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//
// SPDX-License-Identifier: BSD-3-Clause
// Copyright Contributors to the OpenEXR Project.
//

//
// Axis-aligned bounding box
//

#ifndef INCLUDED_IMATHBOX_H
#define INCLUDED_IMATHBOX_H

#include "ImathExport.h"
#include "ImathNamespace.h"

#include "ImathVec.h"

IMATH_INTERNAL_NAMESPACE_HEADER_ENTER

///
/// The `Box<V>` template represents an axis-aligned bounding box defined by
/// minimum and maximum values of type `V`. The `min` and `max` members are
/// public.
///
/// The type `V` is typically an Imath vector (i.e. `V2i`, `V3f`, etc) and must
/// implement an index `operator[]` that returns a type (typically as scalar)
/// that supports assignment, comparison, and arithmetic operators.
///
/// `V` must also provide a constructor that takes a float and/or double for
/// use in initializing the box.
///
/// `V` must also provide a function `V::dimensions()` which returns the
/// number of dimensions in the class (since its assumed its a vector) --
/// preferably, this returns a constant expression, typically 2 or 3.
///

template <class V> class IMATH_EXPORT_TEMPLATE_TYPE Box
{
public:
    /// @{
    /// @name Direct access to bounds

/// The minimum value of the box.
    V min;

/// The maximum value of the box.
    V max;

/// @}

/// @{
    ///	@name Constructors

/// Construct an empty bounding box. This initializes the mimimum to
    /// std::numeric_limits<V::baseType>::max() and the maximum to
    /// std::numeric_limits<V::baseType>::lowest().
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Box () IMATH_NOEXCEPT;

/// Construct a bounding box that contains a single point.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Box (const V& point) IMATH_NOEXCEPT;

/// Construct a bounding box with the given minimum and maximum values.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Box (const V& minV, const V& maxV)
        IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Comparison

/// Equality
    IMATH_HOSTDEVICE constexpr bool
    operator== (const Box<V>& src) const IMATH_NOEXCEPT;

/// Inequality
    IMATH_HOSTDEVICE constexpr bool
    operator!= (const Box<V>& src) const IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Manipulation

/// Set the box to be empty. A box is empty if the mimimum is greater
    /// than the maximum. makeEmpty() sets the mimimum to `V::baseTypeMax()`
    /// and the maximum to `V::baseTypeLowest()`.
    IMATH_HOSTDEVICE void makeEmpty () IMATH_NOEXCEPT;

/// Extend the box to include the given point.
    IMATH_HOSTDEVICE void extendBy (const V& point) IMATH_NOEXCEPT;

/// Extend the box to include the given box.
    IMATH_HOSTDEVICE void extendBy (const Box<V>& box) IMATH_NOEXCEPT;

/// Make the box include the entire range of `V`.
    IMATH_HOSTDEVICE void makeInfinite () IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Query

/// Return the size of the box. The size is of type `V`, defined
    /// as `(max-min)`. An empty box has a size of `V(0)`, i.e. 0 in
    /// each dimension.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 V size () const IMATH_NOEXCEPT;

/// Return the center of the box. The center is defined as
    /// `(max+min)/2`. The center of an empty box is undefined.
    IMATH_HOSTDEVICE constexpr V center () const IMATH_NOEXCEPT;

/// Return true if the given point is inside the box, false otherwise.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
    intersects (const V& point) const IMATH_NOEXCEPT;

/// Return true if the given box is inside the box, false otherwise.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
    intersects (const Box<V>& box) const IMATH_NOEXCEPT;

/// Return the major axis of the box. The major axis is the dimension with
    /// the greatest difference between maximum and minimum.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 unsigned int
    majorAxis () const IMATH_NOEXCEPT;

/// Return true if the box is empty, false otherwise. An empty box's
    /// minimum is greater than its maximum.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool isEmpty () const IMATH_NOEXCEPT;

/// Return true if the box is larger than a single point, false otherwise.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool hasVolume () const IMATH_NOEXCEPT;

/// Return true if the box contains all points, false otherwise.
    /// An infinite box has a mimimum of`V::baseTypeLowest()`
    /// and a maximum of `V::baseTypeMax()`.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool isInfinite () const IMATH_NOEXCEPT;

/// @}
};

//--------------------
// Convenient typedefs
//--------------------

/// 2D box of base type `short`.
typedef Box<V2s> Box2s;

/// 2D box of base type `int`.
typedef Box<V2i> Box2i;

/// 2D box of base type `int64_t`.
typedef Box<V2i64> Box2i64;

/// 2D box of base type `float`.
typedef Box<V2f> Box2f;

/// 2D box of base type `double`.
typedef Box<V2d> Box2d;

/// 3D box of base type `short`.
typedef Box<V3s> Box3s;

/// 3D box of base type `int`.
typedef Box<V3i> Box3i;

/// 3D box of base type `int64_t`.
typedef Box<V3i64> Box3i64;

/// 3D box of base type `float`.
typedef Box<V3f> Box3f;

/// 3D box of base type `double`.
typedef Box<V3d> Box3d;

template <class V>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline Box<V>::Box () IMATH_NOEXCEPT
{
    makeEmpty ();
}

template <class V>
IMATH_HOSTDEVICE
    IMATH_CONSTEXPR14 inline Box<V>::Box (const V& point) IMATH_NOEXCEPT
{
    min = point;
    max = point;
}

template <class V>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline Box<V>::Box (
    const V& minV, const V& maxV) IMATH_NOEXCEPT
{
    min = minV;
    max = maxV;
}

template <class V>
IMATH_HOSTDEVICE constexpr inline bool
Box<V>::operator== (const Box<V>& src) const IMATH_NOEXCEPT
{
    return (min == src.min && max == src.max);
}

template <class V>
IMATH_HOSTDEVICE constexpr inline bool
Box<V>::operator!= (const Box<V>& src) const IMATH_NOEXCEPT
{
    return (min != src.min || max != src.max);
}

template <class V>
IMATH_HOSTDEVICE inline void
Box<V>::makeEmpty () IMATH_NOEXCEPT
{
    min = V (V::baseTypeMax ());
    max = V (V::baseTypeLowest ());
}

template <class V>
IMATH_HOSTDEVICE inline void
Box<V>::makeInfinite () IMATH_NOEXCEPT
{
    min = V (V::baseTypeLowest ());
    max = V (V::baseTypeMax ());
}

template <class V>
IMATH_HOSTDEVICE inline void
Box<V>::extendBy (const V& point) IMATH_NOEXCEPT
{
    for (unsigned int i = 0; i < min.dimensions (); i++)
    {
        if (point[i] < min[i]) min[i] = point[i];

if (point[i] > max[i]) max[i] = point[i];
    }
}

template <class V>
IMATH_HOSTDEVICE inline void
Box<V>::extendBy (const Box<V>& box) IMATH_NOEXCEPT
{
    for (unsigned int i = 0; i < min.dimensions (); i++)
    {
        if (box.min[i] < min[i]) min[i] = box.min[i];

if (box.max[i] > max[i]) max[i] = box.max[i];
    }
}

template <class V>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<V>::intersects (const V& point) const IMATH_NOEXCEPT
{
    for (unsigned int i = 0; i < min.dimensions (); i++)
    {
        if (point[i] < min[i] || point[i] > max[i]) return false;
    }

return true;
}

template <class V>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<V>::intersects (const Box<V>& box) const IMATH_NOEXCEPT
{
    for (unsigned int i = 0; i < min.dimensions (); i++)
    {
        if (box.max[i] < min[i] || box.min[i] > max[i]) return false;
    }

return true;
}

template <class V>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline V
Box<V>::size () const IMATH_NOEXCEPT
{
    if (isEmpty ()) return V (0);

return max - min;
}

template <class V>
IMATH_HOSTDEVICE constexpr inline V
Box<V>::center () const IMATH_NOEXCEPT
{
    return (max + min) / 2;
}

template <class V>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<V>::isEmpty () const IMATH_NOEXCEPT
{
    for (unsigned int i = 0; i < min.dimensions (); i++)
    {
        if (max[i] < min[i]) return true;
    }

return false;
}

template <class V>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<V>::isInfinite () const IMATH_NOEXCEPT
{
    for (unsigned int i = 0; i < min.dimensions (); i++)
    {
        if (min[i] != V::baseTypeLowest () || max[i] != V::baseTypeMax ())
            return false;
    }

return true;
}

template <class V>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<V>::hasVolume () const IMATH_NOEXCEPT
{
    for (unsigned int i = 0; i < min.dimensions (); i++)
    {
        if (max[i] <= min[i]) return false;
    }

return true;
}

template <class V>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline unsigned int
Box<V>::majorAxis () const IMATH_NOEXCEPT
{
    unsigned int major = 0;
    V            s     = size ();

for (unsigned int i = 1; i < min.dimensions (); i++)
    {
        if (s[i] > s[major]) major = i;
    }

return major;
}

//-------------------------------------------------------------------
//
//  Partial class specializations for Imath::Vec2<T> and Imath::Vec3<T>
//
//-------------------------------------------------------------------

template <typename V> class Box;

///
/// The Box<Vec2<T>> template represents a 2D bounding box defined by
/// minimum and maximum values of type Vec2<T>. The min and max members are
/// public.
///

template <class T> class IMATH_EXPORT_TEMPLATE_TYPE Box<Vec2<T>>
{
public:
    /// @{
    /// @name Direct access to bounds

/// The minimum value of the box.
    Vec2<T> min;

/// The maximum value of the box.
    Vec2<T> max;

/// @}

/// @{
    /// @name Constructors and Assignment

/// Empty by default
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Box () IMATH_NOEXCEPT;

/// Construct a bounding box that contains a single point.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Box (const Vec2<T>& point)
        IMATH_NOEXCEPT;

/// Construct a bounding box with the given minimum and maximum points
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14
    Box (const Vec2<T>& minT, const Vec2<T>& maxT) IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Comparison

/// Equality
    IMATH_HOSTDEVICE constexpr bool
    operator== (const Box<Vec2<T>>& src) const IMATH_NOEXCEPT;

/// Inequality
    IMATH_HOSTDEVICE constexpr bool
    operator!= (const Box<Vec2<T>>& src) const IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Manipulation

/// Set the Box to be empty. A Box is empty if the mimimum is
    /// greater than the maximum. makeEmpty() sets the mimimum to
    /// std::numeric_limits<T>::max() and the maximum to
    /// std::numeric_limits<T>::lowest().
    IMATH_HOSTDEVICE void makeEmpty () IMATH_NOEXCEPT;

/// Extend the Box to include the given point.
    IMATH_HOSTDEVICE void extendBy (const Vec2<T>& point) IMATH_NOEXCEPT;

/// Extend the Box to include the given box.
    IMATH_HOSTDEVICE void extendBy (const Box<Vec2<T>>& box) IMATH_NOEXCEPT;

/// Make the box include the entire range of T.
    IMATH_HOSTDEVICE void makeInfinite () IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Query

/// Return the size of the box. The size is of type `V`, defined as
    /// `(max-min)`. An empty box has a size of `V(0)`, i.e. 0 in each dimension.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Vec2<T> size () const IMATH_NOEXCEPT;

