Can I calculate floor(x/y) using only +, -, * and / ?

John_C

Does anyone know if there's a way to calculate floor(x/y) using only the 4 operations; addition, subtraction, multiplication and division?

For example if x=100 & y=7 then x/y = 14.29 and floor(x/y) = 14. Is there any function on x and y using only the 4 simple operators which will give me the the value 14 (or even a close approximation)?

It's a puzzle I came across in work today so thanks in advance for any help!

Yakuza

As a programming problem, you can use loop that subtracts 7 from 100 until the value goes below 0, and return one less than the number of iterations it takes to hit zero.

You can also use a recursive function that keeps going until the divisor drops below zero.
(snarfed from google:)
int divide(int a, int b) {
if (a < 0) return -divide(-a, b);
if (b < 0) return -divide(a, -b);
if (a < b) return 0;
return 1 + divide(a - b, b);
}

John_C

Thanks for the reply.

I don't have the use of conditional statements or recursive functions so it won't fit my needs. I can only use those 4 operators (and brackets to specify priority).

Miggle Kop

I'm not sure if you can do this with just +, -, * and / because they treat all numbers equally and don't have any "preference" for whole numbers. If you can it's going to be some weird function because for example floor(100/7) will give the same answer as floor(100/7.1) and floor(100/7.01).

Davidius

I doubt it is possible.

If you keep x fixed and have the floor function equal a rational function P(y)/Q(y) where P, Q are polynomials then you have P(y)=0 for all y>x implying it has infinitely many roots which is a contradiction.

red_fox

Not possible, the floor is not continuous, and any composition of =,-,* is continuous (and / usually is...)

Miggle Kop

If it can be done it would have to be an infinite power series that approximates a discontinuous function like a Fourier series can do.

John_C

Thanks for the replies. Those contradictions make sense so I guess it's not possible.