641 lines
20 KiB
Plaintext
641 lines
20 KiB
Plaintext
// Copyright John Maddock 2005-2008.
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// Copyright (c) 2006-2008 Johan Rade
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_FPCLASSIFY_HPP
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#define BOOST_MATH_FPCLASSIFY_HPP
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <math.h>
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#include <boost/config/no_tr1/cmath.hpp>
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#include <boost/limits.hpp>
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#include <boost/math/tools/real_cast.hpp>
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#include <boost/type_traits/is_floating_point.hpp>
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#include <boost/math/special_functions/math_fwd.hpp>
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#include <boost/math/special_functions/detail/fp_traits.hpp>
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/*!
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\file fpclassify.hpp
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\brief Classify floating-point value as normal, subnormal, zero, infinite, or NaN.
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\version 1.0
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\author John Maddock
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*/
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/*
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1. If the platform is C99 compliant, then the native floating point
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classification functions are used. However, note that we must only
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define the functions which call std::fpclassify etc if that function
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really does exist: otherwise a compiler may reject the code even though
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the template is never instantiated.
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2. If the platform is not C99 compliant, and the binary format for
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a floating point type (float, double or long double) can be determined
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at compile time, then the following algorithm is used:
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If all exponent bits, the flag bit (if there is one),
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and all significand bits are 0, then the number is zero.
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If all exponent bits and the flag bit (if there is one) are 0,
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and at least one significand bit is 1, then the number is subnormal.
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If all exponent bits are 1 and all significand bits are 0,
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then the number is infinity.
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If all exponent bits are 1 and at least one significand bit is 1,
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then the number is a not-a-number.
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Otherwise the number is normal.
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This algorithm works for the IEEE 754 representation,
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and also for several non IEEE 754 formats.
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Most formats have the structure
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sign bit + exponent bits + significand bits.
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A few have the structure
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sign bit + exponent bits + flag bit + significand bits.
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The flag bit is 0 for zero and subnormal numbers,
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and 1 for normal numbers and NaN.
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It is 0 (Motorola 68K) or 1 (Intel) for infinity.
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To get the bits, the four or eight most significant bytes are copied
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into an uint32_t or uint64_t and bit masks are applied.
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This covers all the exponent bits and the flag bit (if there is one),
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but not always all the significand bits.
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Some of the functions below have two implementations,
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depending on whether all the significand bits are copied or not.
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3. If the platform is not C99 compliant, and the binary format for
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a floating point type (float, double or long double) can not be determined
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at compile time, then comparison with std::numeric_limits values
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is used.
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*/
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#if defined(_MSC_VER) || defined(__BORLANDC__)
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#include <float.h>
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#endif
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#ifdef BOOST_MATH_USE_FLOAT128
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#ifdef __has_include
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#if __has_include("quadmath.h")
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#include "quadmath.h"
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#define BOOST_MATH_HAS_QUADMATH_H
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#endif
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#endif
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#endif
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#ifdef BOOST_NO_STDC_NAMESPACE
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namespace std{ using ::abs; using ::fabs; }
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#endif
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namespace boost{
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//
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// This must not be located in any namespace under boost::math
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// otherwise we can get into an infinite loop if isnan is
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// a #define for "isnan" !
