[Rd] 0.45<0.45 = TRUE (PR#10744)

[(Ted Harding)]

On 12-Feb-08 14:53:19, Gavin Simpson wrote:
> On Tue, 2008-02-12 at 15:35 +0100, labonne at st-pee.inra.fr wrote:
>> Dear developer,
>> 
>> in my version of R (2.4.0) as weel as in a more recent version
>> (2.6.0) on different computers, we found this problem :
> 
> No problem in R. This is the FAQ of all FAQs (Type III SS is
> probably up there as well).

I'm thinking (by now quite strongly) that there is a place
in "Introduction to R" (and maybe other basic documentation)
for an account of arithmetic precision in R (and in digital
computation generally).

A section "Arithmetic Precision in R" near the beginning
would alert people to this issue (there is nothing about it in
"Introduction to R", "R Language Definition", or "R internals").

Once upon a time, poeple who did arithmetic knew about this
from hands-on experience (just when do you break out of the
loop when you are dividing 1 by 3 on a sheet of paper?) -- but
now people press buttons on black boxes, and when they find
that 1/3 calculated in two "mathematically equivalent" ways
comes out with two different values, they believe that there
is a bug in the software.

It would not occur to them, spontaneously, that the computer
is doing the right thing and that they should look in a FAQ
for an explanation of how they do not understand!

I would be willing to contribute to such an explanation;
and probably many others would too. But I feel it should be
coordinated by people who are experts in the internals
of how R handles such things.

Best wishes to all,
Ted.

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Date: 12-Feb-08                                       Time: 15:31:26
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