Towards a modern floating-point environment

Abstract : This work investigates two ways of enlarging the current floating-point environment. The first is to support several implementation versions of each mathematical function (elementary such as $\exp$ or $\log$ and special such as $\erf$ or $\Gamma$), the second one is to provide IEEE754 operations that mix the inputs and the output of different \radixes. As the number of various implementations for each mathematical function is large, this work is focused on code generation. Our code generator supports the huge variety of functions: it generates parametrized implementations for the user-specified functions. So it may be considered as a black-box function generator. This work contains a novel algorithm for domain splitting and an approach to replace branching on reconstruction by a polynomial. This new domain splitting algorithm produces less subdomains and the polynomial degrees on adjacent subdomains do not change much. To produce vectorizable implementations, if-else statements on the reconstruction step have to be avoided. Since the revision of the IEEE754 Standard in 2008 it is possible to mix numbers of different precisions in one operation. However, there is no mechanism that allows users to mix numbers of different radices in one operation. This research starts an examination ofmixed-radix arithmetic with the worst cases search for FMA. A novel algorithm to convert a decimal character sequence of arbitrary length to a binary floating-point number is presented. It is independent of currently-set rounding mode and produces correctly-rounded results.
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Computer Arithmetic. Université Pierre et Marie Curie - Paris VI, 2015. English. < NNT : 2015PA066584 >
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Olga Kupriianova. Towards a modern floating-point environment. Computer Arithmetic. Université Pierre et Marie Curie - Paris VI, 2015. English. < NNT : 2015PA066584 >. <tel-01334024>



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