diff --git a/sprout/valarray/comparison.hpp b/sprout/valarray/comparison.hpp
index 56b8f180..8eb704b8 100644
--- a/sprout/valarray/comparison.hpp
+++ b/sprout/valarray/comparison.hpp
@@ -20,7 +20,7 @@
 #include <sprout/functional/less_equal.hpp>
 #include <sprout/functional/bind2nd.hpp>
 #include <sprout/functional/bind1st.hpp>
-#include <sprout/sized_pit.hpp>
+#include <sprout/sized_pit/sized_pit.hpp>
 
 namespace sprout {
 	//
diff --git a/sprout/valarray/gslice_array.hpp b/sprout/valarray/gslice_array.hpp
index 2ba1f267..e0c19215 100644
--- a/sprout/valarray/gslice_array.hpp
+++ b/sprout/valarray/gslice_array.hpp
@@ -13,6 +13,7 @@
 #include <sprout/utility/swap.hpp>
 #include <sprout/iterator/next.hpp>
 #include <sprout/iterator/index_iterator.hpp>
+#include <sprout/iterator/reverse_iterator.hpp>
 #include <sprout/functional/multiplies.hpp>
 #include <sprout/algorithm/cxx14/copy.hpp>
 #include <sprout/algorithm/cxx14/fill.hpp>
@@ -35,7 +36,11 @@ namespace sprout {
 		SPROUT_CONSTEXPR gslice()
 			: start_(), size_(), stride_()
 		{}
-		SPROUT_CONSTEXPR gslice(std::size_t start, sprout::valarray<std::size_t, N> const& size, sprout::valarray<std::size_t, N> const& stride)
+		SPROUT_CONSTEXPR gslice(
+			std::size_t start,
+			sprout::valarray<std::size_t, N> const& size,
+			sprout::valarray<std::size_t, N> const& stride
+			)
 			: start_(start), size_(size), stride_(stride)
 		{}
 		SPROUT_CONSTEXPR std::size_t start() const {
@@ -64,6 +69,7 @@ namespace sprout {
 		typedef typename valarray_type::difference_type difference_type;
 		typedef typename valarray_type::pointer pointer;
 		typedef sprout::index_iterator<gslice_array const&> iterator;
+		typedef sprout::reverse_iterator<iterator> reverse_iterator;
 	private:
 		typedef sprout::gslice<M> gslice_type;
 		typedef sprout::valarray<size_type, (M < N ? M : N)> indexes_type;
@@ -222,26 +228,51 @@ namespace sprout {
 		end() const {
 			return iterator(*this, size());
 		}
+		SPROUT_CONSTEXPR reverse_iterator
+		rbegin() const {
+			return reverse_iterator(end());
+		}
+		SPROUT_CONSTEXPR reverse_iterator
+		rend() const {
+			return reverse_iterator(begin());
+		}
 		// capacity:
-		SPROUT_CONSTEXPR size_type size() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR size_type
+		size() const SPROUT_NOEXCEPT {
 			return size_.front();
 		}
-		SPROUT_CONSTEXPR bool empty() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR bool
+		empty() const SPROUT_NOEXCEPT {
 			return size() == 0;
 		}
 		// element access:
-		SPROUT_CONSTEXPR reference operator[](size_type i) const {
+		SPROUT_CONSTEXPR reference
+		operator[](size_type i) const {
 			return (*arr_)[index(i)];
 		}
-		SPROUT_CONSTEXPR reference at(size_type i) const {
+		SPROUT_CONSTEXPR reference
+		at(size_type i) const {
 			return arr_->at(index(i));
 		}
-		SPROUT_CONSTEXPR reference front() const {
+		SPROUT_CONSTEXPR reference
+		front() const {
 			return (*this)[0];
 		}
-		SPROUT_CONSTEXPR reference back() const {
+		SPROUT_CONSTEXPR reference
+		back() const {
 			return (*this)[size() - 1];
 		}
+		// others:
