ExtVec.h

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#ifndef DataFormat_Math_ExtVec_H
#define DataFormat_Math_ExtVec_H

#include <type_traits>

#define VECTOR_EXT(N) __attribute__((vector_size(N)))

typedef float VECTOR_EXT(8) cms_float32x2_t;
typedef float VECTOR_EXT(16) cms_float32x4_t;
typedef float VECTOR_EXT(32) cms_float32x8_t;
typedef double VECTOR_EXT(16) cms_float64x2_t;
typedef double VECTOR_EXT(32) cms_float64x4_t;
typedef double VECTOR_EXT(64) cms_float64x8_t;

typedef long double VECTOR_EXT(32) cms_float128x2_t;
typedef long double VECTOR_EXT(64) cms_float128x4_t;
typedef long double VECTOR_EXT(128) cms_float128x8_t;

// template<typename T, int N> using ExtVec =  T __attribute__( ( vector_size( N*sizeof(T) ) ) );

template <typename T, int N>
struct ExtVecTraits {
  //  typedef T __attribute__( ( vector_size( N*sizeof(T) ) ) ) type;
};

template <>
struct ExtVecTraits<float, 2> {
  typedef float VECTOR_EXT(2 * sizeof(float)) type;
};

template <>
struct ExtVecTraits<float, 4> {
  typedef float VECTOR_EXT(4 * sizeof(float)) type;
};

template <>
struct ExtVecTraits<double, 2> {
  typedef double VECTOR_EXT(2 * sizeof(double)) type;
};

template <>
struct ExtVecTraits<double, 4> {
  typedef double VECTOR_EXT(4 * sizeof(double)) type;
};

template <>
struct ExtVecTraits<long double, 2> {
  typedef long double VECTOR_EXT(2 * sizeof(long double)) type;
};

template <>
struct ExtVecTraits<long double, 4> {
  typedef long double VECTOR_EXT(4 * sizeof(long double)) type;
};

template <typename T, int N>
using ExtVec = typename ExtVecTraits<T, N>::type;

template <typename T>
using Vec4 = ExtVec<T, 4>;
template <typename T>
using Vec2 = ExtVec<T, 2>;

// convert V in W
template <typename W, typename V>
inline W convert(V v) {
  // see https://gcc.gnu.org/bugzilla/show_bug.cgi?id=114943
  //  return __builtin_convertvector(v,W);  // nope inefficient in gcc
  typedef typename std::remove_reference<decltype(v[0])>::type T;
  constexpr int N = sizeof(V) / sizeof(T);
  W w;
  for (int i = 0; i != N; ++i)
    w[i] = v[i];
  return w;
}

template <typename V>
inline auto xy(V v) -> Vec2<typename std::remove_reference<decltype(v[0])>::type> {
  typedef typename std::remove_reference<decltype(v[0])>::type T;
  return Vec2<T>{v[0], v[1]};
}

template <typename V>
inline auto zw(V v) -> Vec2<typename std::remove_reference<decltype(v[0])>::type> {
  typedef typename std::remove_reference<decltype(v[0])>::type T;
  return Vec2<T>{v[2], v[3]};
}

template <typename Vec, typename F>
inline Vec apply(Vec v, F f) {
  typedef typename std::remove_reference<decltype(v[0])>::type T;
  constexpr int N = sizeof(Vec) / sizeof(T);
  Vec ret;
  for (int i = 0; i != N; ++i)
    ret[i] = f(v[i]);
  return ret;
}

template <typename Vec>
inline Vec cross3(Vec x, Vec y) {
  //  typedef Vec4<T> Vec;
  // yz - zy, zx - xz, xy - yx, 0
  Vec x1200{x[1], x[2], x[0], x[0]};
  Vec y2010{y[2], y[0], y[1], y[0]};
  Vec x2010{x[2], x[0], x[1], x[0]};
  Vec y1200{y[1], y[2], y[0], y[0]};
  return x1200 * y2010 - x2010 * y1200;
}

template <typename V1, typename V2>
inline auto cross2(V1 x, V2 y) -> typename std::remove_reference<decltype(x[0])>::type {
  return x[0] * y[1] - x[1] * y[0];
}

