Revert "[libc++] [P0879] constexpr std::nth_element, and rewrite its tests."

This reverts commit 207d4be4d9d39fbb9aca30e5d5d11245db9bccc1 due to returning incorrect results. Regression test case posted in D96074.

GitOrigin-RevId: b6ffece32035a90d181101f356bd9c04ea1d3122
diff --git a/include/algorithm b/include/algorithm
index 7220585..a6fceaa 100644
--- a/include/algorithm
+++ b/include/algorithm
@@ -385,11 +385,11 @@
                       RandomAccessIterator result_first, RandomAccessIterator result_last, Compare comp);
 
 template <class RandomAccessIterator>
-    constexpr void                    // constexpr in C++20
+    void
     nth_element(RandomAccessIterator first, RandomAccessIterator nth, RandomAccessIterator last);
 
 template <class RandomAccessIterator, class Compare>
-    constexpr void                    // constexpr in C++20
+    void
     nth_element(RandomAccessIterator first, RandomAccessIterator nth, RandomAccessIterator last, Compare comp);
 
 template <class ForwardIterator, class T>
@@ -3807,7 +3807,7 @@
 // stable, 2-3 compares, 0-2 swaps
 
 template <class _Compare, class _ForwardIterator>
-_LIBCPP_CONSTEXPR_AFTER_CXX11 unsigned
+unsigned
 __sort3(_ForwardIterator __x, _ForwardIterator __y, _ForwardIterator __z, _Compare __c)
 {
     unsigned __r = 0;
@@ -3901,7 +3901,7 @@
 
 // Assumes size > 0
 template <class _Compare, class _BidirectionalIterator>
-_LIBCPP_CONSTEXPR_AFTER_CXX11 void
+void
 __selection_sort(_BidirectionalIterator __first, _BidirectionalIterator __last, _Compare __comp)
 {
     _BidirectionalIterator __lm1 = __last;
@@ -5218,70 +5218,8 @@
 
