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

Why are round/floor/ceiling/truncate limited to real numbers?
What stops them from being extended to all numbers?
Mathematica defines complex floor with:
>* Floor <http://reference.wolfram.com/mathematica/ref/Floor.html> applies
*>* separately to real and imaginary parts of complex numbers
*
Of course, that might just be Mathematica's own idea of what a complex
floor is.
Or am I too simply lazy to define the following?
(define (complex-floor x)
(make-rectangular (floor (real-part x)) (floor (imag-part x))))
Tim
On 10 June 2013 17:18, Bradley Lucier <lucier at math.purdue.edu> wrote:
>* 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
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*>* Racket Users list:
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*>*
*
--
|* Tim Brown <tim.brown at timb.net> | M:+44(0)7771714159 | H:+44(0)1372747875
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