From a59795c9860a9a31e6ccf3555ef0e0ca04a0dd87 Mon Sep 17 00:00:00 2001 From: "H. Peter Anvin" Date: Tue, 2 Oct 2007 17:40:00 -0700 Subject: Use the crc64 we already use as the perfect hash function prehash Use the same crc64 that we already use for the symbol table hash as the perfect hash function prehash. We appear to get radically faster convergence this way, and the crc64 is probably *faster*, since the table likely to be resident in memory. --- perllib/crc64.ph | 158 +++++++++++++++++++ perllib/gensv.pl | 18 +-- perllib/phash.ph | 63 +++----- perllib/random_sv_vectors.ph | 359 ++++++++++++++++++++++++++++++------------- 4 files changed, 442 insertions(+), 156 deletions(-) create mode 100644 perllib/crc64.ph (limited to 'perllib') diff --git a/perllib/crc64.ph b/perllib/crc64.ph new file mode 100644 index 00000000..30a47753 --- /dev/null +++ b/perllib/crc64.ph @@ -0,0 +1,158 @@ +# -*- perl -*- +# +# Pure Perl implementation of the same CRC64 implementation used +# elsewhere in NASM. +# +# Note: Perl may have 32- or 64-bit integers; we need to handle both +# without overflowing into floating point (yuck), so handle them as +# pairs of 32-bit numbers. Ordering is BIGENDIAN. +# + +@crc64_tab = ( + [0x00000000, 0x00000000], [0x7ad870c8, 0x30358979], + [0xf5b0e190, 0x606b12f2], [0x8f689158, 0x505e9b8b], + [0xc038e573, 0x9841b68f], [0xbae095bb, 0xa8743ff6], + [0x358804e3, 0xf82aa47d], [0x4f50742b, 0xc81f2d04], + [0xab28ecb4, 0x6814fe75], [0xd1f09c7c, 0x5821770c], + [0x5e980d24, 0x087fec87], [0x24407dec, 0x384a65fe], + [0x6b1009c7, 0xf05548fa], [0x11c8790f, 0xc060c183], + [0x9ea0e857, 0x903e5a08], [0xe478989f, 0xa00bd371], + [0x7d08ff3b, 0x88be6f81], [0x07d08ff3, 0xb88be6f8], + [0x88b81eab, 0xe8d57d73], [0xf2606e63, 0xd8e0f40a], + [0xbd301a48, 0x10ffd90e], [0xc7e86a80, 0x20ca5077], + [0x4880fbd8, 0x7094cbfc], [0x32588b10, 0x40a14285], + [0xd620138f, 0xe0aa91f4], [0xacf86347, 0xd09f188d], + [0x2390f21f, 0x80c18306], [0x594882d7, 0xb0f40a7f], + [0x1618f6fc, 0x78eb277b], [0x6cc08634, 0x48deae02], + [0xe3a8176c, 0x18803589], [0x997067a4, 0x28b5bcf0], + [0xfa11fe77, 0x117cdf02], [0x80c98ebf, 0x2149567b], + [0x0fa11fe7, 0x7117cdf0], [0x75796f2f, 0x41224489], + [0x3a291b04, 0x893d698d], [0x40f16bcc, 0xb908e0f4], + [0xcf99fa94, 0xe9567b7f], [0xb5418a5c, 0xd963f206], + [0x513912c3, 0x79682177], [0x2be1620b, 0x495da80e], + [0xa489f353, 0x19033385], [0xde51839b, 0x2936bafc], + [0x9101f7b0, 0xe12997f8], [0xebd98778, 0xd11c1e81], + [0x64b11620, 0x8142850a], [0x1e6966e8, 0xb1770c73], + [0x8719014c, 0x99c2b083], [0xfdc17184, 0xa9f739fa], + [0x72a9e0dc, 0xf9a9a271], [0x08719014, 0xc99c2b08], + [0x4721e43f, 0x0183060c], [0x3df994f7, 0x31b68f75], + [0xb29105af, 0x61e814fe], [0xc8497567, 0x51dd9d87], + [0x2c31edf8, 0xf1d64ef6], [0x56e99d30, 