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

Add boost headers

+//  Copyright John Maddock 2005-2008.
+//  Copyright (c) 2006-2008 Johan Rade
+//  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_FPCLASSIFY_HPP
+#define BOOST_MATH_FPCLASSIFY_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <math.h>
+#include <boost/config/no_tr1/cmath.hpp>
+#include <boost/limits.hpp>
+#include <boost/math/tools/real_cast.hpp>
+#include <boost/type_traits/is_floating_point.hpp>
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/special_functions/detail/fp_traits.hpp>
+/*!
+  \file fpclassify.hpp
+  \brief Classify floating-point value as normal, subnormal, zero, infinite, or NaN.
+  \version 1.0
+  \author John Maddock
+ */
+
+/*
+
+1. If the platform is C99 compliant, then the native floating point
+classification functions are used.  However, note that we must only
+define the functions which call std::fpclassify etc if that function
+really does exist: otherwise a compiler may reject the code even though
+the template is never instantiated.
+
+2. If the platform is not C99 compliant, and the binary format for
+a floating point type (float, double or long double) can be determined
+at compile time, then the following algorithm is used:
+
+        If all exponent bits, the flag bit (if there is one),
+        and all significand bits are 0, then the number is zero.
+
+        If all exponent bits and the flag bit (if there is one) are 0,
+        and at least one significand bit is 1, then the number is subnormal.
+
+        If all exponent bits are 1 and all significand bits are 0,
+        then the number is infinity.
+
+        If all exponent bits are 1 and at least one significand bit is 1,
+        then the number is a not-a-number.
+
+        Otherwise the number is normal.
+
+        This algorithm works for the IEEE 754 representation,
+        and also for several non IEEE 754 formats.
+
+    Most formats have the structure
+        sign bit + exponent bits + significand bits.
+
+    A few have the structure
+        sign bit + exponent bits + flag bit + significand bits.
+    The flag bit is 0 for zero and subnormal numbers,
+        and 1 for normal numbers and NaN.
+        It is 0 (Motorola 68K) or 1 (Intel) for infinity.
+
+    To get the bits, the four or eight most significant bytes are copied
+    into an uint32_t or uint64_t and bit masks are applied.
+    This covers all the exponent bits and the flag bit (if there is one),
+    but not always all the significand bits.
+    Some of the functions below have two implementations,
+    depending on whether all the significand bits are copied or not.
+
+3. If the platform is not C99 compliant, and the binary format for
+a floating point type (float, double or long double) can not be determined
+at compile time, then comparison with std::numeric_limits values
+is used.
+
+*/
+
+#if defined(_MSC_VER) || defined(__BORLANDC__)
+#include <float.h>
+#endif
+
+#ifdef BOOST_NO_STDC_NAMESPACE
+  namespace std{ using ::abs; using ::fabs; }
+#endif
+
+namespace boost{
+
+//
+// This must not be located in any namespace under boost::math
+// otherwise we can get into an infinite loop if isnan is
+// a #define for "isnan" !
+//
+namespace math_detail{
+
+#ifdef BOOST_MSVC
+#pragma warning(push)
+#pragma warning(disable:4800)
+#endif
+
+template <class T>
+inline bool is_nan_helper(T t, const boost::true_type&)
+{
+#ifdef isnan
+   return isnan(t);
+#elif defined(BOOST_MATH_DISABLE_STD_FPCLASSIFY) || !defined(BOOST_HAS_FPCLASSIFY)
+   (void)t;
+   return false;
+#else // BOOST_HAS_FPCLASSIFY
+   return (BOOST_FPCLASSIFY_PREFIX fpclassify(t) == (int)FP_NAN);
+#endif
+}
+
+#ifdef BOOST_MSVC
+#pragma warning(pop)
+#endif
+
+template <class T>
+inline bool is_nan_helper(T, const boost::false_type&)
+{
+   return false;
+}
+
+}
+
+namespace math{
+
+namespace detail{
+
+#ifdef BOOST_MATH_USE_STD_FPCLASSIFY
+template <class T>
+inline int fpclassify_imp BOOST_NO_MACRO_EXPAND(T t, const native_tag&)
+{
+   return (std::fpclassify)(t);
+}
+#endif
+
+template <class T>
+inline int fpclassify_imp BOOST_NO_MACRO_EXPAND(T t, const generic_tag<true>&)
+{
+   BOOST_MATH_INSTRUMENT_VARIABLE(t);
+
+   // whenever possible check for Nan's first:
+#if defined(BOOST_HAS_FPCLASSIFY)  && !defined(BOOST_MATH_DISABLE_STD_FPCLASSIFY)
+   if(::boost::math_detail::is_nan_helper(t, ::boost::is_floating_point<T>()))
+      return FP_NAN;
+#elif defined(isnan)
+   if(boost::math_detail::is_nan_helper(t, ::boost::is_floating_point<T>()))
+      return FP_NAN;
+#elif defined(_MSC_VER) || defined(__BORLANDC__)
+   if(::_isnan(boost::math::tools::real_cast<double>(t)))
+      return FP_NAN;
+#endif
+   // std::fabs broken on a few systems especially for long long!!!!
