add compost dft, spectrum, etc

sprout/compost.hpp

@@ -6,6 +6,8 @@
 #include <sprout/compost/effects.hpp>
 #include <sprout/compost/formats.hpp>
 #include <sprout/compost/ranges.hpp>
+#include <sprout/compost/analyses.hpp>
+#include <sprout/compost/utility.hpp>
 #include <sprout/compost/sources.hpp>
 
 #endif	// #ifndef SPROUT_COMPOST_HPP

sprout/compost/analyses.hpp

@@ -0,0 +1,10 @@
+#ifndef SPROUT_COMPOST_ANALYSES_HPP
+#define SPROUT_COMPOST_ANALYSES_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/compost/analyses/dft.hpp>
+#include <sprout/compost/analyses/idft.hpp>
+#include <sprout/compost/analyses/amplitude_spectrum.hpp>
+#include <sprout/compost/analyses/phase_spectrum.hpp>
+
+#endif	// #ifndef SPROUT_COMPOST_ANALYSES_HPP

sprout/compost/analyses/amplitude_spectrum.hpp

@@ -0,0 +1,20 @@
+#ifndef SPROUT_COMPOST_ANALYSES_AMPLITUDE_SPECTRUM_HPP
+#define SPROUT_COMPOST_ANALYSES_AMPLITUDE_SPECTRUM_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/range/adaptor/amplitude_spectrum.hpp>
+
+namespace sprout {
+	namespace compost {
+		namespace analyses {
+			//
+			// amplitude_spectrum
+			//
+			using sprout::adaptors::amplitude_spectrum;
+		}	// namespace analyses
+
+		using sprout::compost::analyses::amplitude_spectrum;
+	}	// namespace compost
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_COMPOST_ANALYSES_AMPLITUDE_SPECTRUM_HPP

sprout/compost/analyses/dft.hpp

@@ -0,0 +1,20 @@
+#ifndef SPROUT_COMPOST_ANALYSES_DFT_HPP
+#define SPROUT_COMPOST_ANALYSES_DFT_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/range/adaptor/dft.hpp>
+
+namespace sprout {
+	namespace compost {
+		namespace analyses {
+			//
+			// dft
+			//
+			using sprout::adaptors::dft;
+		}	// namespace analyses
+
+		using sprout::compost::analyses::dft;
+	}	// namespace compost
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_COMPOST_ANALYSES_DFT_HPP

sprout/compost/analyses/idft.hpp

@@ -0,0 +1,20 @@
+#ifndef SPROUT_COMPOST_ANALYSES_IDFT_HPP
+#define SPROUT_COMPOST_ANALYSES_IDFT_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/range/adaptor/idft.hpp>
+
+namespace sprout {
+	namespace compost {
+		namespace analyses {
+			//
+			// idft
+			//
+			using sprout::adaptors::idft;
+		}	// namespace analyses
+
+		using sprout::compost::analyses::idft;
+	}	// namespace compost
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_COMPOST_ANALYSES_IDFT_HPP

sprout/compost/analyses/phase_spectrum.hpp

@@ -0,0 +1,20 @@
+#ifndef SPROUT_COMPOST_ANALYSES_PHASE_SPECTRUM_HPP
+#define SPROUT_COMPOST_ANALYSES_PHASE_SPECTRUM_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/range/adaptor/phase_spectrum.hpp>
+
+namespace sprout {
+	namespace compost {
+		namespace analyses {
+			//
+			// phase_spectrum
+			//
+			using sprout::adaptors::phase_spectrum;
+		}	// namespace analyses
+
+		using sprout::compost::analyses::phase_spectrum;
+	}	// namespace compost
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_COMPOST_ANALYSES_PHASE_SPECTRUM_HPP

sprout/compost/formats.hpp

@@ -9,5 +9,8 @@
 #include <sprout/compost/formats/effected_each.hpp>
 #include <sprout/compost/formats/effected_left.hpp>
 #include <sprout/compost/formats/effected_right.hpp>
+#include <sprout/compost/formats/as_complex.hpp>
+#include <sprout/compost/formats/as_real.hpp>
+#include <sprout/compost/formats/as_imag.hpp>
 
 #endif	// #ifndef SPROUT_COMPOST_FORMATS_HPP

sprout/compost/formats/as_complex.hpp

@@ -0,0 +1,56 @@
+#ifndef SPROUT_COMPOST_FORMATS_AS_COMPLEX_HPP
+#define SPROUT_COMPOST_FORMATS_AS_COMPLEX_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/complex.hpp>
+#include <sprout/utility/forward.hpp>
+#include <sprout/range/adaptor/transformed.hpp>
+
+namespace sprout {
+	namespace compost {
+		//
+		// to_complex_value
+		//
+		struct to_complex_value {
+		public:
+			template<typename FloatType>
+			SPROUT_CONSTEXPR sprout::complex<FloatType> operator()(FloatType const& x) const {
+				return sprout::complex<FloatType>(x);
+			}
+		};
+
+		namespace formats {
+			//
+			// as_complex_forwarder
+			//
+			class as_complex_forwarder {};
+
+			//
+			// as_complex
+			//
+			namespace {
+				SPROUT_STATIC_CONSTEXPR sprout::compost::formats::as_complex_forwarder as_complex{};
+			}	// anonymous-namespace
+
+			//
+			// operator|
+			//
+			template<typename Range>
+			inline SPROUT_CONSTEXPR auto
+			operator|(Range&& lhs, sprout::compost::formats::as_complex_forwarder const& rhs)
+			-> decltype(
+				sprout::forward<Range>(lhs)
+					| sprout::adaptors::transformed(sprout::compost::to_complex_value())
+				)
+			{
+				return sprout::forward<Range>(lhs)
+					| sprout::adaptors::transformed(sprout::compost::to_complex_value())
+					;
+			}
+		}	// namespace formats
+
+		using sprout::compost::formats::as_complex;
+	}	// namespace compost
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_COMPOST_FORMATS_AS_COMPLEX_HPP

sprout/compost/formats/as_imag.hpp

@@ -0,0 +1,57 @@
+#ifndef SPROUT_COMPOST_FORMATS_AS_IMAG_HPP
+#define SPROUT_COMPOST_FORMATS_AS_IMAG_HPP
+
+#include <utility>
+#include <sprout/config.hpp>
+#include <sprout/complex.hpp>
+#include <sprout/utility/forward.hpp>
+#include <sprout/range/adaptor/transformed.hpp>
+
+namespace sprout {
+	namespace compost {
+		//
+		// to_imag_value
+		//
+		struct to_imag_value {
+		public:
+			template<typename Complex>
+			SPROUT_CONSTEXPR decltype(imag(std::declval<Complex const&>())) operator()(Complex const& x) const {
+				return imag(x);
+			}
+		};
+
+		namespace formats {
+			//
+			// as_imag_forwarder
+			//
+			class as_imag_forwarder {};
+
+			//
+			// as_imag
+			//
+			namespace {
+				SPROUT_STATIC_CONSTEXPR sprout::compost::formats::as_imag_forwarder as_imag{};
+			}	// anonymous-namespace
+
+			//
+			// operator|
+			//
+			template<typename Range>
+			inline SPROUT_CONSTEXPR auto
+			operator|(Range&& lhs, sprout::compost::formats::as_imag_forwarder const& rhs)
+			-> decltype(
+				sprout::forward<Range>(lhs)
+					| sprout::adaptors::transformed(sprout::compost::to_imag_value())
+				)
+			{
+				return sprout::forward<Range>(lhs)
+					| sprout::adaptors::transformed(sprout::compost::to_imag_value())
+					;
+			}
+		}	// namespace formats
+
+		using sprout::compost::formats::as_imag;
+	}	// namespace compost
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_COMPOST_FORMATS_AS_IMAG_HPP

sprout/compost/formats/as_real.hpp

@@ -0,0 +1,57 @@
+#ifndef SPROUT_COMPOST_FORMATS_AS_REAL_HPP
+#define SPROUT_COMPOST_FORMATS_AS_REAL_HPP
+
+#include <utility>
+#include <sprout/config.hpp>
+#include <sprout/complex.hpp>
+#include <sprout/utility/forward.hpp>
+#include <sprout/range/adaptor/transformed.hpp>
+
+namespace sprout {
+	namespace compost {
+		//
+		// to_real_value
+		//
+		struct to_real_value {
+		public:
+			template<typename Complex>
+			SPROUT_CONSTEXPR decltype(real(std::declval<Complex const&>())) operator()(Complex const& x) const {
+				return real(x);
+			}
+		};
+
+		namespace formats {
+			//
+			// as_real_forwarder
+			//
+			class as_real_forwarder {};
+
+			//
+			// as_real
+			//
+			namespace {
+				SPROUT_STATIC_CONSTEXPR sprout::compost::formats::as_real_forwarder as_real{};
+			}	// anonymous-namespace
+
+			//
+			// operator|
+			//
+			template<typename Range>
+			inline SPROUT_CONSTEXPR auto
+			operator|(Range&& lhs, sprout::compost::formats::as_real_forwarder const& rhs)
+			-> decltype(
+				sprout::forward<Range>(lhs)
+					| sprout::adaptors::transformed(sprout::compost::to_real_value())
+				)
+			{
+				return sprout::forward<Range>(lhs)
+					| sprout::adaptors::transformed(sprout::compost::to_real_value())
+					;
+			}
+		}	// namespace formats
+
+		using sprout::compost::formats::as_real;
+	}	// namespace compost
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_COMPOST_FORMATS_AS_REAL_HPP

