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CS6958: HARDWARE RAY TRACING Spring 2014 What is Ray Tracing? A - PowerPoint PPT Presentation

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CS6958: HARDWARE RAY TRACING Spring 2014 What is Ray Tracing? A computer graphic rendering technique that simulates optics Can generate very realistic-looking images Can take a long time to create those images A Tale of Two

  1. Ray Tracing is complex? typedef struct{double x,y,z}vec;vec U,black,amb={.02,.02,.02};struct sphere{ vec cen,colour;double rad,kd,ks,kt,kl,ir}*s,*best,sph[]={0.,6.,.5,1.,1.,1.,.9, .05,.2,.85,0.,1.7,-1.,8.,-.5,1.,.5,.2,1.,.7,.3,0.,.05,1.2,1.,8.,-.5,.1,.8,.8, 1.,.3,.7,0.,0.,1.2,3.,-6.,15.,1.,.8,1.,7.,0.,0.,0.,.6,1.5,-3.,-3.,12.,.8,1., 1.,5.,0.,0.,0.,.5,1.5,};yx;double u,b,tmin,sqrt(),tan();double vdot(A,B)vec A ,B;{return A.x*B.x+A.y*B.y+A.z*B.z;}vec vcomb(a,A,B)double a;vec A,B;{B.x+=a* A.x;B.y+=a*A.y;B.z+=a*A.z;return B;}vec vunit(A)vec A;{return vcomb(1./sqrt( vdot(A,A)),A,black);}struct sphere*intersect(P,D)vec P,D;{best=0;tmin=1e30;s= sph+5;while(s-->sph)b=vdot(D,U=vcomb(-1.,P,s->cen)),u=b*b-vdot(U,U)+s->rad*s ->rad,u=u>0?sqrt(u):1e31,u=b-u>1e-7?b-u:b+u,tmin=u>=1e-7&&u<tmin?best=s,u: tmin;return best;}vec trace(level,P,D)vec P,D;{double d,eta,e;vec N,colour; struct sphere*s,*l;if(!level--)return black;if(s=intersect(P,D));else return amb;colour=amb;eta=s->ir;d= -vdot(D,N=vunit(vcomb(-1.,P=vcomb(tmin,D,P),s->cen )));if(d<0)N=vcomb(-1.,N,black),eta=1/eta,d= -d;l=sph+5;while(l-->sph)if((e=l ->kl*vdot(N,U=vunit(vcomb(-1.,P,l->cen))))>0&&intersect(P,U)==l)colour=vcomb(e ,l->colour,colour);U=s->colour;colour.x*=U.x;colour.y*=U.y;colour.z*=U.z;e=1-eta* eta*(1-d*d);return vcomb(s->kt,e>0?trace(level,P,vcomb(eta,D,vcomb(eta*d-sqrt (e),N,black))):black,vcomb(s->ks,trace(level,P,vcomb(2*d,N,D)),vcomb(s->kd, colour,vcomb(s->kl,U,black))));}main(){puts(“P3\n32 32\n255”);while(yx<32*32) U.x=yx%32-32/2,U.z=32/2-yx++/32,U.y=32/2/tan(25/114.5915590261),U=vcomb(255., trace(3,black,vunit(U)),black),printf("%.0f %.0f %.0f\n",U);}/*minray!*/ Paul Heckbert’s complete ray tracer on the back of his business card (c1989) Does Whitted-style recursive ray tracing with reflections, refraction, two lights…

