Add libc++ and libc++abi to third-party.

third_party/libcxx/include/valarray

+// -*- C++ -*-
+//===-------------------------- valarray ----------------------------------===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP_VALARRAY
+#define _LIBCPP_VALARRAY
+
+/*
+    valarray synopsis
+
+namespace std
+{
+
+template<class T>
+class valarray
+{
+public:
+    typedef T value_type;
+
+    // construct/destroy:
+    valarray();
+    explicit valarray(size_t n);
+    valarray(const value_type& x, size_t n);
+    valarray(const value_type* px, size_t n);
+    valarray(const valarray& v);
+    valarray(valarray&& v) noexcept;
+    valarray(const slice_array<value_type>& sa);
+    valarray(const gslice_array<value_type>& ga);
+    valarray(const mask_array<value_type>& ma);
+    valarray(const indirect_array<value_type>& ia);
+    valarray(initializer_list<value_type> il);
+    ~valarray();
+
+    // assignment:
+    valarray& operator=(const valarray& v);
+    valarray& operator=(valarray&& v) noexcept;
+    valarray& operator=(initializer_list<value_type> il);
+    valarray& operator=(const value_type& x);
+    valarray& operator=(const slice_array<value_type>& sa);
+    valarray& operator=(const gslice_array<value_type>& ga);
+    valarray& operator=(const mask_array<value_type>& ma);
+    valarray& operator=(const indirect_array<value_type>& ia);
+
+    // element access:
+    const value_type& operator[](size_t i) const;
+    value_type&       operator[](size_t i);
+
+    // subset operations:
+    valarray                   operator[](slice s) const;
+    slice_array<value_type>    operator[](slice s);
+    valarray                   operator[](const gslice& gs) const;
+    gslice_array<value_type>   operator[](const gslice& gs);
+    valarray                   operator[](const valarray<bool>& vb) const;
+    mask_array<value_type>     operator[](const valarray<bool>& vb);
+    valarray                   operator[](const valarray<size_t>& vs) const;
+    indirect_array<value_type> operator[](const valarray<size_t>& vs);
+
+    // unary operators:
+    valarray       operator+() const;
+    valarray       operator-() const;
+    valarray       operator~() const;
+    valarray<bool> operator!() const;
+
+    // computed assignment:
+    valarray& operator*= (const value_type& x);
+    valarray& operator/= (const value_type& x);
+    valarray& operator%= (const value_type& x);
+    valarray& operator+= (const value_type& x);
+    valarray& operator-= (const value_type& x);
+    valarray& operator^= (const value_type& x);
+    valarray& operator&= (const value_type& x);
+    valarray& operator|= (const value_type& x);
+    valarray& operator<<=(const value_type& x);
+    valarray& operator>>=(const value_type& x);
+
+    valarray& operator*= (const valarray& v);
+    valarray& operator/= (const valarray& v);
+    valarray& operator%= (const valarray& v);
+    valarray& operator+= (const valarray& v);
+    valarray& operator-= (const valarray& v);
+    valarray& operator^= (const valarray& v);
+    valarray& operator|= (const valarray& v);
+    valarray& operator&= (const valarray& v);
+    valarray& operator<<=(const valarray& v);
+    valarray& operator>>=(const valarray& v);
+
+    // member functions:
+    void swap(valarray& v) noexcept;
+
+    size_t size() const;
+
+    value_type sum() const;
+    value_type min() const;
+    value_type max() const;
+
+    valarray shift (int i) const;
+    valarray cshift(int i) const;
+    valarray apply(value_type f(value_type)) const;
+    valarray apply(value_type f(const value_type&)) const;
+    void resize(size_t n, value_type x = value_type());
+};
+
+class slice
+{
+public:
+    slice();
+    slice(size_t start, size_t size, size_t stride);
+
+    size_t start()  const;
+    size_t size()   const;
+    size_t stride() const;
+};
+
+template <class T>
+class slice_array
+{
+public:
+    typedef T value_type;
+
+    const slice_array& operator=(const slice_array& sa) const;
+    void operator=  (const valarray<value_type>& v) const;
+    void operator*= (const valarray<value_type>& v) const;
+    void operator/= (const valarray<value_type>& v) const;
+    void operator%= (const valarray<value_type>& v) const;
+    void operator+= (const valarray<value_type>& v) const;
+    void operator-= (const valarray<value_type>& v) const;
+    void operator^= (const valarray<value_type>& v) const;
+    void operator&= (const valarray<value_type>& v) const;
+    void operator|= (const valarray<value_type>& v) const;
+    void operator<<=(const valarray<value_type>& v) const;
+    void operator>>=(const valarray<value_type>& v) const;
+
+    void operator=(const value_type& x) const;
+
+    slice_array() = delete;
+};
+
+class gslice
+{
+public:
+    gslice();
+    gslice(size_t start, const valarray<size_t>& size,
+                         const valarray<size_t>& stride);
+
+    size_t           start()  const;
+    valarray<size_t> size()   const;
+    valarray<size_t> stride() const;
+};
+
+template <class T>
+class gslice_array
+{
+public:
+    typedef T value_type;
+
+    void operator=  (const valarray<value_type>& v) const;
+    void operator*= (const valarray<value_type>& v) const;
+    void operator/= (const valarray<value_type>& v) const;
+    void operator%= (const valarray<value_type>& v) const;
+    void operator+= (const valarray<value_type>& v) const;
+    void operator-= (const valarray<value_type>& v) const;
+    void operator^= (const valarray<value_type>& v) const;
+    void operator&= (const valarray<value_type>& v) const;
+    void operator|= (const valarray<value_type>& v) const;
+    void operator<<=(const valarray<value_type>& v) const;
+    void operator>>=(const valarray<value_type>& v) const;
+
+    gslice_array(const gslice_array& ga);
+    ~gslice_array();
+    const gslice_array& operator=(const gslice_array& ga) const;
+    void operator=(const value_type& x) const;
+
+    gslice_array() = delete;
+};
+
+template <class T>
+class mask_array
+{
+public:
+    typedef T value_type;
+
+    void operator=  (const valarray<value_type>& v) const;
+    void operator*= (const valarray<value_type>& v) const;
+    void operator/= (const valarray<value_type>& v) const;
+    void operator%= (const valarray<value_type>& v) const;
+    void operator+= (const valarray<value_type>& v) const;
+    void operator-= (const valarray<value_type>& v) const;
+    void operator^= (const valarray<value_type>& v) const;
+    void operator&= (const valarray<value_type>& v) const;
+    void operator|= (const valarray<value_type>& v) const;
+    void operator<<=(const valarray<value_type>& v) const;
+    void operator>>=(const valarray<value_type>& v) const;
+
+    mask_array(const mask_array& ma);
+    ~mask_array();
+    const mask_array& operator=(const mask_array& ma) const;
+    void operator=(const value_type& x) const;
+
+    mask_array() = delete;
+};
+
+template <class T>
+class indirect_array
+{
+public:
+    typedef T value_type;
+
+    void operator=  (const valarray<value_type>& v) const;
+    void operator*= (const valarray<value_type>& v) const;
+    void operator/= (const valarray<value_type>& v) const;
+    void operator%= (const valarray<value_type>& v) const;
+    void operator+= (const valarray<value_type>& v) const;
+    void operator-= (const valarray<value_type>& v) const;
+    void operator^= (const valarray<value_type>& v) const;
+    void operator&= (const valarray<value_type>& v) const;
+    void operator|= (const valarray<value_type>& v) const;
+    void operator<<=(const valarray<value_type>& v) const;
+    void operator>>=(const valarray<value_type>& v) const;
+
+    indirect_array(const indirect_array& ia);
+    ~indirect_array();
+    const indirect_array& operator=(const indirect_array& ia) const;
+    void operator=(const value_type& x) const;
+
+    indirect_array() = delete;
+};
+
+template<class T> void swap(valarray<T>& x, valarray<T>& y) noexcept;
+
+template<class T> valarray<T> operator* (const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> operator* (const valarray<T>& x, const T& y);
+template<class T> valarray<T> operator* (const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> operator/ (const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> operator/ (const valarray<T>& x, const T& y);
+template<class T> valarray<T> operator/ (const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> operator% (const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> operator% (const valarray<T>& x, const T& y);
+template<class T> valarray<T> operator% (const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> operator+ (const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> operator+ (const valarray<T>& x, const T& y);
+template<class T> valarray<T> operator+ (const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> operator- (const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> operator- (const valarray<T>& x, const T& y);
+template<class T> valarray<T> operator- (const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> operator^ (const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> operator^ (const valarray<T>& x, const T& y);
+template<class T> valarray<T> operator^ (const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> operator& (const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> operator& (const valarray<T>& x, const T& y);
+template<class T> valarray<T> operator& (const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> operator| (const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> operator| (const valarray<T>& x, const T& y);
+template<class T> valarray<T> operator| (const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> operator<<(const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> operator<<(const valarray<T>& x, const T& y);
+template<class T> valarray<T> operator<<(const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> operator>>(const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> operator>>(const valarray<T>& x, const T& y);
+template<class T> valarray<T> operator>>(const T& x, const valarray<T>& y);
+
+template<class T> valarray<bool> operator&&(const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<bool> operator&&(const valarray<T>& x, const T& y);
+template<class T> valarray<bool> operator&&(const T& x, const valarray<T>& y);
+
+template<class T> valarray<bool> operator||(const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<bool> operator||(const valarray<T>& x, const T& y);
+template<class T> valarray<bool> operator||(const T& x, const valarray<T>& y);
+
+template<class T> valarray<bool> operator==(const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<bool> operator==(const valarray<T>& x, const T& y);
+template<class T> valarray<bool> operator==(const T& x, const valarray<T>& y);
+
+template<class T> valarray<bool> operator!=(const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<bool> operator!=(const valarray<T>& x, const T& y);
+template<class T> valarray<bool> operator!=(const T& x, const valarray<T>& y);
+
+template<class T> valarray<bool> operator< (const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<bool> operator< (const valarray<T>& x, const T& y);
+template<class T> valarray<bool> operator< (const T& x, const valarray<T>& y);
+
+template<class T> valarray<bool> operator> (const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<bool> operator> (const valarray<T>& x, const T& y);
+template<class T> valarray<bool> operator> (const T& x, const valarray<T>& y);
+
+template<class T> valarray<bool> operator<=(const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<bool> operator<=(const valarray<T>& x, const T& y);
+template<class T> valarray<bool> operator<=(const T& x, const valarray<T>& y);
+
+template<class T> valarray<bool> operator>=(const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<bool> operator>=(const valarray<T>& x, const T& y);
