path: root/thirdparty/embree/common/simd/vfloat16_avx512.h

// Copyright 2009-2021 Intel Corporation
// SPDX-License-Identifier: Apache-2.0

#pragma once

#define vboolf vboolf_impl
#define vboold vboold_impl
#define vint vint_impl
#define vuint vuint_impl
#define vllong vllong_impl
#define vfloat vfloat_impl
#define vdouble vdouble_impl

namespace embree
{
  /* 16-wide AVX-512 float type */
  template<>
  struct vfloat<16>
  {
    ALIGNED_STRUCT_(64);
    
    typedef vboolf16 Bool;
    typedef vint16   Int;
    typedef vfloat16 Float;

    enum  { size = 16 }; // number of SIMD elements
    union {              // data
      __m512 v; 
      float f[16];
      int i[16];
    };

    ////////////////////////////////////////////////////////////////////////////////
    /// Constructors, Assignment & Cast Operators
    ////////////////////////////////////////////////////////////////////////////////
        
    __forceinline vfloat() {}
    __forceinline vfloat(const vfloat16& t) { v = t; }
    __forceinline vfloat16& operator =(const vfloat16& f) { v = f.v; return *this; }

    __forceinline vfloat(const __m512& t) { v = t; }
    __forceinline operator __m512() const { return v; }
    __forceinline operator __m256() const { return _mm512_castps512_ps256(v); }
    __forceinline operator __m128() const { return _mm512_castps512_ps128(v); }

    __forceinline vfloat(float f) {
      v = _mm512_set1_ps(f);
    }

    __forceinline vfloat(float a, float b, float c, float d) {
      v = _mm512_set4_ps(a, b, c, d);
    }

    __forceinline vfloat(const vfloat4& i) {
      v = _mm512_broadcast_f32x4(i);
    }

    __forceinline vfloat(const vfloat4& a, const vfloat4& b, const vfloat4& c, const vfloat4& d) {
      v = _mm512_castps128_ps512(a);
      v = _mm512_insertf32x4(v, b, 1);
      v = _mm512_insertf32x4(v, c, 2);
      v = _mm512_insertf32x4(v, d, 3);
    }

    __forceinline vfloat(const vboolf16& mask, const vfloat4& a, const vfloat4& b) {
      v = _mm512_broadcast_f32x4(a);
      v = _mm512_mask_broadcast_f32x4(v,mask,b);
    }

    __forceinline vfloat(const vfloat8& i) {
      v = _mm512_castpd_ps(_mm512_broadcast_f64x4(_mm256_castps_pd(i)));
    }

    __forceinline vfloat(const vfloat8& a, const vfloat8& b) {
      v = _mm512_castps256_ps512(a);
#if defined(__AVX512DQ__)
      v = _mm512_insertf32x8(v, b, 1);
#else
      v = _mm512_castpd_ps(_mm512_insertf64x4(_mm512_castps_pd(v), _mm256_castps_pd(b), 1));
#endif
    }

    /* WARNING: due to f64x4 the mask is considered as an 8bit mask */
    /*__forceinline vfloat(const vboolf16& mask, const vfloat8& a, const vfloat8& b) {
      __m512d aa = _mm512_broadcast_f64x4(_mm256_castps_pd(a));
      aa = _mm512_mask_broadcast_f64x4(aa,mask,_mm256_castps_pd(b));
      v = _mm512_castpd_ps(aa);
      }*/
    
    __forceinline explicit vfloat(const vint16& a) {
      v = _mm512_cvtepi32_ps(a);
    }

    __forceinline explicit vfloat(const vuint16& a) {
      v = _mm512_cvtepu32_ps(a);
    }

    ////////////////////////////////////////////////////////////////////////////////
    /// Constants
    ////////////////////////////////////////////////////////////////////////////////

    __forceinline vfloat(ZeroTy)   : v(_mm512_setzero_ps()) {}
    __forceinline vfloat(OneTy)    : v(_mm512_set1_ps(1.0f)) {}
    __forceinline vfloat(PosInfTy) : v(_mm512_set1_ps(pos_inf)) {}
    __forceinline vfloat(NegInfTy) : v(_mm512_set1_ps(neg_inf)) {}
    __forceinline vfloat(StepTy)   : v(_mm512_set_ps(15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0)) {}
    __forceinline vfloat(NaNTy)    : v(_mm512_set1_ps(nan)) {}
    __forceinline vfloat(UndefinedTy) : v(_mm512_undefined_ps()) {}

