From eda5bc26f44ee9a6f83dcf8c91f17296d7fc509d Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Mon, 12 Feb 2024 14:52:43 +0100
Subject: Move into version control

---
 src/armadillo/include/armadillo_bits/traits.hpp | 1315 +++++++++++++++++++++++
 1 file changed, 1315 insertions(+)
 create mode 100644 src/armadillo/include/armadillo_bits/traits.hpp

(limited to 'src/armadillo/include/armadillo_bits/traits.hpp')

diff --git a/src/armadillo/include/armadillo_bits/traits.hpp b/src/armadillo/include/armadillo_bits/traits.hpp
new file mode 100644
index 0000000..bde2200
--- /dev/null
+++ b/src/armadillo/include/armadillo_bits/traits.hpp
@@ -0,0 +1,1315 @@
+// SPDX-License-Identifier: Apache-2.0
+// 
+// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
+// Copyright 2008-2016 National ICT Australia (NICTA)
+// 
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+// http://www.apache.org/licenses/LICENSE-2.0
+// 
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+// ------------------------------------------------------------------------
+
+
+//! \addtogroup traits
+//! @{
+
+
+template<typename T1>
+struct get_pod_type
+  { typedef T1 result; };
+
+template<typename T2>
+struct get_pod_type< std::complex<T2> >
+  { typedef T2 result; };
+
+
+
+template<typename T>
+struct is_Mat_fixed_only
+  {
+  typedef char yes[1];
+  typedef char  no[2];
+  
+  template<typename X> static yes& check(typename X::Mat_fixed_type*);
+  template<typename>   static  no& check(...);
+  
+  static constexpr bool value = ( sizeof(check<T>(0)) == sizeof(yes) );
+  };
+
+
+
+template<typename T>
+struct is_Row_fixed_only
+  {
+  typedef char yes[1];
+  typedef char  no[2];
+  
+  template<typename X> static yes& check(typename X::Row_fixed_type*);
+  template<typename>   static  no& check(...);
+  
+  static constexpr bool value = ( sizeof(check<T>(0)) == sizeof(yes) );
+  };
+
+
+
+template<typename T>
+struct is_Col_fixed_only
+  {
+  typedef char yes[1];
+  typedef char  no[2];
+  
+  template<typename X> static yes& check(typename X::Col_fixed_type*);
+  template<typename>   static  no& check(...);
+  
+  static constexpr bool value = ( sizeof(check<T>(0)) == sizeof(yes) );
+  };
+
+
+
+template<typename T>
+struct is_Mat_fixed
+  { static constexpr bool value = ( is_Mat_fixed_only<T>::value || is_Row_fixed_only<T>::value || is_Col_fixed_only<T>::value ); };
+
+
+
+template<typename T>
+struct is_Mat_only
+  { static constexpr bool value = is_Mat_fixed_only<T>::value; };
+
+template<typename eT>
+struct is_Mat_only< Mat<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_Mat_only< const Mat<eT> >
+  { static constexpr bool value = true; };
+
+
+
+template<typename T>
+struct is_Mat
+  { static constexpr bool value = ( is_Mat_fixed_only<T>::value || is_Row_fixed_only<T>::value || is_Col_fixed_only<T>::value ); };
+
+template<typename eT>
+struct is_Mat< Mat<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_Mat< const Mat<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_Mat< Row<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_Mat< const Row<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_Mat< Col<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_Mat< const Col<eT> >
+  { static constexpr bool value = true; };
+
+
+
+template<typename T>
+struct is_Row
+  { static constexpr bool value = is_Row_fixed_only<T>::value; };
+
+template<typename eT>
+struct is_Row< Row<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_Row< const Row<eT> >
+  { static constexpr bool value = true; };
+
+
+
+template<typename T>
+struct is_Col
+  { static constexpr bool value = is_Col_fixed_only<T>::value; };
+
+template<typename eT>
+struct is_Col< Col<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_Col< const Col<eT> >
+  { static constexpr bool value = true; };
+
+
+
+template<typename T>
+struct is_diagview
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_diagview< diagview<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_diagview< const diagview<eT> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_subview
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_subview< subview<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_subview< const subview<eT> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_subview_row
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_subview_row< subview_row<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_subview_row< const subview_row<eT> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_subview_col