/// Return the center of the box. The center is defined as
    /// `(max+min)/2`. The center of an empty box is undefined.
    IMATH_HOSTDEVICE constexpr Vec2<T> center () const IMATH_NOEXCEPT;

/// Return true if the given point is inside the box, false otherwise.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
    intersects (const Vec2<T>& point) const IMATH_NOEXCEPT;

/// Return true if the given box is inside the box, false otherwise.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
    intersects (const Box<Vec2<T>>& box) const IMATH_NOEXCEPT;

/// Return true if the box is empty, false otherwise. An empty box's
    /// minimum is greater than its maximum.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool isEmpty () const IMATH_NOEXCEPT;

/// Return true if the box is larger than a single point, false otherwise.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool hasVolume () const IMATH_NOEXCEPT;

/// Return true if the box contains all points, false otherwise.
    /// An infinite box has a mimimum of `V::baseTypeMin()`
    /// and a maximum of `V::baseTypeMax()`.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool isInfinite () const IMATH_NOEXCEPT;

/// @}
};

//----------------
//  Implementation
//----------------

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline Box<Vec2<T>>::Box () IMATH_NOEXCEPT
{
    makeEmpty ();
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline Box<Vec2<T>>::Box (
    const Vec2<T>& point) IMATH_NOEXCEPT
{
    min = point;
    max = point;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline Box<Vec2<T>>::Box (
    const Vec2<T>& minT, const Vec2<T>& maxT) IMATH_NOEXCEPT
{
    min = minT;
    max = maxT;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline bool
Box<Vec2<T>>::operator== (const Box<Vec2<T>>& src) const IMATH_NOEXCEPT
{
    return (min == src.min && max == src.max);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline bool
Box<Vec2<T>>::operator!= (const Box<Vec2<T>>& src) const IMATH_NOEXCEPT
{
    return (min != src.min || max != src.max);
}

template <class T>
IMATH_HOSTDEVICE inline void
Box<Vec2<T>>::makeEmpty () IMATH_NOEXCEPT
{
    min = Vec2<T> (Vec2<T>::baseTypeMax ());
    max = Vec2<T> (Vec2<T>::baseTypeLowest ());
}

template <class T>
IMATH_HOSTDEVICE inline void
Box<Vec2<T>>::makeInfinite () IMATH_NOEXCEPT
{
    min = Vec2<T> (Vec2<T>::baseTypeLowest ());
    max = Vec2<T> (Vec2<T>::baseTypeMax ());
}

template <class T>
IMATH_HOSTDEVICE inline void
Box<Vec2<T>>::extendBy (const Vec2<T>& point) IMATH_NOEXCEPT
{
    if (point[0] < min[0]) min[0] = point[0];

if (point[0] > max[0]) max[0] = point[0];

if (point[1] < min[1]) min[1] = point[1];

if (point[1] > max[1]) max[1] = point[1];
}

template <class T>
IMATH_HOSTDEVICE inline void
Box<Vec2<T>>::extendBy (const Box<Vec2<T>>& box) IMATH_NOEXCEPT
{
    if (box.min[0] < min[0]) min[0] = box.min[0];

if (box.max[0] > max[0]) max[0] = box.max[0];

if (box.min[1] < min[1]) min[1] = box.min[1];

if (box.max[1] > max[1]) max[1] = box.max[1];
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<Vec2<T>>::intersects (const Vec2<T>& point) const IMATH_NOEXCEPT
{
    if (point[0] < min[0] || point[0] > max[0] || point[1] < min[1] ||
        point[1] > max[1])
        return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<Vec2<T>>::intersects (const Box<Vec2<T>>& box) const IMATH_NOEXCEPT
{
    if (box.max[0] < min[0] || box.min[0] > max[0] || box.max[1] < min[1] ||
        box.min[1] > max[1])
        return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline Vec2<T>
                 Box<Vec2<T>>::size () const IMATH_NOEXCEPT
{
    if (isEmpty ()) return Vec2<T> (0);

return max - min;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>
Box<Vec2<T>>::center () const IMATH_NOEXCEPT
{
    return (max + min) / 2;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<Vec2<T>>::isEmpty () const IMATH_NOEXCEPT
{
    if (max[0] < min[0] || max[1] < min[1]) return true;

return false;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<Vec2<T>>::isInfinite () const IMATH_NOEXCEPT
{
    if (min[0] != std::numeric_limits<T>::lowest () ||
        max[0] != std::numeric_limits<T>::max () ||
        min[1] != std::numeric_limits<T>::lowest () ||
        max[1] != std::numeric_limits<T>::max ())
        return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<Vec2<T>>::hasVolume () const IMATH_NOEXCEPT
{
    if (max[0] <= min[0] || max[1] <= min[1]) return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline unsigned int
Box<Vec2<T>>::majorAxis () const IMATH_NOEXCEPT
{
    unsigned int major = 0;
    Vec2<T>      s     = size ();

if (s[1] > s[major]) major = 1;

return major;
}

///
/// The Box<Vec3> template represents a 3D bounding box defined by
/// minimum and maximum values of type Vec3.
///
template <class T> class IMATH_EXPORT_TEMPLATE_TYPE Box<Vec3<T>>
{
public:
    /// @{
    /// @name Direct access to bounds

/// The minimum value of the box.
    Vec3<T> min;

/// The maximum value of the box.
    Vec3<T> max;

/// @}

/// @{
    /// @name Constructors

/// Empty by default
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Box () IMATH_NOEXCEPT;

/// Construct a bounding box that contains a single point.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Box (const Vec3<T>& point)
        IMATH_NOEXCEPT;

/// Construct a bounding box with the given minimum and maximum points
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14
    Box (const Vec3<T>& minT, const Vec3<T>& maxT) IMATH_NOEXCEPT;

/// @}

/// Equality
    IMATH_HOSTDEVICE constexpr bool
    operator== (const Box<Vec3<T>>& src) const IMATH_NOEXCEPT;

/// Inequality
    IMATH_HOSTDEVICE constexpr bool
    operator!= (const Box<Vec3<T>>& src) const IMATH_NOEXCEPT;

/// Extend the Box to include the given point.
    IMATH_HOSTDEVICE void extendBy (const Vec3<T>& point) IMATH_NOEXCEPT;
    /// Extend the Box to include the given box.

IMATH_HOSTDEVICE void extendBy (const Box<Vec3<T>>& box) IMATH_NOEXCEPT;

/// Make the box include the entire range of T.
    IMATH_HOSTDEVICE void makeInfinite () IMATH_NOEXCEPT;

/// Return the size of the box. The size is of type `V`, defined as
    /// (max-min). An empty box has a size of V(0), i.e. 0 in each dimension.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Vec3<T> size () const IMATH_NOEXCEPT;

/// Return the center of the box. The center is defined as
    /// (max+min)/2. The center of an empty box is undefined.
    IMATH_HOSTDEVICE constexpr Vec3<T> center () const IMATH_NOEXCEPT;

/// Return true if the given point is inside the box, false otherwise.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
    intersects (const Vec3<T>& point) const IMATH_NOEXCEPT;

/// Return true if the given box is inside the box, false otherwise.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
    intersects (const Box<Vec3<T>>& box) const IMATH_NOEXCEPT;

/// Return true if the box is empty, false otherwise. An empty box's
    /// minimum is greater than its maximum.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool isEmpty () const IMATH_NOEXCEPT;

/// Return true if the box is larger than a single point, false otherwise.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool hasVolume () const IMATH_NOEXCEPT;

/// Return true if the box contains all points, false otherwise.
    /// An infinite box has a mimimum of`V::baseTypeMin()`
    /// and a maximum of `V::baseTypeMax()`.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool isInfinite () const IMATH_NOEXCEPT;
};

//----------------
//  Implementation
//----------------

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline Box<Vec3<T>>::Box () IMATH_NOEXCEPT
{
    makeEmpty ();
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline Box<Vec3<T>>::Box (
    const Vec3<T>& point) IMATH_NOEXCEPT
{
    min = point;
    max = point;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline Box<Vec3<T>>::Box (
    const Vec3<T>& minT, const Vec3<T>& maxT) IMATH_NOEXCEPT
{
    min = minT;
    max = maxT;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline bool
Box<Vec3<T>>::operator== (const Box<Vec3<T>>& src) const IMATH_NOEXCEPT
{
    return (min == src.min && max == src.max);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline bool
Box<Vec3<T>>::operator!= (const Box<Vec3<T>>& src) const IMATH_NOEXCEPT
{
    return (min != src.min || max != src.max);
}

template <class T>
IMATH_HOSTDEVICE inline void
Box<Vec3<T>>::makeEmpty () IMATH_NOEXCEPT
{
    min = Vec3<T> (Vec3<T>::baseTypeMax ());
    max = Vec3<T> (Vec3<T>::baseTypeLowest ());
}

template <class T>
IMATH_HOSTDEVICE inline void
Box<Vec3<T>>::makeInfinite () IMATH_NOEXCEPT
{
    min = Vec3<T> (Vec3<T>::baseTypeLowest ());
    max = Vec3<T> (Vec3<T>::baseTypeMax ());
}

template <class T>
IMATH_HOSTDEVICE inline void
Box<Vec3<T>>::extendBy (const Vec3<T>& point) IMATH_NOEXCEPT
{
    if (point[0] < min[0]) min[0] = point[0];

if (point[0] > max[0]) max[0] = point[0];

if (point[1] < min[1]) min[1] = point[1];

if (point[1] > max[1]) max[1] = point[1];

if (point[2] < min[2]) min[2] = point[2];

if (point[2] > max[2]) max[2] = point[2];
}

template <class T>
IMATH_HOSTDEVICE inline void
Box<Vec3<T>>::extendBy (const Box<Vec3<T>>& box) IMATH_NOEXCEPT
{
    if (box.min[0] < min[0]) min[0] = box.min[0];

if (box.max[0] > max[0]) max[0] = box.max[0];

if (box.min[1] < min[1]) min[1] = box.min[1];

if (box.max[1] > max[1]) max[1] = box.max[1];

if (box.min[2] < min[2]) min[2] = box.min[2];

if (box.max[2] > max[2]) max[2] = box.max[2];
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<Vec3<T>>::intersects (const Vec3<T>& point) const IMATH_NOEXCEPT
{
    if (point[0] < min[0] || point[0] > max[0] || point[1] < min[1] ||
        point[1] > max[1] || point[2] < min[2] || point[2] > max[2])
        return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<Vec3<T>>::intersects (const Box<Vec3<T>>& box) const IMATH_NOEXCEPT
{
    if (box.max[0] < min[0] || box.min[0] > max[0] || box.max[1] < min[1] ||
        box.min[1] > max[1] || box.max[2] < min[2] || box.min[2] > max[2])
        return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline Vec3<T>
                 Box<Vec3<T>>::size () const IMATH_NOEXCEPT
{
    if (isEmpty ()) return Vec3<T> (0);

return max - min;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>
Box<Vec3<T>>::center () const IMATH_NOEXCEPT
{
    return (max + min) / 2;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<Vec3<T>>::isEmpty () const IMATH_NOEXCEPT
{
    if (max[0] < min[0] || max[1] < min[1] || max[2] < min[2]) return true;

return false;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<Vec3<T>>::isInfinite () const IMATH_NOEXCEPT
{
    if (min[0] != std::numeric_limits<T>::lowest () ||
        max[0] != std::numeric_limits<T>::max () ||
        min[1] != std::numeric_limits<T>::lowest () ||
        max[1] != std::numeric_limits<T>::max () ||
        min[2] != std::numeric_limits<T>::lowest () ||
        max[2] != std::numeric_limits<T>::max ())
        return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Box<Vec3<T>>::hasVolume () const IMATH_NOEXCEPT
{
    if (max[0] <= min[0] || max[1] <= min[1] || max[2] <= min[2]) return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline unsigned int
Box<Vec3<T>>::majorAxis () const IMATH_NOEXCEPT
{
    unsigned int major = 0;
    Vec3<T>      s     = size ();

if (s[1] > s[major]) major = 1;

if (s[2] > s[major]) major = 2;

return major;
}

IMATH_INTERNAL_NAMESPACE_HEADER_EXIT

#endif // INCLUDED_IMATHBOX_H

Source code

//
// SPDX-License-Identifier: BSD-3-Clause
// Copyright Contributors to the OpenEXR Project.
//