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//
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namespace math_detail{
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#ifdef BOOST_MSVC
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#pragma warning(push)
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#pragma warning(disable:4800)
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#endif
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template <class T>
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inline bool is_nan_helper(T t, const boost::true_type&)
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{
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#ifdef isnan
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return isnan(t);
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#elif defined(BOOST_MATH_DISABLE_STD_FPCLASSIFY) || !defined(BOOST_HAS_FPCLASSIFY)
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(void)t;
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return false;
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#else // BOOST_HAS_FPCLASSIFY
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return (BOOST_FPCLASSIFY_PREFIX fpclassify(t) == (int)FP_NAN);
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#endif
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}
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#ifdef BOOST_MSVC
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#pragma warning(pop)
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#endif
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template <class T>
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inline bool is_nan_helper(T, const boost::false_type&)
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{
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return false;
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}
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#if defined(BOOST_MATH_USE_FLOAT128)
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#if defined(BOOST_MATH_HAS_QUADMATH_H)
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inline bool is_nan_helper(__float128 f, const boost::true_type&) { return ::isnanq(f); }
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inline bool is_nan_helper(__float128 f, const boost::false_type&) { return ::isnanq(f); }
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#elif defined(BOOST_GNU_STDLIB) && BOOST_GNU_STDLIB && \
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_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
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inline bool is_nan_helper(__float128 f, const boost::true_type&) { return std::isnan(static_cast<double>(f)); }
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inline bool is_nan_helper(__float128 f, const boost::false_type&) { return std::isnan(static_cast<double>(f)); }
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#else
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inline bool is_nan_helper(__float128 f, const boost::true_type&) { return ::isnan(static_cast<double>(f)); }
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inline bool is_nan_helper(__float128 f, const boost::false_type&) { return ::isnan(static_cast<double>(f)); }
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#endif
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#endif
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}
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namespace math{
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namespace detail{
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#ifdef BOOST_MATH_USE_STD_FPCLASSIFY
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template <class T>
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inline int fpclassify_imp BOOST_NO_MACRO_EXPAND(T t, const native_tag&)
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{
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return (std::fpclassify)(t);
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}
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#endif
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template <class T>
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inline int fpclassify_imp BOOST_NO_MACRO_EXPAND(T t, const generic_tag<true>&)
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{
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BOOST_MATH_INSTRUMENT_VARIABLE(t);
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// whenever possible check for Nan's first:
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#if defined(BOOST_HAS_FPCLASSIFY) && !defined(BOOST_MATH_DISABLE_STD_FPCLASSIFY)
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if(::boost::math_detail::is_nan_helper(t, ::boost::is_floating_point<T>()))
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return FP_NAN;
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#elif defined(isnan)
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if(boost::math_detail::is_nan_helper(t, ::boost::is_floating_point<T>()))
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return FP_NAN;
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#elif defined(_MSC_VER) || defined(__BORLANDC__)
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if(::_isnan(boost::math::tools::real_cast<double>(t)))
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return FP_NAN;
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#endif
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// std::fabs broken on a few systems especially for long long!!!!
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T at = (t < T(0)) ? -t : t;
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// Use a process of exclusion to figure out
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// what kind of type we have, this relies on
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// IEEE conforming reals that will treat
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// Nan's as unordered. Some compilers
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// don't do this once optimisations are
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// turned on, hence the check for nan's above.
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if(at <= (std::numeric_limits<T>::max)())
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{
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if(at >= (std::numeric_limits<T>::min)())
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return FP_NORMAL;
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return (at != 0) ? FP_SUBNORMAL : FP_ZERO;
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}
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else if(at > (std::numeric_limits<T>::max)())
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return FP_INFINITE;
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return FP_NAN;
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}
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template <class T>
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inline int fpclassify_imp BOOST_NO_MACRO_EXPAND(T t, const generic_tag<false>&)
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{
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#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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if(std::numeric_limits<T>::is_specialized)
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return fpclassify_imp(t, generic_tag<true>());
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#endif
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//
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// An unknown type with no numeric_limits support,
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// so what are we supposed to do we do here?
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//
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BOOST_MATH_INSTRUMENT_VARIABLE(t);
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return t == 0 ? FP_ZERO : FP_NORMAL;
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}
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template<class T>
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int fpclassify_imp BOOST_NO_MACRO_EXPAND(T x, ieee_copy_all_bits_tag)
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{
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typedef BOOST_DEDUCED_TYPENAME fp_traits<T>::type traits;
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BOOST_MATH_INSTRUMENT_VARIABLE(x);
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BOOST_DEDUCED_TYPENAME traits::bits a;
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traits::get_bits(x,a);
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BOOST_MATH_INSTRUMENT_VARIABLE(a);
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a &= traits::exponent | traits::flag | traits::significand;
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BOOST_MATH_INSTRUMENT_VARIABLE((traits::exponent | traits::flag | traits::significand));
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BOOST_MATH_INSTRUMENT_VARIABLE(a);
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if(a <= traits::significand) {
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if(a == 0)
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return FP_ZERO;
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else
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return FP_SUBNORMAL;
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}
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if(a < traits::exponent) return FP_NORMAL;
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a &= traits::significand;
