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533 lines
15 KiB
533 lines
15 KiB
// 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_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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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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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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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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} |
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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 fp_classify_imp(t, mpl::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) |
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template <> |
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inline int fpclassify_imp<long double> 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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#ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS |
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if(std::numeric_limits<T>::is_specialized && detail::is_generic_tag_false(method())) |
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return detail::fpclassify_imp(t, detail::generic_tag<true>()); |
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return detail::fpclassify_imp(t, method()); |
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#else |
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return detail::fpclassify_imp(t, method()); |
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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 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, mpl::true_()); |
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#endif |
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(void)x; // warning supression. |
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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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template <> |
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inline bool isfinite_impl<long double> 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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return detail::isfinite_impl(x, method()); |
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} |
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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, mpl::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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template <> |
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inline bool isnormal_impl<long double> 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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return detail::isnormal_impl(x, method()); |
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} |
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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, mpl::true_()); |
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#endif |
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(void)x; // warning supression. |
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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&) |
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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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if(a != traits::exponent) |
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return false; |
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traits::set_bits(x,0); |
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return x == 0; |
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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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template <> |
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inline bool isinf_impl<long double> BOOST_NO_MACRO_EXPAND(long double t, const native_tag&) |
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{ |
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return boost::math::detail::isinf_impl(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 bool (isinf)(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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return detail::isinf_impl(x, method()); |
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} |
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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 isnan_impl(T x, native_tag const&) |
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{ |
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return (std::isnan)(x); |
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} |
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#endif |
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template<class T> |
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inline bool isnan_impl(T x, generic_tag<true> const&) |
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{ |
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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 != x; |
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} |
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template<class T> |
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inline bool isnan_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 isnan_impl(x, mpl::true_()); |
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#endif |
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(void)x; // warning supression |
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return false; |
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} |
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template<class T> |
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inline bool isnan_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 isnan_impl(T x, ieee_copy_leading_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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if(a < traits::exponent) |
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return false; |
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a &= traits::significand; |
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traits::set_bits(x,a); |
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return x != 0; |
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} |
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} // namespace detail |
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template<class T> bool (isnan)(T x) |
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{ //!< \brief return true if floating-point type t is NaN (Not A Number). |
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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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return detail::isnan_impl(x, method()); |
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} |
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#ifdef isnan |
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template <> inline bool isnan BOOST_NO_MACRO_EXPAND<float>(float t){ return ::boost::math_detail::is_nan_helper(t, boost::true_type()); } |
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template <> inline bool isnan BOOST_NO_MACRO_EXPAND<double>(double t){ return ::boost::math_detail::is_nan_helper(t, boost::true_type()); } |
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template <> inline bool isnan BOOST_NO_MACRO_EXPAND<long double>(long double t){ return ::boost::math_detail::is_nan_helper(t, boost::true_type()); } |
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#endif |
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} // namespace math |
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} // namespace boost |
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#endif // BOOST_MATH_FPCLASSIFY_HPP |
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