    ////////////////////////////////////////////////////////////////////////////////
    /// Loads and Stores
    ////////////////////////////////////////////////////////////////////////////////

    static __forceinline vfloat16 load (const void* ptr) { return _mm512_load_ps((float*)ptr);  }
    static __forceinline vfloat16 loadu(const void* ptr) { return _mm512_loadu_ps((float*)ptr); }

    static __forceinline vfloat16 load (const vboolf16& mask, const void* ptr) { return _mm512_mask_load_ps (_mm512_setzero_ps(),mask,(float*)ptr); }
    static __forceinline vfloat16 loadu(const vboolf16& mask, const void* ptr) { return _mm512_mask_loadu_ps(_mm512_setzero_ps(),mask,(float*)ptr); }

    static __forceinline void store (void* ptr, const vfloat16& v) { _mm512_store_ps ((float*)ptr,v); }
    static __forceinline void storeu(void* ptr, const vfloat16& v) { _mm512_storeu_ps((float*)ptr,v); }

    static __forceinline void store (const vboolf16& mask, void* ptr, const vfloat16& v) { _mm512_mask_store_ps ((float*)ptr,mask,v); }
    static __forceinline void storeu(const vboolf16& mask, void* ptr, const vfloat16& v) { _mm512_mask_storeu_ps((float*)ptr,mask,v); }

    static __forceinline void store_nt(void* __restrict__ ptr, const vfloat16& a) {
      _mm512_stream_ps((float*)ptr,a);
    }

    static __forceinline vfloat16 broadcast(const float* f) {
      return _mm512_set1_ps(*f);
    }

    template<int scale = 4>
    static __forceinline vfloat16 gather(const float* ptr, const vint16& index) {
      return _mm512_i32gather_ps(index, ptr, scale);
    }

    template<int scale = 4>
    static __forceinline vfloat16 gather(const vboolf16& mask, const float* ptr, const vint16& index) {
      vfloat16 r = zero;
      return _mm512_mask_i32gather_ps(r, mask, index, ptr, scale);
    }

    template<int scale = 4>
    static __forceinline void scatter(float* ptr, const vint16& index, const vfloat16& v) {
      _mm512_i32scatter_ps(ptr, index, v, scale);
    }

    template<int scale = 4>
    static __forceinline void scatter(const vboolf16& mask, float* ptr, const vint16& index, const vfloat16& v) {
      _mm512_mask_i32scatter_ps(ptr, mask, index, v, scale);
    }

    ////////////////////////////////////////////////////////////////////////////////
    /// Array Access
    ////////////////////////////////////////////////////////////////////////////////
    
    __forceinline       float& operator [](size_t index)       { assert(index < 16); return f[index]; }
    __forceinline const float& operator [](size_t index) const { assert(index < 16); return f[index]; }
  };

  ////////////////////////////////////////////////////////////////////////////////
  /// Unary Operators
  ////////////////////////////////////////////////////////////////////////////////

  __forceinline vfloat16 asFloat(const vint16&   a) { return _mm512_castsi512_ps(a); }
  __forceinline vint16   asInt  (const vfloat16& a) { return _mm512_castps_si512(a); }
  __forceinline vuint16  asUInt (const vfloat16& a) { return _mm512_castps_si512(a); }

  __forceinline vint16   toInt  (const vfloat16& a) { return vint16(a); }
  __forceinline vfloat16 toFloat(const vint16&   a) { return vfloat16(a); }

  __forceinline vfloat16 operator +(const vfloat16& a) { return a; }
  __forceinline vfloat16 operator -(const vfloat16& a) { return _mm512_mul_ps(a,vfloat16(-1)); }

  __forceinline vfloat16 abs    (const vfloat16& a) { return _mm512_castsi512_ps(_mm512_and_epi32(_mm512_castps_si512(a),_mm512_set1_epi32(0x7FFFFFFF))); }
  __forceinline vfloat16 signmsk(const vfloat16& a) { return _mm512_castsi512_ps(_mm512_and_epi32(_mm512_castps_si512(a),_mm512_set1_epi32(0x80000000))); }

  __forceinline vfloat16 rcp(const vfloat16& a) {
    const vfloat16 r = _mm512_rcp14_ps(a);
    return _mm512_mul_ps(r, _mm512_fnmadd_ps(r, a, vfloat16(2.0f)));
  }

  __forceinline vfloat16 sqr (const vfloat16& a) { return _mm512_mul_ps(a,a); }
  __forceinline vfloat16 sqrt(const vfloat16& a) { return _mm512_sqrt_ps(a); }

