Architecture and software support in IBM S/390 Parallel Enterprise Servers for IEEE Floating-Point arithmetic

Abbott, P. H.; Brush, D. G.; Clark, Champ; Crone, C. J.; Ehrman, John R.; Ewart, Graham; Goodrich, Clark; Hack, Michel; Kapernick, J. S.; Minchau, B. J.; Shepard, W. C.; Smith, Raymond L.; Tallman, R.; Walkowiak, S.; Watanabe, Akitsugu; White, W. R.

doi:10.1147/rd.435.0723

Cited by 9 publications

(3 citation statements)

References 14 publications

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“…The deceptively-easy task of expressing binary fractional numbers as human-readable decimal numbers led T E X's author to write a famous paper called A Simple Program Whose Proof Isn't [36]. Related articles that finally properly solved the number-base conversion problem have appeared only since 1990 [1,7,21,56,57].…”

Section: Inadequate I/omentioning

confidence: 99%

Preparing Horizon Europe proposals in LaTeX with `heria`

Miller

2024

TUGboat

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T E X has lasted longer than many other computer software technologies.7 Future directions 7.1 XML directions 7.2 Unicode directions Foreword Some of the material in this article may seem old hat to veteran T E X users, but I am writing it with the intention that it can also be read by people who are unfamiliar with T E X and METAFONT, but are nevertheless interested in learning something about the design and history of those programs.

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Section: Inadequate I/omentioning

confidence: 99%

Preparing Horizon Europe proposals in LaTeX with `heria`

Miller

2024

TUGboat

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“…Producing an exact decimal output representation of an internal binary floating-point number, and the correctly-rounded reverse conversion, can require a surprisingly large number of digits: more than 11,000 decimal digits in the quadruple-precision format. The base-conversion problem seems to be viewed by many as trivial, but it is not: it took more than 50 years of computer use before the problem was properly solved in the 1990s [7,8,9,10,11,12,13]. Even today, more than 15 years after the earliest of those papers, most vendors, and most programming languages, fail to guarantee correct base conversion in source code, input, and output.…”

Section: The Base-conversion Problemmentioning

confidence: 99%

“…In 1999, the new IBM mainframe G5 processor added hardware support for IEEE 754 arithmetic (32-bit, 64-bit, and 128-bit formats) [12], while retaining the older hexadecimal arithmetic with its problems of wobbling precision and limited exponent range.…”

Section: The Ieee 754 and 854 Standardsmentioning

confidence: 99%

New Directions in Floating-Point Arithmetic

Beebe

2007

AIP Conference Proceedings

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Abstract. This article briefly describes the history of floating-point arithmetic, the development and features of IEEE standards for such arithmetic, desirable features of new implementations of floating-point hardware, and discusses workin-progress aimed at making decimal floating-point arithmetic widely available across many architectures, operating systems, and programming languages. WHAT IS FLOATING-POINT ARITHMETIC?Floating-point arithmetic is a technique for storing and operating on numbers in a computer where the base, range, and precision of the number system are usually fixed by the computer design.Conceptually, a floating-point number has a sign, an exponent, and a significand (the older term mantissa is now deprecated), allowing a representation of the form . 1/ sign significand base exponent . The base point in the significand may be at the left, or after the first digit, or at the right. The point and the base are implicit in the representation: neither is stored.The sign can be compactly represented by a single bit, and the exponent is most commonly a biased unsigned bitfield, although some historical architectures used a separate exponent sign and an unbiased exponent. Once the sizes of the sign and exponent fields are fixed, all of the remaining storage is available for the significand, although in some older systems, part of this storage is unused, and usually, ignored. On modern systems, the storage order is conceptually sign, exponent, and significand, but addressing conventions on byte-addressable systems (the big endian versus little endian theologies) can alter that order, and some historical designs reordered them, and sometimes split the exponent and significand fields into two interleaved parts. Except when the low-level storage format must be examined by software, such as for binary data exchange, these differences are handled by hardware, and are rarely of concern to programmers.The data size is usually closely related to the computer word size. Indeed, the venerable Fortran programming language mandates a single-precision floating-point format occupying the same storage as an integer, and a doubleprecision format occupying exactly twice the space. This requirement is heavily relied on by Fortran software for array dimensioning, argument passing, and in COMMON and EQUIVALENCE statements for storage alignment and layout. Some vendors later added support for a third format, called quadruple-precision, occupying four words. Wider formats have yet to be offered by commercially-viable architectures, although we address this point later in this article.Floating-point arithmetic can be contrasted with fixed-point arithmetic, where there is no exponent field, and it is the programmer's responsibility to keep track of where the base point lies. Address arithmetic, and signed and unsigned

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A new math library

Beebe

2009

Int J of Quantum Chemistry

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ABSTRACT:The design and development of a new mathematical function library is described. The library extends programming support to decimal, as well as binary, arithmetic, and aims to influence the future evolution of floating-point support in programming languages, libraries, and hardware. It encourages and facilitates research in new computer-arithmetic designs, and the analysis and comparison of historical ones.

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Architecture and software support in IBM S/390 Parallel Enterprise Servers for IEEE Floating-Point arithmetic

Cited by 9 publications

References 14 publications

Preparing Horizon Europe proposals in LaTeX with `heria`

Preparing Horizon Europe proposals in LaTeX with `heria`

New Directions in Floating-Point Arithmetic

A new math library

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Architecture and software support in IBM S/390 Parallel Enterprise Servers for IEEE Floating-Point arithmetic

Cited by 9 publications

References 14 publications

Preparing Horizon Europe proposals in LaTeX with heria

Preparing Horizon Europe proposals in LaTeX with heria

New Directions in Floating-Point Arithmetic

A new math library

Contact Info

Product

Resources

About

Preparing Horizon Europe proposals in LaTeX with `heria`

Preparing Horizon Europe proposals in LaTeX with `heria`