Jamming, von Neumann, or maybe Mauchly

[19-Dec-1991 1302]

The book "From ENIAC to UNIVAC" by Nancy Stern (Digital Press, 1981)
contains an Appendix which is a reprint of "First Draft of a Report
on the EDVAC" by John von Neumann (1945). On page 208 of this book,
in Section 9.4 of von Neumann's Draft, Mauchly is credited with the
following (slightly reworded) rounding rule: for floating point with
p bits of precision, the pth bit of the rounded result is zero if
both the pth and the (p+1)st bits are zeros. Otherwise the pth bit
is forced to one. This rule can be implemented in hardware by ORing
the (p+1)st bit into the pth bit. This rule preserves exactness and
produces an error bound of magnitude ulp/2 for three of the four
possible cases.

This is not quite the same as either of the rules given in
Figueroa's note. This rule, and the rule quoted in IBM's comments on
the LCAS both yield an error bound strictly less than 1 ulp in
magnitude. Both satisfy the LCAS rounding specifications. The rule
quoted from Burks et al. produces an error bound which will be 1 ulp
for an exact result whose pth bit is zero, and hence does not satisfy
the LCAS requirement that an exact result is correctly returned.

Mary Payne