# [racket] a small programming exercise

Here's an interesting data point.
(define (first-digit-fast-1 n)
(if (> 10 n)
n
(let loop ((i 10)
(next 100))
(if (> next n)
(first-digit-fast (floor (/ n i)))
(loop next (* i i))))))
This takes about 13 seconds on my work machine.
If I take advantage of the types:
(define (first-digit-fast-2 n)
(if (and (fixnum? n)
(fix:> 10 n))
n
(let loop ((i 10)
(next 100))
(if (int:> next n)
(first-digit-fast (int:quotient n i))
(loop next (int:* i i))))))
This takes about 3 seconds.
I think the culprit is the call to (floor (/ n i))
The division will allocate an unnecessary rational. The int:quotient
primitive doesn't need to.
I'm pretty sure that Racket has some similar primitives.
--
~jrm