Added boost header

test/external/boost/numeric/interval/arith.hpp

@@ -0,0 +1,305 @@
+/* Boost interval/arith.hpp template implementation file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002-2003 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_ARITH_HPP
+#define BOOST_NUMERIC_INTERVAL_ARITH_HPP
+
+#include <boost/config.hpp>
+#include <boost/numeric/interval/interval.hpp>
+#include <boost/numeric/interval/detail/bugs.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+#include <boost/numeric/interval/detail/division.hpp>
+#include <algorithm>
+
+namespace boost {
+namespace numeric {
+
+/*
+ * Basic arithmetic operators
+ */
+
+template<class T, class Policies> inline
+const interval<T, Policies>& operator+(const interval<T, Policies>& x)
+{
+  return x;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator-(const interval<T, Policies>& x)
+{
+  if (interval_lib::detail::test_input(x))
+    return interval<T, Policies>::empty();
+  return interval<T, Policies>(-x.upper(), -x.lower(), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies>& interval<T, Policies>::operator+=(const interval<T, Policies>& r)
+{
+  if (interval_lib::detail::test_input(*this, r))
+    set_empty();
+  else {
+    typename Policies::rounding rnd;
+    set(rnd.add_down(low, r.low), rnd.add_up(up, r.up));
+  }
+  return *this;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies>& interval<T, Policies>::operator+=(const T& r)
+{
+  if (interval_lib::detail::test_input(*this, r))
+    set_empty();
+  else {
+    typename Policies::rounding rnd;
+    set(rnd.add_down(low, r), rnd.add_up(up, r));
+  }
+  return *this;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies>& interval<T, Policies>::operator-=(const interval<T, Policies>& r)
+{
+  if (interval_lib::detail::test_input(*this, r))
+    set_empty();
+  else {
+    typename Policies::rounding rnd;
+    set(rnd.sub_down(low, r.up), rnd.sub_up(up, r.low));
+  }
+  return *this;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies>& interval<T, Policies>::operator-=(const T& r)
+{
+  if (interval_lib::detail::test_input(*this, r))
+    set_empty();
+  else {
+    typename Policies::rounding rnd;
+    set(rnd.sub_down(low, r), rnd.sub_up(up, r));
+  }
+  return *this;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies>& interval<T, Policies>::operator*=(const interval<T, Policies>& r)
+{
+  return *this = *this * r;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies>& interval<T, Policies>::operator*=(const T& r)
+{
+  return *this = r * *this;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies>& interval<T, Policies>::operator/=(const interval<T, Policies>& r)
+{
+  return *this = *this / r;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies>& interval<T, Policies>::operator/=(const T& r)
+{
+  return *this = *this / r;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator+(const interval<T, Policies>& x,
+                                const interval<T, Policies>& y)
+{
+  if (interval_lib::detail::test_input(x, y))
+    return interval<T, Policies>::empty();
+  typename Policies::rounding rnd;
+  return interval<T,Policies>(rnd.add_down(x.lower(), y.lower()),
+                              rnd.add_up  (x.upper(), y.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator+(const T& x, const interval<T, Policies>& y)
+{
+  if (interval_lib::detail::test_input(x, y))
+    return interval<T, Policies>::empty();
+  typename Policies::rounding rnd;
+  return interval<T,Policies>(rnd.add_down(x, y.lower()),
+                              rnd.add_up  (x, y.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator+(const interval<T, Policies>& x, const T& y)
+{ return y + x; }
+
+template<class T, class Policies> inline
+interval<T, Policies> operator-(const interval<T, Policies>& x,
+                                const interval<T, Policies>& y)
+{
+  if (interval_lib::detail::test_input(x, y))
+    return interval<T, Policies>::empty();
+  typename Policies::rounding rnd;
+  return interval<T,Policies>(rnd.sub_down(x.lower(), y.upper()),
+                              rnd.sub_up  (x.upper(), y.lower()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator-(const T& x, const interval<T, Policies>& y)
+{
+  if (interval_lib::detail::test_input(x, y))
+    return interval<T, Policies>::empty();
+  typename Policies::rounding rnd;
+  return interval<T,Policies>(rnd.sub_down(x, y.upper()),
+                              rnd.sub_up  (x, y.lower()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator-(const interval<T, Policies>& x, const T& y)
+{
+  if (interval_lib::detail::test_input(x, y))
+    return interval<T, Policies>::empty();
+  typename Policies::rounding rnd;
+  return interval<T,Policies>(rnd.sub_down(x.lower(), y),
+                              rnd.sub_up  (x.upper(), y), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator*(const interval<T, Policies>& x,
+                                const interval<T, Policies>& y)
+{
+  BOOST_USING_STD_MIN();
+  BOOST_USING_STD_MAX();
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x, y))
+    return I::empty();
+  typename Policies::rounding rnd;
+  const T& xl = x.lower();
+  const T& xu = x.upper();
+  const T& yl = y.lower();
+  const T& yu = y.upper();
+
+  if (interval_lib::user::is_neg(xl))
+    if (interval_lib::user::is_pos(xu))
+      if (interval_lib::user::is_neg(yl))
+        if (interval_lib::user::is_pos(yu)) // M * M
+          return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.mul_down(xl, yu), rnd.mul_down(xu, yl)),
+                   max BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.mul_up  (xl, yl), rnd.mul_up  (xu, yu)), true);
+        else                    // M * N
+          return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yl), true);
+      else
+        if (interval_lib::user::is_pos(yu)) // M * P
+          return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yu), true);
+        else                    // M * Z
+          return I(static_cast<T>(0), static_cast<T>(0), true);
+    else
+      if (interval_lib::user::is_neg(yl))
+        if (interval_lib::user::is_pos(yu)) // N * M
+          return I(rnd.mul_down(xl, yu), rnd.mul_up(xl, yl), true);
+        else                    // N * N
+          return I(rnd.mul_down(xu, yu), rnd.mul_up(xl, yl), true);
+      else
+        if (interval_lib::user::is_pos(yu)) // N * P
+          return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yl), true);
+        else                    // N * Z
+          return I(static_cast<T>(0), static_cast<T>(0), true);
+  else
+    if (interval_lib::user::is_pos(xu))
+      if (interval_lib::user::is_neg(yl))
+        if (interval_lib::user::is_pos(yu)) // P * M
+          return I(rnd.mul_down(xu, yl), rnd.mul_up(xu, yu), true);
+        else                    // P * N
+          return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yu), true);
+      else
+        if (interval_lib::user::is_pos(yu)) // P * P
+          return I(rnd.mul_down(xl, yl), rnd.mul_up(xu, yu), true);
+        else                    // P * Z
+          return I(static_cast<T>(0), static_cast<T>(0), true);
+    else                        // Z * ?
+      return I(static_cast<T>(0), static_cast<T>(0), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator*(const T& x, const interval<T, Policies>& y)
+{ 
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x, y))
+    return I::empty();
+  typename Policies::rounding rnd;
+  const T& yl = y.lower();
+  const T& yu = y.upper();
+  // x is supposed not to be infinite
+  if (interval_lib::user::is_neg(x))
+    return I(rnd.mul_down(x, yu), rnd.mul_up(x, yl), true);
+  else if (interval_lib::user::is_zero(x))
+    return I(static_cast<T>(0), static_cast<T>(0), true);
+  else
+    return I(rnd.mul_down(x, yl), rnd.mul_up(x, yu), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator*(const interval<T, Policies>& x, const T& y)
+{ return y * x; }
+
+template<class T, class Policies> inline
+interval<T, Policies> operator/(const interval<T, Policies>& x,
+                                const interval<T, Policies>& y)
+{
+  if (interval_lib::detail::test_input(x, y))
+    return interval<T, Policies>::empty();
+  if (zero_in(y))
+    if (!interval_lib::user::is_zero(y.lower()))
+      if (!interval_lib::user::is_zero(y.upper()))
+        return interval_lib::detail::div_zero(x);
+      else
+        return interval_lib::detail::div_negative(x, y.lower());
+    else
+      if (!interval_lib::user::is_zero(y.upper()))
+        return interval_lib::detail::div_positive(x, y.upper());
+      else
+        return interval<T, Policies>::empty();
+  else
+    return interval_lib::detail::div_non_zero(x, y);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator/(const T& x, const interval<T, Policies>& y)
+{
+  if (interval_lib::detail::test_input(x, y))
+    return interval<T, Policies>::empty();
+  if (zero_in(y))
+    if (!interval_lib::user::is_zero(y.lower()))
+      if (!interval_lib::user::is_zero(y.upper()))
+        return interval_lib::detail::div_zero<T, Policies>(x);
+      else
+        return interval_lib::detail::div_negative<T, Policies>(x, y.lower());
+    else
+      if (!interval_lib::user::is_zero(y.upper()))
+        return interval_lib::detail::div_positive<T, Policies>(x, y.upper());
+      else
+        return interval<T, Policies>::empty();
+  else
+    return interval_lib::detail::div_non_zero(x, y);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator/(const interval<T, Policies>& x, const T& y)
+{
+  if (interval_lib::detail::test_input(x, y) || interval_lib::user::is_zero(y))
+    return interval<T, Policies>::empty();
+  typename Policies::rounding rnd;
+  const T& xl = x.lower();
+  const T& xu = x.upper();
+  if (interval_lib::user::is_neg(y))
+    return interval<T, Policies>(rnd.div_down(xu, y), rnd.div_up(xl, y), true);
+  else
+    return interval<T, Policies>(rnd.div_down(xl, y), rnd.div_up(xu, y), true);
+}
+
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_ARITH_HPP

test/external/boost/numeric/interval/arith2.hpp

@@ -0,0 +1,305 @@
+/* Boost interval/arith2.hpp template implementation file
+ *
+ * This header provides some auxiliary arithmetic
+ * functions: fmod, sqrt, square, pov, inverse and
+ * a multi-interval division.
+ *
+ * Copyright 2002-2003 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_ARITH2_HPP
+#define BOOST_NUMERIC_INTERVAL_ARITH2_HPP
+
+#include <boost/config.hpp>
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+#include <boost/numeric/interval/detail/bugs.hpp>
+#include <boost/numeric/interval/detail/division.hpp>
+#include <boost/numeric/interval/arith.hpp>
+#include <boost/numeric/interval/policies.hpp>
+#include <algorithm>
+#include <cassert>
+#include <boost/config/no_tr1/cmath.hpp>
+
+namespace boost {
+namespace numeric {
+
+template<class T, class Policies> inline
+interval<T, Policies> fmod(const interval<T, Policies>& x,
+                           const interval<T, Policies>& y)
+{
+  if (interval_lib::detail::test_input(x, y))
+    return interval<T, Policies>::empty();
+  typename Policies::rounding rnd;
+  typedef typename interval_lib::unprotect<interval<T, Policies> >::type I;
+  T const &yb = interval_lib::user::is_neg(x.lower()) ? y.lower() : y.upper();
+  T n = rnd.int_down(rnd.div_down(x.lower(), yb));
+  return (const I&)x - n * (const I&)y;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> fmod(const interval<T, Policies>& x, const T& y)
+{
+  if (interval_lib::detail::test_input(x, y))
+    return interval<T, Policies>::empty();
+  typename Policies::rounding rnd;
+  typedef typename interval_lib::unprotect<interval<T, Policies> >::type I;
+  T n = rnd.int_down(rnd.div_down(x.lower(), y));
+  return (const I&)x - n * I(y);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> fmod(const T& x, const interval<T, Policies>& y)
+{
+  if (interval_lib::detail::test_input(x, y))
+    return interval<T, Policies>::empty();
+  typename Policies::rounding rnd;
+  typedef typename interval_lib::unprotect<interval<T, Policies> >::type I;
+  T const &yb = interval_lib::user::is_neg(x) ? y.lower() : y.upper();
+  T n = rnd.int_down(rnd.div_down(x, yb));
+  return x - n * (const I&)y;
+}
+
+namespace interval_lib {
+
+template<class T, class Policies> inline
+interval<T, Policies> division_part1(const interval<T, Policies>& x,
+                                     const interval<T, Policies>& y, bool& b)
+{
+  typedef interval<T, Policies> I;
+  b = false;
+  if (detail::test_input(x, y))
+    return I::empty();
+  if (zero_in(y))
+    if (!user::is_zero(y.lower()))
+      if (!user::is_zero(y.upper()))
+        return detail::div_zero_part1(x, y, b);
+      else
+        return detail::div_negative(x, y.lower());
+    else
+      if (!user::is_zero(y.upper()))
+        return detail::div_positive(x, y.upper());
+      else
+        return I::empty();
+  else
+    return detail::div_non_zero(x, y);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> division_part2(const interval<T, Policies>& x,
+                                     const interval<T, Policies>& y, bool b = true)
+{
+  if (!b) return interval<T, Policies>::empty();
+  return detail::div_zero_part2(x, y);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> multiplicative_inverse(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (detail::test_input(x))
+    return I::empty();
+  T one = static_cast<T>(1);
+  typename Policies::rounding rnd;
+  if (zero_in(x)) {
+    typedef typename Policies::checking checking;
+    if (!user::is_zero(x.lower()))
+      if (!user::is_zero(x.upper()))
+        return I::whole();
+      else
+        return I(checking::neg_inf(), rnd.div_up(one, x.lower()), true);
+    else
+      if (!user::is_zero(x.upper()))
+        return I(rnd.div_down(one, x.upper()), checking::pos_inf(), true);
+      else
+        return I::empty();
+  } else 
+    return I(rnd.div_down(one, x.upper()), rnd.div_up(one, x.lower()), true);
+}
+
+namespace detail {
+
+template<class T, class Rounding> inline
+T pow_dn(const T& x_, int pwr, Rounding& rnd) // x and pwr are positive
+{
+  T x = x_;
+  T y = (pwr & 1) ? x_ : static_cast<T>(1);
+  pwr >>= 1;
+  while (pwr > 0) {
+    x = rnd.mul_down(x, x);
+    if (pwr & 1) y = rnd.mul_down(x, y);
+    pwr >>= 1;
+  }
+  return y;
+}
+
+template<class T, class Rounding> inline
+T pow_up(const T& x_, int pwr, Rounding& rnd) // x and pwr are positive
+{
+  T x = x_;
+  T y = (pwr & 1) ? x_ : static_cast<T>(1);
+  pwr >>= 1;
+  while (pwr > 0) {
+    x = rnd.mul_up(x, x);
+    if (pwr & 1) y = rnd.mul_up(x, y);
+    pwr >>= 1;
+  }
+  return y;
+}
+
+} // namespace detail
+} // namespace interval_lib
+
+template<class T, class Policies> inline
+interval<T, Policies> pow(const interval<T, Policies>& x, int pwr)
+{
+  BOOST_USING_STD_MAX();
+  using interval_lib::detail::pow_dn;
+  using interval_lib::detail::pow_up;
+  typedef interval<T, Policies> I;
+
+  if (interval_lib::detail::test_input(x))
+    return I::empty();
+
+  if (pwr == 0)
+    if (interval_lib::user::is_zero(x.lower())
+        && interval_lib::user::is_zero(x.upper()))
+      return I::empty();
+    else
+      return I(static_cast<T>(1));
+  else if (pwr < 0)
+    return interval_lib::multiplicative_inverse(pow(x, -pwr));
+
+  typename Policies::rounding rnd;
+  
+  if (interval_lib::user::is_neg(x.upper())) {        // [-2,-1]
+    T yl = pow_dn(static_cast<T>(-x.upper()), pwr, rnd);
+    T yu = pow_up(static_cast<T>(-x.lower()), pwr, rnd);
+    if (pwr & 1)     // [-2,-1]^1
+      return I(-yu, -yl, true);
+    else             // [-2,-1]^2
+      return I(yl, yu, true);
+  } else if (interval_lib::user::is_neg(x.lower())) { // [-1,1]
+    if (pwr & 1) {   // [-1,1]^1
+      return I(-pow_up(static_cast<T>(-x.lower()), pwr, rnd), pow_up(x.upper(), pwr, rnd), true);
+    } else {         // [-1,1]^2
+      return I(static_cast<T>(0), pow_up(max BOOST_PREVENT_MACRO_SUBSTITUTION(static_cast<T>(-x.lower()), x.upper()), pwr, rnd), true);
+    }
+  } else {                                // [1,2]
+    return I(pow_dn(x.lower(), pwr, rnd), pow_up(x.upper(), pwr, rnd), true);
+  }
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> sqrt(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x) || interval_lib::user::is_neg(x.upper()))
+    return I::empty();
+  typename Policies::rounding rnd;
+  T l = !interval_lib::user::is_pos(x.lower()) ? static_cast<T>(0) : rnd.sqrt_down(x.lower());
+  return I(l, rnd.sqrt_up(x.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> square(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x))
+    return I::empty();
+  typename Policies::rounding rnd;
+  const T& xl = x.lower();
+  const T& xu = x.upper();
+  if (interval_lib::user::is_neg(xu))
+    return I(rnd.mul_down(xu, xu), rnd.mul_up(xl, xl), true);
+  else if (interval_lib::user::is_pos(x.lower()))
+    return I(rnd.mul_down(xl, xl), rnd.mul_up(xu, xu), true);
+  else
+    return I(static_cast<T>(0), (-xl > xu ? rnd.mul_up(xl, xl) : rnd.mul_up(xu, xu)), true);
+}
+
+namespace interval_lib {
+namespace detail {
+
+template< class I > inline
+I root_aux(typename I::base_type const &x, int k) // x and k are bigger than one
+{
+  typedef typename I::base_type T;
+  T tk(k);
+  I y(static_cast<T>(1), x, true);
+  for(;;) {
+    T y0 = median(y);
+    I yy = intersect(y, y0 - (pow(I(y0, y0, true), k) - x) / (tk * pow(y, k - 1)));
+    if (equal(y, yy)) return y;
+    y = yy;
+  }
+}
+
+template< class I > inline // x is positive and k bigger than one
+typename I::base_type root_aux_dn(typename I::base_type const &x, int k)
+{
+  typedef typename I::base_type T;
+  typedef typename I::traits_type Policies;
+  typename Policies::rounding rnd;
+  T one(1);
+  if (x > one) return root_aux<I>(x, k).lower();
+  if (x == one) return one;
+  return rnd.div_down(one, root_aux<I>(rnd.div_up(one, x), k).upper());
+}
+
+template< class I > inline // x is positive and k bigger than one
+typename I::base_type root_aux_up(typename I::base_type const &x, int k)
+{
+  typedef typename I::base_type T;
+  typedef typename I::traits_type Policies;
+  typename Policies::rounding rnd;
+  T one(1);
+  if (x > one) return root_aux<I>(x, k).upper();
+  if (x == one) return one;
+  return rnd.div_up(one, root_aux<I>(rnd.div_down(one, x), k).lower());
+}
+
+} // namespace detail
+} // namespace interval_lib
+
+template< class T, class Policies > inline
+interval<T, Policies> nth_root(interval<T, Policies> const &x, int k)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x)) return I::empty();
+  assert(k > 0);
+  if (k == 1) return x;
+  typename Policies::rounding rnd;
+  typedef typename interval_lib::unprotect<I>::type R;
+  if (!interval_lib::user::is_pos(x.upper())) {
+    if (interval_lib::user::is_zero(x.upper())) {
+      T zero(0);
+      if (!(k & 1) || interval_lib::user::is_zero(x.lower())) // [-1,0]^/2 or [0,0]
+        return I(zero, zero, true);
+      else               // [-1,0]^/3
+        return I(-interval_lib::detail::root_aux_up<R>(-x.lower(), k), zero, true);
+    } else if (!(k & 1)) // [-2,-1]^/2
+      return I::empty();
+    else {               // [-2,-1]^/3
+      return I(-interval_lib::detail::root_aux_up<R>(-x.lower(), k),
+               -interval_lib::detail::root_aux_dn<R>(-x.upper(), k), true);
+    }
+  }
+  T u = interval_lib::detail::root_aux_up<R>(x.upper(), k);
+  if (!interval_lib::user::is_pos(x.lower()))
+    if (!(k & 1) || interval_lib::user::is_zero(x.lower())) // [-1,1]^/2 or [0,1]
+      return I(static_cast<T>(0), u, true);
+    else                 // [-1,1]^/3
+      return I(-interval_lib::detail::root_aux_up<R>(-x.lower(), k), u, true);
+  else                   // [1,2]
+    return I(interval_lib::detail::root_aux_dn<R>(x.lower(), k), u, true);
+}
+
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_ARITH2_HPP

