floating point - Check if a double is evenly divisible by another double in C?

Question

How can I check if a double x is evenly divisible by another double y in C? With integers I would just use modulo, but what would be the correct/best way to do it with doubles?

I know floating point numbers carry with them imprecision, but I'm getting the double from standard input. Maybe I should not scan it as a double straight away but as two integers instead, but where would I go from then?

Answer 1

The standard header math.h defines the following functions:

• double fmod(double x, double y);
• float fmodf(float x, float y);
• long double fmodl(long double x, long double y);

These functions return the result of the remainder of x divided by y. The result has the same sign as that of x. You can use r = fmod(x, y); for double numbers x and y, and check if r == 0. If you want to not test for exact divisibility but add some tolerance, then you can check if r is "close enough" to 0 or y (thanks caf).

fmodf() and fmodl() are new in C99.

Edit: C99 also defines a separate remainder(double x, double y) function, that returns the remainder of x/y. From http://docs.sun.com/source/806-3568/ncg_lib.html:

The remainder(x,y) is the operation specified in IEEE Standard 754-1985. The difference between remainder(x,y) and fmod(x,y) is that the sign of the result returned by remainder(x,y) might not agree with the sign of either x or y, whereas fmod(x,y) always returns a result whose sign agrees with x. Both functions return exact results and do not generate inexact exceptions.

...

When y ≠ 0, the remainder r = x REM y is defined regardless of the rounding mode by the mathematical relation r = x - ny, where n is the integer nearest the exact value of x/y; whenever | n - x/y | = 1/2, then n is even. Thus, the remainder is always exact. If r = 0, its sign shall be that of x. This definition is applicable for all implementations.

(Either fmod() or remainder() should work for you.)