+template<class T> valarray<bool> operator>=(const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> abs (const valarray<T>& x);
+template<class T> valarray<T> acos (const valarray<T>& x);
+template<class T> valarray<T> asin (const valarray<T>& x);
+template<class T> valarray<T> atan (const valarray<T>& x);
+
+template<class T> valarray<T> atan2(const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> atan2(const valarray<T>& x, const T& y);
+template<class T> valarray<T> atan2(const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> cos (const valarray<T>& x);
+template<class T> valarray<T> cosh (const valarray<T>& x);
+template<class T> valarray<T> exp (const valarray<T>& x);
+template<class T> valarray<T> log (const valarray<T>& x);
+template<class T> valarray<T> log10(const valarray<T>& x);
+
+template<class T> valarray<T> pow(const valarray<T>& x, const valarray<T>& y);
+template<class T> valarray<T> pow(const valarray<T>& x, const T& y);
+template<class T> valarray<T> pow(const T& x, const valarray<T>& y);
+
+template<class T> valarray<T> sin (const valarray<T>& x);
+template<class T> valarray<T> sinh (const valarray<T>& x);
+template<class T> valarray<T> sqrt (const valarray<T>& x);
+template<class T> valarray<T> tan (const valarray<T>& x);
+template<class T> valarray<T> tanh (const valarray<T>& x);
+
+template <class T> unspecified1 begin(valarray<T>& v);
+template <class T> unspecified2 begin(const valarray<T>& v);
+template <class T> unspecified1 end(valarray<T>& v);
+template <class T> unspecified2 end(const valarray<T>& v);
+
+}  // std
+
+*/
+
+#include <__config>
+#include <cstddef>
+#include <cmath>
+#include <initializer_list>
+#include <algorithm>
+#include <functional>
+
+#include <__undef_min_max>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+template<class _Tp> class _LIBCPP_TYPE_VIS_ONLY valarray;
+
+class _LIBCPP_TYPE_VIS_ONLY slice
+{
+    size_t __start_;
+    size_t __size_;
+    size_t __stride_;
+public:
+    _LIBCPP_INLINE_VISIBILITY
+    slice()
+        : __start_(0),
+          __size_(0),
+          __stride_(0)
+          {}
+
+    _LIBCPP_INLINE_VISIBILITY
+    slice(size_t __start, size_t __size, size_t __stride)
+        : __start_(__start),
+          __size_(__size),
+          __stride_(__stride)
+          {}
+
+    _LIBCPP_INLINE_VISIBILITY size_t start()  const {return __start_;}
+    _LIBCPP_INLINE_VISIBILITY size_t size()   const {return __size_;}
+    _LIBCPP_INLINE_VISIBILITY size_t stride() const {return __stride_;}
+};
+
+template <class _Tp> class _LIBCPP_TYPE_VIS_ONLY slice_array;
+class _LIBCPP_TYPE_VIS gslice;
+template <class _Tp> class _LIBCPP_TYPE_VIS_ONLY gslice_array;
+template <class _Tp> class _LIBCPP_TYPE_VIS_ONLY mask_array;
+template <class _Tp> class _LIBCPP_TYPE_VIS_ONLY indirect_array;
+
+template <class _Tp>
+_LIBCPP_INLINE_VISIBILITY
+_Tp*
+begin(valarray<_Tp>& __v);
+
+template <class _Tp>
+_LIBCPP_INLINE_VISIBILITY
+const _Tp*
+begin(const valarray<_Tp>& __v);
+
+template <class _Tp>
+_LIBCPP_INLINE_VISIBILITY
+_Tp*
+end(valarray<_Tp>& __v);
+
+template <class _Tp>
+_LIBCPP_INLINE_VISIBILITY
+const _Tp*
+end(const valarray<_Tp>& __v);
+
+template <class _Op, class _A0>
+struct _UnaryOp
+{
+    typedef typename _Op::result_type result_type;
+    typedef typename _A0::value_type value_type;
+
+    _Op __op_;
+    _A0 __a0_;
+
+    _LIBCPP_INLINE_VISIBILITY
+    _UnaryOp(const _Op& __op, const _A0& __a0) : __op_(__op), __a0_(__a0) {}
+
+    _LIBCPP_INLINE_VISIBILITY
+    result_type operator[](size_t __i) const {return __op_(__a0_[__i]);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __a0_.size();}
+};
+
+template <class _Op, class _A0, class _A1>
+struct _BinaryOp
+{
+    typedef typename _Op::result_type result_type;
+    typedef typename _A0::value_type value_type;
+
+    _Op __op_;
+    _A0 __a0_;
+    _A1 __a1_;
+
+    _LIBCPP_INLINE_VISIBILITY
+    _BinaryOp(const _Op& __op, const _A0& __a0, const _A1& __a1)
+        : __op_(__op), __a0_(__a0), __a1_(__a1) {}
+
+    _LIBCPP_INLINE_VISIBILITY
+    value_type operator[](size_t __i) const {return __op_(__a0_[__i], __a1_[__i]);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __a0_.size();}
+};
+
+template <class _Tp>
+class __scalar_expr
+{
+public:
+    typedef _Tp        value_type;
+    typedef const _Tp& result_type;
+private:
+    const value_type& __t_;
+    size_t __s_;
+public:
+    _LIBCPP_INLINE_VISIBILITY
+    explicit __scalar_expr(const value_type& __t, size_t __s) : __t_(__t), __s_(__s) {}
+
+    _LIBCPP_INLINE_VISIBILITY
+    result_type operator[](size_t) const {return __t_;}
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __s_;}
+};
+
+template <class _Tp>
+struct __unary_plus : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return +__x;}
+};
+
+template <class _Tp>
+struct __bit_not  : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return ~__x;}
+};
+
+template <class _Tp>
+struct __bit_shift_left : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x << __y;}
+};
+
+template <class _Tp>
+struct __bit_shift_right : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x >> __y;}
+};
+
+template <class _Tp, class _Fp>
+struct __apply_expr   : unary_function<_Tp, _Tp>
+{
+private:
+    _Fp __f_;
+public:
+    _LIBCPP_INLINE_VISIBILITY
+    explicit __apply_expr(_Fp __f) : __f_(__f) {}
+
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return __f_(__x);}
+};
+
+template <class _Tp>
+struct __abs_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return abs(__x);}
+};
+
+template <class _Tp>
+struct __acos_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return acos(__x);}
+};
+
+template <class _Tp>
+struct __asin_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return asin(__x);}
+};
+
+template <class _Tp>
+struct __atan_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return atan(__x);}
+};
+
+template <class _Tp>
+struct __atan2_expr : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return atan2(__x, __y);}
+};
+
+template <class _Tp>
+struct __cos_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return cos(__x);}
+};
+
+template <class _Tp>
+struct __cosh_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return cosh(__x);}
+};
+
+template <class _Tp>
+struct __exp_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return exp(__x);}
+};
+
+template <class _Tp>
+struct __log_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return log(__x);}
+};
+
+template <class _Tp>
+struct __log10_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return log10(__x);}
+};
+
+template <class _Tp>
+struct __pow_expr : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return pow(__x, __y);}
+};
+
+template <class _Tp>
+struct __sin_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return sin(__x);}
+};
+
+template <class _Tp>
+struct __sinh_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return sinh(__x);}
+};
+
+template <class _Tp>
+struct __sqrt_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return sqrt(__x);}
+};
+
+template <class _Tp>
+struct __tan_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return tan(__x);}
+};
+
+template <class _Tp>
+struct __tanh_expr : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return tanh(__x);}
+};
+
+template <class _ValExpr>
+class __slice_expr
+{
+    typedef typename remove_reference<_ValExpr>::type  _RmExpr;
+public:
+    typedef typename _RmExpr::value_type value_type;
+    typedef value_type result_type;
+
+private:
+    _ValExpr __expr_;
+    size_t __start_;
+    size_t __size_;
+    size_t __stride_;
+
+    _LIBCPP_INLINE_VISIBILITY
+    __slice_expr(const slice& __sl, const _RmExpr& __e)
+        : __expr_(__e),
+          __start_(__sl.start()),
+          __size_(__sl.size()),
+          __stride_(__sl.stride())
+        {}
+public:
+
+    _LIBCPP_INLINE_VISIBILITY
+    result_type operator[](size_t __i) const
+        {return __expr_[__start_ + __i * __stride_];}
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __size_;}
+
+    template <class> friend class _LIBCPP_TYPE_VIS_ONLY valarray;
+};
+
+template <class _ValExpr>
+class __mask_expr;
+
+template <class _ValExpr>
+class __indirect_expr;
+
+template <class _ValExpr>
+class __shift_expr
+{
+    typedef typename remove_reference<_ValExpr>::type  _RmExpr;
+public:
+    typedef typename _RmExpr::value_type value_type;
+    typedef value_type result_type;
+
+private:
+    _ValExpr __expr_;
+    size_t __size_;
+    ptrdiff_t __ul_;
+    ptrdiff_t __sn_;
+    ptrdiff_t __n_;
+    static const ptrdiff_t _Np = static_cast<ptrdiff_t>(
+                                    sizeof(ptrdiff_t) * __CHAR_BIT__ - 1);
+
+    _LIBCPP_INLINE_VISIBILITY
+    __shift_expr(int __n, const _RmExpr& __e)
+        : __expr_(__e),
+          __size_(__e.size()),
+          __n_(__n)
+        {
+            ptrdiff_t __neg_n = static_cast<ptrdiff_t>(__n_ >> _Np);
+            __sn_ = __neg_n | static_cast<ptrdiff_t>(static_cast<size_t>(-__n_) >> _Np);
+            __ul_ = ((__size_ - __n_) & ~__neg_n) | ((__n_ + 1) & __neg_n);
+        }
+public:
+
+    _LIBCPP_INLINE_VISIBILITY
+    result_type operator[](size_t __j) const
+        {
+            ptrdiff_t __i = static_cast<ptrdiff_t>(__j);
+            ptrdiff_t __m = (__sn_ * __i - __ul_) >> _Np;
+            return (__expr_[(__i + __n_) & __m] & __m) | (value_type() & ~__m);
+        }
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __size_;}
+
+    template <class> friend class __val_expr;
+};
+
+template <class _ValExpr>
+class __cshift_expr
+{
+    typedef typename remove_reference<_ValExpr>::type  _RmExpr;
+public:
+    typedef typename _RmExpr::value_type value_type;
+    typedef value_type result_type;
+
+private:
+    _ValExpr __expr_;
+    size_t __size_;
+    size_t __m_;
+    size_t __o1_;
+    size_t __o2_;
+
+    _LIBCPP_INLINE_VISIBILITY
+    __cshift_expr(int __n, const _RmExpr& __e)
+        : __expr_(__e),
+          __size_(__e.size())
+        {
+            __n %= static_cast<int>(__size_);
+            if (__n >= 0)
+            {
+                __m_ = __size_ - __n;
+                __o1_ = __n;
+                __o2_ = __n - __size_;
+            }
+            else
+            {
+                __m_ = -__n;
+                __o1_ = __n + __size_;
+                __o2_ = __n;
+            }
+        }
+public:
+
+    _LIBCPP_INLINE_VISIBILITY
+    result_type operator[](size_t __i) const
+        {
+            if (__i < __m_)
+                return __expr_[__i + __o1_];
+            return __expr_[__i + __o2_];
+        }
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __size_;}
+
+    template <class> friend class __val_expr;
+};
+
+template<class _ValExpr>
+class __val_expr;
+
+template<class _ValExpr>
+struct __is_val_expr : false_type {};
+
+template<class _ValExpr>
+struct __is_val_expr<__val_expr<_ValExpr> > : true_type {};
+
+template<class _Tp>
+struct __is_val_expr<valarray<_Tp> > : true_type {};
+
+template<class _Tp>
+class _LIBCPP_TYPE_VIS_ONLY valarray
+{
+public:
+    typedef _Tp value_type;
+    typedef _Tp result_type;
+
+private:
+    value_type* __begin_;
+    value_type* __end_;
+
+public:
+    // construct/destroy:
+    _LIBCPP_INLINE_VISIBILITY
+    valarray() : __begin_(0), __end_(0) {}
+    explicit valarray(size_t __n);
+    valarray(const value_type& __x, size_t __n);
+    valarray(const value_type* __p, size_t __n);
+    valarray(const valarray& __v);
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+    valarray(valarray&& __v) _NOEXCEPT;
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+#ifndef _LIBCPP_HAS_NO_GENERALIZED_INITIALIZERS
+    valarray(initializer_list<value_type> __il);
+#endif  // _LIBCPP_HAS_NO_GENERALIZED_INITIALIZERS
+    valarray(const slice_array<value_type>& __sa);
+    valarray(const gslice_array<value_type>& __ga);
