From 02340375bee903fe68830cf86c2c207db16ada6b Mon Sep 17 00:00:00 2001
From: Roberto Ierusalimschy <roberto@inf.puc-rio.br>
Date: Fri, 6 Nov 2015 14:07:14 -0200
Subject: [PATCH] janitor work on 'table.sort': added comments, partition code
 moved to a separated function, code conventions updated, etc. No changes at
 all in the logic/algorithm

---
 ltablib.c | 130 +++++++++++++++++++++++++++++++-----------------------
 1 file changed, 76 insertions(+), 54 deletions(-)

diff --git a/ltablib.c b/ltablib.c
index 10a4a3d2..7dae7049 100644
--- a/ltablib.c
+++ b/ltablib.c
@@ -1,5 +1,5 @@
 /*
-** $Id: ltablib.c,v 1.82 2015/09/09 15:42:30 roberto Exp roberto $
+** $Id: ltablib.c,v 1.83 2015/09/17 15:53:50 roberto Exp roberto $
 ** Library for Table Manipulation
 ** See Copyright Notice in lua.h
 */
@@ -12,6 +12,7 @@
 
 #include <limits.h>
 #include <stddef.h>
+#include <time.h>
 
 #include "lua.h"
 
@@ -253,67 +254,88 @@ static int sort_comp (lua_State *L, int a, int b) {
     return lua_compare(L, a, b, LUA_OPLT);
 }
 
