# [racket] (floor (/ ....))

Re:
>* FWIW, I would have at least written:
*>*
*>* ((qty (in-range 0 (add1 (min (floor (/ weight-left weight))
*>* (floor (/ volume-left volume)))))))
*
I have now seen the
(floor (/ a b))
idiom a number of times, and wonder why people prefer it to
(quotient a b)
Normally, to calculate (/ a b) where a and b are exact integers requires
one to calculate (gcd a b) to put the fraction into lowest terms
p/q=(quotient a (gcd a b))/(quotient b (gcd a b)); then, to calculate
(floor p/q), one must calculate (quotient p q).
For large integers of size $N$ bits, (gcd a b) takes $O(N\log^2(N))$
fixnum operations, where quotient takes $O(N\log N)$ operations. This
assumes Fourier-based methods for bignum multiplication; for more direct
methods, the difference in operation count is larger.
In any case, the (floor (/ ...)) idiom takes noticeably more time than
(quotient ...). If one knows that a and b are positive integers, they
give the same results.
This is an argument not to use (floor (/ ...)). Are there arguments in
favor of this idiom?
Brad