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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. | | | 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. |
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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. | | | Most floating point representations in computers use base 2 values, which cannot exactly represent most fractions that are easily represented in base 10. | | | 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. |
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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. | | | Because the description of the radix point is based on decimal digits, the fields in the schematic description refer to decimal digits. | | | Because the description of radix point is based on decimal digits, the fields in the schematic description refer to decimal digits. |
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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. | | | Depending on the calculator design, the number of states might be the same as the number of distinct values that can be displayed. |
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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 problem is, the computer sees each number as having a addition eight zeros on it. | | | The problem with division is basically the same as the problem with multiplication: An unwanted factor crops up in the calculation. |
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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 |
| | Then their Fixed equivalents are nf and mf, where is f is, of course, 65536. | | | Just for comparison, our function for multiplying two Fixed numbers is 3 instructions long and computations are done in registers, whereas FixMul in my LC’s ROM has 47 instructions, and accesses memory many times. | | | 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. |
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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. | | | Therefore a bit-true behavior of the algorithm is specified. | | | All operands of the algorithm are of type fixed. |
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http://www.ert.rwth-aachen.de/Projekte/Tools/FRIDGE/fridge.html
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| | An Introduction to Fixed Point Math |
| | When a fixed point value is positive, this adds one- half away from 0. | | | Rounding to the nearest value, which is what we often associate with rounding (this is what the C language does), is easy primarily because of the 2's complement encoding. | | | Decoding a negative number takes a little bit of thought (you have to do the complement and add one), and the magnitude of a negative number is inversely proportional to the magnitude of its binary representation: -1 = 0xFFFFFFFF but -2147483648 = 0x80000000. |
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http://bookofhook.com/Article/GameDevelopment/AnIntroductiontoFixedPoin.html
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| | Fixed Point of Reference - Activity Based Management Article |
| | Defining a fixed point of reference is a great way to start. | | | "We were created for dependence, not independence."(4) A single vantage point limits our understanding of the world. | | | Without a clearly reliable reference point, ambiguity prevails. |
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http://www.icms.net/fixed_point.htm
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| | Fixed Point Arithmetic |
| | 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. | | | 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. |
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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 |
| | For a function of several variables, the differential is used to show how changes of the independent variables affect the change in the dependent variables. | | | Suppose that the values of these functions in are known at the point | | | In two dimensions, solve the non-linear fixed point system |
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http://math.fullerton.edu/mathews/n2003/FixPointNewtonMod.html
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| | Fixed point math |
| | Floating point is mostly used to work with numbers of different magnitude. | | | The basis of the discussion is how to do navigation on a 'small' computer. | | | The problem is we are so fixed on Base10 numbers that it is |
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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 |
| | 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. | | | Reserving the two extreme ADC values to indicate "under-range" and "over-range," we have to make the mapping shown in Table 1. |
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http://www.embedded.com/98/9804fe2.htm
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| | Fixed-Point Math Speed |
| | Instead of bit-shifting the numerator, we perform the equivalent operation of multiplying by 65536. | | | 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. |
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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 |
| | Additional past support from the Education, Outreach, and Training Partnership for Advanced Computational Infrastructure under the National Computational Science Alliance is gratefully acknowledged. | | | The resulting values of x and g(x) are shown in the plot by bullets and are also shown numerically in the table below. | | | The user selects a problem by choosing one of four preset functions g(x). |
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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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| | 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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| | 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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| | Superior Audio Requires Fixed-Point DSP |
| | The double precision available in the fixed point processor helps the programmer to avoid these problems. | | | An example is the best way to explain how you lose precision when floating-point processors scale data. | | | Often the result of this multiply-and-add is the starting point for the next calculation, so it forms a running total, or an accumulation, of all the results over time. |
