SSEVec.h

Go to the documentation of this file.

#ifndef DataFormat_Math_SSEVec_H
#define DataFormat_Math_SSEVec_H

#if !defined(__arm__) && !defined(__aarch64__) && !defined(__MIC__) && !defined(__powerpc64__) && \
    !defined(__PPC64__) && !defined(__powerpc__) && !defined(__NVCC__) && !defined(__riscv)
#if defined(__GNUC__)
#include <x86intrin.h>
#define CMS_USE_SSE
#ifdef __SSE4_1__
// slower than sse3
// #define CMS_USE_SSE4
#endif
#ifdef __AVX2__
#define CMS_USE_AVX2
#endif /* __AVX2__ */
#endif /* defined(__GNUC__) */
#endif /* !defined(__arm__) && !defined(__aarch64__) && !defined(__MIC__) */

#include <cmath>

namespace mathSSE {
  template <typename T>
  inline T sqrt(T t) {
    return std::sqrt(t);
  }
}  // namespace mathSSE

namespace mathSSE {
#ifdef CMS_USE_SSE
  //dot
  inline __m128 __attribute__((always_inline)) __attribute__((pure)) _mm_dot_ps(__m128 v1, __m128 v2) {
#ifdef CMS_USE_SSE4
    return _mm_dp_ps(v1, v2, 0xff);
#else

    __m128 mul = _mm_mul_ps(v1, v2);
#ifdef __SSE3__
    mul = _mm_hadd_ps(mul, mul);
    return _mm_hadd_ps(mul, mul);
#else
    __m128 swp = _mm_shuffle_ps(mul, mul, _MM_SHUFFLE(1, 0, 3, 2));
    mul = _mm_add_ps(mul, swp);
    swp = _mm_shuffle_ps(mul, mul, _MM_SHUFFLE(2, 3, 0, 1));
    return _mm_add_ps(mul, swp);
#endif
#endif
  }

  // cross (just 3x3)
  inline __m128 __attribute__((always_inline)) __attribute__((pure)) _mm_cross_ps(__m128 v1, __m128 v2) {
    // same order is  _MM_SHUFFLE(3,2,1,0)
    //                                               x2, z1,z1
    __m128 v3 = _mm_shuffle_ps(v2, v1, _MM_SHUFFLE(3, 0, 2, 2));
    //                                               y1, x2,y2
    __m128 v4 = _mm_shuffle_ps(v1, v2, _MM_SHUFFLE(3, 1, 0, 1));

    __m128 v5 = _mm_mul_ps(v3, v4);

    //                                         x1, z2,z2
    v3 = _mm_shuffle_ps(v1, v2, _MM_SHUFFLE(3, 0, 2, 2));
    //                                        y2, x1,y1
    v4 = _mm_shuffle_ps(v2, v1, _MM_SHUFFLE(3, 1, 0, 1));

    v3 = _mm_mul_ps(v3, v4);
    const __m128i neg = _mm_set_epi32(0, 0, 0x80000000, 0);
    __m128i ret = __m128i(_mm_sub_ps(v5, v3));
    return __m128(_mm_xor_si128(ret, neg));
  }
#endif  // CMS_USE_SSE

#ifdef CMS_USE_AVX2
  inline __m256d __attribute__((always_inline)) __attribute__((pure)) _mm256_dot_pd(__m256d v1, __m256d v2) {
    __m256d mul = _mm256_mul_pd(v1, v2);
    mul = _mm256_hadd_pd(mul, mul);
    __m256d tmp = _mm256_permute2f128_pd(mul, mul, 1);
    return _mm256_add_pd(mul, tmp);
  }

  inline __m256d __attribute__((always_inline)) __attribute__((pure)) _mm256_cross_pd(__m256d v1, __m256d v2) {
    __m256d v3 = _mm256_permute2f128_pd(v2, v1, (2 << 4) + 1);
    v3 = _mm256_permute_pd(v3, 0);

