Teaching Approximations (was Re: Microcode, which is a no-go for

[Paul Koning]

> On Jan 8, 2019, at 11:58 PM, Tony Duell via cctalk <cctalk at classiccmp.org> wrote:
> 
> ...
> IIRC one of the manuals for the HP15C had a chapter on 'Why this
> calculator gives the wrong answers'. It covered things like rounding
> errors.
> 
> -tony

That reminds me of a nice old quote.

"An electronic pocket calculator when used by a person unconversant with it will most probably give a wrong answer in 9 decimal places" -- Dr. Anand Prakash, 9 May 1975

Understanding rounding errors is perhaps the most significant part of "numerical methods", a subdivision of computer science not as widely known as it should be.  I remember learning of the work of a scientist at DEC whose work was all about this: making the DEC math libraries not only efficient but accurate to the last bit.  Apparently this isn't anywhere near as common as it should be.  And I wonder how many computer models are used for answering important questions where the answers are significantly affected by numerical errors.  Do the authors of those models know about these considerations?  Maybe.  Do the users of those models know?  Probably not.

	paul