text: // Copyright 2009-2021 Intel Corporation
  // SPDX-License-Identifier: Apache-2.0
  
  #pragma once
  
  #include "../sys/alloc.h"
  #include "math.h"
  #include "../simd/sse.h"
  
  namespace embree
  {
    ////////////////////////////////////////////////////////////////////////////////
    /// SSE Vec2fa Type
    ////////////////////////////////////////////////////////////////////////////////
  
    struct __aligned(16) Vec2fa
    {
      ALIGNED_STRUCT_(16);
  
      typedef float Scalar;
      enum { N = 2 };
      union {
        __m128 m128;
        struct { float x,y,az,aw; };
      };
  
      ////////////////////////////////////////////////////////////////////////////////
      /// Constructors, Assignment & Cast Operators
      ////////////////////////////////////////////////////////////////////////////////
  
      __forceinline Vec2fa( ) {}
      __forceinline Vec2fa( const __m128 a ) : m128(a) {}
  
      __forceinline Vec2fa            ( const Vec2<float>& other  ) { x = other.x; y = other.y; }
      __forceinline Vec2fa& operator =( const Vec2<float>& other ) { x = other.x; y = other.y; return *this; }
  
      __forceinline Vec2fa            ( const Vec2fa& other ) { m128 = other.m128; }
      __forceinline Vec2fa& operator =( const Vec2fa& other ) { m128 = other.m128; return *this; }
  
      __forceinline explicit Vec2fa( const float a ) : m128(_mm_set1_ps(a)) {}
      __forceinline          Vec2fa( const float x, const float y) : m128(_mm_set_ps(y, y, y, x)) {}
  
      __forceinline explicit Vec2fa( const __m128i a ) : m128(_mm_cvtepi32_ps(a)) {}
  
      __forceinline operator const __m128&() const { return m128; }
      __forceinline operator       __m128&()       { return m128; }
  
      ////////////////////////////////////////////////////////////////////////////////
      /// Loads and Stores
      ////////////////////////////////////////////////////////////////////////////////
  
      static __forceinline Vec2fa load( const void* const a ) {
        return Vec2fa(_mm_and_ps(_mm_load_ps((float*)a),_mm_castsi128_ps(_mm_set_epi32(0, 0, -1, -1))));
      }
  
      static __forceinline Vec2fa loadu( const void* const a ) {
        return Vec2fa(_mm_and_ps(_mm_loadu_ps((float*)a),_mm_castsi128_ps(_mm_set_epi32(0, 0, -1, -1))));
      }
  
      static __forceinline void storeu ( void* ptr, const Vec2fa& v ) {
        _mm_storeu_ps((float*)ptr,v);
      }
  
      ////////////////////////////////////////////////////////////////////////////////
      /// Constants
      ////////////////////////////////////////////////////////////////////////////////
  
      __forceinline Vec2fa( ZeroTy   ) : m128(_mm_setzero_ps()) {}
      __forceinline Vec2fa( OneTy    ) : m128(_mm_set1_ps(1.0f)) {}
      __forceinline Vec2fa( PosInfTy ) : m128(_mm_set1_ps(pos_inf)) {}
      __forceinline Vec2fa( NegInfTy ) : m128(_mm_set1_ps(neg_inf)) {}
  
      ////////////////////////////////////////////////////////////////////////////////
      /// Array Access
      ////////////////////////////////////////////////////////////////////////////////
  
      __forceinline const float& operator []( const size_t index ) const { assert(index < 2); return (&x)[index]; }
      __forceinline       float& operator []( const size_t index )       { assert(index < 2); return (&x)[index]; }
    };
  
    ////////////////////////////////////////////////////////////////////////////////
    /// Unary Operators
    ////////////////////////////////////////////////////////////////////////////////
  
    __forceinline Vec2fa operator +( const Vec2fa& a ) { return a; }
    __forceinline Vec2fa operator -( const Vec2fa& a ) {
      const __m128 mask = _mm_castsi128_ps(_mm_set1_epi32(0x80000000));
      return _mm_xor_ps(a.m128, mask);
    }
    __forceinline Vec2fa abs  ( const Vec2fa& a ) {
      const __m128 mask = _mm_castsi128_ps(_mm_set1_epi32(0x7fffffff));
      return _mm_and_ps(a.m128, mask);
    }
    __forceinline Vec2fa sign ( const Vec2fa& a ) {
      return blendv_ps(Vec2fa(one), -Vec2fa(one), _mm_cmplt_ps (a,Vec2fa(zero)));
    }
  
