function count_buckets(values, buckets, i) = if (i == #values) then buckets else let key = values[i]; count = buckets[key]; newbuckets = rep(buckets, count + 1, key) in count_buckets(values, newbuckets, i + 1) \$ function new_location(values, offsets, i) = if (i == #values) then values else let key = values[i]; count = offsets[key]; newvalues = rep(values, count, i); newoffsets = rep(offsets, count + 1, key) in new_location(newvalues, newoffsets, i + 1) \$ function serial_counting_rank(a, bucketsize) = let buckets = dist(0, bucketsize); counts = count_buckets(a, buckets, 0); offsets = plus_scan(counts) in new_location(a, offsets, 0) \$ function get_offsets(buckets, copies) = let trans_buckets = transpose(buckets); scanned_buckets = plus_scan(flatten(trans_buckets)); offsets = transpose(partition(scanned_buckets,{#b : b in trans_buckets})); in offsets \$ function parallel_counting_rank(a, m) = let block_size = isqrt(#a); blocks = group_by(a, block_size); counts = {count_buckets(b, dist(0, m), 0): b in blocks}; offsets = get_offsets(counts, sqrt); ranks = {new_location(b, o, 0): b in blocks; o in offsets}; in flatten(ranks) \$ function radix_rank_r(keys, ranks,bits_per_pass) : ([int],[int],int)->[int] = if any(keys) == all(keys) then permute(index(#ranks), ranks) else let num_buckets = lshift(1, bits_per_pass); mask = num_buckets-1; subkeys = {k and mask: k in keys}; newkeys = {rshift(k, bits_per_pass): k in keys}; index = parallel_counting_rank(subkeys, num_buckets) in radix_rank_r(permute(newkeys, index), permute(ranks, index), bits_per_pass) \$ function radix_rank(v) = radix_rank_r(v, index(#v), 8) \$