add.cpp

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/* Boost test/add.cpp
 * test with symbolic operations if the addition algorithm is correct
 *
 * Copyright 2002-2003 Guillaume Melquiond
 *
 * Distributed under the Boost Software License, Version 1.0.
 * (See accompanying file LICENSE_1_0.txt or
 * copy at http://www.boost.org/LICENSE_1_0.txt)
 */

#include <boost/numeric/interval/interval.hpp>
#include <boost/numeric/interval/arith.hpp>
#include <boost/numeric/interval/rounding.hpp>
#include <boost/numeric/interval/rounded_arith.hpp>
#include <boost/numeric/interval/utility.hpp>
#include <boost/numeric/interval/policies.hpp>
#include <boost/test/minimal.hpp>
#include "bugs.hpp"

typedef enum { EXPR_VAR, EXPR_NEG, EXPR_UP, EXPR_DOWN, EXPR_ADD, EXPR_SUB } e_type;

struct expr;
struct pexpr {
  expr *ptr;
  expr* operator->() { return ptr; }
  pexpr(expr *p = NULL): ptr(p) { }
};

struct expr {
  e_type type;
  int var;
  pexpr e;
  pexpr e1, e2;
};

pexpr var(int v) {
  pexpr e = new expr;
  e->type = EXPR_VAR;
  e->var = v;
  return e;
}

pexpr operator+(pexpr, pexpr);
pexpr operator-(pexpr, pexpr);
pexpr operator-(pexpr);

pexpr operator+(pexpr a, pexpr b) {
  if (a->type == EXPR_NEG) return b - a->e;
  if (b->type == EXPR_NEG) return a - b->e;
  if (a->type == EXPR_VAR && b->type == EXPR_VAR && a->var > b->var) return b + a;
  pexpr c = new expr;
  c->type = EXPR_ADD;
  c->e1 = a;
  c->e2 = b;
  return c;
}

pexpr operator-(pexpr a, pexpr b) {
  if (b->type == EXPR_NEG) return a + b->e;
  pexpr c = new expr;
  c->type = EXPR_SUB;
  c->e1 = a;
  c->e2 = b;
  return c;
}

pexpr down(pexpr a) {
  pexpr e = new expr;
  e->type = EXPR_DOWN;
  e->e = a;
  return e;
}

pexpr up(pexpr a) {
  pexpr e = new expr;
  e->type = EXPR_UP;
  e->e = a;
  return e;
}

pexpr operator-(pexpr a) {
  if (a->type == EXPR_NEG) return a->e;
  if (a->type == EXPR_UP) return down(-a->e);
  if (a->type == EXPR_DOWN) return up(-a->e);
  if (a->type == EXPR_SUB) return a->e2 - a->e1;
  if (a->type == EXPR_ADD) return -a->e1 - a->e2;
  pexpr e = new expr;
  e->type = EXPR_NEG;
  e->e = a;
  return e;
}

bool operator==(pexpr a, pexpr b) {
  if (a->type != b->type) return false;
  if (a->type == EXPR_VAR) return a->var == b->var;
  if (a->type == EXPR_DOWN || a->type == EXPR_UP || a->type == EXPR_NEG)
    return a->e == b->e;
  return a->e1 == b->e1 && a->e2 == b->e2;
}

bool operator<=(pexpr, pexpr) { return true; }

namespace boost {
namespace numeric {
namespace interval_lib {

template<>
struct rounding_control<pexpr> {
  typedef enum { RND_U, RND_M, RND_D } rounding_mode;
  static rounding_mode mode;
  rounding_control() { mode = RND_M; }
  void get_rounding_mode(rounding_mode& m) { m = mode; }
  void set_rounding_mode(rounding_mode m)  { mode = m; }
  void upward()   { mode = RND_U; }
  void downward() { mode = RND_D; }
  pexpr force_rounding(pexpr a) {
    switch (mode) {
    case RND_U: return up(a);
    case RND_D: return down(a);
    default: throw "Unset rounding mode";
    }
  }
};

rounding_control<pexpr>::rounding_mode rounding_control<pexpr>::mode = RND_M;