    __forceinline Vec2fa rcp  ( const Vec2fa& a )
    {
  #if defined(__AVX512VL__)
      const Vec2fa r = _mm_rcp14_ps(a.m128);
  #else
      const Vec2fa r = _mm_rcp_ps(a.m128);
  #endif
  
  #if defined(__AVX2__)
      const Vec2fa h_n = _mm_fnmadd_ps(a, r, vfloat4(1.0));  // First, compute 1 - a * r (which will be very close to 0)
      const Vec2fa res = _mm_fmadd_ps(r, h_n, r);            // Then compute r + r * h_n
  #else
      const Vec2fa h_n = _mm_sub_ps(vfloat4(1.0f), _mm_mul_ps(a, r));  // First, compute 1 - a * r (which will be very close to 0)
      const Vec2fa res = _mm_add_ps(r,_mm_mul_ps(r, h_n));             // Then compute r + r * h_n  
  #endif
  
      return res;
    }
  
    __forceinline Vec2fa sqrt ( const Vec2fa& a ) { return _mm_sqrt_ps(a.m128); }
    __forceinline Vec2fa sqr  ( const Vec2fa& a ) { return _mm_mul_ps(a,a); }
  
    __forceinline Vec2fa rsqrt( const Vec2fa& a )
    {
  #if defined(__AVX512VL__) && !defined(_MSC_VER)
      __m128 r = _mm_rsqrt14_ps(a.m128);
  #else
      __m128 r = _mm_rsqrt_ps(a.m128);
  #endif
      return _mm_add_ps(_mm_mul_ps(_mm_set1_ps(1.5f),r), _mm_mul_ps(_mm_mul_ps(_mm_mul_ps(a, _mm_set1_ps(-0.5f)), r), _mm_mul_ps(r, r)));
    }
  
    __forceinline Vec2fa zero_fix(const Vec2fa& a) {
      return blendv_ps(a, _mm_set1_ps(min_rcp_input), _mm_cmplt_ps (abs(a).m128, _mm_set1_ps(min_rcp_input)));
    }
    __forceinline Vec2fa rcp_safe(const Vec2fa& a) {
      return rcp(zero_fix(a));
    }
    __forceinline Vec2fa log ( const Vec2fa& a ) {
      return Vec2fa(logf(a.x),logf(a.y));
    }
  
    __forceinline Vec2fa exp ( const Vec2fa& a ) {
      return Vec2fa(expf(a.x),expf(a.y));
    }
  
    ////////////////////////////////////////////////////////////////////////////////
    /// Binary Operators
    ////////////////////////////////////////////////////////////////////////////////
  
    __forceinline Vec2fa operator +( const Vec2fa& a, const Vec2fa& b ) { return _mm_add_ps(a.m128, b.m128); }
    __forceinline Vec2fa operator -( const Vec2fa& a, const Vec2fa& b ) { return _mm_sub_ps(a.m128, b.m128); }
    __forceinline Vec2fa operator *( const Vec2fa& a, const Vec2fa& b ) { return _mm_mul_ps(a.m128, b.m128); }
    __forceinline Vec2fa operator *( const Vec2fa& a, const float b ) { return a * Vec2fa(b); }
    __forceinline Vec2fa operator *( const float a, const Vec2fa& b ) { return Vec2fa(a) * b; }
    __forceinline Vec2fa operator /( const Vec2fa& a, const Vec2fa& b ) { return _mm_div_ps(a.m128,b.m128); }
    __forceinline Vec2fa operator /( const Vec2fa& a, const float b        ) { return _mm_div_ps(a.m128,_mm_set1_ps(b)); }
    __forceinline Vec2fa operator /( const        float a, const Vec2fa& b ) { return _mm_div_ps(_mm_set1_ps(a),b.m128); }
  
    __forceinline Vec2fa min( const Vec2fa& a, const Vec2fa& b ) { return _mm_min_ps(a.m128,b.m128); }
    __forceinline Vec2fa max( const Vec2fa& a, const Vec2fa& b ) { return _mm_max_ps(a.m128,b.m128); }
  
  #if defined(__SSE4_1__)
      __forceinline Vec2fa mini(const Vec2fa& a, const Vec2fa& b) {
        const vint4 ai = _mm_castps_si128(a);
        const vint4 bi = _mm_castps_si128(b);
        const vint4 ci = _mm_min_epi32(ai,bi);
        return _mm_castsi128_ps(ci);
      }
  #endif
  
