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shell - Cartesian product of two files (as sets of lines) in GNU/Linux

How can I use shell one-liners and common GNU tools to concatenate lines in two files as in Cartesian product? What is the most succinct, beautiful and "linuxy" way?

For example, if I have two files:

$ cat file1
a
b
$ cat file2
c
d
e

The result should be

a, c
a, d
a, e
b, c
b, d
b, e
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Here's shell script to do it

while read a; do while read b; do echo "$a, $b"; done < file2; done < file1

Though that will be quite slow. I can't think of any precompiled logic to accomplish this. The next step for speed would be to do the above in awk/perl.

awk 'NR==FNR { a[$0]; next } { for (i in a) print i",", $0 }' file1 file2

Hmm, how about this hacky solution to use precompiled logic?

paste -d, <(sed -n "$(yes 'p;' | head -n $(wc -l < file2))" file1) 
          <(cat $(yes 'file2' | head -n $(wc -l < file1)))

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