[COFF] floating point (Re: Old and Tradition was [TUHS] V9 shell

[bakul at bitblocks.com (Bakul Shah)]

> On Feb 12, 2020, at 3:54 PM, Bakul Shah <bakul at bitblocks.com> wrote:
> 
> On Feb 12, 2020, at 3:05 PM, Larry McVoy <lm at mcvoy.com> wrote:
>> 
>> On Wed, Feb 12, 2020 at 04:45:54PM -0600, Charles H Sauer wrote:
>>> If I recall correctly:
>>> - all doctoral candidates ended up taking two semesters of numerical
>>> analysis. I still have two volume n.a. text in the attic (orange, but not
>>> "burnt orange", IIRC).
>>> - numerical analysis was covered on the doctoral qualifying exam.
>> 
>> Pretty sure Madison required that stuff for Masters degrees.  Or maybe
>> undergrad, I feel like I took that stuff pretty early on.
>> 
>> I'm very systems oriented so I can't imagine I would have taking that 
>> willingly.  I hate the whole idea of floating point, just seems so 
>> error prone.
> 
> David Goldberg's article "What every computer scientist should know
> about floating-point arithmetic" is a good one to read:
> https://www.itu.dk/~sestoft/bachelor/IEEE754_article.pdf
> 
> I still have Bill Press's Numerical Recipes book though not opened
> recently (as in not since '80s)!
> 
> It is interesting that older languages such as Lisp & APL have a
> builtin concept of tolerance. Here 0.3 < 0.1 + 0.2 is false. But
> in most modern languages it is true! This is so since 0.1 + 0.2 is
> 0.30000000000000004. In Fortran you'd write something like 
> abs(0.3 - (0.1 + 0.2)) > tolerance. You can do the same in C
> etc.but for some reason it seems to be uncommon :-)

Er... not right. Fl. pt. arithmetic is hard!