From: already5chosen@yahoo.com   
      
   On Sun, 4 Jan 2026 16:45:10 -0000 (UTC)   
   Thomas Koenig  wrote:   
      
   > Michael S  schrieb:   
   > > On Sun, 4 Jan 2026 00:21:31 -0000 (UTC)   
   > > Thomas Koenig  wrote:   
   > >   
   > >>   
   > >> And two decimal flavors, as well, with binary and densely packed   
   > >> decimal encoding of the significand... it's a bit of a mess.   
   > >>   
   > >   
   > > Since both formats have exactly identical semantics, in theory the   
   > > mess is not worse (and not better) than two bytes orders of IEEE   
   > > binary FP.   
   >   
   > Almost.   
   >   
   > IIRC, there is no restriction on the binary mantissa, so its   
   > range is slightly larger for the same number of bits   
   > (1000/1024)**(n/3).   
      
   It's true that there is no restriction, but it does not influence   
   semantics.   
   In binary encoding, when the value of significand exceeds   
   10**(3*J+1)-1 then it is non-canonical representation of zero.   
   It is very similar to how declets in DPD allowed to have all 1024 bit   
   patterns, each pattern has defined numeric value in range [0:999], but   
   1000 patterns are canonical, i.e.allowed both as inputs and as outputs   
   of arithmetic operations and remaining 24 patterns are non-canonical -   
   accepted as inputs, but never produced as outputs.   
      
   --- SoupGate-Win32 v1.05   
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