  #if defined(__SSE4_1__)
      __forceinline Vec2fa maxi(const Vec2fa& a, const Vec2fa& b) {
        const vint4 ai = _mm_castps_si128(a);
        const vint4 bi = _mm_castps_si128(b);
        const vint4 ci = _mm_max_epi32(ai,bi);
        return _mm_castsi128_ps(ci);
      }
  #endif
  
      __forceinline Vec2fa pow ( const Vec2fa& a, const float& b ) {
        return Vec2fa(powf(a.x,b),powf(a.y,b));
      }
  
    ////////////////////////////////////////////////////////////////////////////////
    /// Ternary Operators
    ////////////////////////////////////////////////////////////////////////////////
  
  #if defined(__AVX2__)
    __forceinline Vec2fa madd  ( const Vec2fa& a, const Vec2fa& b, const Vec2fa& c) { return _mm_fmadd_ps(a,b,c); }
    __forceinline Vec2fa msub  ( const Vec2fa& a, const Vec2fa& b, const Vec2fa& c) { return _mm_fmsub_ps(a,b,c); }
    __forceinline Vec2fa nmadd ( const Vec2fa& a, const Vec2fa& b, const Vec2fa& c) { return _mm_fnmadd_ps(a,b,c); }
    __forceinline Vec2fa nmsub ( const Vec2fa& a, const Vec2fa& b, const Vec2fa& c) { return _mm_fnmsub_ps(a,b,c); }
  #else
    __forceinline Vec2fa madd  ( const Vec2fa& a, const Vec2fa& b, const Vec2fa& c) { return a*b+c; }
    __forceinline Vec2fa msub  ( const Vec2fa& a, const Vec2fa& b, const Vec2fa& c) { return a*b-c; }
    __forceinline Vec2fa nmadd ( const Vec2fa& a, const Vec2fa& b, const Vec2fa& c) { return -a*b+c;}
    __forceinline Vec2fa nmsub ( const Vec2fa& a, const Vec2fa& b, const Vec2fa& c) { return -a*b-c; }
  #endif
  
    __forceinline Vec2fa madd  ( const float a, const Vec2fa& b, const Vec2fa& c) { return madd(Vec2fa(a),b,c); }
    __forceinline Vec2fa msub  ( const float a, const Vec2fa& b, const Vec2fa& c) { return msub(Vec2fa(a),b,c); }
    __forceinline Vec2fa nmadd ( const float a, const Vec2fa& b, const Vec2fa& c) { return nmadd(Vec2fa(a),b,c); }
    __forceinline Vec2fa nmsub ( const float a, const Vec2fa& b, const Vec2fa& c) { return nmsub(Vec2fa(a),b,c); }
  
    ////////////////////////////////////////////////////////////////////////////////
    /// Assignment Operators
    ////////////////////////////////////////////////////////////////////////////////
  
    __forceinline Vec2fa& operator +=( Vec2fa& a, const Vec2fa& b ) { return a = a + b; }
    __forceinline Vec2fa& operator -=( Vec2fa& a, const Vec2fa& b ) { return a = a - b; }
    __forceinline Vec2fa& operator *=( Vec2fa& a, const Vec2fa& b ) { return a = a * b; }
    __forceinline Vec2fa& operator *=( Vec2fa& a, const float   b ) { return a = a * b; }
    __forceinline Vec2fa& operator /=( Vec2fa& a, const Vec2fa& b ) { return a = a / b; }
    __forceinline Vec2fa& operator /=( Vec2fa& a, const float   b ) { return a = a / b; }
  
    ////////////////////////////////////////////////////////////////////////////////
    /// Reductions
    ////////////////////////////////////////////////////////////////////////////////
  
    __forceinline float reduce_add(const Vec2fa& v) { return v.x+v.y; }
    __forceinline float reduce_mul(const Vec2fa& v) { return v.x*v.y; }
    __forceinline float reduce_min(const Vec2fa& v) { return min(v.x,v.y); }
    __forceinline float reduce_max(const Vec2fa& v) { return max(v.x,v.y); }
  
    ////////////////////////////////////////////////////////////////////////////////
    /// Comparison Operators
    ////////////////////////////////////////////////////////////////////////////////
  
