Question

Given an n-place integer and an m-place integer. How can I multiply them in LISP using lists, arrays or any other lisp specific data types?

for instance;

a(1)a(2)…a(n)

b(1)b(2)…b(m)

with result of;

r(1)r(2)…r(m+n)

Answer 1

Common Lisp has already bignums natively. Why don’t you use them?

You basically don’t have to declare anything specially, they “magically” happen:

 % sbcl
 This is SBCL 1.0.56.0.debian, an implementation of ANSI Common Lisp.

 * (defun fact (n) (if (< n 1) 1 (* n (fact (- n 1)))))
 FACT

 * (fact 50)
 30414093201713378043612608166064768844377641568960512000000000000

So with a Common Lisp, you basically don’t have to bother…

addenda

And efficient bignum algorithms are a very difficult problem; Efficient algorithms have better complexity than naive ones; you can find difficult books explaining them (the underlying math is pretty hard). See also this answer.

If you want to make a competitive bignum implementation, be prepared to work hard several years, and make it a PhD thesis.