Floating point addition methods and apparatus

A method for adding a plurality of floating point operands, the method comprising:

• receiving the operands at an input of an addition unit;
• adding the operands by the addition unit to provide a first result, the first result being a correct result if the following condition (I) is true:
• (I) the addition operation comprises an effective subtraction of operands which either (1) have equal exponents, or (2) have exponents which differ by 1 and for which the result of the addition operation is to be shifted to be normalized;
• adding the operands by the addition unit to provide a second result, the second result being a correct result if the following condition (II) is true:
• (II) the addition operation comprises an effective addition, or the addition operation comprises an effective subtraction of operands for which one of the following conditions is true:
• (1) the operands' exponents differ by 1 and the addition operation provides a normalized result without normalization, or (2) the operands, exponents differ by more than 1;
• selecting the first result if the condition (I) is true;
• and
• selecting the second result if the condition (II) is true.

A method for providing a floating point unit, the method comprising:

• providing an input for receiving a plurality of floating point operands;
• providing a first subunit for adding the floating point operands and providing a result of the addition;
• providing a second subunit for adding the floating point operands and providing a result of the addition;
• and
• providing a multiplexer for selecting:
• the result from the first subunit if the addition operation comprises an effective subtraction of operands which either (1) have equal exponents, or (2) have exponents which differ by 1 and for which the result of the addition operation is to be shifted to be normalized;
• the result from the second subunit if the addition operation comprises an effective addition, or if the addition operation comprises an effective subtraction of operands for which one of the following conditions is true:
• (1) the operands' exponents differ by 1 and the addition operation provides a normalized result without normalization, or (2) the operands' exponents differ by more than 1.

A floating point unit comprising:

• an input for receiving a plurality of floating point operands;
• and
• a circuit for providing a result of an addition operation on the floating point operands for a case when the addition operation comprises an effective subtraction of operands with unequal exponents or an effective addition, the circuit comprising:
• a circuit for generating a complement signal which is equal to 1 if, and only if, the addition operation comprises an effective subtraction;
• a circuit responsive to the complement signal, for generating a one's complement of a significand of a first operand of the effective subtraction, wherein the first operand has a smaller exponent than a second operand of the effective subtraction;
• and
• an adder for adding:
• (1) the complement signal, (2) the one's complement of the significand of the first operand, and (3) the significand of the second operand, wherein the complement signal is to be added as an end-around carry.

A method for adding floating point operands, the method comprising:

• receiving the operands at an input of an addition unit;
• and
• generating a result of an addition operation on the floating point operands for a case when the addition operation comprises an effective subtraction of operands with unequal exponents or an effective addition, where generating this result comprises:
• generating a complement signal which is equal to 1 if, and only if, the addition operation comprises an effective subtraction;
• in response to the complement signal, generating a one's complement of a significand of a first operand of the effective subtraction, wherein the first operand has a smaller exponent than a second operand of the effective subtraction;
• and
• adding:
• (1) the complement signal, (2) the one's complement of the significand of the first operand, and (3) the significand of the second operand, wherein the complement signal is added as an end-around carry.