From 2df86a7f9cdfb4d4670ffc1801953c6c88464a1e Mon Sep 17 00:00:00 2001
From: Joel Falcou <joel.falcou@lri.fr>
Date: Thu, 9 Nov 2023 17:08:51 +0100
Subject: [PATCH] Fixes around constants generation

* as_real<T> is available
* Add tests for as_real and constants
---
 include/kyosu/functions/abs.hpp               |   4 +-
 include/kyosu/functions/radinpi.hpp           |   4 +-
 include/kyosu/functions/sqr_abs.hpp           |   4 +-
 include/kyosu/types/cayley_dickson.hpp        |  39 ++--
 include/kyosu/types/impl/arithmetic.hpp       |   4 +-
 include/kyosu/types/impl/compounds.hpp        |   4 +-
 include/kyosu/types/impl/detail/besselin.hpp  |   2 +-
 include/kyosu/types/impl/detail/besselj0.hpp  |   4 +-
 include/kyosu/types/impl/detail/besselj1.hpp  |   4 +-
 include/kyosu/types/impl/detail/besseljn.hpp  |   2 +-
 include/kyosu/types/impl/faddeeva.hpp         |   2 +-
 include/kyosu/types/impl/special.hpp          |   8 +-
 include/kyosu/types/traits.hpp                |  31 ++-
 test/unit/infra/as_cayley_dickinson.cpp       | 200 +++++++++---------
 .../infra/{as_real.cpp => as_real_type.cpp}   |  12 +-
 test/unit/infra/constants.cpp                 |  50 +++++
 16 files changed, 224 insertions(+), 150 deletions(-)
 rename test/unit/infra/{as_real.cpp => as_real_type.cpp} (54%)
 create mode 100644 test/unit/infra/constants.cpp

diff --git a/include/kyosu/functions/abs.hpp b/include/kyosu/functions/abs.hpp
index 6d9abbbb..99c0862f 100644
--- a/include/kyosu/functions/abs.hpp
+++ b/include/kyosu/functions/abs.hpp
@@ -51,8 +51,8 @@ namespace kyosu
 //!   @code
 //!   namespace kyosu
 //!   {
-//!      template<kyosu::concepts::cayley_dickson T> constexpr as_real_t<T> abs(T z) noexcept;
-//!      template<eve::floating_ordered_value T>     constexpr T            abs(T z) noexcept;
+//!      template<kyosu::concepts::cayley_dickson T> constexpr as_real_type_t<T>  abs(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr T                  abs(T z) noexcept;
 //!   }
 //!   @endcode
 //!
diff --git a/include/kyosu/functions/radinpi.hpp b/include/kyosu/functions/radinpi.hpp
index 41653cf9..c1eeb2e8 100644
--- a/include/kyosu/functions/radinpi.hpp
+++ b/include/kyosu/functions/radinpi.hpp
@@ -51,8 +51,8 @@ namespace kyosu
 //!   @code
 //!   namespace kyosu
 //!   {
-//!      template<kyosu::concepts::cayley_dickson T> constexpr as_real_t<T> radinpi(T z) noexcept;
-//!      template<eve::floating_ordered_value T>     constexpr T            radinpi(T z) noexcept;
+//!      template<kyosu::concepts::cayley_dickson T> constexpr as_real_type_t<T> radinpi(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr T                 radinpi(T z) noexcept;
 //!   }
 //!   @endcode
 //!
diff --git a/include/kyosu/functions/sqr_abs.hpp b/include/kyosu/functions/sqr_abs.hpp
index 04ab7dd1..962745aa 100644
--- a/include/kyosu/functions/sqr_abs.hpp
+++ b/include/kyosu/functions/sqr_abs.hpp
@@ -51,8 +51,8 @@ namespace kyosu
 //!   @code
 //!   namespace kyosu
 //!   {
-//!      template<kyosu::concepts::cayley_dickson T> constexpr auto sqr_abs(T z) noexcept;
-//!      template<eve::floating_ordered_value T>     constexpr auto sqr_abs(T z) noexcept;
+//!      template<kyosu::concepts::cayley_dickson T> constexpr as_real_type_t<T>  sqr_abs(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr auto               sqr_abs(T z) noexcept;
 //!   }
 //!   @endcode
 //!
diff --git a/include/kyosu/types/cayley_dickson.hpp b/include/kyosu/types/cayley_dickson.hpp
index c0a7eac9..e38db55f 100644
--- a/include/kyosu/types/cayley_dickson.hpp
+++ b/include/kyosu/types/cayley_dickson.hpp
@@ -122,9 +122,9 @@ namespace kyosu
   template<std::size_t I, typename T, unsigned int N>
   constexpr auto get(cayley_dickson<T,N> const& c) noexcept { return kumi::get<I>(c.contents); }
 
