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Even faster integer multiplication
[article]

2014
*
arXiv
*
pre-print

We give a new proof of Fürer's bound for the cost of multiplying n-bit

arXiv:1407.3360v1
fatcat:ldl7p5e6gvfvbdoy4pbe4tftgy
*integers*in the bit complexity model. ... We show that an optimised variant of Fürer's algorithm achieves only K = 16, suggesting that the new algorithm is*faster*than Fürer's by a factor of 2^(log^* n). ... David Harvey, Joris van der Hoeven, Grégoire Lecerf*Even**faster**integer**multiplication*...##
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Even faster integer multiplication

2016
*
Journal of Complexity
*

We give a new proof of Fürer's bound for the cost of multiplying n-bit

doi:10.1016/j.jco.2016.03.001
fatcat:maj3qbr7mrdi3ovtok2pglauei
*integers*in the bit complexity model. ... We show that an optimised variant of Fürer's algorithm achieves only K = 16, suggesting that the new algorithm is*faster*than Fürer's by a factor of 2 log * n . ...*Even**faster**multiplication*In this section, we present an optimised version of the new*integer**multiplication*algorithm. ...##
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Montgomery Multiplier for Faster Cryptosystems

2016
*
Procedia Technology - Elsevier
*

This paper presents a 32-bit implementation of a

doi:10.1016/j.protcy.2016.08.123
fatcat:dlvldhtomzhgnij2utaot5gmrm
*Faster*Montgomery algorithm for performing modular*multiplication*. ... Many hardware and software implementations for*faster*modular*multiplication*have been proposed, Montgomery*Multiplication*Algorithm is recognized as the most efficient among these. ... Modular*Multiplication*Modular*multiplication*problem is defined as the computation of P = A × B (mod m), given the*integers*A, B and m. ...##
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Fast Library for Number Theory: An Introduction
[chapter]

2010
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Lecture Notes in Computer Science
*

Magma is already up to five times

doi:10.1007/978-3-642-15582-6_18
fatcat:i2legnxi3fe2fjjt2msbu5c3hm
*faster*than NTL*even*for polynomial*multiplication*. The Pari library is not usually asymptotically fast and NTL is not threadsafe. ... This implementation is often*faster*than GMP [5] (which is used for smaller*multiplications*), by as much as 30%. ...##
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More Generalized Mersenne Numbers
[chapter]

2004
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Lecture Notes in Computer Science
*

We also show that it is possible to perform long

doi:10.1007/978-3-540-24654-1_24
fatcat:nbfyp7dmrrfatagquqtvg6k4ae
*integer*modular arithmetic without using*multiple*precision operations when t is chosen properly. ... It is shown that such p's lead to fast modular reduction methods which use only a few*integer*additions and subtractions. We further generalize this idea by allowing any*integer*for t. ...*Even*without the KOA, our methods are still*faster*than the classical and the Montgomery algorithms. ...##
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Flexural reticular pigmentation and pruritic papules in a 33-year-old woman

2011
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Clincal and Experimental Dermatology
*

Magma is already up to five times

doi:10.1111/j.1365-2230.2010.03913.x
pmid:21323938
fatcat:o2wi6ja7ubcfrpolzdlqugku34
*faster*than NTL*even*for polynomial*multiplication*. The Pari library is not usually asymptotically fast and NTL is not threadsafe. ... This implementation is often*faster*than GMP [5] (which is used for smaller*multiplications*), by as much as 30%. ...##
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High-Performance Modular Multiplication on the Cell Processor
[chapter]

2010
*
Lecture Notes in Computer Science
*

Typically, the

doi:10.1007/978-3-642-13797-6_2
fatcat:sw6allqzozdpjn7qh3lgyrjhfi
*multiplication*and special reduction are performed sequentially. For the separated*multiplication*step we consider schoolbook and Karatsuba*multiplication*[18] techniques. ...*multiple*computations concurrently; e.g. graphics processing units. ... The SPEs are equipped with a 4-way SIMD multiplier (*even*instruction) which can compute four 16bit*integer**multiplications*simultaneously per clock cycle. ...##
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Strongly Universal String Hashing is Fast

