Intel® MKL and Intel® IPP: Choosing a High Performance FFT
由 Paul L., Jing X., Gennady F. 发布于 2011 年 10 月 30 日，更新于 2019 年 3 月 15 日
Note: This document applies to Intel® MKL 2018.0 or later and Intel® IPP 2018.0 or later.
Objective
The purpose of this document is to help developers determine which FFT, Intel® MKL or Intel® IPP is best suited for their application.
Overview
Fourier transforms are used in signal processing, image processing, physics, statistics, finance, cryptography, and many other areas. The Discrete Fourier transform (DFT) mathematical operation converts a signal from the time domain to the frequency domain and back.
DFT processing time can dominate a software application. Using a fast algorithm, Fast Fourier transform (FFT), reduces the number of arithmetic operations from O(N^{2}) to O(N log_{2} N) operations. Intel® MKL FFT and Intel® IPP FFT are highly optimized for Intel® architecturebased multicore processors using the latest instruction sets, parallelism, and algorithms.
Read further to decide which FFT is best for your application.
Below is a brief summary of the Intel® MKL and Intel® IPP libraries. For additional details on these products, visit the Intel® MKL web site and the Intel® IPP web site.
Table 1: Comparison of Intel® MKL and Intel® IPP Functionality
 Intel MKL  Intel IPP 
Target Applications  Mathematical applications for engineering, scientific and financial applications  Speed performance for imaging, vision, signal, security, and storage applications 
Library Structure 


Linkage Models  Static, dynamic, custom dynamic  Static, dynamic, custom dynamic 
Operating Systems  Windows*, Linux*, macOS*  Windows, Linux, Android, macOS 
Processor Support  IA32 and Intel® 64 architecturebased and compatible platforms  IA32 and Intel® 64 architecturebased and compatible platforms 
Both of these libraries contain the generic code optimized for processors with Intel® Streaming SIMD Extensions (Intel® SSE) and code optimized for processors with Intel® SSE2, SSE3, SSE4.1, SSE4,2, AVX, AVX2 and AVX512 instruction sets
Intel® MKL and Intel® IPP Fourier Transform Feature
The Fourier Transforms provided by MKL and IPP are respectively targeted for the types of applications targeted by MKL (engineering and scientific) and IPP (media and communications). In the table below, we highlight specifics of the MKL and IPP Fourier Transforms that will help you decide which may be best for your application.
Table 2: Comparison of Intel® MKL and Intel® IPP DFT Features
Feature  Intel MKL  Intel IPP 
API  DFT  FFT 
Interfaces  C and Fortran LP64 (64bit long and pointer)  C LP64 only 
Dimensions  1D up to 7D  1D (Signal Processing) 
Transform Sizes  32bit platforms  maximum size is 2^311  FFT  Powers of 2 only (**) DFT 2^{32} maximum size (**) 
Mixed Radix Support  2,3,5,7,11, 13 and several larger kernels (*)  DFT  2,3,5,7,11,13 kernels (*) 
Data Types (See Table 3 for detail)  Real & Complex  Real & Complex 
Scaling  Transforms can be scaled by an arbitrary floating point number (with precision the same as input data)  Integer ("fixed") scaling

Threading  Platform dependent
 1D and 2D

*  Both libraries support arbitrary radix in optimized manner, that is O(N log N), but these specific radixes are better optimized than others.
** the Max Size Limits:
 for double precision complex DFT (64fc) the length upper bound is 67108863 (2^26  1).
 for single precision complex DFT (32fc) the length upper bound is 134217727 (2^27  1).
 for double precision complex FFT(64fc) the length upper bound is 2^27.
 for single precision complex FFT (32fc) the length upper bound is 2^28.
Data Types and Formats
The Intel® MKL and Intel® IPP Fourier transform functions support a variety of data types and formats for storing signal values. Mixed types interfaces are also supported. Please see the product documentation for details.
Table 3: Comparison of Intel® MKL and Intel® IPP Data Types and Formats
Feature  Intel MKL  Intel IPP 
Real FFTs  
Precision  Single, Double  Single, Double 
1D Data Types  Real for all dimensions  Signed short, signed int, float, double 
2D Data Types  Real for all dimensions  Unsigned char, signed int, float 
1D Packed Formats  CCS, Pack, Perm, CCE  CCS, Pack, Perm 
2D Packed Formats  CCS, Pack, Perm, CCE  RCPack2D 
3D Packed Formats  CCE  n/a 
Format Conversion Functions  n/a  n/a 
Complex FFTs  
Precision  Single, Double  Single, Double 
1D Data Types  Complex for all dimensions  Signed short, complex short, signed int, complex integer, complex float, complex double 
2D Data Types  Complex for all dimensions  Complex float 
Formats Legend
CCE  stores the values of the first half of the output complex conjugateeven signal
CCS  same format as CCE format for 1D, is slightly different for multidimensional real transforms
for 2D transforms. CCS, Pack, Perm are not supported for 3D and higher rank
Pack  compact representation of a complex conjugatesymmetric sequence
Perm  same as Pack format for odd lengths, arbitrary permutation of the Pack format for even lengths
RCPack2D  exploits the complex conjugate symmetry of the transformed data to store only half of the resulting Fourier coefficients
Performance
The Intel® MKL and Intel® IPP are optimized for current and future Intel® ® processors, and are specifically tuned for two different usage areas:
 Intel® MKL is suitable for large problem sizes typical to FORTRAN and C/C++ highperformance computing software such as engineering, scientific, and financial applications.
 Intel® IPP is specifically designed for smaller problem sizes including those used in multimedia, data processing, communications, and embedded C/C++ applications.
Choosing the Best FFT for Your Application
Before making a decision, developers must understand the specific requirements and constraints of the application. Developers should consider these questions:
 What are the performance requirements for the application? How performance is measured and what is the measurement criteria? Is a specific benchmark being used? What are the known performance bottlenecks?
 What type of application is being developed? What are the main operations being performed and on what kind of data?
 What API is currently being used in the application for transforms? What programming language(s) is the application code written in?
 Does the FFT output data need to be scaled (normalized)? What type of scaling is required?
 What kind of input and output data does the transform process? What are the valid and invalid values? What type of precision is required?
Summary
Intel® MKL and Intel® IPP both provide optimized Fourier Transform functions. For more detailed information on the FFT APIs, parameters and formats, please refer to the following documents:
 Intel® MKL Reference Manual ( see chapter Fourier Transform Function)
 Intel® IPP Reference Manual Volume 1 Signal Processing and Volume 2 for Image Processing
Get Intel® Performance Libraries for free: https://software.intel.com/enus/performancelibraries
Other Resources
Optimization Notice 

Optimization Notice: Intel’s compilers may or may not optimize to the same degree for nonIntel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessordependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice. Notice revision #20110804 