FM / special_functions

/usr/include/boost/math/special_functions/

/usr/include/boost/math/special_functions

Name	Size	Mode	Actions
detail/	-	0755	rm
acosh.hpp	3693	0644	edit dl rm
airy.hpp	16270	0644	edit dl rm
asinh.hpp	3935	0644	edit dl rm
atanh.hpp	4104	0644	edit dl rm
bernoulli.hpp	5389	0644	edit dl rm
bessel.hpp	28405	0644	edit dl rm
bessel_iterators.hpp	6893	0644	edit dl rm
bessel_prime.hpp	13238	0644	edit dl rm
beta.hpp	52594	0644	edit dl rm
binomial.hpp	2508	0644	edit dl rm
cardinal_b_spline.hpp	4796	0644	edit dl rm
cbrt.hpp	5200	0644	edit dl rm
chebyshev.hpp	4760	0644	edit dl rm
chebyshev_transform.hpp	6209	0644	edit dl rm
cos_pi.hpp	2328	0644	edit dl rm
daubechies_scaling.hpp	15036	0644	edit dl rm
daubechies_wavelet.hpp	9671	0644	edit dl rm
digamma.hpp	22318	0644	edit dl rm
ellint_1.hpp	6700	0644	edit dl rm
ellint_2.hpp	6377	0644	edit dl rm
ellint_3.hpp	12048	0644	edit dl rm
ellint_d.hpp	5965	0644	edit dl rm
ellint_rc.hpp	3135	0644	edit dl rm
ellint_rd.hpp	6280	0644	edit dl rm
ellint_rf.hpp	5255	0644	edit dl rm
ellint_rg.hpp	4125	0644	edit dl rm
ellint_rj.hpp	8862	0644	edit dl rm
erf.hpp	56660	0644	edit dl rm
expint.hpp	75066	0644	edit dl rm
expm1.hpp	11335	0644	edit dl rm
factorials.hpp	8054	0644	edit dl rm
fpclassify.hpp	19871	0644	edit dl rm
gamma.hpp	70488	0644	edit dl rm
gegenbauer.hpp	2015	0644	edit dl rm
hankel.hpp	6994	0644	edit dl rm
hermite.hpp	1778	0644	edit dl rm
heuman_lambda.hpp	2891	0644	edit dl rm
hypergeometric_0F1.hpp	4283	0644	edit dl rm
hypergeometric_1F0.hpp	2383	0644	edit dl rm
hypergeometric_1F1.hpp	31854	0644	edit dl rm
hypergeometric_2F0.hpp	6127	0644	edit dl rm
hypergeometric_pFq.hpp	8518	0644	edit dl rm
hypot.hpp	2246	0644	edit dl rm
jacobi.hpp	1884	0644	edit dl rm
jacobi_elliptic.hpp	10190	0644	edit dl rm
jacobi_zeta.hpp	2273	0644	edit dl rm
laguerre.hpp	3651	0644	edit dl rm
lambert_w.hpp	95998	0644	edit dl rm
lanczos.hpp	312974	0644	edit dl rm
legendre.hpp	11275	0644	edit dl rm
legendre_stieltjes.hpp	6901	0644	edit dl rm
log1p.hpp	16271	0644	edit dl rm
math_fwd.hpp	73671	0644	edit dl rm
modf.hpp	1628	0644	edit dl rm
next.hpp	28961	0644	edit dl rm
nonfinite_num_facets.hpp	18572	0644	edit dl rm
owens_t.hpp	49887	0644	edit dl rm
polygamma.hpp	3209	0644	edit dl rm
pow.hpp	3426	0644	edit dl rm
powm1.hpp	2442	0644	edit dl rm
prime.hpp	91594	0644	edit dl rm
relative_difference.hpp	5455	0644	edit dl rm
round.hpp	4361	0644	edit dl rm
sign.hpp	5648	0644	edit dl rm
sinc.hpp	3409	0644	edit dl rm
sinhc.hpp	4643	0644	edit dl rm
sin_pi.hpp	2311	0644	edit dl rm
spherical_harmonic.hpp	6358	0644	edit dl rm
sqrt1pm1.hpp	1149	0644	edit dl rm
trigamma.hpp	21411	0644	edit dl rm
trunc.hpp	5450	0644	edit dl rm
ulp.hpp	3324	0644	edit dl rm
zeta.hpp	53776	0644	edit dl rm

