From: jacob@jacob.remcomp.fr   
      
   Le 16/01/2021 à 19:54, Richard Fateman a écrit :   
      
   > Is there is a particular important calculation that requires exactly 448   
   bits?   
   > RJF   
   >   
      
   The format I use is seven 64 bit numbers (the mantissa), an exponent of   
   32 bits and a sign of 32 bits making the number 64 bytes wide, a cache   
   line in many processors.   
      
   It is designed for speed, not space. 32 bits to store the sign bit seems   
   ludicrous but it is fast, 32 bits for the exponent is also too much but   
   it is fast. I could have reduced the space and use 32 bits more but the   
   algorithms would need to treat the first part of the mantissa   
   differently, what would really slow down things.   
      
   So, I decided to keep a seven 64 bit integers as mantissa (448 bits)   
   what gives around 135 decimal places.   
      
   The number of atoms in the universe is between 10^78 and 10^82, so this   
   format allows you to couunt each atom and even the numbers of neutrons   
   in each one if you want. It is a fast format, enough for most practical   
   purposes.   
      
   I wanted a very high precision system but with a fixed but large   
   precision...   
      
   This system can run in an inexpensive ARM64 chip (system cost US$ 25)   
   making very high precision calculations available in those systems.   
      
   Now that Apple took the starting ARM train, it shines in the M1, a very   
   fast machine.   
      
      
   Thanks for your time   
      
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