From 2052058357bd14be227674f68aa54e69f4c6257b Mon Sep 17 00:00:00 2001
From: bolero-MURAKAMI <bolero.murakami@gmail.com>
Date: Tue, 10 Oct 2017 02:13:04 +0900
Subject: [PATCH] add numeric algorithm reduce, exclusive_scan, inclusize_scan

---
 sprout/algorithm/fixed/results.hpp            |  34 ++-
 sprout/numeric/adjacent_difference.hpp        |   1 +
 sprout/numeric/cxx14.hpp                      |   2 +
 sprout/numeric/cxx14/exclusive_scan.hpp       |  54 +++++
 sprout/numeric/cxx14/inclusive_scan.hpp       |  59 +++++
 sprout/numeric/exclusive_scan.hpp             |  16 ++
 sprout/numeric/fit.hpp                        |   2 +
 sprout/numeric/fit/exclusive_scan.hpp         |  77 ++++++
 sprout/numeric/fit/inclusive_scan.hpp         | 102 ++++++++
 sprout/numeric/fixed.hpp                      |   2 +
 sprout/numeric/fixed/exclusive_scan.hpp       | 229 ++++++++++++++++++
 sprout/numeric/fixed/inclusive_scan.hpp       | 147 +++++++++++
 sprout/numeric/inclusive_scan.hpp             |  16 ++
 sprout/numeric/iota.hpp                       |   1 +
 sprout/numeric/non_modifying.hpp              |   1 +
 sprout/numeric/partial_sum.hpp                |   1 +
 sprout/numeric/reduce.hpp                     |  42 ++++
 sprout/range/numeric/accumulate.hpp           |   2 +
 sprout/range/numeric/cxx14.hpp                |   2 +
 sprout/range/numeric/cxx14/exclusive_scan.hpp |  42 ++++
 sprout/range/numeric/cxx14/inclusive_scan.hpp |  50 ++++
 sprout/range/numeric/exclusive_scan.hpp       |  15 ++
 sprout/range/numeric/fit.hpp                  |   2 +
 sprout/range/numeric/fit/exclusive_scan.hpp   |  48 ++++
 sprout/range/numeric/fit/inclusive_scan.hpp   |  58 +++++
 sprout/range/numeric/fixed.hpp                |   2 +
 sprout/range/numeric/fixed/exclusive_scan.hpp |  58 +++++
 sprout/range/numeric/fixed/inclusive_scan.hpp |  71 ++++++
 sprout/range/numeric/inclusive_scan.hpp       |  15 ++
 sprout/range/numeric/inner_product.hpp        |   2 +
 sprout/range/numeric/non_modifying.hpp        |   1 +
 sprout/range/numeric/reduce.hpp               |  41 ++++
 sprout/sub_array/container.hpp                |   4 +-
 testspr/trace.hpp                             |  14 +-
 34 files changed, 1195 insertions(+), 18 deletions(-)
 create mode 100644 sprout/numeric/cxx14/exclusive_scan.hpp
 create mode 100644 sprout/numeric/cxx14/inclusive_scan.hpp
 create mode 100644 sprout/numeric/exclusive_scan.hpp
 create mode 100644 sprout/numeric/fit/exclusive_scan.hpp
 create mode 100644 sprout/numeric/fit/inclusive_scan.hpp
 create mode 100644 sprout/numeric/fixed/exclusive_scan.hpp
 create mode 100644 sprout/numeric/fixed/inclusive_scan.hpp
 create mode 100644 sprout/numeric/inclusive_scan.hpp
 create mode 100644 sprout/numeric/reduce.hpp
 create mode 100644 sprout/range/numeric/cxx14/exclusive_scan.hpp
 create mode 100644 sprout/range/numeric/cxx14/inclusive_scan.hpp
 create mode 100644 sprout/range/numeric/exclusive_scan.hpp
 create mode 100644 sprout/range/numeric/fit/exclusive_scan.hpp
 create mode 100644 sprout/range/numeric/fit/inclusive_scan.hpp
 create mode 100644 sprout/range/numeric/fixed/exclusive_scan.hpp
 create mode 100644 sprout/range/numeric/fixed/inclusive_scan.hpp
 create mode 100644 sprout/range/numeric/inclusive_scan.hpp
 create mode 100644 sprout/range/numeric/reduce.hpp

diff --git a/sprout/algorithm/fixed/results.hpp b/sprout/algorithm/fixed/results.hpp
index f242dd8b..ba0a6a4c 100644
--- a/sprout/algorithm/fixed/results.hpp
+++ b/sprout/algorithm/fixed/results.hpp
@@ -12,6 +12,7 @@
 #include <sprout/config.hpp>
 #include <sprout/container/traits.hpp>
 #include <sprout/utility/pair/pair.hpp>
+#include <sprout/type_traits/identity.hpp>
 
 namespace sprout {
 	namespace fixed {
@@ -20,22 +21,33 @@ namespace sprout {
 			// algorithm
 			//
 			template<typename Result>
-			struct algorithm {
-			public:
-				typedef typename sprout::container_construct_traits<Result>::copied_type type;
-			};
+			struct algorithm
+				: public sprout::identity<typename sprout::container_construct_traits<Result>::copied_type>
+			{};
+
+			//
+			// resized_relative
+			//
+			template<typename Result, typename sprout::container_traits<Result>::difference_type RelativeSize>
+			struct resized_relative
+				: public sprout::identity<
+					typename sprout::container_transform_traits<Result>
+						::template rebind_size<sprout::container_traits<Result>::static_size + RelativeSize>::type
+				>
+			{};
 
 			//
 			// shuffle
 			//
 			template<typename Container, typename UniformRandomNumberGenerator>
-			struct shuffle {
-			public:
-				typedef sprout::pair<
-					typename sprout::fixed::results::algorithm<Container>::type,
-					typename std::decay<UniformRandomNumberGenerator>::type
-				> type;
-			};
+			struct shuffle
+				: public sprout::identity<
+					sprout::pair<
+						typename sprout::fixed::results::algorithm<Container>::type,
+						typename std::decay<UniformRandomNumberGenerator>::type
+					>
+				>
+			{};
 		}	// namespace results
 	}	// namespace fixed
 
diff --git a/sprout/numeric/adjacent_difference.hpp b/sprout/numeric/adjacent_difference.hpp
index 3bc1ae5d..d5ec2a55 100644
--- a/sprout/numeric/adjacent_difference.hpp
+++ b/sprout/numeric/adjacent_difference.hpp
@@ -11,5 +11,6 @@
 #include <sprout/config.hpp>
 #include <sprout/numeric/fixed/adjacent_difference.hpp>
 #include <sprout/numeric/fit/adjacent_difference.hpp>
+#include <sprout/numeric/cxx14/adjacent_difference.hpp>
 
 #endif	// #ifndef SPROUT_NUMERIC_ADJACENT_DIFFERENCE_HPP
diff --git a/sprout/numeric/cxx14.hpp b/sprout/numeric/cxx14.hpp
index f95569fe..aabc6108 100644
--- a/sprout/numeric/cxx14.hpp
+++ b/sprout/numeric/cxx14.hpp
@@ -10,6 +10,8 @@
 
