Add tables for crc32_combine(), to speed it up by a factor of 200.

2 files changed, 396 insertions, 92 deletions

diff --git a/crc32.c b/crc32.c
index e72636a..5ccfe09 100644
--- a/crc32.c
+++ b/crc32.c
@@ -1,5 +1,5 @@
 /* crc32.c -- compute the CRC-32 of a data stream
- * Copyright (C) 1995-2006, 2010, 2011, 2012, 2016 Mark Adler
+ * Copyright (C) 1995-2006, 2010, 2011, 2012, 2016, 2018 Mark Adler
  * For conditions of distribution and use, see copyright notice in zlib.h
  *
  * Thanks to Rodney Brown <rbrown64@csc.com.au> for his contribution of faster
@@ -18,7 +18,9 @@
   first call get_crc_table() to initialize the tables before allowing more than
   one thread to use crc32().
 
-  DYNAMIC_CRC_TABLE and MAKECRCH can be #defined to write out crc32.h.
+  DYNAMIC_CRC_TABLE and MAKECRCH can be #defined to write out crc32.h. A main()
+  routine is also produced, so that this one source file can be compiled to an
+  executable.
  */
 
 #ifdef MAKECRCH
@@ -45,20 +47,50 @@
 #endif /* BYFOUR */
 
 /* Local functions for crc concatenation */
-local unsigned long gf2_matrix_times OF((unsigned long *mat,
-                                         unsigned long vec));
-local void gf2_matrix_square OF((unsigned long *square, unsigned long *mat));
+#define GF2_DIM 32      /* dimension of GF(2) vectors (length of CRC) */
+local z_crc_t gf2_matrix_times OF((const z_crc_t *mat, z_crc_t vec));
 local uLong crc32_combine_ OF((uLong crc1, uLong crc2, z_off64_t len2));
 
+/* ========================================================================= */
+local z_crc_t gf2_matrix_times(mat, vec)
+    const z_crc_t *mat;
+    z_crc_t vec;
+{
+    z_crc_t sum;
+
+    sum = 0;
+    while (vec) {
+        if (vec & 1)
+            sum ^= *mat;
+        vec >>= 1;
+        mat++;
+    }
+    return sum;
+}
+
 
 #ifdef DYNAMIC_CRC_TABLE
 
 local volatile int crc_table_empty = 1;
 local z_crc_t FAR crc_table[TBLS][256];
+local z_crc_t FAR crc_comb[GF2_DIM][GF2_DIM];
 local void make_crc_table OF((void));
+local void gf2_matrix_square OF((z_crc_t *square, const z_crc_t *mat));
 #ifdef MAKECRCH
-   local void write_table OF((FILE *, const z_crc_t FAR *));
+   local void write_table OF((FILE *, const z_crc_t FAR *, int));
 #endif /* MAKECRCH */
+
+/* ========================================================================= */
+local void gf2_matrix_square(square, mat)
+    z_crc_t *square;
+    const z_crc_t *mat;
+{
+    int n;
+
+    for (n = 0; n < GF2_DIM; n++)
+        square[n] = gf2_matrix_times(mat, mat[n]);
+}
+
 /*
   Generate tables for a byte-wise 32-bit CRC calculation on the polynomial:
   x^32+x^26+x^23+x^22+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x+1.
@@ -127,6 +159,33 @@ local void make_crc_table()
         }
 #endif /* BYFOUR */
 
