Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Information Disclosure Statement
The information disclosure statements (IDS) submitted on 11/09/2022, 09/28/2023, 03/05/2024, 05/15/2024, 09/13/2024, 06/02/2025, 06/06/2025, and 06/10/2026 are in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered by the examiner.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1-14 are rejected under 35 U.S.C. 101 because the claimed invention is directed to a judicial exception (i.e., a law of nature, a natural phenomenon, or an abstract idea) without significantly more.
Regarding claim 1, under the Alice Framework Step 1, claim 1 falls within the four statutory categories of patentable subject matter identified by 35 USC 101: a process, machine, manufacture, or a composition of matter.
Under the Alice Framework Step 2A prong 1, claim 1 recites an abstract idea, including a mathematical concept. Specifically, claim 1 recites the following mathematical calculations and mathematical formulas:
A method for performing addition and subtraction operations in a k-cluster residue number system, the method comprising: generating an addition and subtraction look-up table comprising 2mi cells for recording values from zero to (mi-1) in an ascending order twice, wherein mi is a coprime integer of a modular set of the k-cluster residue number system; the addition and subtraction look-up table of the k-cluster residue number system; a value recorded in a cell at position Q of the addition and subtraction look-up table when performing an addition operation on two integers A and B, where Q= ( (A mod mi) + (B mod mi) ) ; and a value recorded in a cell at position R of the addition and subtraction look-up table when subtracting an integer X by an integer Y, where R = (X mod mi) - (Y mod mi) = (X mod mi) + (mi - (Y mod mi) ) = rx + (mi - ry) = rx + ry', rx is equal to (X mod mi) , ry is equal to (Y mod mi) , and ry' is equal to (mi- (Y mod mi) ) .
Under the Alice Framework Step 2A prong 2 analysis, claim 1 recites additional elements of, “storing”, “memory”, and “retrieving”. The additional elements describe storing/retrieving data in a memory, which is considered insignificant extra-solution activity see MPEP 2106.04(d)(i), and 2106.05(g). For this reason the additional elements are not integrated into a practical application.
Under the Alice Framework Step 2B, the additional elements of “storing”, “memory” and “retrieving” are describing merely storing data in a memory, which is well-understood, routine, conventional activity, see MPEP 2106.05(d)(II)(iv). For these reasons the additional elements and the claim as a whole do not amount to significantly more than the abstract idea.
Claim 2 is rejected for at least the reasons set forth with respect to claim 1. Claim 2 merely further limits the mathematical concept set forth in claim 1.
Under the Alice Framework Step 2A prong 1, claim 2 recites an abstract idea, including a mathematical concept. Specifically, claim 2 recites the following mathematical calculations and mathematical formulas:
“The method of claim 1 further comprising: generating a multiplication look-up table for the coprime integer mi, wherein the coprime integer mi is not 2, and the multiplication look-up table is composed of S cells, where
S
=
m
i
2
-
1
4
; and the multiplication look-up table.”
Claim 2 recites no further additional elements in the claim limitations which require a Step 2A prong 2 or Step 2B analysis. For these reasons, claim 2 is neither integrated into a practical application nor amounting to significantly more than the abstract idea.
Claim 3 is rejected for at least the reasons set forth with respect to claim 2. Claim 3 merely further limits the mathematical concept set forth in claim 2.
Under the Alice Framework Step 2A prong 1, claim 3 recites an abstract idea, including a mathematical concept. Specifically, claim 3 recites the following mathematical calculations and mathematical formulas:
“The method of claim 2 further comprising: performing a multiplication operation on a multiplicand and a multiplicator using the multiplication look-up table, comprising: determining whether a complement of the multiplicand is greater than or equal to the multiplicator; if it is determined that the complement of the multiplicand is greater than or equal to the multiplicator, perform the following steps: selecting the multiplicand as a column entry and the multiplicator as a row entry, and determining whether the column entry is greater than or equal to the row entry; if it is determined that the column entry is greater than or equal to the row entry, keeping the column entry and the row entry; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; if it is determined that the complement of the multiplicand is less than the multiplicator, perform the following steps: selecting the complement of the multiplicand as the column entry and a complement of the multiplicator as the row entry, and determining whether the column entry is greater than or equal to the complement of the row entry; if it is determined that the column entry is greater than or equal to the complement of the row entry, keeping the column entry and the row entry; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; and a value from the multiplication look-up table as a product of the multiplicand and the multiplicator according to the column entry and the row entry.”