test/external/boost/numeric/interval/arith3.hpp

@@ -0,0 +1,69 @@
+/* Boost interval/arith3.hpp template implementation file
+ *
+ * This headers provides arithmetical functions
+ * which compute an interval given some base
+ * numbers. The resulting interval encloses the
+ * real result of the arithmetic operation.
+ *
+ * Copyright 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_ARITH3_HPP
+#define BOOST_NUMERIC_INTERVAL_ARITH3_HPP
+
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+template<class I> inline
+I add(const typename I::base_type& x, const typename I::base_type& y)
+{
+  typedef typename I::traits_type Policies;
+  if (detail::test_input<typename I::base_type, Policies>(x, y))
+    return I::empty();
+  typename Policies::rounding rnd;
+  return I(rnd.add_down(x, y), rnd.add_up(x, y), true);
+}
+
+template<class I> inline
+I sub(const typename I::base_type& x, const typename I::base_type& y)
+{
+  typedef typename I::traits_type Policies;
+  if (detail::test_input<typename I::base_type, Policies>(x, y))
+    return I::empty();
+  typename Policies::rounding rnd;
+  return I(rnd.sub_down(x, y), rnd.sub_up(x, y), true);
+}
+
+template<class I> inline
+I mul(const typename I::base_type& x, const typename I::base_type& y)
+{
+  typedef typename I::traits_type Policies;
+  if (detail::test_input<typename I::base_type, Policies>(x, y))
+    return I::empty();
+  typename Policies::rounding rnd;
+  return I(rnd.mul_down(x, y), rnd.mul_up(x, y), true);
+}
+
+template<class I> inline
+I div(const typename I::base_type& x, const typename I::base_type& y)
+{
+  typedef typename I::traits_type Policies;
+  if (detail::test_input<typename I::base_type, Policies>(x, y) || user::is_zero(y))
+    return I::empty();
+  typename Policies::rounding rnd;
+  return I(rnd.div_down(x, y), rnd.div_up(x, y), true);
+}
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_ARITH3_HPP

test/external/boost/numeric/interval/checking.hpp

@@ -0,0 +1,130 @@
+/* Boost interval/checking.hpp template implementation file
+ *
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_CHECKING_HPP
+#define BOOST_NUMERIC_INTERVAL_CHECKING_HPP
+
+#include <stdexcept>
+#include <string>
+#include <cassert>
+#include <boost/limits.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+struct exception_create_empty
+{
+  void operator()()
+  {
+    throw std::runtime_error("boost::interval: empty interval created");
+  }
+};
+
+struct exception_invalid_number
+{
+  void operator()()
+  {
+    throw std::invalid_argument("boost::interval: invalid number");
+  }
+};
+
+template<class T>
+struct checking_base
+{
+  static T pos_inf()
+  {
+    assert(std::numeric_limits<T>::has_infinity);
+    return std::numeric_limits<T>::infinity();
+  }
+  static T neg_inf()
+  {
+    assert(std::numeric_limits<T>::has_infinity);
+    return -std::numeric_limits<T>::infinity();
+  }
+  static T nan()
+  {
+    assert(std::numeric_limits<T>::has_quiet_NaN);
+    return std::numeric_limits<T>::quiet_NaN();
+  }
+  static bool is_nan(const T& x)
+  {
+    return std::numeric_limits<T>::has_quiet_NaN && (x != x);
+  }
+  static T empty_lower()
+  {
+    return (std::numeric_limits<T>::has_quiet_NaN ?
+            std::numeric_limits<T>::quiet_NaN() : static_cast<T>(1));
+  }
+  static T empty_upper()
+  {
+    return (std::numeric_limits<T>::has_quiet_NaN ?
+            std::numeric_limits<T>::quiet_NaN() : static_cast<T>(0));
+  }
+  static bool is_empty(const T& l, const T& u)
+  {
+    return !(l <= u); // safety for partial orders
+  }
+};
+
+template<class T, class Checking = checking_base<T>,
+         class Exception = exception_create_empty>
+struct checking_no_empty: Checking
+{
+  static T nan()
+  {
+    assert(false);
+    return Checking::nan();
+  }
+  static T empty_lower()
+  {
+    Exception()();
+    return Checking::empty_lower();
+  }
+  static T empty_upper()
+  {
+    Exception()();
+    return Checking::empty_upper();
+  }
+  static bool is_empty(const T&, const T&)
+  {
+    return false;
+  }
+};
+
+template<class T, class Checking = checking_base<T> >
+struct checking_no_nan: Checking
+{
+  static bool is_nan(const T&)
+  {
+    return false;
+  }
+};
+
+template<class T, class Checking = checking_base<T>,
+         class Exception = exception_invalid_number>
+struct checking_catch_nan: Checking
+{
+  static bool is_nan(const T& x)
+  {
+    if (Checking::is_nan(x)) Exception()();
+    return false;
+  }
+};
+
+template<class T>
+struct checking_strict:
+  checking_no_nan<T, checking_no_empty<T> >
+{};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_CHECKING_HPP

test/external/boost/numeric/interval/compare.hpp

@@ -0,0 +1,19 @@
+/* Boost interval/compare.hpp template implementation file
+ *
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_COMPARE_HPP
+#define BOOST_NUMERIC_INTERVAL_COMPARE_HPP
+
+#include <boost/numeric/interval/compare/certain.hpp>
+#include <boost/numeric/interval/compare/possible.hpp>
+#include <boost/numeric/interval/compare/explicit.hpp>
+#include <boost/numeric/interval/compare/lexicographic.hpp>
+#include <boost/numeric/interval/compare/set.hpp>
+
+#endif // BOOST_NUMERIC_INTERVAL_COMPARE_HPP

test/external/boost/numeric/interval/compare/certain.hpp

@@ -0,0 +1,113 @@
+/* Boost interval/compare/certain.hpp template implementation file
+ *
+ * Copyright 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_COMPARE_CERTAIN_HPP
+#define BOOST_NUMERIC_INTERVAL_COMPARE_CERTAIN_HPP
+
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace compare {
+namespace certain {
+
+template<class T, class Policies1, class Policies2> inline
+bool operator<(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() < y.lower();
+}
+
+template<class T, class Policies> inline
+bool operator<(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() < y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator<=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() <= y.lower();
+}
+
+template<class T, class Policies> inline
+bool operator<=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() <= y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator>(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() > y.upper();
+}
+
+template<class T, class Policies> inline
+bool operator>(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() > y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator>=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() >= y.upper();
+}
+
+template<class T, class Policies> inline
+bool operator>=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() >= y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator==(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() == y.lower() && x.lower() == y.upper();
+}
+
+template<class T, class Policies> inline
+bool operator==(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() == y && x.lower() == y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator!=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() < y.lower() || x.lower() > y.upper();
+}
+
+template<class T, class Policies> inline
+bool operator!=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() < y || x.lower() > y;
+}
+
+} // namespace certain
+} // namespace compare
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_INTERVAL_COMPARE_CERTAIN_HPP

test/external/boost/numeric/interval/compare/explicit.hpp

@@ -0,0 +1,248 @@
+/* Boost interval/compare/explicit.hpp template implementation file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_COMPARE_EXPLICIT_HPP
+#define BOOST_NUMERIC_INTERVAL_COMPARE_EXPLICIT_HPP
+
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+/*
+ * Certainly... operations
+ */
+
+template<class T, class Policies1, class Policies2> inline
+bool cerlt(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.upper() < y.lower();
+}
+
+template<class T, class Policies> inline
+bool cerlt(const interval<T, Policies>& x, const T& y)
+{
+  return x.upper() < y;
+}
+
+template<class T, class Policies> inline
+bool cerlt(const T& x, const interval<T, Policies>& y)
+{
+  return x < y.lower();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool cerle(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.upper() <= y.lower();
+}
+
+template<class T, class Policies> inline
+bool cerle(const interval<T, Policies>& x, const T& y)
+{
+  return x.upper() <= y;
+}
+
+template<class T, class Policies> inline
+bool cerle(const T& x, const interval<T, Policies>& y)
+{
+  return x <= y.lower();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool cergt(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.lower() > y.upper();
+}
+
+template<class T, class Policies> inline
+bool cergt(const interval<T, Policies>& x, const T& y)
+{
+  return x.lower() > y;
+}
+
+template<class T, class Policies> inline
+bool cergt(const T& x, const interval<T, Policies>& y)
+{
+  return x > y.upper();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool cerge(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.lower() >= y.upper();
+}
+
+template<class T, class Policies> inline
+bool cerge(const interval<T, Policies>& x, const T& y)
+{
+  return x.lower() >= y;
+}
+
+template<class T, class Policies> inline
+bool cerge(const T& x, const interval<T, Policies>& y)
+{
+  return x >= y.upper();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool cereq(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.lower() == y.upper() && y.lower() == x.upper();
+}
+
+template<class T, class Policies> inline
+bool cereq(const interval<T, Policies>& x, const T& y)
+{
+  return x.lower() == y && x.upper() == y;
+}
+
+template<class T, class Policies> inline
+bool cereq(const T& x, const interval<T, Policies>& y)
+{
+  return x == y.lower() && x == y.upper();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool cerne(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.upper() < y.lower() || y.upper() < x.lower();
+}
+
+template<class T, class Policies> inline
+bool cerne(const interval<T, Policies>& x, const T& y)
+{
+  return x.upper() < y || y < x.lower();
+}
+
+template<class T, class Policies> inline
+bool cerne(const T& x, const interval<T, Policies>& y)
+{
+  return x < y.lower() || y.upper() < x;
+}
+
+/*
+ * Possibly... comparisons
+ */
+
+template<class T, class Policies1, class Policies2> inline
+bool poslt(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.lower() < y.upper();
+}
+
+template<class T, class Policies> inline
+bool poslt(const interval<T, Policies>& x, const T& y)
+{
+  return x.lower() < y;
+}
+
+template<class T, class Policies> inline
+bool poslt(const T& x, const interval<T, Policies>& y)
+{
+  return x < y.upper();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool posle(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.lower() <= y.upper();
+}
+
+template<class T, class Policies> inline
+bool posle(const interval<T, Policies>& x, const T& y)
+{
+  return x.lower() <= y;
+}
+
+template<class T, class Policies> inline
+bool posle(const T& x, const interval<T, Policies>& y)
+{
+  return x <= y.upper();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool posgt(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.upper() > y.lower();
+}
+
+template<class T, class Policies> inline
+bool posgt(const interval<T, Policies>& x, const T& y)
+{
+  return x.upper() > y;
+}
+
+template<class T, class Policies> inline
+bool posgt(const T& x, const interval<T, Policies> & y)
+{
+  return x > y.lower();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool posge(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.upper() >= y.lower();
+}
+
+template<class T, class Policies> inline
+bool posge(const interval<T, Policies>& x, const T& y)
+{
+  return x.upper() >= y;
+}
+
+template<class T, class Policies> inline
+bool posge(const T& x, const interval<T, Policies>& y)
+{
+  return x >= y.lower();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool poseq(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.upper() >= y.lower() && y.upper() >= x.lower();
+}
+
+template<class T, class Policies> inline
+bool poseq(const interval<T, Policies>& x, const T& y)
+{
+  return x.upper() >= y && y >= x.lower();
+}
+
+template<class T, class Policies> inline
+bool poseq(const T& x, const interval<T, Policies>& y)
+{
+  return x >= y.lower() && y.upper() >= x;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool posne(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return x.upper() != y.lower() || y.upper() != x.lower();
+}
+
+template<class T, class Policies> inline
+bool posne(const interval<T, Policies>& x, const T& y)
+{
+  return x.upper() != y || y != x.lower();
+}
+
+template<class T, class Policies> inline
+bool posne(const T& x, const interval<T, Policies>& y)
+{
+  return x != y.lower() || y.upper() != x;
+}
+
+} // namespace interval_lib
+} // namespace numeric
+} //namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_COMPARE_EXPLICIT_HPP

test/external/boost/numeric/interval/compare/lexicographic.hpp

@@ -0,0 +1,122 @@
+/* Boost interval/compare/lexicographic.hpp template implementation file
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_COMPARE_LEXICOGRAPHIC_HPP
+#define BOOST_NUMERIC_INTERVAL_COMPARE_LEXICOGRAPHIC_HPP
+
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace compare {
+namespace lexicographic {
+
+template<class T, class Policies1, class Policies2> inline
+bool operator<(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  const T& xl = x.lower();
+  const T& yl = y.lower();
+  return xl < yl || (xl == yl && x.upper() < y.upper());
+}
+
+template<class T, class Policies> inline
+bool operator<(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() < y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator<=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  const T& xl = x.lower();
+  const T& yl = y.lower();
+  return xl < yl || (xl == yl && x.upper() <= y.upper());
+}
+
+template<class T, class Policies> inline
+bool operator<=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  const T& xl = x.lower();
+  return xl < y || (xl == y && x.upper() <= y);
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator>(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  const T& xl = x.lower();
+  const T& yl = y.lower();
+  return xl > yl || (xl == yl && x.upper() > y.upper());
+}
+
+template<class T, class Policies> inline
+bool operator>(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  const T& xl = x.lower();
+  return xl > y || (xl == y && x.upper() > y);
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator>=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  const T& xl = x.lower();
+  const T& yl = y.lower();
+  return xl > yl || (xl == yl && x.upper() >= y.upper());
+}
+
+template<class T, class Policies> inline
+bool operator>=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() >= y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator==(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() == y.lower() && x.upper() == y.upper();
+}
+
+template<class T, class Policies> inline
+bool operator==(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() == y && x.upper() == y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator!=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() != y.lower() || x.upper() != y.upper();
+}
+
+template<class T, class Policies> inline
+bool operator!=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() != y || x.upper() != y;
+}
+
+} // namespace lexicographic
+} // namespace compare
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_COMPARE_LEXICOGRAPHIC_HPP

