% This file contains Nesl code for the NAS conjugate gradient (CG) benchmark. It uses a parallel version of MAKEA to build the array, and therefore does not generate an identical array as the original Fortran verson. However, the form of the array is identical and the final results are quite close. As with the Fortran version, two sets of parameters are given, one for a small problem and one for a large problem. The fortran code was written by Robert Schreiber and Horst Simon. There has been no attempt to optimize this code. Don't forget to turn argument checking off before running any timings. % % ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;; ROUTINES FOR MAKING THE INPUT ARRAY ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; % % Makes a cluster of array elements for row i -- used by makea. n is the total number of rows, rcond is the condition number % function MAKE_GROUP(i, n, non_zeros, rcond) = let % generates non_zeros random distinct integers between 0 and n-1% indices = take(remove_duplicates({rand(i): i in dist(n,2*non_zeros)}), non_zeros); % generates a random value between 0.0 and 1.0 for each index % pairs = {i,rand(fl): i in indices; fl in dist(1.0,non_zeros)}; % add diagonal element -- delete any existing diagonal % pairs = {j,v in pairs| i /= j} ++ [(i,.5)]; size = expt(rcond,float(i)/float(n)); % take outer product % result = flatten({{(ix,iy,vx*vy*size) :(ix,vx) in pairs}: (iy,vy) in pairs}) in result \$ % Input is a sequence of (rowindex,columnindex,value) triples Output is compressed sparse row format with duplicates combined. This is a nested sequence in which each subsequence represents a row and consists of a squence of (index,value) pairs, where the index gives the column number of a non-zero element, and value is its value. % function SPARSE(a) = let % collect by rows % rows = int_collect(a); % collect each row by column and combine duplicates % result = {{column_idx, sum(vals): (column_idx,vals) in int_collect(row)}: (row_idx, row) in rows} in result \$ function MAKEA(n, non_zeros, rcond) = let % make group of array elements for each row % triples = flatten({make_group(i,n,non_zeros,rcond): i in [0:n]}); % add identity*rcond to bound the smallest eigenvalue from below % triples = triples ++ {i,i,rcond: i in [0:n]}; % convert to compressed sparse row format % result = sparse(triples) in result \$ % ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;; ROUTINES FOR CONJUGATE GRADIENT ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; % % WARNING: THE REST IS NOT YET DOCUMENTED % function MATVEC(a,x) = let ids,vals = unzip(flatten(a)); newvals = {vals*g:vals;g in x->ids} in {sum(row): row in partition(newvals,{#a:a})} \$ function DOTP(x,y) = sum({x*y:x;y}) \$ function CGSOL_LOOP(a,p,x,r,rho,i) = if (i == 0) then x else let q = matvec(a, p); alpha = rho/dotp(p,q); x = {x + alpha * p:x;p}; rho0 = rho; r = {r - alpha * q:r;q}; rho = dotp(r,r); beta = rho/rho0; p = {beta*p + r:p;r} in cgsol_loop(a,p,x,r,rho,i-1) \$ function CGSOL(a,b,nitcg) = let x = dist(0.0,#b); rho = dotp(b,b); x = cgsol_loop(a,b,x,b,rho,nitcg); r = matvec(a,x); r = {b-r:b;r}; resid = sqrt(dotp(r, r)) in x,resid \$ % ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;; THE OVERALL BENCHMARK ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; % function CGSOL_OUTER_LOOP(a,x,zeta,zeta1,nitcg,i,niter) = let z,resid = cgsol(a,x,nitcg); (zeta1,zeta2) = (zeta,zeta1); zeta = 1. / max_val({abs(z):z}); zetapr = zeta - ((zeta-zeta1)^2 / (zeta - 2.0*zeta1 + zeta2)); % ignore = print_line(@i||-5 ++ @resid||-16 ++ @zetapr||-16); % x = {z*zeta:z} in if (i == niter) then (zetapr,resid) else cgsol_outer_loop(a,x,zeta,zeta1,nitcg,i+1,niter) \$ function print_statistics(a,n,tm,zetapr,resid,nitcg,niter,parameters) = let (nnzchk,zetchk,reschk,timchk) = parameters; matops = 2*sum({#a:a}); opscg = 5*n + matops + nitcg*(matops + 10*n + 2); ops = niter * (opscg + n + 1); flops = 1e-6 * float(ops) / tm; format = (str,val) => (str||30 ++ "=" ++ val||-12 ++ [newline]); line = (format("total number of operations",@ops) ++ format("total execution time", @tm) ++ format("performance in mflops", @flops) ++ format("ratio: this machine/ymp(1cpu)", @(timchk/tm)) ++ [newline] ++ format("computed zeta", @zetapr) ++ format("reference value", @zetchk) ++ [newline] ++ format("computed residual", @resid) ++ format("reference value", @reschk)) in print_line(line) \$ % The following strucutes contain the parameters for the two different sized tests. The parameters are: (n, non_zeros, nnzchk, zetchk, reschk, timchk) % small_parameters = ( 1400, 7, 78148, .10188582986104, 0.6241e-05, 1.0538); large_parameters = (14000, 11, 1853104, .101249586035172, 3.5094e-04, 21.77); function CG(parameters) = let (n,non_zeros,other_parameters) = parameters; niter = 15; % outer iterations % nitcg = 25; % inner iterations % rcond = .1; % condition number % a = makea(n,non_zeros,rcond); ignore = print_line("Final nonzero count: " ++ @sum({#a:a}) ++ [newline]); x = dist(1.0,n); (zeta,zeta1) = (0.,0.); (zetapr,resid),tm = time(cgsol_outer_loop(a,x,zeta,zeta1,nitcg,1,niter)); ignore = print_statistics(a,n,tm,zetapr,resid,nitcg,niter,other_parameters) in t \$ function cg_small(ignore) = cg(small_parameters) \$ function cg_large(ignore) = cg(large_parameters) \$