Jeff Moden (2/16/2013)
If we're going to do this, let's knock the problem right out of the park.
...
We also come to the understanding that we can't directly calculate more than the 70th Fib number using this method because the FLOAT data-type returned by the SQRT function induces rounding errors after the precision of the return reaches just 15 digits.
...
Agreed!
Out of the park 1) Blazing speed, small maximum - Jeff did that!
Out of the park 2) Hardware resource limited maximum
Who's got a CLR arbitrary precision library[/url] for SQL Server?
ETA: A .NET arbitrary precision library, though in alpha stage.
And an integer only .NET arbitrary precision library
Maybe even the .NET 4.0+ native System.Numerics.BigInteger