+		SPROUT_CONSTEXPR iterator
+		nth(size_type i) const {
+			return i < size() ? begin() + i
+				: (throw std::out_of_range("gslice_array<>: index out of range"), iterator())
+				;
+		}
+		SPROUT_CONSTEXPR size_type
+		index_of(iterator p) const SPROUT_NOEXCEPT {
+			return p - begin();
+		}
 	};
 	template<typename T, std::size_t N, std::size_t M>
 	SPROUT_CONSTEXPR_OR_CONST typename sprout::gslice_array<T, N, M>::size_type sprout::gslice_array<T, N, M>::static_size;
diff --git a/sprout/valarray/indirect_array.hpp b/sprout/valarray/indirect_array.hpp
index b72208ec..15498f84 100644
--- a/sprout/valarray/indirect_array.hpp
+++ b/sprout/valarray/indirect_array.hpp
@@ -12,6 +12,7 @@
 #include <sprout/workaround/std/cstddef.hpp>
 #include <sprout/utility/swap.hpp>
 #include <sprout/iterator/index_iterator.hpp>
+#include <sprout/iterator/reverse_iterator.hpp>
 #include <sprout/algorithm/cxx14/copy.hpp>
 #include <sprout/algorithm/cxx14/fill.hpp>
 #include <sprout/valarray/valarray_fwd.hpp>
@@ -32,6 +33,7 @@ namespace sprout {
 		typedef typename valarray_type::difference_type difference_type;
 		typedef typename valarray_type::pointer pointer;
 		typedef sprout::index_iterator<indirect_array const&> iterator;
+		typedef sprout::reverse_iterator<iterator> reverse_iterator;
 	private:
 		typedef sprout::valarray<size_type, M> indexes_type;
 	public:
@@ -160,26 +162,51 @@ namespace sprout {
 		end() const {
 			return iterator(*this, size());
 		}
+		SPROUT_CONSTEXPR reverse_iterator
+		rbegin() const {
+			return reverse_iterator(end());
+		}
+		SPROUT_CONSTEXPR reverse_iterator
+		rend() const {
+			return reverse_iterator(begin());
+		}
 		// capacity:
-		SPROUT_CONSTEXPR size_type size() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR size_type
+		size() const SPROUT_NOEXCEPT {
 			return indexes_.size();
 		}
-		SPROUT_CONSTEXPR bool empty() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR bool
+		empty() const SPROUT_NOEXCEPT {
 			return size() == 0;
 		}
 		// element access:
-		SPROUT_CONSTEXPR reference operator[](size_type i) const {
+		SPROUT_CONSTEXPR reference
+		operator[](size_type i) const {
 			return (*arr_)[indexes_[i]];
 		}
-		SPROUT_CONSTEXPR reference at(size_type i) const {
+		SPROUT_CONSTEXPR reference
+		at(size_type i) const {
 			return arr_->at(indexes_.at(i));
 		}
-		SPROUT_CONSTEXPR reference front() const {
+		SPROUT_CONSTEXPR reference
+		front() const {
 			return (*this)[0];
 		}
-		SPROUT_CONSTEXPR reference back() const {
+		SPROUT_CONSTEXPR reference
+		back() const {
 			return (*this)[size() - 1];
 		}
+		// others:
+		SPROUT_CONSTEXPR iterator
+		nth(size_type i) const {
+			return i < size() ? begin() + i
+				: (throw std::out_of_range("indirect_array<>: index out of range"), iterator())
+				;
+		}
+		SPROUT_CONSTEXPR size_type
+		index_of(iterator p) const SPROUT_NOEXCEPT {
+			return p - begin();
+		}
 	};
 	template<typename T, std::size_t N, std::size_t M>
 	SPROUT_CONSTEXPR_OR_CONST typename sprout::indirect_array<T, N, M>::size_type sprout::indirect_array<T, N, M>::static_size;