  __forceinline vfloat16 rsqrt(const vfloat16& a)
  {
    const vfloat16 r = _mm512_rsqrt14_ps(a);
    return _mm512_fmadd_ps(_mm512_set1_ps(1.5f), r,
                           _mm512_mul_ps(_mm512_mul_ps(_mm512_mul_ps(a, _mm512_set1_ps(-0.5f)), r), _mm512_mul_ps(r, r))); 
  }

  ////////////////////////////////////////////////////////////////////////////////
  /// Binary Operators
  ////////////////////////////////////////////////////////////////////////////////

  __forceinline vfloat16 operator +(const vfloat16& a, const vfloat16& b) { return _mm512_add_ps(a, b); }
  __forceinline vfloat16 operator +(const vfloat16& a, float           b) { return a + vfloat16(b); }
  __forceinline vfloat16 operator +(float           a, const vfloat16& b) { return vfloat16(a) + b; }

  __forceinline vfloat16 operator -(const vfloat16& a, const vfloat16& b) { return _mm512_sub_ps(a, b); }
  __forceinline vfloat16 operator -(const vfloat16& a, float           b) { return a - vfloat16(b); }
  __forceinline vfloat16 operator -(float           a, const vfloat16& b) { return vfloat16(a) - b; }

  __forceinline vfloat16 operator *(const vfloat16& a, const vfloat16& b) { return _mm512_mul_ps(a, b); }
  __forceinline vfloat16 operator *(const vfloat16& a, float           b) { return a * vfloat16(b); }
  __forceinline vfloat16 operator *(float           a, const vfloat16& b) { return vfloat16(a) * b; }

  __forceinline vfloat16 operator /(const vfloat16& a, const vfloat16& b) { return _mm512_div_ps(a,b); }
  __forceinline vfloat16 operator /(const vfloat16& a, float           b) { return a/vfloat16(b); }
  __forceinline vfloat16 operator /(float           a, const vfloat16& b) { return vfloat16(a)/b; }
  
  __forceinline vfloat16 operator &(const vfloat16& a, const vfloat16& b) { return _mm512_and_ps(a,b); }
  __forceinline vfloat16 operator |(const vfloat16& a, const vfloat16& b) { return _mm512_or_ps(a,b); }
  __forceinline vfloat16 operator ^(const vfloat16& a, const vfloat16& b) {
    return  _mm512_castsi512_ps(_mm512_xor_epi32(_mm512_castps_si512(a),_mm512_castps_si512(b))); 
  }
  
  __forceinline vfloat16 min(const vfloat16& a, const vfloat16& b) { return _mm512_min_ps(a,b);  }
  __forceinline vfloat16 min(const vfloat16& a, float           b) { return _mm512_min_ps(a,vfloat16(b)); }
  __forceinline vfloat16 min(const float&    a, const vfloat16& b) { return _mm512_min_ps(vfloat16(a),b); }

  __forceinline vfloat16 max(const vfloat16& a, const vfloat16& b) { return _mm512_max_ps(a,b); }
  __forceinline vfloat16 max(const vfloat16& a, float           b) { return _mm512_max_ps(a,vfloat16(b)); }
  __forceinline vfloat16 max(const float&    a, const vfloat16& b) { return _mm512_max_ps(vfloat16(a),b); }

  __forceinline vfloat16 mini(const vfloat16& a, const vfloat16& b) {
    const vint16 ai = _mm512_castps_si512(a);
    const vint16 bi = _mm512_castps_si512(b);
    const vint16 ci = _mm512_min_epi32(ai,bi);
    return _mm512_castsi512_ps(ci);
  }

  __forceinline vfloat16 maxi(const vfloat16& a, const vfloat16& b) {
    const vint16 ai = _mm512_castps_si512(a);
    const vint16 bi = _mm512_castps_si512(b);
    const vint16 ci = _mm512_max_epi32(ai,bi);
    return _mm512_castsi512_ps(ci);
  }

  ////////////////////////////////////////////////////////////////////////////////
  /// Ternary Operators
  ////////////////////////////////////////////////////////////////////////////////

  __forceinline vfloat16 madd (const vfloat16& a, const vfloat16& b, const vfloat16& c) { return _mm512_fmadd_ps(a,b,c); }
  __forceinline vfloat16 msub (const vfloat16& a, const vfloat16& b, const vfloat16& c) { return _mm512_fmsub_ps(a,b,c); }
  __forceinline vfloat16 nmadd(const vfloat16& a, const vfloat16& b, const vfloat16& c) { return _mm512_fnmadd_ps(a,b,c); }
  __forceinline vfloat16 nmsub(const vfloat16& a, const vfloat16& b, const vfloat16& c) { return _mm512_fnmsub_ps(a,b,c); }
  
