Re: Radians Or Degrees?

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×

The [Rlibm](https://people.cs.rutgers.edu/~sn349/rlibm/) project claims
to get much better performance (basically, in the same ballpark as
not-correctly-rounded implementations).

[ Their key insight is the idea that to get correct rounding, you
  shouldn't try to compute the best approximation of the exact result
  and then round, but you should instead try to compute any
  approximation whose rounding gives the correct result.  ]

My impression was that their performance was good enough that the case
for not-correctly-rounded implementations becomes very weak.

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.

Exactly!
[ Or should I say "Correctly rounded!"?  ]


        Stefan