-  //==================================================================================================================
+  //====================================================================================================================
   // Main function dispatchers
-  //==================================================================================================================
+  //====================================================================================================================
   template<typename... T>
   requires(concepts::cayley_dickson<T> || ... )
   KYOSU_FORCEINLINE   constexpr auto tag_invoke(eve::callable auto const& f, auto, T&&... c) noexcept
@@ -133,9 +133,9 @@ namespace kyosu
     return _::dispatch(f, KYOSU_FWD(c)...);
   }
 
-  //==================================================================================================================
+  //====================================================================================================================
   //  Tag invoke override for if_else - Outside so it can properly deals with the complicated parameters of if_else
-  //==================================================================================================================
+  //====================================================================================================================
   template<typename T, typename F>
   requires(concepts::cayley_dickson<T> || concepts::cayley_dickson<F>)
   KYOSU_FORCEINLINE constexpr auto  tag_invoke( eve::tag_of<kyosu::if_else> const& fn, auto, auto m
@@ -155,9 +155,9 @@ namespace kyosu
     return _::dispatch(f, c, tgt);
   }
 
-  //==================================================================================================================
+  //====================================================================================================================
   //  Tag invoke override for parts extraction - Outside so they can see get<I>(c)
-  //==================================================================================================================
+  //====================================================================================================================
   template<concepts::extractor T, concepts::cayley_dickson C>
   KYOSU_FORCEINLINE constexpr decltype(auto)
   tag_invoke(T const&, auto, C&& c) noexcept
@@ -167,7 +167,7 @@ namespace kyosu
     if constexpr(T::minimum_valid_index == T::maximum_valid_index)
     {
       if constexpr(sz > T::minimum_valid_index) return get<T::minimum_valid_index>(EVE_FWD(c));
-      else                                      return as_real_t<std::remove_cvref_t<C>>{0};
+      else                                      return as_real_type_t<std::remove_cvref_t<C>>{0};
     }
     else
     {
@@ -183,11 +183,22 @@ namespace kyosu
   }
 
   // TODO: Move to tag_invoke when EVE catch up on this front
-  template<typename Tag, eve::floating_scalar_value Type, unsigned int N>
-  KYOSU_FORCEINLINE constexpr auto tagged_dispatch(Tag const&, eve::as<cayley_dickson<Type,N>> const&) noexcept
+  template<typename Tag, concepts::cayley_dickson T>
+  KYOSU_FORCEINLINE constexpr auto tagged_dispatch(Tag const&, eve::as<T> const&) noexcept
   {
     eve::detail::callable_object<Tag> cst;
-    return cayley_dickson<Type,N>( cst(eve::as<Type>{}) );
+    auto val = cst( eve::as<as_real_type_t<T>>{} );
+    using val_t = std::remove_cvref_t<decltype(val)>;
+
+    if constexpr(!eve::floating_value<val_t>) return val;
+    else return as_cayley_dickson_n_t<eve::element_type_t<T>::static_size,val_t>(val);
+  }
+
+  template<typename Tag, typename T>
+  KYOSU_FORCEINLINE constexpr auto tagged_dispatch(Tag const&, as_real<T> const&) noexcept
+  {
+    eve::detail::callable_object<Tag> cst;
+    return cst(typename as_real<T>::target_type{});
   }
 
   //====================================================================================================================
@@ -217,14 +228,6 @@ struct std::tuple_element<I, kyosu::cayley_dickson<T,N>>
   using type = T;
 };
 
-template<typename Wrapper, typename T, unsigned int N>
-struct eve::supports_like<Wrapper,kyosu::cayley_dickson<T,N>>
-      : std::bool_constant<   kyosu::concepts::cayley_dickson<Wrapper>
-                          ||  std::same_as<T, eve::element_type_t<Wrapper>>
-                          ||  plain_scalar_value<Wrapper>
-                          >
-{
-};
 #endif
 
