# n E Z => sin(n*pi) = -1 ?

4 views (last 30 days)
Emirhan Solmaz on 21 Jul 2022
Edited: James Tursa on 21 Jul 2022
the problem is simple at the first glance. if n is an integer, than sin(n*pi) should be "0". But it gives "-0,999".
isInt = @(n) sin(n*pi);
isInt(100000000000000000000000000000);
I get that the number should be small since the computation doesnt go beyond 10^17, but if I give 5, the result is "6*10^-16". Still, is not "0". How can I overcome this problem? is there a method? I need to solve the problem of "integer". It should be "exact integer". I couldn't find a way to get over it. Do you have any idea?

Steven Lord on 21 Jul 2022
Use the sinpi function.
n = 100000000000000000000000000000;
sinpi(n)
ans = 0
James Tursa on 21 Jul 2022
Edited: James Tursa on 21 Jul 2022
"Basicly I need a way to calculate formulas beyond the limits of IEEE. which I suppose it is not possible. is it?"
Yes, it is. Use the Symbolic Toolbox as others have already suggested.
That being said, I suspect that your "algorithm", which you haven't discussed or shown us, may be producing garbage if you need 30 or more decimal digits of precision to calculate results. What else is going into this calculation and are you carrying enough precision in every variable to make the result meaningful? Can you post this code?

Stephen23 on 21 Jul 2022
n = sym(100000000000000000000000000000)
n =
100000000000000000000000000000
sin(n*pi)
ans =
0
##### 1 CommentShowHide None
James Tursa on 21 Jul 2022
Edited: James Tursa on 21 Jul 2022
Note that sym( ) here is doing the conversion based on its calculated "intent" of the user, since the actual number that gets passed to sym( ) isn't 100000000000000000000000000000 but something "nearby" as close as IEEE double precision can represent:
n = 100000000000000000000000000000;
fprintf('%30.0f\n',n);
99999999999999991433150857216
Also, there is another subtle conversion going on in the background. The double precision pi value is converted to its symbolic version based again on its calculated "intent" of the user. That is, here is the actual double precision pi value converted to decimal:
fprintf('%60.55f\n',pi);
3.1415926535897931159979634685441851615905761718750000000
But The product n*pi results in a conversion of this to the "exact" symbolic pi before sin( ) is called:
n = sym(n)
n =
100000000000000000000000000000
n*pi
ans = Personally, I prefer to have these silent conversions made explicit in the code so I don't inadvertently get bit downstream. E.g., I typically would calculate this instead up front and use it downstream so there is no possible ambiguity:
sympi = sym('pi')
sympi =
π

KSSV on 21 Jul 2022
n = vpa(100000000000000000000000000000) ;
vpa(sin(n*pi))
ans =
0.000000000011227417549995295083665533339851
##### 1 CommentShowHide None
John D'Errico on 21 Jul 2022
It is more subtle than you think.
n = vpa(100000000000000000000000000000)
n =
100000000000000000000000000000.0
vpa(sin(n*pi))
ans =
0.000000000011227417549995295083665533339851
vpa(sin(n*pi),100)
ans = There is a difference.

David Hill on 21 Jul 2022
Use symbolics.
function [out] = isInt(n)
n=sym(n);
out=double(sin(n*pi));
end
Call function
o=isInt('10000000000000000000000000000000000000000000000000000000000000000000');
##### 1 CommentShowHide None
Emirhan Solmaz on 21 Jul 2022
I tried it but it gives a vector as long as the decimal, which are not "0". I am sorry but didn't get it.