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if(a == 0) return FP_INFINITE;
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return FP_NAN;
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}
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template<class T>
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int fpclassify_imp BOOST_NO_MACRO_EXPAND(T x, ieee_copy_leading_bits_tag)
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{
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typedef BOOST_DEDUCED_TYPENAME fp_traits<T>::type traits;
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BOOST_MATH_INSTRUMENT_VARIABLE(x);
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BOOST_DEDUCED_TYPENAME traits::bits a;
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traits::get_bits(x,a);
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a &= traits::exponent | traits::flag | traits::significand;
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if(a <= traits::significand) {
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if(x == 0)
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return FP_ZERO;
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else
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return FP_SUBNORMAL;
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}
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if(a < traits::exponent) return FP_NORMAL;
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a &= traits::significand;
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traits::set_bits(x,a);
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if(x == 0) return FP_INFINITE;
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return FP_NAN;
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}
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#if defined(BOOST_MATH_USE_STD_FPCLASSIFY) && (defined(BOOST_MATH_NO_NATIVE_LONG_DOUBLE_FP_CLASSIFY) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS))
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inline int fpclassify_imp BOOST_NO_MACRO_EXPAND(long double t, const native_tag&)
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{
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return boost::math::detail::fpclassify_imp(t, generic_tag<true>());
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}
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#endif
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} // namespace detail
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template <class T>
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inline int fpclassify BOOST_NO_MACRO_EXPAND(T t)
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{
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typedef typename detail::fp_traits<T>::type traits;
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typedef typename traits::method method;
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typedef typename tools::promote_args_permissive<T>::type value_type;
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#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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if(std::numeric_limits<T>::is_specialized && detail::is_generic_tag_false(static_cast<method*>(0)))
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return detail::fpclassify_imp(static_cast<value_type>(t), detail::generic_tag<true>());
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return detail::fpclassify_imp(static_cast<value_type>(t), method());
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#else
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return detail::fpclassify_imp(static_cast<value_type>(t), method());
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#endif
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}
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#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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template <>
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inline int fpclassify<long double> BOOST_NO_MACRO_EXPAND(long double t)
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{
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typedef detail::fp_traits<long double>::type traits;
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typedef traits::method method;
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typedef long double value_type;
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#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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if(std::numeric_limits<long double>::is_specialized && detail::is_generic_tag_false(static_cast<method*>(0)))
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return detail::fpclassify_imp(static_cast<value_type>(t), detail::generic_tag<true>());
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return detail::fpclassify_imp(static_cast<value_type>(t), method());
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#else
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return detail::fpclassify_imp(static_cast<value_type>(t), method());
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#endif
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}
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#endif
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namespace detail {
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#ifdef BOOST_MATH_USE_STD_FPCLASSIFY
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template<class T>
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inline bool isfinite_impl(T x, native_tag const&)
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{
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return (std::isfinite)(x);
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}
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#endif
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template<class T>
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inline bool isfinite_impl(T x, generic_tag<true> const&)
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{
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return x >= -(std::numeric_limits<T>::max)()
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&& x <= (std::numeric_limits<T>::max)();
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}
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template<class T>
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inline bool isfinite_impl(T x, generic_tag<false> const&)
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{
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#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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if(std::numeric_limits<T>::is_specialized)
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return isfinite_impl(x, generic_tag<true>());
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#endif
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(void)x; // warning suppression.
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return true;
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}
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template<class T>
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inline bool isfinite_impl(T x, ieee_tag const&)
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{
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typedef BOOST_DEDUCED_TYPENAME detail::fp_traits<T>::type traits;
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BOOST_DEDUCED_TYPENAME traits::bits a;
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traits::get_bits(x,a);
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a &= traits::exponent;
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return a != traits::exponent;
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}
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#if defined(BOOST_MATH_USE_STD_FPCLASSIFY) && defined(BOOST_MATH_NO_NATIVE_LONG_DOUBLE_FP_CLASSIFY)
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inline bool isfinite_impl BOOST_NO_MACRO_EXPAND(long double t, const native_tag&)
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{
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return boost::math::detail::isfinite_impl(t, generic_tag<true>());
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}
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#endif
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}
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template<class T>
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inline bool (isfinite)(T x)
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{ //!< \brief return true if floating-point type t is finite.
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typedef typename detail::fp_traits<T>::type traits;
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typedef typename traits::method method;
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// typedef typename boost::is_floating_point<T>::type fp_tag;
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typedef typename tools::promote_args_permissive<T>::type value_type;
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return detail::isfinite_impl(static_cast<value_type>(x), method());
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}
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#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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template<>
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inline bool (isfinite)(long double x)
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{ //!< \brief return true if floating-point type t is finite.