Edit: /usr/include/boost/math/special_functions/next.hpp (28961B)

//  (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/special_functions/math_fwd.hpp>
#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>

#include <float.h>

#if !defined(_CRAYC) && !defined(__CUDACC__) && (!defined(__GNUC__) || (__GNUC__ > 3) || ((__GNUC__ == 3) && (__GNUC_MINOR__ > 3)))
#if (defined(_M_IX86_FP) && (_M_IX86_FP >= 2)) || defined(__SSE2__)
#include "xmmintrin.h"
#define BOOST_MATH_CHECK_SSE2
#endif
#endif

namespace boost{ namespace math{

namespace concepts {

class real_concept;
      class std_real_concept;

}

namespace detail{

template <class T>
struct has_hidden_guard_digits;
template <>
struct has_hidden_guard_digits<float> : public boost::false_type {};
template <>
struct has_hidden_guard_digits<double> : public boost::false_type {};
template <>
struct has_hidden_guard_digits<long double> : public boost::false_type {};
#ifdef BOOST_HAS_FLOAT128
template <>
struct has_hidden_guard_digits<__float128> : public boost::false_type {};
#endif
template <>
struct has_hidden_guard_digits<boost::math::concepts::real_concept> : public boost::false_type {};
template <>
struct has_hidden_guard_digits<boost::math::concepts::std_real_concept> : public boost::false_type {};

template <class T, bool b>
struct has_hidden_guard_digits_10 : public boost::false_type {};
template <class T>
struct has_hidden_guard_digits_10<T, true> : public boost::integral_constant<bool, (std::numeric_limits<T>::digits10 != std::numeric_limits<T>::max_digits10)> {};

template <class T>
struct has_hidden_guard_digits 
   : public has_hidden_guard_digits_10<T, 
   std::numeric_limits<T>::is_specialized
   && (std::numeric_limits<T>::radix == 10) >
{};

template <class T>
inline const T& normalize_value(const T& val, const boost::false_type&) { return val; }
template <class T>
inline T normalize_value(const T& val, const boost::true_type&) 
{
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::is_specialized);
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::radix != 2);

boost::intmax_t shift = (boost::intmax_t)std::numeric_limits<T>::digits - (boost::intmax_t)ilogb(val) - 1;
   T result = scalbn(val, shift);
   result = round(result);
   return scalbn(result, -shift); 
}

template <class T>
inline T get_smallest_value(boost::true_type 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();
#ifdef BOOST_MATH_CHECK_SSE2
   return (_mm_getcsr() & (_MM_FLUSH_ZERO_ON | 0x40)) ? tools::min_value<T>() : m;;
#else
   return ((tools::min_value<T>() / 2) == 0) ? tools::min_value<T>() : m;
#endif
}

template <class T>
inline T get_smallest_value(boost::false_type 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>(boost::integral_constant<bool, std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::has_denorm == 1)>());
#else
   return get_smallest_value<T>(boost::integral_constant<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 calc_min_shifted(const boost::true_type&)
{
   BOOST_MATH_STD_USING
   return ldexp(tools::min_value<T>(), tools::digits<T>() + 1);
}
template <class T>
inline T calc_min_shifted(const boost::false_type&)
{
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::is_specialized);
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::radix != 2);

return scalbn(tools::min_value<T>(), std::numeric_limits<T>::digits + 1);
}

template <class T>
inline T get_min_shift_value()
{
   static const T val = calc_min_shifted<T>(boost::integral_constant<bool, !std::numeric_limits<T>::is_specialized || std::numeric_limits<T>::radix == 2>());
   min_shift_initializer<T>::force_instantiate();

return val;
}

template <class T, class Policy>
T float_next_imp(const T& val, const boost::true_type&, 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 == (int)FP_NAN) || (fpclass == (int)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 != (int)FP_SUBNORMAL) && (fpclass != (int)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;
} // float_next_imp
//
// Special version for some base other than 2:
//
template <class T, class Policy>
T float_next_imp(const T& val, const boost::false_type&, const Policy& pol)
{
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::is_specialized);
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::radix != 2);

