proper constexpr functions for older compilers in operations

src/amdis/operations/Arithmetic.hpp

@@ -43,13 +43,13 @@ namespace AMDiS
 #endif
 
     template <class... Int>
-    constexpr int order(Plus, Int... orders)
+    constexpr int order(Plus const&, Int... orders)
     {
       return Math::max(int(orders)...);
     }
 
     template <std::size_t I>
-    constexpr auto partial(Plus, index_t<I>)
+    constexpr auto partial(Plus const&, index_t<I>)
     {
       static_assert((I < 2), "Derivatives of `Plus` only defined for the binary case.");
       return One{};
@@ -66,17 +66,17 @@ namespace AMDiS
         return lhs - rhs;
       }
 
-      friend constexpr int order(Minus, int lhs, int rhs)
+      friend constexpr int order(Minus const&, int lhs, int rhs)
       {
         return Math::max(lhs, rhs);
       }
 
-      friend constexpr auto partial(Minus, index_t<0>)
+      friend constexpr auto partial(Minus const&, index_t<0>)
       {
         return One{};
       }
 
-      friend constexpr auto partial(Minus, index_t<1>)
+      friend constexpr auto partial(Minus const&, index_t<1>)
       {
         return StaticConstant<int,-1>{};
       }
@@ -134,7 +134,7 @@ namespace AMDiS
 
 
     template <class... Int>
-    constexpr int order(Multiplies, Int... orders)
+    constexpr int order(Multiplies const&, Int... orders)
     {
       return Math::sum(int(orders)...);
     }
@@ -142,7 +142,7 @@ namespace AMDiS
     // only for binary *
     // d_0 (x * y) = y, d_1 (x * y) = x
     template <std::size_t I>
-    constexpr auto partial(Multiplies, index_t<I>)
+    constexpr auto partial(Multiplies const&, index_t<I>)
     {
       static_assert((I < 2), "Derivatives of `Multiplies` only defined for the binary case.");
       return Arg<1-I>{};
@@ -160,13 +160,13 @@ namespace AMDiS
       }
 
       // d_0 f(x,y) = 1 / y
-      friend constexpr auto partial(Divides, index_t<0>)
+      friend constexpr auto partial(Divides const&, index_t<0>)
       {
         return compose(Divides{}, One{}, Arg<1>{});
       }
 
       // d_1 f(x,y) = (y - x)/y^2
-      friend constexpr auto partial(Divides, index_t<1>);
+      friend constexpr auto partial(Divides const&, index_t<1>);
     };
 
     // -------------------------------------------------------------------------
@@ -180,12 +180,12 @@ namespace AMDiS
         return -x;
       }
 
-      friend constexpr int order(Negate, int d)
+      friend constexpr int order(Negate const&, int d)
       {
         return d;
       }
 
-      friend constexpr auto partial(Negate, index_t<0>)
+      friend constexpr auto partial(Negate const&, index_t<0>)
       {
         return StaticConstant<int,-1>{};
       }
@@ -238,12 +238,12 @@ namespace AMDiS
         return Math::pow<p>(x);
       }
 
-      friend constexpr int order(PowImpl, int d)
+      friend constexpr int order(PowImpl const&, int d)
       {
         return p*d;
       }
 
-      friend constexpr auto partial(PowImpl, index_t<0>)
+      friend constexpr auto partial(PowImpl const&, index_t<0>)
       {
         return compose(Multiplies{}, StaticConstant<int,p>{}, Pow<p-1>{});
       }
@@ -278,7 +278,7 @@ namespace AMDiS
 #endif
 
     // d_1 f(x,y) = (y - x)/y^2
-    inline constexpr auto partial(Divides, index_t<1>)
+    inline constexpr auto partial(Divides const&, index_t<1>)
     {
       return compose(Divides{}, compose(Minus{}, Arg<1>{}, Arg<0>{}),
                                 compose(Pow<2>{}, Arg<1>{}));
@@ -297,12 +297,12 @@ namespace AMDiS
         return std::pow(x, p_);
       }
 
-      friend constexpr int order(Pow_ P, int d)
+      friend constexpr int order(Pow_ const& P, int d)
       {
         return P.p_ * d;
       }
 
-      friend constexpr auto partial(Pow_ P, index_t<0>)
+      friend constexpr auto partial(Pow_ const& P, index_t<0>)
       {
         return compose(Multiplies{}, Constant<int>{P.p_}, Pow_{P.p_-1});
       }

src/amdis/operations/Basic.hpp

@@ -50,7 +50,7 @@ namespace AMDiS
     }
 
     template <class T, T value, std::size_t J>
-    constexpr auto partial(StaticConstant<T,value>, index_t<J>)
+    constexpr auto partial(StaticConstant<T,value> const&, index_t<J>)
     {
       return Zero{};
     }
@@ -66,12 +66,12 @@ namespace AMDiS
         return x;
       }
 
-      friend constexpr int order(Id, int d)
+      friend constexpr int order(Id const&, int d)
       {
         return d;
       }
 
-      friend auto partial(Id, index_t<0>)
+      friend auto partial(Id const&, index_t<0>)
       {
         return One{};
       }
@@ -111,24 +111,38 @@ namespace AMDiS
 
