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- // Copyright John Maddock 2016
- // Copyright Christopher Kormanyos 2016.
- // Copyright Paul A. Bristow 2016.
- // Use, modification and distribution are subject to the
- // Boost Software License, Version 1.0. (See accompanying file
- // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
- // Contains Quickbook snippets as C++ comments - do not remove.
- // http://gcc.gnu.org/onlinedocs/libquadmath/ GCC Quad-Precision Math Library
- // https://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format
- // https://gcc.gnu.org/onlinedocs/gcc/C_002b_002b-Dialect-Options.html#C_002b_002b-Dialect-Options GNU 3.5 Options Controlling C++ Dialect
- // https://gcc.gnu.org/onlinedocs/gcc/C-Dialect-Options.html#C-Dialect-Options 3.4 Options Controlling C Dialect
- //[float128_includes_1
- #include <boost/cstdfloat.hpp> // For float_64_t, float128_t. Must be first include!
- //#include <boost/config.hpp>
- #include <boost/multiprecision/float128.hpp>
- #include <boost/math/special_functions.hpp> // For gamma function.
- #include <boost/math/constants/constants.hpp> // For constants pi, e ...
- #include <typeinfo> //
- #include <cmath> // for pow function.
- // #include <quadmath.h>
- // C:\program files\gcc-6-win64\lib\gcc\x86_64-w64-mingw32\6.1.1\include\quadmath.h
- // i:\modular-boost\boost\multiprecision\float128.hpp|210| undefined reference to `quadmath_snprintf'.
- //] [/float128_includes_1]
- //[float128_dialect_1
- /*`To make float128 available it is vital to get the dialect and options on the command line correct.
- Quad type is forbidden by all the strict C++ standards, so using or adding -std=c++11 and later standards will prevent its use.
- so explicitly use -std=gnu++11, 1y, 14, 17, or 1z or ...
- For GCC 6.1.1, for example, the default is if no C++ language dialect options are given, is -std=gnu++14.
- See https://gcc.gnu.org/onlinedocs/gcc/C-Dialect-Options.html#C-Dialect-Options
- https://gcc.gnu.org/onlinedocs/gcc/Standards.html#Standards 2 Language Standards Supported by GCC
- g++.exe -Wall -fexceptions -std=gnu++17 -g -fext-numeric-literals -fpermissive -lquadmath
- -II:\modular-boost\libs\math\include -Ii:\modular-boost -c J:\Cpp\float128\float128\float128_example.cpp -o obj\Debug\float128_example.o
- Requires GCC linker option -lquadmath
- If this is missing, then get errors like:
- \modular-boost\boost\multiprecision\float128.hpp|210|undefined reference to `quadmath_snprintf'|
- \modular-boost\boost\multiprecision\float128.hpp|351|undefined reference to `sqrtq'|
- Requires compile option
- -fext-numeric-literals
- If missing, then get errors like:
- \modular-boost\libs\math\include/boost/math/cstdfloat/cstdfloat_types.hpp:229:43: error: unable to find numeric literal operator 'operator""Q'
- A successful build log was:
- 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
- g++.exe -o bin\Debug\float128.exe obj\Debug\float128_example.o -lquadmath
- */
- //] [/float128_dialect_1]
- void show_versions(std::string title)
- {
- std::cout << title << std::endl;
- std::cout << "Platform: " << BOOST_PLATFORM << '\n'
- << "Compiler: " << BOOST_COMPILER << '\n'
- << "STL : " << BOOST_STDLIB << '\n'
- << "Boost : " << BOOST_VERSION / 100000 << "."
- << BOOST_VERSION / 100 % 1000 << "."
- << BOOST_VERSION % 100
- << std::endl;
- #ifdef _MSC_VER
- std::cout << "_MSC_FULL_VER = " << _MSC_FULL_VER << std::endl; // VS 2015 190023026
- #if defined _M_IX86
- std::cout << "(x86)" << std::endl;
- #endif
- #if defined _M_X64
- std::cout << " (x64)" << std::endl;
- #endif
- #if defined _M_IA64
- std::cout << " (Itanium)" << std::endl;
- #endif
- // Something very wrong if more than one is defined (so show them in all just in case)!