Claim 3 recites no further additional elements in the claim limitations which require a Step 2A prong 2 or Step 2B analysis. For these reasons, claim 3 is neither integrated into a practical application nor amounting to significantly more than the abstract idea.
Regarding claim 4, under the Alice Framework Step 1, claim 4 falls within the four statutory categories of patentable subject matter identified by 35 USC 101: a process, machine, manufacture, or a composition of matter.
Under the Alice Framework Step 2A prong 1, claim 4 recites an abstract idea, including a mathematical concept. Specifically, claim 4 recites the following mathematical calculations and mathematical formulas:
A method for performing multiplication operations in a k-cluster residue number system, the method comprising: generating a multiplication look-up table for a coprime integer mi of a modular set of the k-cluster residue number system, wherein the coprime integer mi is not 2, the multiplication
S
=
m
i
2
-
1
4
; the multiplication look-up table in of the k-cluster residue number system; and performing a multiplication operation on a multiplicand and a multiplicator using the multiplication look-up table, comprising: determining whether a complement of the multiplicand is greater than or equal to the multiplicator; if it is determined that the complement of the multiplicand is greater than or equal to the multiplicator, perform the following steps: selecting the multiplicand as a column entry and the multiplicator as a row entry, and determining whether the column entry is greater than or equal to the row entry; if it is determined that the column entry is greater than or equal to the row entry, keeping the column entry and the row entry; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; if it is determined that the complement of the multiplicand is less than the multiplicator, perform the following steps: selecting the complement of the multiplicand as the column entry and a complement of the multiplicator as the row entry, and determining whether the column entry is greater than or equal to the complement of the row entry; if it is determined that the column entry is greater than or equal to the complement of the row entry, keeping the column entry and the row entry ; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; and a value from the multiplication look-up table as a product of the multiplicand and the multiplicator according to the column entry and the row entry.
Under the Alice Framework Step 2A prong 2 analysis, claim 4 recites additional elements of, “storing”, “memory”, and “retrieving”. The additional elements describe storing data in a memory, which is considered insignificant extra-solution activity see MPEP 2106.04(d)(i), and 2106.05(g). For this reason the additional elements are not integrated into a practical application.
Under the Alice Framework Step 2B, the additional elements of “storing”, “memory”, and “retrieving” are describing merely storing data in a memory, which is well-understood, routine, conventional activity, see MPEP 2106.05(d)(II)(iv). For these reasons the additional elements and the claim as a whole do not amount to significantly more than the abstract idea.
Claim 5 is rejected for at least the reasons set forth with respect to claim 4. Claim 5 merely further limits the mathematical concept set forth in claim 4.
Under the Alice Framework Step 2A prong 1, claim 5 recites an abstract idea, including a mathematical concept. Specifically, claim 5 recites the following mathematical calculations and mathematical formulas:
“The method of claim 4 further comprises: generating an addition and subtraction look-up table comprising 2mi cells for recording values from zero to (mi-1) in an ascending order twice; and the addition and subtraction look-up table in the of the k-cluster residue number system.”
Claim 5 recites no further additional elements in the claim limitations which require a Step 2A prong 2 or Step 2B analysis. For these reasons, claim 5 is neither integrated into a practical application nor amounting to significantly more than the abstract idea.
Claim 6 is rejected for at least the reasons set forth with respect to claim 5. Claim 6 merely further limits the mathematical concept set forth in claim 5.
