[PATCH v3 6/7] stdlib: Implement introsort with qsort

[Fangrui Song]

On 2021-09-03, Adhemerval Zanella via Libc-alpha wrote:
>This patch adds a introsort implementation on qsort to avoid worse-case
>performance of quicksort to O(nlog n).  The heapsort fallback used is a
>heapsort based on Linux implementation (commit 22a241ccb2c19962a).  As a
>side note the introsort implementation is similar the one used on
>libstdc++ for std::sort.
>
>Checked on x86_64-linux-gnu.
>---
> stdlib/qsort.c | 94 ++++++++++++++++++++++++++++++++++++++++++++++----
> 1 file changed, 87 insertions(+), 7 deletions(-)
>
>diff --git a/stdlib/qsort.c b/stdlib/qsort.c
>index 5df640362d..8368576aae 100644
>--- a/stdlib/qsort.c
>+++ b/stdlib/qsort.c
>@@ -113,6 +113,7 @@ typedef struct
>   {
>     char *lo;
>     char *hi;
>+    size_t depth;
>   } stack_node;
>
> /* The stack needs log (total_elements) entries (we could even subtract
>@@ -122,23 +123,92 @@ typedef struct
> enum { STACK_SIZE = CHAR_BIT * sizeof (size_t) };
>
> static inline stack_node *
>-push (stack_node *top, char *lo, char *hi)
>+push (stack_node *top, char *lo, char *hi, size_t depth)
> {
>   top->lo = lo;
>   top->hi = hi;
>+  top->depth = depth;
>   return ++top;
> }
>
> static inline stack_node *
>-pop (stack_node *top, char **lo, char **hi)
>+pop (stack_node *top, char **lo, char **hi, size_t *depth)
> {
>   --top;
>   *lo = top->lo;
>   *hi = top->hi;
>+  *depth = top->depth;
>   return top;
> }
>
>
>+/* A fast, small, non-recursive O(nlog n) heapsort, adapted from Linux
>+   lib/sort.c.  Used on introsort implementation as a fallback routine with
>+   worst-case performance of O(nlog n) and worst-case space complexity of
>+   O(1).  */
>+
>+static inline size_t
>+parent (size_t i, unsigned int lsbit, size_t size)
>+{
>+  i -= size;
>+  i -= size & -(i & lsbit);

i -= size & -(i & lsbit); may need a comment that it is logically 

if (i & lsbit) i -= size;

to make i/2 a multiple of size.


>+  return i / 2;
>+}
>+
>+static void
>+heapsort_r (void *base, void *end, size_t size, swap_func_t swap_func,
>+	    __compar_d_fn_t cmp, void *arg)
>+{
>+  size_t num = ((uintptr_t) end - (uintptr_t) base) / size;
>+  size_t n = num * size, a = (num/2) * size;
>+  /* Used to find parent  */
>+  const unsigned int lsbit = size & -size;
>+
>+  /* num < 2 || size == 0.  */
>+  if (a == 0)
>+    return;
>+
>+  for (;;)
>+    {
>+      size_t b, c, d;
>+
>+      if (a != 0)
>+	/* Building heap: sift down --a */
>+	a -= size;
>+      else if (n -= size)
>+	/* Sorting: Extract root to --n */
>+	do_swap (base, base + n, size, swap_func);
>+      else
>+	break;
>+
>+      /* Sift element at "a" down into heap.  This is the "bottom-up" variant,
>+	 which significantly reduces calls to cmp_func(): we find the sift-down
>+	 path all the way to the leaves (one compare per level), then backtrack
>+	 to find where to insert the target element.
>+
>+	 Because elements tend to sift down close to the leaves, this uses fewer
>+	 compares than doing two per level on the way down.  (A bit more than
>+	 half as many on average, 3/4 worst-case.).  */
>+      for (b = a; c = 2 * b + size, (d = c + size) < n;)
>+	b = cmp (base + c, base + d, arg) >= 0 ? c : d;
>+      if (d == n)
>+	/* Special case last leaf with no sibling.  */
>+	b = c;
>+
>+      /* Now backtrack from "b" to the correct location for "a".  */
>+      while (b != a && cmp (base + a, base + b, arg) >= 0)
>+	b = parent (b, lsbit, size);
>+      /* Where "a" belongs.  */
>+      c = b;
>+      while (b != a)
>+	{
>+	  /* Shift it into place.  */
>+	  b = parent (b, lsbit, size);
>+          do_swap (base + b, base + c, size, swap_func);
>+        }

here a tab should be used.

>+    }
>+}
>+
> /* Order size using quicksort.  This implementation incorporates
>    four optimizations discussed in Sedgewick:
>
>@@ -223,7 +293,7 @@ _quicksort (void *const pbase, size_t total_elems, size_t size,
>
>   const size_t max_thresh = MAX_THRESH * size;
>
>-  if (total_elems == 0)
>+  if (total_elems <= 1)
>     /* Avoid lossage with unsigned arithmetic below.  */
>     return;
>
>@@ -235,6 +305,9 @@ _quicksort (void *const pbase, size_t total_elems, size_t size,
>   else
>     swap_func = SWAP_BYTES;
>
>+  /* Maximum depth before quicksort switches to heapsort.  */
>+  size_t depth = 2 * (CHAR_BIT - 1 - __builtin_clzl (total_elems));

With this fixed, the logic LGTM.

>   if (total_elems > MAX_THRESH)
>     {
>       char *lo = base_ptr;
>@@ -242,10 +315,17 @@ _quicksort (void *const pbase, size_t total_elems, size_t size,
>       stack_node stack[STACK_SIZE];
>       stack_node *top = stack;
>
>-      top = push (top, NULL, NULL);
>+      top = push (top, NULL, NULL, depth);
>
>       while (stack < top)
>         {
>+	  if (depth == 0)
>+	    {
>+	      heapsort_r (lo, hi, size, swap_func, cmp, arg);
>+              top = pop (top, &lo, &hi, &depth);
>+	      continue;
>+	    }
>+
>           char *left_ptr;
>           char *right_ptr;
>
>@@ -309,7 +389,7 @@ _quicksort (void *const pbase, size_t total_elems, size_t size,
>             {
>               if ((size_t) (hi - left_ptr) <= max_thresh)
> 		/* Ignore both small partitions. */
>-		top = pop (top, &lo, &hi);
>+		top = pop (top, &lo, &hi, &depth);
>               else
> 		/* Ignore small left partition. */
>                 lo = left_ptr;
>@@ -320,13 +400,13 @@ _quicksort (void *const pbase, size_t total_elems, size_t size,
>           else if ((right_ptr - lo) > (hi - left_ptr))
>             {
> 	      /* Push larger left partition indices. */
>-	      top = push (top, lo, right_ptr);
>+	      top = push (top, lo, right_ptr, depth - 1);
>               lo = left_ptr;
>             }
>           else
>             {
> 	      /* Push larger right partition indices. */
>-	      top = push (top, left_ptr, hi);
>+	      top = push (top, left_ptr, hi, depth - 1);
>               hi = right_ptr;
>             }
>         }
>-- 
>2.30.2
>