BIT Numerical Mathematics

, Volume 35, Issue 3, pp 352–360 | Cite as

Highly accurate tables for elementary functions

  • Wolfram Luther


In this article we describe a fast method to obtain highly accurate tables for all elementary functions by using Bresenham's algorithm. For nearly equally spaced table-points {x i } we construct pairs {f(x i ),g(x i )} such thatf(x i ) is a machine number andg(x i ) is very close to an exactly representable number. By a random sampling in an interval centered onx i we can even find a triplet\(\{ \hat x_i ,f(\hat x_i ),g(\hat x_i )\} \) of nearly machine numbers. The table method together with a polynomial approximation of the function near a table value provides last bit accuracy for more than 99.8% of the argument values without using extended precision calculations [3, 4, 10, 11].

Key words

Accurate table method elementary functions Bresenham's algorithm computer arithmetic 


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Copyright information

© BIT Foundation 1995

Authors and Affiliations

  • Wolfram Luther
    • 1
  1. 1.FB 11, Informatik IIGerhard-Mercator-Universität-Gesamthochschule DuisburgLotharstraße 65Duisburg

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