BOOST_MATH_STD_USING
   boost::intmax_t expon;
   static const char* function = "float_next<%1%>(%1%)";

int fpclass = (boost::math::fpclassify)(val);

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 != (int)FP_SUBNORMAL) && (fpclass != (int)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 scalbn(float_next(T(scalbn(val, 2 * std::numeric_limits<T>::digits)), pol), -2 * std::numeric_limits<T>::digits);
   }

expon = 1 + ilogb(val);
   if(-1 == scalbn(val, -expon) * std::numeric_limits<T>::radix)
      --expon; // reduce exponent when val is a power of base, and negative.
   T diff = scalbn(T(1), expon - std::numeric_limits<T>::digits);
   if(diff == 0)
      diff = detail::get_smallest_value<T>();
   return val + diff;
} // float_next_imp

} // namespace detail

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(detail::normalize_value(static_cast<result_type>(val), typename detail::has_hidden_guard_digits<result_type>::type()), boost::integral_constant<bool, !std::numeric_limits<result_type>::is_specialized || (std::numeric_limits<result_type>::radix == 2)>(), 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 boost::true_type&, 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 == (int)FP_NAN) || (fpclass == (int)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 != (int)FP_SUBNORMAL) && (fpclass != (int)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 == 0.5f)
      --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;
} // float_prior_imp
//
// Special version for bases other than 2:
//
template <class T, class Policy>
T float_prior_imp(const T& val, const boost::false_type&, const Policy& pol)
{
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::is_specialized);
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::radix != 2);

BOOST_MATH_STD_USING
   boost::intmax_t expon;
   static const char* function = "float_prior<%1%>(%1%)";

int fpclass = (boost::math::fpclassify)(val);

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 != (int)FP_SUBNORMAL) && (fpclass != (int)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 scalbn(float_prior(T(scalbn(val, 2 * std::numeric_limits<T>::digits)), pol), -2 * std::numeric_limits<T>::digits);
   }

expon = 1 + ilogb(val);
   T remain = scalbn(val, -expon);
   if(remain * std::numeric_limits<T>::radix == 1)
      --expon; // when val is a power of two we must reduce the exponent
   T diff = scalbn(T(1), expon - std::numeric_limits<T>::digits);
   if(diff == 0)
      diff = detail::get_smallest_value<T>();
   return val - diff;
} // float_prior_imp

} // namespace detail

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(detail::normalize_value(static_cast<result_type>(val), typename detail::has_hidden_guard_digits<result_type>::type()), boost::integral_constant<bool, !std::numeric_limits<result_type>::is_specialized || (std::numeric_limits<result_type>::radix == 2)>(), 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 boost::true_type&, 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 T(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 positive 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:
   //
   (void)frexp(((boost::math::fpclassify)(a) == (int)FP_SUBNORMAL) ? tools::min_value<T>() : a, &expon);
   T upper = ldexp(T(1), expon);
   T result = T(0);
   //
   // 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)
   {
      int expon2;
      (void)frexp(b, &expon2);
      T upper2 = ldexp(T(0.5), expon2);
      result = float_distance(upper2, b);
      result += (expon2 - expon - 1) * ldexp(T(1), tools::digits<T>() - 1);
   }
   //
   // Use compensated double-double addition to avoid rounding
   // errors in the subtraction:
   //
   expon = tools::digits<T>() - expon;
   T mb, x, y, z;
   if(((boost::math::fpclassify)(a) == (int)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;
} // float_distance_imp
//
// Special versions for bases other than 2:
//
template <class T, class Policy>
T float_distance_imp(const T& a, const T& b, const boost::false_type&, const Policy& pol)
{
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::is_specialized);
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::radix != 2);

