Lowest exponent of a CRC polynomial
I have never seen a CRC polynomial without the lowest term x⁰ = 1.
Are there any exceptions I haven't seen yet?
Why do all CRC polynomials have the lowest term x⁰?
crc polynomials
asked Nov 11 at 20:16
Silicomancer
4,05933475
add a comment |
I have never seen a CRC polynomial without the lowest term x⁰ = 1.
Are there any exceptions I haven't seen yet?
Why do all CRC polynomials have the lowest term x⁰?
crc polynomials
asked Nov 11 at 20:16
Silicomancer
4,05933475
add a comment |
I have never seen a CRC polynomial without the lowest term x⁰ = 1.
Are there any exceptions I haven't seen yet?
Why do all CRC polynomials have the lowest term x⁰?
crc polynomials
asked Nov 11 at 20:16
Silicomancer
4,05933475
I have never seen a CRC polynomial without the lowest term x⁰ = 1.
Are there any exceptions I haven't seen yet?
Why do all CRC polynomials have the lowest term x⁰?
crc polynomials
crc polynomials
asked Nov 11 at 20:16
Silicomancer
4,05933475
asked Nov 11 at 20:16
Silicomancer
4,05933475
asked Nov 11 at 20:16
Silicomancer
4,05933475
asked Nov 11 at 20:16
Silicomancer
4,05933475
asked Nov 11 at 20:16
Silicomancer
4,05933475
4,05933475
add a comment |
add a comment |
1 Answer
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A CRC polynomial of the form xn + ... + x0 is used for a n bit CRC (it is used with a borrowless divide of the data bits by the CRC polynomial that produces an n bit remainder, the CRC). If the CRC polynomial is of the form xn + ... + x1 (no x0 term), then it is effectively a n-1 bit CRC.
However, there are cases where common code may use different tables for fast computations of 32 bit or 16 bit CRC's, where the only difference in the main part of the code is the constants. The code is written as if the CRC is of the form x32 + ... + x0, but to allow most of the same code to generate a 16 bit CRC, the polynomial is of the form x32 + ... + x16. There's a final step correction done to shift the final CRC right by 16 bits to place the 16 bit CRC in the proper bits. An example of this is in this 500+ line fast crc32/16 assembly example using pclmulqdq insruction (carryless multiply), which in this case is setup to produce a 16 bit CRC.
answered Nov 11 at 22:07
rcgldr
15.1k31333
add a comment |
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1 Answer
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1 Answer
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active
oldest
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A CRC polynomial of the form xn + ... + x0 is used for a n bit CRC (it is used with a borrowless divide of the data bits by the CRC polynomial that produces an n bit remainder, the CRC). If the CRC polynomial is of the form xn + ... + x1 (no x0 term), then it is effectively a n-1 bit CRC.
However, there are cases where common code may use different tables for fast computations of 32 bit or 16 bit CRC's, where the only difference in the main part of the code is the constants. The code is written as if the CRC is of the form x32 + ... + x0, but to allow most of the same code to generate a 16 bit CRC, the polynomial is of the form x32 + ... + x16. There's a final step correction done to shift the final CRC right by 16 bits to place the 16 bit CRC in the proper bits. An example of this is in this 500+ line fast crc32/16 assembly example using pclmulqdq insruction (carryless multiply), which in this case is setup to produce a 16 bit CRC.
answered Nov 11 at 22:07
rcgldr
15.1k31333
add a comment |
A CRC polynomial of the form xn + ... + x0 is used for a n bit CRC (it is used with a borrowless divide of the data bits by the CRC polynomial that produces an n bit remainder, the CRC). If the CRC polynomial is of the form xn + ... + x1 (no x0 term), then it is effectively a n-1 bit CRC.
However, there are cases where common code may use different tables for fast computations of 32 bit or 16 bit CRC's, where the only difference in the main part of the code is the constants. The code is written as if the CRC is of the form x32 + ... + x0, but to allow most of the same code to generate a 16 bit CRC, the polynomial is of the form x32 + ... + x16. There's a final step correction done to shift the final CRC right by 16 bits to place the 16 bit CRC in the proper bits. An example of this is in this 500+ line fast crc32/16 assembly example using pclmulqdq insruction (carryless multiply), which in this case is setup to produce a 16 bit CRC.
answered Nov 11 at 22:07
rcgldr
15.1k31333
add a comment |
A CRC polynomial of the form xn + ... + x0 is used for a n bit CRC (it is used with a borrowless divide of the data bits by the CRC polynomial that produces an n bit remainder, the CRC). If the CRC polynomial is of the form xn + ... + x1 (no x0 term), then it is effectively a n-1 bit CRC.
However, there are cases where common code may use different tables for fast computations of 32 bit or 16 bit CRC's, where the only difference in the main part of the code is the constants. The code is written as if the CRC is of the form x32 + ... + x0, but to allow most of the same code to generate a 16 bit CRC, the polynomial is of the form x32 + ... + x16. There's a final step correction done to shift the final CRC right by 16 bits to place the 16 bit CRC in the proper bits. An example of this is in this 500+ line fast crc32/16 assembly example using pclmulqdq insruction (carryless multiply), which in this case is setup to produce a 16 bit CRC.
answered Nov 11 at 22:07
rcgldr
15.1k31333
A CRC polynomial of the form xn + ... + x0 is used for a n bit CRC (it is used with a borrowless divide of the data bits by the CRC polynomial that produces an n bit remainder, the CRC). If the CRC polynomial is of the form xn + ... + x1 (no x0 term), then it is effectively a n-1 bit CRC.
However, there are cases where common code may use different tables for fast computations of 32 bit or 16 bit CRC's, where the only difference in the main part of the code is the constants. The code is written as if the CRC is of the form x32 + ... + x0, but to allow most of the same code to generate a 16 bit CRC, the polynomial is of the form x32 + ... + x16. There's a final step correction done to shift the final CRC right by 16 bits to place the 16 bit CRC in the proper bits. An example of this is in this 500+ line fast crc32/16 assembly example using pclmulqdq insruction (carryless multiply), which in this case is setup to produce a 16 bit CRC.
answered Nov 11 at 22:07
rcgldr
15.1k31333
edited Nov 11 at 22:17
answered Nov 11 at 22:07
rcgldr
15.1k31333
answered Nov 11 at 22:07
rcgldr
15.1k31333
answered Nov 11 at 22:07
rcgldr
15.1k31333
15.1k31333
add a comment |
add a comment |
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