sqrt-r of a small ratio

[thomashoullier]

I am trying to compute:

(sqrt-r 241/1212133131231092371897321192837137189237981273)

SQRT-R: attempting to compute the square root of a negative number
    [Condition of type SIMPLE-ERROR]

I can evaluate the number 241/1212133131231092371897321192837137189237981273 on its own without issue or create
it via (/r 241 1212133131231092371897321192837137189237981273).

I am new to the library, is this supposed to be an error?

This is on SBCL 2.2.5 AMD64 compiled for Void Linux.

[stylewarning]

@thomashoullier This sounds like a bug in the internal function raw-approx-cr on rationals. I'll look into it.

[stylewarning]

The problem is that SQRT-R is checking that the argument is definitely positive, not that it is definitively negative. As such, we see the same problem with something that is zero up to the tolerance, such as $\pi-\pi$, i.e.,

(sqrt-r (-r +pi-r+ +pi-r+))

This leads to the same error. It's fixed if we change it to check that the argument is definitively negative, but this could lead to issues when the argument is not definitively negative (i.e., that it is $0$ up to the tolerance, but negative beyond the tolerance).