This is kind of situation where LOOP really shines.<p><pre><code> (defun machin-pi (digits)
"Accurately calculates PI digits using Machin's formula
with fixed point arithmetic and variable digit guarding."
(flet ((arccot (x unity)
(loop
with xsq = (* x x)
for positive = t then (not positive)
for n upfrom 1 by 2
for xpow = (floor (/ unity x)) then (floor xpow xsq)
for term = (floor xpow n)
until (= 0 term)
sum (if positive term (- term)))))
(when (> digits 0)
(let* ((guard (floor (* 10 (log digits 10))))
(unity (expt 10 (+ digits guard)))
(thispi (* 4 (- (* 4 (arccot 5 unity)) (arccot 239 unity)))))
(floor thispi (expt 10 guard))))))</code></pre>