sprout/compost/utility.hpp

@@ -0,0 +1,7 @@
+#ifndef SPROUT_COMPOST_UTILITY_HPP
+#define SPROUT_COMPOST_UTILITY_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/compost/utility/equal_temperament.hpp>
+
+#endif	// #ifndef SPROUT_COMPOST_UTILITY_HPP

sprout/compost/utility/equal_temperament.hpp

@@ -0,0 +1,28 @@
+#ifndef SPROUT_COMPOST_UTILITY_EQUAL_TEMPERAMENT_HPP
+#define SPROUT_COMPOST_UTILITY_EQUAL_TEMPERAMENT_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/math/pow.hpp>
+#include <sprout/type_traits/float_promote.hpp>
+
+namespace sprout {
+	namespace compost {
+		//
+		// equal_temperament_value
+		//
+		template<typename ArithmeticType1, typename ArithmeticType2>
+		SPROUT_CONSTEXPR typename sprout::float_promote<ArithmeticType1, ArithmeticType2>::type
+		equal_temperament_value(ArithmeticType1 i, ArithmeticType2 div) {
+			typedef typename sprout::float_promote<ArithmeticType1, ArithmeticType2>::type type;
+			using sprout::pow;
+			return pow(type(2), type(i) / type(div));
+		}
+		template<typename ArithmeticType>
+		SPROUT_CONSTEXPR typename sprout::float_promote<ArithmeticType, int>::type
+		equal_temperament_value(ArithmeticType i) {
+			return sprout::compost::equal_temperament_value(i, 12);
+		}
+	}	// namespace compost
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_COMPOST_UTILITY_EQUAL_TEMPERAMENT_HPP

sprout/functional/mem_fn.hpp

@@ -48,7 +48,7 @@ namespace sprout {
 	private:
 		typedef Res (Class::*functor)(Args...);
 	private:
-		functor pmf_;
+		Res (Class::*pmf_)(Args...);
 	private:
 		template<typename T>
 		Res call(T& object, Class const volatile*, Args... args) const {
@@ -59,7 +59,7 @@ namespace sprout {
 			return ((*ptr).*pmf_)(sprout::forward<Args>(args)...);
 		}
 	public:
-		explicit SPROUT_CONSTEXPR mem_fn_adaptor(functor pmf)
+		explicit SPROUT_CONSTEXPR mem_fn_adaptor(Res (Class::*pmf)(Args...))
 			: pmf_(pmf)
 		{}
 		Res operator()(Class& object, Args... args) const {
@@ -82,7 +82,7 @@ namespace sprout {
 	private:
 		typedef Res (Class::*functor)(Args...) const;
 	private:
-		functor pmf_;
+		Res (Class::*pmf_)(Args...) const;
 	private:
 		template<typename T>
 		SPROUT_CONSTEXPR Res call(T const& object, Class const volatile*, Args... args) const {
@@ -93,7 +93,7 @@ namespace sprout {
 			return ((*ptr).*pmf_)(sprout::forward<Args>(args)...);
 		}
 	public:
-		explicit SPROUT_CONSTEXPR mem_fn_adaptor(functor pmf)
+		explicit SPROUT_CONSTEXPR mem_fn_adaptor(Res (Class::*pmf)(Args...) const)
 			: pmf_(pmf)
 		{}
 		SPROUT_CONSTEXPR Res operator()(Class const& object, Args... args) const {
@@ -116,7 +116,7 @@ namespace sprout {
 	private:
 		typedef Res (Class::*functor)(Args...) volatile;
 	private:
-		functor pmf_;
+		Res (Class::*pmf_)(Args...) volatile;
 	private:
 		template<typename T>
 		Res call(T& object, Class const volatile*, Args... args) const {
@@ -127,7 +127,7 @@ namespace sprout {
 			return ((*ptr).*pmf_)(sprout::forward<Args>(args)...);
 		}
 	public:
-		explicit SPROUT_CONSTEXPR mem_fn_adaptor(functor pmf)
+		explicit SPROUT_CONSTEXPR mem_fn_adaptor(Res (Class::*pmf)(Args...) volatile)
 			: pmf_(pmf)
 		{}
 		Res operator()(Class volatile& object, Args... args) const {
@@ -150,7 +150,7 @@ namespace sprout {
 	private:
 		typedef Res (Class::*functor)(Args...) const volatile;
 	private:
-		functor pmf_;
+		Res (Class::*pmf_)(Args...) const volatile;
 	private:
 		template<typename T>
 		SPROUT_CONSTEXPR Res call(T const& object, Class const volatile*, Args... args) const {
@@ -161,7 +161,7 @@ namespace sprout {
 			return ((*ptr).*pmf_)(sprout::forward<Args>(args)...);
 		}
 	public:
-		explicit SPROUT_CONSTEXPR mem_fn_adaptor(functor pmf)
+		explicit SPROUT_CONSTEXPR mem_fn_adaptor(Res (Class::*pmf)(Args...) const volatile)
 			: pmf_(pmf)
 		{}
 		SPROUT_CONSTEXPR Res operator()(Class const volatile& object, Args... args) const {

sprout/iterator/clamp_iterator.hpp

@@ -34,14 +34,14 @@ namespace sprout {
 		typedef typename std::iterator_traits<iterator_type>::reference reference;
 	protected:
 		iterator_type current;
-		compare_type comp;
+		Compare comp;
 		value_type low;
 		value_type up;
 	private:
 		public:
 		clamp_iterator() = default;
 		clamp_iterator(clamp_iterator const&) = default;
-		SPROUT_CONSTEXPR clamp_iterator(iterator_type it, value_type const& low, value_type const& up, compare_type comp = compare_type())
+		SPROUT_CONSTEXPR clamp_iterator(iterator_type it, value_type const& low, value_type const& up, Compare comp = Compare())
 			: current(it), comp(comp), low(low), up(up)
 		{}
 		template<typename U, typename V>
@@ -57,7 +57,7 @@ namespace sprout {
 		SPROUT_CONSTEXPR iterator_type const& base() const {
 			return current;
 		}
-		SPROUT_CONSTEXPR compare_type const& compare() const {
+		SPROUT_CONSTEXPR Compare const& compare() const {
 			return comp;
 		}
 		SPROUT_CONSTEXPR value_type const& lower() const {

sprout/iterator/dft.hpp

@@ -0,0 +1,8 @@
+#ifndef SPROUT_ITERATOR_DFT_HPP
+#define SPROUT_ITERATOR_DFT_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/iterator/dft_iterator.hpp>
+#include <sprout/iterator/idft_iterator.hpp>
+
+#endif	// #ifndef SPROUT_ITERATOR_DFT_HPP