  ////////////////////////////////////////////////////////////////////////////////
  /// Assignment Operators
  ////////////////////////////////////////////////////////////////////////////////

  __forceinline vfloat16& operator +=(vfloat16& a, const vfloat16& b) { return a = a + b; }
  __forceinline vfloat16& operator +=(vfloat16& a, float           b) { return a = a + b; }
  
  __forceinline vfloat16& operator -=(vfloat16& a, const vfloat16& b) { return a = a - b; }
  __forceinline vfloat16& operator -=(vfloat16& a, float           b) { return a = a - b; }
  
  __forceinline vfloat16& operator *=(vfloat16& a, const vfloat16& b) { return a = a * b; }
  __forceinline vfloat16& operator *=(vfloat16& a, float           b) { return a = a * b; }

  __forceinline vfloat16& operator /=(vfloat16& a, const vfloat16& b) { return a = a / b; }
  __forceinline vfloat16& operator /=(vfloat16& a, float           b) { return a = a / b; }

  ////////////////////////////////////////////////////////////////////////////////
  /// Comparison Operators + Select
  ////////////////////////////////////////////////////////////////////////////////

  __forceinline vboolf16 operator ==(const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_EQ); }
  __forceinline vboolf16 operator ==(const vfloat16& a, float           b) { return a == vfloat16(b); }
  __forceinline vboolf16 operator ==(float           a, const vfloat16& b) { return vfloat16(a) == b; }

  __forceinline vboolf16 operator !=(const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_NE); }
  __forceinline vboolf16 operator !=(const vfloat16& a, float           b) { return a != vfloat16(b); }
  __forceinline vboolf16 operator !=(float           a, const vfloat16& b) { return vfloat16(a) != b; }

  __forceinline vboolf16 operator < (const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_LT); }
  __forceinline vboolf16 operator < (const vfloat16& a, float           b) { return a <  vfloat16(b); }
  __forceinline vboolf16 operator < (float           a, const vfloat16& b) { return vfloat16(a) <  b; }

  __forceinline vboolf16 operator >=(const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_GE); }
  __forceinline vboolf16 operator >=(const vfloat16& a, float           b) { return a >= vfloat16(b); }
  __forceinline vboolf16 operator >=(float           a, const vfloat16& b) { return vfloat16(a) >= b; }

  __forceinline vboolf16 operator > (const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_GT); }
  __forceinline vboolf16 operator > (const vfloat16& a, float           b) { return a >  vfloat16(b); }
  __forceinline vboolf16 operator > (float           a, const vfloat16& b) { return vfloat16(a) >  b; }

  __forceinline vboolf16 operator <=(const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_LE); }
  __forceinline vboolf16 operator <=(const vfloat16& a, float           b) { return a <= vfloat16(b); }
  __forceinline vboolf16 operator <=(float           a, const vfloat16& b) { return vfloat16(a) <= b; }

  __forceinline vboolf16 eq(const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_EQ); }
  __forceinline vboolf16 ne(const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_NE); }
  __forceinline vboolf16 lt(const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_LT); }
  __forceinline vboolf16 ge(const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_GE); }
  __forceinline vboolf16 gt(const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_GT); }
  __forceinline vboolf16 le(const vfloat16& a, const vfloat16& b) { return _mm512_cmp_ps_mask(a,b,_MM_CMPINT_LE); }

  __forceinline vboolf16 eq(const vboolf16& mask, const vfloat16& a, const vfloat16& b) { return _mm512_mask_cmp_ps_mask(mask,a,b,_MM_CMPINT_EQ); }
  __forceinline vboolf16 ne(const vboolf16& mask, const vfloat16& a, const vfloat16& b) { return _mm512_mask_cmp_ps_mask(mask,a,b,_MM_CMPINT_NE); }
  __forceinline vboolf16 lt(const vboolf16& mask, const vfloat16& a, const vfloat16& b) { return _mm512_mask_cmp_ps_mask(mask,a,b,_MM_CMPINT_LT); }
  __forceinline vboolf16 ge(const vboolf16& mask, const vfloat16& a, const vfloat16& b) { return _mm512_mask_cmp_ps_mask(mask,a,b,_MM_CMPINT_GE); }
  __forceinline vboolf16 gt(const vboolf16& mask, const vfloat16& a, const vfloat16& b) { return _mm512_mask_cmp_ps_mask(mask,a,b,_MM_CMPINT_GT); }
  __forceinline vboolf16 le(const vboolf16& mask, const vfloat16& a, const vfloat16& b) { return _mm512_mask_cmp_ps_mask(mask,a,b,_MM_CMPINT_LE); }
  
