1ITCS 5/4145 Parallel computing, B. Wilkinson, April 11, 2013. CUDAMultiDimBlocks.ppt

CUDA Grids, Blocks, and Threads

These notes will introduce:

•One dimensional and multidimensional grids and blocks•How the grid and block structures are defined in CUDA•Predefined CUDA variables•Adding vectors using one-dimensional structures•Adding/multiplying arrays using 2-dimensional structures

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Grids, Blocks, and Threads

NVIDIA GPUs consist of an array of execution cores, each of which can support a large number of threads, many more than number of cores.

Threads grouped into “blocks”Blocks can be 1, 2, or 3 dimensional

Each kernel call uses a “grid” of blocksGrids can be 1, 2, or 3 dimensional (3-D available for recent GPUs)

Programmer needs to specify grid/block organization on each kernel call (which can be different each time), within limits set by the GPU

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Can be 1, 2, or 3 dimensions(compute capability => 2 see next)

Can be 1, 2 or 3 dimensions

CUDA C programming guide, v 3.2, 2010, NVIDIA

CUDA SIMT Thread StructureAllows flexibility and efficiency in processing 1D, 2-D, and 3-D data on GPU.

Linked to internal organization

Threads in one block execute together.

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NVIDIA defines “compute capabilities”, 1.0, 1.1, … with limits and features supported.

Compute capability1.0 (min) 2.x* 3.0/3.5

Grid:Max dimensionality 2 3 3Max size of each dimension (x, y, z) 65535 65535 231 – 1(no of blocks in each dimension) (2,147,483,647)

Blocks:Max dimensionality 3 3 3Max sizes of x- and y- dimension 512 1024 1024Max size of z- dimension 64 64 64Max number of threads per block overall 512 1024 1024

Device characteristics -- some limitations

coit-grid06 and coit-grid07 have C2050s, compute capability 2.0. coit-grid08.uncc.edu has a K20, compute capability 3.5. Most recent Comp Cap. for April 2013.

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Need to provide each kernel call with values for:

• Number of blocks in each dimension• Threads per block in each dimension

myKernel<<< B, T >>>(arg1, … );

B – a structure that defines number of blocks in grid in each dimension (1D, 2D, or 3D).

T – a structure that defines number of threads in a block in each dimension (1D, 2D, or 3D).

Defining Grid/Block Structure

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1-D grid and/or 1-D blocks

If want a 1-D structure, can use a integer for B and T in:

myKernel<<< B, T >>>(arg1, … );

B – An integer would define a 1D grid of that size

T –An integer would define a 1D block of that size

Example

myKernel<<< 1, 100 >>>(arg1, … );

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CUDA Built-in Variablesfor a 1-D grid and 1-D block

threadIdx.x -- “thread index” within block in “x” dimension

blockIdx.x -- “block index” within grid in “x” dimension

blockDim.x -- “block dimension” in “x” dimension (i.e. number of threads in block in x dimension)

Full global thread ID in x dimension can be computed by:

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

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Example -- x directionA 1-D grid and 1-D block

4 blocks, each having 8 threads

0 1 2 3 4 765 0 1 2 3 4 7650 1 2 3 4 765 0 1 2 3 4 765

threadIdx.x threadIdx.x threadIdx.x

blockIdx.x = 3

threadIdx.x

blockIdx.x = 1blockIdx.x = 0

Derived from Jason Sanders, "Introduction to CUDA C" GPU technology conference, Sept. 20, 2010.

blockIdx.x = 2

gridDim = 4 x 1blockDim = 8 x 1

Global thread ID = blockIdx.x * blockDim.x + threadIdx.x = 3 * 8 + 2 = thread 26 with linear global addressing

Global ID 26

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#define N 2048 // size of vectors#define T 256 // number of threads per block

__global__ void vecAdd(int *a, int *b, int *c) {

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

c[i] = a[i] + b[i];} int main (int argc, char **argv ) {

…

vecAdd<<<N/T, T>>>(devA, devB, devC); // assumes N/T is an integer

…return (0);

}

Code example with a 1-D grid and blocksVector addition

Number of blocks to map each vector across grid, one element of each vector per thread

Note: __global__ CUDA function qualifier.

__ is two underscores

__global__ must return a void

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#define N 2000 // size of vectors#define T 256 // number of threads per block

__global__ void vecAdd(int *a, int *b, int *c) {

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

if (i < N) c[i] = a[i] + b[i]; // allows for more threads than vector elements // some unused

} int main (int argc, char **argv ) {

int blocks = (N + T - 1) / T; // efficient way of rounding to next integer …vecAdd<<<blocks, T>>>(devA, devB, devC); …return (0);

}

If T/N not necessarily an integer:

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Questions

How many threads are created?

How many threads are unused?

What is the maximum number of threads that can be created in a GPU on coit-grid06/7?

On coit-grid08?

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1-D grid and 1-D block suitable for processing one dimensional data

Higher dimensional grids and blocks convenient for higher dimensional data.

