Octuple-precision floating-point format: Difference between revisions

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{{short description|256-bit computer number format}}

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{{use dmy dates|date=December 2022|cs1-dates=y}}

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{{Floating-point}}

{{Computer architecture bit widths}}

In [[computing]], '''octuple precision''' is a binary [[floating-point]]-based [[computer number format]] that occupies 32 [[byte]]s (256 [[bit]]s) in computer memory. This 256-[[bit]] octuple precision is for applications requiring results in higher than [[quadruple precision]]. This format is rarely used and very few environments support it.{{According to whom|date=June 2024}}

The range greatly exceeds what is needed to describe all known physical limitations within the observable universe or precisions better than [[Planck units]].

== IEEE 754 octuple-precision binary floating-point format: binary256 ==

== IEEE 754 octuple-precision binary floating-point format: binary256 ==

In its 2008 revision, the [[IEEE 754]] standard specifies a '''binary256''' format among the ''interchange formats'' (it is not a basic format), as having:

* [[Sign bit]]: 1 bit

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=== Exponent encoding ===

The octuple-precision binary floating-point exponent is encoded using an [[offset binary]] representation, with the zero offset being 262143; also known as exponent bias in the IEEE 754 standard.

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The stored exponents 00000₁₆ and 7FFFF₁₆ are interpreted specially.

{| class="wikitable" style="text-align: center;"

|-

! Exponent !! Significand zero !! Significand non-zero !! Equation

|-

| 00000₁₆ || [[0 (number)|0]], [[−0]] || [[subnormal numbers]] || (-1−1)^signbit × 2^−262142 × 0.significandbits₂

|-

| 00001₁₆, ..., 7FFFE₁₆ ||colspan=2| normalized value || (-1−1)^signbit × 2^{exponent bits₂} × 1.significandbits₂

|-

| 7FFFF₁₆ || ±[[infinity|∞]] || [[NaN]] (quiet, signallingsignaling)

|}

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=== Octuple-precision examples ===

These examples are given in bit ''representation'', in [[hexadecimal]],

of the floating-point value. This includes the sign, (biased) exponent, and significand.

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So the bits beyond the rounding point are <code>0101...</code> which is less than 1/2 of a [[unit in the last place]].

== Implementations ==

Octuple precision is rarely implemented since usage of it is extremely rare. [[Apple Inc.]] had an implementation of addition, subtraction and multiplication of octuple-precision numbers with a 224-bit [[two's complement]] significand and a 32-bit exponent.<ref name="Crandall-Papadopoulos_2002"/> One can use general [[arbitrary-precision arithmetic]] libraries to obtain octuple (or higher) precision, but specialized octuple-precision implementations may achieve higher performance.

=== Hardware support ===

There is no known hardware implementationwith ofnative support for octuple precision.

== See also ==

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}}

== Further reading ==

* {{cite book |author-first=Nelson H. F. |author-last=Beebe |title=The Mathematical-Function Computation Handbook - Programming Using the MathCW Portable Software Library |date=2017-08-22 |___location=Salt Lake City, UT, USA |publisher=[[Springer International Publishing AG]] |edition=1 |lccn=2017947446 |isbn=978-3-319-64109-6 |doi=10.1007/978-3-319-64110-2 }}