General Decimal Arithmetic
[ FAQ  Decimal web links  Bibliography  Arithmetic specification  Formats (encodings)  decNumber C implementation and C++ implementation  DFPAL  Testcases  Summary  Densely Packed Decimal  Speleotrove ] 
Welcome to the new General Decimal Arithmetic website, which is now hosted at speleotrove.com. The page and file names here have not been changed from the names used on the previous website, www2.hursley.ibm.com. 
The problems of binary floatingpoint can be avoided by using base 10 (decimal) exponents and preserving those exponents where possible. This site describes a decimal arithmetic which achieves the necessary results and is suitable for both hardware and software implementation. It brings together the relevant concepts from a number of ANSI, IEEE, ECMA, and ISO standards, and conforms to the decimal formats and arithmetic in the new IEEE 754 standard (‘7542008’), which was published by the IEEE in August 2008.
The decimalencoded formats and arithmetic described in the new standard now have many implementations in hardware and software (see links below), including:
The combination of formats and arithmetic defined here and in the IEEE 754 standard describe a new decimal data type, in various sizes. Notably, this single data type can be used for integer, fixedpoint, and floatingpoint decimal arithmetic, and the design permits compatible fixedsize and arbitraryprecision implementations. Further, most existing numeric data in commercial databases are stored in a decimal form (one or two digits per byte), which can be converted to and from the decimalencoded formats efficiently and easily.
The main features of the arithmetic are summarized below. For the background and rationale for the design of the arithmetic, see Decimal FloatingPoint: Algorism for Computers in the Proceedings of the 16th IEEE Symposium on Computer Arithmetic (Cowlishaw, M. F., 2003).
Reproduced with permission from IBM © Copyright 1997, 2008 by International Business Machines Corporation. Copyright © Mike Cowlishaw 1981, 2009.
Here you will find documentation and downloads for decimal arithmetic, fixedsize decimal formats (encodings) and their performance, the decNumber reference implementation, the decNumber++ implementation for C++, the DFPAL PowerPC abstraction layer, and the languageindependent testcases.
Arithmetic  Version  Description 
Specification
[.html  .pdf] 
1.70 2009.03.25 
Decimal floatingpoint arithmetic, with unrounded and integer arithmetic as a subset (IEEE 754 + IEEE 854 + ANSI X3.274 + ECMA 334 + Java^{[TM]} 5). 
This specification forms the basis for a number of implementations, and also describes the decimal arithmetic in the new IEEE 754 standard. 
Formats  Version  Description 
Specification
[.html  .pdf] 
1.01 2009.03.20 
Concrete decimal formats (bit encodings) suitable for hardware or software implementation of native decimal datatypes; these provide up to 7, 16, or 34 digits of precision. 
Performance
[.html  .pdf] 
1.12 2009.03.21 
Performance measurements on three implementations that support the IEEE 754 decimal formats. 
Sample code
[.html] 
1.00 2003.04.10 
Java^{[TM]} classes which illustrate the decimal encoding of decimal floatingpoint numbers, and the corresponding decoding. 
(The earlier ‘Strawman 1’ proposal, implemented as decSingle and decDouble in early versions of the decNumber package, is available for historical interest in PDF form. See also: A Decimal FloatingPoint Specification, Schwarz et al., 15th IEEE Symposium on Computer Arithmetic [presentation charts].) 
The package is available under a variety of free, open source, and commercial licenses (the ICU license is the simplest and the least restrictive), and is suitable for littleendian or bigendian systems which support 32bit (or wider) integers. It is currently in use on dozens of different platforms, including mainframes, PowerPC, x86, and over 20 varieties of Unix.
decNumber  Version  Description 
Documentation
[.html  .pdf] 
3.61 2009.03.23 
Describes the decNumber package, including a User’s Guide
section with several examples.
Errata (known bugs and fixes since 3.56, 2007.10.12). 
International Components for Unicode (ICU)
decNumber package 
3.61 2008.07.09 
The source code (.h and .c
files), together with the examples, the
ICU license, and the documentation in PDF format.
(The latest package is also mirrored here.) 
IBM alphaWorks
decNumber package 
3.61 2008.07.09 
The source code (.h and .c files), together with the examples, the alphaWorks license, and the documentation in PDF format. (This download is on the IBM alphaWorks site. A commercial license for this software is also available there.) 
GPL open source
decNumber C code decExamples.zip 
3.53 2007.09.07 
‘decNumber C code’ links to the open source code (.h and .c files), part of the GCC project (GPL license). ‘decExamples.zip’ contains the example files referred to in the documentation and also the readme.txt file which has suggestions on how to compile and run the examples. 
More implementations of the arithmetic are listed below. 
decNumber++  Version  Description 
IBM alphaWorks
decNumber++ 
1.00 2006.07.11 
Robert Klarer’s
decNumber++, which implements the interfaces
specified in the forthcoming ISO Technical Report on decimal
arithmetic types in C++:
ISO/IEC
TR 24733: C++ Decimal FloatingPoint Arithmetic Extensions.
(This download is on the IBM alphaWorks site.) 
More implementations of the arithmetic are listed below. 
DFPAL  Version  Description 
Documentation
[.html  as .zip] 
2.20 2008.01.03 
The DFPAL User’s guide with overview, examples, compilation instructions, FAQ, etc. 
Download
DFPAL.zip DFPAL.tar.gz 
2.20 2008.01.03 
The DFPAL source code (.h and .c files), together with the examples, the International Components for Unicode (ICU) license, the documentation in HTML format, etc. 
Testcases  Version  Description 
Documentation
[.html  .pdf] 
2.44 2009.03.24 
Describes the testcase file format, testcase coverage, and testcase sources. 
Download
dectest.zip dectest0.zip 
2.59 2009.10.07 
The extended (dectest.zip) and subset (dectest0.zip) testcase files (containing more than 81,300 tests). These cover all the operations and conversions described in the specifications, and include tests for the decimal encodings. 
See also the IBM Haifa test suite (FPGen). 
The decimal arithmetic described here combines the requirements of both fixedpoint and floatingpoint arithmetic, giving the following advantages:


The links below provide background and related information.
Background & Rationale

Bibliography
Related Decimal Links

Please send any comments or corrections to Mike Cowlishaw (mfc), mfc@uk.ibm.com; see also speleotrove.com. 
Reproduced with permission from IBM © Copyright 1997, 2008 by
International Business Machines Corporation.
Parts © Mike Cowlishaw 1997, 2009.
Java is a trademark of Sun Microsystems Inc. 