OpenCL 快速傅里叶变换（FFTs）参考手册

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clAmdFft.refman.pdf clAmdFft.refman.pdf是AMD（Advanced Micro Devices）提供的一份关于clAmdFft库的说明文档。clAmdFft是一个基于OpenCL的快速傅里叶变换（FFT）库，旨在提供高性能的FFT计算能力。知识点一：OpenCL OpenCL（Open Computing Language）是一种跨平台的并行编程模型，允许开发者使用单个源代码库在多种设备上执行任务，包括中央处理器（CPU）、图形处理器（GPU）和数字信号处理器（DSP）。OpenCL提供了一个统一的编程接口，允许开发者编写高效、可移植的并行代码。知识点二：Fast Fourier Transforms（FFT）快速傅里叶变换（FFT）是一种快速算法，用于计算离散傅里叶变换（DFT）。FFT算法可以将DFT的计算时间从O(n^2)降低到O(n log n)，从而极大地提高了傅里叶变换的计算速度。FFT广泛应用于信号处理、图像处理、数据压缩等领域。知识点三：clAmdFft库 clAmdFft库是AMD提供的一款基于OpenCL的FFT库，旨在提供高性能的FFT计算能力。该库使用OpenCL编程模型，允许开发者在多种设备上执行FFT计算任务。clAmdFft库提供了一个统一的API接口，允许开发者轻松地将FFT计算集成到自己的应用程序中。知识点四：AMD Math Libraries AMD Math Libraries是一组数学库，提供了各种数学函数和算法，包括线性代数、傅里叶变换、随机数生成等。这些库旨在提供高性能的数学计算能力，帮助开发者加速应用程序的开发和优化。知识点五：Khronos和OpenCL Khronos是一个非营利组织，旨在推广和发展OpenCL标准。Khronos负责维护OpenCL规范，确保OpenCL的跨平台兼容性和可扩展性。Apple Inc.是Khronos的成员之一，负责维护OpenCL的商标和Logo。知识点六：Intellectual Property 本文档中提到的各种商标和Logo都是其所属公司的知识产权，包括AMD、ATI、Radeon、FireStream、FirePro、Catalyst、Microsoft、Visual Studio、Windows等。这些商标和Logo只能用于其所属公司的官方产品和服务中，不得用于其他任何目的。 clAmdFft.refman.pdf是AMD提供的一份关于clAmdFft库的说明文档，旨在帮助开发者了解clAmdFft库的使用和开发。该文档涵盖了OpenCL、FFT、clAmdFft库、AMD Math Libraries、Khronos和知识产权等方面的知识点。

AMD ACCELERATED PARALLEL PROCESSING TECHNOLOGY

1-4 Introduction to clAmdFft

Remember to relaunch any new processes that are open, in order to inherit the

new environment variable. On Linux, consider modifying the .bash_rc file (or

shell equivalent) to export a new environment variable every time you log in.

If you are on a Linux system and have used a package manager to install Boost,

you may have to confirm where the Boost include and library files have been

placed. For example, after installing Boost with the Ubuntu Synaptic Package

Manager, the Boost include files are in /usr/include/boost, and the library

files either /usr/lib or /usr/lib64. The CMakeLists.txt file in this project

defaults the BOOST_ROOT value to /usr on Linux; so, if the system is set up

similarly, no further action is necessary. If the system is set up differently, you

may have to set the BOOST_ROOT environmental variable accordingly.

Note that CMake does not recognize version numbers at the end of the library

filename; so, if the package manager only created a

libboost_module_name.so.x.xx.x file (where x.xx.x is the version of Boost),

the user may need to manually create a soft link called

libboost_module_name.so to the versioned

libboost_module_name.so.x.xx.x. See the clAmdFft binary artifacts in the

install directory for an example.

1.2 Introduction to clAmdFft

The FFT is an implementation of the Discrete Fourier Transform (DFT) that

makes use of symmetries in the FFT definition to reduce the mathematical

intensity required from O(N

) to O(N logN) when the sequence length, N, is the

product of small prime factors. Currently, there is no standard API for FFT

routines. Hardware vendors usually provide a set of high-performance FFTs

optimized for their systems: no two vendors employ the same interfaces for their

FFT routines. clAmdFft provides a set of FFT routines that are optimized for AMD

graphics processors, but also are functional across CPU and other compute

devices.

1.2.1 Supported Transform Sizes

clAmdFft supports powers of 2, 3 and 5 sizes. This means that the vector lengths

that can be configured through a plan can be any length that is a power of two,

three, and five; examples include 2

, 2

, 3

, 2

; up to the limit that

the device can support.

1.2.2 Transform Size Limits

Currently, there is an upper bound on the transform size the library supports. This

limit is 2

for single precision and 2

for double precision. This means that the

product of transform lengths must not exceed these values. As an example, a

1D single-precision FFT of size 1024 is valid since 1024 ≤ 2

. Similarly, a 2D

double-precision FFT of size 1024x1024 is also valid, since 1024*1024 ≤ 2

But, a 2D single-precision FFT of size 4096x8192 is not valid because

4096*8192 > 2

AMD ACCELERATED PARALLEL PROCESSING TECHNOLOGY

Introduction to clAmdFft 1-5

1.2.3 Dimensionality

clAmdFft currently supports FFTs of up to three dimensions, given by the enum

clAmdFft-Dim. This enum is a required parameter into

clAmdFftCreateDefaultPlan() to create an initial plan; there is no default for

this parameter. Depending on the dimensionality that the client requests,

clAmdFft uses the formulations shown below to compute the DFT.

The definition of a 1D complex DFT used by clAmdFft is given by:

where x

are the complex data to be transformed, are the transformed data,

and the sign of ± determines the direction of the transform: − for forward, and +

for backward. Note that the user must provided the scaling factor. Typically, the

scale is set to 1 for forward transforms, and for backward transforms.

The definition of a complex 2D DFT used by clAmdFft is given by:

for j = 0,1, . . ., n − 1 and k = 0,1, . . ., m − 1, where x

are the complex data

to be transformed, are the transformed data, and the sign of ± determines

the direction of the transform. Typically, the scale is set to 1 for forward

transforms, and for backward transforms.

The definition of a complex 3D DFT used by clAmdFft is given by:

for j = 0,1, . . ., n − 1 and k = 0,1, . . ., m − 1 and l = 0,1, . . ., p − 1, where x

rqs

are the complex data to be transformed, are the transformed data, and the

sign of ± determines the direction of the transform. Typically, the scale is set to

1 for forward transforms, and for backward transforms.

1.2.4 Setup and Teardown of clAmdFft

clAmdFft is initialized by a call to clAmdFftSetup(), which must be called before

any other API exported from clAmdFft. This allows the library to create resources

used to manage the plans that are created and destroyed by the user. This API

also takes a structure clAmdFftInitSetupData that is initialized by the client to

control the behavior of the library. The corresponding clAmdFftTeardown()

method must be called by the client when it is done using the library. This

instructs clAmdFft to release all resources, including any acquired references to

any OpenCL objects that may have been allocated or passed to it through the

API.

scale

n-1

k=0

∑ X

exp ±i

()

for j = 0, 1, . . .,n − 1

scale

m-1

q=0

∑

exp ±i

π jr

()

n-1

r=0

∑

exp ±i

()

M N

jkl

scale

p-1

s=0

∑

rqs

exp ±i

π jr

()

m-1

q=0

∑

exp ±i

()

n-1

r=0

∑

exp ±i

π kq

()

jkl

M N P

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OpenCL 快速傅里叶变换（FFTs）参考手册

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