gpu computing dr. bo yuan e-mail: yuanb@sz.tsinghua.edu.cn

GPU ComputingGPU Computing

Dr. Bo Yuan

E-mail: yuanb@sz.tsinghua.edu.cn

OverviewOverview

Foundation

Thread

Memory Structure

Intermediate

Kernel

Vector Addition

Matrix Multiplication

Shared Memory

Advanced

Memory Access

Resource Optimization

Dynamic Parallelism

Extension

Floating Point

Stream

Multiple GPUs

Parallel Matlab

What is GPU?What is GPU?

• Graphics Processing Unit

• First GPU: GeForce 256 (1999)

• Connected to motherboard via PCI Express

• High computational density and memory bandwidth

• Massively multithreaded many-core chips

• Traditionally used for real-time rendering

• Several millions units are sold each year.

Graphics CardsGraphics Cards

GPU PipelineGPU Pipeline

Rasterization

Anti-AliasingAnti-Aliasing

Triangle Geometry Aliased Anti-AliasedTriangle Geometry Aliased Anti-Aliased

GPGPUGPGPU

• General-Purpose Computing on GPUs

• Massively Parallel, Simple Operations

• Suitable for compute-intensive engineering problems

• The original problem needs to be cast into native graphics operations.

• Launched through OpenGL or DirectX API calls

• Input data are stored in texture images and issued to the GPU by submitting triangles.

• Highly restricted access to input/output

• Very tedious, limited success with painstaking efforts

Trend of ComputingTrend of Computing

CPU vs. GPUCPU vs. GPU

ALUControl

CPU GPU

Multi-Core Many-Core

Number of ALUs

Memory Bandwidth

Power of the CrowdPower of the Crowd

Instruction Fetch/Dispatch

Instruction L1

Streaming Multiprocessor

Shared Memory

• SM– Streaming Multiprocessor

– Multi-threaded processor core

– Processing unit for thread block

– SPs (Streaming Processor)

– SFUs (Special Function Unit)

• SP– Streaming Processor

– Scalar ALU for a single CUDA thread

• SIMT– Single-Instruction, Multiple-Thread

– Shared instruction fetch per 32 threads (warp)

Need For SpeedNeed For Speed

Green ComputingGreen Computing

Intel Core i7-980XE

SupercomputingSupercomputing

• TITAN, Oak Ridge National Laboratory

• Speed: 24.8 PFLOPS (Theory), 17.6 PFLOPS (Real)

• CPU: AMD Opteron 6274 (18,688 × 16 cores)

• GPU: NVIDIA Tesla K20 (18,688 × 2496 cores)

• Cost: US$ 97 Million

• Power: 9 MW

Personal SupercomputerPersonal Supercomputer

What is CUDA?What is CUDA?

• Compute Unified Device Architecture

• Introduced by NVIDIA in 2007

• Scalable Parallel Programming Model

• Small extensions to standard C/C++

• Enable general-purpose GPU computing

• Straightforward APIs to manage

devices, memory etc.

• Only supports NVIDIA GPUs.

http://developer.nvidia.com/category/zone/cuda-zone

CUDA-Enabled GPUCUDA-Enabled GPU

Load/store

Global Memory

Thread Execution Manager

Input Assembler

Texture Texture Texture Texture Texture Texture Texture TextureTexture

Parallel DataCache

Load/store Load/store Load/store Load/store Load/store

CUDA GPUsCUDA GPUs

ComputeCapability GPUs Cards

2.0 GF100, GF110GeForce GTX 470, GTX 480, GTX 570, GTX 580, GTX

590, Tesla C2050, C2070

2.1GF104, GF114, GF116,

GF108, GF106

GeForce GT 430, GT 440, GTX 460, GTX 550 Ti, GTX

560 Ti, GT 640, GT 630

3.0 GK104, GK106, GK107GeForce GTX 690, GTX 680, GTX 670, GTX 660, GTX

650 Ti, GTX 650

3.5 GK110, GK208GeForce GTX TITAN, GT 640 (Rev. 2), GT 630 (Rev. 2),

Tesla K40, Tesla K20

5.0 GM107, GM108 GeForce GTX 750 Ti, GTX 750, GTX 860M

Fermi ArchitectureFermi Architecture

Kepler ArchitectureKepler Architecture• GeForce GTX 680 (Mar. 22, 2012)

• GK104, 28 nm process

• 3.5 billion transistors on a 294 mm2 die

• CUDA Cores: 1536 (8 SMs X 192 SPs)

• Memory Bandwidth: 192 GB/S

• Peak Performance: 3090 GFLOPS

• TDP: 195W

• Release Price: $499

Maxwell ArchitectureMaxwell Architecture• GeForce GTX 750 Ti (Feb. 18, 2014)

• GM107, 28 nm process

• 1.87 billion transistors on a 148 mm2 die

• CUDA Cores: 640 (5 SMs X 128 Cores)

• Memory Bandwidth: 86.4 GB/S

• Peak Performance: 1306 GFLOPS

• TDP: 60W

• Release Price: $149

CUDA Teaching LabCUDA Teaching Lab

• GTX 750 (GM107)

• Compute Capability: 5.0

• 512 CUDA Cores

• 1GB, 128-bit GDDR5

• 80 GB/S

• 1044 GFLOPS

• TDP: 55W

• RMB 799

• GT 630 (GK208)

• Compute Capability: 3.5

• 384 CUDA Cores

• 2GB, 64-bit GDDR3

• 14.4 GB/S

• 692.7 GFLOPS

• TDP: 25W

• RMB 419

CUDA InstallationCUDA Installationhttps://developer.nvidia.com/cuda-downloads

CUDA: deviceQueryCUDA: deviceQuery

CUDA: bandwidthTestCUDA: bandwidthTest

CUDA ApplicationsCUDA Applications

CUDA ShowcaseCUDA Showcase

Heterogeneous ComputingHeterogeneous Computing

Device

Heterogeneous ComputingHeterogeneous Computing

Grids, Blocks and ThreadsGrids, Blocks and ThreadsHost

Kernel 1

Kernel 2

Device

Grid 1

Block(0, 0)

Block(1, 0)

Block(2, 0)

Block(0, 1)

Block(1, 1)

Block(2, 1)

Grid 2

Block (1, 1)

Thread(0, 1)

Thread(1, 1)

Thread(2, 1)

Thread(3, 1)

Thread(4, 1)

Thread(0, 2)

Thread(1, 2)

Thread(2, 2)

Thread(3, 2)

Thread(4, 2)

Thread(0, 0)

Thread(1, 0)

Thread(2, 0)

Thread(3, 0)

Thread(4, 0)

Thread BlockThread Block

• Threads have thread ID numbers within block.

