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| | Doing It Fast, fixed point arithmetic techniques and fast 3d transforms |
 | | 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. | | | 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. |
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http://www.gameprogrammer.com/4-fixed.html
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| | Hexapedia - Fixed point combinator |
| | A 'fixed point' of a function is a value left 'fixed' by that function; for example, 0 and 1 are fixed points of the squaring function. | | | A fixed point combinator is a function which computes fixed points of other functions. | | | In these formalizations, it is possible to produce a function, often denoted Y, which computes a fixed point of any function it is given. |
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http://www.hexafind.com/encyclopedia/Fixed_point_combinator
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| | 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. |
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http://www.sciencedaily.com/encyclopedia/fixed_point_arithmetic
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| | Fixed Point Math Tutorial |
| | Generating a binary fixed point value in an assembly language program at assembly time is, in theory, simple. | | | When two fixed point numbers are multiplied, the number of digits to the right of the radix point in the product is equal to the sum of the digits to the right of the radix point of multiplier and multiplicand. | | | Division of two fixed point numbers requires that you subtract the number of digits to the right of the radix point in the divisor from those of the dividend to get the position of the radix point in the quotient. |
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http://www.wwnet.net/~stevelim/fixed.html
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| | The Brouwer-Kakutani Fixed Point Theorem |
| | Newton's Method is perhaps the most famous application of the Fixed Point Theorem, and it is very easy to write an algorithm (computer program) to implement it. | | | Once the idea of fixed points is understood, it is amusing to apply the idea to "nonmathematical" maps. | | | That is, self-replicating molecules are an instantiation of the Fixed Point Theorem where the map is the one determined by the laws of Physics and Chemistry. |
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http://underground.musenet.org:8080/utnebury/fixed.point.html
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| | Fixed Point Math |
| | Fixed point math is something that has applications in many, many areas of computer graphics. | | | The idea behind fixed point math is that we pretend that there is a decimal point. | | | Addition and subtraction work are basically the same with fixed point numbers are they do with integer or floats. |
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http://members.aol.com/form1/fixed.htm
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| | 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. | | | fixed(x, p); int x; initial value without decimal point int p; initial precision (default value is zero) fixed(s); const char *s; string to be scanned for initial value |
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http://www.efgh.com/software/fixed.htm
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| | 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. | | | Then their Fixed equivalents are nf and mf, where is f is, of course, 65536. |
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http://www.mactech.com:16080/articles/mactech/Vol.10/10.03/FixedPointMath
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| | Algorithms for the Fixed Point Property |
| | Another variation on the retraction theme is the use of algebraic topology in deriving fixed point theorems initiated by Baclawski and Björner and continued for example by Constantin and Fournier. | | | Walker's relational fixed point property for which the analogous problem has a very satisfying solution also is discussed. | | | While a depth-first search algorithm for a fixed point free map is easily written it is also quite inefficient. |
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http://www.csi.uottawa.ca/ordal/papers/schroder/FINSURVE.html
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| | FRIDGE - Fixed-point pRogrammIng DesiGn Environment |
| | On the fixed-point level, to all operands a fixed word length and a fixed exponent is assigned, while the control structure and the operations of the floating point program remain unchanged. | | | All operands of the algorithm are of type fixed. | | | This allows to ignore the effects of finite word lengths and fixed exponents and to abstract from all implementation details. |
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http://www.ert.rwth-aachen.de/Projekte/Tools/FRIDGE/fridge.html
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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. | | | 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 (binary or radix) point. | | | 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). |
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http://www.sciencedaily.com/encyclopedia/fixed_point_arithmetic
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| | An Introduction to Fixed Point Math |
| | When a fixed point value is positive, this adds one- half away from 0. | | | Fixed point multiplication is a bit uglier, but not too bad -- multiply the two numbers, then shift down by some number of bits to get back into the output format you want. | | | Fixed point is a wonderful way to get around the limitations of systems with slow (or non-existent) floating point units. |
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http://bookofhook.com/Article/GameDevelopment/AnIntroductiontoFixedPoin.html
(965 words)
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| | 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. | | | However, depending on the numbers multiplied, the result can have either 1 or 2 binary digits before the binary point. |
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http://cnx.rice.edu/content/m11054/latest
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| | Fixed Point Iteration and Newton's Method in 2D and 3D |
| | In two dimensions, solve the non-linear fixed point system | | | If the starting point is chosen sufficiently close to the fixed point, then one of the following cases apply. | | | Iterative techniques will now be introduced that extend the fixed point and Newton methods for finding a root of an equation. |
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http://math.fullerton.edu/mathews/n2003/FixPointNewtonMod.html
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| | Fixed point math |
| | Fixed point is definitely a much faster way to handle these calculations. | | | Fixed point is a good way to go, but does require more thought than just | | | Remember, fixed point, in reality, is just integer math. |
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http://www.seattlerobotics.org/encoder/200008/fixedpoint.html
