path: root/thirdparty/embree-aarch64/kernels/builders/heuristic_binning.h

// Copyright 2009-2020 Intel Corporation
// SPDX-License-Identifier: Apache-2.0

#pragma once

#include "priminfo.h"
#include "../../common/algorithms/parallel_reduce.h"
#include "../../common/algorithms/parallel_partition.h"

namespace embree
{
  namespace isa
  { 
    /*! mapping into bins */
    template<size_t BINS>
      struct BinMapping
      {
      public:
        __forceinline BinMapping() {}
        
        /*! calculates the mapping */
        __forceinline BinMapping(size_t N, const BBox3fa& centBounds) 
        {
          num = min(BINS,size_t(4.0f + 0.05f*N));
          assert(num >= 1);
          const vfloat4 eps = 1E-34f;
          const vfloat4 diag = max(eps, (vfloat4) centBounds.size());
          scale = select(diag > eps,vfloat4(0.99f*num)/diag,vfloat4(0.0f));
          ofs  = (vfloat4) centBounds.lower;
        }

        /*! calculates the mapping */
        __forceinline BinMapping(const BBox3fa& centBounds) 
        {
          num = BINS;
          const vfloat4 eps = 1E-34f;
          const vfloat4 diag = max(eps, (vfloat4) centBounds.size());
          scale = select(diag > eps,vfloat4(0.99f*num)/diag,vfloat4(0.0f));
          ofs  = (vfloat4) centBounds.lower;
        }

        /*! calculates the mapping */
        template<typename PrimInfo>
        __forceinline BinMapping(const PrimInfo& pinfo) 
        {
          const vfloat4 eps = 1E-34f;
          num = min(BINS,size_t(4.0f + 0.05f*pinfo.size()));
          const vfloat4 diag = max(eps,(vfloat4) pinfo.centBounds.size());
          scale = select(diag > eps,vfloat4(0.99f*num)/diag,vfloat4(0.0f));
          ofs  = (vfloat4) pinfo.centBounds.lower;
        }

        /*! returns number of bins */
        __forceinline size_t size() const { return num; }
        
        /*! slower but safe binning */
        __forceinline Vec3ia bin(const Vec3fa& p) const 
        {
          const vint4 i = floori((vfloat4(p)-ofs)*scale);
#if 1
          assert(i[0] >= 0 && (size_t)i[0] < num); 
          assert(i[1] >= 0 && (size_t)i[1] < num);
          assert(i[2] >= 0 && (size_t)i[2] < num);
          return Vec3ia(i);
#else
          return Vec3ia(clamp(i,vint4(0),vint4(num-1)));
#endif
        }

        /*! faster but unsafe binning */
        __forceinline Vec3ia bin_unsafe(const Vec3fa& p) const {
          return Vec3ia(floori((vfloat4(p)-ofs)*scale));
        }

        /*! faster but unsafe binning */
        template<typename PrimRef>
        __forceinline Vec3ia bin_unsafe(const PrimRef& p) const {
          return bin_unsafe(p.binCenter());
        }

        /*! faster but unsafe binning */
        template<typename PrimRef, typename BinBoundsAndCenter>
        __forceinline Vec3ia bin_unsafe(const PrimRef& p, const BinBoundsAndCenter& binBoundsAndCenter) const {
          return bin_unsafe(binBoundsAndCenter.binCenter(p));
        }

        template<typename PrimRef>
        __forceinline bool bin_unsafe(const PrimRef& ref,
                                      const vint4&   vSplitPos,
                                      const vbool4&  splitDimMask) const // FIXME: rename to isLeft
        {
          return any(((vint4)bin_unsafe(center2(ref.bounds())) < vSplitPos) & splitDimMask);
        }
        /*! calculates left spatial position of bin */
        __forceinline float pos(const size_t bin, const size_t dim) const {
          return madd(float(bin),1.0f / scale[dim],ofs[dim]);
        }

        /*! returns true if the mapping is invalid in some dimension */
        __forceinline bool invalid(const size_t dim) const {
          return scale[dim] == 0.0f;
        }
        
        /*! stream output */
        friend embree_ostream operator<<(embree_ostream cout, const BinMapping& mapping) {
          return cout << "BinMapping { num = " << mapping.num << ", ofs = " << mapping.ofs << ", scale = " << mapping.scale << "}";
        }
        
      public:
        size_t num;
        vfloat4 ofs,scale;        //!< linear function that maps to bin ID
      };
    
    /*! stores all information to perform some split */
    template<size_t BINS>
      struct BinSplit
      {
        enum
        {
          SPLIT_OBJECT   = 0,
          SPLIT_FALLBACK = 1,
          SPLIT_ENFORCE  = 2, // splits with larger ID are enforced in createLargeLeaf even if we could create a leaf already
          SPLIT_TEMPORAL = 2,
          SPLIT_GEOMID   = 3,
        };

        /*! construct an invalid split by default */
        __forceinline BinSplit()
          : sah(inf), dim(-1), pos(0), data(0) {}

        __forceinline BinSplit(float sah, unsigned data, int dim = 0, float fpos = 0)
          : sah(sah), dim(dim), fpos(fpos), data(data) {}
        
        /*! constructs specified split */
        __forceinline BinSplit(float sah, int dim, int pos, const BinMapping<BINS>& mapping)
          : sah(sah), dim(dim), pos(pos), data(0), mapping(mapping) {}
        
        /*! tests if this split is valid */
        __forceinline bool valid() const { return dim != -1; }
        
        /*! calculates surface area heuristic for performing the split */
        __forceinline float splitSAH() const { return sah; }
        