• Threads use thread ID to select work.

• Threads are assigned to SMs in block granularity.

• Each GT200 SM can have maximum 8 blocks.

• Each GT200 SM can have maximum 1024 threads.

• Threads in the same block can share data and synchronize.

• Threads in different blocks cannot cooperate.

• Each block can execute in any order relative to other blocks.

Thread Id #:0 1 2 3 … m

Thread program

Code ExampleCode Example

Transparent ScalabilityTransparent Scalability

Device

Block 0 Block 1

Block 2 Block 3

Block 4 Block 5

Block 6 Block 7

Kernel grid

Block 0 Block 1

Block 2 Block 3

Block 4 Block 5

Block 6 Block 7

Device

Block 0 Block 1 Block 2 Block 3

Block 4 Block 5 Block 6 Block 7

Memory SpaceMemory SpaceGrid

Global Memory

Block (0, 0)

Shared Memory

Thread (0, 0)

Registers

Thread (1, 0)

Registers

Block (1, 0)

Shared Memory

Thread (0, 0)

Registers

Thread (1, 0)

Registers

Constant Memory

• Each thread can:

– Read/write per-thread registers

– Read/write per-block shared memory

– Read/write per-grid global memory

– Read/only per-grid constant memory

GeForce GTX 680

Memory Bandwidth … 192 GB/S

Single-Precision Floating Point … 4B

Peak Performance … 3090 GFLOPS

Practical Performance … 48 GFLOPS

Hello World!Hello World!

int main(void) {

printf(“Hello World!\n”);

return 0;}

__global__ void mykernel(void) {}

int main(void) {

mykernel<<<1,1>>>();

printf(“Hello World!\n”);

return 0;}

Your first CUDA code!

Device CodeDevice Code

• CUDA keyword __global__ indicates a kernel function that:– Runs on the device.

– Called from the host.

• CUDA keyword __device__ indicates a device function that:– Runs on the device.

– Called from a kernel function or another device function.

• Triple angle brackets <<< >>> indicate a call from host code to device code.– Kernel launch

• nvcc separates source code into two components:– Device functions are processed by NVIDIA compiler.

– Host functions are processed by standard host compiler.

– $ nvcc hello.cu

Addition on DeviceAddition on Device

__global__ void add (int *a, int *b, int *c) {*c=*a+*b;

• add () will execute on the device.

• add () will be called from the host.

• a, b, c must point to device memory.

• We need to allocate memory on GPU.

Memory ManagementMemory Management

• Host and device memories are separate entities.

• Device pointers point to GPU memory.– May be passed to/from host code.

– May not be dereferenced in host code.

• Host pointers point to CPU memory– May be passed to/from device code.

– May not be dereferenced in device code.

• CUDA APIs for handling device memory– cudaMalloc(), cudaFree(), cudaMemcpy()

– C equivalents: malloc(), free(), memcpy()

Addition on Device: main()Addition on Device: main()

int main(void) {int a, b, c; // host copiesint *d_a, *d_b, *d_c; // device copiesint size=sizeof(int);

// Allocate space for device copies of a, b, c cudaMalloc((void **)&d_a, size);

cudaMalloc((void **)&d_b, size);cudaMalloc((void **)&d_c, size);

a=2;b=7;

// Copy inputs to devicecudaMemcpy(d_a, &a, size, cudaMemcpyHostToDevice);cudaMemcpy(d_b, &b, size, cudaMemcpyHostToDevice);

Addition on Device: main()Addition on Device: main()

// Launch add() kernel on GPUadd<<<1,1>>>(d_a,d_b,d_c);

// Copy result back to hostcudaMemcpy(&c, d_c, size, cudaMemcpyDeviceToHost);

// CleanupcudaFree(d_a);

cudaFree(d_b);cudaFree(d_c);

return 0;}

Moving to ParallelMoving to Parallel

• Each call to add() adds two integers.

• With add() running in parallel, we can do vector addition in parallel.

• add<<<nblocks, 1>>>(d_a, d_b, d_c)

• Each parallel invocation of add() is referred to as a block.

• By using blockIdx.x to index into the array, each block handles a different

index.

