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Topic: Modulo operation

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Remainder

Modulo

Modular arithmetic

Chinese remainder theorem

Equality (mathematics)

Equivalence relation

Linear congruential generator

Power of two

Pseudorandom number generator

Algorithm

RANDU

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	SELF-CHECK NUMBER GENERATION - Patent 3686629
		The machine may operate under no program control or under the control of either a first or second program, the state of program control being operator selectable by means of a switch on the keyboard control panel.
		The Self-Check Number DCA operates in conjunction with the Keyboard DCA (or with another data entry DCA, such as a card reader), and may utilize the address validation logic of the Keyboard DCA or internal ADV logic to halt the traffic state sequencer at TS2 until a record length operation is complete.
		It should be noted that with Modulo 10 checking, the check-digit may be generated in the DCA to be placed in buffer memory of the CCU or the check-digit may be previously calculated and appear on the source document.
	www.freepatentsonline.com /3686629.html (6784 words)

	Modulo operation - Wikipedia, the free encyclopedia
		Given two numbers, a and n, a modulo n (abbreviated as a mod n) is the remainder, on division of a by n.
		Modulo operations might be implemented such that division with remainder is calculated each time.
		Modulo — many uses of the word "modulo", all of which grew out of Carl F. Gauss's introduction of modular arithmetic in 1801.
	en.wikipedia.org /wiki/Modulo_operation (541 words)

	System for simultaneous transmission of data blocks or vectors between a memory and one or a number of data-processing ...
		However, the systems which operate in the MIMD mode are subject to many practical difficulties in regard to settlement of conflicts arising from access to data shared between all the processing units, in regard to efficient management of resources, synchronization mechanisms to be employed, and in regard to the management of concurrent processing tasks.
		2, in the case of the element 147, the operation 147 mod 25 produces the result 22 (22 being the remainder of the division of the number 147 by the number 25) and the number 22 corresponds to the number of the physical array in which the element 147 is located.
		The arrival address of this element is obtained by performing the modulo-5 operation on the sequence number 22 which consists in finding the remainder of the division of the sequence number 22 by the number 5, which gives the number 2.
	www.freepatentsonline.com /4731724.html (5385 words)

	5.6 Binary arithmetic operations
		Plain or long integer division yields an integer of the same type; the result is that of mathematical division with the `floor' function applied to the result.
		(modulo) operator yields the remainder from the division of the first argument by the second.
		operator is also overloaded by string and unicode objects to perform string formatting (also known as interpolation).
	docs.python.org /ref/binary.html (477 words)

	modulo@Everything2.com
		To say A equals B modulo C means that A-B is divisible by C. More generally, to say 'X modulo Y' is true means that the difference between X being true and X not being true is a factor of Y. Mathie Jargon.
		In computers, often considered to be an operation on two integers, a and b, the remainder operation a modulo b (or a mod b, or a%b) giving the unique r between 0 and b-1 (inclusive) such that a = r (modulo b).
		The official terminology is a = b (modulo c), but often you know you are operating with a particular modulus, and simply write a = b, e.g.
	everything2.com /index.pl?node=modulo (459 words)

	[No title]
		A pre-decrement and post-decrement unary operator that subtracts 1 from the
		operator creates an object in memory and a reference to that location in memory is assigned to a variable.
		The dot operator is also used to test or set the properties of an object or top-level class, execute a method of an object or top-level class, or create a data structure.
	www.brajeshwar.com /reference/as2/operators.html (7816 words)

	modulo - Search Results - MSN Encarta
		The word modulo (Latin, with respect to a modulus of ___) is the Latin ablative of modulus which itself means "a small measure." It was introduced into mathematics in the book...
		In computing, the modulo operation finds the remainder of division of one number by another.
		Given two numbers, a (the dividend) and n (the divisor), a modulo n (abbreviated as a...
	encarta.msn.com /modulo.html (123 words)

	X.25 and LAPB Commands
		When using modulo 128 mode, the window parameter k should be increased to make use of the ability to send a larger number of frames before acknowledgment is required.
		LAPB overhead is 2 bytes for modulo 8 and 3 bytes for modulo 128.
		Modulo 128 operation is also referred to as extended packet sequence numbering, which allows larger packet windows.
	www.cisco.com /univercd/cc/td/doc/product/software/ios103/rpcr/78996.htm (10919 words)