 #include <sprout/config.hpp>
 #include <sprout/numeric/cxx14/partial_sum.hpp>
+#include <sprout/numeric/cxx14/exclusive_scan.hpp>
+#include <sprout/numeric/cxx14/inclusive_scan.hpp>
 #include <sprout/numeric/cxx14/adjacent_difference.hpp>
 #include <sprout/numeric/cxx14/iota.hpp>
 
diff --git a/sprout/numeric/cxx14/exclusive_scan.hpp b/sprout/numeric/cxx14/exclusive_scan.hpp
new file mode 100644
index 00000000..88058e73
--- /dev/null
+++ b/sprout/numeric/cxx14/exclusive_scan.hpp
@@ -0,0 +1,54 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_NUMERIC_CXX14_EXCLUSIVE_SCAN_HPP
+#define SPROUT_NUMERIC_CXX14_EXCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/utility/move.hpp>
+#include <sprout/iterator/type_traits/is_iterator_of.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/numeric/cxx14/partial_sum.hpp>
+
+namespace sprout {
+	//
+	// 29.8.7 Exclusive scan
+	//
+	template<
+		typename InputIterator, typename OutputIterator, typename T, typename BinaryOperation,
+		typename sprout::enabler_if<sprout::is_iterator_outputable<OutputIterator>::value>::type = sprout::enabler
+	>
+	inline SPROUT_CXX14_CONSTEXPR OutputIterator
+	exclusive_scan(InputIterator first, InputIterator last, OutputIterator result, T init, BinaryOperation binary_op) {
+		typedef typename std::iterator_traits<InputIterator>::value_type value_type;
+		value_type sum = sprout::move(init);
+		*result = sum;
+		if (first == last) {
+			return ++result;
+		}
+		value_type temp = *first;
+		while (++first != last) {
+			sum = binary_op(sum, temp);
+			*++result = sum;
+			temp = *first;
+		}
+		return ++result;
+	}
+	template<
+		typename InputIterator, typename OutputIterator, typename T,
+		typename sprout::enabler_if<sprout::is_iterator_outputable<OutputIterator>::value>::type = sprout::enabler
+	>
+	inline SPROUT_CXX14_CONSTEXPR OutputIterator
+	exclusive_scan(InputIterator first, InputIterator last, OutputIterator result, T init) {
+		return sprout::exclusive_scan(
+			first, last, result, init,
+			NS_SSCRISK_CEL_OR_SPROUT::plus<typename std::iterator_traits<InputIterator>::value_type>()
+			);
+	}
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_NUMERIC_CXX14_EXCLUSIVE_SCAN_HPP
diff --git a/sprout/numeric/cxx14/inclusive_scan.hpp b/sprout/numeric/cxx14/inclusive_scan.hpp
new file mode 100644
index 00000000..8bcf6a21
--- /dev/null
+++ b/sprout/numeric/cxx14/inclusive_scan.hpp
@@ -0,0 +1,59 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_NUMERIC_CXX14_INCLUSIVE_SCAN_HPP
+#define SPROUT_NUMERIC_CXX14_INCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/utility/move.hpp>
+#include <sprout/iterator/type_traits/is_iterator_of.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/numeric/cxx14/partial_sum.hpp>
+
+namespace sprout {
+	//
+	// 29.8.8 Inclusive scan
+	//
+	template<
+		typename InputIterator, typename OutputIterator, typename BinaryOperation, typename T,
+		typename sprout::enabler_if<sprout::is_iterator_outputable<OutputIterator>::value>::type = sprout::enabler
+	>
+	inline SPROUT_CXX14_CONSTEXPR OutputIterator
+	inclusive_scan(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op, T init) {
+		typedef typename std::iterator_traits<InputIterator>::value_type value_type;
+		value_type sum = sprout::move(init);
+		*result = sum;
+		if (first == last) {
+			return ++result;
+		}
+		sum = binary_op(sum, *first);
+		*++result = sum;
+		while (++first != last) {
+			sum = binary_op(sum, *first);
+			*++result = sum;
+		}
+		return ++result;
+	}
+	template<
+		typename InputIterator, typename OutputIterator, typename BinaryOperation,
+		typename sprout::enabler_if<sprout::is_iterator_outputable<OutputIterator>::value>::type = sprout::enabler
+	>
+	inline SPROUT_CXX14_CONSTEXPR OutputIterator
+	inclusive_scan(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op) {
+		return sprout::partial_sum(first, last, result, binary_op);
+	}
+	template<
+		typename InputIterator, typename OutputIterator,
+		typename sprout::enabler_if<sprout::is_iterator_outputable<OutputIterator>::value>::type = sprout::enabler
+	>
+	inline SPROUT_CXX14_CONSTEXPR OutputIterator
+	inclusive_scan(InputIterator first, InputIterator last, OutputIterator result) {
+		return sprout::partial_sum(first, last, result);
+	}
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_NUMERIC_CXX14_INCLUSIVE_SCAN_HPP
diff --git a/sprout/numeric/exclusive_scan.hpp b/sprout/numeric/exclusive_scan.hpp
new file mode 100644
index 00000000..7b01933d
--- /dev/null
+++ b/sprout/numeric/exclusive_scan.hpp
@@ -0,0 +1,16 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_NUMERIC_EXCLUSIVE_SCAN_HPP
+#define SPROUT_NUMERIC_EXCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/numeric/fixed/exclusive_scan.hpp>
+#include <sprout/numeric/fit/exclusive_scan.hpp>
+#include <sprout/numeric/cxx14/exclusive_scan.hpp>
+
+#endif	// #ifndef SPROUT_NUMERIC_EXCLUSIVE_SCAN_HPP
diff --git a/sprout/numeric/fit.hpp b/sprout/numeric/fit.hpp
index 00aebae2..25ab21be 100644
--- a/sprout/numeric/fit.hpp
+++ b/sprout/numeric/fit.hpp
@@ -10,6 +10,8 @@
 
 #include <sprout/config.hpp>
 #include <sprout/numeric/fit/partial_sum.hpp>
+#include <sprout/numeric/fit/exclusive_scan.hpp>
+#include <sprout/numeric/fit/inclusive_scan.hpp>
 #include <sprout/numeric/fit/adjacent_difference.hpp>
 #include <sprout/numeric/fit/iota.hpp>
 