+        /* generate zero operators table for crc32_combine() */
+
+        /* generate the operator to apply a single zero bit to a CRC -- the
+           first row adds the polynomial if the low bit is a 1, and the
+           remaining rows shift the CRC right one bit */
+        k = GF2_DIM - 3;
+        crc_comb[k][0] = 0xedb88320UL;      /* CRC-32 polynomial */
+        z_crc_t row = 1;
+        for (n = 1; n < GF2_DIM; n++) {
+            crc_comb[k][n] = row;
+            row <<= 1;
+        }
+
+        /* generate operators that apply 2, 4, and 8 zeros to a CRC, putting
+           the last one, the operator for one zero byte, at the 0 position */
+        gf2_matrix_square(crc_comb[k + 1], crc_comb[k]);
+        gf2_matrix_square(crc_comb[k + 2], crc_comb[k + 1]);
+        gf2_matrix_square(crc_comb[0], crc_comb[k + 2]);
+
+        /* generate operators for applying 2^n zero bytes to a CRC, filling out
+           the remainder of the table -- the operators repeat after GF2_DIM
+           values of n, so the table only needs GF2_DIM entries, regardless of
+           the size of the length being processed */
+        for (n = 1; n < k; n++)
+            gf2_matrix_square(crc_comb[n], crc_comb[n - 1]);
+
+        /* mark tables as complete, in case someone else is waiting */
         crc_table_empty = 0;
     }
     else {      /* not first */
@@ -134,50 +193,68 @@ local void make_crc_table()
         while (crc_table_empty)
             ;
     }
-
 #ifdef MAKECRCH
-    /* write out CRC tables to crc32.h */
     {
         FILE *out;
 
         out = fopen("crc32.h", "w");
         if (out == NULL) return;
+
+        /* write out CRC table to crc32.h */
         fprintf(out, "/* crc32.h -- tables for rapid CRC calculation\n");
         fprintf(out, " * Generated automatically by crc32.c\n */\n\n");
         fprintf(out, "local const z_crc_t FAR ");
-        fprintf(out, "crc_table[TBLS][256] =\n{\n  {\n");
-        write_table(out, crc_table[0]);
+        fprintf(out, "crc_table[%d][256] =\n{\n  {\n", TBLS);
+        write_table(out, crc_table[0], 256);
 #  ifdef BYFOUR
         fprintf(out, "#ifdef BYFOUR\n");
         for (k = 1; k < 8; k++) {
             fprintf(out, "  },\n  {\n");
-            write_table(out, crc_table[k]);
+            write_table(out, crc_table[k], 256);
         }
         fprintf(out, "#endif\n");
 #  endif /* BYFOUR */
         fprintf(out, "  }\n};\n");
+
+        /* write out zero operator table to crc32.h */
+        fprintf(out, "\nlocal const z_crc_t FAR ");
+        fprintf(out, "crc_comb[%d][%d] =\n{\n  {\n", GF2_DIM, GF2_DIM);
+        write_table(out, crc_comb[0], GF2_DIM);
+        for (k = 1; k < GF2_DIM; k++) {
+            fprintf(out, "  },\n  {\n");
+            write_table(out, crc_comb[k], GF2_DIM);
+        }
+        fprintf(out, "  }\n};\n");
         fclose(out);
     }
 #endif /* MAKECRCH */
 }
 
 #ifdef MAKECRCH
-local void write_table(out, table)
+local void write_table(out, table, k)
     FILE *out;
     const z_crc_t FAR *table;
+    int k;
 {
     int n;
 
-    for (n = 0; n < 256; n++)
+    for (n = 0; n < k; n++)
         fprintf(out, "%s0x%08lxUL%s", n % 5 ? "" : "    ",
                 (unsigned long)(table[n]),
-                n == 255 ? "\n" : (n % 5 == 4 ? ",\n" : ", "));
+                n == k - 1 ? "\n" : (n % 5 == 4 ? ",\n" : ", "));
+}
+
+int main()
+{
+    make_crc_table();
+    return 0;
 }
 #endif /* MAKECRCH */
 
 #else /* !DYNAMIC_CRC_TABLE */
 /* ========================================================================
- * Tables of CRC-32s of all single-byte values, made by make_crc_table().
+ * Tables of CRC-32s of all single-byte values, made by make_crc_table(),
+ * and tables of zero operator matrices for crc32_combine().
  */
 #include "crc32.h"
 #endif /* DYNAMIC_CRC_TABLE */
@@ -338,36 +415,6 @@ local unsigned long crc32_big(crc, buf, len)
 
