On Sat, Apr 22, 2006 at 01:36:07PM -0700, Davide Libenzi wrote:
> Geert, I saw you're using a shift of 55 bits, that gives an degree of the
> root polynomial of 63, that is not prime. Where did you get the root
> polynomial, and why you did not chose 61 as degree of the root?
> Just curious ...
The polynomial was randomly created using code by David Mazieres, that
is part of LBFS. I chose a (irreducible) polynomial of degree 63 as
that was the same as LBFS did. As for my purposes it's best to have
a constant polynomial and I wanted to have all the code for
the computations in the same compilation unit for performance,
I decided to just have a little program print out the tables
and include it directly. The chosen polynomial was 0xb15e234bd3792f63.
Later on I haven't revisited this decision, although I agree that
it'd probably be a good idea to use a polynomial of prime degree,
even though we're not looking for cryptographically strong hashes here.
Below I include new tables for degree 61. The window size of 22 was
found by plotting graphs on a number of largish test cases (30-100MB)
and seeing how the size of the compressed output changed. It is
essential to do all comparisons using gzipped output. I've been
tempted a number of times to include new optimizations, only
to find out that the uncompressed size reduced, but final compressed
size grew. More smaller copies and literal data segments is generally
worse.
-Geert
#define RABIN_POLY 0x25bd5331c0d7096dULL
#define RABIN_DEGREE 61
#define RABIN_SHIFT 53
#define RABIN_WINDOW_SIZE 22
unsigned long long T[256] =
{ 0x0000000000000000ULL, 0x25bd5331c0d7096dULL, 0x4b7aa66381ae12daULL,
0x6ec7f55241791bb7ULL, 0x96f54cc7035c25b4ULL, 0xb3481ff6c38b2cd9ULL,
0xdd8feaa482f2376eULL, 0xf832b99542253e03ULL, 0x0857cabfc66f4205ULL,
0x2dea998e06b84b68ULL, 0x432d6cdc47c150dfULL, 0x66903fed871659b2ULL,
0x9ea28678c53367b1ULL, 0xbb1fd54905e46edcULL, 0xd5d8201b449d756bULL,
0xf065732a844a7c06ULL, 0x10af957f8cde840aULL, 0x3512c64e4c098d67ULL,
0x5bd5331c0d7096d0ULL, 0x7e68602dcda79fbdULL, 0x865ad9b88f82a1beULL,
0xa3e78a894f55a8d3ULL, 0xcd207fdb0e2cb364ULL, 0xe89d2ceacefbba09ULL,
0x18f85fc04ab1c60fULL, 0x3d450cf18a66cf62ULL, 0x5382f9a3cb1fd4d5ULL,