sprout/iterator/dft_iterator.hpp

@@ -0,0 +1,213 @@
+#ifndef SPROUT_ITERATOR_DFT_ITERATOR_HPP
+#define SPROUT_ITERATOR_DFT_ITERATOR_HPP
+
+#include <iterator>
+#include <utility>
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/iterator/next.hpp>
+#include <sprout/iterator/prev.hpp>
+#include <sprout/iterator/distance.hpp>
+#include <sprout/utility/swap.hpp>
+#include <sprout/numeric/dft/dft_element.hpp>
+#include HDR_ITERATOR_SSCRISK_CEL_OR_SPROUT
+
+namespace sprout {
+	//
+	// dft_iterator
+	//
+	template<typename Iterator>
+	class dft_iterator
+		: public std::iterator<
+			std::random_access_iterator_tag,
+			typename std::iterator_traits<Iterator>::value_type,
+			typename std::iterator_traits<Iterator>::difference_type,
+			void,
+			typename std::iterator_traits<Iterator>::value_type
+		>
+	{
+	private:
+		typedef std::iterator<
+			std::random_access_iterator_tag,
+			typename std::iterator_traits<Iterator>::value_type,
+			typename std::iterator_traits<Iterator>::difference_type,
+			void,
+			typename std::iterator_traits<Iterator>::value_type
+		> base_type;
+	public:
+		typedef Iterator iterator_type;
+		typedef typename base_type::iterator_category iterator_category;
+		typedef typename base_type::value_type value_type;
+		typedef typename base_type::difference_type difference_type;
+		typedef typename base_type::pointer pointer;
+		typedef typename base_type::reference reference;
+	private:
+		iterator_type first_;
+		iterator_type last_;
+		difference_type index_;
+		difference_type size_;
+	private:
+		SPROUT_CONSTEXPR dft_iterator(iterator_type first, iterator_type last, difference_type index, difference_type size)
+			: first_(first), last_(last), index_(index)
+			, size_(size)
+		{}
+	public:
+		SPROUT_CONSTEXPR dft_iterator()
+			: first_(), last_(), index_()
+			, size_()
+		{}
+		dft_iterator(dft_iterator const&) = default;
+		SPROUT_CONSTEXPR dft_iterator(iterator_type first, iterator_type last, difference_type index = 0)
+			: first_(first), last_(last), index_(index)
+			, size_(NS_SSCRISK_CEL_OR_SPROUT::distance(first, last))
+		{}
+		SPROUT_CONSTEXPR dft_iterator next() const {
+			return dft_iterator(first_, last_, index_, index_ + 1, size_);
+		}
+		SPROUT_CONSTEXPR dft_iterator prev() const {
+			return dft_iterator(first_, last_, index_, index_ - 1, size_);
+		}
+		void swap(dft_iterator& other)
+		SPROUT_NOEXCEPT_EXPR(SPROUT_NOEXCEPT_EXPR(sprout::swap(first_, other.first_)) && SPROUT_NOEXCEPT_EXPR(sprout::swap(last_, other.last_)))
+		{
+			sprout::swap(first_, other.first_);
+			sprout::swap(last_, other.last_);
+			sprout::swap(index_, other.index_);
+			sprout::swap(size_, other.size_);
+		}
+		friend SPROUT_CONSTEXPR bool operator==(dft_iterator const& lhs, dft_iterator const& rhs) {
+			return lhs.index_ == rhs.index_;
+		}
+		friend SPROUT_CONSTEXPR bool operator!=(dft_iterator const& lhs, dft_iterator const& rhs) {
+			return !(lhs == rhs);
+		}
+		friend SPROUT_CONSTEXPR bool operator<(dft_iterator const& lhs, dft_iterator const& rhs) {
+			return lhs.index_ < rhs.index_;
+		}
+		friend SPROUT_CONSTEXPR bool operator>(dft_iterator const& lhs, dft_iterator const& rhs) {
+			return rhs < lhs;
+		}
+		friend SPROUT_CONSTEXPR bool operator<=(dft_iterator const& lhs, dft_iterator const& rhs) {
+			return !(rhs < lhs);
+		}
+		friend SPROUT_CONSTEXPR bool operator>=(dft_iterator const& lhs, dft_iterator const& rhs) {
+			return !(lhs < rhs);
+		}
+		SPROUT_CONSTEXPR reference operator*() const {
+			return sprout::detail::dft_element_impl(first_, last_, index_, size_);
+		}
+		dft_iterator& operator++() {
+			dft_iterator temp(next());
+			temp.swap(*this);
+			return *this;
+		}
+		dft_iterator operator++(int) {
+			dft_iterator result(*this);
+			++*this;
+			return result;
+		}
+		dft_iterator& operator--() {
+			dft_iterator temp(prev());
+			temp.swap(*this);
+			return *this;
+		}
+		dft_iterator operator--(int) {
+			dft_iterator result(*this);
+			--*this;
+			return result;
+		}
+		SPROUT_CONSTEXPR dft_iterator operator+(difference_type n) const {
+			return dft_iterator(first_, last_, index_, index_ + n, size_);
+		}
+		SPROUT_CONSTEXPR dft_iterator operator-(difference_type n) const {
+			return dft_iterator(first_, last_, index_, index_ - n, size_);
+		}
+		dft_iterator& operator+=(difference_type n) {
+			dft_iterator temp(first_, last_, index_, index_ + n, size_);
+			temp.swap(*this);
+			return *this;
+		}
+		dft_iterator& operator-=(difference_type n) {
+			dft_iterator temp(first_, last_, index_, index_ - n, size_);
+			temp.swap(*this);
+			return *this;
+		}
+		SPROUT_CONSTEXPR reference operator[](difference_type n) const {
+			return sprout::detail::dft_element_impl(first_, last_, index_ + n, size_);
+		}
+		friend SPROUT_CONSTEXPR difference_type operator-(dft_iterator const& lhs, dft_iterator const& rhs) {
+			return lhs.index_ - rhs.index_;
+		}
+		friend SPROUT_CONSTEXPR dft_iterator operator+(difference_type n, dft_iterator const& it) {
+			return it + n;
+		}
+	};
+
+	//
+	// make_dft_iterator
+	//
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR sprout::dft_iterator<Iterator>
+	make_dft_iterator(Iterator first, Iterator last, typename std::iterator_traits<Iterator>::difference_type i = 0) {
+		return sprout::dft_iterator<Iterator>(first, last, i);
+	}
+
+	//
+	// swap
+	//
+	template<typename Iterator>
+	inline void
+	swap(sprout::dft_iterator<Iterator>& lhs, sprout::dft_iterator<Iterator>& rhs)
+	SPROUT_NOEXCEPT_EXPR(SPROUT_NOEXCEPT_EXPR(lhs.swap(rhs)))
+	{
+		lhs.swap(rhs);
+	}
+
+	//
+	// iterator_distance
+	//
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR typename std::iterator_traits<sprout::dft_iterator<Iterator> >::difference_type
+	iterator_distance(sprout::dft_iterator<Iterator> first, sprout::dft_iterator<Iterator> last) {
+		return last - first;
+	}
+
+	//
+	// iterator_next
+	//
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR sprout::dft_iterator<Iterator>
+	iterator_next(sprout::dft_iterator<Iterator> const& it) {
+		return it.next();
+	}
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR sprout::dft_iterator<Iterator>
+	iterator_next(
+		sprout::dft_iterator<Iterator> const& it,
+		typename sprout::dft_iterator<Iterator>::difference_type n
+		)
+	{
+		return it + n;
+	}
+
+	//
+	// iterator_prev
+	//
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR sprout::dft_iterator<Iterator>
+	iterator_prev(sprout::dft_iterator<Iterator> const& it) {
+		return it.prev();
+	}
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR sprout::dft_iterator<Iterator>
+	iterator_prev(
+		sprout::dft_iterator<Iterator> const& it,
+		typename sprout::dft_iterator<Iterator>::difference_type n
+		)
+	{
+		return it - n;
+	}
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_ITERATOR_DFT_ITERATOR_HPP

sprout/iterator/filter_iterator.hpp

@@ -43,10 +43,10 @@ namespace sprout {
 	private:
 		struct private_constructor_tag {};
 	private:
-		static SPROUT_CONSTEXPR iterator_type find_next(iterator_type first, iterator_type last, predicate_type pred) {
+		static SPROUT_CONSTEXPR iterator_type find_next(iterator_type first, iterator_type last, Predicate pred) {
 			return sprout::find_if(first, last, pred);
 		}
-		static SPROUT_CONSTEXPR iterator_type find_prev(iterator_type first, predicate_type pred) {
+		static SPROUT_CONSTEXPR iterator_type find_prev(iterator_type first, Predicate pred) {
 			return pred(*first) ? first
 				: find_prev(sprout::prev(first), pred)
 				;
@@ -54,7 +54,7 @@ namespace sprout {
 	protected:
 		iterator_type current;
 		iterator_type last;
-		predicate_type pred;
+		Predicate pred;
 	private:
 		void satisfy_predicate() {
 			while (current != last && !pred(*current)) {
@@ -66,7 +66,7 @@ namespace sprout {
 				--current;
 			}
 		}
-		SPROUT_CONSTEXPR filter_iterator(predicate_type pred, iterator_type it, iterator_type last, private_constructor_tag)
+		SPROUT_CONSTEXPR filter_iterator(Predicate pred, iterator_type it, iterator_type last, private_constructor_tag)
 			: current(it)
 			, last(last)
 			, pred(pred)
@@ -74,7 +74,7 @@ namespace sprout {
 	public:
 		filter_iterator() = default;
 		filter_iterator(filter_iterator const&) = default;
-		SPROUT_CONSTEXPR filter_iterator(predicate_type pred, iterator_type it, iterator_type last = iterator_type())
+		SPROUT_CONSTEXPR filter_iterator(Predicate pred, iterator_type it, iterator_type last = iterator_type())
 			: current(find_next(it, last, pred))
 			, last(last)
 			, pred(pred)
@@ -97,7 +97,7 @@ namespace sprout {
 		SPROUT_CONSTEXPR iterator_type end() const {
 			return last;
 		}
-		SPROUT_CONSTEXPR predicate_type predicate() const {
+		SPROUT_CONSTEXPR Predicate predicate() const {
 			return pred;
 		}
 		SPROUT_CONSTEXPR reference operator*() const {