• Block can be 2D:– dim3 nblocks(M, N)

– blockIdx.x, blockIdx.y

Vector Addition on DeviceVector Addition on Device

__global__ void add (int *a, int *b, int *c) {c[blockIdx.x]=a[blockIdx.x]+b[blockIdx.x];

c[0]=a[0]+b[0];

Block 0

c[1]=a[1]+b[1];

Block 1

c[2]=a[2]+b[2];

Block 2

c[3]=a[3]+b[3];

Block 3

Vector Addition on Device: main()Vector Addition on Device: main()

# define N 512int main(void) {

int *a, *b, *c; // host copiesint *d_a, *d_b, *d_c; // device copiesint size=N*sizeof(int);

// Allocate space for device copies of a, b, c cudaMalloc((void **)&d_a, size);

cudaMalloc((void **)&d_b, size);cudaMalloc((void **)&d_c, size);

// Allocate space of host copies of a, b, c// Set up initial valuesa=(int *)malloc(size); rand_ints(a, N);b=(int *)malloc(size); rand_ints(b, N);c=(int *)malloc(size); rand_ints(c, N);

Vector Addition on Device: main()Vector Addition on Device: main()

// Copy inputs to devicecudaMemcpy(d_a, a, size, cudaMemcpyHostToDevice);cudaMemcpy(d_b, b, size, cudaMemcpyHostToDevice);

// Launch add() kernel on GPU with N blocksadd<<<N, 1>>(d_a, d_b, d_c);

// Copy results back to hostcudaMemcpy(c, d_c, size, cudaMemcpyDeviceToHost);

// Cleanupfree(a); free(b); free(c);cudaFree(d_a); cudaFree(d_b); cudaFree(d_c);

return 0;}

CUDA ThreadsCUDA Threads

• Each block can be split into parallel threads.

• Threads can be up to 3D:– dim3 nthreads(M, N, P)

– threadIdx.x, threadIdx.y, threadIdx.z

__global__ void add (int *a, int *b, int *c) {c[threadIdx.x]=a[threadIdx.x]+b[threadIdx.x];

add<<<1, N>>>(d_a, d_b, d_c);

Combining Blocks and ThreadsCombining Blocks and Threads

• We have seen parallel vector addition using:– Many blocks with one thread each

– One block with many threads

• Let’s adapt vector addition to use both blocks and threads.– Why bother?

IndexingIndexing

M=8; // 8 threads/blockint index=threadIdx.x+blockIdx.x*M;

int index=threadIdx.x+blockIdx.x*blockDim.x;

__global__ void add (int *a, int *b, int *c) {int index=threadIdx.x+blockIdx.x*blockDim.x;c[index]=a[index]+b[index];

IndexingIndexing

#define N (2048*2048)#define M 512 // THREADS_PER_BLOCK

add<<<N/M, M>>>(d_a, d_b, d_c);

__global__ void add (int *a, int *b, int *c, int n) {

int index=threadIdx.x+blockIdx.x*blockDim.x;

if (index<n)

c[index]=a[index]+b[index];}

add<<<(N+M-1)/M, M>>>(d_a, d_b, d_c, N);

Data Access PatternData Access Pattern

radius radius

output

How many times?

Sharing Data Between ThreadsSharing Data Between Threads

• Each thread generates one output element.– blockDim.x elements per block

• Each input element needs to be read several times.– High I/O cost

• Within a block, threads can share data via shared memory.– Data are not visible to threads in other blocks.

• Extremely fast on-chip memory

• Declared using keyword: __shared__, allocated per block.

• Read (blockDim.x+2*radius)input elements from global to shared memory.

Collaborative ThreadsCollaborative Threads

0 1 2 4 5 63 7 8 9

shared

blockDim.x output elements

Thread 0 produces the values of temp[i], i=0, 3, 13.

Thread 9 requires the values of temp[i], i=9, 10, 11, 12, 13, 14, 15.

Data Race!

void _syncthreads()

T0T0 T0

Kernel SynchronizationKernel Synchronization__global__ void vector_sum(int *in, int *out) {

__shared__ int temp[BLOCK_SIZE+2*RADIUS];

int gindex=threadIdx.x+blockIdx.x*blockDim.x; // global index

int lindex=threadIdx.x+RADIUS; // local index

// Read input elements into shared memory

temp[lindex]=in[gindex];

if (threadIdx.x<RADIUS) { // some extra work

temp[lindex-RADIUS]=in[gindex-RADIUS];

temp[lindex+BLOCK_SIZE]=in[gindex+BLOCK_SIZE];

} __syncthreads();

int offset, result=0;

for (offset=-RADIUS; offset<=RADIUS; offset++)

result+=temp[lindex+offset];

out[gindex]=result;}

void MatrixMulOnHost(float* M, float* N, float* P, int Width){ int i, j, k; float a, b, sum; for (i = 0; i < Width; ++i) for (j = 0; j < Width; ++j) {

sum = 0;for (k = 0; k < Width; ++k) {

a = M[i * width + k]; b = N[k * width + j]; sum += a * b; } P[i * Width + j] = sum; }}

Matrix MultiplicationMatrix Multiplication

WIDTH WIDTH

Host Code Only

Single Thread BlockSingle Thread Blockdim3 dimGrid(1,1);dim3 dimBlock(Width, Width);…MatrixMulKernel<<<dimGrid, dimBlock>>>(Md, Nd, Pd, Width);…

__global__ void MatrixMulKernel(float* Md, float* Nd, float* Pd, int Width){

int k=0; float Pvalue = 0, Melement, Nelement;

for (k = 0; k < Width; ++k) { Melement = Md[threadIdx.y*Width+k]; // Md[threadIdx.y, k] Nelement = Nd[k*Width+threadIdx.x]; // Nd[k, threadIdx.x] Pvalue += Melement * Nelement; } // Pd[threadIdx.y, threadIdx.x] Pd[threadIdx.y*Width+threadIdx.x] = Pvalue; }

Single Thread BlockSingle Thread Block

• What is the maximum size of the matrix?– Each thread computes one element of Pd.

• Each thread:– Loads a row of matrix Md.

– Loads a column of matrix Nd.

– Perform one multiply and addition for each pair

of Md and Nd elements.

• CGMA– Compute to Global Memory Access

Grid 1

Block 1

3 2 5 4

Thread(2, 2)

Multiple BlocksMultiple Blocks

TILE_WIDTH

WIDTHWIDTH

01 TILE_WIDTH-12

TILE_WIDTH-1

• Break Pd into square tiles.

• Each block calculates one tile:– Each threads calculates one element.

– Block size equals to tile size.

• Require both block ID and thread ID.

