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The stored exponents 0000<sub>16</sub> and 7FFF<sub>16</sub> are interpreted specially.
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! Exponent !! Significand zero !! Significand non-zero !! Equation
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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>
== Implementations ==
Quadruple precision is often implemented in software by a variety of techniques (such as 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|lc=on}}, less common (see "[[#Hardware support|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.
=== Computer-language support ===
A separate question is the extent to which quadruple-precision types are directly incorporated into computer [[programming language]]s.
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As of 2024, [[Rust (programming language)|Rust]] is currently working on adding a new <code>f128</code> type for IEEE quadruple-precision 128-bit floats.<ref>{{cite web |last1=Cross |first1=Travis |title=Tracking Issue for f16 and f128 float types |url=https://github.com/rust-lang/rust/issues/116909 |website=GitHub |access-date=2024-07-05}}</ref>
=== Libraries and toolboxes ===
* The [[GNU Compiler Collection|GCC]] quad-precision math library, [https://gcc.gnu.org/onlinedocs/libquadmath libquadmath], provides <code>__float128</code> and <code>__complex128</code> operations.
* The [[Boost (C++ libraries)|Boost]] multiprecision library Boost.Multiprecision provides unified cross-platform C++ interface for <code>__float128</code> and <code>_Quad</code> types, and includes a custom implementation of the standard math library.<ref>{{cite web |title=Boost.Multiprecision – float128 |url=http://www.boost.org/doc/libs/1_58_0/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/float128.html |access-date=2015-06-22}}</ref>
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