Re: Proposal: Trigonometric functions in degrees

Dean Rasheed <dean(dot)a(dot)rasheed(at)gmail(dot)com> writes:
> On 26 October 2015 at 14:18, Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us> wrote:
>> ... but having said that, your argument here is faulty, because 0.9
>> in itself is not exactly representable in binary. You'd be relying
>> on roundoff happening in the right direction to get exact answers
>> from such calculations, for just the same reasons that sind() can't be
>> just "sin(x * scalefactor)" if you want exact-where-possible results.

> It would be relying on the things like the following being exactly true:

> 45 / 0.9 = 50
> 50 * 0.9 = 45
> 90 / 0.9 = 100
> 100 * 0.9 = 90

> which they are on my machine. I thought that this was guaranteed in
> IEEE floating point arithmetic, since one of the inputs and the result
> are exactly representable, and the result is guaranteed to be within
> 0.5ulp. I'm curious now though. Are there any platforms on which the
> above aren't exactly true?

Possibly, but the bigger picture is you're ignoring other cases, such as

regression=# select 30 / 0.9;
?column?
---------------------
33.3333333333333333
(1 row)

which is problematic since sin(30 degrees) = 0.5 is one of the cases
one would like to be exact. (Actually I guess this example shows that
implementing sind in terms of sing would be imprecise, but I'm sure
the reverse holds for some other special angles.)

regards, tom lane