Multiple Blocks: An ExampleMultiple Blocks: An Example

P1,0P0,0

P2,0 P3,0

P0,2 P2,2 P3,2P1,2

P3,1P2,1

P0,3 P2,3 P3,3P1,3

Block(0,0) Block(1,0)

Block(1,1)Block(0,1)

TILE_WIDTH = 2

Pd1,0Md2,0

Md1,0Md0,0

Md3,1 Pd0,1

Pd2,0 Pd3,0

Nd0,3 Nd1,3

Nd1,0Nd0,0

Pd0,2 Pd2,2 Pd3,2Pd1,2

Pd3,1Pd2,1

Pd0,3 Pd2,3 Pd3,3Pd1,3

Multiple Blocks: IndexingMultiple Blocks: Indexing

• TILE_WIDTH

• Block: blockIdx.x, blockIdx.y

• Thread: threadIdx.x, threadIdx.y

• Row: blockIdx.y * TILE_WIDTH + threadIdx.y

• Col: blockIdx.x * TILE_WIDTH + threadIdx.x

(0,0) (1,0) (2,0) (3,0)

(0,1) (1,1) (2,1) (3,1)

(0,2) (1,2) (2,2) (3,2)

(0,3) (1,3) (2,3) (3,3)

blockIdx.y

blockIdx.x threadIdx.x

threadIdx.y

Multiple Blocks: Device CodeMultiple Blocks: Device Code

__global__ void MatrixMulKernel(float* Md, float* Nd, float* Pd, int Width){ // Calculate the row index of the Pd element and Md int Row=blockIdx.y*TILE_WIDTH+threadIdx.y; // Calculate the col index of the Pd element and Nd int Col=blockIdx.x*TILE_WIDTH+threadIdx.x;

int k; float Pvalue = 0; // Each thread computes one element of sub-matrix for (k = 0; k < Width; ++k) Pvalue += Md[Row*Width+k] * Nd[k*Width+Col]; Pd[Row*Width+Col] = Pvalue;}

Block GranularityBlock Granularity

• Each SM in GT200 can take up to 1024 threads and 8 blocks.

• 8×8: 64 threads per block, 1024/64=12 blocks, 64×8=512 threads per SM

• 16×16: 256 threads per block, 1024/256=4 blocks, full capacity!

• 32×32: 1024 threads per block, exceeding the limit of 512 threads/block

t0 t1 t2 … tm

Blocks

SharedMemory

t0 t1 t2 … tmSM 1SM 0

Blocks

Global Memory AccessGlobal Memory Access

T1,0T0,0

T0,1 T1,1

2×2 Thread Block

• Each thread requires one row from Md and

one column from Nd.

• For a k×k thread block, each row/column will

be accessed k times.

• To reduce the global memory I/O, it is

beneficial to load the required data once into

the shared memory.

Splitting MdSplitting Md

Md0,0 Md1,0 Md2,0 Md3,0

Md0,1 Md1,1 Md2,1 Md3,1

Mds0,0 Mds1,0

Mds0,1 Mds1,1

Mds0,0 Mds1,0

Mds0,1 Mds1,1

MdMds Mds

Phase 1 Phase 2

shared shared

• The shared memory per SM is limited (e.g., 64KB).

• Shared among all blocks in the same SM.

• Luckily, not all data needs to be in the shared memory simultaneously.

Shared Memory: Device CodeShared Memory: Device Code__global__ void MatrixMulKernel(float* Md, float* Nd, float* Pd, int

Width){1. __shared__ float Mds[TILE_WIDTH][TILE_WIDTH];2. __shared__ float Nds[TILE_WIDTH][TILE_WIDTH];3. int bx = blockIdx.x; int by = blockIdx.y;4. int tx = threadIdx.x; int ty = threadIdx.y;// Identify the row and column of the Pd element to work on5. int Row = by * TILE_WIDTH + ty;6. int Col = bx * TILE_WIDTH + tx;7. float Pvalue = 0;// Loop over the Md and Nd tiles required to compute the Pd element8. for (int m = 0; m < Width/TILE_WIDTH; ++m) {// Collaboratively load Md and Nd tiles into shared memory9. Mds[ty][tx] = Md[Row*Width + (m*TILE_WIDTH + tx)];10. Nds[ty][tx] = Nd[Col + (m*TILE_WIDTH + ty)*Width];11. __syncthreads(); // Make sure the shared memory is ready

Shared Memory: Device CodeShared Memory: Device Code12. for (int k = 0; k < TILE_WIDTH; ++k)13. Pvalue += Mds[ty][k] * Nds[k][tx];// Make sure all threads have finished working on the shared memory

14. __syncthreads(); }15. Pd[Row*Width+Col] = Pvalue;}

• Each SM in G80 can take up to 768 threads and 8 blocks.

• Each SM has 16KB shared memory.

• For a tile of size 16 × 16, each block requires 16 × 16 × 4 = 1KB for Mds.

• Totally, 2KB are required for each block and 8 blocks can be supported.

• However, since 768/(16 × 16) = 3, only 3 blocks and 6KB will be in use.

Performance ConsiderationsPerformance Considerations

• GPU computing is easy:– Host, Device, Kernel, Block, Thread

– GPU Cards

– Up and running in a few days

• As long as performance is not a major concern:– Various performance bottlenecks

– 10× speedup is often within your reach.

– 100× speedup takes significant amount of tuning efforts.

Thread ExecutionThread Execution

• Conceptually, threads in a block can execute in any order with respect to each other.– Exception: barrier synchronizations

• Each thread block is partitioned into warps.– Hardware cost considerations

– The unit of thread scheduling in SMs

– 32 threads per warp: [0,…, 31], [32,…, 63] …

• All threads in a warp execute the same instruction.

• SM hardware implements zero-overhead thread scheduling.– Can tolerate long-latency operations with several warps around.

– GPU does not require as much chip area for cache memories and branch prediction

mechanisms as CPUs.

