n*

Conformance: SketchyLISP Core

Purpose: Compute the product of two natural numbers.

Arguments:
A - natural number
B - natural number

Implementation:

(define (n* a b)
  (letrec
    ; X*10 where X=/=0
    ((x10
       (lambda (x)
         (list->integer
           (append (integer->list x) '(0d))
           #t)))
     ; Add A to R B times.
     ; A,R are numbers, B is a decimal digit.
     (addn
       (lambda (a b r)
         (cond ((zero? b) r)
           (else (addn a (n- b 1) (n+ a r))))))
     ; R=A*B
     ; B is in reverse order.
     (tms
       (lambda (a b r)
         (cond ((null? b) r)
           (else (tms (x10 a) (cdr b)
                      (addn a (list->integer (list (car b)))
                            r)))))))
    ; avoid leading zeroes in result
    (cond ((zero? a) 0)
      (else (tms a (reverse (integer->list b))
              0)))))

Example:

(n* 4 5) 
=> 20

See also:
digits, nquotient, nremainder, n+, n-, *.