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Interval package: Difference between revisions
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Added library dependency for GNU MPFR
(→What to expect: added notes on speed and accuracy) |
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The [https://sourceforge.net/p/octave/interval/ interval package] provides data types and fundamental operations for real valued interval arithmetic based on the common floating-point format “binary64” a. k. a. double-precision. It aims to be standard compliant with the (upcoming) [http://standards.ieee.org/develop/project/1788.html IEEE 1788] and therefore implements the ''set-based'' interval arithmetic flavor. '''Interval arithmetic''' produces mathematically proven numerical results. | The [https://sourceforge.net/p/octave/interval/ interval package] provides data types and fundamental operations for real valued interval arithmetic based on the common floating-point format “binary64” a. k. a. double-precision. It aims to be standard compliant with the (upcoming) [http://standards.ieee.org/develop/project/1788.html IEEE 1788] and therefore implements the ''set-based'' interval arithmetic flavor. '''Interval arithmetic''' produces mathematically proven numerical results. | ||
Warning: The package has not yet been released. If you want to experience the development version, you may (1) install the (currently deprecated) [http://octave.sourceforge.net/fenv/ fenv package], (2) download a [https://sourceforge.net/p/octave/interval/ci/default/tarball snapshot version of the interval package], (3) navigate to the <code>inst/</code> subfolder and run octave. | Warning: The package has not yet been released. If you want to experience the development version, you may (1) install the (currently deprecated) [http://octave.sourceforge.net/fenv/ fenv package], (2) download a [https://sourceforge.net/p/octave/interval/ci/default/tarball snapshot version of the interval package], (3) install the [http://www.mpfr.org/mpfr-current/#download development library of MPFR] for your system, (4) execute <code>make install</code> in the <code>src/</code> subfolder, (5) navigate to the <code>inst/</code> subfolder and run octave. | ||
== Motivation == | == Motivation == | ||
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== What to expect == | == What to expect == | ||
The interval arithmetic provided by this interval package is '''slow''' | The interval arithmetic provided by this interval package is '''slow''', but '''accurate'''. | ||
''Why is the interval package slow?'' | ''Why is the interval package slow?'' | ||
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Great algorithms and optimizations exist for matrix arithmetic in GNU octave. Good interval versions of these still have to be found and implemented. | Great algorithms and optimizations exist for matrix arithmetic in GNU octave. Good interval versions of these still have to be found and implemented. | ||
''Why is the interval package | ''Why is the interval package accurate?'' | ||
Some basic operations are provided with | Some basic operations are provided by the C library with directed rounding and correctly rounded result: plus, minus, division, multiplication and square root. These are used to build the most basic interval functions. | ||
All other GNU Octave arithmetic functions are not guaranteed to produce accurate results, because they are based on C99 floating-point routines [http://www.gnu.org/software/libc/manual/html_node/Errors-in-Math-Functions.html#Errors-in-Math-Functions]. Their results depend on hardware, system libraries and compilation options. The interval package handles these functions with the help of the [http://www.mpfr.org/ GNU MPFR library]. With MPFR it is possible to compute valid and tight enclosure of the correct results. | |||
== Quick start introduction == | == Quick start introduction == | ||