Tower of numeric types

A method for providing an extensible numeric tower of numeric data types comprising the steps of:

• providing an extensible numeric tower in a memory, the extensible numeric tower representing a structure supporting a plurality of statically defined numeric data types, the plurality of numeric data types each being configured to implement a different but accurate representation of a particular value;
• representing statically defined data types in the extensible numeric tower including:
• a whole number, a quotient of two integers where a denominator is not zero, a finite or infinite decimal expansion, and a real number added to a real number multiplied by an imaginary number;
• enabling the numeric tower to select a particular representation of a particular value based on a numeric operation to perform and providing an extensible set of numeric operations for the numeric tower to perform with the statically defined numeric data types, wherein the numeric tower is configured to allow statically defined data types be adjusted within the structure having the plurality of statically defined data types;
• determining whether a result of the numeric operation will result in an overflow situation when the numeric operation does not fit within a range supported by the particular one of the numeric types and converting to one of the other numeric data types when the numeric operation does not fit within a supported range;
• allowing additional statically defined numeric data types to be added to the plurality of numeric data types by a processing unit.

A method for performing a downward conversion of numeric types based upon an operation performed on at least one statically defined numeric type in a memory coupled to a processing unit, consisting of:

• receiving a request to perform an operation on at least one first particular one of a plurality of statically defined numeric types in a numeric tower in the memory;
• enabling the numeric tower to select a particular representation of a particular value based on a numeric operation to be performed, wherein the numeric tower is configured to allow statically defined data types be adjusted within the structure having the plurality of statically defined data types;
• determining that a result of the operation using the processing unit should be represented using a lower numeric type located in a lower category in the numeric tower as the result of an overflow situation when the numeric operation does not fit within a range supported by the particular one of the numeric types and converting to one of the other numeric data types when the operation does not fit within a supported range;
• performing a downward conversion on the result using the processing unit to find a lower numeric type that can hold the result;
• and
• returning the result in the lower numeric type that can hold the result and be stored in the memory.