Linux includes a bench calculator called bc, which can achieve remarkable arbitrary-precision results in very few lines of code. For ease of running, code can be embedded in a here document:

fib.sh

#!/usr/bin/env bash
BC_LINE_LENGTH=0 bc -q <<end
0;1; for (i=1;i<1000;i++) {g=last;last+=f;f=g;last}
end

The BC_LINE_LENGTH environment variable is used to prevent long lines from being split with a \ continuation character.

The -q flag suppresses the welcome prompt.