0xc1e3c78f], + [0xd9810c68, 0x91bd5c04], [0xa3597ca0, 0xa188d57d], + [0xec09088b, 0x6997f879], [0x96d17843, 0x59a27100], + [0x19b9e91b, 0x09fcea8b], [0x636199d3, 0x39c963f2], + [0xdf7adabd, 0x7a6e2d6f], [0xa5a2aa75, 0x4a5ba416], + [0x2aca3b2d, 0x1a053f9d], [0x50124be5, 0x2a30b6e4], + [0x1f423fce, 0xe22f9be0], [0x659a4f06, 0xd21a1299], + [0xeaf2de5e, 0x82448912], [0x902aae96, 0xb271006b], + [0x74523609, 0x127ad31a], [0x0e8a46c1, 0x224f5a63], + [0x81e2d799, 0x7211c1e8], [0xfb3aa751, 0x42244891], + [0xb46ad37a, 0x8a3b6595], [0xceb2a3b2, 0xba0eecec], + [0x41da32ea, 0xea507767], [0x3b024222, 0xda65fe1e], + [0xa2722586, 0xf2d042ee], [0xd8aa554e, 0xc2e5cb97], + [0x57c2c416, 0x92bb501c], [0x2d1ab4de, 0xa28ed965], + [0x624ac0f5, 0x6a91f461], [0x1892b03d, 0x5aa47d18], + [0x97fa2165, 0x0afae693], [0xed2251ad, 0x3acf6fea], + [0x095ac932, 0x9ac4bc9b], [0x7382b9fa, 0xaaf135e2], + [0xfcea28a2, 0xfaafae69], [0x8632586a, 0xca9a2710], + [0xc9622c41, 0x02850a14], [0xb3ba5c89, 0x32b0836d], + [0x3cd2cdd1, 0x62ee18e6], [0x460abd19, 0x52db919f], + [0x256b24ca, 0x6b12f26d], [0x5fb35402, 0x5b277b14], + [0xd0dbc55a, 0x0b79e09f], [0xaa03b592, 0x3b4c69e6], + [0xe553c1b9, 0xf35344e2], [0x9f8bb171, 0xc366cd9b], + [0x10e32029, 0x93385610], [0x6a3b50e1, 0xa30ddf69], + [0x8e43c87e, 0x03060c18], [0xf49bb8b6, 0x33338561], + [0x7bf329ee, 0x636d1eea], [0x012b5926, 0x53589793], + [0x4e7b2d0d, 0x9b47ba97], [0x34a35dc5, 0xab7233ee], + [0xbbcbcc9d, 0xfb2ca865], [0xc113bc55, 0xcb19211c], + [0x5863dbf1, 0xe3ac9dec], [0x22bbab39, 0xd3991495], + [0xadd33a61, 0x83c78f1e], [0xd70b4aa9, 0xb3f20667], + [0x985b3e82, 0x7bed2b63], [0xe2834e4a, 0x4bd8a21a], + [0x6debdf12, 0x1b863991], [0x1733afda, 0x2bb3b0e8], + [0xf34b3745, 0x8bb86399], [0x8993478d, 0xbb8deae0], + [0x06fbd6d5, 0xebd3716b], [0x7c23a61d, 0xdbe6f812], + [0x3373d236, 0x13f9d516], [0x49aba2fe, 0x23cc5c6f], + [0xc6c333a6, 0x7392c7e4], [0xbc1b436e, 0x43a74e9d], + [0x95ac9329, 0xac4bc9b5], [0xef74e3e1, 0x9c7e40cc], + [0x601c72b9, 0xcc20db47], [0x1ac40271, 0xfc15523e], + [0x5594765a, 0x340a7f3a], [0x2f4c0692, 0x043ff643], + [0xa02497ca, 0x54616dc8], [0xdafce702, 0x6454e4b1], + [0x3e847f9d, 0xc45f37c0], [0x445c0f55, 0xf46abeb9], + [0xcb349e0d, 0xa4342532], [0xb1eceec5, 0x9401ac4b], + [0xfebc9aee, 0x5c1e814f], [0x8464ea26, 0x6c2b0836], + [0x0b0c7b7e, 0x3c7593bd], [0x71d40bb6, 0x0c401ac4], + [0xe8a46c12, 0x24f5a634], [0x927c1cda, 0x14c02f4d], + [0x1d148d82, 0x449eb4c6], [0x67ccfd4a, 0x74ab3dbf], + [0x289c8961, 0xbcb410bb], [0x5244f9a9, 0x8c8199c2], + [0xdd2c68f1, 0xdcdf0249], [0xa7f41839, 0xecea8b30], + [0x438c80a6, 0x4ce15841], [0x3954f06e, 0x7cd4d138], + [0xb63c6136, 0x2c8a4ab3], [0xcce411fe, 0x1cbfc3ca], + [0x83b465d5, 0xd4a0eece], [0xf96c151d, 0xe49567b7], + [0x76048445, 0xb4cbfc3c], [0x0cdcf48d, 