/*
template<typename T> 
T dot_product(Vec4<T>  x, Vec4<T>  y) {
  auto res = x*y;
  T ret=0;
  for (int i=0;i!=4;++i) ret+=res[i];
  return ret;
}
*/

/*
template<typename V, int K> 
inline
V get1(V v) { return (V){v[K]}; }
*/

/*
template<typename T, int N> 
inline
T dot(ExtVec<T,N>  x, ExtVec<T,N>  y) {
  T ret=0;
  for (int i=0;i!=N;++i) ret+=x[i]*y[i];
  return ret;
}
*/

template <typename V>
inline auto dot(V x, V y) -> typename std::remove_reference<decltype(x[0])>::type {
  typedef typename std::remove_reference<decltype(x[0])>::type T;
  constexpr int N = sizeof(V) / sizeof(T);
  T ret = 0;
  for (int i = 0; i != N; ++i)
    ret += x[i] * y[i];
  return ret;
}

template <typename V1, typename V2>
inline auto dot2(V1 x, V2 y) -> typename std::remove_reference<decltype(x[0])>::type {
  return x[0] * y[0] + x[1] * y[1];
}

template <typename V1, typename V2>
inline auto dot3(V1 x, V2 y) -> typename std::remove_reference<decltype(x[0])>::type {
  auto z = x * y;
  return z[0] + z[1] + z[2];
}

typedef Vec2<float> Vec2F;
typedef Vec4<float> Vec4F;
typedef Vec4<float> Vec3F;
typedef Vec2<double> Vec2D;
typedef Vec4<double> Vec3D;
typedef Vec4<double> Vec4D;

/*
template<typename T>
struct As3D {
  Vec4<T> const & v;
  As3D(Vec4<T> const &iv ) : v(iv){}
};
template<typename T>
inline As3D<T> as3D(Vec4<T> const &v ) { return v;}
*/

template <typename V>
struct As3D {
  V const& v;
  As3D(V const& iv) : v(iv) {}
};
template <typename V>
inline As3D<V> as3D(V const& v) {
  return v;
}

// rotations

template <typename T>
struct Rot3 {
  typedef Vec4<T> Vec;
  Vec axis[3];

  constexpr Rot3() : axis{{(Vec){T(1), 0, 0, 0}}, {(Vec){0, T(1), 0, 0}}, {(Vec){0, 0, T(1), 0}}} {}

  constexpr Rot3(Vec4<T> ix, Vec4<T> iy, Vec4<T> iz) : axis{ix, iy, iz} {}

  constexpr Rot3(T xx, T xy, T xz, T yx, T yy, T yz, T zx, T zy, T zz)
      : axis{{(Vec){xx, xy, xz, 0}}, {(Vec){yx, yy, yz, 0}}, {(Vec){zx, zy, zz, 0}}} {}

  constexpr Rot3 transpose() const {
    return Rot3(
        axis[0][0], axis[1][0], axis[2][0], axis[0][1], axis[1][1], axis[2][1], axis[0][2], axis[1][2], axis[2][2]);
  }

  constexpr Vec4<T> x() const { return axis[0]; }
  constexpr Vec4<T> y() const { return axis[1]; }
  constexpr Vec4<T> z() const { return axis[2]; }

  // toLocal...
  constexpr Vec4<T> rotate(Vec4<T> v) const { return transpose().rotateBack(v); }

  // toGlobal...
  constexpr Vec4<T> rotateBack(Vec4<T> v) const { return v[0] * axis[0] + v[1] * axis[1] + v[2] * axis[2]; }

  Rot3 rotate(Rot3 const& r) const {
    Rot3 tr = transpose();
    return Rot3(tr.rotateBack(r.axis[0]), tr.rotateBack(r.axis[1]), tr.rotateBack(r.axis[2]));
  }

  constexpr Rot3 rotateBack(Rot3 const& r) const {
    return Rot3(rotateBack(r.axis[0]), rotateBack(r.axis[1]), rotateBack(r.axis[2]));
  }
};

typedef Rot3<float> Rot3F;

typedef Rot3<double> Rot3D;

template <typename T>
inline constexpr Rot3<T> operator*(Rot3<T> const& rh, Rot3<T> const& lh) {
  return lh.rotateBack(rh);
}

template <typename T>
struct Rot2 {
  typedef Vec2<T> Vec;
  Vec2<T> axis[2];