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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 Computation of Economic Equilibria, Yale University Press, New Haven, CT. | | | The following are fixed point theorems of particular interest in mathematical programming. |
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http://carbon.cudenver.edu/~hgreenbe/glossary/fixedpts.html
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| | IEEE P1076.3 Working Group - Change Proposal |
| | Resolution: Can't be done because arrays in records must have fixed lenghts. | | | Changing the type of "signed" and "unsigned" would cause funcitonal changes in how these types work and cause existing code problems. | | | 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. |
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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 | | | We will assume without loss of generality that | | | Hence P has the fixed point property iff every endomorphism of G has a fixed edge or a fixed vertex. |
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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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| | Fixed-Point Theorems |
| | Brouwer's Theorem made a reapparence in Lionel McKenzie (1959), Hirofumi Uzawa (1962) and, later, in the computational work of Herbert Scarf (1973). | | | (x*)) and thus there would be no fixed point, i.e. | | | Kim C. Border (1985) Fixed Point Theorems with Applications to Economics and Game Theory. |
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http://cepa.newschool.edu/het/essays/math/fixedpoint.htm
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| | Encyclopedia4U - Brouwer fixed point theorem - Encyclopedia Article |
| | It is hoped that this will at least give some idea why the theorem might be expected to be true. | | | The Brouwer fixed point theorem was one of the early achievements of algebraic topology, and is the basis of more general fixed point theorems which are important in functional analysis. | | | ) is a fixed point of the function. |
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http://www.encyclopedia4u.com/b/brouwer-fixed-point-theorem.html
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| | Preprints, R. Baker Kearfott |
| | Empirical Evaluation of Innovations in Interval Branch and Bound Algorithms for Nonlinear Algebraic Systems, in the SIAM Journal on Scientific Computing, 18 (2), pp. | | | On Verifying Feasibility in Equality Constrained Optimization Problems (technical report to supplement the above). | | | On Proving Existence of Feasible Points in Equality Constrained Optimization Problems, Mathematical Programming 83 (1), pp. |
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http://interval.louisiana.edu/preprints.html
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| | least fixed point from FOLDOC |
| | For example, any value is a fixed point of the identity function, (\ x. | | | A function f may have many fixed points (x such that f x = x). | | | The least fixed point is guaranteed to exist for a continuous function over a cpo. |
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http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?least+fixed+point
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| | Fixed Point Theorems with Applications to Economics and Game Theory - Cambridge University Press |
| | Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. | | | Fixed Point Theorems with Applications to Economics and Game Theory | | | This book gives the reader access to the mathematical techniques involved and goes on to apply fixed point theorems to proving the existence of equilibria for economics and for cooperative and non-cooperative games. |
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http://books.cambridge.org/0521388082.htm
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| | Fixed-point Arithmetic |
| | They do this by storing the number as some digits and the position of the decimal point. | | | In this article we're going to use fixed-point decimal numbers because they make the examples simpler. | | | 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. |
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http://www.accu.org/acornsig/public/caugers/volume2/issue6/fixedpoint.html
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| | [No title] |
| | More precisely: (3) Under a continuous map f every point sufficiently close to x is mapped within any preassigned closeness to f(x). | | | The proof of (2) as well as (1), of course, dramatically uses the fact that Under a continuous map points close to each other are mapped into points which are close to each other. | | | Since we assumed that f has no fixed point, f(x) is either to the right of x or f(x) is to the left of x. |
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http://www.mathematik.uni-bielefeld.de/~sillke/NEWS/fixed-point-theorem
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| | Fixed Point Theorems in Mathematical Economics |
| | We will use an algorithm related to Sperner's lemma to find fixed points of mappings of simplices into themselves. | | | For an important class of games, Kakutani's fixed point theorem shows the existence of an equilibrium. | | | We will discuss matrix games as a concrete example. |
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http://www.math.columbia.edu/~welji/seminar/111504.html
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| | Fixed point quotes & quotations |
| | He who stops draws attention to the excess of others, like a fixed point. | | | "The closer a man approaches tragedy the more intense is his concentration of emotion upon the fixed point of his commitment, which is to say the closer he approaches what in life we call fanaticism. | | | When all tend to debauchery, none appears to do so. |
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http://en.thinkexist.com/quotes/with/keyword/fixed_point
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| | Fixed Point Iteration method |
| | Also given below is the code used to create this plots. | | | Given an function, f, and a point a, consider the sequence a, f(a), f(f(a)), f(f(f(a))),... | | | These plots were done with Maple with the script Fixed Point Code |