    __m256d v4 = _mm256_permute2f128_pd(v1, v2, (2 << 4));
    v4 = _mm256_permute_pd(v4, 5);

    __m256d v5 = _mm256_mul_pd(v3, v4);

    v3 = _mm256_permute2f128_pd(v1, v2, (2 << 4) + 1);
    v3 = _mm256_permute_pd(v3, 0);

    v4 = _mm256_permute2f128_pd(v2, v1, (2 << 4));
    v4 = _mm256_permute_pd(v4, 5);

    v3 = _mm256_mul_pd(v3, v4);
    __m256d ret = _mm256_sub_pd(v5, v3);
    const __m256i neg = _mm256_set_epi64x(0, 0, 0x8000000000000000, 0);
    return __m256d(_mm256_xor_si256(__m256i(ret), neg));
  }

#endif  //  CMS_USE_AVX2

  template <typename T>
  struct OldVec {
    T theX;
    T theY;
    T theZ;
    T theW;
  } __attribute__((aligned(16)));
#ifdef CMS_USE_AVX2
  template <>
  struct OldVec<double> {
    double theX;
    double theY;
    double theZ;
    double theW;
  } __attribute__((aligned(32)));
#endif

  template <typename T>
  union Vec4;

  template <typename T>
  union Vec2 {
    Vec2() {
      arr[0] = 0;
      arr[1] = 0;
    }
    Vec2(T f1, T f2) {
      arr[0] = f1;
      arr[1] = f2;
    }
    explicit Vec2(T f1) {
      arr[0] = f1;
      arr[1] = f1;
    }

    void set(T f1, T f2) {
      arr[0] = f1;
      arr[1] = f2;
    }

    template <int N>
    Vec2 get1() const {
      return Vec2(arr[N], arr[N]);
    }

    /*
    Vec2 get1(unsigned int n) const {
      return Vec2(arr[n],arr[n]);
    }
    */

    template <typename U>
    Vec2(Vec2<U> v) {
      arr[0] = v[0];
      arr[1] = v[1];
    }

    inline Vec2(Vec4<T> v4);

    T &operator[](unsigned int n) { return arr[n]; }

    T operator[](unsigned int n) const { return arr[n]; }

    T arr[2];
  };

  template <typename T>
  union Vec4 {
    Vec4() {
      arr[0] = 0;
      arr[1] = 0;
      arr[2] = 0;
      arr[3] = 0;
    }
    Vec4(float f1, float f2, float f3, float f4 = 0) {
      arr[0] = f1;
      arr[1] = f2;
      arr[2] = f3;
      arr[3] = f4;
    }
    explicit Vec4(float f1) { set1(f1); }
    void set(float f1, float f2, float f3, float f4 = 0) {
      arr[0] = f1;
      arr[1] = f2;
      arr[2] = f3;
      arr[3] = f4;
    }
    void set1(float f1) {
      arr[0] = f1;
      arr[1] = f1;
      arr[2] = f1;
      arr[3] = f1;
    }
    template <int N>
    Vec4 get1() const {
      return Vec4(arr[N], arr[N], arr[N], arr[N]);
    }
    /*
    Vec4 get1(unsigned int n) const {
      return Vec4(arr[n],arr[n],arr[n],arr[n]);
    }
    */

    Vec2<T> xy() const { return Vec2<T>(arr[0], arr[1]); }
    Vec2<T> zw() const { return Vec2<T>(arr[2], arr[3]); }

    T __attribute__((aligned(16))) arr[4];
    OldVec<T> o;
  };

  template <typename T>
  inline Vec2<T>::Vec2(Vec4<T> v4) {
    arr[0] = v4[0];
    arr[1] = v4[1];
  }

#ifdef CMS_USE_SSE

  template <>
  union Vec2<double>;
  template <>
  union Vec4<double>;

  template <typename T>
  union Mask2 {};
  template <typename T>
  union Mask4 {};

  template <>
  union Mask4<float> {
    __m128 vec;
    unsigned int __attribute__((aligned(16))) mask[4];
    Mask4() { vec = _mm_setzero_ps(); }
    Mask4(unsigned int m1, unsigned int m2, unsigned int m3, unsigned int m4) {
      mask[0] = m1;
      mask[1] = m2;
      mask[2] = m3;
      mask[3] = m4;
    }
  };

