DFP

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IEEE 854-1987 Notes and differences

• Radix 10000

  IEEE 854 requires the radix to be either 2 or 10. The radix here is 10000, so that requirement is not met, but it is possible that a subclass can be made to make it behave as a radix 10 number. It is my opinion that if it looks and behaves as a radix 10 number then it is one and that requirement would be met.

  The radix of 10000 was chosen because it should be faster to operate on 4 decimal digits at once intead of one at a time. Radix 10 behaviour can be realized by add an additional rounding step to ensure that the number of decimal digits represented is constant.

  The IEEE standard specifically leaves out internal data encoding, so it is reasonable to conclude that such a subclass of this radix 10000 system is merely an encoding of a radix 10 system.

  The supplied subclass rossi.dfp.dfpdec hides this implementation detail and behaves as a decimal number.

• Sub-normal numbers

  IEEE 854 also specifies the existance of "sub-normal" numbers. This class does not contain any such entities. The most significant radix 10000 digit is always non-zero. Instead, we support "gradual underflow" by raising the underflow flag for numbers less with exponent less than expMin, but dont flush to zero until the exponent reaches expMin-DIGITS. Thus the smallest number we can represent would be: 1E(-(minExp-DIGITS-1)*4), eg, for DIGITS=5, minExp=-32767, that would be 1e-131092.

• Implied Radix point

  IEEE 854 defines that the implied radix point lies just to the right of the most significant digit and to the left of the remaining digits. This implementation puts the implied radix point to the left of all digits including the most significant one. The most significant digit here is the one just to the right of the radix point. This is a fine detail and is really only a matter of definition. Any side effects of this can be rendered invisible by a subclass.