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).