CN101276268A - Method for computing remainder of mode number division of integer - Google Patents

Method for computing remainder of mode number division of integer Download PDF

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Publication number
CN101276268A
CN101276268A CNA2008100976969A CN200810097696A CN101276268A CN 101276268 A CN101276268 A CN 101276268A CN A2008100976969 A CNA2008100976969 A CN A2008100976969A CN 200810097696 A CN200810097696 A CN 200810097696A CN 101276268 A CN101276268 A CN 101276268A
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input parameter
divisor
treatment scheme
remainder
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CN101276268B (en
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黄建
徐晶
丁国荣
许炜
范兵
汪进
陈丽萍
张伟伟
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Wuhan Fisee Technology Co., Ltd.
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WUHAN FISEE TECHNOLOGY Co Ltd
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Abstract

The present invention provides a method of counting remainder of module division of integer, relating to a method of counting module, characterized in that the counting step includes following: 1. judging size relation of M and D; 2. changing the dividend M to bit; 3. determining numbers of pipeline treatment the first level input parameter according to the dividend M; 4. checking the remainder table stored in the counting device according to the results of coefficients Mi(i=n-1) of each weight, obtaining ri(i=0,1...n-1); 5. ensuring the input parameter of the pipeline treatment the first level; 6. ensuring pipeline level numbers and amount of sub-treating program of each level; 7. ensuring the input parameter of sub-treating flow; 8. starting the counting process of sub-treating process; 9. judging whether all the sub-treating processes being completed or not, if no, changing to the step 7, otherwise, the finally counting result is value of the remainder. The method of counting remainder of module division of integer adopts a pipeline treatment mode, convenient for hardware implementation, overcoming the deficiency of large counting amount of the traditional iterative method, and having no limit to the divisor and the dividend.