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_subview_col< subview_col<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_subview_col< const subview_col<eT> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_subview_cols
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_subview_cols< subview_cols<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_subview_cols< const subview_cols<eT> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_subview_elem1
+  { static constexpr bool value = false; };
+
+template<typename eT, typename T1>
+struct is_subview_elem1< subview_elem1<eT, T1> >
+  { static constexpr bool value = true; };
+
+template<typename eT, typename T1>
+struct is_subview_elem1< const subview_elem1<eT, T1> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_subview_elem2
+  { static constexpr bool value = false; };
+
+template<typename eT, typename T1, typename T2>
+struct is_subview_elem2< subview_elem2<eT, T1, T2> >
+  { static constexpr bool value = true; };
+
+template<typename eT, typename T1, typename T2>
+struct is_subview_elem2< const subview_elem2<eT, T1, T2> >
+  { static constexpr bool value = true; };
+
+
+
+//
+//
+//
+
+
+
+template<typename T>
+struct is_Cube
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_Cube< Cube<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_Cube< const Cube<eT> >
+  { static constexpr bool value = true; };
+
+template<typename T>
+struct is_subview_cube
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_subview_cube< subview_cube<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_subview_cube< const subview_cube<eT> >
+  { static constexpr bool value = true; };
+
+template<typename T>
+struct is_subview_cube_slices
+  { static constexpr bool value = false; };
+
+template<typename eT, typename T1>
+struct is_subview_cube_slices< subview_cube_slices<eT,T1> >
+  { static constexpr bool value = true; };
+
+template<typename eT, typename T1>
+struct is_subview_cube_slices< const subview_cube_slices<eT,T1> >
+  { static constexpr bool value = true; };
+
+
+//
+//
+//
+
+
+template<typename T>
+struct is_Gen
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename gen_type>
+struct is_Gen< Gen<T1,gen_type> >
+  { static constexpr bool value = true; };
+ 
+template<typename T1, typename gen_type>
+struct is_Gen< const Gen<T1,gen_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_Op
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename op_type>
+struct is_Op< Op<T1,op_type> >
+  { static constexpr bool value = true; };
+ 
+template<typename T1, typename op_type>
+struct is_Op< const Op<T1,op_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_CubeToMatOp
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename op_type>
+struct is_CubeToMatOp< CubeToMatOp<T1,op_type> >
+  { static constexpr bool value = true; };
+ 
+template<typename T1, typename op_type>
+struct is_CubeToMatOp< const CubeToMatOp<T1,op_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_SpToDOp
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename op_type>
+struct is_SpToDOp< SpToDOp<T1,op_type> >
+  { static constexpr bool value = true; };
+ 
+template<typename T1, typename op_type>
+struct is_SpToDOp< const SpToDOp<T1,op_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_SpToDGlue
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename T2, typename glue_type>
+struct is_SpToDGlue< SpToDGlue<T1,T2,glue_type> >
+  { static constexpr bool value = true; };
+ 
+template<typename T1, typename T2, typename glue_type>
+struct is_SpToDGlue< const SpToDGlue<T1,T2,glue_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_eOp
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename eop_type>
+struct is_eOp< eOp<T1,eop_type> >
+  { static constexpr bool value = true; };
+ 
+template<typename T1, typename eop_type>
+struct is_eOp< const eOp<T1,eop_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_mtOp
+  { static constexpr bool value = false; };
+ 
+template<typename eT, typename T1, typename op_type>
+struct is_mtOp< mtOp<eT, T1, op_type> >
+  { static constexpr bool value = true; };
+ 
+template<typename eT, typename T1, typename op_type>
+struct is_mtOp< const mtOp<eT, T1, op_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_Glue
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename T2, typename glue_type>
+struct is_Glue< Glue<T1,T2,glue_type> >
+  { static constexpr bool value = true; };
+
+template<typename T1, typename T2, typename glue_type>