        /*! stream output */
        friend embree_ostream operator<<(embree_ostream cout, const BinSplit& split) {
          return cout << "BinSplit { sah = " << split.sah << ", dim = " << split.dim << ", pos = " << split.pos << "}";
        }
        
      public:
        float sah;                //!< SAH cost of the split
        int dim;                  //!< split dimension
        union { int pos; float fpos; };                  //!< bin index for splitting
        unsigned int data;        //!< extra optional split data
        BinMapping<BINS> mapping; //!< mapping into bins
      };
    
    /*! stores extended information about the split */
    template<typename BBox>
      struct SplitInfoT
    {

      __forceinline SplitInfoT () {}
      
      __forceinline SplitInfoT (size_t leftCount, const BBox& leftBounds, size_t rightCount, const BBox& rightBounds)
	: leftCount(leftCount), rightCount(rightCount), leftBounds(leftBounds), rightBounds(rightBounds) {}
      
    public:
      size_t leftCount,rightCount;
      BBox leftBounds,rightBounds;
    };

    typedef SplitInfoT<BBox3fa> SplitInfo;
    typedef SplitInfoT<LBBox3fa> SplitInfo2;
    
    /*! stores all binning information */
    template<size_t BINS, typename PrimRef, typename BBox>
      struct __aligned(64) BinInfoT
    {		  
      typedef BinSplit<BINS> Split;
      typedef vbool4 vbool;
      typedef vint4 vint;
      typedef vfloat4 vfloat;
      
      __forceinline BinInfoT() {
      }
      
      __forceinline BinInfoT(EmptyTy) {
	clear();
      }

      /*! bin access function */
      __forceinline BBox &bounds(const size_t binID, const size_t dimID)             { return _bounds[binID][dimID]; }
      __forceinline const BBox &bounds(const size_t binID, const size_t dimID) const { return _bounds[binID][dimID]; }

      __forceinline unsigned int &counts(const size_t binID, const size_t dimID)             { return _counts[binID][dimID]; }
      __forceinline const unsigned int &counts(const size_t binID, const size_t dimID) const { return _counts[binID][dimID]; }

      __forceinline vuint4 &counts(const size_t binID)             { return _counts[binID]; }
      __forceinline const vuint4 &counts(const size_t binID) const { return _counts[binID]; }

      /*! clears the bin info */
      __forceinline void clear() 
      {
	for (size_t i=0; i<BINS; i++) {
	  bounds(i,0) = bounds(i,1) = bounds(i,2) = empty;
	  counts(i) = vuint4(zero);
	}
      }
      
      /*! bins an array of primitives */
      __forceinline void bin (const PrimRef* prims, size_t N, const BinMapping<BINS>& mapping)
      {
	if (unlikely(N == 0)) return;
	size_t i; 
	for (i=0; i<N-1; i+=2)
        {
          /*! map even and odd primitive to bin */
          BBox prim0; Vec3fa center0;
          prims[i+0].binBoundsAndCenter(prim0,center0); 
          const vint4 bin0 = (vint4)mapping.bin(center0); 
          
          BBox prim1; Vec3fa center1;
          prims[i+1].binBoundsAndCenter(prim1,center1); 
          const vint4 bin1 = (vint4)mapping.bin(center1); 
          
          /*! increase bounds for bins for even primitive */
          const unsigned int b00 = extract<0>(bin0); bounds(b00,0).extend(prim0); 
          const unsigned int b01 = extract<1>(bin0); bounds(b01,1).extend(prim0); 
          const unsigned int b02 = extract<2>(bin0); bounds(b02,2).extend(prim0); 
          const unsigned int s0 = (unsigned int)prims[i+0].size();
          counts(b00,0)+=s0;
          counts(b01,1)+=s0;
          counts(b02,2)+=s0;

          /*! increase bounds of bins for odd primitive */
          const unsigned int b10 = extract<0>(bin1);  bounds(b10,0).extend(prim1); 
          const unsigned int b11 = extract<1>(bin1);  bounds(b11,1).extend(prim1); 
          const unsigned int b12 = extract<2>(bin1);  bounds(b12,2).extend(prim1); 
          const unsigned int s1 = (unsigned int)prims[i+1].size();
          counts(b10,0)+=s1;
          counts(b11,1)+=s1;
          counts(b12,2)+=s1;
        }
	/*! for uneven number of primitives */
	if (i < N)
        {
          /*! map primitive to bin */
          BBox prim0; Vec3fa center0;
          prims[i].binBoundsAndCenter(prim0,center0); 
          const vint4 bin0 = (vint4)mapping.bin(center0); 
          
          /*! increase bounds of bins */
          const unsigned int s0 = (unsigned int)prims[i].size();
          const int b00 = extract<0>(bin0); counts(b00,0)+=s0; bounds(b00,0).extend(prim0);
          const int b01 = extract<1>(bin0); counts(b01,1)+=s0; bounds(b01,1).extend(prim0);
          const int b02 = extract<2>(bin0); counts(b02,2)+=s0; bounds(b02,2).extend(prim0);
        }
      }

      /*! bins an array of primitives */
      template<typename BinBoundsAndCenter>
        __forceinline void bin (const PrimRef* prims, size_t N, const BinMapping<BINS>& mapping, const BinBoundsAndCenter& binBoundsAndCenter)
      {
	if (N == 0) return;
        
	size_t i; 
	for (i=0; i<N-1; i+=2)
        {
          /*! map even and odd primitive to bin */
          BBox prim0; Vec3fa center0; binBoundsAndCenter.binBoundsAndCenter(prims[i+0],prim0,center0); 
          const vint4 bin0 = (vint4)mapping.bin(center0); 
          BBox prim1; Vec3fa center1; binBoundsAndCenter.binBoundsAndCenter(prims[i+1],prim1,center1); 
          const vint4 bin1 = (vint4)mapping.bin(center1); 
          