sprout/iterator/idft_iterator.hpp

@@ -0,0 +1,213 @@
+#ifndef SPROUT_ITERATOR_IDFT_ITERATOR_HPP
+#define SPROUT_ITERATOR_IDFT_ITERATOR_HPP
+
+#include <iterator>
+#include <utility>
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/iterator/next.hpp>
+#include <sprout/iterator/prev.hpp>
+#include <sprout/iterator/distance.hpp>
+#include <sprout/utility/swap.hpp>
+#include <sprout/numeric/dft/idft_element.hpp>
+#include HDR_ITERATOR_SSCRISK_CEL_OR_SPROUT
+
+namespace sprout {
+	//
+	// idft_iterator
+	//
+	template<typename Iterator>
+	class idft_iterator
+		: public std::iterator<
+			std::random_access_iterator_tag,
+			typename std::iterator_traits<Iterator>::value_type,
+			typename std::iterator_traits<Iterator>::difference_type,
+			void,
+			typename std::iterator_traits<Iterator>::value_type
+		>
+	{
+	private:
+		typedef std::iterator<
+			std::random_access_iterator_tag,
+			typename std::iterator_traits<Iterator>::value_type,
+			typename std::iterator_traits<Iterator>::difference_type,
+			void,
+			typename std::iterator_traits<Iterator>::value_type
+		> base_type;
+	public:
+		typedef Iterator iterator_type;
+		typedef typename base_type::iterator_category iterator_category;
+		typedef typename base_type::value_type value_type;
+		typedef typename base_type::difference_type difference_type;
+		typedef typename base_type::pointer pointer;
+		typedef typename base_type::reference reference;
+	private:
+		iterator_type first_;
+		iterator_type last_;
+		difference_type index_;
+		difference_type size_;
+	private:
+		SPROUT_CONSTEXPR idft_iterator(iterator_type first, iterator_type last, difference_type index, difference_type size)
+			: first_(first), last_(last), index_(index)
+			, size_(size)
+		{}
+	public:
+		SPROUT_CONSTEXPR idft_iterator()
+			: first_(), last_(), index_()
+			, size_()
+		{}
+		idft_iterator(idft_iterator const&) = default;
+		SPROUT_CONSTEXPR idft_iterator(iterator_type first, iterator_type last, difference_type index = 0)
+			: first_(first), last_(last), index_(index)
+			, size_(NS_SSCRISK_CEL_OR_SPROUT::distance(first, last))
+		{}
+		SPROUT_CONSTEXPR idft_iterator next() const {
+			return idft_iterator(first_, last_, index_, index_ + 1, size_);
+		}
+		SPROUT_CONSTEXPR idft_iterator prev() const {
+			return idft_iterator(first_, last_, index_, index_ - 1, size_);
+		}
+		void swap(idft_iterator& other)
+		SPROUT_NOEXCEPT_EXPR(SPROUT_NOEXCEPT_EXPR(sprout::swap(first_, other.first_)) && SPROUT_NOEXCEPT_EXPR(sprout::swap(last_, other.last_)))
+		{
+			sprout::swap(first_, other.first_);
+			sprout::swap(last_, other.last_);
+			sprout::swap(index_, other.index_);
+			sprout::swap(size_, other.size_);
+		}
+		friend SPROUT_CONSTEXPR bool operator==(idft_iterator const& lhs, idft_iterator const& rhs) {
+			return lhs.index_ == rhs.index_;
+		}
+		friend SPROUT_CONSTEXPR bool operator!=(idft_iterator const& lhs, idft_iterator const& rhs) {
+			return !(lhs == rhs);
+		}
+		friend SPROUT_CONSTEXPR bool operator<(idft_iterator const& lhs, idft_iterator const& rhs) {
+			return lhs.index_ < rhs.index_;
+		}
+		friend SPROUT_CONSTEXPR bool operator>(idft_iterator const& lhs, idft_iterator const& rhs) {
+			return rhs < lhs;
+		}
+		friend SPROUT_CONSTEXPR bool operator<=(idft_iterator const& lhs, idft_iterator const& rhs) {
+			return !(rhs < lhs);
+		}
+		friend SPROUT_CONSTEXPR bool operator>=(idft_iterator const& lhs, idft_iterator const& rhs) {
+			return !(lhs < rhs);
+		}
+		SPROUT_CONSTEXPR reference operator*() const {
+			return sprout::detail::idft_element_impl(first_, last_, index_, size_);
+		}
+		idft_iterator& operator++() {
+			idft_iterator temp(next());
+			temp.swap(*this);
+			return *this;
+		}
+		idft_iterator operator++(int) {
+			idft_iterator result(*this);
+			++*this;
+			return result;
+		}
+		idft_iterator& operator--() {
+			idft_iterator temp(prev());
+			temp.swap(*this);
+			return *this;
+		}
+		idft_iterator operator--(int) {
+			idft_iterator result(*this);
+			--*this;
+			return result;
+		}
+		SPROUT_CONSTEXPR idft_iterator operator+(difference_type n) const {
+			return idft_iterator(first_, last_, index_, index_ + n, size_);
+		}
+		SPROUT_CONSTEXPR idft_iterator operator-(difference_type n) const {
+			return idft_iterator(first_, last_, index_, index_ - n, size_);
+		}
+		idft_iterator& operator+=(difference_type n) {
+			idft_iterator temp(first_, last_, index_, index_ + n, size_);
+			temp.swap(*this);
+			return *this;
+		}
+		idft_iterator& operator-=(difference_type n) {
+			idft_iterator temp(first_, last_, index_, index_ - n, size_);
+			temp.swap(*this);
+			return *this;
+		}
+		SPROUT_CONSTEXPR reference operator[](difference_type n) const {
+			return sprout::detail::idft_element_impl(first_, last_, index_ + n, size_);
+		}
+		friend SPROUT_CONSTEXPR difference_type operator-(idft_iterator const& lhs, idft_iterator const& rhs) {
+			return lhs.index_ - rhs.index_;
+		}
+		friend SPROUT_CONSTEXPR idft_iterator operator+(difference_type n, idft_iterator const& it) {
+			return it + n;
+		}
+	};
+
+	//
+	// make_idft_iterator
+	//
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR sprout::idft_iterator<Iterator>
+	make_idft_iterator(Iterator first, Iterator last, typename std::iterator_traits<Iterator>::difference_type i = 0) {
+		return sprout::idft_iterator<Iterator>(first, last, i);
+	}
+
+	//
+	// swap
+	//
+	template<typename Iterator>
+	inline void
+	swap(sprout::idft_iterator<Iterator>& lhs, sprout::idft_iterator<Iterator>& rhs)
+	SPROUT_NOEXCEPT_EXPR(SPROUT_NOEXCEPT_EXPR(lhs.swap(rhs)))
+	{
+		lhs.swap(rhs);
+	}
+
+	//
+	// iterator_distance
+	//
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR typename std::iterator_traits<sprout::idft_iterator<Iterator> >::difference_type
+	iterator_distance(sprout::idft_iterator<Iterator> first, sprout::idft_iterator<Iterator> last) {
+		return last - first;
+	}
+
+	//
+	// iterator_next
+	//
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR sprout::idft_iterator<Iterator>
+	iterator_next(sprout::idft_iterator<Iterator> const& it) {
+		return it.next();
+	}
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR sprout::idft_iterator<Iterator>
+	iterator_next(
+		sprout::idft_iterator<Iterator> const& it,
+		typename sprout::idft_iterator<Iterator>::difference_type n
+		)
+	{
+		return it + n;
+	}
+
+	//
+	// iterator_prev
+	//
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR sprout::idft_iterator<Iterator>
+	iterator_prev(sprout::idft_iterator<Iterator> const& it) {
+		return it.prev();
+	}
+	template<typename Iterator>
+	inline SPROUT_CONSTEXPR sprout::idft_iterator<Iterator>
+	iterator_prev(
+		sprout::idft_iterator<Iterator> const& it,
+		typename sprout::idft_iterator<Iterator>::difference_type n
+		)
+	{
+		return it - n;
+	}
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_ITERATOR_IDFT_ITERATOR_HPP

sprout/iterator/predefined.hpp

@@ -5,5 +5,6 @@
 #include <sprout/iterator/various.hpp>
 #include <sprout/iterator/adaptor.hpp>
 #include <sprout/iterator/wave.hpp>
+#include <sprout/iterator/dft.hpp>
 
 #endif	// #ifndef SPROUT_ITERATOR_PREDEFINED_HPP

sprout/math/cos.hpp

@@ -7,8 +7,8 @@
 #include <sprout/config.hpp>
 #include <sprout/math/detail/config.hpp>
 #include <sprout/math/factorial.hpp>
-#include <sprout/math/fmod.hpp>
 #include <sprout/math/constants.hpp>
+#include <sprout/math/fmod.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
 
 namespace sprout {

sprout/numeric/dft.hpp

@@ -7,6 +7,8 @@
 #include <sprout/numeric/dft/dft_element.hpp>
 #include <sprout/numeric/dft/idft_element.hpp>
 #include <sprout/numeric/dft/spectrum.hpp>
+#include <sprout/numeric/dft/amplitude_spectrum_value.hpp>
+#include <sprout/numeric/dft/phase_spectrum_value.hpp>
 #include <sprout/numeric/dft/wave.hpp>
 
 #endif	// #ifndef SPROUT_NUMERIC_DFT_HPP

sprout/numeric/dft/amplitude_spectrum_value.hpp

@@ -0,0 +1,21 @@
+#ifndef SPROUT_NUMERIC_DFT_AMPLITUDE_SPECTRUM_VALUE_HPP
+#define SPROUT_NUMERIC_DFT_AMPLITUDE_SPECTRUM_VALUE_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/complex.hpp>
+#include <sprout/math/sqrt.hpp>
+
+namespace sprout {
+	//
+	// amplitude_spectrum_value
+	//
+	template<typename T>
+	inline SPROUT_CONSTEXPR typename T::value_type
+	amplitude_spectrum_value(T const& x) {
+		using sprout::real;
+		using sprout::imag;
+		return sprout::sqrt(real(x) * real(x) + imag(x) * imag(x));
+	}
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_NUMERIC_DFT_AMPLITUDE_SPECTRUM_VALUE_HPP

sprout/numeric/dft/detail/dft_element_gen.hpp

@@ -7,12 +7,48 @@
 #include <sprout/iterator/operation.hpp>
 #include <sprout/math/sin.hpp>
 #include <sprout/math/cos.hpp>
+#include HDR_ITERATOR_SSCRISK_CEL_OR_SPROUT
 