	GPU : a Giga@lobal Processing Unit ?? Grid computing for everyone !
		Modulo is the simple operation that gives the remainder of a division between two numbers, e.g.
		The modulo number has to be relative prime to all other elements in the group.
		E.g if you choose 2 as primitive root, and 16 as modulo operator, you won"t get all numbers between 1 and 15 to be generated.
	seeschloss.org /gpu/crypto.php (1233 words)

	3.2 Arithmetic
		The modulo operation is useful in several contexts in shaders, for instance to compute sawtooth stripe functions or to wrap coordinates.
		the “” operator* on matrices is overloaded to mean matrix multiplication, not componentwise multiplication, and “/” is defined to be multiplication by the matrix inverse of the second argument.
		All arithmetic operations return the same type as their arguments, if the arguments are the same type, with the exceptions that subtracting two ShPoints yields an ShVector, and similarily adding an ShVector to an ShPoint returns an ShPoint.
	libsh.org /ref/online/onlinese13.html (814 words)

	Math Forum - Ask Dr. Math
		The word "multiplication" refers to the group operation (which is most certainly not exponentiation), which is "multiplication modulo n." This might be confusing, so I'll explain it in full detail.
		So the binary operation on this set that makes it a group is called "multiplication modulo p." It is not just plain multiplication, because then one would obtain numbers not in the original set, e.g., 20.
		If you are familiar with multiplicative inverses modulo a composite number, then you would know that the only way to do this is to include only those elements that are relatively prime to the modulus, namely {1, 3, 5, 7} and then define the group operation as multiplication modulo 8.
	mathforum.org /library/drmath/view/61646.html (1472 words)

	Duration Scaling
		As an example, if the algorithm's output values are (1, 0, 2, 3) and you use the default duration range of 0 to 5, the division operation will yield the pitch values (1, 0, 3, 5).
		The modulo operation scales the output values into a cyclical pattern throughout the range you provide.
		In general, a modulo b is the integer remainder resulting when a is divided by b.
	musicalgorithms.ewu.edu /learnmore/norm_dur_scale.html (564 words)

	PACER Correction Distributor
		The Division and Modulo Block takes the correction to be distributed, along with the number of Tics available for correction, seen in Table 6-1.
		Because all the divisors are a power of two, the division and modulo operations become simple shifting operations.
		At the same time, the modulo operation uses seven 2-to-1 multiplexers, with the Tic Speed Decoder lines as the seven individual select lines of the appropriate bit position.
	doppler.unl.edu /~drussell/pacer/CD.html (1383 words)

	mod/2 (Site not responding. Last check: )
		This arithmetic operator calculates the modulo operation of both operands.
		If one or both of the operands is a floating point number then the floating point version of the modulo operator is used.
		Before the modulo operation is performed the right operand is checked if it is not 0.
	www.trinc-prolog.com /doc/pl_p215.htm (49 words)

	[No title]
		Key expansion Since we will be dealing with eight-bit byte operations as well as 16-bit word operations, we will use two alternative notations for referring to the key buffer: For word operations, we will refer to the positions of the buffer as K[0],..., K[63]; each K[i] is a 16-bit word.
		Encryption algorithm The encryption operation is defined in terms of primitive "mix" and "mash" operations.
		Decryption algorithm The decryption operation is defined in terms of primitive operations that undo the "mix" and "mash" operations of the encryption algorithm.
	www.ietf.org /rfc/rfc2268.txt (1310 words)

	Class notes CS251B -- Winter 1997
		When it is subject to a Union operation where its representative pointer changes, the size of the new set in which x now lives in is at least twice as large.
		The time of this operation within this setup is given by the distance of the node x to the root.
		This FindSet operation is based on a two-pass method : it first makes one pass up the find path to locate the root and a second pass up the find path to update each node so that it points directly to the root.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic24 (1992 words)

	MS SQL Server - Lesson 7: SQL Operators and Operands
		The modulo operation is used to get the remainder of a division as a natural number.
		For example, when studying the algebraic operations, we saw that the subtraction is not associative and can lead to unpredictable results.
		In the same way, if your operation involves various operators such as a mix of addition(s) and subtraction(s), you can use parentheses to specify how to proceed with the operations, that is, what operation should (must) be performed first.
	www.functionx.com /sqlserver2000/Lesson07b.htm (695 words)

	GPU : a Global Processing Unit - A computing network on a random graph
		Modulo is the simple operation that gives the remainder of a division between two numbers, e.g.
		The modulo number has to be relative prime to all other elements in the group.
		E.g if you choose 2 as primitive root, and 16 as modulo operator, you won"t get all numbers between 1 and 15 to be generated.
	gpu.sourceforge.net /crypto.php (1256 words)

