The cover photograph shows a Cray Y-MP8I
Most readers know that the ABRC's Supercomputing Sub-committee and the SERC's Supercomputing Management Committee have been considering options for increasing the vector-processing capacity available nationally for peer-reviewed research projects. This is a first stage of a longer term programme of upgrades to the national high performance computing facilities, about which the Chairman of the SMC, Professor P G Burke, writes in Future UK Supercomputing below. The outcome of the first stage considerations was a recommendation, which was accepted and approved by the Council of SERC on June 10, for a Cray Y-MP8I/8128 to be located at the Atlas Centre. The Cray X-MP/416, which has been in service for over five years, is to be closed down after the Y-MP has become fully operational.
The new supercomputer will have eight processors, 128 Mwords (1 Gbyte) of memory and 100 Gbytes of disk storage. Each Y-MP processor has about 1.4 times the peak performance of an X-MP processor and is architecturally similar, so the whole machine can be expected to have about 2.8 times the power of the four-processor Cray X-MP/416. The Y-MP is due to be delivered in August. There will then be an installation, commissioning and acceptance period which is expected to last a few weeks, after which the services can begin to be transferred from the X-MP to the Y-MP. More details on the timescale and transition arrangements are given in the article by John Gordon. Our intention is to make the transition as smooth as possible and to bring the new machine into service around the start of the new academic year.
As Chairman of SERC's Supercomputing Management Committee, I am very pleased that we are now proceeding with the first stage of improving the national facilities for high performance computing.
With the installation of the Cray Y-MP8I/8128 at the Atlas Centre, the overall national capacity for conventional supercomputing will be doubled, and I am sure that this will enable substantial progress to be made by many projects which have had to be constrained by competition for limited resources.
The SMC, together with the ABRC Supercomputing Subcommittee which is chaired by Sir Eric Ash, is developing a policy for the provision of further new facilities. The SMC has requested updates of statements on the computational needs of all the Research Councils and it will draw heavily on these in shaping its ideas. Detailed consideration will be given in the next few months to the steps that should be taken on massively parallel computing; we must also ensure that the facilities we provide are adequately equipped with data storage and high performance communications facilities.
The Committee will be holding a Town Meeting in September in which current plans and future possibilities will be discussed with the user community; notice of this meeting can be found later in this newsletter. I hope that the event will provide an opportunity for a wide-ranging exploration of the issues, and I look forward to seeing many of you there.
Early in August, the Atlas Centre will take delivery of a new Cray Y-MP supercomputer. This will have an aggregate peak performance of 2.7 Gflops, nearly three times that of our current X-MP.
The new machine (serial number 1712) is a Y-MP8I/8128
8I to show its eight processor chassis with integrated I/O sub-system,
8 because it has eight processors, and
128 for its 128 MWords of memory.
The architecture of the machine is very similar to the existing Cray X-MP. The clock cycle is reduced from 8.5 nsec to 6.0 nsec and each of the eight processors has a peak performance of 333 Mflops. Cray have designed the Y-MP to reduce memory contention and the performance improvement should be slightly better than the increase in clock speeds.
The new machine's memory size of 128 MWords is a great improvement on that of the X-MP, removing the constraints of memory usage for most users.
Compatibility with the X-MP is excellent and the Y-MP can even run X-MP binary-executable files (with, however, some overhead on memory management).
Another major improvement will be the much greater capacity of the on-line disk storage. The initial configuration will be 47 Gbyte of high speed DD60 disk drives (up to 24 Mbyte/sec) and 53 Gbyte of slower DD61 drives (up to 3 Mbyte/sec). For performance-critical areas like program swap space, the DD60 drives will be striped so that I/O across more than one drive can take place in parallel for a higher bandwidth. We expect most of the DD61 disk space to be used for users' permanent data, and most of the fast DD60 space to be used for important system files, swap space, and the more heavily used temporary files.
The networking of the Y-MP will be similar to that of the X-MP, but as the JANET IP service (JIPS) becomes more widely available, we expect to see a more widespread use of interactive working on the Y-MP. Its greater memory size will allow much more interactive use without an impact on overall system performance. The Y-MP will inherit all the "front-end" connections of the current machine: VM/CMS, VAX/VMS and the RS/6000 UNIX1 front-end.
We intend that the Y-MP service will support all the current user and application code from the X-MP. In order to make the changeover as transparent as possible, the X-MP service will move to UNICOS version 6.1.6 in late July and the Y-MP service will start in late September or early October with exactly the same release levels of operating system and compilers.
