# [PPL-devel] [GIT] ppl/ppl(floating_point): Added "affine from relation" section into definitions.dox.

Fabio (none) Fabio at C1P4
Wed Feb 17 17:03:50 CET 2010

Module: ppl/ppl
Branch: floating_point
Commit: 1e75fbc5ddcda7410ab9a64d7e213bbc2bb20eca
URL:    http://www.cs.unipr.it/git/gitweb.cgi?p=ppl/ppl.git;a=commit;h=1e75fbc5ddcda7410ab9a64d7e213bbc2bb20eca

Author: Fabio <Fabio at 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
--- 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.