Fast floating-point processing in Common Lisp

ABSTRACT

Lisp, one of the oldest higher-level programming languages, has rarely been used for fast numerical (floating-point) computation. We explore the benefits of Common Lisp, an emerging new language standard with some excellent implementations, for numerical computation. We compare it to Fortran in terms of the speed of efficiency of generated code, as well as the structure and convenience of the language. There are a surprising number of advantages to Lisp, especially in cases where a mixture of symbolic and numeric processing is needed.

REFERENCES

• 1: Alfred V. Aho , John E. Hopcroft, The Design and Analysis of Computer Algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1974
• 2: Alfred V. Aho , Ravi Sethi , Jeffrey D. Ullman, Compilers: principles, techniques, and tools, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1986
• 3: E. Anderson , Z. Bai , C. Bischof , J. Demmel , J. Dongarra , J. Du Croz , A. Greenbaum , S. Hammarling , A. McKenney , S. Ostrouchov , D. Sorensen, LAPACK's user's guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992
• 4: BAKER, H.G. 1990. The Nimble Type Inferencer for Common Lisp-84. Nimble Computer Corp., Encino, Calif.
• 5: Ronald F. Boisvert , Sally E. Howe , David K. Kahaner, GAMS: a framework for the management of scientific software, ACM Transactions on Mathematical Software (TOMS), v.11 n.4, p.313-355, Dec. 1985 [doi>10.1145/6187.6188]
• 6: Kevin A. Broughan, SENAC: Lisp as a Platform for Constructing a Problem Solving Environment, Proceedings of the IFIP TC2/WG 2.5 Working Conference on Programming Environments for High-Level Scientific Problem Solving, p.351-361, September 23-27, 1991
• 7: Kevin A. Broughan, SENAC: a high-level interface for the NAG library, ACM Transactions on Mathematical Software (TOMS), v.17 n.4, p.462-480, Dec. 1991 [doi>10.1145/210232.210236]
• 8: BROUGHAN, K.A. 1990a. The SENAC Manuals. Vol. I and II. University of London, London.
• 9: BROUGHAN, K.A. 1990b. Interactive access to subroutine libraries: An interlink for SENAC. In Proceedings of the Internattonal Conference on Computational Techniques and Applications, CTAC-89, J. Horvath, Ed. Hemisphere, Washington, D.C., 145-151.
• 10: BROUGHAN, K. A. 1987. Naglink--A working symbolic/numeric interface. In IFIP TC2 / W.G.2.5 Working Conference on Problem-Solving Environments for Scientific Computing, B. Ford and F. Chatelin, Eds. Elsevier, Amsterdam, 343-350.
• 11: BROUGHAN, K.A. 1986. A symbolic numeric interface for the NAG Library. Newslett. Num. Alg. Group (Aug.), 16-24.
• 12: BROUGHAN, K.A. 1985. The Naglink Manual--An Interface between MACSYMA and NAG. Version 1.0. Development Finance Corp. of New Zealand.
• 13: BROUGHAN, K. A. AND KEADY, G. 1991. Numlink and Naglink: Links to the NAG Library from SENAC and Macsyma. In Proceedings on the Interface between Symbolic and Numeric Computing. Helsinki University, Helsinki, Finland, 19-34.
• 14: K. A. Broughan , G. Keady , T. D. Robb , M. G. Richardson , M. C. Dewar, Some symbolic computing links to the NAG numeric library, ACM SIGSAM Bulletin, v.25 n.3, p.28-37, July 1991 [doi>10.1145/122514.122518]
• 15: BURNET% D.S. 1988. F~nzte Element Analysis Addison-Wesley, Reading, Mass.
• 16: Grant O. Cook, Jr., Code generation in ALPAL using symbolic techniques, Papers from the international symposium on Symbolic and algebraic computation, p.27-35, July 27-29, 1992, Berkeley, California, United States [doi>10.1145/143242.143260]
• 17: John Foderaro, LISP: introduction, Communications of the ACM, v.34 n.9, p.27, Sept. 1991 [doi>10.1145/114669.114670]