- #endif // _MSC_VER
- #ifdef __GNUC__
- //PRINT_MACRO(__GNUC__);
- //PRINT_MACRO(__GNUC_MINOR__);
- //PRINT_MACRO(__GNUC_PATCH__);
- std::cout << "GCC " << __VERSION__ << std::endl;
- //PRINT_MACRO(LONG_MAX);
- #endif // __GNUC__
- return;
- } // void show_version(std::string title)
- int main()
- {
- try
- {
- //[float128_example_3
- // Always use try'n'catch blocks to ensure any error messages are displayed.
- //`Ensure that all possibly significant digits (17) including trailing zeros are shown.
- std::cout.precision(std::numeric_limits<boost::float64_t>::max_digits10);
- std::cout.setf(std::ios::showpoint); // Show all significant trailing zeros.
- //] [/ float128_example_3]
- #ifdef BOOST_FLOAT128_C
- std::cout << "Floating-point type boost::float128_t is available." << std::endl;
- std::cout << " std::numeric_limits<boost::float128_t>::digits10 == "
- << std::numeric_limits<boost::float128_t>::digits10 << std::endl;
- std::cout << " std::numeric_limits<boost::float128_t>::max_digits10 == "
- << std::numeric_limits<boost::float128_t>::max_digits10 << std::endl;
- #else
- std::cout << "Floating-point type boost::float128_t is NOT available." << std::endl;
- #endif
- show_versions("");
- using boost::multiprecision::float128; // Wraps, for example, __float128 or _Quad.
- // or
- //using namespace boost::multiprecision;
- std::cout.precision(std::numeric_limits<float128>::max_digits10); // Show all potentially meaningful digits.
- std::cout.setf(std::ios::showpoint); // Show all significant trailing zeros.
- // float128 pi0 = boost::math::constants::pi(); // Compile fails - need to specify a type for the constant!
- float128 pi1 = boost::math::constants::pi<float128>(); // Returns a constant of type float128.
- std::cout << sqrt(pi1) << std::endl; // 1.77245385090551602729816748334114514
- float128 pi2 = boost::math::constants::pi<__float128>(); // Constant of type __float128 gets converted to float128 on the assignment.
- std::cout << sqrt(pi2) << std::endl; // 1.77245385090551602729816748334114514
- // DIY decimal digit literal constant, with suffix Q.
- float128 pi3 = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348Q;
- std::cout << sqrt(pi3) << std::endl; // 1.77245385090551602729816748334114514
- // Compare to ready-rolled sqrt(pi) constant from Boost.Math:
- std::cout << boost::math::constants::root_pi<float128>() << std::endl; // 1.77245385090551602729816748334114514
- // DIY decimal digit literal constant, without suffix Q, suffering seventeen silent digits loss of precision!
- float128 pi4 = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348;
- std::cout << sqrt(pi4) << std::endl; // 1.77245385090551599275151910313924857
- // float128 variables constructed from a quad-type literal can be declared constexpr if required:
- #ifndef BOOST_NO_CXX11_CONSTEXPR
- constexpr float128 pi_constexpr = 3.1415926535897932384626433832795028841971693993751058Q;
- #endif
- std::cout << pi_constexpr << std::endl; // 3.14159265358979323846264338327950280
- // But sadly functions like sqrt are not yet available constexpr for float128.
- // constexpr float128 root_pi_constexpr = sqrt(pi_constexpr); // Fails - not constexpr (yet).
- // constexpr float128 root_pi_constexpr = std::sqrt(pi_constexpr); // Fails - no known conversion for argument 1 from 'const float128'.
- // constexpr float128 root_pi_constexpr = sqrt(pi_constexpr); // Call to non-constexpr
- // constexpr float128 root_pi_constexpr = boost::math::constants::root_pi(); // Missing type for constant.
- // Best current way to get a constexpr is to use a Boost.Math constant if one is available.
- constexpr float128 root_pi_constexpr = boost::math::constants::root_pi<float128>();
- std::cout << root_pi_constexpr << std::endl; // 1.77245385090551602729816748334114514
- // Note that casts within the sqrt call are NOT NEEDED (nor allowed),
- // since all the variables are the correct type to begin with.
- // std::cout << sqrt<float128>(pi3) << std::endl;
- // But note examples of catastrophic (but hard to see) loss of precision below.
