CN103297196A - Cyclic redundancy check algorithm of non-integral byte data - Google Patents

Abstract

The invention discloses a cyclic redundancy check algorithm of non-integral byte data. The cyclic redundancy check algorithm of the non-integral byte data comprises obtaining a CRC16 value of a fist byte S0 through directly looking up a table of Crcl6-Table [S0]; performing exclusive or on Bn and a n bits higher CH of the CRC16 value a last byte and performing the exclusive or result as a subscript to be looked up the table to obtain Crcl6-Table [(CH+Bn)]; and performing exclusive or on a n bits left shifted (16-n) bits and the table looked up value Crcl6-Table [(CH+Bn)]. The value relationship of n is that n is equal to 8 when an integral byte CRC 16 is calculated and the n is the actual bite when the CRC 16 which not satisfies a bite. The cyclic redundancy check algorithm of the non-integral byte data has the advantages of being applicable to a situation that input information which is a non-integral byte cannot be calculated according to the bites, greatly improving the calculation efficiency, reducing the calculation time, releasing a large number of CPU (Central Processing Unit) resources and reducing power consumption of the CPU.

Description

A kind of cyclic redundancy check (CRC) algorithm of non-whole byte data

Technical field

The present invention relates to a kind of cyclic redundancy check (CRC) algorithm of non-whole byte data.

Background technology

In various data communication, generally all will transmit after the packet, additional data Frame Check Sequence after grouped data (Frame Check Sequence, be called for short FCS) carries out error control, with the correctness of the transmission that guarantees data.In the realization of Frame Check Sequence, cyclic redundancy check (CRC) code (Cyclic Redundancy Code, be called for short CRC) obtained to use widely with its high efficiency, high-performance, be a kind of method that improves data communication reliability that generally adopts in the present data transmission procedure.

Data are in process of transmitting, and the data that transmitting terminal will need to transmit are carried out the CRC check yardage and calculated, and check code is attached to sends together after transmitting data.Receiving terminal need carry out check code to the data that receive with same computational methods and calculate, and then the CRC sign indicating number that calculates and the CRC sign indicating number that receives is compared, if the consistent transfer of data that illustrates is errorless, if inconsistent explanation transfer of data is wrong.

The computational efficiency of CRC and time of delay all are the keys of CRC coding techniques all the time, determine directly whether it can use in the reality.At present, the computational methods of CRC, there is step-by-step calculating and calculates two kinds of distinct modes by byte, calculate the computational efficiency height by byte mode, in the computational process cycle-index for the position mode calculate 1/8, and calculate weak point consuming time and controlled, byte mode is by tabling look-up to finish calculating, weak point consuming time and fixing, calculate by the condition judgment executive mode more than the position mode and to be more suitable for the real-time embedded system, although the byte mode superiority is obvious, but its practical application has the stringent condition requirement: transmission information is necessary for the integer byte, transmission information is that just the having only of service condition that the non-integer byte does not satisfy byte mode uses the position mode to calculate the CRC that transmits information sequence, and efficient is extremely low, seriously restricts the real-time response performance of product.

Summary of the invention

The objective of the invention is to overcome the deficiencies in the prior art, providing a kind of can be to use under the satisfied service condition of calculating by byte mode of non-integer byte in transmission information, improved computational efficiency greatly, shortened computing time, discharged a large amount of cpu resources, reduce the requirement to cpu performance and operation clock, reduced the cyclic redundancy check (CRC) algorithm of a kind of non-whole byte data of CPU power consumption.

The objective of the invention is to be achieved through the following technical solutions: a kind of cyclic redundancy check (CRC) algorithm of non-whole byte data, CRC mathematics essence be to the transmission message polynomial to the complementation of CRC generator polynomial, the generator polynomial of CRC16 is:

G (x)=x ¹⁶+ x ¹²+ x ⁵+ 1, its computational methods are: with 16 0 back of adding S (x) to, just

S (x)=r ¹⁶* S (x), wherein r=2 is the base of binary system multinomial operation, S (x) does division arithmetic to generator polynomial G (x) then, namely carries out the logic xor operation, obtains the remainder part of division at last, is CRC16, abbreviates C as _Reg, and merchant's part is called for short M (x), it may further comprise the steps:

S1: suppose S _mCorresponding CRC16 value is C _Reg, by definition, then:

${\mathrm{CRC}}_{S_m}=(R^2*S_m)\mathrm{Mod}\left(G\left(x\right)\right)=G_{\mathrm{reg}}=\mathrm{Crc}16\_\mathrm{Table}\left[S_m\right]$ (formula 1)

R ²* S _m=M (x) * G (x)+C _Reg(formula 2)

S2: at S _mThe back increases byte information position of less than, n position, forms a new binary system multinomial S' _m, calculate S' _mCRC16, it may further comprise the steps:

S201: at S _mThe back increases byte information position of less than, n position, forms a new binary system multinomial S' _m,

S' _m=r ⁿ* S _m+ B _n(formula 3)

B _nExpression n position binary system multinomial, wherein high-order preceding, low level after.

S202: to S' _mIncrease by 16 0 operations and guarantee that remainder directly is exactly the CRC16 result of data flow:

R ²* S' _m=R ²* (r ⁿ* S _m+ B _n)=r ⁿ* (R ²* S _m)+R ²* B _n(formula 4)

Substituting formula 2 into, formula 4 gets:

R ²*S' _m=rn*(M(x)*G(x)+C _reg)+R ²*B _n

=(r ⁿ* M (x) * G (x))+r ⁿ* C _Reg+ R ²* B _n(formula 5)

Make C _HExpression C _RegHigh n position, C _LExpression C _RegLow (16-n) position,

C _Reg=r ^(16-n)* C _H+ C _L(formula 6)

Formula 6 substitution formulas 5 are got:

R ²* S' _m=(r ⁿ* M (x) * G (x))+R ²* C _H+ r ⁿ* C _L+ R ²* B _n(formula 7)

=(r ⁿ*M(x)*G(x))+R ²*(C _H+B _n)+r ⁿ*C _L

Known by the CRC definition: (r ⁿ* Mod (G (x)) ≡ 0 (formula 8) M (x) * G (x))

$(R^2*(C_H+B_n))\mathrm{Mod}\left(G\left(x\right)\right)={\mathrm{CRC}}_{C_H+B_n}=\mathrm{Crc}16\_\mathrm{Table}[C_H+B_n]$

$(r^n*C_L)\mathrm{Mod}\left(G\left(x\right)\right)=r^n*C_L$

By logic or the associativity of operation, formula 7 and formula 8:

(R ²* S' _m) Mod (G (x))=Crc16_Table[C _H+ B _n]+r ⁿ* C _L(formula 9)

That is:

${\mathrm{CRC}}_{S_m^{\′}}=\mathrm{Crc}16\_\mathrm{Table}\left[(C_H+B_n)\right]+r^n*C_L.$ (formula 10)

S3: by formula 10 as can be known, the CRC16 that calculates current data finishes in two steps, and concrete steps are as follows;

S301: the high n position C that will go up the CRC16 value of a byte _HAnd B _nThe phase XOR, the XOR result tables look-up as subscript and obtains Crc16_Table[(C _H+ B _n)];

S302: will go up behind low (16-n) lt n position of CRC16 of a byte and the value of tabling look-up Crc16_Table[(C _H+ B _n)] the phase XOR.

S4: calculate the CRC16 of random length byte, it may further comprise the steps:

S401: the first byte S of the stream that fetches data ₀As the subscript Crc16_Table[S that tables look-up ₀] obtain S ₀Current C RC16 value;

S402: in order all can be finished CRC16 according to byte by the part that byte is handled and calculate;

S403: the actual bit of getting n and be remaining data is counted substitution formula 10, finishes the calculating of the not enough byte portion C RC16 of residue;

S404: the CRC16 result that the current C RC16 value that obtains in conjunction with S401, S402 and S403, the CRC result who calculates according to byte and not enough byte portion C RC result obtain whole data.

The invention has the beneficial effects as follows:

The present invention can be to use under the satisfied service condition of calculating by byte mode of non-integer byte in transmission information, not only CRC result is correct, and improved computational efficiency greatly, shortened computing time, actual test shows: bring up to 9us from 70us computing time, promoted the real-time response performance, discharged a large amount of cpu resources, reduce the requirement to cpu performance and operation clock, reduced the CPU power consumption.

Embodiment

Technical scheme of the present invention is described in further detail below: a kind of cyclic redundancy check (CRC) algorithm of non-whole byte data, CRC mathematics essence be to the transmission message polynomial to the complementation of CRC generator polynomial, the generator polynomial of CRC16 is:

G (x)=x ¹⁶+ x ¹²+ x ⁵+ 1, its computational methods are: with 16 0 back of adding S (x) to, just

S (x)=r ¹⁶* S (x), wherein r=2 is the base of binary system multinomial operation, S (x) does division arithmetic to generator polynomial G (x) then, namely carries out the logic xor operation, obtains the remainder part of division at last, is CRC16, abbreviates C as _Reg, and merchant's part is called for short M (x), it may further comprise the steps:

S1: suppose S _mCorresponding CRC16 value is C _Reg, by definition, then:

${\mathrm{CRC}}_{S_m}=(R^2*S_m)\mathrm{Mod}\left(G\left(x\right)\right)=G_{\mathrm{reg}}=\mathrm{Crc}16\_\mathrm{Table}\left[S_m\right]$ (formula 1)

R ²* S _m=M (x) * G (x)+C _Reg(formula 2)

S2: at S _mThe back increases byte information position of less than, n position, forms a new binary system multinomial S' _m, calculate S' _mCRC16, it may further comprise the steps:

S201: at S _mThe back increases byte information position of less than, n position, forms a new binary system multinomial S' _m,

S' _m=r ⁿ* S _m+ B _n(formula 3)

B _nExpression n position binary system multinomial, wherein high-order preceding, low level after.

S202: to S' _mIncrease by 16 0 operations and guarantee that remainder directly is exactly the CRC16 result of data flow:

R ²* S' _m=R ²* (r ⁿ* S _m+ B _n)=r ⁿ* (R ²* S _m)+R ²* B _n(formula 4)

Substituting formula 2 into, formula 4 gets:

R ²*S' _m=rn*(M(x)*G(x)+C _reg)+R ²*B _n

=(r ⁿ* M (x) * G (x))+r ⁿ* C _Reg+ R ²* B _n(formula 5)

Make C _HExpression C _RegHigh n position, C _LExpression C _RegLow (16-n) position,

C _Reg=r ^(16-n)* C _H+ C _L(formula 6)

Formula 6 substitution formulas 5 are got:

R ²* S' _m=(r ⁿ* M (x) * G (x))+R ²* C _H+ r ⁿ* C _L+ R ²* B _n(formula 7)

=(r ⁿ*M(x)*G(x))+R ²*(C _H+B _n)+r ⁿ*C _L

Known by the CRC definition: (r ⁿ* Mod (G (x)) ≡ 0 (formula 8) M (x) * G (x))

$(R^2*(C_H+B_n))\mathrm{Mod}\left(G\left(x\right)\right)={\mathrm{CRC}}_{C_H+B_n}=\mathrm{Crc}16\_\mathrm{Table}[C_H+B_n]$

$(r^n*C_L)\mathrm{Mod}\left(G\left(x\right)\right)=r^n*C_L$

By logic or the associativity of operation, formula 7 and formula 8:

(R ²* S' _m) Mod (G (x))=Crc16_Table[C _H+ B _n]+r ⁿ* C _L(formula 9)

That is:

${\mathrm{CRC}}_{S_m^{\′}}=\mathrm{Crc}16\_\mathrm{Table}\left[(C_H+B_n)\right]+r^n*C_L.$ (formula 10)

S3: by formula 10 as can be known, the CRC16 that calculates current data finishes in two steps, and concrete steps are;

S301: the high n position C that will go up the CRC16 value of a byte _HAnd B _nThe phase XOR, the XOR result tables look-up as subscript and obtains Crc16_Table[(C _H+ B _n)];

S302: will go up behind low (16-n) lt n position of CRC16 of a byte and the value of tabling look-up Crc16_Table[(C _H+ B _n)] the phase XOR.

S4: calculate the CRC16 of random length byte, it may further comprise the steps:

S401: the first byte S of the stream that fetches data ₀As the subscript Crc16_Table[S that tables look-up ₀] obtain S ₀Current C RC16 value;

S402: in order all can be finished CRC16 according to byte by the part that byte is handled and calculate;

S403: the actual bit of getting n and be remaining data is counted substitution formula 10, finishes the calculating of the not enough byte portion C RC16 of residue;

S404: the CRC16 result that the current C RC16 value that obtains in conjunction with S401, S402 and S403, the CRC result who calculates according to byte and not enough byte portion C RC result obtain whole data.

