--- a/libgui/src/documentation.cc	Thu Nov 05 12:40:38 2020 -0500
+++ b/libgui/src/documentation.cc	Thu Nov 05 18:43:39 2020 -0500
@@ -36,6 +36,9 @@
 #include <QFileInfo>
 #include <QHelpContentWidget>
 #include <QHelpIndexWidget>
+#if defined (HAVE_QHELPLINK)
+#include <QHelpLink>
+#endif
 #include <QHelpSearchEngine>
 #include <QHelpSearchQueryWidget>
 #include <QHelpSearchResultWidget>
@@ -182,6 +185,10 @@
 
     if (m_help_engine)
       {
+#if defined (HAVE_QHELPLINK)
+        // Help engine uses filters instead of old api since Qt 5.15
+        m_help_engine->setUsesFilterEngine (true);
+#endif
         // Layout contents, index and search
         QTabWidget *navi = new QTabWidget (this);
         navi->setTabsClosable (false);
@@ -227,10 +234,17 @@
 
         navi->addTab (index_all, tr ("Function Index"));
 
+#if defined (HAVE_QHELPLINK)
+        connect (m_help_engine->indexWidget (),
+                 &QHelpIndexWidget::documentActivated,
+                  this, [this](const QHelpLink &link) {
+                        m_doc_browser->handle_index_clicked (link.url);});
+#else
         connect(m_help_engine->indexWidget (),
                 SIGNAL (linkActivated (const QUrl&, const QString&)),
                 m_doc_browser, SLOT(handle_index_clicked (const QUrl&,
                                                           const QString&)));
+#endif
 
         connect (m_filter, SIGNAL (editTextChanged (const QString&)),
                  this, SLOT(filter_update (const QString&)));

--- a/libinterp/corefcn/variables.cc	Thu Nov 05 12:40:38 2020 -0500
+++ b/libinterp/corefcn/variables.cc	Thu Nov 05 18:43:39 2020 -0500
@@ -233,26 +233,70 @@
   // We shouldn't need to look in the global symbol table, since any name
   // that is visible in the current scope will be in the local symbol table.
 
-  // Command line function which Matlab does not support
-  if (search_any)
-    {
-      octave_value val = symtab.find_cmdline_function (name);
-
-      if (val.is_defined ())
-        return 103;
-    }
-
   if (search_any || search_file || search_dir)
     {
-      octave::tree_evaluator& tw = interp.get_evaluator ();
+      bool have_fcn_ext = false;
+
+      std::string xname = name;
+      std::string ext;
+
+      size_t pos = name.rfind ('.');
+
+      if (pos != std::string::npos)
+        {
+          ext = name.substr (pos+1);
 
-      std::string file_name = tw.lookup_autoload (name);
+          if (ext == "m" || ext == "oct" || ext == "mex")
+            {
+              xname = name.substr (0, pos);
+              have_fcn_ext = true;
+            }
+        }
 
-      if (file_name.empty ())
+      std::string file_name;
+
+      if (search_any || search_file)
         {
           octave::load_path& lp = interp.get_load_path ();
 
-          file_name = lp.find_fcn (name);
+          // Class constructor.
+          file_name = lp.find_method (xname, xname);
+
+          if (have_fcn_ext && ! file_name.empty ())
+            {
+              pos = file_name.rfind ('.');
+
+              if (pos != std::string::npos)
+                {
+                  std::string fext = file_name.substr (pos+1);
+
+                  if (ext != fext)
+                    file_name = "";
+                }
+            }
+
+          if (search_any && file_name.empty ())
+            {
+              // Command line function which Matlab does not support
+              octave_value val = symtab.find_cmdline_function (xname);
+
+              if (val.is_defined ())
+                return 103;
+            }
+
+          // Autoloads can only have simple names without extensions.
+
+          if (! have_fcn_ext && file_name.empty ())
+            {
+              octave::tree_evaluator& tw = interp.get_evaluator ();
+
+              file_name = tw.lookup_autoload (name);
+            }
+
+          // Use original name here.
+
+          if (file_name.empty ())
+            file_name = lp.find_fcn (name);
         }
 
