Re: Radians Or Degrees?

Michael S wrote:

On Sat, 16 Mar 2024 01:16:25 +0000
mitchalsup@aol.com (MitchAlsup1) wrote:

Keith Thompson wrote:
 

I can see how computing sin(x) with high precision for "reasonable"
values of x would be useful, but does any of that benefit from being
able to compute sin(2^53) accurately?   

 Because accurate argument reduction reduces the burden on the
programmer to remain within his sandbox.

Not really.

Say you are a programmer and you receive a value like 2^53 from an
Input read and you wan the most accurate possible SIN( of that ).
With high precision argument reduction you have to do (wait for it)
NoThInG !!.
Without high precision argument reduction yo have to do a lot of
programming--programming that I insist should have been done by
the programmer responsible for sin(x).

sin(2**53) is not what programmer wanted, because 2**53 is not the x he
really wanted. It has nothing to do with calculation of sin().

And EvErYtHiNg to do with high precision argument reduction; and
maybe the programmer has no requirement on what he is allowed to
read in from a file and pass onto sin(x).

Since early 1990s, when
Payne and Hanek argument reduction became widely available, there is
no reason NOT to perform argument reduction with great accuracy.
NOTE: you don't HAVE to use Payne and Hanek when simpler strategies
word adequately; but when they do not, you do not have to "Throw up
your hands" and run away.