Under the Alice Framework Step 2A prong 1, claim 6 recites an abstract idea, including a mathematical concept. Specifically, claim 6 recites the following mathematical calculations and mathematical formulas:
“The method of claim 5 further comprises: a value recorded in a cell at position Q of the addition and subtraction look-up table when performing an addition operation on two integers A and B, where Q=((A mod mi) + (B mod mi)).”
Claim 6 recites no further additional elements in the claim limitations which require a Step 2A prong 2 or Step 2B analysis. For these reasons, claim 6 is neither integrated into a practical application nor amounting to significantly more than the abstract idea.
Claim 7 is rejected for at least the reasons set forth with respect to claim 5. Claim 7 merely further limits the mathematical concept set forth in claim 5.
Under the Alice Framework Step 2A prong 1, claim 7 recites an abstract idea, including a mathematical concept. Specifically, claim 7 recites the following mathematical calculations and mathematical formulas:
“The method of claim 5 further comprises: a value recorded in a cell at position R of the addition and subtraction look-up table when subtracting an integer X by an integer Y, where R= (X mod mi) - (Y mod mi) = (X mod mi) + (mi - (Y mod mi) ) = rx + (mi - ry) = (rx + ry' ) , rx is equal to (X mod mi), ry is equal to (Y mod mi), and ry' is equal to (mi- (Y mod mi) ).”
Claim 7 recites no further additional elements in the claim limitations which require a Step 2A prong 2 or Step 2B analysis. For these reasons, claim 7 is neither integrated into a practical application nor amounting to significantly more than the abstract idea.
Regarding claim 8, under the Alice Framework Step 1, claim 8 falls within the four statutory categories of patentable subject matter identified by 35 USC 101: a process, machine, manufacture, or a composition of matter.
Under the Alice Framework Step 2A prong 1, claim 8 recites an abstract idea, including a mathematical concept. Specifically, claim 8 recites the following mathematical calculations and mathematical formulas:
A k-cluster residue number system comprising: a configured to: generate an addition and subtraction look-up table comprising 2mi cells for values from zero to (mi-1) in an ascending order twice, wherein mi is a coprime integer of a modular set of the k-cluster residue number system; in a cell at position Q of the addition and subtraction look-up table when performing an addition operation on two integers A and B, where Q= ( (A mod mi)+ (B mod mi) ) ; and in a cell at position R of the addition and subtraction look-up table when subtracting an integer X by an integer Y, where R=(X mod mi) – (Y mod mi) = (X mod mi) + (mi – (Y mod mi)) = rx + (mi – ry) = (rx + ry’), rx is equal to (X mod mi), ry is equal to (Y mod mi), and ry’ is equal to (mi - (Y mod mi)); and a coupled to the and configured to the addition and subtraction look-up table.
Under the Alice Framework Step 2A prong 2 analysis, claim 4 recites additional elements of, “store”, “processor”, “recording”, “retrieve a value recorded”, “memory”. The additional elements describe storing data in a memory, which is considered insignificant extra-solution activity see MPEP 2106.04(d)(i), and 2106.05(g). For this reason the additional elements are not integrated into a practical application.
Under the Alice Framework Step 2B, the additional elements of “store”, “processor”, “recording”, “retrieve a value recorded”, “memory” are describing merely storing data in a memory, which is well-understood, routine, conventional activity, see MPEP 2106.05(d)(II)(iv). For these reasons the additional elements and the claim as a whole do not amount to significantly more than the abstract idea.
Claim 9 is rejected for at least the reasons set forth with respect to claim 8. Claim 9 merely further limits the mathematical concept set forth in claim 8.
Under the Alice Framework Step 2A prong 1, claim 9 recites an abstract idea, including a mathematical concept. Specifically, claim 9 recites the following mathematical calculations and mathematical formulas:
“The k-cluster residue number system of claim 8, wherein the is further configured to: generate a multiplication look-up table for the coprime integer mi, wherein the coprime integer mi is not 2, and the multiplication look-up table is composed of S cells,
S
=
(
m
i
2
-
1
4
)
; and the multiplication look-up table.”