#ifdef CMS_USE_AVX2
  template <>
  union Mask4<double> {
    __m256d vec;
    unsigned long long __attribute__((aligned(32))) mask[4];
    Mask4() { vec = _mm256_setzero_pd(); }
    Mask4(unsigned long long m1, unsigned long long m2, unsigned long long m3, unsigned long long m4) {
      mask[0] = m1;
      mask[1] = m2;
      mask[2] = m3;
      mask[3] = m4;
    }
  };
#else
  template <>
  union Mask4<double> {
    __m128d vec[2];
    unsigned long long __attribute__((aligned(16))) mask[4];
    Mask4() {
      vec[0] = _mm_setzero_pd();
      vec[1] = _mm_setzero_pd();
    }
    Mask4(unsigned long long m1, unsigned long long m2, unsigned long long m3, unsigned long long m4) {
      mask[0] = m1;
      mask[1] = m2;
      mask[2] = m3;
      mask[3] = m4;
    }
  };
#endif

  template <>
  union Mask2<double> {
    __m128d vec;
    unsigned long long __attribute__((aligned(16))) mask[2];
    Mask2() { vec = _mm_setzero_pd(); }
    Mask2(unsigned long long m1, unsigned long long m2) {
      mask[0] = m1;
      mask[1] = m2;
    }
  };

  template <>
  union Vec4<float> {
    typedef __m128 nativeType;
    __m128 vec;
    float __attribute__((aligned(16))) arr[4];
    OldVec<float> o;

    Vec4(__m128 ivec) : vec(ivec) {}

    Vec4(OldVec<float> const &ivec) : o(ivec) {}

    Vec4() { vec = _mm_setzero_ps(); }

    inline Vec4(Vec4<double> ivec);

    explicit Vec4(float f1) { set1(f1); }

    Vec4(float f1, float f2, float f3, float f4 = 0) { vec = _mm_set_ps(f4, f3, f2, f1); }

    Vec4(Vec2<float> ivec0, Vec2<float> ivec1) {
      arr[0] = ivec0.arr[0];
      arr[1] = ivec0.arr[1];
      arr[2] = ivec1.arr[0];
      arr[3] = ivec1.arr[1];
    }

    Vec4(Vec2<float> ivec0, float f3, float f4 = 0) {
      arr[0] = ivec0.arr[0];
      arr[1] = ivec0.arr[1];
      arr[2] = f3;
      arr[3] = f4;
    }

    Vec4(Vec2<float> ivec0) {
      vec = _mm_setzero_ps();
      arr[0] = ivec0.arr[0];
      arr[1] = ivec0.arr[1];
    }

    // for masking
    void setMask(unsigned int m1, unsigned int m2, unsigned int m3, unsigned int m4) {
      Mask4<float> mask(m1, m2, m3, m4);
      vec = mask.vec;
    }

    void set(float f1, float f2, float f3, float f4 = 0) { vec = _mm_set_ps(f4, f3, f2, f1); }

    void set1(float f1) { vec = _mm_set1_ps(f1); }

    template <int N>
    Vec4 get1() const {
      return _mm_shuffle_ps(vec, vec, _MM_SHUFFLE(N, N, N, N));
    }

    float &operator[](unsigned int n) { return arr[n]; }

    float operator[](unsigned int n) const { return arr[n]; }

    Vec2<float> xy() const { return Vec2<float>(arr[0], arr[1]); }
    Vec2<float> zw() const { return Vec2<float>(arr[2], arr[3]); }
  };

  template <>
  union Vec2<double> {
    typedef __m128d nativeType;
    __m128d vec;
    double __attribute__((aligned(16))) arr[2];

    Vec2(__m128d ivec) : vec(ivec) {}

    Vec2() { vec = _mm_setzero_pd(); }

    inline Vec2(Vec2<float> ivec);

    Vec2(double f1, double f2) { vec = _mm_set_pd(f2, f1); }

    explicit Vec2(double f1) { set1(f1); }

    inline Vec2(Vec4<double> v4);

