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220ecf68c6
libcarla/include/system/boost/math/special_functions/next.hpp
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2024-10-18 13:19:59 +08:00

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// (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 <boost/math/tools/traits.hpp>
#include <type_traits>
#include <cfloat>
#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 std::false_type {};
template <>
struct has_hidden_guard_digits<double> : public std::false_type {};
template <>
struct has_hidden_guard_digits<long double> : public std::false_type {};
#ifdef BOOST_HAS_FLOAT128
template <>
struct has_hidden_guard_digits<__float128> : public std::false_type {};
#endif
template <>
struct has_hidden_guard_digits<boost::math::concepts::real_concept> : public std::false_type {};
template <>
struct has_hidden_guard_digits<boost::math::concepts::std_real_concept> : public std::false_type {};
template <class T, bool b>
struct has_hidden_guard_digits_10 : public std::false_type {};
template <class T>
struct has_hidden_guard_digits_10<T, true> : public std::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 std::false_type&) { return val; }
template <class T>
inline T normalize_value(const T& val, const std::true_type&)
{
static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized.");
static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized.");
std::intmax_t shift = (std::intmax_t)std::numeric_limits<T>::digits - (std::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(std::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(std::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>(std::integral_constant<bool, std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::has_denorm == 1)>());
#else
return get_smallest_value<T>(std::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 std::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 std::false_type&)
{
static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized.");
static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized.");
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>(std::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, bool b = boost::math::tools::detail::has_backend_type<T>::value>
struct exponent_type
{
typedef int type;
};
template <class T>
struct exponent_type<T, true>
{
typedef typename T::backend_type::exponent_type type;
};
template <class T, class Policy>
T float_next_imp(const T& val, const std::true_type&, const Policy& pol)
{
typedef typename exponent_type<T>::type exponent_type;
BOOST_MATH_STD_USING
exponent_type 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 std::false_type&, const Policy& pol)
{
typedef typename exponent_type<T>::type exponent_type;
static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized.");
static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized.");
BOOST_MATH_STD_USING
exponent_type 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 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()), std::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 std::true_type&, const Policy& pol)
{
typedef typename exponent_type<T>::type exponent_type;
BOOST_MATH_STD_USING
exponent_type 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 std::false_type&, const Policy& pol)
{
typedef typename exponent_type<T>::type exponent_type;
static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized.");
static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized.");
BOOST_MATH_STD_USING
exponent_type 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 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()), std::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 std::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_MATH_ASSERT(a >= 0);
BOOST_MATH_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_MATH_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 std::false_type&, const Policy& pol)
{
static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized.");
static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized.");
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_MATH_ASSERT(a >= 0);
BOOST_MATH_ASSERT(b >= a);
std::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)
{
std::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_MATH_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)
{
//
// We allow ONE of a and b to be an integer type, otherwise both must be the SAME type.
//
static_assert(
(std::is_same<T, U>::value
|| (std::is_integral<T>::value && !std::is_integral<U>::value)
|| (!std::is_integral<T>::value && std::is_integral<U>::value)
|| (std::numeric_limits<T>::is_specialized && std::numeric_limits<U>::is_specialized
&& (std::numeric_limits<T>::digits == std::numeric_limits<U>::digits)
&& (std::numeric_limits<T>::radix == std::numeric_limits<U>::radix)
&& !std::numeric_limits<T>::is_integer && !std::numeric_limits<U>::is_integer)),
"Float distance between two different floating point types is undefined.");
BOOST_IF_CONSTEXPR (!std::is_same<T, U>::value)
{
BOOST_IF_CONSTEXPR(std::is_integral<T>::value)
{
return float_distance(static_cast<U>(a), b, pol);
}
else
{
return float_distance(a, static_cast<T>(b), pol);
}
}
else
{
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()), std::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 std::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 std::false_type&, const Policy& pol)
{
static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized.");
static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized.");
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;
}
std::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, std::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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