0x763faa920bc8ddb8ULL, 0x8e0d130749ede3bbULL, 0xabb04036893aead6ULL,
0xc577b564c843f161ULL, 0xe0cae6550894f80cULL, 0x04e279ced96a0179ULL,
0x215f2aff19bd0814ULL, 0x4f98dfad58c413a3ULL, 0x6a258c9c98131aceULL,
0x92173509da3624cdULL, 0xb7aa66381ae12da0ULL, 0xd96d936a5b983617ULL,
0xfcd0c05b9b4f3f7aULL, 0x0cb5b3711f05437cULL, 0x2908e040dfd24a11ULL,
0x47cf15129eab51a6ULL, 0x627246235e7c58cbULL, 0x9a40ffb61c5966c8ULL,
0xbffdac87dc8e6fa5ULL, 0xd13a59d59df77412ULL, 0xf4870ae45d207d7fULL,
0x144decb155b48573ULL, 0x31f0bf8095638c1eULL, 0x5f374ad2d41a97a9ULL,
0x7a8a19e314cd9ec4ULL, 0x82b8a07656e8a0c7ULL, 0xa705f347963fa9aaULL,
0xc9c20615d746b21dULL, 0xec7f55241791bb70ULL, 0x1c1a260e93dbc776ULL,
0x39a7753f530cce1bULL, 0x5760806d1275d5acULL, 0x72ddd35cd2a2dcc1ULL,
0x8aef6ac99087e2c2ULL, 0xaf5239f85050ebafULL, 0xc195ccaa1129f018ULL,
0xe4289f9bd1fef975ULL, 0x09c4f39db2d402f2ULL, 0x2c79a0ac72030b9fULL,
0x42be55fe337a1028ULL, 0x670306cff3ad1945ULL, 0x9f31bf5ab1882746ULL,
0xba8cec6b715f2e2bULL, 0xd44b19393026359cULL, 0xf1f64a08f0f13cf1ULL,
0x0193392274bb40f7ULL, 0x242e6a13b46c499aULL, 0x4ae99f41f515522dULL,
0x6f54cc7035c25b40ULL, 0x976675e577e76543ULL, 0xb2db26d4b7306c2eULL,
0xdc1cd386f6497799ULL, 0xf9a180b7369e7ef4ULL, 0x196b66e23e0a86f8ULL,
0x3cd635d3fedd8f95ULL, 0x5211c081bfa49422ULL, 0x77ac93b07f739d4fULL,
0x8f9e2a253d56a34cULL, 0xaa237914fd81aa21ULL, 0xc4e48c46bcf8b196ULL,
0xe159df777c2fb8fbULL, 0x113cac5df865c4fdULL, 0x3481ff6c38b2cd90ULL,
0x5a460a3e79cbd627ULL, 0x7ffb590fb91cdf4aULL, 0x87c9e09afb39e149ULL,
0xa274b3ab3beee824ULL, 0xccb346f97a97f393ULL, 0xe90e15c8ba40fafeULL,
0x0d268a536bbe038bULL, 0x289bd962ab690ae6ULL, 0x465c2c30ea101151ULL,
0x63e17f012ac7183cULL, 0x9bd3c69468e2263fULL, 0xbe6e95a5a8352f52ULL,
0xd0a960f7e94c34e5ULL, 0xf51433c6299b3d88ULL, 0x057140ecadd1418eULL,
0x20cc13dd6d0648e3ULL, 0x4e0be68f2c7f5354ULL, 0x6bb6b5beeca85a39ULL,
0x93840c2bae8d643aULL, 0xb6395f1a6e5a6d57ULL, 0xd8feaa482f2376e0ULL,
0xfd43f979eff47f8dULL, 0x1d891f2ce7608781ULL, 0x38344c1d27b78eecULL,
0x56f3b94f66ce955bULL, 0x734eea7ea6199c36ULL, 0x8b7c53ebe43ca235ULL,
0xaec100da24ebab58ULL, 0xc006f5886592b0efULL, 0xe5bba6b9a545b982ULL,
0x15ded593210fc584ULL, 0x306386a2e1d8cce9ULL, 0x5ea473f0a0a1d75eULL,
0x7b1920c16076de33ULL, 0x832b99542253e030ULL, 0xa696ca65e284e95dULL,
