"I'm wondering how far, or how deep, this can go without causing Perl to upchuck."
The default recursion depth for subroutines is 100.
You can change this by compiling perl with -DPERL_SUB_DEPTH_WARN=n.
This was introduced in 5.10.1 (see perl5101delta).
You can temporarily ignore the limit with "no warnings 'recursion';"
Searching for "PERL_SUB_DEPTH_WARN" in both of those documents would be the quickest way to locate the relevant information.
"example: in the subroutine SRE_SubRoutineExample, all named variables and arrays start with SRE_ - thus, my $SRE_CompString = "JAPH";"
my variables declared within a subroutine are lexically scoped to that subroutine. You can have a $CompString in every subroutine you write and they will all be different variables. I think you'll probably be creating a rod for your back if you start trying to assign unique prefixes to every variable you declare in every subroutine. It's your back, though :-)
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