Warp SchedulingWarp Scheduling

• Suppose 1 global memory access is needed for every 4 instructions.

• Instruction: 4 clock cycles

• Memory latency: 200 clock cycles

• At least 14 warps are required to keep the units fully utilized.

Flow DivergenceFlow Divergence

warp 8 instruction 11

SM multithreadedWarp scheduler

• SIMT can reduce the cost of fetching and

processing instructions.

• SIMT works well when all threads in a warp

follow the same control flow.

• Multiple sequential passes may be required

for an if-then-else construct.

then else

Flow DivergenceFlow Divergence

• Main performance concern with branching is divergence.– Threads within a thread take different paths.

– The control paths are traversed one at a time.

• How to avoid divergence when the branch condition is a function

of thread ID?– With divergence:

• if (threadIdx.x>2) { }

• Threads 0, 1, and 2 follow a different path than the rest threads in the warp.

– Without divergence:• if (threadIdx.x/WARP_SIZE>=2) { }

• Creates two different paths for threads in a block.

• Branch granularity is a whole multiple of warp size.

• All threads in any given warp follow the same path.

Memory CoalescingMemory Coalescing

• Dynamic Random Access Memory (DRAM)– Each bit is stored in a separate capacitor.

– All storage locations have nearly identical access time.

– In practice, many consecutive locations are accessed in parallel.

– All threads in a warp should access continuous memory locations (coalescing)

to maximize memory bandwidth utilization.

Thread 1

Thread 2

Not coalesced Coalesced

Memory Layout of a Matrix in CMemory Layout of a Matrix in C

M1,0M0,0

M2,1 M3,1

M2,0M1,0M0,0 M3,0 M1,1M0,1 M2,1 M3,1 M1,2M0,2 M2,2 M3,2

M1,2M0,2 M2,2 M3,2

M1,3M0,3 M2,3 M3,3

T0 T1 T2 T3

Time Period 1

T0 T1 T2 T3

Time Period 2

Memory Layout of a Matrix in CMemory Layout of a Matrix in C

M2,0M1,0M0,0 M3,0 M1,1M0,1 M2,1 M3,1 M1,2M0,2 M2,2 M3,2 M1,3M0,3 M2,3 M3,3

T0 T1 T2 T3

Time Period 1

T0 T1 T2 T3

Time Period 2

M1,0M0,0

M2,1 M3,1

M1,2M0,2 M2,2 M3,2

M1,3M0,3 M2,3 M3,3

Shared Memory ArchitectureShared Memory Architecture

• Many threads access memory:

– Shared memory is divided in banks.

– Successive 32-bit words are assigned to successive banks.

– Each bank has a bandwidth of 32 bits per clock cycle.

– G80 has 16 banks: bank=address % 16

– Same as the size of half a warp

• Each memory bank can service one address per cycle.

– Can service as many simultaneous accesses as the number of banks.

• Multiple simultaneous accesses to the same bank may result in a bank conflict.

– Conflicting accesses are serialized.

– No bank conflicts between different half warps.

Bank ConflictsBank Conflicts

• Shared memory is as fast as registers if there are no bank

conflicts.

• The fast case:– If all threads of a half-warp access different banks, there is no

bank conflict.

– If all threads of a half-warp access the identical address, there

is no bank conflict (broadcast).

• The slow case:– Bank Conflict: Multiple threads in the same half-warp access

the same bank.

– Must serialize the accesses.

– Cost = max # of simultaneous accesses to a single bank

Bank 15

Bank 7Bank 6Bank 5Bank 4Bank 3Bank 2Bank 1Bank 0

Bank Addressing ExampleBank Addressing Example

• No Bank Conflicts– Linear addressing

• No Bank Conflicts– Random 1:1 Permutation

Bank 15

Thread 15

Thread 7Thread 6Thread 5Thread 4Thread 3Thread 2Thread 1Thread 0

Bank 15

Thread 15

Bank Addressing ExampleBank Addressing Example

• 2-way Bank Conflicts– Linear addressing

stride = 2

• 8-way Bank Conflicts– Linear addressing

stride = 8

Thread 11Thread 10Thread 9Thread 8

Thread 4Thread 3Thread 2Thread 1Thread 0

Bank 15

Thread 15

Bank 9Bank 8

Bank 15

Bank 7

Bank 2Bank 1Bank 0

Partitioning of SM ResourcesPartitioning of SM Resources

• Execution resources in SM– Registers

– Block Slots (GT200: 8)

– Thread Slots (GT200: 1024)

– Number of 16×16 blocks = 1024/(16×16) = 4

– Determine the number of threads running on a SM.

– Subtle interactions that may cause underutilization of resources

• Register File– Store automatic variables declared in a CUDA kernel.

– G80: 32KB (8192 entries) for each SM

– Dynamically partitioned across all blocks in the same SM.

– Each thread can only access registers assigned to itself.

SM Resources ExampleSM Resources Example

• For 16×16 blocks, if each thread uses 10 registers:– Each block requires 16×16×10 = 2560 registers.

– Number of blocks = 8129/2560 = 3

• If each thread increases the use of registers by 1:– Each block now requires 16×16×11 = 2816 registers.

– Number of blocks = 8129/2816 = 2

– Only two blocks can run on a SM.

– Number of threads drops from 768 to 512

– 1/3 reduction of parallelism due to the single extra automatic variable!

Performance Cliff

Occupancy CalculatorOccupancy Calculator

Instruction MixInstruction Mix

• Each processor core has limited instruction processing bandwidth.

• Every instruction consumes processing bandwidth:– Floating point calculation

– Load instruction

– Branch instruction

• We should try to increase the efficiency of instructions.

for (int k=0; k<BLOCK_SIZE; k++) Pvalue+=Mds[ty][k]*Nds[k][tx];

2 floating point arithmetic instructions

1 loop branch instruction

2 address arithmetic instructions

1 loop counter increment instruction

Instruction MixInstruction Mix

Pvalue+=Mds[ty][0]*Nds[0][tx]+… +Mds[ty][15]*Nds[15][tx];

Loop Unrolling

• Express the dot-product computation as one long multiply-add expression.

