Claims
- 1. A method for performing a minimum computation for an interval multiplication operation, 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 more default NaN (not-a-number) values, computing the minimum involves setting the minimum to negative infinity.
- 2. The method of claim 1,
wherein the minimum is a left endpoint of a resulting interval from the interval multiplication operation; wherein the first floating-point number is the result of a multiplication 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 a multiplication 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 a multiplication 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 a multiplication operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 3. The method 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 method of claim 3, wherein the value representing the empty interval is a non-default NaN value.
- 5. The method 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.
- 6. A method for performing a maximum computation for an interval multiplication operation, 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 more default NaN (not-a-number) values, computing the maximum involves setting the maximum to positive infinity.
- 7. The method of claim 6,
wherein the maximum is a right endpoint of a resulting interval from the interval multiplication operation; wherein the first floating-point number is the result of a multiplication 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 a multiplication 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 a multiplication 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 a multiplication operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 8. The method of claim 6, 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.
- 9. The method of claim 8, wherein the value representing the empty interval is a non-default NaN value.
- 10. The method of claim 6, 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.
- 11. A method for performing a minimum computation for an interval division operation, 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 more default NaN (not-a-number) values, the default NaN values are ignored in computing the minimum.
- 12. The method of claim 11,
wherein the minimum is a left endpoint of a resulting interval from the interval division operation; wherein the first floating-point number is the result of a division 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 a division 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 a division 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 a division operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 13. The method of claim 12, wherein computing the minimum involves setting the minimum to negative infinity, if the second interval contains zero.
- 14. The method of claim 11, 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.
- 15. The method of claim 14, wherein the value representing the empty interval is a non-default NaN value.
- 16. The method of claim 11, 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.
- 17. A method for performing a maximum computation for an interval division operation, 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 more default NaN (not-a-number) values, the default NaN values are ignored in computing the maximum.
- 18. The method of claim 17,
wherein the maximum is a right endpoint of a resulting interval from the interval division operation; wherein the first floating-point number is the result of a division 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 a division 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 a division 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 a division operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 19. The method of claim 18, wherein computing the maximum involves setting the maximum to positive infinity, if the second interval contains zero.
- 20. The method of claim 17, 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.
- 21. The method of claim 20, wherein the value representing the empty interval is a non-default NaN value.
- 22. The method of claim 17, 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.
- 23. 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 multiplication 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 more default NaN (not-a-number) values, computing the minimum involves setting the minimum to negative infinity.
- 24. The computer-readable storage medium of claim 23,
wherein the minimum is a left endpoint of a resulting interval from the interval multiplication operation; wherein the first floating-point number is the result of a multiplication 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 a multiplication 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 a multiplication 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 a multiplication operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 25. The computer-readable storage medium of claim 23, 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.
- 26. The computer-readable storage medium of claim 25, wherein the value representing the empty interval is a non-default NaN value.
- 27. The computer-readable storage medium of claim 23, 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.
- 28. 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 multiplication 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 more default NaN (not-a-number) values, computing the maximum involves setting the maximum to positive infinity.
- 29. The computer-readable storage medium of claim 28,
wherein the maximum is a right endpoint of a resulting interval from the interval multiplication operation; wherein the first floating-point number is the result of a multiplication 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 a multiplication 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 a multiplication 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 a multiplication operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 30. The computer-readable storage medium of claim 28, 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.
- 31. The computer-readable storage medium of claim 30, wherein the value representing the empty interval is a non-default NaN value.
- 32. The computer-readable storage medium of claim 28, 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.
- 33. 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 division 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 more default NaN (not-a-number) values, the default NaN values are ignored in computing the minimum.
- 34. The computer-readable storage medium of claim 33,
wherein the minimum is a left endpoint of a resulting interval from the interval division operation; wherein the first floating-point number is the result of a division 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 a division 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 a division 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 a division operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 35. The computer-readable storage medium of claim 34, wherein computing the minimum involves setting the minimum to negative infinity, if the second interval contains zero.
- 36. The computer-readable storage medium of claim 33, 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.
- 37. The computer-readable storage medium of claim 36, wherein the value representing the empty interval is a non-default NaN value.
- 38. The computer-readable storage medium of claim 33, 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.
- 39. 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 division 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 more default NaN (not-a-number) values, the default NaN values are ignored in computing the maximum.
- 40. The computer-readable storage medium of claim 39,
wherein the maximum is a right endpoint of a resulting interval from the interval division operation; wherein the first floating-point number is the result of a division 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 a division 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 a division 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 a division operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 41. The computer-readable storage medium of claim 40, wherein computing the maximum involves setting the maximum to positive infinity, if the second interval contains zero.