0xc8513f37a3fdf2eaULL, 0xedec6c06632afb87ULL, 0x1389e73b65a805e4ULL,
0x3634b40aa57f0c89ULL, 0x58f34158e406173eULL, 0x7d4e126924d11e53ULL,
0x857cabfc66f42050ULL, 0xa0c1f8cda623293dULL, 0xce060d9fe75a328aULL,
0xebbb5eae278d3be7ULL, 0x1bde2d84a3c747e1ULL, 0x3e637eb563104e8cULL,
0x50a48be72269553bULL, 0x7519d8d6e2be5c56ULL, 0x8d2b6143a09b6255ULL,
0xa8963272604c6b38ULL, 0xc651c7202135708fULL, 0xe3ec9411e1e279e2ULL,
0x03267244e97681eeULL, 0x269b217529a18883ULL, 0x485cd42768d89334ULL,
0x6de18716a80f9a59ULL, 0x95d33e83ea2aa45aULL, 0xb06e6db22afdad37ULL,
0xdea998e06b84b680ULL, 0xfb14cbd1ab53bfedULL, 0x0b71b8fb2f19c3ebULL,
0x2eccebcaefceca86ULL, 0x400b1e98aeb7d131ULL, 0x65b64da96e60d85cULL,
0x9d84f43c2c45e65fULL, 0xb839a70dec92ef32ULL, 0xd6fe525fadebf485ULL,
0xf343016e6d3cfde8ULL, 0x176b9ef5bcc2049dULL, 0x32d6cdc47c150df0ULL,
0x5c1138963d6c1647ULL, 0x79ac6ba7fdbb1f2aULL, 0x819ed232bf9e2129ULL,
0xa42381037f492844ULL, 0xcae474513e3033f3ULL, 0xef592760fee73a9eULL,
0x1f3c544a7aad4698ULL, 0x3a81077bba7a4ff5ULL, 0x5446f229fb035442ULL,
0x71fba1183bd45d2fULL, 0x89c9188d79f1632cULL, 0xac744bbcb9266a41ULL,
0xc2b3beeef85f71f6ULL, 0xe70eeddf3888789bULL, 0x07c40b8a301c8097ULL,
0x227958bbf0cb89faULL, 0x4cbeade9b1b2924dULL, 0x6903fed871659b20ULL,
0x9131474d3340a523ULL, 0xb48c147cf397ac4eULL, 0xda4be12eb2eeb7f9ULL,
0xfff6b21f7239be94ULL, 0x0f93c135f673c292ULL, 0x2a2e920436a4cbffULL,
0x44e9675677ddd048ULL, 0x61543467b70ad925ULL, 0x99668df2f52fe726ULL,
0xbcdbdec335f8ee4bULL, 0xd21c2b917481f5fcULL, 0xf7a178a0b456fc91ULL,
0x1a4d14a6d77c0716ULL, 0x3ff0479717ab0e7bULL, 0x5137b2c556d215ccULL,
0x748ae1f496051ca1ULL, 0x8cb85861d42022a2ULL, 0xa9050b5014f72bcfULL,
0xc7c2fe02558e3078ULL, 0xe27fad3395593915ULL, 0x121ade1911134513ULL,
0x37a78d28d1c44c7eULL, 0x5960787a90bd57c9ULL, 0x7cdd2b4b506a5ea4ULL,
0x84ef92de124f60a7ULL, 0xa152c1efd29869caULL, 0xcf9534bd93e1727dULL,
0xea28678c53367b10ULL, 0x0ae281d95ba2831cULL, 0x2f5fd2e89b758a71ULL,
0x419827bada0c91c6ULL, 0x6425748b1adb98abULL, 0x9c17cd1e58fea6a8ULL,
0xb9aa9e2f9829afc5ULL, 0xd76d6b7dd950b472ULL, 0xf2d0384c1987bd1fULL,
0x02b54b669dcdc119ULL, 0x270818575d1ac874ULL, 0x49cfed051c63d3c3ULL,
0x6c72be34dcb4daaeULL, 0x944007a19e91e4adULL, 0xb1fd54905e46edc0ULL,
