Skip to main content
SpringerLink
Log in

Rational approximations, software and test methods for sine and cosine integrals

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

Rational approximations to the sine integralSi(x) and cosine-integralCi(x) are developed which give an accuracy of 20sf. The robust construction of software for these functions is discussed, together with a test procedure for assessing the performance of such codes. Use of the tests discovers a major error in the netlib library FN codes forSi. Fortran versions of the codes and tests are available by electronic mail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Abramowitz and I.A. Stegun (eds.),Handbook of Mathematical Functions, Dover, New York, 1965.

    Google Scholar 

  2. C.W. Clenshaw, The numerical solution of linear differential equations in Chebyshev series, Proc. Camb. Phil. Soc. 53 (1957) 134–149.

    Google Scholar 

  3. W.J. Cody, Algorithm 665: MACHAR: A subroutine to dynamically determine machine parameters, ACM Trans. Math. Soft., 14 (1988) 303–311.

    Article  Google Scholar 

  4. W.J. Cody, Algorithm 715: SPECFUN — A portable FORTRAN package of special function routines and test drivers, ACM Trans. Math. Softw. 19 (1993) 22–32.

    Article  Google Scholar 

  5. W.J. Cody, W. Fraser and J.F. Hart, Rational Chebyshev approximation using linear equations, Numer. Math. 12 (1968) 242–251.

    Google Scholar 

  6. W.J. Cody and L. Stoltz, The use of Taylor series to test accuracy of function programs, ACM Trans. Math. Soft. 17 (1991) 55–63.

    Article  Google Scholar 

  7. J.J. Dongarra and E. Grosse, Distribution of mathematical software via electronic mail, Comm. ACM 30 (1987) 403–407.

    Article  Google Scholar 

  8. W. Gautschi, Algorithm 282 — derivatives ofe x/x, cosx/x, and sinx/x, Comm. ACM 9 (1966) 272.

    Article  Google Scholar 

  9. W. Gautschi, Computation of successive derivatives off(z)/z, Math. Comp. 20 (1966) 209–214.

    Google Scholar 

  10. W. Gautschi and B.J. Klein, Recursive computation of certain derivatives — a study of error propogation, Comm. ACM 13 (1970) 7–9.

    Article  Google Scholar 

  11. W. Gautschi and B.J. Klein, Remark on Algorithm 282 — Derivatives ofe x/x, cosx/x, and sinx/x, Comm. ACM 13 (1970) 53–54.

    Article  Google Scholar 

  12. J.F. Hart, E.W. Cheney, C.L. Lawson, H.J. Maehhly, C.K. Mesztenyi, J.R. Rice, H.G. Thacher and C. Witzgall,Computer Approximations, Wiley, New York, 1968.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Paisley, High St., PA1 2BE, Paisley, Scotland

    Allan J. MacLeod

Authors
  1. Allan J. MacLeod
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by C. Brezinski and H. Redivo-Zaglia

Rights and permissions

Reprints and permissions

About this article

Cite this article

MacLeod, A.J. Rational approximations, software and test methods for sine and cosine integrals. Numer Algor 12, 259–272 (1996). https://doi.org/10.1007/BF02142806

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02142806

Keywords

Subject classification

Search

Navigation