• Eliminate the loop branch instruction.

• Eliminate the loop counter update.

• Matrix indices are constants rather than a variable.

• With the help of compiler, address arithmetic instructions can be also eliminated!

Dynamic ParallelismDynamic Parallelism

• A child CUDA kernel can be called from within a parent CUDA kernel,

without CPU involvement.

• Extension to flat, single-level of parallelism

• Requires Compute Capability 3.5+

• Benefits:– Simplified CPU/GPU Cooperation

– Dynamic Load Balancing

– Data-Dependent Execution

– Recursive Parallel Algorithms

CPU GPU

What does it mean?What does it mean?

CPU GPU CPU GPU

Dynamic Parallelism

What does it mean?What does it mean?

ExampleExample

__global__ ChildKernel(void* data){ //Operate on data}

__global__ ParentKernel(void *data){ ChildKernel<<<1, 16>>>(data);}

// In Host Code ParentKernel<<<256, 64>>(data);

__global__ RecursiveKernel(void*data){ if(continueRecursion == true) RecursiveKernel<<<64, 16>>>(data); }

Matrix ExampleMatrix Example

for (int i=0; i<N; i++){ for (int j=0; j<M; j++){ convolution_function(i, j); }}

for (int i=0; i<N; i++){ for (int j=0; j<M[i]; j++){ convolution_function(i,j); }}

Oversubscription

__global__ void con_kernel(int i){convolution_function(i, threadIdx.x);

__global__ void dynamic_parallelism_kernel(int *M){ con_kernel<<<1, M[blockIdx.x]>>>(blockIdx.x);}

//In Host Codedynamic_parallelism_kernel<<<N, 1>>>(M);

SynchronizationSynchronization

__global__ void Parent_Kernel() { ... //Kernel code if(threadIdx.x==0){ Child_Kernel<<<1, 256>>>(); // Thread will launch kernel and keep going cudaDeviceSynchronize(); // Make thread wait for Child_Kernel to complete } __syncthreads();//If all threads in the block need Child_Kernel to complete ... //Code that needs data generated by Child_Kernel}

Timing GPU KernelsTiming GPU Kernelsfloat time;

cudaEvent_t start, stop;

cudaEventCreate(&start);

cudaEventCreate(&stop);

cudaEventRecord(start, 0); // Place the start event

kernel <<<..>>>(..); // Returns immediately

cudaEventRecord(stop, 0); // Place the stop event

cudaEventSynchronize(stop); // Make sure stop is reached

cudaEventElapsedTime(&time, start, stop);

cudaEventDestroy(start);

cudaEventDestroy(stop);

stop Kernel start Stream 0

Multiple KernelsMultiple Kernels

// Create two streams

cudaStream_t stream[2];

for (int i=0; i<2; ++i)

cudaStreamCreate(&stream[i]);

// Launch a Kernel from each stream

KernelOne <<<64, 512, 0, stream[0]>>>(..);

KernelTwo <<<64, 512, 0, stream[1]>>>(..);

// Destroy the streams

for (int i=0; i<2; ++i)

cudaStreamDestroy(stream[i]);

• Synchronization is implied for events within the same stream.

• More than one stream can be associated with a GPU.

Multiple GPUsMultiple GPUs

int nDevices;

cudaGetDeviceCount(&nDevices);

cudaDeviceProp prop;

for (int i=0; i<nDevices; i++) {

cudaGetDeviceProperties(&prop, i);

printf("Device Number: %d\n", i);

printf("Device Name: %s\n", prop.name);

printf("Compute Capability: %d.", prop.major);

printf("%d\n", prop.minor);

printf("Memory Bus Width: %d\n", prop.memoryBusWidth);

Streams and Multiple GPUsStreams and Multiple GPUs

• Streams belong to the GPU that was active when they were created.

• Calls to a stream are invalid if the associated GPU is not active.

cudaSetDevice(0);

cudaStreamCreate(&streamA);

cudaSetDevice(1);

cudaStreamCreate(&streamB);

// Launch kernels

KernelOne <<<..., streamA>>>(..); // Invalid!

KernelTwo <<<..., streamB>>>(..); // Valid

Floating Point ConsiderationsFloating Point Considerations

• Numeric values are represented as bit patterns.

• IEEE Floating Point Standard– Sign (S), Exponent (E) and Mantissa (M)

– Each (S, E, M) pattern uniquely identifies a floating point number.

• For each bit pattern, it numeric value is derived as:

– Value = (-1)S × M × {2E}, where 1.0B ≤ M < 10.0B

• The interpretation of S:– S=0: Positive Number

– S=1: Negative Number

Normalized Representation of MNormalized Representation of M

• Subscripts D and B are for decimal place and binary place values respectively.

• Specifying 1.0B ≤ M < 10.0B makes the mantissa value for each floating point

number unique.

– For example: 0.5D = 1.0B × 2-1

– The only valid mantissa value is M=1.0B.

– Neither 10.0B × 2-2 (M = 10.0B) nor 0.1B × 20 (M = 0.1B) qualifies.

– Just like 10.0D × 105, or 0.9D × 10-3 are not valid.

• Because all mantissa values are of the form 1.XX…, we can omit the “1.” part

from the representation.

– The mantissa value of 0.5D in a 2-bit mantissa is 00, by omitting “1.” from 1.00.

– With the IEEE format, an n-bit mantissa is effectively an (n+1)-bit mantissa.

