1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
|
; Scheme 9 from Empty Space, Function Library
; By Nils M Holm, 2009
; Placed in the Public Domain
;
; (integer-sqrt integer) ==> integer
;
; Compute the largest integer value that is not greater than the
; square root of INTEGER.
;
; Example: (integer-sqrt 10) ==> 3
(define (integer-sqrt square)
(letrec
((sqrt2 (lambda (x last)
(cond ((= last x)
x)
((= last (+ 1 x))
(if (> (* x x) square) (- x 1) x))
(else
(sqrt2 (quotient
(+ x (quotient square x))
2)
x))))))
(if (negative? square)
(error "integer-sqrt: negative argument" square)
(sqrt2 square 0))))
|
