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   Message 130,229 of 131,241   
   Terje Mathisen to BGB   
   Re: Tonights Tradeoff   
   10 Nov 25 08:16:07   
   
   From: terje.mathisen@tmsw.no   
      
   BGB wrote:   
   > DIV uses Newton-Raphson   
   > The process of converging is a lot more fiddly than with Binary FP.    
   > Partly as the strategy for generating the initial guess is far less    
   > accurate.   
   >    
   > So, it first uses a loop with hard-coded checks and scales to get it in    
   > the general area, before then letting N-R take over. If the value isn't    
   > close enough (seemingly +/- 25% or so), N-R flies off into space.   
   >    
   > Namely:   
   >    Exponent is wrong:   
   >      Scale by factors of 2 until correct;   
   >    Off by more than 50%, scale by +/- 25%;   
   >    Off by more than 25%, scale by +/- 12.5%;   
   >    Else: Good enough, let normal N-R take over.   
      
   My possibly naive idea would extract the top 9-15 digits from divisor    
   and dividend, convert both to binary FP, do the division and convert back.   
      
   That would reduce the NR step to two or three iterations, right?   
      
   Terje   
      
   --    
   -    
   "almost all programming can be viewed as an exercise in caching"   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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