 namespace sprout {
 	namespace detail {
+		template<typename RandomAccessIterator>
+		inline SPROUT_CONSTEXPR typename std::iterator_traits<RandomAccessIterator>::value_type
+		dft_element_gen_impl_ra(
+			RandomAccessIterator first, RandomAccessIterator last,
+			typename std::iterator_traits<RandomAccessIterator>::value_type::value_type arg,
+			typename std::iterator_traits<RandomAccessIterator>::difference_type pivot,
+			typename std::iterator_traits<RandomAccessIterator>::difference_type k = 0
+			)
+		{
+			typedef typename std::iterator_traits<RandomAccessIterator>::value_type value_type;
+			using sprout::cos;
+			using sprout::sin;
+			return pivot == 0 ? *first * value_type(cos(arg * k), sin(arg * k))
+				: sprout::detail::dft_element_gen_impl_ra(
+					first, sprout::next(first, pivot), arg, pivot / 2, k
+					)
+					+ sprout::detail::dft_element_gen_impl_ra(
+						sprout::next(first, pivot), last, arg, (NS_SSCRISK_CEL_OR_SPROUT::distance(first, last) - pivot) / 2, k + pivot
+						)
+				;
+		}
+		template<typename RandomAccessIterator>
+		inline SPROUT_CONSTEXPR typename std::iterator_traits<RandomAccessIterator>::value_type
+		dft_element_gen_impl(
+			RandomAccessIterator first, RandomAccessIterator last,
+			typename std::iterator_traits<RandomAccessIterator>::value_type::value_type arg,
+			std::random_access_iterator_tag*
+			)
+		{
+			typedef typename std::iterator_traits<RandomAccessIterator>::value_type value_type;
+			return first == last ? value_type()
+				: sprout::detail::dft_element_gen_impl_ra(first, last, arg, NS_SSCRISK_CEL_OR_SPROUT::distance(first, last) / 2)
+				;
+		}
+
 		template<typename InputIterator>
 		inline SPROUT_CONSTEXPR typename std::iterator_traits<InputIterator>::value_type
-		dft_element_gen(
+		dft_element_gen_impl_1(
 			InputIterator first, InputIterator last,
 			typename std::iterator_traits<InputIterator>::value_type::value_type arg,
 			typename std::iterator_traits<InputIterator>::difference_type k = 0,
@@ -25,18 +61,42 @@ namespace sprout {
 			typedef typename std::iterator_traits<InputIterator>::value_type value_type;
 			using sprout::cos;
 			using sprout::sin;
-			return first != last
+			return first == last ? value
-				? value + sprout::detail::dft_element_gen(
+				: value + sprout::detail::dft_element_gen_impl_1(
-					sprout::next(first),
+					sprout::next(first), last,
-					last,
 					arg,
 					k + 1,
 					*first * value_type(cos(theta), sin(theta)),
 					arg * (k + 1)
 					)
-				: value
 				;
 		}
+		template<typename InputIterator>
+		inline SPROUT_CONSTEXPR typename std::iterator_traits<InputIterator>::value_type
+		dft_element_gen_impl(
+			InputIterator first, InputIterator last,
+			typename std::iterator_traits<InputIterator>::value_type::value_type arg,
+			void*
+			)
+		{
+			return sprout::detail::dft_element_gen_impl_1(first, last, arg);
+		}
+
+		template<typename InputIterator>
+		inline SPROUT_CONSTEXPR typename std::iterator_traits<InputIterator>::value_type
+		dft_element_gen(
+			InputIterator first, InputIterator last,
+			typename std::iterator_traits<InputIterator>::value_type::value_type arg,
+			typename std::iterator_traits<InputIterator>::difference_type k = 0,
+			typename std::iterator_traits<InputIterator>::value_type value
+				= typename std::iterator_traits<InputIterator>::value_type(),
+			typename std::iterator_traits<InputIterator>::value_type::value_type theta
+				= typename std::iterator_traits<InputIterator>::value_type::value_type()
+			)
+		{
+			typedef typename std::iterator_traits<InputIterator>::iterator_category* category;
+			return sprout::detail::dft_element_gen_impl(first, last, arg, category());
+		}
 	}	// namespace detail
 }	// namespace sprout
 

sprout/numeric/dft/dft_element.hpp

@@ -1,5 +1,5 @@
-#ifndef SPROUT_NUMERIC_DFT_FIXED_DFT_ELEMENT_HPP
+#ifndef SPROUT_NUMERIC_DFT_DFT_ELEMENT_HPP
-#define SPROUT_NUMERIC_DFT_FIXED_DFT_ELEMENT_HPP
+#define SPROUT_NUMERIC_DFT_DFT_ELEMENT_HPP
 
 #include <iterator>
 #include <sprout/config.hpp>
@@ -38,4 +38,4 @@ namespace sprout {
 	}
 }	// namespace sprout
 
-#endif	// #ifndef SPROUT_NUMERIC_DFT_FIXED_DFT_ELEMENT_HPP
+#endif	// #ifndef SPROUT_NUMERIC_DFT_DFT_ELEMENT_HPP

sprout/numeric/dft/fixed/amplitude_spectrum.hpp

@@ -7,8 +7,7 @@
 #include <sprout/container/functions.hpp>
 #include <sprout/iterator/operation.hpp>
 #include <sprout/algorithm/fixed/result_of.hpp>
-#include <sprout/complex.hpp>
+#include <sprout/numeric/dft/amplitude_spectrum_value.hpp>
-#include <sprout/math/sqrt.hpp>
 #include HDR_ITERATOR_SSCRISK_CEL_OR_SPROUT
 
 namespace sprout {
@@ -24,16 +23,11 @@ namespace sprout {
 				typename sprout::container_traits<Result>::size_type input_size
 				)
 			{
-				using sprout::real;
-				using sprout::imag;
 				return sprout::remake<Result>(
 					result,
 					size,
 					(Indexes >= offset && Indexes < offset + size && Indexes < offset + input_size
-						? sprout::sqrt(
+						? sprout::amplitude_spectrum_value(*sprout::next(first, Indexes))
-							real(*sprout::next(first, Indexes)) * real(*sprout::next(first, Indexes))
-							+ imag(*sprout::next(first, Indexes)) * imag(*sprout::next(first, Indexes))
-							)
 						: *sprout::next(sprout::internal_begin(result), Indexes)
 						)...
 					);

sprout/numeric/dft/fixed/phase_spectrum.hpp

@@ -7,9 +7,7 @@
 #include <sprout/container/functions.hpp>
 #include <sprout/iterator/operation.hpp>
 #include <sprout/algorithm/fixed/result_of.hpp>
-#include <sprout/complex.hpp>
+#include <sprout/numeric/dft/phase_spectrum_value.hpp>
-#include <sprout/math/atan2.hpp>
-#include <sprout/math/llround.hpp>
 #include HDR_ITERATOR_SSCRISK_CEL_OR_SPROUT
 
 namespace sprout {
@@ -31,10 +29,7 @@ namespace sprout {
 					result,
 					size,
 					(Indexes >= offset && Indexes < offset + size && Indexes < offset + input_size
-						? sprout::atan2(
+						? sprout::phase_spectrum_value(*sprout::next(first, Indexes))
-							sprout::llround(imag(*sprout::next(first, Indexes))),
-							sprout::llround(real(*sprout::next(first, Indexes)))
-							)
 						: *sprout::next(sprout::internal_begin(result), Indexes)
 						)...
 					);

sprout/numeric/dft/idft_element.hpp

@@ -1,5 +1,5 @@
-#ifndef SPROUT_NUMERIC_DFT_FIXED_IDFT_ELEMENT_HPP
+#ifndef SPROUT_NUMERIC_DFT_IDFT_ELEMENT_HPP
-#define SPROUT_NUMERIC_DFT_FIXED_IDFT_ELEMENT_HPP
+#define SPROUT_NUMERIC_DFT_IDFT_ELEMENT_HPP
 
 #include <iterator>
 #include <sprout/config.hpp>
@@ -40,4 +40,4 @@ namespace sprout {
 	}
 }	// namespace sprout
 
-#endif	// #ifndef SPROUT_NUMERIC_DFT_FIXED_IDFT_ELEMENT_HPP
+#endif	// #ifndef SPROUT_NUMERIC_DFT_IDFT_ELEMENT_HPP

sprout/numeric/dft/phase_spectrum_value.hpp

@@ -0,0 +1,22 @@
+#ifndef SPROUT_NUMERIC_DFT_PHASE_SPECTRUM_VALUE_HPP
+#define SPROUT_NUMERIC_DFT_PHASE_SPECTRUM_VALUE_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/complex.hpp>
+#include <sprout/math/atan2.hpp>
+#include <sprout/math/llround.hpp>
+
+namespace sprout {
+	//
+	// phase_spectrum_value
+	//
+	template<typename T>
+	inline SPROUT_CONSTEXPR typename T::value_type
+	phase_spectrum_value(T const& x) {
+		using sprout::real;
+		using sprout::imag;
+		return sprout::atan2(sprout::llround(imag(x)), sprout::llround(real(x)));
+	}
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_NUMERIC_DFT_PHASE_SPECTRUM_VALUE_HPP

sprout/numeric/non_modifying.hpp

@@ -4,5 +4,7 @@
 #include <sprout/config.hpp>
 #include <sprout/numeric/accumulate.hpp>
 #include <sprout/numeric/inner_product.hpp>
+#include <sprout/numeric/unstable_accumulate.hpp>
+#include <sprout/numeric/unstable_inner_product.hpp>
 