diff --git a/sprout/valarray/logical.hpp b/sprout/valarray/logical.hpp
index 5a69764a..cfcba55e 100644
--- a/sprout/valarray/logical.hpp
+++ b/sprout/valarray/logical.hpp
@@ -16,7 +16,7 @@
 #include <sprout/functional/logical_or.hpp>
 #include <sprout/functional/bind2nd.hpp>
 #include <sprout/functional/bind1st.hpp>
-#include <sprout/sized_pit.hpp>
+#include <sprout/sized_pit/sized_pit.hpp>
 
 namespace sprout {
 	//
diff --git a/sprout/valarray/mask_array.hpp b/sprout/valarray/mask_array.hpp
index 241839d2..b73d95a5 100644
--- a/sprout/valarray/mask_array.hpp
+++ b/sprout/valarray/mask_array.hpp
@@ -12,6 +12,7 @@
 #include <sprout/workaround/std/cstddef.hpp>
 #include <sprout/utility/swap.hpp>
 #include <sprout/iterator/index_iterator.hpp>
+#include <sprout/iterator/reverse_iterator.hpp>
 #include <sprout/algorithm/count.hpp>
 #include <sprout/algorithm/cxx14/copy.hpp>
 #include <sprout/algorithm/cxx14/fill.hpp>
@@ -34,6 +35,7 @@ namespace sprout {
 		typedef typename valarray_type::difference_type difference_type;
 		typedef typename valarray_type::pointer pointer;
 		typedef sprout::index_iterator<mask_array const&> iterator;
+		typedef sprout::reverse_iterator<iterator> reverse_iterator;
 	private:
 		typedef sprout::valarray<bool, M> mask_type;
 		typedef sprout::valarray<size_type, (M < N ? M : N)> indexes_type;
@@ -168,26 +170,51 @@ namespace sprout {
 		end() const {
 			return iterator(*this, size());
 		}
+		SPROUT_CONSTEXPR reverse_iterator
+		rbegin() const {
+			return reverse_iterator(end());
+		}
+		SPROUT_CONSTEXPR reverse_iterator
+		rend() const {
+			return reverse_iterator(begin());
+		}
 		// capacity:
-		SPROUT_CONSTEXPR size_type size() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR size_type
+		size() const SPROUT_NOEXCEPT {
 			return indexes_.size();
 		}
-		SPROUT_CONSTEXPR bool empty() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR bool
+		empty() const SPROUT_NOEXCEPT {
 			return size() == 0;
 		}
 		// element access:
-		SPROUT_CONSTEXPR reference operator[](size_type i) const {
+		SPROUT_CONSTEXPR reference
+		operator[](size_type i) const {
 			return (*arr_)[indexes_[i]];
 		}
-		SPROUT_CONSTEXPR reference at(size_type i) const {
+		SPROUT_CONSTEXPR reference
+		at(size_type i) const {
 			return arr_->at(indexes_.at(i));
 		}
-		SPROUT_CONSTEXPR reference front() const {
+		SPROUT_CONSTEXPR reference
+		front() const {
 			return (*this)[0];
 		}
-		SPROUT_CONSTEXPR reference back() const {
+		SPROUT_CONSTEXPR reference
+		back() const {
 			return (*this)[size() - 1];
 		}
+		// others:
+		SPROUT_CONSTEXPR iterator
+		nth(size_type i) const {
+			return i < size() ? begin() + i
+				: (throw std::out_of_range("mask_array<>: index out of range"), iterator())
+				;
+		}
+		SPROUT_CONSTEXPR size_type
+		index_of(iterator p) const SPROUT_NOEXCEPT {
+			return p - begin();
+		}
 	};
 	template<typename T, std::size_t N, std::size_t M>
 	SPROUT_CONSTEXPR_OR_CONST typename sprout::mask_array<T, N, M>::size_type sprout::mask_array<T, N, M>::static_size;
diff --git a/sprout/valarray/slice_array.hpp b/sprout/valarray/slice_array.hpp
