Saturation Arithmetic

Saturation arithmetic - Wikipedia, the free encyclopedia
Additionally, saturation arithmetic enables efficient algorithms for many ... Saturation arithmetic for integers has also implemented in software for a number ...
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Bug ID: 4466549 Add saturation/overflow integer arithmetic
java:classes_lang, Add saturation/overflow integer arithmetic,State: 11-Closed,Reported: 05-JUN-2001,Release Reported Against: merlin-beta
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Synthesis of saturation arithmetic architectures
Synthesis of saturation arithmetic architectures. Full text. Pdf (392 KB) Source ... Signal processing, saturation arithmetic, synthesis. Collaborative Colleagues: ...
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Data processing system having a saturation arithmetic operation ...
A data processing system includes an instruction decoder for decoding a string of instructions including an arithmetic operation instruction, an arithmetic operation ...
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Saturation - Wikipedia, the free encyclopedia
Saturation (chemistry), multiple definitions for chemistry ... Saturation arithmetic, in arithmetic, a version of arithmetic in which all ...
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saturation: Definition from Answers.com
saturation n. The act or process of saturating. The condition of being saturated. ... Saturation arithmetic, in arithmetic, a version of arithmetic in which all ...
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Saturation Arithmetic VIs (FPGA Module) - LabVIEW FPGA Module 8.2 Help
Saturation Arithmetic VIs (FPGA Module) "Table of Contents. LabVIEW FPGA Module ... Use the Saturation Arithmetic VIs to handle or avoid integer overflow when ...
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SIMD architectures: Page 3
Saturated arithmetic ... SIMD implementations under discussion share is support for saturated arithmetic. ... (remember the saturated arithmetic discussion) ...
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Truncated Online Arithmetic with Applications to Communication Systems
saturated arithmetic is used when LSBs are important. simplify the operations, the choice of ... arithmetic for saturation and truncated online arithmetic for ...
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SECTION 4 DATA ARITHMETIC LOGIC UNIT
The data representation, rounding, and saturation arithmetic used within the ... Limiting (Saturation Arithmetic) ... called saturation arithmetic. The value ...
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Saturation arithmetic is a version of arithmetic in which all operations such as addition and multiplication are limited to a fixed range between a minimum and maximum value. If the result of an operation is greater than the maximum it is set ("clamped") to the maximum, while if it is below the minimum it is clamped to the minimum. The name comes from how the value becomes "saturated" once it reaches the extreme values; further additions to a maximum or subtractions from a minimum will not change the result.

For example, if the valid range of values is from -100 to 100, the following operations produce the following values:

60 + 43 = 100
(60 + 43) - 150 = -50
43 - 150 = -100
60 + (43 - 150) = -40
10 × 11 = 100
99 × 99 = 100
30 × (5 - 1) = 100
30×5 - 30×1 = 70

As can be seen from these examples, familiar properties like associativity and distributivity fail in saturation arithmetic. This makes it unpleasant to deal with in abstract mathematics, but it has an important role to play in digital hardware and algorithms.

Typically, early computer microprocessors did not implement integer arithmetic operations using saturation arithmetic; instead, they used the easier-to-implement modular arithmetic, in which values exceeding the maximum value "Integer overflow" to the minimum value, like the hours on a clock passing from 12 to 1. In hardware, modular arithmetic with a minimum of zero and a maximum of 2n can be implemented by simply discarding all but the lowest n bits.

However, although more difficult to implement, saturation arithmetic has numerous practical advantages. The result is as numerically close to the true answer as possible; it's considerably less surprising to get an answer of 127 instead of 130 than to get an answer of -126 instead of 130. It also enables overflow of additions and multiplications to be detected consistently without an overflow bit or excessive computation by simple comparison with the maximum or minimum value (provided the datum is not permitted to take on these values).

Additionally, saturation arithmetic enables efficient algorithms for many problems, particularly in digital signal processing. For example, adjusting the volume level of a sound signal can result in overflow, and saturation causes significantly less distortion to the sound than wrap-around. In the words of researchers G. A. Constantinides et al:

Saturation arithmetic operations are available on many modern platforms, and in particular was one of the extensions made by the Intel MMX platform, specifically for such signal processing applications.

Saturation arithmetic for integers has also implemented in software for a number of programming languages including C (programming language), C++, Eiffel (programming language), and most notably Ada programming language, which has built-in support for saturation arithmetic. This helps programmers anticipate and understand the effects of overflow better. On the other hand, saturation is challenging to implement efficiently in software on a machine with only modular arithmetic operations, since simple implementations require branches that create huge pipeline delays.

Although saturation arithmetic is less popular for integer arithmetic in hardware, the IEEE floating-point standard, the most popular abstraction for dealing with approximate real numbers, uses a form of saturation in which overflow is converted into "infinity" or "negative infinity", and any other operation on this result continues to produce the same value. This has the advantage over simple saturation that later operations which decrease the value will not end up producing a "reasonable" result, such as in the computation \sqrt{x^2-y^2}.

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External links

SARITH: Safe ARITHmetic - A Progress Report: Report on a saturation arithmetic component for Eiffel (programming language).

Saturation arithmetic - Wikipedia, the free encyclopedia
Saturation arithmetic is a version of arithmetic in which all operations such as addition and multiplication are limited to a fixed range between a minimum and maximum value.

Saturation - Wikipedia, the free encyclopedia
... stronger magnetic field; Oxygen saturation, a clinical measure of the amount of oxygen in a patient's blood; Saturation (telecommunications), a number of meanings; Saturation arithmetic ...

Synthesis of saturation arithmetic architectures
G. A. Constantinides: Imperial College of Science, Technology and Medicine, London, United Kingtom: P. Y. K. Cheung: Imperial College of Science, Technology and Medicine, London ...

Presburger Arithmetic and Pseudo-Recursive Saturation
Presburger Arithmetic and Pseudo-Recursive Saturation by David Llewellyn-Jones A thesis submitted to the University of Birmingham for the degree of PhD in the Faculty of Sciences ...

saturation - definition of saturation by the Free Online Dictionary ...
sat·u·ra·tion (s ch-r sh n) n. 1. a. The act or process of saturating. b. The ... Saturation arithmetic Saturation attack saturation bombing saturation bombing

Saturation Arithmetic Palette Details (FPGA Module) - LabVIEW FPGA ...
Note The information in this topic is subject to change with each version of the LabVIEW FPGA Module.

Saturation (chemistry) - Hutchinson encyclopedia article about ...
saturated solution. In physics and chemistry, a solution obtained when a solvent ... Saturation arithmetic Saturation attack: saturation bombing saturation bombing

Saturation - Simple English Wikipedia, the free encyclopedia
... stronger magnetic field; Oxygen saturation, a clinical measure of the amount of oxygen in a patient's blood; Saturation (telecommunications), a number of meanings; Saturation arithmetic ...

saturation - definition of saturation in the Medical dictionary - by ...
saturation /sat·u·ra·tion/ (sach?ah-ra´shun) 1. the state of being saturated ... Saturation arithmetic Saturation attack saturation bombing saturation bombing

Saturation Arithmetic VIs (FPGA Module) - LabVIEW FPGA Module 8.5 Help
Owning Palette: FPGA Math & Analysis VIs, Numeric Functions. Use the Saturation Arithmetic VIs to handle or avoid integer overflow when performing mathematical operations.