    // Try to find the best approximation of the ratio that we can.  Our
    // approach is as follows.  Figure out the number of bits to the right
    // we need to shift the numerator and denominator, rounding up or down
    // in the process, such that the result can be reduced to fit into 32
    // bits.
    //
    // This approach tends to beat out a just-shift-until-it-fits approach,
    // as well as an always-shift-then-reduce approach, but _none_ of these
    // approaches always finds the best solution.
    //
    // TODO(johngro) : figure out if it is reasonable to actually compute