Re: Radians Or Degrees?

Stefan Monnier wrote:

There are groups who have shown that exactly rounded trancendental
functions are in fact achievable with maybe 3X reduced performance.

That much?  I had the impression it was significantly cheaper.

The J. M. Muller book indicates about 2× to 2.5×

At which cost in tables sizes?

Making transcendental faster is always a tradeoff between table size
and speed. SIN() COS() can use 10-term polynomials when the reduced argument is -¼pi..+¼pi, on the other hand, when the reduced argument
is ±0.008 a 3 term polynomial is just as accurate but you need 128×3
tables.

My impression was that it wasn't costly in that respect, but since my
recollection seems to be off on the performance, maybe it's off here
as well.

ITANIC did rather well, here, because it had 2 FMAC units and could use
both for the polynomials.

The critical point here is definition of what considered exact. If
'exact' is measured only on y side of y=foo(x), disregarding
possible imprecision on the x side then you are very likely to end up
with results that are slower to calculate, but not at all more useful
from point of view of engineer or physicist. Exactly like Payne-Hanek
or Mitch's equivalent of Payne-Hanek.

I don't know what are/were the motivations for the people working on
exact transcendentals, but they have applications unrelated to the fact
that they're "better": the main benefit (from this here PL guy) is that
it gives them a reliable, reproducible semantics.
Bit-for-bit reproducibility makes several things much easier.

Consider moving an application which uses libm from machine to machine.
When libm is correctly rounded, there is no issue at all; not so other-
wise.

        Stefan