+    valarray(const mask_array<value_type>& __ma);
+    valarray(const indirect_array<value_type>& __ia);
+    ~valarray();
+
+    // assignment:
+    valarray& operator=(const valarray& __v);
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+    valarray& operator=(valarray&& __v) _NOEXCEPT;
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+#ifndef _LIBCPP_HAS_NO_GENERALIZED_INITIALIZERS
+    valarray& operator=(initializer_list<value_type>);
+#endif  // _LIBCPP_HAS_NO_GENERALIZED_INITIALIZERS
+    valarray& operator=(const value_type& __x);
+    valarray& operator=(const slice_array<value_type>& __sa);
+    valarray& operator=(const gslice_array<value_type>& __ga);
+    valarray& operator=(const mask_array<value_type>& __ma);
+    valarray& operator=(const indirect_array<value_type>& __ia);
+    template <class _ValExpr>
+        valarray& operator=(const __val_expr<_ValExpr>& __v);
+
+    // element access:
+    _LIBCPP_INLINE_VISIBILITY
+    const value_type& operator[](size_t __i) const {return __begin_[__i];}
+
+    _LIBCPP_INLINE_VISIBILITY
+    value_type&       operator[](size_t __i)       {return __begin_[__i];}
+
+    // subset operations:
+    __val_expr<__slice_expr<const valarray&> >    operator[](slice __s) const;
+    slice_array<value_type>                       operator[](slice __s);
+    __val_expr<__indirect_expr<const valarray&> > operator[](const gslice& __gs) const;
+    gslice_array<value_type>   operator[](const gslice& __gs);
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+    __val_expr<__indirect_expr<const valarray&> > operator[](gslice&& __gs) const;
+    gslice_array<value_type>                      operator[](gslice&& __gs);
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+    __val_expr<__mask_expr<const valarray&> >     operator[](const valarray<bool>& __vb) const;
+    mask_array<value_type>                        operator[](const valarray<bool>& __vb);
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+    __val_expr<__mask_expr<const valarray&> >     operator[](valarray<bool>&& __vb) const;
+    mask_array<value_type>                        operator[](valarray<bool>&& __vb);
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+    __val_expr<__indirect_expr<const valarray&> > operator[](const valarray<size_t>& __vs) const;
+    indirect_array<value_type>                    operator[](const valarray<size_t>& __vs);
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+    __val_expr<__indirect_expr<const valarray&> > operator[](valarray<size_t>&& __vs) const;
+    indirect_array<value_type>                    operator[](valarray<size_t>&& __vs);
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+    // unary operators:
+    valarray       operator+() const;
+    valarray       operator-() const;
+    valarray       operator~() const;
+    valarray<bool> operator!() const;
+
+    // computed assignment:
+    valarray& operator*= (const value_type& __x);
+    valarray& operator/= (const value_type& __x);
+    valarray& operator%= (const value_type& __x);
+    valarray& operator+= (const value_type& __x);
+    valarray& operator-= (const value_type& __x);
+    valarray& operator^= (const value_type& __x);
+    valarray& operator&= (const value_type& __x);
+    valarray& operator|= (const value_type& __x);
+    valarray& operator<<=(const value_type& __x);
+    valarray& operator>>=(const value_type& __x);
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        valarray&
+    >::type
+    operator*= (const _Expr& __v);
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        valarray&
+    >::type
+    operator/= (const _Expr& __v);
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        valarray&
+    >::type
+    operator%= (const _Expr& __v);
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        valarray&
+    >::type
+    operator+= (const _Expr& __v);
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        valarray&
+    >::type
+    operator-= (const _Expr& __v);
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        valarray&
+    >::type
+    operator^= (const _Expr& __v);
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        valarray&
+    >::type
+    operator|= (const _Expr& __v);
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        valarray&
+    >::type
+    operator&= (const _Expr& __v);
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        valarray&
+    >::type
+    operator<<= (const _Expr& __v);
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        valarray&
+    >::type
+    operator>>= (const _Expr& __v);
+
+    // member functions:
+    void swap(valarray& __v) _NOEXCEPT;
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return static_cast<size_t>(__end_ - __begin_);}
+
+    value_type sum() const;
+    value_type min() const;
+    value_type max() const;
+
+    valarray shift (int __i) const;
+    valarray cshift(int __i) const;
+    valarray apply(value_type __f(value_type)) const;
+    valarray apply(value_type __f(const value_type&)) const;
+    void     resize(size_t __n, value_type __x = value_type());
+
+private:
+    template <class> friend class _LIBCPP_TYPE_VIS_ONLY valarray;
+    template <class> friend class _LIBCPP_TYPE_VIS_ONLY slice_array;
+    template <class> friend class _LIBCPP_TYPE_VIS_ONLY gslice_array;
+    template <class> friend class _LIBCPP_TYPE_VIS_ONLY mask_array;
+    template <class> friend class __mask_expr;
+    template <class> friend class _LIBCPP_TYPE_VIS_ONLY indirect_array;
+    template <class> friend class __indirect_expr;
+    template <class> friend class __val_expr;
+
+    template <class _Up>
+    friend
+    _Up*
+    begin(valarray<_Up>& __v);
+
+    template <class _Up>
+    friend
+    const _Up*
+    begin(const valarray<_Up>& __v);
+
+    template <class _Up>
+    friend
+    _Up*
+    end(valarray<_Up>& __v);
+
+    template <class _Up>
+    friend
+    const _Up*
+    end(const valarray<_Up>& __v);
+};
+
+_LIBCPP_EXTERN_TEMPLATE(_LIBCPP_FUNC_VIS valarray<size_t>::valarray(size_t))
+_LIBCPP_EXTERN_TEMPLATE(_LIBCPP_FUNC_VIS valarray<size_t>::~valarray())
+_LIBCPP_EXTERN_TEMPLATE(_LIBCPP_FUNC_VIS void valarray<size_t>::resize(size_t, size_t))
+
+template <class _Op, class _Tp>
+struct _UnaryOp<_Op, valarray<_Tp> >
+{
+    typedef typename _Op::result_type result_type;
+    typedef _Tp value_type;
+
+    _Op __op_;
+    const valarray<_Tp>& __a0_;
+
+    _LIBCPP_INLINE_VISIBILITY
+    _UnaryOp(const _Op& __op, const valarray<_Tp>& __a0) : __op_(__op), __a0_(__a0) {}
+
+    _LIBCPP_INLINE_VISIBILITY
+    result_type operator[](size_t __i) const {return __op_(__a0_[__i]);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __a0_.size();}
+};
+
+template <class _Op, class _Tp, class _A1>
+struct _BinaryOp<_Op, valarray<_Tp>, _A1>
+{
+    typedef typename _Op::result_type result_type;
+    typedef _Tp value_type;
+
+    _Op __op_;
+    const valarray<_Tp>& __a0_;
+    _A1 __a1_;
+
+    _LIBCPP_INLINE_VISIBILITY
+    _BinaryOp(const _Op& __op, const valarray<_Tp>& __a0, const _A1& __a1)
+        : __op_(__op), __a0_(__a0), __a1_(__a1) {}
+
+    _LIBCPP_INLINE_VISIBILITY
+    value_type operator[](size_t __i) const {return __op_(__a0_[__i], __a1_[__i]);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __a0_.size();}
+};
+
+template <class _Op, class _A0, class _Tp>
+struct _BinaryOp<_Op, _A0, valarray<_Tp> >
+{
+    typedef typename _Op::result_type result_type;
+    typedef _Tp value_type;
+
+    _Op __op_;
+    _A0 __a0_;
+    const valarray<_Tp>& __a1_;
+
+    _LIBCPP_INLINE_VISIBILITY
+    _BinaryOp(const _Op& __op, const _A0& __a0, const valarray<_Tp>& __a1)
+        : __op_(__op), __a0_(__a0), __a1_(__a1) {}
+
+    _LIBCPP_INLINE_VISIBILITY
+    value_type operator[](size_t __i) const {return __op_(__a0_[__i], __a1_[__i]);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __a0_.size();}
+};
+
+template <class _Op, class _Tp>
+struct _BinaryOp<_Op, valarray<_Tp>, valarray<_Tp> >
+{
+    typedef typename _Op::result_type result_type;
+    typedef _Tp value_type;
+
+    _Op __op_;
+    const valarray<_Tp>& __a0_;
+    const valarray<_Tp>& __a1_;
+
+    _LIBCPP_INLINE_VISIBILITY
+    _BinaryOp(const _Op& __op, const valarray<_Tp>& __a0, const valarray<_Tp>& __a1)
+        : __op_(__op), __a0_(__a0), __a1_(__a1) {}
+
+    _LIBCPP_INLINE_VISIBILITY
+    value_type operator[](size_t __i) const {return __op_(__a0_[__i], __a1_[__i]);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __a0_.size();}
+};
+
+// slice_array
+
+template <class _Tp>
+class _LIBCPP_TYPE_VIS_ONLY slice_array
+{
+public:
+    typedef _Tp value_type;
+
+private:
+    value_type* __vp_;
+    size_t __size_;
+    size_t __stride_;
+
+public:
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator*=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator/=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator%=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator+=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator-=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator^=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator&=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator|=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator<<=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator>>=(const _Expr& __v) const;
+
+    const slice_array& operator=(const slice_array& __sa) const;
+
+    void operator=(const value_type& __x) const;
+
+private:
+    _LIBCPP_INLINE_VISIBILITY
+    slice_array(const slice& __sl, const valarray<value_type>& __v)
+        : __vp_(const_cast<value_type*>(__v.__begin_ + __sl.start())),
+          __size_(__sl.size()),
+          __stride_(__sl.stride())
+        {}
+
+    template <class> friend class valarray;
+    template <class> friend class sliceExpr;
+};
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+const slice_array<_Tp>&
+slice_array<_Tp>::operator=(const slice_array& __sa) const
+{
+    value_type* __t = __vp_;
+    const value_type* __s = __sa.__vp_;
+    for (size_t __n = __size_; __n; --__n, __t += __stride_, __s += __sa.__stride_)
+        *__t = *__s;
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+slice_array<_Tp>::operator=(const _Expr& __v) const
+{
+    value_type* __t = __vp_;
+    for (size_t __i = 0; __i < __size_; ++__i, __t += __stride_)
+        *__t = __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+slice_array<_Tp>::operator*=(const _Expr& __v) const
+{
+    value_type* __t = __vp_;
+    for (size_t __i = 0; __i < __size_; ++__i, __t += __stride_)
+        *__t *= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+slice_array<_Tp>::operator/=(const _Expr& __v) const
+{
+    value_type* __t = __vp_;
+    for (size_t __i = 0; __i < __size_; ++__i, __t += __stride_)
+        *__t /= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+slice_array<_Tp>::operator%=(const _Expr& __v) const
+{
+    value_type* __t = __vp_;
+    for (size_t __i = 0; __i < __size_; ++__i, __t += __stride_)
+        *__t %= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+slice_array<_Tp>::operator+=(const _Expr& __v) const
+{
+    value_type* __t = __vp_;
+    for (size_t __i = 0; __i < __size_; ++__i, __t += __stride_)
+        *__t += __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+slice_array<_Tp>::operator-=(const _Expr& __v) const
+{
+    value_type* __t = __vp_;
+    for (size_t __i = 0; __i < __size_; ++__i, __t += __stride_)
+        *__t -= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+slice_array<_Tp>::operator^=(const _Expr& __v) const
+{
+    value_type* __t = __vp_;
+    for (size_t __i = 0; __i < __size_; ++__i, __t += __stride_)
+        *__t ^= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+slice_array<_Tp>::operator&=(const _Expr& __v) const
+{
+    value_type* __t = __vp_;
+    for (size_t __i = 0; __i < __size_; ++__i, __t += __stride_)
