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59 lines
3.7 KiB
Plaintext
59 lines
3.7 KiB
Plaintext
The compressor achieves an average compression rate of 60% of the
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original size which is on par with "gzip". It seems that you cannot do
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much better for compressing compiled binaries. This means that the
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break even point for using compressed images is reached, once the
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uncompressed size approaches 1.5kB. We can stuff more than 12kB into
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an 8kB EPROM and more than 25kB into an 16kB EPROM. As there is only
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32kB of RAM for both the uncompressed image and its BSS area, this
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means that 32kB EPROMs will hardly ever be required.
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The compression algorithm uses a 4kB ring buffer for buffering the
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uncompressed data. Before compression starts, the ring buffer is
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filled with spaces (ASCII character 0x20). The algorithm tries to
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find repeated input sequences of a maximum length of 60 bytes. All
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256 different input bytes plus the 58 (60 minus a threshold of 2)
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possible repeat lengths form a set of 314 symbols. These symbols are
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adaptively Huffman encoded. The algorithm starts out with a Huffmann
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tree that assigns equal code lengths to each of the 314 symbols
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(slightly favoring the repeat symbols over symbols for regular input
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characters), but it will be changed whenever the frequency of any of
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the symbols changes. Frequency counts are kept in 16bit words until
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the total number of compressed codes totals 2^15. Then, all frequency
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counts will be halfed (rounding to the bigger number). For unrepeated
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characters (symbols 0..255) the Huffman code is written to the output
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stream. For repeated characters the Huffmann code, which denotes the
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length of the repeated character sequence, is written out and then the
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index in the ring buffer is computed. From this index, the algorithm
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computes the offset relative to the current index into the ring
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buffer. Thus, for typical input data, one would expect that short to
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medium range offsets are more frequent than extremely short or medium
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range to long range offsets. Thus the 12bit (for a 4kB buffer) offset
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value is statically Huffman encoded using a precomputed Huffman tree
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that favors those offset values that are deemed to be more
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frequent. The Huffman encoded offset is written to the output data
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stream, directly following the code that determines the length of
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repeated characters.
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This algorithm, as implemented in the C example code, looks very good
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and its operating parameters are already well optimized. This also
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explains why it achieves compression ratios comparable with
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"gzip". Depending on the input data, it sometimes excells considerably
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beyond what "gzip -9" does, but this phenomenon does not appear to be
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typical. There are some flaws with the algorithm, such as the limited
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buffer sizes, the adaptive Huffman tree which takes very long to
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change, if the input characters experience a sudden change in
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distribution, and the static Huffman tree for encoding offsets into
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the buffer. The slow changes of the adaptive Huffman tree are
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partially counteracted by artifically keeping a 16bit precision for
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the frequency counts, but this does not come into play until 32kB of
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compressed data is output, so it does not have any impact on our use
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for "etherboot", because the BOOT Prom does not support uncompressed
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data of more then 32kB (c.f. doc/spec.doc).
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Nonetheless, these problems do not seem to affect compression of
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compiled programs very much. Mixing object code with English text,
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would not work too well though, and the algorithm should be reset in
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between. Actually, we might gain a little improvement, if text and
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data segments were compressed individually, but I have not
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experimented with this option, yet.
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