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**Parallelizing and Optimizing Programs for GPU Acceleration using CUDA**

Martin Burtscher Department of Computer Science

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**CUDA Optimization Tutorial**

Martin Burtscher Tutorial slides CUDA Optimization Tutorial

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**High-end CPU-GPU Comparison**

Xeon E5-2687W Kepler GTX 680 Cores 8 (superscalar) (simple) Active threads 2 per core ~11 per core Frequency GHz 1.0 GHz Peak performance (SP) 397 GFlop/s GFlop/s Peak mem. bandwidth 51 GB/s 192 GB/s Maximum power 150 W W* Price $ $500* Release dates Xeon: March 2012 Kepler: March 2012 *entire card Intel Nvidia CUDA Optimization Tutorial

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**GPU Advantages Performance Main memory bandwidth**

8x as many operations executed per second Main memory bandwidth 4x as many bytes transferred per second Cost-, energy-, and size-efficiency 29x as much performance per dollar 6x as much performance per watt 11x as much performance per area (based on peak values) CUDA Optimization Tutorial

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**GPU Disadvantages Clearly, we should be using GPUs all the time**

So why aren’t we? GPUs can only execute some types of code fast Need lots of data parallelism, data reuse, & regularity GPUs are harder to program and tune than CPUs In part because of poor tool support In part because of their architecture In part because of poor support for irregular codes CUDA Optimization Tutorial

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**Outline (Part I) Introduction GPU programming N-body example**

Porting and tuning Other considerations Conclusions Hightechreview.com CUDA Optimization Tutorial

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**CUDA Programming Model**

Non-graphics programming Uses GPU as massively parallel co-processor SIMT (single-instruction multiple-threads) model Thousands of threads needed for full efficiency C/C++ with extensions Function launch Calling functions on GPU Memory management GPU memory allocation, copying data to/from GPU Declaration qualifiers Device, shared, local, etc. Special instructions Barriers, fences, etc. Keywords threadIdx, blockIdx GPU CPU PCI-Express bus CUDA Optimization Tutorial

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**Calling GPU Kernels Kernels are functions that run on the GPU**

Callable by CPU code CPU can continue processing while GPU runs kernel KernelName<<<m, n>>>(arg1, arg2, ...); Launch configuration (programmer selectable) GPU spawns m blocks with n threads (i.e., m*n threads total) that run a copy of the same function Normal function parameters: passed conventionally Different address space, should never pass CPU pointers CUDA Optimization Tutorial

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**GPU Architecture GPUs consist of Streaming Multiprocessors (SMs)**

1 to 30 SMs per chip (run blocks) SMs contain Processing Elements (PEs) 8, 32, or 192 PEs per SM (run threads) Global Memory Shared Memory Adapted from NVIDIA CUDA Optimization Tutorial

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**Block Scalability Hardware can assign blocks to SMs in any order**

A kernel with enough blocks scales across GPUs Not all blocks may be resident at the same time GPU with 2 SMs Block 0 Block 1 Block 2 Block 3 Block 4 Block 5 Block 6 Block 7 Kernel GPU with 4 SMs time Adapted from NVIDIA CUDA Optimization Tutorial

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**GPU Memories Separate from CPU memory Visible GPU memory types**

CPU can access GPU’s global & constant mem. via PCIe bus Requires slow explicit transfer Visible GPU memory types Registers (per thread) Local mem. (per thread) Shared mem. (per block) Software-controlled cache Global mem. (per kernel) Constant mem. (read only) Slow communic. between blocks GPU Global + Local Memory (DRAM) Block (0, 0) Shared Memory (SRAM) Thread (0, 0) Registers Thread (1, 0) Block (1, 0) CPU Constant Memory (DRAM, cached) Adapted from NVIDIA CUDA Optimization Tutorial

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**SM Internals (Fermi and Kepler)**

Caches Software-controlled shared memory Hardware-controlled incoherent L1 data cache 64 kB combined size, can be split 16/48, 32/32, 48/16 Synchronization support Fast hardware barrier within block (__syncthreads()) Fence instructions: memory consistency & coherency Special operations Thread voting (warp-based reduction operations) CUDA Optimization Tutorial

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**Block and Thread Allocation Limits**

Blocks assigned to SMs Until first limit reached Threads assigned to PEs Hardware limits 8/16 active blocks/SM 1024, 1536, or 2048 resident threads/SM 512 or 1024 threads/blk 16k, 32k, or 64k regs/SM 16 kB or 48 kB shared memory per SM 216-1 or blks/kernel t0 t1 t2 … tm Blocks PE Shared Memory MT IU SM 1 SM 0 Adapted from NVIDIA CUDA Optimization Tutorial

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**Warp-based Execution 32 contiguous threads form a warp**

Execute same instruction in same cycle (or disabled) Warps are scheduled out-of-order with respect to each other to hide latencies Thread divergence Some threads in warp jump to different PC than others Hardware runs subsets of warp until they re-converge Results in reduction of parallelism (performance loss) CUDA Optimization Tutorial

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**Thread Divergence Non-divergent code Divergent code**

if (threadID >= 32) { some_code; } else { other_code; } Divergent code if (threadID >= 13) { some_code; } else { other_code; } Thread ID: … Thread ID: … disabled disabled Adapted from NVIDIA Adapted from NVIDIA CUDA Optimization Tutorial