 #include <kyosu/types/impl/io.hpp>
diff --git a/include/kyosu/types/impl/arithmetic.hpp b/include/kyosu/types/impl/arithmetic.hpp
index 31d99e32..b0a4d4f6 100644
--- a/include/kyosu/types/impl/arithmetic.hpp
+++ b/include/kyosu/types/impl/arithmetic.hpp
@@ -250,7 +250,7 @@ namespace kyosu::_
   KYOSU_FORCEINLINE constexpr
   auto dispatch(eve::tag_of<kyosu::proj> const&, C c) noexcept
   {
-    using real_t = eve::as<as_real_t<C>>;
+    using real_t = eve::as<as_real_type_t<C>>;
     constexpr auto P = kyosu::dimension_v<C>;
     if constexpr (P == 2)
       return if_else(is_infinite(c)
@@ -417,7 +417,7 @@ namespace kyosu::_
     {
       r_t x = convert(xx, eve::as<r_t>());
       auto dfma = /*d*/(fma);
-      r_t  that(eve::zero(eve::as<as_real_t<r_t>>()));
+      r_t  that(eve::zero(eve::as<as_real_type_t<r_t>>()));
       auto next = [&](auto that, auto arg) { return dfma(x, that, arg); };
       ((that = next(that, cs)), ...);
       return that;
diff --git a/include/kyosu/types/impl/compounds.hpp b/include/kyosu/types/impl/compounds.hpp
index 58f288a6..5586d9e1 100644
--- a/include/kyosu/types/impl/compounds.hpp
+++ b/include/kyosu/types/impl/compounds.hpp
@@ -77,7 +77,7 @@ namespace kyosu
       auto ria  = kumi::split(self ,kumi::index<sz>);
       auto rib  = kumi::split(other,kumi::index<sz>);
 
-      using cd_t = as_cayley_dickson_n_t<sz,as_real_t<Self>,as_real_t<Other>>;
+      using cd_t = as_cayley_dickson_n_t<sz,as_real_type_t<Self>,as_real_type_t<Other>>;
       cd_t  ra{get<0>(ria)}, ia{get<1>(ria)}
           , rb{get<0>(rib)}, ib{get<1>(rib)};
 
@@ -91,7 +91,7 @@ namespace kyosu
       constexpr auto idx  = kumi::index<sz>;
       auto ria  = kumi::split(self,idx);
 
-      using cd_t = as_cayley_dickson_n_t<sz,as_real_t<Self>,as_real_t<Other>>;
+      using cd_t = as_cayley_dickson_n_t<sz,as_real_type_t<Self>,as_real_type_t<Other>>;
       cd_t ra{get<0>(ria)}, ia{get<1>(ria)};
       self = as_cayley_dickson_t<Self,Other>{kumi::cat(ra * other,ia * conj(other))};
     }
diff --git a/include/kyosu/types/impl/detail/besselin.hpp b/include/kyosu/types/impl/detail/besselin.hpp
index 3e33b171..925b7595 100644
--- a/include/kyosu/types/impl/detail/besselin.hpp
+++ b/include/kyosu/types/impl/detail/besselin.hpp
@@ -19,7 +19,7 @@ namespace kyosu::_
   {
     if constexpr(concepts::complex<Z> )
     {
-      using e_t = as_real_t<Z>;
+      using e_t = as_real_type_t<Z>;
       auto miton = [](N n){
         if (n%4 == 0) return complex(eve::one(eve::as<e_t>()));
         else if (n%4 == 1) return  complex(eve::zero(eve::as<e_t>()), eve::mone(eve::as<e_t>()));
diff --git a/include/kyosu/types/impl/detail/besselj0.hpp b/include/kyosu/types/impl/detail/besselj0.hpp
index 3196307f..0fc16f93 100644
--- a/include/kyosu/types/impl/detail/besselj0.hpp
+++ b/include/kyosu/types/impl/detail/besselj0.hpp
@@ -17,7 +17,7 @@ namespace kyosu::_
   {
     if constexpr(concepts::complex<Z> )
     {
-      using e_t = as_real_t<Z>;
+      using e_t = as_real_type_t<Z>;
       using u_t = eve::underlying_type_t<e_t>;
       auto saz = kyosu::sqr_abs(z);
 
@@ -110,7 +110,7 @@ namespace kyosu::_
 
       if( eve::any(notdone) )
       {
-        notdone = next_interval(ascending_series_cyl_j0, notdone, saz <= as_real_t<Z>(144), r, z);
+        notdone = next_interval(ascending_series_cyl_j0, notdone, saz <= as_real_type_t<Z>(144), r, z);
         if( eve::any(notdone) )
         {
           last_interval(semiconvergent_series_cyl_j0, notdone, r, z);
diff --git a/include/kyosu/types/impl/detail/besselj1.hpp b/include/kyosu/types/impl/detail/besselj1.hpp
index 891f6361..599d0aaf 100644
--- a/include/kyosu/types/impl/detail/besselj1.hpp
+++ b/include/kyosu/types/impl/detail/besselj1.hpp
@@ -17,7 +17,7 @@ namespace kyosu::_
   {
     if constexpr(concepts::complex<Z> )
     {
-      using e_t = as_real_t<Z>;
+      using e_t = as_real_type_t<Z>;
       using u_t = eve::underlying_type_t<e_t>;
       auto saz = kyosu::sqr_abs(z);
 
