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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: comp.lang.c,comp.arch
Subject: Re: Radians Or Degrees?
Date: Fri, 15 Mar 2024 14:26:56 -0700
Organization: A noiseless patient Spider
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On 3/15/2024 2:16 PM, Keith Thompson wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>> On 3/15/2024 3:23 AM, Terje Mathisen wrote:
>>> Michael, I for the main part agree with you here, i.e. calculating
>>> sin(x) with x larger than 2^53 or so, is almost certainly stupid.
>> [...]
>>
>> ;^D tooooooo big. :^)
>>
>> Now, wrt the results, arbitrary precision for trig is useful, in
>> say... Deep fractal zooms...
>>
>> Zooming in really deep in say something like this, well the precision
>> of trig can become an issue:
>>
>> https://paulbourke.net/fractals/multijulia/
>>
>> Trig would be used, say, in rectangular to-from polar forms wrt
>> getting the n-ary roots of a complex number?
> 
> 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? 

Nope. :^) Fwiw, my fractals deal with zooming in and the numbers 
comprising their initial state is tiny compared to 2^53. For instance 
take these initial states for my multijulia fractal:

____________
c0 = {0.5,0.0}, c1 = {-5.5,0.0}

c0 = {0.0,1.0}, c1 = {0.0,-1.0}

c0 = {0.726514,0.240242}, c1 = {0.171039,0.235043}

c0 = {-1.444991,0.139179}, c1 = {-0.063294,-1.401774}

c0 = {1,0}, c1 = {-1,0}

c0 = {-.75, .06 }, c1 = {-.45, .6 }

c0 = {-1,0}, c1 = {1,0}, c2 = {0,-1}, c3 = {0,1}
____________

Notice how the numbers are small? However, if we zoom in enough, then 
2^53 might become an issue..


>  (Since I'm posting to
> comp.lang.c, I'll mention that "^" is meant to be exponentation, not
> bitwise xor.)
> 

Indeed.