diff --git a/sprout/numeric/fit/exclusive_scan.hpp b/sprout/numeric/fit/exclusive_scan.hpp
new file mode 100644
index 00000000..38b43033
--- /dev/null
+++ b/sprout/numeric/fit/exclusive_scan.hpp
@@ -0,0 +1,77 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_NUMERIC_FIT_EXCLUSIVE_SCAN_HPP
+#define SPROUT_NUMERIC_FIT_EXCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/iterator/distance.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/numeric/fixed/exclusive_scan.hpp>
+#include <sprout/algorithm/fit/results.hpp>
+#include <sprout/sub_array/sub_array.hpp>
+#include <sprout/sub_array/sub.hpp>
+#include <sprout/iterator/type_traits/category.hpp>
+
+namespace sprout {
+	namespace fit {
+		namespace detail {
+			template<typename InputIterator, typename Result, typename T>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			exclusive_scan_impl(
+				InputIterator const& first, InputIterator const& last, Result const& result, T init,
+				typename sprout::container_traits<Result>::difference_type offset
+				)
+			{
+				typedef typename std::iterator_traits<InputIterator>::difference_type diff_type;
+				return sprout::sub_copy(
+					sprout::get_internal(sprout::fixed::exclusive_scan(first, last, result, init)),
+					offset,
+					offset + NS_SSCRISK_CEL_OR_SPROUT::min<diff_type>(sprout::distance(first, last), sprout::size(result))
+					);
+			}
+		}	// namespace detail
+		//
+		// exclusive_scan
+		//
+		template<typename InputIterator, typename Result, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+		exclusive_scan(InputIterator first, InputIterator last, Result const& result, T init) {
+			static_assert(sprout::is_forward_iterator<InputIterator>::value, "Sorry, not implemented.");
+			return sprout::fit::detail::exclusive_scan_impl(first, last, result, init, sprout::internal_begin_offset(result));
+		}
+
+		namespace detail {
+			template<typename InputIterator, typename Result, typename T, typename BinaryOperation>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			exclusive_scan_impl(
+				InputIterator const& first, InputIterator const& last, Result const& result, T init, BinaryOperation binary_op,
+				typename sprout::container_traits<Result>::difference_type offset
+				)
+			{
+				typedef typename std::iterator_traits<InputIterator>::difference_type diff_type;
+				return sprout::sub_copy(
+					sprout::get_internal(sprout::fixed::exclusive_scan(first, last, result, init, binary_op)),
+					offset,
+					offset + NS_SSCRISK_CEL_OR_SPROUT::min<diff_type>(sprout::distance(first, last), sprout::size(result))
+					);
+			}
+		}	// namespace detail
+		//
+		// exclusive_scan
+		//
+		template<typename InputIterator, typename Result, typename T, typename BinaryOperation>
+		inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+		exclusive_scan(InputIterator first, InputIterator last, Result const& result, T init, BinaryOperation binary_op) {
+			static_assert(sprout::is_forward_iterator<InputIterator>::value, "Sorry, not implemented.");
+			return sprout::fit::detail::exclusive_scan_impl(first, last, result, init, binary_op, sprout::internal_begin_offset(result));
+		}
+	}	// namespace fit
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_NUMERIC_FIT_EXCLUSIVE_SCAN_HPP
diff --git a/sprout/numeric/fit/inclusive_scan.hpp b/sprout/numeric/fit/inclusive_scan.hpp
new file mode 100644
index 00000000..ac05543a
--- /dev/null
+++ b/sprout/numeric/fit/inclusive_scan.hpp
@@ -0,0 +1,102 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_NUMERIC_FIT_INCLUSIVE_SCAN_HPP
+#define SPROUT_NUMERIC_FIT_INCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/iterator/distance.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/numeric/fixed/inclusive_scan.hpp>
+#include <sprout/algorithm/fit/results.hpp>
+#include <sprout/sub_array/sub_array.hpp>
+#include <sprout/sub_array/sub.hpp>
+#include <sprout/iterator/type_traits/category.hpp>
+
+namespace sprout {
+	namespace fit {
+		namespace detail {
+			template<typename InputIterator, typename Result>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			inclusive_scan_impl(
+				InputIterator const& first, InputIterator const& last, Result const& result,
+				typename sprout::container_traits<Result>::difference_type offset
+				)
+			{
+				return sprout::sub_copy(
+					sprout::get_internal(sprout::fixed::inclusive_scan(first, last, result)),
+					offset,
+					offset + sprout::fit_size(result, sprout::distance(first, last))
+					);
+			}
+		}	// namespace detail
+		//
+		// inclusive_scan
+		//
+		template<typename InputIterator, typename Result>
+		inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+		inclusive_scan(InputIterator first, InputIterator last, Result const& result) {
+			static_assert(sprout::is_forward_iterator<InputIterator>::value, "Sorry, not implemented.");
+			return sprout::fit::detail::inclusive_scan_impl(first, last, result, sprout::internal_begin_offset(result));
+		}
+
+		namespace detail {
+			template<typename InputIterator, typename Result, typename BinaryOperation>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			inclusive_scan_impl(
+				InputIterator const& first, InputIterator const& last, Result const& result, BinaryOperation binary_op,
+				typename sprout::container_traits<Result>::difference_type offset
+				)
+			{
+				typedef typename std::iterator_traits<InputIterator>::difference_type diff_type;
+				return sprout::sub_copy(
+					sprout::get_internal(sprout::fixed::inclusive_scan(first, last, result, binary_op)),
+					offset,
+					offset + NS_SSCRISK_CEL_OR_SPROUT::min<diff_type>(sprout::distance(first, last), sprout::size(result))
+					);
+			}
+		}	// namespace detail
+		//
+		// inclusive_scan
+		//
+		template<typename InputIterator, typename Result, typename BinaryOperation>
+		inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+		inclusive_scan(InputIterator first, InputIterator last, Result const& result, BinaryOperation binary_op) {
+			static_assert(sprout::is_forward_iterator<InputIterator>::value, "Sorry, not implemented.");
+			return sprout::fit::detail::inclusive_scan_impl(first, last, result, binary_op, sprout::internal_begin_offset(result));
+		}
+
+		namespace detail {
+			template<typename InputIterator, typename Result, typename BinaryOperation, typename T>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			inclusive_scan_impl(
+				InputIterator const& first, InputIterator const& last, Result const& result, BinaryOperation binary_op, T init,
+				typename sprout::container_traits<Result>::difference_type offset
+				)
+			{
+				typedef typename std::iterator_traits<InputIterator>::difference_type diff_type;
+				return sprout::sub_copy(
+					sprout::get_internal(sprout::fixed::inclusive_scan(first, last, result, binary_op, init)),
+					offset,
+					offset + NS_SSCRISK_CEL_OR_SPROUT::min<diff_type>(sprout::distance(first, last) + 1, sprout::size(result))
+					);
+			}
+		}	// namespace detail
+		//
+		// inclusive_scan
+		//
+		template<typename InputIterator, typename Result, typename BinaryOperation, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+		inclusive_scan(InputIterator first, InputIterator last, Result const& result, BinaryOperation binary_op, T init) {
+			static_assert(sprout::is_forward_iterator<InputIterator>::value, "Sorry, not implemented.");
+			return sprout::fit::detail::inclusive_scan_impl(first, last, result, binary_op, init, sprout::internal_begin_offset(result));
+		}
+	}	// namespace fit
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_NUMERIC_FIT_INCLUSIVE_SCAN_HPP
diff --git a/sprout/numeric/fixed.hpp b/sprout/numeric/fixed.hpp
index ddf953a4..017bd453 100644
--- a/sprout/numeric/fixed.hpp
+++ b/sprout/numeric/fixed.hpp
@@ -10,6 +10,8 @@
 
 #include <sprout/config.hpp>
 #include <sprout/numeric/fixed/partial_sum.hpp>
+#include <sprout/numeric/fixed/exclusive_scan.hpp>
+#include <sprout/numeric/fixed/inclusive_scan.hpp>
 #include <sprout/numeric/fixed/adjacent_difference.hpp>
 #include <sprout/numeric/fixed/iota.hpp>
 