Excess Encoding of EExcess Encoding of E

Decimal Value Two’s Complement Excess-3

Reserved 100 111

-3 101 000

-2 110 001

-1 111 010

0 000 011

1 001 100

2 010 101

3 011 110

In an n-bit exponent representation, 2n-1-1 is added to its two's complement to form its excess representation.

(-1)S × 1.M × 2(E-2^(n-1)+1)

Representable NumbersRepresentable NumbersNo-zero Abrupt Underflow Denormalization

E M S=0 S=1 S=0 S=1 S=0 S=1

00 00 2-1 -(2-1) 0 0 0 0

01 2-1+1*2-3 -(2-1+1*2-3) 0 0 1*2-2 -1*2-2

10 2-1+2*2-3 -(2-1+2*2-3) 0 0 2*2-2 -2*2-2

11 2-1+3*2-3 -(2-1+3*2-3) 0 0 3*2-2 -3*2-2

01 00 20 -(20) 20 -(20) 20 -(20)

01 20+1*2-2 -(20+1*2-2) 20+1*2-2 -(20+1*2-2) 20+1*2-2 -(20+1*2-2)

10 20+2*2-2 -(20+2*2-2) 20+2*2-2 -(20+2*2-2) 20+2*2-2 -(20+2*2-2)

11 20+3*2-2 -(20+3*2-2) 20+3*2-2 -(20+3*2-2) 20+3*2-2 -(20+3*2-2)

10 00 21 -(21) 21 -(21) 21 -(21)

01 21+1*2-1 -(21+1*2-1) 21+1*2-1 -(21+1*2-1) 21+1*2-1 -(21+1*2-1)

10 21+2*2-1 -(21+2*2-1) 21+2*2-1 -(21+2*2-1) 21+2*2-1 -(21+2*2-1)

11 21+3*2-1 -(21+3*2-1) 21+3*2-1 -(21+3*2-1) 21+3*2-1 -(21+3*2-1)

11 Reserved Pattern

Representable NumbersRepresentable Numbers

• The exponent bits define the major intervals of representable numbers.

• The mantissa bits define the number of representable numbers in each interval.

• Zero is not representable in this format.

• Representable numbers become closer to each other toward 0.

• There is a gap in representable numbers in the vicinity of 0.

1 2 30

Representing ZeroRepresenting Zero

• Abrupt Underflow– Treats all bit patters with E=0 as 0.

– Takes away several representable numbers near zero and lumps them all into 0.

1 2 30

• Denormalization– Relaxes the normalization requirement for numbers very close to 0.

– Whenever E=0, the mantissa is assumed to be 0.xx.

– The exponent is assumed to be the same as the previous interval.

0.M × 2-2^(n-1)+2

0 00 01 (S E M) 0.01 X 20 = 2-2

Accuracy and RoundingAccuracy and Rounding

• 1.00 × 2-2 + 1.00 × 21 = 0.001 × 21 + 1.00 × 21 = 1.001 × 21 ≈ 1.00 × 21 (Error = 0.001 × 21)

• 1.00 × 20 +1.00 × 20 + 1.00 × 2-2 + 1.00 × 2-2 = 1.00 × 21 + 1.00 × 2-2 + 1.00 × 2-2 = 1.00 × 21 + 1.00 × 2-2 = 1.00 × 21

• [1.00 × 20 +1.00 × 20 ]+ [1.00 × 2-2 + 1.00 × 2-2]= 1.00 × 21 + 1.00 × 2-1 = 1.01 × 21

• Sorting data in ascending order may help achieve greater accuracy.– Numbers with similar numerical values are close to each other.

Single vs. Double PrecisionSingle vs. Double Precision

• GPUs were traditionally not good at double precision calculation.– Requires compute capability 1.3 or above.

– Around 1/8 of single precision performance.

– Improved greatly to 1/2 with Fermi architecture.

• Important to avoid using double precision when it is not necessary.– Add ‘f’ specifier on float literals:

• Y=X*0.123; // double assumed

• Y=X*0.123f; // float explicit

– Use float version of standard library functions:

• Y=sin(X); // double assumed

• Y=sinf(X); // single precision explicit

Matlab in ParallelMatlab in Parallel

• Matlab: Numerical Computing Environment

• Parallel Computing Toolbox (PCT)

• Offload work from one MATLAB session (client) to other MATLAB sessions (workers).

• Run as many as eight MATLAB workers (2011b) on your local machine in addition to your MATLAB client session.

http://www.mathworks.cn/cn/help/distcomp/index.html

ParforParfor

• Parallel for-loop

• The parfor body is executed on the client and workers.

• The data on which parfor operates is sent from the client to workers, and the

results are sent back to the client and pieced together.

• MATLAB workers evaluate iterations in no particular order, and independently

of each other.

• Classification of Variables– Loop, Sliced, Reduction, Broadcast, Temporary

Classification of VariablesClassification of Variables

r=rand(1,10);

parfor i=1:10

z=z+i;

b(i)=r(i);

if i<=c

d=2*a;

temporary loop

reduction

broadcast

slicedsliced

Parfor ExampleParfor Example

X=zeros(1,N);for i = 1:N x(i)=sin(i/N*2*pi);end

X=zeros(1,N);matlabpool open local 8 % create 8 workers parfor i = 1:N X(i)=sin(i/N*2*pi);endmatlabpool close % close all workers

parallelization

Notes on ParforNotes on Parfor

• Each loop must be independent of other loops.

• In the Windows Task Manager, there are multiple Matlab processes:– Higher CPU Usage

– Higher Memory Usage

• It incurs significant overhead: only works with long loop iterations and/or

time consuming calculations.

• Be prepared to be surprised:– Some Matlab functions are already optimized for multithreading.

– The practical speedup value is generally quite moderate.

GPU Accelerated MatlabGPU Accelerated Matlab

• Matlab users can now easily enjoy the benefits of GPU computing.

• Capabilities– Evaluating built-in functions on the GPU.– Running MATLAB code on the GPU.

