Fixed point arithmetic

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Topic: Fixed point arithmetic

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	Fixed-point arithmetic - Wikipedia, the free encyclopedia
		Fixed point operations assume that the binary point in a number is always between two specific bits in the field.
		This assumption is important when performing fixed point operations which are likely to produce values with more bits than either of the operands (for instance, multiplication, where the product could potentially have as many bits as the sum of the number of bits in the two operands).
		When multiplying two fixed point numbers with the same format, for instance with I integer bits, and Q fractional bits, the answer could have up to 2I integer bits, and 2Q number of fractional bits.
	www.sciencedaily.com /encyclopedia/fixed_point_arithmetic (965 words)

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	www.answers-zone.com /article/Fixed-point_arithmetic (382 words)

	Fixed point - Wikipedia, the free encyclopedia
		Fixed-point arithmetic — manner of doing arithmetic on computers: a fixed number of decimal (or binary) digits is kept after the decimal point, any remaining digits are rounded.
		Conformal field theory is a different description of a fixed point in the context of the renormalization group, for example see infrared fixed point
		Fixed point has many meanings in science, most of them mathematical.
	en.wikipedia.org /wiki/Fixed_point (147 words)

	Fixed point - Wikipedia, the free encyclopedia
		Fixed-point arithmetic — manner of doing arithmetic on computers: a fixed number of decimal (or binary) digits is kept after the decimal point, any remaining digits are rounded.
		Fixed point — a number x that makes f(x) = x.
		Fixed point has many meanings in science, most of them mathematical.
	en.wikipedia.org /wiki/Fixed_point (147 words)

	DictF12.html
		A method of calculation in which the computer does not consider the location of the decimal or radix point because the point is given a fixed position.
		A type of arithmetic in which the operands and results of all arithmetic operations must be properly scaled so as to have a magnitude between certain fixed values.
		] Interferometer in which light from a point source is collimated and multiply reflected between a plane mirror and the partially silvered inner surface of a parallel plane plate, and is viewed in reflection.
	www.accessscience.com /Dictionary/F/F12/DictF12.html (147 words)

	Credit Fix
		Fixed-point arithmetic — manner of doing arithmetic on computers: a fixed number of decimal (or binary) digits is kept after the decimal point, any remaining digits are rounded.
		Fixed point — a number ''x'' that makes ''f''(''x'') = ''x''.
		''Fixed point'' has many meanings in science, most of them mathematical.
	www.wwwtln.com /finance/56/credit-fix.html (590 words)

	Floating Point Arithmetic
		The step which actually performs the operation can result in another kind of error: overflows can occur in floating point arithmetic as well as in fixed, but they are detected in the exponent rather than the significand.
		In order to illustrate some of the details of floating point arithmetic, we will consider an imaginary floating point format in which the exponent is stored in 5 bits, the significand is stored in 10 bits, and 1 bit is used to store the sign of the number.
		Floating point arithmetic derives its name from something that happens when you use exponential notation.
	www.rwc.uc.edu /koehler/comath/14.html (590 words)

	Unsigned and Signed Integers
		Integer arithmetic on computers is often called "fixed point" arithmetic and the integers themselves are often called fixed point numbers.
		Real numbers on computers (which may have fractional parts) are often called "floating point" numbers, and they are the subject of the next section.
		This document may be freely reproduced provided that this copyright notice is included.
	www.rwc.uc.edu /koehler/comath/13.html (590 words)

	DictF12.html
		A method of calculation in which the computer does not consider the location of the decimal or radix point because the point is given a fixed position.
		A type of arithmetic in which the operands and results of all arithmetic operations must be properly scaled so as to have a magnitude between certain fixed values.
		] Interferometer in which light from a point source is collimated and multiply reflected between a plane mirror and the partially silvered inner surface of a parallel plane plate, and is viewed in reflection.
	accessscience.com /Dictionary/F/F12/DictF12.html (590 words)

	Hypertext Ada 95 Rationale - Part Three - Chapter G
		Support for fixed point types is patchy, due to the difficulty of dealing accurately with multiplications and divisions having "incompatible smalls" as well as fixed point multiplications, divisions, and conversions yielding a result of an integer or floating point type.
		While this would further simplify the semantics of floating point arithmetic, it would not eliminate the interval orientation of the accuracy requirements if variations in rounding mode from one implementation to another and the use of extended registers are both to be tolerated.
		The machine numbers of a floating point type are somewhat informally defined as the values of the type that are capable of being represented to full accuracy in all unconstrained variables of the type.
	www.adaic.org /standards/95rat/RAThtml/rat95-p3-g.html (590 words)

