# weima learns to program

my attempt to do the exercises in sicp.

## Thursday, June 26, 2008

### sicp exercise 1.17

;  Exercise 1.17. The exponentiation algorithms in this section are based on performing exponentiation by
;  means of repeated multiplication. In a similar way, one can perform integer multiplication by means of
;  repeated addition. The following multiplication procedure (in which it is assumed that our language can
;  only add, not multiply) is analogous to the expt procedure:
;  (define (* a b)
;    (if (= b 0)
;      0
;      (+ a (* a (- b 1)))))
;  This algorithm takes a number of steps that is linear in b. Now suppose we include, together with addition,
;  operations double, which doubles an integer, and halve, which divides an (even) integer by 2. Using
;  these, design a multiplication procedure analogous to fast-expt that uses a logarithmic number of
;  steps.

(define (double a) (+ a a))
(define (halve a) (/ a 2))

(define (fast-mul-recur a b)
(cond ((= b 0) 0)
((even? b) (fast-mul-recur (double a) (halve b)))
(else (+ (fast-mul-recur (double a) (halve (- b 1))) a))))

(display (fast-mul-recur 10 9)) (newline)
(display (fast-mul-recur 99999 99999)) (newline)
(display (fast-mul-recur 9999999999999999999999999 9999999999999999999999999)) (newline)