diff --git a/include/kyosu/cayley.hpp b/include/kyosu/cayley.hpp
new file mode 100644
index 00000000..c4ea1332
--- /dev/null
+++ b/include/kyosu/cayley.hpp
@@ -0,0 +1,80 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+//======================================================================================================================
+//! @defgroup functions cayley Functions
+//! @brief Functions performing computations over all cayley-dicson types, complex, quaternions and octonions...
+//======================================================================================================================
+#include <kyosu/cayley/abs.hpp>
+#include <kyosu/cayley/ceil.hpp>
+#include <kyosu/cayley/conj.hpp>
+#include <kyosu/cayley/cos.hpp>
+#include <kyosu/cayley/cosh.hpp>
+#include <kyosu/cayley/cot.hpp>
+#include <kyosu/cayley/coth.hpp>
+#include <kyosu/cayley/convert.hpp>
+#include <kyosu/cayley/csc.hpp>
+#include <kyosu/cayley/csch.hpp>
+#include <kyosu/cayley/dec.hpp>
+#include <kyosu/cayley/dist.hpp>
+#include <kyosu/cayley/exp.hpp>
+#include <kyosu/cayley/exp2.hpp>
+#include <kyosu/cayley/exp10.hpp>
+#include <kyosu/cayley/expm1.hpp>
+#include <kyosu/cayley/expmx2.hpp>
+#include <kyosu/cayley/expx2.hpp>
+#include <kyosu/cayley/exp_i.hpp>
+#include <kyosu/cayley/exp_ipi.hpp>
+#include <kyosu/cayley/floor.hpp>
+#include <kyosu/cayley/frac.hpp>
+#include <kyosu/cayley/if_else.hpp>
+#include <kyosu/cayley/inc.hpp>
+#include <kyosu/cayley/ipart.hpp>
+#include <kyosu/cayley/is_denormal.hpp>
+#include <kyosu/cayley/is_equal.hpp>
+#include <kyosu/cayley/is_eqz.hpp>
+#include <kyosu/cayley/is_finite.hpp>
+#include <kyosu/cayley/is_infinite.hpp>
+#include <kyosu/cayley/is_nan.hpp>
+#include <kyosu/cayley/is_nez.hpp>
+#include <kyosu/cayley/is_not_denormal.hpp>
+#include <kyosu/cayley/is_not_equal.hpp>
+#include <kyosu/cayley/is_not_finite.hpp>
+#include <kyosu/cayley/is_not_infinite.hpp>
+#include <kyosu/cayley/is_not_nan.hpp>
+#include <kyosu/cayley/is_not_real.hpp>
+#include <kyosu/cayley/is_real.hpp>
+#include <kyosu/cayley/jpart.hpp>
+#include <kyosu/cayley/kpart.hpp>
+#include <kyosu/cayley/lerp.hpp>
+#include <kyosu/cayley/log.hpp>
+#include <kyosu/cayley/log1p.hpp>
+#include <kyosu/cayley/log10.hpp>
+#include <kyosu/cayley/log2.hpp>
+#include <kyosu/cayley/minus.hpp>
+#include <kyosu/cayley/nearest.hpp>
+#include <kyosu/cayley/oneminus.hpp>
+#include <kyosu/cayley/pure.hpp>
+#include <kyosu/cayley/purepart.hpp>
+#include <kyosu/cayley/real.hpp>
+#include <kyosu/cayley/rec.hpp>
+#include <kyosu/cayley/reldist.hpp>
+#include <kyosu/cayley/sec.hpp>
+#include <kyosu/cayley/sech.hpp>
+#include <kyosu/cayley/sign.hpp>
+#include <kyosu/cayley/sin.hpp>
+#include <kyosu/cayley/sincos.hpp>
+#include <kyosu/cayley/sinh.hpp>
+#include <kyosu/cayley/sinhcosh.hpp>
+#include <kyosu/cayley/sqr_abs.hpp>
+#include <kyosu/cayley/sqr.hpp>
+#include <kyosu/cayley/sqrt.hpp>
+#include <kyosu/cayley/tan.hpp>
+#include <kyosu/cayley/tanh.hpp>
+#include <kyosu/cayley/trunc.hpp>
diff --git a/include/kyosu/complex/impl/predicates.hpp b/include/kyosu/complex/impl/predicates.hpp
new file mode 100644
index 00000000..5667c272
--- /dev/null
+++ b/include/kyosu/complex/impl/predicates.hpp
@@ -0,0 +1,19 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+#include <eve/module/core.hpp>
+
+namespace kyosu::_
+{
+  template<kyosu::concepts::complex C>
+  KYOSU_FORCEINLINE constexpr
+  auto dispatch(eve::tag_of<kyosu::conj> const&, C const& c) noexcept
+  {
+    return is_eqz(kyosu::real(c));
+  }
+}
diff --git a/include/kyosu/complex/is_imag.hpp b/include/kyosu/complex/is_imag.hpp
new file mode 100644
index 00000000..f6dd8a39
--- /dev/null
+++ b/include/kyosu/complex/is_imag.hpp
@@ -0,0 +1,74 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_is_imag : eve::elementwise
+  {
+    using callable_tag_type = callable_is_imag;
+
+    KYOSU_DEFERS_CALLABLE(is_imag_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept { return eve::is_eqz(v); }
+
+    template<typename T>
+    KYOSU_FORCEINLINE auto operator()(T const& target) const noexcept -> decltype(eve::tag_invoke(*this, target))
+    {
+      return eve::tag_invoke(*this, target);
+    }
+
+    template<typename... T>
+    eve::unsupported_call<callable_is_imag(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var is_imag
+//!   @brief test if the parameter is imag.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<kyosu::concepts::complex T> constexpr auto is_imag(T z) noexcept;
+//!      template<eve::ordered_value T>       constexpr auto is_imag(T z) noexcept;
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z` : Value to process.
+//!
+//!   **Return value**
+//!
+//!     Returns elementwise true the real part of the argument is zero.
