#!/usr/bin/env python3
# This is an implementation of the algorithm described in
#
# [ACI10] C. Ancourt, F. Coelho and F. Irigoin, A modular static analysis
# approach to affine loop invariants detection (2010), pp. 3 - 16, NSAD 2010.
#
# to compute the transitive closure of an affine transformer. A refined version
# of this algorithm is implemented in PIPS.
from linpy import *
class Transformer:
def __new__(cls, polyhedron, range_symbols, domain_symbols):
self = object().__new__(cls)
self.polyhedron = polyhedron
self.range_symbols = range_symbols
self.domain_symbols = domain_symbols
return self
@property
def symbols(self):
return self.range_symbols + self.domain_symbols
def star(self):
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):
polyhedron &= Eq(dx, xprime - x)
polyhedron = polyhedron.project(self.symbols)
equalities, inequalities = [], []
for equality in polyhedron.equalities:
equality += (k-1) * equality.constant
equalities.append(equality)
for inequality in polyhedron.inequalities:
inequality += (k-1) * inequality.constant
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):
polyhedron &= Eq(dx, xprime - x)
polyhedron = polyhedron.project(delta_symbols)
return Transformer(polyhedron, self.range_symbols, self.domain_symbols)
if __name__ == '__main__':
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)