CADNA: a library for estimating round-off error propagation
The CADNA library enables one to estimate round-off error propagation using a probabilistic approach. With CADNA the numerical quality of any simulation program can be controlled. Furthermore by detecting all the instabilities which may occur at run time, a numerical debugging of the user code can b...
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| Vydáno v: | Computer physics communications Ročník 178; číslo 12; s. 933 - 955 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
15.06.2008
Elsevier |
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| ISSN: | 0010-4655, 1879-2944 |
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| Abstract | The CADNA library enables one to estimate round-off error propagation using a probabilistic approach. With CADNA the numerical quality of any simulation program can be controlled. Furthermore by detecting all the instabilities which may occur at run time, a numerical debugging of the user code can be performed. CADNA provides new numerical types on which round-off errors can be estimated. Slight modifications are required to control a code with CADNA, mainly changes in variable declarations, input and output. This paper describes the features of the CADNA library and shows how to interpret the information it provides concerning round-off error propagation in a code.
Program title:CADNA
Catalogue identifier:AEAT_v1_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/AEAT_v1_0.html
Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland
Licensing provisions:Standard CPC licence,
http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.:53 420
No. of bytes in distributed program, including test data, etc.:566 495
Distribution format:tar.gz
Programming language:Fortran
Computer:PC running LINUX with an i686 or an ia64 processor, UNIX workstations including SUN, IBM
Operating system:LINUX, UNIX
Classification:4.14, 6.5, 20
Nature of problem:A simulation program which uses floating-point arithmetic generates round-off errors, due to the rounding performed at each assignment and at each arithmetic operation. Round-off error propagation may invalidate the result of a program. The CADNA library enables one to estimate round-off error propagation in any simulation program and to detect all numerical instabilities that may occur at run time.
Solution method:The CADNA library [1] implements Discrete Stochastic Arithmetic [2–4] which is based on a probabilistic model of round-off errors. The program is run several times with a random rounding mode generating different results each time. From this set of results, CADNA estimates the number of exact significant digits in the result that would have been computed with standard floating-point arithmetic.
Restrictions:CADNA requires a Fortran 90 (or newer) compiler. In the program to be linked with the CADNA library, round-off errors on complex variables cannot be estimated. Furthermore array functions such as
product or
sum must not be used. Only the arithmetic operators and the
abs,
min,
max and
sqrt functions can be used for arrays.
Running time:The version of a code which uses CADNA runs at least three times slower than its floating-point version. This cost depends on the computer architecture and can be higher if the detection of numerical instabilities is enabled. In this case, the cost may be related to the number of instabilities detected.
References:
[1]
The CADNA library, URL address:
http://www.lip6.fr/cadna.
[2]
J.-M. Chesneaux, L'arithmétique Stochastique et le Logiciel CADNA, Habilitation á diriger des recherches, Université Pierre et Marie Curie, Paris, 1995.
[3]
J. Vignes, A stochastic arithmetic for reliable scientific computation, Math. Comput. Simulation 35 (1993) 233–261.
[4]
J. Vignes, Discrete stochastic arithmetic for validating results of numerical software, Numer. Algorithms 37 (2004) 377–390. |
|---|---|
| AbstractList | The CADNA library enables one to estimate round-off error propagation using a probabilistic approach. With CADNA the numerical quality of any simulation program can be controlled. Furthermore by detecting all the instabilities which may occur at run time, a numerical debugging of the user code can be performed. CADNA provides new numerical types on which round-off errors can be estimated. Slight modifications are required to control a code with CADNA, mainly changes in variable declarations, input and output. This paper describes the features of the CADNA library and shows how to interpret the information it provides concerning round-off error propagation in a code. The CADNA library enables one to estimate round-off error propagation using a probabilistic approach. With CADNA the numerical quality of any simulation program can be controlled. Furthermore by detecting all the instabilities which may occur at run time, a numerical debugging of the user code can be performed. CADNA provides new numerical types on which round-off errors can be estimated. Slight modifications are required to control a code with CADNA, mainly changes in variable declarations, input and output. This paper describes the features of the CADNA library and shows how to interpret the information it provides concerning round-off error propagation in a code. Program title:CADNA Catalogue identifier:AEAT_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEAT_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:53 420 No. of bytes in distributed program, including test data, etc.:566 495 Distribution format:tar.gz Programming language:Fortran Computer:PC running LINUX with an i686 or an ia64 processor, UNIX workstations including SUN, IBM Operating system:LINUX, UNIX Classification:4.14, 6.5, 20 Nature of problem:A simulation program which uses floating-point arithmetic generates round-off errors, due to the rounding performed at each assignment and at each arithmetic operation. Round-off error propagation may invalidate the result of a program. The CADNA library enables one to estimate round-off error propagation in any simulation program and to detect all numerical instabilities