but why did the 'print log(2)' example fail?

Definitely a bug in that particular version of bigint. I get the same on Cygwin, and also on ActivePerl 5.8.8 (build 822, bigint-0.07):

C:\_32>perl -Mbigint -le "print log(2)"
Can't use an undefined value as an ARRAY reference at C:/perl58_M/lib/
+Math/BigIn
t/Calc.pm line 1338.

C:\_32>perl -Mbigint -e "print $bigint::VERSION"
0.07
[download]

But on ActivePerl 5.10.0 (build 1001, bigint-0.22) I get the correct output:

C:\_32>perl -Mbigint -le "print log(2)"
0

C:\_32>perl -Mbigint -e "print $bigint::VERSION"
0.22
[download]

Try updating to a later bigint version (0.22 or later, if possible).

Cheers,
Rob