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diff --git a/FAQ.lz77 b/FAQ.lz77 new file mode 100644 index 0000000..7bd7e0a --- /dev/null +++ b/FAQ.lz77 @@ -0,0 +1,207 @@ + + + +Q: What is the lz77 compression? What is the terminology you used? +A: The lz77 compression is a quite simple algorithm, which works in stream. + You have to "copy" the uncompressed bytes from the stream, and sometime, + you encounter what I've called "restart blocks" which tells two things: + a backward jump, and a lenght. The jump value tells you of how many bytes + you have to "rewind", and the length tells you how many bytes you have to + copy from there. For example if you have the compressed stream: + + One Ring to rule them all, <J:27,L:12>find<J:28,L:5>. + + then you will decompress it by: + + One Ring to rule them all, One Ring to find them. + + because when you hit the <J:27,L:12>, it tells you to copy 12 bytes from + 27 bytes backward, and when you hit the <J:28,L:5>, it tells you to + copy 5 bytes from 28 bytes backward. + + + +Q: What are the differences between lz77, lzss and lzw? +A: The lzw is the algorithm name implemented by PKZIP, and thus by WinZIP. + But it uses basically the same scheme as the lz77 algorithm. The lzss + is the name for a fixed maximum backward length window algorithm. + I've named my stuff 'lz77' because it's the generic name for it. + The lzw is in fact two algorithms in one: the Huffman and the lz77. + + + +Q: How is the file stored? +A: From a general manner, you have a 4 bytes length to know where to stop + when you are uncompressing. As you may have noticed, you have normal + bytes and compressed blocks. So you can have a bitmap which tells you + if the bytes are normal bytes or restart blocks. As an example, let's + look the Lord of the Rings compression: + + |Bitmaps | Datas + |--------|---------------------------|--------| + |00000000| 4f 6e 65 20 52 69 6e 67 |One Ring| + |00000000| 20 74 6f 20 72 75 6c 65 | to rule| + |00000000| 20 74 68 65 6d 20 61 6c | them al| + |00010000| 6c 2c 20<1b 90>66 69 6e 64|l, ..find| + |10000000|<1b 20>2e |...| + + If you have a 0 in the bitmap, then you know you have to simply copy the + byte you find, and if you have a 1, you have to read the two next bytes, + 'unpack' them to find the backward jump and the length, then copy the + corresponding bytes. As an exercise, try to find how I've 'packed' the + length and the backward jump into the above array. + + Since you need two bytes to write a restart block, you will have to add + three to the unpacked length. + + Here is the final form of the packed file: + +0000: 31 00 00 00 00 4F 6E 65 20 52 69 6E 67 00 20 74 1 One Ring t +0010: 6F 20 72 75 6C 65 00 20 74 68 65 6D 20 61 6C 08 o rule them al. +0020: 6C 2C 20 1B 90 66 69 6E 64 01 1B 20 2E l, ..find.. .. + + Note how the bitmaps are stored. + + + +Q: How are the jump and length packed? +A: You may find infos on the net like: + + O3 O2 O1 O0 L3 L2 L1 L0 | OB OA O9 O8 O7 O6 O5 O4 + + This means that the two infos are packed like this: the offset (jump) has the + four lower bits in the four upper bits of the first byte, then the eight upper + bits are directly stored into the second byte. Thus, the backward jump is + stored on 12 bits. The length is stored in four bits, and they are stored in + the four lower bits of the first byte. So the length may vary from 3 to 18. + + + +Q: What is the relationship between the schemes into the software and the + thing you pasted above? +A: It's quite easy. The computation formula is the following: + + decomp_length = shift(val1 & scheme.l_mask_1, scheme.l_shft_1) | + shift(val2 & scheme.l_mask_2, scheme.l_shft_2); + decomp_jump = shift(val1 & scheme.j_mask_1, scheme.j_shft_1) | + shift(val2 & scheme.j_mask_2, scheme.j_shft_2); + + + So, if you want to write the eight parameters for the above thingy, you + will have to set them to this: + + l_mask_1 = 0x0f | l_mask_2 = 0x00 | j_mask_1 = 0xf0 | j_mask_2 = 0xff + l_shft_1 = 0 | l_shft_2 = 0 | j_shft_1 = -4 | j_shft_2 = 4 + + What is he most difficult to understand is the jump value. We want to build + the jump value as: OB OA O9 O8 O7 O6 O5 O4 O3 O2 O1 O0. + + Let's first work on the first byte. + -) We have to only keep the Ox bits + -) Then we have to move them to