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A brief review of the Zlib development is given. Emphasized is the Zlib nerve system which uses the One-Step Index Pointers (OSIP'S) for efficient compu- tation and flexible use of the Truncated Power Series Algebra (TPSA). Also emphasized is the treatment of parameterized maps with an object-oriented language (e.g. C++). A parameterized map can be a Vector Power Series (Vps) or a Lie generator represented by an exponent of a Truncated Power Series (Tps) of which each coefficient is an object of truncated power series. fast computational speed for nonlinear analyses of high-order power-series maps of the Superconducting Super Collider (SSC) lattices. Since Supercomputers, such as Cray computers, were used, the algorithms used for manipulating truncated power series and Lie algebras were optimized for scalar, vector, and parallel computing. Of the most important part in achieving such optimization was the Zlib nerve system consisted of One-Step Index Pointers for optimized computation of TPSA routines such as multiplication, concatenation, partial derivative, Taylor map tracking, etc. Memories for the One-Step Index Pointers and necessary internal auxiliary arrays were dynamically allocated at the minimum required level per user's input for the maximum order and number of variables. By the time of the CAP93 Conference, there were more than 200 dynamically usable subroutines in Zlib Fortran version for TPSA and Lie algebraic mapping analysis (2). In late 1993, upon termination of the SSC, about 20% of the Zlib Fortran subrou- tines were faithfully translated into C++ codes that form two fundamental classes of the TPSA (3). These two classes were named ZSeries and ZMap which handles the algebra of truncated power series and Vector truncated power series respectively and have been included in Malitsky's Unified Library (4). Recently at SLAC, aiming at further development for mapping analysis, the two classes ZSeries and ZMap have been rewritten and named as Tps and Vps and added or to be added upon them are many other classes for treating Lie algebras. Many of these classes are translated or to be translated from Zlib Fortran version developed in early 90's.

Zlib: A numerical library for optimal design of truncated power series algebra and map parameterization routines