## Quad-Double Arithmetic: Algorithms, Implementation, and Application (2000)

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Citations: | 8 - 1 self |

### BibTeX

@MISC{Hida00quad-doublearithmetic:,

author = {Yozo Hida and Xiaoye S. Li and David H. Bailey},

title = {Quad-Double Arithmetic: Algorithms, Implementation, and Application},

year = {2000}

}

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### Abstract

A quad-double number is an unevaluated sum of four IEEE double precision numbers, capable of representing at least 212 bits of signi cand. Algorithms for various arithmetic operations (including the four basic operations and various algebraic and transcendental operations) are presented. A C++ implementation of these algorithms is also described, as well as an application of this quad-double library.

### Citations

2197 |
The art of computer programming
- Knuth
- 1973
(Show Context)
Citation Context ...e work. 2 Preliminaries In this section, we present some basic properties and algorithms of IEEE floating point arithmetic used in quad-double arithmetic. These results are based on Dekker [7], Knuth =-=[9]-=-, Priest [10], Shewchuk [11], and others. In fact, many of the algorithms and diagrams are directly taken from, or based on, Shewchuk's paper. All basic arithmetics are assumed to be performed in IEEE... |

1496 | The C++ Programming Language
- Stroustrup
- 1997
(Show Context)
Citation Context ...where the addition routine knows where to put the result directly. This problem is somewhat alleviated by inlining, but not completely eliminated. There are techniques to avoid these kinds of copying =-=[12]-=-, but they have their own overheads associated with them and is not practical for quad-double with only 32 bytes of data 1 . 9 Application: Vortex Roll-Up Simulation The quad-double library was succes... |

134 | Adaptive precision floating-point arithmetic and fast robust geometric predicates
- Shewchuk
- 1997
(Show Context)
Citation Context ...e numbers in a multiple-component format, where a number is expressed as unevaluated sums of ordinary floating-point words, each with its own significand and exponent. Examples of this format include =-=[7, 10, 11]-=-. The multiple-digit approach can represent a much larger range of numbers, whereas the multiple-component approach has the advantage in speed. We note that many applications would get full benefit fr... |

105 |
A Floating-point Technique for Extending the Available Precision
- Dekker
- 1971
(Show Context)
Citation Context ...e numbers in a multiple-component format, where a number is expressed as unevaluated sums of ordinary floating-point words, each with its own significand and exponent. Examples of this format include =-=[7, 10, 11]-=-. The multiple-digit approach can represent a much larger range of numbers, whereas the multiple-component approach has the advantage in speed. We note that many applications would get full benefit fr... |

66 | A Fortran-90 Based Multiprecision System
- Bailey
- 1995
(Show Context)
Citation Context ...re represented. Some libraries store numbers in a multiple-digit format, with a sequence of digits coupled with a single exponent, such as the symbolic computation package Mathematica, Bailey's MPFUN =-=[2]-=-, Brent's MP [4] and GNU MP [8]. An alternative approach is to store numbers in a multiple-component format, where a number is expressed as unevaluated sums of ordinary floating-point words, each with... |

26 | On Properties of Floating Point Arithmetics: Numerical Stability and the Cost of Accurate Computations
- Priest
- 1992
(Show Context)
Citation Context ...e numbers in a multiple-component format, where a number is expressed as unevaluated sums of ordinary floating-point words, each with its own significand and exponent. Examples of this format include =-=[7, 10, 11]-=-. The multiple-digit approach can represent a much larger range of numbers, whereas the multiple-component approach has the advantage in speed. We note that many applications would get full benefit fr... |

19 |
A Fortran Multiple Precision Arithmetic Package
- Brent
- 1978
(Show Context)
Citation Context ...Some libraries store numbers in a multiple-digit format, with a sequence of digits coupled with a single exponent, such as the symbolic computation package Mathematica, Bailey's MPFUN [2], Brent's MP =-=[4]-=- and GNU MP [8]. An alternative approach is to store numbers in a multiple-component format, where a number is expressed as unevaluated sums of ordinary floating-point words, each with its own signifi... |

7 | Multiple Precision, Multiple Processor Vortex Sheet Roll-Up Computation
- Bailey, Krasny, et al.
- 1993
(Show Context)
Citation Context ...em and is not practical for quad-double with only 32 bytes of data 1 . 9 Application: Vortex Roll-Up Simulation The quad-double library was successfully used in a parallel vortex roll-up simulation 2 =-=[3]-=-, which uses various transcendental functions as well as basic arithmetics. On a test on the NERSC IBM SP, using 256 Power3 processors, the quad-double version runs about four times as fast as the mul... |

6 | Adaptive precision arithmetic and fast robust geometric predicates - Shewchuk - 1997 |

5 |
A fortran-90 double-double library. Available at http://www.nersc.gov/ ~dhbailey/mpdist/mpdist.html
- Bailey
- 2001
(Show Context)
Citation Context ...adruple) the working precision, without the need for arbitrary precision. The algorithms for this kind of "fixed" precision can be made significantly faster than those for arbitrary precisio=-=n. Bailey [1] and Brigg-=-s [5] have developed algorithms and software for "double-double" precision, twice the double precision. They used the multiple-component format, where a doubledouble number is represented as... |

5 |
Doubledouble floating point arithmetic. http://www-epidem.plantsci.cam.ac.uk /âˆ¼kbriggs/doubledouble.html
- Briggs
- 1998
(Show Context)
Citation Context ...rking precision, without the need for arbitrary precision. The algorithms for this kind of "fixed" precision can be made significantly faster than those for arbitrary precision. Bailey [1] a=-=nd Briggs [5] have deve-=-loped algorithms and software for "double-double" precision, twice the double precision. They used the multiple-component format, where a doubledouble number is represented as an unevaluated... |

5 |
MPFUN++: A Multiple Precision Floating Point Computation Package in C
- Chatterjee, Harjono
- 1998
(Show Context)
Citation Context ... constants such as #, #/2, #/4, e, log 2 are provided as qd real:: pi, qd real:: pi2, qd real:: pi4, qd real:: e, and qd real:: log2. These were computed using an arbitrary precision package (MPFUN++ =-=[6]-=-), and therefore are accurate to the last bit. 7.2 Building To build the library, edit the files make.inc (for platform specific options) and make.config (for library build options) and then type make... |

3 | Doubledouble point arithmetic. http://www-epidem.plantsci.cam.ac.uk /kbriggs/doubledouble.html - Briggs - 1998 |

2 | MPFUN++: A multiple precision point computation package in C - Chatterjee - 1998 |