test/external/boost/numeric/interval/compare/possible.hpp

@@ -0,0 +1,113 @@
+/* Boost interval/compare/possible.hpp template implementation file
+ *
+ * Copyright 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_COMPARE_POSSIBLE_HPP
+#define BOOST_NUMERIC_INTERVAL_COMPARE_POSSIBLE_HPP
+
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace compare {
+namespace possible {
+
+template<class T, class Policies1, class Policies2> inline
+bool operator<(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() < y.upper();
+}
+
+template<class T, class Policies> inline
+bool operator<(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() < y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator<=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() <= y.upper();
+}
+
+template<class T, class Policies> inline
+bool operator<=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() <= y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator>(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() > y.lower();
+}
+
+template<class T, class Policies> inline
+bool operator>(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() > y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator>=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() >= y.lower();
+}
+
+template<class T, class Policies> inline
+bool operator>=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.upper() >= y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator==(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() <= y.upper() && x.upper() >= y.lower();
+}
+
+template<class T, class Policies> inline
+bool operator==(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() <= y && x.upper() >= y;
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator!=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() != y.upper() || x.upper() != y.lower();
+}
+
+template<class T, class Policies> inline
+bool operator!=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  return x.lower() != y || x.upper() != y;
+}
+
+} // namespace possible
+} // namespace compare
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_INTERVAL_COMPARE_POSSIBLE_HPP

test/external/boost/numeric/interval/compare/set.hpp

@@ -0,0 +1,101 @@
+/* Boost interval/compare/set.hpp template implementation file
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_COMPARE_SET_HPP
+#define BOOST_NUMERIC_INTERVAL_COMPARE_SET_HPP
+
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+#include <boost/numeric/interval/utility.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace compare {
+namespace set {
+
+template<class T, class Policies1, class Policies2> inline
+bool operator<(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return proper_subset(x, y);
+}
+
+template<class T, class Policies> inline
+bool operator<(const interval<T, Policies>& x, const T& y)
+{
+  throw comparison_error();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator<=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return subset(x, y);
+}
+
+template<class T, class Policies> inline
+bool operator<=(const interval<T, Policies>& x, const T& y)
+{
+  throw comparison_error();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator>(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return proper_subset(y, x);
+}
+
+template<class T, class Policies> inline
+bool operator>(const interval<T, Policies>& x, const T& y)
+{
+  throw comparison_error();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator>=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return subset(y, x);
+}
+
+template<class T, class Policies> inline
+bool operator>=(const interval<T, Policies>& x, const T& y)
+{
+  throw comparison_error();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator==(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return equal(y, x);
+}
+
+template<class T, class Policies> inline
+bool operator==(const interval<T, Policies>& x, const T& y)
+{
+  throw comparison_error();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool operator!=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  return !equal(y, x);
+}
+
+template<class T, class Policies> inline
+bool operator!=(const interval<T, Policies>& x, const T& y)
+{
+  throw comparison_error();
+}
+
+} // namespace set
+} // namespace compare
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_COMPARE_SET_HPP

test/external/boost/numeric/interval/compare/tribool.hpp

@@ -0,0 +1,138 @@
+/* Boost interval/compare/tribool.hpp template implementation file
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_COMPARE_TRIBOOL_HPP
+#define BOOST_NUMERIC_INTERVAL_COMPARE_TRIBOOL_HPP
+
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+#include <boost/logic/tribool.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace compare {
+namespace tribool {
+
+template<class T, class Policies1, class Policies2> inline
+logic::tribool operator<(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.upper() < y.lower()) return true;
+  if (x.lower() >= y.upper()) return false;
+  return logic::indeterminate;
+}
+
+template<class T, class Policies> inline
+logic::tribool operator<(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.upper() < y) return true;
+  if (x.lower() >= y) return false;
+  return logic::indeterminate;
+}
+
+template<class T, class Policies1, class Policies2> inline
+logic::tribool operator<=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.upper() <= y.lower()) return true;
+  if (x.lower() > y.upper()) return false;
+  return logic::indeterminate;
+}
+
+template<class T, class Policies> inline
+logic::tribool operator<=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.upper() <= y) return true;
+  if (x.lower() > y) return false;
+  return logic::indeterminate;
+}
+
+template<class T, class Policies1, class Policies2> inline
+logic::tribool operator>(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.lower() > y.upper()) return true;
+  if (x.upper() <= y.lower()) return false;
+  return logic::indeterminate;
+}
+
+template<class T, class Policies> inline
+logic::tribool operator>(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.lower() > y) return true;
+  if (x.upper() <= y) return false;
+  return logic::indeterminate;
+}
+
+template<class T, class Policies1, class Policies2> inline
+logic::tribool operator>=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.lower() >= y.upper()) return true;
+  if (x.upper() < y.lower()) return false;
+  return logic::indeterminate;
+}
+
+template<class T, class Policies> inline
+logic::tribool operator>=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.lower() >= y) return true;
+  if (x.upper() < y) return false;
+  return logic::indeterminate;
+}
+
+template<class T, class Policies1, class Policies2> inline
+logic::tribool operator==(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.upper() == y.lower() && x.lower() == y.upper()) return true;
+  if (x.upper() < y.lower() || x.lower() > y.upper()) return false;
+  return logic::indeterminate;
+}
+
+template<class T, class Policies> inline
+logic::tribool operator==(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.upper() == y && x.lower() == y) return true;
+  if (x.upper() < y || x.lower() > y) return false;
+  return logic::indeterminate;
+}
+
+template<class T, class Policies1, class Policies2> inline
+logic::tribool operator!=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.upper() < y.lower() || x.lower() > y.upper()) return true;
+  if (x.upper() == y.lower() && x.lower() == y.upper()) return false;
+  return logic::indeterminate;
+}
+
+template<class T, class Policies> inline
+logic::tribool operator!=(const interval<T, Policies>& x, const T& y)
+{
+  if (detail::test_input(x, y)) throw comparison_error();
+  if (x.upper() < y || x.lower() > y) return true;
+  if (x.upper() == y && x.lower() == y) return false;
+  return logic::indeterminate;
+}
+
+} // namespace tribool
+} // namespace compare
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_INTERVAL_COMPARE_TRIBOOL_HPP

test/external/boost/numeric/interval/constants.hpp

@@ -0,0 +1,85 @@
+/* Boost interval/constants.hpp template implementation file
+ *
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_CONSTANTS_HPP
+#define BOOST_NUMERIC_INTERVAL_CONSTANTS_HPP
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace constants {
+
+// These constants should be exactly computed.
+// Decimal representations wouldn't do it since the standard doesn't
+// specify the rounding (even nearest) that should be used.
+
+static const float pi_f_l = 13176794.0f/(1<<22);
+static const float pi_f_u = 13176795.0f/(1<<22);
+static const double pi_d_l = (3373259426.0 + 273688.0 / (1<<21)) / (1<<30);
+static const double pi_d_u = (3373259426.0 + 273689.0 / (1<<21)) / (1<<30);
+
+template<class T> inline T pi_lower() { return 3; }
+template<class T> inline T pi_upper() { return 4; }
+template<class T> inline T pi_half_lower() { return 1; }
+template<class T> inline T pi_half_upper() { return 2; }
+template<class T> inline T pi_twice_lower() { return 6; }
+template<class T> inline T pi_twice_upper() { return 7; }
+
+template<> inline float pi_lower<float>() { return pi_f_l; }
+template<> inline float pi_upper<float>() { return pi_f_u; }
+template<> inline float pi_half_lower<float>() { return pi_f_l / 2; }
+template<> inline float pi_half_upper<float>() { return pi_f_u / 2; }
+template<> inline float pi_twice_lower<float>() { return pi_f_l * 2; }
+template<> inline float pi_twice_upper<float>() { return pi_f_u * 2; }
+
+template<> inline double pi_lower<double>() { return pi_d_l; }
+template<> inline double pi_upper<double>() { return pi_d_u; }
+template<> inline double pi_half_lower<double>() { return pi_d_l / 2; }
+template<> inline double pi_half_upper<double>() { return pi_d_u / 2; }
+template<> inline double pi_twice_lower<double>() { return pi_d_l * 2; }
+template<> inline double pi_twice_upper<double>() { return pi_d_u * 2; }
+
+template<> inline long double pi_lower<long double>() { return pi_d_l; }
+template<> inline long double pi_upper<long double>() { return pi_d_u; }
+template<> inline long double pi_half_lower<long double>() { return pi_d_l / 2; }
+template<> inline long double pi_half_upper<long double>() { return pi_d_u / 2; }
+template<> inline long double pi_twice_lower<long double>() { return pi_d_l * 2; }
+template<> inline long double pi_twice_upper<long double>() { return pi_d_u * 2; }
+
+} // namespace constants
+
+template<class I> inline
+I pi()
+{
+  typedef typename I::base_type T;
+  return I(constants::pi_lower<T>(),
+           constants::pi_upper<T>(), true);
+}
+
+template<class I> inline
+I pi_half()
+{
+  typedef typename I::base_type T;
+  return I(constants::pi_half_lower<T>(),
+           constants::pi_half_upper<T>(), true);
+}
+
+template<class I> inline
+I pi_twice()
+{
+  typedef typename I::base_type T;
+  return I(constants::pi_twice_lower<T>(),
+           constants::pi_twice_upper<T>(), true);
+}
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_CONSTANTS_HPP

test/external/boost/numeric/interval/detail/alpha_rounding_control.hpp

@@ -0,0 +1,113 @@
+/* Boost interval/detail/alpha_rounding_control.hpp file
+ *
+ * Copyright 2005 Felix H<>fling, 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_ALPHA_ROUNDING_CONTROL_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_ALPHA_ROUNDING_CONTROL_HPP
+
+#if !defined(alpha) && !defined(__alpha__)
+#error This header only works on Alpha CPUs.
+#endif
+
+#if defined(__GNUC__) || defined(__digital__) || defined(__DECCXX)
+
+#include <float.h> // write_rnd() and read_rnd()
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+namespace detail {
+#if defined(__GNUC__ )
+    typedef union {
+    ::boost::long_long_type imode;
+    double dmode;
+    } rounding_mode_struct;
+
+    // set bits 59-58 (DYN),
+    // clear all exception bits and disable overflow (51) and inexact exceptions (62)
+    static const rounding_mode_struct mode_upward      = { 0x4C08000000000000LL };
+    static const rounding_mode_struct mode_downward    = { 0x4408000000000000LL };
+    static const rounding_mode_struct mode_to_nearest  = { 0x4808000000000000LL };
+    static const rounding_mode_struct mode_toward_zero = { 0x4008000000000000LL };
+
+    struct alpha_rounding_control
+    {
+    typedef double rounding_mode;
+
+    static void set_rounding_mode(const rounding_mode mode)
+    { __asm__ __volatile__ ("mt_fpcr %0" : : "f"(mode)); }
+
+    static void get_rounding_mode(rounding_mode& mode)
+    { __asm__ __volatile__ ("mf_fpcr %0" : "=f"(mode)); }
+
+    static void downward()    { set_rounding_mode(mode_downward.dmode);    }
+    static void upward()      { set_rounding_mode(mode_upward.dmode);      }
+    static void to_nearest()  { set_rounding_mode(mode_to_nearest.dmode);  }
+    static void toward_zero() { set_rounding_mode(mode_toward_zero.dmode); }
+    };
+#elif defined(__digital__) || defined(__DECCXX)
+
+#if defined(__DECCXX) && !(defined(__FLT_ROUNDS) && __FLT_ROUNDS == -1)
+#error Dynamic rounding mode not enabled. See cxx man page for details.
+#endif
+
+    struct alpha_rounding_control
+    {
+    typedef unsigned int rounding_mode;
+
+    static void set_rounding_mode(const rounding_mode& mode)  { write_rnd(mode); }
+    static void get_rounding_mode(rounding_mode& mode)  { mode = read_rnd(); }
+
+    static void downward()    { set_rounding_mode(FP_RND_RM); }
+    static void upward()      { set_rounding_mode(FP_RND_RP); }
+    static void to_nearest()  { set_rounding_mode(FP_RND_RN); }
+    static void toward_zero() { set_rounding_mode(FP_RND_RZ); }
+    };
+#endif
+} // namespace detail
+
+extern "C" {
+  float rintf(float);
+  double rint(double);
+  long double rintl(long double);
+}
+
+template<>
+struct rounding_control<float>:
+  detail::alpha_rounding_control
+{
+  static float force_rounding(const float r)
+  { volatile float _r = r; return _r; }
+  static float to_int(const float& x) { return rintf(x); }
+};
+
+template<>
+struct rounding_control<double>:
+  detail::alpha_rounding_control
+{
+  static const double & force_rounding(const double& r) { return r; }
+  static double to_int(const double& r) { return rint(r); }
+};
+
+template<>
+struct rounding_control<long double>:
+  detail::alpha_rounding_control
+{
+  static const long double & force_rounding(const long double& r) { return r; }
+  static long double to_int(const long double& r) { return rintl(r); }
+};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#undef BOOST_NUMERIC_INTERVAL_NO_HARDWARE
+#endif
+
+#endif /* BOOST_NUMERIC_INTERVAL_DETAIL_ALPHA_ROUNDING_CONTROL_HPP */

test/external/boost/numeric/interval/detail/bcc_rounding_control.hpp

@@ -0,0 +1,57 @@
+/* Boost interval/detail/bcc_rounding_control.hpp file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_BCC_ROUNDING_CONTROL_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_BCC_ROUNDING_CONTROL_HPP
+
+#ifndef __BORLANDC__
+#  error This header is only intended for Borland C++.
+#endif
+
+#ifndef _M_IX86
+#  error This header only works on x86 CPUs.
+#endif
+
+#include <float.h>      // Borland C++ rounding control
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace detail {
+
+#ifndef BOOST_NUMERIC_INTERVAL_KEEP_EXCEPTIONS_FOR_BCC
+extern "C" { unsigned int _RTLENTRY _fm_init(void); }
+
+struct borland_workaround {
+  borland_workaround() { _fm_init(); }
+};
+
+static borland_workaround borland_workaround_exec;
+#endif // BOOST_NUMERIC_INTERVAL_KEEP_EXCEPTIONS_FOR_BCC
+
+__inline double rint(double)
+{ __emit__(0xD9); __emit__(0xFC); /* asm FRNDINT */ }
+
+struct x86_rounding
+{
+  typedef unsigned int rounding_mode;
+  static void get_rounding_mode(rounding_mode& mode)
+  { mode = _control87(0, 0); }
+  static void set_rounding_mode(const rounding_mode mode)
+  { _control87(mode, 0xffff); } 
+  static double to_int(const double& x) { return rint(x); }
+};
+
+} // namespace detail
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif /* BOOST_NUMERIC_INTERVAL_DETAIL_BCC_ROUNDING_CONTROL_HPP */

