What does it mean to have a negative accuracy number?
I understand 0``128
to mean "the number zero to 128 decimal points". Mathematica corroborates this:
In[1]:= 0``128 < 1
(* Out[1]= True *)
In[2]:= 0``128 < 0
(* Out[2]= False *)
In[3]:= Accuracy[0``128]
(* Out[3]= 128. *)
But then I have no idea what "negative accuracy" is:
In[1]:= 0``-128 < 1
(* Out[1]= False *)
In[2]:= 0``-128 > 1
(* Out[2]= False *)
In[3]:= 0``-128 == 1
(* Out[3]= True *) (* Why????? *)
In[4]:= Accuracy[0``-128]
(* Out[4]= -128. *)
Context: these values are showing up in a system of ~10000 equations, as the result of computing 100s of expressions of the form
$$ \sum_i \frac{\textrm{numer}}{\textrm{denom}} \textrm{basis}_i, $$
where both numer and denom are randomly generated complex numbers, with 200 digit precision. I then collect coefficients of the (symbolic) $\textrm{basis}_i$'s to form algebraic equations.
The 0``128
objects appear in only a handful of the total number of equations, so I don't yet know what causes the 0``-128
's to appear.