Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: Guide and Reference

Overview of ESSL

This section gives an overview of the ESSL capabilities and requirements.

ESSL is a state-of-the-art collection of subroutines providing a wide range of mathematical functions for many different scientific and engineering applications. Its primary characteristics are performance, functional capability, and usability.

Performance and Functional Capability

The mathematical subroutines, in nine computational areas, are tuned for performance on the RS/6000. The computational areas are:

• Linear Algebra Subprograms
• Matrix Operations
• Linear Algebraic Equations
• Eigensystem Analysis
• Fourier Transforms, Convolutions and Correlations, and Related Computations
• Sorting and Searching
• Interpolation
• Numerical Quadrature
• Random Number Generation

ESSL provides two run-time libraries:

• The ESSL Symmetric Multi-Processing (SMP) Library provides thread-safe versions of the ESSL subroutines for use on all SMP (for example, 604e or 630) processors. In addition, a subset of these subroutines are also multithreaded versions; that is, they support the shared memory parallel processing programming model. For a list of the multithreaded subroutines in the ESSL SMP Library, see Table 21.
• The ESSL Serial Library provides thread-safe versions of the ESSL subroutines for use on all processors. You may use this library to develop your own multithreaded applications.

All libraries are designed to provide high levels of performance for numerically intensive computing jobs on these respective processors. All versions provide mathematically equivalent results.

The ESSL Serial Library and the ESSL SMP Library support both 32-bit environment and 64-bit environment applications.

The ESSL subroutines can be called from application programs written in Fortran, C, |and C++. ESSL runs under the AIX operating system.

Usability

ESSL is designed for usability:

• It has an easy-to-use call interface.
• If your existing application programs use the ESSL Serial library, you only need to re-link your program to take advantage of the increased performance of the ESSL SMP Library.
• It supports a 64-bit environment.

  64-bit applications can be created on any system, but can only run on 64-bit hardware.

  The data model used for |the 64-bit environment is referred to as LP64. This data model supports 32-bit integers and 64-bit pointers. In accordance with the LP64 data model, all ESSL integer arguments remain |32-bit except for the iusadr argument for ERRSET. See ERRSET--ESSL ERRSET Subroutine for ESSL.

• It has informative error-handling capabilities, enabling you to calculate auxiliary storage sizes and transform lengths.
• An online book that can be displayed using an Hypertext Markup Language (HTML) document browser, is available for use with ESSL.

The Variety of Mathematical Functions

This section describes the mathematical functions included in ESSL.

Areas of Application

ESSL provides a variety of mathematical functions for many different types of scientific and engineering applications. Some of the industries using these applications are: Aerospace, Automotive, Electronics, Petroleum, Finance, Utilities, and Research. Examples of applications in these industries are:

What ESSL Provides

The subroutines provided in ESSL, summarized in Table 1, fall into the following groups:

• Nine major areas of mathematical computation, providing the computations commonly used by the industry applications listed above
• Utilities, performing general-purpose functions

To help you select the ESSL subroutines that fulfill your needs for performance, accuracy, storage, and so forth, see Selecting an ESSL Subroutine.

Table 1. Summary of ESSL Subroutines

ESSL--Processing Capabilities

ESSL provides two run-time libraries, the ESSL SMP Library and the ESSL Serial Library. These libraries are designed to provide high levels of performance for numerically intensive computing jobs on the |IBM pSeries and RS/6000 processors. To order the IBM Engineering and Scientific Subroutine Library for AIX, specify program number 5765-C42. Most of the subroutine calls are compatible with those in the ESSL/370 product.

Accuracy of the Computations

ESSL provides accuracy comparable to libraries using equivalent algorithms with identical precision formats. Both short- and long-precision real versions of the subroutines are provided in most areas of ESSL. In some areas, short- and long-precision complex versions are also provided, and, occasionally, an integer version is provided. The data types operated on by the short-precision, long-precision, and integer versions of the subroutines are |ANSI/IEEE 32-bit and 64-bit binary floating-point format, and 32-bit integer. See the ANSI/IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Standard 754-1985, for more detail. (There are ESSL-specific rules that apply to the results of computations on workstation processors using the ANSI/IEEE standards. For details, see What Data Type Standards Are Used by ESSL, and What Exceptions Should You Know About?.)

For more information on accuracy, see Getting the Best Accuracy.

High Performance of ESSL

Algorithms: The ESSL subroutines have been designed to provide high performance. (See references [30], [41], and [42].) To achieve this performance, the subroutines use state-of-the-art algorithms tailored to specific operational characteristics of the hardware, such as cache size, Translation Lookaside Buffer (TLB) size, and page size.

Most subroutines use the following techniques to optimize performance:

• Managing the cache and TLB efficiently so the hit ratios are maximized; that is, data is blocked so it stays in the cache or TLB for its computation.
• Accessing data stored contiguously--that is, using stride-1 computations.
• Exploiting the large number of available floating-point registers.
• Using algorithms that minimize paging.
• On the SMP processors:
  • The ESSL SMP Library is designed to exploit the processing power and shared memory of the SMP processor. In addition, a subset of the ESSL SMP subroutines have been coded to take advantage of increased performance from multithreaded (parallel) programming techniques. For a list of the multithreaded subroutines in the ESSL SMP Library, see Table 21.
  • Choosing the number of threads depends on the problem size, the specific subroutine being called, and the number of physical processors you are running on. To achieve optimal performance, experimentation is necessary; however, picking the number of threads equal to the number of online processors generally provides good performance in most cases. In some cases, performance may increase if you choose the number of threads to be less than the number of online processors.

    |You should use either the XL Fortran XLSMPOPTS or the |OMP_NUM_THREADS environment variable to specify the number of threads you want |to create.

• |On the POWER4 processor: |
  • |Structuring the ESSL subroutines so, where applicable, the compiled code |fully utilizes the dual floating-point execution units. Because two |Multiply-Add instructions can be executed each cycle, neglecting overhead, |this allows four floating-point operations per cycle to be performed.
  • |Structuring the ESSL subroutines so, where applicable, the compiled code |takes full advantage of the hardware data prefetching. |
• On the POWER3 and POWER3-II processors:
  • Structuring the ESSL subroutines so, where applicable, the compiled code fully utilizes the dual floating-point execution units. Because two Multiply-Add instructions can be executed each cycle, neglecting overhead, this allows four floating-point operations per cycle to be performed.
  • Structuring the ESSL subroutines so, where applicable, the compiled code takes full advantage of the hardware data prefetching.
• On the POWER processor:
  • Using algorithms that balance floating-point operations with loads in the innermost loop.
  • Using algorithms that minimize stores in the innermost loops.
  • Structuring the ESSL subroutines so, where applicable, the compiled code uses the Multiply-Add instructions. Neglecting overhead, these instructions perform two floating-point operations per cycle.

Mathematical Techniques: All areas of ESSL use state-of-the-art mathematical techniques to achieve high performance. For example, the matrix-vector linear algebra subprograms operate on a higher-level data structure, matrix-vector rather than vector-scalar. As a result, they optimize performance directly for your program and indirectly through those ESSL subroutines using them.

The Fortran Language Interface to the Subroutines

The ESSL subroutines follow standard Fortran calling conventions and must run in the Fortran run-time environment. When ESSL subroutines are called from a program in a language other than Fortran, such as C, C++, or PL/I, the Fortran conventions must be used. This applies to all aspects of the interface, such as the linkage conventions and the data conventions. For example, array ordering must be consistent with Fortran array ordering techniques. Data and linkage conventions for each language are given in Chapter 4, Coding Your Program.