test/external/boost/numeric/interval/detail/bugs.hpp

@@ -0,0 +1,79 @@
+/* Boost interval/detail/bugs.hpp file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_BUGS
+#define BOOST_NUMERIC_INTERVAL_DETAIL_BUGS
+
+#include <boost/config.hpp>
+
+#if defined(__GLIBC__) && (defined(__USE_MISC) || defined(__USE_XOPEN_EXTENDED) || defined(__USE_ISOC99)) && !defined(__ICC)
+#  define BOOST_HAS_INV_HYPERBOLIC
+#endif
+
+#ifdef BOOST_NO_STDC_NAMESPACE
+#  define BOOST_NUMERIC_INTERVAL_using_math(a) using ::a
+#  ifdef BOOST_HAS_INV_HYPERBOLIC
+#    define BOOST_NUMERIC_INTERVAL_using_ahyp(a) using ::a
+#  endif
+#else
+#  define BOOST_NUMERIC_INTERVAL_using_math(a) using std::a
+#  if defined(BOOST_HAS_INV_HYPERBOLIC)
+#    if defined(__GLIBCPP__) || defined(__GLIBCXX__)
+#    define BOOST_NUMERIC_INTERVAL_using_ahyp(a) using ::a
+#    else
+#    define BOOST_NUMERIC_INTERVAL_using_ahyp(a) using std::a
+#  endif
+#  endif
+#endif
+
+#if defined(__COMO__) || defined(BOOST_INTEL)
+#  define BOOST_NUMERIC_INTERVAL_using_max(a) using std::a
+#elif defined(BOOST_NO_STDC_NAMESPACE)
+#  define BOOST_NUMERIC_INTERVAL_using_max(a) using ::a
+#else
+#  define BOOST_NUMERIC_INTERVAL_using_max(a) using std::a
+#endif
+
+#ifndef BOOST_NUMERIC_INTERVAL_using_ahyp
+#  define BOOST_NUMERIC_INTERVAL_using_ahyp(a)
+#endif
+
+#if defined(__GNUC__) && (__GNUC__ <= 2)
+// cf PR c++/1981 for a description of the bug
+#include <algorithm>
+#include <boost/config/no_tr1/cmath.hpp>
+namespace boost {
+namespace numeric {
+  using std::min;
+  using std::max;
+  using std::sqrt;
+  using std::exp;
+  using std::log;
+  using std::cos;
+  using std::tan;
+  using std::asin;
+  using std::acos;
+  using std::atan;
+  using std::ceil;
+  using std::floor;
+  using std::sinh;
+  using std::cosh;
+  using std::tanh;
+# undef BOOST_NUMERIC_INTERVAL_using_max
+# undef BOOST_NUMERIC_INTERVAL_using_math
+# define BOOST_NUMERIC_INTERVAL_using_max(a)
+# define BOOST_NUMERIC_INTERVAL_using_math(a)
+# undef BOOST_NUMERIC_INTERVAL_using_ahyp
+# define BOOST_NUMERIC_INTERVAL_using_ahyp(a)
+} // namespace numeric
+} // namespace boost
+#endif
+
+#endif // BOOST_NUMERIC_INTERVAL_DETAIL_BUGS

test/external/boost/numeric/interval/detail/c99_rounding_control.hpp

@@ -0,0 +1,50 @@
+/* Boost interval/detail/c99_rounding_control.hpp file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_C99_ROUNDING_CONTROL_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_C99_ROUNDING_CONTROL_HPP
+
+#include <boost/numeric/interval/detail/c99sub_rounding_control.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+template<>
+struct rounding_control<float>:
+  detail::c99_rounding_control
+{
+  static float force_rounding(float const &r)
+  { volatile float r_ = r; return r_; }
+};
+
+template<>
+struct rounding_control<double>:
+  detail::c99_rounding_control
+{
+  static double force_rounding(double const &r)
+  { volatile double r_ = r; return r_; }
+};
+
+template<>
+struct rounding_control<long double>:
+  detail::c99_rounding_control
+{
+  static long double force_rounding(long double const &r)
+  { volatile long double r_ = r; return r_; }
+};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#undef BOOST_NUMERIC_INTERVAL_NO_HARDWARE
+
+#endif // BOOST_NUMERIC_INTERVAL_DETAIL_C99_ROUNDING_CONTROL_HPP

test/external/boost/numeric/interval/detail/c99sub_rounding_control.hpp

@@ -0,0 +1,43 @@
+/* Boost interval/detail/c99sub_rounding_control.hpp file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_C99SUB_ROUNDING_CONTROL_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_C99SUB_ROUNDING_CONTROL_HPP
+
+#include <boost/detail/fenv.hpp>      // ISO C 99 rounding mode control
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace detail {
+
+extern "C" { double rint(double); }
+
+struct c99_rounding_control
+{
+  typedef int rounding_mode;
+
+  static void set_rounding_mode(rounding_mode mode)  { fesetround(mode); }
+  static void get_rounding_mode(rounding_mode &mode) { mode = fegetround(); }
+  static void downward()    { set_rounding_mode(FE_DOWNWARD);   }
+  static void upward()      { set_rounding_mode(FE_UPWARD);     }
+  static void to_nearest()  { set_rounding_mode(FE_TONEAREST);  }
+  static void toward_zero() { set_rounding_mode(FE_TOWARDZERO); }
+
+  template<class T>
+  static T to_int(const T& r) { return rint(r); }
+};
+
+} // namespace detail
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_DETAIL_C99SUB_ROUBDING_CONTROL_HPP

test/external/boost/numeric/interval/detail/division.hpp

@@ -0,0 +1,194 @@
+/* Boost interval/detail/division.hpp file
+ *
+ * Copyright 2003 Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP
+
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+#include <boost/numeric/interval/detail/bugs.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+#include <boost/numeric/interval/rounded_arith.hpp>
+#include <algorithm>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace detail {
+
+template<class T, class Policies> inline
+interval<T, Policies> div_non_zero(const interval<T, Policies>& x,
+                                   const interval<T, Policies>& y)
+{
+  // assert(!in_zero(y));
+  typename Policies::rounding rnd;
+  typedef interval<T, Policies> I;
+  const T& xl = x.lower();
+  const T& xu = x.upper();
+  const T& yl = y.lower();
+  const T& yu = y.upper();
+  if (::boost::numeric::interval_lib::user::is_neg(xu))
+    if (::boost::numeric::interval_lib::user::is_neg(yu))
+      return I(rnd.div_down(xu, yl), rnd.div_up(xl, yu), true);
+    else
+      return I(rnd.div_down(xl, yl), rnd.div_up(xu, yu), true);
+  else if (::boost::numeric::interval_lib::user::is_neg(xl))
+    if (::boost::numeric::interval_lib::user::is_neg(yu))
+      return I(rnd.div_down(xu, yu), rnd.div_up(xl, yu), true);
+    else
+      return I(rnd.div_down(xl, yl), rnd.div_up(xu, yl), true);
+  else
+    if (::boost::numeric::interval_lib::user::is_neg(yu))
+      return I(rnd.div_down(xu, yu), rnd.div_up(xl, yl), true);
+    else
+      return I(rnd.div_down(xl, yu), rnd.div_up(xu, yl), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> div_non_zero(const T& x, const interval<T, Policies>& y)
+{
+  // assert(!in_zero(y));
+  typename Policies::rounding rnd;
+  typedef interval<T, Policies> I;
+  const T& yl = y.lower();
+  const T& yu = y.upper();
+  if (::boost::numeric::interval_lib::user::is_neg(x))
+    return I(rnd.div_down(x, yl), rnd.div_up(x, yu), true);
+  else
+    return I(rnd.div_down(x, yu), rnd.div_up(x, yl), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> div_positive(const interval<T, Policies>& x, const T& yu)
+{
+  // assert(::boost::numeric::interval_lib::user::is_pos(yu));
+  if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
+      ::boost::numeric::interval_lib::user::is_zero(x.upper()))
+    return x;
+  typename Policies::rounding rnd;
+  typedef interval<T, Policies> I;
+  const T& xl = x.lower();
+  const T& xu = x.upper();
+  typedef typename Policies::checking checking;
+  if (::boost::numeric::interval_lib::user::is_neg(xu))
+    return I(checking::neg_inf(), rnd.div_up(xu, yu), true);
+  else if (::boost::numeric::interval_lib::user::is_neg(xl))
+    return I(checking::neg_inf(), checking::pos_inf(), true);
+  else
+    return I(rnd.div_down(xl, yu), checking::pos_inf(), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> div_positive(const T& x, const T& yu)
+{
+  // assert(::boost::numeric::interval_lib::user::is_pos(yu));
+  typedef interval<T, Policies> I;
+  if (::boost::numeric::interval_lib::user::is_zero(x))
+    return I(static_cast<T>(0), static_cast<T>(0), true);
+  typename Policies::rounding rnd;
+  typedef typename Policies::checking checking;
+  if (::boost::numeric::interval_lib::user::is_neg(x))
+    return I(checking::neg_inf(), rnd.div_up(x, yu), true);
+  else
+    return I(rnd.div_down(x, yu), checking::pos_inf(), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> div_negative(const interval<T, Policies>& x, const T& yl)
+{
+  // assert(::boost::numeric::interval_lib::user::is_neg(yl));
+  if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
+      ::boost::numeric::interval_lib::user::is_zero(x.upper()))
+    return x;
+  typename Policies::rounding rnd;
+  typedef interval<T, Policies> I;
+  const T& xl = x.lower();
+  const T& xu = x.upper();
+  typedef typename Policies::checking checking;
+  if (::boost::numeric::interval_lib::user::is_neg(xu))
+    return I(rnd.div_down(xu, yl), checking::pos_inf(), true);
+  else if (::boost::numeric::interval_lib::user::is_neg(xl))
+    return I(checking::neg_inf(), checking::pos_inf(), true);
+  else
+    return I(checking::neg_inf(), rnd.div_up(xl, yl), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> div_negative(const T& x, const T& yl)
+{
+  // assert(::boost::numeric::interval_lib::user::is_neg(yl));
+  typedef interval<T, Policies> I;
+  if (::boost::numeric::interval_lib::user::is_zero(x))
+    return I(static_cast<T>(0), static_cast<T>(0), true);
+  typename Policies::rounding rnd;
+  typedef typename Policies::checking checking;
+  if (::boost::numeric::interval_lib::user::is_neg(x))
+    return I(rnd.div_down(x, yl), checking::pos_inf(), true);
+  else
+    return I(checking::neg_inf(), rnd.div_up(x, yl), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> div_zero(const interval<T, Policies>& x)
+{
+  if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
+      ::boost::numeric::interval_lib::user::is_zero(x.upper()))
+    return x;
+  else return interval<T, Policies>::whole();
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> div_zero(const T& x)
+{
+  if (::boost::numeric::interval_lib::user::is_zero(x))
+    return interval<T, Policies>(static_cast<T>(0), static_cast<T>(0), true);
+  else return interval<T, Policies>::whole();
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> div_zero_part1(const interval<T, Policies>& x,
+                                     const interval<T, Policies>& y, bool& b)
+{
+  // assert(::boost::numeric::interval_lib::user::is_neg(y.lower()) && ::boost::numeric::interval_lib::user::is_pos(y.upper()));
+  if (::boost::numeric::interval_lib::user::is_zero(x.lower()) && ::boost::numeric::interval_lib::user::is_zero(x.upper()))
+    { b = false; return x; }
+  typename Policies::rounding rnd;
+  typedef interval<T, Policies> I;
+  const T& xl = x.lower();
+  const T& xu = x.upper();
+  const T& yl = y.lower();
+  const T& yu = y.upper();
+  typedef typename Policies::checking checking;
+  if (::boost::numeric::interval_lib::user::is_neg(xu))
+    { b = true;  return I(checking::neg_inf(), rnd.div_up(xu, yu), true); }
+  else if (::boost::numeric::interval_lib::user::is_neg(xl))
+    { b = false; return I(checking::neg_inf(), checking::pos_inf(), true); }
+  else
+    { b = true;  return I(checking::neg_inf(), rnd.div_up(xl, yl), true); }
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> div_zero_part2(const interval<T, Policies>& x,
+                                     const interval<T, Policies>& y)
+{
+  // assert(::boost::numeric::interval_lib::user::is_neg(y.lower()) && ::boost::numeric::interval_lib::user::is_pos(y.upper()) && (div_zero_part1(x, y, b), b));
+  typename Policies::rounding rnd;
+  typedef interval<T, Policies> I;
+  typedef typename Policies::checking checking;
+  if (::boost::numeric::interval_lib::user::is_neg(x.upper()))
+    return I(rnd.div_down(x.upper(), y.lower()), checking::pos_inf(), true);
+  else
+    return I(rnd.div_down(x.lower(), y.upper()), checking::pos_inf(), true);
+}
+
+} // namespace detail
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP

test/external/boost/numeric/interval/detail/ia64_rounding_control.hpp

@@ -0,0 +1,83 @@
+/* Boost interval/detail/ia64_rounding_control.hpp file
+ *
+ * Copyright 2006-2007 Boris Gubenko
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_IA64_ROUNDING_CONTROL_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_IA64_ROUNDING_CONTROL_HPP
+
+#if !defined(ia64) && !defined(__ia64) && !defined(__ia64__)
+#error This header only works on ia64 CPUs.
+#endif
+
+#if defined(__hpux)
+
+#   include <fenv.h>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace detail {
+
+
+    struct ia64_rounding_control
+    {
+    typedef unsigned int rounding_mode;
+
+    static void set_rounding_mode(const rounding_mode& mode)  { 
+fesetround(mode); }
+    static void get_rounding_mode(rounding_mode& mode)  { mode = fegetround(); }
+
+    static void downward()    { set_rounding_mode(FE_DOWNWARD); }
+    static void upward()      { set_rounding_mode(FE_UPWARD); }
+    static void to_nearest()  { set_rounding_mode(FE_TONEAREST); }
+    static void toward_zero() { set_rounding_mode(FE_TOWARDZERO); }
+    };
+
+} // namespace detail
+
+extern "C" {
+  float rintf(float);
+  double rint(double);
+  long double rintl(long double);
+}
+
+template<>
+struct rounding_control<float>:
+  detail::ia64_rounding_control
+{
+  static float force_rounding(const float r)
+  { volatile float _r = r; return _r; }
+  static float to_int(const float& x) { return rintf(x); }
+};
+
+template<>
+struct rounding_control<double>:
+  detail::ia64_rounding_control
+{
+  static const double & force_rounding(const double& r) { return r; }
+  static double to_int(const double& r) { return rint(r); }
+};
+
+template<>
+struct rounding_control<long double>:
+  detail::ia64_rounding_control
+{
+  static const long double & force_rounding(const long double& r) { return r; }
+  static long double to_int(const long double& r) { return rintl(r); }
+};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#undef BOOST_NUMERIC_INTERVAL_NO_HARDWARE
+
+#endif /* __hpux */
+
+#endif /* BOOST_NUMERIC_INTERVAL_DETAIL_IA64_ROUNDING_CONTROL_HPP */
+

test/external/boost/numeric/interval/detail/interval_prototype.hpp

@@ -0,0 +1,41 @@
+/* Boost interval/detail/interval_prototype.hpp file
+ *
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_INTERVAL_PROTOTYPE_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_INTERVAL_PROTOTYPE_HPP
+
+namespace boost {
+namespace numeric {
+
+namespace interval_lib {
+
+template<class T> struct rounded_math;
+template<class T> struct checking_strict;
+class comparison_error;
+template<class Rounding, class Checking> struct policies;
+
+/*
+ * default policies class
+ */
+
+template<class T>
+struct default_policies
+{
+  typedef policies<rounded_math<T>, checking_strict<T> > type;
+};
+    
+} // namespace interval_lib
+
+template<class T, class Policies = typename interval_lib::default_policies<T>::type >
+class interval;  
+
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_DETAIL_INTERVAL_PROTOTYPE_HPP

test/external/boost/numeric/interval/detail/msvc_rounding_control.hpp

@@ -0,0 +1,100 @@
+/* Boost interval/detail/msvc_rounding_control.hpp file
+ *
+ * Copyright 2000 Maarten Keijzer
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_MSVC_ROUNDING_CONTROL_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_MSVC_ROUNDING_CONTROL_HPP
+
+#ifndef _MSC_VER
+#  error This header is only intended for MSVC, but might work for Borland as well
+#endif
+
+#include <float.h>      // MSVC rounding control
+
+// Although the function is called _control87, it seems to work for
+// other FPUs too, so it does not have to be changed to _controlfp.
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace detail {
+
+#if BOOST_MSVC < 1400 || defined(WIN64)
+extern "C" { double rint(double); }
+#else
+inline double rint(double x)
+{
+_asm FLD [x] ;
+_asm FRNDINT ;
+//_asm RET ;
+}
+#endif
+
+struct x86_rounding
+{
+  static unsigned int hard2msvc(unsigned short m) {
+    unsigned int n = 0;
+    if (m & 0x01) n |= _EM_INVALID;
+    if (m & 0x02) n |= _EM_DENORMAL;
+    if (m & 0x04) n |= _EM_ZERODIVIDE;
+    if (m & 0x08) n |= _EM_OVERFLOW;
+    if (m & 0x10) n |= _EM_UNDERFLOW;
+    if (m & 0x20) n |= _EM_INEXACT;
+    switch (m & 0x300) {
+    case 0x000: n |= _PC_24; break;
+    case 0x200: n |= _PC_53; break;
+    case 0x300: n |= _PC_64; break;
+    }
+    switch (m & 0xC00) {
+    case 0x000: n |= _RC_NEAR; break;
+    case 0x400: n |= _RC_DOWN; break;
+    case 0x800: n |= _RC_UP;   break;
+    case 0xC00: n |= _RC_CHOP; break;
+    }
+    if (m & 0x1000) n |= _IC_AFFINE; // only useful on 287
+    return n;
+  }
+
+  static unsigned short msvc2hard(unsigned int n) {
+    unsigned short m = 0;
+    if (n & _EM_INVALID)    m |= 0x01;
+    if (n & _EM_DENORMAL)   m |= 0x02;
+    if (n & _EM_ZERODIVIDE) m |= 0x04;
+    if (n & _EM_OVERFLOW)   m |= 0x08;
+    if (n & _EM_UNDERFLOW)  m |= 0x10;
+    if (n & _EM_INEXACT)    m |= 0x20;
+    switch (n & _MCW_RC) {
+    case _RC_NEAR: m |= 0x000; break;
+    case _RC_DOWN: m |= 0x400; break;
+    case _RC_UP:   m |= 0x800; break;
+    case _RC_CHOP: m |= 0xC00; break;
+    }
+    switch (n & _MCW_PC) {
+    case _PC_24: m |= 0x000; break;
+    case _PC_53: m |= 0x200; break;
+    case _PC_64: m |= 0x300; break;
+    }
+    if ((n & _MCW_IC) == _IC_AFFINE) m |= 0x1000;
+    return m;
+  }
+
+  typedef unsigned short rounding_mode;
+  static void get_rounding_mode(rounding_mode& mode)
+  { mode = msvc2hard(_control87(0, 0)); }
+  static void set_rounding_mode(const rounding_mode mode)
+  { _control87(hard2msvc(mode), _MCW_EM | _MCW_RC | _MCW_PC | _MCW_IC); }
+  static double to_int(const double& x) { return rint(x); }
+};
+
+} // namespace detail
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif /* BOOST_NUMERIC_INTERVAL_DETAIL_MSVC_ROUNDING_CONTROL_HPP */