          /*! increase bounds for bins for even primitive */
          const unsigned int s0 = prims[i+0].size();
          const int b00 = extract<0>(bin0); counts(b00,0)+=s0; bounds(b00,0).extend(prim0);
          const int b01 = extract<1>(bin0); counts(b01,1)+=s0; bounds(b01,1).extend(prim0);
          const int b02 = extract<2>(bin0); counts(b02,2)+=s0; bounds(b02,2).extend(prim0);
          
          /*! increase bounds of bins for odd primitive */
          const unsigned int s1 = prims[i+1].size();
          const int b10 = extract<0>(bin1); counts(b10,0)+=s1; bounds(b10,0).extend(prim1);
          const int b11 = extract<1>(bin1); counts(b11,1)+=s1; bounds(b11,1).extend(prim1);
          const int b12 = extract<2>(bin1); counts(b12,2)+=s1; bounds(b12,2).extend(prim1);
        }
	
	/*! for uneven number of primitives */
	if (i < N)
        {
          /*! map primitive to bin */
          BBox prim0; Vec3fa center0; binBoundsAndCenter.binBoundsAndCenter(prims[i+0],prim0,center0); 
          const vint4 bin0 = (vint4)mapping.bin(center0); 
          
          /*! increase bounds of bins */
          const unsigned int s0 = prims[i+0].size();
          const int b00 = extract<0>(bin0); counts(b00,0)+=s0; bounds(b00,0).extend(prim0);
          const int b01 = extract<1>(bin0); counts(b01,1)+=s0; bounds(b01,1).extend(prim0);
          const int b02 = extract<2>(bin0); counts(b02,2)+=s0; bounds(b02,2).extend(prim0);
        }
      }
      
      __forceinline void bin(const PrimRef* prims, size_t begin, size_t end, const BinMapping<BINS>& mapping) {
	bin(prims+begin,end-begin,mapping);
      }

      template<typename BinBoundsAndCenter>
        __forceinline void bin(const PrimRef* prims, size_t begin, size_t end, const BinMapping<BINS>& mapping, const BinBoundsAndCenter& binBoundsAndCenter) {
	bin<BinBoundsAndCenter>(prims+begin,end-begin,mapping,binBoundsAndCenter);
      }

      /*! merges in other binning information */
      __forceinline void merge (const BinInfoT& other, size_t numBins)
      {
		
	for (size_t i=0; i<numBins; i++) 
        {
          counts(i) += other.counts(i);
          bounds(i,0).extend(other.bounds(i,0));
          bounds(i,1).extend(other.bounds(i,1));
          bounds(i,2).extend(other.bounds(i,2));
        }
      }

      /*! reduces binning information */
      static __forceinline const BinInfoT reduce (const BinInfoT& a, const BinInfoT& b, const size_t numBins = BINS)
      {
        BinInfoT c;
	for (size_t i=0; i<numBins; i++) 
        {
          c.counts(i) = a.counts(i)+b.counts(i);
          c.bounds(i,0) = embree::merge(a.bounds(i,0),b.bounds(i,0));
          c.bounds(i,1) = embree::merge(a.bounds(i,1),b.bounds(i,1));
          c.bounds(i,2) = embree::merge(a.bounds(i,2),b.bounds(i,2));
        }
        return c;
      }
      
      /*! finds the best split by scanning binning information */
      __forceinline Split best(const BinMapping<BINS>& mapping, const size_t blocks_shift) const
      {
	/* sweep from right to left and compute parallel prefix of merged bounds */
	vfloat4 rAreas[BINS];
	vuint4 rCounts[BINS];
	vuint4 count = 0; BBox bx = empty; BBox by = empty; BBox bz = empty;
	for (size_t i=mapping.size()-1; i>0; i--)
        {
          count += counts(i);
          rCounts[i] = count;
          bx.extend(bounds(i,0)); rAreas[i][0] = expectedApproxHalfArea(bx);
          by.extend(bounds(i,1)); rAreas[i][1] = expectedApproxHalfArea(by);
          bz.extend(bounds(i,2)); rAreas[i][2] = expectedApproxHalfArea(bz);
          rAreas[i][3] = 0.0f;
        }
	/* sweep from left to right and compute SAH */
	vuint4 blocks_add = (1 << blocks_shift)-1;
	vuint4 ii = 1; vfloat4 vbestSAH = pos_inf; vuint4 vbestPos = 0; 
	count = 0; bx = empty; by = empty; bz = empty;
	for (size_t i=1; i<mapping.size(); i++, ii+=1)
        {
          count += counts(i-1);
          bx.extend(bounds(i-1,0)); float Ax = expectedApproxHalfArea(bx);
          by.extend(bounds(i-1,1)); float Ay = expectedApproxHalfArea(by);
          bz.extend(bounds(i-1,2)); float Az = expectedApproxHalfArea(bz);
          const vfloat4 lArea = vfloat4(Ax,Ay,Az,Az);
          const vfloat4 rArea = rAreas[i];
          const vuint4 lCount = (count     +blocks_add) >> (unsigned int)(blocks_shift); // if blocks_shift >=1 then lCount < 4B and could be represented with an vint4, which would allow for faster vfloat4 conversions.
          const vuint4 rCount = (rCounts[i]+blocks_add) >> (unsigned int)(blocks_shift);
          const vfloat4 sah = madd(lArea,vfloat4(lCount),rArea*vfloat4(rCount));
          //const vfloat4 sah = madd(lArea,vfloat4(vint4(lCount)),rArea*vfloat4(vint4(rCount)));

          vbestPos = select(sah < vbestSAH,ii ,vbestPos);
          vbestSAH = select(sah < vbestSAH,sah,vbestSAH);
        }
	