0x84fe7545], + [0x6fbd6d5e, 0xbd3716b7], [0x15651d96, 0x8d029fce], + [0x9a0d8cce, 0xdd5c0445], [0xe0d5fc06, 0xed698d3c], + [0xaf85882d, 0x2576a038], [0xd55df8e5, 0x15432941], + [0x5a3569bd, 0x451db2ca], [0x20ed1975, 0x75283bb3], + [0xc49581ea, 0xd523e8c2], [0xbe4df122, 0xe51661bb], + [0x3125607a, 0xb548fa30], [0x4bfd10b2, 0x857d7349], + [0x04ad6499, 0x4d625e4d], [0x7e751451, 0x7d57d734], + [0xf11d8509, 0x2d094cbf], [0x8bc5f5c1, 0x1d3cc5c6], + [0x12b59265, 0x35897936], [0x686de2ad, 0x05bcf04f], + [0xe70573f5, 0x55e26bc4], [0x9ddd033d, 0x65d7e2bd], + [0xd28d7716, 0xadc8cfb9], [0xa85507de, 0x9dfd46c0], + [0x273d9686, 0xcda3dd4b], [0x5de5e64e, 0xfd965432], + [0xb99d7ed1, 0x5d9d8743], [0xc3450e19, 0x6da80e3a], + [0x4c2d9f41, 0x3df695b1], [0x36f5ef89, 0x0dc31cc8], + [0x79a59ba2, 0xc5dc31cc], [0x037deb6a, 0xf5e9b8b5], + [0x8c157a32, 0xa5b7233e], [0xf6cd0afa, 0x9582aa47], + [0x4ad64994, 0xd625e4da], [0x300e395c, 0xe6106da3], + [0xbf66a804, 0xb64ef628], [0xc5bed8cc, 0x867b7f51], + [0x8aeeace7, 0x4e645255], [0xf036dc2f, 0x7e51db2c], + [0x7f5e4d77, 0x2e0f40a7], [0x05863dbf, 0x1e3ac9de], + [0xe1fea520, 0xbe311aaf], [0x9b26d5e8, 0x8e0493d6], + [0x144e44b0, 0xde5a085d], [0x6e963478, 0xee6f8124], + [0x21c64053, 0x2670ac20], [0x5b1e309b, 0x16452559], + [0xd476a1c3, 0x461bbed2], [0xaeaed10b, 0x762e37ab], + [0x37deb6af, 0x5e9b8b5b], [0x4d06c667, 0x6eae0222], + [0xc26e573f, 0x3ef099a9], [0xb8b627f7, 0x0ec510d0], + [0xf7e653dc, 0xc6da3dd4], [0x8d3e2314, 0xf6efb4ad], + [0x0256b24c, 0xa6b12f26], [0x788ec284, 0x9684a65f], + [0x9cf65a1b, 0x368f752e], [0xe62e2ad3, 0x06bafc57], + [0x6946bb8b, 0x56e467dc], [0x139ecb43, 0x66d1eea5], + [0x5ccebf68, 0xaecec3a1], [0x2616cfa0, 0x9efb4ad8], + [0xa97e5ef8, 0xcea5d153], [0xd3a62e30, 0xfe90582a], + [0xb0c7b7e3, 0xc7593bd8], [0xca1fc72b, 0xf76cb2a1], + [0x45775673, 0xa732292a], [0x3faf26bb, 0x9707a053], + [0x70ff5290, 0x5f188d57], [0x0a272258, 0x6f2d042e], + [0x854fb300, 0x3f739fa5], [0xff97c3c8, 0x0f4616dc], + [0x1bef5b57, 0xaf4dc5ad], [0x61372b9f, 0x9f784cd4], + [0xee5fbac7, 0xcf26d75f], [0x9487ca0f, 0xff135e26], + [0xdbd7be24, 0x370c7322], [0xa10fceec, 0x0739fa5b], + [0x2e675fb4, 0x576761d0], [0x54bf2f7c, 0x6752e8a9], + [0xcdcf48d8, 0x4fe75459], [0xb7173810, 0x7fd2dd20], + [0x387fa948, 0x2f8c46ab], [0x42a7d980, 0x1fb9cfd2], + [0x0df7adab, 0xd7a6e2d6], [0x772fdd63, 0xe7936baf], + [0xf8474c3b, 0xb7cdf024], [0x829f3cf3, 0x87f8795d], + [0x66e7a46c, 0x27f3aa2c], [0x1c3fd4a4, 0x17c62355], + [0x935745fc, 0x4798b8de], [0xe98f3534, 0x77ad31a7], + [0xa6df411f, 0xbfb21ca3], [0xdc0731d7, 0x8f8795da], + [0x536fa08f, 0xdfd90e51], [0x29b7d047, 0xefec8728] + ); + +sub crc64($$) { + my ($cv, $str) = @_; + my $c; + my @cc = @$cv; + $cc[0] %= 4294967296; + $cc[1] %= 4294967296; + + foreach $c (unpack("C*", $str)) { + my @ct = @{$crc64_tab[($cc[1] & 0xff) ^ $c]}; + + $cc[1] = $ct[1] ^ + ((($cc[1] & 0xffffff00) >> 8) | (($cc[0] & 0xff) << 24)); + $cc[0] = $ct[0] ^ (($cc[0] & 0xffffff00) >> 8); + } + + return @cc; +} diff --git a/perllib/gensv.pl b/perllib/gensv.pl index 2790b0ea..b80ccbe6 100755 --- a/perllib/gensv.pl +++ b/perllib/gensv.pl @@ -15,19 +15,11 @@ $outl = ' '; for ($i = 0; $i < $n; $i++) { - do { - die if (sysread(UR, $x4, 4) != 4); - @n = unpack("C*", $x4); - - $n[0] &= 31; - $n[1] &= 31; - $n[2] &= 31; - $n[3] &= 31; - } while ($n[0] == 0 || $n[1] == 0 || $n[2] == 0 || $n[3] == 0 || - $n[0] == $n[3] || $n[1] == $n[2]); - - $xl = sprintf(" [%d,%d,%d,%d]%s", - $n[0], $n[1], $n[2], $n[3], + die if (sysread(UR, $x8, 8) != 8); + @n = unpack("V*", $x8); + + $xl = sprintf(" [0x%08x, 0x%08x]%s", + $n[0], $n[1], ($i == $n-1) ? '' : ','); if (length($outl.$xl) > $maxlen) { print $outl, "\n"; diff --git a/perllib/phash.ph b/perllib/phash.ph index 3bb3a05b..487b12ee 100644 --- a/perllib/phash.ph +++ b/perllib/phash.ph @@ -8,25 +8,7 @@ use Graph::Undirected; require 'random_sv_vectors.ph'; - -# -# Truncate to 32-bit integer -# -sub int32($) { - my($x) = @_; - - return int($x) % 4294967296; -} - -# -# 32-bit rotate -# -sub rot($$) { - my($v,$s) = @_; - - $v = int32($v); - return int32(($v << $s)|($v >> (32-$s))); -} +require 'crc64.ph'; # # Compute the prehash for a key @@ -35,20 +17,11 @@ sub rot($$) { # sub prehash($$$) { my($key, $n, $sv) = @_; - my $c; - my $k1 = 0, $k2 = 0; - my $ko1, $ko2; - my($s0, $s1, $s2, $s3) = @{$sv}; - - foreach $c (unpack("C*", $key)) { - $ko1 = $k1; $ko2 = $k2; - $k1 = int32(rot($ko1,$s0)^int32(rot($ko2, $s1)+$c)); - $k2 = int32(rot($ko2,$s2)^int32(rot($ko1, $s3)+$c)); - } + my @c = crc64($sv, $key); # Create a bipartite graph... - $k1 = (($k1 & ($n-1)) << 1) + 0; - $k2 = (($k2 & ($n-1)) << 1) + 1; + $k1 = (($c[1] & ($n-1)) << 1) + 0; # low word + $k2 = (($c[0] & ($n-1)) << 1) + 1; # high word return ($k1, $k2); } @@ -81,10 +54,10 @@ sub walk_graph($$$) { # # Generate the function assuming a given N. # -# gen_hash_n(N, sv, \%data) +# gen_hash_n(N, sv, \%data, run) # -sub gen_hash_n($$$) { - my($n, $sv, $href) = @_; +sub gen_hash_n($$$$) { + my($n, $sv, $href, $run) = @_; my @keys = keys(%{$href}); my $i, $sv, @g; my $gr; @@ -103,8 +76,10 @@ sub gen_hash_n($$$) { if ($gr->has_edge($pf1, $pf2)) { my $xkey = $gr->get_edge_attribute($pf1, $pf2, "key"); my ($xp1, $xp2) = prehash($xkey, $n, $sv); - print STDERR "Collision: $pf1=$pf2 $k with "; - print STDERR "$xkey ($xp1,$xp2)\n"; + if (defined($run)) { + print STDERR "$run: Collision: $pf1=$pf2 $k with "; + print STDERR "$xkey ($xp1,$xp2)\n"; + } return; } @@ -117,11 +92,15 @@ sub gen_hash_n($$$) { # At this point, we're good if the graph is acyclic. if ($gr->is_cyclic) { - print STDERR "Graph is cyclic\n"; + if (defined($run)) { + print STDERR "$run: Graph is cyclic\n"; + } return; } - print STDERR "Graph OK, computing vertices...