From: already5chosen@yahoo.com   
      
   On Tue, 4 Nov 2025 16:52:18 +0100   
   Terje Mathisen  wrote:   
      
   > Scott Lurndal wrote:   
   > > Michael S  writes:   
   > >> On Mon, 03 Nov 2025 15:22:44 GMT   
   > >> scott@slp53.sl.home (Scott Lurndal) wrote:   
   > >   
   > >>> By decimal FP, do you mean BCD?  I.e. a format where   
   > >>> you have a BCD exponent sign digit (BCD 'C' or 'D')   
   > >>> followed by two BCD exponent digits, followed by a   
   > >>> mantissa sign digit ('C' or 'D') followed by a variable   
   > >>> number of mantissa digits (1 to 100)?   
   > >>   
   > >> I am pretty sure that by decimal FP Terje means decimal FP :-). As   
   > >> defined in IEEE 754 (formerly it was in 854, but since 2008 it   
   > >> became a part of the main standard).   
   > >> IEEE 754 has two options for encoding of mantissa, IBM's DPD which   
   > >> is a clever variation of Base 1000 and Intel's binary.   
   > >> DPD encoding is considered preferable for hardware implementations   
   > >> while binary encoding is easier for software implementations.   
   > >> BCD is not an option, it's information density is insufficient to   
   > >> supply required semantics in given size of container.   
   > >   
   > > How so?  The B3500 supported 100 digit (400 bit) signed mantissa and   
   > > a two digit signed exponent using a BCD representation.   
   >   
   > It is needed to be comparable to binary FP:   
   >   
   > A 64-bit double provides 54 mantissa bits, this corresponds to 16+   
   > decimal digits, while fp128 gives us 113 bits or a smidgen over 34   
   > digits.   
   >   
   > The corresponding 128-bit DFP format also provides 34 decimal digts,   
   > with an exponent range which covers 10^-6143 to 10^6144, while the 15   
   > exponent bits in binary128 covers 2^-16k to 2^16k, corresponding to   
   > 5.9e(+/-)4931.   
   >   
   > I.e. the DFP format has the same precision and a larger range than   
   > BFP.   
   >   
   > Terje   
   >   
      
   Nitpick:   
   In the best case, i.e. cases where mantissa of BFP is close to 2 and MS   
   digit of DFP =9, [relative] precision is indeed almost identical.   
   But in the worst case, i.e. cases where mantissa of BFP is close to 1   
   and MS digit of DFP =1, [relative] precision of BFP is 5 times better.   
      
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