extendedprecision

Extended precision refers to floating-point formats that provide more precision than the standard single (32-bit) or double (64-bit) representations. It is used to reduce rounding errors, improve the accuracy of numerical methods, and mitigate error accumulation in iterative computations. In practice, extended precision often means a larger significand or a wider exponent than the usual 32- or 64-bit formats, sometimes at the cost of speed or portability.

One common historical form is the 80-bit extended precision used by the x87 floating-point unit. It uses 1 sign bit, 15 exponent bits with a bias of 16383, and a 64-bit significand, where the leading bit is explicit. This yields about 64 bits of precision and a wider range than standard double precision. In some architectures and languages, this 80-bit type is accessible as a long double and may be mapped differently by compilers and ABIs.

IEEE 754-2008 introduced binary128, often called quadruple precision, as another form of extended precision. It uses 1 sign bit, 15 exponent bits (bias 16383), and 112 fraction bits, giving a precision of 113 bits. Other implementations may provide even larger or software-emulated extended formats, but binary128 represents a widely standardized option.

In programming, the presence and size of extended precision depend on the language, compiler, and hardware. The long double type in C/C++ is commonly used to access extended precision, but its exact size can vary by platform. Extended precision offers improved numerical accuracy at the expense of performance and portability, and where portability is critical, software libraries or arbitrary-precision arithmetic may be preferred.