//
// 2D, 3D and 4D point/vector class templates
//

#ifndef INCLUDED_IMATHVEC_H
#define INCLUDED_IMATHVEC_H

#include "ImathExport.h"
#include "ImathNamespace.h"
#include "ImathTypeTraits.h"

#include "ImathMath.h"

#include <iostream>
#include <limits>
#include <cstdint>
#include <stdexcept>

#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
// suppress exception specification warnings
#    pragma warning(push)
#    pragma warning(disable : 4290)
#endif

IMATH_INTERNAL_NAMESPACE_HEADER_ENTER

template <class T> class Vec2;
template <class T> class Vec3;
template <class T> class Vec4;

/// Enum for the Vec4 to Vec3 conversion constructor
enum IMATH_EXPORT_ENUM InfException
{
    INF_EXCEPTION
};

///
/// 2-element vector
///

template <class T> class IMATH_EXPORT_TEMPLATE_TYPE Vec2
{
public:
    /// @{
    /// @name Direct access to elements

T x, y;

/// @}

/// Element access by index.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 T& operator[] (int i) IMATH_NOEXCEPT;

/// Element access by index.
    IMATH_HOSTDEVICE constexpr const T& operator[] (int i) const IMATH_NOEXCEPT;

/// @{
    ///	@name Constructors and Assignment

/// Uninitialized by default
    IMATH_HOSTDEVICE Vec2 () IMATH_NOEXCEPT;

/// Initialize to a scalar `(a,a)`
    IMATH_HOSTDEVICE constexpr explicit Vec2 (T a) IMATH_NOEXCEPT;

/// Initialize to given elements `(a,b)`
    IMATH_HOSTDEVICE constexpr Vec2 (T a, T b) IMATH_NOEXCEPT;

/// Copy constructor
    IMATH_HOSTDEVICE constexpr Vec2 (const Vec2& v) IMATH_NOEXCEPT;

/// Construct from Vec2 of another base type
    template <class S>
    IMATH_HOSTDEVICE constexpr Vec2 (const Vec2<S>& v) IMATH_NOEXCEPT;

/// Assignment
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec2&
    operator= (const Vec2& v) IMATH_NOEXCEPT;

/// Destructor
    ~Vec2 () IMATH_NOEXCEPT = default;

/// @}

#if IMATH_FOREIGN_VECTOR_INTEROP
    /// @{
    /// @name Interoperability with other vector types
    ///
    /// Construction and assignment are allowed from other classes that
    /// appear to be equivalent vector types, provided that they have either
    /// a subscripting operator, or data members .x and .y, that are of the
    /// same type as the elements of this vector, and their size appears to
    /// be the right number of elements.
    ///
    /// This functionality is disabled for gcc 4.x, which seems to have a
    /// compiler bug that results in spurious errors. It can also be
    /// disabled by defining IMATH_FOREIGN_VECTOR_INTEROP to be 0 prior to
    /// including any Imath header files.
    ///

template <typename V, IMATH_ENABLE_IF (has_xy<V, T>::value)>
    IMATH_HOSTDEVICE explicit constexpr Vec2 (const V& v) IMATH_NOEXCEPT
        : Vec2 (T (v.x), T (v.y))
    {}

template <
        typename V,
        IMATH_ENABLE_IF (has_subscript<V, T, 2>::value && !has_xy<V, T>::value)>
    IMATH_HOSTDEVICE explicit Vec2 (const V& v) : Vec2 (T (v[0]), T (v[1]))
    {}

template <typename V, IMATH_ENABLE_IF (has_xy<V, T>::value)>
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec2&
    operator= (const V& v) IMATH_NOEXCEPT
    {
        x = T (v.x);
        y = T (v.y);
        return *this;
    }

template <
        typename V,
        IMATH_ENABLE_IF (has_subscript<V, T, 2>::value && !has_xy<V, T>::value)>
    IMATH_HOSTDEVICE const Vec2& operator= (const V& v)
    {
        x = T (v[0]);
        y = T (v[1]);
        return *this;
    }
#endif

/// @{
    /// @name Compatibility with Sb

/// Set the value
    template <class S> IMATH_HOSTDEVICE void setValue (S a, S b) IMATH_NOEXCEPT;

/// Set the value
    template <class S>
    IMATH_HOSTDEVICE void setValue (const Vec2<S>& v) IMATH_NOEXCEPT;

/// Return the value in `a` and `b`
    template <class S>
    IMATH_HOSTDEVICE void getValue (S& a, S& b) const IMATH_NOEXCEPT;

/// Return the value in `v`
    template <class S>
    IMATH_HOSTDEVICE void getValue (Vec2<S>& v) const IMATH_NOEXCEPT;

/// Return a raw pointer to the array of values
    IMATH_HOSTDEVICE T* getValue () IMATH_NOEXCEPT;

/// Return a raw pointer to the array of values
    IMATH_HOSTDEVICE const T* getValue () const IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Arithmetic and Comparison

/// Equality
    template <class S>
    IMATH_HOSTDEVICE constexpr bool
    operator== (const Vec2<S>& v) const IMATH_NOEXCEPT;

/// Inequality
    template <class S>
    IMATH_HOSTDEVICE constexpr bool
    operator!= (const Vec2<S>& v) const IMATH_NOEXCEPT;

/// Compare two matrices and test if they are "approximately equal":
    /// @return True if the coefficients of this and `m` are the same
    /// with an absolute error of no more than e, i.e., for all i, j:
    ///
    ///     abs (this[i][j] - m[i][j]) <= e
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
    equalWithAbsError (const Vec2<T>& v, T e) const IMATH_NOEXCEPT;

/// Compare two matrices and test if they are "approximately equal":
    /// @return True if the coefficients of this and m are the same with
    /// a relative error of no more than e, i.e., for all i, j:
    ///
    ///     abs (this[i] - v[i][j]) <= e * abs (this[i][j])
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
    equalWithRelError (const Vec2<T>& v, T e) const IMATH_NOEXCEPT;

/// Dot product
    IMATH_HOSTDEVICE constexpr T dot (const Vec2& v) const IMATH_NOEXCEPT;

/// Dot product
    IMATH_HOSTDEVICE constexpr T operator^ (const Vec2& v) const IMATH_NOEXCEPT;

/// Right-handed cross product, i.e. z component of
    /// Vec3 (this->x, this->y, 0) % Vec3 (v.x, v.y, 0)
    IMATH_HOSTDEVICE constexpr T cross (const Vec2& v) const IMATH_NOEXCEPT;

/// Right-handed cross product, i.e. z component of
    /// Vec3 (this->x, this->y, 0) % Vec3 (v.x, v.y, 0)
    IMATH_HOSTDEVICE constexpr T operator% (const Vec2& v) const IMATH_NOEXCEPT;

/// Component-wise addition
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec2&
    operator+= (const Vec2& v) IMATH_NOEXCEPT;

/// Component-wise addition
    IMATH_HOSTDEVICE constexpr Vec2
    operator+ (const Vec2& v) const IMATH_NOEXCEPT;

/// Component-wise subtraction
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec2&
    operator-= (const Vec2& v) IMATH_NOEXCEPT;

/// Component-wise subtraction
    IMATH_HOSTDEVICE constexpr Vec2
    operator- (const Vec2& v) const IMATH_NOEXCEPT;

/// Component-wise multiplication by -1
    IMATH_HOSTDEVICE constexpr Vec2 operator- () const IMATH_NOEXCEPT;

/// Component-wise multiplication by -1
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec2& negate () IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec2&
    operator*= (const Vec2& v) IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec2&
    operator*= (T a) IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE constexpr Vec2
    operator* (const Vec2& v) const IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE constexpr Vec2 operator* (T a) const IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec2&
    operator/= (const Vec2& v) IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec2&
    operator/= (T a) IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE constexpr Vec2
    operator/ (const Vec2& v) const IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE constexpr Vec2 operator/ (T a) const IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Query and Manipulation

/// Return the Euclidean norm
    IMATH_HOSTDEVICE T length () const IMATH_NOEXCEPT;

/// Return the square of the Euclidean norm, i.e. the dot product
    /// with itself.
    IMATH_HOSTDEVICE constexpr T length2 () const IMATH_NOEXCEPT;

/// Normalize in place. If length()==0, return a null vector.
    IMATH_HOSTDEVICE const Vec2& normalize () IMATH_NOEXCEPT;

/// Normalize in place. If length()==0, throw an exception.
    const Vec2& normalizeExc ();

/// Normalize without any checks for length()==0. Slightly faster
    /// than the other normalization routines, but if v.length() is
    /// 0.0, the result is undefined.
    IMATH_HOSTDEVICE const Vec2& normalizeNonNull () IMATH_NOEXCEPT;

/// Return a normalized vector. Does not modify *this.
    IMATH_HOSTDEVICE Vec2<T> normalized () const IMATH_NOEXCEPT;

/// Return a normalized vector. Does not modify *this. Throw an
    /// exception if length()==0.
    Vec2<T> normalizedExc () const;

/// Return a normalized vector. Does not modify *this, and does
    /// not check for length()==0. Slightly faster than the other
    /// normalization routines, but if v.length() is 0.0, the result
    /// is undefined.
    IMATH_HOSTDEVICE Vec2<T> normalizedNonNull () const IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Numeric Limits

/// Largest possible negative value
    IMATH_HOSTDEVICE constexpr static T baseTypeLowest () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::lowest ();
    }

/// Largest possible positive value
    IMATH_HOSTDEVICE constexpr static T baseTypeMax () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::max ();
    }

/// Smallest possible positive value
    IMATH_HOSTDEVICE constexpr static T baseTypeSmallest () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::min ();
    }

/// Smallest possible e for which 1+e != 1
    IMATH_HOSTDEVICE constexpr static T baseTypeEpsilon () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::epsilon ();
    }

