comparison DEPENDENCIES/generic/include/boost/numeric/interval/transc.hpp @ 16:2665513ce2d3

Add boost headers

+/* Boost interval/transc.hpp template implementation file
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002 Hervé Brönnimann, 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