The Y-MP hardware can run existing X-MP binaries without any change, but with the restriction that they can only be loaded on 16 MWord boundaries in real memory and can only use four processors for multi-tasking. As memory at address zero is used by the operating system code, there can be only seven X-MP binaries loaded on a 128 MWord machine. Running existing binaries will be acceptable for the first month or two of the new service, but there will then be some pressure to recompile to produce true Y-MP binaries. No changes to program source code should be necessary, but now is a good time to start looking for your source so that you will be able to recompile when the time comes.
As part of the new installation Cray are providing additional application software. Cray's Multi Purpose Graphics Software (primarily aimed at engineers with Silicon Graphics workstations, including the Indigo) which has recently been mounted on the X-MP will be included in the Y-MP package, as will Unichem, Cray's integrated chemistry package, also supporting Silicon Graphics workstations. Both MPGS and Unichem can run across the JIPS service to users' own workstations.
We have also ordered Gaussian 92 for installation on the Y-MP. Gaussian 92 claims to be far more efficient than previous versions and can make use of the multiple processors and large memory available on the Cray. If any of the other applications we support have Y-MP-specific versions we shall try to obtain them.
General graphics support will be easier on the Y-MP through the inclusion of CVT (Cray Visualisation Toolkit) which contains the OSF/Motif library so that Motif applications can now be built directly under UNICOS.
The existing front-end station software on VM/CMS and VAX/VMS will continue to be available, but for a transition period only. The station protocol is proprietary to Cray, does not run over wide area networks and has a syntax (CRSUBMIT etc.) which is unique to Cray. As part of the move to open and portable systems we intend to move to RQS (Remote Queuing System) and will run RQS and the existing station software alongside each other for a few months.
RQS has the same syntax as the NQS software used both to submit batch jobs from an interactive UNICOS session and in versions of NQS available on workstations and mini-supercomputers from other suppliers. Full guidance on moving to RQS will be given well in advance of the removal of the station software and after the start of the production Y-MP service.
Earlier this year an IBM RS/6000 model 550 was purchased to act as a UNIX front-end for the Atlas Centre Cray. It is now available as a general user service for any registered Cray user who wishes to use it.
The UNIX front-end complements the existing VM and VMS front-ends and allows you to choose the front-end which best suits your needs. But, I can hear you ask, lithe Cray itself runs UNIX, so why do we need a UNIX front-end?" Well, although the Cray is attached to JIPS (the JANET IP Service), it has no direct X.25 access, so that the many users on JANET with no JIPS access cannot log-in directly to the Cray. The UNIX front-end has both IP and X.25 access across JANET.
Another justification for a UNIX front-end is the Cray itself: because it requires contiguous real memory for a process address space and swaps complete processes in and out instead of paging, the Cray can support fewer processes than a comparable paging machine. It can be tuned to give excellent interactive performance, but this would always be at the expense of batch throughput, as there is an overhead in the repeated swapping and interrupt handling which characterise an interactive workload. In the circumstances, even with the increased CPU power and memory of the Y-MP, it seems sensible to target the general housekeeping tasks of editing, file management, and job submission to a separate machine, leaving the Cray to do what it does best: high performance numerically-intensive floating point work.
So, what kind of service does this machine (known as UK.AC.RL.UNIXFE) offer?
The basic tools that are provided initially are:
In addition to this basic service, all the usual facilities of a UNIX service are available. We have ordered the NAG Fortran + Graphics libraries, Pacific Sierra's Fortran 90 to 77 converter (both directions), the NAG Fortran 90 to C converter, and the UNIRAS Graphics software. If you have any suggestions for software suitable for a Cray front-end then contact me with them.
After reading so far, you might ask, Will I ever need to use the Cray interactively? Well, if you wish to interact with a Cray job and you have not developed a client-server version of your code, then you will still need to login. There are also a number of Cray-specific tools such as ATEXPERT, A TSCOPE, and the symbolic debugger cdbx, which require a UNICOS session to run them.
For these you can log into the Cray and have the tool display its output in an X-window on your local workstation.
Cray users who wish to use the UNIX front-end should contact Resource Management to have their userids registered.
By the time you read this, the Atlas Centre will have more than doubled the storage capacity in its Automatic Cartridge Store by taking delivery of a second Library Storage Module, or silo, from StorageTek. The new silo is physically identical to the existing one with its own robot arm, cartridge access port and storage slots for 6000 cartridge tapes. It is not planned to buy any more tape drives, at least initially, but instead to move one of the two existing drives (each of which has four transports) on to the new silo. Both sets of transports will be shared between the IBM and Cray mainframes so that the whole ACS can be used by both the VM and UNICOS operating systems. The ACS will continue to be used mainly for data migration, backups and transparent tape staging.