Claim 9 recites no further additional elements in the claim limitations which require a Step 2A prong 2 or Step 2B analysis. For these reasons, claim 9 is neither integrated into a practical application nor amounting to significantly more than the abstract idea.
Claim 10 is rejected for at least the reasons set forth with respect to claim 9. Claim 10 merely further limits the mathematical concept set forth in claim 9.
Under the Alice Framework Step 2A prong 1, claim 10 recites an abstract idea, including a mathematical concept. Specifically, claim 10 recites the following mathematical calculations and mathematical formulas:
“The k-cluster residue number system of claim 9, wherein the is further configured to: perform a multiplication operation on a multiplicand and a multiplicator using the multiplication look-up table by performing the following steps: determining whether a complement of the multiplicand is greater than or equal to the multiplicator; if it is determined that the complement of the multiplicand is greater than or equal to the multiplicator, perform the following steps: selecting the multiplicand as a column entry and the multiplicator as a row entry, and determining whether the column entry is greater than or equal to the row entry; if it is determined that the column entry is greater than or equal to the row entry, keeping the column entry and the row entry; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; if it is determined that the complement of the multiplicand is less than the multiplicator, perform the following steps: selecting the complement of the multiplicand as the column entry and a complement of the multiplicator as the row entry, and determining whether the column entry is greater than or equal to the complement of the row entry; if it is determined that the column entry is greater than or equal to the complement of the row entry, keeping the column entry and the row entry; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; and a value from the multiplication look-up table as a product of the multiplicand and the multiplicator according to the column entry and the row entry.”
Under the Alice Framework Step 2A prong 2 analysis, claim 10 recites additional elements of, “retrieving”. The additional elements describe retrieving data in a memory, which is considered insignificant extra-solution activity see MPEP 2106.04(d)(i), and 2106.05(g). For this reason the additional elements are not integrated into a practical application.
Under the Alice Framework Step 2B, the additional elements of “retrieving” are describing merely retrieving data in a memory, which is well-understood, routine, conventional activity, see MPEP 2106.05(d)(II)(iv). For these reasons the additional elements and the claim as a whole do not amount to significantly more than the abstract idea.
Regarding claim 11, under the Alice Framework Step 1, claim 11 falls within the four statutory categories of patentable subject matter identified by 35 USC 101: a process, machine, manufacture, or a composition of matter.
Under the Alice Framework Step 2A prong 1, claim 11 recites an abstract idea, including a mathematical concept. Specifically, claim 11 recites the following mathematical calculations and mathematical formulas:
A k-cluster residue number system, comprising: a configured to: generate a multiplication look-up table for a coprime integer mi of a modular set of the k-cluster residue number system, wherein the coprime integer mi is not 2, and the multiplication look-up table is composed of S cells,
S
=
(
m
i
2
-
1
4
)
; and perform a multiplication operation on a multiplicand and a multiplicator using the multiplication look-up table by performing the following steps: determining whether a complement of the multiplicand is greater than or equal to the multiplicator; if it is determined that the complement of the multiplicand is greater than or equal to the multiplicator, perform the following steps: selecting the multiplicand as a column entry and the multiplicator as a row entry, and determining whether the column entry is greater than or equal to the row entry; if it is determined that the column entry is greater than or equal to the row entry, keeping the column entry and the row entry; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; if it is determined that the complement of the multiplicand is less than the multiplicator, perform the following steps: selecting the complement of the multiplicand as the column entry and a complement of the multiplicator as the row entry, and determining whether the column entry is greater than or equal to the complement of the row entry; if it is determined that the column entry is greater than or equal to the complement of the row entry, keeping the column entry and the row entry; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; and a value from the multiplication look-up table as a product of the multiplicand and the multiplicator according to the column entry and the row entry; and a coupled to the and configured to the multiplication look-up table.
