comparison DEPENDENCIES/generic/include/boost/math/special_functions/next.hpp @ 16:2665513ce2d3

Add boost headers

+//  (C) Copyright John Maddock 2008.
+//  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_SPECIAL_NEXT_HPP
+#define BOOST_MATH_SPECIAL_NEXT_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/math/special_functions/fpclassify.hpp>
+#include <boost/math/special_functions/sign.hpp>
+#include <boost/math/special_functions/trunc.hpp>
+
+#ifdef BOOST_MSVC
+#include <float.h>
+#endif
+
+namespace boost{ namespace math{
+
+namespace detail{
+
+template <class T>
+inline T get_smallest_value(mpl::true_ const&)
+{
+   //
+   // numeric_limits lies about denorms being present - particularly
+   // when this can be turned on or off at runtime, as is the case
+   // when using the SSE2 registers in DAZ or FTZ mode.
+   //
+   static const T m = std::numeric_limits<T>::denorm_min();
+   return ((tools::min_value<T>() - m) == tools::min_value<T>()) ? tools::min_value<T>() : m;
+}
+
+template <class T>
+inline T get_smallest_value(mpl::false_ const&)
+{
+   return tools::min_value<T>();
+}
+
+template <class T>
+inline T get_smallest_value()
+{
+#if defined(BOOST_MSVC) && (BOOST_MSVC <= 1310)
+   return get_smallest_value<T>(mpl::bool_<std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::has_denorm == 1)>());
+#else
+   return get_smallest_value<T>(mpl::bool_<std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::has_denorm == std::denorm_present)>());
+#endif
+}
+
+//
+// Returns the smallest value that won't generate denorms when
+// we calculate the value of the least-significant-bit:
+//
+template <class T>
+T get_min_shift_value();
+
+template <class T>
+struct min_shift_initializer
+{
+   struct init
+   {
+      init()
+      {
+         do_init();
+      }
+      static void do_init()
+      {
+         get_min_shift_value<T>();
+      }
+      void force_instantiate()const{}
+   };
+   static const init initializer;
+   static void force_instantiate()
+   {
+      initializer.force_instantiate();
+   }
+};
+
+template <class T>
+const typename min_shift_initializer<T>::init min_shift_initializer<T>::initializer;
+
+
+template <class T>
+inline T get_min_shift_value()
+{
+   BOOST_MATH_STD_USING
+   static const T val = ldexp(tools::min_value<T>(), tools::digits<T>() + 1);
+   min_shift_initializer<T>::force_instantiate();
+
+   return val;
+}
+
+template <class T, class Policy>
+T float_next_imp(const T& val, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   int expon;
+   static const char* function = "float_next<%1%>(%1%)";
+
+   int fpclass = (boost::math::fpclassify)(val);
+
+   if((fpclass == FP_NAN) || (fpclass == FP_INFINITE))
+   {
+      if(val < 0)
+         return -tools::max_value<T>();
+      return policies::raise_domain_error<T>(
+         function,
+         "Argument must be finite, but got %1%", val, pol);
+   }
+
+   if(val >= tools::max_value<T>())
+      return policies::raise_overflow_error<T>(function, 0, pol);
+
+   if(val == 0)
+      return detail::get_smallest_value<T>();
+
+   if((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO) && (fabs(val) < detail::get_min_shift_value<T>()) && (val != -tools::min_value<T>()))
+   {
+      //
+      // Special case: if the value of the least significant bit is a denorm, and the result
+      // would not be a denorm, then shift the input, increment, and shift back.
+      // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set.
+      //
+      return ldexp(float_next(T(ldexp(val, 2 * tools::digits<T>())), pol), -2 * tools::digits<T>());
+   }
+
+   if(-0.5f == frexp(val, &expon))
+      --expon; // reduce exponent when val is a power of two, and negative.