\n"; + if (defined($run)) { + print STDERR "$run: Graph OK, computing vertices...\n"; + } # Now we need to assign values to each vertex, so that for each # edge, the sum of the values for the two vertices give the value @@ -144,7 +123,10 @@ sub gen_hash_n($$$) { # print STDERR "Vertex ", $i, ": ", $g[$i], "\n"; # } - print STDERR "Done: n = $n, sv = [", join(',', @$sv), "]\n"; + if (defined($run)) { + printf STDERR "$run: Done: n = $n, sv = [0x%08x, 0x%08x]\n", + $$sv[0], $$sv[1]; + } return ($n, $sv, \@g); } @@ -159,6 +141,7 @@ sub gen_perfect_hash($) { my @keys = keys(%{$href}); my @hashinfo; my $n, $i, $j, $sv, $maxj; + my $run = 1; # Minimal power of 2 value for N with enough wiggle room. # The scaling constant must be larger than 0.5 in order for the @@ -176,7 +159,7 @@ sub gen_perfect_hash($) { print STDERR "Trying n = $n...\n"; for ($j = 0; $j < $maxj; $j++) { $sv = $random_sv_vectors[$j]; - @hashinfo = gen_hash_n($n, $sv, $href); + @hashinfo = gen_hash_n($n, $sv, $href, $run++); return @hashinfo if (defined(@hashinfo)); } $n <<= 1; diff --git a/perllib/random_sv_vectors.ph b/perllib/random_sv_vectors.ph index 30df929a..ae67d1f9 100644 --- a/perllib/random_sv_vectors.ph +++ b/perllib/random_sv_vectors.ph @@ -1,106 +1,259 @@ @random_sv_vectors = ( - [19,10,28,8], [19,13,14,5], [29,12,9,13], [19,18,27,7], [26,29,15,30], - [19,3,2,14], [12,12,11,27], [21,7,22,16], [5,31,11,11], [18,8,27,6], - [14,10,24,15], [9,4,15,3], [18,19,17,5], [17,22,9,3], [6,22,27,4], - [12,20,18,23], [29,15,5,7], [2,2,8,1], [29,9,14,8], [8,13,6,20], - [25,24,28,11], [4,7,21,24], [29,15,24,28], [3,2,29,17], [23,5,19,24], - [6,1,17,16], [17,13,12,3], [15,15,8,3], [21,9,10,1], [17,10,26,28], - [6,13,18,20], [5,7,21,23], [3,11,4,4], [25,23,1,16], [26,7,26,19], - [18,16,24,30], [4,5,31,13], [12,28,3,14], [27,23,29,30], [17,26,6,8], - [29,10,4,26], [26,5,13,6], [24,6,16,18], [20,23,28,25], [28,22,8,27], - [16,15,18,12], [6,17,11,17], [11,20,31,5], [7,24,7,23], [13,29,6,3], - [4,23,11,29], [31,6,9,28], [3,1,7,13], [11,26,18,3], [27,19,10,1], - [29,8,3,17], [7,25,20,21], [16,10,22,29], [15,5,6,28], [17,31,7,21], - [25,23,19,7], [1,15,9,23], [21,2,22,19], [11,14,23,21], [31,12,30,11], - [24,13,27,9], [29,17,25,1], [4,3,16,22], [1,19,16,20], [20,21,27,9], - [2,21,22,12], [29,18,11,17], [14,25,5,29], [12,3,21,22], [2,12,8,1], - [29,25,4,28], [15,7,27,14], [4,22,10,11], [15,23,16,10], [2,19,15,17], - [16,21,20,5], [7,21,7,24], [28,16,7,8], [14,19,31,20], [17,16,10,19], - [21,20,10,16], [31,4,30,5], [2,23,29,31], [22,22,18,12], [22,22,16,4], - [19,27,22,5], [23,16,26,22], [9,13,22