US4272827A
Expired / Lapsed
US
⏱️ 0.0 years remaining
Division processing method system having 2N-bit precision
Assignee: Fujitsu Ltd
•
Filing: 1979-03-16
•
Granted: 1981-06-09
•
Expires: 1999-03-16
Abstract
Abstract A division processing system performs 2N-bit precision division processing by effectively using division processing circuitry with N-bit precision. The system performs the division with 2N-bit precision as follows: <IMAGE> (n=N: the number of digit positions in selected binary numbers A, B, C and D). The above expression is approximated to the form of Q1+Q2x2-n (Q1, Q2: binary numbers). The binary numbers Q1 and Q2 are respectively operated on by the division processing circuitry with N-bit precision. By effective control, the error caused during the division processing of Q1 is used as a part of the data for performing the division processing of Q2, thus effectively transferring any error evolving during the processing of Q1 to Q2. The function is performed in a system having only four registers, each of N-bit capacity (precision), and an operation register, multiplication circuitry, division circuitry, and a shift circuit, affording proper control of data transfer between the registers.
Inventors
- 👤 Norio Inui
- 👤 Noriaki Kume
- 👤 Tetsuro Okamoto
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-30 05:53
CPC Classifications
G; G06; G06F; G06F7/00; G06F7/38; G06F7/48; G06F7/52; G06F7/535; G06F2207/00; G06F2207/535; G06F2207/5355
Claims Analysis
Total Claims: 16
Claim 1
Independent Claim
181 words
A method for performing division processing with 2 N-bit precision utilizing only N-bit precision components which perform at least multiplication processing and division processing, wherein the division function to be performed with 2 N-bit precision is expressed as: ##EQU22## (n=N, the number of digit positions in each of the selected binary numbers A, B, C and D) and wherein the answer to said division function is represented by: Q.sub.1 +Q.sub.2 ×2-n where Q 1 and Q 2 are binary quotients each of N bits; the method comprising the steps of: approximating said binary quotient Q 1 , in accordance with division processing of N-bit precision, to produce a Q 1 approximation which includes an error value; operating on said Q 1 approximation in accordance with said N-bit precision division processing and in conjunction with said A, B, C and D terms so as to calculate an approximation of said quotient Q 2 ; and generating said binary quotient Q 1 , from said Q 1 approximation in conjunction with said A and C terms, in accordance with N-bit precision division processing.
Claim 2
Independent Claim
181 words
A method for performing division processing with 2 N-bit precision utilizing only N-bit precision components which perform at least multiplication processing and division processing, wherein the division function to be performed with 2 N-bit precision is expressed as: ##EQU22## (n=N, the number of digit positions in each of the selected binary numbers A, B, C and D) and wherein the answer to said division function is represented by: Q.sub.1 +Q.sub.2 ×2-n where Q 1 and Q 2 are binary quotients each of N bits; the method comprising the steps of: approximating said binary quotient Q 1 , in accordance with division processing of N-bit precision, to produce a Q 1 approximation which includes an error value; operating on said Q 1 approximation in accordance with said N-bit precision division processing and in conjunction with said A, B, C and D terms so as to calculate an approximation of said quotient Q 2 ; and generating said binary quotient Q 1 , from said Q 1 approximation in conjunction with said A and C terms, in accordance with N-bit precision division processing.
Claim 3
Dependent Claim
67 words
A method as recited in claim 1, further comprising the step of calculating said Q 2 quotient based on the value of at least the term D, and wherein said operating step comprises extracting the error value from said Q 1 approximation, and transferring said extracted error value to the term D in said Q 2 quotient, whereby said approximation of said quotient Q 2 is calculated.
Claim 4
Dependent Claim
67 words
A method as recited in claim 1, further comprising the step of calculating said Q 2 quotient based on the value of at last the term B, and wherein said operating step comprises extracting the error value from said Q 1 approximation, and transferring said extracted error value to the term B in said Q 2 quotient, whereby said approximation of said quotient Q 2 is calculated.
