/* Test Box::bounded_affine_preimage().
   Copyright (C) 2001-2009 Roberto Bagnara <bagnara@cs.unipr.it>

This file is part of the Parma Polyhedra Library (PPL).

The PPL 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.

The PPL 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.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02111-1307, USA.

For the most up-to-date information see the Parma Polyhedra Library
site: http://www.cs.unipr.it/ppl/ . */

#include "ppl_test.hh"

namespace {

// Affine image variable is neither expression, denominator 1.
bool
test01() {
  Variable x(0);
  Variable y(1);

  TBox box(3);
  box.add_constraint(x <= 2);
  box.add_constraint(y <= 2);

  print_constraints(box, "*** box ***");

  C_Polyhedron ph(box);

  box.bounded_affine_preimage(x, y, y+1);
  ph.bounded_affine_preimage(x, y, y+1);

  bool ok = check_result(box, Rational_Box(ph));

  print_constraints(box, "*** box.bounded_affine_preimage(x, y, y+1) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph.bounded_affine_preimage("
                    "x, y, y+1)) ***");

  return ok;
}

// Affine preimage variable is in the lb_expr but not the ub_expr;
// negative denominator.

// Illustrates where, when the corresponding polyhedron (still with
// non-relational constraints) is used to compute the
// transformation, we get more precise results.  This is due to the
// relational constraint obtained from comparing the lhs expression
// with the rhs expression.
bool
test02() {
  Variable A(0);
  Variable B(1);
  Variable C(2);
  Variable D(3);
  Variable E(4);

  TBox box(5);
  box.add_constraint(B <= 0);
  box.add_constraint(B >= -2);
  box.add_constraint(C <= 1);

  print_constraints(box, "*** box ***");

  C_Polyhedron ph(box);

  box.bounded_affine_preimage(B, 3*E - 5*D + A - 3*B, 4*A -2*C + 3, -3);
  ph.bounded_affine_preimage(B, 3*E - 5*D + A - 3*B, 4*A -2*C + 3, -3);

  Rational_Box known_result(5);
  known_result.add_constraint(C <= 1);

  bool ok = check_result(box, known_result);

  print_constraints(box, "*** box.bounded_affine_preimage(B, "
                    "3*E - 5*D + A - 3*B, 4*A - 2*C + 3, -3) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph.bounded_affine_preimage(B, "
                    "3*E - 5*D + A - 3*B, 4*A - 2*C + 3, -3)) ***");

  return ok;
}

// Affine preimage variable is in lb_expr but not ub_expr, negative
// denominator.
bool
test03() {
  Variable A(0);
  Variable B(1);
  Variable C(2);
  Variable D(3);
  Variable E(4);

  TBox box(5);
  box.add_constraint(A <= 1);
  box.add_constraint(B <= 1);
  box.add_constraint(C == 1);

  print_constraints(box, "*** box ***");

  C_Polyhedron ph(box);

  box.bounded_affine_preimage(C, 3*D - E, 2*C + 1, -5);
  ph.bounded_affine_preimage(C, 3*D - E, 2*C + 1, -5);

  bool ok = check_result(box, Rational_Box(ph));

  print_constraints(box, "*** box.bounded_affine_preimage(C, "
                    "3*D - E, 2*C + 1, -5) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph).bounded_affine_preimage(C, "
                    "3*D - E, 2*C + 1, -5) ***");

  return ok;
}

// Affine preimage variable is in ub_expr but not lb_expr, positive
// denominator and negative coefficient for the transformed variable.
bool
test04() {
  Variable A(0);
  Variable B(1);
  Variable C(2);
  Variable D(3);
  Variable E(4);

  TBox box(5);
  box.add_constraint(A <= 0);
  box.add_constraint(B <= 15);

  print_constraints(box, "*** box ***");

  C_Polyhedron ph(box);

  box.bounded_affine_preimage(B, -B - 2, 7*D - E + 5, 3);
  ph.bounded_affine_preimage(B, -B - 2, 7*D - E + 5, 3);

  bool ok = check_result(box, Rational_Box(ph));

  print_constraints(box, "*** box.bounded_affine_preimage(B, "
                    "-B - 2, 7*D - E + 5, 3) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph).bounded_affine_preimage(B, "
                    "-B - 2, 7*D - E + 5, 3) ***");

  return ok;
}

// Affine preimage variable is in ub_expr but not lb_expr, negative
// denominator and negative coefficient for the transformed variable.
bool
test05() {
  Variable A(0);

  TBox box(1);
  box.add_constraint(A <= 4);
  box.add_constraint(A >= -6);

  print_constraints(box, "*** box ***");