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 T(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 positive 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);

boost::intmax_t 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:
   //
   expon = 1 + ilogb(((boost::math::fpclassify)(a) == (int)FP_SUBNORMAL) ? tools::min_value<T>() : a);
   T upper = scalbn(T(1), expon);
   T result = T(0);
   //
   // 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)
   {
      boost::intmax_t expon2 = 1 + ilogb(b);
      T upper2 = scalbn(T(1), expon2 - 1);
      result = float_distance(upper2, b);
      result += (expon2 - expon - 1) * scalbn(T(1), std::numeric_limits<T>::digits - 1);
   }
   //
   // Use compensated double-double addition to avoid rounding
   // errors in the subtraction:
   //
   expon = std::numeric_limits<T>::digits - expon;
   T mb, x, y, z;
   if(((boost::math::fpclassify)(a) == (int)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 = scalbn(a, std::numeric_limits<T>::digits);
      T b2 = scalbn(b, std::numeric_limits<T>::digits);
      mb = -(std::min)(T(scalbn(upper, std::numeric_limits<T>::digits)), b2);
      x = a2 + mb;
      z = x - a2;
      y = (a2 - (x - z)) + (mb - z);

expon -= std::numeric_limits<T>::digits;
   }
   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 += scalbn(x, expon) + scalbn(y, expon);
   //
   // Result must be an integer:
   //
   BOOST_ASSERT(result == floor(result));
   return result;
} // float_distance_imp

} // namespace detail

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(detail::normalize_value(static_cast<result_type>(a), typename detail::has_hidden_guard_digits<result_type>::type()), detail::normalize_value(static_cast<result_type>(b), typename detail::has_hidden_guard_digits<result_type>::type()), boost::integral_constant<bool, !std::numeric_limits<result_type>::is_specialized || (std::numeric_limits<result_type>::radix == 2)>(), 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 boost::true_type&, 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 == (int)FP_NAN) || (fpclass == (int)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;
   (void)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))
      {
         return 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;
} // float_advance_imp
//
// Special version for bases other than 2:
//
template <class T, class Policy>
T float_advance_imp(T val, int distance, const boost::false_type&, const Policy& pol)
{
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::is_specialized);
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::radix != 2);

BOOST_MATH_STD_USING
   //
   // Error handling:
   //
   static const char* function = "float_advance<%1%>(%1%, int)";

int fpclass = (boost::math::fpclassify)(val);

if((fpclass == (int)FP_NAN) || (fpclass == (int)FP_INFINITE))
      return policies::raise_domain_error<T>(
         function,
         "Argument val must be finite, but got %1%", val, pol);

boost::intmax_t expon = 1 + ilogb(val);
   T limit = scalbn(T(1), distance < 0 ? expon - 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 /= std::numeric_limits<T>::radix;
         expon--;
      }
      else
      {
         limit *= std::numeric_limits<T>::radix;
         expon++;
      }
      limit_distance = float_distance(val, limit);
      if(distance && (limit_distance == 0))
      {
         return 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);
      }
   }
   /*expon = 1 + ilogb(val);
   if((1 == scalbn(val, 1 + expon)) && (distance < 0))
      --expon;*/
   T diff = 0;
   if(val != 0)
      diff = distance * scalbn(T(1), expon - std::numeric_limits<T>::digits);
   if(diff == 0)
      diff = distance * detail::get_smallest_value<T>();
   return val += diff;
} // float_advance_imp

} // namespace detail

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(detail::normalize_value(static_cast<result_type>(val), typename detail::has_hidden_guard_digits<result_type>::type()), distance, boost::integral_constant<bool, !std::numeric_limits<result_type>::is_specialized || (std::numeric_limits<result_type>::radix == 2)>(), 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<>());
}

}} // boost math namespaces

#endif // BOOST_MATH_SPECIAL_NEXT_HPP

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