diff --git a/sprout/numeric/fixed/exclusive_scan.hpp b/sprout/numeric/fixed/exclusive_scan.hpp
new file mode 100644
index 00000000..400df854
--- /dev/null
+++ b/sprout/numeric/fixed/exclusive_scan.hpp
@@ -0,0 +1,229 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_NUMERIC_FIXED_EXCLUSIVE_SCAN_HPP
+#define SPROUT_NUMERIC_FIXED_EXCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/iterator/type_traits/is_iterator_of.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/algorithm/fixed/results.hpp>
+#include <sprout/pit/pit.hpp>
+#include <sprout/detail/container_complate.hpp>
+#include <sprout/numeric/fixed/exclusive_scan.hpp>
+
+namespace sprout {
+	namespace fixed {
+		namespace detail {
+			template<typename InputIterator, typename Result, typename... Args>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				sprout::container_traits<Result>::static_size == sizeof...(Args) + 1,
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			exclusive_scan_impl_1(
+				InputIterator const&, InputIterator const&, Result const& result,
+				typename sprout::container_traits<Result>::size_type,
+				typename sprout::container_traits<Result>::value_type const& value,
+				typename sprout::container_traits<Result>::value_type const& temp,
+				Args const&... args
+				)
+			{
+				return sprout::remake<Result>(result, sprout::size(result), args..., value);
+			}
+			template<typename InputIterator, typename Result, typename... Args>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				sprout::container_traits<Result>::static_size != sizeof...(Args) + 1,
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			exclusive_scan_impl_1(
+				InputIterator const& first, InputIterator const& last, Result const& result,
+				typename sprout::container_traits<Result>::size_type size,
+				typename sprout::container_traits<Result>::value_type const& value,
+				typename sprout::container_traits<Result>::value_type const& temp,
+				Args const&... args
+				)
+			{
+				return first != last && sizeof...(Args) + 1 < size
+					? exclusive_scan_impl_1(sprout::next(first), last, result, size, value + temp, *first, args..., value)
+					: sprout::detail::container_complate(result, args..., value)
+					;
+			}
+			template<typename InputIterator, typename Result, typename T>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				sprout::container_traits<Result>::static_size == 0,
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			exclusive_scan_impl(
+				InputIterator, InputIterator, Result const& result, T,
+				typename sprout::container_traits<Result>::size_type
+				)
+			{
+				return sprout::detail::container_complate(result);
+			}
+			template<typename InputIterator, typename Result, typename T>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				sprout::container_traits<Result>::static_size == 1,
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			exclusive_scan_impl(
+				InputIterator, InputIterator, Result const& result, T init,
+				typename sprout::container_traits<Result>::size_type
+				)
+			{
+				return sprout::detail::container_complate(result, init);
+			}
+			template<typename InputIterator, typename Result, typename T>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				(sprout::container_traits<Result>::static_size > 1),
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			exclusive_scan_impl(
+				InputIterator const& first, InputIterator const& last, Result const& result, T init,
+				typename sprout::container_traits<Result>::size_type size
+				)
+			{
+				return first != last
+					? exclusive_scan_impl_1(sprout::next(first), last, result, size, init, *first)
+					: sprout::detail::container_complate(result, init)
+					;
+			}
+		}	// namespace detail
+		//
+		// exclusive_scan
+		//
+		template<typename InputIterator, typename Result, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+		exclusive_scan(InputIterator first, InputIterator last, Result const& result, T init) {
+			return sprout::fixed::detail::exclusive_scan_impl(first, last, result, init, sprout::size(result));
+		}
+		template<typename Result, typename InputIterator, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+		exclusive_scan(InputIterator first, InputIterator last, T init) {
+			return sprout::fixed::exclusive_scan<Result>(first, last, sprout::pit<Result>(), init);
+		}
+
+		namespace detail {
+			template<typename InputIterator, typename Result, typename BinaryOperation, typename... Args>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				sprout::container_traits<Result>::static_size == sizeof...(Args) + 1,
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			exclusive_scan_impl_1(
+				InputIterator const&, InputIterator const&, Result const& result, BinaryOperation,
+				typename sprout::container_traits<Result>::size_type,
+				typename sprout::container_traits<Result>::value_type const& value,
+				typename sprout::container_traits<Result>::value_type const& temp,
+				Args const&... args
+				)
+			{
+				return sprout::remake<Result>(result, sprout::size(result), args..., value);
+			}
+			template<typename InputIterator, typename Result, typename BinaryOperation, typename... Args>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				sprout::container_traits<Result>::static_size != sizeof...(Args) + 1,
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			exclusive_scan_impl_1(
+				InputIterator const& first, InputIterator const& last, Result const& result, BinaryOperation binary_op,
+				typename sprout::container_traits<Result>::size_type size,
+				typename sprout::container_traits<Result>::value_type const& value,
+				typename sprout::container_traits<Result>::value_type const& temp,
+				Args const&... args
+				)
+			{
+				return first != last && sizeof...(Args) + 1 < size
+					? exclusive_scan_impl_1(sprout::next(first), last, result, binary_op, size, binary_op(value, temp), *first, args..., value)
+					: sprout::detail::container_complate(result, args..., value)
+					;
+			}
+			template<typename InputIterator, typename Result, typename T, typename BinaryOperation>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				sprout::container_traits<Result>::static_size == 0,
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			exclusive_scan_impl(
+				InputIterator, InputIterator, Result const& result, T, BinaryOperation,
+				typename sprout::container_traits<Result>::size_type
+				)
+			{
+				return sprout::detail::container_complate(result);
+			}
+			template<typename InputIterator, typename Result, typename T, typename BinaryOperation>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				sprout::container_traits<Result>::static_size == 1,
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			exclusive_scan_impl(
+				InputIterator, InputIterator, Result const& result, T init, BinaryOperation,
+				typename sprout::container_traits<Result>::size_type
+				)
+			{
+				return sprout::detail::container_complate(result, init);
+			}
+			template<typename InputIterator, typename Result, typename T, typename BinaryOperation>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				(sprout::container_traits<Result>::static_size > 1),
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			exclusive_scan_impl(
+				InputIterator const& first, InputIterator const& last, Result const& result, T init, BinaryOperation binary_op,
+				typename sprout::container_traits<Result>::size_type size
+				)
+			{
+				return first != last
+					? exclusive_scan_impl_1(sprout::next(first), last, result, binary_op, size, init, *first)
+					: sprout::detail::container_complate(result, init)
+					;
+			}
+		}	// namespace detail
+		//
+		// exclusive_scan
+		//
+		template<typename InputIterator, typename Result, typename T, typename BinaryOperation>
+		inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+		exclusive_scan(InputIterator first, InputIterator last, Result const& result, T init, BinaryOperation binary_op) {
+			return sprout::fixed::detail::exclusive_scan_impl(first, last, result, init, binary_op, sprout::size(result));
+		}
+		template<typename Result, typename InputIterator, typename T, typename BinaryOperation>
+		inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+		exclusive_scan(InputIterator first, InputIterator last, T init, BinaryOperation binary_op) {
+			return sprout::fixed::exclusive_scan(first, last, sprout::pit<Result>(), init, binary_op);
+		}
+	}	// namespace fixed
+
+	template<
+		typename InputIterator, typename Result, typename T,
+		typename sprout::enabler_if<!sprout::is_iterator_outputable<Result>::value>::type = sprout::enabler
+	>