,31], [14,5,8,18], [22,9,14,17], - [22,20,8,10], [27,20,19,15], [8,29,27,18], [11,3,12,14], [29,29,19,25], - [12,11,8,26], [24,8,27,19], [2,5,9,25], [24,28,7,28], [9,6,8,12], - [8,1,15,3], [9,31,13,6], [7,29,8,22], [27,2,17,10], [25,22,23,13], - [15,30,2,17], [28,20,11,3], [13,31,17,15], [18,19,1,26], [14,4,17,29], - [20,6,5,24], [23,17,25,16], [30,11,31,20], [24,29,17,1], [28,5,27,18], - [23,13,24,8], [19,19,16,24], [4,25,20,13], [17,19,1,12], [13,5,25,3], - [16,6,17,7], [18,21,8,31], [16,25,4,9], [18,14,12,22], [21,8,17,22], - [30,14,30,28], [23,9,15,5], [1,8,21,11], [4,25,7,24], [12,31,18,21], - [17,24,15,18], [5,7,31,30], [3,5,3,31], [18,29,28,28], [3,29,15,4], - [5,18,26,31], [31,27,24,4], [4,16,18,18], [17,25,15,12], [13,19,28,7], - [26,20,25,10], [18,12,1,2], [9,17,3,21], [25,25,6,27], [14,8,31,21], - [15,21,14,3], [27,15,4,30], [1,8,11,25], [7,8,3,26], [18,8,19,25], - [11,19,25,24], [15,22,4,8], [8,28,4,18], [29,1,8,26], [16,27,4,10], - [14,11,10,25], [13,3,14,14], [29,25,5,8], [5,19,11,3], [27,31,20,29], - [11,6,4,22], [31,7,27,11], [30,27,13,11], [21,15,21,31], [15,26,5,23], - [9,25,23,19], [23,28,22,31], [14,11,8,19], [18,8,28,2], [15,19,17,24], - [2,18,8,18], [21,30,15,18], [10,21,31,26], [11,6,18,6], [19,31,10,12], - [25,31,1,10], [26,12,8,8], [14,23,29,4], [4,26,11,18], [17,16,7,11], - [15,12,24,18], [8,30,20,4], [3,16,23,12], [21,28,12,19], [22,3,28,5], - [6,7,23,28], [30,22,8,27], [17,27,17,2], [24,29,20,25], [7,21,2,11], - [25,8,31,4], [24,11,21,14], [25,13,2,24], [11,14,2,24], [26,16,6,12], - [13,27,24,19], [11,27,10,5], [30,19,23,18], [14,16,4,21], [9,26,5,24], - [28,19,1,6], [21,29,28,4], [31,6,20,9], [11,3,8,28], [17,10,20,10], - [13,11,28,6], [18,8,13,11], [13,29,4,5], [23,24,3,10], [12,30,20,21], - [15,9,30,9], [3,2,22,25], [31,19,30,9], [9,15,14,23], [24,19,16,2], - [10,28,16,18], [12,4,16,23], [16,28,2,12], [7,17,8,15], [5,20,1,2], - [12,18,21,15], [28,25,20,18], [25,18,13,7], [1,9,11,21], [5,3,1,26], - [21,5,25,12], [30,28,24,7], [16,21,10,15], [29,21,9,17], [27,24,30,25], - [31,4,25,4], [14,21,13,6], [3,15,13,21], [6,6,14,9], [10,6,30,20], - [23,28,31,22], [30,11,25,2], [22,25,21,10], [10,11,31,11], [6,9,22,10], - [14,19,9,16], [17,17,7,20], [10,1,8,1], [29,18,10,14], [2,3,19,17], - [28,14,21,14], [1,14,3,5], [31,14,22,22], [13,26,13,31], [5,23,12,25], - [25,21,13,19], [11,2,12,21], [16,1,13,24], [6,2,4,8], [19,12,9,29], - [2,19,20,7], [6,18,25,16], [12,14,15,19], [5,20,22,31], [12,15,13,8], - [10,10,12,26], [3,28,1,23], [20,6,24,4], [29,26,27,3], [3,22,20,21], - [4,21,6,8], [19,18,8,11], [27,26,2,3], [9,30,26,31], [29,2,20,31], - [14,18,7,4], [29,18,19,16], [28,20,13,4], [18,23,12,26], [25,24,6,27], - [7,30,21,26], [18,9,24,13], [21,3,13,14], [26,5,7,12], [10,6,16,16], - [15,7,4,11], [11,