Complex multiplication and division follow Fortran rules. Range reduction is done as part of complex division, but there is no checking whether the result of a complex multiplication or division is NaN + I*NaN, with an attempt to rescue the situation in that case.
The default is -fno-cx-fortran-rules.
Comments
One trick that I happened upon was speeding up complex multiplication (like a factor of 5) under gcc with the --enable-cx-fortran switch.
-fcx-fortran-rules
[1] https://gcc.gnu.org/onlinedocs/gcc-9.3.0/gcc/Optimize-Option...