How to write floating-point value to custom logic???

Except that such code breaks the 'strict aliasing' rules of C, and gcc might optimise away the assignment.

Better would be a cast on the LHS, eg:

*(volatile float *)SQRT_BASE = data_in;

An alternative is to define a C structure, and variable of a type that matches the IO device, and then get the linker to assign a fixed address (or use a pointer). eg:

extern struct {
    volatile float  sqrt_in;
    volatile float  sqrt_out;
} *sqrt_device = (void *)(1u << 31 | SQRT_BASE);
    ...
    sqrt_device->sqrt_in = data_in;
    delay();
    printf("%f\n", sqrt_device->sqrt_out);

IMHO using structures to access hardware devices is much less error prone than trying to use constants and access macros.

Although not 100% portable, it is portable enough.