Processing 2-D arrays might use a two dimensional grid and two dimensional block

Might need higher dimensions because of limitation on sizes of block in each dimension

CUDA provided with built-in variables and structures to define number of blocks in grid in each dimension and number of threads in a block in each dimension.

Higher dimensional grids/blocks

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CUDA Vector Types/Structures

unit3 and dim3 – can be considered essentially as CUDA-defined structures of unsigned integers: x, y, z, i.e.

struct unit3 { x; y; z; };struct dim3 { x; y; z; };

Used to define grid of blocks and threads, see next.

Unassigned structure components automatically set to 1.There are other CUDA vector types.

Built-in CUDA data types and structures

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Built-in Variables forGrid/Block Sizes

dim3 gridDim -- Grid dimensions, x, y, z.

Number of blocks in grid = gridDim.x * gridDim.y * gridDim.z

dim3 blockDim -- Size of block dimensions x, y, and z.

Number of threads in a block =

blockDim.x * blockDim.y * blockDim.z

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To set values in each dimensions, use for example:

dim3 grid(16, 16); // Grid -- 16 x 16 blocksdim3 block(32, 32); // Block -- 32 x 32 threads…myKernel<<<grid, block>>>(...);

which sets:

gridDim.x = 16gridDim.y = 16gridDim.z = 1blockDim.x = 32blockDim.y = 32blockDim.z = 1

Example Initializing Values

when kernel called

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CUDA Built-in Variablesfor Grid/Block Indices

uint3 blockIdx -- block index within grid:

blockIdx.x, blockIdx.y, blockIdx.z

uint3 threadIdx -- thread index within block:

blockIdx.x, blockIdx.y, blockId.z

2-D: Full global thread ID in x and y dimensions can be computed by:

x = blockIdx.x * blockDim.x + threadIdx.x;y = blockIdx.y * blockDim.y + threadIdx.y;

CUDA structures

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2-D Grids and 2-D blocks

threadID.x

threadID.y

Thread

blockIdx.x * blockDim.x + threadIdx.x

blockIdx.y * blockDim.y + threadIdx.y

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Flattening arrays onto linear memory

Generally memory allocated dynamically on device (GPU) and we cannot not use two-dimensional indices (e.g. a[row][column]) to access array as we might otherwise. (Why?)

We will need to know how the array is laid out in memory and then compute the distance from the beginning of the array.

C uses row-major order --- rows are stored one after the other in memory, i.e. row 0 then row 1 etc.

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Flattening an array

Number of columns, N

columnArray element

a[row][column] = a[offset]

offset = column + row * N

where N is number of column in array

row * number of columns

row

0

0

N-1

Note: Another way to flatten array is:

offset = row + column * N

We will come back to this later as it does have very significant consequences on performance.

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

int row = blockIdx.y*blockDim.y+threadIdx.y;

int index = col + row * N;

a[index] = …

Using CUDA variables

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Example using 2-D grid and 2-D blocksAdding two arrays

Corresponding elements of each array added together to form element of third array

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CUDA version using 2-D grid and 2-D blocksAdding two arrays

#define N 2048 // size of arrays

__global__void addMatrix (int *a, int *b, int *c) {int col = blockIdx.x*blockDim.x+threadIdx.x;int row =blockIdx.y*blockDim.y+threadIdx.y;int index = col + row * N;

if ( col < N && row < N) c[index]= a[index] + b[index];}

int main() {...dim3 block (16,16);dim3 grid (N/block.x, N/block.y);

addMatrix<<<grid, block>>>(devA, devB, devC);…

}

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Matrix Multiplication

Matrix multiplication is an important application in HPC and appears in many applications

C = A * B

where A, B, and C are matrices (two-dimensional arrays.

A restricted case is when B has only one column -- matrix-vector multiplication, which appears in representation of linear equations and partial differential equations

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Matrix multiplication, C = A x B

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Assume matrices square (N x N matrices).

for (i = 0; i < N; i++)for (j = 0; j < N; j++) {

c[i][j] = 0;for (k = 0; k < N; k++)

c[i][j] = c[i][j] + a[i][k] * b[k][j];}

Requires n3 multiplications and n3 additionsSequential time complexity of O(n3). Very easy to parallelize.

