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+// 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 upgrade_val
+//! @{
+
+
+
+//! upgrade_val is used to ensure an operation such as multiplication is possible between two types.
+//! values are upgraded only where necessary.
+
+template<typename T1, typename T2>
+struct upgrade_val
+  {
+  typedef typename promote_type<T1,T2>::result T1_result;
+  typedef typename promote_type<T1,T2>::result T2_result;
+  
+  arma_inline
+  static
+  typename promote_type<T1,T2>::result
+  apply(const T1 x)
+    {
+    typedef typename promote_type<T1,T2>::result out_type;
+    return out_type(x);
+    }
+  
+  arma_inline
+  static
+  typename promote_type<T1,T2>::result
+  apply(const T2 x)
+    {
+    typedef typename promote_type<T1,T2>::result out_type;
+    return out_type(x);
+    }
+  
+  };
+
+
+// template<>
+template<typename T>
+struct upgrade_val<T,T>
+  {
+  typedef T T1_result;
+  typedef T T2_result;
+  
+  arma_inline static const T& apply(const T& x) { return x; }
+  };
+
+
+//! upgrade a type to allow multiplication with a complex type
+//! eg. the int in "int * complex<double>" is upgraded to a double
+// template<>
+template<typename T, typename T2>
+struct upgrade_val< std::complex<T>, T2 >
+  {
+  typedef std::complex<T> T1_result;
+  typedef T               T2_result;
+  
+  arma_inline static const std::complex<T>& apply(const std::complex<T>& x) { return x;    }
+  arma_inline static       T                apply(const T2 x)               { return T(x); }
+  };
+
+
+// template<>
+template<typename T1, typename T>
+struct upgrade_val< T1, std::complex<T> >
+  {
+  typedef T               T1_result;
+  typedef std::complex<T> T2_result;
+  
+  arma_inline static       T                apply(const T1 x)               { return T(x); }
+  arma_inline static const std::complex<T>& apply(const std::complex<T>& x) { return x;    }
+  };
+
+
+//! ensure we don't lose precision when multiplying a complex number with a higher precision real number
+template<>
+struct upgrade_val< std::complex<float>, double >
+  {
+  typedef std::complex<double> T1_result;
+  typedef double               T2_result;
+  
+  arma_inline static const std::complex<double> apply(const std::complex<float>& x) { return std::complex<double>(x); }
+  arma_inline static       double               apply(const double x)               { return x; }
+  };
+
+
+template<>
+struct upgrade_val< double, std::complex<float> >
+  {
+  typedef double              T1_result;
+  typedef std::complex<float> T2_result;
+  
+  arma_inline static       double               apply(const double x)               { return x; }
+  arma_inline static const std::complex<double> apply(const std::complex<float>& x) { return std::complex<double>(x); }
+  };
+
+
+//! ensure we don't lose precision when multiplying complex numbers with different underlying types
+template<>
+struct upgrade_val< std::complex<float>, std::complex<double> >
+  {
+  typedef std::complex<double> T1_result;
+  typedef std::complex<double> T2_result;
+  
+  arma_inline static const std::complex<double>  apply(const std::complex<float>&  x) { return std::complex<double>(x); }
+  arma_inline static const std::complex<double>& apply(const std::complex<double>& x) { return x; }
+  };
+
+
+template<>
+struct upgrade_val< std::complex<double>, std::complex<float> >
+  {
+  typedef std::complex<double> T1_result;
+  typedef std::complex<double> T2_result;
+  
+  arma_inline static const std::complex<double>& apply(const std::complex<double>& x) { return x; }
+  arma_inline static const std::complex<double>  apply(const std::complex<float>&  x) { return std::complex<double>(x); }
+  };
+
+
+//! work around limitations in the complex class (at least as present in gcc 4.1 & 4.3)
+template<>
+struct upgrade_val< std::complex<double>, float >
+  {
+  typedef std::complex<double> T1_result;
+  typedef double               T2_result;
+  
+  arma_inline static const std::complex<double>& apply(const std::complex<double>& x) { return x; }
+  arma_inline static       double                apply(const float x)                 { return double(x); }
+  };
+
+
+template<>
+struct upgrade_val< float, std::complex<double> >
+  {
+  typedef double               T1_result;
+  typedef std::complex<double> T2_result;
+  
+  arma_inline static       double                apply(const float x)                 { return double(x); }
+  arma_inline static const std::complex<double>& apply(const std::complex<double>& x) { return x; }
+  };
+
+
+
+//! @}