2013
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Computer journal
*

Moreover, conventional wisdom is that hash functions with fewer

doi:10.1093/comjnl/bxt070
fatcat:ihslalyvrbc63njznfrhcbtxgy
*multiplications*are*faster*. Yet we find that they may fail to be*faster*due to operation pipelining. ... Our tests include hash functions designed for processors with the Carry-Less*Multiplication*(CLMUL) instruction set. We also prove, using accessible proofs, the strong universality of our families. ... Yet another alternative, Multilinear (2-by-2), was slightly*faster*(≈ 15%) for 32-bit hashing on the mobile ARM-based processors*even*though it requires twice as many*multiplications*as Multilinear-HM. ...##
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Fast Implementation of 4-bit Convolutional Neural Networks for Mobile Devices
[article]

2020
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arXiv
*
pre-print

It shows 2.9 times speedup compared to standard floating-point

arXiv:2009.06488v2
fatcat:pojrbhq6cnearmrheyxi7tmxni
*multiplication*and is 1.5 times*faster*than 8-bit quantized one. ... However, their advantages are apparent for FPGA and ASIC devices, while general-purpose processor architectures are not always able to perform low-bit*integer*computations efficiently. ... We can see that*multiplication*of 32-bit*integers*and floating point values takes almost the same time,*multiplication*of 4-bit unsigned*integers*works approximately 2.4 times*faster*than that of 32-bit ...##
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Software Optimization of Decorrelation Module
[chapter]

2000
*
Lecture Notes in Computer Science
*

This paper investigates software optimization of special

doi:10.1007/3-540-46513-8_13
fatcat:iwfephzrxfh5rbrhcl3wbxe76m
*multiplication*. In particular we concentrate on ax + b mod 2 64 + 13 mod 2 64 which is the bottleneck operation in the DFC cipher. ... These methods are*faster*than using four*integer**multiplications*. The only problem is to convert from*integers*to floats. ...*Even*hand-written bytecode, which should produce*faster*code, does not have a noticeable speedup. ...##
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Faster remainder by direct computation: Applications to compilers and software libraries

2019
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Software, Practice & Experience
*

On common processors,

doi:10.1002/spe.2689
fatcat:ujlp4nxjzjhctgmq32oreanpsa
*integer**multiplication*is many times*faster*than*integer*division. ... If the divisor is known in advance---or if repeated*integer*divisions will be performed with the same divisor---it can be beneficial to substitute a less costly*multiplication*for an expensive division ... Given an*integer*numerator and an*integer*divisor , the quotient ( ) and the remainder ( ) are always*integers**even*when the fraction ∕ is not an*integer*. ...##
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Number Theoretic Transforms for Fast Digital Computation

2019
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International Journal of Research in Advent Technology
*

The aim of this study is to show that Number Theoretic Transforms (NTTs) can be really beneficial in terms of error free and

doi:10.32622/ijrat.752019106
fatcat:s6crqwmhlrdftgx7gg2pjcn6na
*faster*computation. ... This is much simpler than complex domain*multiplications*; hence FNT is*faster*than FFT. ... If*multiplicative*inverse exists for all nonzero*integers*in then becomes field. [4] [5] . ...##
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How Fast Can We Multiply Large Integers on an Actual Computer?
[article]

2014
*
arXiv
*
pre-print

We provide two complexity measures that can be used to measure the running time of algorithms to compute

arXiv:1402.1811v1
fatcat:73lp23v6enevrfnyj52iy6jj5y
*multiplications*of long*integers*. ... The random access machine with unit or logarithmic cost is not adequate for measuring the complexity of a task like*multiplication*of long*integers*. ...*Even*without*multiplication*, length T (n)*integers*can be produced in time T (n), resulting in unrealistically cheap additions. ...##
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Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications

2014
*
Journal of Applied Mathematics
*

The proposed

doi:10.1155/2014/107109
fatcat:xnciccnokvgtliq5sk2n74kw7e
*multiplication*algorithm is also 2.3 to 3.9 and 7 to 2.4 times*faster*for multiplying 32-bit and 8-Kbit numbers, respectively. ... We present a modified version of the classical*multiplication*and squaring algorithms based on the Big-ones to improve the efficiency of big*integer**multiplication*and squaring in number theory based cryptosystems ... The proposed*multiplication*algorithm is about 2.3 times*faster*than CM MUL for multiplying 32-bit numbers and about 3 times*faster*for multiplying 64-bit numbers. ...##
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Efficient Multiple-Precision Evaluation of Elementary Functions

1989
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Mathematics of Computation
*

Because this improvement is fairly simple, the resulting algorithms are

doi:10.2307/2008657
fatcat:wqyzslhqrfa6dfvolicoh2diy4
*faster*than those in [3]*even*at low precision. Exponential and Related Functions. ... . , Sjpl requires one*multiplication*to get the next power of xi, j divisions by an*integer*, and j additions. ...
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