[CWI]

The Library NUMAL of ALGOL 60 Procedures in Numerical Mathematics (Preamble)


Preamble to the historical NUMAL files, by Jan Kok [external link], CWI, Amsterdam.
[The history of NUMAL] [Earlier work] [Fields covered] [Focus] [Status today] [Availability] [References] [Address]

The history of NUMAL

In the years 1973 - 1979 a systematically organized library of ALGOL 60 procedures in Numerical Mathematics was assembled, called NUMAL. The work of implementing numerical algorithms and documenting the implementations was directed by P.W. Hemker of the Mathematisch Centrum at Amsterdam (Mathematical Centre - MC) and carried out by a large group of (numerical) mathematicians from the MC and the Dutch Universities of Amsterdam and Groningen.

In the sixties the MC was an influential center regarding the scientific use of early-day computers. It had played a keyrole in the construction of computers in The Netherlands and taken part in the design of ALGOL 60. The MC was providing computer services to the academic world: its Electrologica X1 and X8 computers were available for testing and running programs written in ALGOL 60. When large computer centers were created for the Dutch universities, the availability of ALGOL 60 compilers was a logical requirement, and it was found equally logical that several early collections of ALGOL 60 procedures for subareas of numerical mathematics would be united (and extended) to a complete and coherent mathematical software library.

One may suspect it was also hoped that with the obvious advantages of ALGOL 60 for developing new software the library would achieve a prominent place in the scientific world among its equivalents, such as were developed in Fortran by IMSL and NAG.

What resulted was, first, a systematic classification of all possible branches of numerical mathematics, including sectors for auxiliary procedures like manipulating vectors and matrices which fitted with the design characteristic of modularity and would allow a certain level of a common programming style. Next, a library of ALGOL 60 procedures was created starting with the earlier collections: procedures were incorporated when sufficiently supplemented with uniform documentation, and the growing library was further extended with the results of ongoing research. See [Hemker, 1977] for background of this library construction effort.

But ALGOL 60 did not become very popular and with the decreasing interest in ALGOL 60 the justification for continuing development and maintenance of NUMAL disappeared, together with the support for the MC to carry out most of the work. When this became apparent, the MC terminated the project (in 1980) with the publication in book form (MC Syllabus 47) of the whole manual together with the systematic classification and a KWIC index:

P.W. Hemker (ed.): NUMAL, Numerical procedures in ALGOL 60, MC Amsterdam, 1981, MC Syllabus 47.1 - 47.7.

One year later, J. Kok and D.T. Winter carried out the fifth and last revision of the NUMAL library and manual, to make NUMAL sources satisfy the more severe language requirements of a new ALGOL 60 compiler; at the same time they corrected typos and reorganized the on-line manual.

What is made accessible here are the following original, unchanged texts (please note that much additional information in these texts is not valid any more, such as about tapes or even the address of the MC):

Earlier work

In the early days a couple of procedure collections were produced at the MC such as the Zonneveld collection for (systems of) ODEs and the Dekker, resp. Dekker & Hoffmann collections for linear algebra problems (see references), and similar sets for double precision and complex numbers. An older collection (AP 200) contained a set of ALGOL 60 procedures for use on the X1 machine, e.g. for zero finding (real and complex), elliptic integrals and quadrature. Apart from these sets the MC had also available collections of statistical and plotting routines in ALGOL 60.

Other, international sources were Collected Algorithms from the Comm.ACM, Wilkinson & Reinsch, and the journals BIT and Numerische Mathematik. And finally, the procedure euler for summing an alternating infinite series had already been published in the defining Report on ALGOL 60.

Fields covered

The areas for which procedures were present include: system calls, elementary and special functions, vector and matrix manipulation including double precision and complex arithmetic, long integer arithmetic, fourier series, linear systems of general and special forms, including overdetermined systems, singular value decomposition, eigenvalue / eigenvector problems, zero finding, nonlinear systems, quadrature, approximation, summation of series, ordinary and partial differential equations (initial and boundary value problems). Not treated were problems belonging to statistics or operation control, or other computer science methods although a sorting procedure could be found.

Focus

The library was developed, tested and used mainly on successive CDC machines available to the Dutch academic world, under successive versions (version 3 to 5) of their ALGOL compilers. This is still reflected in the employment of the code conventions for calling pre-compiled library procedures. Computer architecture properties concerning floating-point precision are less conspicuous as the prevailing programming style was that for iterative methods the user had to provide tolerances through procedure parameters (hence, only the defaults and examples showed the CDC preference).

Status today

As mentioned before, development ended around 1980, and maintenance stopped some years later when the ALGOL services at the Amsterdam Academic Computer Center (SARA) ended. Subsets of the library had a prolonged, but less well-known life by their conversion (by MC) for subset libraries in Pascal, Algol 68 and Ada. Independently, H.T. Lau supervised a mainly automatic conversion of the whole NUMAL library to Fortran and, more recently, to C.

Availability

The Stichting Mathematisch Centrum at Amsterdam has granted permission to incorporate the complete NUMAL library manual into this CDROM. It may be freely used. It may be copied, provided that the name NUMAL and the attribution to the Stichting Mathematisch Centrum at Amsterdam are retained.

References

  1. T.J. Dekker: ALGOL 60 procedures in numerical algebra, part 1, MC Amsterdam, 1968, MC Tract 22.
  2. T.J. Dekker & W. Hoffmann: ALGOL 60 procedures in numerical algebra, part 2, MC Amsterdam, 1968, MC Tract 23.
  3. P.W. Hemker: Criteria for transportable ALGOL libraries, pp. 145-157, in: W. Cowell (ed.), Portability of numerical software, 1977, Lecture Notes in Computer Science 57, Springer Verlag.
  4. P.W. Hemker (ed.): NUMAL, Numerical procedures in ALGOL 60, MC Amsterdam, 1980, MC Syllabus 47.1 - 47.7.
  5. H.T. Lau: A numerical library in C for scientists and engineers, 1995, CRC Press, Boca Raton.
  6. P. Naur (ed.): Revised Report on the Algorithmic Language ALGOL 60, 1962, A/S Regnecentralen, Copenhagen.
  7. J.H. Wilkinson & C. Reinsch: Linear algebra, Handbook for automatic computation, Vol. 2, 1971, Springer Verlag.
  8. J.A. Zonneveld: Automatic numerical integration, MC Amsterdam, 1964, MC Tract 8.

Address:

CWI [external link]
P.O. Box 94079
NL - 1090 GB Amsterdam
The Netherlands
MC: the institute MC is now (since 1983) called: CWI - Centrum voor Wiskunde en Informatica (Centre for Mathematics and Computer Science). The institute belongs to the Foundation Stichting Mathematisch Centrum.
To CWI's Home Page [external link]
Mail To: Jan.Kok@cwi.nl [external link]