+   T at = (t < T(0)) ? -t : t;
+
+   // Use a process of exclusion to figure out
+   // what kind of type we have, this relies on
+   // IEEE conforming reals that will treat
+   // Nan's as unordered.  Some compilers
+   // don't do this once optimisations are
+   // turned on, hence the check for nan's above.
+   if(at <= (std::numeric_limits<T>::max)())
+   {
+      if(at >= (std::numeric_limits<T>::min)())
+         return FP_NORMAL;
+      return (at != 0) ? FP_SUBNORMAL : FP_ZERO;
+   }
+   else if(at > (std::numeric_limits<T>::max)())
+      return FP_INFINITE;
+   return FP_NAN;
+}
+
+template <class T>
+inline int fpclassify_imp BOOST_NO_MACRO_EXPAND(T t, const generic_tag<false>&)
+{
+#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
+   if(std::numeric_limits<T>::is_specialized)
+      return fpclassify_imp(t, generic_tag<true>());
+#endif
+   //
+   // An unknown type with no numeric_limits support,
+   // so what are we supposed to do we do here?
+   //
+   BOOST_MATH_INSTRUMENT_VARIABLE(t);
+
+   return t == 0 ? FP_ZERO : FP_NORMAL;
+}
+
+template<class T>
+int fpclassify_imp BOOST_NO_MACRO_EXPAND(T x, ieee_copy_all_bits_tag)
+{
+   typedef BOOST_DEDUCED_TYPENAME fp_traits<T>::type traits;
+
+   BOOST_MATH_INSTRUMENT_VARIABLE(x);
+
+   BOOST_DEDUCED_TYPENAME traits::bits a;
+   traits::get_bits(x,a);
+   BOOST_MATH_INSTRUMENT_VARIABLE(a);
+   a &= traits::exponent | traits::flag | traits::significand;
+   BOOST_MATH_INSTRUMENT_VARIABLE((traits::exponent | traits::flag | traits::significand));
+   BOOST_MATH_INSTRUMENT_VARIABLE(a);
+
+   if(a <= traits::significand) {
+      if(a == 0)
+         return FP_ZERO;
+      else
+         return FP_SUBNORMAL;
+   }
+
+   if(a < traits::exponent) return FP_NORMAL;
+
+   a &= traits::significand;
+   if(a == 0) return FP_INFINITE;
+
+   return FP_NAN;
+}
+
+template<class T>
+int fpclassify_imp BOOST_NO_MACRO_EXPAND(T x, ieee_copy_leading_bits_tag)
+{
+   typedef BOOST_DEDUCED_TYPENAME fp_traits<T>::type traits;
+
+   BOOST_MATH_INSTRUMENT_VARIABLE(x);
+
+   BOOST_DEDUCED_TYPENAME traits::bits a;
+   traits::get_bits(x,a);
+   a &= traits::exponent | traits::flag | traits::significand;
+
+   if(a <= traits::significand) {
+      if(x == 0)
+         return FP_ZERO;
+      else
+         return FP_SUBNORMAL;
+   }
+
+   if(a < traits::exponent) return FP_NORMAL;
+
+   a &= traits::significand;
+   traits::set_bits(x,a);
+   if(x == 0) return FP_INFINITE;
+
+   return FP_NAN;
+}
+
+#if defined(BOOST_MATH_USE_STD_FPCLASSIFY) && (defined(BOOST_MATH_NO_NATIVE_LONG_DOUBLE_FP_CLASSIFY) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS))
+inline int fpclassify_imp BOOST_NO_MACRO_EXPAND(long double t, const native_tag&)
+{
+   return boost::math::detail::fpclassify_imp(t, generic_tag<true>());
+}
+#endif
+
+}  // namespace detail
+
+template <class T>
+inline int fpclassify BOOST_NO_MACRO_EXPAND(T t)
+{
+   typedef typename detail::fp_traits<T>::type traits;
+   typedef typename traits::method method;
+   typedef typename tools::promote_args_permissive<T>::type value_type;