	Fixed point - Wikipedia, the free encyclopedia
		Fixed-point arithmetic — manner of doing arithmetic on computers: a fixed number of decimal (or binary) digits is kept after the decimal point, any remaining digits are rounded.
		Fixed point — a number x that makes f(x) = x.
		Fixed point has many meanings in science, most of them mathematical.
	en.wikipedia.org /wiki/Fixed_point (117 words)

	Doing It Fast, fixed point arithmetic techniques and fast 3d transforms
		When we want to use fixed point arithmetic in a program we have to decide what format to use and how to implement it within the programming language we are using.
		The integer square root of a fixed point number divided by the square root of 2 to the F power where F is the number of bits of fraction in the fixed point number is the square root of the original fixed point number.
		A fixed point number is called fixed point because the decimal point (I'm going to use decimal numbers in the first part of this discussion) is in a fixed location in the number.
	www.gameprogrammer.com /4-fixed.html (117 words)

	Fixed-point arithmetic
		In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after the decimal (or binary or hexadecimal) point.
		For example, a fixed-point number with 4 digits after the decimal point could be used to store numbers such as 1.3467, 281243.3234 and 0.1000, but would round 1.0301789 to 1.0302 and 0.0000654 to 0.0001.
		Most floating point representations in computers use base 2 values, which cannot exactly represent most fractions that are easily represented in base 10.
	www.sciencedaily.com /encyclopedia/fixed_point_arithmetic (117 words)

	Fixed Point Math
		In this article we will explore several aspects of Mac programming: fixed point arithmetic in assembly, 3-d transformations, perspective and parallel projections, backplane elimination, offscreen bitmaps, and animation.
		We will use 32-bit fixed point numbers, with the integer part in the higher word, and the fractional part in the lower word.
		We say that points with positive (counter-clockwise) orientation lie on a visible plane, otherwise they line on the backplane, and the triangle is not drawn.
	www.mactech.com:16080 /articles/mactech/Vol.10/10.03/FixedPointMath (117 words)

	A Calculated Look at Fixed-Point Arithmetic
		There are a fixed number of digits after the decimal point; the resolution is explicit.
		In this case, the decimal point is really an illusion-there are always two decimal places, so instead of working with numbers in the range 0.00 to 50.00 we actually use 0 to 5,000 (the values are scaled up by a factor of 100).
		Certainly none of the small 4- and 8-bit microcontrollers support floating point, even though these are precisely the processors that are going to be at the heart of many apparently "real-number" applications.
	www.embedded.com /98/9804fe2.htm (117 words)

	IEEE P1076.3 Working Group - Change Proposal
		Normally the fixed point representation will be "ufixed (7 downto -8)" however may people expressed the need for "ufixed (-8 to 7)" to be supported and to be treated as having the same direction as the downto example.
		Create two fixed point representations, one for "signed" and one for "unsigned".
		Their behavior will be similar to that of the signed and unsigned arithmetic in numeric_std.
	www.vhdl.org /vhdlsynth/proposals/dave_p3.html (117 words)

	A Fixed-Point Arithmetic Package
		The precision of a fixed-point number is the number of digits to the right of the decimal point, and it normally stays the same when computations are performed on the number.
		Fixed-point numbers, which have a specified number of digits to the right of the decimal point, are common in many kinds of applications, but they seem to have been omitted from most computer programming libraries.
		If the fixed::ALIGN option is included, then the result will be padded with enough leading blanks so the decimal point will appear in the same position, no matter what the value and precision of the fixed-point number.
	www.efgh.com /software/fixed.htm (117 words)

	Fixed Point Arithmetic
		This handout explains how numbers are represented in the fixed point TI C6211 DSP processor.
		The point is that there is no meaning inherent in a binary word, although most people are tempted to think of them as positive integers.
		ignoring the binary points, then perform sign extension by putting enough 1s (if the result is negative) or 0s (if the result is nonnegative), then put the binary point to obtain a Q-6 number.
	cnx.rice.edu /content/m11054/latest (117 words)

	Fixed-point Arithmetic
		If you're prepared to lose the wide range of numbers that floating-point gives, you can speed things up by fixing the position of the decimal point and using integer arithmetic operations.
		In this article we're going to use fixed-point decimal numbers because they make the examples simpler.
		Floating-point numbers allow you to deal with an extremely wide range of numbers: from the very small to the very large.
	www.accu.org /acornsig/public/caugers/volume2/issue6/fixedpoint.html (117 words)