Description

A kind of method of remainder of modulus division of computes integer
Technical field
The present invention relates to calculate the method for modulus, specifically a kind of method of remainder of modulus division of computes integer.
Background technology
The modulus value n of integer m is designated as it m mod n usually.Ask the modulus of integer that very big realistic meaning is arranged, because all need to ask the modulus of integer under many circumstances, such as at some load-balancing method, packet switch and transmission, digital massage volume/decoding, computer graphics, division arithmetic is medium.
Problem aspect in the algorithm of existing delivery, having two:
1) traditional algorithm realizes that by iteration the mode of this iteration makes to calculate needs very big calculated amount.If divisor D=2N-1 (N is a natural number) is a n position integer, dividend M is for being less than or equal to (D-1) 2Any positive integer, be 2n position integer when promptly M is maximum, traditional alternative manner needs 6n condition test, 2n time multiplication (or displacement) and 2n sub-addition.Therefore entire method needs 10n time also do not comprise assign operation.This shows that calculated amount is big, but dividend and divisor can be got arbitrary value.
2) patent 99109437.9 proposes a kind of non-alternative manner that calculates the remainder of modulus division, has solved the big problem of calculated amount that causes owing to iteration, and this algorithm does not rely on the figure place of modulo operation divisor.The value that it is exactly divisor that but this algorithm has two preconditions must equal 2N-1 (N is a natural number), and the value of dividend should be less than or equal to (D-1) 2, but more than or equal to 0.This just illustrates that this computing method can not be applied to dividend and divisor is that arbitrary value gets situation.
Summary of the invention
The objective of the invention is to overcome above-mentioned weak point, a kind of method of remainder of modulus division of computes integer is provided, this method adopts pipeline processing mode, being convenient to hardware realizes, overcome the big deficiency of calculated amount of traditional alternative manner, and do not had specific restriction for divisor and dividend.
For reaching above purpose, the technical scheme that the present invention takes is:
A kind of method of remainder of modulus division of computes integer is characterized in that: its calculation procedure is as follows:
(1) obtain dividend M, divisor D by the input equipment that is connected with calculation element or by the memory device that is connected with calculation element, judge the magnitude relationship of M and D: if M<D, then remainder R=M finishes to calculate, otherwise changes (2);
(2) convert dividend M to binary digit M=M 0* 2 0+ M 1* 2 1+ ... + M N-1* 2 N-1, obtain the coefficient M of each weights i(i=0 n-1) and binary figure place n;
(3) determine the number of the 1st grade of input parameter of pipeline processes according to dividend M: if 2 j<M≤2 2j, wherein j for the set 1,2,4 ..., 2 mIn a value, m is a natural number, so the number N=2j of the 1st grade of input parameter of pipeline processes;
(4) according to the coefficient M of each weights iThe result look into the remainder table that is stored in the calculation element, obtain r i(i=0,1 ... n-1): work as M i=1 (obtains during i=0~n-1) that divisor D is expert at and M in the remainder table iCorresponding weights 2 iThe value r of column i, work as M i=0 o'clock, r i=0;
(5) determine the input parameter of the 1st grade of pipeline processes: know that by (3) the 1st grade of pipeline processes has N input parameter, by (2) the figure place n when knowing that dividend is expressed as scale-of-two, this N input parameter R so 1i(i=0 ... N-1) parameters R of the n in 1i(i=0 ... n-1) be resulting r in (4) i(i=0,1 ... n-1) value, a remaining N-n input value is 0, i.e. R 1i=0 (i=n ... N-1);
(6) determine the quantity of pipeline series and every grade of sub-handling procedure: know that by (3) the 1st level production line handles the number N=2j of input parameter, then N=2 q, i.e. j=2 Q-1, pipeline processes progression is q so, the 1st level production line is handled 2 Q-1Individual sub-treatment scheme, by that analogy, the k level production line is handled 2 Q-k+1Individual input parameter has 2 Q-kIndividual sub-treatment scheme;
(7) determine the input parameter of sub-treatment scheme: each sub-treatment scheme has two input parameters, handles always having 2 for the k level production line Q-k+1Individual input parameter R Ki(i=0,1 ..., 2 Q-k+1-1), with this 2 Q-k+1Individual input parameter divides into groups in twos, as 2 Q-kThe input of individual sub-treatment scheme, i.e. i-1, i (i=2,4,6 ... 2 Q-k+1) individual parameters R K (i-2), R K (i-1)Two input parameters as i/2 sub-treatment scheme;
(8) computation process of the sub-treatment scheme of beginning: at first with these two input parameter additions, with must be more than or equal to 0 and less than the divisor of twice, judge then and with the size of divisor, if gained and less than divisor, so after the addition and as the input parameter of next stage, if gained and more than or equal to divisor and less than the divisor of twice, so with and deduct divisor, with the input parameter of this difference as next stage;
(9) the sub-treatment scheme that judges whether all grades all disposes, and do not change step (7), otherwise final calculation result is the value of remainder.
The present invention has the following advantages:
1. the employing pipeline processing mode is convenient to hardware and is realized,
2. overcome the big deficiency of calculated amount of traditional alternative manner,
3. there is not specific restriction for divisor and dividend.
Description of drawings
The present invention has following accompanying drawing:
Fig. 1 is the process flow diagram of remainder of the modulus division of computes integer;
Fig. 2 is the processing logic process flow diagram of the sub-treatment scheme of streamline;
Fig. 3 is the process flow diagram of the sub-treatment scheme of single-stage of streamline;
Embodiment
Below in conjunction with accompanying drawing the present invention is described in further detail.
Fig. 1 is the process flow diagram of remainder of the modulus division of computes integer, and as shown in Figure 1, its calculation procedure is as follows:
(1) obtain dividend M, divisor D by the input equipment that is connected with calculation element or by the memory device that is connected with calculation element, judge the magnitude relationship of M and D: if M<D, then remainder R=M finishes to calculate, otherwise changes (2);
(2) convert dividend M to binary digit M=M 0* 2 0+ M 1* 2 1+ ... + M N-1* 2 N-1, obtain the coefficient M of each weights i(i=0 n-1) and binary figure place n;
(3) determine the number of the 1st grade of input parameter of pipeline processes according to dividend M: if 2 j<M≤2 2j, wherein j for the set 1,2,4 ..., 2 mIn a value, m is a natural number, so the number N=2j of the 1st grade of input parameter of pipeline processes;
(4) according to the coefficient M of each weights iThe result look into the remainder table that is stored in the calculation element, obtain r i(i=0,1 ... n-1): work as M i=1 (obtains during i=0~n-1) that divisor D is expert at and M in the remainder table iCorresponding weights 2 iThe value r of column i, work as M i=0 o'clock, r i=0;
(5) determine the input parameter of the 1st grade of pipeline processes: know that by (3) the 1st grade of pipeline processes has N input parameter, by (2) the figure place n when knowing that dividend is expressed as scale-of-two, this N input parameter R so 1i(i=0 ... N-1) parameters R of the n in 1i(i=0 ... n-1) be resulting r in (4) i(i=0,1 ... n-1) value, a remaining N-n input value is 0, i.e. R 1i=0 (i=n ... N-1);
(6) determine the quantity of pipeline series and every grade of sub-handling procedure: know that by (3) the 1st level production line handles the number N=2j of input parameter, then N=2 q, i.e. j=2 Q-1, pipeline processes progression is q so, the 1st level production line is handled 2 Q-1Individual sub-treatment scheme, by that analogy, the k level production line is handled 2 Q-k+1Individual input parameter has 2 Q-kIndividual sub-treatment scheme;
(7) determine the input parameter of sub-treatment scheme: each sub-treatment scheme has two input parameters, handles always having 2 for the k level production line Q-k+1Individual input parameter R Ki(i=0,1 ..., 2 Q-k+1-1), with this 2 Q-k+1Individual input parameter divides into groups in twos, as 2 Q-kThe input of individual sub-treatment scheme, i.e. i-1, i (i=2,4,6 ... 2 Q-k+1) individual parameters R K (i-2), R K (i-1)Two input parameters as i/2 sub-treatment scheme;
(8) computation process of the sub-treatment scheme of beginning: at first with these two input parameter additions, with must be more than or equal to 0 and less than the divisor of twice, judge then and with the size of divisor, if gained and less than divisor, so after the addition and as the input parameter of next stage, if gained and more than or equal to divisor and less than the divisor of twice, so with and deduct divisor, with the input parameter of this difference as next stage;
(9) the sub-treatment scheme that judges whether all grades all disposes, and do not change step (7), otherwise final calculation result is the value of remainder.
Fig. 2 has provided the processing logic flow process of the sub-treatment scheme of streamline, i.e. the process flow diagram of whole sub-treatment schemees, and Fig. 3 has provided the process flow diagram of the sub-treatment scheme of single-stage of streamline, i.e. the process flow diagram of the sub-treatment scheme of each in each level production line.Said remainder table can adopt existing techniques in realizing, and for example the remainder table can adopt the form of table 1:
The structure of table 1 remainder table
Figure A20081009769600081
Wherein each divisor of line display D tabulates and shows all scale-of-two weights 2 i, r iIt is the binary digit 2 of its column iThe mould value of being expert at divisor D, i.e. r i=2 iMod D.
Table 2 is a specific embodiment of remainder table:
Table 2 remainder table
Figure A20081009769600082
Below in conjunction with table 2, accompanying drawing, further specify computing method of the present invention by specific embodiment:
Suppose to obtain dividend M=29, divisor D=3 by the input equipment that is connected with calculation element or by the memory device that is connected with calculation element, the remainder table that is stored in the calculation element stores the information shown in the table 2, and its concrete calculation procedure is:
(1) magnitude relationship of judgement M and D, because 29>3, change (2);
(2) dividend 29 is converted into 11101, i.e. 29=1 * 2 0+ 0 * 2 1+ 1 * 2 2+ 1 * 2 3+ 1 * 2 4, M then 0=1, M 1=0, M 2=1, M 3=1, M 4=1, figure place n=5;
(3) determine the number of the 1st grade of input parameter of pipeline processes according to dividend M: when j=4, satisfy 2 4=16<29≤2 8=256, and 4 for the set { 1,2,4,8,16 ... 2 mIn a value, the number N=2j=8 of the 1st grade of input parameter of pipeline processes then;
