[Cfp-interest 2107] Re: Subnormals in decimal

[David Hough CFP]

If C model numbers don't include subnormals then
I wonder if something like this would work:

 The minimum normal magnitude in a format
 is the smallest positive model number in that format.
 Normal numbers in a format are those with finite magnitudes greater
 than or equal to the minimum normal magnitude.
 Subnormal numbers in a format are those with finite magnitudes greater
 than zero and less than the minimum normal magnitude.
 Thus all finite numbers in a format are just one of zero, subnormal, or normal.

 Footnote: The distinction among zero, subnormal, and normal is based solely
 on the magnitude of the number, not on encoding. 
 Some formats permit multiple encodings of the same number.
 Encodings can be distinguished as normalized or unnormalized.
 Normalized encodings of model numbers
 have the maximum significand and minimum exponent 
 among encodings of the same model number. 
 Unnormalized encodings of model
 numbers have a smaller significand or larger exponent
 than the corresponding normalized encoding.
 Encodings of non-model numbers might be considered normalized or unnormalized
 as defined by an implementation.

 In IEEE 754 basic binary formats, the normal numbers have unique,
 and thus normalized, encodings,
 and the subnormal numbers are considered to have
 unnormalized encodings, sometimes called denormalized.   
 Thus "normal" and "normalized" are sometimes used interchangeably, 
 as are "subnormal" and "unnormalized" and "denormalized",
 but that is incorrect for many other formats, 
 including 754 basic decimal formats.