Added boost header

test/external/boost/math/special_functions/log1p.hpp

@@ -0,0 +1,471 @@
+//  (C) Copyright John Maddock 2005-2006.
+//  Use, modification and distribution are subject to 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_MATH_LOG1P_INCLUDED
+#define BOOST_MATH_LOG1P_INCLUDED
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/config/no_tr1/cmath.hpp>
+#include <math.h> // platform's ::log1p
+#include <boost/limits.hpp>
+#include <boost/math/tools/config.hpp>
+#include <boost/math/tools/series.hpp>
+#include <boost/math/tools/rational.hpp>
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/math/special_functions/math_fwd.hpp>
+
+#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
+#  include <boost/static_assert.hpp>
+#else
+#  include <boost/assert.hpp>
+#endif
+
+namespace boost{ namespace math{
+
+namespace detail
+{
+  // Functor log1p_series returns the next term in the Taylor series
+  //   pow(-1, k-1)*pow(x, k) / k
+  // each time that operator() is invoked.
+  //
+  template <class T>
+  struct log1p_series
+  {
+     typedef T result_type;
+
+     log1p_series(T x)
+        : k(0), m_mult(-x), m_prod(-1){}
+
+     T operator()()
+     {
+        m_prod *= m_mult;
+        return m_prod / ++k;
+     }
+
+     int count()const
+     {
+        return k;
+     }
+
+  private:
+     int k;
+     const T m_mult;
+     T m_prod;
+     log1p_series(const log1p_series&);
+     log1p_series& operator=(const log1p_series&);
+  };
+
+// Algorithm log1p is part of C99, but is not yet provided by many compilers.
+//
+// This version uses a Taylor series expansion for 0.5 > x > epsilon, which may
+// require up to std::numeric_limits<T>::digits+1 terms to be calculated. 
+// It would be much more efficient to use the equivalence:
+//   log(1+x) == (log(1+x) * x) / ((1-x) - 1)
+// Unfortunately many optimizing compilers make such a mess of this, that 
+// it performs no better than log(1+x): which is to say not very well at all.
+//
+template <class T, class Policy>
+T log1p_imp(T const & x, const Policy& pol, const mpl::int_<0>&)
+{ // The function returns the natural logarithm of 1 + x.
+   typedef typename tools::promote_args<T>::type result_type;
+   BOOST_MATH_STD_USING
+
+   static const char* function = "boost::math::log1p<%1%>(%1%)";
+
+   if(x < -1)
+      return policies::raise_domain_error<T>(
+         function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
+   if(x == -1)
+      return -policies::raise_overflow_error<T>(
+         function, 0, pol);
+
+   result_type a = abs(result_type(x));
+   if(a > result_type(0.5f))
+      return log(1 + result_type(x));
+   // Note that without numeric_limits specialisation support, 
+   // epsilon just returns zero, and our "optimisation" will always fail:
+   if(a < tools::epsilon<result_type>())
+      return x;
+   detail::log1p_series<result_type> s(x);
+   boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) && !BOOST_WORKAROUND(__EDG_VERSION__, <= 245)
+   result_type result = tools::sum_series(s, policies::get_epsilon<result_type, Policy>(), max_iter);
+#else
+   result_type zero = 0;
+   result_type result = tools::sum_series(s, policies::get_epsilon<result_type, Policy>(), max_iter, zero);
+#endif
+   policies::check_series_iterations<T>(function, max_iter, pol);
+   return result;
+}
+
+template <class T, class Policy>
+T log1p_imp(T const& x, const Policy& pol, const mpl::int_<53>&)
+{ // The function returns the natural logarithm of 1 + x.
+   BOOST_MATH_STD_USING
+
+   static const char* function = "boost::math::log1p<%1%>(%1%)";
+
+   if(x < -1)
+      return policies::raise_domain_error<T>(
+         function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
+   if(x == -1)
+      return -policies::raise_overflow_error<T>(
+         function, 0, pol);
+
+   T a = fabs(x);
+   if(a > 0.5f)
+      return log(1 + x);
+   // Note that without numeric_limits specialisation support, 
+   // epsilon just returns zero, and our "optimisation" will always fail:
+   if(a < tools::epsilon<T>())
+      return x;
+
+   // Maximum Deviation Found:                     1.846e-017
+   // Expected Error Term:                         1.843e-017
+   // Maximum Relative Change in Control Points:   8.138e-004
+   // Max Error found at double precision =        3.250766e-016
+   static const T P[] = {    
+       0.15141069795941984e-16L,
+       0.35495104378055055e-15L,
+       0.33333333333332835L,
+       0.99249063543365859L,
+       1.1143969784156509L,
+       0.58052937949269651L,
+       0.13703234928513215L,
+       0.011294864812099712L
+     };
+   static const T Q[] = {    
+       1L,
+       3.7274719063011499L,
+       5.5387948649720334L,
+       4.159201143419005L,
+       1.6423855110312755L,
+       0.31706251443180914L,
+       0.022665554431410243L,
+       -0.29252538135177773e-5L
+     };
+
+   T result = 1 - x / 2 + tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);
+   result *= x;
+
+   return result;
+}
+
+template <class T, class Policy>
+T log1p_imp(T const& x, const Policy& pol, const mpl::int_<64>&)
+{ // The function returns the natural logarithm of 1 + x.