- 42. The computer-readable storage medium of claim 39, 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.
- 43. The computer-readable storage medium of claim 42, wherein the value representing the empty interval is a non-default NaN value.
- 44. The computer-readable storage medium of claim 39, 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.
- 45. An apparatus that performs a minimum computation for an interval multiplication operation, comprising:
an input that is configured to receive 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 a computing mechanism that is configured to compute a minimum of the at least four floating-point numbers; wherein if the at least four floating-point numbers include one or more default NaN (not-a-number) values, computing the minimum involves setting the minimum to negative infinity.
- 46. The apparatus of claim 45,
wherein the minimum is a left endpoint of a resulting interval from the interval multiplication operation; wherein the first floating-point number is the result of a multiplication 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 a multiplication 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 a multiplication 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 a multiplication operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 47. The apparatus of claim 45, wherein the computing mechanism is configured to set 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.
- 48. The apparatus of claim 47, wherein the value representing the empty interval is a non-default NaN value.
- 49. The apparatus of claim 45, wherein if none of the at least four floating-point numbers is a default NaN value or a value representing the empty interval, the computing mechanism is configured to select the minimum of the at least four floating-point numbers.
- 50. An apparatus that performs a maximum computation for an interval multiplication operation, comprising:
an input that is configured to receive 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 a computing mechanism that is configured to compute a maximum of the at least four floating-point numbers; wherein if the at least four floating-point numbers include one or more default NaN (not-a-number) values, computing the maximum involves setting the maximum to positive infinity.
- 51. The apparatus of claim 50,
wherein the maximum is a right endpoint of a resulting interval from the interval multiplication operation; wherein the first floating-point number is the result of a multiplication 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 a multiplication 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 a multiplication 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 a multiplication operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 52. The apparatus of claim 50, wherein the computing mechanism is configured to set 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.
- 53. The apparatus of claim 50, wherein the value representing the empty interval is a non-default NaN value.
- 54. The apparatus of claim 50, wherein if none of the at least four floating-point numbers is a default NaN value or a value representing the empty interval, the computing mechanism is configured to select the maximum of the at least four floating-point numbers.
- 55. An apparatus that performs a minimum computation for an interval division operation, comprising:
an input that is configured to receive 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 a computing mechanism that is configured to compute a minimum of the at least four floating-point numbers; wherein if the at least four floating-point numbers include one or more default NaN (not-a-number) values, the default NaN values are ignored in computing the minimum.
- 56. The apparatus of claim 55,
wherein the minimum is a left endpoint of a resulting interval from the interval division operation; wherein the first floating-point number is the result of a division 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 a division 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 a division 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 a division operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 57. The apparatus of claim 56, wherein if the second interval contains zero, the computing mechanism is configured to set the minimum to negative infinity.
- 58. The apparatus of claim 55, wherein the computing mechanism is configured to set 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.
- 59. The apparatus of claim 58, wherein the value representing the empty interval is a non-default NaN value.
- 60. The apparatus of claim 55, wherein if none of the at least four floating-point numbers is a default NaN value or a value representing the empty interval, the computing mechanism is configured to select the minimum of the at least four floating-point numbers.
- 61. An apparatus that performs a maximum computation for an interval division operation, comprising:
an input that is configured to receive 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 a computing mechanism that is configured to compute a maximum of the at least four floating-point numbers; wherein if the at least four floating-point numbers include one or more default NaN (not-a-number) values, the default NaN values are ignored in computing the maximum.
- 62. The apparatus of claim 61,
wherein the maximum is a right endpoint of a resulting interval from the interval division operation; wherein the first floating-point number is the result of a division 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 a division 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 a division 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 a division operation between the right endpoint of the first interval and the right endpoint of the second interval.
- 63. The apparatus of claim 62, wherein if the second interval contains zero, the computing mechanism is configured to set the maximum to positive infinity.
- 64. The apparatus of claim 61, wherein the computing mechanism is configured to set 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.
- 65. The apparatus of claim 64, wherein the value representing the empty interval is a non-default NaN value.
- 66. The apparatus of claim 61, wherein if none of the at least four floating-point numbers is a default NaN value or a value representing the empty interval, the computing mechanism is configured to select the maximum of the at least four floating-point numbers.
RELATED APPLICATION
[0001] The subject matter of this application is related to the subject matter in a pending non-provisional application by the same inventor as the instant application and filed on Mar. 26, 2001 entitled, “Minimum and Maximum Operations to Facilitate Interval Multiplication and/or Interval Division,” Ser. No. 09/818,021 (Attorney Docket No. SUN-P5608-SPL).