    __forceinline bool operator ==( const Vec2fa& a, const Vec2fa& b ) { return (_mm_movemask_ps(_mm_cmpeq_ps (a.m128, b.m128)) & 3) == 3; }
    __forceinline bool operator !=( const Vec2fa& a, const Vec2fa& b ) { return (_mm_movemask_ps(_mm_cmpneq_ps(a.m128, b.m128)) & 3) != 0; }
  
    ////////////////////////////////////////////////////////////////////////////////
    /// Euclidian Space Operators
    ////////////////////////////////////////////////////////////////////////////////
  
  #if defined(__SSE4_1__)
    __forceinline float dot ( const Vec2fa& a, const Vec2fa& b ) {
      return _mm_cvtss_f32(_mm_dp_ps(a,b,0x3F));
    }
  #else
    __forceinline float dot ( const Vec2fa& a, const Vec2fa& b ) {
      return reduce_add(a*b);
    }
  #endif
  
    __forceinline Vec2fa cross ( const Vec2fa& a ) {
      return Vec2fa(-a.y,a.x);
    }
  
    __forceinline float  sqr_length ( const Vec2fa& a )                { return dot(a,a); }
    __forceinline float  rcp_length ( const Vec2fa& a )                { return rsqrt(dot(a,a)); }
    __forceinline float  rcp_length2( const Vec2fa& a )                { return rcp(dot(a,a)); }
    __forceinline float  length   ( const Vec2fa& a )                  { return sqrt(dot(a,a)); }
    __forceinline Vec2fa normalize( const Vec2fa& a )                  { return a*rsqrt(dot(a,a)); }
    __forceinline float  distance ( const Vec2fa& a, const Vec2fa& b ) { return length(a-b); }
  
    ////////////////////////////////////////////////////////////////////////////////
    /// Select
    ////////////////////////////////////////////////////////////////////////////////
  
    __forceinline Vec2fa select( bool s, const Vec2fa& t, const Vec2fa& f ) {
      __m128 mask = s ? _mm_castsi128_ps(_mm_cmpeq_epi32(_mm_setzero_si128(), _mm_setzero_si128())) : _mm_setzero_ps();
      return blendv_ps(f, t, mask);
    }
  
    __forceinline Vec2fa lerp(const Vec2fa& v0, const Vec2fa& v1, const float t) {
      return madd(1.0f-t,v0,t*v1);
    }
  
    __forceinline int maxDim ( const Vec2fa& a )
    {
      const Vec2fa b = abs(a);
      if (b.x > b.y) return 0;
      else return 1;
    }
  
    ////////////////////////////////////////////////////////////////////////////////
    /// Rounding Functions
    ////////////////////////////////////////////////////////////////////////////////
  
  #if defined(__aarch64__)
    //__forceinline Vec2fa trunc(const Vec2fa& a) { return vrndq_f32(a); }
    __forceinline Vec2fa floor(const Vec2fa& a) { return vrndmq_f32(a); }
    __forceinline Vec2fa ceil (const Vec2fa& a) { return vrndpq_f32(a); }
  #elif defined (__SSE4_1__)
    //__forceinline Vec2fa trunc( const Vec2fa& a ) { return _mm_round_ps(a, _MM_FROUND_TO_NEAREST_INT); }
    __forceinline Vec2fa floor( const Vec2fa& a ) { return _mm_round_ps(a, _MM_FROUND_TO_NEG_INF    ); }
    __forceinline Vec2fa ceil ( const Vec2fa& a ) { return _mm_round_ps(a, _MM_FROUND_TO_POS_INF    ); }
  #else
    //__forceinline Vec2fa trunc( const Vec2fa& a ) { return Vec2fa(truncf(a.x),truncf(a.y),truncf(a.z)); }
    __forceinline Vec2fa floor( const Vec2fa& a ) { return Vec2fa(floorf(a.x),floorf(a.y)); }
    __forceinline Vec2fa ceil ( const Vec2fa& a ) { return Vec2fa(ceilf (a.x),ceilf (a.y)); }
  #endif
  
    ////////////////////////////////////////////////////////////////////////////////
    /// Output Operators
    ////////////////////////////////////////////////////////////////////////////////
  
    __forceinline embree_ostream operator<<(embree_ostream cout, const Vec2fa& a) {
      return cout << "(" << a.x << ", " << a.y << ")";
    }
  
    typedef Vec2fa Vec2fa_t;
  }
  