计算机程序的构造和解释 折半查找法

#lang racket

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

(define (close-enough? x y)
(< (abs (- x y)) 0.000000000000001))

(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)))))

;: 求pi 的值：
(half-interval-method sin 2.0 4.0)

(half-interval-method (lambda (x) (- (* x x x) (* 2 x) 3))
1.0 2.0)