Robust sign comparison

[ivan-pi]

https://github.com/jacobwilliams/roots-fortran/blob/60524bc4f491a50ae1b2e538e1e486551812b9db/src/root_module.F90#L1837

I noticed the sign comparison is performed inconsistently; i.e. in some places as fa*fc < 0 and in some places you extract the sign explicitly like above.

The latter option is in agreement with what Kahaner, Moler, & Nash have to say about this:

The original SLATEC FZERO from Shampine & Watts does it like this:

IF (SIGN(1.0E0,FB) .NE. SIGN(1.0E0,FC)) ...

Leaving the underflow issues aside, the sign version seems to generate a few instructions less than your branching isign function. Moreover, gfortran and ifx produce branchless instructions when using the sign intrinsic: https://godbolt.org/z/E41P9c4Mz

As a matter of clarity, the sign comparison could also be abstracted as a function or operator, e.g.

if (sne(fb,fc)) ...  ! sign not equal

or

if( fb .oppsign. fc) ...   ! opposite sign

but I guess this is more a matter of taste (I'm not advocating for it, but the compilers seem able to inline such operators just fine).