Spyke

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math

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f(w,t)=sin(wt)/w. Help make defined at w = 0.

People are being kind of rude, sorry about that.

I also think they aren't understanding your problem. You have a function f(w,t) = sin(wt)/w which is well defined everywhere (in the sense of limits at w=0 ), but for which the naive implementation (compute sin(wt), then divide by w) gives the "wrong" output for w=0 (an error instead of t).

Note that the function sin(x)/x has a name, sinc(x). Using this to rewrite your function gives f(w,t) = sin(wt)/w = tsin(wt)/(wt) = tsinc(wt).

Now you just need to find a quality implementation of sinc from a math library.

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Not everything can be done in constant time, that's O(k)

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T = O(n) means that there exists a single constant k such that T < kn for all sufficiently large n. Therefore O(n!^2) is not the the same as O(n!), but for example both 10n!, 10000n!, n! + n^2 (note the plus) are O(n!).

Another way to think about this: suppose you believe that O(n) and O(n^2) are distinct. Now plug in only numbers that are factorials (2, 6, 24, ...).