  2. Andrew Kensler’s business-card C++ RT #include <stdlib.h> // card > aek.ppm � #include <stdio.h> � #include <math.h> � typedef int i;typedef float f;struct v{ � f x,y,z;v operator+(v r){return v(x+r.x � ,y+r.y,z+r.z);}v operator*(f r){return � v(x*r,y*r,z*r);}f operator%(v r){return � x*r.x+y*r.y+z*r.z;}v(){}v operator^(v r � ){return v(y*r.z-z*r.y,z*r.x-x*r.z,x*r. � y-y*r.x);}v(f a,f b,f c){x=a;y=b;z=c;}v � operator!(){return*this*(1/sqrt(*this%* � this));}};i G[]={247570,280596,280600, � 249748,18578,18577,231184,16,16};f R(){ � return(f)rand()/RAND_MAX;}i T(v o,v d,f � &t,v&n){t=1e9;i m=0;f p=-o.z/d.z;if(.01 � <p)t=p,n=v(0,0,1),m=1;for(i k=19;k--;) � for(i j=9;j--;)if(G[j]&1<<k){v p=o+v(-k � ,0,-j-4);f b=p%d,c=p%p-1,q=b*b-c;if(q>0 � ){f s=-b-sqrt(q);if(s<t&&s>.01)t=s,n=!( � p+d*t),m=2;}}return m;}v S(v o,v d){f t � ;v n;i m=T(o,d,t,n);if(!m)return v(.7, � .6,1)*pow(1-d.z,4);v h=o+d*t,l=!(v(9+R( � ),9+R(),16)+h*-1),r=d+n*(n%d*-2);f b=l% � n;if(b<0||T(h,l,t,n))b=0;f p=pow(l%r*(b � >0),99);if(m&1){h=h*.2;return((i)(ceil( � h.x)+ceil(h.y))&1?v(3,1,1):v(3,3,3))*(b � *.2+.1);}return v(p,p,p)+S(h,r)*.5;}i � main(){printf("P6 512 512 255 ");v g=!v � (-6,-16,0),a=!(v(0,0,1)^g)*.002,b=!(g^a � )*.002,c=(a+b)*-256+g;for(i y=512;y--;) � for(i x=512;x--;){v p(13,13,13);for(i r � =64;r--;){v t=a*(R()-.5)*99+b*(R()-.5)* � 99;p=S(v(17,16,8)+t,!(t*-1+(a*(R()+x)+b � *(y+R())+c)*16))*3.5+p;}printf("%c%c%c" � ,(i)p.x,(i)p.y,(i)p.z);}} �

  3. Andrew Kensler’s business-card C++ RT #include <stdlib.h> // card > aek.ppm � #include <stdio.h> � #include <math.h> � typedef int i;typedef float f;struct v{ � f x,y,z;v operator+(v r){return v(x+r.x � ,y+r.y,z+r.z);}v operator*(f r){return � v(x*r,y*r,z*r);}f operator%(v r){return � x*r.x+y*r.y+z*r.z;}v(){}v operator^(v r � ){return v(y*r.z-z*r.y,z*r.x-x*r.z,x*r. � y-y*r.x);}v(f a,f b,f c){x=a;y=b;z=c;}v � operator!(){return*this*(1/sqrt(*this%* � this));}};i G[]={247570,280596,280600, � 249748,18578,18577,231184,16,16};f R(){ � return(f)rand()/RAND_MAX;}i T(v o,v d,f � &t,v&n){t=1e9;i m=0;f p=-o.z/d.z;if(.01 � <p)t=p,n=v(0,0,1),m=1;for(i k=19;k--;) � for(i j=9;j--;)if(G[j]&1<<k){v p=o+v(-k � ,0,-j-4);f b=p%d,c=p%p-1,q=b*b-c;if(q>0 � ){f s=-b-sqrt(q);if(s<t&&s>.01)t=s,n=!( � p+d*t),m=2;}}return m;}v S(v o,v d){f t � ;v n;i m=T(o,d,t,n);if(!m)return v(.7, � .6,1)*pow(1-d.z,4);v h=o+d*t,l=!(v(9+R( � ),9+R(),16)+h*-1),r=d+n*(n%d*-2);f b=l% � n;if(b<0||T(h,l,t,n))b=0;f p=pow(l%r*(b � >0),99);if(m&1){h=h*.2;return((i)(ceil( � h.x)+ceil(h.y))&1?v(3,1,1):v(3,3,3))*(b � *.2+.1);}return v(p,p,p)+S(h,r)*.5;}i � main(){printf("P6 512 512 255 ");v g=!v � (-6,-16,0),a=!(v(0,0,1)^g)*.002,b=!(g^a � )*.002,c=(a+b)*-256+g;for(i y=512;y--;) � for(i x=512;x--;){v p(13,13,13);for(i r � =64;r--;){v t=a*(R()-.5)*99+b*(R()-.5)* � 99;p=S(v(17,16,8)+t,!(t*-1+(a*(R()+x)+b � *(y+R())+c)*16))*3.5+p;}printf("%c%c%c" � ,(i)p.x,(i)p.y,(i)p.z);}} �

  4. A Hierarchy of Ray Tracers Ray casting 1. Ray casting with shadows 2. Whitted-style recursive ray tracing 3. Cook-style distribution ray tracing 4. Path tracing for indirect illumination 5. (global illumination) … even more advanced techniques… 6.

