(mod-expt r i m) is the result of raising the number r to
the integer power i and then taking the residue mod m. That is,
(mod-expt r i m) is equal to (mod (expt r i) m).
The guard for (mod-expt r i m) is that r is a rational
number and i is an integer; if r is 0 then i is
nonnegative; and m is a non-zero rational number.
In some implementations (GCL Version 2.7.0 as of this writing), this
function is highly optimized when r and i are natural numbers, not
both zero, and m is a positive integer. For other Lisp implementations,
consider using function mod-expt-fast, defined in the community book
arithmetic-3/floor-mod/mod-expt-fast.lisp, which should still provide
significantly improved performance over this function.
(defun mod-expt (base exp mod)
(declare (xargs :guard (and (real/rationalp base)
(not (and (eql base 0) (< exp 0)))
(not (eql mod 0)))))
(mod (expt base exp) mod))