The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A Fortran Multiple-Precision Arithmetic Package
ACM Transactions on Mathematical Software (TOMS)
Automatic error analysis for determining precision
Communications of the ACM
An arbitrary precision real arithmetic package in REDUCE
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Symbolic-Numeric Interface: a review (in absentia)
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
The MACSYMA “big-floating-point” arithmetic system
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Interval arithmetic applied to polynomial remainder sequences
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
SAC-1 variable precision floating point arithmetic
ACM '75 Proceedings of the 1975 annual conference
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The efficiency of evaluation is investigated on two "big-float" systems, our LISP-interpreter-based system and Brent's FORTRAN-compiler-based system. The test problems are computations of constants e and pi, and functions sqrt(x) and exp(x). We found that speeds of big-float addition, subtraction and multiplication on our LISP-based system are nearly the same as or rather faster than those on the FORTRAN-based system. This high efficiency of basic arithmetic operations in our system is essentially due to the efficient big-integer routines in a host LISP-system written in an assembly language. Evaluation speeds of the test problems themselves on the LISP-based system are, on an average, 1.5 times slower than those on the FORTRAN-based system. The ratio of the evaluation speeds depends, however, very much on how the routines of test problems are programmed. Therefore, we conclude that the speed of a LISP-based big-float system can be reduced to within two times of that of a FORTRAN-based system.