	/* find best dimension */
	float bestSAH = inf;
	int   bestDim = -1;
	int   bestPos = 0;
	for (int dim=0; dim<3; dim++) 
        {
          /* ignore zero sized dimensions */
          if (unlikely(mapping.invalid(dim)))
            continue;
          
          /* test if this is a better dimension */
          if (vbestSAH[dim] < bestSAH && vbestPos[dim] != 0) {
            bestDim = dim;
            bestPos = vbestPos[dim];
            bestSAH = vbestSAH[dim];
          }
        }
	return Split(bestSAH,bestDim,bestPos,mapping);
      }
      
      /*! calculates extended split information */
      __forceinline void getSplitInfo(const BinMapping<BINS>& mapping, const Split& split, SplitInfoT<BBox>& info) const 
      {
	if (split.dim == -1) {
	  new (&info) SplitInfoT<BBox>(0,empty,0,empty);
	  return;
	}
	
	size_t leftCount = 0;
	BBox leftBounds = empty;
	for (size_t i=0; i<(size_t)split.pos; i++) {
	  leftCount += counts(i,split.dim);
	  leftBounds.extend(bounds(i,split.dim));
	}
	size_t rightCount = 0;
	BBox rightBounds = empty;
	for (size_t i=split.pos; i<mapping.size(); i++) {
	  rightCount += counts(i,split.dim);
	  rightBounds.extend(bounds(i,split.dim));
	}
	new (&info) SplitInfoT<BBox>(leftCount,leftBounds,rightCount,rightBounds);
      }

      /*! gets the number of primitives left of the split */
      __forceinline size_t getLeftCount(const BinMapping<BINS>& mapping, const Split& split) const
      {
        if (unlikely(split.dim == -1)) return -1;

        size_t leftCount = 0;
        for (size_t i = 0; i < (size_t)split.pos; i++) {
          leftCount += counts(i, split.dim);
        }
        return leftCount;
      }

      /*! gets the number of primitives right of the split */
      __forceinline size_t getRightCount(const BinMapping<BINS>& mapping, const Split& split) const
      {
        if (unlikely(split.dim == -1)) return -1;

        size_t rightCount = 0;
        for (size_t i = (size_t)split.pos; i<mapping.size(); i++) {
          rightCount += counts(i, split.dim);
        }
        return rightCount;
      }

    private:
      BBox _bounds[BINS][3]; //!< geometry bounds for each bin in each dimension
      vuint4   _counts[BINS];    //!< counts number of primitives that map into the bins
    };

#if defined(__AVX512ER__) // KNL

   /*! mapping into bins */
   template<>
     struct BinMapping<16>
   {
   public:
     __forceinline BinMapping() {}
      
     /*! calculates the mapping */
     template<typename PrimInfo>
     __forceinline BinMapping(const PrimInfo& pinfo)
     {
       num = 16;
       const vfloat4 eps = 1E-34f;
       const vfloat4 diag = max(eps,(vfloat4) pinfo.centBounds.size());
       scale = select(diag > eps,vfloat4(0.99f*num)/diag,vfloat4(0.0f));
       ofs  = (vfloat4) pinfo.centBounds.lower;
       scale16 = scale;
       ofs16 = ofs;
     }

     /*! returns number of bins */
     __forceinline size_t size() const { return num; }

     __forceinline vint16 bin16(const Vec3fa& p) const {
       return vint16(vint4(floori((vfloat4(p)-ofs)*scale)));
     }

     __forceinline vint16 bin16(const vfloat16& p) const {
       return floori((p-ofs16)*scale16);
     }

     __forceinline int bin_unsafe(const PrimRef& ref,
                                  const vint16&  vSplitPos,
                                  const vbool16& splitDimMask) const // FIXME: rename to isLeft
     {
       const vfloat16 lower(*(vfloat4*)&ref.lower);
       const vfloat16 upper(*(vfloat4*)&ref.upper);
       const vfloat16 p = lower + upper;
       const vint16 i = floori((p-ofs16)*scale16);
       return lt(splitDimMask,i,vSplitPos);
     }

     /*! returns true if the mapping is invalid in some dimension */
     __forceinline bool invalid(const size_t dim) const {
       return scale[dim] == 0.0f;
     }
        
    public:
      size_t num;
      vfloat4 ofs,scale;         //!< linear function that maps to bin ID
      vfloat16 ofs16,scale16;    //!< linear function that maps to bin ID
    };

    /* 16 bins in-register binner */
    template<typename PrimRef>
      struct __aligned(64) BinInfoT<16,PrimRef,BBox3fa>
    {
      typedef BinSplit<16> Split;
      typedef vbool16 vbool;
      typedef vint16 vint;
      typedef vfloat16 vfloat;
      