test/external/boost/numeric/interval/detail/ppc_rounding_control.hpp

@@ -0,0 +1,99 @@
+/* Boost interval/detail/ppc_rounding_control.hpp file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ * Copyright 2005 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_PPC_ROUNDING_CONTROL_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_PPC_ROUNDING_CONTROL_HPP
+
+#if !defined(powerpc) && !defined(__powerpc__) && !defined(__ppc__)
+#error This header only works on PPC CPUs.
+#endif
+
+#if defined(__GNUC__ ) || (__IBMCPP__ >= 700)
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace detail {
+
+typedef union {
+   ::boost::long_long_type imode;
+  double dmode;
+} rounding_mode_struct;
+
+static const rounding_mode_struct mode_upward      = { 0xFFF8000000000002LL };
+static const rounding_mode_struct mode_downward    = { 0xFFF8000000000003LL };
+static const rounding_mode_struct mode_to_nearest  = { 0xFFF8000000000000LL };
+static const rounding_mode_struct mode_toward_zero = { 0xFFF8000000000001LL };
+
+struct ppc_rounding_control
+{
+  typedef double rounding_mode;
+
+  static void set_rounding_mode(const rounding_mode mode)
+  { __asm__ __volatile__ ("mtfsf 255,%0" : : "f"(mode)); }
+
+  static void get_rounding_mode(rounding_mode& mode)
+  { __asm__ __volatile__ ("mffs %0" : "=f"(mode)); }
+
+  static void downward()    { set_rounding_mode(mode_downward.dmode);    }
+  static void upward()      { set_rounding_mode(mode_upward.dmode);      }
+  static void to_nearest()  { set_rounding_mode(mode_to_nearest.dmode);  }
+  static void toward_zero() { set_rounding_mode(mode_toward_zero.dmode); }
+};
+
+} // namespace detail
+
+// Do not declare the following C99 symbols if <math.h> provides them.
+// Otherwise, conflicts may occur, due to differences between prototypes.
+#if !defined(_ISOC99_SOURCE) && !defined(__USE_ISOC99)
+extern "C" {
+  float rintf(float);
+  double rint(double);
+}
+#endif
+
+template<>
+struct rounding_control<float>:
+  detail::ppc_rounding_control
+{
+  static float force_rounding(const float r)
+  {
+    float tmp;
+    __asm__ __volatile__ ("frsp %0, %1" : "=f" (tmp) : "f" (r));
+    return tmp;
+  }
+  static float to_int(const float& x) { return rintf(x); }
+};
+
+template<>
+struct rounding_control<double>:
+  detail::ppc_rounding_control
+{
+  static const double & force_rounding(const double& r) { return r; }
+  static double to_int(const double& r) { return rint(r); }
+};
+
+template<>
+struct rounding_control<long double>:
+  detail::ppc_rounding_control
+{
+  static const long double & force_rounding(const long double& r) { return r; }
+  static long double to_int(const long double& r) { return rint(r); }
+};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#undef BOOST_NUMERIC_INTERVAL_NO_HARDWARE
+#endif
+
+#endif /* BOOST_NUMERIC_INTERVAL_DETAIL_PPC_ROUNDING_CONTROL_HPP */

test/external/boost/numeric/interval/detail/sparc_rounding_control.hpp

@@ -0,0 +1,112 @@
+/* Boost interval/detail/sparc_rounding_control.hpp file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ *
+ * The basic code in this file was kindly provided by Jeremy Siek.
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_SPARC_ROUNDING_CONTROL_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_SPARC_ROUNDING_CONTROL_HPP
+
+#if !defined(sparc) && !defined(__sparc__)
+#  error This header is only intended for SPARC CPUs.
+#endif
+
+#ifdef __SUNPRO_CC
+#  include <ieeefp.h>
+#endif
+
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace detail {
+
+struct sparc_rounding_control
+{
+  typedef unsigned int rounding_mode;
+
+  static void set_rounding_mode(const rounding_mode& mode)
+  {
+#   if defined(__GNUC__)
+    __asm__ __volatile__("ld %0, %%fsr" : : "m"(mode));
+#   elif defined (__SUNPRO_CC)
+    fpsetround(fp_rnd(mode));
+#   elif defined(__KCC)
+    asm("sethi %hi(mode), %o1");
+    asm("ld [%o1+%lo(mode)], %fsr");
+#   else
+#     error Unsupported compiler for Sparc rounding control.
+#   endif
+  }
+
+  static void get_rounding_mode(rounding_mode& mode)
+  {
+#   if defined(__GNUC__)
+    __asm__ __volatile__("st %%fsr, %0" : "=m"(mode));
+#   elif defined (__SUNPRO_CC)
+    mode = fpgetround();
+#   elif defined(__KCC)
+#     error KCC on Sun SPARC get_round_mode: please fix me
+    asm("st %fsr, [mode]");
+#   else
+#     error Unsupported compiler for Sparc rounding control.
+#   endif
+  }
+
+#if defined(__SUNPRO_CC)
+  static void downward()    { set_rounding_mode(FP_RM); }
+  static void upward()      { set_rounding_mode(FP_RP); }
+  static void to_nearest()  { set_rounding_mode(FP_RN); }
+  static void toward_zero() { set_rounding_mode(FP_RZ); }
+#else
+  static void downward()    { set_rounding_mode(0xc0000000); }
+  static void upward()      { set_rounding_mode(0x80000000); }
+  static void to_nearest()  { set_rounding_mode(0x00000000); }
+  static void toward_zero() { set_rounding_mode(0x40000000); }
+#endif
+};
+
+} // namespace detail
+
+extern "C" {
+  float rintf(float);
+  double rint(double);
+}
+
+template<>
+struct rounding_control<float>:
+  detail::sparc_rounding_control
+{
+  static const float& force_rounding(const float& x) { return x; }
+  static float to_int(const float& x) { return rintf(x); }
+};
+
+template<>
+struct rounding_control<double>:
+  detail::sparc_rounding_control
+{
+  static const double& force_rounding(const double& x) { return x; }
+  static double to_int(const double& x) { return rint(x); }
+};
+
+template<>
+struct rounding_control<long double>:
+  detail::sparc_rounding_control
+{
+  static const long double& force_rounding(const long double& x) { return x; }
+  static long double to_int(const long double& x) { return rint(x); }
+};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#undef BOOST_NUMERIC_INTERVAL_NO_HARDWARE
+
+#endif /* BOOST_NUMERIC_INTERVAL_DETAIL_SPARC_ROUNDING_CONTROL_HPP */

test/external/boost/numeric/interval/detail/test_input.hpp

@@ -0,0 +1,76 @@
+/* Boost interval/detail/test_input.hpp file
+ *
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_TEST_INPUT_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_TEST_INPUT_HPP
+
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace user {
+
+template<class T> inline
+bool is_zero(T const &v) { return v == static_cast<T>(0); }
+
+template<class T> inline
+bool is_neg (T const &v) { return v <  static_cast<T>(0); }
+
+template<class T> inline
+bool is_pos (T const &v) { return v >  static_cast<T>(0); }
+
+} // namespace user
+
+namespace detail {
+
+template<class T, class Policies> inline
+bool test_input(const interval<T, Policies>& x) {
+  typedef typename Policies::checking checking;
+  return checking::is_empty(x.lower(), x.upper());
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool test_input(const interval<T, Policies1>& x, const interval<T, Policies2>& y) {
+  typedef typename Policies1::checking checking1;
+  typedef typename Policies2::checking checking2;
+  return checking1::is_empty(x.lower(), x.upper()) ||
+         checking2::is_empty(y.lower(), y.upper());
+}
+
+template<class T, class Policies> inline
+bool test_input(const T& x, const interval<T, Policies>& y) {
+  typedef typename Policies::checking checking;
+  return checking::is_nan(x) || checking::is_empty(y.lower(), y.upper());
+}
+
+template<class T, class Policies> inline
+bool test_input(const interval<T, Policies>& x, const T& y) {
+  typedef typename Policies::checking checking;
+  return checking::is_empty(x.lower(), x.upper()) || checking::is_nan(y);
+}
+
+template<class T, class Policies> inline
+bool test_input(const T& x) {
+  typedef typename Policies::checking checking;
+  return checking::is_nan(x);
+}
+
+template<class T, class Policies> inline
+bool test_input(const T& x, const T& y) {
+  typedef typename Policies::checking checking;
+  return checking::is_nan(x) || checking::is_nan(y);
+}
+
+} // namespace detail
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_DETAIL_TEST_INPUT_HPP

test/external/boost/numeric/interval/detail/x86_rounding_control.hpp

@@ -0,0 +1,108 @@
+/* Boost interval/detail/x86_rounding_control.hpp file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_X86_ROUNDING_CONTROL_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_X86_ROUNDING_CONTROL_HPP
+
+#ifdef __GNUC__
+#  include <boost/numeric/interval/detail/x86gcc_rounding_control.hpp>
+#elif defined(__BORLANDC__)
+#  include <boost/numeric/interval/detail/bcc_rounding_control.hpp>
+#elif defined(_MSC_VER)
+#  include <boost/numeric/interval/detail/msvc_rounding_control.hpp>
+#elif defined(__MWERKS__) || defined(__ICC) || defined (__SUNPRO_CC)
+#  define BOOST_NUMERIC_INTERVAL_USE_C99_SUBSYSTEM
+#  include <boost/numeric/interval/detail/c99sub_rounding_control.hpp>
+#else
+#  error Unsupported C++ compiler.
+#endif
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+namespace detail {
+
+#ifdef BOOST_NUMERIC_INTERVAL_USE_C99_SUBSYSTEM
+typedef c99_rounding_control x86_rounding_control;
+#undef BOOST_NUMERIC_INTERVAL_USE_C99_SUBSYSTEM
+#else
+struct fpu_rounding_modes
+{
+  unsigned short to_nearest;
+  unsigned short downward;
+  unsigned short upward;
+  unsigned short toward_zero;
+};
+
+// exceptions masked, extended precision
+// hardware default is 0x037f (0x1000 only has a meaning on 287)
+static const fpu_rounding_modes rnd_mode = { 0x137f, 0x177f, 0x1b7f, 0x1f7f };
+
+struct x86_rounding_control: x86_rounding
+{
+  static void to_nearest()  { set_rounding_mode(rnd_mode.to_nearest);  }
+  static void downward()    { set_rounding_mode(rnd_mode.downward);    }
+  static void upward()      { set_rounding_mode(rnd_mode.upward);      }
+  static void toward_zero() { set_rounding_mode(rnd_mode.toward_zero); }
+};
+#endif // BOOST_NUMERIC_INTERVAL_USE_C99_SUBSYSTEM
+
+} // namespace detail
+
+template<>
+struct rounding_control<float>: detail::x86_rounding_control
+{
+  static float force_rounding(const float& r) 
+  { volatile float r_ = r; return r_; }
+};
+
+template<>
+struct rounding_control<double>: detail::x86_rounding_control
+{
+  /*static double force_rounding(double r) 
+  { asm volatile ("" : "+m"(r) : ); return r; }*/
+  static double force_rounding(const double& r) 
+  { volatile double r_ = r; return r_; }
+};
+
+namespace detail {
+
+template<bool>
+struct x86_rounding_control_long_double;
+
+template<>
+struct x86_rounding_control_long_double<false>: x86_rounding_control
+{
+  static long double force_rounding(long double const &r)
+  { volatile long double r_ = r; return r_; }
+};
+
+template<>
+struct x86_rounding_control_long_double<true>: x86_rounding_control
+{
+  static long double const &force_rounding(long double const &r)
+  { return r; }
+};
+
+} // namespace detail
+
+template<>
+struct rounding_control<long double>:
+  detail::x86_rounding_control_long_double< (sizeof(long double) >= 10) >
+{};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#undef BOOST_NUMERIC_INTERVAL_NO_HARDWARE
+
+#endif /* BOOST_NUMERIC_INTERVAL_DETAIL_X86_ROUNDING_CONTROL_HPP */

test/external/boost/numeric/interval/detail/x86gcc_rounding_control.hpp

@@ -0,0 +1,51 @@
+/* Boost interval/detail/x86gcc_rounding_control.hpp file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_X86GCC_ROUNDING_CONTROL_HPP
+#define BOOST_NUMERIC_INTERVAL_DETAIL_X86GCC_ROUNDING_CONTROL_HPP
+
+#ifndef __GNUC__
+#  error This header only works with GNU CC.
+#endif
+
+#ifndef __i386__
+#  error This header only works on x86 CPUs.
+#endif
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+namespace detail {
+
+struct x86_rounding
+{
+  typedef unsigned short rounding_mode;
+
+  static void set_rounding_mode(const rounding_mode& mode)
+  { __asm__ __volatile__ ("fldcw %0" : : "m"(mode)); }
+
+  static void get_rounding_mode(rounding_mode& mode)
+  { __asm__ __volatile__ ("fnstcw %0" : "=m"(mode)); }
+
+  template<class T>
+  static T to_int(T r)
+  {
+    T r_;
+    __asm__ ("frndint" : "=&t"(r_) : "0"(r));
+    return r_;
+  }
+};
+
+} // namespace detail
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif /* BOOST_NUMERIC_INTERVAL_DETAIL_X86GCC_ROUNDING_CONTROL_HPP */

test/external/boost/numeric/interval/ext/integer.hpp

@@ -0,0 +1,70 @@
+/* Boost interval/ext/integer.hpp template implementation file
+ *
+ * Copyright 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_EXT_INTEGER_HPP
+#define BOOST_NUMERIC_INTERVAL_EXT_INTEGER_HPP
+
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+
+namespace boost {
+namespace numeric {
+
+template<class T, class Policies> inline
+interval<T, Policies> operator+ (const interval<T, Policies>& x, int y)
+{
+  return x + static_cast<T>(y);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator+ (int x, const interval<T, Policies>& y)
+{
+  return static_cast<T>(x) + y;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator- (const interval<T, Policies>& x, int y)
+{
+  return x - static_cast<T>(y);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator- (int x, const interval<T, Policies>& y)
+{
+  return static_cast<T>(x) - y;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator* (const interval<T, Policies>& x, int y)
+{
+  return x * static_cast<T>(y);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator* (int x, const interval<T, Policies>& y)
+{
+  return static_cast<T>(x) * y;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator/ (const interval<T, Policies>& x, int y)
+{
+  return x / static_cast<T>(y);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> operator/ (int x, const interval<T, Policies>& y)
+{
+  return static_cast<T>(x) / y;
+}
+
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_EXT_INTEGER_HPP