  __forceinline vfloat16 select(const vboolf16& s, const vfloat16& t, const vfloat16& f) {
    return _mm512_mask_blend_ps(s, f, t);
  }

  __forceinline vfloat16 lerp(const vfloat16& a, const vfloat16& b, const vfloat16& t) {
    return madd(t,b-a,a);
  }

  ////////////////////////////////////////////////////////////////////////////////
  /// Rounding Functions
  ////////////////////////////////////////////////////////////////////////////////
  
  __forceinline vfloat16 floor(const vfloat16& a) {
    return _mm512_floor_ps(a);
  }
  __forceinline vfloat16 ceil (const vfloat16& a) {
    return _mm512_ceil_ps(a);
  }
  __forceinline vfloat16 round (const vfloat16& a) {
    return _mm512_roundscale_ps(a, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
  }
  __forceinline vint16 floori (const vfloat16& a) {
    return _mm512_cvt_roundps_epi32(a, _MM_FROUND_TO_NEG_INF | _MM_FROUND_NO_EXC);
  }

  ////////////////////////////////////////////////////////////////////////////////
  /// Movement/Shifting/Shuffling Functions
  ////////////////////////////////////////////////////////////////////////////////

  __forceinline vfloat16 unpacklo(const vfloat16& a, const vfloat16& b) { return _mm512_unpacklo_ps(a, b); }
  __forceinline vfloat16 unpackhi(const vfloat16& a, const vfloat16& b) { return _mm512_unpackhi_ps(a, b); }

  template<int i>
  __forceinline vfloat16 shuffle(const vfloat16& v) {
    return _mm512_permute_ps(v, _MM_SHUFFLE(i, i, i, i));
  }

  template<int i0, int i1, int i2, int i3>
  __forceinline vfloat16 shuffle(const vfloat16& v) {
    return _mm512_permute_ps(v, _MM_SHUFFLE(i3, i2, i1, i0));
  }

  template<int i>
  __forceinline vfloat16 shuffle4(const vfloat16& v) {
    return _mm512_shuffle_f32x4(v, v ,_MM_SHUFFLE(i, i, i, i));
  }

  template<int i0, int i1, int i2, int i3>
  __forceinline vfloat16 shuffle4(const vfloat16& v) {
    return _mm512_shuffle_f32x4(v, v, _MM_SHUFFLE(i3, i2, i1, i0));
  }

  __forceinline vfloat16 interleave4_even(const vfloat16& a, const vfloat16& b) {
    return _mm512_castsi512_ps(_mm512_mask_permutex_epi64(_mm512_castps_si512(a), mm512_int2mask(0xcc), _mm512_castps_si512(b), (_MM_PERM_ENUM)0x4e));
  }

  __forceinline vfloat16 interleave4_odd(const vfloat16& a, const vfloat16& b) {
    return _mm512_castsi512_ps(_mm512_mask_permutex_epi64(_mm512_castps_si512(b), mm512_int2mask(0x33), _mm512_castps_si512(a), (_MM_PERM_ENUM)0x4e));
  }

  __forceinline vfloat16 permute(vfloat16 v, __m512i index) {
    return _mm512_castsi512_ps(_mm512_permutexvar_epi32(index, _mm512_castps_si512(v)));
  }

  __forceinline vfloat16 reverse(const vfloat16& v) {
    return permute(v,_mm512_setr_epi32(15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0));
  }

  template<int i>
  __forceinline vfloat16 align_shift_right(const vfloat16& a, const vfloat16& b) {
    return _mm512_castsi512_ps(_mm512_alignr_epi32(_mm512_castps_si512(a),_mm512_castps_si512(b),i)); 
  };

  template<int i>
  __forceinline vfloat16 mask_align_shift_right(const vboolf16& mask, vfloat16& c, const vfloat16& a, const vfloat16& b) {
    return _mm512_castsi512_ps(_mm512_mask_alignr_epi32(_mm512_castps_si512(c),mask,_mm512_castps_si512(a),_mm512_castps_si512(b),i)); 
  };
 
  __forceinline vfloat16 shift_left_1(const vfloat16& a) {
    vfloat16 z = zero;
    return mask_align_shift_right<15>(0xfffe,z,a,a);
  }

