Floating point - Revision history

Jnc: Link normalized

2024-03-17T16:34:44Z

Link normalized

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

2023-10-23T04:42:59Z

‎External links: +Floating-Point Formats

Jnc: +cat

2018-12-16T04:11:44Z

+cat

Jnc: Mention FPPs

2018-05-14T00:29:17Z

Mention FPPs

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.

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 * 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==

← Older revision		Revision as of 04:42, 23 October 2023
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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.
		+
		+	==External links==
		+
		+	* [http://employees.oneonta.edu/zhangs/csci201/general%20Floating%20Point%20Format.htm Floating-Point Formats] - good overview

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

← 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]]

← 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.