The new silo is being attached physically to the old one with a device called a Pass Through Port which allows the two robots to exchange cartridges, passing them from one silo to the other. This means that any of the 12,000 cartridges in the combined ACS can be read or written in any of the eight tape transports.
The new silo is being populated initially with longer length tapes which have a capacity of about 300 Mbytes compared with the original 3480 capacity of about 200 Mbytes. There are even longer tapes which will be tested, but assuming an average tape capacity of 300 Mbytes, the total capacity of both silos would be 3.6 terabytes. A future development planned by StorageTek is to increase the tape density by going from 18 tracks to 36 which would double the capacity again.
AXIOM is installed on the RS/6000 system in the Atlas Centre, with a single user licence which allows use by one person at a time, but is available to any user who can access the RS/6000 system from a terminal running X-Windows. For further information please contact Jonathan Wheeler, preferably by sending electronic mail to JFWt@UK.AC.RL.IB.
Since digital computers first became available, computational mathematics has been largely concerned with numerical analysis. Numerical methods have improved and evolved and have enabled the solution of problems that were previously impractical, if not impossible. Whilst the numerical solution of many mathematical models often produces satisfactory results, there are many areas that can benefit from a different approach, namely the treatment of those models in a symbolic form.
Recent advances in hardware performance and software technology have made the symbolic approach feasible even for potentially large and complex problems. Systems which support symbolic techniques effectively are at the forefront of a diffuse but profound revolution in computational mathematics, building upon established and recent mathematical theory and opening up new possibilities to people in almost every industry. Such systems represent a major step in the evolution of indispensable tools for engineers and scientists: from slide-rule and hand calculator, via general purpose scientific programming languages, towards integrated problem-solving environments incorporating symbolic and other computational techniques.
There are many real-life situations where a numerical solution is required, (for example, the prediction of physical variables such as position, time and quantity). However, investigation of the underlying principles expressed in symbolic form is required to achieve a more profound insight.
Mathematical models are used to represent these real-life situations. In order to evaluate the model and to use it effectively to predict behaviour, it is necessary to analyse and solve the model. Only for the simplest cases are analytic solutions readily available using pencil and paper. Many models are more complex, and until recently, numerical techniques have provided the only practical approach, giving specific numeric results for a given set of initial data.
Now powerful computers and symbolic systems have combined to provide the user with analytic solutions to more complicated models. Such solutions can display the explicit sensitivity of the model solution to initial data and can give further insight into model refinement.
Symbolic algebra is a basic tool of mathematics. For centuries, mathematicians have been representing the world (and later, the universe), using formulae, incorporating symbols to represent variables, constants and mathematical operations.
The use of symbolic algebra and associated analytic methods has created a wealth of knowledge and insight in mathematics, science and engineering. Before symbolic solvers, the vast majority of mathematical work required the analyst to have a strong understanding of the underlying mathematical principles involved. Moreover, the work was very laborious and error prone, with even routine tasks, for example finding the integral of a function, often taking many hours by hand.
Symbolic solvers are packages that can perform symbolic algebra. The user's problem is posed in the language of mathematics, algebraically. The problem can then be investigated symbolically and the solution given in symbolic form, or a message given as to why the operation cannot be performed, (such as the detection of a singularity in a function to be integrated). Symbolic solvers perform algebraic manipulations such as: polynomial factorisation, summation of series, symbolic integration and differentiation, and matrix operations.
Symbolic solvers give the user direct access to the knowledge base of the world's leading mathematicians, producing exact and reliable results. They are important tools for the analyst in mathematics, science, engineering and finance, opening up new fields of study and enabling new insights into existing areas.
Symbolic solvers have already been used to great effect in a wide and diverse range of applications including: high energy physics, celestial mechanics, group theory, number theory, non-linear control systems, spacecraft dynamics, computational chemistry, robotics, geometrical modelling, financial modelling, radar design and mathematical biology.
Symbolic solvers allow the user to specify models that can be changed and improved quickly and easily. Financial institutions have been quick to realise the advantages offered, constructing complex and powerful economic models of economies and markets, realising that competitive advantage is gained from the analysis of information and the insight this provides. Symbolic solvers are ideal for creating adaptive, flexible predictive models that are easy to construct and simple to use.