+        *__t &= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+slice_array<_Tp>::operator|=(const _Expr& __v) const
+{
+    value_type* __t = __vp_;
+    for (size_t __i = 0; __i < __size_; ++__i, __t += __stride_)
+        *__t |= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+slice_array<_Tp>::operator<<=(const _Expr& __v) const
+{
+    value_type* __t = __vp_;
+    for (size_t __i = 0; __i < __size_; ++__i, __t += __stride_)
+        *__t <<= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+slice_array<_Tp>::operator>>=(const _Expr& __v) const
+{
+    value_type* __t = __vp_;
+    for (size_t __i = 0; __i < __size_; ++__i, __t += __stride_)
+        *__t >>= __v[__i];
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+void
+slice_array<_Tp>::operator=(const value_type& __x) const
+{
+    value_type* __t = __vp_;
+    for (size_t __n = __size_; __n; --__n, __t += __stride_)
+        *__t = __x;
+}
+
+// gslice
+
+class _LIBCPP_TYPE_VIS gslice
+{
+    valarray<size_t> __size_;
+    valarray<size_t> __stride_;
+    valarray<size_t> __1d_;
+
+public:
+    _LIBCPP_INLINE_VISIBILITY
+    gslice() {}
+
+    _LIBCPP_INLINE_VISIBILITY
+    gslice(size_t __start, const valarray<size_t>& __size,
+                           const valarray<size_t>& __stride)
+        : __size_(__size),
+          __stride_(__stride)
+        {__init(__start);}
+
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+    _LIBCPP_INLINE_VISIBILITY
+    gslice(size_t __start, const valarray<size_t>&  __size,
+                                 valarray<size_t>&& __stride)
+        : __size_(__size),
+          __stride_(move(__stride))
+        {__init(__start);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    gslice(size_t __start,       valarray<size_t>&& __size,
+                           const valarray<size_t>&  __stride)
+        : __size_(move(__size)),
+          __stride_(__stride)
+        {__init(__start);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    gslice(size_t __start,       valarray<size_t>&& __size,
+                                 valarray<size_t>&& __stride)
+        : __size_(move(__size)),
+          __stride_(move(__stride))
+        {__init(__start);}
+
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+//  gslice(const gslice&)            = default;
+//  gslice(gslice&&)                 = default;
+//  gslice& operator=(const gslice&) = default;
+//  gslice& operator=(gslice&&)      = default;
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t           start()  const {return __1d_.size() ? __1d_[0] : 0;}
+
+    _LIBCPP_INLINE_VISIBILITY
+    valarray<size_t> size()   const {return __size_;}
+
+    _LIBCPP_INLINE_VISIBILITY
+    valarray<size_t> stride() const {return __stride_;}
+
+private:
+    void __init(size_t __start);
+
+    template <class> friend class gslice_array;
+    template <class> friend class valarray;
+    template <class> friend class __val_expr;
+};
+
+// gslice_array
+
+template <class _Tp>
+class _LIBCPP_TYPE_VIS_ONLY gslice_array
+{
+public:
+    typedef _Tp value_type;
+
+private:
+    value_type*      __vp_;
+    valarray<size_t> __1d_;
+
+public:
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator*=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator/=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator%=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator+=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator-=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator^=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator&=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator|=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator<<=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator>>=(const _Expr& __v) const;
+
+    const gslice_array& operator=(const gslice_array& __ga) const;
+
+    void operator=(const value_type& __x) const;
+
+//  gslice_array(const gslice_array&)            = default;
+//  gslice_array(gslice_array&&)                 = default;
+//  gslice_array& operator=(const gslice_array&) = default;
+//  gslice_array& operator=(gslice_array&&)      = default;
+
+private:
+    _LIBCPP_INLINE_VISIBILITY
+    gslice_array(const gslice& __gs, const valarray<value_type>& __v)
+        : __vp_(const_cast<value_type*>(__v.__begin_)),
+          __1d_(__gs.__1d_)
+        {}
+
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+    _LIBCPP_INLINE_VISIBILITY
+    gslice_array(gslice&& __gs, const valarray<value_type>& __v)
+        : __vp_(const_cast<value_type*>(__v.__begin_)),
+          __1d_(move(__gs.__1d_))
+        {}
+
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+    template <class> friend class valarray;
+};
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+gslice_array<_Tp>::operator=(const _Expr& __v) const
+{
+    typedef const size_t* _Ip;
+    size_t __j = 0;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i, ++__j)
+        __vp_[*__i] = __v[__j];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+gslice_array<_Tp>::operator*=(const _Expr& __v) const
+{
+    typedef const size_t* _Ip;
+    size_t __j = 0;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i, ++__j)
+        __vp_[*__i] *= __v[__j];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+gslice_array<_Tp>::operator/=(const _Expr& __v) const
+{
+    typedef const size_t* _Ip;
+    size_t __j = 0;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i, ++__j)
+        __vp_[*__i] /= __v[__j];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+gslice_array<_Tp>::operator%=(const _Expr& __v) const
+{
+    typedef const size_t* _Ip;
+    size_t __j = 0;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i, ++__j)
+        __vp_[*__i] %= __v[__j];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+gslice_array<_Tp>::operator+=(const _Expr& __v) const
+{
+    typedef const size_t* _Ip;
+    size_t __j = 0;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i, ++__j)
+        __vp_[*__i] += __v[__j];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+gslice_array<_Tp>::operator-=(const _Expr& __v) const
+{
+    typedef const size_t* _Ip;
+    size_t __j = 0;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i, ++__j)
+        __vp_[*__i] -= __v[__j];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+gslice_array<_Tp>::operator^=(const _Expr& __v) const
+{
+    typedef const size_t* _Ip;
+    size_t __j = 0;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i, ++__j)
+        __vp_[*__i] ^= __v[__j];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+gslice_array<_Tp>::operator&=(const _Expr& __v) const
+{
+    typedef const size_t* _Ip;
+    size_t __j = 0;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i, ++__j)
+        __vp_[*__i] &= __v[__j];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+gslice_array<_Tp>::operator|=(const _Expr& __v) const
+{
+    typedef const size_t* _Ip;
+    size_t __j = 0;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i, ++__j)
+        __vp_[*__i] |= __v[__j];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+gslice_array<_Tp>::operator<<=(const _Expr& __v) const
+{
+    typedef const size_t* _Ip;
+    size_t __j = 0;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i, ++__j)
+        __vp_[*__i] <<= __v[__j];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+gslice_array<_Tp>::operator>>=(const _Expr& __v) const
+{
+    typedef const size_t* _Ip;
+    size_t __j = 0;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i, ++__j)
+        __vp_[*__i] >>= __v[__j];
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+const gslice_array<_Tp>&
+gslice_array<_Tp>::operator=(const gslice_array& __ga) const
+{
+    typedef const size_t* _Ip;
+    const value_type* __s = __ga.__vp_;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_, __j = __ga.__1d_.__begin_;
+            __i != __e; ++__i, ++__j)
+        __vp_[*__i] = __s[*__j];
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+void
+gslice_array<_Tp>::operator=(const value_type& __x) const
+{
+    typedef const size_t* _Ip;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i)
+        __vp_[*__i] = __x;
+}
+
+// mask_array
+
+template <class _Tp>
+class _LIBCPP_TYPE_VIS_ONLY mask_array
+{
+public:
+    typedef _Tp value_type;
+
+private:
+    value_type*      __vp_;
+    valarray<size_t> __1d_;
+
+public:
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator*=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator/=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator%=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator+=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator-=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator^=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator&=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator|=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator<<=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator>>=(const _Expr& __v) const;
+
+    const mask_array& operator=(const mask_array& __ma) const;
+
+    void operator=(const value_type& __x) const;
+
+//  mask_array(const mask_array&)            = default;
+//  mask_array(mask_array&&)                 = default;
+//  mask_array& operator=(const mask_array&) = default;
+//  mask_array& operator=(mask_array&&)      = default;
+
+private:
+    _LIBCPP_INLINE_VISIBILITY
+    mask_array(const valarray<bool>& __vb, const valarray<value_type>& __v)
+        : __vp_(const_cast<value_type*>(__v.__begin_)),
+          __1d_(static_cast<size_t>(count(__vb.__begin_, __vb.__end_, true)))
+          {
+              size_t __j = 0;
+              for (size_t __i = 0; __i < __vb.size(); ++__i)
+                  if (__vb[__i])
+                      __1d_[__j++] = __i;
+          }
+
+    template <class> friend class valarray;
+};
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+mask_array<_Tp>::operator=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] = __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+mask_array<_Tp>::operator*=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] *= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+mask_array<_Tp>::operator/=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] /= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+mask_array<_Tp>::operator%=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] %= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+mask_array<_Tp>::operator+=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] += __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+mask_array<_Tp>::operator-=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] -= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+mask_array<_Tp>::operator^=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] ^= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+mask_array<_Tp>::operator&=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] &= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+mask_array<_Tp>::operator|=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] |= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+mask_array<_Tp>::operator<<=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] <<= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+mask_array<_Tp>::operator>>=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] >>= __v[__i];
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+const mask_array<_Tp>&
+mask_array<_Tp>::operator=(const mask_array& __ma) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] = __ma.__vp_[__1d_[__i]];
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+void
+mask_array<_Tp>::operator=(const value_type& __x) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] = __x;
+}
+
+template <class _ValExpr>
+class __mask_expr
+{
+    typedef typename remove_reference<_ValExpr>::type  _RmExpr;
+public:
+    typedef typename _RmExpr::value_type value_type;
+    typedef value_type result_type;
+
+private:
+    _ValExpr __expr_;
+    valarray<size_t> __1d_;
+
+    _LIBCPP_INLINE_VISIBILITY
+    __mask_expr(const valarray<bool>& __vb, const _RmExpr& __e)
+        : __expr_(__e),
+          __1d_(static_cast<size_t>(count(__vb.__begin_, __vb.__end_, true)))
+          {
+              size_t __j = 0;
+              for (size_t __i = 0; __i < __vb.size(); ++__i)
+                  if (__vb[__i])
+                      __1d_[__j++] = __i;
+          }
+
+public:
+    _LIBCPP_INLINE_VISIBILITY
+    result_type operator[](size_t __i) const
+        {return __expr_[__1d_[__i]];}
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __1d_.size();}
+
+    template <class> friend class valarray;
+};
+
+// indirect_array
+
+template <class _Tp>
+class _LIBCPP_TYPE_VIS_ONLY indirect_array
+{
+public:
+    typedef _Tp value_type;
+
+private:
+    value_type*      __vp_;
+    valarray<size_t> __1d_;
+
+public:
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator*=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator/=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator%=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator+=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator-=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator^=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator&=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator|=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator<<=(const _Expr& __v) const;
+
+    template <class _Expr>
+    typename enable_if
+    <
+        __is_val_expr<_Expr>::value,
+        void
+    >::type
+    operator>>=(const _Expr& __v) const;
+
+    const indirect_array& operator=(const indirect_array& __ia) const;
+
+    void operator=(const value_type& __x) const;
+
+//  indirect_array(const indirect_array&)            = default;
+//  indirect_array(indirect_array&&)                 = default;
+//  indirect_array& operator=(const indirect_array&) = default;
+//  indirect_array& operator=(indirect_array&&)      = default;
+
+private:
+     _LIBCPP_INLINE_VISIBILITY
+   indirect_array(const valarray<size_t>& __ia, const valarray<value_type>& __v)
+        : __vp_(const_cast<value_type*>(__v.__begin_)),
+          __1d_(__ia)
+        {}
+
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+    _LIBCPP_INLINE_VISIBILITY
+    indirect_array(valarray<size_t>&& __ia, const valarray<value_type>& __v)
+        : __vp_(const_cast<value_type*>(__v.__begin_)),
+          __1d_(move(__ia))
+        {}
+
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+    template <class> friend class valarray;
+};
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+indirect_array<_Tp>::operator=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] = __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+indirect_array<_Tp>::operator*=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] *= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+indirect_array<_Tp>::operator/=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] /= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+indirect_array<_Tp>::operator%=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] %= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+indirect_array<_Tp>::operator+=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] += __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+indirect_array<_Tp>::operator-=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] -= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+indirect_array<_Tp>::operator^=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] ^= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+indirect_array<_Tp>::operator&=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] &= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+indirect_array<_Tp>::operator|=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] |= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+indirect_array<_Tp>::operator<<=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] <<= __v[__i];
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    void
+>::type
+indirect_array<_Tp>::operator>>=(const _Expr& __v) const
+{
+    size_t __n = __1d_.size();
+    for (size_t __i = 0; __i < __n; ++__i)
+        __vp_[__1d_[__i]] >>= __v[__i];
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+const indirect_array<_Tp>&
+indirect_array<_Tp>::operator=(const indirect_array& __ia) const
+{
+    typedef const size_t* _Ip;
+    const value_type* __s = __ia.__vp_;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_, __j = __ia.__1d_.__begin_;
+            __i != __e; ++__i, ++__j)
+        __vp_[*__i] = __s[*__j];
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+void
+indirect_array<_Tp>::operator=(const value_type& __x) const
+{
+    typedef const size_t* _Ip;
+    for (_Ip __i = __1d_.__begin_, __e = __1d_.__end_; __i != __e; ++__i)
+        __vp_[*__i] = __x;
+}
+
+template <class _ValExpr>
+class __indirect_expr
+{
+    typedef typename remove_reference<_ValExpr>::type  _RmExpr;
+public:
+    typedef typename _RmExpr::value_type value_type;
+    typedef value_type result_type;
+
+private:
+    _ValExpr __expr_;
+    valarray<size_t> __1d_;
+
+    _LIBCPP_INLINE_VISIBILITY
+    __indirect_expr(const valarray<size_t>& __ia, const _RmExpr& __e)
+        : __expr_(__e),
+          __1d_(__ia)
+          {}
+
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+    _LIBCPP_INLINE_VISIBILITY
+    __indirect_expr(valarray<size_t>&& __ia, const _RmExpr& __e)
+        : __expr_(__e),
+          __1d_(move(__ia))
+          {}
+
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+public:
+    _LIBCPP_INLINE_VISIBILITY
+    result_type operator[](size_t __i) const
+        {return __expr_[__1d_[__i]];}
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __1d_.size();}
+
+    template <class> friend class _LIBCPP_TYPE_VIS_ONLY valarray;
+};
+
+template<class _ValExpr>
+class __val_expr
+{
+    typedef typename remove_reference<_ValExpr>::type  _RmExpr;
+
+    _ValExpr __expr_;
+public:
+    typedef typename _RmExpr::value_type value_type;
+    typedef typename _RmExpr::result_type result_type;
+
+    _LIBCPP_INLINE_VISIBILITY
+    explicit __val_expr(const _RmExpr& __e) : __expr_(__e) {}
+
+    _LIBCPP_INLINE_VISIBILITY
+    result_type operator[](size_t __i) const
+        {return __expr_[__i];}
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<__slice_expr<_ValExpr> > operator[](slice __s) const
+        {return __val_expr<__slice_expr<_ValExpr> >(__expr_, __s);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<__indirect_expr<_ValExpr> > operator[](const gslice& __gs) const
+        {return __val_expr<__indirect_expr<_ValExpr> >(__expr_, __gs.__1d_);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<__mask_expr<_ValExpr> > operator[](const valarray<bool>& __vb) const
+        {return __val_expr<__mask_expr<_ValExpr> >(__expr_, __vb);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<__indirect_expr<_ValExpr> > operator[](const valarray<size_t>& __vs) const
+        {return __val_expr<__indirect_expr<_ValExpr> >(__expr_, __vs);}
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<_UnaryOp<__unary_plus<value_type>, _ValExpr> >
+    operator+() const
+    {
+        typedef _UnaryOp<__unary_plus<value_type>, _ValExpr> _NewExpr;
+        return __val_expr<_NewExpr>(_NewExpr(__unary_plus<value_type>(), __expr_));
+    }
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<_UnaryOp<negate<value_type>, _ValExpr> >
+    operator-() const
+    {
+        typedef _UnaryOp<negate<value_type>, _ValExpr> _NewExpr;
+        return __val_expr<_NewExpr>(_NewExpr(negate<value_type>(), __expr_));
+    }
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<_UnaryOp<__bit_not<value_type>, _ValExpr> >
+    operator~() const
+    {
+        typedef _UnaryOp<__bit_not<value_type>, _ValExpr> _NewExpr;
+        return __val_expr<_NewExpr>(_NewExpr(__bit_not<value_type>(), __expr_));
+    }
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<_UnaryOp<logical_not<value_type>, _ValExpr> >
+    operator!() const
+    {
+        typedef _UnaryOp<logical_not<value_type>, _ValExpr> _NewExpr;
+        return __val_expr<_NewExpr>(_NewExpr(logical_not<value_type>(), __expr_));
+    }
+
+    operator valarray<result_type>() const;
+
+    _LIBCPP_INLINE_VISIBILITY
+    size_t size() const {return __expr_.size();}
+
+    _LIBCPP_INLINE_VISIBILITY
+    result_type sum() const
+    {
+        size_t __n = __expr_.size();
+        result_type __r = __n ? __expr_[0] : result_type();
+        for (size_t __i = 1; __i < __n; ++__i)
+            __r += __expr_[__i];
+        return __r;
+    }
+
+    _LIBCPP_INLINE_VISIBILITY
+    result_type min() const
+    {
+        size_t __n = size();
+        result_type __r = __n ? (*this)[0] : result_type();
+        for (size_t __i = 1; __i < __n; ++__i)
+        {
+            result_type __x = __expr_[__i];
+            if (__x < __r)
+                __r = __x;
+        }
+        return __r;
+    }
+
+    _LIBCPP_INLINE_VISIBILITY
+    result_type max() const
+    {
+        size_t __n = size();
+        result_type __r = __n ? (*this)[0] : result_type();
+        for (size_t __i = 1; __i < __n; ++__i)
+        {
+            result_type __x = __expr_[__i];
+            if (__r < __x)
+                __r = __x;
+        }
+        return __r;
+    }
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<__shift_expr<_ValExpr> > shift (int __i) const
+        {return __val_expr<__shift_expr<_ValExpr> >(__shift_expr<_ValExpr>(__i, __expr_));}
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<__cshift_expr<_ValExpr> > cshift(int __i) const
+        {return __val_expr<__cshift_expr<_ValExpr> >(__cshift_expr<_ValExpr>(__i, __expr_));}
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<_UnaryOp<__apply_expr<value_type, value_type(*)(value_type)>, _ValExpr> >
+    apply(value_type __f(value_type)) const
+    {
+        typedef __apply_expr<value_type, value_type(*)(value_type)> _Op;
+        typedef _UnaryOp<_Op, _ValExpr> _NewExpr;
+        return __val_expr<_NewExpr>(_NewExpr(_Op(__f), __expr_));
+    }
+
+    _LIBCPP_INLINE_VISIBILITY
+    __val_expr<_UnaryOp<__apply_expr<value_type, value_type(*)(const value_type&)>, _ValExpr> >
+    apply(value_type __f(const value_type&)) const
+    {
+        typedef __apply_expr<value_type, value_type(*)(const value_type&)> _Op;
+        typedef _UnaryOp<_Op, _ValExpr> _NewExpr;
+        return __val_expr<_NewExpr>(_NewExpr(_Op(__f), __expr_));
+    }
+};
+
+template<class _ValExpr>
+__val_expr<_ValExpr>::operator valarray<__val_expr::result_type>() const
+{
+    valarray<result_type> __r;
+    size_t __n = __expr_.size();
+    if (__n)
+    {
+        __r.__begin_ =
+            __r.__end_ =
+                static_cast<result_type*>(::operator new(__n * sizeof(result_type)));
+        for (size_t __i = 0; __i != __n; ++__r.__end_, ++__i)
+            ::new (__r.__end_) result_type(__expr_[__i]);
+    }
+    return __r;
+}
+
+// valarray
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>::valarray(size_t __n)
+    : __begin_(0),
+      __end_(0)
+{
+    resize(__n);
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>::valarray(const value_type& __x, size_t __n)
+    : __begin_(0),
+      __end_(0)
+{
+    resize(__n, __x);
+}
+
+template <class _Tp>
+valarray<_Tp>::valarray(const value_type* __p, size_t __n)
+    : __begin_(0),
+      __end_(0)
+{
+    if (__n)
+    {
+        __begin_ = __end_ = static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        try
+        {
+#endif  // _LIBCPP_NO_EXCEPTIONS
+            for (; __n; ++__end_, ++__p, --__n)
+                ::new (__end_) value_type(*__p);
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        }
+        catch (...)
