The IBM POWER4 is a new microprocessor organized in a system structure that includes new technology to form systems. The name POWER4 as used in this context refers not only to a chip, but also to the structure used to interconnect chips to form systems. In this paper we describe the processor microarchitecture as well as the interconnection architecture employed to form systems up to a 32-way symmetric multiprocessor.

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A set of stiffly stable, cychc composite multlstep methods, expressed as l t a,~ymt+j-h ~ fl,jYmt+j=O with ~= 1,. ,l, j=--k+~ ]--I of orders 3 through 7 is established Each method exhibits better stability properties than those of the backward dffferentmtlon formula of the same order. A new varmble-step-slze, variable-order integration algorithm incorporating these new cyclic methods is described This algorithm, realized as a Fortran program, is ideally suited for the numemcal mtegratmn of stiff systems of first order ordinary differential equations y = f(y, t) wherein the Jacobian matrix fy(y, t) has complex eigenvalues near the Imaginary axis Numermal results to support th~s clmm are presented, mcludmg a comparison of the new program with GEAR, Hmdmarsh's tuned versmn of Gear's widely accepted computer program DIFSUB, and with EPISODE, Byrne and Hmdmarsh's counterpart of DIFSUB and GEAR using a varmble-step form of the backward dffferentmuon formulas.Key Words and Phrases stiff dffferentml equatmns, stiffly stable methods, composite multlstep methods, cyclic methods, numerical mtegratlon, ordinary differential equatmns, initial value problems, multlstep formulas, numermal mtegratmn program, Fortran code STINT CR Categorms 5 16, 5 17 The Algorithm. STINT. STiff {differential equatmns) INTegrator. ACM Trans Math. Software 4, 4 {Dec. 1978), 399-403.

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and ZDENEK PICEL equations)Key Words and Phrases. stiff dlfferentml equations, stiffly stable methods, composite mulhstep methods, cyclic methods, numerical integration, ordinary differential equations, initial value problems, multistep formulas, numerical integration program, Fortran code STINT CR Categories-5.16, 5 17 Language' Fortran DESCRIPTION T h e a l g o r i t h m given here is a c o m p l e m e n t to [1] where the t h e o r e t i c a l developm e n t a n d test results are described. REFERENCES [1] TENDLER, J.M., BICKART, T.A., AND PICEL, Z. A stiffly stable integration process using cyclic composite methods. ACM Trans. Math. Software 4, 4 (Dec. 1978), 339-368. ALGORITHM [ S u m m a r y i n f o r m a t i o n a n d p a r t of the listing is p r i n t e d here. T h e c o m p l e t e listing is available from t h e A C M A l g o r i t h m s D i s t r i b u t i o n Service (see inside