 // nth_element
 
-template<class _Compare, class _RandomAccessIterator>
-_LIBCPP_CONSTEXPR_AFTER_CXX11 bool
-__nth_element_find_guard(_RandomAccessIterator& __i, _RandomAccessIterator& __j,
-                         _RandomAccessIterator& __m, _Compare __comp)
-{
-    // manually guard downward moving __j against __i
-    while (--__j != __i)
-    {
-        if (__comp(*__j, *__m))
-        {
-            return true;
-        }
-    }
-    return false;
-}
-
-template<class _Compare, class _RandomAccessIterator>
-_LIBCPP_CONSTEXPR_AFTER_CXX11 bool
-__nth_element_partloop(_RandomAccessIterator __first, _RandomAccessIterator __last,
-                       _RandomAccessIterator& __i, _RandomAccessIterator& __j,
-                       unsigned& __n_swaps, _Compare __comp)
-{
-    // *__first == *__m, *__m <= all other elements
-    // Partition instead into [__first, __i) == *__first and *__first < [__i, __last)
-    ++__i;  // __first + 1
-    __j = __last;
-    if (!__comp(*__first, *--__j))  // we need a guard if *__first == *(__last-1)
-    {
-        while (true)
-        {
-            if (__i == __j)
-                return true;  // [__first, __last) all equivalent elements
-            if (__comp(*__first, *__i))
-            {
-                swap(*__i, *__j);
-                ++__n_swaps;
-                ++__i;
-                break;
-            }
-            ++__i;
-        }
-    }
-    // [__first, __i) == *__first and *__first < [__j, __last) and __j == __last - 1
-    if (__i == __j)
-        return true;
-    while (true)
-    {
-        while (!__comp(*__first, *__i))
-            ++__i;
-        while (__comp(*__first, *--__j))
-            ;
-        if (__i >= __j)
-            break;
-        swap(*__i, *__j);
-        ++__n_swaps;
-        ++__i;
-    }
-    // [__first, __i) == *__first and *__first < [__i, __last)
-    // The first part is sorted.
-    return false;
-}
-
 template <class _Compare, class _RandomAccessIterator>
-_LIBCPP_CONSTEXPR_AFTER_CXX11 void
+void
 __nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last, _Compare __comp)
 {
     // _Compare is known to be a reference type
@@ -5289,7 +5227,7 @@
     const difference_type __limit = 7;
     while (true)
     {
-        // __restart: -- this is the target of a "continue" below
+    __restart:
         if (__nth == __last)
             return;
         difference_type __len = __last - __first;
@@ -5329,19 +5267,61 @@
         if (!__comp(*__i, *__m))  // if *__first == *__m
         {
             // *__first == *__m, *__first doesn't go in first part
-            if (_VSTD::__nth_element_find_guard<_Compare>(__i, __j, __m, __comp)) {
-                swap(*__i, *__j);
-                ++__n_swaps;
-                // found guard for downward moving __j, now use unguarded partition
-            } else if (_VSTD::__nth_element_partloop<_Compare>(__first, __last, __i, __j, __n_swaps, __comp)) {
-                return;
-            } else if (__nth < __i) {
-                return;
-            } else {
-                // __nth_element the second part
-                // _VSTD::__nth_element<_Compare>(__i, __nth, __last, __comp);
-                __first = __i;
-                continue;  // i.e., goto __restart
+            // manually guard downward moving __j against __i
+            while (true)
+            {
+                if (__i == --__j)
+                {
+                    // *__first == *__m, *__m <= all other elements
+                    // Partition instead into [__first, __i) == *__first and *__first < [__i, __last)
+                    ++__i;  // __first + 1
+                    __j = __last;
+                    if (!__comp(*__first, *--__j))  // we need a guard if *__first == *(__last-1)
+                    {
+                        while (true)
+                        {
+                            if (__i == __j)
+                                return;  // [__first, __last) all equivalent elements
+                            if (__comp(*__first, *__i))
+                            {
+                                swap(*__i, *__j);
+                                ++__n_swaps;
+                                ++__i;
+                                break;
+                            }
+                            ++__i;
+                        }
+                    }
+                    // [__first, __i) == *__first and *__first < [__j, __last) and __j == __last - 1
+                    if (__i == __j)
+                        return;
+                    while (true)
+                    {
+                        while (!__comp(*__first, *__i))
+                            ++__i;
+                        while (__comp(*__first, *--__j))
+                            ;
+                        if (__i >= __j)
+                            break;
+                        swap(*__i, *__j);
+                        ++__n_swaps;
+                        ++__i;
+                    }
+                    // [__first, __i) == *__first and *__first < [__i, __last)
+                    // The first part is sorted,
+                    if (__nth < __i)
+                        return;
+                    // __nth_element the second part
+                    // _VSTD::__nth_element<_Compare>(__i, __nth, __last, __comp);
+                    __first = __i;
+                    goto __restart;
+                }
+                if (__comp(*__j, *__m))
+                {
+                    swap(*__i, *__j);
+                    ++__n_swaps;
+                    break;  // found guard for downward moving __j, now use unguarded partition
+                }
             }
         }
         ++__i;
@@ -5385,16 +5365,15 @@
             {
                 // Check for [__first, __i) already sorted
                 __j = __m = __first;
-                while (true)
+                while (++__j != __i)
                 {
-                    if (++__j == __i)
-                        // [__first, __i) sorted
-                        return;
                     if (__comp(*__j, *__m))
                         // not yet sorted, so sort
-                        break;
+                        goto not_sorted;
                     __m = __j;
                 }
+                // [__first, __i) sorted
+                return;
             }
             else
             {
@@ -5402,16 +5381,16 @@
                 __j = __m = __i;
                 while (++__j != __last)
                 {
-                    if (++__j == __last)
-                        // [__i, __last) sorted
-                        return;
                     if (__comp(*__j, *__m))
                         // not yet sorted, so sort
-                        break;
+                        goto not_sorted;
                     __m = __j;
                 }
+                // [__i, __last) sorted
+                return;
             }
         }
+not_sorted:
         // __nth_element on range containing __nth
         if (__nth < __i)
         {
@@ -5427,7 +5406,7 @@
 }
 
 template <class _RandomAccessIterator, class _Compare>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
+inline _LIBCPP_INLINE_VISIBILITY
 void
 nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last, _Compare __comp)
 {
@@ -5436,7 +5415,7 @@
 }
 
 template <class _RandomAccessIterator>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
+inline _LIBCPP_INLINE_VISIBILITY
 void
 nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last)
 {