Symbolic solvers provide a tool that dramatically increases the productivity of the mathematical scientist and engineer. In mathematical research, for example, symbolic solvers are invaluable for testing conjectures, gathering insight through computational experiments and overcoming computational bottlenecks leading to the next stage of research. Cryptographers find symbolic facilities for elliptic curve factorization, finite fields, and discrete logarithms useful. Symbolic solvers can help solve some boundary value problems that occur in the modelling of many physical situations, including the flow of gases and fluids, electrical and magnetic fields.
Newly developed algorithms from the symbolic solver research community have led to unprecedented problem solving power. For example, symbolic solvers can locate all solutions of systems of polynomial equations and compute them to any user-specified accuracy. For systems with an infinite number of solutions, the dimension of the solutions space can be calculated along with a description of each irreducible component. Among the triumphs of research are those which have led to complete algorithms for calculus and differential equations. A decision procedure can produce closed form solutions for integrals where they exist, thus obviating the need for tables which are necessarily incomplete. Differential equations can be solved either in closed form or by series expansions. Closed form expressions for limits and summations can also be computed.
The analysis of many mathematical problems is best performed using a combination of symbolic and numerical techniques. The numerical solution of equations and functions can be difficult, and simple analytical approximations can make the solutions unusable. Symbolic solvers can recast the model in terms of functions that can be calculated accurately by forward or backward recursion.
The advent of the modem digital computer made possible the solution of large problems using numerical techniques. This spurred the development of a new branch of mathematics known as numerical analysis, which studies the behaviour of numerical methods under the conditions of inexact computer arithmetic. New numerical techniques were discovered and developed.
Symbolic computation remained traditionally manual. However, recent advances in hardware and programming technology have enabled computers to perform symbolic computation with speed and accuracy.
In summary, numerical techniques use actual data values in a mathematical problem and employ specialised techniques to minimise the effects of inexact computer arithmetic. The results are expressed numerically.
Symbolic computation uses different techniques, in general, to manipulate formulae and symbols and bears a much closer affinity to pencil and paper mathematical techniques. Typically, results are expressed in terms of formulae and symbols.
AXIOM is the powerful new symbolic solver developed (under the name Scratchpad) at IBM's T J Watson Research Facility, Yorktown Heights, New York, in collaboration with experts around the world. It is:
AXIOM is believed to be unique among computer algebra systems in its consistent, hierarchical, object-oriented approach to datatypes and operations defined on them. Users and system implementers alike use AXIOM's abstract data type programming language to modify or extend existing facilities.
Fundamental concepts in the design of AXIOM are domains, categories and packages.
Every computational object in AXIOM belongs to one, and only one, domain. Domains correspond to the usual notion of abstract datatypes in the modem theory of programming languages, in that a domain is a set of values and a set of exported operations for the creation and manipulation of these values. AXIOM has the usual datatypes (e.g. integers, floats, strings, lists, hash tables, input files), as well as algebraic ones (e.g. polynomials, matrices, fractions, power series).
Datatypes are parameterized, dynamically constructed, and can combine with others in any meaningful way, e.g. lists of floats, fractions of polynomials with integer coefficients, matrices of matrices of power series, infinite streams of cardinal numbers. AXIOM domains are defined in the AXIOM programming language and converted into machine code by its compiler, representing a set of values with a set of exported operations which can be performed upon them.
Categories are second-order types which serve to define useful classification worlds for domains, such as algebraic constructs (e.g. groups, rings, fields), and data structures (e.g. homogeneous aggregates, collections, dictionaries). The categories of a given world are arranged in a family-tree (formally, a directed acyclic graph). Each category inherits the properties of all its ancestors. Thus, for example, the category of ordered rings inherits the properties of the category of rings and those of the ordered sets. Categories provide a database of algebraic knowledge and ensure mathematical correctness, (e.g. that matrices of polynomials is correct but polynomials of hash tables is not; and also that the multiply operation for polynomials of continued fractions is commutative, but that for matrices of power series is not).
Facilities for integration, group theory and the solution of linear, polynomial or differential equations are provided by packages. Packages are domains whose exported operations depend solely on their parameters and other explicit domains, for example, a package for solving systems of equations of polynomials over any field, e.g. floats, rational numbers, complex rational functions, or power series. Using packages, algorithms can be defined in their natural algebraic setting and compiled for run-time efficiency.
The structure of AXIOM consists of a Kernel and a Library of over 500 loadable modules. The Kernel itself knows very little algebra. Most of the algebraic knowledge - for example, the definitions of categories and domains - is supplied by the Library, which is written in a high-level language and compiled into machine code for speed of execution. This is the result of a continuing effort by many expert mathematicians around the world. Updates and extensions of the Library will be distributed with each release of AXIOM.