 #endif	// #ifndef SPROUT_NUMERIC_NON_MODIFYIING_HPP

sprout/numeric/unstable_accumulate.hpp

@@ -0,0 +1,81 @@
+#ifndef SPROUT_NUMERIC_UNSTABLE_ACCUMLATE_HPP
+#define SPROUT_NUMERIC_UNSTABLE_ACCUMLATE_HPP
+
+#include <iterator>
+#include <sprout/config.hpp>
+#include <sprout/numeric/accumulate.hpp>
+#include HDR_FUNCTIONAL_SSCRISK_CEL_OR_SPROUT
+#include HDR_ITERATOR_SSCRISK_CEL_OR_SPROUT
+
+namespace sprout {
+	//
+	// unstable_accumulate
+	//
+	namespace detail {
+		template<typename T, typename RandomAccessIterator, typename BinaryOperation>
+		inline SPROUT_CONSTEXPR T
+		unstable_accumulate_ra(
+			RandomAccessIterator first, RandomAccessIterator last, BinaryOperation binary_op,
+			typename std::iterator_traits<RandomAccessIterator>::difference_type pivot
+			)
+		{
+			return pivot == 0 ? *first
+				: binary_op(
+					sprout::detail::unstable_accumulate_ra<T>(
+						first, sprout::next(first, pivot), binary_op,
+						pivot / 2
+						),
+					sprout::detail::unstable_accumulate_ra<T>(
+						sprout::next(first, pivot), last, binary_op,
+						(NS_SSCRISK_CEL_OR_SPROUT::distance(first, last) - pivot) / 2
+						)
+					)
+				;
+		}
+		template<typename RandomAccessIterator, typename T, typename BinaryOperation>
+		inline SPROUT_CONSTEXPR T
+		unstable_accumulate(
+			RandomAccessIterator first, RandomAccessIterator last, T init, BinaryOperation binary_op,
+			std::random_access_iterator_tag*
+			)
+		{
+			return first == last ? init
+				: binary_op(
+					init,
+					sprout::detail::unstable_accumulate_ra<T>(
+						first, last, binary_op,
+						NS_SSCRISK_CEL_OR_SPROUT::distance(first, last) / 2
+						)
+					)
+				;
+		}
+
+		template<typename InputIterator, typename T, typename BinaryOperation>
+		inline SPROUT_CONSTEXPR T
+		unstable_accumulate(
+			InputIterator first, InputIterator last, T init, BinaryOperation binary_op,
+			void*
+			)
+		{
+			return sprout::accumulate(first, last, init, binary_op);
+		}
+	}	// namespace detail
+
+	template<typename InputIterator, typename T, typename BinaryOperation>
+	inline SPROUT_CONSTEXPR T
+	unstable_accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op) {
+		typedef typename std::iterator_traits<InputIterator>::iterator_category* category;
+		return sprout::detail::unstable_accumulate(first, last, init, binary_op, category());
+	}
+
+	template<typename InputIterator, typename T>
+	inline SPROUT_CONSTEXPR T
+	unstable_accumulate(InputIterator first, InputIterator last, T init) {
+		return sprout::unstable_accumulate(
+			first, last, init,
+			NS_SSCRISK_CEL_OR_SPROUT::plus<typename std::iterator_traits<InputIterator>::value_type>()
+			);
+	}
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_NUMERIC_UNSTABLE_ACCUMLATE_HPP

sprout/numeric/unstable_inner_product.hpp

@@ -0,0 +1,89 @@
+#ifndef SPROUT_NUMERIC_UNSTABLE_INNNER_PRODUCT_HPP
+#define SPROUT_NUMERIC_UNSTABLE_INNNER_PRODUCT_HPP
+
+#include <iterator>
+#include <sprout/config.hpp>
+#include <sprout/numeric/inner_product.hpp>
+#include HDR_FUNCTIONAL_SSCRISK_CEL_OR_SPROUT
+#include HDR_ITERATOR_SSCRISK_CEL_OR_SPROUT
+
+namespace sprout {
+	//
+	// unstable_inner_product
+	//
+	namespace detail {
+		template<typename T, typename RandomAccessIterator1, typename RandomAccessIterator2, typename BinaryOperation1, typename BinaryOperation2>
+		inline SPROUT_CONSTEXPR T
+		unstable_inner_product_ra(
+			RandomAccessIterator1 first1, RandomAccessIterator1 last1, RandomAccessIterator2 first2,
+			BinaryOperation1 binary_op1, BinaryOperation2 binary_op2,
+			typename std::iterator_traits<RandomAccessIterator1>::difference_type pivot
+			)
+		{
+			return pivot == 0 ? binary_op2(*first1, *first2)
+				: binary_op1(
+					sprout::detail::unstable_inner_product_ra<T>(
+						first1, sprout::next(first1, pivot), first2, binary_op1, binary_op2,
+						pivot / 2
+						),
+					sprout::detail::unstable_inner_product_ra<T>(
+						sprout::next(first1, pivot), last1, sprout::next(first2, pivot), binary_op1, binary_op2,
+						(NS_SSCRISK_CEL_OR_SPROUT::distance(first1, last1) - pivot) / 2
+						)
+					)
+				;
+		}
+		template<typename RandomAccessIterator1, typename RandomAccessIterator2, typename T, typename BinaryOperation1, typename BinaryOperation2>
+		inline SPROUT_CONSTEXPR T
+		unstable_inner_product(
+			RandomAccessIterator1 first1, RandomAccessIterator1 last1, RandomAccessIterator2 first2, T init,
+			BinaryOperation1 binary_op1, BinaryOperation2 binary_op2,
+			std::random_access_iterator_tag*
+			)
+		{
+			return first1 == last1 ? init
+				: binary_op1(
+					init,
+					sprout::detail::unstable_inner_product_ra<T>(
+						first1, last1, first2, binary_op1, binary_op2,
+						NS_SSCRISK_CEL_OR_SPROUT::distance(first1, last1) / 2
+						)
+					)
+				;
+		}
+
+		template<typename InputIterator1, typename InputIterator2, typename T, typename BinaryOperation1, typename BinaryOperation2>
+		inline SPROUT_CONSTEXPR T
+		unstable_inner_product(
+			InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init,
+			BinaryOperation1 binary_op1, BinaryOperation2 binary_op2,
+			void*
+			)
+		{
+			return sprout::inner_product(first1, last1, first2, init, binary_op1, binary_op2);
+		}
+	}	// namespace detail
+
+	template<typename InputIterator1, typename InputIterator2, typename T, typename BinaryOperation1, typename BinaryOperation2>
+	inline SPROUT_CONSTEXPR T
+	unstable_inner_product(
+		InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init,
+		BinaryOperation1 binary_op1, BinaryOperation2 binary_op2
+		)
+	{
+		typedef typename std::iterator_traits<InputIterator1>::iterator_category* category;
+		return sprout::detail::unstable_inner_product(first1, last1, first2, init, binary_op1, binary_op2, category());
+	}
+
+	template<typename InputIterator1, typename InputIterator2, typename T>
+	inline SPROUT_CONSTEXPR T
+	unstable_inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init) {
+		return sprout::unstable_inner_product(
+			first1, last1, first2, init,
+			sprout::plus<typename std::iterator_traits<InputIterator1>::value_type>(),
+			NS_SSCRISK_CEL_OR_SPROUT::multiplies<typename std::iterator_traits<InputIterator1>::value_type>()
+			);
+	}
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_NUMERIC_UNSTABLE_INNNER_PRODUCT_HPP

sprout/range/adaptor/amplitude_spectrum.hpp

@@ -0,0 +1,103 @@
+#ifndef SPROUT_RANGE_ADAPTOR_AMPLITUDE_SPECTRUM_HPP
+#define SPROUT_RANGE_ADAPTOR_AMPLITUDE_SPECTRUM_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/pit.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/iterator/transform_iterator.hpp>
+#include <sprout/range/adaptor/detail/adapted_range_default.hpp>
+#include <sprout/range/algorithm/copy.hpp>
+#include <sprout/type_traits/lvalue_reference.hpp>
+#include <sprout/utility/forward.hpp>
+#include <sprout/utility/lvalue_forward.hpp>
+#include <sprout/numeric/dft/amplitude_spectrum_value.hpp>
+
+namespace sprout {
+	namespace adaptors {
+		namespace detail {
+			template<typename T>
+			class amplitude_spectrum_value {
+			public:
+				typedef typename T::value_type result_type;
+				typedef T argument_type;
+			public:
+				SPROUT_CONSTEXPR result_type operator()(T const& value) const {
+					return sprout::amplitude_spectrum_value(value);
+				}
+			};
+		}	// namespace detail
+		//
+		// amplitude_spectrum_range
+		//
+		template<typename Range>
+		class amplitude_spectrum_range
+			: public sprout::adaptors::detail::adapted_range_default<
+				Range,
+				sprout::transform_iterator<
+					sprout::adaptors::detail::amplitude_spectrum_value<typename sprout::container_traits<Range>::value_type>,
+					typename sprout::container_traits<Range>::iterator
+				>
+			>
+		{
+		public:
+			typedef sprout::adaptors::detail::adapted_range_default<
+				Range,
+				sprout::transform_iterator<
+					sprout::adaptors::detail::amplitude_spectrum_value<typename sprout::container_traits<Range>::value_type>,
+					typename sprout::container_traits<Range>::iterator
+				>
+			> base_type;
+			typedef typename base_type::range_type range_type;
+			typedef typename base_type::iterator iterator;
+			typedef typename base_type::value_type value_type;
+		public:
+			amplitude_spectrum_range() = default;
+			amplitude_spectrum_range(amplitude_spectrum_range const&) = default;
+			explicit SPROUT_CONSTEXPR amplitude_spectrum_range(range_type& range)
+				: base_type(
+					iterator(sprout::begin(range), typename iterator::functor_type()),
+					iterator(sprout::end(range), typename iterator::functor_type())
+					)
+			{}
+		};
+
+		//
+		// amplitude_spectrum_forwarder
+		//
+		class amplitude_spectrum_forwarder {};
+
+		//
+		// amplitude_spectrum
+		//
+		namespace {
+			SPROUT_STATIC_CONSTEXPR sprout::adaptors::amplitude_spectrum_forwarder amplitude_spectrum{};
+		}	// anonymous-namespace
+
+		//
+		// operator|
+		//
+		template<typename Range>
+		inline SPROUT_CONSTEXPR sprout::adaptors::amplitude_spectrum_range<
+			typename std::remove_reference<typename sprout::lvalue_reference<Range>::type>::type
+		>
+		operator|(Range&& lhs, amplitude_spectrum_forwarder) {
+			return sprout::adaptors::amplitude_spectrum_range<
+				typename std::remove_reference<typename sprout::lvalue_reference<Range>::type>::type
+			>(
+				sprout::lvalue_forward<Range>(lhs)
+				);
+		}
+	}	// namespace adaptors
+
+	//
+	// container_construct_traits
+	//
+	template<typename Range>
+	struct container_construct_traits<sprout::adaptors::amplitude_spectrum_range<Range> >
+		: public sprout::container_construct_traits<typename sprout::adaptors::amplitude_spectrum_range<Range>::base_type>
+	{};
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_ADAPTOR_AMPLITUDE_SPECTRUM_HPP

