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Integer Division Using Reciprocals
 In Proceedings of the Tenth Symposium on Computer Arithmetic
, 1991
"... As logic density increases, more and more functionality is moving into hardware. Several years ago, it was uncommon to find more than minimal support in a processor for integer multiplication and division. Now, several processors have multipliers included within the central processing unit on one in ..."
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Cited by 8 (0 self)
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As logic density increases, more and more functionality is moving into hardware. Several years ago, it was uncommon to find more than minimal support in a processor for integer multiplication and division. Now, several processors have multipliers included within the central processing unit on one
Prescaled Integer Division
"... We describe a high radix integer division algorithm where the divisor is prescaled and the quotient is postscaled without modifying the dividend to obtain an identity ¢¤£¦¥¨§�©������� § with the quotient ¥¨§ differing from the desired integer quotient ¥ only in its lowest order high radix digit. Her ..."
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We describe a high radix integer division algorithm where the divisor is prescaled and the quotient is postscaled without modifying the dividend to obtain an identity ¢¤£¦¥¨§�©������� § with the quotient ¥¨§ differing from the desired integer quotient ¥ only in its lowest order high radix digit
Bidirectional Exact Integer Division
 J. SYMBOLIC COMPUTATION
, 1994
"... Division of integers is called exact if the remainder is zero. We show that the highorder part and the loworder part of the exact quotient can be computed independently from each other. A sequential implementation of this algorithm is up to twice as fast as ordinary exact division and four times ..."
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Cited by 6 (2 self)
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Division of integers is called exact if the remainder is zero. We show that the highorder part and the loworder part of the exact quotient can be computed independently from each other. A sequential implementation of this algorithm is up to twice as fast as ordinary exact division and four times
Integer Division is in NC¹
, 1995
"... An NC¹ circuit for division of binary numbers is presented. By results of Beame, Cook and Hoover this also shows that iterated product and powering are in NC¹, and by a result of Borodin all three operations are in logspace. This settles an open issue in parallel and space bounded arithmetic comple ..."
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An NC¹ circuit for division of binary numbers is presented. By results of Beame, Cook and Hoover this also shows that iterated product and powering are in NC¹, and by a result of Borodin all three operations are in logspace. This settles an open issue in parallel and space bounded arithmetic
Practical Integer Division with Karatsuba Complexity
 Proc. ISSAC'97, 339341
, 1997
"... Combining Karatsuba multiplication with a technique developed by Krandick for computing the highorder part of the quotient, we obtain an integer division algorithm which is only two times slower, on average, than Karatsuba multiplication. The main idea is to delay part of the dividend update until ..."
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Cited by 11 (1 self)
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Combining Karatsuba multiplication with a technique developed by Krandick for computing the highorder part of the quotient, we obtain an integer division algorithm which is only two times slower, on average, than Karatsuba multiplication. The main idea is to delay part of the dividend update until
On Secure Twoparty Integer Division
"... Abstract. We consider the problem of secure integer division: given two Paillier encryptions of ℓbit values n and d, determine an encryption of ⌊ n ⌋ without leaking any information about n or d. We propose two new d protocols solving this problem. The first requires O(ℓ) arithmetic operation on en ..."
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Abstract. We consider the problem of secure integer division: given two Paillier encryptions of ℓbit values n and d, determine an encryption of ⌊ n ⌋ without leaking any information about n or d. We propose two new d protocols solving this problem. The first requires O(ℓ) arithmetic operation
Integer Division, Clock Arithmetic, and Congruences
"... to division, we face a choice: we can either say that 1 \Xi 2 is 1 2 (or 0.5), and be forced to work in the complicated world of fractions, or we can recall another definition of division, say that 1 \Xi 2 is "0, with remainder 1", and continue to work among the natural numbers. At this p ..."
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. At this point, we prefer the latter! We need, therefore, to remember the definition of integer division: when m is divided by n, we obtain two integers, q and r, called the quotient and remainder, respectively, with r between 0 and n \Gamma 1, such that the equation m = nq + r is satisfied. The number r
OPTIMAL SIZE INTEGER DIVISION CIRCUITS
, 1988
"... Division is a fundamental problem for arithmetic and algebraic computation. This paper describes Boolean circuits (of bounded fanin) for integer division ( nding reciprocals) that have size O(M (n)) and depth O(log n log log n), where M(n) is the size complexity ofO(log n) depth integer multiplicat ..."
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Cited by 11 (2 self)
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Division is a fundamental problem for arithmetic and algebraic computation. This paper describes Boolean circuits (of bounded fanin) for integer division ( nding reciprocals) that have size O(M (n)) and depth O(log n log log n), where M(n) is the size complexity ofO(log n) depth integer
Results 1  10
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184,435