	Modular Arithmetic - Wolfram Demonstrations Project
		Because 0 is always represented by fl and 1 by white, it makes these values easy to spot in the table.
		For example, to determine which numbers have multiplicative inverses mod 12, you simply need to move the modulus slider to 12, the operation to times, and then determine which rows of the table have the white "1" square.
		By using this Demonstration, you can see a wide range of values and different operations for modular arithmetic, which is quite useful for those beginning to study algebra/number theory.
	demonstrations.wolfram.com /ModularArithmetic (170 words)

	Efficient techniques for sharing a secret - US Patent 7167565
		The custodian performs an exponent/modulo operation each time one of the keys is received from one of the secret owners.
		Alternatively, n+1 keys are created by the custodian, and the custodian retains one key after distributing the remaining n keys to the secret owners.
		The custodian performs another exponent/modulo operation using the entry retrieved from the database in order to reconstruct the original secret.
	www.patentstorm.us /patents/7167565.html (342 words)

	The Grinnell Scheme Web: The modulo procedure
		In mathematics, these subsets are called equivalence classes modulo n.
		procedure examines the first operand and determines which of the equivalence classes modulo n it belongs to (where n is the second operand).
		operation gets a negative operand, its behavior depends on the instruction set of the central processing unit of the computer on which the operation is performed.
	www.math.grin.edu /~stone/scheme-web/modulo.html (405 words)

	Citations: Regular VLSI architectures for multiplication modulo - Curiger, Bonnenberg, Kaeslin (ResearchIndex)
		2.1 Multiplication Modulo 2 n 1 Of the basic operations used in the IDEA algorithm, multiplication modulo 2 16 1 is the most complicated and occupies most of the hardware.
		....the importance of the combinatorial delay and area consumption of the multiplication modulo (2 16 1) units which are crucial to the entire system.
		A modulo (2 n 1) multiplier architecture with modulo reduced, Booth recoded partial products and with concurrent modulo reduction during carry save addition is proposed in [3] and improved in [9] It is shown in [13] that modulo (2 n 1) multipliers with highly regular modulo carry save....
	citeseer.ist.psu.edu /context/165530/0 (996 words)

	Modulo Operation
		The modulo is determined by the pitch range, and a couple
		modulo N if and only if their difference (A – B) is exactly divisible by N. In which case we could write A = B (Mod N).
		This means we are operating in Mod 7
	www.ewu.edu /prime/Modulo1.htm (593 words)

	Arithmetic operators - SGP Baltie 4 C# - help
		Result of this operation is opposite value to the original one.
		Result of this operation is typical subtraction of the operands.
		Modulo is remainder after division of the left expression by the right expression.
	www.sgpsys.com /doc/b4/en-US/arithmetic_operators(ArithmeticOperators).html (351 words)

	The Rabin-Karp Algorithm
		Luckily, we can exploit an important property of the modulo operation- taking the modulus of intermediate steps of an addition, multiplication, or subtraction calculation has no effect on the outcome of the calculation.
		This means that by performing the modulo operation early and often, we can compute the modulus of the results of operations on very large numbers without actually ever worrying about the size of the numbers, as long as the modulus we are using is not very large.
		However, the modulus operation can be eliminated from the algorithm by choosing a different hashing function that has the same property that it is easy to compute from the previous string, yet does not require so many modulo operations.
	www.eecs.harvard.edu /~ellard/Q-97/HTML/root/node43.html (1480 words)

	David Stiller’s blog » Blog Archive » Lesser Known Operators: Modulo (%)
		Modulo is one of the multiplicative operators, a category whose members take two operands and perform a multiplication, division, or modulo operation on them.
		Modulo tells you right away which is which: if a number mod 2 equals zero, it’s even.
		The thing about operators is that they’re usually just punctuation marks, which makes them a bit tougher to locate.
	www.quip.net /blog/2006/flash/actionscript-20/lesser-known-operators-modulo (1183 words)

	Legacy:Useful Maths Functions - Unreal Wiki
		The modulo operator is defined as the remainder after integer division of its first argument by its second argument.
		In IEEE 754 the remainder operation is a rounding division, not a truncating division, and therefore complies with the historical definition based on equivalence classes.
		We are talking about (at least) 12 interpreter operations for the shifting version as opposed to 6 for the log version, which means half as many runs through a potentially fairly complicated (with OO and all) interpreter loop.
	wiki.beyondunreal.com /wiki/Useful_Maths_Functions (3017 words)

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