Are arithmetic operations on double variables holding integer values exact?

Question

Let's say I've got two integer values stored in double variables, e. g.:

double x = 100.0;
double y = 7.0;

May I safely assume that any arithmetic operation on these two double variables that would yield an integer result, will return an exact integer value (as a double)? That is, will for example all of:

x + y = 107.0
x - y = 93.0
x * y = 700.0

return the exact integer values, or will be there some accuracy problems? Like x*y being 699.99995 or so?

The general question: Is it true that any arithmetic operation on two double variables holding integer values that would yield an integer result will return the exact integer value (as a double)?

I'm asking this in a Java context, but I assume it's similar in other languages, too.

Answer 1

As long as the integer result of your operation can be exactly represented as a double, you will get an exact result, but as soon as the integer result exceeds the number of bits available in the mantissa (i.e. 52+1 = 53 bits), it will be rounded.

Answer 2

In general, the answer is No. However, I strongly recommend reading David Goldberg’s "What Every Computer Scientist Should Know About Floating-Point Arithmetic" - it never hurts to know the things from the inside.