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Topic: Binary logarithm

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Logarithm

Big O notation

Binary search tree

Analysis of algorithms

Irrational number

Natural logarithm

Fundamental theorem of algebra

Computational complexity theory

Real number

Number

Spline (mathematics)

Polynomial

Cubic equation

Imaginary number

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	Logarithm - Wikipedia, the free encyclopedia
		Logarithms to various bases: red is to base e, green is to base 10, and purple is to base 1.7.
		One simply found the logarithms of both numbers (multiply and divide) or the first number (power or root, where one number is already an exponent) in a table of common logarithms, performed a simpler operation on those, and found the result on a table.
		This he followed, in 1624, by his Arithmetica Logarithmica, containing the logarithms of all integers from 1 to 20,000 and from 90,000 to 100,000 to fourteen places of decimals, together with a learned introduction, in which the theory and use of logarithms are fully developed.
	en.wikipedia.org /wiki/Logarithm (2054 words)

	Logarithm - Open Encyclopedia (Site not responding. Last check: 2007-10-21)
		Logarithms are numbers that are substituted in computation for other numbers, to which they bear such a relation that the operations to be performed on the latter are represented by simpler operations performed on the former.
		Logarithms are useful in order to solve equations in which the unknown appears in the exponent, and they often occur as the solution of differential equations because of their simple derivatives.
		Binary logarithms are useful in determining characteristics of the time or space complexity of such algorithms.
	open-encyclopedia.com /Logarithm (1894 words)

	Representation of numbers (Site not responding. Last check: 2007-10-21)
		Before discussing the binary system, a review of the decimal (ten possible digits) system is in order, because many of the concepts of the binary system will be easier to understand when introduced alongside their decimal counterpart.
		Binary representations of positive can be understood in the same way as their decimal counterparts.
		Signed binary fractions are easily extended to include all numbers by representing the number to the left of the decimal point as a 2's complement integer, and the number to the right of the decimal point as a positive fraction.
	www.swarthmore.edu /NatSci/echeeve1/Ref/BinaryMath/NumSys.html (2515 words)

	Logarithm - FreeEncyclopedia (Site not responding. Last check: 2007-10-21)
		Before the widespread availability of electronic computers, logarithms were widely used as a calculating aid, both with tables of logarithms and slide rules.
		Logarithms are also useful in order to solve equations in which the unknown appears in the exponent, and they often occur as the solution of differential equations because of their simple derivatives.
		Binary logarithms are useful in determining functions that exhibit this behaviour.
	openproxy.ath.cx /lo/Logarithm.html (420 words)

	Binary logarithm -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Binary logarithm also frequently appears in the (Click link for more info and facts about analysis of algorithms) analysis of algorithms.
		This idea is used in the analysis of several (A precise rule (or set of rules) specifying how to solve some problem) algorithms and ((computer science) the organization of data (and its storage allocations in a computer)) data structures.
		For example in (Click link for more info and facts about binary search) binary search, the size of the problem to be solved is halved in each iterations, therefore roughly lg n iterations are needed to obtain a problem of size 1, which is solved easily in constant time.
	www.absoluteastronomy.com /encyclopedia/B/Bi/Binary_logarithm.htm (507 words)

	Logarithm - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-21)
		The word logarithm, which is due to Napier, is formed from λoγoς (logos), ratio, and αριθμoς (arithmos), number, and means a number that indicates a ratio.
		In current usage, nearly any unstated base of a logarithm, except in certain applications, is assumed to be 10.
		The base of the logarithm is hardly ever mentioned explicitly when analyzing the asymptotic complexity of algorithms in terms of Big O notation, since for all valid bases b and c.
	encyclopedia.learnthis.info /l/lo/logarithm.html (1706 words)

	Binary logarithm: Definition and Links by Encyclopedian.com - All about Binary logarithm
		Algorithms and data structures that are binary in nature, like Binary search trees and binary partition halving, make use of the lg n property.
		Binary partition halving can split an array in lg n time.
		Also, binary algorithms that are multiplied by a linear term are sometimes called linearithmic (n lg n).
	www.encyclopedian.com /bi/Binary-logarithm.html (208 words)

	Encyclopedia: Iterated logarithm
		is often used to indicate the binary iterated logarithm, which iterates the binary logarithm instead.
		The iterated logarithm is useful in analysis of algorithms and their computational complexity, appearing in the time and space complexity bounds of many algorithms such as:
		For all practical purposes, the iterated logarithm may be considered to be a constant.
	www.nationmaster.com /encyclopedia/Iterated-logarithm (281 words)

