Quadruple-precision floating-point format special characteristics: 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 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. Quadruple precision is often implemented in software by a variety of techniques (such as
Quadruple-precision floating-point format the double-double technique above, although that technique does not implement IEEE quadruple precision), since direct hardware support for quadruple precision is, as of 2016, less common (see "Hardware support" below). One can use general arbitrary-precision arithmetic libraries to obtain quadruple (or higher) precision, but specialized quadruple-precision implementations may achieve higher performance. A separate question is the extent to which quadruple-precision types are directly incorporated into computer programming languages. Quadruple precision is specified in Fortran by the codice_2 (module codice_3 from Fortran 2008 must be used, the constant codice_4 is equal to 16 on most processors), or as codice_5, or in