 #endif /* BYFOUR */
 
-#define GF2_DIM 32      /* dimension of GF(2) vectors (length of CRC) */
-
-/* ========================================================================= */
-local unsigned long gf2_matrix_times(mat, vec)
-    unsigned long *mat;
-    unsigned long vec;
-{
-    unsigned long sum;
-
-    sum = 0;
-    while (vec) {
-        if (vec & 1)
-            sum ^= *mat;
-        vec >>= 1;
-        mat++;
-    }
-    return sum;
-}
-
-/* ========================================================================= */
-local void gf2_matrix_square(square, mat)
-    unsigned long *square;
-    unsigned long *mat;
-{
-    int n;
-
-    for (n = 0; n < GF2_DIM; n++)
-        square[n] = gf2_matrix_times(mat, mat[n]);
-}
-
 /* ========================================================================= */
 local uLong crc32_combine_(crc1, crc2, len2)
     uLong crc1;
@@ -375,53 +422,18 @@ local uLong crc32_combine_(crc1, crc2, len2)
     z_off64_t len2;
 {
     int n;
-    unsigned long row;
-    unsigned long even[GF2_DIM];    /* even-power-of-two zeros operator */
-    unsigned long odd[GF2_DIM];     /* odd-power-of-two zeros operator */
-
-    /* degenerate case (also disallow negative lengths) */
-    if (len2 <= 0)
-        return crc1;
-
-    /* put operator for one zero bit in odd */
-    odd[0] = 0xedb88320UL;          /* CRC-32 polynomial */
-    row = 1;
-    for (n = 1; n < GF2_DIM; n++) {
-        odd[n] = row;
-        row <<= 1;
-    }
 
-    /* put operator for two zero bits in even */
-    gf2_matrix_square(even, odd);
-
-    /* put operator for four zero bits in odd */
-    gf2_matrix_square(odd, even);
-
-    /* apply len2 zeros to crc1 (first square will put the operator for one
-       zero byte, eight zero bits, in even) */
-    do {
-        /* apply zeros operator for this bit of len2 */
-        gf2_matrix_square(even, odd);
-        if (len2 & 1)
-            crc1 = gf2_matrix_times(even, crc1);
-        len2 >>= 1;
-
-        /* if no more bits set, then done */
-        if (len2 == 0)
-            break;
-
-        /* another iteration of the loop with odd and even swapped */
-        gf2_matrix_square(odd, even);
-        if (len2 & 1)
-            crc1 = gf2_matrix_times(odd, crc1);
-        len2 >>= 1;
-
-        /* if no more bits set, then done */
-    } while (len2 != 0);
-
-    /* return combined crc */
-    crc1 ^= crc2;
-    return crc1;
+#ifdef DYNAMIC_CRC_TABLE
+    if (crc_table_empty)
+        make_crc_table();
+#endif /* DYNAMIC_CRC_TABLE */
+
+    if (len2 > 0)
+        /* operator for 2^n zeros repeats every GF2_DIM n values */
+        for (n = 0; len2; n = (n + 1) % GF2_DIM, len2 >>= 1)
+            if (len2 & 1)
+                crc1 = gf2_matrix_times(crc_comb[n], crc1);
+    return crc1 ^ crc2;
 }
 
 /* ========================================================================= */
diff --git a/crc32.h b/crc32.h
index 9e0c778..64ee8ea 100644
--- a/crc32.h
+++ b/crc32.h
@@ -2,7 +2,7 @@
  * Generated automatically by crc32.c
  */
 