+   BOOST_MATH_STD_USING
+
+   static const char* function = "boost::math::log1p<%1%>(%1%)";
+
+   if(x < -1)
+      return policies::raise_domain_error<T>(
+         function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
+   if(x == -1)
+      return -policies::raise_overflow_error<T>(
+         function, 0, pol);
+
+   T a = fabs(x);
+   if(a > 0.5f)
+      return log(1 + x);
+   // Note that without numeric_limits specialisation support, 
+   // epsilon just returns zero, and our "optimisation" will always fail:
+   if(a < tools::epsilon<T>())
+      return x;
+
+   // Maximum Deviation Found:                     8.089e-20
+   // Expected Error Term:                         8.088e-20
+   // Maximum Relative Change in Control Points:   9.648e-05
+   // Max Error found at long double precision =   2.242324e-19
+   static const T P[] = {    
+      -0.807533446680736736712e-19L,
+      -0.490881544804798926426e-18L,
+      0.333333333333333373941L,
+      1.17141290782087994162L,
+      1.62790522814926264694L,
+      1.13156411870766876113L,
+      0.408087379932853785336L,
+      0.0706537026422828914622L,
+      0.00441709903782239229447L
+   };
+   static const T Q[] = {    
+      1L,
+      4.26423872346263928361L,
+      7.48189472704477708962L,
+      6.94757016732904280913L,
+      3.6493508622280767304L,
+      1.06884863623790638317L,
+      0.158292216998514145947L,
+      0.00885295524069924328658L,
+      -0.560026216133415663808e-6L
+   };
+
+   T result = 1 - x / 2 + tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);
+   result *= x;
+
+   return result;
+}
+
+template <class T, class Policy>
+T log1p_imp(T const& x, const Policy& pol, const mpl::int_<24>&)
+{ // The function returns the natural logarithm of 1 + x.
+   BOOST_MATH_STD_USING
+
+   static const char* function = "boost::math::log1p<%1%>(%1%)";
+
+   if(x < -1)
+      return policies::raise_domain_error<T>(
+         function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
+   if(x == -1)
+      return -policies::raise_overflow_error<T>(
+         function, 0, pol);
+
+   T a = fabs(x);
+   if(a > 0.5f)
+      return log(1 + x);
+   // Note that without numeric_limits specialisation support, 
+   // epsilon just returns zero, and our "optimisation" will always fail:
+   if(a < tools::epsilon<T>())
+      return x;
+
+   // Maximum Deviation Found:                     6.910e-08
+   // Expected Error Term:                         6.910e-08
+   // Maximum Relative Change in Control Points:   2.509e-04
+   // Max Error found at double precision =        6.910422e-08
+   // Max Error found at float precision =         8.357242e-08
+   static const T P[] = {    
+      -0.671192866803148236519e-7L,
+      0.119670999140731844725e-6L,
+      0.333339469182083148598L,
+      0.237827183019664122066L
+   };
+   static const T Q[] = {    
+      1L,
+      1.46348272586988539733L,
+      0.497859871350117338894L,
+      -0.00471666268910169651936L
+   };
+
+   T result = 1 - x / 2 + tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);
+   result *= x;
+
+   return result;
+}
+
+} // namespace detail
+
+template <class T, class Policy>
+inline typename tools::promote_args<T>::type log1p(T x, const Policy&)
+{ 
+   typedef typename tools::promote_args<T>::type result_type;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   typedef typename policies::precision<result_type, Policy>::type precision_type;
+   typedef typename policies::normalise<
+      Policy, 
+      policies::promote_float<false>, 
+      policies::promote_double<false>, 
+      policies::discrete_quantile<>,
+      policies::assert_undefined<> >::type forwarding_policy;
+
+   typedef typename mpl::if_<
+      mpl::less_equal<precision_type, mpl::int_<0> >,
+      mpl::int_<0>,
+      typename mpl::if_<
+         mpl::less_equal<precision_type, mpl::int_<53> >,
+         mpl::int_<53>,  // double
+         typename mpl::if_<
+            mpl::less_equal<precision_type, mpl::int_<64> >,
+            mpl::int_<64>, // 80-bit long double
+            mpl::int_<0> // too many bits, use generic version.