(4) the coefficient M of each weights that obtain according to (2) iThe result look into the remainder table, obtain r i(i=0,1 ... n-1): know M by (2) 0=1, M 2=1, M 3=1, M 4=1, the 1st, 3,4,5 row of looking into the remainder table obtain r 0=1, r 2=1, r 3=2, r 4=1, and M 1=0 r so 1=0, so r iValue be:
r 0=1,r 1=0,r 2=1,r 3=2,r 4=1;
(5) determine the input parameter of the 1st grade of pipeline processes: know that by (3) the 1st grade of pipeline processes has N=8 input parameter, figure place n=5 when knowing that by (2) dividend 29 is expressed as scale-of-two.This 8 input parameter R so 1i(i=0 ... 7) 5 parameters R in 1i(i=0 ... n-1) be resulting r in (4) i(i=0,1 ... n-1) value, i.e. R 10=1, R 11=0, R 12=1, R 13=2, R 14=1,3 remaining input values are 0, i.e. R 15=0, R 16=0, R 17=0;
(6) determine the quantity of pipeline series and every grade of sub-handling procedure: know that by (3) the 1st level production line handles the number N=2j=8=2 of input parameter 3, i.e. q=3, then j=2 3-1=2 2=4, pipeline processes progression is q=3 so, and the 1st level production line is handled 2 Q-1=4 sub-treatment schemees, by that analogy, the 2nd level production line is handled 2 Q-k+1=2 3-2+1=4 input parameters have 2 Q-k=2 3-2=2 sub-treatment schemees, the 3rd level pipeline processes has 2 Q-k+1=2 3-3+1=2 input parameters have 2 Q-k=2 3-3=1 sub-treatment scheme;
(7) determine the input parameter of sub-treatment scheme: handle for the 1st level production line, have 2 Q-k+1=2 3-1+1=8 input parameter R 1i(i=0,1 ..., 7), these 8 input parameters are divided into groups in twos, as 2 Q-k=2 3-1The input of=4 sub-treatment schemees, promptly the 1st, 2 (i-1, i (i=2,4,6 ... 2 Q-k+1)) individual parameters R 10, R 11(R K (i-2), R K (i-1)) as two input parameters of the 1st sub-treatment scheme, the 3rd, 4 parameters R 12, R 13As two input parameters of the 2nd sub-treatment scheme, the 5th, 6 parameters R 14, R 15As two input parameters of the 3rd sub-treatment scheme, the 7th, 8 parameters R 16, R 17Two input parameters as the 4th sub-treatment scheme;
(8) computation process of the sub-treatment scheme of beginning: in the 1st level production line, two input parameters of the 1st sub-treatment scheme are R 10, R 11, R 10+ R 11=0+1=1, gained and less than divisor, R then 20=1; In the 1st level production line, two input parameters of the 2nd sub-treatment scheme are R 12, R 13, R 12+ R 13=1+2=3, gained and equal divisor and less than the divisor of twice, then with and deduct divisor 3-3=0,0 less than divisor, then R 21=3-3=0; In the 1st level production line, two input parameters of the 3rd sub-treatment scheme are R 14, R 15, R 14+ R 15=1+0=1, then R 22=1; In the 1st level production line, two input parameters of the 4th sub-treatment scheme are R 16, R 17, R 16+ R 17=0, R then 23=0; So far finished the whole sub-treatment scheme of the 1st level production line; R 20=1, R 21=0, R 22=1, R 23=0;
(9) the sub-treatment scheme that judges whether all grades all disposes, because pipeline processes progression is 3, so change step (7);
(7) determine the input parameter of sub-treatment scheme: handle for the 2nd level production line, have 2 Q-k+1=2 3-2+1=4 input parameter R KiDivide into groups these 4 input parameters, in twos as 2 (i=0,1,2,3) Q-k=2 3-2The input of=2 sub-treatment schemees, i.e. the 1st, 2 parameters R 20, R 21As two input parameters of the 1st sub-treatment scheme, the 3rd, 4 parameters R 22, R 23Two input parameters as the 2nd sub-treatment scheme;
(8) computation process of the sub-treatment scheme of beginning: in the 2nd level production line, two input parameters of the 1st sub-treatment scheme are R 20, R 21, R 20+ R 21=1, gained and less than divisor, R then 30=1; In the 2nd level production line, two input parameters of the 2nd sub-treatment scheme are R 22, R 23, R 22+ R 23=1, gained and less than divisor, R then 31=1; So far finished the whole sub-treatment scheme of the 2nd level production line; R 30=1, R 31=1;
(9) the sub-treatment scheme that judges whether all grades all disposes, because pipeline processes progression is 3, so change step (7);
(7) determine the input parameter of sub-treatment scheme:, have 2 for the 3rd level pipeline processes Q-k+1=2 3-3+1=2 input parameter R Ki(i=0,1) is divided into one group with these 2 input parameters, as 2 Q-k=2 3-3The input of=1 sub-treatment scheme, i.e. the 1st, 2 parameters R 30, R 31Two input parameters as the 1st sub-treatment scheme;
(8) computation process of the sub-treatment scheme of beginning: in the 3rd level streamline, two input parameters of the 1st sub-treatment scheme are R 30, R 31, R 30+ R 31=2, gained and less than divisor; So far finished the whole sub-treatment scheme of 3rd level streamline;
(9) the sub-treatment scheme that judges whether all grades all disposes, because pipeline processes progression is 3, so the sub-treatment scheme of all grades all disposes so remainder R=R 30+ R 31=2, i.e. 29 mod 3=2.By this specific embodiment as can be known: the method for the modulus of computes integer of the present invention (remainder of division) is feasible, and the result is accurately.The method of the modulus of computes integer of the present invention adopts pipeline processing mode, is convenient to hardware and realizes that system overhead is little, computing velocity is fast, overcome the big deficiency of calculated amount of traditional alternative manner, and do not had specific restriction, very wide application prospect has been arranged for divisor and dividend.

