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Unrestricted algorithms for reciprocals and square roots

  • Part II Numerical Mathematics
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Abstract

Algorithms are presented for the computation of reciprocals of nonzero real numbers and square roots of positive numbers. There are no restrictions on the range of the numbers or on the precision that may be demanded in the results.

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References

  1. R. P. Brent,Multiple-precision zero-finding methods and the complexity of elementary function evaluation. InAnalytic Computational Complexity (Edited by J. F. Traub), Academic Press, New York, 1976, pp. 151–176.

    Google Scholar 

  2. R. P. Brent,The complexity of multiple-precision arithmetic. InThe Complexity of Computational Problem Solving (Edited by R. S. Anderssen and R. P. Brent), University of Queensland Press, Brisbane, 1976, pp. 126–165.

    Google Scholar 

  3. R. P. Brent,A Fortran multiple-precision arithmetic package, ACM Trans. Math. Softw., 4 (1978), pp. 57–70.

    Google Scholar 

  4. R. P. Brent,Algorithm 524. MP, A Fortran multiple-precision arithmetic package, ACM Trans. Math. Softw., 4 (1978), pp. 71–81.

    Google Scholar 

  5. C. W. Clenshaw and F. W. J. Olver,An unrestricted algorithm for the exponential function, SIAM J. Numer. Anal., 17 (1980), pp. 310–331.

    Google Scholar 

  6. C. W. Clenshaw and F. W. J. Olver,Beyond floating point, J. Assoc. Comput. Mach., 31 (1984), pp. 319–328.

    Google Scholar 

  7. C. W. Clenshaw and F. W. J. Olver,Level-index arithmetic operations, SIAM J. Numer. Anal. [In Press.]

  8. T. E. Hull and A. Abrham,Properly rounded variable precision square root, ACM Trans. Math. Softw., 11 (1985), pp. 229–237.

    Google Scholar 

  9. F. W. J. Olver,A new approach to error arithmetic, SIAM J. Numer. Anal., 15 (1978), pp. 368–393.

    Google Scholar 

  10. F. W. J. Olver,Further developments of rp and ap error analysis, IMA J. Numer. Anal., 2 (1982), pp. 249–274.

    Google Scholar 

  11. J. M. Yohe,Interval bounds for square roots and the cube roots, Computing, 11 (1973), pp. 51–57.

    Google Scholar 

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Clenshaw, C.W., Olver, F.W.J. Unrestricted algorithms for reciprocals and square roots. BIT 26, 475–492 (1986). https://doi.org/10.1007/BF01935054

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  • DOI: https://doi.org/10.1007/BF01935054

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