C H A P T E R 1

Introduction

Sun Performance Library is a set of optimized, high-speed mathematical subroutines for solving linear algebra and other numerically intensive problems. Sun Performance Library is based on a collection of public domain applications available from Netlib at http://www.netlib.org. Sun has enhanced these public domain applications and bundled them as the Sun Performance Library.

The Sun Performance Library User's Guide explains the Sun-specific enhancements to the base applications available from Netlib. Reference material describing the base routines is available from Netlib and the Society for Industrial and Applied Mathematics (SIAM).

Libraries Included With Sun Performance Library

Sun Performance Library contains enhanced versions of the following standard libraries:

LAPACK version 3.0 - For solving linear algebra problems.

BLAS1 (Basic Linear Algebra Subprograms) - For performing vector-vector operations.

BLAS2 - For performing matrix-vector operations.

BLAS3 - For performing matrix-matrix operations.

The BLAS1, BLAS2, and BLAS3 libraries do not have version numbers. There has been only one version of the BLAS routines on Netlib.

Note - LINPACK has been removed from Sun Performance Library. LAPACK version 3.0 supersedes LINPACK and all previous versions of LAPACK. If the LINPACK routines are still needed, the LINPACK library and documentation can be obtained from http://www.netlib.org.

Sun Performance Library is available in both static and dynamic library versions optimized for the V8, V8+, and V9 architectures. Sun Performance Library supports static and shared libraries on Solaris 7, Solaris 8, and Solaris 9 and adds support for multiple processors.

Sun Performance Library LAPACK routines have been compiled with a Fortran 95 compiler and remain compatible with the Netlib LAPACK version 3.0 library. The Sun Performance Library versions of these routines perform the same operations as the Fortran callable routines and have the same interface as the standard Netlib versions.

LAPACK contains driver, computational, and auxiliary routines. Sun Performance Library does not support the auxiliary routines, because auxiliary routines can change or be removed from LAPACK without notice. Because the auxiliary routines are not supported, they are not documented in the Sun Performance Library User's Guide or the section 3P man pages.

Many auxiliary routines contain LA as the second and third characters in the routine name; however, some do not. Appendix B of the LAPACK Users' Guide contains a list of auxiliary routines.

Auxiliary routines are available in the shared (dynamic) libraries and the static libraries. However, there is no guarantee that auxiliary routines will continue to be available in any form in future versions of the Sun Performance Library.

Netlib

Netlib is an online repository of mathematical software, papers, and databases maintained by AT&T Bell Laboratories, the University of Tennessee, Oak Ridge National Laboratory, and professionals from around the world.

Netlib provides many libraries, in addition to the libraries used in Sun Performance Library. While some of these libraries can appear similar to libraries used with Sun Performance Library, they can be different from, and incompatible with Sun Performance Library.

Using routines from other libraries can produce compatibility problems, not only with Sun Performance Library routines, but also with the base Netlib LAPACK routines. When using routines from other libraries, refer to the documentation provided with those libraries.

For example, Netlib provides a CLAPACK library, but the CLAPACK interfaces differ from the C interfaces included with Sun Performance Library. A LAPACK 90 library package is also available on Netlib. The LAPACK 90 library contains interfaces that differ from the Sun Performance Library Fortran 95 interfaces and the Netlib LAPACK version 3.0 interfaces. If using LAPACK 90, refer to the documentation provided with that library.

For the base libraries supported by Sun Performance Library, Netlib provides detailed information that can supplement this user's guide. The LAPACK 3.0 Users' Guide describes LAPACK algorithms and how to use the routines, but it does not describe the Sun Performance Library extensions made to the base routines.

Sun Performance Library Features

Sun Performance Library routines can increase application performance on both serial and MP platforms, because the serial speed of many Sun Performance Library routines has been increased, and, for SPARC, many routines have been parallelized that might be serial in other products. Sun Performance Library routines also have SPARC® specific optimizations that are not present in the base Netlib libraries.

Sun Performance Library provides the following optimizations and extensions to the base Netlib libraries:

Extensions that support Fortran 95 and C language interfaces

Fortran 95 language features, including type independence, compile time checking, and optional arguments.

