Re: Radians Or Degrees?

Steven G. Kargl wrote:

On Wed, 20 Mar 2024 18:21:47 +0200, Michael S wrote:

On Wed, 20 Mar 2024 09:54:36 -0400
Stefan Monnier <monnier@iro.umontreal.ca> 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× 

 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).
 

 I had only read the 1st page.
It sounds like they are not particularly interested in IEEE binary64
which appears to be the major point of interest of math libs of
conventional languages.
 

I skimmed their logf(x) implementation.  Their technique will
fall a part for binary64 (and other higher precisions).  With
logf(x), they combine an argument step with table look-up and
a 5th-order polynomial approximation.  The polynomial is computed
in double precision, and provides the correct rounding.  For
binary64, the polynomial would require many more terms and double-double or binary128 evaluation. 

The first 7 terms of the DP polynomial do not require FP128, whereas
the last 3 do/will.
Whereas: HW with 64-bits of fraction does not need FP128 at all.
64-bits of fraction with 64-bit coefficients added into a 128-bit accumulator is more than sufficient.
Note FP64 has 53-bits of fraction.....