• 18: FODERARO, J. K., SKLOWER, K. L., AND LAYER, K. 1983. The Franz L~sp Manual. Univ. of California, Berkeley, Calif.
• 19: Brian Ford, Transportable numerical software, Problems and Methodologies in Mathematical Software Production, International Seminar, p.128-140, November 03-08, 1980
• 20: FRANZ. 1991. Allegro CL Users Guide, Release 4.0. Franz Inc., Berkeley, Calif.
• 21: Norbert Kajler, CAS/PI: a portable and extensible interface for computer algebra systems, Papers from the international symposium on Symbolic and algebraic computation, p.376-386, July 27-29, 1992, Berkeley, California, United States [doi>10.1145/143242.143359]
• 22: Donald E. Knuth, The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1997
• 23: Douglas H. Lanam, An algebraic front-end for the production and use of numeric programs, Proceedings of the fourth ACM symposium on Symbolic and algebraic computation, p.223-227, August 05-07, 1981, Snowbird, Utah, United States [doi>10.1145/800206.806400]
• 24: C. L. Lawson , R. J. Hanson , D. R. Kincaid , F. T. Krogh, Basic Linear Algebra Subprograms for Fortran Usage, ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.308-323, Sept. 1979 [doi>10.1145/355841.355847]
• 25: LUCID, INC. 1991. Lucid Common L~sp/Sun Advanced User's Guide, Release 4.0. Lucid, Inc., Menlo Park, Calif.
• 26: Robert A. MacLachlan, The Python compiler for CMU Common Lisp, Proceedings of the 1992 ACM conference on LISP and functional programming, p.235-246, June 22-24, 1992, San Francisco, California, United States
• 27: Roy E. Marsten, The Design of the XMP Linear Programming Library, ACM Transactions on Mathematical Software (TOMS), v.7 n.4, p.481-497, Dec. 1981 [doi>10.1145/355972.355976]
• 28: MATt~LAB GROUP. 1977. The Macsyma Reference Manual, Version 9. Mathlab Group, Lab. for Computer Science, MIT, Cambridge, Mass.
• 29: John McCarthy, LISP 1.5 Programmer's Manual, The MIT Press, 1962
• 30: MESZTENY, C. AND W~TZaALL, C. 1967. Stable evaluation of polynomials. J. Res. NGt. Bur. Stand.-B 71B, I (Jan.), 11-17.
• 31: PRESS, W. H., FLANNERY. B. P., TEUKOLSKY, S. A., AND VETTERLINa, W.T. 1989. Numerical Recipes. Cambridge University Press, Cambridge, U K.
• 32: W. C. Schou , K. A. Broughan, The risch algorithms of MACSYMA and SENAC, ACM SIGSAM Bulletin, v.23 n.3, p.19-22, July 1989 [doi>10.1145/74646.74649]
• 33: Guy L. Steele, Jr., Common LISP: the language (2nd ed.), Digital Press, Newton, MA, 1990
• 34: Paul S. Wang, FINGER: a symbolic system for automatic generation of numerical programs in finite element analysis, Journal of Symbolic Computation, v.2 n.3, p.305-316, Sept. 1986 [doi>10.1016/S0747-7171(86)80029-3]
• 35: WHITE, J.L. 1979. NIL: A perspective. In Proceedings of the 1979 MACSYMA Users' Conference. MIT, Cambridge, Mass.
• 36: W~ITE, J.L. 1977. Lisp: Program is Data: A historical perspective on MACLISP. In Proceedings of the 1977 MACSYMA Users' Conference. MIT, Cambridge, Mass., 181-189.
• 37: WroTH, M. C. 1980. On the automation of computational physics Ph.D. dissertation, Davis School of Applied Science, Univ. of California, Berkeley, Cahf.

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: Common Lisp

Additional Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.4 Processors
          Subjects: Optimization; Compilers; Interpreters

  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Efficiency; Portability**

General Terms:
Languages, Performance, Standardization

Keywords:
C programming language, Common Lisp, Fortran, Lisp, compiler optimization, floating-point arithmetic, numerical algorithms, symbolic computation