2,25,3], [26,22,28,5], [8,4,30,10], [27,27,13,11], - [14,24,21,24], [14,26,16,20], [22,29,20,3], [7,24,3,4], [30,23,17,27], - [4,19,27,16], [18,31,10,8], [10,11,27,29], [24,16,13,1], [23,16,24,2], - [14,14,10,6], [25,16,11,17], [30,6,14,15], [8,24,30,13], [31,13,20,24], - [20,16,21,24], [7,1,17,16], [22,1,30,26], [25,18,23,11], [2,14,18,4], - [28,27,29,25], [30,16,4,11], [15,13,14,21], [8,16,18,17], [4,14,11,14], - [4,3,18,18], [9,21,2,23], [2,13,9,26], [12,19,21,7], [9,18,7,11], - [1,29,11,26], [23,5,31,27], [30,5,25,2], [11,4,21,20], [30,18,29,6], - [19,3,12,28], [25,9,12,23], [1,5,6,22], [13,8,28,26], [3,6,31,10], - [15,17,19,17], [7,8,31,29], [29,1,7,11], [15,15,1,16], [20,18,27,27], - [22,14,11,25], [15,8,22,11], [15,10,7,22], [19,5,21,25], [11,23,26,4], - [23,21,8,7], [10,3,18,17], [13,11,4,26], [5,11,2,1], [27,18,7,26], - [14,7,12,21], [6,3,7,23], [15,16,6,8], [6,31,16,29], [9,10,25,10], - [10,28,23,4], [21,3,8,31], [29,28,20,12], [20,10,7,31], [23,11,25,6], - [2,10,2,1], [25,3,18,24], [29,11,5,3], [26,3,7,28], [13,4,3,19], - [1,16,19,17], [15,12,1,16], [8,18,7,19], [21,3,5,11], [26,18,3,19], - [10,21,25,29], [12,22,24,22], [31,12,7,6], [20,7,6,13], [1,11,7,17], - [28,25,22,25], [21,4,20,11], [14,26,11,31], [4,30,7,1], [28,26,1,9], - [21,29,31,17], [25,17,14,4], [26,31,30,28], [4,23,2,12], [5,26,31,18], - [11,7,1,14], [19,6,2,20], [17,12,3,28], [25,17,12,8], [30,2,30,3], - [6,10,16,1], [21,24,13,26], [17,13,2,16], [12,16,12,17], [25,14,19,5], - [11,7,3,1], [7,9,7,31], [2,6,7,14], [24,12,8,28], [25,25,22,31], - [9,7,11,31], [20,8,4,23], [25,16,11,24], [2,19,20,17], [13,4,19,6], - [21,6,19,1], [29,21,12,23], [15,13,28,17], [31,11,20,25], [4,20,9,24], - [5,25,11,20], [21,25,31,12], [5,20,23,7], [27,26,3,17], [1,4,7,13], - [8,7,25,20], [20,4,24,14], [13,7,6,5], [14,17,23,22], [20,16,15,26], - [21,28,30,17], [13,1,7,15], [29,24,17,20], [22,20,16,5], [17,25,10,6], - [14,1,18,13], [8,26,31,7], [28,29,3,10], [27,12,15,16], [13,14,20,5], - [26,9,16,5], [10,12,15,23], [30,31,9,15], [15,6,7,31], [15,30,10,31], - [21,31,3,1], [20,8,22,8], [17,15,26,5], [31,6,11,10], [6,30,27,5], - [7,29,10,15], [16,10,27,22], [2,2,31,15], [20,22,26,27], [12,16,20,21], - [8,15,31,7], [4,30,23,28], [18,8,19,14], [30,26,11,7], [5,26,18,25], - [5,21,14,8], [20,30,3,31], [25,19,5,5], [29,7,2,18], [16,18,2,17], - [13,15,25,19], [24,1,24,30], [23,5,11,13], [30,25,5,25], [18,16,20,28], - [3,26,5,10], [4,12,20,20], [14,7,27,12], [7,26,15,18], [30,29,16,13], - [20,23,30,2], [30,27,23,21], [27,30,12,22], [31,22,25,2], [9,28,1,2], - [8,2,23,15], [1,16,31,2], [3,24,5,6], [27,14,30,20], [29,18,16,12], - [22,17,3,16], [14,20,1,19], [18,16,11,30], [27,16,23,24], [20,27,10,19], - [7,4,11,13], [24,23,24,16], [3,24,19,16], [22,11,29,12], [17,16,28,11], - [11