    // for masking
    void setMask(unsigned long long m1, unsigned long long m2) {
      Mask2<double> mask(m1, m2);
      vec = mask.vec;
    }

    void set(double f1, double f2) { vec = _mm_set_pd(f2, f1); }

    void set1(double f1) { vec = _mm_set1_pd(f1); }

    template <int N>
    Vec2 get1() const {
      return Vec2(arr[N], arr[N]);
    }
    /*
    Vec2 get1(unsigned int n) const {
      return Vec2(arr[n],arr[n]);
    }
    */
    double &operator[](unsigned int n) { return arr[n]; }
    double operator[](unsigned int n) const { return arr[n]; }
  };

#ifdef CMS_USE_AVX2
}  // namespace mathSSE
#include "private/AVXVec.h"

namespace mathSSE {
#else
  template <>
  union Vec4<double> {
    __m128d vec[2];
    double __attribute__((aligned(16))) arr[4];
    OldVec<double> o;

    Vec4(__m128d ivec[]) {
      vec[0] = ivec[0];
      vec[1] = ivec[1];
    }

    Vec4(__m128d ivec0, __m128d ivec1) {
      vec[0] = ivec0;
      vec[1] = ivec1;
    }

    Vec4() {
      vec[0] = _mm_setzero_pd();
      vec[1] = _mm_setzero_pd();
    }

    Vec4(Vec4<float> ivec) {
      vec[0] = _mm_cvtps_pd(ivec.vec);
      vec[1] = _mm_cvtps_pd(_mm_shuffle_ps(ivec.vec, ivec.vec, _MM_SHUFFLE(1, 0, 3, 2)));
    }

    explicit Vec4(double f1) { set1(f1); }

    Vec4(double f1, double f2, double f3, double f4 = 0) {
      arr[0] = f1;
      arr[1] = f2;
      arr[2] = f3;
      arr[3] = f4;
    }

    Vec4(Vec2<double> ivec0, Vec2<double> ivec1) {
      vec[0] = ivec0.vec;
      vec[1] = ivec1.vec;
    }

    Vec4(Vec2<double> ivec0, double f3, double f4 = 0) {
      vec[0] = ivec0.vec;
      arr[2] = f3;
      arr[3] = f4;
    }

    Vec4(Vec2<double> ivec0) {
      vec[0] = ivec0.vec;
      vec[1] = _mm_setzero_pd();
    }

    Vec4(OldVec<double> const &ivec) : o(ivec) {}

    // for masking
    void setMask(unsigned long long m1, unsigned long long m2, unsigned long long m3, unsigned long long m4) {
      Mask4<double> mask(m1, m2, m3, m4);
      vec[0] = mask.vec[0];
      vec[1] = mask.vec[1];
    }

    void set(double f1, double f2, double f3, double f4 = 0) {
      arr[0] = f1;
      arr[1] = f2;
      arr[2] = f3;
      arr[3] = f4;
    }

    void set1(double f1) { vec[0] = vec[1] = _mm_set1_pd(f1); }

    template <int N>
    Vec4 get1() const {
      return Vec4(arr[N], arr[N], arr[N], arr[N]);
    }

    double &operator[](unsigned int n) { return arr[n]; }

    double operator[](unsigned int n) const { return arr[n]; }

    Vec2<double> xy() const { return vec[0]; }
    Vec2<double> zw() const { return vec[1]; }
  };

  inline Vec4<float>::Vec4(Vec4<double> ivec) {
    vec = _mm_cvtpd_ps(ivec.vec[0]);
    __m128 v2 = _mm_cvtpd_ps(ivec.vec[1]);
    vec = _mm_shuffle_ps(vec, v2, _MM_SHUFFLE(1, 0, 1, 0));
  }
#endif  // CMS_USE_AVX2

#endif  // CMS_USE_SSE

  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;
  }

}  // namespace mathSSE

#ifdef CMS_USE_SSE

//float op

inline bool operator==(mathSSE::Vec4F a, mathSSE::Vec4F b) {
  return _mm_movemask_ps(_mm_cmpeq_ps(a.vec, b.vec)) == 0xf;
}

inline mathSSE::Vec4F cmpeq(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_cmpeq_ps(a.vec, b.vec); }

inline mathSSE::Vec4F cmpgt(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_cmpgt_ps(a.vec, b.vec); }

