General-Purpose Computation on Graphics Hardware

General-Purpose Computation on Graphics Hardware David Luebke University of Virginia

Course Introduction • The GPU on commodity video cards has evolved into an extremely flexible and powerful processor • Programmability • Precision • Power • We are interested in how to harness that power for general-purpose computation

Motivation: Computational Power • GPUs are fast… • 3 GHz Pentium4 theoretical: 6 GFLOPS, 5.96 GB/sec peak • GeForceFX 5900 observed: 20 GFLOPS, 25.3 GB/sec peak • GeForce 6800 Ultra observed: 53 GFLOPS, 35.2 GB/sec peak • GPUs are getting faster, faster • CPUs: annual growth  1.5× decade growth  60× • GPUs: annual growth > 2.0× decade growth > 1000 Courtesy Kurt Akeley,Ian Buck & Tim Purcell, GPU Gems (see course notes)

Motivation:Computational Power GPU CPU Courtesy Naga Govindaraju

Motivation:Computational Power GPU multiplies per second NVIDIA NV30, 35, 40 ATI R300, 360, 420 GFLOPS Pentium 4 July 01 Jan 02 July 02 Jan 03 July 03 Jan 04 Courtesy Ian Buck

An Aside: Computational Power • Why are GPUs getting faster so fast? • Arithmetic intensity: the specialized nature of GPUs makes it easier to use additional transistors for computation not cache • Economics: multi-billion dollar video game market is a pressure cooker that drives innovation

Motivation:Flexible and precise • Modern GPUs are deeply programmable • Programmable pixel, vertex, video engines • Solidifying high-level language support • Modern GPUs support high precision • 32 bit floating point throughout the pipeline • High enough for many (not all) applications

Motivation:The Potential of GPGPU • The power and flexibility of GPUs makes them an attractive platform for general-purpose computation • Example applications range from in-game physics simulation to conventional computational science • Goal: make the inexpensive power of the GPU available to developers as a sort of computational coprocessor

The Problem:Difficult To Use • GPUs designed for and driven by video games • Programming model is unusual & tied to computer graphics • Programming environment is tightly constrained • Underlying architectures are: • Inherently parallel • Rapidly evolving (even in basic feature set!) • Largely secret • Can’t simply “port” code written for the CPU!

GPU Fundamentals:The Graphics Pipeline • A simplified graphics pipeline • Note that pipe widths vary • Many caches, FIFOs, and so on not shown CPU GPU Graphics State Application Transform Rasterizer Shade VideoMemory(Textures) Vertices(3D) Xformed,LitVertices(2D) Fragments(pre-pixels) Finalpixels(Color, Depth) Render-to-texture

Programmable vertex processor! Programmable pixel processor! GPU Fundamentals:The Modern Graphics Pipeline CPU GPU Graphics State VertexProcessor FragmentProcessor Application VertexProcessor Rasterizer PixelProcessor VideoMemory(Textures) Vertices(3D) Xformed,LitVertices(2D) Fragments(pre-pixels) Finalpixels(Color, Depth) Render-to-texture

GPU Pipeline: Transform • Vertex Processor (multiple operate in parallel) • Transform from “world space” to “image space” • Compute per-vertex lighting

GPU Pipeline: Rasterizer • Rasterizer • Convert geometric rep. (vertex) to image rep. (fragment) • Fragment = image fragment • Pixel + associated data: color, depth, stencil, etc. • Interpolate per-vertex quantities across pixels

GPU Pipeline: Shade • Fragment Processors (multiple in parallel) • Compute a color for each pixel • Optionally read colors from textures (images)

Importance of Data Parallelism • GPU: Each vertex / fragment is independent • Temporary registers are zeroed • No static data • No read-modify-write buffers • Data parallel processing • Best for ALU-heavy architectures: GPUs • Multiple vertex & pixel pipelines • Hide memory latency (with more computation) Courtesy of Ian Buck

Arithmetic Intensity • Lots of ops per word transferred • GPGPU demands high arithmetic intensity for peak performance • Ex: solving systems of linear equations • Physically-based simulation on lattices • All-pairs shortest paths Courtesy of Pat Hanrahan

Data Streams & Kernels • Streams • Collection of records requiring similar computation • Vertex positions, Voxels, FEM cells, etc. • Provide data parallelism • Kernels • Functions applied to each element in stream • Transforms, PDE, … • No dependencies between stream elements • Encourage high arithmetic intensity Courtesy of Ian Buck

