Floating point system with improved support of interval arithmetic

A method of enhancing support of an interval computation when performing a floating point arithmetic operation, comprising the steps, performed by a processor, of:

• receiving a first floating point operand;
• receiving a second floating point operand;
• executing the floating point arithmetic operation on the first floating point operand and the second floating point operand;
• determining whether a NaN substitution is necessary;
• producing a floating point result if the NaN substitution is determined to be unnecessary;
• and
• substituting an alternative value as the floating point result if the NaN substitution is determined to be necessary,
• wherein the substituting step further comprises:
• setting the floating point result to the alternative value if the floating point arithmetic operation is subtraction, and the first floating point operand and the second floating point operand, respectively, are from the group comprising:
• (1) negative infinity and negative infinity;
• and (2) positive infinity and positive infinity.

A method of enhancing support of an interval computation when performing a floating point arithmetic operation, comprising the steps, performed by a processor, of:

• receiving a first floating point operand;
• receiving a second floating point operand;
• executing the floating point arithmetic operation on the first floating point operand and the second floating point operand;
• determining whether a NaN substitution is necessary;
• producing a floating point result if the NaN substitution is determined to be unnecessary;
• and
• substituting an alternative value as the floating point result if the NaN substitution is determined to be necessary,
• wherein the substituting step further comprises:
• setting the floating point result to the alternative value if the floating point arithmetic operation is multiplication, and the first floating point operand and the second floating point operand are an infinity and a zero.

A method of enhancing support of an interval computation when performing a floating point arithmetic operation, comprising the steps, performed by a processor, of:

• receiving a first floating point operand;
• receiving a second floating point operand;
• executing the floating point arithmetic operation on the first floating point operand and the second floating point operand;
• determining whether a NaN substitution is necessary;
• producing a floating point result if the NaN substitution is determined to be unnecessary;
• and
• substituting an alternative value as the floating point result if the NaN substitution is determined to be necessary,
• wherein the substituting step further comprises:
• setting the floating point result to the alternative value if the floating point arithmetic operation is division, and the first floating point operand and the second floating point operand are a first infinity and a second infinity.

A method of enhancing support of an interval computation when performing a floating point arithmetic operation, comprising the steps, performed by a processor, of:

• receiving a first floating point operand;
• receiving a second floating point operand;
• executing the floating point arithmetic operation on the first floating point operand and the second floating point operand;
• determining whether a NaN substitution is necessary;
• producing a floating point result if the NaN substitution is determined to be unnecessary;
• and
• substituting an alternative value as the floating point result if the NaN substitution is determined to be necessary,
• wherein the substituting step further comprises:
• setting the floating point result to the alternative value if the floating point arithmetic operation is division, and the first floating point operand and the second floating point operand are a first zero and a second zero.