### Abstract

This paper is concerned with floating-point filters for a two dimensional orientation problem which is a basic problem in the field of computational geometry. If this problem is only approximately solved by floating-point arithmetic, then an incorrect result may be obtained due to accumulation of rounding errors. A floating-point filter can quickly guarantee the correctness of the computed result if the problem is well-conditioned. In this paper, a simple semi-static floating-point filter which handles floating-point exceptions such as overflow and underflow by only one branch is developed. In addition, an improved fully-static filter is developed.

Original language | English |
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Journal | BIT Numerical Mathematics |

DOIs | |

Publication status | Accepted/In press - 2015 Jul 25 |

### Fingerprint

### Keywords

- Computational geometry
- Floating-point arithmetic
- Floating-point filter

### ASJC Scopus subject areas

- Computer Networks and Communications
- Software
- Applied Mathematics
- Computational Mathematics

### Cite this

*BIT Numerical Mathematics*. https://doi.org/10.1007/s10543-015-0574-9

**Simple floating-point filters for the two-dimensional orientation problem.** / Ozaki, Katsuhisa; Bünger, Florian; Ogita, Takeshi; Oishi, Shin’ichi; Rump, Siegfried M.

Research output: Contribution to journal › Article

*BIT Numerical Mathematics*. https://doi.org/10.1007/s10543-015-0574-9

}

TY - JOUR

T1 - Simple floating-point filters for the two-dimensional orientation problem

AU - Ozaki, Katsuhisa

AU - Bünger, Florian

AU - Ogita, Takeshi

AU - Oishi, Shin’ichi

AU - Rump, Siegfried M.

PY - 2015/7/25

Y1 - 2015/7/25

N2 - This paper is concerned with floating-point filters for a two dimensional orientation problem which is a basic problem in the field of computational geometry. If this problem is only approximately solved by floating-point arithmetic, then an incorrect result may be obtained due to accumulation of rounding errors. A floating-point filter can quickly guarantee the correctness of the computed result if the problem is well-conditioned. In this paper, a simple semi-static floating-point filter which handles floating-point exceptions such as overflow and underflow by only one branch is developed. In addition, an improved fully-static filter is developed.

AB - This paper is concerned with floating-point filters for a two dimensional orientation problem which is a basic problem in the field of computational geometry. If this problem is only approximately solved by floating-point arithmetic, then an incorrect result may be obtained due to accumulation of rounding errors. A floating-point filter can quickly guarantee the correctness of the computed result if the problem is well-conditioned. In this paper, a simple semi-static floating-point filter which handles floating-point exceptions such as overflow and underflow by only one branch is developed. In addition, an improved fully-static filter is developed.

KW - Computational geometry

KW - Floating-point arithmetic

KW - Floating-point filter

UR - http://www.scopus.com/inward/record.url?scp=84937882728&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937882728&partnerID=8YFLogxK

U2 - 10.1007/s10543-015-0574-9

DO - 10.1007/s10543-015-0574-9

M3 - Article

AN - SCOPUS:84937882728

JO - BIT

JF - BIT

SN - 0006-3835

ER -