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290 lines
12 KiB
C++
290 lines
12 KiB
C++
// Copyright John Maddock 2016
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// Copyright Christopher Kormanyos 2016.
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// Copyright Paul A. Bristow 2016.
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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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// Contains Quickbook snippets as C++ comments - do not remove.
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// http://gcc.gnu.org/onlinedocs/libquadmath/ GCC Quad-Precision Math Library
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// https://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format
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// https://gcc.gnu.org/onlinedocs/gcc/C_002b_002b-Dialect-Options.html#C_002b_002b-Dialect-Options GNU 3.5 Options Controlling C++ Dialect
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// https://gcc.gnu.org/onlinedocs/gcc/C-Dialect-Options.html#C-Dialect-Options 3.4 Options Controlling C Dialect
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//[float128_includes_1
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#include <boost/cstdfloat.hpp> // For float_64_t, float128_t. Must be first include!
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//#include <boost/config.hpp>
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#include <boost/multiprecision/float128.hpp>
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#include <boost/math/special_functions.hpp> // For gamma function.
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#include <boost/math/constants/constants.hpp> // For constants pi, e ...
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#include <typeinfo> //
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#include <cmath> // for pow function.
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// #include <quadmath.h>
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// C:\program files\gcc-6-win64\lib\gcc\x86_64-w64-mingw32\6.1.1\include\quadmath.h
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// i:\modular-boost\boost\multiprecision\float128.hpp|210| undefined reference to `quadmath_snprintf'.
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//] [/float128_includes_1]
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//[float128_dialect_1
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/*`To make float128 available it is vital to get the dialect and options on the command line correct.
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Quad type is forbidden by all the strict C++ standards, so using or adding -std=c++11 and later standards will prevent its use.
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so explicitly use -std=gnu++11, 1y, 14, 17, or 1z or ...
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For GCC 6.1.1, for example, the default is if no C++ language dialect options are given, is -std=gnu++14.
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See https://gcc.gnu.org/onlinedocs/gcc/C-Dialect-Options.html#C-Dialect-Options
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https://gcc.gnu.org/onlinedocs/gcc/Standards.html#Standards 2 Language Standards Supported by GCC
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g++.exe -Wall -fexceptions -std=gnu++17 -g -fext-numeric-literals -fpermissive -lquadmath
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-II:\modular-boost\libs\math\include -Ii:\modular-boost -c J:\Cpp\float128\float128\float128_example.cpp -o obj\Debug\float128_example.o
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Requires GCC linker option -lquadmath
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If this is missing, then get errors like:
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\modular-boost\boost\multiprecision\float128.hpp|210|undefined reference to `quadmath_snprintf'|
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\modular-boost\boost\multiprecision\float128.hpp|351|undefined reference to `sqrtq'|
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Requires compile option
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-fext-numeric-literals
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If missing, then get errors like:
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\modular-boost\libs\math\include/boost/math/cstdfloat/cstdfloat_types.hpp:229:43: error: unable to find numeric literal operator 'operator""Q'
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A successful build log was:
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g++.exe -Wall -std=c++11 -fexceptions -std=gnu++17 -g -fext-numeric-literals -II:\modular-boost\libs\math\include -Ii:\modular-boost -c J:\Cpp\float128\float128\float128_example.cpp -o obj\Debug\float128_example.o
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g++.exe -o bin\Debug\float128.exe obj\Debug\float128_example.o -lquadmath
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*/
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//] [/float128_dialect_1]
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void show_versions(std::string title)
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{
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std::cout << title << std::endl;
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std::cout << "Platform: " << BOOST_PLATFORM << '\n'
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<< "Compiler: " << BOOST_COMPILER << '\n'
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<< "STL : " << BOOST_STDLIB << '\n'
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<< "Boost : " << BOOST_VERSION / 100000 << "."
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<< BOOST_VERSION / 100 % 1000 << "."
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<< BOOST_VERSION % 100
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<< std::endl;
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#ifdef _MSC_VER
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std::cout << "_MSC_FULL_VER = " << _MSC_FULL_VER << std::endl; // VS 2015 190023026
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#if defined _M_IX86
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std::cout << "(x86)" << std::endl;
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#endif
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#if defined _M_X64
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std::cout << " (x64)" << std::endl;
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#endif
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#if defined _M_IA64
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std::cout << " (Itanium)" << std::endl;
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#endif
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// Something very wrong if more than one is defined (so show them in all just in case)!
