Abstract
Many hardware-oriented algorithms computing the usual elementary functions (sine, cosine, exponential, logarithm, ...) only use shifts and additions. In this paper, we present new algorithms using shifts, adds and “small multiplications” (i. e. multiplications by few-digit-numbers). These CORDIC-like algorithms compute the elementary functions in radix 2p (instead of the standard radix 2) and use table look-ups. The number of the required steps to compute functions with a given accuracy is reduced and since we use a quick “small multiplier”, the computation time is reduced.
Zusammenfassung
Viele hardware-orientierte Algorithmen zur Berechnung der üblichen Elementarfunktionen (Sinus, Cosinus, Exponentialfunktion, Logarithmus, ...) benützen nur Shifts und Additionen. In dieser Arbeit stellen wir neue Algorithmen vor, die zusätzlich noch “kleine Multiplikationen” (mit Zahlen von wenigen Stellen) benützen. Diese CORDIC-artigen Algorithmen berechnen die Elementarfunktionen in der Basis 2p (statt der standardbasis 2) und benützen Wertetabellen. Da-durch wird die Anzahl der für eine bestimmte Genauigkeit notwendigen Schritte reduziert und bei der Verwendung einer schnellen “kleinen Multiplikation” auch die Rechenzeit.
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This work has been partially supported by the French “Réseau doctoral en architecture des ordinateurs”.
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Merrheim, X. The computation of elementary functions in radix 2p . Computing 53, 219–232 (1994). https://doi.org/10.1007/BF02307375
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DOI: https://doi.org/10.1007/BF02307375