Update

thiele.lisp

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+
+; Thiele's interpolation formula
+; ==============================
+
+(defun $thiele (u v)
+  (loop for rh on
+    (loop for w on (cdr u) ; we build rho with axes transposed
+          ; first, building column 1 and 2
+          for r = (list
+                    (loop for a on u
+                          for b on v
+                          while (cdr a)
+                          collect (div (sub (car a) (cadr a))
+                                       (sub (car b) (cadr b)))) v)
+          ; then building starting from column 3
+                then (cons
+                       (loop for a1 in u
+                             for a2 in w
+                             for y1 on (car r)
+                             for y2 in (cdr (cadr r))
+                             collect (add (div (sub a1 a2)
+                                               (sub (car y1) (cadr y1)))
+                                        y2)) r)
+          ; finally get the row 1
+                ; finally (return (loop for i in r ; i is already a 1-list
+                ;                       for j = i then (cons (car i) j)
+                ;                       finally (return j))))
+                finally (return (nreverse (mapcar #'car r))))
+        for k in (cdr u)
+        with a = 0
+        do (setf a (add a (div (sub 'x k)
+                               (sub (caddr rh) (car rh)))))
+        finally (return (add (car v)
+                             (div (sub 'x (car u))
+                                  (sub (cadr rh) a))))))