From: johnl@taugh.com   
      
   According to David Schultz  :   
   >This reminds me of when I took a numerical analysis course. (The many   
   >ways that computer calculations can go wrong and how to deal with it.)   
   >The professor said that the schools IBM (360 or 370, ca. 1980) was   
   >perfect for the course because of the defects in its floating point   
   >system. Guard digits and rounding sorts of things as near as I can recall.   
      
   The 360's floating point is a famous and somewhat puzzling failure, considering   
   how much else they got right.   
      
   It does hex normalization rather than binary. They assumed that   
   leading digits are evenly distributed so there's be on average one   
   zero bit, but in fact they're geometrically distributed, so on average   
   there's two. They got one bit back by making the exponent units of 16   
   rather than 2, but that's still one bit gone. It truncated rather than   
   rounding, another bit gone.  They also truncated rather than rounding   
   results.   
      
   Originally there wre no guard digits which made the results comically   
   bad but IBM retrofitted them at great cost to all the installed machines.   
      
   IEEE floating point can be seen as a reaction to that, how do you use   
   the same number of bits but get good results.   
      
   --   
   Regards,   
   John Levine, johnl@taugh.com, Primary Perpetrator of "The Internet for   
   Dummies",   
   Please consider the environment before reading this e-mail. https://jl.ly   
      
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