Decimal fixed-point arithmetic
The module decimalfp provides a Decimal number type which can represent decimal numbers of arbitrary magnitude and arbitrary precision, i.e. any number of fractional digits.
decimalfp.Decimal instances are created by giving a value (default: 0) and a precision (i.e the number of fractional digits, default: None).
If precision is given, it must be of type int and >= 0.
If value is given, it must either be a string (type str or unicode in Python 2.x, bytes or str in Python 3.x), an instance of number.Integral (for example int or long in Python 2.x, int in Python 3.x), number.Rational (for example fractions.Fraction), decimal.Decimal or float or be convertable to a float or an int.
If a string is given as value, it must be a string in one of two formats:
- [+|-]<int>[.<frac>][<e|E>[+|-]<exp>] or
The value is always adjusted to the given precision or the precision is calculated from the given value, if no precision is given.
When the given precision is lower than the precision of the given value, the result is rounded, according to the rounding mode of the current context held by the standard module decimal (which defaults to ROUND_HALF_EVEN, in contrast to the round function in Python 2.x !!!).
When no precision is given and the given value is a float or a numbers.Rational (but no Decimal), the Decimal constructor tries to convert value exactly. But, for performance reasons, this is done only up a fixed limit of fractional digits. This limit defaults to 32 and is accessible as decimalfp.LIMIT_PREC. If value can not be represented as a Decimal within this limit, an exception is raised.
Decimal does not deal with infinity, division by 0 always raises a ZeroDivisionError. Likewise, infinite instances of type float or decimal.Decimal can not be converted to Decimal instances. The same is true for the ‘not a number’ instances of these types.
When importing decimalfp, its Decimal type is registered in Pythons numerical stack as number.Rational. It supports all operations defined for that base class and its instances can be mixed in computations with instances of all numeric types mentioned above.
All numerical operations give an exact result, i.e. they are not automatically constraint to the precision of the operands or to a number of significant digits (like the floating-point Decimal type from the standard module decimal). When the result can not exactly be represented by a Decimal instance within the limit given by decimalfp.LIMIT_PREC, an instance of fractions.Fraction is returned.
Decimal supports rounding via the built-in function round using the same rounding mode as the float type by default (i.e. ROUND_HALF_UP in Pyhton 2.x and ROUND_HALF_EVEN in Python 3.x). In addition, via the method adjusted a Decimal with a different precision can be derived, supporting all rounding modes defined by the standard library module decimal.
For more details see the documentation provided with the source distribution or here.