Under the Alice Framework Step 2A prong 2 analysis, claim 11 recites additional elements of, “retrieving”, “processor”, “memory”, and “store”. The additional elements describe storing/retrieving data in a memory, which is considered insignificant extra-solution activity see MPEP 2106.04(d)(i), and 2106.05(g). For this reason the additional elements are not integrated into a practical application.
Under the Alice Framework Step 2B, the additional elements of “retrieving”, “processor”, “memory”, and “store” are describing merely storing/retrieving data in a memory, which is well-understood, routine, conventional activity, see MPEP 2106.05(d)(II)(iv). For these reasons the additional elements and the claim as a whole do not amount to significantly more than the abstract idea.
Claim 12 is rejected for at least the reasons set forth with respect to claim 11. Claim 12 merely further limits the mathematical concept set forth in claim 11.
Under the Alice Framework Step 2A prong 1, claim 12 recites an abstract idea, including a mathematical concept. Specifically, claim 12 recites the following mathematical calculations and mathematical formulas:
“The k-cluster residue number system of claim 11, wherein the is further configured to: generate an addition and subtraction look-up table comprising 2mi cells for recording values from zero to (mi-1) in an ascending order twice; and the addition and subtraction look-up table in the of the k-cluster residue number system.”
Claim 12 recites no further additional elements in the claim limitations which require a Step 2A prong 2 or Step 2B analysis. For these reasons, claim 12 is neither integrated into a practical application nor amounting to significantly more than the abstract idea.
Claim 13 is rejected for at least the reasons set forth with respect to claim 12. Claim 13 merely further limits the mathematical concept set forth in claim 12.
Under the Alice Framework Step 2A prong 1, claim 13 recites an abstract idea, including a mathematical concept. Specifically, claim 13 recites the following mathematical calculations and mathematical formulas:
“The k-cluster residue number system of claim 12, wherein the is further configured to: a value in a cell at position Q of the addition and subtraction look-up table when performing an addition operation on two integers A and B, where Q= ( (A mod mi) + (B mod mi )).”
Under the Alice Framework Step 2A prong 2 analysis, claim 13 recites additional elements of, “retrieve”, and “recorded”. The additional elements describe storing/retrieving data in a memory, which is considered insignificant extra-solution activity see MPEP 2106.04(d)(i), and 2106.05(g). For this reason the additional elements are not integrated into a practical application.
Under the Alice Framework Step 2B, the additional elements of “retrieve”, and “recorded” are describing merely storing/retrieving data in a memory, which is well-understood, routine, conventional activity, see MPEP 2106.05(d)(II)(iv). For these reasons the additional elements and the claim as a whole do not amount to significantly more than the abstract idea.
Claim 14 is rejected for at least the reasons set forth with respect to claim 12. Claim 14 merely further limits the mathematical concept set forth in claim 12.
Under the Alice Framework Step 2A prong 1, claim 14 recites an abstract idea, including a mathematical concept. Specifically, claim 14 recites the following mathematical calculations and mathematical formulas:
“The k-cluster residue number system of claim 12, wherein the is further configured to: a value in a cell at position R of the addition and subtraction look-up table when subtracting an integer X by an integer Y, where R= (X mod mi) - (Y mod mi) = (X mod mi) + (mi - (Y mod mi) ) = rx + (mi - ry) = (rx + ry'), rx is equal to (X mod mi) , ry is equal to (Y mod mi) , and ry' is equal to (mi- (Y mod mi) ).”
Under the Alice Framework Step 2A prong 2 analysis, claim 14 recites additional elements of, “retrieve”, and “recorded”. The additional elements describe storing/retrieving data in a memory, which is considered insignificant extra-solution activity see MPEP 2106.04(d)(i), and 2106.05(g). For this reason the additional elements are not integrated into a practical application.