+        {
+            resize(0);
+            throw;
+        }
+#endif  // _LIBCPP_NO_EXCEPTIONS
+    }
+}
+
+template <class _Tp>
+valarray<_Tp>::valarray(const valarray& __v)
+    : __begin_(0),
+      __end_(0)
+{
+    if (__v.size())
+    {
+        __begin_ = __end_ = static_cast<value_type*>(::operator new(__v.size() * sizeof(value_type)));
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        try
+        {
+#endif  // _LIBCPP_NO_EXCEPTIONS
+            for (value_type* __p = __v.__begin_; __p != __v.__end_; ++__end_, ++__p)
+                ::new (__end_) value_type(*__p);
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        }
+        catch (...)
+        {
+            resize(0);
+            throw;
+        }
+#endif  // _LIBCPP_NO_EXCEPTIONS
+    }
+}
+
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>::valarray(valarray&& __v) _NOEXCEPT
+    : __begin_(__v.__begin_),
+      __end_(__v.__end_)
+{
+    __v.__begin_ = __v.__end_ = nullptr;
+}
+
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+#ifndef _LIBCPP_HAS_NO_GENERALIZED_INITIALIZERS
+
+template <class _Tp>
+valarray<_Tp>::valarray(initializer_list<value_type> __il)
+    : __begin_(0),
+      __end_(0)
+{
+    size_t __n = __il.size();
+    if (__n)
+    {
+        __begin_ = __end_ = static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        try
+        {
+#endif  // _LIBCPP_NO_EXCEPTIONS
+            for (const value_type* __p = __il.begin(); __n; ++__end_, ++__p, --__n)
+                ::new (__end_) value_type(*__p);
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        }
+        catch (...)
+        {
+            resize(0);
+            throw;
+        }
+#endif  // _LIBCPP_NO_EXCEPTIONS
+    }
+}
+
+#endif  // _LIBCPP_HAS_NO_GENERALIZED_INITIALIZERS
+
+template <class _Tp>
+valarray<_Tp>::valarray(const slice_array<value_type>& __sa)
+    : __begin_(0),
+      __end_(0)
+{
+    size_t __n = __sa.__size_;
+    if (__n)
+    {
+        __begin_ = __end_ = static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        try
+        {
+#endif  // _LIBCPP_NO_EXCEPTIONS
+            for (const value_type* __p = __sa.__vp_; __n; ++__end_, __p += __sa.__stride_, --__n)
+                ::new (__end_) value_type(*__p);
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        }
+        catch (...)
+        {
+            resize(0);
+            throw;
+        }
+#endif  // _LIBCPP_NO_EXCEPTIONS
+    }
+}
+
+template <class _Tp>
+valarray<_Tp>::valarray(const gslice_array<value_type>& __ga)
+    : __begin_(0),
+      __end_(0)
+{
+    size_t __n = __ga.__1d_.size();
+    if (__n)
+    {
+        __begin_ = __end_ = static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        try
+        {
+#endif  // _LIBCPP_NO_EXCEPTIONS
+            typedef const size_t* _Ip;
+            const value_type* __s = __ga.__vp_;
+            for (_Ip __i = __ga.__1d_.__begin_, __e = __ga.__1d_.__end_;
+                    __i != __e; ++__i, ++__end_)
+                ::new (__end_) value_type(__s[*__i]);
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        }
+        catch (...)
+        {
+            resize(0);
+            throw;
+        }
+#endif  // _LIBCPP_NO_EXCEPTIONS
+    }
+}
+
+template <class _Tp>
+valarray<_Tp>::valarray(const mask_array<value_type>& __ma)
+    : __begin_(0),
+      __end_(0)
+{
+    size_t __n = __ma.__1d_.size();
+    if (__n)
+    {
+        __begin_ = __end_ = static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        try
+        {
+#endif  // _LIBCPP_NO_EXCEPTIONS
+            typedef const size_t* _Ip;
+            const value_type* __s = __ma.__vp_;
+            for (_Ip __i = __ma.__1d_.__begin_, __e = __ma.__1d_.__end_;
+                    __i != __e; ++__i, ++__end_)
+                ::new (__end_) value_type(__s[*__i]);
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        }
+        catch (...)
+        {
+            resize(0);
+            throw;
+        }
+#endif  // _LIBCPP_NO_EXCEPTIONS
+    }
+}
+
+template <class _Tp>
+valarray<_Tp>::valarray(const indirect_array<value_type>& __ia)
+    : __begin_(0),
+      __end_(0)
+{
+    size_t __n = __ia.__1d_.size();
+    if (__n)
+    {
+        __begin_ = __end_ = static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        try
+        {
+#endif  // _LIBCPP_NO_EXCEPTIONS
+            typedef const size_t* _Ip;
+            const value_type* __s = __ia.__vp_;
+            for (_Ip __i = __ia.__1d_.__begin_, __e = __ia.__1d_.__end_;
+                    __i != __e; ++__i, ++__end_)
+                ::new (__end_) value_type(__s[*__i]);
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        }
+        catch (...)
+        {
+            resize(0);
+            throw;
+        }
+#endif  // _LIBCPP_NO_EXCEPTIONS
+    }
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>::~valarray()
+{
+    resize(0);
+}
+
+template <class _Tp>
+valarray<_Tp>&
+valarray<_Tp>::operator=(const valarray& __v)
+{
+    if (this != &__v)
+    {
+        if (size() != __v.size())
+            resize(__v.size());
+        _VSTD::copy(__v.__begin_, __v.__end_, __begin_);
+    }
+    return *this;
+}
+
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator=(valarray&& __v) _NOEXCEPT
+{
+    resize(0);
+    __begin_ = __v.__begin_;
+    __end_ = __v.__end_;
+    __v.__begin_ = nullptr;
+    __v.__end_ = nullptr;
+    return *this;
+}
+
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+#ifndef _LIBCPP_HAS_NO_GENERALIZED_INITIALIZERS
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator=(initializer_list<value_type> __il)
+{
+    if (size() != __il.size())
+        resize(__il.size());
+    _VSTD::copy(__il.begin(), __il.end(), __begin_);
+    return *this;
+}
+
+#endif  // _LIBCPP_HAS_NO_GENERALIZED_INITIALIZERS
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator=(const value_type& __x)
+{
+    _VSTD::fill(__begin_, __end_, __x);
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator=(const slice_array<value_type>& __sa)
+{
+    value_type* __t = __begin_;
+    const value_type* __s = __sa.__vp_;
+    for (size_t __n = __sa.__size_; __n; --__n, __s += __sa.__stride_, ++__t)
+        *__t = *__s;
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator=(const gslice_array<value_type>& __ga)
+{
+    typedef const size_t* _Ip;
+    value_type* __t = __begin_;
+    const value_type* __s = __ga.__vp_;
+    for (_Ip __i = __ga.__1d_.__begin_, __e = __ga.__1d_.__end_;
+                    __i != __e; ++__i, ++__t)
+        *__t = __s[*__i];
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator=(const mask_array<value_type>& __ma)
+{
+    typedef const size_t* _Ip;
+    value_type* __t = __begin_;
+    const value_type* __s = __ma.__vp_;
+    for (_Ip __i = __ma.__1d_.__begin_, __e = __ma.__1d_.__end_;
+                    __i != __e; ++__i, ++__t)
+        *__t = __s[*__i];
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator=(const indirect_array<value_type>& __ia)
+{
+    typedef const size_t* _Ip;
+    value_type* __t = __begin_;
+    const value_type* __s = __ia.__vp_;
+    for (_Ip __i = __ia.__1d_.__begin_, __e = __ia.__1d_.__end_;
+                    __i != __e; ++__i, ++__t)
+        *__t = __s[*__i];
+    return *this;
+}
+
+template <class _Tp>
+template <class _ValExpr>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator=(const __val_expr<_ValExpr>& __v)
+{
+    size_t __n = __v.size();
+    if (size() != __n)
+        resize(__n);
+    value_type* __t = __begin_;
+    for (size_t __i = 0; __i != __n; ++__t, ++__i)
+        *__t = result_type(__v[__i]);
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+__val_expr<__slice_expr<const valarray<_Tp>&> >
+valarray<_Tp>::operator[](slice __s) const
+{
+    return __val_expr<__slice_expr<const valarray&> >(__slice_expr<const valarray&>(__s, *this));
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+slice_array<_Tp>
+valarray<_Tp>::operator[](slice __s)
+{
+    return slice_array<value_type>(__s, *this);
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+__val_expr<__indirect_expr<const valarray<_Tp>&> >
+valarray<_Tp>::operator[](const gslice& __gs) const
+{
+    return __val_expr<__indirect_expr<const valarray&> >(__indirect_expr<const valarray&>(__gs.__1d_, *this));
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+gslice_array<_Tp>
+valarray<_Tp>::operator[](const gslice& __gs)
+{
+    return gslice_array<value_type>(__gs, *this);
+}
+
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+__val_expr<__indirect_expr<const valarray<_Tp>&> >
+valarray<_Tp>::operator[](gslice&& __gs) const
+{
+    return __val_expr<__indirect_expr<const valarray&> >(__indirect_expr<const valarray&>(move(__gs.__1d_), *this));
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+gslice_array<_Tp>
+valarray<_Tp>::operator[](gslice&& __gs)
+{
+    return gslice_array<value_type>(move(__gs), *this);
+}
+
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+__val_expr<__mask_expr<const valarray<_Tp>&> >
+valarray<_Tp>::operator[](const valarray<bool>& __vb) const
+{
+    return __val_expr<__mask_expr<const valarray&> >(__mask_expr<const valarray&>(__vb, *this));
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+mask_array<_Tp>
+valarray<_Tp>::operator[](const valarray<bool>& __vb)
+{
+    return mask_array<value_type>(__vb, *this);
+}
+
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+__val_expr<__mask_expr<const valarray<_Tp>&> >
+valarray<_Tp>::operator[](valarray<bool>&& __vb) const
+{
+    return __val_expr<__mask_expr<const valarray&> >(__mask_expr<const valarray&>(move(__vb), *this));
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+mask_array<_Tp>
+valarray<_Tp>::operator[](valarray<bool>&& __vb)
+{
+    return mask_array<value_type>(move(__vb), *this);
+}
+
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+__val_expr<__indirect_expr<const valarray<_Tp>&> >
+valarray<_Tp>::operator[](const valarray<size_t>& __vs) const
+{
+    return __val_expr<__indirect_expr<const valarray&> >(__indirect_expr<const valarray&>(__vs, *this));
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+indirect_array<_Tp>
+valarray<_Tp>::operator[](const valarray<size_t>& __vs)
+{
+    return indirect_array<value_type>(__vs, *this);
+}
+
+#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+__val_expr<__indirect_expr<const valarray<_Tp>&> >
+valarray<_Tp>::operator[](valarray<size_t>&& __vs) const
+{
+    return __val_expr<__indirect_expr<const valarray&> >(__indirect_expr<const valarray&>(move(__vs), *this));
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+indirect_array<_Tp>