     // -------------------------------------------------------------------------
 
+
+    template <class T0, class... Ts>
+    inline constexpr decltype(auto) get_element(index_t<0>, T0&& t0, Ts&&... /*ts*/)
+    {
+      return FWD(t0);
+    }
+
+    template <std::size_t J, class T0, class... Ts>
+    inline constexpr decltype(auto) get_element(index_t<J>, T0&& /*t0*/, Ts&&... ts)
+    {
+      static_assert(J <= sizeof...(Ts), "");
+      return get_element(index_t<J-1>{}, FWD(ts)...);
+    }
+
     template <std::size_t I>
     struct Arg
     {
       template <class... Ts>
       constexpr auto&& operator()(Ts&&... args) const
       {
-        return std::get<I>(std::forward_as_tuple(FWD(args)...));
+        return get_element(index_t<I>{}, FWD(args)...);
       }
     };
 
     template <std::size_t I, class... Int>
     constexpr int order(Arg<I> const&, Int... orders)
     {
-      return std::get<I>(std::forward_as_tuple(orders...));
+      return get_element(index_t<I>{}, orders...);
     }
 
     template <std::size_t I, std::size_t J>
-    constexpr auto partial(Arg<I>, index_t<J>)
+    constexpr auto partial(Arg<I> const&, index_t<J>)
     {
       return StaticConstant<int,(I==J ? 1 : 0)>{};
     }
@@ -144,7 +158,7 @@ namespace AMDiS
         return vec[I];
       }
 
-      friend constexpr int order(Get, int d)
+      friend constexpr int order(Get const&, int d)
       {
         return d;
       }
@@ -162,7 +176,7 @@ namespace AMDiS
         return vec[i_];
       }
 
-      friend constexpr int order(Get_, int d)
+      friend constexpr int order(Get_ const&, int d)
       {
         return d;
       }

src/amdis/operations/CMath.hpp

@@ -27,7 +27,7 @@
           return DERIV ;                                      \
         }                                                     \
       };                                                      \
-      friend constexpr auto partial(NAME, index_t<0>)         \
+      friend constexpr auto partial(NAME const&, index_t<0>)  \
       {                                                       \
         return Derivative{} ;                                 \
       }                                                       \
@@ -52,7 +52,7 @@ namespace AMDiS
         return (x > T{0} ? T{1} : T{-1});
       }
 
-      friend constexpr auto partial(Signum, index_t<0>)
+      friend constexpr auto partial(Signum const&, index_t<0>)
       {
         return Zero{};
       }
@@ -91,14 +91,14 @@ namespace AMDiS
       }
 
       // -y/(Math::sqr(x) + Math::sqr(y))
-      constexpr friend auto partial(Atan2, index_t<0>)
+      constexpr friend auto partial(Atan2 const&, index_t<0>)
       {
         return compose(Divides{}, compose(Negate{}, Arg<1>{}),
           compose(Plus{}, compose(Pow<2>{}, Arg<0>{}), compose(Pow<2>{}, Arg<1>{})));
       }
 
       // x/(Math::sqr(x) + Math::sqr(y));
-      constexpr friend auto partial(Atan2, index_t<1>)
+      constexpr friend auto partial(Atan2 const&, index_t<1>)
       {
         return compose(Divides{}, Arg<0>{},
           compose(Plus{}, compose(Pow<2>{}, Arg<0>{}), compose(Pow<2>{}, Arg<1>{})));
@@ -131,7 +131,7 @@ namespace AMDiS
         T lo_, hi_;
       };
 
-      constexpr friend auto partial(Clamp c, index_t<0>)
+      constexpr friend auto partial(Clamp const& c, index_t<0>)
       {
         return DClamp{c.lo_,c.hi_};
       }

src/amdis/operations/FieldMatVec.hpp

@@ -23,17 +23,17 @@ namespace AMDiS
         return lhs.dot(rhs);
       }
 
-      friend constexpr int order(Dot, int d1, int d2)
+      friend constexpr int order(Dot const&, int d1, int d2)
       {
         return d1 + d2;
       }
 
-      friend constexpr auto partial(Dot, index_t<0>)
+      friend constexpr auto partial(Dot const&, index_t<0>)
       {
         return Arg<1>{};
       }
 
-      friend constexpr auto partial(Dot, index_t<1>)
+      friend constexpr auto partial(Dot const&, index_t<1>)
       {
         return Arg<0>{};
       }
@@ -50,12 +50,12 @@ namespace AMDiS
         return unary_dot(vec);
       }
 
-      friend constexpr int order(UnaryDot, int d)
+      friend constexpr int order(UnaryDot const&, int d)
       {
         return 2*d;
       }
 
-      friend auto partial(UnaryDot, index_t<0>)
+      friend auto partial(UnaryDot const&, index_t<0>)
       {
         return compose(Multiplies{}, StaticConstant<int,2>{}, Id{});
       }
@@ -88,7 +88,7 @@ namespace AMDiS
         return trans(mat);
       }
 
-      friend constexpr int order(Trans, int d)
+      friend constexpr int order(Trans const&, int d)
       {
         return d;
       }

src/amdis/operations/MaxMin.hpp

@@ -34,7 +34,8 @@ namespace AMDiS
       template <class T, class S>
       constexpr auto operator()(T const& lhs, S const& rhs) const
       {
-        return Math::max(std::abs(lhs), std::abs(rhs));
+        using std::abs;
+        return Math::max(abs(lhs), abs(rhs));
       }
     };
 
@@ -46,7 +47,8 @@ namespace AMDiS
       template <class T, class S>
       constexpr auto operator()(T const& lhs, S const& rhs) const
       {
-        return Math::min(std::abs(lhs), std::abs(rhs));
+        using std::abs;
+        return Math::min(abs(lhs), abs(rhs));
       }
     };