test/external/boost/numeric/interval/ext/x86_fast_rounding_control.hpp

@@ -0,0 +1,70 @@
+/* Boost interval/detail/x86gcc_rounding_control.hpp file
+ *
+ * This header provides a rounding control policy
+ * that avoids flushing results to memory. In
+ * order for this optimization to be reliable, it
+ * should be used only when no underflow or
+ * overflow would happen without it. Indeed, only
+ * values in range are correctly rounded.
+ *
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_EXT_X86_FAST_ROUNDING_CONTROL_HPP
+#define BOOST_NUMERIC_INTERVAL_EXT_X86_FAST_ROUNDING_CONTROL_HPP
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+namespace detail {
+
+// exceptions masked, expected precision (the mask is 0x0300)
+static const fpu_rounding_modes rnd_mode_f = { 0x107f, 0x147f, 0x187f, 0x1c7f };
+static const fpu_rounding_modes rnd_mode_d = { 0x127f, 0x167f, 0x1a7f, 0x1e7f };
+static const fpu_rounding_modes rnd_mode_l = { 0x137f, 0x177f, 0x1b7f, 0x1f7f };
+
+} // namespace detail
+
+template<class T>
+struct x86_fast_rounding_control;
+
+template<>
+struct x86_fast_rounding_control<float>: detail::x86_rounding
+{
+  static void to_nearest()  { set_rounding_mode(detail::rnd_mode_f.to_nearest);  }
+  static void downward()    { set_rounding_mode(detail::rnd_mode_f.downward);    }
+  static void upward()      { set_rounding_mode(detail::rnd_mode_f.upward);      }
+  static void toward_zero() { set_rounding_mode(detail::rnd_mode_f.toward_zero); }
+  static const float& force_rounding(const float& r) { return r; }
+};
+
+template<>
+struct x86_fast_rounding_control<double>: detail::x86_rounding
+{
+  static void to_nearest()  { set_rounding_mode(detail::rnd_mode_d.to_nearest);  }
+  static void downward()    { set_rounding_mode(detail::rnd_mode_d.downward);    }
+  static void upward()      { set_rounding_mode(detail::rnd_mode_d.upward);      }
+  static void toward_zero() { set_rounding_mode(detail::rnd_mode_d.toward_zero); }
+  static const double& force_rounding(const double& r) { return r; }
+};
+
+template<>
+struct x86_fast_rounding_control<long double>: detail::x86_rounding
+{
+  static void to_nearest()  { set_rounding_mode(detail::rnd_mode_l.to_nearest);  }
+  static void downward()    { set_rounding_mode(detail::rnd_mode_l.downward);    }
+  static void upward()      { set_rounding_mode(detail::rnd_mode_l.upward);      }
+  static void toward_zero() { set_rounding_mode(detail::rnd_mode_l.toward_zero); }
+  static const long double& force_rounding(const long double& r) { return r; }
+};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_EXT_X86_FAST_ROUNDING_CONTROL_HPP

test/external/boost/numeric/interval/hw_rounding.hpp

@@ -0,0 +1,70 @@
+/* Boost interval/hw_rounding.hpp template implementation file
+ *
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ * Copyright 2005 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_HW_ROUNDING_HPP
+#define BOOST_NUMERIC_INTERVAL_HW_ROUNDING_HPP
+
+#include <boost/numeric/interval/rounding.hpp>
+#include <boost/numeric/interval/rounded_arith.hpp>
+
+#define BOOST_NUMERIC_INTERVAL_NO_HARDWARE
+
+// define appropriate specialization of rounding_control for built-in types
+#if defined(__x86_64__) && (defined(__USE_ISOC99) || defined(__APPLE__))
+#  include <boost/numeric/interval/detail/c99_rounding_control.hpp>
+#elif defined(__i386__) || defined(_M_IX86) || defined(__BORLANDC__) || defined(_M_X64)
+#  include <boost/numeric/interval/detail/x86_rounding_control.hpp>
+#elif defined(powerpc) || defined(__powerpc__) || defined(__ppc__)
+#  include <boost/numeric/interval/detail/ppc_rounding_control.hpp>
+#elif defined(sparc) || defined(__sparc__)
+#  include <boost/numeric/interval/detail/sparc_rounding_control.hpp>
+#elif defined(alpha) || defined(__alpha__)
+#  include <boost/numeric/interval/detail/alpha_rounding_control.hpp>
+#elif defined(ia64) || defined(__ia64) || defined(__ia64__)
+#  include <boost/numeric/interval/detail/ia64_rounding_control.hpp>
+#endif
+
+#if defined(BOOST_NUMERIC_INTERVAL_NO_HARDWARE) && (defined(__USE_ISOC99) || defined(__MSL__))
+#  include <boost/numeric/interval/detail/c99_rounding_control.hpp>
+#endif
+
+#if defined(BOOST_NUMERIC_INTERVAL_NO_HARDWARE)
+#  undef BOOST_NUMERIC_INTERVAL_NO_HARDWARE
+#  error Boost.Numeric.Interval: Please specify rounding control mechanism.
+#endif
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+/*
+ * Three specializations of rounded_math<T>
+ */
+
+template<>
+struct rounded_math<float>
+  : save_state<rounded_arith_opp<float> >
+{};
+
+template<>
+struct rounded_math<double>
+  : save_state<rounded_arith_opp<double> >
+{};
+
+template<>
+struct rounded_math<long double>
+  : save_state<rounded_arith_opp<long double> >
+{};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_HW_ROUNDING_HPP

test/external/boost/numeric/interval/interval.hpp

@@ -0,0 +1,450 @@
+/* Boost interval/interval.hpp header file
+ *
+ * Copyright 2002-2003 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_INTERVAL_HPP
+#define BOOST_NUMERIC_INTERVAL_INTERVAL_HPP
+
+#include <stdexcept>
+#include <string>
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+
+namespace boost {
+namespace numeric {
+
+namespace interval_lib {
+    
+class comparison_error
+  : public std::runtime_error 
+{
+public:
+  comparison_error()
+    : std::runtime_error("boost::interval: uncertain comparison")
+  { }
+};
+
+} // namespace interval_lib
+
+/*
+ * interval class
+ */
+
+template<class T, class Policies>
+class interval
+{
+private:
+  struct interval_holder;
+  struct number_holder;
+public:
+  typedef T base_type;
+  typedef Policies traits_type;
+
+  T const &lower() const;
+  T const &upper() const;
+
+  interval();
+  interval(T const &v);
+  template<class T1> interval(T1 const &v);
+  interval(T const &l, T const &u);
+  template<class T1, class T2> interval(T1 const &l, T2 const &u);
+  interval(interval<T, Policies> const &r);
+  template<class Policies1> interval(interval<T, Policies1> const &r);
+  template<class T1, class Policies1> interval(interval<T1, Policies1> const &r);
+
+  interval &operator=(T const &v);
+  template<class T1> interval &operator=(T1 const &v);
+  interval &operator=(interval<T, Policies> const &r);
+  template<class Policies1> interval &operator=(interval<T, Policies1> const &r);
+  template<class T1, class Policies1> interval &operator=(interval<T1, Policies1> const &r);
+ 
+  void assign(const T& l, const T& u);
+
+  static interval empty();
+  static interval whole();
+  static interval hull(const T& x, const T& y);
+
+  interval& operator+= (const T& r);
+  interval& operator+= (const interval& r);
+  interval& operator-= (const T& r);
+  interval& operator-= (const interval& r);
+  interval& operator*= (const T& r);
+  interval& operator*= (const interval& r);
+  interval& operator/= (const T& r);
+  interval& operator/= (const interval& r);
+
+  bool operator< (const interval_holder& r) const;
+  bool operator> (const interval_holder& r) const;
+  bool operator<= (const interval_holder& r) const;
+  bool operator>= (const interval_holder& r) const;
+  bool operator== (const interval_holder& r) const;
+  bool operator!= (const interval_holder& r) const;
+
+  bool operator< (const number_holder& r) const;
+  bool operator> (const number_holder& r) const;
+  bool operator<= (const number_holder& r) const;
+  bool operator>= (const number_holder& r) const;
+  bool operator== (const number_holder& r) const;
+  bool operator!= (const number_holder& r) const;
+
+  // the following is for internal use only, it is not a published interface
+  // nevertheless, it's public because friends don't always work correctly.
+  interval(const T& l, const T& u, bool): low(l), up(u) {}
+  void set_empty();
+  void set_whole();
+  void set(const T& l, const T& u);
+
+private:
+  struct interval_holder {
+    template<class Policies2>
+    interval_holder(const interval<T, Policies2>& r)
+      : low(r.lower()), up(r.upper())
+    {
+      typedef typename Policies2::checking checking2;
+      if (checking2::is_empty(low, up))
+        throw interval_lib::comparison_error();
+    }
+
+    const T& low;
+    const T& up;
+  };
+
+  struct number_holder {
+    number_holder(const T& r) : val(r)
+    {
+      typedef typename Policies::checking checking;
+      if (checking::is_nan(r))
+        throw interval_lib::comparison_error();
+    }
+    
+    const T& val;
+  };
+
+  typedef typename Policies::checking checking;
+  typedef typename Policies::rounding rounding;
+
+  T low;
+  T up;
+};
+
+template<class T, class Policies> inline
+interval<T, Policies>::interval():
+  low(static_cast<T>(0)), up(static_cast<T>(0))
+{}
+
+template<class T, class Policies> inline
+interval<T, Policies>::interval(T const &v): low(v), up(v)
+{
+  if (checking::is_nan(v)) set_empty();
+}
+
+template<class T, class Policies> template<class T1> inline
+interval<T, Policies>::interval(T1 const &v)
+{
+  if (checking::is_nan(v)) set_empty();
+  else {
+    rounding rnd;
+    low = rnd.conv_down(v);
+    up  = rnd.conv_up  (v);
+  }
+}
+
+template<class T, class Policies> template<class T1, class T2> inline
+interval<T, Policies>::interval(T1 const &l, T2 const &u)
+{
+  if (checking::is_nan(l) || checking::is_nan(u) || !(l <= u)) set_empty();
+  else {
+    rounding rnd;
+    low = rnd.conv_down(l);
+    up  = rnd.conv_up  (u);
+  }
+}
+
+template<class T, class Policies> inline
+interval<T, Policies>::interval(T const &l, T const &u): low(l), up(u)
+{
+  if (checking::is_nan(l) || checking::is_nan(u) || !(l <= u))
+    set_empty();
+}
+
+
+template<class T, class Policies> inline
+interval<T, Policies>::interval(interval<T, Policies> const &r): low(r.lower()), up(r.upper())
+{}
+
+template<class T, class Policies> template<class Policies1> inline
+interval<T, Policies>::interval(interval<T, Policies1> const &r): low(r.lower()), up(r.upper())
+{
+  typedef typename Policies1::checking checking1;
+  if (checking1::is_empty(r.lower(), r.upper())) set_empty();
+}
+
+template<class T, class Policies> template<class T1, class Policies1> inline
+interval<T, Policies>::interval(interval<T1, Policies1> const &r)
+{
+  typedef typename Policies1::checking checking1;
+  if (checking1::is_empty(r.lower(), r.upper())) set_empty();
+  else {
+    rounding rnd;
+    low = rnd.conv_down(r.lower());
+    up  = rnd.conv_up  (r.upper());
+  }
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> &interval<T, Policies>::operator=(T const &v)
+{
+  if (checking::is_nan(v)) set_empty();
+  else low = up = v;
+  return *this;
+}
+
+template<class T, class Policies> template<class T1> inline
+interval<T, Policies> &interval<T, Policies>::operator=(T1 const &v)
+{
+  if (checking::is_nan(v)) set_empty();
+  else {
+    rounding rnd;
+    low = rnd.conv_down(v);
+    up  = rnd.conv_up  (v);
+  }
+  return *this;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> &interval<T, Policies>::operator=(interval<T, Policies> const &r)
+{
+  low = r.lower();
+  up  = r.upper();
+  return *this;
+}
+
+template<class T, class Policies> template<class Policies1> inline
+interval<T, Policies> &interval<T, Policies>::operator=(interval<T, Policies1> const &r)
+{
+  typedef typename Policies1::checking checking1;
+  if (checking1::is_empty(r.lower(), r.upper())) set_empty();
+  else {
+    low = r.lower();
+    up  = r.upper();
+  }
+  return *this;
+}
+
+template<class T, class Policies> template<class T1, class Policies1> inline
+interval<T, Policies> &interval<T, Policies>::operator=(interval<T1, Policies1> const &r)
+{
+  typedef typename Policies1::checking checking1;
+  if (checking1::is_empty(r.lower(), r.upper())) set_empty();
+  else {
+    rounding rnd;
+    low = rnd.conv_down(r.lower());
+    up  = rnd.conv_up  (r.upper());
+  }
+  return *this;
+}
+
+template<class T, class Policies> inline
+void interval<T, Policies>::assign(const T& l, const T& u)
+{
+  if (checking::is_nan(l) || checking::is_nan(u) || !(l <= u))
+    set_empty();
+  else set(l, u);
+}
+
+template<class T, class Policies> inline
+void interval<T, Policies>::set(const T& l, const T& u)
+{
+  low = l;
+  up  = u;
+}
+
+template<class T, class Policies> inline
+void interval<T, Policies>::set_empty()
+{
+  low = checking::empty_lower();
+  up  = checking::empty_upper();
+}
+
+template<class T, class Policies> inline
+void interval<T, Policies>::set_whole()
+{
+  low = checking::neg_inf();
+  up  = checking::pos_inf();
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> interval<T, Policies>::hull(const T& x, const T& y)
+{
+  bool bad_x = checking::is_nan(x);
+  bool bad_y = checking::is_nan(y);
+  if (bad_x)
+    if (bad_y) return interval::empty();
+    else       return interval(y, y, true);
+  else
+    if (bad_y) return interval(x, x, true);
+  if (x <= y) return interval(x, y, true);
+  else        return interval(y, x, true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> interval<T, Policies>::empty()
+{
+  return interval<T, Policies>(checking::empty_lower(),
+                               checking::empty_upper(), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> interval<T, Policies>::whole()
+{
+  return interval<T, Policies>(checking::neg_inf(), checking::pos_inf(), true);
+}
+
+template<class T, class Policies> inline
+const T& interval<T, Policies>::lower() const
+{
+  return low;
+}
+
+template<class T, class Policies> inline
+const T& interval<T, Policies>::upper() const
+{
+  return up;
+}
+
+/*
+ * interval/interval comparisons
+ */
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator< (const interval_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (up < r.low) return true;
+    else if (low >= r.up) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator> (const interval_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (low > r.up) return true;
+    else if (up <= r.low) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator<= (const interval_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (up <= r.low) return true;
+    else if (low > r.up) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator>= (const interval_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (low >= r.up) return true;
+    else if (up < r.low) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator== (const interval_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (up == r.low && low == r.up) return true;
+    else if (up < r.low || low > r.up) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator!= (const interval_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (up < r.low || low > r.up) return true;
+    else if (up == r.low && low == r.up) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+/*
+ * interval/number comparisons
+ */
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator< (const number_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (up < r.val) return true;
+    else if (low >= r.val) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator> (const number_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (low > r.val) return true;
+    else if (up <= r.val) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator<= (const number_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (up <= r.val) return true;
+    else if (low > r.val) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator>= (const number_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (low >= r.val) return true;
+    else if (up < r.val) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator== (const number_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (up == r.val && low == r.val) return true;
+    else if (up < r.val || low > r.val) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+template<class T, class Policies> inline
+bool interval<T, Policies>::operator!= (const number_holder& r) const
+{
+  if (!checking::is_empty(low, up)) {
+    if (up < r.val || low > r.val) return true;
+    else if (up == r.val && low == r.val) return false;
+  }
+  throw interval_lib::comparison_error();
+}
+
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_INTERVAL_HPP

test/external/boost/numeric/interval/io.hpp

@@ -0,0 +1,41 @@
+/* Boost interval/io.hpp header file
+ *
+ * This file is only meant to provide a quick
+ * implementation of the output operator. It is
+ * provided for test programs that aren't even
+ * interested in the precision of the results.
+ * A real progam should define its own operators
+ * and never include this header.
+ *
+ * Copyright 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_IO_HPP
+#define BOOST_NUMERIC_INTERVAL_IO_HPP
+
+#include <boost/numeric/interval/interval.hpp>
+#include <boost/numeric/interval/utility.hpp>
+#include <ostream>
+
+namespace boost {
+namespace numeric {
+
+template<class CharType, class CharTraits, class T, class Policies>
+std::basic_ostream<CharType, CharTraits> &operator<<
+  (std::basic_ostream<CharType, CharTraits> &stream,
+   interval<T, Policies> const &value)
+{
+  if (empty(value))
+    return stream << "[]";
+  else
+    return stream << '[' << lower(value) << ',' << upper(value) << ']';
+}
+
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_IO_HPP