+struct is_Glue< const Glue<T1,T2,glue_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_eGlue
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename T2, typename eglue_type>
+struct is_eGlue< eGlue<T1,T2,eglue_type> >
+  { static constexpr bool value = true; };
+
+template<typename T1, typename T2, typename eglue_type>
+struct is_eGlue< const eGlue<T1,T2,eglue_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_mtGlue
+  { static constexpr bool value = false; };
+ 
+template<typename eT, typename T1, typename T2, typename glue_type>
+struct is_mtGlue< mtGlue<eT, T1, T2, glue_type> >
+  { static constexpr bool value = true; };
+
+template<typename eT, typename T1, typename T2, typename glue_type>
+struct is_mtGlue< const mtGlue<eT, T1, T2, glue_type> >
+  { static constexpr bool value = true; };
+
+
+//
+//
+
+
+template<typename T>
+struct is_glue_times
+  { static constexpr bool value = false; };
+
+template<typename T1, typename T2>
+struct is_glue_times< Glue<T1,T2,glue_times> >
+  { static constexpr bool value = true; };
+
+template<typename T1, typename T2>
+struct is_glue_times< const Glue<T1,T2,glue_times> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_glue_times_diag
+  { static constexpr bool value = false; };
+
+template<typename T1, typename T2>
+struct is_glue_times_diag< Glue<T1,T2,glue_times_diag> >
+  { static constexpr bool value = true; };
+
+template<typename T1, typename T2>
+struct is_glue_times_diag< const Glue<T1,T2,glue_times_diag> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_op_diagmat
+  { static constexpr bool value = false; };
+ 
+template<typename T1>
+struct is_op_diagmat< Op<T1,op_diagmat> >
+  { static constexpr bool value = true; };
+
+template<typename T1>
+struct is_op_diagmat< const Op<T1,op_diagmat> >
+  { static constexpr bool value = true; };
+
+
+//
+//
+
+
+template<typename T>
+struct is_Mat_trans
+  { static constexpr bool value = false; };
+
+template<typename T1>
+struct is_Mat_trans< Op<T1,op_htrans> >
+  { static constexpr bool value = is_Mat<T1>::value; };
+
+template<typename T1>
+struct is_Mat_trans< Op<T1,op_htrans2> >
+  { static constexpr bool value = is_Mat<T1>::value; };
+
+
+//
+//
+
+
+template<typename T>
+struct is_GenCube
+  { static constexpr bool value = false; };
+ 
+template<typename eT, typename gen_type>
+struct is_GenCube< GenCube<eT,gen_type> >
+  { static constexpr bool value = true; };
+ 
+
+template<typename T>
+struct is_OpCube
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename op_type>
+struct is_OpCube< OpCube<T1,op_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_eOpCube
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename eop_type>
+struct is_eOpCube< eOpCube<T1,eop_type> >
+  { static constexpr bool value = true; };
+ 
+
+template<typename T>
+struct is_mtOpCube
+  { static constexpr bool value = false; };
+ 
+template<typename eT, typename T1, typename op_type>
+struct is_mtOpCube< mtOpCube<eT, T1, op_type> >
+  { static constexpr bool value = true; };
+ 
+
+template<typename T>
+struct is_GlueCube
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename T2, typename glue_type>
+struct is_GlueCube< GlueCube<T1,T2,glue_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_eGlueCube
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename T2, typename eglue_type>
+struct is_eGlueCube< eGlueCube<T1,T2,eglue_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_mtGlueCube
+  { static constexpr bool value = false; };
+ 
+template<typename eT, typename T1, typename T2, typename glue_type>
+struct is_mtGlueCube< mtGlueCube<eT, T1, T2, glue_type> >
+  { static constexpr bool value = true; };
+
+
+//
+//
+//
+
+
+template<typename T1>
+struct is_arma_type2
+  {
+  static constexpr bool value
+  =  is_Mat<T1>::value
+  || is_Gen<T1>::value
+  || is_Op<T1>::value
+  || is_Glue<T1>::value
+  || is_eOp<T1>::value
+  || is_eGlue<T1>::value
+  || is_mtOp<T1>::value
+  || is_mtGlue<T1>::value
+  || is_diagview<T1>::value
+  || is_subview<T1>::value
+  || is_subview_row<T1>::value
+  || is_subview_col<T1>::value
+  || is_subview_cols<T1>::value
+  || is_subview_elem1<T1>::value
+  || is_subview_elem2<T1>::value
+  || is_CubeToMatOp<T1>::value
+  || is_SpToDOp<T1>::value
+  || is_SpToDGlue<T1>::value
+  ;
+  };
+
+
+
+// due to rather baroque C++ rules for proving constant expressions,
+// certain compilers may get confused with the combination of conditional inheritance, nested classes and the shenanigans in is_Mat_fixed_only.
