exp(2,l-1)) next(fac[2*j*s-1]) = fac[2*j*s-1] * fac[(2*j-1)*s-1]; } pause; } // top-down traversal requires time log(N)-1 // with N-log(N)-1 work and N/2 processors for(i=1..M-1) { let(l = M-i) for(j=1..exp(2,i)-1) { let(s = exp(2,l-1)) next(fac[(2*j+1)*s-1]) = fac[(2*j+1)*s-1] * fac[2*j*s-1]; } pause; } // signal the termination emit(rdy); } drivenby { await(rdy); }