TABLE OF CONTENTS The first American Venus probe was lost due to a program fault caused by the inadvertent substitution of a statement of the form D0 3 I = 1.3 for one of the form D0 3 I = 1, 3.
- JIM HORNING, Note on Program Reliability [21] (1979)
Numerical subroutines should deliver results that satisfy simple, useful mathematical laws whenever possible.
- DONALD E. KNUTH, The Art of Computer Programming, Volume 2, Seminumerical Algorithms (1998)
No method of solving a computational problem is really available to a user until it is completely described in an algebraic computing language and made completely reliable. Before that, there are indeterminate aspects in any algorithm.
- GEORGE E. FORSYTHE, Today's Computational Methods of Linear Algebra (1967)
The extended precision calculation of pi has substantial application as a test of the "global integrity" of a supercomputer ... Such calculations ... are apparently now used routinely to check supercomputers before they leave the factory. A large-scale calculation of pi is entirely unforgiving; it soaks into all parts of the machine and a single bit awry leaves detectable consequences.
- J. M. BORWEIN, P. B. BORWEIN, and D. H. BAILEY, Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989)
[21]Quoted, with further details, in Tropp [1159, 1984].
In this chapter we discuss some miscellaneous aspects of floating point arithmetic that have an impact on software development.
