Some progress ... Since this is an OpenGL app I had been
setting Set8087CW($133F) to prevent FPU errors from showing as exceptions.
When I omit Set8087CW I get EDivByZero an exception, but my program is
still in an unusable state.

Since this error occurs in the SSE XMM registers, I think I should also be
using the SetSSECSR function. Does anyone have any details about how this
function works in relation to XMM registers and rounding or divide by zero
errors and how it could be applied in my situation?
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