valarray

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  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = asin(__x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> atan(const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = atan(__x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> atan2(const valarray<_Tp>& __x,
                           const valarray<_Tp>& __y) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = atan2(__x[__i], __y[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> atan2(const valarray<_Tp>& __x, const _Tp& __c) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = atan2(__x[__i], __c);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> atan2(const _Tp& __c, const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = atan2(__c, __x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> cos(const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = cos(__x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> cosh(const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = cosh(__x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> exp(const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = exp(__x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> log(const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = log(__x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> log10(const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = log10(__x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> pow(const valarray<_Tp>& __x,
                           const valarray<_Tp>& __y) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = pow(__x[__i], __y[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> pow(const valarray<_Tp>& __x, const _Tp& __c) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = pow(__x[__i], __c);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> pow(const _Tp& __c, const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = pow(__c, __x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> sin(const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = sin(__x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> sinh(const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = sinh(__x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> sqrt(const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = sqrt(__x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> tan(const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = tan(__x[__i]);
  return __tmp;
}

template <class _Tp>
inline valarray<_Tp> tanh(const valarray<_Tp>& __x) {
  typedef typename valarray<_Tp>::_NoInit _NoInit;
  valarray<_Tp> __tmp(__x.size(), _NoInit());
  for (size_t __i = 0; __i < __x.size(); ++__i)
    __tmp[__i] = tanh(__x[__i]);
  return __tmp;
}

//----------------------------------------------------------------------
// slice and slice_array

class slice {
public:
  slice() : _M_start(0), _M_length(0), _M_stride(0) {}
  slice(size_t __start, size_t __length, size_t __stride)
    : _M_start(__start), _M_length(__length), _M_stride(__stride)
    {}

  size_t start()  const { return _M_start; }
  size_t size()   const { return _M_length; }
  size_t stride() const { return _M_stride; }

   
private:
  size_t _M_start;
  size_t _M_length;
  size_t _M_stride;
};

template <class _Tp>
class slice_array {
  friend class valarray<_Tp>;
public:
  typedef _Tp value_type;

  void operator=(const valarray<value_type>& __x) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] = __x[__i];
  }

  void operator*=(const valarray<value_type>& __x) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] *= __x[__i];
  }

  void operator/=(const valarray<value_type>& __x) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] /= __x[__i];
  }

  void operator%=(const valarray<value_type>& __x) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] %= __x[__i];
  }

  void operator+=(const valarray<value_type>& __x) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] += __x[__i];
  }

  void operator-=(const valarray<value_type>& __x) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] -= __x[__i];
  }

  void operator^=(const valarray<value_type>& __x) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] ^= __x[__i];
  }

  void operator&=(const valarray<value_type>& __x) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] &= __x[__i];
  }

  void operator|=(const valarray<value_type>& __x) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] |= __x[__i];
  }

  void operator<<=(const valarray<value_type>& __x) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] <<= __x[__i];
  }

  void operator>>=(const valarray<value_type>& __x) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] >>= __x[__i];
  }

  void operator=(const value_type& __c) const {
    size_t __index = _M_slice.start();
    for (size_t __i = 0;
         __i < _M_slice.size();
         ++__i, __index += _M_slice.stride())
      _M_array[__index] = __c;
  }

  ~slice_array() {}

private:
  slice_array(const slice& __slice, valarray<_Tp>& __array)
    : _M_slice(__slice), _M_array(__array)
    {}

  slice          _M_slice;
  valarray<_Tp>& _M_array;

private:                        // Disable assignment and default constructor
  slice_array();
};

// valarray member functions dealing with slice and slice_array

template <class _Tp>
inline valarray<_Tp>::valarray(const slice_array<_Tp>& __x)
  : _Valarray_base<_Tp>(__x._M_slice.size())
{
  typedef typename __type_traits<_Tp>::has_trivial_default_constructor
          _Is_Trivial;
  _M_initialize(_Is_Trivial());  
  *this = __x;
}