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| | Fixed point class & Intels GPP [PocketMatrix >> mobile devices] |
| | I created my own Fixed point class, in which I called functions of the Intel(R) Graphics Performance Primitives Library Version. | | | Fixed point class and Intels GPP [PocketMatrix >> mobile devices] | | | Post subject: Re: Fixed point class and Intels GPP |
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http://www.pocketmatrix.com/forums/viewtopic.php?p=266297
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| | A Calculated Look at Fixed-Point Arithmetic |
| | There are a fixed number of digits after the decimal point; the resolution is explicit. | | | When formatting the display value, consideration must be given to the effective position of the decimal point. | | | For instance, a number which is stored and manipulated such that its stored value is 1,000 times larger than the number it represents would have three fixed decimal places. |
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http://www.embedded.com/98/9804fe2.htm
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| | Fixed-Point Math Speed |
| | After executing this instruction, a6 will contain the previous value of a6 and a7 will point to the return address. | | | Notice that the function parameters are declared as Real instead of Fixed. | | | This instruction also causes the stack pointer to point to the returned value thereby de-allocating the stack space originally allocated for x. |
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http://mactech.com:16080/articles/mactech/Vol.13/13.11/Fixed-PointMathSpeed
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| | Symposium Program |
| | It is demonstrated for our Indium fixed point, that the overall estimated uncertainty can be lowered from 1.74 mK to 1.10 mK (k=2) due to a reduction of the chemical impurity contribution to the uncertainty. | | | During these tests, between four and five SPRTs were simultaneously mounted in the copper comparator block which held the modular fixed point cells, so that the same SPRTs could be calibrated at the cryogenic fixed points of ITS-90 and the new calibrations could be compared to the original ones. | | | A brief review is given of techniques and apparatuses used, source and purity of the fixed points in this range, cell designs and uncertainties of our realization. |
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http://www.cstl.nist.gov/div836/836.05/thermometry/symposium/program.htm
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| | Fixed Point Iteration |
| | The iterates may or may not converge to the fixed point x = g(x), which is the intersection of the curve g(x) and the line y = x, and the convergence may be relatively slow (linear) or fast (quadratic). | | | The four examples provided, all of which are fixed point problems equivalent to the same nonlinear equation f (x) = 0, demonstrate nonconvergence, monotonic linear convergence, alternating linear convergence, and quadratic convergence, respectively. | | | The successive steps of fixed point iteration are then carried out sequentially by repeatedly clicking on NEXT or on the currently highlighted step. |
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http://www.cse.uiuc.edu/eot/modules/nonlinear_eqns/FixedPoint
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| | Brouwer |
| | In other words, one might say that one solves an equation iff one finds a fixed point of some relevant transformation of an analogous mathematical space. | | | [A11] Karamadian, S. Fixed points, algorithms and applications, Acad. | | | [A3] Example from Shashkin, Y.A.: Fixed Points, Am. |
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http://hypatia.math.uri.edu/~kulenm/mth381pr/fixedpoint/fixedpoint.html
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| | MTH 207 Lab Lesson 15 - Fixed Point Iteration |
| | Implement the fixed point algorithm and use it to find the roots of the the functions in the previous question (where possible). | | | MTH 207 Lab Lesson 15 - Fixed Point Iteration | | | Use your fixed point algorithm from the last question to solve the equation |
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http://www.scs.ryerson.ca/~danziger/labs/less15.htm
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| | Fixed Point Theorems |
| | A continuous function that maps a disk into itself has a fixed point. | | | A continous function that maps [0,1] into itself has a fixed point. | | | The mathematical analysis of this question usually relies on fixed point theorems. |
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http://www.applet-magic.com/fixed.htm
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| | Superior Audio Requires Fixed-Point DSP |
| | The double precision available in the fixed point processor helps the programmer to avoid these problems. | | | What they fail to point out is the "rest of the story," which is that the 24-bit fixed-point DSP box can operate in "double-precision" mode, making it a 48-bit box. | | | Another possibility is if the floating point DSPs evolve to offer significantly more processing power for the same price (enough to overcome the low-frequency, high-Q issues in firmware) and offer a compatible peripheral chip set, then this could tip the scales even if they still offer only a 32-bit fixed numerical format. |
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http://www.rane.com/note153.html
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| | Fixed Points |
| | Fixed Points: Algorithms and Applications, Academic Press, New York, NY. | | | The following are fixed point theorems of particular interest in mathematical programming. | | | A fixed point of F is x in X such that x is in F(x). |
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http://carbon.cudenver.edu/~hgreenbe/glossary/fixedpts.html
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| | 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". | | | Resolution: Can't be done because arrays in records must have fixed lenghts. |
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http://www.vhdl.org/vhdlsynth/proposals/dave_p3.html
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| | Fixed Point Theorems/Reflection Conditions |
| | Theorem 3.19 obviously leads to an algorithm for a sufficient condition for the fixed point property: Dismantle P via | | | Hence P has the fixed point property iff every endomorphism of G has a fixed edge or a fixed vertex. | | | However by Theorem 3.21 P has the fixed point property iff P is connected and has no crowns and no infinite fences. |
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http://www.csi.uottawa.ca/ordal/papers/schroder/node13.html
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| | FIXED-POINT - Definition |
| | fixed point combinator, fixed-point notation, fixed-point number, fixed-point part, fixed-point representation system | | | The fixed point of a function, f is any value, x for which f x = x. | | | The fixed point combinator, written as either "fix" or "Y" will return the fixed point of a function. |
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http://www.hyperdictionary.com/computing/fixed-point
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