[algo] Add stable sort algorithm, using merge sort.

algo.lua

@@ -139,4 +139,74 @@ function algo.bsearchr(array, what, less)
     return lo + ofs
 end
 
+local function merge(array, lo, mid, hi, less, workspace)
+    local i, j, k
+    i = 1
+
+    -- Copy first half of array to auxiliary array
+    for j = lo,mid do
+        workspace[i] = array[j]
+        i = i + 1
+    end
+
+    i = 1
+    j = mid + 1
+    k = lo
+    while k < j and j <= hi do
+        local v = array[j]
+        local el = workspace[i]
+
+        if less(v, el) then
+            array[k] = v
+            j = j + 1
+        else
+            array[k] = el
+            i = i + 1
+        end
+        k = k + 1
+    end
+
+    -- Copy back any remaining elements of first half
+    for k = k,j-1 do
+        array[k] = workspace[i]
+        i = i + 1
+    end
+end
+
+local function mergesort(array, lo, hi, less, workspace)
+    if hi - lo < 72 then
+        _insertionsort(array, lo, hi, less)
+    else
+        local mid = floor((lo + hi)/2)
+
+        mergesort(array, lo, mid, less, workspace)
+        mergesort(array, mid + 1, hi, less, workspace)
+        merge(array, lo, mid, hi, less, workspace)
+    end
+end
+
+--- Array stable sort, uses Merge Sort - O(n*log(n)).
+--
+-- Algorithm is a slightly altered version of stable_sort(),
+-- posted on Lua-L by Steve Fisher on 02 May 2013 22:10:50
+-- https://lua-users.org/lists/lua-l/2013-05/msg00038.html
+--
+-- This implementation uses an auxiliary buffer of size O(n/2).
+--
+-- @tparam table array Array to be sorted.
+-- @tparam[opt=operator <] function less comparison function, takes 2 arguments,
+--                                  returns true if its first argument is
+--                                  less than its second argument,
+--                                  false otherwise.
+-- @tparam[opt={}] table use an existing workspace buffer instead of allocating one.
+function algo.stablesort(array, less, workspace)
+    local n = #array
+
+    less = less or lt
+    workspace = workspace or {}
+    workspace[floor((n+1)/2)] = array[1]   -- preallocate some room
+
+    mergesort(array, 1, n, less, workspace)
+end
+
 return algo