#ifdef __SSE3__
inline mathSSE::Vec4F hadd(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_hadd_ps(a.vec, b.vec); }
#endif

inline mathSSE::Vec4F operator-(mathSSE::Vec4F a) {
  const __m128 neg = _mm_set_ps(-0.0, -0.0, -0.0, -0.0);
  return _mm_xor_ps(a.vec, neg);
}

inline mathSSE::Vec4F operator&(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_and_ps(a.vec, b.vec); }
inline mathSSE::Vec4F operator|(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_or_ps(a.vec, b.vec); }
inline mathSSE::Vec4F operator^(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_xor_ps(a.vec, b.vec); }
inline mathSSE::Vec4F andnot(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_andnot_ps(a.vec, b.vec); }

inline mathSSE::Vec4F operator+(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_add_ps(a.vec, b.vec); }

inline mathSSE::Vec4F operator-(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_sub_ps(a.vec, b.vec); }

inline mathSSE::Vec4F operator*(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_mul_ps(a.vec, b.vec); }

inline mathSSE::Vec4F operator/(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_div_ps(a.vec, b.vec); }

inline mathSSE::Vec4F min(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_min_ps(a.vec, b.vec); }

inline mathSSE::Vec4F max(mathSSE::Vec4F a, mathSSE::Vec4F b) { return _mm_max_ps(a.vec, b.vec); }

inline mathSSE::Vec4F operator*(float a, mathSSE::Vec4F b) { return _mm_mul_ps(_mm_set1_ps(a), b.vec); }

inline mathSSE::Vec4F operator*(mathSSE::Vec4F b, float a) { return _mm_mul_ps(_mm_set1_ps(a), b.vec); }

inline mathSSE::Vec4F operator/(mathSSE::Vec4F b, float a) { return _mm_div_ps(b.vec, _mm_set1_ps(a)); }

inline float dot(mathSSE::Vec4F a, mathSSE::Vec4F b) {
  using mathSSE::_mm_dot_ps;
  float s;
  _mm_store_ss(&s, _mm_dot_ps(a.vec, b.vec));
  return s;
}

inline float dot3(mathSSE::Vec4F a, mathSSE::Vec4F b) { return dot(a, b); }

inline mathSSE::Vec4F cross(mathSSE::Vec4F a, mathSSE::Vec4F b) {
  using mathSSE::_mm_cross_ps;
  return _mm_cross_ps(a.vec, b.vec);
}

inline float dotxy(mathSSE::Vec4F a, mathSSE::Vec4F b) {
  mathSSE::Vec4F mul = a * b;
#ifdef __SSE3__
  mul = hadd(mul, mul);
#else
  __m128 swp = _mm_shuffle_ps(mul.vec, mul.vec, _MM_SHUFFLE(2, 3, 0, 1));
  mul.vec = _mm_add_ps(mul.vec, swp);
#endif
  float s;
  _mm_store_ss(&s, mul.vec);
  return s;
}

//
// float op 2d (use the 4d one...)
//
inline mathSSE::Vec4F operator-(mathSSE::Vec2F a) { return -mathSSE::Vec4F(a); }

inline mathSSE::Vec4F operator+(mathSSE::Vec2F a, mathSSE::Vec2F b) { return mathSSE::Vec4F(a) + mathSSE::Vec4F(b); }

inline mathSSE::Vec4F operator-(mathSSE::Vec2F a, mathSSE::Vec2F b) { return mathSSE::Vec4F(a) - mathSSE::Vec4F(b); }

inline mathSSE::Vec4F operator*(mathSSE::Vec2F a, mathSSE::Vec2F b) { return mathSSE::Vec4F(a) * mathSSE::Vec4F(b); }

inline mathSSE::Vec4F operator/(mathSSE::Vec2F a, mathSSE::Vec2F b) { return mathSSE::Vec4F(a) / mathSSE::Vec4F(b); }

inline mathSSE::Vec4F min(mathSSE::Vec2F a, mathSSE::Vec2F b) { return min(mathSSE::Vec4F(a), mathSSE::Vec4F(b)); }