the right. + + The mask is here to suppress the unwanted bits. So for our case, the mask is + 0xf0 since it's the four high bits. The shift is here to move the bits. A + negative value means to move them to the right, and a positive means to the + left. So since we have to make the bits go to the four lower bits, we have + a shift of -4 + + For the second byte: + -) We keep all the bits, but + -) we have to make room for the four bits from the first byte. + + The mask don't have to suppress anything, so it's set to 0xff. And now, the + shift is set to 4 to make enough room. + + Finally, the software will build the jump with those four parameters. + + +Q: What are the others parameters? +A: You have: + + 1iscomp overlap negative 16bits opposite + + This will change the behaviour of the compression/decompression algorithm. + + The 1iscomp will inverse the bitmap from the default. The default is, a 1 in + the bitmap is uncompressed. + + The overlap is a boolean to tell the compressor to use the overlap trick. + Some roms does use it, but is a little hard to explain here. + + This is the same for the negative trick. + + The 16bits behavior is quite specific to the FF6 PSX. Everything is coded + using 16 bits words instead of 8 bits words. And thus, the compression + algorithm is more difficult. As for now, it's broken. + + The opposite behavior is to compute the jump offset in a different way. + Instead of taking it as the backward jump value, it will be an offset + from the maximum backward jump possible. + + + +Q: What are the overlap and the negative tricks? +A: You really want to know? *sigh* + Ok, here we go. The negative is still the simplier to understand. When you + are uncompressing a lz77 stream, you read backward jumps and lengths. The + maximum value for a jump and a length are determined on how the two infos + are packed into the restart block. + + For example, if you have 12 bits for the jump and 4 for the length, you will + have a maximum of 0xfff for the jump and 18 for the length (18 because it's + 0xf + 3) + + Here comes the negative trick: when you are uncompressing the first bytes, + you will still be able to have a jump which is *beyond* the beginning of the + decompressed file. Later, when your file will grow up, this won't be possible + anymore of course, since its size will be over the maximum jump size. + + So, sometime, you can consider that *if* you have a negative value, it's not + a fault: you just read zeros. Understood? BTW, most of the case, the negative + restart will be very near the begin of the file. So if you have to copy five + bytes distant of 1000 bytes from the beginning of the file, *this* is + probably a fault, or a misunderstood scheme. + + + Next, the overlap trick. It's more difficult to understand though. You have + to understand the decompressor's algorithm a bit. When it hits a restart + block, it computes the jump and the length, then it will begin to copy the + bytes from the old decompressed datas, one byte after the other. + + So the trick is here: when you are copying the bytes, the algorithm will + be able to reuse them immediately for the current copy, since they are + already written. The restart block will use "itself". + + Let's have an example: + + If you want to compress the stream: + + 123123123123 + + you will have two solutions. Either with, either without the overlap trick. + Without the overlap trick, here is the compressed stream: + + 123123<J:6,L:6> + + This is obvious hu? Now, with the overlap trick: + + 123<J:3,L:9> + + Try to take a piece of paper and to decompress those two thingy, maybe this + will help you understand. + + + +Q: When do I have to active the overlap and negative tricks? +A: Well, for the decompressor, it's not really necessary, because it won't + crash if the flags are not enabled. But it will warn you so you will be + able to know that the tricks are enabled into the lz77 stream. So if you + see that those tricks are enabled, then active the flags so the compressor + will be able to take care of them. + + Something else: you may also test if the tricks are working. Maybe they + wasn't used when your original lz77 stream was created, but the decompression + algorithm used by the game *maybe* is able to handle them. + + |