that may occur at run time. Solution method:The CADNA library [1] implements Discrete Stochastic Arithmetic [2–4] which is based on a probabilistic model of round-off errors. The program is run several times with a random rounding mode generating different results each time. From this set of results, CADNA estimates the number of exact significant digits in the result that would have been computed with standard floating-point arithmetic. Restrictions:CADNA requires a Fortran 90 (or newer) compiler. In the program to be linked with the CADNA library, round-off errors on complex variables cannot be estimated. Furthermore array functions such as product or sum must not be used. Only the arithmetic operators and the abs, min, max and sqrt functions can be used for arrays. Running time:The version of a code which uses CADNA runs at least three times slower than its floating-point version. This cost depends on the computer architecture and can be higher if the detection of numerical instabilities is enabled. In this case, the cost may be related to the number of instabilities detected. References: [1] The CADNA library, URL address: http://www.lip6.fr/cadna. [2] J.-M. Chesneaux, L'arithmétique Stochastique et le Logiciel CADNA, Habilitation á diriger des recherches, Université Pierre et Marie Curie, Paris, 1995. [3] J. Vignes, A stochastic arithmetic for reliable scientific computation, Math. Comput. Simulation 35 (1993) 233–261. [4] J. Vignes, Discrete stochastic arithmetic for validating results of numerical software, Numer. Algorithms 37 (2004) 377–390. |
| Author | Chesneaux, Jean-Marie Jézéquel, Fabienne |
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| Keywords | 02.70.-c Round-off errors Discrete Stochastic Arithmetic CADNA CESTAC method Numerical validation Floating-point arithmetic |
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| References | Vignes (bib003) December 2004; 37 Chesneaux (bib004) 1990 Vignes (bib008) 1986; 303 J.-M. Chesneaux, L'arithmétique stochastique et le logiciel CADNA. Habilitation à diriger des recherches, Université Pierre et Marie Curie, Paris, November 1995 Muller (bib010) 1989 Vignes (bib005) 1993; 35 Scott, Jézéquel, Denis, Chesneaux (bib007) 2007; 176 Rump (bib009) 1988 (bib001) 1985; 22 Vignes, La Porte (bib006) 1974 10.1016/j.cpc.2008.02.003_bib002 Rump (10.1016/j.cpc.2008.02.003_bib009) 1988 (10.1016/j.cpc.2008.02.003_bib001) 1985 Chesneaux (10.1016/j.cpc.2008.02.003_bib004) 1990 Vignes (10.1016/j.cpc.2008.02.003_bib006) 1974 Vignes (10.1016/j.cpc.2008.02.003_bib008) 1986; 303 Vignes (10.1016/j.cpc.2008.02.003_bib003) 2004; 37 Vignes (10.1016/j.cpc.2008.02.003_bib005) 1993; 35 Scott (10.1016/j.cpc.2008.02.003_bib007) 2007; 176 Muller (10.1016/j.cpc.2008.02.003_bib010) 1989 |
| References_xml | – volume: 176 start-page: 507 year: 2007 end-page: 521 ident: bib007 article-title: Numerical ‘health check’ for scientific codes: the CADNA approach publication-title: Comput. Phys. Comm. – volume: 37 start-page: 377 year: December 2004 end-page: 390 ident: bib003 article-title: Discrete stochastic arithmetic for validating results of numerical software publication-title: Numer. Algorithms – volume: 35 start-page: 233 year: 1993 end-page: 261 ident: bib005 article-title: A stochastic arithmetic for reliable scientific computation publication-title: Math. Comput. Simulation – year: 1988 ident: bib009 article-title: Reliability in Computing. The Role of Interval Methods in Scientific Computing – volume: 303 start-page: 997 year: 1986 end-page: 1000 ident: bib008 article-title: Zéro mathématique et zéro informatique publication-title: C. R. Acad. Sci. Paris Sér. I Math. – reference: J.-M. Chesneaux, L'arithmétique stochastique et le logiciel CADNA. Habilitation à diriger des recherches, Université Pierre et Marie Curie, Paris, November 1995 – year: 1989 ident: bib010 article-title: Arithmétique des Ordinateurs – volume: 22 start-page: 9 year: 1985 end-page: 25 ident: bib001 publication-title: IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Standard 754-1985 – start-page: 19 year: 1990 end-page: 30 ident: bib004 article-title: Study of the computing accuracy by using probabilistic approach publication-title: Contribution to Computer Arithmetic and Self-Validating Numerical Methods – start-page: 610 year: 1974 end-page: 614 ident: bib006 article-title: Error analysis in computing publication-title: Information Processing 1974 – volume: 176 start-page: 507 issue: 8 year: 2007 ident: 10.1016/j.cpc.2008.02.003_bib007 article-title: Numerical ‘health check’ for scientific codes: the CADNA approach publication-title: Comput. Phys. Comm. doi: 10.1016/j.cpc.2007.01.005 – volume: 35 start-page: 233 year: 1993 ident: 10.1016/j.cpc.2008.02.003_bib005 article-title: A stochastic arithmetic for reliable scientific computation publication-title: Math. Comput. Simulation doi: 10.1016/0378-4754(93)90003-D – year: 1988 ident: 10.1016/j.cpc.2008.02.003_bib009 – start-page: 19 year: 1990 ident: 10.1016/j.cpc.2008.02.003_bib004 article-title: Study of the computing accuracy by using probabilistic approach – year: 1989 ident: 10.1016/j.cpc.2008.02.003_bib010 – volume: 37 start-page: 377 issue: 1–4 year: 2004 ident: 10.1016/j.cpc.2008.02.003_bib003 article-title: Discrete stochastic arithmetic for validating results of numerical software publication-title: Numer. Algorithms doi: 10.1023/B:NUMA.0000049483.75679.ce – start-page: 610 year: 1974 ident: 10.1016/j.cpc.2008.02.003_bib006 article-title: Error analysis in computing – volume: 303 start-page: 997 year: 1986 ident: 10.1016/j.cpc.2008.02.003_bib008 article-title: Zéro mathématique et zéro informatique publication-title: C. R. Acad. Sci. Paris Sér. I Math. – year: 1985 ident: 10.1016/j.cpc.2008.02.003_bib001 – ident: 10.1016/j.cpc.2008.02.003_bib002 |
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| SubjectTerms | CADNA CESTAC method Computer Science Discrete Stochastic Arithmetic Floating-point arithmetic Numerical validation Round-off errors |
| Title | CADNA: a library for estimating round-off error propagation |
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