Module: ppl/ppl Branch: master Commit: a36b05302ae483bff5778a75ec5d1abe632db241 URL: http://www.cs.unipr.it/git/gitweb.cgi?p=ppl/ppl.git;a=commit;h=a36b05302ae48...
Author: Patricia Hill p.m.hill@leeds.ac.uk Date: Mon May 11 11:56:02 2009 +0100
Added a _draft_ description of the wrap operator for grids.
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doc/definitions.dox | 41 +++++++++++++++++++++++++++++++++++++++++ 1 files changed, 41 insertions(+), 0 deletions(-)
diff --git a/doc/definitions.dox b/doc/definitions.dox index 75d30ce..a1cc335 100644 --- a/doc/definitions.dox +++ b/doc/definitions.dox @@ -2313,6 +2313,47 @@ A grid \f$\cL\f$ <EM>subsumes</EM> a (polyhedron) ray or line \f$g\f$ if adding the corresponding grid line to any grid generator system representing \f$\cL\f$ does not change \f$\cL\f$.
+\subsection Wrapping_Operator Wrapping Operator + +The operator <CODE>wrap_assign</CODE> provided by the library, allows +for the wrapping of a subset of the set of space dimensions so to fit +the given bounded integer type and have the specified overflow behavior. + +Suppose \f$\cL \in \Gset_n\f$ is a grid and \f$J\f$ a subset of the +set of space dimensions \f${0, \ldots, n-1}\f$. +Suppose also that the width of the bounded integer type is \f$w\f$ so that +the range of values can be \f$0 - 2^w-1\f$ if the type is unsigned +and \f$-2^{w-1} - 2^{w-1} - 1\f$ otherwise. +Consider a space dimension \f$j \in J\f$. + +If the value in \f$\cL\f$ for the dimension \f$j\f$ is bounded and +hence a constant, no wrapping can take place; in this case the +grid is unchanged. + +Otherwise the value for the dimension \f$j\f$ will be unbounded and +the result of the operation will depend on which of +three possible overflow behaviors has been specified. + +- Overflow impossible: in this case, it is known that no wrapping can + occur; if the grid has exactly one possible value for the given + bounded integer type, then the dimension \f$j\f$ is set equal to + that value, otherwise, the grid is unchanged. + +- Overflow undefined: in this case, the wrapped value can be any + integer within the range of the bounded integer type, so that the + parameter \f$(0, \ldots, 0, v_j, 0, \dots, 0)\f$, where + \f$v_j = 1\f$ is added to the generator system. + +- Overflow wraps: in this case, the \f$j\f$ dimension can be wrapped to + a value modulo \f$2^w\f$, so that the parameter + \f$(0, \ldots, 0, v_j, 0, \dots, 0)\f$, where \f$v_j = 2^w\f$ + is added to the generator system. + +Note that the <CODE>wrap_assign</CODE> is intended for dimensions that +can take integral values; if this not the case for any of the +dimensions in \f$J\f$ for the grid \f$\cL\f$, the behavior is +undefined. + \subsection Grid_Widening Widening Operators
The library provides <EM>grid widening</EM> operators for the domain of grids.