+#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
+   if(std::numeric_limits<T>::is_specialized && detail::is_generic_tag_false(static_cast<method*>(0)))
+      return detail::fpclassify_imp(static_cast<value_type>(t), detail::generic_tag<true>());
+   return detail::fpclassify_imp(static_cast<value_type>(t), method());
+#else
+   return detail::fpclassify_imp(static_cast<value_type>(t), method());
+#endif
+}
+
+#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+template <>
+inline int fpclassify<long double> BOOST_NO_MACRO_EXPAND(long double t)
+{
+   typedef detail::fp_traits<long double>::type traits;
+   typedef traits::method method;
+   typedef long double value_type;
+#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
+   if(std::numeric_limits<long double>::is_specialized && detail::is_generic_tag_false(static_cast<method*>(0)))
+      return detail::fpclassify_imp(static_cast<value_type>(t), detail::generic_tag<true>());
+   return detail::fpclassify_imp(static_cast<value_type>(t), method());
+#else
+   return detail::fpclassify_imp(static_cast<value_type>(t), method());
+#endif
+}
+#endif
+
+namespace detail {
+
+#ifdef BOOST_MATH_USE_STD_FPCLASSIFY
+    template<class T>
+    inline bool isfinite_impl(T x, native_tag const&)
+    {
+        return (std::isfinite)(x);
+    }
+#endif
+
+    template<class T>
+    inline bool isfinite_impl(T x, generic_tag<true> const&)
+    {
+        return x >= -(std::numeric_limits<T>::max)()
+            && x <= (std::numeric_limits<T>::max)();
+    }
+
+    template<class T>
+    inline bool isfinite_impl(T x, generic_tag<false> const&)
+    {
+#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
+      if(std::numeric_limits<T>::is_specialized)
+         return isfinite_impl(x, generic_tag<true>());
+#endif
+       (void)x; // warning supression.
+       return true;
+    }
+
+    template<class T>
+    inline bool isfinite_impl(T x, ieee_tag const&)
+    {
+        typedef BOOST_DEDUCED_TYPENAME detail::fp_traits<T>::type traits;
+        BOOST_DEDUCED_TYPENAME traits::bits a;
+        traits::get_bits(x,a);
+        a &= traits::exponent;
+        return a != traits::exponent;
+    }
+
+#if defined(BOOST_MATH_USE_STD_FPCLASSIFY) && defined(BOOST_MATH_NO_NATIVE_LONG_DOUBLE_FP_CLASSIFY)
+inline bool isfinite_impl BOOST_NO_MACRO_EXPAND(long double t, const native_tag&)
+{
+   return boost::math::detail::isfinite_impl(t, generic_tag<true>());
+}
+#endif
+
+}
+
+template<class T>
+inline bool (isfinite)(T x)
+{ //!< \brief return true if floating-point type t is finite.
+   typedef typename detail::fp_traits<T>::type traits;
+   typedef typename traits::method method;
+   // typedef typename boost::is_floating_point<T>::type fp_tag;
+   typedef typename tools::promote_args_permissive<T>::type value_type;
+   return detail::isfinite_impl(static_cast<value_type>(x), method());
+}
+
+#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+template<>
+inline bool (isfinite)(long double x)
+{ //!< \brief return true if floating-point type t is finite.