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http://www.cecm.sfu.ca/~kghare/numeric/fixed_point.html
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| | Concise Course on Fixed Point Theorems/K.Goebel |
| | Suggestions for future research projects are selected from those problems I have encountered, and in some cases invented myself, during my over thirty years working in this field. | | | Indeed, many important branches of the fixed point theory are mentioned only briefly if at all. | | | I was advised that my class would consist of graduate students ranging from beginning to advanced, with some near the completion of their degrees. |
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http://www.ybook.co.jp/pub/goebel.htm
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| | MSN Encarta - Dictionary - fixed point |
| | Search for "fixed point" in all of MSN Encarta | | | invariable temperature standard: a temperature that has a fixed value under specific conditions and can be used to calibrate instruments, e.g. | | | Click here to search all of MSN Encarta |
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http://encarta.msn.com/encnet/features/dictionary/DictionaryResults.aspx?refid=1861611872
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| | Babes |
| | An International Journal on Fixed Point Theory, Computation and Applications | | | Fixed Point Theory publishes important research and expository papers devoted to the theory, computation and applications of the fixed points. | | | Submission of a paper implies that it has not been published elsewherand is not under consideration for publication elsewhere. |
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http://www.math.ubbcluj.ro/~nodeacj/sfptcj.htm
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| | FRIDGE: A Fixed-Point Design and Simulation Environment |
| | These requirements have been the motivation for FRIDGE (Fixed-point pRogrammIng DesiGn Environment), a design environment for the specification, evaluation and implementation of fixed-point systems. | | | FRIDGE offers a seamless design flow from a floating- point description to a fixed-point implementation. | | | Within this paper we focus on two core capabilities of FRIDGE: (1) the concept of an interactive, automated transformation of floating-point programs written in ANSI-C into fixed-point specifications, based on an interpolative approach. |
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http://csdl2.computer.org/persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/date/1998/8359/00/8359toc.xml&DOI=10.1109/DATE.1998.655893
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| | IAppli Fixed Point Math Library |
| | Note, I am not a numerical methods or computer arithmetic hacker. | | | This is an implementation of a simple fixed point math library for the IAppli (CLDC) Java platform. | | | If anyone knows a good implementation for fixed point exponential, please email me. |
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http://www.ai.mit.edu/people/hqm/imode/fplib/index.html
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| | Temperature Calibration from Isothermal Technology |
| | Isothermal Technology Ltd is involved with the research, development and manufacture of | | | Equipment produced includes Standard Platinum Resistance Thermometers, fixed point cells and associated equipment which are used in metrology laboratories throughout the world. | | | Industrial temperature calibration equipment includes portable dry block calibrators, thermocouple referencing and more. |
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http://www.isotech.co.uk
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| | Fixed-Point Literature |
| | A Methodology and Design Environment for DSP ASIC Fixed Point Refinement | | | Proceedings of the International Conference on Acoustics, Speech and Signal Processing 1997 | | | Automatic Floating to Fixed Point Translation and its Application to Post-Rendering 3D Warping |
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http://www.ert.rwth-aachen.de/Projekte/Tools/FRIDGE/FixedPointLiterature.html
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| | Pond Engineering: Setting the standard of Performance... |
| | We also do custom engineering to meet your every need. | | | Click on the Links to explore our product line from argon triple points, water triple points, and cells and maintence system. | | | Please contact us today.Precision Thermemtry, Primary Metrology, Temperature Metrology, Fixed Point, Fixed Points, ITS-90, SPRT, Water Triple Point, Argon Triple Point, Mercury Triple Point, Argon Triple Points, Water Triple Points, Mercury Triple Points, Precision Thermometer |
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http://www.pondengineering.com
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| | PlanetMath: fixed point |
| | This is version 5 of fixed point, born on 2002-03-08, modified 2003-09-17. | | | See Also: Banach fixed point theorem, Brouwer fixed point theorem, Schauder fixed point theorem, fixed point property, Tarski-Knaster theorem | | | , is a point that remains constant upon application of that function, i.e.: |
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http://planetmath.org/encyclopedia/FixedPoint.html
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| | Mudd Math Fun Facts: Brouwer Fixed Point Theorem |
| | Fixed point theorems are some of the most important theorems in all of mathematics. | | | One of the most useful theorems in mathematics is an amazing topological result known as the Brouwer Fixed Point Theorem. | | | Among other applications, they are used to show the existence of solutions to differential equations, as well as the existence of equilibria in game theory. |
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http://www.math.hmc.edu/funfacts/ffiles/20002.7.shtml
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| | PlanetMath: hyperbolic fixed point |
| | This is version 3 of hyperbolic fixed point, born on 2003-07-27, modified 2003-07-29. | | | (Dynamical systems and ergodic theory :: Smooth dynamical systems: general theory :: Fixed points, periodic points, fixed-point index theory) | | | is said to be a hyperbolic fixed point if |
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http://planetmath.org/encyclopedia/HyperbolicFixedPoint.html
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