Module: ppl/ppl Branch: floating_point Commit: 1e75fbc5ddcda7410ab9a64d7e213bbc2bb20eca URL: http://www.cs.unipr.it/git/gitweb.cgi?p=ppl/ppl.git;a=commit;h=1e75fbc5ddcda...
Author: Fabio <Fabio@C1P4.(none)> Date: Wed Feb 17 17:02:05 2010 +0100
Added "affine from relation" section into definitions.dox. Fixed a reference to "affine from relation".
---
doc/definitions.dox | 22 ++++++++++++++++++++++ src/Polyhedron.defs.hh | 2 +- 2 files changed, 23 insertions(+), 1 deletions(-)
diff --git a/doc/definitions.dox b/doc/definitions.dox index f5437ad..48fd25d 100644 --- a/doc/definitions.dox +++ b/doc/definitions.dox @@ -1463,6 +1463,28 @@ is defined as \Bigr). \f]
+\subsection affine_form_relation Affine Form Relations. +Let \f$\mathbb{F}_{\mathrm{f}}\f$ be the set of floating point numbers +representables in a certain +format \f$\mathrm{f}\f$ and let \f$\mathbb{I}_\mathrm{f}\f$ be the set of +real intervals with bounds in \f$\mathbb{F}_{\mathrm{f}}\f$. +We can define a <EM>floating-point interval linear form</EM> +\f$\langle\vect{\alpha}, \vect{x}\rangle + + \beta\f$ +as: + \f[\left<\vect{\alpha}, \vect{x}\right> + \beta = + \alpha_0x_0 + \ldots + + \alpha_{n-1}x_{n-1} + \beta,\f] + +where \f$\beta\f$, \f$\vect{\alpha}_k \in \mathbb{I}_{\mathrm{f}}\f$ +for each \f$k = 0, \ldots, n - 1\f$. + +Given a such linear form \f$\mathrm{lf}\f$ and a primed variable \f$x'_k\f$ the +<EM>affine form image</EM> operator computes the bounded affine image of a +polyhedron \f$\cP\f$ under \f$\mathrm{lb} \leq x'_k \leq \mathrm{ub}\f$, where +\f$\mathrm{lb}\f$ and \f$\mathrm{ub}\f$ are the upper and lower bound +of \f$\mathrm{lf}\f$ respectively. + \subsection Generalized_Affine_Relations Generalized Affine Relations. Similarly, the <EM>generalized affine relation</EM> \f$\phi = (\mathrm{lhs}' \relsym \mathrm{rhs})\f$, where diff --git a/src/Polyhedron.defs.hh b/src/Polyhedron.defs.hh index 09233d0..8981831 100644 --- a/src/Polyhedron.defs.hh +++ b/src/Polyhedron.defs.hh @@ -1222,7 +1222,7 @@ public: // FIXME: To be completed. /*! Assigns to \p *this the - \ref Single_Update_Affine_Form_Functions "affine form image" + \ref affine_form_relation "affine form image" of \p *this under the function mapping variable \p var into the affine expression(s) specified by \p lf.