Claim 5
Independent Claim
176 words
A method for performing division processing with 2 N-bit precision utilizing only N-bit precision components which perform at least multiplication processing and division processing, wherein the division function to be performed with 2 N-bit precision is expressed as: ##EQU23## (n=N, the number of digit position in each of the selected binary numbers A, B, C and D) and wherein the answer to said division function is represented by: Q.sub.1 +Q.sub.2 ×2-n where Q 1 and Q 2 are binary quotients each of N bits; the method comprising the steps of: calculating binary quotient C/A, in accordance with division processing of N-bit precision, to produce a Q 1 approximation which includes an error value; operating on said C/A quotient in accordance with said N-bit precision division processing and in accordance with said A, B, C and D terms so as to calculate an approximation of said quotient Q 2 ; and generating said binary quotient Q 1 from said binary quotient C/A in conjunction with said A and C terms in accordance with N-bit precision division processing.
Claim 6
Independent Claim
176 words
A method for performing division processing with 2 N-bit precision utilizing only N-bit precision components which perform at least multiplication processing and division processing, wherein the division function to be performed with 2 N-bit precision is expressed as: ##EQU23## (n=N, the number of digit position in each of the selected binary numbers A, B, C and D) and wherein the answer to said division function is represented by: Q.sub.1 +Q.sub.2 ×2-n where Q 1 and Q 2 are binary quotients each of N bits; the method comprising the steps of: calculating binary quotient C/A, in accordance with division processing of N-bit precision, to produce a Q 1 approximation which includes an error value; operating on said C/A quotient in accordance with said N-bit precision division processing and in accordance with said A, B, C and D terms so as to calculate an approximation of said quotient Q 2 ; and generating said binary quotient Q 1 from said binary quotient C/A in conjunction with said A and C terms in accordance with N-bit precision division processing.
Claim 7
Dependent Claim
243 words
A method as recited in claim 4 utilizing a decoder circuit and an adder, wherein said step of calculating C/A includes: decoding the value A to define a value R 0 such that the product A×R 0 approaches a value of 1, determining a first error value as the error of A×R 0 relative to said value of 1, processing the said first error value to derive a further term R 1 where the product A×R 0 ×R 1 more closely approaches the value of 1, deriving a further error value as the error of A×R 0 ×R 1 relative to said value of 1, deriving successively, such further error values to define a product A×R 0 ×R 1 ×R 2 . . . approaching the value of 1 to a desired degree, and performing the multiplication C×R 0 ×R 1 ×R 2 . . . to produce the quotient C/A; and wherein the method includes the additional step of storing the quotient result of the operation C/A; and wherein said operating step comprises: extracting said error value from the C/A quotient by performing C-A×(C/A) to produce said error value included in C/A, transferring said error value to the term D to define a term D", performing the multiplication D"×R 0 ×R 1 ×R 2 . . . , determining the value BC/A 2 , and performing the operations (D"/A)-(BC/A 2 ), whereby to derive said approximation of said quotient Q 2 .
Claim 8
Dependent Claim
62 words
A method as recited in claim 4, wherein said operating step comprises: extracting said error value from the C/A quotient, and transferring the error value to the term B to produce a term B", performing the operation B"C/A 2 , storing the resultant value of the operation B"C/A 2 , determining the value D/A, and performing subtraction to produce (D/A)-(B"C/A 2 ).
Claim 9
Dependent Claim
62 words
A method as recited in claim 4, wherein said operating step comprises: extracting said error value from the C/A quotient, and transferring the error value to the term D to produce a term D", performing the operation BC/A 2 , storing the resultant value of the operation BC/A 2 , determining the value D"/A, and performing subtraction to produce (D"/A)-(BC/A 2 ).
