extracted sorting into a separate file. may later replace the unstable sort in the TSM table by a stable sort

sort.lua

@@ -0,0 +1,84 @@
+local private, public = {}, {}
+Aux.sort = public
+
+public.LT = {}
+public.EQ = {}
+public.GT = {}
+
+-- stable sorting
+function public.merge_sort(A, comp)
+    local n = getn(A)
+    local B = {}
+
+    local width = 1
+    while width <= n do
+
+        for i=1, n, 2 * width do
+            private.merge(A, i, min(i + width, n), min(i + 2 * width - 1, n), B, comp)
+        end
+
+        private.copy_array(B, A, n)
+
+        width = 2 * width
+    end
+end
+
+function private.merge(A, start1, start2, last, B, comp)
+    local i1 = start1
+    local i2 = start2
+
+    for i=start1,last do
+        if i1 < start2 and (i2 > last or comp(A[i1], A[i2]) == public.LT or comp(A[i1], A[i2]) == public.EQ) then
+            B[i] = A[i1]
+            i1 = i1 + 1
+        else
+            B[i] = A[i2]
+            i2 = i2 + 1
+        end
+    end
+end
+
+function private.copy_array(A, B, n)
+    for i=1,n do
+        B[i] = A[i]
+    end
+end
+
+function public.invert_order(ordering)
+    if ordering == public.LT then
+        return public.GT
+    elseif ordering == public.GT then
+        return public.LT
+    else
+        return public.EQ
+    end
+end
+
+function public.compare(a, b, nil_ordering)
+    nil_ordering = nil_ordering or public.EQ
+    if not a and b then
+        return nil_ordering
+    elseif a and not b then
+        return public.invert_order(nil_ordering)
+    elseif not a and not b then
+        return public.EQ
+    elseif a < b then
+        return public.LT
+    elseif a > b then
+        return public.GT
+    else
+        return public.EQ
+    end
+end
+
+function public.compare_from_lt(comp)
+    return function(a, b)
+        if comp(a, b) then
+            return public.LT
+        elseif comp(b, a) then
+            return public.GT
+        else
+            return public.EQ
+        end
+    end
+end