AXIOM has an Interpreter for interactive use. Users can write their own functions and programs that use the existing Library. AXIOM will compile or interpret such user code transparently. The Compiler emphasises strict type-checking, whilst the Interpreter is oriented towards ease of use. An enhanced Library Compiler will be available to users with Version 2 of AXIOM, allowing domains and packages to be added in a convenient and consistent manner.
AXIOM's mathematical facilities include arbitrary precision numbers, factorisation of polynomials, symbolic solution of algebraic and differential equations, symbolic differentiation and integration, limits, power series, transforms, linear algebra, group theory, number theory and a lot more.
Often additional valuable insights can be gained by employing numeric techniques in association with a powerful symbolic system such as AXIOM. Work has started to link the NAG FORTRAN Library with AXIOM Version 2 to combine the best of the symbolic and numerical worlds into one comprehensive system. The NAG FORTRAN Library contains over 1000 numerical algorithms.
AXIOM features a powerful on-line documentation and help system called HyperDoc. HyperDoc is a mouse-driven hypertext system that runs under AIXwindows. The User's Guide is available in HyperDoc complete with graphics, active AXIOM commands and hypertext links. In addition, a Tutorial session and an introductory Basic Commands section are included. Users can write their own HyperDoc pages and link them to the system documentation. The Browser is a powerful HyperDoc utility that is used to examine the hierarchical structure of the AXIOM Library. Every single Library module and operation is accessible. The Browser can also display the appropriate Library source files (where available).
AXIOM has an integral Graphics System which runs under AIXwindows. AXIOM transparently sends graphics information to the Graphics System when requested to produce a graph. The graph then appears in a separate window. The user can manipulate it by using an interactive mouse-driven control panel or by issuing AXIOM commands. Two- and three-dimensional graphs can be produced while various co louring, shading, lighting and perspective options can be specified. Graphics can be included in HyperDoc documents where the same degree of control is available. Graphs can be output in Bitmap, PostScript and Pixmap format for hard-copy generation.
The Interpreter reads and analyses input expressions from the user and dynamically builds AXIOM structures in response to this input in order to perform indicated computations. The Interpreter uses sophisticated type-inferencing to determine appropriate types, searches the Library for appropriate operations, resolves type mismatches, and selects the correct operation. Output from computations is available in two-dimensional form, TeX, and FORTRAN. Users can trace AXIOM Library functions, internal Interpreter functions, and user-defined functions. Facilities are provided to maintain several interpreter workspaces concurrently, execute operating system commands, and to save results in a history file.
A hard-copy version of the documentation is available in book form as an AXIOM user's guide, published by Springer-Verlag. Copies are available via NAG or through the publisher's bookseller outlets. The AXIOM book provides a comprehensive guide to the use of the system, and features a large number of examples and graphical illustrations.
AXIOM is marketed and supported by NAG. It currently runs on the IBM RISC System/6000, a comprehensive family of powerful workstations supported by a very large range of applications software. The RISC System/6000 family operates under AIX (IBM's open systems operating system) and supports X-windows in addition to many other industry standards. Versions for other IBM platforms which support AIX and AIXwindows are also planned. The minimum requirements to support AXIOM on the IBM RISC System/6000 are:
The distribution medium is a quarter inch cartridge tape or 8mm DAT.
AXIOM's design, performance, power and range make it a very powerful computer algebra system. The general availability of the IBM RISC System/6000, the primary development platform for AXIOM, makes AXIOM's facilities accessible to the people who need it - at their desk.
AXIOM incorporates HyperDoc - a powerful, on-line, help, tutorial and browser system providing easy-to-use, comprehensive documentation. The extensive use of a graphical user interface throughout the system and the efficient organisation of the on-line documentation helps the user climb the learning curve quickly and confidently.
Extensions planned for Version 2 include an enhanced AXIOM compiler (to provide improved performance for creating tailored extensions to the Library, in an object-oriented framework) and a link to the NAG Fortran Library (to create an integrated system of even greater scope and power).
In common with many technologies, MULTIMEDIA has created a vast jargon to shroud the subject in mystery and protect its acolytes. This is a brief explanation of some of the more common acronyms, but beware: new systems seem to be appearing daily so no responsibility is accepted if the latest one is missing!
Warning: Each description of a topic starts with facts, (generally corresponding to Norman Wiseman's original article) but comments are then given on some of the topics. The CD formats are defined by a set of Coloured Books (no relation!).