@@ -111,7 +111,7 @@ namespace kyosu::_
 
       if( eve::any(notdone) )
       {
-        notdone = next_interval(ascending_series_cyl_j1, notdone, saz <= as_real_t<Z>(144), r, z);
+        notdone = next_interval(ascending_series_cyl_j1, notdone, saz <= as_real_type_t<Z>(144), r, z);
         if( eve::any(notdone) )
         {
           last_interval(semiconvergent_series_cyl_j1, notdone, r, z);
diff --git a/include/kyosu/types/impl/detail/besseljn.hpp b/include/kyosu/types/impl/detail/besseljn.hpp
index f976dcbf..fd9b484d 100644
--- a/include/kyosu/types/impl/detail/besseljn.hpp
+++ b/include/kyosu/types/impl/detail/besseljn.hpp
@@ -35,7 +35,7 @@ namespace kyosu::_
       }
       else
       {
-        using e_t = as_real_t<Z>;
+        using e_t = as_real_type_t<Z>;
         using u_t = eve::underlying_type_t<e_t>;
         auto n = u_t(eve::abs(nn));
         auto az = kyosu::abs(z);
diff --git a/include/kyosu/types/impl/faddeeva.hpp b/include/kyosu/types/impl/faddeeva.hpp
index 16860fcc..93ae5576 100644
--- a/include/kyosu/types/impl/faddeeva.hpp
+++ b/include/kyosu/types/impl/faddeeva.hpp
@@ -17,7 +17,7 @@ namespace kyosu::_
   {
     if constexpr(concepts::complex<Z> )
     {
-      using v_t = as_real_t<Z>;
+      using v_t = as_real_type_t<Z>;
       using real_t = eve::element_type_t<v_t>;
       auto const   sqrtpi = eve::sqrt_pi(eve::as<real_t>());
       auto const iosqrtpi = complex(real_t(0), eve::rec(sqrtpi));
diff --git a/include/kyosu/types/impl/special.hpp b/include/kyosu/types/impl/special.hpp
index 415c2cb7..c1b24774 100644
--- a/include/kyosu/types/impl/special.hpp
+++ b/include/kyosu/types/impl/special.hpp
@@ -23,7 +23,7 @@ namespace kyosu::_
       // 15 sig. digits for 0<=real(z)<=171
       // coeffs should sum to about g*g/2+23/24
       //
-      using r_t = eve::element_type_t<as_real_t<Z>>;
+      using r_t = eve::element_type_t<as_real_type_t<Z>>;
       auto  g=r_t(607)/r_t(128);
       // best results when 4<=g<=5
       constexpr int N = 15;
@@ -98,7 +98,7 @@ namespace kyosu::_
       // 15 sig. digits for 0<=real(z)<=171
       // coeffs should sum to about g*g/2+23/24
       //
-      using r_t = eve::element_type_t<as_real_t<Z>>;
+      using r_t = eve::element_type_t<as_real_type_t<Z>>;
       auto  g=r_t(607)/r_t(128);
       // best results when 4<=g<=5
       constexpr int N = 15;
@@ -165,7 +165,7 @@ namespace kyosu::_
       // 15 sig. digits for 0<=real(z)<=171
       // coeffs should sum to about g*g/2+23/24
       //
-      using r_t = eve::element_type_t<as_real_t<Z>>;
+      using r_t = eve::element_type_t<as_real_type_t<Z>>;
       auto  g=r_t(607)/r_t(128);
       // best results when 4<=g<=5
       constexpr int N = 15;
@@ -263,7 +263,7 @@ namespace kyosu::_
       // 15 sig. digits for 0<=real(z)<=171
       // coeffs should sum to about g*g/2+23/24
       //
-      using v_t = kyosu::as_real_t<Z>;
+      using v_t = kyosu::as_real_type_t<Z>;
       using real_t = eve::element_type_t<v_t>;
       auto k = real_t(kk);
       auto [rz, iz] = z;
diff --git a/include/kyosu/types/traits.hpp b/include/kyosu/types/traits.hpp
index 161f4ae9..46b2739b 100644
--- a/include/kyosu/types/traits.hpp
+++ b/include/kyosu/types/traits.hpp
@@ -7,6 +7,7 @@
 //======================================================================================================================
 #pragma once
 
+#include <eve/as.hpp>
 #include <bit>
 
 namespace kyosu
@@ -63,11 +64,11 @@ namespace kyosu
   template<concepts::cayley_dickson T>
   inline constexpr auto dimension_v<T> = eve::element_type_t<std::remove_cvref_t<T>>::static_size;
 
