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>-- val1 = 9007199254740992
>val1 is the first value, on my system (Windows NT on Duron), where an
>increment of 1 isn't signifiant.

Yes, 9007199254740992 = 2^53.
On Intel machines (and most others) doubles are represented using the IEEE 754
standard, which has 52 bits for the mantissa. (There's a hidden bit and so
the precision is actually 53 bits.) For an explantion, see

For single-precision floats, the limit would be 2^24.