Re: Radians Or Degrees?

On Sat, 16 Mar 2024 17:22:50 +0000
mitchalsup@aol.com (MitchAlsup1) wrote:

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).
 

I never met programmers that wants do anything of this sort.
Programmers that I meet in real world could sometimes want something
else. They could want, for example, to draw 1000 points of wave of blue
LED with frequency 663.42 THz (663.42e12 Hz) with step of 10 nm (1e-8 m)
starting at distance of 1 million km. Well, not really, but at least I
can imagine them wanting to do it*.
Will double precision sin() routine that does perfect argument
reduction be any more helpful for their task then sin() implementation
that makes no effort at all beyound simple modulo 2*pi? No, they both
would be the same.
May be, sinpi() that does a perfect reduction more or less by
definition, be more helpful?
For naive folks - not at all.
For advanced folks - yes, but just a little. It still wouldn't be easy.
And among programmers that I know naives outnumber advanced by more
than factor of 10.

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* - For more real case, they could want to draw the same wave at
distance of 2m using single-precision arithmetic.