Implementing Matrix MultiplicationSequential Code

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CUDA Kernelfor multiplying two arrays

__global__ void gpu_matrixmult(int *gpu_a, int *gpu_b, int *gpu_c, int N) {

int k, sum = 0;

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

int row = threadIdx.y + blockDim.y * blockIdx.y;

if (col < N && row < N) {

for (k = 0; k < N; k++)

sum += a[row * N + k] * b[k * N + col];

c[row * N + col] = sum;

}

}

In this example, one thread computes one C element and the number of threads must equal or greater than the number of elements

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Sequential version with flattened arraysfor comparison

void cpu_matrixmult(int *cpu_a, int *cpu_b, int *cpu_c, int N) {

int i, j, k, sum;

for (row =0; row < N; row++) // row of a

for (col =0; col < N; col++) { // column of b

sum = 0;

for(k = 0; k < N; k++)

sum += cpu_a[row * N + k] * cpu_b[k * N + col];

cpu_c[row * N + col] = sum;

}

}

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Matrix mapped on 2-D Grids and 2-D blocks

threadID.x

threadID.y

blockIdx.x * blockDim.x + threadIdx.x

blockIdx.y * blockDim.y + threadIdx.y

A[][column]

A[row][] Thread

Arrays mapped onto structure, one element per thread

Array

Grid

Block

Basically array divided into “tiles” and one tile mapped onto one block

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// Matrix addition program MatrixMult.cu, Barry Wilkinson, Dec. 28, 2010.#include <stdio.h>#include <cuda.h>#include <stdlib.h>

__global__ void gpu_matrixmult(int *gpu_a, int *gpu_b, int *gpu_c, int N) {…

}

void cpu_matrixmult(int *cpu_a, int *cpu_b, int *cpu_c, int N) {…

}

int main(int argc, char *argv[]) {int i, j; // loop countersint Grid_Dim_x=1, Grid_Dim_y=1; //Grid structure valuesint Block_Dim_x=1, Block_Dim_y=1; //Block structure valuesint noThreads_x, noThreads_y; // number of threads available in device, each dimensionint noThreads_block; // number of threads in a blockint N = 10; // size of array in each dimensionint *a,*b,*c,*d;int *dev_a, *dev_b, *dev_c;int size; // number of bytes in arrayscudaEvent_t start, stop; // using cuda events to measure timefloat elapsed_time_ms; // which is applicable for asynchronous code also

/* --------------------ENTER INPUT PARAMETERS AND ALLOCATE DATA -----------------------*/… // keyboard input

dim3 Grid(Grid_Dim_x, Grid_Dim_x); //Grid structuredim3 Block(Block_Dim_x,Block_Dim_y); //Block structure, threads/block limited by specific devicesize = N * N * sizeof(int); // number of bytes in total in arrays

a = (int*) malloc(size); //dynamically allocated memory for arrays on hostb = (int*) malloc(size);c = (int*) malloc(size); // results from GPUd = (int*) malloc(size); // results from CPU… // load arrays with some numbers

Complete Program(several slides)

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/* ------------- COMPUTATION DONE ON GPU ----------------------------*/

cudaMalloc((void**)&dev_a, size); // allocate memory on devicecudaMalloc((void**)&dev_b, size);cudaMalloc((void**)&dev_c, size);

cudaMemcpy(dev_a, a , size ,cudaMemcpyHostToDevice);cudaMemcpy(dev_b, b , size ,cudaMemcpyHostToDevice);

cudaEventRecord(start, 0); // here start time, after memcpy

gpu_matrixmult<<<Grid,Block>>>(dev_a,dev_b,dev_c,N);cudaMemcpy(c, dev_c, size , cudaMemcpyDeviceToHost);

cudaEventRecord(stop, 0); // measuse end timecudaEventSynchronize(stop);cudaEventElapsedTime(&elapsed_time_ms, start, stop );

printf("Time to calculate results on GPU: %f ms.\n", elapsed_time_ms);

Where you measure time will make a big difference

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/* ------------- COMPUTATION DONE ON HOST CPU ----------------------------*/

cudaEventRecord(start, 0); // use same timing*

cpu_matrixmult(a,b,d,N); // do calculation on host

cudaEventRecord(stop, 0); // measure end timecudaEventSynchronize(stop);cudaEventElapsedTime(&elapsed_time_ms, start, stop );

printf("Time to calculate results on CPU: %f ms.\n", elapsed_time_ms); // exe. time

/* ------------------- check device creates correct results -----------------*/…/* --------------------- repeat program ----------------------------------------*/… // while loop to repeat calc with different parameters/* -------------- clean up ---------------------------------------*/

free(a); free(b); free(c);cudaFree(dev_a);cudaFree(dev_b);cudaFree(dev_c);cudaEventDestroy(start);cudaEventDestroy(stop);return 0;

}

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Some PreliminariesEffects of First Launch

Program is written so that can repeat with different parameters without stopping program – to eliminate effect of first kernel launch

Also might take advantage of caching – seems not significant as first launch

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Some results

Random numbers 0- 9

32 x 32 array

1 blockof 32 x 32 threads

Speedup = 1.65,First time Answer

Check both CPU and GPU same answers

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Some results

32 x 32 array

1 blockof 32 x 32 threads

Speedup = 2.12Second time

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Some results

32 x 32 array

1 blockof 32 x 32 threads

Speedup = 2.16Third time

Subsequently can vary 2.12 – 2.18

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Some results

256 x 256 array

8 blocksof 32 x 32 threads

Speedup = 151.86

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Some results

1024 x 1024 array

32 blocksof 32 x 32 threads

Speedup = 860.9

Questions