; the sum of two squares

(define (isqrt n)
  (let loop ((x n) (y (quotient (+ n 1) 2)))
    (if (<= 0 (- y x) 1) x
      (loop y (quotient (+ y (quotient n y)) 2)))))

(define (squares n)
  (let loop ((x (isqrt n)) (y 0) (zs '()))
    (cond ((< x y) zs)
          ((< (+ (* x x) (* y y)) n) (loop x (+ y 1) zs))
          ((< n (+ (* x x) (* y y))) (loop (- x 1) y zs))
          (else (loop (- x 1) (+ y 1) (cons (list x y) zs))))))

(display (squares 50)) (newline)
(display (squares 48612265)) (newline)
(display (squares 999)) (newline)