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cfloating-pointieee-754c89floor

Does floor() return something that's exactly representable?

In C89, floor() returns a double. Is the following guaranteed to work?

double d = floor(3.0 + 0.5);
int x = (int) d;
assert(x == 3);

My concern is that the result of floor might not be exactly representable in IEEE 754. So d gets something like 2.99999, and x ends up being 2.

For the answer to this question to be yes, all integers within the range of an int have to be exactly representable as doubles, and floor must always return that exactly represented value.

Solution

  • All integers can have exact floating point representation if your floating point type supports the required mantissa bits. Since double uses 53 bits for mantissa, it can store all 32-bit ints exactly. After all, you could just set the value as mantissa with zero exponent.