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4 Elementary FunctionsComputation

§4.48 Software

  1. §4.48(i) Introduction
  2. §4.48(ii) Interval Arithmetic
  3. §4.48(iii) General Precision
  4. §4.48(iv) Lambert W-Function
  5. §4.48(v) Testing

§4.48(i) Introduction

All scientific programming languages, libraries, and systems support computation of at least some of the elementary functions in standard floating-point arithmetic (§3.1(i)). These will not be listed here.

Here we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter when the arithmetic is nonstandard. Links to research literature for the Lambert W-function and for test software are included also. Citations in bulleted lists refer to papers for which research software has been made available and can be downloaded via the Web. References to research software that is available in other ways is listed separately.

A more complete list of available software for computing these functions is found in the Software Index; again, software that uses only standard floating-point arithmetic is excluded. For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C4).

§4.48(ii) Interval Arithmetic

  • Kearfott et al. (1994). Fortran.

  • Kearfott (1996). Fortran 90.

  • Neher (2007). C++.

See also Loenko (2001), Yohe (1979).

§4.48(iii) General Precision

  • Brent (1978a). Fortran.

  • Smith (1991). Fortran.

  • Bailey (1993). Fortran.

  • Smith (1998). Fortran.

  • Smith (2011). Fortran.

See also Bailey (1995), Hull and Abrham (1986), Xu and Li (1994).

§4.48(iv) Lambert W-Function

  • Barry et al. (1995a). Fortran.

  • Lawrence et al. (2012). C.

See also Fritsch et al. (1973).

§4.48(v) Testing

  • Cody (1993a). Fortran.