# lapack(7) [osx man page]

ACCELERATE(7) BSD Miscellaneous Information Manual ACCELERATE(7)NAME

Accelerate vecLib vImage Neon vMathLib BLAS LAPACK vDSP Vector Computation Extended Math LibraryThis man page introduces the Accelerate umbrella framework, its constituent libraries and programming support in Mac OS X.--DESCRIPTION

The Accelerate framework (/System/Library/Frameworks/Accelerate.framework) contains thousands of hand tuned high performance library routines for common problems in signal and image processing and general and scientific computing. These routines are provided to help developers and Apple frameworks alike make better use of onboard hardware SIMD vector engines (such as SSE and Neon) and multiple processors for best per- formance, without the need to invest in the complexity that SIMD and multithreaded programming sometimes requires. A typical Accelerate.framework function will be presented as a single function that accomplishes a taske.g. do a discrete Fourier trans- form, or blur an image, or perhaps just multiply two arrays of floats together. Once called, a typical Accelerate.framework function will examine available hardware and select a tuned version of the algorithm for best performance on that hardware for that problem size, image shape, etc. That function will usually be hand-tuned vectorized code (i.e. uses SSE or Neon). For large enough problems, the function may automatically split up the work across multiple processors using Grand Central Dispatch (GCD) or pthreads, all without involvement of the caller. The speedups so obtained can be quite significant due to impressive synergies between SIMD vector engines and multithreading. Vec- torization typically will enchance performance many fold--2, 4, or even 10 fold improvement is normal. Multithreading can then further accelerate your code many fold according to the number of processors on your system. Some vectorized, multithreaded Accelerate.framework functions run hundreds of times faster than their scalar, single threaded counterparts! Accelerate.framework is intended to help you towards greater application performance regardless of your current investment in high perfor- mance technologies. If you have already written your own threading engine, you can use methods such as the kvImageDoNotTile flag or the VECLIB_MAXIMUM_THREADS environment variable to disable internal multithreading so that it does not contend with your threading engine. If you have pseudo-real-time scheduling needs, Accelerate.framework functions that otherwise might allocate their own temporary memory on the heap allow you to pass in preallocated temporary buffers, so as to avoid potential locking in malloc. If you are interested in writing your own vector code, perhaps to speed up areas of your application which is not covered by Accelerate functionality, the framework headers provide cross platform vector types that you can use to enhance the portability of some vector code and facilitate debugging, as well as a number of basic library routines to make writing vector code easier, such as the interfaces found in vMathLib, a library of math routines (e.g. sin, cos, pow, etc.) for SIMD vectors. To use Accelerate.framework headers: #include <Accelerate/Accelerate.h> To link to Accelerate.framework, simply add--Accelerate to your compiler line: cc-frameworkAccelerate my_file.c For help with linking to frameworks in Xcode, see also: http://developer.apple.com/library/mac/#documentation/MacOSX/Conceptual/BPFrameworks/Tasks/IncludingFrameworks.html-frameworkFor further information: Browse a comprehensive introduction to the Accelerate framework: http://developer.apple.com/performance/accelerateframework.htmlAccelerate Umbrella FrameworkThe Accelerate umbrella framework encompasses all the libraries provided with MacOS X that Apple has optimized for high performance vector and numerical computing. Subsequent sections describe the sub-frameworks that comprise the Accelerate framework. Please link to Accelerate.framework. The positioning of interfaces within sub-frameworks and libraries within Accelerate.framework is subject to change.vImage FrameworkThis framework is designed to provide a suite of image processing primitives. Convolutions, Morphological operators, and Geometric transforms (e.g. scale, shear, warp, rotate) are provided. Alpha compositing and histogram operations are also supported, in addition to various conver- sion routines between different image formats. vImage uses your image data in place without costly packing and unpacking from wrapper objects, using a simple descriptor of the image using base address, height, width and row bytes (to allow for tiling and row padding). Four core formats are supported: Planar8 - a single channel, 8-bit per channel image ARGB8888 - a four channel, 8-bit per channel image.* PlanarF - a single channel, floating point image. ARGBFFFF - a four channel, floating point image.* *Most functions are channel order agnostic, but where it matters, RGBA and BGRA forms may also be provided. Other formats are supported by conversion to core format prior to applying various vImage functions. The conversion cost is typically very small, and is in many cases faster than attempting to do the conversion just in time within the function, because many redundant conversions to a arithmetic format usable by the core vector units, some hidden from you, can be avoided. The formats provided reflect core performance competencies of the vector hardware rather than the wide diversity of image formats out there. For more information, see: http://developer.apple.com/library/mac/#documentation/Performance/Conceptual/vImage/Introduction/Introduction.htmlvecLib FrameworkThe vecLib framework is a collection of facilities covering digital signal processing (vDSP), matrix computations (BLAS), numerical linear algebra (LAPACK) and mathematical routines (vForce/vMathLib) The vDSP, BLAS and LAPACK components of vecLib run on the scalar and vector domain. vecLib automatically detects the presence of the vector engine and uses it. vMathLib mirrors the existing scalar libm on the vector engine. vMathLib runs only on the vector engine. For more information, see: http://developer.apple.com/library/mac/#documentation/Performance/Conceptual/vecLib/Reference/reference.htmlvDSPThe vDSP Library provides mathematical functions for applications such as speech, sound, audio, and video processing, diagnostic medical imaging, radar signal processing, seismic analysis, and scientific data processing. The vDSP functions operate on real and complex data types. The functions include data type conversions, fast Fourier transforms (FFTs), and vector-to-vector and vector-to-scalar operations. The vDSP functions have been implemented in two ways: as vectorized code, using the vector unit on the ARM and Intel microprocessors, and as scalar code, which runs on all machines. Vector code often has special alignment restrictions. If your data is not properly aligned it is common for vDSP to use the scalar path as a fallback. For best results on Intel, align your data to a multiple of 16 bytes. (Malloc natu- rally aligns memory blocks that it allocates to 16 bytes on MacOS X.) It is noteworthy that vDSP's FFTs are one of the fastest implementations of the Discrete Fourier Transforms available anywhere. The vDSP Library itself is included as part of vecLib in Mac OS X. The header file, vDSP.h, defines data types used by the vDSP functions and symbols accepted as flag arguments to vDSP functions. vDSP functions are available in single and double precision. Note that only the single precision is vectorized on ARM due to the underlying instruction set architecture of the vector engine on board. The Intel vector unit supports both single and double precision, so double preci- sion operations can be vectorized on Intel processors. For more information about vDSP see: <http://developer.apple.com/hardwaredrivers/ve/downloads/vDSP_Library.pdf>BLAS