+// below we explicitly ensure the type is forced to be const, which seems to eliminate the confusion.
+template<typename T1>
+struct is_arma_type
+  {
+  static constexpr bool value = is_arma_type2<const T1>::value;
+  };
+
+
+
+template<typename T1>
+struct is_arma_cube_type
+  {
+  static constexpr bool value
+  =  is_Cube<T1>::value
+  || is_GenCube<T1>::value
+  || is_OpCube<T1>::value
+  || is_eOpCube<T1>::value
+  || is_mtOpCube<T1>::value
+  || is_GlueCube<T1>::value
+  || is_eGlueCube<T1>::value
+  || is_mtGlueCube<T1>::value
+  || is_subview_cube<T1>::value
+  || is_subview_cube_slices<T1>::value
+  ;
+  };
+
+
+
+//
+//
+//
+
+
+
+template<typename T>
+struct is_SpMat
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_SpMat< SpMat<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_SpMat< SpCol<eT> >
+  { static constexpr bool value = true; };
+
+template<typename eT>
+struct is_SpMat< SpRow<eT> >
+  { static constexpr bool value = true; };
+
+
+
+template<typename T>
+struct is_SpRow
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_SpRow< SpRow<eT> >
+  { static constexpr bool value = true; };
+
+
+
+template<typename T>
+struct is_SpCol
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_SpCol< SpCol<eT> >
+  { static constexpr bool value = true; };
+
+
+
+template<typename T>
+struct is_SpSubview
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_SpSubview< SpSubview<eT> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_SpSubview_col
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_SpSubview_col< SpSubview_col<eT> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_SpSubview_col_list
+  { static constexpr bool value = false; };
+
+template<typename eT, typename T1>
+struct is_SpSubview_col_list< SpSubview_col_list<eT,T1> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_SpSubview_row
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_SpSubview_row< SpSubview_row<eT> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_spdiagview
+  { static constexpr bool value = false; };
+
+template<typename eT>
+struct is_spdiagview< spdiagview<eT> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_SpOp
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename op_type>
+struct is_SpOp< SpOp<T1,op_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_SpGlue
+  { static constexpr bool value = false; };
+ 
+template<typename T1, typename T2, typename glue_type>
+struct is_SpGlue< SpGlue<T1,T2,glue_type> >
+  { static constexpr bool value = true; };
+ 
+
+template<typename T>
+struct is_mtSpOp
+  { static constexpr bool value = false; };
+ 
+template<typename eT, typename T1, typename spop_type>
+struct is_mtSpOp< mtSpOp<eT, T1, spop_type> >
+  { static constexpr bool value = true; };
+
+
+template<typename T>
+struct is_mtSpGlue
+  { static constexpr bool value = false; };
+ 
+template<typename eT, typename T1, typename T2, typename spglue_type>
+struct is_mtSpGlue< mtSpGlue<eT, T1, T2, spglue_type> >
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_arma_sparse_type
+  {
+  static constexpr bool value
+  =  is_SpMat<T1>::value
+  || is_SpSubview<T1>::value
+  || is_SpSubview_col<T1>::value
+  || is_SpSubview_col_list<T1>::value
+  || is_SpSubview_row<T1>::value
+  || is_spdiagview<T1>::value
+  || is_SpOp<T1>::value
+  || is_SpGlue<T1>::value
+  || is_mtSpOp<T1>::value
+  || is_mtSpGlue<T1>::value
+  ;
+  };
+
+
+
+//
+//
+//
+
+
+template<typename T1, typename T2>
+struct is_same_type
+  {
+  static constexpr bool value = false;
+  static constexpr bool yes   = false;
+  static constexpr bool no    = true;
+  };
+
+
+template<typename T1>
+struct is_same_type<T1,T1>
+  {
+  static constexpr bool value = true;
+  static constexpr bool yes   = true;
+  static constexpr bool no    = false;
+  };
+
+
+
+//
+//
+//
+
+
+template<typename T1>
+struct is_u8
+  { static constexpr bool value = false; };
+
+template<>
+struct is_u8<u8>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_s8