Example: Simulation Grid • Common GPGPU computation style • Textures represent computational grids = streams • Many computations map to grids • Matrix algebra • Image & Volume processing • Physical simulation • Global Illumination • ray tracing, photon mapping, radiosity • Non-grid streams can be mapped to grids

Stream Computation • Grid Simulation algorithm • Made up of steps • Each step updates entire grid • Must complete before next step can begin • Grid is a stream, steps are kernels • Kernel applied to each stream element

Scatter vs. Gather • Grid communication • Grid cells share information

Computational Resources Inventory • Programmable parallel processors • Vertex & Fragment pipelines • Rasterizer • Mostly useful for interpolating addresses (texture coordinates) and per-vertex constants • Texture unit • Read-only memory interface • Render to texture • Write-only memory interface

Vertex Processor • Fully programmable (SIMD / MIMD) • Processes 4-vectors (RGBA / XYZW) • Capable of scatter but not gather • Can change the location of current vertex • Cannot read info from other vertices • Can only read a small constant memory • Future hardware enables gather! • Vertex textures

Fragment Processor • Fully programmable (SIMD) • Processes 4-vectors (RGBA / XYZW) • Random access memory read (textures) • Capable of gather but not scatter • No random access memory writes • Output address fixed to a specific pixel • Typically more useful than vertex processor • More fragment pipelines than vertex pipelines • RAM read • Direct output

CPU-GPU Analogies • CPU programming is familiar • GPU programming is graphics-centric • Analogies can aid understanding

CPU-GPU Analogies CPU GPU Stream / Data Array = Texture Memory Read = Texture Sample

CPU-GPU Analogies Loop body / kernel / algorithm step = Fragment Program CPU GPU

Feedback • Each algorithm step depend on the results of previous steps • Each time step depends on the results of the previous time step

CPU-GPU Analogies . . . Grid[i][j]= x; . . . Array Write = Render to Texture CPU GPU

GPU Simulation Overview • Analogies lead to implementation • Algorithm steps are fragment programs • Computational “kernels” • Current state variables stored in textures • Feedback via render to texture • One question: how do we invoke computation?

Invoking Computation • Must invoke computation at each pixel • Just draw geometry! • Most common GPGPU invocation is a full-screen quad

Typical “Grid” Computation • Initialize “view” (so that pixels:texels::1:1) glMatrixMode(GL_MODELVIEW);glLoadIdentity();glMatrixMode(GL_PROJECTION);glLoadIdentity();glOrtho(0, 1, 0, 1, 0, 1);glViewport(0, 0, outTexResX, outTexResY); • For each algorithm step: • Activate render-to-texture • Setup input textures, fragment program • Draw a full-screen quad (1x1)

Branching Techniques • Fragment program branches can be expensive • No true fragment branching on NV3X & R3X0 • Better to move decisions up the pipeline • Replace with math • Occlusion Query • Domain decomposition • Z-cull • Pre-computation

Branching with OQ • Use it for iteration termination Do { // outer loop on CPU BeginOcclusionQuery { // Render with fragment program that // discards fragments that satisfy // termination criteria } EndQuery } While query returns > 0 • Can be used for subdivision techniques • Demo later

Domain Decomposition • Avoid branches where outcome is fixed • One region is always true, another false • Separate FPs for each region, no branches • Example: boundaries

Z-Cull • In early pass, modify depth buffer • Write depth=0 for pixels that should not be modified by later passes • Write depth=1 for rest • Subsequent passes • Enable depth test (GL_LESS) • Draw full-screen quad at z=0.5 • Only pixels with previous depth=1 will be processed • Can also use early stencil test • Not available on NV3X • Depth replace disables ZCull

Pre-computation • Pre-compute anything that will not change every iteration! • Example: arbitrary boundaries • When user draws boundaries, compute texture containing boundary info for cells • Reuse that texture until boundaries modified • Combine with Z-cull for higher performance!

High-level Shading Languages • Cg, HLSL, & GLSlang • Cg: • http://www.nvidia.com/cg • HLSL: • http://msdn.microsoft.com/library/default.asp?url=/library/en-us/directx9_c/directx/graphics/reference/highlevellanguageshaders.asp • GLSlang: • http://www.3dlabs.com/support/developer/ogl2/whitepapers/index.html …. MULR R0.xyz, R0.xxx, R4.xyxx; MOVR R5.xyz, -R0.xyzz; DP3R R3.x, R0.xyzz, R3.xyzz; … float3 cPlastic = Cd * (cAmbi + cDiff) + Cs*cSpec