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**Parallel Memory Accesses**

Coalesced main memory access (16/32x faster) Under some conditions, HW combines multiple (half) warp memory accesses into a single coalesced access CC 1.3: 64-byte aligned 64-byte line (any permutation) CC 2.x+3.0: 128-byte aligned 128-byte line (cached) Bank-conflict-free shared memory access (16/32) No superword alignment or contiguity requirements CC 1.3: 16 different banks per half warp or same word CC 2.x+3.0 : 32 different banks + 1-word broadcast each CUDA Optimization Tutorial

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**Coalesced Main Memory Accesses**

single coalesced access one and two coalesced accesses* NVIDIA NVIDIA CUDA Optimization Tutorial

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**Outline Introduction GPU programming N-body example Porting and tuning**

Other considerations Conclusions NASA/JPL-Caltech/SSC CUDA Optimization Tutorial

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**N-body Simulation Time evolution of physical system**

System consists of bodies “n” is the number of bodies Bodies interact via pair-wise forces Many systems can be modeled in this way Star/galaxy clusters (gravitational force) Particles (electric force, magnetic force) RUG Cornell CUDA Optimization Tutorial

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**Simple N-body Algorithm**

Initialize body masses, positions, and velocities Iterate over time steps { Accumulate forces acting on each body Update body positions and velocities based on force } Output result More sophisticated n-body algorithms exist Barnes Hut algorithm (covered in Part II) Fast Multipole Method (FMM) CUDA Optimization Tutorial

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**Key Loops (Pseudo Code)**

bodySet = ...; // input for timestep do { // sequential foreach Body b1 in bodySet { // O(n2) parallel foreach Body b2 in bodySet { if (b1 != b2) { b1.addInteractionForce(b2); } foreach Body b in bodySet { // O(n) parallel b.Advance(); // output result CUDA Optimization Tutorial

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**Force Calculation C Code**

struct Body { float mass, posx, posy, posz; // mass and 3D position float velx, vely, velz, accx, accy, accz; // 3D velocity & accel } *body; for (i = 0; i < nbodies; i++) { . . . for (j = 0; j < nbodies; j++) { if (i != j) { dx = body[j].posx - px; // delta x dy = body[j].posy - py; // delta y dz = body[j].posz - pz; // delta z dsq = dx*dx + dy*dy + dz*dz; // distance squared dinv = 1.0f / sqrtf(dsq + epssq); // inverse distance scale = body[j].mass * dinv * dinv * dinv; // scaled force ax += dx * scale; // accumulate x contribution of accel ay += dy * scale; az += dz * scale; // ditto for y and z } CUDA Optimization Tutorial

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**Outline Introduction GPU programming N-body example Porting and tuning**

Other considerations Conclusions CUDA Optimization Tutorial

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**N-body Algorithm Suitability for GPU**

Lots of data parallelism Force calculations are independent Should be able to keep SMs and PEs busy Sufficient memory access regularity All force calculations access body data in same order* Should have lots of coalesced memory accesses Sufficient code regularity All force calculations are identical* There should be little thread divergence Plenty of data reuse O(n2) operations on O(n) data CPU/GPU transfer time is insignificant CUDA Optimization Tutorial

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**C to CUDA Conversion Two CUDA kernels Benefits Force calculation**

Advance position and velocity Benefits Force calculation requires over 99.9% of runtime Primary target for acceleration Advancing kernel unimportant to runtime But allows to keep data on GPU during entire simulation Minimizes GPU/CPU transfers CUDA Optimization Tutorial

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C to CUDA Conversion __global__ void ForceCalcKernel(int nbodies, struct Body *body, ...) { } __global__ void AdvancingKernel(int nbodies, struct Body *body, ...) { int main(...) { Body *body, *bodyl; cudaMalloc((void**)&bodyl, sizeof(Body)*nbodies); cudaMemcpy(bodyl, body, sizeof(Body)*nbodies, cuda…HostToDevice); for (timestep = ...) { ForceCalcKernel<<<1, 1>>>(nbodies, bodyl, ...); AdvancingKernel<<<1, 1>>>(nbodies, bodyl, ...); cudaMemcpy(body, bodyl, sizeof(Body)*nbodies, cuda…DeviceToHost); cudaFree(bodyl); Indicates GPU kernel that CPU can call Separate address spaces, need two pointers Allocate memory on GPU Copy CPU data to GPU Call GPU kernel with 1 block and 1 thread per block Copy GPU data back to CPU CUDA Optimization Tutorial

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**Evaluation Methodology**

Systems and compilers CC 1.3: Quadro FX 5800, nvcc 3.2 30 SMs, 240 PEs, 1.3 GHz, resident threads CC 2.0: Tesla C2050, nvcc 3.2 14 SMs, 448 PEs, 1.15 GHz, resident threads CC 3.0: GeForce GTX 680, nvcc 4.2 8 SMs, 1536 PEs, 1.0 GHz, resident threads Inputs and metric 1k, 10k, or 100k star clusters (Plummer model) Median runtime of three experiments, excluding I/O CUDA Optimization Tutorial