The Basic Linear Algebra Subroutines (BLAS) are high quality, industry standard routines for performing basic vector and matrix operations. Level 1 BLAS consists of vector-vector operations, Level 2 BLAS consists of matrix-vector operations, and Level 3 BLAS have matrix-matrix operations. The efficiency, portability, and the wide adoption of the BLAS have made them commonplace in the development of high quality linear algebra software such as LAPACK and in other technologies requiring fast vector and matrix calculations. All of the industry stan- dard FORTRAN and C BLAS entry points, as well as some common extensions, are exported by the vecLib framework. For more information refer to: <http://www.netlib.org/blas/faq.html>LAPACK

LAPACK provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigen- value problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision. LAPACK in vecLib makes full use of the optimized BLAS and fully benefits from their performance. All the industry standard FORTRAN LAPACK entry points are exported from the vecLib framework. C programs may make calls to the FORTRAN entry points using the prototypes set out in "/System/Library/Frameworks/vecLib.framework/Headers/clapack.h". For more information, please see: <http://www.netlib.org/lapack/index.html> LAPACK follows FORTRAN calling conventions (even when called from C code). Users must be aware that ALL arguments are passed by reference. This includes all scalar arguments such as matrix dimensions and scale factors. Additionally, please note that two-dimensional arrays such as matrices are stored in column-major order; this differs from how C programmers customarily lay out such arrays. For more information refer to <http://www.netlib.org/clapack/readme>.SEE ALSO

You may also be interested in the system math library, which provides high-quality implementations of basic mathematical functions like exp, log, pow, sin, cos... See math(3) for more information.BUGS

Accelerate.framework is not magic! It will not vectorize or multithread your code for you, just because you linked against the framework. You have to actually call the functions exported by the Accelerate.framework, and then only those functions from the framework that you called will be Accelerated.MacOS XMay 1, 2007 MacOS X