Claims (1)

1. the method for the remainder of the modulus division of a computes integer, it is characterized in that: its calculation procedure is as follows:
(1) obtain dividend M, divisor D by the input equipment that is connected with calculation element or by the memory device that is connected with calculation element, judge the magnitude relationship of M and D: if M<D, then remainder R=M finishes to calculate, otherwise changes (2);
(2) convert dividend M to binary digit M=M 0* 2 0+ M 1* 2 1+ ... + M N-1* 2 N-1, obtain the coefficient M of each weights i(i=0 n-1) and binary figure place n;
(3) determine the number of the 1st grade of input parameter of pipeline processes according to dividend M: if 2 j<M≤2 2j, wherein j for the set 1,2,4 ..., 2 mIn a value, m is a natural number,
The number N=2j of the 1st grade of input parameter of pipeline processes so;
(4) according to the coefficient M of each weights iThe result look into the remainder table that is stored in the calculation element, obtain r i(i=0,1 ... n-1): work as M i=1 (obtains during i=0~n-1) that divisor D is expert at and M in the remainder table iCorresponding weights 2 iThe value r of column i, work as M i=0 o'clock, r i=0;
(5) determine the input parameter of the 1st grade of pipeline processes: know that by (3) the 1st grade of pipeline processes has N input parameter, by (2) the figure place n when knowing that dividend is expressed as scale-of-two, this N input parameter R so 1i(i=0 ... N-1) parameters R of the n in 1i(i=0 ... n-1) be resulting r in (4) i(i=0,1 ... n-1) value, a remaining N-n input value is 0, i.e. R 1i=0 (i=n ... N-1);
(6) determine the quantity of pipeline series and every grade of sub-handling procedure: know that by (3) the 1st level production line handles the number N=2j of input parameter, then N=2 q, i.e. j=2 Q-1, pipeline processes progression is q so, the 1st level production line is handled 2 Q-1Individual sub-treatment scheme, by that analogy, the k level production line is handled 2 Q-k+1Individual input parameter has 2 Q-kIndividual sub-treatment scheme;
(7) determine the input parameter of sub-treatment scheme: each sub-treatment scheme has two input parameters, handles always having 2 for the k level production line Q-k+1Individual input parameter R Ki(i=0,1 ..., 2 Q-k+1-1), with this 2 Q-k+1Individual input parameter divides into groups in twos, as 2 Q-kThe input of individual sub-treatment scheme, i.e. i-1, i (i=2,4,6 ... 2 Q-k+1) individual parameters R K (i-2), R K (i-1)Two input parameters as i/2 sub-treatment scheme;
(8) computation process of the sub-treatment scheme of beginning: at first with these two input parameter additions, with must be more than or equal to 0 and less than the divisor of twice, judge then and with the size of divisor, if gained and less than divisor, so after the addition and as the input parameter of next stage, if gained and more than or equal to divisor and less than the divisor of twice, so with and deduct divisor, with the input parameter of this difference as next stage;
(9) the sub-treatment scheme that judges whether all grades all disposes, and do not change step (7), otherwise final calculation result is the value of remainder.
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CN110088727A (en) * 2016-12-12 2019-08-02 皇家飞利浦有限公司 It is arranged to calculate the electronic computing device of the product of integer
CN111813375A (en) * 2020-08-14 2020-10-23 Oppo广东移动通信有限公司 Modulo arithmetic processing method and related product

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CN111813375A (en) * 2020-08-14 2020-10-23 Oppo广东移动通信有限公司 Modulo arithmetic processing method and related product

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