Package org.apache.commons.math.dfp
Another floating point class. This one is built using radix 10000 which is 10^{4}, so its almost decimal.
The design goals here are:
 Decimal math, or close to it
 Settable precision (but no mix between numbers using different settings)
 Portability. Code should be keep as portable as possible.
 Performance
 Accuracy  Results should always be +/ 1 ULP for basic algebraic operation
 Comply with IEEE 8541987 as much as possible. (See IEEE 8541987 notes below)
Trade offs:
 Memory foot print. I'm using more memory than necessary to represent numbers to get better performance.
 Digits are bigger, so rounding is a greater loss. So, if you really need 12 decimal digits, better use 4 base 10000 digits there can be one partially filled.
Numbers are represented in the following form:
n = sign × mant × (radix)^{exp};where sign is ±1, mantissa represents a fractional number between zero and one. mant[0] is the least significant digit. exp is in the range of 32767 to 32768
IEEE 8541987 Notes and differences
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 subclassed 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 instead of one at a time. Radix 10 behavior 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.
IEEE 854 also specifies the existence of "subnormal" numbers. This class does not contain any such entities. The most significant radix 10000 digit is always nonzero. Instead, we support "gradual underflow" by raising the underflow flag for numbers less with exponent less than expMin, but don't flush to zero until the exponent reaches MIN_EXPdigits. Thus the smallest number we can represent would be: 1E((MIN_EXPdigits1)*4), eg, for digits=5, MIN_EXP=32767, that would be 1e131092.
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.

Class Summary Class Description Dfp Decimal floating point library for JavaDfpDec Subclass ofDfp
which hides the radix10000 artifacts of the superclass.DfpField Field for Decimal floating point instances.DfpMath Mathematical routines for use withDfp
. 
Enum Summary Enum Description DfpField.RoundingMode Enumerate for rounding modes.