Claim 10
Independent Claim
213 words
A system for performing division processing with 2 N-bit precision, wherein the division function to be performed with 2 N-bit precision is expressed as: ##EQU24## (n=N, the number of digit positions in each of the selected binary numbers A, B, C and D) and wherein the answer to said division function is represented by Q 1 +Q 2 ×2 -n , where Q 1 and Q 2 are each N-bit binary quotients said system comprising: means for division processing at least two of said selected binary numbers, in accordance with division processing of N bit precision, to produce a Q 1 approximation; means for receiving said Q 1 approximation from said division processing means and for calculating an error value relating said Q 1 approximation to said Q 1 quotient; means for storing said Q 1 approximation from said division processing means and said error value from said error value calculating means; additional means for processing said selected binary numbers in accordance with said error value from said error value calculating means, and in accordance with division processing of N-bit precision, to produce an approximation of said Q 2 quotient; and further means for generating said binary quotient Q 1 from said Q 1 approximation in conjunction with said A and C terms.
Claim 11
Independent Claim
213 words
A system for performing division processing with 2 N-bit precision, wherein the division function to be performed with 2 N-bit precision is expressed as: ##EQU24## (n=N, the number of digit positions in each of the selected binary numbers A, B, C and D) and wherein the answer to said division function is represented by Q 1 +Q 2 ×2 -n , where Q 1 and Q 2 are each N-bit binary quotients said system comprising: means for division processing at least two of said selected binary numbers, in accordance with division processing of N bit precision, to produce a Q 1 approximation; means for receiving said Q 1 approximation from said division processing means and for calculating an error value relating said Q 1 approximation to said Q 1 quotient; means for storing said Q 1 approximation from said division processing means and said error value from said error value calculating means; additional means for processing said selected binary numbers in accordance with said error value from said error value calculating means, and in accordance with division processing of N-bit precision, to produce an approximation of said Q 2 quotient; and further means for generating said binary quotient Q 1 from said Q 1 approximation in conjunction with said A and C terms.
Claim 12
Dependent Claim
42 words
A system as recited in claim 8, wherein said Q 1 approximation=C/A and said Q 2 approximation=(D"/A)-(BC/A 2 ); and said additional means for division processing comprises means for transferring said error value to D so as to define said term D".
Claim 13
Dependent Claim
42 words
A system as recited in claim 8, wherein said Q 1 approximation=C/A and said Q 2 approximation=(D/A)-(B"C/A 2 ); and said additional means for division processing comprises means for transferring said error value to B so as to define the term B".
Claim 14
Dependent Claim
179 words
A system as recited in claim 8, wherein said Q 1 approximation=C/A; and said means for division processing to produce said Q 1 approximation comprises: means for decoding the value A to define a value R 0 such that the product A×R 0 approaches a value of 1; means for determining a first error value as the error of A×R 0 with respect to said value of 1; means for processing said first error value from said first error value determining means to derive a further term R 1 where the product A×R 0 ×R 1 more closely approaches the value of 1; means for determining a further error value as the error of A×R 0 ×R 1 with respect to said value of 1; means for successively deriving such further error values to define a product A×R 0 ×R 1 ×R 2 . . . approaching the value of 1 to a desired degree; and means for performing the multiplication C×R 0 ×R 1 ×R 2 . . . to produce the quotient C/A and said error value.
Claim 15
Dependent Claim
75 words
A system as recited in claim 11, wherein said additional means for processing said selected binary numbers comprises: means for transferring said error value to the binary number D, thereby defining a term D"; means for performing the multiplication D"×R 0 ×R 1 ×R 2 . . . to obtain D"/A; means for determining the value BC/A 2 ; and means for performing the operation D"/A-BC/A 2 to obtain the approximation of Q 2 .
Claim 16
Dependent Claim
75 words
A system as recited in claim 11, wherein said additional means for processing said selected binary numbers comprises: means for transferring said error value to the binary number B, thereby defining a term B"; means for performing the multiplication D×R 0 ×R 1 ×R 2 . . . to obtain D/A; means for determining the value B"C/A 2 ; and means for performing the operating D/A-B"C/A 2 to obtain the approximation of Q 2 .
References Cited (Backward Citations)
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1984-06-08 | 1984-12-08 | 1985-06-09 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1988-06-08 | 1988-12-08 | 1989-06-09 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1992-06-08 | 1992-12-08 | 1993-06-09 | $7700.00 | Window Closed / Lapsed |