diff DEPENDENCIES/generic/include/boost/numeric/interval/arith2.hpp @ 16:2665513ce2d3

Add boost headers
author Chris Cannam
date Tue, 05 Aug 2014 11:11:38 +0100
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/DEPENDENCIES/generic/include/boost/numeric/interval/arith2.hpp	Tue Aug 05 11:11:38 2014 +0100
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+/* 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 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_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