0xdf3aa1c21f3ff677ULL, 0xfa87f2f3dfe8ff1aULL, 0x1eaf6d680e16066fULL,
0x3b123e59cec10f02ULL, 0x55d5cb0b8fb814b5ULL, 0x7068983a4f6f1dd8ULL,
0x885a21af0d4a23dbULL, 0xade7729ecd9d2ab6ULL, 0xc32087cc8ce43101ULL,
0xe69dd4fd4c33386cULL, 0x16f8a7d7c879446aULL, 0x3345f4e608ae4d07ULL,
0x5d8201b449d756b0ULL, 0x783f528589005fddULL, 0x800deb10cb2561deULL,
0xa5b0b8210bf268b3ULL, 0xcb774d734a8b7304ULL, 0xeeca1e428a5c7a69ULL,
0x0e00f81782c88265ULL, 0x2bbdab26421f8b08ULL, 0x457a5e74036690bfULL,
0x60c70d45c3b199d2ULL, 0x98f5b4d08194a7d1ULL, 0xbd48e7e14143aebcULL,
0xd38f12b3003ab50bULL, 0xf6324182c0edbc66ULL, 0x065732a844a7c060ULL,
0x23ea61998470c90dULL, 0x4d2d94cbc509d2baULL, 0x6890c7fa05dedbd7ULL,
0x90a27e6f47fbe5d4ULL, 0xb51f2d5e872cecb9ULL, 0xdbd8d80cc655f70eULL,
0xfe658b3d0682fe63ULL
};
unsigned long long U[256] =
{ 0x0000000000000000ULL, 0x067b86c43d6a6cb0ULL, 0x0cf70d887ad4d960ULL,
0x0a8c8b4c47beb5d0ULL, 0x19ee1b10f5a9b2c0ULL, 0x1f959dd4c8c3de70ULL,
0x151916988f7d6ba0ULL, 0x1362905cb2170710ULL, 0x166165102b846cedULL,
0x101ae3d416ee005dULL, 0x1a9668985150b58dULL, 0x1cedee5c6c3ad93dULL,
0x0f8f7e00de2dde2dULL, 0x09f4f8c4e347b29dULL, 0x03787388a4f9074dULL,
0x0503f54c99936bfdULL, 0x097f991197dfd0b7ULL, 0x0f041fd5aab5bc07ULL,
0x05889499ed0b09d7ULL, 0x03f3125dd0616567ULL, 0x1091820162766277ULL,
0x16ea04c55f1c0ec7ULL, 0x1c668f8918a2bb17ULL, 0x1a1d094d25c8d7a7ULL,
0x1f1efc01bc5bbc5aULL, 0x19657ac58131d0eaULL, 0x13e9f189c68f653aULL,
0x1592774dfbe5098aULL, 0x06f0e71149f20e9aULL, 0x008b61d57498622aULL,
0x0a07ea993326d7faULL, 0x0c7c6c5d0e4cbb4aULL, 0x12ff32232fbfa16eULL,
0x1484b4e712d5cddeULL, 0x1e083fab556b780eULL, 0x1873b96f680114beULL,
0x0b112933da1613aeULL, 0x0d6aaff7e77c7f1eULL, 0x07e624bba0c2caceULL,
0x019da27f9da8a67eULL, 0x049e5733043bcd83ULL, 0x02e5d1f73951a133ULL,
0x08695abb7eef14e3ULL, 0x0e12dc7f43857853ULL, 0x1d704c23f1927f43ULL,
0x1b0bcae7ccf813f3ULL, 0x118741ab8b46a623ULL, 0x17fcc76fb62cca93ULL,
0x1b80ab32b86071d9ULL, 0x1dfb2df6850a1d69ULL, 0x1777a6bac2b4a8b9ULL,
0x110c207effdec409ULL, 0x026eb0224dc9c319ULL, 0x041536e670a3afa9ULL,
0x0e99bdaa371d1a79ULL, 0x08e23b6e0a7776c9ULL, 0x0de1ce2293e41d34ULL,
0x0b9a48e6ae8e7184ULL, 0x0116c3aae930c454ULL, 0x076d456ed45aa8e4ULL,
0x140fd532664daff4ULL, 0x127453f65b27c344ULL, 0x18f8d8ba1c997694ULL,