inline mathSSE::Vec4F max(mathSSE::Vec2F a, mathSSE::Vec2F b) { return ::max(mathSSE::Vec4F(a), mathSSE::Vec4F(b)); }

inline mathSSE::Vec4F operator*(mathSSE::Vec2F a, float s) { return s * mathSSE::Vec4F(a); }

inline mathSSE::Vec4F operator*(float s, mathSSE::Vec2F a) { return s * mathSSE::Vec4F(a); }

inline mathSSE::Vec4F operator/(mathSSE::Vec2F a, float s) { return mathSSE::Vec4F(a) / s; }

inline float dot(mathSSE::Vec2F a, mathSSE::Vec2F b) __attribute__((always_inline)) __attribute__((pure));

inline float dot(mathSSE::Vec2F a, mathSSE::Vec2F b) { return a.arr[0] * b.arr[0] + a.arr[1] * b.arr[1]; }

inline float cross(mathSSE::Vec2F a, mathSSE::Vec2F b) __attribute__((always_inline)) __attribute__((pure));

inline float cross(mathSSE::Vec2F a, mathSSE::Vec2F b) { return a.arr[0] * b.arr[1] - a.arr[1] * b.arr[0]; }

// double op 2d
//

inline mathSSE::Vec2D::Vec2(Vec4D v4) {
#ifdef CMS_USE_AVX2
  vec = _mm256_castpd256_pd128(v4.vec);
#else
  vec = v4.vec[0];
#endif
}

inline mathSSE::Vec2D::Vec2(Vec2F ivec) {
  arr[0] = ivec.arr[0];
  arr[1] = ivec.arr[1];
}

inline mathSSE::Vec2D operator-(mathSSE::Vec2D a) {
  const __m128d neg = _mm_set_pd(-0.0, -0.0);
  return _mm_xor_pd(a.vec, neg);
}

inline mathSSE::Vec2D operator&(mathSSE::Vec2D a, mathSSE::Vec2D b) { return _mm_and_pd(a.vec, b.vec); }
inline mathSSE::Vec2D operator|(mathSSE::Vec2D a, mathSSE::Vec2D b) { return _mm_or_pd(a.vec, b.vec); }
inline mathSSE::Vec2D operator^(mathSSE::Vec2D a, mathSSE::Vec2D b) { return _mm_xor_pd(a.vec, b.vec); }
inline mathSSE::Vec2D andnot(mathSSE::Vec2D a, mathSSE::Vec2D b) { return _mm_andnot_pd(a.vec, b.vec); }

#ifdef __SSE3__
inline mathSSE::Vec2D hadd(mathSSE::Vec2D a, mathSSE::Vec2D b) { return _mm_hadd_pd(a.vec, b.vec); }
#endif

inline mathSSE::Vec2D operator+(mathSSE::Vec2D a, mathSSE::Vec2D b) { return _mm_add_pd(a.vec, b.vec); }

inline mathSSE::Vec2D operator-(mathSSE::Vec2D a, mathSSE::Vec2D b) { return _mm_sub_pd(a.vec, b.vec); }

inline mathSSE::Vec2D operator*(mathSSE::Vec2D a, mathSSE::Vec2D b) { return _mm_mul_pd(a.vec, b.vec); }

inline mathSSE::Vec2D operator/(mathSSE::Vec2D a, mathSSE::Vec2D b) { return _mm_div_pd(a.vec, b.vec); }

inline mathSSE::Vec2D min(mathSSE::Vec2D a, mathSSE::Vec2D b) { return _mm_min_pd(a.vec, b.vec); }

inline mathSSE::Vec2D max(mathSSE::Vec2D a, mathSSE::Vec2D b) { return _mm_max_pd(a.vec, b.vec); }

inline mathSSE::Vec2D operator*(double a, mathSSE::Vec2D b) { return _mm_mul_pd(_mm_set1_pd(a), b.vec); }

inline mathSSE::Vec2D operator*(mathSSE::Vec2D b, double a) { return _mm_mul_pd(_mm_set1_pd(a), b.vec); }

inline mathSSE::Vec2D operator/(mathSSE::Vec2D b, double a) { return _mm_div_pd(b.vec, _mm_set1_pd(a)); }