      __forceinline BinInfoT() {
      }
      
      __forceinline BinInfoT(EmptyTy) {
	clear();
      }
      
      /*! clears the bin info */
      __forceinline void clear() 
      {
        lower[0] = lower[1] = lower[2] = pos_inf;
        upper[0] = upper[1] = upper[2] = neg_inf;
        count[0] = count[1] = count[2] = 0;
      }


      static __forceinline vfloat16 prefix_area_rl(const vfloat16 min_x,
                                                   const vfloat16 min_y,
                                                   const vfloat16 min_z,
                                                   const vfloat16 max_x,
                                                   const vfloat16 max_y,
                                                   const vfloat16 max_z)
      {
        const vfloat16 r_min_x = reverse_prefix_min(min_x);
        const vfloat16 r_min_y = reverse_prefix_min(min_y);
        const vfloat16 r_min_z = reverse_prefix_min(min_z);
        const vfloat16 r_max_x = reverse_prefix_max(max_x);
        const vfloat16 r_max_y = reverse_prefix_max(max_y);
        const vfloat16 r_max_z = reverse_prefix_max(max_z);
        const vfloat16 dx = r_max_x - r_min_x;
        const vfloat16 dy = r_max_y - r_min_y;
        const vfloat16 dz = r_max_z - r_min_z;
        const vfloat16 area_rl = madd(dx,dy,madd(dx,dz,dy*dz));
        return area_rl;
      }

      static __forceinline vfloat16 prefix_area_lr(const vfloat16 min_x,
                                                   const vfloat16 min_y,
                                                   const vfloat16 min_z,
                                                   const vfloat16 max_x,
                                                   const vfloat16 max_y,
                                                   const vfloat16 max_z)
      {
        const vfloat16 r_min_x = prefix_min(min_x);
        const vfloat16 r_min_y = prefix_min(min_y);
        const vfloat16 r_min_z = prefix_min(min_z);
        const vfloat16 r_max_x = prefix_max(max_x);
        const vfloat16 r_max_y = prefix_max(max_y);
        const vfloat16 r_max_z = prefix_max(max_z);
        const vfloat16 dx = r_max_x - r_min_x;
        const vfloat16 dy = r_max_y - r_min_y;
        const vfloat16 dz = r_max_z - r_min_z;
        const vfloat16 area_lr = madd(dx,dy,madd(dx,dz,dy*dz));
        return area_lr;
      }


      /*! bins an array of primitives */
      __forceinline void bin (const PrimRef* prims, size_t N, const BinMapping<16>& mapping)
      {
        if (unlikely(N == 0)) return;

        const vfloat16 init_min(pos_inf);
        const vfloat16 init_max(neg_inf);

        vfloat16 min_x0,min_x1,min_x2;
        vfloat16 min_y0,min_y1,min_y2;
        vfloat16 min_z0,min_z1,min_z2;
        vfloat16 max_x0,max_x1,max_x2;
        vfloat16 max_y0,max_y1,max_y2;
        vfloat16 max_z0,max_z1,max_z2;
        vuint16 count0,count1,count2;

        min_x0 = init_min;
        min_x1 = init_min;
        min_x2 = init_min;
        min_y0 = init_min;
        min_y1 = init_min;
        min_y2 = init_min;
        min_z0 = init_min;
        min_z1 = init_min;
        min_z2 = init_min;

        max_x0 = init_max;
        max_x1 = init_max;
        max_x2 = init_max;
        max_y0 = init_max;
        max_y1 = init_max;
        max_y2 = init_max;
        max_z0 = init_max;
        max_z1 = init_max;
        max_z2 = init_max;

        count0 = zero;
        count1 = zero;
        count2 = zero;

        const vint16 step16(step);
        size_t i;
	for (i=0; i<N-1; i+=2)
        {
          /*! map even and odd primitive to bin */
          const BBox3fa primA = prims[i+0].bounds();
          const vfloat16 centerA = vfloat16((vfloat4)primA.lower) + vfloat16((vfloat4)primA.upper);
          const vint16 binA = mapping.bin16(centerA);

          const BBox3fa primB = prims[i+1].bounds();
          const vfloat16 centerB = vfloat16((vfloat4)primB.lower) + vfloat16((vfloat4)primB.upper); 
          const vint16 binB = mapping.bin16(centerB);

          /* A */
          {
            const vfloat16 b_min_x = prims[i+0].lower.x;
            const vfloat16 b_min_y = prims[i+0].lower.y;
            const vfloat16 b_min_z = prims[i+0].lower.z;
            const vfloat16 b_max_x = prims[i+0].upper.x;
            const vfloat16 b_max_y = prims[i+0].upper.y;
            const vfloat16 b_max_z = prims[i+0].upper.z;

            const vint16 bin0 = shuffle<0>(binA);
            const vint16 bin1 = shuffle<1>(binA);
            const vint16 bin2 = shuffle<2>(binA);

            const vbool16 m_update_x = step16 == bin0;
            const vbool16 m_update_y = step16 == bin1;
            const vbool16 m_update_z = step16 == bin2;

            assert(popcnt((size_t)m_update_x) == 1);
            assert(popcnt((size_t)m_update_y) == 1);
            assert(popcnt((size_t)m_update_z) == 1);