+         >::type
+      >::type
+   >::type tag_type;
+   return policies::checked_narrowing_cast<result_type, forwarding_policy>(
+      detail::log1p_imp(static_cast<value_type>(x), forwarding_policy(), tag_type()), "boost::math::log1p<%1%>(%1%)");
+}
+
+#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564))
+// These overloads work around a type deduction bug:
+inline float log1p(float z)
+{
+   return log1p<float>(z);
+}
+inline double log1p(double z)
+{
+   return log1p<double>(z);
+}
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+inline long double log1p(long double z)
+{
+   return log1p<long double>(z);
+}
+#endif
+#endif
+
+#ifdef log1p
+#  ifndef BOOST_HAS_LOG1P
+#     define BOOST_HAS_LOG1P
+#  endif
+#  undef log1p
+#endif
+
+#if defined(BOOST_HAS_LOG1P) && !(defined(__osf__) && defined(__DECCXX_VER))
+#  ifdef BOOST_MATH_USE_C99
+template <class Policy>
+inline float log1p(float x, const Policy& pol)
+{ 
+   if(x < -1)
+      return policies::raise_domain_error<float>(
+         "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
+   if(x == -1)
+      return -policies::raise_overflow_error<float>(
+         "log1p<%1%>(%1%)", 0, pol);
+   return ::log1pf(x); 
+}
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+template <class Policy>
+inline long double log1p(long double x, const Policy& pol)
+{ 
+   if(x < -1)
+      return policies::raise_domain_error<long double>(
+         "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
+   if(x == -1)
+      return -policies::raise_overflow_error<long double>(
+         "log1p<%1%>(%1%)", 0, pol);
+   return ::log1pl(x); 
+}
+#endif
+#else
+template <class Policy>
+inline float log1p(float x, const Policy& pol)
+{ 
+   if(x < -1)
+      return policies::raise_domain_error<float>(
+         "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
+   if(x == -1)
+      return -policies::raise_overflow_error<float>(
+         "log1p<%1%>(%1%)", 0, pol);
+   return ::log1p(x); 
+}
+#endif
+template <class Policy>
+inline double log1p(double x, const Policy& pol)
+{ 
+   if(x < -1)
+      return policies::raise_domain_error<double>(
+         "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
+   if(x == -1)
+      return -policies::raise_overflow_error<double>(
+         "log1p<%1%>(%1%)", 0, pol);
+   return ::log1p(x); 
+}
+#elif defined(_MSC_VER) && (BOOST_MSVC >= 1400)
+//
+// You should only enable this branch if you are absolutely sure
+// that your compilers optimizer won't mess this code up!!
+// Currently tested with VC8 and Intel 9.1.
+//
+template <class Policy>
+inline double log1p(double x, const Policy& pol)
+{
+   if(x < -1)
+      return policies::raise_domain_error<double>(
+         "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
+   if(x == -1)
+      return -policies::raise_overflow_error<double>(
+         "log1p<%1%>(%1%)", 0, pol);
+   double u = 1+x;
+   if(u == 1.0) 
+      return x; 
+   else
+      return ::log(u)*(x/(u-1.0));
+}
+template <class Policy>
+inline float log1p(float x, const Policy& pol)
+{
+   return static_cast<float>(boost::math::log1p(static_cast<double>(x), pol));
+}
+#ifndef _WIN32_WCE
+//
+// For some reason this fails to compile under WinCE...
+// Needs more investigation.
+//
+template <class Policy>
+inline long double log1p(long double x, const Policy& pol)
+{
+   if(x < -1)
+      return policies::raise_domain_error<long double>(
+         "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
+   if(x == -1)
+      return -policies::raise_overflow_error<long double>(
+         "log1p<%1%>(%1%)", 0, pol);
+   long double u = 1+x;
+   if(u == 1.0) 
+      return x; 
+   else
+      return ::logl(u)*(x/(u-1.0));
+}
+#endif
+#endif
+
+template <class T>
+inline typename tools::promote_args<T>::type log1p(T x)
+{
+   return boost::math::log1p(x, policies::policy<>());
+}
+//
+// Compute log(1+x)-x:
+//
+template <class T, class Policy>
+inline typename tools::promote_args<T>::type 
+   log1pmx(T x, const Policy& pol)
+{
+   typedef typename tools::promote_args<T>::type result_type;
+   BOOST_MATH_STD_USING
+   static const char* function = "boost::math::log1pmx<%1%>(%1%)";
+
+   if(x < -1)
+      return policies::raise_domain_error<T>(
+         function, "log1pmx(x) requires x > -1, but got x = %1%.", x, pol);
+   if(x == -1)
+      return -policies::raise_overflow_error<T>(
+         function, 0, pol);
+
+   result_type a = abs(result_type(x));
+   if(a > result_type(0.95f))
+      return log(1 + result_type(x)) - result_type(x);
+   // Note that without numeric_limits specialisation support, 
+   // epsilon just returns zero, and our "optimisation" will always fail:
+   if(a < tools::epsilon<result_type>())
+      return -x * x / 2;
+   boost::math::detail::log1p_series<T> s(x);
+   s();
+   boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
+#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+   T zero = 0;
+   T result = boost::math::tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, zero);
+#else
+   T result = boost::math::tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter);
+#endif
+   policies::check_series_iterations<T>(function, max_iter, pol);
+   return result;
+}
+
+template <class T>
+inline typename tools::promote_args<T>::type log1pmx(T x)
+{
+   return log1pmx(x, policies::policy<>());
+}
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_LOG1P_INCLUDED
+
+
+