  __forceinline vfloat16 shift_right_1(const vfloat16& x) {
    return align_shift_right<1>(zero,x);
  }

  __forceinline float toScalar(const vfloat16& v) { return mm512_cvtss_f32(v); }


  template<int i> __forceinline vfloat16 insert4(const vfloat16& a, const vfloat4& b) { return _mm512_insertf32x4(a, b, i); }

  template<int N, int i>
  vfloat<N> extractN(const vfloat16& v);

  template<> __forceinline vfloat4 extractN<4,0>(const vfloat16& v) { return _mm512_castps512_ps128(v);    }
  template<> __forceinline vfloat4 extractN<4,1>(const vfloat16& v) { return _mm512_extractf32x4_ps(v, 1); }
  template<> __forceinline vfloat4 extractN<4,2>(const vfloat16& v) { return _mm512_extractf32x4_ps(v, 2); }
  template<> __forceinline vfloat4 extractN<4,3>(const vfloat16& v) { return _mm512_extractf32x4_ps(v, 3); }

  template<> __forceinline vfloat8 extractN<8,0>(const vfloat16& v) { return _mm512_castps512_ps256(v);    }
  template<> __forceinline vfloat8 extractN<8,1>(const vfloat16& v) { return _mm512_extractf32x8_ps(v, 1); }

  template<int i> __forceinline vfloat4 extract4   (const vfloat16& v) { return _mm512_extractf32x4_ps(v, i); }
  template<>      __forceinline vfloat4 extract4<0>(const vfloat16& v) { return _mm512_castps512_ps128(v);    }

  template<int i> __forceinline vfloat8 extract8   (const vfloat16& v) { return _mm512_extractf32x8_ps(v, i); }
  template<>      __forceinline vfloat8 extract8<0>(const vfloat16& v) { return _mm512_castps512_ps256(v);    }

  ////////////////////////////////////////////////////////////////////////////////
  /// Transpose
  ////////////////////////////////////////////////////////////////////////////////

  __forceinline void transpose(const vfloat16& r0, const vfloat16& r1, const vfloat16& r2, const vfloat16& r3,
                               vfloat16& c0, vfloat16& c1, vfloat16& c2, vfloat16& c3)
  {
    vfloat16 a0a2_b0b2 = unpacklo(r0, r2);
    vfloat16 c0c2_d0d2 = unpackhi(r0, r2);
    vfloat16 a1a3_b1b3 = unpacklo(r1, r3);
    vfloat16 c1c3_d1d3 = unpackhi(r1, r3);

    c0 = unpacklo(a0a2_b0b2, a1a3_b1b3);
    c1 = unpackhi(a0a2_b0b2, a1a3_b1b3);
    c2 = unpacklo(c0c2_d0d2, c1c3_d1d3);
    c3 = unpackhi(c0c2_d0d2, c1c3_d1d3);
  }

  __forceinline void transpose(const vfloat4& r0,  const vfloat4& r1,  const vfloat4& r2,  const vfloat4& r3,
                               const vfloat4& r4,  const vfloat4& r5,  const vfloat4& r6,  const vfloat4& r7,
                               const vfloat4& r8,  const vfloat4& r9,  const vfloat4& r10, const vfloat4& r11,
                               const vfloat4& r12, const vfloat4& r13, const vfloat4& r14, const vfloat4& r15,
                               vfloat16& c0, vfloat16& c1, vfloat16& c2, vfloat16& c3)
  {
    return transpose(vfloat16(r0, r4, r8, r12), vfloat16(r1, r5, r9, r13), vfloat16(r2, r6, r10, r14), vfloat16(r3, r7, r11, r15),
                     c0, c1, c2, c3);
  }

  __forceinline void transpose(const vfloat16& r0, const vfloat16& r1, const vfloat16& r2, const vfloat16& r3,
                               const vfloat16& r4, const vfloat16& r5, const vfloat16& r6, const vfloat16& r7,
                               vfloat16& c0, vfloat16& c1, vfloat16& c2, vfloat16& c3,
                               vfloat16& c4, vfloat16& c5, vfloat16& c6, vfloat16& c7)
  {
    vfloat16 a0a1a2a3_e0e1e2e3, b0b1b2b3_f0f1f2f3, c0c1c2c3_g0g1g2g3, d0d1d2d3_h0h1h2h3;
    transpose(r0, r1, r2, r3, a0a1a2a3_e0e1e2e3, b0b1b2b3_f0f1f2f3, c0c1c2c3_g0g1g2g3, d0d1d2d3_h0h1h2h3);