• Requirements– Matlab 2014a (Recommended)– NVIDIA CUDA-enabled devices with compute capability of 1.3 or greater– NVIDIA CUDA device driver 3.1 or greater

• Check the GPU environment– gpuDeviceCount: number of available GPU devices– gpuDevice: select and query GPU device

Create Data on GPUCreate Data on GPU

• Transferring data between workspace and GPU:

• Directly creating GPU data:

M = rand(6);G = gpuArray(single(M));N = gather(G);

Workspace GPU

G = ones(100,100,50, 'single', 'gpuArray'); size(G) 100 100 50 classUnderlying(G) single

Execute Code on GPUExecute Code on GPU

• Run Built-In Functions

• Run Element-Wise Matlab Code

X = rand(1000,'single','gpuArray');

Gfft = fft(X);

Y = gather(Gfft);

function c = myCal(rawdata, gain, offst)

c = (rawdata .* gain) + offst;

meas = ones(1000)*3; // CPU

gn = rand(1000,'gpuArray')/100; // GPU

offs = rand(1000,'gpuArray')/50; // GPU

corrected = arrayfun(@myCal,meas,gn,offs);

results = gather(corrected);

Timing GPU CodeTiming GPU Code

A = rand(1024,'gpuArray');fh = @()fft(A); gputimeit(fh);

gd = gpuDevice(); tic(); B = fft(A); wait(gd); t = toc();

A = rand(12000,400,'gpuArray'); B = rand(400,12000,'gpuArray'); f = @()A*B; t = gputimeit(f);

X = rand(1000,'gpuArray'); f = @()svd(X); t1 = gputimeit(f,1);t3 = gputimeit(f,3) ;

Testing Host-GPU BandwidthTesting Host-GPU BandwidthsizeOfDouble = 8; sizes = power(2, 14:28);

sendTimes = inf(size(sizes)); gatherTimes =

inf(size(sizes));

for i=1:numel(sizes)

numElements = sizes(i)/sizeOfDouble;

hostData = randi([0 9], numElements, 1);

gpuData = gpuArray.randi([0 9], numElements, 1);

sendFcn = @()gpuArray(hostData);

sendTimes(i) = gputimeit(sendFcn);

gatherFcn = @()gather(gpuData);

gatherTimes(i) = gputimeit(gatherFcn);

sendBandwidth = (sizes./sendTimes)/1e9;

[maxSendBandwidth, maxSendIdx] = max(sendBandwidth);

gatherBandwidth = (sizes./gatherTimes)/1e9;

[maxGatherBandwidth, maxGatherIdx] =

max(gatherBandwidth);

Testing Host-GPU BandwidthTesting Host-GPU Bandwidth

5Data Transfer Bandwidth

Array size (bytes)

Send to GPU

Gather from GPU

Testing CPU BandwidthTesting CPU Bandwidth

sizeOfDouble = 8; sizes = power(2, 14:28);

memoryTimesHost = inf(size(sizes));

hostData = randi([0 9], numElements, 1);

plusFcn = @()plus(hostData, 1.0);

memoryTimesHost(i) = timeit(plusFcn);

memoryBandwidthHost =

2*(sizes./memoryTimesHost)/1e9;

[maxBWHost, maxBWIdxHost] =

max(memoryBandwidthHost);

Testing GPU BandwidthTesting GPU Bandwidth

memoryTimesGPU = inf(size(sizes));

gpuData = gpuArray.randi([0 9], numElements, 1);

plusFcn = @()plus(gpuData, 1.0);

memoryTimesGPU(i) = gputimeit(plusFcn);

memoryBandwidthGPU = 2*(sizes./memoryTimesGPU)/1e9;

[maxBWGPU, maxBWIdxGPU] = max(memoryBandwidthGPU);

Bandwidth: CPU vs. GPUBandwidth: CPU vs. GPU

150Read+Write Bandwidth

Array size (bytes)

Testing Matrix MultiplicationTesting Matrix Multiplication

sizes = power(2, 12:2:24); N = sqrt(sizes);

mmTimesHost = inf(size(sizes));

mmTimesGPU = inf(size(sizes));

A = rand(N(i), N(i)); B = rand(N(i), N(i));

mmTimesHost(i) = timeit(@()A*B);

A = gpuArray(A); B = gpuArray(B);

mmTimesGPU(i) = gputimeit(@()A*B);

mmGFlopsHost = (2*N.^3 - N.^2)./mmTimesHost/1e9;

[maxGFlopsHost,maxGFlopsHostIdx] = max(mmGFlopsHost);

mmGFlopsGPU = (2*N.^3 - N.^2)./mmTimesGPU/1e9;

[maxGFlopsGPU,maxGFlopsGPUIdx] = max(mmGFlopsGPU);

1000Double precision matrix-matrix multiply

Matrix size (numel)

3000Single precision matrix-matrix multiply

Matrix size (numel)

ReviewReview

• What are the differences among MPI, OpenMP and CUDA?

• Why is GPU suitable for high performance computing?

• What is the general framework of CUDA programming?

• What is a kernel function and how to call it from the host code?

• What is the advantage of splitting a block into threads?

• Why do we need multiple thread blocks?

• What are the major memory types in CUDA?

• When should we use shared memory?

• What resource factors are critical to GPU programming?

ReviewReview

• What is a warp and why do we need it?

• What is flow divergence and how to avoid it?

• What is bank conflict?

• What is instruction mix?

• What are the benefits of Dynamic Parallelism?

• How to measure the performance of GPU code?

• How to run kernel functions in parallel?

• How is a floating point number represented in the IEEE format?

• How to execute Matlab code on GPU?

gpu computing dr. bo yuan e-mail: yuanb@sz.tsinghua.edu.cn

watt slide

rasterization slide

cores gpu

cuda cores

gpu computing

cores memory bandwidth

cudaenabled gpu

cuda gpus

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