+  { static constexpr bool value = false; };
+
+template<>
+struct is_s8<s8>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_u16
+  { static constexpr bool value = false; };
+
+template<>
+struct is_u16<u16>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_s16
+  { static constexpr bool value = false; };
+
+template<>
+struct is_s16<s16>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_u32
+  { static constexpr bool value = false; };
+
+template<>
+struct is_u32<u32>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_s32
+  { static constexpr bool value = false; };
+
+template<>
+struct is_s32<s32>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_u64
+  { static constexpr bool value = false; };
+
+template<>
+struct is_u64<u64>
+  { static constexpr bool value = true; };
+
+
+template<typename T1>
+struct is_s64
+  { static constexpr bool value = false; };
+
+template<>
+struct is_s64<s64>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_ulng_t
+  { static constexpr bool value = false; };
+
+template<>
+struct is_ulng_t<ulng_t>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_slng_t
+  { static constexpr bool value = false; };
+
+template<>
+struct is_slng_t<slng_t>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_ulng_t_32
+  { static constexpr bool value = false; };
+
+template<>
+struct is_ulng_t_32<ulng_t>
+  { static constexpr bool value = (sizeof(ulng_t) == 4); };
+
+
+
+template<typename T1>
+struct is_slng_t_32
+  { static constexpr bool value = false; };
+
+template<>
+struct is_slng_t_32<slng_t>
+  { static constexpr bool value = (sizeof(slng_t) == 4); };
+
+
+
+template<typename T1>
+struct is_ulng_t_64
+  { static constexpr bool value = false; };
+
+template<>
+struct is_ulng_t_64<ulng_t>
+  { static constexpr bool value = (sizeof(ulng_t) == 8); };
+
+
+
+template<typename T1>
+struct is_slng_t_64
+  { static constexpr bool value = false; };
+
+template<>
+struct is_slng_t_64<slng_t>
+  { static constexpr bool value = (sizeof(slng_t) == 8); };
+
+
+
+template<typename T1>
+struct is_uword
+  { static constexpr bool value = false; };
+
+template<>
+struct is_uword<uword>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_sword
+  { static constexpr bool value = false; };
+
+template<>
+struct is_sword<sword>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_float
+  { static constexpr bool value = false; };
+
+template<>
+struct is_float<float>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_double
+  { static constexpr bool value = false; };
+
+template<>
+struct is_double<double>
+  { static constexpr bool value = true; };
+
+
+
+template<typename T1>
+struct is_real
+  {
+  static constexpr bool value = false;
+  static constexpr bool yes   = false;
+  static constexpr bool no    = true;
+  };
+
+template<>
+struct is_real<float>
+  {
+  static constexpr bool value = true;
+  static constexpr bool yes   = true;
+  static constexpr bool no    = false;
+  };
+  
+template<>
+struct is_real<double>
+  {
+  static constexpr bool value = true;
+  static constexpr bool yes   = true;
+  static constexpr bool no    = false;
+  };
+
+
+
+
+template<typename T1>
+struct is_cx
+  {
+  static constexpr bool value = false;
+  static constexpr bool yes   = false;
+  static constexpr bool no    = true;
+  };
+
+// template<>
+template<typename T>
+struct is_cx< std::complex<T> >
+  {
+  static constexpr bool value = true;
+  static constexpr bool yes   = true;
+  static constexpr bool no    = false;
+  };
+
+
+
+template<typename T1>
+struct is_cx_float
+  {
+  static constexpr bool value = false;
+  static constexpr bool yes   = false;
+  static constexpr bool no    = true;
+  };
+
+template<>
+struct is_cx_float< std::complex<float> >
+  {
+  static constexpr bool value = true;
+  static constexpr bool yes   = true;
+  static constexpr bool no    = false;
+  };
+
+
+
+template<typename T1>
+struct is_cx_double
+  {
+  static constexpr bool value = false;