  constexpr Rot2() : axis{{(Vec){T(1), 0}}, {(Vec){0, T(1)}}} {}

  constexpr Rot2(Vec2<T> ix, Vec2<T> iy) : axis{ix, iy} {}

  constexpr Rot2(T xx, T xy, T yx, T yy) : Rot2((Vec){xx, xy}, (Vec){yx, yy}) {}

  constexpr Rot2 transpose() const { return Rot2(axis[0][0], axis[1][0], axis[0][1], axis[1][1]); }

  constexpr Vec2<T> x() const { return axis[0]; }
  constexpr Vec2<T> y() const { return axis[1]; }

  // toLocal...
  constexpr Vec2<T> rotate(Vec2<T> v) const { return transpose().rotateBack(v); }

  // toGlobal...
  constexpr Vec2<T> rotateBack(Vec2<T> v) const { return v[0] * axis[0] + v[1] * axis[1]; }

  Rot2 rotate(Rot2 const& r) const {
    Rot2 tr = transpose();
    return Rot2(tr.rotateBack(r.axis[0]), tr.rotateBack(r.axis[1]));
  }

  constexpr Rot2 rotateBack(Rot2 const& r) const { return Rot2(rotateBack(r.axis[0]), rotateBack(r.axis[1])); }
};

typedef Rot2<float> Rot2F;

typedef Rot2<double> Rot2D;

template <typename T>
inline constexpr Rot2<T> operator*(Rot2<T> const& rh, Rot2<T> const& lh) {
  return lh.rotateBack(rh);
}

#include <iosfwd>
std::ostream& operator<<(std::ostream& out, Vec2D const& v);
std::ostream& operator<<(std::ostream& out, Vec2F const& v);
std::ostream& operator<<(std::ostream& out, Vec4F const& v);
std::ostream& operator<<(std::ostream& out, Vec4D const& v);

std::ostream& operator<<(std::ostream& out, As3D<Vec4F> const& v);
std::ostream& operator<<(std::ostream& out, As3D<Vec4D> const& v);

std::ostream& operator<<(std::ostream& out, Rot3F const& v);
std::ostream& operator<<(std::ostream& out, Rot3D const& v);
std::ostream& operator<<(std::ostream& out, Rot2F const& v);
std::ostream& operator<<(std::ostream& out, Rot2D const& v);

#ifdef USE_INLINE_IO
#include <ostream>
std::ostream& operator<<(std::ostream& out, ::Vec4F const& v) {
  return out << '(' << v[0] << ", " << v[1] << ", " << v[2] << ", " << v[3] << ')';
}
std::ostream& operator<<(std::ostream& out, ::Vec4D const& v) {
  return out << '(' << v[0] << ", " << v[1] << ", " << v[2] << ", " << v[3] << ')';
}
std::ostream& operator<<(std::ostream& out, ::Vec2F const& v) { return out << '(' << v[0] << ", " << v[1] << ')'; }
std::ostream& operator<<(std::ostream& out, ::Vec2D const& v) { return out << '(' << v[0] << ", " << v[1] << ')'; }

std::ostream& operator<<(std::ostream& out, ::As3D<Vec4F> const& v) {
  return out << '(' << v.v[0] << ", " << v.v[1] << ", " << v.v[2] << ')';
}

std::ostream& operator<<(std::ostream& out, ::As3D<Vec4D> const& v) {
  return out << '(' << v.v[0] << ", " << v.v[1] << ", " << v.v[2] << ')';
}

std::ostream& operator<<(std::ostream& out, ::Rot3F const& r) {
  return out << as3D(r.axis[0]) << '\n' << as3D(r.axis[1]) << '\n' << as3D(r.axis[2]);
}

std::ostream& operator<<(std::ostream& out, ::Rot3D const& r) {
  return out << as3D(r.axis[0]) << '\n' << as3D(r.axis[1]) << '\n' << as3D(r.axis[2]);
}

std::ostream& operator<<(std::ostream& out, ::Rot2F const& r) { return out << r.axis[0] << '\n' << r.axis[1]; }

std::ostream& operator<<(std::ostream& out, ::Rot2D const& r) { return out << r.axis[0] << '\n' << r.axis[1]; }
#endif

#endif