lisp - Blocked Matrix Multiplication -

i trying create function performs blocked matrix multiplication in allegrocl, keep getting array-index errors. believe due indicies being 0-19 side of 20 x 20 block matrix, i'm unsure of how fix it.

error: array index 20 big dimension 20 while accessing #. [condition type: type-error]

any or direction appreciated. below code far.

(defun bmmul (a b)   (let* ((m (car (array-dimensions a)))          (n (cadr (array-dimensions a)))          (l (cadr (array-dimensions b)))          (u 0)          (c (make-array `(,m ,l) :initial-element 0)))     (loop p 0 (- m n)           (loop (+ 0 1) n                 (setf u (aref c 0))                 (loop k p (- (+ p n) 1)                       (setf u (* (aref k) (aref b k 0))))                 (setf (aref c 0) u)))     c)) 

in general, when looping on array index, go :from 0 :below n, n array dimension, when dimension 20, index goes 0 , including 19.

another problem seems in innermost loop, want incf, not setf. not need temporary variable (u) there, incf array cell directly.

finally, not feel structured loops correctly, not expect see hardcoded 0 index there. innermost loop body should (incf (aref c j) (* (aref k) (aref b k j))), regardless of whether ordinary or blocked multiplication.