+   T diff = ldexp(T(1), expon - tools::digits<T>());
+   if(diff == 0)
+      diff = detail::get_smallest_value<T>();
+   return val + diff;
+}
+
+}
+
+template <class T, class Policy>
+inline typename tools::promote_args<T>::type float_next(const T& val, const Policy& pol)
+{
+   typedef typename tools::promote_args<T>::type result_type;
+   return detail::float_next_imp(static_cast<result_type>(val), pol);
+}
+
+#if 0 //def BOOST_MSVC
+//
+// We used to use ::_nextafter here, but doing so fails when using
+// the SSE2 registers if the FTZ or DAZ flags are set, so use our own
+// - albeit slower - code instead as at least that gives the correct answer.
+//
+template <class Policy>
+inline double float_next(const double& val, const Policy& pol)
+{
+   static const char* function = "float_next<%1%>(%1%)";
+
+   if(!(boost::math::isfinite)(val) && (val > 0))
+      return policies::raise_domain_error<double>(
+         function,
+         "Argument must be finite, but got %1%", val, pol);
+
+   if(val >= tools::max_value<double>())
+      return policies::raise_overflow_error<double>(function, 0, pol);
+
+   return ::_nextafter(val, tools::max_value<double>());
+}
+#endif
+
+template <class T>
+inline typename tools::promote_args<T>::type float_next(const T& val)
+{
+   return float_next(val, policies::policy<>());
+}
+
+namespace detail{
+
+template <class T, class Policy>
+T float_prior_imp(const T& val, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   int expon;
+   static const char* function = "float_prior<%1%>(%1%)";
+
+   int fpclass = (boost::math::fpclassify)(val);
+
+   if((fpclass == FP_NAN) || (fpclass == FP_INFINITE))
+   {
+      if(val > 0)
+         return tools::max_value<T>();
+      return policies::raise_domain_error<T>(
+         function,
+         "Argument must be finite, but got %1%", val, pol);
+   }
+
+   if(val <= -tools::max_value<T>())
+      return -policies::raise_overflow_error<T>(function, 0, pol);
+
+   if(val == 0)
+      return -detail::get_smallest_value<T>();
+
+   if((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO) && (fabs(val) < detail::get_min_shift_value<T>()) && (val != tools::min_value<T>()))
+   {
+      //
+      // Special case: if the value of the least significant bit is a denorm, and the result
+      // would not be a denorm, then shift the input, increment, and shift back.
+      // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set.
+      //
+      return ldexp(float_prior(T(ldexp(val, 2 * tools::digits<T>())), pol), -2 * tools::digits<T>());
+   }
+
+   T remain = frexp(val, &expon);
+   if(remain == 0.5)
+      --expon; // when val is a power of two we must reduce the exponent
+   T diff = ldexp(T(1), expon - tools::digits<T>());
+   if(diff == 0)
+      diff = detail::get_smallest_value<T>();
+   return val - diff;
+}
+
+}
+
+template <class T, class Policy>
+inline typename tools::promote_args<T>::type float_prior(const T& val, const Policy& pol)
+{
+   typedef typename tools::promote_args<T>::type result_type;
+   return detail::float_prior_imp(static_cast<result_type>(val), pol);
+}
+
+#if 0 //def BOOST_MSVC
+//
+// We used to use ::_nextafter here, but doing so fails when using
+// the SSE2 registers if the FTZ or DAZ flags are set, so use our own
+// - albeit slower - code instead as at least that gives the correct answer.