,23,9,16], [20,12,22,24], [31,27,2,7], [28,12,9,19], [12,28,11,21], - [16,4,31,6], [16,1,26,25], [14,15,22,26], [12,18,11,10], [28,14,26,1], - [24,29,24,7], [2,21,8,22], [27,6,25,9], [5,31,16,3], [7,10,22,23], - [1,18,11,13], [24,20,21,6], [22,26,21,28], [11,23,24,26], [28,4,3,22], - [6,16,5,19], [26,1,13,1], [7,16,27,12], [10,18,20,13], [3,28,23,15], - [16,14,11,13], [30,12,27,26], [18,23,20,3], [24,17,25,20], [18,10,3,20], - [15,2,1,5], [15,29,27,7] + [0x4f75e86a, 0xa619a221], [0x4211d883, 0x375af6e6], + [0x7657d667, 0x6333e69f], [0x51306ad6, 0xe87a75b2], + [0x818469e6, 0x19a9e82d], [0x623da09e, 0x169c4031], + [0xc3012f83, 0xbdf48dd0], [0xfcbb1f89, 0x0c51d7c9], + [0xe1e3397b, 0x8ff4d865], [0x0ac918f1, 0x4f9ec6bb], + [0xbe18da0f, 0xd87be655], [0x0f0e0e53, 0xf1288c8b], + [0xf9d28c2b, 0xf8ab94c8], [0xcfabcfae, 0x6d08b1dc], + [0xe496f39b, 0x548e8257], [0xd21e139e, 0x721b5256], + [0xbdc4bf74, 0x03160c9e], [0xd19ef1b3, 0x0ca3b520], + [0x8f52dfbd, 0x4c7a6224], [0xc67399be, 0xbb88e496], + [0x334cdf5b, 0x4a7884e6], [0x46b89a7a, 0xaafbd448], + [0x0f5f12a1, 0x3694d0f1], [0x376fd093, 0xd0dac844], + [0xcc21a4bd, 0x11fb3780], [0x0fdf4036, 0x5b51fc12], + [0x4f8ffd03, 0xea2579a6], [0x8f8cc719, 0x7c11acb4], + [0x2fe1ee56, 0x9c781da6], [0x4db1da0d, 0xb65cb4e3], + [0x70b53ff6, 0x98f35a3e], [0x9bf52704, 0x66c9f702], + [0x9ea4aa9c, 0xa45cb773], [0x1b745933, 0x0e4df7c1], + [0xd9f3cc40, 0x78b8e00f], [0x131620ea, 0x6c693290], + [0xbc0e10dd, 0x2d8de15e], [0x3e7684e5, 0x15358338], + [0x427f025b, 0x1bea99b8], [0x9e36e80a, 0x5cc209f7], + [0xe96ecd24, 0x164c80ad], [0x2a0fd487, 0x34ae53a8], + [0x374d10ad, 0xf8ba703e], [0xc7b7025c, 0x726fd38c], + [0xc9c71681, 0x749fe58c], [0x54c146f9, 0xcf5d5eed], + [0xdd63a845, 0x5b409a2b], [0x6c1eb5df, 0x236f3d7a], + [0x3f26e454, 0x6c6ddbda], [0xde49583e, 0x854d25f8], + [0x77cc1c8b, 0xb9f44f2f], [0x504d08d7, 0x8a15f37b], + [0x0fa90449, 0x767c45e6], [0x353dd4f6, 0x3945abc3], + [0x279cc804, 0x9aca2078], [0xc0889e29, 0x0887bc4b], + [0x6befcf7a, 0x34579438], [0xa1e96c99, 0x4e8d958e], + [0x7e92c701, 0x8cafd3e4], [0x88194b29, 0x549baa5b], + [0x37d5a863, 0x6d158281], [0xe39bfd81, 0xeeba2b1f], + [0xf0b45736, 0x909cd899], [0x36528974, 0x3864d47c], + [0xe8c776af, 0x9a09b791], [0x2178fa44, 0x283993fb], + [0x7705f641, 0x6b77e579], [0x3be99f1a, 0xddb55ee7], + [0x933e4adf, 0x8bf2a4d5], [0x60bd229f, 0x553a1880], + [0xf71eecc0, 0x44540d74], [0x0b2e0f02, 0x51f94819], + [0x9acb45f1, 0x56ff9489], [0x55deac30, 0xf40bd69f], + [0xc7c65da9, 0x6e98523f], [0xd20df531, 0x73229a8b], + [0x56736755, 0x58f1155e], [0x6bd03660, 0x75c2d26c], + [0x62228cdc, 0x49ea4855], [0x0856f45a, 0xd59f5a1e], + [0x2b2e8407, 0x508bb429], [0xa24b81e7, 0xd2c1752b], + [0xc1eedb28, 0xf5dc5ff0], [0xb177d794, 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