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#endif // _MSC_VER
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#ifdef __GNUC__
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//PRINT_MACRO(__GNUC__);
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//PRINT_MACRO(__GNUC_MINOR__);
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//PRINT_MACRO(__GNUC_PATCH__);
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std::cout << "GCC " << __VERSION__ << std::endl;
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//PRINT_MACRO(LONG_MAX);
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#endif // __GNUC__
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return;
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} // void show_version(std::string title)
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int main()
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{
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try
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{
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//[float128_example_3
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// Always use try'n'catch blocks to ensure any error messages are displayed.
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//`Ensure that all possibly significant digits (17) including trailing zeros are shown.
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std::cout.precision(std::numeric_limits<boost::float64_t>::max_digits10);
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std::cout.setf(std::ios::showpoint); // Show all significant trailing zeros.
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//] [/ float128_example_3]
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#ifdef BOOST_FLOAT128_C
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std::cout << "Floating-point type boost::float128_t is available." << std::endl;
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std::cout << " std::numeric_limits<boost::float128_t>::digits10 == "
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<< std::numeric_limits<boost::float128_t>::digits10 << std::endl;
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std::cout << " std::numeric_limits<boost::float128_t>::max_digits10 == "
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<< std::numeric_limits<boost::float128_t>::max_digits10 << std::endl;
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#else
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std::cout << "Floating-point type boost::float128_t is NOT available." << std::endl;
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#endif
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show_versions("");
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using boost::multiprecision::float128; // Wraps, for example, __float128 or _Quad.
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// or
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//using namespace boost::multiprecision;
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std::cout.precision(std::numeric_limits<float128>::max_digits10); // Show all potentially meaningful digits.
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std::cout.setf(std::ios::showpoint); // Show all significant trailing zeros.
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// float128 pi0 = boost::math::constants::pi(); // Compile fails - need to specify a type for the constant!
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float128 pi1 = boost::math::constants::pi<float128>(); // Returns a constant of type float128.
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std::cout << sqrt(pi1) << std::endl; // 1.77245385090551602729816748334114514
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float128 pi2 = boost::math::constants::pi<__float128>(); // Constant of type __float128 gets converted to float128 on the assignment.
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std::cout << sqrt(pi2) << std::endl; // 1.77245385090551602729816748334114514
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// DIY decimal digit literal constant, with suffix Q.
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float128 pi3 = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348Q;
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std::cout << sqrt(pi3) << std::endl; // 1.77245385090551602729816748334114514
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// Compare to ready-rolled sqrt(pi) constant from Boost.Math:
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std::cout << boost::math::constants::root_pi<float128>() << std::endl; // 1.77245385090551602729816748334114514
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// DIY decimal digit literal constant, without suffix Q, suffering seventeen silent digits loss of precision!
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float128 pi4 = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348;
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std::cout << sqrt(pi4) << std::endl; // 1.77245385090551599275151910313924857
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// float128 variables constructed from a quad-type literal can be declared constexpr if required:
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#ifndef BOOST_NO_CXX11_CONSTEXPR
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constexpr float128 pi_constexpr = 3.1415926535897932384626433832795028841971693993751058Q;
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#endif
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std::cout << pi_constexpr << std::endl; // 3.14159265358979323846264338327950280
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// But sadly functions like sqrt are not yet available constexpr for float128.
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// constexpr float128 root_pi_constexpr = sqrt(pi_constexpr); // Fails - not constexpr (yet).
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// constexpr float128 root_pi_constexpr = std::sqrt(pi_constexpr); // Fails - no known conversion for argument 1 from 'const float128'.
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// constexpr float128 root_pi_constexpr = sqrt(pi_constexpr); // Call to non-constexpr
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// constexpr float128 root_pi_constexpr = boost::math::constants::root_pi(); // Missing type for constant.
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// Best current way to get a constexpr is to use a Boost.Math constant if one is available.
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constexpr float128 root_pi_constexpr = boost::math::constants::root_pi<float128>();
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std::cout << root_pi_constexpr << std::endl; // 1.77245385090551602729816748334114514
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// Note that casts within the sqrt call are NOT NEEDED (nor allowed),
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// since all the variables are the correct type to begin with.
