Method and apparatus for representing arithmetic intervals within a computer system

A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for representing an interval within a computer system to facilitate implementing efficient arithmetic operations using the interval, the method comprising:

• receiving a representation of the interval, the representation including a first floating-point number representing a first endpoint of the interval and a second floating-point number representing a second endpoint of the interval;
• and
• performing an arithmetic operation using the interval and using a floating-point arithmetic unit to produce a result;
• wherein if the first endpoint is negative infinity and the second endpoint is finite, performing the arithmetic operation involves treating the first endpoint as a number less than the smallest negative floating-point number and greater than negative infinity to represent a result of a negative overflow toward negative infinity;
• wherein if the second endpoint is positive infinity and the first endpoint is finite, performing the arithmetic operation involves treating the first endpoint as a number greater than the largest positive floating-point number and less than positive infinity to represent a result of a positive overflow toward positive infinity.

An apparatus for representing an interval within a computer system to facilitate implementing efficient arithmetic operations using the interval, the apparatus comprising:

• a receiving mechanism that is configured to receive a representation of the interval, the representation including a first floating-point number representing a first endpoint of the interval and a second floating-point number representing a second endpoint of the interval;
• and
• an execution mechanism that is configured to perform an arithmetic operation using the interval and using a floating-point arithmetic unit to produce a result;
• wherein if the first endpoint is negative infinity and the second endpoint finite, the execution mechanism is configured to treat the first endpoint as a number less than the smallest negative floating-point number and greater than negative infinity to represent a result of a negative overflow toward negative infinity;
• wherein if the second endpoint is positive infinity and the first endpoint is finite, the execution mechanism is configured to treat first endpoint as a number greater than the largest positive floating-point number and less than positive infinity to represent a result of a positive overflow toward positive infinity.