title: Dealing with very small numbers in R
body: <p>I need to calculate a list of very small numbers such as </p>
  
  <p>(0.1)^1000, 0.2^(1200), </p>
  
  <p>and then normalize them so they will sum up to one
  i.e. </p>
  
  <p>a1 = 0.1^1000,
  a2 = 0.2^1200</p>
  
  <p>And I want to calculate 
  a1' =  a1/(a1+a2), 
  a2'=a2(a1+a2).</p>
  
  <p>I'm running into underflow problems, as I get a1=0. How can I get around this?
  Theoretically I could deal with logs, and then log(a1) = 1000*log(0.l) would be a way to represent a1 without underflow problems - But in order to normalize I would need to get 
  log(a1+a2) - which I can't compute since I can't represent a1 directly.</p>
  
  <p>I'm programming with R - as far as I can tell there is no data type such Decimal in c# which
  allows you to get better than double-precision value. </p>
  
  <p>Any suggestions will be appreciated, thanks</p>