-  template<typename T>                  struct as_real                          { using type = T; };
-  template<typename T,unsigned int Dim> struct as_real<cayley_dickson<T,Dim>>   { using type = T; };
-  template<typename T,typename N>       struct as_real<eve::wide<T,N>>
+  template<typename T>                  struct as_real_type                          { using type = T; };
+  template<typename T,unsigned int Dim> struct as_real_type<cayley_dickson<T,Dim>>   { using type = T; };
+  template<typename T,typename N>       struct as_real_type<eve::wide<T,N>>
   {
-    using type = eve::wide<typename as_real<T>::type,N>;
+    using type = eve::wide<typename as_real_type<T>::type,N>;
   };
 
   //====================================================================================================================
@@ -76,7 +77,7 @@ namespace kyosu
   //! @tparam T Type to convert to a real type.
   //====================================================================================================================
   template<typename T>
-  using as_real_t = typename as_real<T>::type;
+  using as_real_type_t = typename as_real_type<T>::type;
 
   template<unsigned int Dim, typename... Ts>
   struct  as_cayley_dickson_n;
@@ -127,6 +128,26 @@ namespace kyosu
   template<typename... Ts>
   using as_cayley_dickson_t = typename as_cayley_dickson<Ts...>::type;
 
+  using eve::as;
+
+  //====================================================================================================================
+  //! @struct as_real
+  //! @brief Lightweight type-wrapper of real value type
+  //!
+  //! Wraps the real type associed to `T` into a constexpr, trivially constructible empty class to optimize passing type
+  //! parameters via object instead of via template parameters.
+  //!
+  //! @tparam T Type to wrap
+  //====================================================================================================================
+  template<typename T> struct as_real
+  {
+    using type        = as_real_type_t<T>;
+    using target_type = eve::as<type>;
+
+    constexpr as_real()          noexcept {}
+    constexpr as_real(T const&)  noexcept {}
+  };
+
   //====================================================================================================================
   //!  @}
   //====================================================================================================================
diff --git a/test/unit/infra/as_cayley_dickinson.cpp b/test/unit/infra/as_cayley_dickinson.cpp
index 9a19c20f..e9cbe52a 100644
--- a/test/unit/infra/as_cayley_dickinson.cpp
+++ b/test/unit/infra/as_cayley_dickinson.cpp
@@ -8,117 +8,117 @@
 #include <kyosu/kyosu.hpp>
 #include <test.hpp>
 
-// TTS_CASE( "Check as_cayley_dickson_n<N,T> with scalar reals")
-// {
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, std::int32_t > ), kyosu::complex<float>    );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, float        > ), kyosu::complex<float>    );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, std::int64_t > ), kyosu::complex<double>   );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, double       > ), kyosu::complex<double>   );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, std::int32_t > ), kyosu::quaternion<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, float        > ), kyosu::quaternion<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, std::int64_t > ), kyosu::quaternion<double>);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, double       > ), kyosu::quaternion<double>);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, std::int32_t > ), kyosu::octonion<float>   );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, float        > ), kyosu::octonion<float>   );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, std::int64_t > ), kyosu::octonion<double>  );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, double       > ), kyosu::octonion<double>  );
-// };
+TTS_CASE( "Check as_cayley_dickson_n<N,T> with scalar reals")
+{
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, std::int32_t > ), kyosu::complex_t<float>    );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, float        > ), kyosu::complex_t<float>    );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, std::int64_t > ), kyosu::complex_t<double>   );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, double       > ), kyosu::complex_t<double>   );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, std::int32_t > ), kyosu::quaternion_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, float        > ), kyosu::quaternion_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, std::int64_t > ), kyosu::quaternion_t<double>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, double       > ), kyosu::quaternion_t<double>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, std::int32_t > ), kyosu::octonion_t<float>   );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, float        > ), kyosu::octonion_t<float>   );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, std::int64_t > ), kyosu::octonion_t<double>  );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, double       > ), kyosu::octonion_t<double>  );
+};
 
-// TTS_CASE( "Check as_cayley_dickson_n<N,T> with scalar non-reals")
-// {
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::complex<float>  > ), kyosu::complex<float>    );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::complex<double> > ), kyosu::complex<double>   );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::complex<float>  > ), kyosu::quaternion<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::complex<double> > ), kyosu::quaternion<double>);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::complex<float>  > ), kyosu::octonion<float>   );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::complex<double> > ), kyosu::octonion<double>  );
+TTS_CASE( "Check as_cayley_dickson_n<N,T> with scalar non-reals")
+{
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::complex_t<float>  > ), kyosu::complex_t<float>    );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::complex_t<double> > ), kyosu::complex_t<double>   );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::complex_t<float>  > ), kyosu::quaternion_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::complex_t<double> > ), kyosu::quaternion_t<double>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::complex_t<float>  > ), kyosu::octonion_t<float>   );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::complex_t<double> > ), kyosu::octonion_t<double>  );
 