/// @}

/// Return the number of dimensions, i.e. 2
    IMATH_HOSTDEVICE constexpr static unsigned int dimensions () IMATH_NOEXCEPT
    {
        return 2;
    }

/// The base type: In templates that accept a parameter `V`, you
    /// can refer to `T` as `V::BaseType`
    typedef T BaseType;

private:
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 T lengthTiny () const IMATH_NOEXCEPT;
};

///
/// 3-element vector
///

template <class T> class IMATH_EXPORT_TEMPLATE_TYPE Vec3
{
public:
    /// @{
    /// @name Direct access to elements

T x, y, z;

/// @}

/// Element access by index.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 T& operator[] (int i) IMATH_NOEXCEPT;

/// Element access by index.
    IMATH_HOSTDEVICE constexpr const T& operator[] (int i) const IMATH_NOEXCEPT;

/// @{
    ///	@name Constructors and Assignment

/// Uninitialized by default
    IMATH_HOSTDEVICE Vec3 () IMATH_NOEXCEPT;

/// Initialize to a scalar `(a,a,a)`
    IMATH_HOSTDEVICE constexpr explicit Vec3 (T a) IMATH_NOEXCEPT;

/// Initialize to given elements `(a,b,c)`
    IMATH_HOSTDEVICE constexpr Vec3 (T a, T b, T c) IMATH_NOEXCEPT;

/// Copy constructor
    IMATH_HOSTDEVICE constexpr Vec3 (const Vec3& v) IMATH_NOEXCEPT;

/// Construct from Vec3 of another base type
    template <class S>
    IMATH_HOSTDEVICE constexpr Vec3 (const Vec3<S>& v) IMATH_NOEXCEPT;

/// Vec4 to Vec3 conversion: divide x, y and z by w, even if w is
    /// 0.  The result depends on how the environment handles
    /// floating-point exceptions.
    template <class S>
    IMATH_HOSTDEVICE explicit constexpr Vec3 (const Vec4<S>& v) IMATH_NOEXCEPT;

/// Vec4 to Vec3 conversion: divide x, y and z by w.  Throws an
    /// exception if w is zero or if division by w would overflow.
    template <class S>
    explicit IMATH_HOSTDEVICE IMATH_CONSTEXPR14
    Vec3 (const Vec4<S>& v, InfException);

/// Assignment
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3&
    operator= (const Vec3& v) IMATH_NOEXCEPT;

/// Destructor
    ~Vec3 () IMATH_NOEXCEPT = default;

/// @}

#if IMATH_FOREIGN_VECTOR_INTEROP
    /// @{
    /// @name Interoperability with other vector types
    ///
    /// Construction and assignment are allowed from other classes that
    /// appear to be equivalent vector types, provided that they have either
    /// a subscripting operator, or data members .x, .y, .z, that are of the
    /// same type as the elements of this vector, and their size appears to
    /// be the right number of elements.
    ///
    /// This functionality is disabled for gcc 4.x, which seems to have a
    /// compiler bug that results in spurious errors. It can also be
    /// disabled by defining IMATH_FOREIGN_VECTOR_INTEROP to be 0 prior to
    /// including any Imath header files.
    ///

template <typename V, IMATH_ENABLE_IF (has_xyz<V, T>::value)>
    IMATH_HOSTDEVICE explicit constexpr Vec3 (const V& v) IMATH_NOEXCEPT
        : Vec3 (T (v.x), T (v.y), T (v.z))
    {}

template <
        typename V,
        IMATH_ENABLE_IF (
            has_subscript<V, T, 3>::value && !has_xyz<V, T>::value)>
    IMATH_HOSTDEVICE explicit Vec3 (const V& v)
        : Vec3 (T (v[0]), T (v[1]), T (v[2]))
    {}

/// Interoperability assignment from another type that behaves as if it
    /// were an equivalent vector.
    template <typename V, IMATH_ENABLE_IF (has_xyz<V, T>::value)>
    IMATH_HOSTDEVICE const Vec3& operator= (const V& v) IMATH_NOEXCEPT
    {
        x = T (v.x);
        y = T (v.y);
        z = T (v.z);
        return *this;
    }

template <
        typename V,
        IMATH_ENABLE_IF (
            has_subscript<V, T, 3>::value && !has_xyz<V, T>::value)>
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3& operator= (const V& v)
    {
        x = T (v[0]);
        y = T (v[1]);
        z = T (v[2]);
        return *this;
    }
    /// @}
#endif

/// @{
    /// @name Compatibility with Sb

/// Set the value
    template <class S>
    IMATH_HOSTDEVICE void setValue (S a, S b, S c) IMATH_NOEXCEPT;

/// Set the value
    template <class S>
    IMATH_HOSTDEVICE void setValue (const Vec3<S>& v) IMATH_NOEXCEPT;

/// Return the value in `a`, `b`, and `c`
    template <class S>
    IMATH_HOSTDEVICE void getValue (S& a, S& b, S& c) const IMATH_NOEXCEPT;

/// Return the value in `v`
    template <class S>
    IMATH_HOSTDEVICE void getValue (Vec3<S>& v) const IMATH_NOEXCEPT;

/// Return a raw pointer to the array of values
    IMATH_HOSTDEVICE T* getValue () IMATH_NOEXCEPT;

/// Return a raw pointer to the array of values
    IMATH_HOSTDEVICE const T* getValue () const IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Arithmetic and Comparison

/// Equality
    template <class S>
    IMATH_HOSTDEVICE constexpr bool
    operator== (const Vec3<S>& v) const IMATH_NOEXCEPT;

/// Inequality
    template <class S>
    IMATH_HOSTDEVICE constexpr bool
    operator!= (const Vec3<S>& v) const IMATH_NOEXCEPT;

/// Dot product
    IMATH_HOSTDEVICE constexpr T dot (const Vec3& v) const IMATH_NOEXCEPT;

/// Dot product
    IMATH_HOSTDEVICE constexpr T operator^ (const Vec3& v) const IMATH_NOEXCEPT;

/// Right-handed cross product
    IMATH_HOSTDEVICE constexpr Vec3 cross (const Vec3& v) const IMATH_NOEXCEPT;

/// Right-handed cross product
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3&
    operator%= (const Vec3& v) IMATH_NOEXCEPT;

/// Right-handed cross product
    IMATH_HOSTDEVICE constexpr Vec3
    operator% (const Vec3& v) const IMATH_NOEXCEPT;

/// Component-wise addition
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3&
    operator+= (const Vec3& v) IMATH_NOEXCEPT;

/// Component-wise addition
    IMATH_HOSTDEVICE constexpr Vec3
    operator+ (const Vec3& v) const IMATH_NOEXCEPT;

/// Component-wise subtraction
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3&
    operator-= (const Vec3& v) IMATH_NOEXCEPT;

/// Component-wise subtraction
    IMATH_HOSTDEVICE constexpr Vec3
    operator- (const Vec3& v) const IMATH_NOEXCEPT;

/// Component-wise multiplication by -1
    IMATH_HOSTDEVICE constexpr Vec3 operator- () const IMATH_NOEXCEPT;

/// Component-wise multiplication by -1
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3& negate () IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3&
    operator*= (const Vec3& v) IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3&
    operator*= (T a) IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE constexpr Vec3
    operator* (const Vec3& v) const IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE constexpr Vec3 operator* (T a) const IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3&
    operator/= (const Vec3& v) IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3&
    operator/= (T a) IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE constexpr Vec3
    operator/ (const Vec3& v) const IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE constexpr Vec3 operator/ (T a) const IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Query and Manipulation

/// Return the Euclidean norm
    IMATH_HOSTDEVICE T length () const IMATH_NOEXCEPT;

/// Return the square of the Euclidean norm, i.e. the dot product
    /// with itself.
    IMATH_HOSTDEVICE constexpr T length2 () const IMATH_NOEXCEPT;

/// Normalize in place. If length()==0, return a null vector.
    IMATH_HOSTDEVICE const Vec3& normalize () IMATH_NOEXCEPT;

/// Normalize in place. If length()==0, throw an exception.
    const Vec3& normalizeExc ();

/// Return a normalized vector. Does not modify *this.
    IMATH_HOSTDEVICE Vec3<T>
    normalized () const IMATH_NOEXCEPT; // does not modify *this

/// Return a normalized vector. Does not modify *this. Throw an
    /// exception if length()==0.
    Vec3<T> normalizedExc () const;

/// @}

/// @{
    /// @name Numeric Limits

/// Largest possible negative value
    IMATH_HOSTDEVICE constexpr static T baseTypeLowest () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::lowest ();
    }

/// Largest possible positive value
    IMATH_HOSTDEVICE constexpr static T baseTypeMax () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::max ();
    }

/// Smallest possible positive value
    IMATH_HOSTDEVICE constexpr static T baseTypeSmallest () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::min ();
    }

/// Smallest possible e for which 1+e != 1
    IMATH_HOSTDEVICE constexpr static T baseTypeEpsilon () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::epsilon ();
    }

/// @}

/// Return the number of dimensions, i.e. 3
    IMATH_HOSTDEVICE constexpr static unsigned int dimensions () IMATH_NOEXCEPT
    {
        return 3;
    }

/// The base type: In templates that accept a parameter `V`, you
    /// can refer to `T` as `V::BaseType`
    typedef T BaseType;

private:
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 T lengthTiny () const IMATH_NOEXCEPT;
};

///
/// 4-element vector
///

template <class T> class IMATH_EXPORT_TEMPLATE_TYPE Vec4
{
public:
    /// @{
    /// @name Direct access to elements

T x, y, z, w;

/// @}

/// Element access by index.
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 T& operator[] (int i) IMATH_NOEXCEPT;

/// Element access by index.
    IMATH_HOSTDEVICE constexpr const T& operator[] (int i) const IMATH_NOEXCEPT;

/// @{
    ///	@name Constructors and Assignment

/// Uninitialized by default
    IMATH_HOSTDEVICE Vec4 () IMATH_NOEXCEPT; // no initialization

/// Initialize to a scalar `(a,a,a,a)`
    IMATH_HOSTDEVICE constexpr explicit Vec4 (T a) IMATH_NOEXCEPT;

/// Initialize to given elements `(a,b,c,d)`
    IMATH_HOSTDEVICE constexpr Vec4 (T a, T b, T c, T d) IMATH_NOEXCEPT;

/// Copy constructor
    IMATH_HOSTDEVICE constexpr Vec4 (const Vec4& v) IMATH_NOEXCEPT;

/// Construct from Vec4 of another base type
    template <class S>
    IMATH_HOSTDEVICE constexpr Vec4 (const Vec4<S>& v) IMATH_NOEXCEPT;

/// Vec3 to Vec4 conversion, sets w to 1.
    template <class S>
    IMATH_HOSTDEVICE explicit constexpr Vec4 (const Vec3<S>& v) IMATH_NOEXCEPT;

/// Assignment
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec4&
    operator= (const Vec4& v) IMATH_NOEXCEPT;

/// Destructor
    ~Vec4 () IMATH_NOEXCEPT = default;

