Floating_Point_Expression_templates.hh

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/* Floating_Point_Expression class implementation:
   non-inline template functions.
   Copyright (C) 2001-2010 Roberto Bagnara <bagnara@cs.unipr.it>
   Copyright (C) 2010-2016 BUGSENG srl (http://bugseng.com)

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://bugseng.com/products/ppl/ . */

#ifndef PPL_Floating_Point_Expression_templates_hh
#define PPL_Floating_Point_Expression_templates_hh 1

#include "Linear_Form_defs.hh"
#include <cmath>

namespace Parma_Polyhedra_Library {

template<typename FP_Interval_Type, typename FP_Format>
void
Floating_Point_Expression<FP_Interval_Type, FP_Format>
::relative_error(const FP_Linear_Form& lf, FP_Linear_Form& result) {

  FP_Interval_Type error_propagator;
  boundary_type lb = -pow(FP_Format::BASE,
  -static_cast<typename Floating_Point_Expression<FP_Interval_Type, FP_Format>
  ::boundary_type>(FP_Format::MANTISSA_BITS));
  error_propagator.build(i_constraint(GREATER_OR_EQUAL, lb),
                         i_constraint(LESS_OR_EQUAL, -lb));

  // Handle the inhomogeneous term.
  const FP_Interval_Type* current_term = &lf.inhomogeneous_term();
  assert(current_term->is_bounded());

  FP_Interval_Type
    current_multiplier(std::max(std::abs(current_term->lower()),
                                std::abs(current_term->upper())));
  FP_Linear_Form current_result_term(current_multiplier);
  current_result_term *= error_propagator;
  result = FP_Linear_Form(current_result_term);

  // Handle the other terms.
  dimension_type dimension = lf.space_dimension();
  for (dimension_type i = 0; i < dimension; ++i) {
    current_term = &lf.coefficient(Variable(i));
    assert(current_term->is_bounded());
    current_multiplier
      = FP_Interval_Type(std::max(std::abs(current_term->lower()),
                                  std::abs(current_term->upper())));
    current_result_term = FP_Linear_Form(Variable(i));
    current_result_term *= current_multiplier;
    current_result_term *= error_propagator;
    result += current_result_term;
  }

  return;
}

template<typename FP_Interval_Type, typename FP_Format>
void
Floating_Point_Expression<FP_Interval_Type, FP_Format>
::intervalize(const FP_Linear_Form& lf,
              const FP_Interval_Abstract_Store& store,
              FP_Interval_Type& result) {
  result = FP_Interval_Type(lf.inhomogeneous_term());
  dimension_type dimension = lf.space_dimension();
  assert(dimension <= store.space_dimension());
  for (dimension_type i = 0; i < dimension; ++i) {
    FP_Interval_Type current_addend = lf.coefficient(Variable(i));
    const FP_Interval_Type& curr_int = store.get_interval(Variable(i));
    current_addend *= curr_int;
    result += current_addend;
  }

  return;
}

template<typename FP_Interval_Type, typename FP_Format>
FP_Interval_Type
Floating_Point_Expression<FP_Interval_Type, FP_Format>
::compute_absolute_error() {
  typedef typename Floating_Point_Expression<FP_Interval_Type, FP_Format>
    ::boundary_type Boundary;
  boundary_type omega;
  omega = std::max(pow(static_cast<Boundary>(FP_Format::BASE),
                       static_cast<Boundary>(1 - FP_Format::EXPONENT_BIAS
                                             - FP_Format::MANTISSA_BITS)),
                   std::numeric_limits<Boundary>::denorm_min());
  FP_Interval_Type result;
  result.build(i_constraint(GREATER_OR_EQUAL, -omega),
               i_constraint(LESS_OR_EQUAL, omega));
  return result;
}

} // namespace Parma_Polyhedra_Library

#endif // !defined(PPL_Floating_Point_Expression_templates_hh)