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::quaternion<float>  > ), kyosu::complex<float>    );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::quaternion<double> > ), kyosu::complex<double>   );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::quaternion<float>  > ), kyosu::quaternion<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::quaternion<double> > ), kyosu::quaternion<double>);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::quaternion<float>  > ), kyosu::octonion<float>   );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::quaternion<double> > ), kyosu::octonion<double>  );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::quaternion_t<float>  > ), kyosu::complex_t<float>    );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::quaternion_t<double> > ), kyosu::complex_t<double>   );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::quaternion_t<float>  > ), kyosu::quaternion_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::quaternion_t<double> > ), kyosu::quaternion_t<double>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::quaternion_t<float>  > ), kyosu::octonion_t<float>   );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::quaternion_t<double> > ), kyosu::octonion_t<double>  );
 
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::octonion<float>  > ), kyosu::complex<float>    );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::octonion<double> > ), kyosu::complex<double>   );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::octonion<float>  > ), kyosu::quaternion<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::octonion<double> > ), kyosu::quaternion<double>);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::octonion<float>  > ), kyosu::octonion<float>   );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::octonion<double> > ), kyosu::octonion<double>  );
-// };
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::octonion_t<float>  > ), kyosu::complex_t<float>    );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, kyosu::octonion_t<double> > ), kyosu::complex_t<double>   );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::octonion_t<float>  > ), kyosu::quaternion_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, kyosu::octonion_t<double> > ), kyosu::quaternion_t<double>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::octonion_t<float>  > ), kyosu::octonion_t<float>   );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, kyosu::octonion_t<double> > ), kyosu::octonion_t<double>  );
+};
 
-// TTS_CASE( "Check as_cayley_dickson_n<N,Ts...> with mixed scalar")
-// {
-//   using kyosu::complex;
-//   using kyosu::quaternion;
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<float> , complex<float>> ), complex<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<float> , int           > ), complex<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<float> , std::int64_t  > ), complex<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<float> , float         > ), complex<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<float> , double        > ), complex<float> );
+TTS_CASE( "Check as_cayley_dickson_n<N,Ts...> with mixed scalar")
+{
+  using kyosu::complex_t;
+  using kyosu::quaternion_t;
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<float> , complex_t<float>> ), complex_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<float> , int           > ), complex_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<float> , std::int64_t  > ), complex_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<float> , float         > ), complex_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<float> , double        > ), complex_t<float> );
 
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<float> , complex<float>> ), complex<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, int            , complex<float>> ), complex<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, std::int64_t   , complex<float>> ), complex<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, float          , complex<float>> ), complex<float> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, double         , complex<float>> ), complex<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<float> , complex_t<float>> ), complex_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, int            , complex_t<float>> ), complex_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, std::int64_t   , complex_t<float>> ), complex_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, float          , complex_t<float>> ), complex_t<float> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, double         , complex_t<float>> ), complex_t<float> );
 
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<double>, complex<double>>), complex<double> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<double>, int           > ), complex<double> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<double>, std::int64_t  > ), complex<double> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<double>, float         > ), complex<double> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<double>, double        > ), complex<double> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<double>, complex_t<double>>), complex_t<double> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<double>, int           > ), complex_t<double> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<double>, std::int64_t  > ), complex_t<double> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<double>, float         > ), complex_t<double> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<double>, double        > ), complex_t<double> );
 
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex<double>, complex<double>> ), complex<double> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, int            , complex<double>> ), complex<double> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, std::int64_t   , complex<double>> ), complex<double> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, float          , complex<double>> ), complex<double> );
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, double         , complex<double>> ), complex<double> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, complex_t<double>, complex_t<double>> ), complex_t<double> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, int            , complex_t<double>> ), complex_t<double> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, std::int64_t   , complex_t<double>> ), complex_t<double> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, float          , complex_t<double>> ), complex_t<double> );
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, double         , complex_t<double>> ), complex_t<double> );
 
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, complex<double>, quaternion<double>> ), quaternion<double> );
-// };
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, complex_t<double>, quaternion_t<double>> ), quaternion_t<double> );
+};
 
-// TTS_CASE( "Check as_cayley_dickson_n<N,T> on SIMD reals")
-// {
-//   using eve::wide;
+TTS_CASE( "Check as_cayley_dickson_n<N,T> on SIMD reals")
+{
+  using eve::wide;
 