inline double dot(mathSSE::Vec2D a, mathSSE::Vec2D b) __attribute__((always_inline)) __attribute__((pure));

inline double dot(mathSSE::Vec2D a, mathSSE::Vec2D b) {
  __m128d res = _mm_mul_pd(a.vec, b.vec);
#ifdef __SSE3__
  res = _mm_hadd_pd(res, res);
#else
  res = _mm_add_sd(_mm_shuffle_pd(res, res, 1), res);
#endif
  double s;
  _mm_store_sd(&s, res);
  return s;
}

inline double cross(mathSSE::Vec2D a, mathSSE::Vec2D b) __attribute__((always_inline)) __attribute__((pure));

inline double cross(mathSSE::Vec2D a, mathSSE::Vec2D b) {
  __m128d res = _mm_shuffle_pd(b.vec, b.vec, 1);
  res = _mm_mul_pd(a.vec, res);
  res = _mm_sub_sd(res, _mm_shuffle_pd(res, res, 1));
  double s;
  _mm_store_sd(&s, res);
  return s;
}

#ifndef CMS_USE_AVX2
// double op 3d

#ifdef __SSE3__
// consistent with AVX...
inline mathSSE::Vec4D hadd(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  return mathSSE::Vec4D(hadd(mathSSE::Vec2D(a.vec[0]), mathSSE::Vec2D(b.vec[0])),
                        hadd(mathSSE::Vec2D(a.vec[1]), mathSSE::Vec2D(b.vec[1])));
}
#endif

inline bool operator==(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  return _mm_movemask_pd(_mm_cmpeq_pd(a.vec[0], b.vec[0])) == 0x3 &&
         _mm_movemask_pd(_mm_cmpeq_pd(a.vec[1], b.vec[1])) == 0x3;
}

inline mathSSE::Vec4D operator-(mathSSE::Vec4D a) {
  const __m128d neg = _mm_set_pd(-0.0, -0.0);
  return mathSSE::Vec4D(_mm_xor_pd(a.vec[0], neg), _mm_xor_pd(a.vec[1], neg));
}

inline mathSSE::Vec4D operator+(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  return mathSSE::Vec4D(_mm_add_pd(a.vec[0], b.vec[0]), _mm_add_pd(a.vec[1], b.vec[1]));
}

inline mathSSE::Vec4D operator-(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  return mathSSE::Vec4D(_mm_sub_pd(a.vec[0], b.vec[0]), _mm_sub_pd(a.vec[1], b.vec[1]));
}
inline mathSSE::Vec4D operator*(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  return mathSSE::Vec4D(_mm_mul_pd(a.vec[0], b.vec[0]), _mm_mul_pd(a.vec[1], b.vec[1]));
}
inline mathSSE::Vec4D operator/(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  return mathSSE::Vec4D(_mm_div_pd(a.vec[0], b.vec[0]), _mm_div_pd(a.vec[1], b.vec[1]));
}

inline mathSSE::Vec4D min(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  using namespace mathSSE;
  return mathSSE::Vec4D(::min(mathSSE::Vec2D(a.vec[0]), mathSSE::Vec2D(b.vec[0])),
                        ::min(mathSSE::Vec2D(a.vec[1]), mathSSE::Vec2D(b.vec[1])));
}

inline mathSSE::Vec4D max(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  using namespace mathSSE;
  return mathSSE::Vec4D(::max(mathSSE::Vec2D(a.vec[0]), mathSSE::Vec2D(b.vec[0])),
                        ::max(mathSSE::Vec2D(a.vec[1]), mathSSE::Vec2D(b.vec[1])));
}

inline mathSSE::Vec4D operator*(double a, mathSSE::Vec4D b) {
  __m128d res = _mm_set1_pd(a);
  return mathSSE::Vec4D(_mm_mul_pd(res, b.vec[0]), _mm_mul_pd(res, b.vec[1]));
}

inline mathSSE::Vec4D operator*(mathSSE::Vec4D b, double a) {
  __m128d res = _mm_set1_pd(a);
  return mathSSE::Vec4D(_mm_mul_pd(res, b.vec[0]), _mm_mul_pd(res, b.vec[1]));
}

inline mathSSE::Vec4D operator/(mathSSE::Vec4D b, double a) {
  a = 1. / a;
  return a * b;
}

