code: def _computeFractionForSampleSize(sampleSizeLowerBound, total, withReplacement):
          
          fraction = float(sampleSizeLowerBound) / total
          if withReplacement:
              numStDev = 5
              if (sampleSizeLowerBound < 12):
                  numStDev = 9
              return fraction + numStDev * sqrt(fraction / total)
          else:
              delta = 0.00005
              gamma = - log(delta) / total
              return min(1, fraction + gamma + sqrt(gamma * gamma + 2 * gamma * fraction))
docs: Returns a sampling rate that guarantees a sample of
          size >= sampleSizeLowerBound 99.99% of the time.
  
          How the sampling rate is determined:
          Let p = num / total, where num is the sample size and total is the
          total number of data points in the RDD. We're trying to compute
          q > p such that
            - when sampling with replacement, we're drawing each data point
              with prob_i ~ Pois(q), where we want to guarantee
              Pr[s < num] < 0.0001 for s = sum(prob_i for i from 0 to
              total), i.e. the failure rate of not having a sufficiently large
              sample < 0.0001. Setting q = p + 5 * sqrt(p/total) is sufficient
              to guarantee 0.9999 success rate for num > 12, but we need a
              slightly larger q (9 empirically determined).
            - when sampling without replacement, we're drawing each data point
              with prob_i ~ Binomial(total, fraction) and our choice of q
              guarantees 1-delta, or 0.9999 success rate, where success rate is
              defined the same as in sampling with replacement.