Consistent API across the different libraries in Sun Performance Library

Compatibility with LAPACK 1, LAPACK 2.0, and LAPACK 3.0 libraries

Increased performance, and in some cases, greater accuracy

Optimizations for specific SPARC instruction set architectures

Support for 64-bit enabled Solaris operating environment

Support for parallel processing compiler options for SPARC

Support for multiple processor hardware options

Mathematical Routines

The Sun Performance Library routines are used to solve the following types of linear algebra and numerical problems:

Elementary vector and matrix operations - Vector and matrix products; plane rotations; 1, 2-, and infinity-norms; rank-1, 2, k, and 2k updates

Linear systems - Solve full-rank systems, compute error bounds, solve Sylvester equations, refine a computed solution, equilibrate a coefficient matrix

Least squares - Full-rank, generalized linear regression, rank-deficient, linear equality constrained

Eigenproblems - Eigenvalues, generalized eigenvalues, eigenvectors, generalized eigenvectors, Schur vectors, generalized Schur vectors

Matrix factorizations or decompositions - SVD, generalized SVD, QL and LQ, QR and RQ, Cholesky, LU, Schur, LDL^T and UDU^T

Support operations - Condition number, in-place or out-of-place transpose, inverse, determinant, inertia

Sparse matrices - Solve symmetric, structurally symmetric, and unsymmetric coefficient matrices using direct methods and a choice of fill-reducing ordering algorithms, and user-specified orderings

Convolution and correlation in one and two dimensions

Fast Fourier transforms, Fourier synthesis, cosine and quarter-wave cosine transforms, cosine and quarter-wave sine transforms

Complex vector FFTs and FFTs in two and three dimensions

Compatibility With Previous LAPACK Versions

The Sun Performance Library routines that are based on LAPACK support the expanded capabilities and improved algorithms in LAPACK 3.0, but are completely compatible with both LAPACK l and LAPACK 2.0. Maintaining compatibility with previous LAPACK versions:

Reduces linking errors due to changes in subroutine names or argument lists.

Ensures results are consistent with results generated with previous LAPACK versions.

Minimizes programs terminating due to differences between argument lists.

Getting Started With Sun Performance Library

This section shows the most basic compiler options used to compile an application that uses the Sun Performance Library routines.

To use the Sun Performance Library, type one of the following commands.

my_system% f95 -dalign my_file.f -xlic_lib=sunperf

my_system% cc -dalign my_file.c -xlic_lib=sunperf

Because Sun Performance Library routines are compiled with -dalign, the -dalign option should be used for compilation of all files if any routine in the program makes a Sun Performance Library call. If -dalign cannot be used, enabling Trap 6, described in the section Enabling Trap 6, is a low-performance workaround that allows misaligned data.

Sun Performance Library is linked into an application with the -xlic_lib switch rather than the -l switch that is used to link in other libraries. The -xlic_lib switch gives the same effect as if -l was used to specify the Sun Performance Library and added -l switches for all of the supporting libraries that Sun Performance Library requires.

To summarize, use the following:

-dalign on all files at compile time or enable trap 6

The same command line options for compiling and linking

-xlic_lib=sunperf

Additional compiler options exist that optimize application performance for the following:

Specific SPARC instruction set architectures, as described in Compiling for SPARC Platforms.

Parallel processing for SPARC platforms, as described in Parallel Processing on SPARC Platforms.

Enabling Trap 6

If an application cannot be compiled using -dalign, enable trap 6 to provide a handler for misaligned data. To enable trap 6 on SPARC, do the following:

1. Place this assembly code in a file called trap6_handler.s.

	.global trap6_handler_

	.text

	.align 4

trap6_handler_:

	retl

	ta    6

2. Assemble trap6_handler.s.

my_system% fbe trap6_handler.s

The first parallelizable subroutine invoked from Sun Performance Library will call a routine named trap6_handler_. If a trap6_handler_ is not specified, Sun Performance Library will call a default handler that does nothing. Not supplying a handler for any misaligned data will cause a trap that will be fatal. (fbe (1) is the Solaris assembler for SPARC platforms.)

3. Include trap6_handler.o on the command line.

my_system% f95 any.f trap6_handler.o -xlic_lib=sunperf