+	inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+	exclusive_scan(InputIterator first, InputIterator last, Result const& result, T init) {
+		return sprout::fixed::exclusive_scan(first, last, result, init);
+	}
+	template<typename Result, typename InputIterator, typename T>
+	inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+	exclusive_scan(InputIterator first, InputIterator last, T init) {
+		return sprout::fixed::exclusive_scan<Result>(first, last, init);
+	}
+
+	template<
+		typename InputIterator, typename Result, typename T, typename BinaryOperation,
+		typename sprout::enabler_if<!sprout::is_iterator_outputable<Result>::value>::type = sprout::enabler
+	>
+	inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+	exclusive_scan(InputIterator first, InputIterator last, Result const& result, T init, BinaryOperation binary_op) {
+		return sprout::fixed::exclusive_scan(first, last, result, init, binary_op);
+	}
+	template<typename Result, typename InputIterator, typename T, typename BinaryOperation>
+	inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+	exclusive_scan(InputIterator first, InputIterator last, T init, BinaryOperation binary_op) {
+		return sprout::fixed::exclusive_scan<Result>(first, last, init, binary_op);
+	}
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_NUMERIC_FIXED_EXCLUSIVE_SCAN_HPP
diff --git a/sprout/numeric/fixed/inclusive_scan.hpp b/sprout/numeric/fixed/inclusive_scan.hpp
new file mode 100644
index 00000000..b247d036
--- /dev/null
+++ b/sprout/numeric/fixed/inclusive_scan.hpp
@@ -0,0 +1,147 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_NUMERIC_FIXED_INCLUSIVE_SCAN_HPP
+#define SPROUT_NUMERIC_FIXED_INCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/iterator/type_traits/is_iterator_of.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/algorithm/fixed/results.hpp>
+#include <sprout/pit/pit.hpp>
+#include <sprout/detail/container_complate.hpp>
+#include <sprout/numeric/fixed/partial_sum.hpp>
+
+namespace sprout {
+	namespace fixed {
+		//
+		// inclusive_scan
+		//
+		template<typename InputIterator, typename Result>
+		inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+		inclusive_scan(InputIterator first, InputIterator last, Result const& result) {
+			return sprout::fixed::partial_sum(first, last, result);
+		}
+		template<typename Result, typename InputIterator>
+		inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+		inclusive_scan(InputIterator first, InputIterator last) {
+			return sprout::fixed::partial_sum<Result>(first, last);
+		}
+
+		template<typename InputIterator, typename Result, typename BinaryOperation>
+		inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+		inclusive_scan(InputIterator first, InputIterator last, Result const& result, BinaryOperation binary_op) {
+			return sprout::fixed::partial_sum(first, last, result, binary_op);
+		}
+		template<typename Result, typename InputIterator, typename BinaryOperation>
+		inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+		inclusive_scan(InputIterator first, InputIterator last, BinaryOperation binary_op) {
+			return sprout::fixed::partial_sum<Result>(first, last, binary_op);
+		}
+
+		namespace detail {
+			template<typename InputIterator, typename Result, typename BinaryOperation, typename T>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				sprout::container_traits<Result>::static_size == 0,
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			inclusive_scan_impl(
+				InputIterator, InputIterator, Result const& result, BinaryOperation, T,
+				typename sprout::container_traits<Result>::size_type
+				)
+			{
+				return sprout::remake<Result>(result, sprout::size(result));
+			}
+			template<typename InputIterator, typename Result, typename BinaryOperation, typename T>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				sprout::container_traits<Result>::static_size == 1,
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			inclusive_scan_impl(
+				InputIterator, InputIterator, Result const& result, BinaryOperation, T init,
+				typename sprout::container_traits<Result>::size_type
+				)
+			{
+				return sprout::remake<Result>(result, sprout::size(result), init);
+			}
+			template<typename InputIterator, typename Result, typename BinaryOperation, typename T>
+			inline SPROUT_CONSTEXPR typename std::enable_if<
+				(sprout::container_traits<Result>::static_size > 1),
+				typename sprout::fixed::results::algorithm<Result>::type
+			>::type
+			inclusive_scan_impl(
+				InputIterator const& first, InputIterator const& last, Result const& result, BinaryOperation binary_op, T init,
+				typename sprout::container_traits<Result>::size_type size
+				)
+			{
+				return first != last
+					? partial_sum_impl_1(first, last, result, binary_op, size, init)
+					: sprout::detail::container_complate(result, init)
+					;
+			}
+		}	// namespace detail
+		//
+		// inclusive_scan
+		//
+		template<typename InputIterator, typename Result, typename BinaryOperation, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+		inclusive_scan(InputIterator first, InputIterator last, Result const& result, BinaryOperation binary_op, T init) {
+			return sprout::fixed::detail::inclusive_scan_impl(first, last, result, binary_op, init, sprout::size(result));
+		}
+		template<typename Result, typename InputIterator, typename BinaryOperation, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+		inclusive_scan(InputIterator first, InputIterator last, BinaryOperation binary_op, T init) {
+			return sprout::fixed::inclusive_scan(first, last, sprout::pit<Result>(), binary_op, init);
+		}
+	}	// namespace fixed
+
+	template<
+		typename InputIterator, typename Result,
+		typename sprout::enabler_if<!sprout::is_iterator_outputable<Result>::value>::type = sprout::enabler
+	>
+	inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+	inclusive_scan(InputIterator first, InputIterator last, Result const& result) {
+		return sprout::fixed::inclusive_scan(first, last, result);
+	}
+	template<typename Result, typename InputIterator>
+	inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+	inclusive_scan(InputIterator first, InputIterator last) {
+		return sprout::fixed::inclusive_scan<Result>(first, last);
+	}
+
+	template<
+		typename InputIterator, typename Result, typename BinaryOperation,
+		typename sprout::enabler_if<!sprout::is_iterator_outputable<Result>::value>::type = sprout::enabler
+	>
+	inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+	inclusive_scan(InputIterator first, InputIterator last, Result const& result, BinaryOperation binary_op) {
+		return sprout::fixed::inclusive_scan(first, last, result, binary_op);
+	}
+	template<typename Result, typename InputIterator, typename BinaryOperation>
+	inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+	inclusive_scan(InputIterator first, InputIterator last, BinaryOperation binary_op) {
+		return sprout::fixed::inclusive_scan<Result>(first, last, binary_op);
+	}
+
+	template<
+		typename InputIterator, typename Result, typename BinaryOperation, typename T,
+		typename sprout::enabler_if<!sprout::is_iterator_outputable<Result>::value>::type = sprout::enabler
+	>
+	inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+	inclusive_scan(InputIterator first, InputIterator last, Result const& result, BinaryOperation binary_op, T init) {
+		return sprout::fixed::inclusive_scan(first, last, result, binary_op, init);
+	}
+	template<typename Result, typename InputIterator, typename BinaryOperation, typename T>
+	inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+	inclusive_scan(InputIterator first, InputIterator last, BinaryOperation binary_op, T init) {
+		return sprout::fixed::inclusive_scan<Result>(first, last, binary_op, init);
+	}
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_NUMERIC_FIXED_INCLUSIVE_SCAN_HPP
diff --git a/sprout/numeric/inclusive_scan.hpp b/sprout/numeric/inclusive_scan.hpp
new file mode 100644
index 00000000..71878889
--- /dev/null
+++ b/sprout/numeric/inclusive_scan.hpp
@@ -0,0 +1,16 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_NUMERIC_INCLUSIVE_SCAN_HPP
+#define SPROUT_NUMERIC_INCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/numeric/fixed/inclusive_scan.hpp>
+#include <sprout/numeric/fit/inclusive_scan.hpp>
+#include <sprout/numeric/cxx14/inclusive_scan.hpp>
+
+#endif	// #ifndef SPROUT_NUMERIC_INCLUSIVE_SCAN_HPP
diff --git a/sprout/numeric/iota.hpp b/sprout/numeric/iota.hpp
index 7c53e6de..4059fbd6 100644
--- a/sprout/numeric/iota.hpp
+++ b/sprout/numeric/iota.hpp
@@ -11,5 +11,6 @@
 #include <sprout/config.hpp>
 #include <sprout/numeric/fixed/iota.hpp>
 #include <sprout/numeric/fit/iota.hpp>
+#include <sprout/numeric/cxx14/iota.hpp>
 
