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Construction of Parallel Addition Algorithms by the Extending Window Method - results

Legerský, Jan; Svobodová, Milena

An algebraic number \(\beta \in \mathbb{C}\) with no conjugate of modulus 1 can serve as the base of a numeration system \((\beta, \mathcal{A})\) with parallel addition, i.e., the sum of two operands represented in base \(\beta\) with digits from \(\mathcal{A}\) is calculated in constant time, irrespective of the length of the operands.

In the paper Construction of Algorithms for Parallel Addition, a so-called Extending Window Method is introduced. This method is an algorithm to construct Parallel Addition algorithms. See the paper for the details, or the project website.

We present here the results of this method for selected numeration systems, see the implementation.

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Avizienis.zip
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Chow-Robertson.zip
md5:f1d8e470fc08678fdef9595574e3d9ae
26.0 kB Download
complexQuadraticBases_integerAlphabet.zip
md5:ba1b359004eedb6b5ea4ef1c0983d0f2
665.5 kB Download
complexQuadraticBases_non-integerAlphabet.zip
md5:c76fe9725007821e7153806bfd20d67d
236.2 MB Download
cubicRootOfSeven.zip
md5:64955b0e2d8884f171ccdd85d7679162
91.7 MB Download
cubicRootOfTwo.zip
md5:c360bd45cb3949875c2fc00aba86fb65
233.5 kB Download
Eisenstein.zip
md5:a6d43d608e665aa5b600724fcbffe06c
4.9 MB Download
fifthRootOfSix_positiveAlphabet_smallB.zip
md5:c73844b6a4b6a1ce6a5f305a46741551
663.0 kB Download
fourthRootOfFive_positiveAlphabet.zip
md5:c5d8a98c5cead9b8f9c3c632c1b28f72
1.1 GB Download
fourthRootOfFive_positiveAlphabet_smallB.zip
md5:f6facbd70d4c15a15b4a7ae033990b04
65.5 kB Download
fourthRootOfFive_symmetricAlphabet_smallB.zip
md5:165cb635c9d8c19757c76ec3f600bedd
707.8 MB Download
Knuth.zip
md5:60776e2c75a21faa1826848924a17718
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negativeIntegerBase.zip
md5:ef04804e29c246569825f913a7e431e1
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Penney.zip
md5:2a04481f5c953c9775d4155eac60cc18
74.1 MB Download
positiveIntegerBase.zip
md5:d0cffdec8f1762a9c9029553c731b37f
34.0 kB Download
realQuadraticBases_integerAlphabet_positive.zip
md5:784094eabeb3bb8bc550f6eb542a5ac0
6.8 MB Download
realQuadraticBases_integerAlphabet_symmetric.zip
md5:93fa8f9e9c7e1e9b9820d9789fc21ffb
6.1 MB Download
realQuadraticBases_non-integerAlphabet.zip
md5:361161c8e015ac99f8b303639c381f99
52.2 MB Download
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