Octuple-precision floating-point format: Difference between revisions

Revision as of 19:22, 8 June 2015

Revision as of 21:02, 8 June 2015

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

In its 2008 revision, the [[IEEE 754]] standard specifies a '''binary256binary 256''' format among the ''interchange formats'' (it is not a basic format), as having:

* [[Sign bit]]: 1 bit

* [[Exponent]] width: 19 bits

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The format is written with an implicit lead bit with value 1 unless the exponent is all zeros. Thus only 236 bits of the [[significand]] appear in the memory format, but the total precision is 237 bits (approximately 71 decimal digits: {{nowrap|log₁₀(2²³⁷) ≈ 71.344}}).

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The bits are laid out as follows (as you can see, it is so super-massive that it goes off the page, thus this visually demonstrates that common implementation of this would produce lots of lag):

The bits are laid out as follows:

[[File:Octuple precisionpersision visual demontration.png|1000px|Octuple precisionpersision visual demonstrationdemontration]]

[[File:Octuple precision visual demontration.png|1000px|Octuple precision visual demonstration]]

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=== Exponent encoding ===

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=== Hardware support ===

There is little to no hardware support for octuple-precision arithmetic. The requirements in-order to transport this piece of data are as follows.

* [[8-bit|8-bit architecture]] (statistical extrapolation since it would take 1/8 of the entire memory just to store 1 octuple precision numeral so it would be impractical) - 32 separate packages of information (at least) in order to transport this across the main data bus

* [[16-bit|x16 architecture]] - 16 separate packages of information (at least) in order to transport this across the main data bus

* [[x86|x86 architecture]] - 8 separate packages of information (at least) in order to transport this across the main data bus

* [[x86-64|x64 architecture]] - 4 separate packages of information (at least) in order to transport this across the main data bus

<br />

So, usage of this on modern architecture computers would create tremendous lag compared to other precision arithmetic.

== See also ==

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{{reflist}}

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[[Category:Binary arithmetic]]