+//!     For Caley-Dickson types of dimension greater than 2 use is_pure.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/is_imag.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_is_imag is_imag = {};
+}
diff --git a/include/kyosu/functions.hpp b/include/kyosu/functions.hpp
index b5072b0c..0cc002c8 100644
--- a/include/kyosu/functions.hpp
+++ b/include/kyosu/functions.hpp
@@ -12,6 +12,7 @@
 //! @brief Functions performing computations over complex, quaternions and octonions.
 //======================================================================================================================
 #include <kyosu/functions/abs.hpp>
+#include <kyosu/functions/average.hpp>
 #include <kyosu/functions/ceil.hpp>
 #include <kyosu/functions/conj.hpp>
 #include <kyosu/functions/cos.hpp>
@@ -40,6 +41,7 @@
 #include <kyosu/functions/is_equal.hpp>
 #include <kyosu/functions/is_eqz.hpp>
 #include <kyosu/functions/is_finite.hpp>
+#include <kyosu/functions/is_imag.hpp>
 #include <kyosu/functions/is_infinite.hpp>
 #include <kyosu/functions/is_nan.hpp>
 #include <kyosu/functions/is_nez.hpp>
diff --git a/include/kyosu/functions/average.hpp b/include/kyosu/functions/average.hpp
new file mode 100644
index 00000000..d8f85591
--- /dev/null
+++ b/include/kyosu/functions/average.hpp
@@ -0,0 +1,78 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+namespace kyosu::tags
+{
+  struct callable_average : eve::elementwise
+  {
+    using callable_tag_type = callable_average;
+
+    KYOSU_DEFERS_CALLABLE(average_);
+
+    static KYOSU_FORCEINLINE auto deferred_call(auto
+                                               , eve::ordered_value auto const& v0
+                                               , eve::ordered_value auto const& v1) noexcept
+    {
+      return eve::average(v0, v1);
+    }
+
+    KYOSU_FORCEINLINE auto operator()(auto const& target0, auto const& target1) const noexcept
+    -> decltype(eve::tag_invoke(*this, target0, target1))
+    {
+      return eve::tag_invoke(*this, target0, target1);
+    }
+
+    template<typename... T>
+    eve::unsupported_call<callable_average(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var average
+//!   @brief Computes the average of the two parameters.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto average(T0 z0, T1, z1) noexcept;
+//!      template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1>             > constexpr auto average(T0 z0, T1, z1) noexcept;
+//!      template<kyosu::concepts::cayley_dickson T0,  eve::ordered_value T1             > constexpr auto average(T0 z0, T1, z1) noexcept;
+//!      template<eve::ordered_value T0, ordered_value T1>                               > constexpr auto average(T0 z0, T1, z1) noexcept;
+///!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z0, z1` : Value to process.
+//!
+//!   **Return value**
+//!
+//!     Returns the average of the two arguments .
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/average.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_average average = {};
+}
diff --git a/include/kyosu/functions/is_imag.hpp b/include/kyosu/functions/is_imag.hpp
new file mode 100644
index 00000000..33190eaf
--- /dev/null
+++ b/include/kyosu/functions/is_imag.hpp
@@ -0,0 +1,73 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_is_imag : eve::elementwise
+  {
+    using callable_tag_type = callable_is_imag;
+
+    KYOSU_DEFERS_CALLABLE(is_imag_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept { return eve::is_eqz(v); }
+
+    template<typename T>
+    KYOSU_FORCEINLINE auto operator()(T const& target) const noexcept -> decltype(eve::tag_invoke(*this, target))
+    {
+      return eve::tag_invoke(*this, target);
+    }
+
+    template<typename... T>
+    eve::unsupported_call<callable_is_imag(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var is_imag
+//!   @brief test if the complex parameter is pure imaginary.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<kyosu::concepts::cayley_dickson T> constexpr auto is_imag(T z) noexcept;
+//!      template<eve::ordered_value T>              constexpr auto is_imag(T z) noexcept;
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z` : Value to process.
+//!
+//!   **Return value**
+//!
+//!     Returns the value of real(z) == 0.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/is_imag.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_is_imag is_imag = {};
+}
diff --git a/include/kyosu/types/cayley_dickson.hpp b/include/kyosu/types/cayley_dickson.hpp
index 69487e50..6ab99347 100644
--- a/include/kyosu/types/cayley_dickson.hpp
+++ b/include/kyosu/types/cayley_dickson.hpp
@@ -15,6 +15,7 @@
 #include <kyosu/types/impl/predicates.hpp>
 #include <kyosu/types/impl/math.hpp>
 #include <kyosu/types/impl/trigo.hpp>
+#include <kyosu/types/impl/complex/predicates.hpp>
 #include <bit>
 