0x1e835e7e21f31a24ULL, 0x004337779fa84bb1ULL, 0x0638b1b3a2c22701ULL,
0x0cb43affe57c92d1ULL, 0x0acfbc3bd816fe61ULL, 0x19ad2c676a01f971ULL,
0x1fd6aaa3576b95c1ULL, 0x155a21ef10d52011ULL, 0x1321a72b2dbf4ca1ULL,
0x16225267b42c275cULL, 0x1059d4a389464becULL, 0x1ad55fefcef8fe3cULL,
0x1caed92bf392928cULL, 0x0fcc49774185959cULL, 0x09b7cfb37ceff92cULL,
0x033b44ff3b514cfcULL, 0x0540c23b063b204cULL, 0x093cae6608779b06ULL,
0x0f4728a2351df7b6ULL, 0x05cba3ee72a34266ULL, 0x03b0252a4fc92ed6ULL,
0x10d2b576fdde29c6ULL, 0x16a933b2c0b44576ULL, 0x1c25b8fe870af0a6ULL,
0x1a5e3e3aba609c16ULL, 0x1f5dcb7623f3f7ebULL, 0x19264db21e999b5bULL,
0x13aac6fe59272e8bULL, 0x15d1403a644d423bULL, 0x06b3d066d65a452bULL,
0x00c856a2eb30299bULL, 0x0a44ddeeac8e9c4bULL, 0x0c3f5b2a91e4f0fbULL,
0x12bc0554b017eadfULL, 0x14c783908d7d866fULL, 0x1e4b08dccac333bfULL,
0x18308e18f7a95f0fULL, 0x0b521e4445be581fULL, 0x0d29988078d434afULL,
0x07a513cc3f6a817fULL, 0x01de95080200edcfULL, 0x04dd60449b938632ULL,
0x02a6e680a6f9ea82ULL, 0x082a6dcce1475f52ULL, 0x0e51eb08dc2d33e2ULL,
0x1d337b546e3a34f2ULL, 0x1b48fd9053505842ULL, 0x11c476dc14eeed92ULL,
0x17bff01829848122ULL, 0x1bc39c4527c83a68ULL, 0x1db81a811aa256d8ULL,
0x173491cd5d1ce308ULL, 0x114f170960768fb8ULL, 0x022d8755d26188a8ULL,
0x04560191ef0be418ULL, 0x0eda8adda8b551c8ULL, 0x08a10c1995df3d78ULL,
0x0da2f9550c4c5685ULL, 0x0bd97f9131263a35ULL, 0x0155f4dd76988fe5ULL,
0x072e72194bf2e355ULL, 0x144ce245f9e5e445ULL, 0x12376481c48f88f5ULL,
0x18bbefcd83313d25ULL, 0x1ec06909be5b5195ULL, 0x00866eef3f509762ULL,
0x06fde82b023afbd2ULL, 0x0c71636745844e02ULL, 0x0a0ae5a378ee22b2ULL,
0x196875ffcaf925a2ULL, 0x1f13f33bf7934912ULL, 0x159f7877b02dfcc2ULL,
0x13e4feb38d479072ULL, 0x16e70bff14d4fb8fULL, 0x109c8d3b29be973fULL,
0x1a1006776e0022efULL, 0x1c6b80b3536a4e5fULL, 0x0f0910efe17d494fULL,
0x0972962bdc1725ffULL, 0x03fe1d679ba9902fULL, 0x05859ba3a6c3fc9fULL,
0x09f9f7fea88f47d5ULL, 0x0f82713a95e52b65ULL, 0x050efa76d25b9eb5ULL,
0x03757cb2ef31f205ULL, 0x1017ecee5d26f515ULL, 0x166c6a2a604c99a5ULL,
0x1ce0e16627f22c75ULL, 0x1a9b67a21a9840c5ULL, 0x1f9892ee830b2b38ULL,
0x19e3142abe614788ULL, 0x136f9f66f9dff258ULL, 0x151419a2c4b59ee8ULL,
0x067689fe76a299f8ULL, 0x000d0f3a4bc8f548ULL, 0x0a8184760c764098ULL,
0x0cfa02b2311c2c28ULL, 0x12795ccc10ef360cULL, 0x1402da082d855abcULL,
0x1e8e51446a3bef6cULL, 0x18f5d780575183dcULL, 0x0b9747dce54684ccULL,
0x0decc118d82ce87cULL, 0x07604a549f925dacULL, 0x011bcc90a2f8311cULL,
0x041839dc3b6b5ae1ULL, 0x0263bf1806013651ULL, 0x08ef345441bf8381ULL,
0x0e94b2907cd5ef31ULL, 0x1df622cccec2e821ULL, 0x1b8da408f3a88491ULL,
0x11012f44b4163141ULL, 0x177aa980897c5df1ULL, 0x1b06c5dd8730e6bbULL,
0x1d7d4319ba5a8a0bULL, 0x17f1c855fde43fdbULL, 0x118a4e91c08e536bULL,
0x02e8decd7299547bULL, 0x049358094ff338cbULL, 0x0e1fd345084d8d1bULL,
0x086455813527e1abULL, 0x0d67a0cdacb48a56ULL, 0x0b1c260991dee6e6ULL,
0x0190ad45d6605336ULL, 0x07eb2b81eb0a3f86ULL, 0x1489bbdd591d3896ULL,
0x12f23d1964775426ULL, 0x187eb65523c9e1f6ULL, 0x1e0530911ea38d46ULL,
0x00c55998a0f8dcd3ULL, 0x06bedf5c9d92b063ULL, 0x0c325410da2c05b3ULL,
0x0a49d2d4e7466903ULL, 0x192b428855516e13ULL, 0x1f50c44c683b02a3ULL,
0x15dc4f002f85b773ULL, 0x13a7c9c412efdbc3ULL, 0x16a43c888b7cb03eULL,
0x10dfba4cb616dc8eULL, 0x1a533100f1a8695eULL, 0x1c28b7c4ccc205eeULL,
0x0f4a27987ed502feULL, 0x0931a15c43bf6e4eULL, 0x03bd2a100401db9eULL,
0x05c6acd4396bb72eULL, 0x09bac08937270c64ULL, 0x0fc1464d0a4d60d4ULL,
0x054dcd014df3d504ULL, 0x03364bc57099b9b4ULL, 0x1054db99c28ebea4ULL,
0x162f5d5dffe4d214ULL, 0x1ca3d611b85a67c4ULL, 0x1ad850d585300b74ULL,
0x1fdba5991ca36089ULL, 0x19a0235d21c90c39ULL, 0x132ca8116677b9e9ULL,
0x15572ed55b1dd559ULL, 0x0635be89e90ad249ULL, 0x004e384dd460bef9ULL,
0x0ac2b30193de0b29ULL, 0x0cb935c5aeb46799ULL, 0x123a6bbb8f477dbdULL,
0x1441ed7fb22d110dULL, 0x1ecd6633f593a4ddULL, 0x18b6e0f7c8f9c86dULL,
0x0bd470ab7aeecf7dULL, 0x0daff66f4784a3cdULL, 0x07237d23003a161dULL,
0x0158fbe73d507aadULL, 0x045b0eaba4c31150ULL, 0x0220886f99a97de0ULL,
0x08ac0323de17c830ULL, 0x0ed785e7e37da480ULL, 0x1db515bb516aa390ULL,
0x1bce937f6c00cf20ULL, 0x114218332bbe7af0ULL, 0x17399ef716d41640ULL,
0x1b45f2aa1898ad0aULL, 0x1d3e746e25f2c1baULL, 0x17b2ff22624c746aULL,
0x11c979e65f2618daULL, 0x02abe9baed311fcaULL, 0x04d06f7ed05b737aULL,
0x0e5ce43297e5c6aaULL, 0x082762f6aa8faa1aULL, 0x0d2497ba331cc1e7ULL,
0x0b5f117e0e76ad57ULL, 0x01d39a3249c81887ULL, 0x07a81cf674a27437ULL,
0x14ca8caac6b57327ULL, 0x12b10a6efbdf1f97ULL, 0x183d8122bc61aa47ULL,
0x1e4607e6810bc6f7ULL
};
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