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// std::cout << sqrt<float128>(pi3) << std::endl;
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// But note examples of catastrophic (but hard to see) loss of precision below.
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// Note also that the library functions, here sqrt, is NOT defined using std::sqrt,
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// so that the correct overload is found using Argument Dependent LookUp (ADL).
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float128 ee = boost::math::constants::e<float128>();
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std::cout << ee << std::endl; // 2.71828182845904523536028747135266231
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float128 e1 = exp(1.Q); // Note argument to exp is type float128.
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std::cout << e1 << std::endl; // 2.71828182845904523536028747135266231
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// Beware - it is all too easy to silently get a much lower precision by mistake.
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float128 e1d = exp(1.); // Caution - only double 17 decimal digits precision!
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std::cout << e1d << std::endl; // 2.71828182845904509079559829842764884
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float128 e1i = exp(1); // Caution int promoted to double so only 17 decimal digits precision!
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std::cout << e1i << std::endl; // 2.71828182845904509079559829842764884
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float f1 = 1.F;
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float128 e1f = exp(f1); // Caution float so only 6 decimal digits precision out of 36!
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std::cout << e1f << std::endl; // 2.71828174591064453125000000000000000
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// In all these cases you get what you asked for and not what you expected or wanted.
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// Casting is essential if you start with a lower precision type.
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float128 e1q = exp(static_cast<float128>(f1)); // Full 36 decimal digits precision!
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std::cout << e1q << std::endl; // 2.71828182845904523536028747135266231
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float128 e1qc = exp((float128)f1); // Full 36 decimal digits precision!
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std::cout << e1qc << std::endl; // 2.71828182845904523536028747135266231
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float128 e1qcc = exp(float128(f1)); // Full 36 decimal digits precision!
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std::cout << e1qcc << std::endl; // 2.71828182845904523536028747135266231
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//float128 e1q = exp<float128>(1.); // Compile fails.
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// std::cout << e1q << std::endl; //
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// http://en.cppreference.com/w/cpp/language/typeid
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// The name()is implementation-dependent mangled, and may not be able to be output.
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// The example showing output using one of the implementations where type_info::name prints full type names;
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// filter through c++filt -t if using gcc or similar.
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//[float128_type_info
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const std::type_info& tifu128 = typeid(__float128); // OK.
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//std::cout << tifu128.name() << std::endl; // On GCC, aborts (because not printable string).
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//std::cout << typeid(__float128).name() << std::endl; // Aborts -
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// string name cannot be output.
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const std::type_info& tif128 = typeid(float128); // OK.
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std::cout << tif128.name() << std::endl; // OK.
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std::cout << typeid(float128).name() << std::endl; // OK.
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const std::type_info& tpi = typeid(pi1); // OK using GCC 6.1.1.
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// (from GCC 5 according to http://gcc.gnu.org/bugzilla/show_bug.cgi?id=43622)
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std::cout << tpi.name() << std::endl; // OK, Output implementation-dependent mangled name:
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// N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
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//] [/float128_type_info]
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}
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catch (std::exception ex)
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{ // Display details about why any exceptions are thrown.
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std::cout << "Thrown exception " << ex.what() << std::endl;
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}
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} // int main()
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/*
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[float128_output
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-std=c++11 or -std=c++17 don't work
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Floating-point type boost::float128_t is NOT available.
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Platform: Win32
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Compiler: GNU C++ version 6.1.1 20160609
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STL : GNU libstdc++ version 20160609
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Boost : 1.62.0
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GCC 6.1.1 20160609
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Added -fext-numeric-literals to
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-std=gnu++11 -fext-numeric-literals -lquadmath
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Floating-point type boost::float128_t is available.
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std::numeric_limits<boost::float128_t>::digits10 == 33
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std::numeric_limits<boost::float128_t>::max_digits10 == 36
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Platform: Win32
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Compiler: GNU C++ version 6.1.1 20160609
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STL : GNU libstdc++ version 20160609
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Boost : 1.62.0
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GCC 6.1.1 20160609
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1.77245385090551602729816748334114514
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1.77245385090551602729816748334114514
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1.77245385090551602729816748334114514
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1.77245385090551602729816748334114514
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N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
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N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
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N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
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Process returned 0 (0x0) execution time : 0.033 s
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Press any key to continue.
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//] [/float128_output]
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*/
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