Remarks on Algorithms Implemented in Some C++ Libraries for Floating-Point Conversions and Interval Arithmetic

<p>Rounded interval arithmetic is very easy to implement by means of directed rounding arithmetic operators. Such operators are available in the IEEE floating point arithmetic of the transputer. When a few small pieces of assembly language code are used to access the directed rounding operators, the four basic rounded interval arithmetic operators can easily be expressed in the programming language Occam.</p><p>The performance of this implementation is assessed and it is shown that the time consuming part of the calculation are not the directed rounding floating point operations as one might have expected. Most of the time is spent with transport of operands to and from the on-chip floating point unit and the procedure call/parameter passing overhead. Based on this experience the implementation is improved. This implementation runs with 0.15 MIOPS (Million Interval Operations Per Second) or 0.30 MFLOPS on an example interval calculation proposed by Moore. Furthermore, it is demonstrated that an advanced interval language compiler may provide a performance of 0.30 MIOPS or 0.59 MFLOPS on this example calculation.</p>

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Design of floating point units for interval arithmetic

2009 Ph.D. Research in Microelectronics and Electronics ◽

10.1109/rme.2009.5201307 ◽

2009 ◽

Cited By ~ 1

Author(s):

Alexandru Amaricai ◽

Mircea Vladutiu ◽

Oana Boncalo

Keyword(s):

Interval Arithmetic ◽

Floating Point

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The Use of Floating-Point and Interval Arithmetic in the Computation of Error Bounds

IEEE Transactions on Computers ◽

10.1109/tc.1983.1676245 ◽

1983 ◽

Vol C-32 (4) ◽

pp. 411-417

Author(s):

Lozier

Keyword(s):

Error Bounds ◽

Interval Arithmetic ◽

Floating Point

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Interval Versions of Central-Difference Method for Solving the Poisson Equation in Proper and Directed Interval Arithmetic

Foundations of Computing and Decision Sciences ◽

10.2478/fcds-2013-0009 ◽

2013 ◽

Vol 38 (3) ◽

pp. 193-206 ◽

Cited By ~ 5

Author(s):

Tomasz Hoffmann ◽

Andrzej Marciniak ◽

Barbara Szyszka

Keyword(s):

Poisson Equation ◽

Interval Arithmetic ◽

Difference Method ◽

Floating Point ◽

Rounding Errors ◽

Central Difference ◽

Interval Method ◽

The Poisson Equation ◽

Central Difference Method ◽

The One

Abstract To study the Poisson equation, the central-difference method is often used. This method has the local truncation error of order O(h2 +k2), where h and k are mesh constants. Using this method in conventional floating-point arithmetic, we get solutions including the method, representation and rounding errors. Therefore, we propose interval versions of the central-difference method in proper and directed interval arithmetic. Applying such methods in floating-point interval arithmetic allows one to obtain solutions including all possible numerical errors. We present numerical examples from which it follows that the presented interval method in directed interval arithmetic is a little bit better than the one in proper interval arithmetic, i.e. the intervals of solutions are smaller. It appears that applying both proper and directed interval arithmetic the exact solutions belong to the interval solutions obtained.

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