/// @}

#if IMATH_FOREIGN_VECTOR_INTEROP
    /// @{
    /// @name Interoperability with other vector types
    ///
    /// Construction and assignment are allowed from other classes that
    /// appear to be equivalent vector types, provided that they have either
    /// a subscripting operator, or data members .x, .y, .z, .w that are of
    /// the same type as the elements of this vector, and their size appears
    /// to be the right number of elements.
    ///
    /// This functionality is disabled for gcc 4.x, which seems to have a
    /// compiler bug that results in spurious errors. It can also be
    /// disabled by defining IMATH_FOREIGN_VECTOR_INTEROP to be 0 prior to
    /// including any Imath header files.
    ///

template <typename V, IMATH_ENABLE_IF (has_xyzw<V, T>::value)>
    IMATH_HOSTDEVICE explicit constexpr Vec4 (const V& v) IMATH_NOEXCEPT
        : Vec4 (T (v.x), T (v.y), T (v.z), T (v.w))
    {}

template <
        typename V,
        IMATH_ENABLE_IF (
            has_subscript<V, T, 4>::value && !has_xyzw<V, T>::value)>
    IMATH_HOSTDEVICE explicit Vec4 (const V& v)
        : Vec4 (T (v[0]), T (v[1]), T (v[2]), T (v[3]))
    {}

template <typename V, IMATH_ENABLE_IF (has_xyzw<V, T>::value)>
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec4&
    operator= (const V& v) IMATH_NOEXCEPT
    {
        x = T (v.x);
        y = T (v.y);
        z = T (v.z);
        w = T (v.w);
        return *this;
    }

template <
        typename V,
        IMATH_ENABLE_IF (
            has_subscript<V, T, 4>::value && !has_xyzw<V, T>::value)>
    IMATH_HOSTDEVICE const Vec4& operator= (const V& v)
    {
        x = T (v[0]);
        y = T (v[1]);
        z = T (v[2]);
        w = T (v[3]);
        return *this;
    }
    /// @}
#endif

/// @{
    /// @name Arithmetic and Comparison

/// Equality
    template <class S>
    IMATH_HOSTDEVICE constexpr bool
    operator== (const Vec4<S>& v) const IMATH_NOEXCEPT;

/// Inequality
    template <class S>
    IMATH_HOSTDEVICE constexpr bool
    operator!= (const Vec4<S>& v) const IMATH_NOEXCEPT;

/// Dot product
    IMATH_HOSTDEVICE constexpr T dot (const Vec4& v) const IMATH_NOEXCEPT;

/// Dot product
    IMATH_HOSTDEVICE constexpr T operator^ (const Vec4& v) const IMATH_NOEXCEPT;

/// Component-wise addition
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec4&
    operator+= (const Vec4& v) IMATH_NOEXCEPT;

/// Component-wise addition
    IMATH_HOSTDEVICE constexpr Vec4
    operator+ (const Vec4& v) const IMATH_NOEXCEPT;

/// Component-wise subtraction
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec4&
    operator-= (const Vec4& v) IMATH_NOEXCEPT;

/// Component-wise subtraction
    IMATH_HOSTDEVICE constexpr Vec4
    operator- (const Vec4& v) const IMATH_NOEXCEPT;

/// Component-wise multiplication by -1
    IMATH_HOSTDEVICE constexpr Vec4 operator- () const IMATH_NOEXCEPT;

/// Component-wise multiplication by -1
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec4& negate () IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec4&
    operator*= (const Vec4& v) IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec4&
    operator*= (T a) IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE constexpr Vec4
    operator* (const Vec4& v) const IMATH_NOEXCEPT;

/// Component-wise multiplication
    IMATH_HOSTDEVICE constexpr Vec4 operator* (T a) const IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec4&
    operator/= (const Vec4& v) IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec4&
    operator/= (T a) IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE constexpr Vec4
    operator/ (const Vec4& v) const IMATH_NOEXCEPT;

/// Component-wise division
    IMATH_HOSTDEVICE constexpr Vec4 operator/ (T a) const IMATH_NOEXCEPT;

/// @}

/// @{
    /// @name Query and Manipulation

/// Return the Euclidean norm
    IMATH_HOSTDEVICE T length () const IMATH_NOEXCEPT;

/// Return the square of the Euclidean norm, i.e. the dot product
    /// with itself.
    IMATH_HOSTDEVICE constexpr T length2 () const IMATH_NOEXCEPT;

/// Normalize in place. If length()==0, return a null vector.
    IMATH_HOSTDEVICE const Vec4& normalize () IMATH_NOEXCEPT; // modifies *this

/// Normalize in place. If length()==0, throw an exception.
    const Vec4& normalizeExc ();

/// Return a normalized vector. Does not modify *this.
    IMATH_HOSTDEVICE Vec4<T>
    normalized () const IMATH_NOEXCEPT; // does not modify *this

/// Return a normalized vector. Does not modify *this. Throw an
    /// exception if length()==0.
    Vec4<T> normalizedExc () const;

/// @}

/// @{
    /// @name Numeric Limits

/// Largest possible negative value
    IMATH_HOSTDEVICE constexpr static T baseTypeLowest () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::lowest ();
    }

/// Largest possible positive value
    IMATH_HOSTDEVICE constexpr static T baseTypeMax () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::max ();
    }

/// Smallest possible positive value
    IMATH_HOSTDEVICE constexpr static T baseTypeSmallest () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::min ();
    }

/// Smallest possible e for which 1+e != 1
    IMATH_HOSTDEVICE constexpr static T baseTypeEpsilon () IMATH_NOEXCEPT
    {
        return std::numeric_limits<T>::epsilon ();
    }

/// @}

/// Return the number of dimensions, i.e. 4
    IMATH_HOSTDEVICE constexpr static unsigned int dimensions () IMATH_NOEXCEPT
    {
        return 4;
    }

/// The base type: In templates that accept a parameter `V`, you
    /// can refer to `T` as `V::BaseType`
    typedef T BaseType;

private:
    IMATH_HOSTDEVICE IMATH_CONSTEXPR14 T lengthTiny () const IMATH_NOEXCEPT;
};

/// Stream output, as "(x y)"
template <class T> std::ostream& operator<< (std::ostream& s, const Vec2<T>& v);

/// Stream output, as "(x y z)"
template <class T> std::ostream& operator<< (std::ostream& s, const Vec3<T>& v);

/// Stream output, as "(x y z w)"
template <class T> std::ostream& operator<< (std::ostream& s, const Vec4<T>& v);

/// Reverse multiplication: S * Vec2<T>
template <class T>
IMATH_HOSTDEVICE constexpr Vec2<T>
operator* (T a, const Vec2<T>& v) IMATH_NOEXCEPT;

/// Reverse multiplication: S * Vec3<T>
template <class T>
IMATH_HOSTDEVICE constexpr Vec3<T>
operator* (T a, const Vec3<T>& v) IMATH_NOEXCEPT;

/// Reverse multiplication: S * Vec4<T>
template <class T>
IMATH_HOSTDEVICE constexpr Vec4<T>
operator* (T a, const Vec4<T>& v) IMATH_NOEXCEPT;

//-------------------------
// Typedefs for convenience
//-------------------------

/// Vec2 of short
typedef Vec2<short> V2s;

/// Vec2 of integer
typedef Vec2<int> V2i;

/// Vec2 of int64_t
typedef Vec2<int64_t> V2i64;

/// Vec2 of float
typedef Vec2<float> V2f;

/// Vec2 of double
typedef Vec2<double> V2d;

/// Vec3 of short
typedef Vec3<short> V3s;

/// Vec3 of integer
typedef Vec3<int> V3i;

/// Vec3 of int64_t
typedef Vec3<int64_t> V3i64;

/// Vec3 of float
typedef Vec3<float> V3f;

/// Vec3 of double
typedef Vec3<double> V3d;

/// Vec4 of short
typedef Vec4<short> V4s;

/// Vec4 of integer
typedef Vec4<int> V4i;

/// Vec4 of int64_t
typedef Vec4<int64_t> V4i64;

/// Vec4 of float
typedef Vec4<float> V4f;

/// Vec4 of double
typedef Vec4<double> V4d;

//----------------------------------------------------------------------------
// Specializations for VecN<short>, VecN<int>
//
// Normalize and length don't make sense for integer vectors, so disable them.
//----------------------------------------------------------------------------

/// @cond Doxygen_Suppress

// Vec2<short>
template <>
IMATH_HOSTDEVICE short Vec2<short>::length () const IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE const Vec2<short>&
                       Vec2<short>::normalize () IMATH_NOEXCEPT = delete;
template <> const Vec2<short>& Vec2<short>::normalizeExc ()     = delete;
template <>
IMATH_HOSTDEVICE const Vec2<short>&
                       Vec2<short>::normalizeNonNull () IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE Vec2<short>
                 Vec2<short>::normalized () const IMATH_NOEXCEPT = delete;
template <> Vec2<short> Vec2<short>::normalizedExc () const      = delete;
template <>
IMATH_HOSTDEVICE Vec2<short>
Vec2<short>::normalizedNonNull () const IMATH_NOEXCEPT = delete;

// Vec2<int>
template <>
IMATH_HOSTDEVICE int Vec2<int>::length () const IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE const       Vec2<int>&
                             Vec2<int>::normalize () IMATH_NOEXCEPT = delete;
template <> const Vec2<int>& Vec2<int>::normalizeExc ()             = delete;
template <>
IMATH_HOSTDEVICE const Vec2<int>&
                       Vec2<int>::normalizeNonNull () IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE      Vec2<int>
                      Vec2<int>::normalized () const IMATH_NOEXCEPT = delete;
template <> Vec2<int> Vec2<int>::normalizedExc () const             = delete;
template <>
IMATH_HOSTDEVICE Vec2<int>
                 Vec2<int>::normalizedNonNull () const IMATH_NOEXCEPT = delete;

// Vec2<int64_t>
template <>
IMATH_HOSTDEVICE int64_t Vec2<int64_t>::length () const IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE const Vec2<int64_t>&
                       Vec2<int64_t>::normalize () IMATH_NOEXCEPT = delete;
template <> const Vec2<int64_t>& Vec2<int64_t>::normalizeExc ()   = delete;
template <>
IMATH_HOSTDEVICE const Vec2<int64_t>&
Vec2<int64_t>::normalizeNonNull () IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE Vec2<int64_t>
                 Vec2<int64_t>::normalized () const IMATH_NOEXCEPT = delete;
template <> Vec2<int64_t> Vec2<int64_t>::normalizedExc () const    = delete;
template <>
IMATH_HOSTDEVICE Vec2<int64_t>
Vec2<int64_t>::normalizedNonNull () const IMATH_NOEXCEPT = delete;

// Vec3<short>
template <>
IMATH_HOSTDEVICE short Vec3<short>::length () const IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE const Vec3<short>&
                       Vec3<short>::normalize () IMATH_NOEXCEPT = delete;
template <> const Vec3<short>& Vec3<short>::normalizeExc ()     = delete;
template <>
IMATH_HOSTDEVICE const Vec3<short>&
                       Vec3<short>::normalizeNonNull () IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE Vec3<short>
                 Vec3<short>::normalized () const IMATH_NOEXCEPT = delete;
template <> Vec3<short> Vec3<short>::normalizedExc () const      = delete;
template <>
IMATH_HOSTDEVICE Vec3<short>
Vec3<short>::normalizedNonNull () const IMATH_NOEXCEPT = delete;