sprout/range/adaptor/clamped.hpp

@@ -45,14 +45,14 @@ namespace sprout {
 				range_type& range,
 				value_type const& low,
 				value_type const& up,
-				compare_type comp = compare_type()
+				Compare comp = Compare()
 				)
 				: base_type(
 					iterator(sprout::begin(range), low, up, comp),
 					iterator(sprout::end(range), low, up, comp)
 					)
 			{}
-			SPROUT_CONSTEXPR compare_type compare() const {
+			SPROUT_CONSTEXPR Compare compare() const {
 				return base_type::begin().compare();
 			}
 			SPROUT_CONSTEXPR value_type lower() const {
@@ -72,14 +72,14 @@ namespace sprout {
 			typedef Value value_type;
 			typedef Compare compare_type;
 		private:
-			compare_type comp_;
+			Compare comp_;
 			value_type low_;
 			value_type up_;
 		public:
-			SPROUT_CONSTEXPR clamp_holder(value_type const& low, value_type const& up, compare_type comp = compare_type())
+			SPROUT_CONSTEXPR clamp_holder(value_type const& low, value_type const& up, Compare comp = Compare())
 				: comp_(comp), low_(low), up_(up)
 			{}
-			SPROUT_CONSTEXPR compare_type const& compare() const {
+			SPROUT_CONSTEXPR Compare const& compare() const {
 				return comp_;
 			}
 			SPROUT_CONSTEXPR value_type const& lower() const {

sprout/range/adaptor/dft.hpp

@@ -0,0 +1,83 @@
+#ifndef SPROUT_RANGE_ADAPTOR_DFT_HPP
+#define SPROUT_RANGE_ADAPTOR_DFT_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/pit.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/iterator/dft_iterator.hpp>
+#include <sprout/range/adaptor/detail/adapted_range_default.hpp>
+#include <sprout/range/algorithm/copy.hpp>
+#include <sprout/type_traits/lvalue_reference.hpp>
+#include <sprout/utility/forward.hpp>
+#include <sprout/utility/lvalue_forward.hpp>
+
+namespace sprout {
+	namespace adaptors {
+		//
+		// dft_range
+		//
+		template<typename Range>
+		class dft_range
+			: public sprout::adaptors::detail::adapted_range_default<
+				Range,
+				sprout::dft_iterator<typename sprout::container_traits<Range>::iterator>
+			>
+		{
+		public:
+			typedef sprout::adaptors::detail::adapted_range_default<
+				Range,
+				sprout::dft_iterator<typename sprout::container_traits<Range>::iterator>
+			> base_type;
+			typedef typename base_type::range_type range_type;
+			typedef typename base_type::iterator iterator;
+		public:
+			dft_range() = default;
+			dft_range(dft_range const&) = default;
+			explicit SPROUT_CONSTEXPR dft_range(range_type& range)
+				: base_type(
+					iterator(sprout::begin(range), sprout::end(range)),
+					iterator(sprout::begin(range), sprout::end(range), sprout::size(range))
+					)
+			{}
+		};
+
+		//
+		// dft_forwarder
+		//
+		class dft_forwarder {};
+
+		//
+		// dft
+		//
+		namespace {
+			SPROUT_STATIC_CONSTEXPR sprout::adaptors::dft_forwarder dft{};
+		}	// anonymous-namespace
+
+		//
+		// operator|
+		//
+		template<typename Range>
+		inline SPROUT_CONSTEXPR sprout::adaptors::dft_range<
+			typename std::remove_reference<typename sprout::lvalue_reference<Range>::type>::type
+		>
+		operator|(Range&& lhs, sprout::adaptors::dft_forwarder) {
+			return sprout::adaptors::dft_range<
+				typename std::remove_reference<typename sprout::lvalue_reference<Range>::type>::type
+			>(
+				sprout::lvalue_forward<Range>(lhs)
+				);
+		}
+	}	// namespace adaptors
+
+	//
+	// container_construct_traits
+	//
+	template<typename Range>
+	struct container_construct_traits<sprout::adaptors::dft_range<Range> >
+		: public sprout::container_construct_traits<typename sprout::adaptors::dft_range<Range>::base_type>
+	{};
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_ADAPTOR_DFT_HPP

sprout/range/adaptor/filtered.hpp

@@ -42,7 +42,7 @@ namespace sprout {
 		public:
 			filtered_range() = default;
 			filtered_range(filtered_range const&) = default;
-			SPROUT_CONSTEXPR filtered_range(predicate_type pred, range_type& range)
+			SPROUT_CONSTEXPR filtered_range(Predicate pred, range_type& range)
 				: base_type(
 					iterator(pred, sprout::begin(range), sprout::end(range)),
 					iterator(pred, sprout::end(range), sprout::end(range))
@@ -58,14 +58,14 @@ namespace sprout {
 		public:
 			typedef Predicate predicate_type;
 		private:
-			predicate_type pred_;
+			Predicate pred_;
 		public:
 			filter_holder() = default;
 			filter_holder(filter_holder const&) = default;
-			SPROUT_CONSTEXPR filter_holder(predicate_type pred)
+			SPROUT_CONSTEXPR filter_holder(Predicate pred)
 				: pred_(pred)
 			{}
-			SPROUT_CONSTEXPR predicate_type predicate() const {
+			SPROUT_CONSTEXPR Predicate predicate() const {
 				return pred_;
 			}
 		};

sprout/range/adaptor/idft.hpp

@@ -0,0 +1,83 @@
+#ifndef SPROUT_RANGE_ADAPTOR_IDFT_HPP
+#define SPROUT_RANGE_ADAPTOR_IDFT_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/pit.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/iterator/idft_iterator.hpp>
+#include <sprout/range/adaptor/detail/adapted_range_default.hpp>
+#include <sprout/range/algorithm/copy.hpp>
+#include <sprout/type_traits/lvalue_reference.hpp>
+#include <sprout/utility/forward.hpp>
+#include <sprout/utility/lvalue_forward.hpp>
+
+namespace sprout {
+	namespace adaptors {
+		//
+		// idft_range
+		//
+		template<typename Range>
+		class idft_range
+			: public sprout::adaptors::detail::adapted_range_default<
+				Range,
+				sprout::idft_iterator<typename sprout::container_traits<Range>::iterator>
+			>
+		{
+		public:
+			typedef sprout::adaptors::detail::adapted_range_default<
+				Range,
+				sprout::idft_iterator<typename sprout::container_traits<Range>::iterator>
+			> base_type;
+			typedef typename base_type::range_type range_type;
+			typedef typename base_type::iterator iterator;
+		public:
+			idft_range() = default;
+			idft_range(idft_range const&) = default;
+			explicit SPROUT_CONSTEXPR idft_range(range_type& range)
+				: base_type(
+					iterator(sprout::begin(range), sprout::end(range)),
+					iterator(sprout::begin(range), sprout::end(range), sprout::size(range))
+					)
+			{}
+		};
+
+		//
+		// idft_forwarder
+		//
+		class idft_forwarder {};
+
+		//
+		// idft
+		//
+		namespace {
+			SPROUT_STATIC_CONSTEXPR sprout::adaptors::idft_forwarder idft{};
+		}	// anonymous-namespace
+
+		//
+		// operator|
+		//
+		template<typename Range>
+		inline SPROUT_CONSTEXPR sprout::adaptors::idft_range<
+			typename std::remove_reference<typename sprout::lvalue_reference<Range>::type>::type
+		>
+		operator|(Range&& lhs, sprout::adaptors::idft_forwarder) {
+			return sprout::adaptors::idft_range<
+				typename std::remove_reference<typename sprout::lvalue_reference<Range>::type>::type
+			>(
+				sprout::lvalue_forward<Range>(lhs)
+				);
+		}
+	}	// namespace adaptors
+
+	//
+	// container_construct_traits
+	//
+	template<typename Range>
+	struct container_construct_traits<sprout::adaptors::idft_range<Range> >
+		: public sprout::container_construct_traits<typename sprout::adaptors::idft_range<Range>::base_type>
+	{};
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_ADAPTOR_IDFT_HPP