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typedef detail::fp_traits<long double>::type traits;
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typedef traits::method method;
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//typedef boost::is_floating_point<long double>::type fp_tag;
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typedef long double value_type;
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return detail::isfinite_impl(static_cast<value_type>(x), method());
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}
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#endif
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//------------------------------------------------------------------------------
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namespace detail {
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#ifdef BOOST_MATH_USE_STD_FPCLASSIFY
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template<class T>
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inline bool isnormal_impl(T x, native_tag const&)
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{
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return (std::isnormal)(x);
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}
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#endif
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template<class T>
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inline bool isnormal_impl(T x, generic_tag<true> const&)
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{
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if(x < 0) x = -x;
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return x >= (std::numeric_limits<T>::min)()
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&& x <= (std::numeric_limits<T>::max)();
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}
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template<class T>
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inline bool isnormal_impl(T x, generic_tag<false> const&)
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{
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#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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if(std::numeric_limits<T>::is_specialized)
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return isnormal_impl(x, generic_tag<true>());
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#endif
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return !(x == 0);
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}
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template<class T>
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inline bool isnormal_impl(T x, ieee_tag const&)
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{
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typedef BOOST_DEDUCED_TYPENAME detail::fp_traits<T>::type traits;
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BOOST_DEDUCED_TYPENAME traits::bits a;
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traits::get_bits(x,a);
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a &= traits::exponent | traits::flag;
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return (a != 0) && (a < traits::exponent);
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}
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#if defined(BOOST_MATH_USE_STD_FPCLASSIFY) && defined(BOOST_MATH_NO_NATIVE_LONG_DOUBLE_FP_CLASSIFY)
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inline bool isnormal_impl BOOST_NO_MACRO_EXPAND(long double t, const native_tag&)
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{
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return boost::math::detail::isnormal_impl(t, generic_tag<true>());
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}
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#endif
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}
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template<class T>
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inline bool (isnormal)(T x)
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{
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typedef typename detail::fp_traits<T>::type traits;
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typedef typename traits::method method;
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//typedef typename boost::is_floating_point<T>::type fp_tag;
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typedef typename tools::promote_args_permissive<T>::type value_type;
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return detail::isnormal_impl(static_cast<value_type>(x), method());
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}
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#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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template<>
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inline bool (isnormal)(long double x)
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{
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typedef detail::fp_traits<long double>::type traits;
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typedef traits::method method;
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//typedef boost::is_floating_point<long double>::type fp_tag;
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typedef long double value_type;
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return detail::isnormal_impl(static_cast<value_type>(x), method());
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}
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#endif
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//------------------------------------------------------------------------------
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namespace detail {
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#ifdef BOOST_MATH_USE_STD_FPCLASSIFY
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template<class T>
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inline bool isinf_impl(T x, native_tag const&)
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{
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return (std::isinf)(x);
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}
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#endif
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template<class T>
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inline bool isinf_impl(T x, generic_tag<true> const&)
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{
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(void)x; // in case the compiler thinks that x is unused because std::numeric_limits<T>::has_infinity is false
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return std::numeric_limits<T>::has_infinity
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&& ( x == std::numeric_limits<T>::infinity()
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|| x == -std::numeric_limits<T>::infinity());
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}
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template<class T>
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inline bool isinf_impl(T x, generic_tag<false> const&)
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{
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#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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if(std::numeric_limits<T>::is_specialized)
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return isinf_impl(x, generic_tag<true>());
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#endif
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(void)x; // warning suppression.
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return false;
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}
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template<class T>
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inline bool isinf_impl(T x, ieee_copy_all_bits_tag const&)
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{
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typedef BOOST_DEDUCED_TYPENAME fp_traits<T>::type traits;
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BOOST_DEDUCED_TYPENAME traits::bits a;
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traits::get_bits(x,a);
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a &= traits::exponent | traits::significand;
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return a == traits::exponent;
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}
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template<class T>
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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
|
|
#if defined(BOOST_MATH_USE_FLOAT128) && defined(BOOST_MATH_HAS_QUADMATH_H)
|
|
template<>
|
|
inline bool (isinf)(__float128 x)
|
|
{
|
|
return ::isinfq(x);
|
|
}
|
|
#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 suppression
|
|
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
|
|
#if defined(BOOST_MATH_USE_FLOAT128) && defined(BOOST_MATH_HAS_QUADMATH_H)
|
|
template<>
|
|
inline bool (isnan)(__float128 x)
|
|
{
|
|
return ::isnanq(x);
|
|
}
|
|
#endif
|
|
|
|
} // namespace math
|
|
} // namespace boost
|
|
|
|
#endif // BOOST_MATH_FPCLASSIFY_HPP
|
|
|