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<std::int32_t >> ), wide<kyosu::complex<float>    >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<float        >> ), wide<kyosu::complex<float>    >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<std::int64_t >> ), wide<kyosu::complex<double>   >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<double       >> ), wide<kyosu::complex<double>   >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<std::int32_t >> ), wide<kyosu::quaternion<float> >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<float        >> ), wide<kyosu::quaternion<float> >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<std::int64_t >> ), wide<kyosu::quaternion<double>>);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<double       >> ), wide<kyosu::quaternion<double>>);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<std::int32_t >> ), wide<kyosu::octonion<float>   >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<float        >> ), wide<kyosu::octonion<float>   >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<std::int64_t >> ), wide<kyosu::octonion<double>  >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<double       >> ), wide<kyosu::octonion<double>  >);
-// };
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<std::int32_t >> ), wide<kyosu::complex_t<float>    >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<float        >> ), wide<kyosu::complex_t<float>    >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<std::int64_t >> ), wide<kyosu::complex_t<double>   >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<double       >> ), wide<kyosu::complex_t<double>   >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<std::int32_t >> ), wide<kyosu::quaternion_t<float> >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<float        >> ), wide<kyosu::quaternion_t<float> >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<std::int64_t >> ), wide<kyosu::quaternion_t<double>>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<double       >> ), wide<kyosu::quaternion_t<double>>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<std::int32_t >> ), wide<kyosu::octonion_t<float>   >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<float        >> ), wide<kyosu::octonion_t<float>   >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<std::int64_t >> ), wide<kyosu::octonion_t<double>  >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<double       >> ), wide<kyosu::octonion_t<double>  >);
+};
 
-// TTS_CASE( "Check as_cayley_dickson_n<N,T> on SIMD non-reals")
-// {
-//   using eve::wide;
+TTS_CASE( "Check as_cayley_dickson_n<N,T> on SIMD non-reals")
+{
+  using eve::wide;
 
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::complex<float>     >> ), wide<kyosu::complex<float>  >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::complex<double>    >> ), wide<kyosu::complex<double> >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::quaternion<float>  >> ), wide<kyosu::complex<float>  >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::quaternion<double> >> ), wide<kyosu::complex<double> >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::octonion<float>    >> ), wide<kyosu::complex<float>  >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::octonion<double>   >> ), wide<kyosu::complex<double> >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::complex_t<float>     >> ), wide<kyosu::complex_t<float>  >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::complex_t<double>    >> ), wide<kyosu::complex_t<double> >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::quaternion_t<float>  >> ), wide<kyosu::complex_t<float>  >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::quaternion_t<double> >> ), wide<kyosu::complex_t<double> >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::octonion_t<float>    >> ), wide<kyosu::complex_t<float>  >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<2, wide<kyosu::octonion_t<double>   >> ), wide<kyosu::complex_t<double> >);
 
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::complex<float>     >> ), wide<kyosu::quaternion<float> >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::complex<double>    >> ), wide<kyosu::quaternion<double>>);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::quaternion<float>  >> ), wide<kyosu::quaternion<float> >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::quaternion<double> >> ), wide<kyosu::quaternion<double>>);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::octonion<float>    >> ), wide<kyosu::quaternion<float> >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::octonion<double>   >> ), wide<kyosu::quaternion<double>>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::complex_t<float>     >> ), wide<kyosu::quaternion_t<float> >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::complex_t<double>    >> ), wide<kyosu::quaternion_t<double>>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::quaternion_t<float>  >> ), wide<kyosu::quaternion_t<float> >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::quaternion_t<double> >> ), wide<kyosu::quaternion_t<double>>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::octonion_t<float>    >> ), wide<kyosu::quaternion_t<float> >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<4, wide<kyosu::octonion_t<double>   >> ), wide<kyosu::quaternion_t<double>>);
 
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::complex<float>     >> ), wide<kyosu::octonion<float> >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::complex<double>    >> ), wide<kyosu::octonion<double>>);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::quaternion<float>  >> ), wide<kyosu::octonion<float> >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::quaternion<double> >> ), wide<kyosu::octonion<double>>);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::octonion<float>    >> ), wide<kyosu::octonion<float> >);
-//   TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::octonion<double>   >> ), wide<kyosu::octonion<double>>);
-// };
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::complex_t<float>     >> ), wide<kyosu::octonion_t<float> >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::complex_t<double>    >> ), wide<kyosu::octonion_t<double>>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::quaternion_t<float>  >> ), wide<kyosu::octonion_t<float> >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::quaternion_t<double> >> ), wide<kyosu::octonion_t<double>>);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::octonion_t<float>    >> ), wide<kyosu::octonion_t<float> >);
+  TTS_TYPE_IS((kyosu::as_cayley_dickson_n_t<8, wide<kyosu::octonion_t<double>   >> ), wide<kyosu::octonion_t<double>>);
+};
diff --git a/test/unit/infra/as_real.cpp b/test/unit/infra/as_real_type.cpp
similarity index 54%
rename from test/unit/infra/as_real.cpp
rename to test/unit/infra/as_real_type.cpp
index 8382e339..a7cfde69 100644
--- a/test/unit/infra/as_real.cpp
+++ b/test/unit/infra/as_real_type.cpp
@@ -8,16 +8,16 @@
 #include <kyosu/kyosu.hpp>
 #include <test.hpp>
 