// Vec3<int>
template <>
IMATH_HOSTDEVICE int Vec3<int>::length () const IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE const       Vec3<int>&
                             Vec3<int>::normalize () IMATH_NOEXCEPT = delete;
template <> const Vec3<int>& Vec3<int>::normalizeExc ()             = delete;
template <>
IMATH_HOSTDEVICE const Vec3<int>&
                       Vec3<int>::normalizeNonNull () IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE      Vec3<int>
                      Vec3<int>::normalized () const IMATH_NOEXCEPT = delete;
template <> Vec3<int> Vec3<int>::normalizedExc () const             = delete;
template <>
IMATH_HOSTDEVICE Vec3<int>
                 Vec3<int>::normalizedNonNull () const IMATH_NOEXCEPT = delete;

// Vec3<int64_t>
template <>
IMATH_HOSTDEVICE int64_t Vec3<int64_t>::length () const IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE const Vec3<int64_t>&
                       Vec3<int64_t>::normalize () IMATH_NOEXCEPT = delete;
template <> const Vec3<int64_t>& Vec3<int64_t>::normalizeExc ()   = delete;
template <>
IMATH_HOSTDEVICE const Vec3<int64_t>&
Vec3<int64_t>::normalizeNonNull () IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE Vec3<int64_t>
                 Vec3<int64_t>::normalized () const IMATH_NOEXCEPT = delete;
template <> Vec3<int64_t> Vec3<int64_t>::normalizedExc () const    = delete;
template <>
IMATH_HOSTDEVICE Vec3<int64_t>
Vec3<int64_t>::normalizedNonNull () const IMATH_NOEXCEPT = delete;

// Vec4<short>
template <>
IMATH_HOSTDEVICE short Vec4<short>::length () const IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE const Vec4<short>&
                       Vec4<short>::normalize () IMATH_NOEXCEPT = delete;
template <> const Vec4<short>& Vec4<short>::normalizeExc ()     = delete;
template <>
IMATH_HOSTDEVICE const Vec4<short>&
                       Vec4<short>::normalizeNonNull () IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE Vec4<short>
                 Vec4<short>::normalized () const IMATH_NOEXCEPT = delete;
template <> Vec4<short> Vec4<short>::normalizedExc () const      = delete;
template <>
IMATH_HOSTDEVICE Vec4<short>
Vec4<short>::normalizedNonNull () const IMATH_NOEXCEPT = delete;

// Vec4<int>
template <>
IMATH_HOSTDEVICE int Vec4<int>::length () const IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE const       Vec4<int>&
                             Vec4<int>::normalize () IMATH_NOEXCEPT = delete;
template <> const Vec4<int>& Vec4<int>::normalizeExc ()             = delete;
template <>
IMATH_HOSTDEVICE const Vec4<int>&
                       Vec4<int>::normalizeNonNull () IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE      Vec4<int>
                      Vec4<int>::normalized () const IMATH_NOEXCEPT = delete;
template <> Vec4<int> Vec4<int>::normalizedExc () const             = delete;
template <>
IMATH_HOSTDEVICE Vec4<int>
                 Vec4<int>::normalizedNonNull () const IMATH_NOEXCEPT = delete;

// Vec4<int64_t>
template <>
IMATH_HOSTDEVICE int64_t Vec4<int64_t>::length () const IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE const Vec4<int64_t>&
                       Vec4<int64_t>::normalize () IMATH_NOEXCEPT = delete;
template <> const Vec4<int64_t>& Vec4<int64_t>::normalizeExc ()   = delete;
template <>
IMATH_HOSTDEVICE const Vec4<int64_t>&
Vec4<int64_t>::normalizeNonNull () IMATH_NOEXCEPT = delete;
template <>
IMATH_HOSTDEVICE Vec4<int64_t>
                 Vec4<int64_t>::normalized () const IMATH_NOEXCEPT = delete;
template <> Vec4<int64_t> Vec4<int64_t>::normalizedExc () const    = delete;
template <>
IMATH_HOSTDEVICE Vec4<int64_t>
Vec4<int64_t>::normalizedNonNull () const IMATH_NOEXCEPT = delete;

/// @endcond Doxygen_Suppress

//------------------------
// Implementation of Vec2:
//------------------------

template <class T>
IMATH_CONSTEXPR14 IMATH_HOSTDEVICE inline T&
Vec2<T>::operator[] (int i) IMATH_NOEXCEPT
{
    return (&x)[i]; // NOSONAR - suppress SonarCloud bug report.
}

template <class T>
constexpr IMATH_HOSTDEVICE inline const T&
Vec2<T>::operator[] (int i) const IMATH_NOEXCEPT
{
    return (&x)[i]; // NOSONAR - suppress SonarCloud bug report.
}

template <class T> IMATH_HOSTDEVICE inline Vec2<T>::Vec2 () IMATH_NOEXCEPT
{
    // empty, and not constexpr because data is uninitialized.
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>::Vec2 (T a) IMATH_NOEXCEPT : x (a),
                                                                       y (a)
{}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>::Vec2 (T a, T b) IMATH_NOEXCEPT
    : x (a),
      y (b)
{}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>::Vec2 (const Vec2& v) IMATH_NOEXCEPT
    : x (v.x),
      y (v.y)
{}

template <class T>
template <class S>
IMATH_HOSTDEVICE constexpr inline Vec2<T>::Vec2 (const Vec2<S>& v)
    IMATH_NOEXCEPT : x (T (v.x)),
                     y (T (v.y))
{}

template <class T>
IMATH_CONSTEXPR14 IMATH_HOSTDEVICE inline const Vec2<T>&
Vec2<T>::operator= (const Vec2& v) IMATH_NOEXCEPT
{
    x = v.x;
    y = v.y;
    return *this;
}

template <class T>
template <class S>
IMATH_HOSTDEVICE inline void
Vec2<T>::setValue (S a, S b) IMATH_NOEXCEPT
{
    x = T (a);
    y = T (b);
}

template <class T>
template <class S>
IMATH_HOSTDEVICE inline void
Vec2<T>::setValue (const Vec2<S>& v) IMATH_NOEXCEPT
{
    x = T (v.x);
    y = T (v.y);
}

template <class T>
template <class S>
IMATH_HOSTDEVICE inline void
Vec2<T>::getValue (S& a, S& b) const IMATH_NOEXCEPT
{
    a = S (x);
    b = S (y);
}

template <class T>
template <class S>
IMATH_HOSTDEVICE inline void
Vec2<T>::getValue (Vec2<S>& v) const IMATH_NOEXCEPT
{
    v.x = S (x);
    v.y = S (y);
}

template <class T>
IMATH_HOSTDEVICE inline T*
Vec2<T>::getValue () IMATH_NOEXCEPT
{
    return (T*) &x;
}

template <class T>
IMATH_HOSTDEVICE inline const T*
Vec2<T>::getValue () const IMATH_NOEXCEPT
{
    return (const T*) &x;
}

template <class T>
template <class S>
IMATH_HOSTDEVICE constexpr inline bool
Vec2<T>::operator== (const Vec2<S>& v) const IMATH_NOEXCEPT
{
    return x == v.x && y == v.y;
}

template <class T>
template <class S>
IMATH_HOSTDEVICE constexpr inline bool
Vec2<T>::operator!= (const Vec2<S>& v) const IMATH_NOEXCEPT
{
    return x != v.x || y != v.y;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Vec2<T>::equalWithAbsError (const Vec2<T>& v, T e) const IMATH_NOEXCEPT
{
    for (int i = 0; i < 2; i++)
        if (!IMATH_INTERNAL_NAMESPACE::equalWithAbsError ((*this)[i], v[i], e))
            return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Vec2<T>::equalWithRelError (const Vec2<T>& v, T e) const IMATH_NOEXCEPT
{
    for (int i = 0; i < 2; i++)
        if (!IMATH_INTERNAL_NAMESPACE::equalWithRelError ((*this)[i], v[i], e))
            return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline T
Vec2<T>::dot (const Vec2& v) const IMATH_NOEXCEPT
{
    return x * v.x + y * v.y;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline T
Vec2<T>::operator^ (const Vec2& v) const IMATH_NOEXCEPT
{
    return dot (v);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline T
Vec2<T>::cross (const Vec2& v) const IMATH_NOEXCEPT
{
    return x * v.y - y * v.x;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline T
Vec2<T>::operator% (const Vec2& v) const IMATH_NOEXCEPT
{
    return x * v.y - y * v.x;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec2<T>&
Vec2<T>::operator+= (const Vec2& v) IMATH_NOEXCEPT
{
    x += v.x;
    y += v.y;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>
Vec2<T>::operator+ (const Vec2& v) const IMATH_NOEXCEPT
{
    return Vec2 (x + v.x, y + v.y);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec2<T>&
Vec2<T>::operator-= (const Vec2& v) IMATH_NOEXCEPT
{
    x -= v.x;
    y -= v.y;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>
Vec2<T>::operator- (const Vec2& v) const IMATH_NOEXCEPT
{
    return Vec2 (x - v.x, y - v.y);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>
Vec2<T>::operator- () const IMATH_NOEXCEPT
{
    return Vec2 (-x, -y);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec2<T>&
                 Vec2<T>::negate () IMATH_NOEXCEPT
{
    x = -x;
    y = -y;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec2<T>&
Vec2<T>::operator*= (const Vec2& v) IMATH_NOEXCEPT
{
    x *= v.x;
    y *= v.y;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec2<T>&
Vec2<T>::operator*= (T a) IMATH_NOEXCEPT
{
    x *= a;
    y *= a;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>
Vec2<T>::operator* (const Vec2& v) const IMATH_NOEXCEPT
{
    return Vec2 (x * v.x, y * v.y);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>
Vec2<T>::operator* (T a) const IMATH_NOEXCEPT
{
    return Vec2 (x * a, y * a);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec2<T>&
Vec2<T>::operator/= (const Vec2& v) IMATH_NOEXCEPT
{
    x /= v.x;
    y /= v.y;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec2<T>&
Vec2<T>::operator/= (T a) IMATH_NOEXCEPT
{
    x /= a;
    y /= a;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>
Vec2<T>::operator/ (const Vec2& v) const IMATH_NOEXCEPT
{
    return Vec2 (x / v.x, y / v.y);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>
Vec2<T>::operator/ (T a) const IMATH_NOEXCEPT
{
    return Vec2 (x / a, y / a);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline T
Vec2<T>::lengthTiny () const IMATH_NOEXCEPT
{
    T absX = std::abs (x);
    T absY = std::abs (y);

T max = absX;

if (max < absY) max = absY;

if (IMATH_UNLIKELY (max == T (0))) return T (0);