       size_t len = file_name.length ();
@@ -303,14 +347,9 @@
         return 0;
     }
 
-  if (search_any || search_builtin)
-    {
-      if (symtab.is_built_in_function_name (name))
-        return 5;
-
-      if (search_builtin)
-        return 0;
-    }
+  if ((search_any || search_builtin)
+      && symtab.is_built_in_function_name (name))
+    return 5;
 
   return 0;
 }
@@ -497,6 +536,14 @@
 %!assert (exist ("fftw", "file"), 3)
 %!assert (exist ("fftw", "builtin"), 0)
 
+%!assert (exist ("ftp"), 2);
+%!assert (exist ("ftp.m"), 2);
+%!assert (exist ("@ftp/ftp"), 2);
+%!assert (exist ("@ftp/ftp.m"), 2);
+
+%!assert (exist ("inputParser"), 2);
+%!assert (exist ("inputParser.m"), 2);
+
 %!assert (exist ("sin"), 5)
 %!assert (exist ("sin", "builtin"), 5)
 %!assert (exist ("sin", "file"), 0)

--- a/m4/acinclude.m4	Thu Nov 05 12:40:38 2020 -0500
+++ b/m4/acinclude.m4	Thu Nov 05 18:43:39 2020 -0500
@@ -431,6 +431,37 @@
   fi
 ])
 dnl
+dnl Check whether the structure QtHelpLink is defined. Then,
+dnl QHelpIndexWidget emits documentActivates instead of linkActivated.
+dnl This structure/signal was introduced in Qt 5.15.
+dnl
+dnl FIXME: Delete this entirely when we drop support for Qt 5.14 or older.
+dnl
+AC_DEFUN([OCTAVE_CHECK_FUNC_QHELPLINK], [
+  AC_CACHE_CHECK([for QHelpLink],
+    [octave_cv_func_qhelplink],
+    [AC_LANG_PUSH(C++)
+    ac_octave_save_CPPFLAGS="$CPPFLAGS"
+    ac_octave_save_CXXFLAGS="$CXXFLAGS"
+    CPPFLAGS="$QT_CPPFLAGS $CXXPICFLAG $CPPFLAGS"
+    CXXFLAGS="$CXXPICFLAG $CPPFLAGS"
+    AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
+        #include <QHelpLink>
+        ]], [[
+        QHelpLink link;
+        ]])],
+      octave_cv_func_qhelplink=yes,
+      octave_cv_func_qhelplink=no)
+    CPPFLAGS="$ac_octave_save_CPPFLAGS"
+    CXXFLAGS="$ac_octave_save_CXXFLAGS"
+    AC_LANG_POP(C++)
+  ])
+  if test $octave_cv_func_qhelplink = yes; then
+    AC_DEFINE(HAVE_QHELPLINK, 1,
+      [Define to 1 if you have the `QHelpLink' structure.])
+  fi
+])
+dnl
 dnl Check whether the Qt class QScreen has the devicePixelRatio member function.
 dnl This member function was introduced in Qt 5.5.
 dnl
@@ -1863,6 +1894,7 @@
     OCTAVE_CHECK_FUNC_QFONTMETRICS_HORIZONTAL_ADVANCE
     OCTAVE_CHECK_FUNC_QGUIAPPLICATION_SETDESKTOPFILENAME
     OCTAVE_CHECK_FUNC_QHELPSEARCHQUERYWIDGET_SEARCHINPUT
+    OCTAVE_CHECK_FUNC_QHELPLINK
     OCTAVE_CHECK_FUNC_QLIST_ITERATOR_CONSTRUCTOR
     OCTAVE_CHECK_FUNC_QSCREEN_DEVICEPIXELRATIO