index 9b65d804..a06f5700 100644
--- a/sprout/valarray/slice_array.hpp
+++ b/sprout/valarray/slice_array.hpp
@@ -12,6 +12,7 @@
 #include <sprout/workaround/std/cstddef.hpp>
 #include <sprout/utility/swap.hpp>
 #include <sprout/iterator/index_iterator.hpp>
+#include <sprout/iterator/reverse_iterator.hpp>
 #include <sprout/algorithm/cxx14/copy.hpp>
 #include <sprout/algorithm/cxx14/fill.hpp>
 #include <sprout/valarray/valarray_fwd.hpp>
@@ -58,6 +59,7 @@ namespace sprout {
 		typedef typename valarray_type::difference_type difference_type;
 		typedef typename valarray_type::pointer pointer;
 		typedef sprout::index_iterator<slice_array const&> iterator;
+		typedef sprout::reverse_iterator<iterator> reverse_iterator;
 	public:
 		SPROUT_STATIC_CONSTEXPR size_type static_size = valarray_type::static_size;
 	private:
@@ -183,26 +185,51 @@ namespace sprout {
 		end() const {
 			return iterator(*this, size());
 		}
+		SPROUT_CONSTEXPR reverse_iterator
+		rbegin() const {
+			return reverse_iterator(end());
+		}
+		SPROUT_CONSTEXPR reverse_iterator
+		rend() const {
+			return reverse_iterator(begin());
+		}
 		// capacity:
-		SPROUT_CONSTEXPR size_type size() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR size_type
+		size() const SPROUT_NOEXCEPT {
 			return slice_.size();
 		}
-		SPROUT_CONSTEXPR bool empty() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR bool
+		empty() const SPROUT_NOEXCEPT {
 			return size() == 0;
 		}
 		// element access:
-		SPROUT_CONSTEXPR reference operator[](size_type i) const {
+		SPROUT_CONSTEXPR reference
+		operator[](size_type i) const {
 			return (*arr_)[slice_.start() + slice_.stride() * i];
 		}
-		SPROUT_CONSTEXPR reference at(size_type i) const {
+		SPROUT_CONSTEXPR reference
+		at(size_type i) const {
 			return arr_->at(slice_.start() + slice_.stride() * i);
 		}
-		SPROUT_CONSTEXPR reference front() const {
+		SPROUT_CONSTEXPR reference
+		front() const {
 			return (*this)[0];
 		}
-		SPROUT_CONSTEXPR reference back() const {
+		SPROUT_CONSTEXPR reference
+		back() const {
 			return (*this)[size() - 1];
 		}
+		// others:
+		SPROUT_CONSTEXPR iterator
+		nth(size_type i) const {
+			return i < size() ? begin() + i
+				: (throw std::out_of_range("slice_array<>: index out of range"), iterator())
+				;
+		}
+		SPROUT_CONSTEXPR size_type
+		index_of(iterator p) const SPROUT_NOEXCEPT {
+			return p - begin();
+		}
 	};
 	template<typename T, std::size_t N>
 	SPROUT_CONSTEXPR_OR_CONST typename sprout::slice_array<T, N>::size_type sprout::slice_array<T, N>::static_size;
diff --git a/sprout/valarray/valarray.hpp b/sprout/valarray/valarray.hpp
index d70179cb..84a449cc 100644
--- a/sprout/valarray/valarray.hpp
+++ b/sprout/valarray/valarray.hpp
@@ -53,6 +53,7 @@
 #include <sprout/valarray/gslice_array.hpp>
 #include <sprout/valarray/mask_array.hpp>
 #include <sprout/valarray/indirect_array.hpp>
+#include <sprout/sized_pit/sized_pit.hpp>
 
 namespace sprout {
 	namespace detail {
@@ -453,119 +454,152 @@ namespace sprout {
 		}
 
 		// modifiers (array):
-		SPROUT_CXX14_CONSTEXPR void fill(const_reference value) {