//
    // Do not replace the divisions by max with multiplications by 1/max.
    // Computing 1/max can overflow but the divisions below will always
    // produce results less than or equal to 1.
    //

absX /= max;
    absY /= max;

return max * std::sqrt (absX * absX + absY * absY);
}

template <class T>
IMATH_HOSTDEVICE inline T
Vec2<T>::length () const IMATH_NOEXCEPT
{
    T length2 = dot (*this);

if (IMATH_UNLIKELY (length2 < T (2) * std::numeric_limits<T>::min ()))
        return lengthTiny ();

return std::sqrt (length2);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline T
Vec2<T>::length2 () const IMATH_NOEXCEPT
{
    return dot (*this);
}

template <class T>
IMATH_HOSTDEVICE inline const Vec2<T>&
Vec2<T>::normalize () IMATH_NOEXCEPT
{
    T l = length ();

if (IMATH_LIKELY (l != T (0)))
    {
        //
        // Do not replace the divisions by l with multiplications by 1/l.
        // Computing 1/l can overflow but the divisions below will always
        // produce results less than or equal to 1.
        //

x /= l;
        y /= l;
    }

return *this;
}

template <class T>
inline const Vec2<T>&
Vec2<T>::normalizeExc ()
{
    T l = length ();

if (IMATH_UNLIKELY (l == T (0)))
        throw std::domain_error ("Cannot normalize null vector.");

x /= l;
    y /= l;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE inline const Vec2<T>&
Vec2<T>::normalizeNonNull () IMATH_NOEXCEPT
{
    T l = length ();
    x /= l;
    y /= l;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE inline Vec2<T>
Vec2<T>::normalized () const IMATH_NOEXCEPT
{
    T l = length ();

if (IMATH_UNLIKELY (l == T (0))) return Vec2 (T (0));

return Vec2 (x / l, y / l);
}

template <class T>
inline Vec2<T>
Vec2<T>::normalizedExc () const
{
    T l = length ();

if (IMATH_UNLIKELY (l == T (0)))
        throw std::domain_error ("Cannot normalize null vector.");

return Vec2 (x / l, y / l);
}

template <class T>
IMATH_HOSTDEVICE inline Vec2<T>
Vec2<T>::normalizedNonNull () const IMATH_NOEXCEPT
{
    T l = length ();
    return Vec2 (x / l, y / l);
}

//-----------------------
// Implementation of Vec3
//-----------------------

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline T&
Vec3<T>::operator[] (int i) IMATH_NOEXCEPT
{
    return (&x)[i]; // NOSONAR - suppress SonarCloud bug report.
}

template <class T>
IMATH_HOSTDEVICE constexpr inline const T&
Vec3<T>::operator[] (int i) const IMATH_NOEXCEPT
{
    return (&x)[i]; // NOSONAR - suppress SonarCloud bug report.
}

template <class T> IMATH_HOSTDEVICE inline Vec3<T>::Vec3 () IMATH_NOEXCEPT
{
    // empty, and not constexpr because data is uninitialized.
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>::Vec3 (T a) IMATH_NOEXCEPT : x (a),
                                                                       y (a),
                                                                       z (a)
{}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>::Vec3 (T a, T b, T c) IMATH_NOEXCEPT
    : x (a),
      y (b),
      z (c)
{}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>::Vec3 (const Vec3& v) IMATH_NOEXCEPT
    : x (v.x),
      y (v.y),
      z (v.z)
{}

template <class T>
template <class S>
IMATH_HOSTDEVICE constexpr inline Vec3<T>::Vec3 (const Vec3<S>& v)
    IMATH_NOEXCEPT : x (T (v.x)),
                     y (T (v.y)),
                     z (T (v.z))
{}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec3<T>&
Vec3<T>::operator= (const Vec3& v) IMATH_NOEXCEPT
{
    x = v.x;
    y = v.y;
    z = v.z;
    return *this;
}

template <class T>
template <class S>
IMATH_HOSTDEVICE constexpr inline Vec3<T>::Vec3 (const Vec4<S>& v)
    IMATH_NOEXCEPT : x (T (v.x / v.w)),
                     y (T (v.y / v.w)),
                     z (T (v.z / v.w))
{}

template <class T>
template <class S>
IMATH_HOSTDEVICE
    IMATH_CONSTEXPR14 inline Vec3<T>::Vec3 (const Vec4<S>& v, InfException)
{
    T vx = T (v.x);
    T vy = T (v.y);
    T vz = T (v.z);
    T vw = T (v.w);

T absW = (vw >= T (0)) ? vw : -vw;

if (absW < 1)
    {
        T m = baseTypeMax () * absW;

if (vx <= -m || vx >= m || vy <= -m || vy >= m || vz <= -m || vz >= m)
            throw std::domain_error ("Cannot normalize point at infinity.");
    }

x = vx / vw;
    y = vy / vw;
    z = vz / vw;
}

template <class T>
template <class S>
IMATH_HOSTDEVICE inline void
Vec3<T>::setValue (S a, S b, S c) IMATH_NOEXCEPT
{
    x = T (a);
    y = T (b);
    z = T (c);
}

template <class T>
template <class S>
IMATH_HOSTDEVICE inline void
Vec3<T>::setValue (const Vec3<S>& v) IMATH_NOEXCEPT
{
    x = T (v.x);
    y = T (v.y);
    z = T (v.z);
}

template <class T>
template <class S>
IMATH_HOSTDEVICE inline void
Vec3<T>::getValue (S& a, S& b, S& c) const IMATH_NOEXCEPT
{
    a = S (x);
    b = S (y);
    c = S (z);
}

template <class T>
template <class S>
IMATH_HOSTDEVICE inline void
Vec3<T>::getValue (Vec3<S>& v) const IMATH_NOEXCEPT
{
    v.x = S (x);
    v.y = S (y);
    v.z = S (z);
}

template <class T>
IMATH_HOSTDEVICE inline T*
Vec3<T>::getValue () IMATH_NOEXCEPT
{
    return (T*) &x;
}

template <class T>
IMATH_HOSTDEVICE inline const T*
Vec3<T>::getValue () const IMATH_NOEXCEPT
{
    return (const T*) &x;
}

template <class T>
template <class S>
IMATH_HOSTDEVICE constexpr inline bool
Vec3<T>::operator== (const Vec3<S>& v) const IMATH_NOEXCEPT
{
    return x == v.x && y == v.y && z == v.z;
}

template <class T>
template <class S>
IMATH_HOSTDEVICE constexpr inline bool
Vec3<T>::operator!= (const Vec3<S>& v) const IMATH_NOEXCEPT
{
    return x != v.x || y != v.y || z != v.z;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Vec3<T>::equalWithAbsError (const Vec3<T>& v, T e) const IMATH_NOEXCEPT
{
    for (int i = 0; i < 3; i++)
        if (!IMATH_INTERNAL_NAMESPACE::equalWithAbsError ((*this)[i], v[i], e))
            return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Vec3<T>::equalWithRelError (const Vec3<T>& v, T e) const IMATH_NOEXCEPT
{
    for (int i = 0; i < 3; i++)
        if (!IMATH_INTERNAL_NAMESPACE::equalWithRelError ((*this)[i], v[i], e))
            return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline T
Vec3<T>::dot (const Vec3& v) const IMATH_NOEXCEPT
{
    return x * v.x + y * v.y + z * v.z;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline T
Vec3<T>::operator^ (const Vec3& v) const IMATH_NOEXCEPT
{
    return dot (v);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>
Vec3<T>::cross (const Vec3& v) const IMATH_NOEXCEPT
{
    return Vec3 (y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec3<T>&
Vec3<T>::operator%= (const Vec3& v) IMATH_NOEXCEPT
{
    T a = y * v.z - z * v.y;
    T b = z * v.x - x * v.z;
    T c = x * v.y - y * v.x;
    x   = a;
    y   = b;
    z   = c;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>
Vec3<T>::operator% (const Vec3& v) const IMATH_NOEXCEPT
{
    return Vec3 (y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec3<T>&
Vec3<T>::operator+= (const Vec3& v) IMATH_NOEXCEPT
{
    x += v.x;
    y += v.y;
    z += v.z;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>
Vec3<T>::operator+ (const Vec3& v) const IMATH_NOEXCEPT
{
    return Vec3 (x + v.x, y + v.y, z + v.z);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec3<T>&
Vec3<T>::operator-= (const Vec3& v) IMATH_NOEXCEPT
{
    x -= v.x;
    y -= v.y;
    z -= v.z;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>
Vec3<T>::operator- (const Vec3& v) const IMATH_NOEXCEPT
{
    return Vec3 (x - v.x, y - v.y, z - v.z);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>
Vec3<T>::operator- () const IMATH_NOEXCEPT
{
    return Vec3 (-x, -y, -z);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec3<T>&
                 Vec3<T>::negate () IMATH_NOEXCEPT
{
    x = -x;
    y = -y;
    z = -z;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec3<T>&
Vec3<T>::operator*= (const Vec3& v) IMATH_NOEXCEPT
{
    x *= v.x;
    y *= v.y;
    z *= v.z;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec3<T>&
Vec3<T>::operator*= (T a) IMATH_NOEXCEPT
{
    x *= a;
    y *= a;
    z *= a;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>
Vec3<T>::operator* (const Vec3& v) const IMATH_NOEXCEPT
{
    return Vec3 (x * v.x, y * v.y, z * v.z);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>
Vec3<T>::operator* (T a) const IMATH_NOEXCEPT
{
    return Vec3 (x * a, y * a, z * a);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec3<T>&
Vec3<T>::operator/= (const Vec3& v) IMATH_NOEXCEPT
{
    x /= v.x;
    y /= v.y;
    z /= v.z;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec3<T>&
Vec3<T>::operator/= (T a) IMATH_NOEXCEPT
{
    x /= a;
    y /= a;
    z /= a;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>
Vec3<T>::operator/ (const Vec3& v) const IMATH_NOEXCEPT
{
    return Vec3 (x / v.x, y / v.y, z / v.z);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>
Vec3<T>::operator/ (T a) const IMATH_NOEXCEPT
{
    return Vec3 (x / a, y / a, z / a);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline T
Vec3<T>::lengthTiny () const IMATH_NOEXCEPT
{
    T absX = (x >= T (0)) ? x : -x;
    T absY = (y >= T (0)) ? y : -y;
    T absZ = (z >= T (0)) ? z : -z;

T max = absX;

if (max < absY) max = absY;

if (max < absZ) max = absZ;

if (IMATH_UNLIKELY (max == T (0))) return T (0);

absX /= max;
    absY /= max;
    absZ /= max;

return max * std::sqrt (absX * absX + absY * absY + absZ * absZ);
}

template <class T>
IMATH_HOSTDEVICE inline T
Vec3<T>::length () const IMATH_NOEXCEPT
{
    T length2 = dot (*this);

if (IMATH_UNLIKELY (length2 < T (2) * std::numeric_limits<T>::min ()))
        return lengthTiny ();

return std::sqrt (length2);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline T
Vec3<T>::length2 () const IMATH_NOEXCEPT
{
    return dot (*this);
}

template <class T>
IMATH_HOSTDEVICE inline const Vec3<T>&
Vec3<T>::normalize () IMATH_NOEXCEPT
{
    T l = length ();

x /= l;
        y /= l;
        z /= l;
    }

return *this;
}

template <class T>
inline const Vec3<T>&
Vec3<T>::normalizeExc ()
{
    T l = length ();

if (IMATH_UNLIKELY (l == T (0)))
        throw std::domain_error ("Cannot normalize null vector.");

x /= l;
    y /= l;
    z /= l;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE inline const Vec3<T>&
Vec3<T>::normalizeNonNull () IMATH_NOEXCEPT
{
    T l = length ();
    x /= l;
    y /= l;
    z /= l;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE inline Vec3<T>
Vec3<T>::normalized () const IMATH_NOEXCEPT
{
    T l = length ();

if (IMATH_UNLIKELY ((l == T (0)))) return Vec3 (T (0));

return Vec3 (x / l, y / l, z / l);
}

template <class T>
inline Vec3<T>
Vec3<T>::normalizedExc () const
{
    T l = length ();

if (IMATH_UNLIKELY (l == T (0)))
        throw std::domain_error ("Cannot normalize null vector.");

return Vec3 (x / l, y / l, z / l);
}

template <class T>
IMATH_HOSTDEVICE inline Vec3<T>
Vec3<T>::normalizedNonNull () const IMATH_NOEXCEPT
{
    T l = length ();
    return Vec3 (x / l, y / l, z / l);
}