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**1-Thread Performance Problem size Slowdown rel. to CPU Performance**

n=10000, step=1 n=3000, step=1 Slowdown rel. to CPU CC 1.3: 72.4 CC 2.0: 36.7 CC 3.0: 68.1 (Note: comparing different GPUs to different CPUs) Performance 1 thread is one to two orders of magnitude slower on GPU than CPU Reasons No caches (CC 1.3) Not superscalar Slower clock frequency No SMT latency hiding CUDA Optimization Tutorial

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**Using N Threads Approach Threading Eliminate outer loop**

Instantiate n copies of inner loop, one per body Threading Blocks can only hold 512 or 1024 threads Up to 8/16 blocks can be resident in an SM at a time SM can hold 1024, 1536, or 2048 threads We use 256 threads per block (works for all of our GPUs) Need multiple blocks Last block may not need all of its threads CUDA Optimization Tutorial

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Using N Threads __global__ void ForceCalcKernel(int nbodies, struct Body *body, ...) { for (i = 0; i < nbodies; i++) { i = threadIdx.x + blockIdx.x * blockDim.x; // compute i if (i < nbodies) { // in case last block is only partially used for (j = ...) { } __global__ void AdvancingKernel(int nbodies,...) // same changes #define threads 256 int main(...) { int blocks = (nbodies + threads - 1) / threads; // compute block cnt for (timestep = ...) { ForceCalcKernel<<<1, 1blocks, threads>>>(nbodies, bodyl, ...); AdvancingKernel<<<1, 1blocks, threads>>>(nbodies, bodyl, ...); CUDA Optimization Tutorial

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**N Thread Speedup Relative to 1 GPU thread Performance**

CC 1.3: 7781 (240 PEs) CC 2.0: 6495 (448 PEs) CC 3.0: (1536 PEs) Relative to 1 CPU thread CC 1.3: 107.5 CC 2.0: 176.7 CC 3.0: 176.2 Performance Speedup much higher than number of PEs (32, 14.5, and 7.9 times) Due to SMT latency hiding Per-core performance CPU core delivers up to 4.4, 5, and 8.7 times as much performance as a GPU core (PE) CUDA Optimization Tutorial

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**Using Scalar Arrays Data structure conversion Optimize data structure**

Arrays of structs are bad for coalescing Bodies’ elements (e.g., mass fields) are not adjacent Optimize data structure Use multiple scalar arrays, one per field (need 10) Results in code bloat but often much better speed CUDA Optimization Tutorial

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Using Scalar Arrays __global__ void ForceCalcKernel(int nbodies, float *mass, ...) { // change all “body[k].blah” to “blah[k]” } __global__ void AdvancingKernel(int nbodies, float *mass, ...) { int main(...) { float *mass, *posx, *posy, *posz, *velx, *vely, *velz, *accx, *accy,*accz; float *massl, *posxl, *posyl, *poszl, *velxl, *velyl, *velzl, ...; mass = (float *)malloc(sizeof(float) * nbodies); // etc cudaMalloc((void**)&massl, sizeof(float)*nbodies); // etc cudaMemcpy(massl, mass, sizeof(float)*nbodies, cuda…HostToDevice); // etc for (timestep = ...) { ForceCalcKernel<<<blocks, threads>>>(nbodies, massl, posxl, ...); AdvancingKernel<<<blocks, threads>>>(nbodies, massl, posxl, ...); cudaMemcpy(mass, massl, sizeof(float)*nbodies, cuda…DeviceToHost); // etc CUDA Optimization Tutorial

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**Scalar Array Speedup Problem size Performance Relative to struct**

n=100000, step=1 n=300000, step=1 Relative to struct CC 1.3: 0.83 CC 2.0: 0.96 CC 3.0: 0.82 Performance Threads access same memory locations, not adjacent ones Always combined but not really coalesced access Slowdowns may be due to DRAM page/TLB misses Scalar arrays Still needed (see later) CUDA Optimization Tutorial

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**Constant Kernel Parameters**

Lots of parameters due to scalar arrays All but one parameter never change their value Constant memory “Pass” parameters only once Copy them into GPU’s constant memory Performance implications Reduced parameter passing overhead Constant memory has hardware cache CUDA Optimization Tutorial

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**Constant Kernel Parameters**

__constant__ int nbodiesd; __constant__ float dthfd, epssqd, float *massd, *posxd, ...; __global__ void ForceCalcKernel(int step) { // rename affected variables (add “d” to name) } __global__ void AdvancingKernel() { int main(...) { cudaMemcpyToSymbol(massd, &massl, sizeof(void *)); // etc for (timestep = ...) { ForceCalcKernel<<<1, 1>>>(step); AdvancingKernel<<<1, 1>>>(); CUDA Optimization Tutorial

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**Constant Mem. Parameter Speedup**

Problem size n=1000, step=10000 n=3000, step=10000 Speedup CC 1.3: 1.015 CC 2.0: 1.016 CC 3.0: 0.971 Performance Minimal perf. impact May be useful for very short kernels that are often invoked Benefit Less shared memory used on CC 1.3 devices CUDA Optimization Tutorial

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**Using the RSQRTF Instruction**

Slowest kernel operation Computing one over the square root is very slow GPU has slightly imprecise but fast 1/sqrt instruction (frequently used in graphics code to calculate inverse of distance to a point) IEEE floating-point accuracy compliance CC 1.x is not entirely compliant CC 2.x and above are compliant but also offer faster non-compliant instructions CUDA Optimization Tutorial