            min_x0 = mask_min(m_update_x,min_x0,min_x0,b_min_x);
            min_y0 = mask_min(m_update_x,min_y0,min_y0,b_min_y);
            min_z0 = mask_min(m_update_x,min_z0,min_z0,b_min_z);
            // ------------------------------------------------------------------------      
            max_x0 = mask_max(m_update_x,max_x0,max_x0,b_max_x);
            max_y0 = mask_max(m_update_x,max_y0,max_y0,b_max_y);
            max_z0 = mask_max(m_update_x,max_z0,max_z0,b_max_z);
            // ------------------------------------------------------------------------
            min_x1 = mask_min(m_update_y,min_x1,min_x1,b_min_x);
            min_y1 = mask_min(m_update_y,min_y1,min_y1,b_min_y);
            min_z1 = mask_min(m_update_y,min_z1,min_z1,b_min_z);      
            // ------------------------------------------------------------------------      
            max_x1 = mask_max(m_update_y,max_x1,max_x1,b_max_x);
            max_y1 = mask_max(m_update_y,max_y1,max_y1,b_max_y);
            max_z1 = mask_max(m_update_y,max_z1,max_z1,b_max_z);
            // ------------------------------------------------------------------------
            min_x2 = mask_min(m_update_z,min_x2,min_x2,b_min_x);
            min_y2 = mask_min(m_update_z,min_y2,min_y2,b_min_y);
            min_z2 = mask_min(m_update_z,min_z2,min_z2,b_min_z);
            // ------------------------------------------------------------------------      
            max_x2 = mask_max(m_update_z,max_x2,max_x2,b_max_x);
            max_y2 = mask_max(m_update_z,max_y2,max_y2,b_max_y);
            max_z2 = mask_max(m_update_z,max_z2,max_z2,b_max_z);
            // ------------------------------------------------------------------------
            count0 = mask_add(m_update_x,count0,count0,vuint16(1));
            count1 = mask_add(m_update_y,count1,count1,vuint16(1));
            count2 = mask_add(m_update_z,count2,count2,vuint16(1));      
          }


          /* B */
          {
            const vfloat16 b_min_x = prims[i+1].lower.x;
            const vfloat16 b_min_y = prims[i+1].lower.y;
            const vfloat16 b_min_z = prims[i+1].lower.z;
            const vfloat16 b_max_x = prims[i+1].upper.x;
            const vfloat16 b_max_y = prims[i+1].upper.y;
            const vfloat16 b_max_z = prims[i+1].upper.z;

            const vint16 bin0 = shuffle<0>(binB);
            const vint16 bin1 = shuffle<1>(binB);
            const vint16 bin2 = shuffle<2>(binB);

            const vbool16 m_update_x = step16 == bin0;
            const vbool16 m_update_y = step16 == bin1;
            const vbool16 m_update_z = step16 == bin2;

            assert(popcnt((size_t)m_update_x) == 1);
            assert(popcnt((size_t)m_update_y) == 1);
            assert(popcnt((size_t)m_update_z) == 1);

            min_x0 = mask_min(m_update_x,min_x0,min_x0,b_min_x);
            min_y0 = mask_min(m_update_x,min_y0,min_y0,b_min_y);
            min_z0 = mask_min(m_update_x,min_z0,min_z0,b_min_z);
            // ------------------------------------------------------------------------      
            max_x0 = mask_max(m_update_x,max_x0,max_x0,b_max_x);
            max_y0 = mask_max(m_update_x,max_y0,max_y0,b_max_y);
            max_z0 = mask_max(m_update_x,max_z0,max_z0,b_max_z);
            // ------------------------------------------------------------------------
            min_x1 = mask_min(m_update_y,min_x1,min_x1,b_min_x);
            min_y1 = mask_min(m_update_y,min_y1,min_y1,b_min_y);
            min_z1 = mask_min(m_update_y,min_z1,min_z1,b_min_z);      
            // ------------------------------------------------------------------------      
            max_x1 = mask_max(m_update_y,max_x1,max_x1,b_max_x);
            max_y1 = mask_max(m_update_y,max_y1,max_y1,b_max_y);
            max_z1 = mask_max(m_update_y,max_z1,max_z1,b_max_z);
            // ------------------------------------------------------------------------
            min_x2 = mask_min(m_update_z,min_x2,min_x2,b_min_x);
            min_y2 = mask_min(m_update_z,min_y2,min_y2,b_min_y);
            min_z2 = mask_min(m_update_z,min_z2,min_z2,b_min_z);
            // ------------------------------------------------------------------------      
            max_x2 = mask_max(m_update_z,max_x2,max_x2,b_max_x);
            max_y2 = mask_max(m_update_z,max_y2,max_y2,b_max_y);
            max_z2 = mask_max(m_update_z,max_z2,max_z2,b_max_z);
            // ------------------------------------------------------------------------
            count0 = mask_add(m_update_x,count0,count0,vuint16(1));
            count1 = mask_add(m_update_y,count1,count1,vuint16(1));
            count2 = mask_add(m_update_z,count2,count2,vuint16(1));      
          }

        }

        if (i < N)
        {
          const BBox3fa prim0 = prims[i].bounds();
          const vfloat16 center0 = vfloat16((vfloat4)prim0.lower) + vfloat16((vfloat4)prim0.upper); 
          const vint16 bin = mapping.bin16(center0);

          const vfloat16 b_min_x = prims[i].lower.x;
          const vfloat16 b_min_y = prims[i].lower.y;
          const vfloat16 b_min_z = prims[i].lower.z;
          const vfloat16 b_max_x = prims[i].upper.x;
          const vfloat16 b_max_y = prims[i].upper.y;
          const vfloat16 b_max_z = prims[i].upper.z;

          const vint16 bin0 = shuffle<0>(bin);
          const vint16 bin1 = shuffle<1>(bin);
          const vint16 bin2 = shuffle<2>(bin);

          const vbool16 m_update_x = step16 == bin0;
          const vbool16 m_update_y = step16 == bin1;
          const vbool16 m_update_z = step16 == bin2;

          assert(popcnt((size_t)m_update_x) == 1);
          assert(popcnt((size_t)m_update_y) == 1);
          assert(popcnt((size_t)m_update_z) == 1);

