An Implementation of a FIR Filter on a GPU

1
An Implementation of a FIR Filter on a GPU

• Alexey Smirnov and Tzi-cker Chiueh
• ECSL Research Seminar
• 9/13/05

2
Outline

• Introduction
• GPU Computing Overview
• Related Work
• FIR Filter Definition
• FIR Filter Implementation on GPU
• Performance Evaluation
• Conclusion

3
Introduction

• Numerical algorithms often perform repeated
  computations on vectors of elements.
• Parallel computation improves performance.
• x86 MMX, SSE, SSE2, SSE3.
• Video cards are now programmable.

4
Computation and Bandwidth Rates

• Video cards have higher GFLOPs rate and memory
  bandwidth compared to CPU.
• However, data copying between main memory and
  video memory can reduce performance.

5
GPU Computing Background

• Rendering pipeline
• User program defines vertex and texture
  coordinates.
• Vertex processor converts vertex attributes from
  world coordinate system into screen coordinate
  system.
• Fragment processor computes color of each output
  pixel using textures and color.
• Interpolation defines coordinates and color for
  each pixel.
• Vertex and fragment processors are programmable
  for example in C-like language Cg.

6
Rendering APIs

• OpenGL (Linux, Windows, MacOS) and DirectX
  (Windows).
• OpenGL extensions allow to use advanced features
  of a video card.
• NV_float_buffer supports floating-point textures.
• ARB_render_texture allows to render to a texture
  instead of the screen.

7
GPU Program Architecture

• Create floating-point textures that contain input
  data and load them into video memory
• Load the fragment program and enable
  multi-texturing
• Define vertex and texture coordinates
• Draw the figure to an off-screen buffer
• If the results were rendered to an off-screen
  buffer then copy the image to a texture using
  glCopyTexSubImage2D().
• Go to step 3 if more iterations needed.
• Use glGetTexImage() to copy data from video
  memory to main memory.

8
Input Data Representation

• Matrices are represented as textures naturally.
  Four elements per pixel (R, G, B, A).
• Vectors are wrapped into matrices. Textures have
  maximum dimensions.

9
Related Work

• Four papers describing matrix multiplication
• Linear algebra operations
• Array sorting
• FFT
• Earlier papers concluded that the CPU is more
  efficient then GPU.
• Recent video cards, e.g. GeForce 7800 and ATI
  X800 XT do better than CPU.

10
FIR Filter Definition

• Finite Impulse Response (FIR) filter is used in
  audio processing.
• We modified GNU Radio an open-source software
  implementing Software Defined Radio.

11
Other Relevant Transformations

• Hilbert transformation

• Frequency translation FIR filter

12
FIR Filter on a GPU
13
FIR Filters Loop

• Initialization

• Loop iteration

14
FIR Filters Loop

• O(j1)O(j)MI

• Final output value is computed as

15
Fragment Program
16
Optimizations

• Break loop into two to get rid of conditional
  expression
• Unroll loop body w/ and w/o conditional
  expression
• Process two rows of input and textures
• Use different texture units in unrolled loops
• Nothing of the above improved performance.

17
Performance Evaluation FIR Filter
18
Performance of FreqXlating FIR Filter
19
Performance of Hilbert Transformation
20
Conclusion

• Not everything improves from GPU optimization.
• CPU optimization tricks do not work on GPU.
• Texture upload/download takes up to 60 of total
  time.
• GPU computation can take several seconds compared
  to millisecond time to render a frame in a game.

21
Future Work

• QoS for GPU can application specify maximum
  latency or share of GPU resources?
• Work offload from CPU to GPU is it possible to
  build a compiler that can automatically decide
  what is worth GPU optimization?
• Debugging support a lot of tools for Windows,
  none for Linux.