test/external/boost/numeric/interval/limits.hpp

@@ -0,0 +1,51 @@
+/* Boost interval/limits.hpp template implementation file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002-2003 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_LIMITS_HPP
+#define BOOST_NUMERIC_INTERVAL_LIMITS_HPP
+
+#ifndef BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION
+
+#include <boost/config.hpp>
+#include <boost/limits.hpp>
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+
+namespace std {
+
+template<class T, class Policies>
+class numeric_limits<boost::numeric::interval<T, Policies> >
+  : public numeric_limits<T>
+{
+private:
+  typedef boost::numeric::interval<T, Policies> I;
+  typedef numeric_limits<T> bl;
+public:
+  static I min BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return I((bl::min)(), (bl::min)()); }
+  static I max BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return I((bl::max)(), (bl::max)()); }
+  static I epsilon() throw() { return I(bl::epsilon(), bl::epsilon()); }
+
+  BOOST_STATIC_CONSTANT(float_round_style, round_style = round_indeterminate);
+  BOOST_STATIC_CONSTANT(bool, is_iec559 = false);
+
+  static I infinity () throw() { return I::whole(); }
+  static I quiet_NaN() throw() { return I::empty(); }
+  static I signaling_NaN() throw()
+  { return I(bl::signaling_NaN(), bl::signaling_Nan()); }
+  static I denorm_min() throw()
+  { return I(bl::denorm_min(), bl::denorm_min()); }
+private:
+  static I round_error();    // hide this on purpose, not yet implemented
+};
+
+} // namespace std
+
+#endif
+
+#endif // BOOST_NUMERIC_INTERVAL_LIMITS_HPP

test/external/boost/numeric/interval/policies.hpp

@@ -0,0 +1,75 @@
+/* Boost interval/policies.hpp template implementation file
+ *
+ * Copyright 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_POLICIES_HPP
+#define BOOST_NUMERIC_INTERVAL_POLICIES_HPP
+
+#include <boost/numeric/interval/interval.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+/*
+ * policies class
+ */
+
+template<class Rounding, class Checking>
+struct policies
+{
+  typedef Rounding rounding;
+  typedef Checking checking;
+};
+
+/*
+ * policies switching classes
+ */
+
+template<class OldInterval, class NewRounding>
+class change_rounding
+{
+  typedef typename OldInterval::base_type T;
+  typedef typename OldInterval::traits_type p;
+  typedef typename p::checking checking;
+public:
+  typedef interval<T, policies<NewRounding, checking> > type;
+};
+
+template<class OldInterval, class NewChecking>
+class change_checking
+{
+  typedef typename OldInterval::base_type T;
+  typedef typename OldInterval::traits_type p;
+  typedef typename p::rounding rounding;
+public:
+  typedef interval<T, policies<rounding, NewChecking> > type;
+};
+
+/*
+ * Protect / unprotect: control whether the rounding mode is set/reset
+ * at each operation, rather than once and for all.
+ */
+
+template<class OldInterval>
+class unprotect
+{
+  typedef typename OldInterval::base_type T;
+  typedef typename OldInterval::traits_type p;
+  typedef typename p::rounding r;
+  typedef typename r::unprotected_rounding newRounding;
+public:
+  typedef typename change_rounding<OldInterval, newRounding>::type type;
+};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_INTERVAL_POLICIES_HPP

test/external/boost/numeric/interval/rounded_arith.hpp

@@ -0,0 +1,120 @@
+/* Boost interval/rounded_arith.hpp template implementation file
+ *
+ * Copyright 2002-2003 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_ROUNDED_ARITH_HPP
+#define BOOST_NUMERIC_INTERVAL_ROUNDED_ARITH_HPP
+
+#include <boost/numeric/interval/rounding.hpp>
+#include <boost/numeric/interval/detail/bugs.hpp>
+#include <boost/config/no_tr1/cmath.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+/*
+ * Three classes of rounding: exact, std, opp
+ * See documentation for details.
+ */
+
+template<class T, class Rounding>
+struct rounded_arith_exact: Rounding {
+  void init() { }
+  template<class U> T conv_down(U const &v) { return v; }
+  template<class U> T conv_up  (U const &v) { return v; }
+  T add_down (const T& x, const T& y) { return x + y; }
+  T add_up   (const T& x, const T& y) { return x + y; }
+  T sub_down (const T& x, const T& y) { return x - y; }
+  T sub_up   (const T& x, const T& y) { return x - y; }
+  T mul_down (const T& x, const T& y) { return x * y; }
+  T mul_up   (const T& x, const T& y) { return x * y; }
+  T div_down (const T& x, const T& y) { return x / y; }
+  T div_up   (const T& x, const T& y) { return x / y; }
+  T median   (const T& x, const T& y) { return (x + y) / 2; }
+  T sqrt_down(const T& x)
+  { BOOST_NUMERIC_INTERVAL_using_math(sqrt); return sqrt(x); }
+  T sqrt_up  (const T& x)
+  { BOOST_NUMERIC_INTERVAL_using_math(sqrt); return sqrt(x); }
+  T int_down (const T& x)
+  { BOOST_NUMERIC_INTERVAL_using_math(floor); return floor(x); }
+  T int_up   (const T& x)
+  { BOOST_NUMERIC_INTERVAL_using_math(ceil); return ceil(x); }
+};
+
+template<class T, class Rounding>
+struct rounded_arith_std: Rounding {
+# define BOOST_DN(EXPR) this->downward();   return this->force_rounding(EXPR)
+# define BOOST_NR(EXPR) this->to_nearest(); return this->force_rounding(EXPR)
+# define BOOST_UP(EXPR) this->upward();     return this->force_rounding(EXPR)
+  void init() { }
+  template<class U> T conv_down(U const &v) { BOOST_DN(v); }
+  template<class U> T conv_up  (U const &v) { BOOST_UP(v); }
+  T add_down(const T& x, const T& y) { BOOST_DN(x + y); }
+  T sub_down(const T& x, const T& y) { BOOST_DN(x - y); }
+  T mul_down(const T& x, const T& y) { BOOST_DN(x * y); }
+  T div_down(const T& x, const T& y) { BOOST_DN(x / y); }
+  T add_up  (const T& x, const T& y) { BOOST_UP(x + y); }
+  T sub_up  (const T& x, const T& y) { BOOST_UP(x - y); }
+  T mul_up  (const T& x, const T& y) { BOOST_UP(x * y); }
+  T div_up  (const T& x, const T& y) { BOOST_UP(x / y); }
+  T median(const T& x, const T& y) { BOOST_NR((x + y) / 2); }
+  T sqrt_down(const T& x)
+  { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_DN(sqrt(x)); }
+  T sqrt_up  (const T& x)
+  { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_UP(sqrt(x)); }
+  T int_down(const T& x) { this->downward(); return to_int(x); }
+  T int_up  (const T& x) { this->upward();   return to_int(x); }
+# undef BOOST_DN
+# undef BOOST_NR
+# undef BOOST_UP
+};
+  
+template<class T, class Rounding>
+struct rounded_arith_opp: Rounding {
+  void init() { this->upward(); }
+# define BOOST_DN(EXPR) \
+    this->downward(); \
+    T r = this->force_rounding(EXPR); \
+    this->upward(); \
+    return r
+# define BOOST_NR(EXPR) \
+    this->to_nearest(); \
+    T r = this->force_rounding(EXPR); \
+    this->upward(); \
+    return r
+# define BOOST_UP(EXPR) return this->force_rounding(EXPR)
+# define BOOST_UP_NEG(EXPR) return -this->force_rounding(EXPR)
+  template<class U> T conv_down(U const &v) { BOOST_UP_NEG(-v); }
+  template<class U> T conv_up  (U const &v) { BOOST_UP(v); }
+  T add_down(const T& x, const T& y) { BOOST_UP_NEG((-x) - y); }
+  T sub_down(const T& x, const T& y) { BOOST_UP_NEG(y - x); }
+  T mul_down(const T& x, const T& y) { BOOST_UP_NEG(x * (-y)); }
+  T div_down(const T& x, const T& y) { BOOST_UP_NEG(x / (-y)); }
+  T add_up  (const T& x, const T& y) { BOOST_UP(x + y); }
+  T sub_up  (const T& x, const T& y) { BOOST_UP(x - y); }
+  T mul_up  (const T& x, const T& y) { BOOST_UP(x * y); }
+  T div_up  (const T& x, const T& y) { BOOST_UP(x / y); }
+  T median  (const T& x, const T& y) { BOOST_NR((x + y) / 2); }
+  T sqrt_down(const T& x)
+  { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_DN(sqrt(x)); }
+  T sqrt_up  (const T& x)
+  { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_UP(sqrt(x)); }
+  T int_down(const T& x) { return -to_int(-x); }
+  T int_up  (const T& x) { return to_int(x); }
+# undef BOOST_DN
+# undef BOOST_NR
+# undef BOOST_UP
+# undef BOOST_UP_NEG
+};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_ROUNDED_ARITH_HPP

test/external/boost/numeric/interval/rounded_transc.hpp

@@ -0,0 +1,140 @@
+/* Boost interval/rounded_transc.hpp template implementation file
+ *
+ * Copyright 2002-2003 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_ROUNDED_TRANSC_HPP
+#define BOOST_NUMERIC_INTERVAL_ROUNDED_TRANSC_HPP
+
+#include <boost/numeric/interval/rounding.hpp>
+#include <boost/numeric/interval/detail/bugs.hpp>
+#include <boost/config/no_tr1/cmath.hpp>
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+template<class T, class Rounding>
+struct rounded_transc_exact: Rounding
+{
+# define BOOST_NUMERIC_INTERVAL_new_func(f) \
+    T f##_down(const T& x) { BOOST_NUMERIC_INTERVAL_using_math(f); return f(x); } \
+    T f##_up  (const T& x) { BOOST_NUMERIC_INTERVAL_using_math(f); return f(x); }
+  BOOST_NUMERIC_INTERVAL_new_func(exp)
+  BOOST_NUMERIC_INTERVAL_new_func(log)
+  BOOST_NUMERIC_INTERVAL_new_func(sin)
+  BOOST_NUMERIC_INTERVAL_new_func(cos)
+  BOOST_NUMERIC_INTERVAL_new_func(tan)
+  BOOST_NUMERIC_INTERVAL_new_func(asin)
+  BOOST_NUMERIC_INTERVAL_new_func(acos)
+  BOOST_NUMERIC_INTERVAL_new_func(atan)
+  BOOST_NUMERIC_INTERVAL_new_func(sinh)
+  BOOST_NUMERIC_INTERVAL_new_func(cosh)
+  BOOST_NUMERIC_INTERVAL_new_func(tanh)
+# undef BOOST_NUMERIC_INTERVAL_new_func
+# define BOOST_NUMERIC_INTERVAL_new_func(f) \
+    T f##_down(const T& x) { BOOST_NUMERIC_INTERVAL_using_ahyp(f); return f(x); } \
+    T f##_up  (const T& x) { BOOST_NUMERIC_INTERVAL_using_ahyp(f); return f(x); }
+  BOOST_NUMERIC_INTERVAL_new_func(asinh)
+  BOOST_NUMERIC_INTERVAL_new_func(acosh)
+  BOOST_NUMERIC_INTERVAL_new_func(atanh)
+# undef BOOST_NUMERIC_INTERVAL_new_func
+};
+  
+template<class T, class Rounding>
+struct rounded_transc_std: Rounding
+{
+# define BOOST_NUMERIC_INTERVAL_new_func(f) \
+    T f##_down(const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_math(f); \
+      this->downward(); return this->force_rounding(f(x)); } \
+    T f##_up  (const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_math(f); \
+      this->upward(); return this->force_rounding(f(x)); }
+  BOOST_NUMERIC_INTERVAL_new_func(exp)
+  BOOST_NUMERIC_INTERVAL_new_func(log)
+  BOOST_NUMERIC_INTERVAL_new_func(sin)
+  BOOST_NUMERIC_INTERVAL_new_func(cos)
+  BOOST_NUMERIC_INTERVAL_new_func(tan)
+  BOOST_NUMERIC_INTERVAL_new_func(asin)
+  BOOST_NUMERIC_INTERVAL_new_func(acos)
+  BOOST_NUMERIC_INTERVAL_new_func(atan)
+  BOOST_NUMERIC_INTERVAL_new_func(sinh)
+  BOOST_NUMERIC_INTERVAL_new_func(cosh)
+  BOOST_NUMERIC_INTERVAL_new_func(tanh)
+# undef BOOST_NUMERIC_INTERVAL_new_func
+# define BOOST_NUMERIC_INTERVAL_new_func(f) \
+    T f##_down(const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_ahyp(f); \
+      this->downward(); return this->force_rounding(f(x)); } \
+    T f##_up  (const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_ahyp(f); \
+      this->upward(); return this->force_rounding(f(x)); }
+  BOOST_NUMERIC_INTERVAL_new_func(asinh)
+  BOOST_NUMERIC_INTERVAL_new_func(acosh)
+  BOOST_NUMERIC_INTERVAL_new_func(atanh)
+# undef BOOST_NUMERIC_INTERVAL_new_func
+};
+
+template<class T, class Rounding>
+struct rounded_transc_opp: Rounding
+{
+# define BOOST_NUMERIC_INTERVAL_new_func(f) \
+    T f##_down(const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_math(f); \
+      this->downward(); T y = this->force_rounding(f(x)); \
+      this->upward(); return y; } \
+    T f##_up  (const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_math(f); \
+      return this->force_rounding(f(x)); }
+  BOOST_NUMERIC_INTERVAL_new_func(exp)
+  BOOST_NUMERIC_INTERVAL_new_func(log)
+  BOOST_NUMERIC_INTERVAL_new_func(cos)
+  BOOST_NUMERIC_INTERVAL_new_func(acos)
+  BOOST_NUMERIC_INTERVAL_new_func(cosh)
+# undef BOOST_NUMERIC_INTERVAL_new_func
+# define BOOST_NUMERIC_INTERVAL_new_func(f) \
+    T f##_down(const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_math(f); \
+      return -this->force_rounding(-f(x)); } \
+    T f##_up  (const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_math(f); \
+      return this->force_rounding(f(x)); }
+  BOOST_NUMERIC_INTERVAL_new_func(sin)
+  BOOST_NUMERIC_INTERVAL_new_func(tan)
+  BOOST_NUMERIC_INTERVAL_new_func(asin)
+  BOOST_NUMERIC_INTERVAL_new_func(atan)
+  BOOST_NUMERIC_INTERVAL_new_func(sinh)
+  BOOST_NUMERIC_INTERVAL_new_func(tanh)
+# undef BOOST_NUMERIC_INTERVAL_new_func
+# define BOOST_NUMERIC_INTERVAL_new_func(f) \
+    T f##_down(const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_ahyp(f); \
+      this->downward(); T y = this->force_rounding(f(x)); \
+      this->upward(); return y; } \
+    T f##_up  (const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_ahyp(f); \
+      return this->force_rounding(f(x)); }
+  BOOST_NUMERIC_INTERVAL_new_func(asinh)
+  BOOST_NUMERIC_INTERVAL_new_func(atanh)
+# undef BOOST_NUMERIC_INTERVAL_new_func
+# define BOOST_NUMERIC_INTERVAL_new_func(f) \
+    T f##_down(const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_ahyp(f); \
+      return -this->force_rounding(-f(x)); } \
+    T f##_up  (const T& x) \
+    { BOOST_NUMERIC_INTERVAL_using_ahyp(f); \
+      return this->force_rounding(f(x)); }
+  BOOST_NUMERIC_INTERVAL_new_func(acosh)
+# undef BOOST_NUMERIC_INTERVAL_new_func
+};
+  
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_ROUNDED_TRANSC_HPP

