bug with fast_float, imag and sqrt : NotANumber isn't fine.

[sagetrac-fmaltey]

I'm looking at the float result of y by fast_float for m=0.0 :

var('m')
y=imag(sqrt(1+sqrt(m-1)))
fast_float (y, m)(0)     # I get nan

Now I try the constant function (without m),
the value must be the previous one for m=0.

z=imag(sqrt(1+sqrt(-1)))
fast_float(z,m)(0)  # I get the right 0.45...=2^(1/4)*sin(pi/8)

I feel (but I can't prove) that this bug is near from the #7165 bug I found in parametric_plot [that maybe calls fast_float in this case].

When I read the y.imag() value, there is at the end a fuzzy ...*sqrt(abs(sqrt(m-1)+1))
This sqrt(m-1) is Not_A_Number if m=0 because fast_float only uses real numbers. So this call might be replaced by an other expression, with real part and imaginary part.

There is no expression as sqrt(1+sqrt(-1)) in z.imag() and Sage runs right.

F.

Component: symbolics

Stopgaps: todo

Issue created by migration from https://trac.sagemath.org/ticket/10087

[sagetrac-jakobkroeker]

Stopgaps: todo