+valarray<_Tp>::operator[](valarray<size_t>&& __vs)
+{
+    return indirect_array<value_type>(move(__vs), *this);
+}
+
+#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
+
+template <class _Tp>
+valarray<_Tp>
+valarray<_Tp>::operator+() const
+{
+    valarray<value_type> __r;
+    size_t __n = size();
+    if (__n)
+    {
+        __r.__begin_ =
+            __r.__end_ =
+                static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+        for (const value_type* __p = __begin_; __n; ++__r.__end_, ++__p, --__n)
+            ::new (__r.__end_) value_type(+*__p);
+    }
+    return __r;
+}
+
+template <class _Tp>
+valarray<_Tp>
+valarray<_Tp>::operator-() const
+{
+    valarray<value_type> __r;
+    size_t __n = size();
+    if (__n)
+    {
+        __r.__begin_ =
+            __r.__end_ =
+                static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+        for (const value_type* __p = __begin_; __n; ++__r.__end_, ++__p, --__n)
+            ::new (__r.__end_) value_type(-*__p);
+    }
+    return __r;
+}
+
+template <class _Tp>
+valarray<_Tp>
+valarray<_Tp>::operator~() const
+{
+    valarray<value_type> __r;
+    size_t __n = size();
+    if (__n)
+    {
+        __r.__begin_ =
+            __r.__end_ =
+                static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+        for (const value_type* __p = __begin_; __n; ++__r.__end_, ++__p, --__n)
+            ::new (__r.__end_) value_type(~*__p);
+    }
+    return __r;
+}
+
+template <class _Tp>
+valarray<bool>
+valarray<_Tp>::operator!() const
+{
+    valarray<bool> __r;
+    size_t __n = size();
+    if (__n)
+    {
+        __r.__begin_ =
+            __r.__end_ =
+                static_cast<bool*>(::operator new(__n * sizeof(bool)));
+        for (const value_type* __p = __begin_; __n; ++__r.__end_, ++__p, --__n)
+            ::new (__r.__end_) bool(!*__p);
+    }
+    return __r;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator*=(const value_type& __x)
+{
+    for (value_type* __p = __begin_; __p != __end_; ++__p)
+        *__p *= __x;
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator/=(const value_type& __x)
+{
+    for (value_type* __p = __begin_; __p != __end_; ++__p)
+        *__p /= __x;
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator%=(const value_type& __x)
+{
+    for (value_type* __p = __begin_; __p != __end_; ++__p)
+        *__p %= __x;
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator+=(const value_type& __x)
+{
+    for (value_type* __p = __begin_; __p != __end_; ++__p)
+        *__p += __x;
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator-=(const value_type& __x)
+{
+    for (value_type* __p = __begin_; __p != __end_; ++__p)
+        *__p -= __x;
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator^=(const value_type& __x)
+{
+    for (value_type* __p = __begin_; __p != __end_; ++__p)
+        *__p ^= __x;
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator&=(const value_type& __x)
+{
+    for (value_type* __p = __begin_; __p != __end_; ++__p)
+        *__p &= __x;
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator|=(const value_type& __x)
+{
+    for (value_type* __p = __begin_; __p != __end_; ++__p)
+        *__p |= __x;
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator<<=(const value_type& __x)
+{
+    for (value_type* __p = __begin_; __p != __end_; ++__p)
+        *__p <<= __x;
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+valarray<_Tp>&
+valarray<_Tp>::operator>>=(const value_type& __x)
+{
+    for (value_type* __p = __begin_; __p != __end_; ++__p)
+        *__p >>= __x;
+    return *this;
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    valarray<_Tp>&
+>::type
+valarray<_Tp>::operator*=(const _Expr& __v)
+{
+    size_t __i = 0;
+    for (value_type* __t = __begin_; __t != __end_ ; ++__t, ++__i)
+        *__t *= __v[__i];
+    return *this;
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    valarray<_Tp>&
+>::type
+valarray<_Tp>::operator/=(const _Expr& __v)
+{
+    size_t __i = 0;
+    for (value_type* __t = __begin_; __t != __end_ ; ++__t, ++__i)
+        *__t /= __v[__i];
+    return *this;
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    valarray<_Tp>&
+>::type
+valarray<_Tp>::operator%=(const _Expr& __v)
+{
+    size_t __i = 0;
+    for (value_type* __t = __begin_; __t != __end_ ; ++__t, ++__i)
+        *__t %= __v[__i];
+    return *this;
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    valarray<_Tp>&
+>::type
+valarray<_Tp>::operator+=(const _Expr& __v)
+{
+    size_t __i = 0;
+    for (value_type* __t = __begin_; __t != __end_ ; ++__t, ++__i)
+        *__t += __v[__i];
+    return *this;
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    valarray<_Tp>&
+>::type
+valarray<_Tp>::operator-=(const _Expr& __v)
+{
+    size_t __i = 0;
+    for (value_type* __t = __begin_; __t != __end_ ; ++__t, ++__i)
+        *__t -= __v[__i];
+    return *this;
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    valarray<_Tp>&
+>::type
+valarray<_Tp>::operator^=(const _Expr& __v)
+{
+    size_t __i = 0;
+    for (value_type* __t = __begin_; __t != __end_ ; ++__t, ++__i)
+        *__t ^= __v[__i];
+    return *this;
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    valarray<_Tp>&
+>::type
+valarray<_Tp>::operator|=(const _Expr& __v)
+{
+    size_t __i = 0;
+    for (value_type* __t = __begin_; __t != __end_ ; ++__t, ++__i)
+        *__t |= __v[__i];
+    return *this;
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    valarray<_Tp>&
+>::type
+valarray<_Tp>::operator&=(const _Expr& __v)
+{
+    size_t __i = 0;
+    for (value_type* __t = __begin_; __t != __end_ ; ++__t, ++__i)
+        *__t &= __v[__i];
+    return *this;
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    valarray<_Tp>&
+>::type
+valarray<_Tp>::operator<<=(const _Expr& __v)
+{
+    size_t __i = 0;
+    for (value_type* __t = __begin_; __t != __end_ ; ++__t, ++__i)
+        *__t <<= __v[__i];
+    return *this;
+}
+
+template <class _Tp>
+template <class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    valarray<_Tp>&
+>::type
+valarray<_Tp>::operator>>=(const _Expr& __v)
+{
+    size_t __i = 0;
+    for (value_type* __t = __begin_; __t != __end_ ; ++__t, ++__i)
+        *__t >>= __v[__i];
+    return *this;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+void
+valarray<_Tp>::swap(valarray& __v) _NOEXCEPT
+{
+    _VSTD::swap(__begin_, __v.__begin_);
+    _VSTD::swap(__end_, __v.__end_);
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp
+valarray<_Tp>::sum() const
+{
+    if (__begin_ == __end_)
+        return value_type();
+    const value_type* __p = __begin_;
+    _Tp __r = *__p;
+    for (++__p; __p != __end_; ++__p)
+        __r += *__p;
+    return __r;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp
+valarray<_Tp>::min() const
+{
+    if (__begin_ == __end_)
+        return value_type();
+    return *_VSTD::min_element(__begin_, __end_);
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp
+valarray<_Tp>::max() const
+{
+    if (__begin_ == __end_)
+        return value_type();
+    return *_VSTD::max_element(__begin_, __end_);
+}
+
+template <class _Tp>
+valarray<_Tp>
+valarray<_Tp>::shift(int __i) const
+{
+    valarray<value_type> __r;
+    size_t __n = size();
+    if (__n)
+    {
+        __r.__begin_ =
+            __r.__end_ =
+                static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+        const value_type* __sb;
+        value_type* __tb;
+        value_type* __te;
+        if (__i >= 0)
+        {
+            __i = _VSTD::min(__i, static_cast<int>(__n));
+            __sb = __begin_ + __i;
+            __tb = __r.__begin_;
+            __te = __r.__begin_ + (__n - __i);
+        }
+        else
+        {
+            __i = _VSTD::min(-__i, static_cast<int>(__n));
+            __sb = __begin_;
+            __tb = __r.__begin_ + __i;
+            __te = __r.__begin_ + __n;
+        }
+        for (; __r.__end_ != __tb; ++__r.__end_)
+            ::new (__r.__end_) value_type();
+        for (; __r.__end_ != __te; ++__r.__end_, ++__sb)
+            ::new (__r.__end_) value_type(*__sb);
+        for (__te = __r.__begin_ + __n; __r.__end_ != __te; ++__r.__end_)
+            ::new (__r.__end_) value_type();
+    }
+    return __r;
+}
+
+template <class _Tp>
+valarray<_Tp>
+valarray<_Tp>::cshift(int __i) const
+{
+    valarray<value_type> __r;
+    size_t __n = size();
+    if (__n)
+    {
+        __r.__begin_ =
+            __r.__end_ =
+                static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+        __i %= static_cast<int>(__n);
+        const value_type* __m = __i >= 0 ? __begin_ + __i : __end_ + __i;
+        for (const value_type* __s = __m; __s != __end_; ++__r.__end_, ++__s)
+            ::new (__r.__end_) value_type(*__s);
+        for (const value_type* __s = __begin_; __s != __m; ++__r.__end_, ++__s)
+            ::new (__r.__end_) value_type(*__s);
+    }
+    return __r;
+}
+
+template <class _Tp>
+valarray<_Tp>
+valarray<_Tp>::apply(value_type __f(value_type)) const
+{
+    valarray<value_type> __r;
+    size_t __n = size();
+    if (__n)
+    {
+        __r.__begin_ =
+            __r.__end_ =
+                static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+        for (const value_type* __p = __begin_; __n; ++__r.__end_, ++__p, --__n)
+            ::new (__r.__end_) value_type(__f(*__p));
+    }
+    return __r;
+}
+
+template <class _Tp>
+valarray<_Tp>
+valarray<_Tp>::apply(value_type __f(const value_type&)) const
+{
+    valarray<value_type> __r;
+    size_t __n = size();
+    if (__n)
+    {
+        __r.__begin_ =
+            __r.__end_ =
+                static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+        for (const value_type* __p = __begin_; __n; ++__r.__end_, ++__p, --__n)
+            ::new (__r.__end_) value_type(__f(*__p));
+    }
+    return __r;
+}
+
+template <class _Tp>
+void
+valarray<_Tp>::resize(size_t __n, value_type __x)
+{
+    if (__begin_ != nullptr)
+    {
+        while (__end_ != __begin_)
+            (--__end_)->~value_type();
+        ::operator delete(__begin_);
+        __begin_ = __end_ = nullptr;
+    }
+    if (__n)
+    {
+        __begin_ = __end_ = static_cast<value_type*>(::operator new(__n * sizeof(value_type)));
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        try
+        {
+#endif  // _LIBCPP_NO_EXCEPTIONS
+            for (; __n; --__n, ++__end_)
+                ::new (__end_) value_type(__x);
+#ifndef _LIBCPP_NO_EXCEPTIONS
+        }
+        catch (...)