- // Note also that the library functions, here sqrt, is NOT defined using std::sqrt,
- // so that the correct overload is found using Argument Dependent LookUp (ADL).
- float128 ee = boost::math::constants::e<float128>();
- std::cout << ee << std::endl; // 2.71828182845904523536028747135266231
- float128 e1 = exp(1.Q); // Note argument to exp is type float128.
- std::cout << e1 << std::endl; // 2.71828182845904523536028747135266231
- // Beware - it is all too easy to silently get a much lower precision by mistake.
- float128 e1d = exp(1.); // Caution - only double 17 decimal digits precision!
- std::cout << e1d << std::endl; // 2.71828182845904509079559829842764884
- float128 e1i = exp(1); // Caution int promoted to double so only 17 decimal digits precision!
- std::cout << e1i << std::endl; // 2.71828182845904509079559829842764884
- float f1 = 1.F;
- float128 e1f = exp(f1); // Caution float so only 6 decimal digits precision out of 36!
- std::cout << e1f << std::endl; // 2.71828174591064453125000000000000000
- // In all these cases you get what you asked for and not what you expected or wanted.
- // Casting is essential if you start with a lower precision type.
- float128 e1q = exp(static_cast<float128>(f1)); // Full 36 decimal digits precision!
- std::cout << e1q << std::endl; // 2.71828182845904523536028747135266231
- float128 e1qc = exp((float128)f1); // Full 36 decimal digits precision!
- std::cout << e1qc << std::endl; // 2.71828182845904523536028747135266231
- float128 e1qcc = exp(float128(f1)); // Full 36 decimal digits precision!
- std::cout << e1qcc << std::endl; // 2.71828182845904523536028747135266231
- //float128 e1q = exp<float128>(1.); // Compile fails.
- // std::cout << e1q << std::endl; //
- // http://en.cppreference.com/w/cpp/language/typeid
- // The name()is implementation-dependent mangled, and may not be able to be output.
- // The example showing output using one of the implementations where type_info::name prints full type names;
- // filter through c++filt -t if using gcc or similar.
- //[float128_type_info
- const std::type_info& tifu128 = typeid(__float128); // OK.
- //std::cout << tifu128.name() << std::endl; // On GCC, aborts (because not printable string).
- //std::cout << typeid(__float128).name() << std::endl; // Aborts -
- // string name cannot be output.
- const std::type_info& tif128 = typeid(float128); // OK.
- std::cout << tif128.name() << std::endl; // OK.
- std::cout << typeid(float128).name() << std::endl; // OK.
- const std::type_info& tpi = typeid(pi1); // OK using GCC 6.1.1.
- // (from GCC 5 according to http://gcc.gnu.org/bugzilla/show_bug.cgi?id=43622)
- std::cout << tpi.name() << std::endl; // OK, Output implementation-dependent mangled name:
- // N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
- //] [/float128_type_info]
- }
- catch (std::exception ex)
- { // Display details about why any exceptions are thrown.
- std::cout << "Thrown exception " << ex.what() << std::endl;
- }
- } // int main()
- /*
- [float128_output
- -std=c++11 or -std=c++17 don't work
- Floating-point type boost::float128_t is NOT available.
- Platform: Win32
- Compiler: GNU C++ version 6.1.1 20160609
- STL : GNU libstdc++ version 20160609
- Boost : 1.62.0
- GCC 6.1.1 20160609
- Added -fext-numeric-literals to
- -std=gnu++11 -fext-numeric-literals -lquadmath
- Floating-point type boost::float128_t is available.
- std::numeric_limits<boost::float128_t>::digits10 == 33
- std::numeric_limits<boost::float128_t>::max_digits10 == 36
- Platform: Win32
- Compiler: GNU C++ version 6.1.1 20160609
- STL : GNU libstdc++ version 20160609
- Boost : 1.62.0
- GCC 6.1.1 20160609
- 1.77245385090551602729816748334114514
- 1.77245385090551602729816748334114514
- 1.77245385090551602729816748334114514
- 1.77245385090551602729816748334114514
- N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
- N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
- N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
- Process returned 0 (0x0) execution time : 0.033 s
- Press any key to continue.
- //] [/float128_output]
- */
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