Question

I know about weird stuff with precision errors, but I can’t fathom,

Why is (long)9223372036854665200d giving me 9223372036854665216 ?

Answer 1

9223372036854665200d is a constant of type double. However, 9223372036854665200 does not fit in a double without loss of precision. A double only has 52 bits of mantissa, whereas the number in question requires 63 bits to be represented exactly.

The nearest double to 9223372036854665200d is the number whose mantissa equals 1.1111111111111111111111111111111111111111111110010100 in binary and whose exponent is 63 (decimal). This number is none other than 9223372036854665216 (call it U).

If we decrease the mantissa one notch to 1.1...0011, we get 9223372036854664192 (call it L).

The original number is between L and U and is much closer to U than it is to L

Finally, if you think that this truncation of the mantissa ought to result in a number that ends in a bunch of zeros, you’re right. Only it happens in binary, not in decimal: U in base-16 is 0x7ffffffffffe5000 and L is 0x7ffffffffffe4c00.