+        {
+            resize(0);
+            throw;
+        }
+#endif  // _LIBCPP_NO_EXCEPTIONS
+    }
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+void
+swap(valarray<_Tp>& __x, valarray<_Tp>& __y) _NOEXCEPT
+{
+    __x.swap(__y);
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<multiplies<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator*(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<multiplies<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(multiplies<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<multiplies<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator*(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<multiplies<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(multiplies<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<multiplies<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator*(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<multiplies<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(multiplies<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<divides<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator/(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<divides<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(divides<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<divides<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator/(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<divides<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(divides<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<divides<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator/(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<divides<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(divides<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<modulus<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator%(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<modulus<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(modulus<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<modulus<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator%(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<modulus<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(modulus<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<modulus<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator%(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<modulus<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(modulus<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<plus<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator+(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<plus<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(plus<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<plus<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator+(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<plus<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(plus<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<plus<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator+(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<plus<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(plus<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<minus<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator-(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<minus<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(minus<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<minus<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator-(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<minus<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(minus<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<minus<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator-(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<minus<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(minus<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<bit_xor<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator^(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<bit_xor<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(bit_xor<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<bit_xor<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator^(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<bit_xor<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(bit_xor<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<bit_xor<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator^(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<bit_xor<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(bit_xor<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<bit_and<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator&(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<bit_and<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(bit_and<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<bit_and<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator&(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<bit_and<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(bit_and<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<bit_and<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator&(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<bit_and<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(bit_and<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<bit_or<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator|(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<bit_or<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(bit_or<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<bit_or<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator|(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<bit_or<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(bit_or<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<bit_or<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator|(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<bit_or<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(bit_or<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<__bit_shift_left<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator<<(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<__bit_shift_left<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(__bit_shift_left<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<__bit_shift_left<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator<<(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<__bit_shift_left<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(__bit_shift_left<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<__bit_shift_left<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator<<(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<__bit_shift_left<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__bit_shift_left<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<__bit_shift_right<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator>>(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<__bit_shift_right<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(__bit_shift_right<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<__bit_shift_right<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator>>(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<__bit_shift_right<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(__bit_shift_right<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<__bit_shift_right<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator>>(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<__bit_shift_right<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__bit_shift_right<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<logical_and<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator&&(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<logical_and<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(logical_and<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<logical_and<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator&&(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<logical_and<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(logical_and<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<logical_and<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator&&(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<logical_and<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(logical_and<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<logical_or<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator||(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<logical_or<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(logical_or<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<logical_or<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator||(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<logical_or<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(logical_or<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<logical_or<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator||(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<logical_or<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(logical_or<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<equal_to<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator==(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<equal_to<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(equal_to<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<equal_to<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator==(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<equal_to<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(equal_to<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<equal_to<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator==(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<equal_to<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(equal_to<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<not_equal_to<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator!=(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<not_equal_to<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(not_equal_to<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<not_equal_to<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator!=(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<not_equal_to<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(not_equal_to<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<not_equal_to<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator!=(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<not_equal_to<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(not_equal_to<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<less<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator<(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<less<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(less<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<less<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator<(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<less<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(less<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<less<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator<(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<less<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(less<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<greater<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator>(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<greater<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(greater<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<greater<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator>(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<greater<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(greater<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<greater<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator>(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<greater<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(greater<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<less_equal<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator<=(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<less_equal<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(less_equal<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<less_equal<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator<=(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<less_equal<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(less_equal<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<less_equal<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator<=(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<less_equal<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(less_equal<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<greater_equal<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+operator>=(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<greater_equal<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(greater_equal<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<greater_equal<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+operator>=(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<greater_equal<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(greater_equal<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<greater_equal<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+operator>=(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<greater_equal<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(greater_equal<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__abs_expr<typename _Expr::value_type>, _Expr> >
+>::type
+abs(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__abs_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__abs_expr<value_type>(), __x));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__acos_expr<typename _Expr::value_type>, _Expr> >
+>::type
+acos(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__acos_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__acos_expr<value_type>(), __x));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__asin_expr<typename _Expr::value_type>, _Expr> >
+>::type
+asin(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__asin_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__asin_expr<value_type>(), __x));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__atan_expr<typename _Expr::value_type>, _Expr> >
+>::type
+atan(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__atan_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__atan_expr<value_type>(), __x));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<__atan2_expr<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+atan2(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<__atan2_expr<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(__atan2_expr<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<__atan2_expr<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+atan2(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<__atan2_expr<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(__atan2_expr<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<__atan2_expr<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+atan2(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<__atan2_expr<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__atan2_expr<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__cos_expr<typename _Expr::value_type>, _Expr> >
+>::type
+cos(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__cos_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__cos_expr<value_type>(), __x));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__cosh_expr<typename _Expr::value_type>, _Expr> >
+>::type
+cosh(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__cosh_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__cosh_expr<value_type>(), __x));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__exp_expr<typename _Expr::value_type>, _Expr> >
+>::type
+exp(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__exp_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__exp_expr<value_type>(), __x));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__log_expr<typename _Expr::value_type>, _Expr> >
+>::type
+log(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__log_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__log_expr<value_type>(), __x));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__log10_expr<typename _Expr::value_type>, _Expr> >
+>::type
+log10(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__log10_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__log10_expr<value_type>(), __x));
+}
+
+template<class _Expr1, class _Expr2>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr1>::value && __is_val_expr<_Expr2>::value,
+    __val_expr<_BinaryOp<__pow_expr<typename _Expr1::value_type>, _Expr1, _Expr2> >
+>::type
+pow(const _Expr1& __x, const _Expr2& __y)
+{
+    typedef typename _Expr1::value_type value_type;
+    typedef _BinaryOp<__pow_expr<value_type>, _Expr1, _Expr2> _Op;
+    return __val_expr<_Op>(_Op(__pow_expr<value_type>(), __x, __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<__pow_expr<typename _Expr::value_type>,
+               _Expr, __scalar_expr<typename _Expr::value_type> > >
+>::type
+pow(const _Expr& __x, const typename _Expr::value_type& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<__pow_expr<value_type>, _Expr, __scalar_expr<value_type> > _Op;
+    return __val_expr<_Op>(_Op(__pow_expr<value_type>(),
+                           __x, __scalar_expr<value_type>(__y, __x.size())));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_BinaryOp<__pow_expr<typename _Expr::value_type>,
+               __scalar_expr<typename _Expr::value_type>, _Expr> >
+>::type
+pow(const typename _Expr::value_type& __x, const _Expr& __y)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _BinaryOp<__pow_expr<value_type>, __scalar_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__pow_expr<value_type>(),
+                           __scalar_expr<value_type>(__x, __y.size()), __y));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__sin_expr<typename _Expr::value_type>, _Expr> >
+>::type
+sin(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__sin_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__sin_expr<value_type>(), __x));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__sinh_expr<typename _Expr::value_type>, _Expr> >
+>::type
+sinh(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__sinh_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__sinh_expr<value_type>(), __x));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__sqrt_expr<typename _Expr::value_type>, _Expr> >
+>::type
+sqrt(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__sqrt_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__sqrt_expr<value_type>(), __x));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__tan_expr<typename _Expr::value_type>, _Expr> >
+>::type
+tan(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__tan_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__tan_expr<value_type>(), __x));
+}
+
+template<class _Expr>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    __is_val_expr<_Expr>::value,
+    __val_expr<_UnaryOp<__tanh_expr<typename _Expr::value_type>, _Expr> >
+>::type
+tanh(const _Expr& __x)
+{
+    typedef typename _Expr::value_type value_type;
+    typedef _UnaryOp<__tanh_expr<value_type>, _Expr> _Op;
+    return __val_expr<_Op>(_Op(__tanh_expr<value_type>(), __x));
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp*
+begin(valarray<_Tp>& __v)
+{
+    return __v.__begin_;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+const _Tp*
+begin(const valarray<_Tp>& __v)
+{
+    return __v.__begin_;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp*
+end(valarray<_Tp>& __v)
+{
+    return __v.__end_;
+}
+
+template <class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+const _Tp*
+end(const valarray<_Tp>& __v)
+{
+    return __v.__end_;
+}
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif  // _LIBCPP_VALARRAY