X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/197818714e75c2353ed8b7c9fec653f1212f13ae..d585b06ccf67b2837519f4b48c6800dcdb924d9d:/examples/nsad2010.py

diff --git a/examples/nsad2010.py b/examples/nsad2010.py
index 91a85b4..3de2ebd 100755
--- a/examples/nsad2010.py
+++ b/examples/nsad2010.py
@@ -1,23 +1,14 @@
 #!/usr/bin/env python3
+
+# This is an implementation of the algorithm described in
 #
-# Copyright 2014 MINES ParisTech
-#
-# This file is part of LinPy.
-#
-# LinPy is free software: you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation, either version 3 of the License, or
-# (at your option) any later version.
-#
-# LinPy is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-# GNU General Public License for more details.
+# [ACI10] C. Ancourt, F. Coelho and F. Irigoin, A modular static analysis
+# approach to affine loop invariants detection (2010), pp. 3 - 16, NSAD 2010.
 #
-# You should have received a copy of the GNU General Public License
-# along with LinPy.  If not, see <http://www.gnu.org/licenses/>.
+# to compute the transitive closure of an affine transformer. A refined version
+# of this algorithm is implemented in PIPS.
 
-from linpy import *
+from linpy import Dummy, Eq, Ge, Polyhedron, symbols
 
 
 class Transformer:
@@ -37,7 +28,8 @@ class Transformer:
         delta_symbols = [symbol.asdummy() for symbol in self.range_symbols]
         k = Dummy('k')
         polyhedron = self.polyhedron
-        for x, xprime, dx in zip(self.range_symbols, self.domain_symbols, delta_symbols):
+        for x, xprime, dx in zip(
+                self.range_symbols, self.domain_symbols, delta_symbols):
             polyhedron &= Eq(dx, xprime - x)
         polyhedron = polyhedron.project(self.symbols)
         equalities, inequalities = [], []
@@ -49,15 +41,16 @@ class Transformer:
             inequalities.append(inequality)
         polyhedron = Polyhedron(equalities, inequalities) & Ge(k, 0)
         polyhedron = polyhedron.project([k])
-        for x, xprime, dx in zip(self.range_symbols, self.domain_symbols, delta_symbols):
+        for x, xprime, dx in zip(
+                self.range_symbols, self.domain_symbols, delta_symbols):
             polyhedron &= Eq(dx, xprime - x)
         polyhedron = polyhedron.project(delta_symbols)
         return Transformer(polyhedron, self.range_symbols, self.domain_symbols)
 
 
 if __name__ == '__main__':
-    i, iprime, j, jprime = symbols("i i' j j'")
-    transformer = Transformer(Eq(iprime, i + 2) & Eq(jprime, j + 1),
-        [i, j], [iprime, jprime])
+    i0, i, j0, j = symbols('i0 i j0 j')
+    transformer = Transformer(Eq(i, i0 + 2) & Eq(j, j0 + 1),
+                              [i0, j0], [i, j])
     print('T  =', transformer.polyhedron)
     print('T* =', transformer.star().polyhedron)