Jeroen Demeyer on Mon, 24 Feb 2014 21:36:57 +0100 |
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Documentation of precision |
On 2014-02-24 21:20, Bill Allombert wrote:
""" By definition, 0.E n returns a real 0 of exponent n, whereas 0. returns a real 0 "of default precision" (of exponent -realprecision), see Section [Label: se:whatzero], behaving like the machine epsilon for the current default accuracy: any float of smaller absolute value is indistinguishable from 0. """ which is exactly what happen in your example.
I don't find it very clear. I think the user's manual would benefit from explicitly mentioning that
1. t_REALs are interpreted as some kind of intervals, they represent a number with an error term (unlike for example MPFR).
2. The precision for zero is absolute, while the precision for non-zero numbers is relative. One particular consequence is that a + e for very small e is *not* the same as a + 0, where a, e and 0 have the same precision (I was not aware of this).
Cheers, Jeroen.