From d1fc657c1fe7b4ad70452cb37b13a377fa831e56 Mon Sep 17 00:00:00 2001
From: bolero-MURAKAMI <bolero.murakami@gmail.com>
Date: Fri, 18 Apr 2014 19:33:48 +0900
Subject: [PATCH] fix fft implementation

---
 sprout/complex.hpp             |  1 +
 sprout/complex/complex.hpp     |  6 ++---
 sprout/complex/type_traits.hpp | 42 ++++++++++++++++++++++++++++++++++
 sprout/complex/values.hpp      |  4 ++--
 sprout/numeric/fft/fft.hpp     | 36 +++++++++++++++++++----------
 5 files changed, 72 insertions(+), 17 deletions(-)
 create mode 100644 sprout/complex/type_traits.hpp

diff --git a/sprout/complex.hpp b/sprout/complex.hpp
index ebf8decf..2bc5f937 100644
--- a/sprout/complex.hpp
+++ b/sprout/complex.hpp
@@ -16,5 +16,6 @@
 #include <sprout/complex/hash.hpp>
 #include <sprout/complex/nearest.hpp>
 #include <sprout/complex/udl.hpp>
+#include <sprout/complex/type_traits.hpp>
 
 #endif	// #ifndef SPROUT_COMPLEX_HPP
diff --git a/sprout/complex/complex.hpp b/sprout/complex/complex.hpp
index 0edd5509..3c05d066 100644
--- a/sprout/complex/complex.hpp
+++ b/sprout/complex/complex.hpp
@@ -15,9 +15,9 @@ namespace sprout {
 	class complex;
 
 	namespace detail {
-		template<typename T>
-		inline SPROUT_CONSTEXPR T
-		complex_norm(sprout::complex<T> const& x) {
+		template<typename Complex>
+		inline SPROUT_CONSTEXPR typename Complex::value_type
+		complex_norm(Complex const& x) {
 			return x.real() * x.real() + x.imag() * x.imag();
 		}
 	}	// namespace detail
diff --git a/sprout/complex/type_traits.hpp b/sprout/complex/type_traits.hpp
new file mode 100644
index 00000000..0ad74b3e
--- /dev/null
+++ b/sprout/complex/type_traits.hpp
@@ -0,0 +1,42 @@
+/*=============================================================================
+  Copyright (c) 2011-2014 Bolero MURAKAMI
+  https://github.com/bolero-MURAKAMI/Sprout
+
+  Distributed under the Boost Software License, Version 1.0. (See accompanying
+  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================*/
+#ifndef SPROUT_COMPLEX_TYPE_TRAITS_HPP
+#define SPROUT_COMPLEX_TYPE_TRAITS_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/complex/complex.hpp>
+#include <sprout/type_traits/integral_constant.hpp>
+
+namespace sprout {
+	//
+	// is_complex
+	//
+	template<typename T>
+	struct is_complex
+		: public sprout::false_type
+	{};
+	template<typename T>
+	struct is_complex<T const>
+		: public sprout::is_complex<T>
+	{};
+	template<typename T>
+	struct is_complex<T const volatile>
+		: public sprout::is_complex<T>
+	{};
+	template<typename T>
+	struct is_complex<sprout::complex<T> >
+		: public sprout::true_type
+	{};
+
+#if SPROUT_USE_VARIABLE_TEMPLATES
+	template<typename T>
+	SPROUT_STATIC_CONSTEXPR bool is_complex_v = sprout::is_complex<T>::value;
+#endif	// #if SPROUT_USE_VARIABLE_TEMPLATES
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_COMPLEX_TYPE_TRAITS_HPP
diff --git a/sprout/complex/values.hpp b/sprout/complex/values.hpp
index 7a41dc5c..2d8aaec2 100644
--- a/sprout/complex/values.hpp
+++ b/sprout/complex/values.hpp
@@ -33,12 +33,12 @@ namespace sprout {
 		return x.imag();
 	}
 	template<typename T>
-	inline SPROUT_CXX14_CONSTEXPR T&
+	inline SPROUT_CONSTEXPR T&
 	real(sprout::complex<T>& x) {
 		return x.real();
 	}
 	template<typename T>
-	inline SPROUT_CXX14_CONSTEXPR T&
+	inline SPROUT_CONSTEXPR T&
 	imag(sprout::complex<T>& x) {
 		return x.imag();
 	}
diff --git a/sprout/numeric/fft/fft.hpp b/sprout/numeric/fft/fft.hpp
index e4224dc4..3448d757 100644
--- a/sprout/numeric/fft/fft.hpp
+++ b/sprout/numeric/fft/fft.hpp
@@ -51,10 +51,14 @@ namespace sprout {
 					first[j] += first[j1];
 					value_type x3 = first[j3] - first[j2];
 					first[j2] += first[j3];
-					real(first[j1]) = real(x1) - imag(x3);
-					imag(first[j1]) = imag(x1) + real(x3);
-					real(first[j3]) = real(x1) + imag(x3);
-					imag(first[j3]) = imag(x1) - real(x3);
+					first[j1] = value_type(
+						real(x1) - imag(x3),
+						imag(x1) + real(x3)
+						);
+					first[j3] = value_type(
+						real(x1) + imag(x3),
+						imag(x1) - real(x3)
+						);
 				}
 			}
 			if (m == size) {
@@ -73,12 +77,16 @@ namespace sprout {
 					first[j2] += first[j3];
 					elem_type x0r = real(x1) - imag(x3);
 					elem_type x0i = imag(x1) + real(x3);
-					real(first[j1]) = w1r * (x0r + x0i);
-					imag(first[j1]) = w1r * (x0i - x0r);
+					first[j1] = value_type(
+						w1r * (x0r + x0i),
+						w1r * (x0i - x0r)
+						);
 					x0r = real(x1) + imag(x3);
 					x0i = imag(x1) - real(x3);
-					real(first[j3]) = w1r * (-x0r + x0i);
-					imag(first[j3]) = w1r * (-x0i - x0r);
+					first[j3] = value_type(
+						w1r * (-x0r + x0i),
+						w1r * (-x0i - x0r)
+						);
 				}
 			}
 			for (difference_type i = 2 * m; i < size; i += m) {
@@ -99,12 +107,16 @@ namespace sprout {
 						first[j2] += first[j3];
 						elem_type x0r = real(x1) - imag(x3);
 						elem_type x0i = imag(x1) + real(x3);
-						real(first[j1]) = w1r * x0r - w1i * x0i;
-						imag(first[j1]) = w1r * x0i + w1i * x0r;
+						first[j1] = value_type(
+							w1r * x0r - w1i * x0i,
+							w1r * x0i + w1i * x0r
+							);
 						x0r = real(x1) + imag(x3);
 						x0i = imag(x1) - real(x3);
-						real(first[j3]) = w3r * x0r - w3i * x0i;
-						imag(first[j3]) = w3r * x0i + w3i * x0r;
+						first[j3] = value_type(
+							w3r * x0r - w3i * x0i,
+							w3r * x0i + w3i * x0r
+							);
 					}
 				}
 			}