 #endif	// #ifndef SPROUT_NUMERIC_IOTA_HPP
diff --git a/sprout/numeric/non_modifying.hpp b/sprout/numeric/non_modifying.hpp
index 927adcaa..1dff6adc 100644
--- a/sprout/numeric/non_modifying.hpp
+++ b/sprout/numeric/non_modifying.hpp
@@ -10,6 +10,7 @@
 
 #include <sprout/config.hpp>
 #include <sprout/numeric/accumulate.hpp>
+#include <sprout/numeric/reduce.hpp>
 #include <sprout/numeric/inner_product.hpp>
 
 #endif	// #ifndef SPROUT_NUMERIC_NON_MODIFYIING_HPP
diff --git a/sprout/numeric/partial_sum.hpp b/sprout/numeric/partial_sum.hpp
index 4673a488..30a2fe1b 100644
--- a/sprout/numeric/partial_sum.hpp
+++ b/sprout/numeric/partial_sum.hpp
@@ -11,5 +11,6 @@
 #include <sprout/config.hpp>
 #include <sprout/numeric/fixed/partial_sum.hpp>
 #include <sprout/numeric/fit/partial_sum.hpp>
+#include <sprout/numeric/cxx14/partial_sum.hpp>
 
 #endif	// #ifndef SPROUT_NUMERIC_PARTIAL_SUM_HPP
diff --git a/sprout/numeric/reduce.hpp b/sprout/numeric/reduce.hpp
new file mode 100644
index 00000000..f6db96fc
--- /dev/null
+++ b/sprout/numeric/reduce.hpp
@@ -0,0 +1,42 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_NUMERIC_REDUCE_HPP
+#define SPROUT_NUMERIC_REDUCE_HPP
+
+#include <iterator>
+#include <sprout/config.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/numeric/accumulate.hpp>
+
+namespace sprout {
+	//
+	// reduce
+	//
+	//	recursion depth:
+	//		O(log N)
+	//
+	template<typename InputIterator>
+	inline SPROUT_CONSTEXPR typename std::iterator_traits<InputIterator>::value_type
+	reduce(InputIterator first, InputIterator last) {
+		return sprout::accumulate(first, last, typename std::iterator_traits<InputIterator>::value_type());
+	}
+
+	template<typename InputIterator, typename T>
+	inline SPROUT_CONSTEXPR T
+	reduce(InputIterator first, InputIterator last, T init) {
+		return sprout::accumulate(first, last, init);
+	}
+
+	template<typename InputIterator, typename T, typename BinaryOperation>
+	inline SPROUT_CONSTEXPR T
+	reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op) {
+		return sprout::accumulate(first, last, init, binary_op);
+	}
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_NUMERIC_REDUCE_HPP
diff --git a/sprout/range/numeric/accumulate.hpp b/sprout/range/numeric/accumulate.hpp
index 5ccfe0ca..c3893cf6 100644
--- a/sprout/range/numeric/accumulate.hpp
+++ b/sprout/range/numeric/accumulate.hpp
@@ -9,10 +9,12 @@
 #define SPROUT_RANGE_NUMERIC_ACCUMLATE_HPP
 
 #include <sprout/config.hpp>
+#include <sprout/container/functions.hpp>
 #include <sprout/numeric/accumulate.hpp>
 
 namespace sprout {
 	namespace range {
+
 		// 26.7.2 Accumulate
 		template<typename InputRange, typename T, typename BinaryOperation>
 		inline SPROUT_CONSTEXPR T
diff --git a/sprout/range/numeric/cxx14.hpp b/sprout/range/numeric/cxx14.hpp
index adb8d38c..38c9df8f 100644
--- a/sprout/range/numeric/cxx14.hpp
+++ b/sprout/range/numeric/cxx14.hpp
@@ -10,6 +10,8 @@
 
 #include <sprout/config.hpp>
 #include <sprout/range/numeric/cxx14/partial_sum.hpp>
+#include <sprout/range/numeric/cxx14/exclusive_scan.hpp>
+#include <sprout/range/numeric/cxx14/inclusive_scan.hpp>
 #include <sprout/range/numeric/cxx14/adjacent_difference.hpp>
 #include <sprout/range/numeric/cxx14/iota.hpp>
 
diff --git a/sprout/range/numeric/cxx14/exclusive_scan.hpp b/sprout/range/numeric/cxx14/exclusive_scan.hpp
new file mode 100644
index 00000000..4c0bb4d8
--- /dev/null
+++ b/sprout/range/numeric/cxx14/exclusive_scan.hpp
@@ -0,0 +1,42 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_RANGE_NUMERIC_CXX14_EXCLUSIVE_SCAN_HPP
+#define SPROUT_RANGE_NUMERIC_CXX14_EXCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/iterator/type_traits/is_iterator_of.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/numeric/cxx14/exclusive_scan.hpp>
+
+namespace sprout {
+	namespace range {
+		//
+		// exclusive_scan
+		//
+		template<
+			typename InputRange, typename OutputIterator, typename T,
+			typename sprout::enabler_if<sprout::is_iterator_outputable<OutputIterator>::value>::type = sprout::enabler
+		>
+		inline SPROUT_CONSTEXPR OutputIterator
+		exclusive_scan(InputRange const& rng, OutputIterator result, T init) {
+			return sprout::exclusive_scan(sprout::begin(rng), sprout::end(rng), result, init);
+		}
+		template<
+			typename InputRange, typename OutputIterator, typename T, typename BinaryOperation,
+			typename sprout::enabler_if<sprout::is_iterator_outputable<OutputIterator>::value>::type = sprout::enabler
+		>
+		inline SPROUT_CONSTEXPR OutputIterator
+		exclusive_scan(InputRange const& rng, OutputIterator result, T init, BinaryOperation binary_op) {
+			return sprout::exclusive_scan(sprout::begin(rng), sprout::end(rng), result, init, binary_op);
+		}
+	}	// namespace range
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_NUMERIC_CXX14_EXCLUSIVE_SCAN_HPP
diff --git a/sprout/range/numeric/cxx14/inclusive_scan.hpp b/sprout/range/numeric/cxx14/inclusive_scan.hpp
new file mode 100644
index 00000000..ee7ab3ad
--- /dev/null
+++ b/sprout/range/numeric/cxx14/inclusive_scan.hpp
@@ -0,0 +1,50 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_RANGE_NUMERIC_CXX14_INCLUSIVE_SCAN_HPP
+#define SPROUT_RANGE_NUMERIC_CXX14_INCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/iterator/type_traits/is_iterator_of.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/numeric/cxx14/inclusive_scan.hpp>
+
+namespace sprout {
+	namespace range {
+		//
+		// inclusive_scan
+		//
+		template<
+			typename InputRange, typename OutputIterator,
+			typename sprout::enabler_if<sprout::is_iterator_outputable<OutputIterator>::value>::type = sprout::enabler
+		>
+		inline SPROUT_CONSTEXPR OutputIterator
+		inclusive_scan(InputRange const& rng, OutputIterator result) {
+			return sprout::inclusive_scan(sprout::begin(rng), sprout::end(rng), result);
+		}
+		template<
+			typename InputRange, typename OutputIterator, typename BinaryOperation,
+			typename sprout::enabler_if<sprout::is_iterator_outputable<OutputIterator>::value>::type = sprout::enabler
+		>
+		inline SPROUT_CONSTEXPR OutputIterator
+		inclusive_scan(InputRange const& rng, OutputIterator result, BinaryOperation binary_op) {
+			return sprout::inclusive_scan(sprout::begin(rng), sprout::end(rng), result, binary_op);
+		}
+		template<
+			typename InputRange, typename OutputIterator, typename BinaryOperation, typename T,
+			typename sprout::enabler_if<sprout::is_iterator_outputable<OutputIterator>::value>::type = sprout::enabler
+		>
+		inline SPROUT_CONSTEXPR OutputIterator
+		inclusive_scan(InputRange const& rng, OutputIterator result, BinaryOperation binary_op, T init) {
+			return sprout::inclusive_scan(sprout::begin(rng), sprout::end(rng), result, binary_op, init);
+		}
+	}	// namespace range
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_NUMERIC_CXX14_INCLUSIVE_SCAN_HPP
diff --git a/sprout/range/numeric/exclusive_scan.hpp b/sprout/range/numeric/exclusive_scan.hpp
new file mode 100644
index 00000000..a17f08d3
--- /dev/null
+++ b/sprout/range/numeric/exclusive_scan.hpp
@@ -0,0 +1,15 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_RANGE_NUMERIC_EXCLUSIVE_SCAN_HPP
+#define SPROUT_RANGE_NUMERIC_EXCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/range/numeric/fixed/exclusive_scan.hpp>
+#include <sprout/range/numeric/fit/exclusive_scan.hpp>
+
+#endif	// #ifndef SPROUT_RANGE_NUMERIC_EXCLUSIVE_SCAN_HPP
diff --git a/sprout/range/numeric/fit.hpp b/sprout/range/numeric/fit.hpp
index 6a997bb8..93c07c5c 100644
--- a/sprout/range/numeric/fit.hpp
+++ b/sprout/range/numeric/fit.hpp
@@ -10,6 +10,8 @@
 
 #include <sprout/config.hpp>
 #include <sprout/range/numeric/fit/partial_sum.hpp>
+#include <sprout/range/numeric/fit/exclusive_scan.hpp>
+#include <sprout/range/numeric/fit/inclusive_scan.hpp>
 #include <sprout/range/numeric/fit/adjacent_difference.hpp>
 
