Claims
- 1-10 (Canceled).
- 11. A method for performing extremum 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 computing the minimum includes computing the minimum in an arithmetic unit for intervals; 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. The method of claim 11, further comprising:
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.
- 23-32 (Canceled).
- 33. A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for performing extremum 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. The computer-readable storage medium of claim 33, the method further comprising:
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.
- 45-54 (Canceled).
- 55. An apparatus that performs extremum 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. The apparatus of claim 55 wherein:
the input is further 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; the computing mechanism is further configured to compute a maximum of the at least four floating-point numbers; and 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 26 Mar. 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).
Divisions (1)
|
Number |
Date |
Country |
Parent |
09854096 |
May 2001 |
US |
Child |
10850078 |
May 2004 |
US |