Quadruple-precision floating-point format: Difference between revisions

Revision as of 14:09, 29 July 2025

Revision as of 08:37, 1 August 2025

Line 112:

* Because of the reason above, it is possible to represent values like {{nowrap|1 + 2⁻¹⁰⁷⁴}}, which is the smallest representable number greater than 1.

In addition to the double-double arithmetic, it is also possible to generate triple-double or quad-double arithmetic if higher precision is required without any higher precision floating-point library. They are represented as a sum of three (or four) double-precision values respectively. They can represent operations with at least 159/161 and 212/215 bits respectively. A natural extension to an arbitrary number of terms (though limited by the exponent range) is called ''floating-point expansions''.

A similar technique can be used to produce a '''double-quad arithmetic''', which is represented as a sum of two quadruple-precision values. They can represent operations with at least 226 (or 227) bits.<ref>sourceware.org [http://sourceware.org/ml/libc-alpha/2012-03/msg01024.html Re: The state of glibc libm]</ref>