 Floating-point overflow

Floating-point overflow occurs when the magnitude of a computed result exceeds the largest finite representable floating-point number. Large values of an exponential function are a common source. In a normalized weighted sum, replacing exponentials $e^{r_i}$ by $e^{r_i-r_{\max }}$ before division prevents this particular overflow while leaving the normalized weights unchanged; this is an application of the log-sum-exp construction.