	Doing It Fast, fixed point arithmetic techniques and fast 3d transforms
		The integer square root of a fixed point number divided by the square root of 2 to the F power where F is the number of bits of fraction in the fixed point number is the square root of the original fixed point number.
		A fixed point number is called fixed point because the decimal point (I'm going to use decimal numbers in the first part of this discussion) is in a fixed location in the number.
		For example, you might have a table of sines in 2.30 binary fixed point format (in a binary format the numbers are the number of bits, not the number of digits) that you want to multiply by numbers in an 18.14 format.
	www.gameprogrammer.com /4-fixed.html (117 words)

	Doing It Fast, fixed point arithmetic techniques and fast 3d transforms
		Floating point arithmetic is easy to use and it comes closer to working the way we expect arithmetic to work than any other kind of arithmetic we can use in programs.
		The integer square root of a fixed point number divided by the square root of 2 to the F power where F is the number of bits of fraction in the fixed point number is the square root of the original fixed point number.
		A fixed point number is called fixed point because the decimal point (I'm going to use decimal numbers in the first part of this discussion) is in a fixed location in the number.
	www.gameprogrammer.com /4-fixed.html (117 words)

	A Calculated Look at Fixed-Point Arithmetic
		There are a fixed number of digits after the decimal point; the resolution is explicit.
		In this case, the decimal point is really an illusion-there are always two decimal places, so instead of working with numbers in the range 0.00 to 50.00 we actually use 0 to 5,000 (the values are scaled up by a factor of 100).
		Certainly none of the small 4- and 8-bit microcontrollers support floating point, even though these are precisely the processors that are going to be at the heart of many apparently "real-number" applications.
	www.embedded.com /98/9804fe2.htm (117 words)

	Fixed-point arithmetic
		In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after the decimal (or binary or hexadecimal) point.
		For example, a fixed-point number with 4 digits after the decimal point could be used to store numbers such as 1.3467, 281243.3234 and 0.1000, but would round 1.0301789 to 1.0302 and 0.0000654 to 0.0001.
		As long as the numeric value uses only the number of digits specified after the decimal point, fixed-point values can exactly represent all values up to its maximum value (determined by the number of bits in its representation).
	www.sciencedaily.com /encyclopedia/fixed_point_arithmetic (117 words)

	Fixed
		Fixed point In fixed point (mathematics) In renormalization group In fixed-point arithmetic.
		Fixed point combinator A fixed point combinator is a function which computes fixed pointss of other functions.
		Fixed shooter A fixed shooter is a game where the player has limited control of their character and the focus is almost...
	www.brainyencyclopedia.com /topics/fixed.html (117 words)

	Provability Logic
		From a philosophical point of view, provability logic is interesting because the concept of provability in a fixed theory of arithmetic has a unique and non-problematic meaning, other than concepts like necessity and knowledge studied in modal and epistemic logic.
		The main "modal" result about provability logic is the fixed point theorem, which D. de Jongh and G. Sambin independently proved in 1975.
		GL This formula B is called a fixed point of A(p).
	plato.stanford.edu /entries/logic-provability (117 words)

	Mathematics Program Information
		The following topics will be discussed: Early number systems, arithmetic and geometry; classical Greek mathematics; mathematics in the middle ages; the development of analytic geometry, calculus and probability theory; the renaissance of number theory; non-Euclidean geometries and the age of rigor in analysis, logic and set theory.
		For prerequisite purposes, this course is equivalent to the Finite Mathematics OAC.
		For entry into the Mathematics program, it is recommended that secondary school students include the following courses in their program at the OAC level: Calculus and one other mathematics.
	www.cs.laurentian.ca /calendar/cal_math.html (117 words)

	Programmer's Guide to TinyLine 2D API
		Fixed point arithmetic is as fast as integer operations.
		The position of the binary point is the means by which fixed-point values are scaled and interpreted.
		In TinyLine 2D user space coordinates are fixed point numbers.
	www.tinyline.com /2d/guide (117 words)

	Fixed-point arithmetic
		In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after the decimal (or binary or hexadecimal) point.
		For example, a fixed-point number with 4 digits after the decimal point could be used to store numbers such as 1.3467, 281243.3234 and 0.1000, but would round 1.0301789 to 1.0302 and 0.0000654 to 0.0001.
		Most floating point representations in computers use base 2 values, which cannot exactly represent most fractions that are easily represented in base 10.
	www.sciencedaily.com /encyclopedia/fixed_point_arithmetic (117 words)

	General Decimal Arithmetic
		The arithmetic permits a single representation of decimal numbers, whether they be integers, fixed-point (scaled), or floating-point; this minimizes conversion overheads.
		The arithmetic was designed as a decimal extended floating-point arithmetic, directly implementing the rules that people are taught at school.
		The working precision of the arithmetic is not determined by the representation, but is freely selectable within the limits of the representation as required for the problem being solved.
	www2.hursley.ibm.com /decimal (117 words)

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Topic: Fixed point arithmetic

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