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If I was trying really hard to be miserly with the clock cycles
I might try something else that didn't require the evaluation
of 2 different transcendental functions.
I disagree, because exp() and sinh() are both transcendental
functions. One exp() and one sinh() is no worse than two exp()s.
BTW FWIW I prefer the name sinhc(x) = sinh(x)/x which is
perhaps not perfect, but it is memorable, in analogy to the
established name sinc(x) = sin(x)/x.