// SPDX-License-Identifier: Apache-2.0
// 
// Copyright 2008-2016 Conrad Sanderson (https://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
// https://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
  {
  using yes = char[1];
  using no  = char[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
  {
  using yes = char[1];
  using no  = char[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
  {
  using yes = char[1];
  using no  = char[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_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 T>
struct is_mtSpReduceOp
  { static constexpr bool value = false; };
 
template<typename eT, typename T1, typename op_type>
struct is_mtSpReduceOp< mtSpReduceOp<eT, T1, op_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
  || is_mtSpReduceOp<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_fp16
  {
  static constexpr bool value = false;
  static constexpr bool yes   = false;
  static constexpr bool no    = true;
  };

#ifdef ARMA_HAVE_FP16
template<>
struct is_fp16<fp16>
  {
  static constexpr bool value = true;
  static constexpr bool yes   = true;
  static constexpr bool no    = false;
  };
#endif



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;
  };

#ifdef ARMA_HAVE_FP16
template<>
struct is_real<fp16>
  {
  static constexpr bool value = true;
  static constexpr bool yes   = true;
  static constexpr bool no    = false;
  };
#endif



template<typename T1>
struct is_blas_real
  {
  static constexpr bool value = false;
  static constexpr bool yes   = false;
  static constexpr bool no    = true;
  };

template<>
struct is_blas_real<float>
  {
  static constexpr bool value = true;
  static constexpr bool yes   = true;
  static constexpr bool no    = false;
  };
  
template<>
struct is_blas_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_blas_cx
  {
  static constexpr bool value = false;
  static constexpr bool yes   = false;
  static constexpr bool no    = true;
  };

template<>
struct is_blas_cx< std::complex<float> >
  {
  static constexpr bool value = true;
  static constexpr bool yes   = true;
  static constexpr bool no    = false;
  };

template<>
struct is_blas_cx< std::complex<double> >
  {
  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_cx_fp16
  {
  static constexpr bool value = false;
  static constexpr bool yes   = false;
  static constexpr bool no    = true;
  };

#ifdef ARMA_HAVE_FP16
template<>
struct is_cx_fp16< std::complex<fp16> >
  {
  static constexpr bool value = true;
  static constexpr bool yes   = true;
  static constexpr bool no    = false;
  };
#endif



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 ||
    is_fp16<T1>::value ||
    is_cx_fp16<T1>::value;
  };



template<typename T1>
struct is_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_real_or_cx
  {
  static constexpr bool value = false;
  };


template<> struct is_real_or_cx<              float   > { static constexpr bool value = true; };
template<> struct is_real_or_cx<              double  > { static constexpr bool value = true; };
template<> struct is_real_or_cx< std::complex<float>  > { static constexpr bool value = true; };
template<> struct is_real_or_cx< std::complex<double> > { static constexpr bool value = true; };

#if defined(ARMA_HAVE_FP16)
template<> struct is_real_or_cx<              fp16    > { static constexpr bool value = true; };
template<> struct is_real_or_cx< std::complex<fp16>   > { static constexpr bool value = true; };
#endif




//

struct 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
  {
  using yes = char[1];
  using no  = char[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
  {
  using yes = char[1];
  using no  = char[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) );
  };




template<typename T1>
struct is_sym_expr
  {
  static constexpr bool eval(const T1&)  { return false; }
  };

template<typename eT>
struct is_sym_expr< Glue< Mat<eT>, Op<Mat<eT>, op_htrans>, glue_times > >
  {
  static
  arma_inline
  bool
  eval(const Glue< Mat<eT>, Op<Mat<eT>, op_htrans>, glue_times >& expr)
    {
    const Mat<eT>& X = expr.A;
    const Mat<eT>& Y = expr.B.m;
    
    return (&X == &Y);
    }
  };

template<typename eT>
struct is_sym_expr< Glue< Op<Mat<eT>, op_htrans>, Mat<eT>, glue_times > >
  {
  static
  arma_inline
  bool
  eval(const Glue< Op<Mat<eT>, op_htrans>, Mat<eT>, glue_times >& expr)
    {
    const Mat<eT>& X = expr.A.m;
    const Mat<eT>& Y = expr.B;
    
    return (&X == &Y);
    }
  };

template<typename T1>
struct is_sym_expr< Op<T1, op_symmatu> >
  {
  static
  arma_inline
  bool
  eval(const Op<T1, op_symmatu>&)
    {
    return true;
    }
  };

template<typename T1>
struct is_sym_expr< Op<T1, op_symmatl> >
  {
  static
  arma_inline
  bool
  eval(const Op<T1, op_symmatl>&)
    {
    return true;
    }
  };


//! @}
