Digital Arithmetic Ercegovac, Milos D; Lang, Tomás; Lang, Tom S ...
2004, 2003, 2003-09-15T00:00:00, 2003-09-15
eBook
Digital arithmetic plays an important role in the design of general-purpose digital processors and of embedded systems for signal processing, graphics, and communications. In spite of a mature body ...of knowledge in digital arithmetic, each new generation of processors or digital systems creates new arithmetic design problems. Designers, researchers, and graduate students will find solid solutions to these problems in this comprehensive, state-of-the-art exposition of digital arithmetic. The authors, two of the field's leading experts, deliver a unified treatment of digital arithmetic, tying underlying theory to design practice in a technology-independent manner. They consistently use an algorithmic approach in defining arithmetic operations, illustrate concepts with examples of designs at the logic level, and discuss cost/performance characteristics throughout. Readers will find this book a definitive reference and a consistent teaching tool for developing a deep understanding of the "arithmetic style" of algorithms and designs.
Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to ...rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for graduate teaching: problems and exercises are scattered throughout the text and a solutions manual is available for instructors.
Modern Computer Arithmetic Brent, Richard P.; Zimmermann, Paul
11/2010, Letnik:
v.Series Number 18
eBook
Odprti dostop
Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics ...such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions to selected exercises are available from the authors.
Kao u prethodna dva članka nastavljamo s vizualnim i kratkim dokazima.
Ovaj članak, kao i prethodna dva, posvećujemo našim dragim prijateljima,
učiteljima i profesorima Borisu Pavkoviću ( ...1931.-2006.) i akademiku
Sibi Mardešiću (1927.-2016.). Kao njihovi studenti, koautori i kolege
znamo da su obojica voljela i cijenila kratke, elegantne i jednostavne
dokaze.
Matematikom do ideja za uzorke Duraković, Amra; Kapić, Selma
Osječki matematički list,
12/2015, Letnik:
15, Številka:
1
Paper
Odprti dostop
Modularna aritmetika predstavlja aritmeticki sustav kod koga se brojevi "vraćaju u krug" nakon što dostignu određenu vrijednost - modul. U ovom članku ćemo opisati jednu od primjena modularne ...aritmetike.
Untuk membangun sebuah algoritma kriptografi, banyak konsep aritmatika yang dibutuhkan. ElGamalenkripsi misalnya, dapat didefinisikan melalui grup siklikKeahlian, konsep aritmatika biasa. ...Jikapenggunaan aritmatika ini dikaitkan dengan aspek keamanan, maka membutuhkan besarpekerjaan komputasi. Tesis ini bertujuan untuk membangun algoritma aritmatika sebagai alternatifaritmatika yang dapat diterapkan pada skema kriptografi apa pun, terutama skema kunci publik.Algoritma ini dikenakan dari medan hingga )5). Dengan demikian, prosedur untuk membangunalgoritma aritmatika adalah sebagai berikut. Langkah pertama adalah memilih polinomial primitif)ܼ߳ݔ)ܯݔ dari tingkat yang lebih rendah. Langkah kedua adalah mencari akar primitif M(α) = 0, sehinggapersamaan )ݔ = (0 memiliki akar di )5). Algoritma aritmatika yang dihasilkan adalahprosedur komputasi untuk operasi standar di )5):penjumlahan, perkalian, pembagian,inversi, dan eksponensial. Dapat disimpulkan bahwa algoritma aritmatika yang dibangun5(ܨܩ) lebih baik daripada algoritma standar karena beberapa operasi dapat dikurangi dengan menggunakanpolinomial primitif atau sifat grup siklik, dan menggunakan pengurangan nol.
This paper describes porting LuaJIT compiler to MIPS32 architecture without floating-point unit (FPU). Porting is done by adding software implementation of floating-point arithmetic. It also includes ...enabling dual number mode for LuaJIT on MIPS32 architecture.
Model autodavača (autoencodera) je jedan od najtipičnijih modela temeljitog učenja koji se najčešće koriste u učenju neupravljačkog obilježja za mnoge aplikacije kao što su prepoznavanje, ...identifikacija i pretraživanje. Algoritmi autodavača predstavljaju opsežne računarske zadatke. Stvaranje opsežnog modela autodavača može zadovoljiti potrebe u analizi ogromnog broja podataka. Međutim, vrijeme učenja katkada postaje nepodnošljivo, što dovodi do potrebe istraživanja nekih platformi hardvera za ubrzavanje, kao što je FPGA. Verzije softvera autodavača često koriste izraze jednostruke ili dvostruke preciznosti. Ali implementiranje jedinica s promjenjivom točkom je vrlo skupo za postavljanje u FPGA. Kod implementacije autodavača na hardver stoga se često primjenjuje aritmetika nepromjenjive točke. No često se zanemaruje gubitak točnosti i nije proučavan u ranijim radovima. Ima tek nekoliko radova koji se bave akceleratorima koji koriste fiksne širine bita na drugim modelima neuronskih mreža. U našem se radu daje opsežna procjena prikaza preciznosti implikacija nepromjenjive točke na autodavač, postizanje najbolje značajke i područja učinkovitosti. Metoda konverzije formata podataka, metode blokiranja matrice i aproksimacija kompleksnim funkcijama predstavljaju ključne razmatrane čimbenike u skladu s mjestom implementacije hardvera. U radu se procjenjuju metoda simulacije konverzije podataka, blokiranje matrice različitim paralelizmom i jednostavna metoda evaluacije. Rezultati su pokazali da je širina bita s nepromjenjivom točkom uistinu utjecala na učinkovitost autodavača. Višestruki čimbenici mogu postići suprotan učinak. Svaki čimbenik može imati dvostruki učinak odbacivanja "brojnih" informacija i "korisnih" informacija u isto vrijeme. Područje predstavljanja treba pažljivo odabrati u skladu s računarskim paralelizmom. Rezultat je također pokazao da se primjenom aritmetike nepromjenjive točke može garantirati preciznost algoritma autodavača i postići prihvatljiva brzina konvergencije.
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