// mix algebra (creates ambiguities...)
/*
inline mathSSE::Vec4D operator+(mathSSE::Vec4D a, mathSSE::Vec4F b) {
  return a + mathSSE::Vec4D(b);
}
inline mathSSE::Vec4D operator+(mathSSE::Vec4D b, mathSSE::Vec4F a) {
  return a + mathSSE::Vec4D(b);
}
inline mathSSE::Vec4D operator-(mathSSE::Vec4D a, mathSSE::Vec4F b) {
  return a - mathSSE::Vec4D(b);
}
inline mathSSE::Vec4D operator-(mathSSE::Vec4D b, mathSSE::Vec4F a) {
  return a - mathSSE::Vec4D(b);
}
*/

inline double dot(mathSSE::Vec4D a, mathSSE::Vec4D b) __attribute__((always_inline)) __attribute__((pure));

inline double __attribute__((always_inline)) __attribute__((pure)) dot3(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  return dot(a, b);
}

inline double dot(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  __m128d res = _mm_add_sd(_mm_mul_pd(a.vec[0], b.vec[0]), _mm_mul_sd(a.vec[1], b.vec[1]));
  res = _mm_add_sd(_mm_unpackhi_pd(res, res), res);
  double s;
  _mm_store_sd(&s, res);
  return s;
}

inline mathSSE::Vec4D cross(mathSSE::Vec4D a, mathSSE::Vec4D b) __attribute__((always_inline)) __attribute__((pure));

inline mathSSE::Vec4D cross(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  const __m128i neg = _mm_set_epi64x(0, 0x8000000000000000);
  // lh .z * rh .x , lh .z * rh .y
  __m128d l1 = _mm_mul_pd(_mm_unpacklo_pd(a.vec[1], a.vec[1]), b.vec[0]);
  // rh .z * lh .x , rh .z * lh .y
  __m128d l2 = _mm_mul_pd(_mm_unpacklo_pd(b.vec[1], b.vec[1]), a.vec[0]);
  __m128d m1 = _mm_sub_pd(l1, l2);                // l1 - l2
  m1 = _mm_shuffle_pd(m1, m1, 1);                 // switch the elements
  m1 = __m128d(_mm_xor_si128(__m128i(m1), neg));  // change the sign of the first element
  // lh .x * rh .y , lh .y * rh .x
  l1 = _mm_mul_pd(a.vec[0], _mm_shuffle_pd(b.vec[0], b.vec[0], 1));
  // lh .x * rh .y - lh .y * rh .x
  __m128d m2 = _mm_sub_sd(l1, _mm_unpackhi_pd(l1, l1));
  return mathSSE::Vec4D(m1, m2);
}

inline double __attribute__((always_inline)) __attribute__((pure)) dotxy(mathSSE::Vec4D a, mathSSE::Vec4D b) {
  return dot(a.xy(), b.xy());
}

#endif  // CMS_USE_AVX2

// sqrt
namespace mathSSE {
  template <>
  inline Vec4F sqrt(Vec4F v) {
    return _mm_sqrt_ps(v.vec);
  }
  template <>
  inline Vec2F sqrt(Vec2F v) {
    return sqrt(Vec4F(v));
  }
  template <>
  inline Vec2D sqrt(Vec2D v) {
    return _mm_sqrt_pd(v.vec);
  }
#ifdef CMS_USE_AVX2
  template <>
  inline Vec4D sqrt(Vec4D v) {
    return _mm256_sqrt_pd(v.vec);
  }
#else
  template <>
  inline Vec4D sqrt(Vec4D v) {
    return Vec4D(_mm_sqrt_pd(v.vec[0]), _mm_sqrt_pd(v.vec[1]));
  }
#endif
}  // namespace mathSSE

#endif  // CMS_USE_SSE

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

std::ostream &operator<<(std::ostream &out, mathSSE::As3D<float> const &v);
std::ostream &operator<<(std::ostream &out, mathSSE::As3D<double> const &v);

#endif  // DataFormat_Math_SSEVec_H