A Portable Fortran Program to Find the Euclidean Norm of a Vector
ACM Transactions on Mathematical Software (TOMS)
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
More on algorithms that reveal properties of floating point arithmetic units
Communications of the ACM
| Hi-index | 0.00 |
The proposed IEEE Floating Point Standard, which is being prepared with unprecedented reliance on the advice of experienced numerical analysts, appears to be the answer to long-standing pleas for sensible floating-point arithmetic systems. The committee drafting the standard has not settled some of the details, but it has agreed that the standard is intended to encourage high-quality numerical programming. To this end the committee agrees on basic arithmetic operations that round correctly and are otherwise clean and free of anomalies. Many of us applaud that accomplishment and eagerly await the appearance of standard-conforming machines. Our frustrations with arithmetic systems in which multiplication is not commutative, in which X+X differs from 2.0×X by a decimal place or more, and in which the least significant half of a double precision number underflows and flushes to zero independent of the most significant half thus abruptly dropping the computation to single precision (without warning, of course) are almost over. The new machines will have none of these or the even more exotic mathematical atrocities existing in our current machines. But our joy at the dream we see materializing before our eyes must be tempered by the realization that the new machines will not solve all of our problems immediately and may even introduce a few new ones.