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Nbit unsigned division via nbit multiplyadd
 in 17th IEEE Symposium on Computer Arithmetic
, 2005
"... Integer division on modern processors is expensive compared to multiplication. Previous algorithms for performing unsigned division by an invariant divisor, via reciprocal approximation, suffer in the worst case from a common requirement for n+1 bit multiplication, which typically must be synthesize ..."
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Cited by 6 (0 self)
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Integer division on modern processors is expensive compared to multiplication. Previous algorithms for performing unsigned division by an invariant divisor, via reciprocal approximation, suffer in the worst case from a common requirement for n+1 bit multiplication, which typically must
Division by Invariant Integers Using Multiplication
 In Proceedings of the SIGPLAN '94 Conference on Programming Language Design and Implementation
, 1994
"... Integer division remains expensive on today's processors as the cost of integer multiplication declines. We present code sequences for division by arbitrary nonzero integer constants and runtime invariants using integer multiplication. The algorithms assume a two's complement architectur ..."
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Cited by 49 (1 self)
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architecture. Most also require that the upper half of an integer product be quickly accessible. We treat unsigned division, signed division where the quotient rounds towards zero, signed division where the quotient rounds towards #, and division where the result is known a priori to be exact. We give some
Design of Approximate Unsigned Integer Nonrestoring Divider for Inexact Computing
"... This paper proposes several approximate divider designs; two different levels of approximation (cell and array levels) are investigated for nonrestoring division. Three approximate subtractor cells are proposed and designed for the basic subtraction; these cells mitigate accuracy in subtraction wit ..."
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This paper proposes several approximate divider designs; two different levels of approximation (cell and array levels) are investigated for nonrestoring division. Three approximate subtractor cells are proposed and designed for the basic subtraction; these cells mitigate accuracy in subtraction
Software Integer Division
"... Abstract Early computers omitted instructions for integer multiplication and division, requiring these operations to be synthesized in software. Even some modern RISC and DSP architectures are deficient in the case of division. Therefore software methods for performing integer division continue to ..."
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to be of interest. We consider typical architectures based on two's complement binary arithmetic and present various methods of performing single precision unsigned integer division in software. In addition to methods based on the standard testsubtractshift approach, we present a method and variants based
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 10 (0 self)
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the reciprocal, however, the quotient obtained often suffers from offby one errors, requiring a correction step. This paper describes the design decisions we made when architecting integer division for a new 64 bit machine. The result is a fast and economical scheme for computing both unsigned and signed
Improved division by invariant integers
 IEEE Transactions on Computers
"... AbstractThis paper considers the problem of dividing a twoword integer by a singleword integer, together with a few extensions and applications. Due to lack of efficient division instructions in current processors, the division is performed as a multiplication using a precomputed singleword app ..."
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Cited by 4 (0 self)
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AbstractThis paper considers the problem of dividing a twoword integer by a singleword integer, together with a few extensions and applications. Due to lack of efficient division instructions in current processors, the division is performed as a multiplication using a precomputed single
1Improved division by invariant integers
"... Abstract—This paper considers the problem of dividing a twoword integer by a singleword integer, together with a few extensions and applications. Due to lack of efficient division instructions in current processors, the division is performed as a multiplication using a precomputed singleword appr ..."
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Abstract—This paper considers the problem of dividing a twoword integer by a singleword integer, together with a few extensions and applications. Due to lack of efficient division instructions in current processors, the division is performed as a multiplication using a precomputed single
ROUNDED CONSTANT DIVISION VIA ADDSHIFT IN VERILOG
"... Abstract: An implementation of division in hardware is expensive. One of the alternatives is by replacing it with cheaper adder and shifter. This paper presents the condition of addshift schemes that had been modifiedfrom existing algorithm. The constant denominators are 3, 5, 6, 7 and 9. The modi ..."
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. The modifications are to eliminate the integer multiplication and to round the unsigned result to the nearest integer. The comparison results of the outputs between C++ and Verilog codes are used to verify the accuracy of the division process. Verilog code needs to be changed for any incorrect results. The required
doi:10.1093/comjnl/bxm082 Efficient Algorithms for Integer Division by Constants Using Multiplication
"... We present a complete analysis of the integer division of a single unsigned dividend word by a single unsigned divisor word based on doubleword multiplication of the dividend by an inverse of the divisor. The wellknown advantage of this method yields runtime efficiency, if the inverse of the divi ..."
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Cited by 1 (1 self)
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We present a complete analysis of the integer division of a single unsigned dividend word by a single unsigned divisor word based on doubleword multiplication of the dividend by an inverse of the divisor. The wellknown advantage of this method yields runtime efficiency, if the inverse
Systolic, LinearArray Multiplier for a Class of RightShift Algorithms
, 1994
"... A very simple multiplier cell is developed for use in a linear, purely systolic array forming a digitserial multiplier for unsigned or 2'complement operands. Each cell produces two digitproduct terms and accumulates these into a previous sum of the same weight, developing the product least si ..."
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Cited by 30 (0 self)
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A very simple multiplier cell is developed for use in a linear, purely systolic array forming a digitserial multiplier for unsigned or 2'complement operands. Each cell produces two digitproduct terms and accumulates these into a previous sum of the same weight, developing the product least
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