Floating point - Revision history

Jnc: /* External links */ +A Test of a Computer’s Floating-Point Arithmetic Unit

2026-10-17T10:53:21Z

External links: +A Test of a Computer’s Floating-Point Arithmetic Unit

← Older revision		Revision as of 10:53, 17 October 2026
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	In all four, there is actually one more bit of mantissa than shown, because they are usually stored in [[normalization\|normalized]] form (i.e. the mantissa is constrained to be between 1/2 and 1, without any leading 0's to the right of the 'point'), and so there is always a '1' there, which is not stored.		In all four, there is actually one more bit of mantissa than shown, because they are usually stored in [[normalization\|normalized]] form (i.e. the mantissa is constrained to be between 1/2 and 1, without any leading 0's to the right of the 'point'), and so there is always a '1' there, which is not stored.

			==Further reading==

			* N. L. Schryer, [https://www.tuhs.org/Archive/Documentation/TechReports/Bell_Labs/CSTRs/89.pdf A Test of a Computer’s Floating-Point Arithmetic Unit], Computing Science Technical Report No. 89, AT&T Bell Laboratories, Murray Hill, 1981 - tough going in parts for non-mathematicians, but interesting; reports on a wide range of machines extant as of the time of writing

	==External links==		==External links==

Jnc: Link normalized

2024-03-17T16:34:44Z

Link normalized

← Older revision		Revision as of 16:34, 17 March 2024
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	* Octuple-precision: 19+236		* Octuple-precision: 19+236

	In all four, there is actually one more bit of mantissa than shown, because they are usually stored in 'normalized' form (i.e. the mantissa is constrained to be between 1/2 and 1, without any leading 0's to the right of the 'point'), and so there is always a '1' there, which is not stored.		In all four, there is actually one more bit of mantissa than shown, because they are usually stored in [[normalization\|normalized]] form (i.e. the mantissa is constrained to be between 1/2 and 1, without any leading 0's to the right of the 'point'), and so there is always a '1' there, which is not stored.

	==External links==		==External links==

Jnc: /* External links */ +Floating-Point Formats

2023-10-23T04:42:59Z

External links: +Floating-Point Formats

← Older revision		Revision as of 04:42, 23 October 2023
Line 13:		Line 13:

	In all four, there is actually one more bit of mantissa than shown, because they are usually stored in 'normalized' form (i.e. the mantissa is constrained to be between 1/2 and 1, without any leading 0's to the right of the 'point'), and so there is always a '1' there, which is not stored.		In all four, there is actually one more bit of mantissa than shown, because they are usually stored in 'normalized' form (i.e. the mantissa is constrained to be between 1/2 and 1, without any leading 0's to the right of the 'point'), and so there is always a '1' there, which is not stored.

			==External links==

			* [http://employees.oneonta.edu/zhangs/csci201/general%20Floating%20Point%20Format.htm Floating-Point Formats] - good overview

	[[Category: Theory]]		[[Category: Theory]]

Jnc: +cat

2018-12-16T04:11:44Z

+cat

← Older revision		Revision as of 04:11, 16 December 2018
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	In all four, there is actually one more bit of mantissa than shown, because they are usually stored in 'normalized' form (i.e. the mantissa is constrained to be between 1/2 and 1, without any leading 0's to the right of the 'point'), and so there is always a '1' there, which is not stored.		In all four, there is actually one more bit of mantissa than shown, because they are usually stored in 'normalized' form (i.e. the mantissa is constrained to be between 1/2 and 1, without any leading 0's to the right of the 'point'), and so there is always a '1' there, which is not stored.

			[[Category: Theory]]

Jnc: Mention FPPs

2018-05-14T00:29:17Z

Mention FPPs

← Older revision		Revision as of 00:29, 14 May 2018
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	'''Floating point''' is a term used to describe computer support for real numbers; originally performed in software, it is now invariably done in hardware. Most implementations are fixed accuracy, and thus may truncate or round some results. It is possible to use floating point for irrational numbers as well, provided the user is prepared to accept the slight loss of accuracy.		'''Floating point''' is a term used to describe computer support for real numbers; originally performed in [[software]], it is now invariably done in [[hardware]], often in a special [[floating point processor]].

			Most implementations are fixed accuracy, and thus may truncate or round some results. It is possible to use floating point for irrational numbers as well, provided the user is prepared to accept the slight loss of accuracy.

	Most hardware implementations of floating point uses three fields - a sign bit, an exponent, and a mantissa (fractional part); i.e. floating point numbers are represented in the form .X * 2^Y, where Y can be negative or positive.		Most hardware implementations of floating point uses three fields - a sign bit, an exponent, and a mantissa (fractional part); i.e. floating point numbers are represented in the form .X * 2^Y, where Y can be negative or positive.

Jnc: A reasonable start

2016-11-14T00:56:45Z

A reasonable start

New page

'''Floating point''' is a term used to describe computer support for real numbers; originally performed in software, it is now invariably done in hardware. Most implementations are fixed accuracy, and thus may truncate or round some results. It is possible to use floating point for irrational numbers as well, provided the user is prepared to accept the slight loss of accuracy.

Most hardware implementations of floating point uses three fields - a sign bit, an exponent, and a mantissa (fractional part); i.e. floating point numbers are represented in the form .X * 2^Y, where Y can be negative or positive.

Historically, different architectures devised their own floating point specifications (e.g. [[FP11 floating point]]), but there are now IEEE standards for floating point. The following formats (each with one sign bit, and exponent and mantissa bits as given) for storing floating point numbers exist:

* Single-precision: 8+23
* Double-precision: 11+52
* Quadruple-precision: 15+112
* Octuple-precision: 19+236

In all four, there is actually one more bit of mantissa than shown, because they are usually stored in 'normalized' form (i.e. the mantissa is constrained to be between 1/2 and 1, without any leading 0's to the right of the 'point'), and so there is always a '1' there, which is not stored.