	Signed binary logarithm system - Patent 5940312
		It is therefore an object of the present invention to provide an instruction for computing the binary logarithm of most significant bit of a signed binary number in a single instruction cycle time.
		The output unsigned binary number comprises a fixed number of successive bits with a zero as an output most significant bit and the result of each of the exclusive-or operations as successive output lower significant bits.
		An apparatus for implementing the alternative binary logarithm of most significant bit instruction comprises a plurality of successive two input exclusive-or gates, each with one of the lower significant bits connected as a first input and the next successively lower significant bit connected as a second input.
	www.freepatentsonline.com /5940312.html (3923 words)

	GNU libavl 2.0.1
		binary search tree: A binary tree (see binary tree) with the additional property that the key in each node's left child is less than the node's key, and that the key in each node's right child is greater than the node's key.
		binary tree: A data structure that is either an {empty (@pxref{{empty}) tree} or consists of a root (see root), a left subtree (see left subtree), and a right subtree (see right subtree).
		Every node is the root of a binary tree, but "root" is most often used to refer to a node that is not a child (see child) of any other node.
	www.delorie.com /gnu/docs/avl/libavl_276.html (1909 words)

	Binary Logarithm Template (Site not responding. Last check: 2007-10-21)
		The program static_log2_test.cpp is a simplistic demonstration of the results from instantiating various examples of the binary logarithm class template.
		The truncated logarithm can be considered the highest power-of-two in a value, which corresponds to the value's highest set bit (for binary integers).
		The original version of the Boost binary logarithm class template was written by Daryle Walker and then enhanced by Giovanni Bajo with support for compilers without partial template specialization.
	www.boost.org /libs/integer/doc/static_log2.html (325 words)

	Binary logarithm
		n are called Binary logarithms or Base 2 logarithms.
		Base 2 logarithms are frequently written lg n.
		The text of this article is licensed under the GFDL.
	www.ebroadcast.com.au /lookup/encyclopedia/bi/Binary_logarithm.html (197 words)

	exponential function
		The inverse of the exponential function is the logarithmic function or logarithm.
		For 2 as the base of the logarithm the binary logarithm lb(x) is the case.
		In the time of the logarithmic tables the cologarithm was used to prevent negative results.
	www.2dcurves.com /exponential/exponentiale.html (869 words)

	CSCI 1300, Thursday, March 20, 1997 (Site not responding. Last check: 2007-10-21)
		Consequently for an element to travel all the way to its correct place in the sorted array it takes an number of operations that is equal to the number of bits in the subscripts, e.g., 7 for an array of size 128, 10 for an array of size 1024.
		This is called the "binary logarithm" of the array size.
		Spending a number of operations per element that is (proportional to) the logarithm of the array size is unavoidable unless you are dealing with special data.
	www.cs.colorado.edu /~karl/1300.spring97/970320.html (380 words)

	Logarithm - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-21)
		The method of logarithms was first propounded in 1614, in a book entitled Mirifici Logarithmorum Canonis Descriptio, by John Napier (latinized Neperus), Baron of Merchiston?
		The base of the logarithm is hardly ever mentioned explicitly when analyzing the asymptotic complexity of algorithms in terms of Big O notation, since O(log
		, a Dutch computer; but in his table, which appeared in 1628, the logarithms were given to only ten places of decimals.
	xahlee.org /_p/wiki/Logarithm.html (1864 words)

	Binary logarithm (Site not responding. Last check: 2007-10-21)
		Logarithms in the form log2n are called Binary logarithms or Base 2 logarithms.
		All is still licensed under the GNU FDL.
		A and her beauty thrilled him, with the passionate, almost sensuous was read out by the Public Prosecutor, and listened to by the accused -.
	www.termsdefined.net /bi/binary-logarithm.html (389 words)

	History of Logarithm Tables (Site not responding. Last check: 2007-10-21)
		The essential property of a system of logarithms is that the sum of the logarithms of any two or more numbers is the logarithm of their product.
		Hence the use of a table of logarithms enables a computer to substitute addition and subtraction for the more laborious operations of multiplication and division, and likewise multiplication and division for involution and evolution.
		In mathematical notation ‘the logarithm of’ is expressed by the abbreviation ‘log’ prefixed to numeral figures or algebraical symbols.
	www.ankatang.demon.co.uk /logs.html (628 words)

	Logarithm
		Logarithmic Descriptions of Whitehead Groups and Class Groups for P Groups (Memoirs of the American Mathematical Society, 392)
		To calculate the value for a logarithm of non base 10, the following formula will do a change of base so that a value may be obtained, assuming that a, b, and k are all positive real numbers and that and
		Binary logarithms are useful in determining characteristics of functions, such as the order of such functions that exhibit this behaviour.
	news-server.org /l/lo/logarithm.html (668 words)

	flooble :: perplexus :: Algorithms : Just by hand, only by hand, nothing but by hand?
		To express as binary, you just double the fraction; the digit to the left of the decimal point will be the first binary digit after the binary point.
		Remembering that adding exponents (or logarithms) corresponds to multiplying numbers, this binary representation means that we have to multiply the fourth root of 10 by the 32nd root of 10 and by the 64th root of 10 and the 256th root of 10, etc. (whichever positions have a 1 in the binary representation).
		However, the fourth root of 10 is less than 2, so 2 is divided by the fourth root of 10 and the quotient is placed under the 2 and a 1 is appended to the binary representation of the log.
	www.flooble.com /perplexus/show.php?pid=2060&cid=16169 (751 words)