    vfloat16 a4a5a6a7_e4e5e6e7, b4b5b6b7_f4f5f6f7, c4c5c6c7_g4g5g6g7, d4d5d6d7_h4h5h6h7;
    transpose(r4, r5, r6, r7, a4a5a6a7_e4e5e6e7, b4b5b6b7_f4f5f6f7, c4c5c6c7_g4g5g6g7, d4d5d6d7_h4h5h6h7);

    c0 = interleave4_even(a0a1a2a3_e0e1e2e3, a4a5a6a7_e4e5e6e7);
    c1 = interleave4_even(b0b1b2b3_f0f1f2f3, b4b5b6b7_f4f5f6f7);
    c2 = interleave4_even(c0c1c2c3_g0g1g2g3, c4c5c6c7_g4g5g6g7);
    c3 = interleave4_even(d0d1d2d3_h0h1h2h3, d4d5d6d7_h4h5h6h7);
    c4 = interleave4_odd (a0a1a2a3_e0e1e2e3, a4a5a6a7_e4e5e6e7);
    c5 = interleave4_odd (b0b1b2b3_f0f1f2f3, b4b5b6b7_f4f5f6f7);
    c6 = interleave4_odd (c0c1c2c3_g0g1g2g3, c4c5c6c7_g4g5g6g7);
    c7 = interleave4_odd (d0d1d2d3_h0h1h2h3, d4d5d6d7_h4h5h6h7);
  }

  __forceinline void transpose(const vfloat8& r0,  const vfloat8& r1,  const vfloat8& r2,  const vfloat8& r3,
                               const vfloat8& r4,  const vfloat8& r5,  const vfloat8& r6,  const vfloat8& r7,
                               const vfloat8& r8,  const vfloat8& r9,  const vfloat8& r10, const vfloat8& r11,
                               const vfloat8& r12, const vfloat8& r13, const vfloat8& r14, const vfloat8& r15,
                               vfloat16& c0, vfloat16& c1, vfloat16& c2, vfloat16& c3,
                               vfloat16& c4, vfloat16& c5, vfloat16& c6, vfloat16& c7)
  {
    return transpose(vfloat16(r0, r8),  vfloat16(r1, r9),  vfloat16(r2, r10), vfloat16(r3, r11),
                     vfloat16(r4, r12), vfloat16(r5, r13), vfloat16(r6, r14), vfloat16(r7, r15),
                     c0, c1, c2, c3, c4, c5, c6, c7);
  }

  ////////////////////////////////////////////////////////////////////////////////
  /// Reductions
  ////////////////////////////////////////////////////////////////////////////////

  __forceinline vfloat16 vreduce_add2(vfloat16 x) {                      return x + shuffle<1,0,3,2>(x); }
  __forceinline vfloat16 vreduce_add4(vfloat16 x) { x = vreduce_add2(x); return x + shuffle<2,3,0,1>(x); }
  __forceinline vfloat16 vreduce_add8(vfloat16 x) { x = vreduce_add4(x); return x + shuffle4<1,0,3,2>(x); }
  __forceinline vfloat16 vreduce_add (vfloat16 x) { x = vreduce_add8(x); return x + shuffle4<2,3,0,1>(x); }

  __forceinline vfloat16 vreduce_min2(vfloat16 x) {                      return min(x, shuffle<1,0,3,2>(x)); }
  __forceinline vfloat16 vreduce_min4(vfloat16 x) { x = vreduce_min2(x); return min(x, shuffle<2,3,0,1>(x)); }
  __forceinline vfloat16 vreduce_min8(vfloat16 x) { x = vreduce_min4(x); return min(x, shuffle4<1,0,3,2>(x)); }
  __forceinline vfloat16 vreduce_min (vfloat16 x) { x = vreduce_min8(x); return min(x, shuffle4<2,3,0,1>(x)); }

  __forceinline vfloat16 vreduce_max2(vfloat16 x) {                      return max(x, shuffle<1,0,3,2>(x)); }
  __forceinline vfloat16 vreduce_max4(vfloat16 x) { x = vreduce_max2(x); return max(x, shuffle<2,3,0,1>(x)); }
  __forceinline vfloat16 vreduce_max8(vfloat16 x) { x = vreduce_max4(x); return max(x, shuffle4<1,0,3,2>(x)); }
  __forceinline vfloat16 vreduce_max (vfloat16 x) { x = vreduce_max8(x); return max(x, shuffle4<2,3,0,1>(x)); }