  C_Polyhedron ph(box);

  box.bounded_affine_preimage(A, A - 3, A, -1);
  ph.bounded_affine_preimage(A, A - 3, A, -1);

  bool ok = check_result(box, Rational_Box(ph));

  print_constraints(box, "*** box.bounded_affine_preimage(A, "
                    "A - 3, A, -1) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph).bounded_affine_preimage(A, "
                    "A - 3, A, -1) ***");

  return ok;
}

// Affine preimage variable is in both expressions, the ub_expr and
// lb_expr are bounded by the box, and negative coefficient for the
// transformed variable.
bool
test06() {
  Variable x(0);
  Variable y(1);

  TBox box(2);
  box.add_constraint(x <= 1);
  box.add_constraint(x >= 0);
  box.add_constraint(y <= 2);
  box.add_constraint(y >= -1);

  print_constraints(box, "*** box ***");

  C_Polyhedron ph(box);

  box.bounded_affine_preimage(x, -2*x + 1, -2*x + 2);
  ph.bounded_affine_preimage(x, -2*x + 1, -2*x + 2);

  bool ok = check_result(box, Rational_Box(ph));

  print_constraints(box,
                    "*** box.bounded_affine_preimage("
                    "x, -2*x+1, -2*x+2) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph).bounded_affine_preimage("
                    "x, -2*x+1, -2*x+2) ***");

  return ok;
}

// Affine preimage variable is in both expressions, the ub_expr and
// lb_expr are bounded by the box, negative denominator.
bool
test07() {
  Variable x(0);
  Variable y(1);

  TBox box(2);
  box.add_constraint(x <= 1);
  box.add_constraint(x >= 0);
  box.add_constraint(y <= 2);
  box.add_constraint(y >= -1);

  print_constraints(box, "*** box ***");
  C_Polyhedron ph(box);
  box.bounded_affine_preimage(x, x + y, x + y, -1);
  ph.bounded_affine_preimage(x, x + y, x + y, -1);

  bool ok = check_result(box, Rational_Box(ph));

  print_constraints(box,
                    "*** box.bounded_affine_preimage("
                    "x, -2*x+y+1, -2*x+y+1, -1) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph).bounded_affine_preimage("
                    "x, -2*x+y+1, -2*x+y+1, -1) ***");

  return ok;
}

// Affine preimage variable is in both expressions, the ub_expr and
// lb_expr are bounded by the box, lower bound is open.
bool
test08() {
  Variable x(0);
  Variable y(1);

  TBox box(2);
  box.add_constraint(x <= 1);
  box.add_constraint(x > 0);
  box.add_constraint(y <= 3);
  box.add_constraint(y >= -8);

  print_constraints(box, "*** box ***");
  NNC_Polyhedron ph(box);
  box.bounded_affine_preimage(x, -2*x + y, -2*x + 2*y + 1);
  ph.bounded_affine_preimage(x, -2*x + y, -2*x + 2*y + 1);

  bool ok = check_result(box, Rational_Box(ph));

  print_constraints(box,
                    "*** box.bounded_affine_preimage("
                    "x, -2*x+y, -2*x+2*y+1) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph).bounded_affine_preimage("
                    "x, -2*x+y, -2*x+2*y+1) ***");

  return ok;
}

// Affine preimage variable is in both expressions, the ub_expr has a
// maximum value but the lb_expr has no minimum, negative denominator.
bool
test09() {
  Variable x(0);
  Variable y(1);

  TBox box(3);
  box.add_constraint(10*x <= 2);
  box.add_constraint(y <= 2);

  print_constraints(box, "*** box ***");
  C_Polyhedron ph(box);
  box.bounded_affine_preimage(x, x + 5, x + 4, -1);
  ph.bounded_affine_preimage(x, x + 5, x + 4, -1);

  bool ok = check_result(box, Rational_Box(ph),
                         "2.84e-07", "2.84e-07", "2.84e-07");

  print_constraints(box,
                    "*** box.bounded_affine_preimage("
                    "x, x + 5, x + 4, -1) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph).bounded_affine_preimage("
                    "x, x + 5, x + 4, -1) ***");

  return ok;
}

// Affine preimage variable is in both expressions, the ub_expr has
// a maximum value (which is open) but the lb_expr has no minimum
// Negative coefficient for the transformed variable and negative
// denominator.
bool
test10() {
  Variable x(0);
  Variable y(1);

  TBox box(3);
  box.add_constraint(x < 2);
  box.add_constraint(x > 0);
  box.add_constraint(y <= 2);

  print_constraints(box, "*** box ***");
  NNC_Polyhedron ph(box);
  box.bounded_affine_preimage(x, -x + 5, -x + 4, -1);
  ph.bounded_affine_preimage(x, -x + 5, -x + 4, -1);

  bool ok = check_result(box, Rational_Box(ph));

  print_constraints(box,
                    "*** box.bounded_affine_preimage("
                    "x, -x + 5, x + 4, -1) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph).bounded_affine_preimage("
                    "x, -x + 5, x + 4, -1) ***");
  return ok;
}

