An Optimized Diffusion Depth Of Field Solver (DDOF)

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2 An Optimized Diffusion Depth Of Field Solver (DDOF) Holger Gruen AMD 28th February 2011 AMD s Favorite Effects 2

3 Agenda Motivation Recap of a high-level explanation of DDOF Recap of earlier DDOF solvers A Vanilla Cyclic Reduction(CR) DDOF solver A DX11 optimized CR solver for DDOF Results 28th February 2011 AMD s Favorite Effects 3

4 Motivation Solver presented at GDC 2010 [RS2010] has some weaknesses Great implementation but memory reqs and runtime too high for many game developers Looking for faster and memory efficient solver 28th February 2011 AMD s Favorite Effects 4

5 Diffusion DOF recap 1 DDOF is an enhanced way of blurring a picture taking an arbitrary CoC at a pixel into account Interprets input image as a heat distribution Uses the CoC at a pixel to derive a per pixel heat conductivity CoC=Circle of Confusion 28th February 2011 AMD s Favorite Effects 5

6 Diffusion DOF recap 2 Blurring is done by time stepping a differential equation that models the diffusion of heat ADI method used to arrive at a separable solution for stepping Need to solve tri-diagonal linear system for each row and then each colum of the input 28th February 2011 AMD s Favorite Effects 6

7 DDOF Tri-diagonal system row/col of input image derived from CoC at each pixel of an input row/col resulting blurred row/col b1 c1 0 y1 x1 a b c y x a 3 b3 c 3 y 3 x 3 0 a n b n y n x n 28th February 2011 AMD s Favorite Effects 7

8 Solver recap 1 The GDC2010 solver [RS2010] is a hybrid solver Performs three PCR steps upfront Performs serial Sweep algorithm to solve small resulting systems Check [ZCO2010] for details on other hybrid solvers 28th February 2011 AMD s Favorite Effects 8

9 Solver recap 2 The GDC2010 solver [RS2010] has drawbacks It uses a large UAV as a RW scratch-pad to store the modified coefficients of the sweep algorithm GPUs without RW cache will suffer For high resolutions three PCR steps produce tri-diagonal system of substantial size This means a serial (sweep) algorithm is run on a big system 28th February 2011 AMD s Favorite Effects 9

10 Solver recap 3 Cyclic Reduction (CR) solver Used by [Kass2006] in the original DDOF paper Runs in two phases 1. reduction phase 2. backward substitution phase 28th February 2011 AMD s Favorite Effects 10

11 Solver recap 4 According to [ZCO2010]: CR solver has lowest computational complexity of all solvers It suffers from lack of parallelism though At the end of the reduction phase At the start of the backwards substitution phase 28th February 2011 AMD s Favorite Effects 11

12 Passes of a Vanilla CR Solver X abc Y Input image Pass 1: construct from CoC Blurred image b c 0 y x a 2 b2 c 2 y Solve for 2 x the Stop at size 1 first y 2 a 3 b3 c 3 y 3 x 3 0 a n bn y n x n 28th February 2011 AMD s Favorite Effects 12

13 Vanilla Solver Results Higher performance than reported in [Bavoil2010] (~6 ms vs. ~8ms at 1600x1200) Memory footprint prohibitively high >200 MB at 1600x1200 Need an answer to tackling the lack of parallelism problem answer given in [ZCO2010] 28th February 2011 AMD s Favorite Effects 13

14 Vanilla CR Solver X abc Input image Pass 1: construct from CoC This is Stop what at kills size 1 parallelism Solve for the first y Y Blurred image 28th February 2011 AMD s Favorite Effects 14

15 Keeping the parallelism high X abc Y Input image Pass 1: construct from CoC Blurred image Stop at a reasonable size Solve for Y at that resolution to have a big enough parallel workload (e.g using PCR see [ZCO2010]) 28th February 2011 AMD s Favorite Effects 15

16 Memory Optimizations 1 X abc Input image Pass 1: construct from CoC Stop at a reasonable size Solve for Y at that resolution Y Blurred image 28th February 2011 AMD s Favorite Effects 16

17 Memory Optimizations 1 X abc rgab32f rgab32f rgab32f rgab32f Stop at a reasonable size Solve for Y at that resolution Y rgba32f rgab32f 28th February 2011 AMD s Favorite Effects 17

18 Memory Optimizations 1 X abc rgab16f rgab32f rgab16f Stop at a This saves some significant reasonable amount of memory - We found size no artifacts rgab32f for going from rgba32f to rgba16f Solve for Y at that resolution Y rgba16f rgab16f 28th February 2011 AMD s Favorite Effects 18

19 Memory Optimizations 2 X abc rgab16f rgab32f rgab16f This does again save a significant amount of memory rgab32f as this is the biggest surface used by the solver Stop at a reasonable size Solve for Y at that resolution Y rgba16f rgab16f 28th February 2011 AMD s Favorite Effects 19

20 Memory Optimizations 2 X abc rgab16f Skip abc construction pass and compute abc on-the-fly during 1. reduction pass rgab16f rgab32f Stop at a reasonable size Solve for Y at that resolution Y rgba16f rgab16f 28th February 2011 AMD s Favorite Effects 20

21 Intermediate Results 1600x1200 Solver Time in ms Memory in Megabytes HD5870 GTX480 GDC2010 hybrid solver on GTX480 ~ [Bavoil 2010] Standard Solver (already skips high res abc construction) ~132 ~117 (guesstimate) 28th February 2011 AMD s Favorite Effects 21

22 Memory Optimizations 3 X abc rgab16f Skip abc construction pass compute abc during 1. reduction pass rgab16f rgab32f Stop at a Yet again this saves a reasonable significant amount of size memory! Solve for Y at that resolution Y rgba16f rgab16f 28th February 2011 AMD s Favorite Effects 22

23 Memory Optimizations 3 X abc Y rgab16f Skip abc construction pass compute abc during 1. reduction pass rgba16f 4 Reduce 4-to-1 in a special first reduction pass Substitute 1-to-4 in a special substitution pass Stop at a reasonable size Solve for Y at that resolution 4 28th February 2011 AMD s Favorite Effects 23

24 Intermediate Results 1600x1200 Solver Time in ms Memory in Megabytes HD5870 GTX480 GDC2010 hybrid solver on GTX480 ~ [Bavoil 2010] Standard Solver (already skips high res abc construction) ~132 4 to-1 Reduction ~73 ~117 (guesstimate) 28th February 2011 AMD s Favorite Effects 24

25 DX11 Memory Optimizations 1 X abc Y rgab16f Skip abc construction pass compute abc during 1. reduction pass rgba16f 4 Reduce 4-to-1 in a special first reduction pass Substitute 1-to-4 in a special substitution pass Stop at a reasonable size Solve for Y at that resolution 4 28th February 2011 AMD s Favorite Effects 25

26 DX11 Memory Optimizations 1 X abc Y rgab16f Skip abc construction pass compute abc during 1. reduction pass rgba16f 4 Reduce 4-to-1 in a special first reduction pass Substitute 1-to-4 in a special substitution pass Pack abc and X into one rgba_uint surface Stop at a reasonable size Solve for Y at that resolution 4 28th February 2011 AMD s Favorite Effects 26

27 Using SM5 for data packing X abc rgab16f rgab32f pack x,y channel (f32tof16(x.x) + (f32tof16(x.y) << 16)) uint uint uint uint 28th February 2011 AMD s Favorite Effects 27

28 Using SM5 for data packing X rgab16f uint uint abc rgab32f higher 27 bits of x channel (asuint(abc.x) &0xFFFFFFC0) (f32tof16(x.z) & 0x3F)) uint uint Steal 6 lowest mantissa bits of abc.x to store some bits of X.z 28th February 2011 AMD s Favorite Effects 28

29 Using SM5 for data packing X rgab16f uint uint abc rgab32f higher 27 bits of y channel (asuint(abc.y) &0xFFFFFFC0) ((f32tof16(x.z) >>6 )& 0x3F)) uint uint Steal 6 lowest mantissa bits of abc.y to store some bits of X.z 28th February 2011 AMD s Favorite Effects 29

30 SM5 Memory Optimizations 1 X rgab16f uint uint abc rgab32f higher 27 bits of z channel (asuint(abc.z) &0xFFFFFFC0) ((f32tof16(x.z) >>12 )& 0x3F)) uint uint Steal 6 lowest mantissa bits of abc.z to store some bits of X.z 28th February 2011 AMD s Favorite Effects 30

31 Sample Screenshot 28th February 2011 AMD s Favorite Effects 31

32 Abs(Packed-Unpacked) x 255.0f 28th February 2011 AMD s Favorite Effects 32

33 DX11 Memory Optimizations 2 Solver does a horizonal and vertical pass Chain of lower res RTs needs to be there twice Horizontal reduction/substitution chain Vertical reduction/substitution chain How can DX11 help? 28th February 2011 AMD s Favorite Effects 33

34 DX11 Memory Optimizations 2 UAVs allow us to reuse data of the horizontal chain for the vertical chain A proof of concept implementation shows that this works nicely but impacts the runtime significantly ~40% lower fps Stayed with RTs as memory was already quite low Use only if you are really concerned about memory 28th February 2011 AMD s Favorite Effects 34

35 Final Results 1600x1200 Solver Time in ms Memory in Megabytes HD5870 GTX480 GDC2010 hybrid solver on GTX480 ~ [Bavoil 2010] Standard Solver (already skips high res abc construction) ~132 4 to-1 Reduction ~73 4-to-1 Reduction + SM5 Packing ~58 ~117 (guesstimate,) 28th February 2011 AMD s Favorite Effects 35

36 Future Work Look into CS acceleration of the solver 4-to-1 reduction pass 1-to-4 substitution pass Look into using heat diffusion for other effects e.g. Motion blur 28th February 2011 AMD s Favorite Effects 36

37 Conclusion Optimized CR solver is fast and mem-efficient Used in Dragon Age 2 4aGames considering its use for new projects Detailed description in Game Engine Gems 2 Mail me (holger.gruen@amd.com) if you want access to the sources 28th February 2011 AMD s Favorite Effects 37

38 References [Kass2006] Interactive depth of field using simulated diffusion on a GPU Michael Kass, Pixar Animation studios, Pixar technical memo #06-01 [ZCO2010] Fast Tridiagonal Solvers on the GPU Y. Zhang, J. Cohen, J. D. Owens, PPoPP 2010 [RS2010] DX11 Effects in Metro 2033: The Last Refuge A. Rege, O. Shishkovtsov, GDC 2010 [Bavoil2010] Modern Real-Time Rendering Techniques, L. Bavoil, FGO th February 2011 AMD s Favorite Effects 38

39 Backup 28th February 2011 AMD s Favorite Effects 39

40 Results 1920x1200 Solver Time in ms Memory in Megabytes HD5870 GTX480 Standard Solver (already skips high res abc construction) ~158 4 to-1 Reduction ~88 4-to-1 Reduction + SM5 Packing ~70 28th February 2011 AMD s Favorite Effects 40