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Implementation of Float128 type

Overloading template functions with float128_t
Exponential function

Since few compilers implement a true 128-bit floating-point, and language features like the suffix Q (which may need an option -fext-numeric-literals to enable), and C++ Standard library functions are as-yet missing or incomplete in C++11, this Boost.Math implementation wraps __float128 provided by the GCC compiler GCC floating-point types or the _Quad type provided by the Intel compiler.

This is provided to in order to demonstrate, and users to evaluate, the feasibility and benefits of higher-precision floating-point, especially to allow use of the full <cmath> and Boost.Math library of functions and distributions at high precision.

(It is also possible to use Boost.Math with Boost.Multiprecision decimal and binary, but since these are entirely software solutions, allowing much higher precision or arbitrary precision, they are likely to be slower).

We also provide (we believe full) support for <limits>, <cmath>, I/O stream operations in <iostream>, and <complex>.

As a prototype for a future C++ standard, we place all these in namespace std. This contravenes the existing C++ standard of course, so selecting any compiler that promises to check conformance will fail.

[Tip] Tip

For GCC, compile with -std=gnu++11 or -std=gnu++03 and do not use -std=stdc++11 or any 'strict' options, as these turn off full support for __float128. These requirements also apply to the Intel compiler on Linux, for Intel on Windows you need to compile with -Qoption,cpp,--extended_float_type -DBOOST_MATH_USE_FLOAT128 in order to activate 128-bit floating point support.

The __float128 type is provided by the libquadmath library on GCC or by Intel's FORTRAN library with Intel C++. THey also provide a full set of <cmath> functions in namespace std.

Using C __float128 quadmath type


The source code is at quadmath_snprintf.c.

Using C++ float128 quadmath type

For C++ programs, you will want to use the C++ type float128

See example at cstdfloat_example.cpp.

A typical invocation of the compiler is

g++ -O3 -std=gnu++11 test.cpp -I/c/modular-boost -lquadmath -o test.exe
[Tip] Tip

If you are trying to use the develop branch of Boost.Math, then make -I/c/modular-boost/libs/math/include the first include directory.

g++ -O3 -std=gnu++11 test.cpp -I/c/modular-boost/libs/math/include -I/c/modular-boost -lquadmath -o test.exe
[Note] Note

So far, the only missing detail that we had noted was in trying to use <typeinfo>, for example for std::cout << typeid<__float_128>.name();.

Link fails: undefined reference to typeinfo for __float128.

See GCC Bug 43622 - no C++ typeinfo for __float128. But this is reported (Marc Glisse 2015-04-04 ) fixed in GCC 5 (and above).

For example, with GCC6.1.1 this works as expected to a mangled string name, and output (if possible - not always).

const std::type_info& tifu128 = typeid(__float128); // OK.
//std::cout << << 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 << << std::endl; // OK.
std::cout << typeid(float128).name() << std::endl; // OK.

const std::type_info& tpi = typeid(pi1); // OK GCC 6.1.1 (from GCC 5 according to
std::cout << << std::endl; // Output mangled name:

// N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE