Decimal Hardware Multiplier

Decimal Arithmetic ◽

Decimal Numbers ◽

Decimal Multiplication ◽

IEEE-754 2008 has extended the standard with decimal floating-point arithmetic. Human-centric applications, like financial and commercial, depend on decimal arithmetic since the results must match exactly those obtained by human calculations without being subject to errors caused by decimal to binary conversions. Decimal multiplication is a fundamental operation utilized in many algorithms, and it is referred in the standard IEEE-754 2008. Decimal multiplication has an inherent difficulty associated with the representation of decimal numbers using a binary number system. Both bit and digit carries, as well as invalid results, must be considered in decimal multiplication in order to produce the correct result. This chapter focuses on algorithms for hardware implementation of decimal multiplication. Both decimal fixed-point and floating-point multiplication are described, including iterative and parallel solutions.

Decimal Hardware Multiplier

Encyclopedia of Information Science and Technology, Fourth Edition ◽

10.4018/978-1-5225-2255-3.ch400 ◽

2018 ◽

pp. 4607-4618

Author(s):

Mário Pereira Vestias

Keyword(s):

Number System ◽

Floating Point ◽

Binary Number ◽

Correct Result ◽

Fundamental Operation ◽

Decimal Arithmetic ◽

Decimal Numbers ◽

Decimal Multiplication ◽

IEEE-754 2008 has extended the standard with decimal floating point arithmetic. Human-centric applications, like financial and commercial, depend on decimal arithmetic since the results must match exactly those obtained by human calculations without being subject to errors caused by decimal to binary conversions. Decimal Multiplication is a fundamental operation utilized in many algorithms and it is referred in the standard IEEE-754 2008. Decimal multiplication has an inherent difficulty associated with the representation of decimal numbers using a binary number system. Both bit and digit carries, as well as invalid results, must be considered in decimal multiplication in order to produce the correct result. This article focuses on algorithms for hardware implementation of decimal multiplication. Both decimal fixed-point and floating-point multiplication are described, including iterative and parallel solutions.

Floating-Point Arithmetic Algorithms in the Symmetric Residue Number System

IEEE Transactions on Computers ◽

10.1109/t-c.1974.223772 ◽

1974 ◽

Vol C-23 (1) ◽

pp. 9-20 ◽

Cited By ~ 13

Author(s):

E. Kinoshita ◽

H. Kosako ◽

Y. Kojima

Keyword(s):

Number System ◽

Residue Number System ◽

Floating Point ◽

Residue Number ◽

Specification for binary floating point arithmetic for microprocessor systems

10.3403/00218955u ◽

2015 ◽

Keyword(s):

Floating Point ◽

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

Numerical algorithms for high-performance computational science

10.1098/rsta.2019.0066 ◽

2020 ◽

Vol 378 (2166) ◽

pp. 20190066 ◽

Cited By ~ 2

Author(s):

Jack Dongarra ◽

Laura Grigori ◽

Nicholas J. Higham

Keyword(s):

High Performance ◽

Numerical Algorithms ◽

Computational Science ◽

Floating Point ◽

Important Criterion ◽

Data Movement ◽

High Performance Computers ◽

Point Arithmetic ◽

Speed And Accuracy

A number of features of today’s high-performance computers make it challenging to exploit these machines fully for computational science. These include increasing core counts but stagnant clock frequencies; the high cost of data movement; use of accelerators (GPUs, FPGAs, coprocessors), making architectures increasingly heterogeneous; and multi- ple precisions of floating-point arithmetic, including half-precision. Moreover, as well as maximizing speed and accuracy, minimizing energy consumption is an important criterion. New generations of algorithms are needed to tackle these challenges. We discuss some approaches that we can take to develop numerical algorithms for high-performance computational science, with a view to exploiting the next generation of supercomputers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.