(use-modules (srfi srfi-1))

(define default-algebra
  (list
   ;; Binary addition
   (cons #:add +)
   ;; Binary multiplication
   (cons #:multiply *)
   ;; Binary subtraction
   (cons #:subtract -)))

(define (make-iir a-in  ;; a_1..a_n-1
                  b-in  ;; b_0..b_n-1
                . rest) ;; algebra
  (let* (;; Algebra that has at least addition and multiplication.
         (algebra (if (null? rest) default-algebra (car rest)))

         ;; Extract operations from algebra for easier use. This also
         ;; conveniently causes an error if a necessary operation is
         ;; missing.
         (add (cdr (assq #:add algebra)))
         (mul (cdr (assq #:multiply algebra)))

         ;; Output side coefficients, with values for the latest
         ;; samples placed last.
         (a (reverse a-in))
         ;; Input side coefficients. Same order as in output side.
         (b (reverse b-in))

         ;; Lengths of coefficient sets
         (Na (length a))
         (Nb (length b))

         ;; Delay lines. Cars have the oldest value and ends have the
         ;; most recent ones.
         (x (make-list      Nb  0))
         (y (make-list (+ 1 Na) 0))

         ;; References to the last pairs
         (last-x (last-pair x))
         (last-y (last-pair y)))

    (lambda (x0)
      ;; Input delay line propagation
      (set-cdr! last-x (cons #f '()))
      (set! last-x (cdr last-x))
      (set! x (cdr x))

      ;; Insert the new X value
      (set-car! last-x x0)

      ;; Output delay line propagation
      (set-cdr! last-y (cons #f '()))
      (set! last-y (cdr last-y))
      (set! y (cdr y))

      ;; Compute and insert new Y value
      (set-car! last-y
                ;; The output value is computed here.
                (- (fold add 0 (map mul x b))
                   (fold add 0 (map mul y a))))

      (car last-y))))

(define (make-fir b-in)
  (make-iir '() b-in))