Under the Alice Framework Step 2B, the additional elements of “retrieve”, and “recorded” are describing merely storing/retrieving data in a memory, which is well-understood, routine, conventional activity, see MPEP 2106.05(d)(II)(iv). For these reasons the additional elements and the claim as a whole do not amount to significantly more than the abstract idea.
Allowable Subject Matter
Claims 1-14 would be allowable if rewritten or amended to overcome the rejection(s) under 35 U.S.C. 101 set forth in this Office action.
The following is a statement of reasons for the indication of allowable subject matter:
Regarding claim 1, the applicant claims a method for performing operations in a k-cluster residue number system, the method comprising:
A method for performing addition and subtraction operations in a k-cluster residue number system, the method comprising: generating an addition and subtraction look-up table comprising 2mi cells for recording values from zero to (mi-1) in an ascending order twice, wherein mi is a coprime integer of a modular set of the k-cluster residue number system; storing the addition and subtraction look-up table in a memory of the k-cluster residue number system; retrieving a value recorded in a cell at position Q of the addition and subtraction look-up table when performing an addition operation on two integers A and B, where Q= ( (A mod mi) + (B mod mi) ) ; and retrieving a value recorded in a cell at position R of the addition and subtraction look-up table when subtracting an integer X by an integer Y, where R = (X mod mi) - (Y mod mi) = (X mod mi) + (mi - (Y mod mi) ) = rx + (mi - ry) = rx + ry', rx is equal to (X mod mi) , ry is equal to (Y mod mi) , and ry' is equal to (mi- (Y mod mi) ) .
The primary reason for indication of allowable subject matter is the above italicized claim limitations in combination with the remaining claim limitations including intervening claims.
Regarding claim 4, the applicant claims a method for performing operations in a k-cluster residue number system, the method comprising:
A method for performing multiplication operations in a k-cluster residue number system, the method comprising: generating a multiplication look-up table for a coprime integer mi of a modular set of the k-cluster residue number system, wherein the coprime integer mi is not 2, the multiplication look-up table is composed of S cells,
S
=
m
i
2
-
1
4
; and storing the multiplication look-up table in a memory of the k-cluster residue number system; and performing a multiplication operation on a multiplicand and a multiplicator using the multiplication look-up table, comprising: determining whether a complement of the multiplicand is greater than or equal to the multiplicator; if it is determined that the complement of the multiplicand is greater than or equal to the multiplicator, perform the following steps: selecting the multiplicand as a column entry and the multiplicator as a row entry, and determining whether the column entry is greater than or equal to the row entry; if it is determined that the column entry is greater than or equal to the row entry, keeping the column entry and the row entry; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; if it is determined that the complement of the multiplicand is less than the multiplicator, perform the following steps: selecting the complement of the multiplicand as the column entry and a complement of the multiplicator as the row entry, and determining whether the column entry is greater than or equal to the complement of the row entry; if it is determined that the column entry is greater than or equal to the complement of the row entry, keeping the column entry and the row entry ; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; and retrieving a value from the multiplication look-up table as a product of the multiplicand and the multiplicator according to the column entry and the row entry.
The primary reason for indication of allowable subject matter is the above italicized claim limitations in combination with the remaining claim limitations including intervening claims.
Regarding claim 8, the applicant claims a k-cluster residue number system, the system comprising:
A k-cluster residue number system comprising: a processor configured to: generate an addition and subtraction look-up table comprising 2mi cells for recording values from zero to (mi-1) in an ascending order twice, wherein mi is a coprime integer of a modular set of the k-cluster residue number system; retrieve a value recorded in a cell at position Q of the addition and subtraction look-up table when performing an addition operation on two integers A and B, where Q= ( (A mod mi)+ (B mod mi) ) ; and retrieve a value recorded in a cell at position R of the addition and subtraction look-up table when subtracting an integer X by an integer Y, where R=(X mod mi) - (Y mod mi) = (X mod mi) + (mi – (Y mod mi)) = rx + (mi - ry) = (rx + ry’), rx is equal to (X mod mi), ry is equal to (Y mod mi), and ry’ is equal to (mi – ( Y mod mi)); and a memory coupled to the processor and configured to store the addition and subtraction look-up table.