// Affine preimage variable is in both expressions, the ub_expr has a
// maximum value but the lb_expr has no minimum. Box is closed
// and the affine preimage has a denominator > 1.
bool
test11() {
  Variable x(0);
  Variable y(1);

  TBox box(3);
  box.add_constraint(x <= 2);
  box.add_constraint(y <= 2);

  print_constraints(box, "*** box ***");
  C_Polyhedron ph(box);
  box.bounded_affine_preimage(y, 2*x, 2*x, 2);
  ph.bounded_affine_preimage(y, 2*x, 2*x, 2);

  bool ok = check_result(box, Rational_Box(ph));

  print_constraints(box,
                    "*** box.bounded_affine_preimage("
                    "y, 2*x, 2*x, 2) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph).bounded_affine_preimage("
                    "y, 2*x, 2*x, 2) ***");

  return ok;
}

// Affine preimage variable is in both expressions, the ub_expr has a
// maximum value but the lb_expr has no minimum. Box is not closed
// and the affine preimage has a denominator > 1.
bool
test12() {
  Variable x(0);
  Variable y(1);

  TBox box(3);
  box.add_constraint(x < 2);
  box.add_constraint(y <= 2);

  print_constraints(box, "*** box ***");
  NNC_Polyhedron ph(box);
  box.bounded_affine_preimage(x, 2*x - 2, 5*x + 2, 2);
  ph.bounded_affine_preimage(x, 2*x - 2, 5*x + 2, 2);

  bool ok = check_result(box, Rational_Box(ph),
                         "3.98e-08", "3.98e-08", "3.98e-08");

  print_constraints(box,
                    "*** box .bounded_affine_preimage("
                    "x, 2*x-2, 5*x+2, 2) ***");
  print_constraints(Rational_Box(ph),
                    "*** Rational_Box(ph).bounded_affine_preimage("
                    "x, 2*x-2, 5*x+2, 2) ***");

  return ok;
}

bool
test13() {
  Variable x(0);
  Variable y(1);
  Variable z(2);

  TBox box(2);
  box.add_constraint(x >= 1);

  try {
    // This is an incorrect use of the method
    // Box::bounded_affine_preimage(v, lb_expr, ub_expr, d): it is
    // illegal to apply it to an expression whose space dimension is
    // greater than the box's space dimension.
    box.bounded_affine_preimage(y, x, z);
  }
  catch (std::invalid_argument& e) {
    nout << "std::invalid_argument: " << endl;
    return true;
  }
  catch (...) {
  }
  return false;
}

bool
test14() {
  Variable x(0);
  Variable y(1);
  Variable z(2);

  TBox box(2);
  box.add_constraint(x >= 1);

  try {
    // This is an incorrect use of the method
    // Box::bounded_affine_preimage(v, lb_expr, ub_expr, d): it is illegal
    // to apply it to an expression whose space dimension is
    // greater than the box's space dimension.
    box.bounded_affine_preimage(y, z, x);
  }
  catch (std::invalid_argument& e) {
    nout << "std::invalid_argument: " << endl;
    return true;
  }
  catch (...) {
  }
  return false;
}

bool
test15() {
  Variable x(0);
  Variable y(1);

  TBox box(2);
  box.add_constraint(x >= 1);

  try {
    // This is an incorrect use of the method
    // Box::bounded_affine_preimage(v, lb_expr, ub_expr, d): it is illegal
    // to apply it to a expression with the denominator
    // equal to zero.
    Coefficient d = 0;
    box.bounded_affine_preimage(x, Linear_Expression(0), x + 1, d);
  }
  catch (std::invalid_argument& e) {
    nout << "std::invalid_argument: " << endl;
    return true;
  }
  catch (...) {
  }
  return false;
}

bool
test16() {
  Variable x(0);
  Variable y(1);

  TBox box(1);
  box.add_constraint(x >= 1);

  try {
    // This is an invalid used of the method
    // Box::bounded_affine_preimage(v, lb_expr, ub_epxr, d): it is illegal to
    // apply the method to a variable that is not in the space of
    // the polyhedron.
    box.bounded_affine_preimage(y, x + 1, Linear_Expression(8));
  }
  catch (std::invalid_argument& e) {
    nout << "std::invalid_argument: " << endl;
    return true;
  }
  catch (...) {
  }
  return false;
}

} // namespace

BEGIN_MAIN
  DO_TEST(test01);
  DO_TEST(test02);
  DO_TEST(test03);
  DO_TEST(test04);
  DO_TEST(test05);
  DO_TEST(test06);
  DO_TEST(test07);
  DO_TEST(test08);
  DO_TEST_MAY_OVERFLOW_IF_INEXACT(test09, TBox);
  DO_TEST(test10);
  DO_TEST(test11);
  DO_TEST(test12);
  DO_TEST(test13);
  DO_TEST(test14);
  DO_TEST(test15);
  DO_TEST(test16);
END_MAIN