          min_x0 = mask_min(m_update_x,min_x0,min_x0,b_min_x);
          min_y0 = mask_min(m_update_x,min_y0,min_y0,b_min_y);
          min_z0 = mask_min(m_update_x,min_z0,min_z0,b_min_z);
          // ------------------------------------------------------------------------      
          max_x0 = mask_max(m_update_x,max_x0,max_x0,b_max_x);
          max_y0 = mask_max(m_update_x,max_y0,max_y0,b_max_y);
          max_z0 = mask_max(m_update_x,max_z0,max_z0,b_max_z);
          // ------------------------------------------------------------------------
          min_x1 = mask_min(m_update_y,min_x1,min_x1,b_min_x);
          min_y1 = mask_min(m_update_y,min_y1,min_y1,b_min_y);
          min_z1 = mask_min(m_update_y,min_z1,min_z1,b_min_z);      
          // ------------------------------------------------------------------------      
          max_x1 = mask_max(m_update_y,max_x1,max_x1,b_max_x);
          max_y1 = mask_max(m_update_y,max_y1,max_y1,b_max_y);
          max_z1 = mask_max(m_update_y,max_z1,max_z1,b_max_z);
          // ------------------------------------------------------------------------
          min_x2 = mask_min(m_update_z,min_x2,min_x2,b_min_x);
          min_y2 = mask_min(m_update_z,min_y2,min_y2,b_min_y);
          min_z2 = mask_min(m_update_z,min_z2,min_z2,b_min_z);
          // ------------------------------------------------------------------------      
          max_x2 = mask_max(m_update_z,max_x2,max_x2,b_max_x);
          max_y2 = mask_max(m_update_z,max_y2,max_y2,b_max_y);
          max_z2 = mask_max(m_update_z,max_z2,max_z2,b_max_z);
          // ------------------------------------------------------------------------
          count0 = mask_add(m_update_x,count0,count0,vuint16(1));
          count1 = mask_add(m_update_y,count1,count1,vuint16(1));
          count2 = mask_add(m_update_z,count2,count2,vuint16(1));      
        }

        lower[0] = Vec3vf16( min_x0, min_y0, min_z0 );
        lower[1] = Vec3vf16( min_x1, min_y1, min_z1 );
        lower[2] = Vec3vf16( min_x2, min_y2, min_z2 );

        upper[0] = Vec3vf16( max_x0, max_y0, max_z0 );
        upper[1] = Vec3vf16( max_x1, max_y1, max_z1 );
        upper[2] = Vec3vf16( max_x2, max_y2, max_z2 );

        count[0] = count0;
        count[1] = count1;
        count[2] = count2;
      }

      __forceinline void bin(const PrimRef* prims, size_t begin, size_t end, const BinMapping<16>& mapping) {
	bin(prims+begin,end-begin,mapping);
      }

      /*! merges in other binning information */
      __forceinline void merge (const BinInfoT& other, size_t numBins)
      {
        for (size_t i=0; i<3; i++)
        {
          lower[i]  = min(lower[i],other.lower[i]);
          upper[i]  = max(upper[i],other.upper[i]);
          count[i] += other.count[i];
        }
      }

      /*! reducesr binning information */
      static __forceinline const BinInfoT reduce (const BinInfoT& a, const BinInfoT& b)
      {
        BinInfoT c;
	for (size_t i=0; i<3; i++) 
        {
          c.counts[i] = a.counts[i] + b.counts[i];
          c.lower[i]  = min(a.lower[i],b.lower[i]);
          c.upper[i]  = max(a.upper[i],b.upper[i]);
        }
        return c;
      }

      /*! finds the best split by scanning binning information */
      __forceinline Split best(const BinMapping<16>& mapping, const size_t blocks_shift) const
      {
	/* find best dimension */
	float bestSAH = inf;
	int   bestDim = -1;
	int   bestPos = 0;
	const vuint16 blocks_add = (1 << blocks_shift)-1;
        const vfloat16 inf(pos_inf);
	for (size_t dim=0; dim<3; dim++) 
        {
          /* ignore zero sized dimensions */
          if (unlikely(mapping.invalid(dim)))
            continue;

          const vfloat16 rArea16 = prefix_area_rl(lower[dim].x,lower[dim].y,lower[dim].z, upper[dim].x,upper[dim].y,upper[dim].z);
          const vfloat16 lArea16 = prefix_area_lr(lower[dim].x,lower[dim].y,lower[dim].z, upper[dim].x,upper[dim].y,upper[dim].z);
          const vuint16  lCount16 = prefix_sum(count[dim]);
          const vuint16  rCount16 = reverse_prefix_sum(count[dim]); 

          /* compute best split in this dimension */
          const vfloat16 leftArea  = lArea16;
          const vfloat16 rightArea = align_shift_right<1>(zero,rArea16);
          const vuint16 lC = lCount16;
          const vuint16 rC = align_shift_right<1>(zero,rCount16);
          const vuint16 leftCount  = ( lC + blocks_add) >> blocks_shift;
          const vuint16 rightCount = ( rC + blocks_add) >> blocks_shift;
          const vbool16 valid = (leftArea < inf) & (rightArea < inf) & vbool16(0x7fff); // handles inf entries
          const vfloat16 sah = select(valid,madd(leftArea,vfloat16(leftCount),rightArea*vfloat16(rightCount)),vfloat16(pos_inf));
          /* test if this is a better dimension */
          if (any(sah < vfloat16(bestSAH))) 
          {
            const size_t index = select_min(sah);            
            assert(index < 15);
            assert(sah[index] < bestSAH);
            bestDim = dim;
            bestPos = index+1;
            bestSAH = sah[index];
          }
        }
	
	return Split(bestSAH,bestDim,bestPos,mapping);

      }

      /*! calculates extended split information */
      __forceinline void getSplitInfo(const BinMapping<16>& mapping, const Split& split, SplitInfo& info) const 
      {
	if (split.dim == -1) {
	  new (&info) SplitInfo(0,empty,0,empty);
	  return;
	}
	// FIXME: horizontal reduction!