test/external/boost/numeric/interval/rounding.hpp

@@ -0,0 +1,101 @@
+/* Boost interval/rounding.hpp template implementation file
+ *
+ * Copyright 2002-2003 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_ROUNDING_HPP
+#define BOOST_NUMERIC_INTERVAL_ROUNDING_HPP
+
+namespace boost {
+namespace numeric {
+namespace interval_lib {
+
+/*
+ * Default rounding_control class (does nothing)
+ */
+
+template<class T>
+struct rounding_control
+{
+  typedef int rounding_mode;
+  static void get_rounding_mode(rounding_mode&) {}
+  static void set_rounding_mode(rounding_mode)  {}
+  static void upward()     {}
+  static void downward()   {}
+  static void to_nearest() {}
+  static const T& to_int(const T& x)         { return x; }
+  static const T& force_rounding(const T& x) { return x; }
+};
+
+/*
+ * A few rounding control classes (exact/std/opp: see documentation)
+ *   rounded_arith_* control the rounding of the arithmetic operators
+ *   rounded_transc_* control the rounding of the transcendental functions
+ */
+
+template<class T, class Rounding = rounding_control<T> >
+struct rounded_arith_exact;
+
+template<class T, class Rounding = rounding_control<T> >
+struct rounded_arith_std;
+
+template<class T, class Rounding = rounding_control<T> >
+struct rounded_arith_opp;
+
+template<class T, class Rounding>
+struct rounded_transc_dummy;
+
+template<class T, class Rounding = rounded_arith_exact<T> > 
+struct rounded_transc_exact;
+
+template<class T, class Rounding = rounded_arith_std<T> > 
+struct rounded_transc_std;
+
+template<class T, class Rounding = rounded_arith_opp<T> > 
+struct rounded_transc_opp;
+
+/*
+ * State-saving classes: allow to set and reset rounding control
+ */
+
+namespace detail {
+
+template<class Rounding>
+struct save_state_unprotected: Rounding
+{
+  typedef save_state_unprotected<Rounding> unprotected_rounding;
+};
+
+} // namespace detail
+
+template<class Rounding>
+struct save_state: Rounding
+{
+  typename Rounding::rounding_mode mode;
+  save_state() {
+    this->get_rounding_mode(mode);
+    this->init();
+  }
+  ~save_state() { this->set_rounding_mode(mode); }
+  typedef detail::save_state_unprotected<Rounding> unprotected_rounding;
+};
+  
+template<class Rounding>
+struct save_state_nothing: Rounding
+{
+  typedef save_state_nothing<Rounding> unprotected_rounding;
+};
+  
+template<class T>
+struct rounded_math: save_state_nothing<rounded_arith_exact<T> >
+{};
+
+} // namespace interval_lib
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_ROUNDING_HPP

test/external/boost/numeric/interval/transc.hpp

@@ -0,0 +1,232 @@
+/* Boost interval/transc.hpp template implementation file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_TRANSC_HPP
+#define BOOST_NUMERIC_INTERVAL_TRANSC_HPP
+
+#include <boost/config.hpp>
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+#include <boost/numeric/interval/detail/bugs.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+#include <boost/numeric/interval/rounding.hpp>
+#include <boost/numeric/interval/constants.hpp>
+#include <boost/numeric/interval/arith.hpp>
+#include <boost/numeric/interval/arith2.hpp>
+#include <algorithm>
+
+namespace boost {
+namespace numeric {
+
+template<class T, class Policies> inline
+interval<T, Policies> exp(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x))
+    return I::empty();
+  typename Policies::rounding rnd;
+  return I(rnd.exp_down(x.lower()), rnd.exp_up(x.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> log(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x) ||
+      !interval_lib::user::is_pos(x.upper()))
+    return I::empty();
+  typename Policies::rounding rnd;
+  typedef typename Policies::checking checking;
+  T l = !interval_lib::user::is_pos(x.lower())
+             ? checking::neg_inf() : rnd.log_down(x.lower());
+  return I(l, rnd.log_up(x.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> cos(const interval<T, Policies>& x)
+{
+  if (interval_lib::detail::test_input(x))
+    return interval<T, Policies>::empty();
+  typename Policies::rounding rnd;
+  typedef interval<T, Policies> I;
+  typedef typename interval_lib::unprotect<I>::type R;
+
+  // get lower bound within [0, pi]
+  const R pi2 = interval_lib::pi_twice<R>();
+  R tmp = fmod((const R&)x, pi2);
+  if (width(tmp) >= pi2.lower())
+    return I(static_cast<T>(-1), static_cast<T>(1), true); // we are covering a full period
+  if (tmp.lower() >= interval_lib::constants::pi_upper<T>())
+    return -cos(tmp - interval_lib::pi<R>());
+  T l = tmp.lower();
+  T u = tmp.upper();
+
+  BOOST_USING_STD_MIN();
+  // separate into monotone subintervals
+  if (u <= interval_lib::constants::pi_lower<T>())
+    return I(rnd.cos_down(u), rnd.cos_up(l), true);
+  else if (u <= pi2.lower())
+    return I(static_cast<T>(-1), rnd.cos_up(min BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.sub_down(pi2.lower(), u), l)), true);
+  else
+    return I(static_cast<T>(-1), static_cast<T>(1), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> sin(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x))
+    return I::empty();
+  typename Policies::rounding rnd;
+  typedef typename interval_lib::unprotect<I>::type R;
+  I r = cos((const R&)x - interval_lib::pi_half<R>());
+  (void)&rnd;
+  return r;
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> tan(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x))
+    return I::empty();
+  typename Policies::rounding rnd;
+  typedef typename interval_lib::unprotect<I>::type R;
+
+  // get lower bound within [-pi/2, pi/2]
+  const R pi = interval_lib::pi<R>();
+  R tmp = fmod((const R&)x, pi);
+  const T pi_half_d = interval_lib::constants::pi_half_lower<T>();
+  if (tmp.lower() >= pi_half_d)
+    tmp -= pi;
+  if (tmp.lower() <= -pi_half_d || tmp.upper() >= pi_half_d)
+    return I::whole();
+  return I(rnd.tan_down(tmp.lower()), rnd.tan_up(tmp.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> asin(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x)
+     || x.upper() < static_cast<T>(-1) || x.lower() > static_cast<T>(1))
+    return I::empty();
+  typename Policies::rounding rnd;
+  T l = (x.lower() <= static_cast<T>(-1))
+             ? -interval_lib::constants::pi_half_upper<T>()
+             : rnd.asin_down(x.lower());
+  T u = (x.upper() >= static_cast<T>(1) )
+             ?  interval_lib::constants::pi_half_upper<T>()
+             : rnd.asin_up  (x.upper());
+  return I(l, u, true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> acos(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x)
+     || x.upper() < static_cast<T>(-1) || x.lower() > static_cast<T>(1))
+    return I::empty();
+  typename Policies::rounding rnd;
+  T l = (x.upper() >= static_cast<T>(1) )
+          ? static_cast<T>(0)
+          : rnd.acos_down(x.upper());
+  T u = (x.lower() <= static_cast<T>(-1))
+          ? interval_lib::constants::pi_upper<T>()
+          : rnd.acos_up  (x.lower());
+  return I(l, u, true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> atan(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x))
+    return I::empty();
+  typename Policies::rounding rnd;
+  return I(rnd.atan_down(x.lower()), rnd.atan_up(x.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> sinh(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x))
+    return I::empty();
+  typename Policies::rounding rnd;
+  return I(rnd.sinh_down(x.lower()), rnd.sinh_up(x.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> cosh(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x))
+    return I::empty();
+  typename Policies::rounding rnd;
+  if (interval_lib::user::is_neg(x.upper()))
+    return I(rnd.cosh_down(x.upper()), rnd.cosh_up(x.lower()), true);
+  else if (!interval_lib::user::is_neg(x.lower()))
+    return I(rnd.cosh_down(x.lower()), rnd.cosh_up(x.upper()), true);
+  else
+    return I(static_cast<T>(1), rnd.cosh_up(-x.lower() > x.upper() ? x.lower() : x.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> tanh(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x))
+    return I::empty();
+  typename Policies::rounding rnd;
+  return I(rnd.tanh_down(x.lower()), rnd.tanh_up(x.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> asinh(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x))
+    return I::empty();
+  typename Policies::rounding rnd;
+  return I(rnd.asinh_down(x.lower()), rnd.asinh_up(x.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> acosh(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x) || x.upper() < static_cast<T>(1))
+    return I::empty();
+  typename Policies::rounding rnd;
+  T l = x.lower() <= static_cast<T>(1) ? static_cast<T>(0) : rnd.acosh_down(x.lower());
+  return I(l, rnd.acosh_up(x.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> atanh(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x)
+      || x.upper() < static_cast<T>(-1) || x.lower() > static_cast<T>(1))
+    return I::empty();
+  typename Policies::rounding rnd;
+  typedef typename Policies::checking checking;
+  T l = (x.lower() <= static_cast<T>(-1))
+             ? checking::neg_inf() : rnd.atanh_down(x.lower());
+  T u = (x.upper() >= static_cast<T>(1) )
+             ? checking::pos_inf() : rnd.atanh_up  (x.upper());
+  return I(l, u, true);
+}
+
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_TRANSC_HPP

test/external/boost/numeric/interval/utility.hpp

@@ -0,0 +1,337 @@
+/* Boost interval/utility.hpp template implementation file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002-2003 Herv<72> Br<42>nnimann, Guillaume Melquiond, Sylvain Pion
+ *
+ * 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)
+ */
+
+#ifndef BOOST_NUMERIC_INTERVAL_UTILITY_HPP
+#define BOOST_NUMERIC_INTERVAL_UTILITY_HPP
+
+#include <boost/config.hpp>
+#include <boost/numeric/interval/detail/interval_prototype.hpp>
+#include <boost/numeric/interval/detail/test_input.hpp>
+#include <boost/numeric/interval/detail/bugs.hpp>
+#include <algorithm>
+#include <utility>
+
+/*
+ * Implementation of simple functions
+ */
+
+namespace boost {
+namespace numeric {
+
+/*
+ * Utility Functions
+ */
+
+template<class T, class Policies> inline
+const T& lower(const interval<T, Policies>& x)
+{
+  return x.lower();
+}
+
+template<class T, class Policies> inline
+const T& upper(const interval<T, Policies>& x)
+{
+  return x.upper();
+}
+
+template<class T, class Policies> inline
+T checked_lower(const interval<T, Policies>& x)
+{
+  if (empty(x)) {
+    typedef typename Policies::checking checking;
+    return checking::nan();
+  }
+  return x.lower();
+}
+
+template<class T, class Policies> inline
+T checked_upper(const interval<T, Policies>& x)
+{
+  if (empty(x)) {
+    typedef typename Policies::checking checking;
+    return checking::nan();
+  }
+  return x.upper();
+}
+
+template<class T, class Policies> inline
+T width(const interval<T, Policies>& x)
+{
+  if (interval_lib::detail::test_input(x)) return static_cast<T>(0);
+  typename Policies::rounding rnd;
+  return rnd.sub_up(x.upper(), x.lower());
+}
+
+template<class T, class Policies> inline
+T median(const interval<T, Policies>& x)
+{
+  if (interval_lib::detail::test_input(x)) {
+    typedef typename Policies::checking checking;
+    return checking::nan();
+  }
+  typename Policies::rounding rnd;
+  return rnd.median(x.lower(), x.upper());
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> widen(const interval<T, Policies>& x, const T& v)
+{
+  if (interval_lib::detail::test_input(x))
+    return interval<T, Policies>::empty();
+  typename Policies::rounding rnd;
+  return interval<T, Policies>(rnd.sub_down(x.lower(), v),
+                               rnd.add_up  (x.upper(), v), true);
+}
+
+/*
+ * Set-like operations
+ */
+
+template<class T, class Policies> inline
+bool empty(const interval<T, Policies>& x)
+{
+  return interval_lib::detail::test_input(x);
+}
+
+template<class T, class Policies> inline
+bool zero_in(const interval<T, Policies>& x)
+{
+  if (interval_lib::detail::test_input(x)) return false;
+  return (!interval_lib::user::is_pos(x.lower())) &&
+         (!interval_lib::user::is_neg(x.upper()));
+}
+
+template<class T, class Policies> inline
+bool in_zero(const interval<T, Policies>& x) // DEPRECATED
+{
+  return zero_in<T, Policies>(x);
+}
+
+template<class T, class Policies> inline
+bool in(const T& x, const interval<T, Policies>& y)
+{
+  if (interval_lib::detail::test_input(x, y)) return false;
+  return y.lower() <= x && x <= y.upper();
+}
+
+template<class T, class Policies> inline
+bool subset(const interval<T, Policies>& x,
+            const interval<T, Policies>& y)
+{
+  if (empty(x)) return true;
+  return !empty(y) && y.lower() <= x.lower() && x.upper() <= y.upper();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool proper_subset(const interval<T, Policies1>& x,
+                   const interval<T, Policies2>& y)
+{
+  if (empty(y)) return false;
+  if (empty(x)) return true;
+  return y.lower() <= x.lower() && x.upper() <= y.upper() &&
+         (y.lower() != x.lower() || x.upper() != y.upper());
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool overlap(const interval<T, Policies1>& x,
+             const interval<T, Policies2>& y)
+{
+  if (interval_lib::detail::test_input(x, y)) return false;
+  return (x.lower() <= y.lower() && y.lower() <= x.upper()) ||
+         (y.lower() <= x.lower() && x.lower() <= y.upper());
+}
+
+template<class T, class Policies> inline
+bool singleton(const interval<T, Policies>& x)
+{
+ return !empty(x) && x.lower() == x.upper();
+}
+
+template<class T, class Policies1, class Policies2> inline
+bool equal(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
+{
+  if (empty(x)) return empty(y);
+  return !empty(y) && x.lower() == y.lower() && x.upper() == y.upper();
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> intersect(const interval<T, Policies>& x,
+                                const interval<T, Policies>& y)
+{
+  BOOST_USING_STD_MIN();
+  BOOST_USING_STD_MAX();
+  if (interval_lib::detail::test_input(x, y))
+    return interval<T, Policies>::empty();
+  const T& l = max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower());
+  const T& u = min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper());
+  if (l <= u) return interval<T, Policies>(l, u, true);
+  else        return interval<T, Policies>::empty();
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> hull(const interval<T, Policies>& x,
+                           const interval<T, Policies>& y)
+{
+  BOOST_USING_STD_MIN();
+  BOOST_USING_STD_MAX();
+  bool bad_x = interval_lib::detail::test_input(x);
+  bool bad_y = interval_lib::detail::test_input(y);
+  if (bad_x)
+    if (bad_y) return interval<T, Policies>::empty();
+    else       return y;
+  else
+    if (bad_y) return x;
+  return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()),
+                               max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> hull(const interval<T, Policies>& x, const T& y)
+{
+  BOOST_USING_STD_MIN();
+  BOOST_USING_STD_MAX();
+  bool bad_x = interval_lib::detail::test_input(x);
+  bool bad_y = interval_lib::detail::test_input<T, Policies>(y);
+  if (bad_y)
+    if (bad_x) return interval<T, Policies>::empty();
+    else       return x;
+  else
+    if (bad_x) return interval<T, Policies>(y, y, true);
+  return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y),
+                               max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> hull(const T& x, const interval<T, Policies>& y)
+{
+  BOOST_USING_STD_MIN();
+  BOOST_USING_STD_MAX();
+  bool bad_x = interval_lib::detail::test_input<T, Policies>(x);
+  bool bad_y = interval_lib::detail::test_input(y);
+  if (bad_x)
+    if (bad_y) return interval<T, Policies>::empty();
+    else       return y;
+  else
+    if (bad_y) return interval<T, Policies>(x, x, true);
+  return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()),
+                               max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true);
+}
+
+template<class T> inline
+interval<T> hull(const T& x, const T& y)
+{
+  return interval<T>::hull(x, y);
+}
+
+template<class T, class Policies> inline
+std::pair<interval<T, Policies>, interval<T, Policies> >
+bisect(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x))
+    return std::pair<I,I>(I::empty(), I::empty());
+  const T m = median(x);
+  return std::pair<I,I>(I(x.lower(), m, true), I(m, x.upper(), true));
+}
+
+/*
+ * Elementary functions
+ */
+
+template<class T, class Policies> inline
+T norm(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x)) {
+    typedef typename Policies::checking checking;
+    return checking::nan();
+  }
+  BOOST_USING_STD_MAX();
+  return max BOOST_PREVENT_MACRO_SUBSTITUTION(static_cast<T>(-x.lower()), x.upper());
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> abs(const interval<T, Policies>& x)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x))
+    return I::empty();
+  if (!interval_lib::user::is_neg(x.lower())) return x;
+  if (!interval_lib::user::is_pos(x.upper())) return -x;
+  BOOST_USING_STD_MAX();
+  return I(static_cast<T>(0), max BOOST_PREVENT_MACRO_SUBSTITUTION(static_cast<T>(-x.lower()), x.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x,
+                                                            const interval<T, Policies>& y)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x, y))
+    return I::empty();
+  BOOST_USING_STD_MAX();
+  return I(max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()), max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, const T& y)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x, y))
+    return I::empty();
+  BOOST_USING_STD_MAX();
+  return I(max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y), max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const T& x, const interval<T, Policies>& y)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x, y))
+    return I::empty();
+  BOOST_USING_STD_MAX();
+  return I(max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()), max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x,
+                                                            const interval<T, Policies>& y)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x, y))
+    return I::empty();
+  BOOST_USING_STD_MIN();
+  return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()), min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, const T& y)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x, y))
+    return I::empty();
+  BOOST_USING_STD_MIN();
+  return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y), min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true);
+}
+
+template<class T, class Policies> inline
+interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const T& x, const interval<T, Policies>& y)
+{
+  typedef interval<T, Policies> I;
+  if (interval_lib::detail::test_input(x, y))
+    return I::empty();
+  BOOST_USING_STD_MIN();
+  return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()), min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true);
+}
+
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_INTERVAL_UTILITY_HPP