+//
+template <class Policy>
+inline double float_prior(const double& val, const Policy& pol)
+{
+   static const char* function = "float_prior<%1%>(%1%)";
+
+   if(!(boost::math::isfinite)(val) && (val < 0))
+      return policies::raise_domain_error<double>(
+         function,
+         "Argument must be finite, but got %1%", val, pol);
+
+   if(val <= -tools::max_value<double>())
+      return -policies::raise_overflow_error<double>(function, 0, pol);
+
+   return ::_nextafter(val, -tools::max_value<double>());
+}
+#endif
+
+template <class T>
+inline typename tools::promote_args<T>::type float_prior(const T& val)
+{
+   return float_prior(val, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type nextafter(const T& val, const U& direction, const Policy& pol)
+{
+   typedef typename tools::promote_args<T, U>::type result_type;
+   return val < direction ? boost::math::float_next<result_type>(val, pol) : val == direction ? val : boost::math::float_prior<result_type>(val, pol);
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type nextafter(const T& val, const U& direction)
+{
+   return nextafter(val, direction, policies::policy<>());
+}
+
+namespace detail{
+
+template <class T, class Policy>
+T float_distance_imp(const T& a, const T& b, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   //
+   // Error handling:
+   //
+   static const char* function = "float_distance<%1%>(%1%, %1%)";
+   if(!(boost::math::isfinite)(a))
+      return policies::raise_domain_error<T>(
+         function,
+         "Argument a must be finite, but got %1%", a, pol);
+   if(!(boost::math::isfinite)(b))
+      return policies::raise_domain_error<T>(
+         function,
+         "Argument b must be finite, but got %1%", b, pol);
+   //
+   // Special cases:
+   //
+   if(a > b)
+      return -float_distance(b, a, pol);
+   if(a == b)
+      return 0;
+   if(a == 0)
+      return 1 + fabs(float_distance(static_cast<T>((b < 0) ? T(-detail::get_smallest_value<T>()) : detail::get_smallest_value<T>()), b, pol));
+   if(b == 0)
+      return 1 + fabs(float_distance(static_cast<T>((a < 0) ? T(-detail::get_smallest_value<T>()) : detail::get_smallest_value<T>()), a, pol));
+   if(boost::math::sign(a) != boost::math::sign(b))
+      return 2 + fabs(float_distance(static_cast<T>((b < 0) ? T(-detail::get_smallest_value<T>()) : detail::get_smallest_value<T>()), b, pol))
+         + fabs(float_distance(static_cast<T>((a < 0) ? T(-detail::get_smallest_value<T>()) : detail::get_smallest_value<T>()), a, pol));
+   //
+   // By the time we get here, both a and b must have the same sign, we want
+   // b > a and both postive for the following logic:
+   //
+   if(a < 0)
+      return float_distance(static_cast<T>(-b), static_cast<T>(-a), pol);
+
+   BOOST_ASSERT(a >= 0);
+   BOOST_ASSERT(b >= a);
+
+   int expon;
+   //
+   // Note that if a is a denorm then the usual formula fails
+   // because we actually have fewer than tools::digits<T>()
+   // significant bits in the representation:
+   //
+   frexp(((boost::math::fpclassify)(a) == FP_SUBNORMAL) ? tools::min_value<T>() : a, &expon);
+   T upper = ldexp(T(1), expon);
+   T result = 0;
+   expon = tools::digits<T>() - expon;
+   //
+   // If b is greater than upper, then we *must* split the calculation
+   // as the size of the ULP changes with each order of magnitude change:
+   //
+   if(b > upper)
+   {
+      result = float_distance(upper, b);
+   }
+   //
+   // Use compensated double-double addition to avoid rounding
+   // errors in the subtraction:
+   //
+   T mb, x, y, z;
+   if(((boost::math::fpclassify)(a) == FP_SUBNORMAL) || (b - a < tools::min_value<T>()))
+   {
+      //
+      // Special case - either one end of the range is a denormal, or else the difference is.
+      // The regular code will fail if we're using the SSE2 registers on Intel and either
+      // the FTZ or DAZ flags are set.