	size_t leftCount = 0;
	BBox3fa leftBounds = empty;
	for (size_t i=0; i<(size_t)split.pos; i++) {
	  leftCount += count[split.dim][i];
          Vec3fa bounds_lower(lower[split.dim].x[i],lower[split.dim].y[i],lower[split.dim].z[i]);
          Vec3fa bounds_upper(upper[split.dim].x[i],upper[split.dim].y[i],upper[split.dim].z[i]);
	  leftBounds.extend(BBox3fa(bounds_lower,bounds_upper));
	}
	size_t rightCount = 0;
	BBox3fa rightBounds = empty;
	for (size_t i=split.pos; i<mapping.size(); i++) {
	  rightCount += count[split.dim][i];
          Vec3fa bounds_lower(lower[split.dim].x[i],lower[split.dim].y[i],lower[split.dim].z[i]);
          Vec3fa bounds_upper(upper[split.dim].x[i],upper[split.dim].y[i],upper[split.dim].z[i]);
	  rightBounds.extend(BBox3fa(bounds_lower,bounds_upper));
	}
	new (&info) SplitInfo(leftCount,leftBounds,rightCount,rightBounds);
      }

      /*! gets the number of primitives left of the split */
      __forceinline size_t getLeftCount(const BinMapping<16>& mapping, const Split& split) const
      {
        if (unlikely(split.dim == -1)) return -1;

        size_t leftCount = 0;
        for (size_t i = 0; i < (size_t)split.pos; i++) {
          leftCount += count[split.dim][i];
        }
        return leftCount;
      }

      /*! gets the number of primitives right of the split */
      __forceinline size_t getRightCount(const BinMapping<16>& mapping, const Split& split) const
      {
        if (unlikely(split.dim == -1)) return -1;

        size_t rightCount = 0;
        for (size_t i = (size_t)split.pos; i<mapping.size(); i++) {
          rightCount += count[split.dim][i];
        }
        return rightCount;
      }
            
    private:
      Vec3vf16 lower[3];
      Vec3vf16 upper[3];
      vuint16   count[3];
    };
#endif
  }

  template<typename BinInfoT, typename BinMapping, typename PrimRef>
  __forceinline void bin_parallel(BinInfoT& binner, const PrimRef* prims, size_t begin, size_t end, size_t blockSize, size_t parallelThreshold, const BinMapping& mapping)
  {
    if (likely(end-begin < parallelThreshold)) {
      binner.bin(prims,begin,end,mapping);
    } else {
      binner = parallel_reduce(begin,end,blockSize,binner,
                              [&](const range<size_t>& r) -> BinInfoT { BinInfoT binner(empty); binner.bin(prims + r.begin(), r.size(), mapping); return binner; },
                              [&](const BinInfoT& b0, const BinInfoT& b1) -> BinInfoT { BinInfoT r = b0; r.merge(b1, mapping.size()); return r; });
    }
  }

  template<typename BinBoundsAndCenter, typename BinInfoT, typename BinMapping, typename PrimRef>
  __forceinline void bin_parallel(BinInfoT& binner, const PrimRef* prims, size_t begin, size_t end, size_t blockSize, size_t parallelThreshold, const BinMapping& mapping, const BinBoundsAndCenter& binBoundsAndCenter)
  {
    if (likely(end-begin < parallelThreshold)) {
      binner.bin(prims,begin,end,mapping,binBoundsAndCenter);
    } else {
      binner = parallel_reduce(begin,end,blockSize,binner,
                              [&](const range<size_t>& r) -> BinInfoT { BinInfoT binner(empty); binner.bin(prims + r.begin(), r.size(), mapping, binBoundsAndCenter); return binner; },
                              [&](const BinInfoT& b0, const BinInfoT& b1) -> BinInfoT { BinInfoT r = b0; r.merge(b1, mapping.size()); return r; });
    }
  }

  template<bool parallel, typename BinInfoT, typename BinMapping, typename PrimRef>
  __forceinline void bin_serial_or_parallel(BinInfoT& binner, const PrimRef* prims, size_t begin, size_t end, size_t blockSize, const BinMapping& mapping)
  {
    if (!parallel) {
      binner.bin(prims,begin,end,mapping);
    } else {
      binner = parallel_reduce(begin,end,blockSize,binner,
                              [&](const range<size_t>& r) -> BinInfoT { BinInfoT binner(empty); binner.bin(prims + r.begin(), r.size(), mapping); return binner; },
                              [&](const BinInfoT& b0, const BinInfoT& b1) -> BinInfoT { BinInfoT r = b0; r.merge(b1, mapping.size()); return r; });
    }
  }

  template<bool parallel, typename BinBoundsAndCenter, typename BinInfoT, typename BinMapping, typename PrimRef>
  __forceinline void bin_serial_or_parallel(BinInfoT& binner, const PrimRef* prims, size_t begin, size_t end, size_t blockSize, const BinMapping& mapping, const BinBoundsAndCenter& binBoundsAndCenter)
  {
    if (!parallel) {
      binner.bin(prims,begin,end,mapping,binBoundsAndCenter);
    } else {
      binner = parallel_reduce(begin,end,blockSize,binner,
                              [&](const range<size_t>& r) -> BinInfoT { BinInfoT binner(empty); binner.bin(prims + r.begin(), r.size(), mapping, binBoundsAndCenter); return binner; },
                              [&](const BinInfoT& b0, const BinInfoT& b1) -> BinInfoT { BinInfoT r = b0; r.merge(b1, mapping.size()); return r; });
    }
  }
}