  __forceinline float reduce_add(const vfloat16& v) { return toScalar(vreduce_add(v)); }
  __forceinline float reduce_min(const vfloat16& v) { return toScalar(vreduce_min(v)); }
  __forceinline float reduce_max(const vfloat16& v) { return toScalar(vreduce_max(v)); }
 
  __forceinline size_t select_min(const vfloat16& v) { 
    return bsf(_mm512_kmov(_mm512_cmp_epi32_mask(_mm512_castps_si512(v),_mm512_castps_si512(vreduce_min(v)),_MM_CMPINT_EQ)));
  }

  __forceinline size_t select_max(const vfloat16& v) { 
    return bsf(_mm512_kmov(_mm512_cmp_epi32_mask(_mm512_castps_si512(v),_mm512_castps_si512(vreduce_max(v)),_MM_CMPINT_EQ)));
  }

  __forceinline size_t select_min(const vboolf16& valid, const vfloat16& v) 
  { 
    const vfloat16 a = select(valid,v,vfloat16(pos_inf)); 
    const vbool16 valid_min = valid & (a == vreduce_min(a));
    return bsf(movemask(any(valid_min) ? valid_min : valid)); 
  }

  __forceinline size_t select_max(const vboolf16& valid, const vfloat16& v) 
  { 
    const vfloat16 a = select(valid,v,vfloat16(neg_inf)); 
    const vbool16 valid_max = valid & (a == vreduce_max(a));
    return bsf(movemask(any(valid_max) ? valid_max : valid)); 
  }
  
  __forceinline vfloat16 prefix_sum(const vfloat16& a) 
  {
    const vfloat16 z(zero);
    vfloat16 v = a;
    v = v + align_shift_right<16-1>(v,z);
    v = v + align_shift_right<16-2>(v,z);
    v = v + align_shift_right<16-4>(v,z);
    v = v + align_shift_right<16-8>(v,z);
    return v;  
  }

  __forceinline vfloat16 reverse_prefix_sum(const vfloat16& a) 
  {
    const vfloat16 z(zero);
    vfloat16 v = a;
    v = v + align_shift_right<1>(z,v);
    v = v + align_shift_right<2>(z,v);
    v = v + align_shift_right<4>(z,v);
    v = v + align_shift_right<8>(z,v);
    return v;  
  }

  __forceinline vfloat16 prefix_min(const vfloat16& a)
  {
    const vfloat16 z(pos_inf);
    vfloat16 v = a;
    v = min(v,align_shift_right<16-1>(v,z));
    v = min(v,align_shift_right<16-2>(v,z));
    v = min(v,align_shift_right<16-4>(v,z));
    v = min(v,align_shift_right<16-8>(v,z));
    return v;  
  }

  __forceinline vfloat16 prefix_max(const vfloat16& a)
  {
    const vfloat16 z(neg_inf);
    vfloat16 v = a;
    v = max(v,align_shift_right<16-1>(v,z));
    v = max(v,align_shift_right<16-2>(v,z));
    v = max(v,align_shift_right<16-4>(v,z));
    v = max(v,align_shift_right<16-8>(v,z));
    return v;  
  }


  __forceinline vfloat16 reverse_prefix_min(const vfloat16& a)
  {
    const vfloat16 z(pos_inf);
    vfloat16 v = a;
    v = min(v,align_shift_right<1>(z,v));
    v = min(v,align_shift_right<2>(z,v));
    v = min(v,align_shift_right<4>(z,v));
    v = min(v,align_shift_right<8>(z,v));
    return v;  
  }

  __forceinline vfloat16 reverse_prefix_max(const vfloat16& a)
  {
    const vfloat16 z(neg_inf);
    vfloat16 v = a;
    v = max(v,align_shift_right<1>(z,v));
    v = max(v,align_shift_right<2>(z,v));
    v = max(v,align_shift_right<4>(z,v));
    v = max(v,align_shift_right<8>(z,v));
    return v;  
  }

  __forceinline vfloat16 rcp_safe(const vfloat16& a) {
    return rcp(select(a != vfloat16(zero), a, vfloat16(min_rcp_input)));
  }

  ////////////////////////////////////////////////////////////////////////////////
  /// Output Operators
  ////////////////////////////////////////////////////////////////////////////////
  
  __forceinline embree_ostream operator <<(embree_ostream cout, const vfloat16& v)
  {
    cout << "<" << v[0];
    for (int i=1; i<16; i++) cout << ", " << v[i];
    cout << ">";
    return cout;
  }
}

#undef vboolf
#undef vboold
#undef vint
#undef vuint
#undef vllong
#undef vfloat
#undef vdouble