// Behavior is undefined if __x and *this have different sizes
template <class _Tp>
valarray<_Tp>& valarray<_Tp>::operator=(const slice_array<_Tp>& __x)
{
  size_t __index = __x._M_slice.start();
  for (size_t __i = 0;
       __i < __x._M_slice.size();
       ++__i, __index += __x._M_slice.stride())
    (*this)[__i] = __x._M_array[__index];
  return *this;
}

template <class _Tp>
valarray<_Tp> valarray<_Tp>::operator[](slice __slice) const {
  valarray<_Tp> __tmp(__slice.size(), _NoInit());
  size_t __index = __slice.start();
  for (size_t __i = 0;
       __i < __slice.size();
       ++__i, __index += __slice.stride())
    __tmp[__i] = (*this)[__index];
  return __tmp;
}

template <class _Tp>
inline slice_array<_Tp> valarray<_Tp>::operator[](slice __slice) {
  return slice_array<_Tp>(__slice, *this);
}

//----------------------------------------------------------------------
// gslice and gslice_array

struct _Gslice_Iter;

class gslice {
  friend struct _Gslice_Iter;
public:
  gslice() : _M_start(0), _M_lengths(0), _M_strides(0) {}
  gslice(size_t __start,
         const valarray<size_t>& __lengths, const valarray<size_t>& __strides)
    : _M_start(__start), _M_lengths(__lengths), _M_strides(__strides)
    {}

  size_t start()            const { return _M_start; }
  valarray<size_t> size()   const { return _M_lengths; }
  valarray<size_t> stride() const { return _M_strides; }

  // Extension: check for an empty gslice.
  bool _M_empty() const { return _M_lengths.size() == 0; }

  // Extension: number of indices this gslice represents.  (For a degenerate
  // gslice, they're not necessarily all distinct.)
  size_t _M_size() const {
    return !this->_M_empty()
      ? accumulate(_M_lengths._M_first + 1,
                   _M_lengths._M_first + _M_lengths._M_size,
                   _M_lengths[0],
                   multiplies<size_t>())
      : 0;
  }

private:
  size_t _M_start;
  valarray<size_t> _M_lengths;
  valarray<size_t> _M_strides;
};

// This is not an STL iterator.  It is constructed from a gslice, and it
// steps through the gslice indices in sequence.  See 23.3.6 of the C++
// standard, paragraphs 2-3, for an explanation of the sequence.  At
// each step we get two things: the ordinal (i.e. number of steps taken),
// and the one-dimensional index.

struct _Gslice_Iter {
  _Gslice_Iter(const gslice& __gslice)
    : _M_step(0), _M_1d_idx(__gslice.start()),
      _M_indices(size_t(0), __gslice._M_lengths.size()),
      _M_gslice(__gslice)
    {}
    
  bool _M_done() const { return _M_indices[0] == _M_gslice._M_lengths[0]; }

  bool _M_incr() {
    size_t __dim = _M_indices.size() - 1;
    ++_M_step;
    while (true) {
      _M_1d_idx += _M_gslice._M_strides[__dim];
      if (++_M_indices[__dim] != _M_gslice._M_lengths[__dim])
        return true;
      else if (__dim != 0) {
        _M_1d_idx -=
          _M_gslice._M_strides[__dim] * _M_gslice._M_lengths[__dim];
        _M_indices[__dim] = 0;
        --__dim;
      }
      else
        return false;
    }
  }

  size_t _M_step;
  size_t _M_1d_idx;

  valarray<size_t> _M_indices;
  const gslice& _M_gslice;
};

template <class _Tp>
class gslice_array {
  friend class valarray<_Tp>;
public:
  typedef _Tp value_type;

  void operator= (const valarray<value_type>& __x) const {
    if (!_M_gslice._M_empty()) {
      _Gslice_Iter __i(_M_gslice);
      do _M_array[__i._M_1d_idx] = __x[__i._M_step]; while(__i._M_incr());
    }
  }

  void operator*= (const valarray<value_type>& __x) const {
    if (!_M_gslice._M_empty()) {
      _Gslice_Iter __i(_M_gslice);
      do _M_array[__i._M_1d_idx] *= __x[__i._M_step]; while(__i._M_incr());
    }
  }

  void operator/= (const valarray<value_type>& __x) const {
    if (!_M_gslice._M_empty()) {
      _Gslice_Iter __i(_M_gslice);
      do _M_array[__i._M_1d_idx] /= __x[__i._M_step]; while(__i._M_incr());
    }
  }