  5. 1: Ray Casting ¨ A 3D line query to determine visibility ¤ Rays are cast from the eye point through each pixel into the scene ¤ Intersection point of nearest object is returned

  6. 2: Ray Casting with Shadows ¨ At each intersection point, cast another ray in the direction of the light source ¤ Checks whether the point is in shadow

  7. 3: Whitted-Style Ray Tracing ¨ Recursively cast rays to account for reflections and refractions

  8. 3: Whitted-Style Ray Tracing Ray casting with shadows Whitted-style ray tracing

  9. Classic Whitted Examples

  10. 4: Distribution Ray Tracing ¨ AKA Cook-Style Ray Tracing ¤ Rays can be cast through a lens with area (i.e. not just a pinhole) n Depth of field ¤ secondary rays directions can be perturbed n Glossy reflections ¤ Shadow rays can be aimed at area light sources n Soft shadows ¤ Can also add time to the ray n Motion blur

  11. 4: Distribution Ray Tracing

  12. 4: Distribution Ray Tracing

  13. 4: Distribution Ray Tracing

  14. 5: Path Tracing ¨ At each intersection point, cast a ray in a random direction to see if any light comes from there ¤ With enough oversampling, this results in solving the “rendering equation” ¤ Fills in the “ambient” shadowed spaces with indirect lighting

  15. 5: Path Tracing

  16. 5: Path Tracing

  17. 5: Path Tracing Whitted ray tracing Path Tracing

  18. Lots more to it… ¨ But this hierarchy helps me keep things straight ¤ Ambient occlusion, ray bundles, beam tracing, photon mapping, metropolis light transport, etc. etc. etc. ¨ Material properties involve other huge set of issues that can impact realism ¤ BRDF: Bidirectional Reflectance Distribution Function ¤ BSDF: Bidirectional Scattering Distribution Function ¤ BTDF: Bidirectional Transmission Distribution Function ¤ BSSRDF: Bidirectional Scattering Surface Reflectance Distribution Function

  19. So – use GPUs to ray trace… ¨ … Problem solved? ¨ Unfortunately no – Ray Tracing isn’t as friendly to SIMD parallelism as Z-buffer rasterization ¨ Cast rays into scene ¨ Intersect with all objects, return first hit ¨ Independent rays processed in parallel ¤ Additional rays can handle optical effects

  20. So – use GPUs to ray trace… ¨ … Problem solved? ¨ Unfortunately no – Ray Tracing isn’t as friendly to SIMD parallelism as Z-buffer rasterization ¨ Cast rays into scene ¨ Intersect with all objects, return first hit ¨ Independent rays processed in parallel ¤ Additional rays can handle optical effects

  21. Acceleration Structures ¨ Hierarchical partitions that help eliminate large numbers of primitives from that intersection step ¤ Surround scene objects with partitions that are easy to test for intersection ¤ If you miss the partition, you don’t need to test anything inside that partition ¤ Changes that linear search step into logarithmic search ¤ BUT – adds data-dependent branching…

  22. Acceleration Structures ¨ Partition the scene into easy to intersect units ¤ Tree-Based n Bounding Volume Hierarchy (BVH) n Axis-aligned or Object-aligned n KD-Tree n Binary Space Partitioning Tree (BSP Tree) ¤ Grid-Based n Oct-tree n Uniform Grids n Multi-Grids

  23. Bounding Volume Hierarchy Tom Funkhouser, Princeton

  24. Bounding Volume Hierarchy Tom Funkhouser, Princeton

  25. Ray Tracing Algorithm Phases ¨ Traversal ¤ Intersect the ray with bounding objects to eliminate as much as you can ¨ Intersection ¤ At the leaf nodes, intersect the ray with actual geometry (triangles, spheres, patches, etc.) ¨ Shading ¤ Figure out what color/light contribution that intersected point adds to the scene

