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In a big application, wouldn't rounding to a random direction (a feature GNU MP supports) be the most accurate probabilistically? If you round up or down all yo
by gnulinux 4y ago
In a big application, wouldn't rounding to a random direction (a feature GNU MP supports) be the most accurate probabilistically? If you round up or down all your numbers and you perform a lot of arithmetic operations, you create a lot of bias.
- pertymcpert 4y agoMaybe, but having random "accurate" behavior in a program is generally worse than being incorrect all of the time.
- klyrs 4y agoConsider the logarithm. In almost any interval, rounding down will be more accurate than rounding up the majority of the time -- so random rounding will bias you away from an accurate result. Random rounding can be a good idea, but it's not always a good idea. Random rounding is an okay default, but having fine-grain control over rounding direction is vastly superior to always sticking to the default. For another example, interval arithmetic is a really cool approach to keeping an eye on your accuracy. There, you want to round your upper bounds up, and round your lower bounds down.