...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
#include <boost/multiprecision/float128.hpp>
namespace boost{ namespace multiprecision{ class float128_backend; typedef number<float128_backend, et_off> float128; }} // namespaces
The float128
number type
is a very thin wrapper around GCC's __float128
or Intel's _Quad
data types
and provides an real-number type that is a drop-in replacement for the
native C++ floating-point types, but with a 113 bit mantissa, and compatible
with FORTRAN's 128-bit QUAD real.
All the usual standard library and std::numeric_limits
support are available, performance should be equivalent to the underlying
native types: for example the LINPACK benchmarks for GCC's __float128
and boost::multiprecision::float128
both achieved 5.6 MFLOPS[3].
As well as the usual conversions from arithmetic and string types, instances
of float128
are copy constructible
and assignable from GCC's __float128
and Intel's _Quad
data
types.
It's also possible to access the underlying __float128
or _Quad
type via the
data()
member function of float128_backend
.
Things you should know when using this type:
float128
s
have the value zero.
number
on this backend
move aware.
constexpr
aware - basic constexpr arithmetic is supported from C++14 and onwards,
comparisons, plus the functions fabs
,
abs
, fpclassify
, isnormal
,
isfinite
, isinf
and isnan
are also supported if either the compiler implements C++20's std::is_constant_evaluated()
,
or if the compiler is GCC.
_Quad
as the underlying type: this is a current limitation of our code. Round
tripping when using __float128
as the underlying type is possible (both for GCC and Intel).
std::runtime_error
being thrown if the string can not be interpreted as a valid floating-point
number.
float128
can be
used as a literal type (constexpr support).
float128
can be
used for full constexpr
arithmetic from C++14 and later with GCC. The functions abs
, fabs
,
fpclassify
, isnan
, isinf
,
isfinite
and isnormal
are also constexpr
,
but the transcendental functions are not.
__float128
if it's available and
_Quad
if not. You can
override the default by defining either BOOST_MP_USE_FLOAT128
or BOOST_MP_USE_QUAD
.
_Quad
type, the code must be compiled with the compiler option -Qoption,cpp,--extended_float_type
.
gcc
,
you need to use the flag --std=gnu++11/14/17
,
as the suffix 'Q' is a GNU extension. Compilation fails with the flag
--std=c++11/14/17
unless you also use -fext-numeric-literals
.
libquadmath.dll
with the link command -lquadmath
and ensure that the DLL
is visible by the linker. If you are using the B2/bjam build system
then commands<linkflags>-lQUADMATH
and <linkflags>-L"path/to/lib"
will be needed.
std::numeric_limits<float128>
and extremely close but
not identical to those from the equivalent precision and
range multiprecision types std::numeric_limits<cpp_bin_float_quad>
and std::numeric_limits<cpp_dec_float_quad>
.
#include <boost/multiprecision/float128.hpp> #include <boost/math/special_functions/gamma.hpp> #include <iostream> int main() { using namespace boost::multiprecision; // Potential to cause name collisions? // using boost::multiprecision::float128; // is safer.
The type float128 provides operations at 128-bit precision with Quadruple-precision
floating-point format and have full std::numeric_limits
support:
float128 b = 2;
There are 15 bits of (biased) binary exponent and 113-bits of significand precision
std::cout << std::numeric_limits<float128>::digits << std::endl;
or 33 decimal places:
std::cout << std::numeric_limits<float128>::digits10 << std::endl;
We can use any C++ std library function, so let's show all the at-most 36 potentially significant digits, and any trailing zeros, as well:
std::cout.setf(std::ios_base::showpoint); // Include any trailing zeros. std::cout << std::setprecision(std::numeric_limits<float128>::max_digits10) << log(b) << std::endl; // Shows log(2) = 0.693147180559945309417232121458176575
We can also use any function from Boost.Math, for example, the 'true gamma'
function tgamma
:
std::cout << boost::math::tgamma(b) << std::endl;
And since we have an extended exponent range, we can generate some really large numbers here (4.02387260077093773543702433923004111e+2564):
std::cout << boost::math::tgamma(float128(1000)) << std::endl;
We can declare constants using GCC or Intel's native types, and literals
with the Q suffix, and these can be declared constexpr
if required:
// std::numeric_limits<float128>::max_digits10 = 36 constexpr float128 pi = 3.14159265358979323846264338327950288Q; std::cout.precision(std::numeric_limits<float128>::max_digits10); std::cout << "pi = " << pi << std::endl; //pi = 3.14159265358979323846264338327950280
Values for std::numeric_limits<float128>
are:
GCC 8.1.0 Type name is float128_t: Type is g std::is_fundamental<> = true boost::multiprecision::detail::is_signed<> = true boost::multiprecision::detail::is_unsigned<> = false boost::multiprecision::detail::is_integral<> = false boost::multiprecision::detail::is_arithmetic<> = true std::is_const<> = false std::is_trivial<> = true std::is_standard_layout<> = true std::is_pod<> = true std::numeric_limits::<>is_exact = false std::numeric_limits::<>is bounded = true std::numeric_limits::<>is_modulo = false std::numeric_limits::<>is_iec559 = true std::numeric_limits::<>traps = false std::numeric_limits::<>tinyness_before = false std::numeric_limits::<>max() = 1.18973149535723176508575932662800702e+4932 std::numeric_limits::<>min() = 3.36210314311209350626267781732175260e-4932 std::numeric_limits::<>lowest() = -1.18973149535723176508575932662800702e+4932 std::numeric_limits::<>min_exponent = -16381 std::numeric_limits::<>max_exponent = 16384 std::numeric_limits::<>epsilon() = 1.92592994438723585305597794258492732e-34 std::numeric_limits::<>radix = 2 std::numeric_limits::<>digits = 113 std::numeric_limits::<>digits10 = 33 std::numeric_limits::<>max_digits10 = 36 std::numeric_limits::<>has denorm = true std::numeric_limits::<>denorm min = 6.47517511943802511092443895822764655e-4966 std::denorm_loss = false limits::has_signaling_NaN == false std::numeric_limits::<>quiet_NaN = nan std::numeric_limits::<>infinity = inf