Claims (1)

1. the cyclic redundancy check (CRC) algorithm of a non-whole byte data, CRC mathematics essence be to the transmission message polynomial to the complementation of CRC generator polynomial, the generator polynomial of CRC16 is: G (x)=x ¹⁶+ x ¹²+ x ⁵+ 1, its computational methods are: with 16 0 back of adding S (x) to, and S (x)=r just ¹⁶* S (x), wherein r=2 is the base of binary system multinomial operation, S (x) does division arithmetic to generator polynomial G (x) then, namely carries out the logic xor operation, obtains the remainder part of division at last, is CRC16, abbreviates C as _Reg, and merchant's part is called for short M (x), it is characterized in that: it may further comprise the steps:

S1: suppose S _mCorresponding CRC16 value is C _Reg, by definition, then:

${\mathrm{CRC}}_{S_m}=(R^2*S_m)\mathrm{Mod}\left(G\left(x\right)\right)=G_{\mathrm{reg}}=\mathrm{Crc}16\_\mathrm{Table}\left[S_m\right]$ (formula 1)

R ²* S _m=M (x) * G (x)+C _Reg(formula 2)

S2: at S _mThe back increases byte information position of less than, n position, forms a new binary system multinomial S' _m, calculate S' _mCRC16, it may further comprise the steps:

S201: at S _mThe back increases byte information position of less than, n position, forms a new binary system multinomial S' _m,

S' _m=r ⁿ* S _m+ B _n(formula 3)

B _nExpression n position binary system multinomial, wherein high-order preceding, low level after.

S202: to S' _mIncrease by 16 0 operations and guarantee that remainder directly is exactly the CRC16 result of data flow:

R ²* S' _m=R ²* (r ⁿ* S _m+ B _n)=r ⁿ* (R ²* S _m)+R ²* B _n(formula 4)

Substituting formula 2 into, formula 4 gets:

R ²*S' _m=rn*(M(x)*G(x)+C _reg)+R ²*B _n

=(r ⁿ* M (x) * G (x))+r ⁿ* C _Reg+ R ²* B _n(formula 5)

Make C _HExpression C _RegHigh n position, C _LExpression C _RegLow (16-n) position,

C _Reg=r ^(16-n)* C _H+ C _L(formula 6)

Formula 6 substitution formulas 5 are got:

R ²* S' _m=(r ⁿ* M (x) * G (x))+R ²* C _H+ r ⁿ* C _L+ R ²* B _n(formula 7)

=(r ⁿ*M(x)*G(x))+R ²*(C _H+B _n)+r ⁿ*C _L

Known by the CRC definition: (r ⁿ* Mod (G (x)) ≡ 0 (formula 8) M (x) * G (x))

$(R^2*(C_H+B_n))\mathrm{Mod}\left(G\left(x\right)\right)={\mathrm{CRC}}_{C_H+B_n}=\mathrm{Crc}16\_\mathrm{Table}[C_H+B_n]$

$(r^n*C_L)\mathrm{Mod}\left(G\left(x\right)\right)=r^n*C_L$

By logic or the associativity of operation, formula 7 and formula 8:

(R ²* S' _m) Mod (G (x))=Crc16_Table[C _H+ B _n]+r ⁿ* C _L(formula 9)

That is:

${\mathrm{CRC}}_{S_m^{\′}}=\mathrm{Crc}16\_\mathrm{Table}\left[(C_H+B_n)\right]+r^n*C_L.$ (formula 10)

S3: by formula 10 as can be known, the CRC16 that calculates current data finishes in two steps, and concrete steps are as follows;

S301: the high n position C that will go up the CRC16 value of a byte _HAnd B _nThe phase XOR, the XOR result tables look-up as subscript and obtains Crc16_Table[(C _H+ B _n)];

S302: will go up behind low (16-n) lt n position of CRC16 of a byte and the value of tabling look-up Crc16_Table[(C _H+ B _n)] the phase XOR.

S4: calculate the CRC16 of random length byte, it may further comprise the steps:

S401: the first byte S of the stream that fetches data ₀As the subscript Crc16_Table[S that tables look-up ₀] obtain S ₀Current C RC16 value;

S402: in order all can be finished CRC16 according to byte by the part that byte is handled and calculate;

S403: the actual bit of getting n and be remaining data is counted substitution formula 10, finishes the calculating of the not enough byte portion C RC16 of residue;

S404: the CRC16 result that the current C RC16 value that obtains in conjunction with S401, S402 and S403, the CRC result who calculates according to byte and not enough byte portion C RC result obtain whole data.