+   typedef detail::fp_traits<long double>::type traits;
+   typedef traits::method method;
+   typedef boost::is_floating_point<long double>::type fp_tag;
+   typedef long double value_type;
+   return detail::isfinite_impl(static_cast<value_type>(x), method());
+}
+#endif
+
+//------------------------------------------------------------------------------
+
+namespace detail {
+
+#ifdef BOOST_MATH_USE_STD_FPCLASSIFY
+    template<class T>
+    inline bool isnormal_impl(T x, native_tag const&)
+    {
+        return (std::isnormal)(x);
+    }
+#endif
+
+    template<class T>
+    inline bool isnormal_impl(T x, generic_tag<true> const&)
+    {
+        if(x < 0) x = -x;
+        return x >= (std::numeric_limits<T>::min)()
+            && x <= (std::numeric_limits<T>::max)();
+    }
+
+    template<class T>
+    inline bool isnormal_impl(T x, generic_tag<false> const&)
+    {
+#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
+      if(std::numeric_limits<T>::is_specialized)
+         return isnormal_impl(x, generic_tag<true>());
+#endif
+       return !(x == 0);
+    }
+
+    template<class T>
+    inline bool isnormal_impl(T x, ieee_tag const&)
+    {
+        typedef BOOST_DEDUCED_TYPENAME detail::fp_traits<T>::type traits;
+        BOOST_DEDUCED_TYPENAME traits::bits a;
+        traits::get_bits(x,a);
+        a &= traits::exponent | traits::flag;
+        return (a != 0) && (a < traits::exponent);
+    }
+
+#if defined(BOOST_MATH_USE_STD_FPCLASSIFY) && defined(BOOST_MATH_NO_NATIVE_LONG_DOUBLE_FP_CLASSIFY)
+inline bool isnormal_impl BOOST_NO_MACRO_EXPAND(long double t, const native_tag&)
+{
+   return boost::math::detail::isnormal_impl(t, generic_tag<true>());
+}
+#endif
+
+}
+
+template<class T>
+inline bool (isnormal)(T x)
+{
+   typedef typename detail::fp_traits<T>::type traits;
+   typedef typename traits::method method;
+   //typedef typename boost::is_floating_point<T>::type fp_tag;
+   typedef typename tools::promote_args_permissive<T>::type value_type;
+   return detail::isnormal_impl(static_cast<value_type>(x), method());
+}
+
+#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+template<>
+inline bool (isnormal)(long double x)
+{
+   typedef detail::fp_traits<long double>::type traits;
+   typedef traits::method method;
+   typedef boost::is_floating_point<long double>::type fp_tag;
+   typedef long double value_type;
+   return detail::isnormal_impl(static_cast<value_type>(x), method());
+}
+#endif
+
+//------------------------------------------------------------------------------
+
+namespace detail {
+
+#ifdef BOOST_MATH_USE_STD_FPCLASSIFY
+    template<class T>
+    inline bool isinf_impl(T x, native_tag const&)
+    {
+        return (std::isinf)(x);
+    }
+#endif
+
+    template<class T>
+    inline bool isinf_impl(T x, generic_tag<true> const&)
+    {
+        (void)x; // in case the compiler thinks that x is unused because std::numeric_limits<T>::has_infinity is false
+        return std::numeric_limits<T>::has_infinity
+            && ( x == std::numeric_limits<T>::infinity()
+                 || x == -std::numeric_limits<T>::infinity());
+    }
+
+    template<class T>
+    inline bool isinf_impl(T x, generic_tag<false> const&)
+    {
+#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
+      if(std::numeric_limits<T>::is_specialized)
+         return isinf_impl(x, generic_tag<true>());
+#endif
+        (void)x; // warning supression.
