16 May 1999 15:14:31 -0400

Related articles |
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Rounding with Div and Mod operators william.rayer@virgin.net (William Rayer) (1999-05-09) |

Re: Rounding with Div and Mod operators wclodius@aol.com (1999-05-16) |

Re: Rounding with Div and Mod operators ucapjab@ucl.ac.uk (Jonathan Barker) (1999-05-16) |

Re: Rounding with Div and Mod operators nr@labrador.cs.virginia.edu (Norman Ramsey) (1999-05-16) |

Re: Rounding with Div and Mod operators guerby@acm.org (Laurent Guerby) (1999-05-16) |

Re: Rounding with Div and Mod operators anton@mips.complang.tuwien.ac.at (1999-05-16) |

Re: Rounding with Div and Mod operators Scott.Daniels@Acm.Org (Scott.David.Daniels) (1999-05-16) |

Re: Rounding with Div and Mod operators cdg@nullstone.com (Christopher Glaeser) (1999-05-16) |

Re: Rounding with Div and Mod operators johan.persson@mbox319.swipnet.se (Johan Persson) (1999-05-16) |

Re: Rounding with Div and Mod operators genew@shuswap.net (1999-05-20) |

Re: Rounding with Div and Mod operators sofkam@rpi.edu (1999-05-20) |

Re: Rounding with Div and Mod operators drh@microsoft.com (Dave Hanson) (1999-05-20) |

[8 later articles] |

From: | anton@mips.complang.tuwien.ac.at (Anton Ertl) |

Newsgroups: | comp.compilers |

Date: | 16 May 1999 15:14:31 -0400 |

Organization: | Institut fuer Computersprachen, Technische Universitaet Wien |

References: | 99-05-039 |

Keywords: | arithmetic, design |

"William Rayer" <william.rayer@virgin.net> writes:

*> n = (n div d) * d + (n mod d)*

*>*

*> What is interesting about this rule is there seem to be two ways of*

*> rounding that satisfy it when n or d are negative - either we round*

*> integers to the next lowest value or we round towards zero.*

The first is called floored division, the second symmetric division.

*> My question is: which rounding system is preferred and does it matter?*

It does matter in some applications. Which one is preferred depends

on the application, but in most cases that I have come across floored

division is preferred.

Therefore several languages have come up with operations for both

options: Ada has mod and rem (I don't know how it defines /), Forth

has fm/mod (floored) and sm/rem (symmetric).

And here's a little gem I have from Andrew Haley for doing floored

division of a double-precision integer by a single-precision integer

with single-precision results in terms of unsigned division; the

signed number representation is 2s complement:

denomsign=denom;

if (denom < 0) {

denom = -denom;

num = -num;

*}*

if (num < 0)

num.hi += denom; /* single-precision add to the most significant part of

the numerator. */

quot = num u/ denom;

rem = num u% denom;

if (denomsign<0)

rem = -rem;

- anton

--

M. Anton Ertl Some things have to be seen to be believed

anton@mips.complang.tuwien.ac.at Most things have to be believed to be seen

http://www.complang.tuwien.ac.at/anton/home.html

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