From: terje.mathisen@tmsw.no   
      
   Thomas Koenig wrote:   
   > MitchAlsup  schrieb:   
   >>   
   >> Terje Mathisen  posted:   
   >   
   >>> Actually, for the five required basic operations, you can always do the   
   >>> op in the next higher precision, then round again down to the target,   
   >>> and get exactly the same result.   
   >>   
   >> https://guillaume.melquiond.fr/doc/05-imacs17_1-article.pdf   
   >   
   > The PowerISA version 3.0 introduced rounding to odd for its 128-bit   
   > floating point arithmetic, for that very reason (I assume).   
      
   Rounding to odd is basically the same as rounding to sticky, i.e if   
   there are any trailing 1 bits in the exact result, then put that in the   
   ulp position.   
      
   We have known since before the 1978 ieee754 standard that guard+sticky   
   (plus sign and ulp) is enough to get the rounding correct in all modes.   
      
   The single exception is when rounding up from the maximum magnitude   
   value to inf should be suppressed, there you do in fact need to check   
   all the bits.   
      
   Terje   
      
   --   
   -    
   "almost all programming can be viewed as an exercise in caching"   
      
   --- SoupGate-Win32 v1.05   
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