-TTS_CASE_TPL( "Check as_real behavior on real types", kyosu::real_types)
+TTS_CASE_TPL( "Check as_real_type_t behavior on real types", kyosu::real_types)
 <typename T>(tts::type<T>)
 {
-  TTS_TYPE_IS(kyosu::as_real_t<T>, T);
+  TTS_TYPE_IS(kyosu::as_real_type_t<T>, T);
 };
 
-TTS_CASE_TPL( "Check as_real behavior on non-real types", kyosu::real_types)
+TTS_CASE_TPL( "Check as_real_type_t behavior on non-real types", kyosu::real_types)
 <typename T>(tts::type<T>)
 {
-  TTS_TYPE_IS(kyosu::as_real_t<kyosu::complex_t<T>>    , T);
-  TTS_TYPE_IS(kyosu::as_real_t<kyosu::quaternion_t<T>> , T);
-  TTS_TYPE_IS(kyosu::as_real_t<kyosu::octonion_t<T>>   , T);
+  TTS_TYPE_IS(kyosu::as_real_type_t<kyosu::complex_t<T>>    , T);
+  TTS_TYPE_IS(kyosu::as_real_type_t<kyosu::quaternion_t<T>> , T);
+  TTS_TYPE_IS(kyosu::as_real_type_t<kyosu::octonion_t<T>>   , T);
 };
diff --git a/test/unit/infra/constants.cpp b/test/unit/infra/constants.cpp
new file mode 100644
index 00000000..2f65cd60
--- /dev/null
+++ b/test/unit/infra/constants.cpp
@@ -0,0 +1,50 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#include <kyosu/kyosu.hpp>
+#include <test.hpp>
+
+TTS_CASE_TPL( "Check as_real behavior on real types", kyosu::real_types)
+<typename T>(tts::type<T>)
+{
+  T x = {};
+
+  TTS_EQUAL(eve::half(kyosu::as_real<T>{}), T{0.5});
+  TTS_EQUAL(eve::half(kyosu::as_real(x)), T{0.5});
+};
+
+TTS_CASE_TPL( "Check as_real behavior on non-real types", kyosu::real_types)
+<typename T>(tts::type<T>)
+{
+  kyosu::complex_t<T>     cx = {};
+  kyosu::quaternion_t<T>  qx = {};
+  kyosu::octonion_t<T>    ox = {};
+
+  TTS_EQUAL(eve::half(kyosu::as_real<kyosu::complex_t<T>>{}), T{0.5});
+  TTS_EQUAL(eve::half(kyosu::as_real<kyosu::quaternion_t<T>>{}), T{0.5});
+  TTS_EQUAL(eve::half(kyosu::as_real<kyosu::octonion_t<T>>{}), T{0.5});
+
+  TTS_EQUAL(eve::half(kyosu::as_real(cx)), T{0.5});
+  TTS_EQUAL(eve::half(kyosu::as_real(qx)), T{0.5});
+  TTS_EQUAL(eve::half(kyosu::as_real(ox)), T{0.5});
+};
+
+TTS_CASE_TPL( "Check as behavior on non-real types", kyosu::real_types)
+<typename T>(tts::type<T>)
+{
+  kyosu::complex_t<T>     cx = {};
+  kyosu::quaternion_t<T>  qx = {};
+  kyosu::octonion_t<T>    ox = {};
+
+  TTS_EQUAL(eve::half(kyosu::as<kyosu::complex_t<T>>{})   , kyosu::complex_t<T>(0.5));
+  TTS_EQUAL(eve::half(kyosu::as<kyosu::quaternion_t<T>>{}), kyosu::quaternion_t<T>{0.5});
+  TTS_EQUAL(eve::half(kyosu::as<kyosu::octonion_t<T>>{})  , kyosu::octonion_t<T>{0.5});
+
+  TTS_EQUAL(eve::half(kyosu::as(cx)),kyosu::complex_t<T>(0.5));
+  TTS_EQUAL(eve::half(kyosu::as(qx)),kyosu::quaternion_t<T>{0.5});
+  TTS_EQUAL(eve::half(kyosu::as(ox)),kyosu::octonion_t<T>{0.5});
+};