🚀 go-pugleaf

In <mlK/wQ9ytpDN084yn@csn.net>, thads@csn.net (Thad Smith) writes:
>In article <4ddev4$1vg@stingray.mcnc.org>,
>coats@mcnc.org (Carlie Coats) wrote:
>
>>>14.5:	What's a good way to check for "close enough" floating-point
>>>	equality?
>
>> A safer test is of the form
>>
>>    | a - b | / sqrt( a^2 + b^2 + delta ) < epsilon
>
>This criteria, plus the squared version which uses squares, seems
>to be too much effort with no payback.

Check out "The Art of Computer Programming" by Donald Knuth,
Volume 2 "Seminumerical Alogrithms" starting on page 213 (2nd
edition) the section "4.2.2 Accuracy of Floating Point Arithmetic".

Knuth expounds on a bit of theory (easily followed) and the winds
up with very precise methods for floating point comparision and
the properties that hold.  You really need to read the section to
fully understand the formulae.  But it seems to be reasonably
definitive, outside of possible special application considerations.

BTW, none of the methods suggested so far are the ones that
Knuth recommends.


Michael Lee Finney