 namespace kyosu
@@ -99,16 +100,6 @@ namespace kyosu
       return that;
     }
 
-    //==================================================================================================================
-    // Main function dispatchers
-    //==================================================================================================================
-    KYOSU_FORCEINLINE
-    friend constexpr auto tag_invoke(eve::callable auto const& f, auto, eve::like<cayley_dickson> auto&&... c) noexcept
-                  -> decltype(_::dispatch(f, KYOSU_FWD(c)...))
-    {
-      return _::dispatch(f, KYOSU_FWD(c)...);
-    }
-
     //==================================================================================================================
     //  Tuple-like behavior
     //==================================================================================================================
@@ -126,6 +117,17 @@ 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
+                  ->  decltype(_::dispatch(f, KYOSU_FWD(c)...))
+  {
+    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
   //==================================================================================================================
@@ -148,7 +150,6 @@ namespace kyosu
     return _::dispatch(f, c, tgt);
   }
 
-
   //==================================================================================================================
   //  Tag invoke override for parts extraction - Outside so they can see get<I>(c)
   //==================================================================================================================
diff --git a/include/kyosu/types/impl/arithmetic.hpp b/include/kyosu/types/impl/arithmetic.hpp
index 58914280..72d6cf7e 100644
--- a/include/kyosu/types/impl/arithmetic.hpp
+++ b/include/kyosu/types/impl/arithmetic.hpp
@@ -9,7 +9,7 @@
 
 #include <eve/module/core.hpp>
 #include <eve/module/math.hpp>
-
+#include <iostream>
 namespace kyosu::_
 {
   template<typename C>
@@ -119,17 +119,21 @@ namespace kyosu::_
     }
   }
 
-  template<concepts::cayley_dickson  C0, concepts::cayley_dickson  C1>
+  template<typename  C0, typename  C1>
   KYOSU_FORCEINLINE constexpr
   auto dispatch(eve::tag_of<kyosu::dist> const&, C0 const & c0, C1 const &  c1) noexcept
   {
     return kyosu::abs(c0-c1);
   }
 