+		SPROUT_CXX14_CONSTEXPR void
+		fill(const_reference value) {
 			impl_.array_.fill(value);
 		}
-		SPROUT_CONSTEXPR valarray fill(const_reference value) const {
+		SPROUT_CONSTEXPR valarray
+		fill(const_reference value) const {
 			return valarray(value, size());
 		}
-		SPROUT_CXX14_CONSTEXPR void assign(const_reference value) {
+		SPROUT_CXX14_CONSTEXPR void
+		assign(const_reference value) {
 			impl_.array_.assign(value);
 		}
-		SPROUT_CONSTEXPR valarray assign(const_reference value) const {
+		SPROUT_CONSTEXPR valarray
+		assign(const_reference value) const {
 			return valarray(value, size());
 		}
 		// iterators (array):
-		SPROUT_CXX14_CONSTEXPR iterator begin() SPROUT_NOEXCEPT {
+		SPROUT_CXX14_CONSTEXPR iterator
+		begin() SPROUT_NOEXCEPT {
 			return impl_.array_.begin();
 		}
-		SPROUT_CONSTEXPR const_iterator begin() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR const_iterator
+		begin() const SPROUT_NOEXCEPT {
 			return impl_.array_.begin();
 		}
-		SPROUT_CXX14_CONSTEXPR iterator end() SPROUT_NOEXCEPT {
+		SPROUT_CXX14_CONSTEXPR iterator
+		end() SPROUT_NOEXCEPT {
 			return impl_.array_.begin() + size();
 		}
-		SPROUT_CONSTEXPR const_iterator end() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR const_iterator
+		end() const SPROUT_NOEXCEPT {
 			return impl_.array_.begin() + size();
 		}
-		SPROUT_CXX14_CONSTEXPR reverse_iterator rbegin() SPROUT_NOEXCEPT {
+		SPROUT_CXX14_CONSTEXPR reverse_iterator
+		rbegin() SPROUT_NOEXCEPT {
 			return impl_.array_.rend() - size();
 		}
-		SPROUT_CONSTEXPR const_reverse_iterator rbegin() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR const_reverse_iterator
+		rbegin() const SPROUT_NOEXCEPT {
 			return impl_.array_.rend() - size();
 		}
-		SPROUT_CXX14_CONSTEXPR reverse_iterator rend() SPROUT_NOEXCEPT {
+		SPROUT_CXX14_CONSTEXPR reverse_iterator
+		rend() SPROUT_NOEXCEPT {
 			return impl_.array_.rend();
 		}
-		SPROUT_CONSTEXPR const_reverse_iterator rend() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR const_reverse_iterator
+		rend() const SPROUT_NOEXCEPT {
 			return impl_.array_.rend();
 		}
-		SPROUT_CONSTEXPR const_iterator cbegin() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR const_iterator
+		cbegin() const SPROUT_NOEXCEPT {
 			return impl_.array_.cbegin();
 		}
-		SPROUT_CONSTEXPR const_iterator cend() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR const_iterator
+		cend() const SPROUT_NOEXCEPT {
 			return impl_.array_.cbegin() + size();
 		}
-		SPROUT_CONSTEXPR const_reverse_iterator crbegin() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR const_reverse_iterator
+		crbegin() const SPROUT_NOEXCEPT {
 			return impl_.array_.crend() - size();
 		}
-		SPROUT_CONSTEXPR const_reverse_iterator crend() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR const_reverse_iterator
+		crend() const SPROUT_NOEXCEPT {
 			return impl_.array_.crend();
 		}
 		// capacity (array):
-		SPROUT_CONSTEXPR size_type max_size() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR size_type
+		max_size() const SPROUT_NOEXCEPT {
 			return impl_.array_.max_size();
