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### floating-point Numbers

The following back-ends provide floating-point arithmetic:

Backend Type | Header | Radix | Dependencies | Pros | Cons
--- | --- | --- | --- | --- | ---
`cpp_bin_float<N>` | boost/multiprecision/cpp_bin_float.hpp | 2 | None | Header only, all C++ implementation. Boost licence. | Approximately 2x slower than the MPFR or GMP libraries.
`cpp_dec_float<N>` | boost/multiprecision/cpp_dec_float.hpp | 10 | None | Header only, all C++ implementation. Boost licence. | Approximately 2x slower than the MPFR or GMP libraries.
`mpf_float<N>` | boost/multiprecision/gmp.hpp | 2 | GMP | Very fast and efficient back-end. | Dependency on GNU licensed GMP library.
`mpfr_float<N>` | boost/multiprecision/mpfr.hpp | 2 | GMP and MPFR | Very fast and efficient back-end, with its own standard library implementation. | Dependency on GNU licensed GMP and MPFR libraries.
`float128` | boost/multiprecision/float128.hpp | 2 | Either libquadmath or the Intel C++ Math library. | Very fast and efficient back-end for 128-bit floating-point values (113-bit mantissa, equivalent to FORTRAN's QUAD real) | Depends on the compiler being either recent GCC or Intel C++ versions.