GPGPU Languages • Why do we want them? • Make programming GPUs easier! • Don’t need to know OpenGL, DirectX, or ATI/NV extensions • Simplify common operations • Focus on the algorithm, not on the implementation • Sh • University of Waterloo • http://libsh.sourceforge.net • http://www.cgl.uwaterloo.ca • Brook • Stanford University • http://brook.sourceforge.net • http://graphics.stanford.edu

Brook: general purpose streaming language • stream programming model • enforce data parallel computing • streams • encourage arithmetic intensity • kernels • C with stream extensions • GPU = streaming coprocessor

.br Brook source files brcc source to source compiler brt Brook run-time library system outline

Brook languagestreams • streams • collection of records requiring similar computation • particle positions, voxels, FEM cell, … float3 positions<200>; float3 velocityfield<100,100,100>; • similar to arrays, but… • index operations disallowed: position[i] • read/write stream operators streamRead (positions, p_ptr); streamWrite (velocityfield, v_ptr); • encourage data parallelism

Brook languagekernels • kernels • functions applied to streams • similar to for_all construct kernel void foo (float a<>, float b<>, out float result<>) { result = a + b; } float a<100>; float b<100>; float c<100>; foo(a,b,c); for (i=0; i<100; i++) c[i] = a[i]+b[i];

Brook languagekernels • kernels • functions applied to streams • similar to for_all construct kernel void foo (float a<>, float b<>, out float result<>) { result = a + b; } • no dependencies between stream elements • encourage high arithmetic intensity

Brook languagekernels • kernels arguments • input/output streams • constant parameters • gather streams • iterator streams kernel void foo (float a<>, float b<>, float t, float array[], iter float n<>, out float result<>) { result = array[a] + t*b + n; } float a<100>; float b<100>; float c<100>; float array<25> iter float n<100> = iter(0, 10); foo(a,b,3.2f,array,n,c);

Brook languagekernels • ray triangle intersection kernel void krnIntersectTriangle(Ray ray<>, Triangle tris[], RayState oldraystate<>, GridTrilist trilist[], out Hit candidatehit<>) { float idx, det, inv_det; float3 edge1, edge2, pvec, tvec, qvec; if(oldraystate.state.y > 0) { idx = trilist[oldraystate.state.w].trinum; edge1 = tris[idx].v1 - tris[idx].v0; edge2 = tris[idx].v2 - tris[idx].v0; pvec = cross(ray.d, edge2); det = dot(edge1, pvec); inv_det = 1.0f/det; tvec = ray.o - tris[idx].v0; candidatehit.data.y = dot( tvec, pvec ) * inv_det; qvec = cross( tvec, edge1 ); candidatehit.data.z = dot( ray.d, qvec ) * inv_det; candidatehit.data.x = dot( edge2, qvec ) * inv_det; candidatehit.data.w = idx; } else { candidatehit.data = float4(0,0,0,-1); } }

Brook languagereductions • reductions • compute single value from a stream reduce void sum (float a<>, reduce float r<>) r += a; } float a<100>; float r; sum(a,r); r = a[0]; for (int i=1; i<100; i++) r += a[i];

Brook languagereductions • reductions • associative operations only (a+b)+c = a+(b+c) • sum, multiply, max, min, OR, AND, XOR • matrix multiply

Brook languagereductions • multi-dimension reductions • stream “shape” differences resolved by reduce function reduce void sum (float a<>, reduce float r<>) r += a; } float a<20>; float r<5>; sum(a,r); for (int i=0; i<5; i++) r[i] = a[i*4]; for (int j=1; j<4; j++) r[i] += a[i*4 + j];

Brook languagestream repeat & stride • kernel arguments of different shape • resolved by repeat and stride kernel void foo (float a<>, float b<>, out float result<>); float a<20>; float b<5>; float c<10>; foo(a,b,c); foo(a[0], b[0], c[0]) foo(a[2], b[0], c[1]) foo(a[4], b[1], c[2]) foo(a[6], b[1], c[3]) foo(a[8], b[2], c[4]) foo(a[10], b[2], c[5]) foo(a[12], b[3], c[6]) foo(a[14], b[3], c[7]) foo(a[16], b[4], c[8]) foo(a[18], b[4], c[9])

Brook languagematrix vector multiply kernel void mul (float a<>, float b<>, out float result<>) { result = a*b; } reduce void sum (float a<>, reduce float result<>) { result += a; } float matrix<20,10>; float vector<1, 10>; float tempmv<20,10>; float result<20, 1>; mul(matrix,vector,tempmv); sum(tempmv,result); M T V = V V

General-Purpose Computation on Graphics Hardware