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**Using the RSQRT Instruction**

for (i = 0; i < nbodies; i++) { for (j = 0; j < nbodies; j++) { if (i != j) { dx = body[j].posx - px; dy = body[j].posy - py; dz = body[j].posz - pz; dsq = dx*dx + dy*dy + dz*dz; dinv = 1.0f / sqrtf(dsq + epssq); dinv = rsqrtf(dsq + epssq); scale = body[j].mass * dinv * dinv * dinv; ax += dx * scale; ay += dy * scale; az += dz * scale; } CUDA Optimization Tutorial

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**RSQRT Speedup Problem size Performance Speedup n=100000, step=1**

CC 1.3: 0.99 CC 2.0: 1.83 CC 3.0: 1.64 Performance No change for CC 1.3 Compiler automatically uses less precise RSQRTF as most FP ops are not fully precise anyhow 83% speedup for CC 2.0 Over entire application Compiler defaults to precise instructions Explicit use of RSQRTF indicates imprecision okay CUDA Optimization Tutorial

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**Using 2 Loops to Avoid If Statement**

“if (i != j)” causes thread divergence Break loop into two loops to avoid if statement for (j = 0; j < nbodies; j++) { if (i != j) { dx = body[j].posx - px; dy = body[j].posy - py; dz = body[j].posz - pz; dsq = dx*dx + dy*dy + dz*dz; dinv = rsqrtf(dsq + epssq); scale = body[j].mass * dinv * dinv * dinv; ax += dx * scale; ay += dy * scale; az += dz * scale; } CUDA Optimization Tutorial

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**Using 2 Loops to Avoid If Statement**

for (j = 0; j < i; j++) { dx = body[j].posx - px; dy = body[j].posy - py; dz = body[j].posz - pz; dsq = dx*dx + dy*dy + dz*dz; dinv = rsqrtf(dsq + epssq); scale = body[j].mass * dinv * dinv * dinv; ax += dx * scale; ay += dy * scale; az += dz * scale; } for (j = i+1; j < nbodies; j++) { CUDA Optimization Tutorial

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**Loop Duplication Speedup**

Problem size n=100000, step=1 n=300000, step=1 Speedup CC 1.3: 0.55 CC 2.0: 1.00 CC 3.0: 1.00 Performance No change for 2.0 & 3.0 Divergence moved to loop 45% slowdown for CC 1.3 Unclear why Discussion Not a useful optimization Code bloat A little divergence is okay (only 1 in 3125 iterations) CUDA Optimization Tutorial

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**Blocking using Shared Memory**

Code is memory bound Each warp streams in all bodies’ masses and positions Block inner loop Read block of mass & position info into shared mem Requires barriers (fast hardware barrier within SM) Advantage A lot fewer main memory accesses Remaining main memory accesses are fully coalesced (due to usage of scalar arrays) CUDA Optimization Tutorial

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**Blocking using Shared Memory**

__shared__ float posxs[threads], posys[threads], poszs[…], masss[…]; j = 0; for (j1 = 0; j1 < nbodiesd; j1 += THREADS) { // first part of loop idx = tid + j1; if (idx < nbodiesd) { // each thread copies 4 words (fully coalesced) posxs[id] = posxd[idx]; posys[id] = posyd[idx]; poszs[id] = poszd[idx]; masss[id] = massd[idx]; } __syncthreads(); // wait for all copying to be done bound = min(nbodiesd - j1, THREADS); for (j2 = 0; j2 < bound; j2++, j++) { // second part of loop if (i != j) { dx = posxs[j2] – px; dy = posys[j2] – py; dz = poszs[j2] - pz; dsq = dx*dx + dy*dy + dz*dz; dinv = rsqrtf(dsq + epssqd); scale = masss[j2] * dinv * dinv * dinv; ax += dx * scale; ay += dy * scale; az += dz * scale; __syncthreads(); // wait for all force calculations to be done CUDA Optimization Tutorial

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**Blocking Speedup Problem size Performance Discussion Speedup**

n=100000, step=1 n=300000, step=1 Speedup CC 1.3: 3.7 CC 2.0: 1.1 CC 3.0: 1.6 Performance Great speedup for CC 1.3 Some speedup for others Has hardware data cache Discussion Very important optimization for memory bound code Even with L1 cache CUDA Optimization Tutorial

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**Loop Unrolling CUDA compiler Use pragma to unroll (and pad arrays)**

Generally good at unrolling loops with fixed bounds Does not unroll inner loop of our example code Use pragma to unroll (and pad arrays) #pragma unroll 8 for (j2 = 0; j2 < bound; j2++, j++) { if (i != j) { dx = posxs[j2] – px; dy = posys[j2] – py; dz = poszs[j2] - pz; dsq = dx*dx + dy*dy + dz*dz; dinv = rsqrtf(dsq + epssqd); scale = masss[j2] * dinv * dinv * dinv; ax += dx * scale; ay += dy * scale; az += dz * scale; } CUDA Optimization Tutorial

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**Loop Unrolling Speedup**

Problem size n=100000, step=1 n=300000, step=1 Speedup CC 1.3: 1.07 CC 2.0: 1.16 CC 3.0: 1.07 Performance Noticeable speedup All three GPUs Discussion Can be useful May increase register usage, which may lower maximum number of threads per block and result in slowdown CUDA Optimization Tutorial