 		}
-		SPROUT_CONSTEXPR bool empty() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR bool
+		empty() const SPROUT_NOEXCEPT {
 			return size() != 0;
 		}
 		// element access (array):
-		SPROUT_CXX14_CONSTEXPR reference at(size_type i) {
+		SPROUT_CXX14_CONSTEXPR reference
+		at(size_type i) {
 			return i < size() ? (*this)[i]
 				: (throw std::out_of_range("valarray<>: index out of range"), (*this)[i])
 				;
 		}
-		SPROUT_CONSTEXPR const_reference at(size_type i) const {
+		SPROUT_CONSTEXPR const_reference
+		at(size_type i) const {
 			return i < size() ? (*this)[i]
 				: (throw std::out_of_range("valarray<>: index out of range"), (*this)[i])
 				;
 		}
-		SPROUT_CXX14_CONSTEXPR reference front() {
+		SPROUT_CXX14_CONSTEXPR reference
+		front() {
 			return impl_.array_.front();
 		}
-		SPROUT_CONSTEXPR const_reference front() const {
+		SPROUT_CONSTEXPR const_reference
+		front() const {
 			return impl_.array_.front();
 		}
-		SPROUT_CXX14_CONSTEXPR reference back() {
+		SPROUT_CXX14_CONSTEXPR reference
+		back() {
 			return (*this)[size() - 1];
 		}
-		SPROUT_CONSTEXPR const_reference back() const {
+		SPROUT_CONSTEXPR const_reference
+		back() const {
 			return (*this)[size() - 1];
 		}
 
-		SPROUT_CXX14_CONSTEXPR pointer data() SPROUT_NOEXCEPT {
+		SPROUT_CXX14_CONSTEXPR pointer
+		data() SPROUT_NOEXCEPT {
 			return impl_.array_.data();
 		}
-		SPROUT_CONSTEXPR const_pointer data() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR const_pointer
+		data() const SPROUT_NOEXCEPT {
 			return impl_.array_.data();
 		}
-		SPROUT_CXX14_CONSTEXPR pointer c_array() SPROUT_NOEXCEPT {
+		SPROUT_CXX14_CONSTEXPR pointer
+		c_array() SPROUT_NOEXCEPT {
 			return impl_.array_.c_array();
 		}
-		SPROUT_CONSTEXPR const_pointer c_array() const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR const_pointer
+		c_array() const SPROUT_NOEXCEPT {
 			return impl_.array_.c_array();
 		}
 		// others (array):
-		SPROUT_CXX14_CONSTEXPR void rangecheck(size_type i) const {
+		SPROUT_CXX14_CONSTEXPR void
+		rangecheck(size_type i) const {
 			return i >= size() ? throw std::out_of_range("valarray<>: index out of range")
 				: (void)0
 				;
 		}
 
-		SPROUT_CXX14_CONSTEXPR iterator nth(size_type i) {
+		SPROUT_CXX14_CONSTEXPR iterator
+		nth(size_type i) {
 			return i < size() ? begin() + i
 				: (throw std::out_of_range("valarray<>: index out of range"), iterator())
 				;
 		}
-		SPROUT_CONSTEXPR const_iterator nth(size_type i) const {
+		SPROUT_CONSTEXPR const_iterator
+		nth(size_type i) const {
 			return i < size() ? begin() + i
 				: (throw std::out_of_range("valarray<>: index out of range"), const_iterator())
 				;
 		}
-		SPROUT_CXX14_CONSTEXPR size_type index_of(iterator p) SPROUT_NOEXCEPT {
+		SPROUT_CXX14_CONSTEXPR size_type
+		index_of(iterator p) SPROUT_NOEXCEPT {
 			return impl_.array_.index_of(p);
 		}
-		SPROUT_CONSTEXPR size_type index_of(const_iterator p) const SPROUT_NOEXCEPT {
+		SPROUT_CONSTEXPR size_type
+		index_of(const_iterator p) const SPROUT_NOEXCEPT {
 			return impl_.array_.index_of(p);
 		}
 	};