[libcxx][gardening] Move all algorithms into their own headers.

This is a fairly mechanical change, it just moves each algorithm into its own header. This is a NFC.

Note: during this change, I burned down all the includes, so this follows "include only and exactly what you use."

Differential Revision: https://reviews.llvm.org/D103583

NOKEYCHECK=True
GitOrigin-RevId: 7ed7d4ccb8991e2b5b95334b508f8cec2faee737
diff --git a/include/functional b/include/functional
index 62e9b89..6e9a334 100644
--- a/include/functional
+++ b/include/functional
@@ -509,6 +509,7 @@
 #include <__config>
 #include <__debug>
 #include <__functional_base>
+#include <__functional/search.h>
 #include <concepts>
 #include <exception>
 #include <memory>
@@ -3110,88 +3111,6 @@
 
 // struct hash<T*> in <memory>
 
-template <class _BinaryPredicate, class _ForwardIterator1, class _ForwardIterator2>
-pair<_ForwardIterator1, _ForwardIterator1> _LIBCPP_CONSTEXPR_AFTER_CXX11
-__search(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
-         _ForwardIterator2 __first2, _ForwardIterator2 __last2, _BinaryPredicate __pred,
-         forward_iterator_tag, forward_iterator_tag)
-{
-    if (__first2 == __last2)
-        return _VSTD::make_pair(__first1, __first1);  // Everything matches an empty sequence
-    while (true)
-    {
-        // Find first element in sequence 1 that matchs *__first2, with a mininum of loop checks
-        while (true)
-        {
-            if (__first1 == __last1)  // return __last1 if no element matches *__first2
-                return _VSTD::make_pair(__last1, __last1);
-            if (__pred(*__first1, *__first2))
-                break;
-            ++__first1;
-        }
-        // *__first1 matches *__first2, now match elements after here
-        _ForwardIterator1 __m1 = __first1;
-        _ForwardIterator2 __m2 = __first2;
-        while (true)
-        {
-            if (++__m2 == __last2)  // If pattern exhausted, __first1 is the answer (works for 1 element pattern)
-                return _VSTD::make_pair(__first1, __m1);
-            if (++__m1 == __last1)  // Otherwise if source exhaused, pattern not found
-                return _VSTD::make_pair(__last1, __last1);
-            if (!__pred(*__m1, *__m2))  // if there is a mismatch, restart with a new __first1
-            {
-                ++__first1;
-                break;
-            }  // else there is a match, check next elements
-        }
-    }
-}
-
-template <class _BinaryPredicate, class _RandomAccessIterator1, class _RandomAccessIterator2>
-_LIBCPP_CONSTEXPR_AFTER_CXX11
-pair<_RandomAccessIterator1, _RandomAccessIterator1>
-__search(_RandomAccessIterator1 __first1, _RandomAccessIterator1 __last1,
-         _RandomAccessIterator2 __first2, _RandomAccessIterator2 __last2, _BinaryPredicate __pred,
-           random_access_iterator_tag, random_access_iterator_tag)
-{
-    typedef typename iterator_traits<_RandomAccessIterator1>::difference_type _D1;
-    typedef typename iterator_traits<_RandomAccessIterator2>::difference_type _D2;
-    // Take advantage of knowing source and pattern lengths.  Stop short when source is smaller than pattern
-    const _D2 __len2 = __last2 - __first2;
-    if (__len2 == 0)
-        return _VSTD::make_pair(__first1, __first1);
-    const _D1 __len1 = __last1 - __first1;
-    if (__len1 < __len2)
-        return _VSTD::make_pair(__last1, __last1);
-    const _RandomAccessIterator1 __s = __last1 - (__len2 - 1);  // Start of pattern match can't go beyond here
-
-    while (true)
-    {
-        while (true)
-        {
-            if (__first1 == __s)
-                return _VSTD::make_pair(__last1, __last1);
-            if (__pred(*__first1, *__first2))
-                break;
-            ++__first1;
-        }
-
-        _RandomAccessIterator1 __m1 = __first1;
-        _RandomAccessIterator2 __m2 = __first2;
-         while (true)
-         {
-             if (++__m2 == __last2)
-                 return _VSTD::make_pair(__first1, __first1 + __len2);
-             ++__m1;          // no need to check range on __m1 because __s guarantees we have enough source
-             if (!__pred(*__m1, *__m2))
-             {
-                 ++__first1;
-                 break;
-             }
-         }
-    }
-}
-
 #if _LIBCPP_STD_VER > 14
 
 // default searcher