-static void auxsort (lua_State *L, int l, int u) {
-  while (l < u) {  /* for tail recursion */
-    int i, j;
-    /* sort elements a[l], a[(l+u)/2] and a[u] */
-    lua_geti(L, 1, l);
-    lua_geti(L, 1, u);
-    if (sort_comp(L, -1, -2))  /* a[u] < a[l]? */
-      set2(L, l, u);  /* swap a[l] - a[u] */
+
+/*
+** Does the partition: Pivot P is at the top of the stack.
+** precondition: a[lo] <= P == a[up-1] <= a[up],
+** so it only needs to do the partition from lo + 1 to up - 2.
+** Pos-condition: a[lo .. i - 1] <= a[i] == P <= a[i + 1 .. up]
+** returns 'i'.
+*/
+static int partition (lua_State *L, int lo, int up) {
+  int i = lo;  /* will be incremented before first use */
+  int j = up - 1;  /* will be decremented before first use */
+  /* loop invariant: a[lo .. i] <= P <= a[j .. up] */
+  for (;;) {
+    /* next loop: repeat ++i while a[i] < P */
+    while (lua_geti(L, 1, ++i), sort_comp(L, -1, -2)) {
+      if (i >= up)
+        luaL_error(L, "invalid order function for sorting");
+      lua_pop(L, 1);  /* remove a[i] */
+    }
+    /* after the loop, a[i] >= P and a[lo .. i - 1] < P */
+    /* next loop: repeat --j while P < a[j] */
+    while (lua_geti(L, 1, --j), sort_comp(L, -3, -1)) {
+      if (j < lo)
+        luaL_error(L, "invalid order function for sorting");
+      lua_pop(L, 1);  /* remove a[j] */
+    }
+    /* after the loop, a[j] <= P and a[j + 1 .. up] >= P */
+    if (j < i) {  /* no elements out of place? */
+      /* a[lo .. i - 1] <= P <= a[j + 1 .. i .. up] */
+      lua_pop(L, 1);  /* pop a[j] */
+      /* swap pivot (a[up - 1]) with a[i] to satisfy pos-condition */
+      set2(L, up - 1, i);
+      return i;
+    }
+    /* otherwise, swap a[i] - a[j] to restore invariant and repeat */
+    set2(L, i, j);
+  }
+}
+
+
+static void auxsort (lua_State *L, int lo, int up) {
+  while (lo < up) {  /* loop for tail recursion */
+    int p;
+    /* sort elements 'lo', '(lo + up)/2' and 'up' */
+    lua_geti(L, 1, lo);
+    lua_geti(L, 1, up);
+    if (sort_comp(L, -1, -2))  /* a[up] < a[lo]? */
+      set2(L, lo, up);  /* swap a[lo] - a[up] */
     else
-      lua_pop(L, 2);
-    if (u-l == 1) break;  /* only 2 elements */
-    i = (l+u)/2;
-    lua_geti(L, 1, i);
-    lua_geti(L, 1, l);
-    if (sort_comp(L, -2, -1))  /* a[i]<a[l]? */
-      set2(L, i, l);
+      lua_pop(L, 2);  /* remove both values */
+    if (up - lo == 1)  /* only 2 elements? */
+      return;  /* already sorted */
+    p = (lo + up)/2;
+    lua_geti(L, 1, p);
+    lua_geti(L, 1, lo);
+    if (sort_comp(L, -2, -1))  /* a[p] < a[lo]? */
+      set2(L, p, lo);  /* swap a[p] - a[lo] */
     else {
-      lua_pop(L, 1);  /* remove a[l] */
-      lua_geti(L, 1, u);
-      if (sort_comp(L, -1, -2))  /* a[u]<a[i]? */
-        set2(L, i, u);
+      lua_pop(L, 1);  /* remove a[lo] */
+      lua_geti(L, 1, up);
+      if (sort_comp(L, -1, -2))  /* a[up] < a[p]? */
+        set2(L, p, up);  /* swap a[up] - a[p] */
       else
         lua_pop(L, 2);
     }
-    if (u-l == 2) break;  /* only 3 elements */
-    lua_geti(L, 1, i);  /* Pivot */
-    lua_pushvalue(L, -1);
-    lua_geti(L, 1, u-1);
-    set2(L, i, u-1);
-    /* a[l] <= P == a[u-1] <= a[u], only need to sort from l+1 to u-2 */
-    i = l; j = u-1;
-    for (;;) {  /* invariant: a[l..i] <= P <= a[j..u] */
-      /* repeat ++i until a[i] >= P */
-      while (lua_geti(L, 1, ++i), sort_comp(L, -1, -2)) {
-        if (i>=u) luaL_error(L, "invalid order function for sorting");
-        lua_pop(L, 1);  /* remove a[i] */
-      }
-      /* repeat --j until a[j] <= P */
-      while (lua_geti(L, 1, --j), sort_comp(L, -3, -1)) {
-        if (j<=l) luaL_error(L, "invalid order function for sorting");
-        lua_pop(L, 1);  /* remove a[j] */
-      }
-      if (j<i) {
-        lua_pop(L, 3);  /* pop pivot, a[i], a[j] */
-        break;
-      }
-      set2(L, i, j);
-    }
-    lua_geti(L, 1, u-1);
-    lua_geti(L, 1, i);
-    set2(L, u-1, i);  /* swap pivot (a[u-1]) with a[i] */
-    /* a[l..i-1] <= a[i] == P <= a[i+1..u] */
-    /* adjust so that smaller half is in [j..i] and larger one in [l..u] */
-    if (i-l < u-i) {
-      j=l; i=i-1; l=i+2;
+    if (up - lo == 2)  /* only 3 elements? */
+      return;  /* already sorted */
+    lua_geti(L, 1, p);  /* get middle element (Pivot) */
+    lua_pushvalue(L, -1);  /* push Pivot */
+    lua_geti(L, 1, up - 1);  /* push a[up - 1] */
+    set2(L, p, up - 1);  /* swap Pivot (a[p]) with a[up - 1] */
+    p = partition(L, lo, up);
+    /* a[lo .. p - 1] <= a[p] == P <= a[p + 1 .. up] */
+    if (p - lo < up - p) {  /* lower interval is smaller? */
+      auxsort(L, lo, p - 1);  /* call recursively for lower interval */
+      lo = p + 1;  /* tail call for [p + 1 .. up] (upper interval) */
     }
     else {
-      j=i+1; i=u; u=j-2;
+      auxsort(L, p + 1, up);  /* call recursively for upper interval */
+      up = p - 1;  /* tail call for [lo .. p - 1]  (lower interval) */
     }
-    auxsort(L, j, i);  /* call recursively the smaller one */
-  }  /* repeat the routine for the larger one */
+  }  /* tail call auxsort(L, lo, up) */
 }
 
 static int sort (lua_State *L) {