+      //
+      T a2 = ldexp(a, tools::digits<T>());
+      T b2 = ldexp(b, tools::digits<T>());
+      mb = -(std::min)(T(ldexp(upper, tools::digits<T>())), b2);
+      x = a2 + mb;
+      z = x - a2;
+      y = (a2 - (x - z)) + (mb - z);
+
+      expon -= tools::digits<T>();
+   }
+   else
+   {
+      mb = -(std::min)(upper, b);
+      x = a + mb;
+      z = x - a;
+      y = (a - (x - z)) + (mb - z);
+   }
+   if(x < 0)
+   {
+      x = -x;
+      y = -y;
+   }
+   result += ldexp(x, expon) + ldexp(y, expon);
+   //
+   // Result must be an integer:
+   //
+   BOOST_ASSERT(result == floor(result));
+   return result;
+}
+
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type float_distance(const T& a, const U& b, const Policy& pol)
+{
+   typedef typename tools::promote_args<T, U>::type result_type;
+   return detail::float_distance_imp(static_cast<result_type>(a), static_cast<result_type>(b), pol);
+}
+
+template <class T, class U>
+typename tools::promote_args<T, U>::type float_distance(const T& a, const U& b)
+{
+   return boost::math::float_distance(a, b, policies::policy<>());
+}
+
+namespace detail{
+
+template <class T, class Policy>
+T float_advance_imp(T val, int distance, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   //
+   // Error handling:
+   //
+   static const char* function = "float_advance<%1%>(%1%, int)";
+
+   int fpclass = (boost::math::fpclassify)(val);
+
+   if((fpclass == FP_NAN) || (fpclass == FP_INFINITE))
+      return policies::raise_domain_error<T>(
+         function,
+         "Argument val must be finite, but got %1%", val, pol);
+
+   if(val < 0)
+      return -float_advance(-val, -distance, pol);
+   if(distance == 0)
+      return val;
+   if(distance == 1)
+      return float_next(val, pol);
+   if(distance == -1)
+      return float_prior(val, pol);
+
+   if(fabs(val) < detail::get_min_shift_value<T>())
+   {
+      //
+      // Special case: if the value of the least significant bit is a denorm,
+      // implement in terms of float_next/float_prior.
+      // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set.
+      //
+      if(distance > 0)
+      {
+         do{ val = float_next(val, pol); } while(--distance);
+      }
+      else
+      {
+         do{ val = float_prior(val, pol); } while(++distance);
+      }
+      return val;
+   }
+
+   int expon;
+   frexp(val, &expon);
+   T limit = ldexp((distance < 0 ? T(0.5f) : T(1)), expon);
+   if(val <= tools::min_value<T>())
+   {
+      limit = sign(T(distance)) * tools::min_value<T>();
+   }
+   T limit_distance = float_distance(val, limit);
+   while(fabs(limit_distance) < abs(distance))
+   {
+      distance -= itrunc(limit_distance);
+      val = limit;
+      if(distance < 0)
+      {
+         limit /= 2;
+         expon--;
+      }
+      else
+      {
+         limit *= 2;
+         expon++;
+      }
+      limit_distance = float_distance(val, limit);
+      if(distance && (limit_distance == 0))
+      {
+         policies::raise_evaluation_error<T>(function, "Internal logic failed while trying to increment floating point value %1%: most likely your FPU is in non-IEEE conforming mode.", val, pol);
+      }
+   }
+   if((0.5f == frexp(val, &expon)) && (distance < 0))
+      --expon;
+   T diff = 0;
+   if(val != 0)
+      diff = distance * ldexp(T(1), expon - tools::digits<T>());
+   if(diff == 0)
+      diff = distance * detail::get_smallest_value<T>();
+   return val += diff;
+}
+
+}
+
+template <class T, class Policy>
+inline typename tools::promote_args<T>::type float_advance(T val, int distance, const Policy& pol)
+{
+   typedef typename tools::promote_args<T>::type result_type;
+   return detail::float_advance_imp(static_cast<result_type>(val), distance, pol);
+}
+
+template <class T>
+inline typename tools::promote_args<T>::type float_advance(const T& val, int distance)
+{
+   return boost::math::float_advance(val, distance, policies::policy<>());
+}
+
+}} // namespaces
+
+#endif // BOOST_MATH_SPECIAL_NEXT_HPP
+