sprout/range/adaptor/phase_spectrum.hpp

@@ -0,0 +1,103 @@
+#ifndef SPROUT_RANGE_ADAPTOR_PHASE_SPECTRUM_HPP
+#define SPROUT_RANGE_ADAPTOR_PHASE_SPECTRUM_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/pit.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/iterator/transform_iterator.hpp>
+#include <sprout/range/adaptor/detail/adapted_range_default.hpp>
+#include <sprout/range/algorithm/copy.hpp>
+#include <sprout/type_traits/lvalue_reference.hpp>
+#include <sprout/utility/forward.hpp>
+#include <sprout/utility/lvalue_forward.hpp>
+#include <sprout/numeric/dft/phase_spectrum_value.hpp>
+
+namespace sprout {
+	namespace adaptors {
+		namespace detail {
+			template<typename T>
+			class phase_spectrum_value {
+			public:
+				typedef typename T::value_type result_type;
+				typedef T argument_type;
+			public:
+				SPROUT_CONSTEXPR result_type operator()(T const& value) const {
+					return sprout::phase_spectrum_value(value);
+				}
+			};
+		}	// namespace detail
+		//
+		// phase_spectrum_range
+		//
+		template<typename Range>
+		class phase_spectrum_range
+			: public sprout::adaptors::detail::adapted_range_default<
+				Range,
+				sprout::transform_iterator<
+					sprout::adaptors::detail::phase_spectrum_value<typename sprout::container_traits<Range>::value_type>,
+					typename sprout::container_traits<Range>::iterator
+				>
+			>
+		{
+		public:
+			typedef sprout::adaptors::detail::adapted_range_default<
+				Range,
+				sprout::transform_iterator<
+					sprout::adaptors::detail::phase_spectrum_value<typename sprout::container_traits<Range>::value_type>,
+					typename sprout::container_traits<Range>::iterator
+				>
+			> base_type;
+			typedef typename base_type::range_type range_type;
+			typedef typename base_type::iterator iterator;
+			typedef typename base_type::value_type value_type;
+		public:
+			phase_spectrum_range() = default;
+			phase_spectrum_range(phase_spectrum_range const&) = default;
+			explicit SPROUT_CONSTEXPR phase_spectrum_range(range_type& range)
+				: base_type(
+					iterator(sprout::begin(range), typename iterator::functor_type()),
+					iterator(sprout::end(range), typename iterator::functor_type())
+					)
+			{}
+		};
+
+		//
+		// phase_spectrum_forwarder
+		//
+		class phase_spectrum_forwarder {};
+
+		//
+		// phase_spectrum
+		//
+		namespace {
+			SPROUT_STATIC_CONSTEXPR sprout::adaptors::phase_spectrum_forwarder phase_spectrum{};
+		}	// anonymous-namespace
+
+		//
+		// operator|
+		//
+		template<typename Range>
+		inline SPROUT_CONSTEXPR sprout::adaptors::phase_spectrum_range<
+			typename std::remove_reference<typename sprout::lvalue_reference<Range>::type>::type
+		>
+		operator|(Range&& lhs, phase_spectrum_forwarder) {
+			return sprout::adaptors::phase_spectrum_range<
+				typename std::remove_reference<typename sprout::lvalue_reference<Range>::type>::type
+			>(
+				sprout::lvalue_forward<Range>(lhs)
+				);
+		}
+	}	// namespace adaptors
+
+	//
+	// container_construct_traits
+	//
+	template<typename Range>
+	struct container_construct_traits<sprout::adaptors::phase_spectrum_range<Range> >
+		: public sprout::container_construct_traits<typename sprout::adaptors::phase_spectrum_range<Range>::base_type>
+	{};
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_ADAPTOR_PHASE_SPECTRUM_HPP

sprout/range/adaptor/replaced.hpp

@@ -20,7 +20,7 @@ namespace sprout {
 			class replace_value {
 			public:
 				typedef T const& result_type;
-				typedef T const& first_argument_type;
+				typedef T const& argument_type;
 			private:
 				T old_;
 				T new_;
@@ -61,7 +61,7 @@ namespace sprout {
 		public:
 			replaced_range() = default;
 			replaced_range(replaced_range const&) = default;
-			explicit SPROUT_CONSTEXPR replaced_range(range_type& range, value_type const& old_value, value_type const& new_value)
+			SPROUT_CONSTEXPR replaced_range(range_type& range, value_type const& old_value, value_type const& new_value)
 				: base_type(
 					iterator(sprout::begin(range), typename iterator::functor_type(old_value, new_value)),
 					iterator(sprout::end(range), typename iterator::functor_type(old_value, new_value))

sprout/range/adaptor/replaced_if.hpp

@@ -21,7 +21,7 @@ namespace sprout {
 			public:
 				typedef Predicate predicate_type;
 				typedef T const& result_type;
-				typedef T const& first_argument_type;
+				typedef T const& argument_type;
 			private:
 				Predicate pred_;
 				T new_;
@@ -63,7 +63,7 @@ namespace sprout {
 		public:
 			replaced_if_range() = default;
 			replaced_if_range(replaced_if_range const&) = default;
-			explicit SPROUT_CONSTEXPR replaced_if_range(range_type& range, predicate_type pred, value_type const& new_value)
+			SPROUT_CONSTEXPR replaced_if_range(range_type& range, Predicate pred, value_type const& new_value)
 				: base_type(
 					iterator(sprout::begin(range), typename iterator::functor_type(pred, new_value)),
 					iterator(sprout::end(range), typename iterator::functor_type(pred, new_value))
@@ -80,14 +80,14 @@ namespace sprout {
 			typedef Predicate predicate_type;
 			typedef T value_type;
 		private:
-			predicate_type pred_;
+			Predicate pred_;
 			value_type new_;
 		public:
-			SPROUT_CONSTEXPR replace_if_holder(predicate_type pred, value_type const& new_value)
+			SPROUT_CONSTEXPR replace_if_holder(Predicate pred, value_type const& new_value)
 				: pred_(pred)
 				, new_(new_value)
 			{}
-			SPROUT_CONSTEXPR predicate_type const& predicate() const {
+			SPROUT_CONSTEXPR Predicate const& predicate() const {
 				return pred_;
 			}
 			SPROUT_CONSTEXPR value_type const& new_value() const {

sprout/range/adaptor/wave.hpp

@@ -6,5 +6,9 @@
 #include <sprout/range/adaptor/sawtooth_wave.hpp>
 #include <sprout/range/adaptor/triangle_wave.hpp>
 #include <sprout/range/adaptor/square_wave.hpp>
+#include <sprout/range/adaptor/dft.hpp>
+#include <sprout/range/adaptor/idft.hpp>
+#include <sprout/range/adaptor/amplitude_spectrum.hpp>
+#include <sprout/range/adaptor/phase_spectrum.hpp>
 
 #endif	// #ifndef SPROUT_RANGE_ADAPTOR_WAVE_HPP

sprout/range/numeric/dft.hpp

@@ -4,6 +4,8 @@
 #include <sprout/config.hpp>
 #include <sprout/range/numeric/dft/dft.hpp>
 #include <sprout/range/numeric/dft/idft.hpp>
+#include <sprout/range/numeric/dft/dft_element.hpp>
+#include <sprout/range/numeric/dft/idft_element.hpp>
 #include <sprout/range/numeric/dft/spectrum.hpp>
 
 #endif	// #ifndef SPROUT_RANGE_NUMERIC_DFT_HPP

sprout/range/numeric/dft/dft_element.hpp

@@ -0,0 +1,22 @@
+#ifndef SPROUT_RANGE_NUMERIC_DFT_DFT_ELEMENT_HPP
+#define SPROUT_RANGE_NUMERIC_DFT_DFT_ELEMENT_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/numeric/dft/dft_element.hpp>
+
+namespace sprout {
+	namespace range {
+		//
+		// dft_element
+		//
+		template<typename Input>
+		inline SPROUT_CONSTEXPR typename sprout::container_traits<Input>::value_type
+		dft_element(Input const& input, typename sprout::container_traits<Input>::difference_type i) {
+			return sprout::dft_element(sprout::begin(input), sprout::end(input), i);
+		}
+	}	// namespace range
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_NUMERIC_DFT_DFT_ELEMENT_HPP

sprout/range/numeric/dft/fit/spectrum.hpp

@@ -22,4 +22,7 @@ namespace sprout {
 	}	// namespace range
 }	// namespace sprout
 
+#include <sprout/range/numeric/dft/fit/amplitude_spectrum.hpp>
+#include <sprout/range/numeric/dft/fit/phase_spectrum.hpp>
+
 #endif	// #ifndef SPROUT_RANGE_NUMERIC_DFT_FIT_SPECTRUM_HPP

sprout/range/numeric/dft/fixed/spectrum.hpp

@@ -24,4 +24,7 @@ namespace sprout {
 	}	// namespace range
 }	// namespace sprout
 
+#include <sprout/range/numeric/dft/fixed/amplitude_spectrum.hpp>
+#include <sprout/range/numeric/dft/fixed/phase_spectrum.hpp>
+
 #endif	// #ifndef SPROUT_RANGE_NUMERIC_DFT_FIXED_SPECTRUM_HPP

sprout/range/numeric/dft/idft_element.hpp

@@ -0,0 +1,22 @@
+#ifndef SPROUT_RANGE_NUMERIC_DFT_IDFT_ELEMENT_HPP
+#define SPROUT_RANGE_NUMERIC_DFT_IDFT_ELEMENT_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/numeric/dft/idft_element.hpp>
+
+namespace sprout {
+	namespace range {
+		//
+		// idft_element
+		//
+		template<typename Input>
+		inline SPROUT_CONSTEXPR typename sprout::container_traits<Input>::value_type
+		idft_element(Input const& input, typename sprout::container_traits<Input>::difference_type i) {
+			return sprout::idft_element(sprout::begin(input), sprout::end(input), i);
+		}
+	}	// namespace range
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_NUMERIC_DFT_IDFT_ELEMENT_HPP