What causes a trap in IEEE-754 floating-point?

In the ANSI/IEEE Std 754-1985 (IEEE Standard for Binary Floating-point Arithmetic), and the ANSI/IEEE Std 854-1987 (IEEE Standard for Radix-Independent Floating-Point Arithmetic), is signaling a trap an "edge-triggered" or a "level-sensitive" event? Does it matter if an exception is signaled by an arithmetic operation versus a user setting a status flag?