Thu, 4 Jun 2009 06:21:41 +0000 (UTC)

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what is the dependence vector joefoxreal@gmail.com (Eric Fisher) (2009-06-04) |

Re: what is the dependence vector xueyunzhi@gmail.com (yunzhi) (2009-06-05) |

Re: what is the dependence vector joefoxreal@gmail.com (Eric Fisher) (2009-06-08) |

From: | Eric Fisher <joefoxreal@gmail.com> |

Newsgroups: | comp.compilers |

Date: | Thu, 4 Jun 2009 06:21:41 +0000 (UTC) |

Organization: | A poorly-installed InterNetNews site |

Posted-Date: | 04 Jun 2009 15:47:35 EDT |

Hi

I'm reading the paper "A Data Locality Optimizing Algorithm", by

Michael E. Wolf and Monica S. Lam. In section 2, it describes the

dependence vector as,

*>>"*

a generalization of distance and direction vectors.

A dependence vector in an n-nested loop is denoted by a vector

d=(d1,d2,...,dn)

each component di is a possibly infinite range of integers, represented

by [di_min, di_max], where

di_min b Z b* {-b}, di_max b Z b* {b} and di_min b $ di_max

<<"

Here, a n-nested loop corresponds to a finite convex polyhedron of

iteration space Zn (n power).

a) What does di mean? Does it mean the dependence of loop i? I think the

dependence should refer to two statements.

*>>"*

A single dependence vector therefore represents a set of distance

vectors, called its distance vector set:

N5(d)={(e1,...,en) | ei b Z and di_min b $ ei b $ di_max}

"

<<"

b) Here, what does 'N5(d)' mean? What does 'N5' mean?

*>>"*

The dependence vector d is also a distance vector if each of its

components is a degenerate range consisting of a singleton value, that

is, di_min=di_max.

<<"

c) What does this sentence above mean?

Too more questions about dependence representations.

Cheers

Eric Fisher

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