Minimum and maximum operations to facilitate interval multiplication and/or interval division

1. A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for performing a minimum computation for an interval operation, the method comprising:

receiving at least four floating-point numbers, including a first floating-point number, a second floating-point number, a third floating-point number and a fourth floating-point number; and

computing a minimum of the at least four floating-point numbers;

wherein if the at least four floating-point numbers include one or two default NaN (not-a-number) values and the remaining values are not default NaN values, the default NaN values are ignored in computing the minimum.

2. The computer-readable storage medium of claim 1 ,

wherein the minimum is a left endpoint of a resulting interval of the interval operation;

wherein the first floating-point number is the result of an operation between the left endpoint of a first interval and the left endpoint of a second interval;

wherein the second floating-point number is the result of the operation between the left endpoint of the first interval and the right endpoint of the second interval;

wherein the third floating-point number is the result of the operation between the right endpoint of the first interval and the left endpoint of the second interval; and

wherein the fourth floating-point number is the result of the operation between the right endpoint of the first interval and the right endpoint of the second interval.

3. The computer-readable storage medium of claim 1 , wherein computing the minimum involves setting the minimum to a value representing the empty interval, if any of the at least four floating-point numbers contain the value representing the empty interval.

4. The computer-readable storage medium of claim 3 , wherein the value representing the empty interval is a non-default NaN value.

5. The computer-readable storage medium of claim 2 , wherein computing the minimum involves setting the minimum to negative infinity if the first floating-point number is a default NaN value and the fourth floating-point number is the default NaN value.

6. The computer-readable storage medium of claim 2 , wherein computing the minimum involves setting the minimum to negative infinity if the second floating-point number is a default NaN value and the third floating-point number is the default NaN value.

7. The computer-readable storage medium of claim 1 , wherein if none of the at least four floating-point numbers is a default NaN value or a value representing the empty interval, computing the minimum involves selecting the minimum of the at least four floating-point numbers.

8. The computer-readable storage medium of claim 2 , wherein the operation can include one of a multiplication operation and a division operation.

9. A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for performing a maximum computation for an interval operation, the method comprising:

receiving at least four floating-point numbers, including a first floating-point number, a second floating-point number, a third floating-point number and a fourth floating-point number; and

computing a maximum of the at least four floating-point numbers;

wherein if the at least four floating-point numbers include one or two default NaN (not-a-number) values and the remaining values are not default NaN values, the default NaN values are ignored in computing the maximum.

10. The computer-readable storage medium of claim 9 ,

wherein the maximum is a right endpoint of a resulting interval of the interval operation;

wherein the first floating-point number is the result of an operation between the left endpoint of a first interval and the left endpoint of a second interval;

wherein the second floating-point number is the result of the operation between the left endpoint of the first interval and the right endpoint of the second interval;

wherein the third floating-point number is the result of the operation between the right endpoint of the first interval and the left endpoint of the second interval; and

wherein the fourth floating-point number is the result of the operation between the right endpoint of the first interval and the right endpoint of the second interval.

11. The computer-readable storage medium of claim 9 , wherein computing the maximum involves setting the maximum to a value representing the empty interval, if any of the at least four floating-point numbers contain the value representing the empty interval.

12. The computer-readable storage medium of claim 11 , wherein the value representing the empty interval is a non-default NaN value.

13. The computer-readable storage medium of claim 10 , wherein computing the maximum involves setting the maximum to positive infinity if the first floating-point number is a default NaN value and the fourth floating-point number is the default NaN value.

14. The computer-readable storage medium of claim 10 , wherein computing the maximum involves setting the maximum to positive infinity if the second floating-point number is a default NaN value and the third floating-point number is the default NaN value.

15. The computer-readable storage medium of claim 9 , wherein if none of the at least four floating-point numbers is a default NaN value or a value representing the empty interval, computing the maximum involves selecting the maximum of the at least four floating-point numbers.

16. The computer-readable storage medium of claim 10 , wherein the operation can include one of a multiplication operation and a division operation.