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**CC 2.0 Absolute Performance**

Problem size n=100000, step=1 Runtime 612 ms FP operations 326.7 GFlop/s Main mem throughput 1.035 GB/s Not peak performance Only 32% of 1030 GFlop/s Peak assumes FMA every cycle 3 sub (1c), 3 fma (1c), 1 rsqrt (8c), 3 mul (1c), 3 fma (1c) = 20c for 20 Flop 63% of realistic peak of GFlop/s Assumes no non-FP operations With int ops = 31c for 20 Flop 99% of actual peak of GFlop/s CUDA Optimization Tutorial

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**Eliminating the If Statement**

Algorithmic optimization Potential softening parameter avoids division by zero If-statement is not necessary and can be removed Eliminates thread divergence for (j2 = 0; j2 < bound; j2++, j++) { if (i != j) { dx = posxs[j2] – px; dy = posys[j2] – py; dz = poszs[j2] - pz; dsq = dx*dx + dy*dy + dz*dz; dinv = rsqrtf(dsq + epssqd); scale = masss[j2] * dinv * dinv * dinv; ax += dx * scale; ay += dy * scale; az += dz * scale; } CUDA Optimization Tutorial

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**If Elimination Speedup**

Problem size n=100000, step=1 n=300000, step=1 Speedup CC 1.3: 1.38 CC 2.0: 1.54 CC 3.0: 1.64 Performance Large speedup All three GPUs Discussion No thread divergence Allows compiler to schedule code much better CUDA Optimization Tutorial

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**Rearranging Terms Generated code is suboptimal**

Compiler does not emit as many fused multiply-add (FMA) instructions as it could Rearrange terms in expressions to help compiler Need to check generated assembly code for (j2 = 0; j2 < bound; j2++, j++) { dx = posxs[j2] – px; dy = posys[j2] – py; dz = poszs[j2] - pz; dsq = dx*dx + dy*dy + dz*dz; dinv = rsqrtf(dsq + epssqd); dsq = dx*dx + (dy*dy + (dz*dz + epssqd)); dinv = rsqrtf(dsq); scale = masss[j2] * dinv * dinv * dinv; ax += dx * scale; ay += dy * scale; az += dz * scale; } CUDA Optimization Tutorial

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**FMA Speedup Problem size Performance Discussion Speedup**

n=100000, step=1 n=300000, step=1 Speedup CC 1.3: 1.03 CC 2.0: 1.05 CC 3.0: 1.06 Performance Small speedup All three GPUs Discussion Seemingly needless transformations can make a difference CUDA Optimization Tutorial

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**Higher Unroll Factor Problem size Unroll 128 times Performance Speedup**

n=100000, step=1 n=300000, step=1 Speedup CC 1.3: 1.01 CC 2.0: 1.04 CC 3.0: 0.93 Unroll 128 times Avoid looping overhead Now that there are no ifs Performance Little speedup/slowdown Discussion Carefully choose unroll factor (manually tune) CUDA Optimization Tutorial

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**Compiler Flags Problem size -use_fast_math Performance Speedup**

n=100000, step=1 n=300000, step=1 Speedup CC 1.3: 1.00 CC 2.0: 1.18 CC 3.0: 1.15 -use_fast_math “-ftz=true” suffices (flush denormals to zero) Makes SP FP operations faster except on CC 1.3 Performance Significant speedup Discussion Use faster but less precise operations when prudent CUDA Optimization Tutorial

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**Final Absolute Performance**

CC 2.0 Fermi GTX 480 Problem size n=100000, step=1 Runtime 296.1 ms FP operations 675.6 GFlop/s (SP) 66% of peak performance 261.1 GFlops/s (DP) Main mem throughput 2.139 GB/s CC 3.0 Kepler GTX 680 Problem size n=300000, step=1 Runtime 1073 ms FP operations GFlop/s (SP) 54% of peak performance 88.7 GFlops/s (DP) Main mem throughput 5.266 GB/s CUDA Optimization Tutorial

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**Outline Introduction GPU programming N-body example Porting and tuning**

Other considerations Conclusions gamedsforum.ca Thepcreport.net CUDA Optimization Tutorial

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**Things to Consider Minimize PCIe transfers Locks and synchronization**

Implementing entire algorithm on GPU, even some slow serial code sections, might be overall win Can stream data to/from GPU while computing Locks and synchronization Lightweight locks & fast barriers possible within SM Slow across different SMs L1 data caches are not coherent Use volatile & fences to avoid deadlocks CUDA Optimization Tutorial

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**Warp-based Execution Problem Thread divergence**

// wrong on GPU, correct on CPU do { cnt = 0; if (ready[i] != 0) cnt++; if (ready[j] != 0) cnt++; } while (cnt < 2); ready[k] = 1; // correct if (cnt == 2) ready[k] = 1; Problem Thread divergence Loop exiting threads wait for other threads in warp to also exit “ready[k] = 1” is not executed until all threads in warp are done with loop Possible deadlock CUDA Optimization Tutorial

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**Hybrid Execution CPU always needed for program launch and I/O**

