Sign in
Author

Conference

Journal

Organization

Year

DOI
Look for results that meet for the following criteria:
since
equal to
before
between
and
Search in all fields of study
Limit my searches in the following fields of study
Agriculture Science
Arts & Humanities
Biology
Chemistry
Computer Science
Economics & Business
Engineering
Environmental Sciences
Geosciences
Material Science
Mathematics
Medicine
Physics
Social Science
Multidisciplinary
Keywords
(6)
Error Analysis
Error Estimate
Floating Point
Floating Point Arithmetic
Inner Product
Digital Number
Related Publications
(2)
On the precision attainable with various floatingpoint number systems
Representation Error for Real Numbers in Binary Computer Arithmetic
Subscribe
Academic
Publications
A statistical study of the accuracy of floating point number systems
A statistical study of the accuracy of floating point number systems,10.1145/362003.362013,Communications of The ACM,H. Kuki,W. J. Cody
Edit
A statistical study of the accuracy of floating point number systems
(
Citations: 21
)
BibTex

RIS

RefWorks
Download
H. Kuki
,
W. J. Cody
This paper presents the statistical results of tests of the accuracy of certain arithmetic systems in evaluating sums, products and inner products, and analytic error estimates for some of the computations. The arithmetic systems studied are 6digit hexadecimal and 22digit binary
floating point
number representations combined with the usual chop and round modes of arithmetic with various numbers of guard digits, and with a modified round mode with guard digits. In a certain sense, arithmetic systems differing only in their use of binary or hexadecimal number representations are shown to be approximately statistically equivalent in accuracy. Further, the usual round mode with guard digits is shown to be statistically superior in accuracy to the usual chop mode in all cases save one. The modified round mode is found to be superior to the chop mode in all cases.
Journal:
Communications of The ACM  CACM
, vol. 16, no. 4, pp. 223230, 1973
DOI:
10.1145/362003.362013
Cumulative
Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
(
portal.acm.org
)
(
portal.acm.org
)
(
portal.acm.org
)
(
portal.acm.org
)
(
www.informatik.unitrier.de
)
More »
Citation Context
(9)
...The reduction in precision caused by using only a small number of guard digits is discussed by Kuki and Cody [
18
]...
...Thus we prefer rms to other probabilistic measures of precision such as the expected value of   (McKeeman [21]), the expected value of log2   (Kuki and Codi [
18
]), and the expected error in “units in the last place” (Kahan [15])...
...The rounding rule for systems S1 to S5 is the “R*mode” of Kuki and Cody [
18
]: fl(x) is defined to be the floatingpoint number closest to x, and ties are broken by choosing fl(x) so that its least significant fraction bit is one...
...A number z was drawn from a uniform distribution on [0,1], then numbers x1,...,xn were drawn independently from a uniform distribution on [ Z,Z], where Z = 256z is a scale factor used to avoid a bias in favour of any of the number systems (see Kuki and Cody [
18
])...
Richard P. Brent
.
On the precision attainable with various floatingpoint number systems
...corresponding binary system, but this is not necessarily the case (see [
22
])...
William J. Cody
.
Basic concepts for computational software
...One result that might have broad interest concerns the behavior of the mean value of multiplicative error as a function of the base fl. What had been observed empirically for even base by Cody [2] and by Kukl and Cody [
10
], and had been proven theoretically in [6], is that two guard flits are better than one when postmultlphcatlve normalization occurs before symmetric rounding...
...Of course adding a second guard flit (or even just a fifth binary guard bit) would further reduce the mean error, by an order of magmtude in u. This was observed by Cody [2] and by Kuki and Cody [
10
]...
Joaquín Bustoz
,
et al.
Improved Trailing Digits Estimates Applied to Optimal Computer Arithme...
...We use R*rounding [15,
33
] after postnormalization, with four guard digits...
Richard P. Brent
.
A Fortran MultiplePrecision Arithmetic Package
...We use R*rounding [15,
33
] after postnormalization, with four guard digits...
RICHARD P. BRENT
.
A Fortran MultiplePrecision Arithmetic
References
(8)
On the precision attainable with various floatingpoint number systems
(
Citations: 20
)
Richard P. Brent
Journal:
Computing Research Repository  CORR
, vol. abs/1004.3, 2010
On Local Roundoff Errors in FloatingPoint Arithmetic
(
Citations: 36
)
Toyohisa Kaneko
,
Bede Liu
Journal:
Journal of The ACM  JACM
, vol. 20, no. 3, pp. 391398, 1973
Roundoff Error Distribution in FixedPoint Multiplication and a Remark about the Rounding Rule
(
Citations: 17
)
Minoru Urabe
Journal:
Siam Journal on Numerical Analysis  SIAM J NUMER ANAL
, vol. 5, no. 2, pp. 202210, 1968
Rounding errors in algebraic processes
(
Citations: 544
)
James Hardy Wilkinson
Conference:
World Computer Congress  IFIP
, pp. 4453, 1959
Tests of probabilistic models for propagation of roundoff errors
(
Citations: 17
)
T. E. Hull
,
J. Richard Swenson
Journal:
Communications of The ACM  CACM
, vol. 9, no. 2, pp. 108113, 1966
Sort by:
Citations
(21)
On the precision attainable with various floatingpoint number systems
(
Citations: 20
)
Richard P. Brent
Journal:
Computing Research Repository  CORR
, vol. abs/1004.3, 2010
Modern Computer Arithmetic
(
Citations: 8
)
Richard P. Brent
,
Paul Zimmermann
Published in 2010.
FloatingPoint Arithmetic
Nicolas Brisebarre
,
Florent de Dinechin
,
ClaudePierre Jeannerod
,
Vincent Lefèvre
,
Guillaume Melquiond
,
JeanMichel Muller
,
Nathalie Revol
,
Damien Stehlé
,
Serge Torres
Published in 2009.
Formalization of Continuous Probability Distributions
(
Citations: 14
)
Osman Hasan
,
Sofiène Tahar
Conference:
Conference on Automated Deduction  CADE
, pp. 318, 2007
Higher Radix FloatingPoint Representations for FPGABased Arithmetic
(
Citations: 8
)
Bryan C. Catanzaro
,
Brent E. Nelson
Conference:
FieldProgrammable Custom Computing Machines  FCCM
, pp. 161170, 2005