+        return false;
+    }
+
+    template<class T>
+    inline bool isinf_impl(T x, ieee_copy_all_bits_tag const&)
+    {
+        typedef BOOST_DEDUCED_TYPENAME fp_traits<T>::type traits;
+
+        BOOST_DEDUCED_TYPENAME traits::bits a;
+        traits::get_bits(x,a);
+        a &= traits::exponent | traits::significand;
+        return a == traits::exponent;
+    }
+
+    template<class T>
+    inline bool isinf_impl(T x, ieee_copy_leading_bits_tag const&)
+    {
+        typedef BOOST_DEDUCED_TYPENAME fp_traits<T>::type traits;
+
+        BOOST_DEDUCED_TYPENAME traits::bits a;
+        traits::get_bits(x,a);
+        a &= traits::exponent | traits::significand;
+        if(a != traits::exponent)
+            return false;
+
+        traits::set_bits(x,0);
+        return x == 0;
+    }
+
+#if defined(BOOST_MATH_USE_STD_FPCLASSIFY) && defined(BOOST_MATH_NO_NATIVE_LONG_DOUBLE_FP_CLASSIFY)
+inline bool isinf_impl BOOST_NO_MACRO_EXPAND(long double t, const native_tag&)
+{
+   return boost::math::detail::isinf_impl(t, generic_tag<true>());
+}
+#endif
+
+}   // namespace detail
+
+template<class T>
+inline bool (isinf)(T x)
+{
+   typedef typename detail::fp_traits<T>::type traits;
+   typedef typename traits::method method;
+   // typedef typename boost::is_floating_point<T>::type fp_tag;
+   typedef typename tools::promote_args_permissive<T>::type value_type;
+   return detail::isinf_impl(static_cast<value_type>(x), method());
+}
+
+#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+template<>
+inline bool (isinf)(long double x)
+{
+   typedef detail::fp_traits<long double>::type traits;
+   typedef traits::method method;
+   typedef boost::is_floating_point<long double>::type fp_tag;
+   typedef long double value_type;
+   return detail::isinf_impl(static_cast<value_type>(x), method());
+}
+#endif
+
+//------------------------------------------------------------------------------
+
+namespace detail {
+
+#ifdef BOOST_MATH_USE_STD_FPCLASSIFY
+    template<class T>
+    inline bool isnan_impl(T x, native_tag const&)
+    {
+        return (std::isnan)(x);
+    }
+#endif
+
+    template<class T>
+    inline bool isnan_impl(T x, generic_tag<true> const&)
+    {
+        return std::numeric_limits<T>::has_infinity
+            ? !(x <= std::numeric_limits<T>::infinity())
+            : x != x;
+    }
+
+    template<class T>
+    inline bool isnan_impl(T x, generic_tag<false> const&)
+    {
+#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
+      if(std::numeric_limits<T>::is_specialized)
+         return isnan_impl(x, generic_tag<true>());
+#endif
+        (void)x; // warning supression
+        return false;
+    }
+
+    template<class T>
+    inline bool isnan_impl(T x, ieee_copy_all_bits_tag const&)
+    {
+        typedef BOOST_DEDUCED_TYPENAME fp_traits<T>::type traits;
+
+        BOOST_DEDUCED_TYPENAME traits::bits a;
+        traits::get_bits(x,a);
+        a &= traits::exponent | traits::significand;
+        return a > traits::exponent;
+    }
+
+    template<class T>
+    inline bool isnan_impl(T x, ieee_copy_leading_bits_tag const&)
+    {
+        typedef BOOST_DEDUCED_TYPENAME fp_traits<T>::type traits;
+
+        BOOST_DEDUCED_TYPENAME traits::bits a;
+        traits::get_bits(x,a);
+
+        a &= traits::exponent | traits::significand;
+        if(a < traits::exponent)
+            return false;
+
+        a &= traits::significand;
+        traits::set_bits(x,a);
+        return x != 0;
+    }
+
+}   // namespace detail
+
+template<class T>
+inline bool (isnan)(T x)
+{ //!< \brief return true if floating-point type t is NaN (Not A Number).
+   typedef typename detail::fp_traits<T>::type traits;
+   typedef typename traits::method method;
+   // typedef typename boost::is_floating_point<T>::type fp_tag;
+   return detail::isnan_impl(x, method());
+}
+
+#ifdef isnan
+template <> inline bool isnan BOOST_NO_MACRO_EXPAND<float>(float t){ return ::boost::math_detail::is_nan_helper(t, boost::true_type()); }
+template <> inline bool isnan BOOST_NO_MACRO_EXPAND<double>(double t){ return ::boost::math_detail::is_nan_helper(t, boost::true_type()); }
+template <> inline bool isnan BOOST_NO_MACRO_EXPAND<long double>(long double t){ return ::boost::math_detail::is_nan_helper(t, boost::true_type()); }
+#elif defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS)
+template<>
+inline bool (isnan)(long double x)
+{ //!< \brief return true if floating-point type t is NaN (Not A Number).
+   typedef detail::fp_traits<long double>::type traits;
+   typedef traits::method method;
+   typedef boost::is_floating_point<long double>::type fp_tag;
+   return detail::isnan_impl(x, method());
+}
+#endif
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_FPCLASSIFY_HPP
+