CPU much faster on serial program segments GPU 10 times faster than CPU on parallel code Running 10% of problem on CPU is hardly worthwhile Complicates programming and requires data transfer Best CPU data structure is often not best for GPU PCIe bandwidth much lower than GPU bandwidth 1.6 to 6.5 GB/s versus 192 GB/s But can send data while CPU & GPU are computing Merging CPU and GPU on same die (e.g., AMD’s Fusion APU) makes finer grain switching possible CUDA Optimization Tutorial

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**Outline Introduction GPU programming N-body example Porting and tuning**

Other considerations Conclusions gamedsforum.ca CUDA Optimization Tutorial

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**Summary and Conclusions (Part I)**

Step-by-step porting and tuning of CUDA code Example: n-body simulation GPUs have very powerful hardware But only exploitable with some codes Even harder to program and optimize than CPU hardware CUDA Optimization Tutorial

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**Martin Burtscher Department of Computer Science**

Parallelizing and Optimizing Programs for GPU Acceleration using CUDA (Part II) Martin Burtscher Department of Computer Science

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**Mapping Regular Code to GPUs**

Regular codes Operate on array- and matrix-based data structures Exhibit mostly strided memory access patterns Have relatively predictable control flow (control flow behavior is mainly determined by input size) Largely independent computations Many regular codes are easy to port to GPUs E.g., matrix codes executing many ops/word Dense matrix operations (level 2 and 3 BLAS) Stencil codes (PDE solvers) LLNL CUDA Optimization Tutorial

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**Mapping Irregular Code to GPUs**

Irregular codes Build, traverse, and update dynamic data structures (trees, graphs, linked lists, priority queues, etc.) Exhibit pointer-chasing memory access patterns Have complex control flow (control flow behavior depends on input values and changes dynamically) Many important scientific programs are irregular E.g., n-body simulation, data clustering, SAT solving, social networks, discrete-event simulation, meshing, … Need case studies on how to best map irreg codes FSU CUDA Optimization Tutorial

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**Example: N-body Simulation**

Irregular Barnes Hut algorithm Repeatedly builds unbalanced tree and performs complex traversals on it Our implementation Designed for GPUs (not just port of CPU code) First GPU implementation of entire BH algorithm Results GPU is 21 times faster than CPU (6 cores) on this code CUDA Optimization Tutorial

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**Outline Introduction Barnes Hut algorithm CUDA implementation**

Experimental results Conclusions NASA/JPL-Caltech/SSC CUDA Optimization Tutorial

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**Barnes Hut Idea Precise force calculation Barnes and Hut (1986)**

Requires O(n2) operations (O(n2) body pairs) Computationally intractable for large n Barnes and Hut (1986) Algorithm to approximately compute forces Bodies’ initial position & velocity are also approximate Requires only O(n log n) operations Idea is to “combine” far away bodies Error should be small because force 1/distance2 CUDA Optimization Tutorial

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**Barnes Hut Algorithm Set bodies’ initial position and velocity**

Iterate over time steps Compute bounding box around bodies Subdivide space until at most one body per cell Record this spatial hierarchy in an octree Compute mass and center of mass of each cell Compute force on bodies by traversing octree Stop traversal path when encountering a leaf (body) or an internal node (cell) that is far enough away Update each body’s position and velocity CUDA Optimization Tutorial

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Build Tree (Level 1) Compute bounding box around all bodies → tree root CUDA Optimization Tutorial

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**Build Tree (Level 2) Subdivide space until at most one body per cell**

CUDA Optimization Tutorial

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**Build Tree (Level 3) Subdivide space until at most one body per cell**

CUDA Optimization Tutorial

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**Build Tree (Level 4) Subdivide space until at most one body per cell**

CUDA Optimization Tutorial

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**Build Tree (Level 5) Subdivide space until at most one body per cell**

CUDA Optimization Tutorial

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**Compute Cells’ Center of Mass**

For each internal cell, compute sum of mass and weighted average of position of all bodies in subtree; example shows two cells only CUDA Optimization Tutorial

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**Compute Forces Compute force, for example, acting upon green body**

CUDA Optimization Tutorial

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**Compute Force (short distance)**

Scan tree depth first from left to right; green portion already completed CUDA Optimization Tutorial

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**Compute Force (down one level)**

Red center of mass is too close, need to go down one level CUDA Optimization Tutorial

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**Compute Force (long distance)**

Blue center of mass is far enough away CUDA Optimization Tutorial

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**Compute Force (skip subtree)**

Therefore, entire subtree rooted in the blue cell can be skipped CUDA Optimization Tutorial

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Pseudocode bodySet = ... foreach timestep do { bounding_box = new Bounding_Box(); foreach Body b in bodySet { bounding_box.include(b); } octree = new Octree(bounding_box); octree.Insert(b); cellList = octree.CellsByLevel(); foreach Cell c in cellList { c.Summarize(); b.ComputeForce(octree); b.Advance(); CUDA Optimization Tutorial

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**Complexity and Parallelism**

bodySet = ... foreach timestep do { // O(n log n) + ordered sequential bounding_box = new Bounding_Box(); foreach Body b in bodySet { // O(n) parallel reduction bounding_box.include(b); } octree = new Octree(bounding_box); foreach Body b in bodySet { // O(n log n) top-down tree building octree.Insert(b); cellList = octree.CellsByLevel(); foreach Cell c in cellList { // O(n) + ordered bottom-up traversal c.Summarize(); foreach Body b in bodySet { // O(n log n) fully parallel b.ComputeForce(octree); foreach Body b in bodySet { // O(n) fully parallel b.Advance(); CUDA Optimization Tutorial