-  template<concepts::cayley_dickson  C0, concepts::cayley_dickson  C1>
+  template<typename  C0, typename  C1>
   KYOSU_FORCEINLINE constexpr
   auto dispatch(eve::tag_of<kyosu::reldist> const&, C0 const & c0, C1 const & c1) noexcept
   {
+//     using r_t = kyosu::as_cayley_dickson_t<C0,C1>;
+//     using er_t = eve::element_type_t<r_t>;
+//     auto cc0 = kyosu::convert(c0, eve::as<er_t>());
+//     auto cc1 = kyosu::convert(c1, eve::as<er_t>());
     return kyosu::dist(c0, c1)/eve::max(kyosu::abs(c0), kyosu::abs(c1), eve::one(eve::as(abs(c0))));
   }
 
@@ -201,4 +205,19 @@ namespace kyosu::_
   {
     return kyosu::if_else(kyosu::is_nez(c), c/abs(c), C(0));
   }
+
+  template<typename  C0, typename  C1>
+  KYOSU_FORCEINLINE constexpr
+  auto dispatch(eve::tag_of<kyosu::average> const&, C0 const & c0, C1 const &  c1) noexcept
+  {
+    using r_t = kyosu::as_cayley_dickson_t<C0,C1>;
+    using er_t = eve::element_type_t<r_t>;
+    return r_t{kumi::map([](auto const& e, auto const& f) { return eve::average(e, f); }
+                         , kyosu::convert(c0, eve::as<er_t>())
+                         , kyosu::convert(c1, eve::as<er_t>())
+                        )
+        };
+  }
+
+
 }
diff --git a/include/kyosu/types/impl/complex/predicates.hpp b/include/kyosu/types/impl/complex/predicates.hpp
new file mode 100644
index 00000000..9398fbcc
--- /dev/null
+++ b/include/kyosu/types/impl/complex/predicates.hpp
@@ -0,0 +1,21 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <eve/module/core.hpp>
+
+namespace kyosu::_
+{
+  template<kyosu::concepts::complex C>
+  KYOSU_FORCEINLINE constexpr
+  auto dispatch(eve::tag_of<kyosu::is_imag> const&, C const& c) noexcept
+  {
+    return eve::is_eqz(kyosu::real(c));
+  }
+
+}
diff --git a/include/kyosu/types/impl/trigo.hpp b/include/kyosu/types/impl/trigo.hpp
index 60ac6b15..a2c3d651 100644
--- a/include/kyosu/types/impl/trigo.hpp
+++ b/include/kyosu/types/impl/trigo.hpp
@@ -35,7 +35,7 @@ namespace kyosu::_
     else
     {
       auto e = kyosu::exp(z);
-      return eve::average(e, rec(e));
+      return kyosu::average(e, rec(e));
     }
   }
 
