ch1-3-3-half-interval-method.scm

; Ch 1.3.3 Procedures as General Methods: Finding roots of 
; equations by half-interval method

(define (search f neg-point pos-point)
    (let ((midpoint (average neg-point pos-point)))
      (if (close-enough? neg-point pos-point)
          midpoint
          (let ((test-value (f midpoint)))
            (cond ((positive? test-value)
                   (search f neg-point midpoint))
                  ((negative? test-value)
                   (search f midpoint pos-point))
                  (else midpoint))))))

                  
(define (close-enough? x y)
    (< (abs (- x y)) 0.001))

    
(define (average x y) (/ (+ x y) 2))

    
(define (half-interval-method f a b)
    (let ((a-value (f a))
          (b-value (f b)))
      (cond ((and (negative? a-value) (positive? b-value))
             (search f a b))
            ((and (negative? b-value) (positive? a-value))
             (search f b a))
            (else
             (error "Values are not of opposite sign." a b)))))