+  static constexpr bool yes   = false;
+  static constexpr bool no    = true;
+  };
+
+template<>
+struct is_cx_double< std::complex<double> >
+  {
+  static constexpr bool value = true;
+  static constexpr bool yes   = true;
+  static constexpr bool no    = false;
+  };
+
+
+
+template<typename T1>
+struct is_supported_elem_type
+  {
+  static constexpr bool value = \
+    is_u8<T1>::value ||
+    is_s8<T1>::value ||
+    is_u16<T1>::value ||
+    is_s16<T1>::value ||
+    is_u32<T1>::value ||
+    is_s32<T1>::value ||
+    is_u64<T1>::value ||
+    is_s64<T1>::value ||
+    is_ulng_t<T1>::value ||
+    is_slng_t<T1>::value ||
+    is_float<T1>::value ||
+    is_double<T1>::value ||
+    is_cx_float<T1>::value ||
+    is_cx_double<T1>::value;
+  };
+
+
+
+template<typename T1>
+struct is_supported_blas_type
+  {
+  static constexpr bool value = \
+    is_float<T1>::value ||
+    is_double<T1>::value ||
+    is_cx_float<T1>::value ||
+    is_cx_double<T1>::value;
+  };
+
+
+
+template<typename T1>
+struct has_blas_float_bug
+  {
+  #if defined(ARMA_BLAS_FLOAT_BUG)
+    static constexpr bool value = is_float<typename get_pod_type<T1>::result>::value;
+  #else
+    static constexpr bool value = false;
+  #endif
+  };
+
+
+
+template<typename T>
+struct is_signed
+  {
+  static constexpr bool value = true;
+  };
+
+
+template<> struct is_signed<u8>     { static constexpr bool value = false; };
+template<> struct is_signed<u16>    { static constexpr bool value = false; };
+template<> struct is_signed<u32>    { static constexpr bool value = false; };
+template<> struct is_signed<u64>    { static constexpr bool value = false; };
+template<> struct is_signed<ulng_t> { static constexpr bool value = false; };
+
+
+template<typename T>
+struct is_non_integral
+  {
+  static constexpr bool value = false;
+  };
+
+
+template<> struct is_non_integral<              float   > { static constexpr bool value = true; };
+template<> struct is_non_integral<              double  > { static constexpr bool value = true; };
+template<> struct is_non_integral< std::complex<float>  > { static constexpr bool value = true; };
+template<> struct is_non_integral< std::complex<double> > { static constexpr bool value = true; };
+
+
+
+
+//
+
+class arma_junk_class;
+
+template<typename T1, typename T2>
+struct force_different_type
+  {
+  typedef T1 T1_result;
+  typedef T2 T2_result;
+  };
+  
+
+template<typename T1>
+struct force_different_type<T1,T1>
+  {
+  typedef T1              T1_result;
+  typedef arma_junk_class T2_result;
+  };
+  
+  
+
+//
+
+
+template<typename T1>
+struct resolves_to_vector_default
+  {
+  static constexpr bool value = false;
+  static constexpr bool yes   = false;
+  static constexpr bool no    = true;
+  };
+
+template<typename T1>
+struct resolves_to_vector_test
+  {
+  static constexpr bool value =  (T1::is_col || T1::is_row || T1::is_xvec);
+  static constexpr bool yes   =  (T1::is_col || T1::is_row || T1::is_xvec);
+  static constexpr bool no    = ((T1::is_col || T1::is_row || T1::is_xvec) == false);
+  };
+
+
+template<typename T1, bool condition>
+struct resolves_to_vector_redirect {};
+
+template<typename T1>
+struct resolves_to_vector_redirect<T1, false> { typedef resolves_to_vector_default<T1> result; };
+
+template<typename T1>
+struct resolves_to_vector_redirect<T1, true>  { typedef resolves_to_vector_test<T1>    result; };
+
+
+template<typename T1>
+struct resolves_to_vector : public resolves_to_vector_redirect<T1, is_arma_type<T1>::value>::result {};
+
+template<typename T1>
+struct resolves_to_sparse_vector : public resolves_to_vector_redirect<T1, is_arma_sparse_type<T1>::value>::result {};
+
+//
+
+template<typename T1>
+struct resolves_to_rowvector_default { static constexpr bool value = false;      };
+
+template<typename T1>
+struct resolves_to_rowvector_test    { static constexpr bool value = T1::is_row; };
+
+
+template<typename T1, bool condition>
