Consider the n-ary function 
,
along with the functions 
and
which overestimate the error of 
,
an accurate model of 
.
The function 
overestimates the amount by which exceeds
while 
overestimates the amount by which exceeds
:
A simple implementation of 
would proceed as follows:
would proceed as follows:
and 
would be computed concurrently with 
and would use partial results computed during the computation of .
If necessary, table lookup may be used to handle infinite arguments.
As an example, consider a model , of ,
which guarantees:
than 
.
The functions
,
where 
and 
give the floating-point number
immediately preceding and succeeding x, respectively:
| Jeff Tupper | March 1996 |