The concept itself seems to be easy—a CRC is just the remainder of a particular type of division. The steps of the algorithm are very simple:. And from that description, the code pretty much follows:. Although, this is the rare case where it's easier to write it in assembly that it is in C, since we have access to the carry bit when shifting, which makes it easier to check:. Note: the core of the algorithm in assembly is four instructionsthe C compiler didn't do quite as good a job from the six lines of C comprising the core of the algorithmit's about six times the object code.

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The concept itself seems to be easy—a CRC is just the remainder of a particular type of division. The steps of the algorithm are very simple:. And from that description, the code pretty much follows:. Although, this is the rare case where it's easier to write it in assembly that it is in C, since we have access to the carry bit when shifting, which makes it easier to check:. Note: the core of the algorithm in assembly is four instructionsthe C compiler didn't do quite as good a job from the six lines of C comprising the core of the algorithmit's about six times the object code.

What is not shown in the code above either version is the agumentation step of adding additional 0-bits to the message—that's left up to the caller of these routines. Both of these routines give the same result. Other implementations I did based upon the Guide also give the same results. And they're consistent with the results of the reference code given in the Guide. So far so good. Okay, so the bits are fed in backwards. That can be compensated for.

Also, the standard CRC algorithm mandates that the initial value of the remainder is all one bits, not zero bits. Easy to fix. And that the final remainder is to be exclusived-or'ed with all ones. Again, easy to do.

It all seems pretty straightforward. And since the zlib library uses the CRC, we can link that in as a baseline to compare results. I didn't think the code I wrote for reflected CRCs was that unreasonable based upon the information in the Guide, but I guess I was wrong for some of them.

Oh, and getting back to the non-reflected code—I didn't initialize the results properly, nor did I exclusive-or the results. Okay, now I'm horribly confused. But I'm concerned that the routines that require additional zero bits aren't the same in this case. There has to be some subtle difference between the two in this case that I don't see, and isn't mentioned in the Guide at all. Another thing I noticed by looking deeply into the abyss that is CRC, is that my first implementation of CRC is flawed —I don't exclusive-or the results with all ones at the end.

I suspect that the code I based mine on didn't bother with the exclusive-or when returning the CRC, but instead did that elsewhere in the codebase. It's not a bug per se , but according to Numerical Recipes in C :. Second, one can add XOR any M- bit constant K to the CRC before it is transmitted … This has the advantage of detecting another kind of erorr that the CRC would otherwise not find: deletion of an initial 1 bit in the message with spurious insertion of a 1 bit at the end of the block.

The result is that there's a type of corruption that I won't catch. This code was the basis for the CRC implementation in a few programs at work oops but again, I don't think it's an outright show-stopping bug.

At some point, I may go through some of this on paper, one bit at a time, to see what's going on math-wise with the reflected and non-reflected table implementations with non-0 initial values. The dates are the permanent links to that day's entries or entry, if there is only one entry. The titles are the permanent links to that entry only.

You can also specify the entire month by leaving off the day portion. You can even select an arbitrary portion of time. It's an experiment in using color shading to denote the distance a link is from here.

If you don't notice it, don't worry; it's not all that important. All Rights Reserved. The steps of the algorithm are very simple: Load the remainder with zero bits. Augment the message by appending zero bits equal to the size of the remainder to the end of it.

While more message bits Shift the remainder left by one bit, reading the next bit of the augmented message into bit position 0 of the remainder.

If a 1 bit popped out of the remainder during the previous step, XOR the result with the polynomial We now have the remainder. It's not a bug per se , but according to Numerical Recipes in C : Second, one can add XOR any M- bit constant K to the CRC before it is transmitted … This has the advantage of detecting another kind of erorr that the CRC would otherwise not find: deletion of an initial 1 bit in the message with spurious insertion of a 1 bit at the end of the block.

Impudence kottke. You have my permission to link freely to any entry here. Go ahead, I won't bite. I promise.

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## The Boston Diaries

Much of theliterature on CRCs, and in particular on their table-drivenimplementations, is a little obscure or at least seems so to me. This document is an attempt to provide a clear and simple no-nonsenseexplanation of CRCs and to absolutely nail down every detail of theoperation of their high-speed implementations. The model algorithm can beparameterized to behave like most of the CRC implementations around,and so acts as a good reference for describing particular algorithms. A low-speed implementation of the model CRC algorithm is provided inthe C programming language. Lastly there is a section giving two formsof high-speed table driven implementations, and providing a programthat generates CRC lookup tables.

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## CRC校驗的精彩介紹（A PAINLESS GUIDE TO CRC ERROR DETECTION ALGORITHMS）

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. Williams Published Computer Science. In a kinetic sculpture apparatus, the lower end of a pendulum provides a scribe having a tapered tip that penetrates the surface of a bed of fine, particulate material to make an intricate pattern in the bed whose configuration is determined by the location of the pendulum's primary horizontal axis, the position from which the pendulum is released, and the depth of penetration of the tip of the scribe.