 #endif	// #ifndef SPROUT_RANGE_NUMERIC_FIT_HPP
diff --git a/sprout/range/numeric/fit/exclusive_scan.hpp b/sprout/range/numeric/fit/exclusive_scan.hpp
new file mode 100644
index 00000000..145c8102
--- /dev/null
+++ b/sprout/range/numeric/fit/exclusive_scan.hpp
@@ -0,0 +1,48 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_RANGE_NUMERIC_FIT_EXCLUSIVE_SCAN_HPP
+#define SPROUT_RANGE_NUMERIC_FIT_EXCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/algorithm/fit/results.hpp>
+#include <sprout/numeric/fit/exclusive_scan.hpp>
+
+namespace sprout {
+	namespace range {
+		namespace fit {
+			//
+			// exclusive_scan
+			//
+			template<typename InputRange, typename Result, typename T>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			exclusive_scan(InputRange const& rng, Result const& result, T init) {
+				return sprout::fit::exclusive_scan(sprout::begin(rng), sprout::end(rng), result, init);
+			}
+			template<typename InputRange, typename Result, typename T, typename BinaryOperation>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			exclusive_scan(InputRange const& rng, Result const& result, T init, BinaryOperation binary_op) {
+				return sprout::fit::exclusive_scan(sprout::begin(rng), sprout::end(rng), result, init, binary_op);
+			}
+
+			template<typename Result, typename InputRange, typename T>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			exclusive_scan(InputRange const& rng, T init) {
+				return sprout::fit::exclusive_scan<Result>(sprout::begin(rng), sprout::end(rng), init);
+			}
+			template<typename Result, typename InputRange, typename T, typename BinaryOperation>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			exclusive_scan(InputRange const& rng, T init, BinaryOperation binary_op) {
+				return sprout::fit::exclusive_scan<Result>(sprout::begin(rng), sprout::end(rng), init, binary_op);
+			}
+		}	// namespace fit
+	}	// namespace range
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_NUMERIC_FIT_EXCLUSIVE_SCAN_HPP
diff --git a/sprout/range/numeric/fit/inclusive_scan.hpp b/sprout/range/numeric/fit/inclusive_scan.hpp
new file mode 100644
index 00000000..be1f7072
--- /dev/null
+++ b/sprout/range/numeric/fit/inclusive_scan.hpp
@@ -0,0 +1,58 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_RANGE_NUMERIC_FIT_INCLUSIVE_SCAN_HPP
+#define SPROUT_RANGE_NUMERIC_FIT_INCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/algorithm/fit/results.hpp>
+#include <sprout/numeric/fit/inclusive_scan.hpp>
+
+namespace sprout {
+	namespace range {
+		namespace fit {
+			//
+			// inclusive_scan
+			//
+			template<typename InputRange, typename Result>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng, Result const& result) {
+				return sprout::fit::inclusive_scan(sprout::begin(rng), sprout::end(rng), result);
+			}
+			template<typename InputRange, typename Result, typename BinaryOperation>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng, Result const& result, BinaryOperation binary_op) {
+				return sprout::fit::inclusive_scan(sprout::begin(rng), sprout::end(rng), result, binary_op);
+			}
+			template<typename InputRange, typename Result, typename BinaryOperation, typename T>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng, Result const& result, BinaryOperation binary_op, T init) {
+				return sprout::fit::inclusive_scan(sprout::begin(rng), sprout::end(rng), result, binary_op, init);
+			}
+
+			template<typename Result, typename InputRange>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng) {
+				return sprout::fit::inclusive_scan<Result>(sprout::begin(rng), sprout::end(rng));
+			}
+			template<typename Result, typename InputRange, typename BinaryOperation>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng, BinaryOperation binary_op) {
+				return sprout::fit::inclusive_scan<Result>(sprout::begin(rng), sprout::end(rng), binary_op);
+			}
+			template<typename Result, typename InputRange, typename BinaryOperation, typename T>
+			inline SPROUT_CONSTEXPR typename sprout::fit::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng, BinaryOperation binary_op, T init) {
+				return sprout::fit::inclusive_scan<Result>(sprout::begin(rng), sprout::end(rng), binary_op, init);
+			}
+		}	// namespace fit
+	}	// namespace range
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_NUMERIC_FIT_INCLUSIVE_SCAN_HPP
diff --git a/sprout/range/numeric/fixed.hpp b/sprout/range/numeric/fixed.hpp
index cfa71bcf..914d1d2e 100644
--- a/sprout/range/numeric/fixed.hpp
+++ b/sprout/range/numeric/fixed.hpp
@@ -10,6 +10,8 @@
 
 #include <sprout/config.hpp>
 #include <sprout/range/numeric/fixed/partial_sum.hpp>
+#include <sprout/range/numeric/fixed/exclusive_scan.hpp>
+#include <sprout/range/numeric/fixed/inclusive_scan.hpp>
 #include <sprout/range/numeric/fixed/adjacent_difference.hpp>
 
 #endif	// #ifndef SPROUT_RANGE_NUMERIC_FIXED_HPP
diff --git a/sprout/range/numeric/fixed/exclusive_scan.hpp b/sprout/range/numeric/fixed/exclusive_scan.hpp
new file mode 100644
index 00000000..16ddd617
--- /dev/null
+++ b/sprout/range/numeric/fixed/exclusive_scan.hpp
@@ -0,0 +1,58 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_RANGE_NUMERIC_FIXED_EXCLUSIVE_SCAN_HPP
+#define SPROUT_RANGE_NUMERIC_FIXED_EXCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/iterator/type_traits/is_iterator_of.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/algorithm/fixed/results.hpp>
+#include <sprout/numeric/fixed/exclusive_scan.hpp>
+
+namespace sprout {
+	namespace range {
+		namespace fixed {
+			//
+			// exclusive_scan
+			//
+			template<
+				typename InputRange, typename Result, typename T,
+				typename sprout::enabler_if<!sprout::is_iterator_outputable<Result>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+			exclusive_scan(InputRange const& rng, Result const& result, T init) {
+				return sprout::fixed::exclusive_scan(sprout::begin(rng), sprout::end(rng), result, init);
+			}
+			template<
+				typename InputRange, typename Result, typename T, typename BinaryOperation,
+				typename sprout::enabler_if<!sprout::is_iterator_outputable<Result>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+			exclusive_scan(InputRange const& rng, Result const& result, T init, BinaryOperation binary_op) {
+				return sprout::fixed::exclusive_scan(sprout::begin(rng), sprout::end(rng), result, init, binary_op);
+			}
+
+			template<typename Result, typename InputRange, typename T>
+			inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+			exclusive_scan(InputRange const& rng, T init) {
+				return sprout::fixed::exclusive_scan<Result>(sprout::begin(rng), sprout::end(rng), init);
+			}
+			template<typename Result, typename InputRange, typename T, typename BinaryOperation>
+			inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+			exclusive_scan(InputRange const& rng, T init, BinaryOperation binary_op) {
+				return sprout::fixed::exclusive_scan<Result>(sprout::begin(rng), sprout::end(rng), init, binary_op);
+			}
+		}	// namespace fixed
+
+		using sprout::range::fixed::exclusive_scan;
+	}	// namespace range
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_NUMERIC_FIXED_EXCLUSIVE_SCAN_HPP
diff --git a/sprout/range/numeric/fixed/inclusive_scan.hpp b/sprout/range/numeric/fixed/inclusive_scan.hpp
new file mode 100644
index 00000000..35f677fd
--- /dev/null
+++ b/sprout/range/numeric/fixed/inclusive_scan.hpp
@@ -0,0 +1,71 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_RANGE_NUMERIC_FIXED_INCLUSIVE_SCAN_HPP
+#define SPROUT_RANGE_NUMERIC_FIXED_INCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/container/traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/iterator/type_traits/is_iterator_of.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/algorithm/fixed/results.hpp>
+#include <sprout/numeric/fixed/inclusive_scan.hpp>
+
+namespace sprout {
+	namespace range {
+		namespace fixed {
+			//
+			// inclusive_scan
+			//
+			template<
+				typename InputRange, typename Result,
+				typename sprout::enabler_if<!sprout::is_iterator_outputable<Result>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng, Result const& result) {
+				return sprout::fixed::inclusive_scan(sprout::begin(rng), sprout::end(rng), result);
+			}
+			template<
+				typename InputRange, typename Result, typename BinaryOperation,
+				typename sprout::enabler_if<!sprout::is_iterator_outputable<Result>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng, Result const& result, BinaryOperation binary_op) {
+				return sprout::fixed::inclusive_scan(sprout::begin(rng), sprout::end(rng), result, binary_op);
+			}
+			template<
+				typename InputRange, typename Result, typename BinaryOperation, typename T,
+				typename sprout::enabler_if<!sprout::is_iterator_outputable<Result>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng, Result const& result, BinaryOperation binary_op, T init) {
+				return sprout::fixed::inclusive_scan(sprout::begin(rng), sprout::end(rng), result, binary_op, init);
+			}
+
+			template<typename Result, typename InputRange>
+			inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng) {
+				return sprout::fixed::inclusive_scan<Result>(sprout::begin(rng), sprout::end(rng));
+			}
+			template<typename Result, typename InputRange, typename BinaryOperation>
+			inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng, BinaryOperation binary_op) {
+				return sprout::fixed::inclusive_scan<Result>(sprout::begin(rng), sprout::end(rng), binary_op);
+			}
+			template<typename Result, typename InputRange, typename BinaryOperation, typename T>
+			inline SPROUT_CONSTEXPR typename sprout::fixed::results::algorithm<Result>::type
+			inclusive_scan(InputRange const& rng, BinaryOperation binary_op, T init) {
+				return sprout::fixed::inclusive_scan<Result>(sprout::begin(rng), sprout::end(rng), binary_op, init);
+			}
+		}	// namespace fixed
+
+		using sprout::range::fixed::inclusive_scan;
+	}	// namespace range
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_NUMERIC_FIXED_INCLUSIVE_SCAN_HPP
diff --git a/sprout/range/numeric/inclusive_scan.hpp b/sprout/range/numeric/inclusive_scan.hpp
new file mode 100644
index 00000000..30b9f159
--- /dev/null
+++ b/sprout/range/numeric/inclusive_scan.hpp
@@ -0,0 +1,15 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_RANGE_NUMERIC_INCLUSIVE_SCAN_HPP
+#define SPROUT_RANGE_NUMERIC_INCLUSIVE_SCAN_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/range/numeric/fixed/inclusive_scan.hpp>
+#include <sprout/range/numeric/fit/inclusive_scan.hpp>
+
+#endif	// #ifndef SPROUT_RANGE_NUMERIC_INCLUSIVE_SCAN_HPP
diff --git a/sprout/range/numeric/inner_product.hpp b/sprout/range/numeric/inner_product.hpp
index 07bbf413..4ab56821 100644
--- a/sprout/range/numeric/inner_product.hpp
+++ b/sprout/range/numeric/inner_product.hpp
@@ -9,10 +9,12 @@
 #define SPROUT_RANGE_NUMERIC_INNER_PRODUCT_HPP
 