//-----------------------
// Implementation of Vec4
//-----------------------

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline T&
Vec4<T>::operator[] (int i) IMATH_NOEXCEPT
{
    return (&x)[i]; // NOSONAR - suppress SonarCloud bug report.
}

template <class T>
IMATH_HOSTDEVICE constexpr inline const T&
Vec4<T>::operator[] (int i) const IMATH_NOEXCEPT
{
    return (&x)[i]; // NOSONAR - suppress SonarCloud bug report.
}

template <class T> IMATH_HOSTDEVICE inline Vec4<T>::Vec4 () IMATH_NOEXCEPT
{
    // empty, and not constexpr because data is uninitialized.
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec4<T>::Vec4 (T a) IMATH_NOEXCEPT : x (a),
                                                                       y (a),
                                                                       z (a),
                                                                       w (a)
{}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec4<T>::Vec4 (T a, T b, T c, T d)
    IMATH_NOEXCEPT : x (a),
                     y (b),
                     z (c),
                     w (d)
{}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec4<T>::Vec4 (const Vec4& v) IMATH_NOEXCEPT
    : x (v.x),
      y (v.y),
      z (v.z),
      w (v.w)
{}

template <class T>
template <class S>
IMATH_HOSTDEVICE constexpr inline Vec4<T>::Vec4 (const Vec4<S>& v)
    IMATH_NOEXCEPT : x (T (v.x)),
                     y (T (v.y)),
                     z (T (v.z)),
                     w (T (v.w))
{}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec4<T>&
Vec4<T>::operator= (const Vec4& v) IMATH_NOEXCEPT
{
    x = v.x;
    y = v.y;
    z = v.z;
    w = v.w;
    return *this;
}

template <class T>
template <class S>
IMATH_HOSTDEVICE constexpr inline Vec4<T>::Vec4 (const Vec3<S>& v)
    IMATH_NOEXCEPT : x (T (v.x)),
                     y (T (v.y)),
                     z (T (v.z)),
                     w (T (1))
{}

template <class T>
template <class S>
IMATH_HOSTDEVICE constexpr inline bool
Vec4<T>::operator== (const Vec4<S>& v) const IMATH_NOEXCEPT
{
    return x == v.x && y == v.y && z == v.z && w == v.w;
}

template <class T>
template <class S>
IMATH_HOSTDEVICE constexpr inline bool
Vec4<T>::operator!= (const Vec4<S>& v) const IMATH_NOEXCEPT
{
    return x != v.x || y != v.y || z != v.z || w != v.w;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Vec4<T>::equalWithAbsError (const Vec4<T>& v, T e) const IMATH_NOEXCEPT
{
    for (int i = 0; i < 4; i++)
        if (!IMATH_INTERNAL_NAMESPACE::equalWithAbsError ((*this)[i], v[i], e))
            return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline bool
Vec4<T>::equalWithRelError (const Vec4<T>& v, T e) const IMATH_NOEXCEPT
{
    for (int i = 0; i < 4; i++)
        if (!IMATH_INTERNAL_NAMESPACE::equalWithRelError ((*this)[i], v[i], e))
            return false;

return true;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline T
Vec4<T>::dot (const Vec4& v) const IMATH_NOEXCEPT
{
    return x * v.x + y * v.y + z * v.z + w * v.w;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline T
Vec4<T>::operator^ (const Vec4& v) const IMATH_NOEXCEPT
{
    return dot (v);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec4<T>&
Vec4<T>::operator+= (const Vec4& v) IMATH_NOEXCEPT
{
    x += v.x;
    y += v.y;
    z += v.z;
    w += v.w;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec4<T>
Vec4<T>::operator+ (const Vec4& v) const IMATH_NOEXCEPT
{
    return Vec4 (x + v.x, y + v.y, z + v.z, w + v.w);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec4<T>&
Vec4<T>::operator-= (const Vec4& v) IMATH_NOEXCEPT
{
    x -= v.x;
    y -= v.y;
    z -= v.z;
    w -= v.w;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec4<T>
Vec4<T>::operator- (const Vec4& v) const IMATH_NOEXCEPT
{
    return Vec4 (x - v.x, y - v.y, z - v.z, w - v.w);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec4<T>
Vec4<T>::operator- () const IMATH_NOEXCEPT
{
    return Vec4 (-x, -y, -z, -w);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec4<T>&
                 Vec4<T>::negate () IMATH_NOEXCEPT
{
    x = -x;
    y = -y;
    z = -z;
    w = -w;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec4<T>&
Vec4<T>::operator*= (const Vec4& v) IMATH_NOEXCEPT
{
    x *= v.x;
    y *= v.y;
    z *= v.z;
    w *= v.w;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec4<T>&
Vec4<T>::operator*= (T a) IMATH_NOEXCEPT
{
    x *= a;
    y *= a;
    z *= a;
    w *= a;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec4<T>
Vec4<T>::operator* (const Vec4& v) const IMATH_NOEXCEPT
{
    return Vec4 (x * v.x, y * v.y, z * v.z, w * v.w);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec4<T>
Vec4<T>::operator* (T a) const IMATH_NOEXCEPT
{
    return Vec4 (x * a, y * a, z * a, w * a);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec4<T>&
Vec4<T>::operator/= (const Vec4& v) IMATH_NOEXCEPT
{
    x /= v.x;
    y /= v.y;
    z /= v.z;
    w /= v.w;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline const Vec4<T>&
Vec4<T>::operator/= (T a) IMATH_NOEXCEPT
{
    x /= a;
    y /= a;
    z /= a;
    w /= a;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec4<T>
Vec4<T>::operator/ (const Vec4& v) const IMATH_NOEXCEPT
{
    return Vec4 (x / v.x, y / v.y, z / v.z, w / v.w);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec4<T>
Vec4<T>::operator/ (T a) const IMATH_NOEXCEPT
{
    return Vec4 (x / a, y / a, z / a, w / a);
}

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline T
Vec4<T>::lengthTiny () const IMATH_NOEXCEPT
{
    T absX = (x >= T (0)) ? x : -x;
    T absY = (y >= T (0)) ? y : -y;
    T absZ = (z >= T (0)) ? z : -z;
    T absW = (w >= T (0)) ? w : -w;

T max = absX;

if (max < absY) max = absY;

if (max < absZ) max = absZ;

if (max < absW) max = absW;

if (IMATH_UNLIKELY (max == T (0))) return T (0);

absX /= max;
    absY /= max;
    absZ /= max;
    absW /= max;

return max *
           std::sqrt (absX * absX + absY * absY + absZ * absZ + absW * absW);
}

template <class T>
IMATH_HOSTDEVICE inline T
Vec4<T>::length () const IMATH_NOEXCEPT
{
    T length2 = dot (*this);

if (IMATH_UNLIKELY (length2 < T (2) * std::numeric_limits<T>::min ()))
        return lengthTiny ();

return std::sqrt (length2);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline T
Vec4<T>::length2 () const IMATH_NOEXCEPT
{
    return dot (*this);
}

template <class T>
IMATH_HOSTDEVICE const inline Vec4<T>&
Vec4<T>::normalize () IMATH_NOEXCEPT
{
    T l = length ();

x /= l;
        y /= l;
        z /= l;
        w /= l;
    }

return *this;
}

template <class T>
const inline Vec4<T>&
Vec4<T>::normalizeExc ()
{
    T l = length ();

if (IMATH_UNLIKELY (l == T (0)))
        throw std::domain_error ("Cannot normalize null vector.");

x /= l;
    y /= l;
    z /= l;
    w /= l;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE inline const Vec4<T>&
Vec4<T>::normalizeNonNull () IMATH_NOEXCEPT
{
    T l = length ();
    x /= l;
    y /= l;
    z /= l;
    w /= l;
    return *this;
}

template <class T>
IMATH_HOSTDEVICE inline Vec4<T>
Vec4<T>::normalized () const IMATH_NOEXCEPT
{
    T l = length ();

if (IMATH_UNLIKELY (l == T (0))) return Vec4 (T (0));

return Vec4 (x / l, y / l, z / l, w / l);
}

template <class T>
inline Vec4<T>
Vec4<T>::normalizedExc () const
{
    T l = length ();

if (IMATH_UNLIKELY (l == T (0)))
        throw std::domain_error ("Cannot normalize null vector.");

return Vec4 (x / l, y / l, z / l, w / l);
}

template <class T>
IMATH_HOSTDEVICE inline Vec4<T>
Vec4<T>::normalizedNonNull () const IMATH_NOEXCEPT
{
    T l = length ();
    return Vec4 (x / l, y / l, z / l, w / l);
}

//-----------------------------
// Stream output implementation
//-----------------------------

template <class T>
std::ostream&
operator<< (std::ostream& s, const Vec2<T>& v)
{
    return s << '(' << v.x << ' ' << v.y << ')';
}

template <class T>
std::ostream&
operator<< (std::ostream& s, const Vec3<T>& v)
{
    return s << '(' << v.x << ' ' << v.y << ' ' << v.z << ')';
}

template <class T>
std::ostream&
operator<< (std::ostream& s, const Vec4<T>& v)
{
    return s << '(' << v.x << ' ' << v.y << ' ' << v.z << ' ' << v.w << ')';
}

//-----------------------------------------
// Implementation of reverse multiplication
//-----------------------------------------

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec2<T>
operator* (T a, const Vec2<T>& v) IMATH_NOEXCEPT
{
    return Vec2<T> (a * v.x, a * v.y);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec3<T>
operator* (T a, const Vec3<T>& v) IMATH_NOEXCEPT
{
    return Vec3<T> (a * v.x, a * v.y, a * v.z);
}

template <class T>
IMATH_HOSTDEVICE constexpr inline Vec4<T>
operator* (T a, const Vec4<T>& v) IMATH_NOEXCEPT
{
    return Vec4<T> (a * v.x, a * v.y, a * v.z, a * v.w);
}

#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
#    pragma warning(pop)
#endif

IMATH_INTERNAL_NAMESPACE_HEADER_EXIT

#endif // INCLUDED_IMATHVEC_H