	Binary logarithm - Enpsychlopedia (Site not responding. Last check: 2007-10-21)
		The binary logarithm is often used in computer science and information theory (where it is frequently written lg n), because it is closely connected to the binary numeral system.
		The number of digits (bits) in the binary representation of a positive integer n is the integral part of lg n + 1, i.e.
		The base of the logarithm in expressions such as O(log n) or O(n log n) is therefore not important.
	www.grohol.com /psypsych/Binary_logarithm (391 words)

	Rane Professional Audio Reference (B)
		binary A condition in which there are two possible states; for example, the binary number system (base-2) using the digits 0 and 1.
		binary logarithm A logarithm based on the powers of 2 (aka base 2).
		[The original term binary unit was coined by John Tukey of Bell Laboratories to represent the basic unit of information as defined by Shannon as a message representing one of two states.] 2.
	www.rane.com /par-b.html (5615 words)

	Design of VLSI Systems (Site not responding. Last check: 2007-10-21)
		The logarithmic time is attained using one depth of a binary tree instead of two in the case of Brent and Kung.
		Once the reproduction of the binary tree is made m times to the right, the only thing to do is to remove the cells at the negative bit positions and the adder is finished.
		The logarithm and antilogarithm curves are approximated by linear segments.
	www.vlsi.wpi.edu /webcourse/ch06/ch06.html (8434 words)

	Numerical algorithms II: elementary functions
		However, sometimes only the integer part of the logarithm is needed and the logarithm is taken with respect to an integer base.
		Since the internal representation of floating-point numbers is usually in binary, the integer part of the binary logarithm can be usually implemented as a constant-time operation.
		Exp(x)!by binary reduction"> This method is based on the binary splitting technique and is described in [Haible et al.
	yacas.sourceforge.net /Algochapter5.html (10274 words)

	logarithm - yourDictionary.com - American Heritage Dictionary
		The power to which a base, such as 10, must be raised to produce a given number.
		= a, the logarithm of a, with n as the base, is x; symbolically, log
		The kinds most often used are the common logarithm (base 10), the natural logarithm (base e), and the binary logarithm (base 2).
	www.yourdictionary.com /ahd/l/l0229600.html (65 words)

	OptiVec: log2 (Site not responding. Last check: 2007-10-21)
		The logarithm of the argument to the basis 2 is calculated and the result returned.
		In C/C++, the handling of both errors can be modified via _matherr or _matherrl, resp.
		The binary logarithm of the argument is returned.
	www.optivec.com /vecfuncs/_log2.htm (65 words)

	CodingForums.com - c maths
		And I've seen far more literature using lg as base 2; to an extent that I could believe that lg is also accepted notation for the binary logarithm, and not the base 10 algorithm.
		06-03-2004 12:07 AM Actually, I've never seen 'lg' being used for binary logarithms before, but on the other hand I'm not that interested in math to have read that very many different sources.
		As for your information, the books we used in gymnasial math seems to derive mainly from Swedish mathematical journals and sciences encyclopedias that in turn have centuries of history, deriving back to primarily two works: The journal Acta Mathematica (not sure about that spelling) by a number of famous Swedish mathematicians, and the Encyclopedia.
	www.codingforums.com /printthread.php?t=39513 (678 words)

	anadict assignment
		An anagram of a word is a different word formed using the same characters that comprise the original word.
		An anagram dictionary showing all words that can be constructed using a given set of letters is useful for certain kinds of word puzzles and games.
		Each entry in such a dictionary contains a key giving a the set of letters in alphabetic order, and one or more words that can be formed using the letters found in the key.
	www.links.net /vita/swat/course/unixc/ana.assign.html (705 words)

	CMOS VLSI Implementation of a Low-Power Logarithmic Converter (Site not responding. Last check: 2007-10-21)
		The converter is implemented using combinational logic only and it calculates a logarithm approximation in a single clock cycle.
		Unlike other complex logarithm correcting algorithms, three unique algorithms are developed and implemented with low-power and fast circuits that reduce the maximum percent errors that result from binary-to-binary logarithm conversion to 0.9299 percent, 0.4314 percent, and 0.1538 percent.
		Simulations of the CMOS design for the 32-bit logarithmic converter, operating at {\rm V_{DD}} equal to 5 volts, run at 55 MHz, and the converter consumes 20 milliwatts.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/trans/tc/&toc=comp/trans/tc/2003/11/tytoc.xml&DOI=10.1109/TC.2003.1244940 (677 words)

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