} // namespace interval_lib
} // namespace numeric
} // namespace boost

template<class I>
bool test_neg() {
  I a(var(0), var(1));
  return equal(-a, I(-var(1), -var(0)));
}

template<class I>
bool test_add() {
  I a(var(0), var(1)), b(var(2), var(3));
  return equal(a + b, I(down(var(0) + var(2)), up(var(1) + var(3))));
}

template<class I>
bool test_add1() {
  I a(var(0), var(1));
  return equal(a + var(2), I(down(var(0) + var(2)), up(var(1) + var(2))));
}

template<class I>
bool test_add2() {
  I a(var(0), var(1));
  return equal(var(2) + a, I(down(var(0) + var(2)), up(var(1) + var(2))));
}

template<class I>
bool test_sub() {
  I a(var(0), var(1)), b(var(2), var(3));
  return equal(a - b, I(down(var(0) - var(3)), up(var(1) - var(2))));
}

template<class I>
bool test_sub1() {
  I a(var(0), var(1));
  return equal(a - var(2), I(down(var(0) - var(2)), up(var(1) - var(2))));
}

template<class I>
bool test_sub2() {
  I a(var(0), var(1));
  return equal(var(2) - a, I(down(var(2) - var(1)), up(var(2) - var(0))));
}

template<class I>
bool test_addeq() {
  I a(var(0), var(1)), b(var(2), var(3));
  return equal(a += b, I(down(var(0) + var(2)), up(var(1) + var(3))));
}

template<class I>
bool test_addeq1() {
  I a(var(0), var(1));
  return equal(a += var(2), I(down(var(0) + var(2)), up(var(1) + var(2))));
}

template<class I>
bool test_subeq() {
  I a(var(0), var(1)), b(var(2), var(3));
  return equal(a -= b, I(down(var(0) - var(3)), up(var(1) - var(2))));
}

template<class I>
bool test_subeq1() {
  I a(var(0), var(1));
  return equal(a -= var(2), I(down(var(0) - var(2)), up(var(1) - var(2))));
}

struct my_checking
{
  static pexpr pos_inf() { throw; }
  static pexpr neg_inf() { throw; }
  static pexpr nan() { throw; }
  static bool is_nan(const pexpr&) { return false; }
  static pexpr empty_lower() { throw; }
  static pexpr empty_upper() { throw; }
  static bool is_empty(const pexpr&, const pexpr&) { return false; }
};

template<class Rounding>
struct my_interval {
private:
  typedef boost::numeric::interval_lib::save_state<Rounding> my_rounding;
  typedef boost::numeric::interval_lib::policies<my_rounding, my_checking> my_policies;
public:
  typedef boost::numeric::interval<pexpr, my_policies> type;
};

int test_main(int, char *[]) {
  typedef my_interval<boost::numeric::interval_lib::rounded_arith_std<pexpr> >::type I1;
  typedef my_interval<boost::numeric::interval_lib::rounded_arith_opp<pexpr> >::type I2;
  BOOST_CHECK((test_neg<I1>()));
  BOOST_CHECK((test_neg<I2>()));
  BOOST_CHECK((test_add<I1>()));
  BOOST_CHECK((test_add<I2>()));
  BOOST_CHECK((test_add1<I1>()));
  BOOST_CHECK((test_add1<I2>()));
  BOOST_CHECK((test_add2<I1>()));
  BOOST_CHECK((test_add2<I2>()));
  BOOST_CHECK((test_sub<I1>()));
  BOOST_CHECK((test_sub<I2>()));
  BOOST_CHECK((test_sub1<I1>()));
  BOOST_CHECK((test_sub1<I2>()));
  BOOST_CHECK((test_sub2<I1>()));
  BOOST_CHECK((test_sub2<I2>()));
  BOOST_CHECK((test_addeq<I1>()));
  BOOST_CHECK((test_addeq<I2>()));
  BOOST_CHECK((test_addeq1<I1>()));
  BOOST_CHECK((test_addeq1<I2>()));
  BOOST_CHECK((test_subeq<I1>()));
  BOOST_CHECK((test_subeq<I2>()));
  BOOST_CHECK((test_subeq1<I1>()));
  BOOST_CHECK((test_subeq1<I2>()));
  return 0;
}