The primary reason for indication of allowable subject matter is the above italicized claim limitations in combination with the remaining claim limitations including intervening claims.
Regarding claim 11, the applicant claims a k-cluster residue number system, the system comprising:
A k-cluster residue number system, comprising: a processor configured to: generate a multiplication look-up table for a coprime integer mi of a modular set of the k-cluster residue number system, wherein the coprime integer mi is not 2, and the multiplication look-up table is composed of S cells,
S
=
m
i
2
-
1
4
; and perform a multiplication operation on a multiplicand and a multiplicator using the multiplication look-up table by performing the following steps: determining whether a complement of the multiplicand is greater than or equal to the multiplicator; if it is determined that the complement of the multiplicand is greater than or equal to the multiplicator, perform the following steps: selecting the multiplicand as a column entry and the multiplicator as a row entry, and determining whether the column entry is greater than or equal to the row entry; if it is determined that the column entry is greater than or equal to the row entry, keeping the column entry and the row entry; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; if it is determined that the complement of the multiplicand is less than the multiplicator, perform the following steps: selecting the complement of the multiplicand as the column entry and a complement of the multiplicator as the row entry, and determining whether the column entry is greater than or equal to the complement of the row entry; if it is determined that the column entry is greater than or equal to the complement of the row entry, keeping the column entry and the row entry; and if it is determined that the column entry is less than the row entry, interchanging the column entry and the row entry; and retrieving a value from the multiplication look-up table as a product of the multiplicand and the multiplicator according to the column entry and the row entry; and a memory coupled to the processor and configured to store the multiplication look-up table.
The primary reason for indication of allowable subject matter is the above italicized claim limitations in combination with the remaining claim limitations including intervening claims.
Olsen (U.S. Patent Application Publication 2013/0311532 A1), hereinafter “Olsen” discloses a residue number arithmetic logic unit which supports addition, subtraction, multiplication and division operations ([0165]; Table 1). Furthermore, Olsen discloses storing look-up table result data after operations performed ([0229]). Furthermore, Olsen discloses addition, subtraction, and multiplication look-up tables (Table 2A; Table 2B; Table 2C). Furthermore, Olsen discloses, as part of multiplication operation, finding a complement value of an operand and comparing the complement in a series of steps (Fig. 15D; Fig 16A; [0614]). However, Olsen fails to teach or suggest the italicized claim limitations in combination with the remaining claim limitations as referenced above.
Mellott (U.S. Patent 7523151 B1), hereinafter “Mellott” discloses a residue number system arithmetic operating system which supports addition, subtraction, and multiplication operations (Column 5 lines 54-56 regarding Chinese remainder theorem). Furthermore, Mellot discloses mathematical functions performed by using look up tables (Column 9 lines 22-32). However, Mellott fails to teach or suggest the italicized claim limitations in combination with the remaining claim limitations as referenced above.
Rossi et al. (U.S. Patent Application Publication 2020/0310761 A1) hereinafter, “Rossi” discloses a residue number system which supports addition, subtraction and multiplication operations ([0277]). Furthermore, Rossi discloses multiplication operations may be performed utilizing look-up tables ([0333]). However, Rossi fails to teach or suggest the italicized claim limitations in combination with the remaining claim limitations as referenced above.
Conclusion
Any inquiry concerning this communication or earlier communications from the examiner should be directed to JEROME ANTHONY KLOSTERMAN II whose telephone number is (571)272-0541. The examiner can normally be reached Monday - Friday 8:30am - 3:30pm ET.
Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice.
If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Andrew Caldwell can be reached at 571-272-3702. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000.
/J.A.K./ Examiner, Art Unit 2182 /EMILY E LAROCQUE/ Primary Examiner, Art Unit 2182
Prosecution Insights