diff --git a/test/doc/average.cpp b/test/doc/average.cpp
new file mode 100644
index 00000000..0e579556
--- /dev/null
+++ b/test/doc/average.cpp
@@ -0,0 +1,51 @@
+#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+
+int main()
+{
+  using kyosu::average;
+  using kyosu::complex;
+  using kyosu::quaternion;
+  using e_t = float;
+  using c_t = complex<float>;
+  using q_t = quaternion<float>;
+  using we_t = eve::wide<float, eve::fixed<2>>;
+  using wc_t = eve::wide<complex<float>, eve::fixed<2>>;
+  using wq_t = eve::wide<quaternion<float>, eve::fixed<2>>;
+
+  std::cout << "Real:        "<< "\n";
+  e_t e0(1);
+  e_t e1(2);
+  std::cout << e0 << ", " << e1 << " -> "  << average(e0, e1) << "\n";
+  std::cout << e0 << ", " << e0 << " -> "  << average(e0, e0) << "\n";
+  we_t we0(e0);
+  we_t we1(e1);
+  std::cout << we0 << ", " << we1 << " -> " << average(we0, we1) << "\n";
+
+  std::cout << "Complex:     "<< "\n";
+  c_t c0(1, 5);
+  c_t c1(5, 9);
+  std::cout << c0 << ", " << c1 << " -> "  << average(c0, c1) << "\n";
+  std::cout << c0 << ", " << c0 << " -> "  << average(c0, c0) << "\n";
+  wc_t wc0(c0, c1);
+  wc_t wc1(c1, c1);
+  std::cout << wc0 << ", " << wc1 << " -> " << average(wc0, wc1) << "\n";
+
+  std::cout << "Quaternion:  "<< "\n";
+  q_t q0(1, 5, 2, 3);
+  q_t q1(5, 9, 6, 7);
+  std::cout << q0 << ", " << q1 << " -> "  << average(q0, q1) << "\n";
+  std::cout << q0 << ", " << q0 << " -> "  << average(q0, q0) << "\n";
+  wq_t wq0(q0, q1);
+  wq_t wq1(q1, q1);
+  std::cout << wq0 << ", " << wq1 << " -> " << average(wq0, wq1) << "\n";
+
+  std::cout << "Mixed:  "<< "\n";
+  std::cout << kyosu::average(c0, q1) << std::endl;
+  std::cout << kyosu::average(e0, q1) << std::endl;
+  std::cout << kyosu::average(c0, wq1) << std::endl;
+  std::cout << kyosu::average(we0, q1) << std::endl;
+
+  return 0;
+}
diff --git a/test/doc/dist.cpp b/test/doc/dist.cpp
index 7db417d4..c10b2fde 100644
--- a/test/doc/dist.cpp
+++ b/test/doc/dist.cpp
@@ -37,6 +37,8 @@ int main()
   wq_t wq0(q0);
   wq_t wq1(q1);
   std::cout << wq0 << ", " << wq1 << " -> " << dist(wq0, wq1) << "\n";
+  std::cout << wq0 << ", " << q1 << " -> " << dist(wq0, q1) << "\n";
+  std::cout << wq0 << ", " << e1 << " -> " << dist(wq0, e1) << "\n";
 
   return 0;
 }
diff --git a/test/doc/reldist.cpp b/test/doc/reldist.cpp
index 6ebc78c5..20e7a96c 100644
--- a/test/doc/reldist.cpp
+++ b/test/doc/reldist.cpp
@@ -37,6 +37,8 @@ int main()
   wq_t wq0(q0);
   wq_t wq1(q1);
   std::cout << wq0 << ", " << wq1 << " -> " << reldist(wq0, wq1) << "\n";
+  std::cout << wq0 << ", " << q1 << " -> " << reldist(wq0, q1) << "\n";
+  std::cout << wq0 << ", " << e1 << " -> " << reldist(wq0, e1) << "\n";
 
   return 0;
 }
diff --git a/test/unit/complex/is_imag.cpp b/test/unit/complex/is_imag.cpp
new file mode 100644
index 00000000..7b8a49d0
--- /dev/null
+++ b/test/unit/complex/is_imag.cpp
@@ -0,0 +1,44 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#include <kyosu/kyosu.hpp>
+#include <test.hpp>
+#include <complex>
+
+template < typename T >
+auto cv(std::complex < T > const &sc)
+{
+  return kyosu::to_complex(sc.real(), sc.imag());
+}
+
+TTS_CASE_WITH( "Check behavior of cos on scalar"
+        , tts::bunch<kyosu::scalar_real_types>
+        , tts::generate( tts::randoms(-10, 10), tts::randoms(-10, 10))
+        )
+  <typename T>(T const& a0, T const& a1 )
+{
+  using e_t = typename T::value_type;
+  using kc_t = kyosu::as_complex_t<e_t>;
+  for(size_t i = 0; i < a0.size(); ++i)
+  {
+    auto e = a0[i];
+    auto f = a1[i];
+    auto z = kc_t(e, f);
+    TTS_EQUAL(kyosu::is_imag(z), eve::is_eqz(kyosu::real(z)));
+  }
+};
+
+TTS_CASE_WITH( "Check behavior of cos on wide"
+             , kyosu::simd_real_types
+             , tts::generate( tts::between(-10, 10)
+                            , tts::between(-10, 10))
+             )
+  <typename T>(T const& a0, T const& a1 )
+{
+  auto z = kyosu::to_complex(a0, a1);
+  TTS_EQUAL(kyosu::is_imag(z), eve::is_eqz(kyosu::real(z)));
+};