>> Another good good way to think of IEEE I was presented once with, and >> which kind of gave me a ah-ah moment, is the fact that numbers with >> exact representation fall on the nodes of grid, and there's plenty of >> "space" in between the nodes for values which cannot be exactly >> represented. The "spacing" of the grid varies depending on the >> magnitude of your number (i.e. the exponent) and the size of the >> mantissa (i.e. how small your 1/2^i fractions get). IEEE is complex... >> I'm not an expert, but hopefully the above helps. --DD >> > >Very true, and a corollary is that using a fixed tolerance for floating point >comparisons (like 1e-14 suggested elsewhere in this thread) doesn't work in >general. > It's fine if you know the magnitude of the numbers you're comparing, but once > you get to numbers above 100, abs(f1 - f2) < 1e-14 becomes the same as saying > f1 == f2, because even a single bit of error at this magnitude will be larger > than 1e-14.
>Some languages provide a way to determine the distance between a given >floating point value and the next largest representable number (eg the Math.ulp > function in java), but I'm not sure if SQL provides such? Or if its even in > scope... Once the binary representation of an integer value becomes longer than the mantissa, even integers will start to fall into the space in between adjacent floating point values... asql> select (9007199254740992.0 + 1.0) - (9007199254740992.0 + 2.0); (9007199254740992.0 + 1.0) - (9007199254740992.0 + 2.0) ------------------------------------------------------- -2.0 asql> select (9007199254740992.0 + 1.0) - (9007199254740992.0); (9007199254740992.0 + 1.0) - (9007199254740992.0) ------------------------------------------------- 0.0 ___________________________________________ Gunter Hick Software Engineer Scientific Games International GmbH FN 157284 a, HG Wien Klitschgasse 2-4, A-1130 Vienna, Austria Tel: +43 1 80100 0 E-Mail: hick at scigames.at This communication (including any attachments) is intended for the use of the intended recipient(s) only and may contain information that is confidential, privileged or legally protected. Any unauthorized use or dissemination of this communication is strictly prohibited. If you have received this communication in error, please immediately notify the sender by return e-mail message and delete all copies of the original communication. Thank you for your cooperation.
