Subsections

• 3.2.1 $\clubsuit$ Atlas for Computing Mathematical Functions [Tho97]
• 3.2.2 $\clubsuit$ C Mathematical Function Handbook [Bak92]
• 3.2.3 $\clubsuit$ Computation of Special Functions [ZJ96]
• 3.2.4 $\clubsuit$ Mathematical Function Library for Microsoft Fortran or C [ULI90]
• 3.2.5 $\clubsuit$ Methods and Programs for Mathematical Functions [Mos89]

3.2 Intermediate Libraries

Under this heading we place software that is in some sense intermediate between software packages, which embody original research contributions, and comprehensive libraries (§3.3 below). The libraries we consider here provide support only for mathematical functions. Furthermore, they are largely restricted to codification of existing algorithms with all their advantages--and limitations.

3.2.1 $\clubsuit$ Atlas for Computing Mathematical Functions [Tho97]

The purpose of this book with CD-ROM is to provide C or Fortran 90 source code for most of the functions included in the NBS Handbook of Mathematical Functions [AS64]. It claims ``most of the functions are computed ...to an accuracy of at least 10 decimal digits.'' The functions are computed for real variables only.

3.2.2 $\clubsuit$ C Mathematical Function Handbook [Bak92]

This volume with diskette is keyed to the NBS Handbook of Mathematical Functions [AS64]. Most chapters of the NBS Handbook have a counterpart here in which brief introductory material is followed by C code listings. A complex arithmetic package is included since C supports only real and integer arithmetic. The author advocates the use of C because it ``is rapidly becoming the lingua franca of the computer world'' and ``algorithms written in C should be very portable''. He has written two other books on C programming for technical applications.

3.2.3 $\clubsuit$ Computation of Special Functions [ZJ96]

This book with included diskette provides Fortran 77 code for most of the functions in the NBS Handbook of Mathematical Functions [AS64]. For many of the functions, codes are supplied for complex as well as real arguments. In some cases complex parameters are supported also.

3.2.4 $\clubsuit$ Mathematical Function Library for Microsoft Fortran or C [ULI90]

These volumes exist to ``provide users with a comprehensive set of mathematical function routines to assist them in solving their mathematical problems on IBM PC/XT/AT or compatibles.'' Each consists of a looseleaf manual with diskettes. The documentation for each function gives usage instructions, input range, accuracy, definition of the function, algorithm, sample program and sample results. The functions are evaluated only for real arguments. The diskettes contain a compiled library in microprocessor assembly code for use with Microsoft compilers and the Fortran or C source code for use with other compilers.

3.2.5 $\clubsuit$ Methods and Programs for Mathematical Functions [Mos89]

This volume with separate diskette of C programs presents a selection of special functions with real arguments and integer or real parameters. The programs are designed for double precision, and tables of test results included for every function typically show absolute or relative errors (whichever is appropriate) of the order of $10^{-16}$. Where polynomial or rational approximations are used, the expansion coefficients were generated in multiple precision using C programs that are given in the book. The programs have been collected under the heading ``cephes'' and are downloadable free-of-charge from Netlib; see http://gams.nist.gov/serve.cgi/Package/CEPHES/.