+struct resolves_to_rowvector_redirect {};
+
+template<typename T1>
+struct resolves_to_rowvector_redirect<T1, false> { typedef resolves_to_rowvector_default<T1> result; };
+
+template<typename T1>
+struct resolves_to_rowvector_redirect<T1, true>  { typedef resolves_to_rowvector_test<T1>    result; };
+
+
+template<typename T1>
+struct resolves_to_rowvector : public resolves_to_rowvector_redirect<T1, is_arma_type<T1>::value>::result {};
+
+//
+
+template<typename T1>
+struct resolves_to_colvector_default { static constexpr bool value = false;      };
+
+template<typename T1>
+struct resolves_to_colvector_test    { static constexpr bool value = T1::is_col; };
+
+
+template<typename T1, bool condition>
+struct resolves_to_colvector_redirect {};
+
+template<typename T1>
+struct resolves_to_colvector_redirect<T1, false> { typedef resolves_to_colvector_default<T1> result; };
+
+template<typename T1>
+struct resolves_to_colvector_redirect<T1, true>  { typedef resolves_to_colvector_test<T1>    result; };
+
+
+template<typename T1>
+struct resolves_to_colvector : public resolves_to_colvector_redirect<T1, is_arma_type<T1>::value>::result {};
+
+
+
+template<typename T1>
+struct is_outer_product
+  { static constexpr bool value = false; };
+
+template<typename T1, typename T2>
+struct is_outer_product< Glue<T1,T2,glue_times> >
+  { static constexpr bool value = (resolves_to_colvector<T1>::value && resolves_to_rowvector<T2>::value); };
+
+
+
+template<typename T1>
+struct has_op_inv_any
+  { static constexpr bool value = false; };
+
+template<typename T1>
+struct has_op_inv_any< Op<T1,op_inv_gen_full> >
+  { static constexpr bool value = true;  };
+
+template<typename T1>
+struct has_op_inv_any< Op<T1,op_inv_spd_full> >
+  { static constexpr bool value = true;  };
+
+template<typename T1>
+struct has_op_inv_any< Op<T1,op_inv_gen_default> >
+  { static constexpr bool value = true;  };
+
+template<typename T1>
+struct has_op_inv_any< Op<T1,op_inv_spd_default> >
+  { static constexpr bool value = true;  };
+
+template<typename T1, typename T2>
+struct has_op_inv_any< Glue<Op<T1,op_inv_gen_full>, T2, glue_times> >
+  { static constexpr bool value = true;  };
+
+template<typename T1, typename T2>
+struct has_op_inv_any< Glue<Op<T1,op_inv_spd_full>, T2, glue_times> >
+  { static constexpr bool value = true;  };
+
+template<typename T1, typename T2>
+struct has_op_inv_any< Glue<Op<T1,op_inv_gen_default>, T2, glue_times> >
+  { static constexpr bool value = true;  };
+
+template<typename T1, typename T2>
+struct has_op_inv_any< Glue<Op<T1,op_inv_spd_default>, T2, glue_times> >
+  { static constexpr bool value = true;  };
+
+template<typename T1, typename T2>
+struct has_op_inv_any< Glue<T1, Op<T2,op_inv_gen_full>, glue_times> >
+  { static constexpr bool value = true;  };
+
+template<typename T1, typename T2>
+struct has_op_inv_any< Glue<T1, Op<T2,op_inv_spd_full>, glue_times> >
+  { static constexpr bool value = true;  };
+
+template<typename T1, typename T2>
+struct has_op_inv_any< Glue<T1, Op<T2,op_inv_gen_default>, glue_times> >
+  { static constexpr bool value = true;  };
+
+template<typename T1, typename T2>
+struct has_op_inv_any< Glue<T1, Op<T2,op_inv_spd_default>, glue_times> >
+  { static constexpr bool value = true;  };
+
+
+
+
+template<typename T>
+struct has_nested_op_traits
+  {
+  typedef char yes[1];
+  typedef char  no[2];
+  
+  template<typename X> static yes& check(typename X::template traits<void>*);
+  template<typename>   static  no& check(...);
+  
+  static constexpr bool value = ( sizeof(check<T>(0)) == sizeof(yes) );
+  };
+
+template<typename T>
+struct has_nested_glue_traits
+  {
+  typedef char yes[1];
+  typedef char  no[2];
+  
+  template<typename X> static yes& check(typename X::template traits<void,void>*);
+  template<typename>   static  no& check(...);
+  
+  static constexpr bool value = ( sizeof(check<T>(0)) == sizeof(yes) );
+  };
+
+
+//! @}
-- 
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