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**Outline Introduction Barnes Hut algorithm CUDA implementation**

Experimental results Conclusions CUDA Optimization Tutorial

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**Efficient GPU Code Large amounts of data parallelism**

Coalesced main memory accesses Little thread divergence Relatively little synchronization between blocks Little CPU/GPU data transfer Efficient use of shared memory Thepcreport.net CUDA Optimization Tutorial

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**Main BH Implementation Challenges**

Uses irregular tree-based data structure Initially little parallelism Little coalescing Load imbalance Complex recursive traversals Recursion not well supported Lots of thread divergence Memory-bound pointer-chasing operations Not enough computation to hide latency CUDA Optimization Tutorial

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**Six GPU Kernels Read initial data and transfer to GPU**

for each timestep do { Compute bounding box around bodies (not irregular) Build hierarchical decomposition, i.e., octree Summarize body information in internal octree nodes Approximately sort bodies by spatial location (optional) Compute forces acting on each body with help of octree Update body positions and velocities (not irregular) } Transfer result from GPU and output CUDA Optimization Tutorial

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**Global Optimizations Make code iterative (recursion not supported*)**

Keep data on GPU between kernel calls Use array elements instead of heap nodes One aligned array per field for coalesced accesses CUDA Optimization Tutorial

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**Global Optimizations (cont.)**

Maximize thread count (round down to warp size) Maximize resident block count (all SMs filled) Pass kernel parameters through constant memory Use special allocation order Alias arrays (56 B/node) Use index arithmetic Persistent blocks & threads Unroll loops over children CUDA Optimization Tutorial

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**Kernel 1: Bounding Box (Regular)**

Optimizations Fully coalesced Fully cached No bank conflicts Minimal divergence Built-in min and max 2 red/mem, 6 red/bar Bodies load balanced 512*3 threads per SM Reduction operation CUDA Optimization Tutorial

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**Kernel 2: Build Octree (Irregular)**

Optimizations Only lock leaf “pointers” Lock-free fast path Light-weight lock release No re-traverse after lock acquire failure Combined memory fence Re-compute position during traversal Separate init kernels 512*3 threads per SM Top-down tree building CUDA Optimization Tutorial

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**Kernel 2: Build Octree (cont.)**

// initialize cell = find_insertion_point(body); // no locks, cache cell child = get_insertion_index(cell, body); if (child != locked) { // skip atomic if already locked if (child == null) { // fast path (frequent) if (null == atomicCAS(&cell[child], null, body)) { // lock-free insertion // move on to next body } } else { if (child == atomicCAS(&cell[child], child, lock)) { // acquire lock // build subtree with new and existing body flag = true; __syncthreads(); // optional barrier __threadfence(); // make data visible if (flag) { cell[child] = new_subtree; // insert subtree and releases lock CUDA Optimization Tutorial

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**Kernel 3: Summarize Subtrees (Irreg.)**

Bottom-up tree traversal Optimizations Scan avoids deadlock Use mass as flag + fence No locks, no atomics Use wait-free first pass Cache the ready info Piggyback on traversal Count bodies in subtrees No parent “pointers” 128*6 threads per SM CUDA Optimization Tutorial

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**Kernel 4: Sort Bodies (Irregular)**

Top-down tree traversal Optimizations (Similar to Kernel 3) Scan avoids deadlock Use data field as flag No locks, no atomics Use counts from Kernel 3 Piggyback on traversal Move nulls to back Throttle warps with optional barrier 64*6 threads per SM CUDA Optimization Tutorial

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**Kernel 5: Force Calculation (Irregular)**

Multiple prefix traversals Optimizations Group similar work together Uses sorting to minimize size of prefix union in each warp Early out (nulls in back) Traverse whole union to avoid divergence (warp voting) Lane 0 controls iteration stack for entire warp (fits in shmem) Minimize volatile accesses Use fast 1/sqrtf instruction Cache tree-level-based data 256*5 threads per SM CUDA Optimization Tutorial

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**Architectural Support**

Coalesced memory accesses & lockstep execution All threads in warp read same tree node at same time Only one mem access per warp instead of 32 accesses Warp-based execution Enables data sharing in warps w/o synchronization RSQRTF instruction Quickly computes good approximation of 1/sqrtf(x) Warp voting instructions Quickly perform reduction operations within a warp CUDA Optimization Tutorial

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**Kernel 6: Advance Bodies (Regular)**

Optimizations Fully coalesced, no divergence Load balanced, 1024*1 threads per SM Straightforward streaming CUDA Optimization Tutorial

97
**Outline Introduction Barnes Hut algorithm CUDA implementation**

Experimental results Conclusions CUDA Optimization Tutorial

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**Evaluation Methodology**

Implementations CUDA/GPU: Barnes Hut and O(n2) algorithms OpenMP/CPU: Barnes Hut algorithm (derived from CUDA) Pthreads/CPU: Barnes Hut algorithm (SPLASH-2 suite) Systems and compilers nvcc 4.0 (-O3 -arch=sm_20 -ftz=true*) GeForce GTX 480, 1.4 GHz, 15 SMs, 32 cores per SM gcc (-O3 -fopenmp* -ffast-math*) Xeon X5690, 3.46 GHz, 6 cores, 2 threads per core Inputs and metric 5k, 50k, 500k, and 5M star clusters (Plummer model) Best runtime of three experiments, excluding I/O CUDA Optimization Tutorial