 #include <sprout/config.hpp>
+#include <sprout/container/functions.hpp>
 #include <sprout/numeric/inner_product.hpp>
 
 namespace sprout {
 	namespace range {
+
 		// 26.7.3 Inner product
 		template<typename InputRange1, typename InputRange2, typename T, typename BinaryOperation1, typename BinaryOperation2>
 		inline SPROUT_CONSTEXPR T
diff --git a/sprout/range/numeric/non_modifying.hpp b/sprout/range/numeric/non_modifying.hpp
index 1d94c876..ee3f5bda 100644
--- a/sprout/range/numeric/non_modifying.hpp
+++ b/sprout/range/numeric/non_modifying.hpp
@@ -10,6 +10,7 @@
 
 #include <sprout/config.hpp>
 #include <sprout/range/numeric/accumulate.hpp>
+#include <sprout/range/numeric/reduce.hpp>
 #include <sprout/range/numeric/inner_product.hpp>
 
 #endif	// #ifndef SPROUT_RANGE_NUMERIC_NON_MODIFYIING_HPP
diff --git a/sprout/range/numeric/reduce.hpp b/sprout/range/numeric/reduce.hpp
new file mode 100644
index 00000000..15672e00
--- /dev/null
+++ b/sprout/range/numeric/reduce.hpp
@@ -0,0 +1,41 @@
+/*=============================================================================
+  Copyright (c) 2011-2017 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_RANGE_NUMERIC_REDUCE_HPP
+#define SPROUT_RANGE_NUMERIC_REDUCE_HPP
+
+#include <iterator>
+#include <sprout/config.hpp>
+#include <sprout/container/container_traits.hpp>
+#include <sprout/container/functions.hpp>
+#include <sprout/numeric/reduce.hpp>
+
+namespace sprout {
+	namespace range {
+
+		// 29.8.3 Reduce
+		template<typename InputRange, typename T, typename BinaryOperation>
+		inline SPROUT_CONSTEXPR T
+		reduce(InputRange const& range, T init, BinaryOperation binary_op) {
+			return sprout::reduce(sprout::begin(range), sprout::end(range), init, binary_op);
+		}
+
+		template<typename InputRange, typename T>
+		inline SPROUT_CONSTEXPR T
+		reduce(InputRange const& range, T init) {
+			return sprout::reduce(sprout::begin(range), sprout::end(range), init);
+		}
+
+		template<typename InputRange>
+		inline SPROUT_CONSTEXPR typename std::iterator_traits<typename sprout::container_traits<InputRange>::iterator>::value_type
+		reduce(InputRange const& range) {
+			return sprout::reduce(sprout::begin(range), sprout::end(range));
+		}
+	}	// namespace range
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_RANGE_NUMERIC_REDUCE_HPP
diff --git a/sprout/sub_array/container.hpp b/sprout/sub_array/container.hpp
index 8117dbe1..3fcf9eb4 100644
--- a/sprout/sub_array/container.hpp
+++ b/sprout/sub_array/container.hpp
@@ -85,7 +85,7 @@ namespace sprout {
 		public:
 			typedef sprout::sub_array<
 				typename sprout::container_transform_traits<
-					typename std::remove_reference<Container>::type
+					typename sprout::container_construct_traits<Container>::copied_type
 				>::template rebind_size<Size>::type
 			> type;
 		};
@@ -94,7 +94,7 @@ namespace sprout {
 		public:
 			typedef sprout::sub_array<
 				typename sprout::container_transform_traits<
-					typename std::remove_reference<Container>::type
+					typename sprout::container_construct_traits<Container>::copied_type
 				>::template rebind_type<Type>::type
 			> type;
 		};
diff --git a/testspr/trace.hpp b/testspr/trace.hpp
index 6fa195b7..5e883e71 100644
--- a/testspr/trace.hpp
+++ b/testspr/trace.hpp
@@ -155,14 +155,18 @@ namespace testspr {
 			SPROUT_NON_CONSTEXPR comparable_function(function_type const& f)
 				: func_(f)
 			{}
-			SPROUT_NON_CONSTEXPR bool operator()(trace_stack const& t) {
+			SPROUT_NON_CONSTEXPR bool operator()(trace_stack const& t) const {
 				return func_(t);
 			}
-			SPROUT_NON_CONSTEXPR bool operator==(function_type const& rhs) {
-				return func_.target_type() == rhs.target_type();
+			SPROUT_NON_CONSTEXPR bool operator==(function_type const& rhs) const {
+				return func_ == nullptr ? rhs == nullptr
+					: rhs == nullptr ? false
+					: func_.target_type() == rhs.target_type()
+						&& func_.target<bool (testspr::trace_stack const&)>() == rhs.target<bool (testspr::trace_stack const&)>()
+					;
 			}
-			SPROUT_NON_CONSTEXPR bool operator!=(function_type const& rhs) {
-				return func_.target_type() != rhs.target_type();
+			SPROUT_NON_CONSTEXPR bool operator!=(function_type const& rhs) const {
+				return !(*this == rhs);
 			}
 		};
 	private: