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 2 Existing Scope and |
 Toward a Revised NBS |
4 Prospectus
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2 Existing Scope and |
Toward a Revised NBS |
4 Prospectus
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In the introduction to this report an allusion was made to an unfolding revolution in information technology which is marking a new technological transition. This revolution is being driven by technological advances in hardware, software, and especially in digital communications. This report is not the place to try to define or describe this revolution in general terms. Everyone is well aware of its existence and of its potential for dramatic impacts in book publishing, journal publishing, interpersonal communication, and dissemination of all kinds of information. Indeed, the impact has already been enormous. In mathematical publishing, LATEX3is used routinely to typeset arbitrarily complex material. Diskettes and compact disks (CD-ROMs) are distributed with published books to provide relevant computer files to the purchaser. Automated repositories are used to obtain software documents and other material by a simple electronic request; the requester is the only human in the transaction. These are examples of one-way communication from an author to a reader or `information consumer' in which new technology results in an improved product. The information transferred (mathematical text, graphs, tables of numbers, programs) is prepared in advance in the expectation that it will meet future needs, and of course there are always unanticipated needs that are not met.
What is needed to meet unanticipated needs is a mechanism that can generate and deliver information on demand. This is achievable using the World Wide Web (WWW) in conjunction with computer programs. In a typical transaction, the consumer enters a request for information on a `question page,' and an `information provider' returns an `answer page.' The answer page could be a simple image of a record extracted from a database (reminiscent of one-way communication between an author and a reader), or it could be generated by an arbitrarily complicated computation. To get beyond the traditional concept of a fixed and immutable publication, the term digital library4has come into use.
There are opportunities and obstacles in applying digital library technology to the subject matter of the NBS Handbook. The overall opportunity is to provide to the widest possible audience an authoritative and up-to-date resource center for special functions. We envision constructing a resource center, or digital library, in two major stages. The first stage will be similar in concept to the existing handbook with as many extensions as possible in the direction of dynamic generation of information. A large database of static answer pages will be constructed and used as the basis for satisfying information requests. The same database could serve as the basis for books and CD-ROMs. An immediate advantage of CD-ROMs and the WWW over books is the possibility of downloading crucial artifacts, such as symbolic code for mathematical formulas, into documents and computer programs. In this initial stage a major obstacle will be in connection with the numerical tables. First, the precision and range of the existing tables are inadequate to current needs, particularly when used to validate numerical software. Second, software packages exist that can compute vastly extended numerical tables--but the state of the art in software packages today is such that reliability of the computed values remains open to question. The decision of what to include in the way of numerical tables, if any, will be difficult. References without endorsement to algorithms and software can be given and will be useful but a completely satisfactory outcome with respect to the numerical tables is not likely in the initial stage.
In the second stage we envision making a serious attempt to overcome the numerical tables obstacle. The idea is to develop a standard reference library of numerical software that is capable of computing function values to at least quadruple precision over very large ranges of the input arguments and parameters. But we require even more--that the accuracy of quadruple precision is reliable in the sense that all errors arising from truncation and rounding are monitored and kept under strict control. This requirement is necessary to uphold the standard of authoritativeness that is desirable for a genuine successor to the NBS Handbook. The library will be used to generate numerical tables on demand.
The obstacles to the construction of such a library are mathematical and computational. Algorithms with strict bounds on truncation and rounding errors are not generally available for special functions. The techniques of interval analysis are applicable here but most of the effort in that field has been in other directions. The flaws in computer arithmetic systems, such as their vulnerability to underflow and overflow, make it difficult to construct robust and reliable software. But these obstacles provide an opportunity for creative mathematicians and computer scientists to contribute toward the solution of an important problem: replacing standard tables with standard software of comparable quality.
The use of standard tables to validate computer software was mentioned earlier. A large effort to develop advanced test procedures for mathematical software is underway in the Information Technology Laboratory at NIST. One component of this effort is a Software Test Service for Special Functions5. This service will use the WWW to help software users and developers craft detailed tests based on comparison to a standard. The most important missing piece is a standard reference library for special functions. Stopgap measures are being used until such software becomes available. As the second stage of our anticipated project progresses, the test service is expected to become an integral part of the NIST Digital Library of Mathematical Functions.
Graphics, applications of special functions, and the role of symbolic processing are important also. For graphics, as with tables, dynamic generation of information promises useful benefits. For example, fixed graphs could be replaced by graphical objects that could be manipulated (rotated, enlarged, viewed in cross sections, etc.) under the control of commands given by the user. In the area of applications, an exciting opportunity exists to improve communication between mathematicians and scientists. The notation and normalization conventions used in different fields can lead to irritating difficulties in understanding as well as actual errors. We envision a set of application digital libraries that call upon the Digital Library of Mathematical Functions for standard data. These data will be translated into a form that is immediately meaningful to scientists in the application area. Toward this end, and as a prototype for future developments, our project plan includes construction of application digital libraries of electromagnetism and quantum physics by the Electron and Optical Physics Division of NIST. Finally, symbolic processing is expected to be useful also in helping users resolve differences in notation and normalization, and for other purposes. User controls, as in the case of manipulating graphs, are applicable here as well.
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