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**Nodes Touched per Activity (5M Input)**

Kernel “activities” K1: pair reduction K2: tree insertion K3: bottom-up step K4: top-down step K5: prefix traversal K6: integration step Max tree depth ≤ 22 Cells have 3.1 children Prefix ≤ 6,315 nodes (≤ 0.1% of 7.4 million) BH algorithm & sorting to min. union work well CUDA Optimization Tutorial

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**Available Amorphous Data Parallelism**

Almost every “round” has lots of activities without data dependencies that can be processed in parallel bounding box tree building summarization sorting force calc. integration CUDA Optimization Tutorial

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**Runtime Comparison GPU BH inefficiency BH vs. O(n2) algorithm**

5k input too small for 5,760 to 23,040 threads BH vs. O(n2) algorithm O(n2) faster with fewer than about 15k bodies GPU (5M input) 21.1x faster than OpenMP 23.2x faster than Pthreads CUDA Optimization Tutorial

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**Kernel Performance for 5M Input**

$200 GPU delivers 228 GFlops/s on irregular code GPU chip is 2.7 to 23.5 times faster than CPU chip GPU hardware is better suited for BH than CPU hw But difficult and very time consuming to program CUDA Optimization Tutorial

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**Kernel Speedups Optimizations that are generally applicable**

Optimizations for irregular kernels CUDA Optimization Tutorial

104
**Outline Introduction Barnes Hut algorithm CUDA implementation**

Experimental results Conclusions CUDA Optimization Tutorial

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**Optimization Summary Reduce main memory accesses**

Share data within warp, combine memory fences & traversals, re-compute data, avoid volatile accesses Minimize thread divergence Group similar work together, force synchronicity Implement entire algorithm on and for GPU Avoid data transfers & data structure inefficiencies, wait-free pre-pass, scan entire prefix union CUDA Optimization Tutorial

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**Optimization Summary (cont.)**

Exploit hardware features Fast synchronization & thread startup, special instrs., coalesced memory accesses, even lockstep execution Use light-weight locking and synchronization Minimize locks, reuse fields, and use fence + store ops Maximize parallelism Parallelize every step within and across SMs CUDA Optimization Tutorial

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**CPU/GPU Implementation Comparison**

Irregular CPU code Dynamically (incrementally) allocated shared data structures Structure-based shared data structures Logical lock-based implementation Global/local worklists Recursive or iterative implementation Irregular GPU code Statically (wholly) allocated shared data structures Multiple-array-based shared data structures Lock-free implementation (Implicit) local worklists Iterative implementation CUDA Optimization Tutorial

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**Useful GPU Hardware Features**

Wide parallelism Great for exploiting large amounts of parallelism Massive multithreading Ideal for hiding latency of irregular mem. accesses Fast thread startup Essential when launching thousands of threads Shared memory Fast data sharing Useful for local worklists HW support for reduction and synchronization Makes otherwise costly operations very fast Coalesced accesses Memory access combining is useful in irregular codes Lockstep execution Can share data without explicit synchronization Allows to consolidate iteration stacks CUDA Optimization Tutorial

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**Challenges with GPUs Warp-based execution Data structure layout**

Often requires sorting of work or algorithm change Data structure layout Best layout for CPU differs from best layout for GPU SoA can be tedious to code and deal with (parameter passing) Separate memory space Slow transfers Pack/unpack data Incoherent L1 caches May need to explicitly manage data (fences) Poor recursion support Need to make code iterative and maintain explicit iteration stacks Thread and block counts Hierarchy complicates implementation Optimal counts have to be (auto-)tuned CUDA Optimization Tutorial

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**Running Irregular Algorithms on GPUs**

Mandatory Need vast amounts of data parallelism Can do large chunks of computation on GPU Very Important Cautious implementation DS can be expressed through fixed arrays Uses local worklists that can be statically populated Important Scheduling is independent of previous activities Easy to sort activities by similarity (if needed) Beneficial Easy to express iteratively Has statically known range of neighborhoods DS size (or bound) can be determined based on input CUDA Optimization Tutorial

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Conclusions Irregularity does not necessarily prevent high-performance on GPUs Entire Barnes Hut algorithm implemented on GPU Builds and traverses unbalanced octree GPU is 21.1 times (float) and 9.1 times (double) faster than high-end 6-core Xeon Code directly for GPU, do not merely adjust CPU code Requires different data and code structures Benefits from different algorithmic modifications CUDA Optimization Tutorial

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**Acknowledgments Hardware Funding OpenMP code Collaborator**

NVIDIA Corp. and Intel Corp. Funding NVIDIA Corp. and Texas State University OpenMP code Ricardo Alves (Universidade do Minho, Portugal) Collaborator Keshav Pingali (University of Texas at Austin) CUDA Optimization Tutorial

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**CUDA Optimization Tutorial**

Martin Burtscher Barnes Hut CUDA code Tutorial slides CUDA Optimization Tutorial

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