  26. Ray Tracing Algorithm Phases ¨ Traversal ¤ Tree traversal – does NOT map well to SIMD parallelism ¨ Intersection ¤ FP operations – maps fine to SIMD ¨ Shading ¤ Some trig, some FP – maps fine to SIMD

  27. Ray Tracing Algorithm Phases ¨ Traversal ¤ Tree traversal – does NOT map well to SIMD parallelism ¤ 64%-84% of run time ¨ Intersection ¤ FP operations – maps fine to SIMD ¤ 8% - 30% of run time ¨ Shading ¤ Some trig, some FP – maps fine to SIMD ¤ 1% to 8% of run time

  28. Gaming Possibilities

  29. iRay – NVIDIA’s GPU ray tracer 1 minute

  30. iRay – NVIDIA’s GPU ray tracer 30 minutes

  31. iRay – NVIDIA’s GPU ray tracer 4 hours

  32. iRay GPU ray tracing - 2011

  33. Ray Tracing Hardware? ¨ There have been a few academic projects ¤ Saarland University – SaarCor and RPU ¤ University of Illinois at Urbana-Champaign – Rigel ¤ University of Wisconsin, Madison – Copernicus ¤ KAIST, Korea – MRTP mobile RT ¤ University of Utah - TRaX

  34. TRaX: Threaded Ray eXecution ¨ If you could build a GPU that was customized for ray tracing, what would it look like? ¤ Probably have lots of floating point units ¤ NVIDA/ATI GPUs organize them as wide SIMD n For example, 32 threads in a “warp” n Great if all 32 threads truly do the exact same thing n Not so great if they branch… ¤ TRaX takes a more MIMD/SPMD approach n Let the multiple threads each have their own PC n Letting the threads be out of sync has benefits…

  35. SIMD Execution … � SWI � � r6,r1,232 � SWI � � r6,r1,236 � LWI � � r3,r1,240 � ORI � � r5,r0,114 � ORI � � r6,r0,106 � FPINVSQRT � r5,r5 � Bleid � r23,$0BB0 � FPDIV � r5,r6,r5 � ORI � � r7,r0,-107 � FPDIV � r5,r6,r5 � ORI � � r8,r0,110 � ORI � � r9,r0,107 � FPMUL � r7,r5,r7 � SWI � � r7,r1,400 � … �

  36. SIMD Execution Thread Number 0 2 3 4 5 7 1 6 … � … � … � … � … � … � … � … � SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� … � … � … � … � … � … � … � … �

  37. SIMD Execution Thread Number 0 2 3 4 5 7 1 6 … � … � … � … � … � … � … � … � SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� … � … � … � … � … � … � … � … �

  38. SIMD Execution Thread Number 0 2 3 4 5 7 1 6 … � … � … � … � … � … � … � … � SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� … � … � … � … � … � … � … � … �

  39. SIMD Execution Thread Number 0 2 3 4 5 7 1 6 … � … � … � … � … � … � … � … � SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� … � … � … � … � … � … � … � … �

  40. SIMD Execution Thread Number 0 2 3 4 5 7 1 6 … � … � … � … � … � … � … � … � SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� … � … � … � … � … � … � … � … �

  41. SIMD Execution Thread Number 0 2 3 4 5 7 1 6 … � … � … � … � … � … � … � … � SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� … � … � … � … � … � … � … � … �

  42. SIMD Execution – Resource Replication Thread Number 0 2 3 4 5 7 1 6 … � … � … � … � … � … � … � … � SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� … � … � … � … � … � … � … � … �

  43. SIMD Execution Thread Number 0 2 3 4 5 7 1 6 … � … � … � … � … � … � … � … � SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� … � … � … � … � … � … � … � … �

  44. SIMD Execution Thread Number 0 2 3 4 5 7 1 6 … � … � … � … � … � … � … � … � SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� … � … � … � … � … � … � … � … �

  45. SIMD Execution Thread Number 0 2 3 4 5 7 1 6 … � … � … � … � … � … � … � … � SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� … � … � … � … � … � … � … � … �

  46. SIMD Execution Thread Number 0 2 3 4 5 7 1 6 … � … � … � … � … � … � … � … � SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� SWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� LWI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� ORI �� FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � FPINVSQRT � Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� Bleid �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� FPDIV �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� ORI � �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� FPMUL �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� SWI � �� … � … � … � … � … � … � … � … �

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