Standard double precision floating point arithmetic is good to about 16 significant digits. So trying to do what you are doing to an accuracy of more than approximately 1e-15 is plain and simply impossible.
to illustrate, try funct=single(sin(2*pi*a(1:500))); this will convert your number to a single precision floating point, which is accurate to about 7 significant digits. You should find that your code is good only to about 1e-6.
the only way you can succeed is to use something with more precision than a double . I don't know of a way to do it natively in matlab. A google search turned this up: http://www.advanpix.com/ might be a good place to start. Or you might need to try something like a computer algebra system (e.g. Maple) that has native support for arbitrary precision arithmetic.