-local const z_crc_t FAR crc_table[TBLS][256] =
+local const z_crc_t FAR crc_table[8][256] =
 {
   {
     0x00000000UL, 0x77073096UL, 0xee0e612cUL, 0x990951baUL, 0x076dc419UL,
@@ -439,3 +439,295 @@ local const z_crc_t FAR crc_table[TBLS][256] =
 #endif
   }
 };
+
+local const z_crc_t FAR crc_comb[32][32] =
+{
+  {
+    0x77073096UL, 0xee0e612cUL, 0x076dc419UL, 0x0edb8832UL, 0x1db71064UL,
+    0x3b6e20c8UL, 0x76dc4190UL, 0xedb88320UL, 0x00000001UL, 0x00000002UL,
+    0x00000004UL, 0x00000008UL, 0x00000010UL, 0x00000020UL, 0x00000040UL,
+    0x00000080UL, 0x00000100UL, 0x00000200UL, 0x00000400UL, 0x00000800UL,
+    0x00001000UL, 0x00002000UL, 0x00004000UL, 0x00008000UL, 0x00010000UL,
+    0x00020000UL, 0x00040000UL, 0x00080000UL, 0x00100000UL, 0x00200000UL,
+    0x00400000UL, 0x00800000UL
+  },
+  {
+    0x191b3141UL, 0x32366282UL, 0x646cc504UL, 0xc8d98a08UL, 0x4ac21251UL,
+    0x958424a2UL, 0xf0794f05UL, 0x3b83984bUL, 0x77073096UL, 0xee0e612cUL,
+    0x076dc419UL, 0x0edb8832UL, 0x1db71064UL, 0x3b6e20c8UL, 0x76dc4190UL,
+    0xedb88320UL, 0x00000001UL, 0x00000002UL, 0x00000004UL, 0x00000008UL,
+    0x00000010UL, 0x00000020UL, 0x00000040UL, 0x00000080UL, 0x00000100UL,
+    0x00000200UL, 0x00000400UL, 0x00000800UL, 0x00001000UL, 0x00002000UL,
+    0x00004000UL, 0x00008000UL
+  },
+  {
+    0xb8bc6765UL, 0xaa09c88bUL, 0x8f629757UL, 0xc5b428efUL, 0x5019579fUL,
+    0xa032af3eUL, 0x9b14583dUL, 0xed59b63bUL, 0x01c26a37UL, 0x0384d46eUL,
+    0x0709a8dcUL, 0x0e1351b8UL, 0x1c26a370UL, 0x384d46e0UL, 0x709a8dc0UL,
+    0xe1351b80UL, 0x191b3141UL, 0x32366282UL, 0x646cc504UL, 0xc8d98a08UL,
+    0x4ac21251UL, 0x958424a2UL, 0xf0794f05UL, 0x3b83984bUL, 0x77073096UL,
+    0xee0e612cUL, 0x076dc419UL, 0x0edb8832UL, 0x1db71064UL, 0x3b6e20c8UL,
+    0x76dc4190UL, 0xedb88320UL
+  },
+  {
+    0xccaa009eUL, 0x4225077dUL, 0x844a0efaUL, 0xd3e51bb5UL, 0x7cbb312bUL,
+    0xf9766256UL, 0x299dc2edUL, 0x533b85daUL, 0xa6770bb4UL, 0x979f1129UL,
+    0xf44f2413UL, 0x33ef4e67UL, 0x67de9cceUL, 0xcfbd399cUL, 0x440b7579UL,
+    0x8816eaf2UL, 0xcb5cd3a5UL, 0x4dc8a10bUL, 0x9b914216UL, 0xec53826dUL,
+    0x03d6029bUL, 0x07ac0536UL, 0x0f580a6cUL, 0x1eb014d8UL, 0x3d6029b0UL,
+    0x7ac05360UL, 0xf580a6c0UL, 0x30704bc1UL, 0x60e09782UL, 0xc1c12f04UL,
+    0x58f35849UL, 0xb1e6b092UL
+  },
+  {
+    0xae689191UL, 0x87a02563UL, 0xd4314c87UL, 0x73139f4fUL, 0xe6273e9eUL,
+    0x173f7b7dUL, 0x2e7ef6faUL, 0x5cfdedf4UL, 0xb9fbdbe8UL, 0xa886b191UL,
+    0x8a7c6563UL, 0xcf89cc87UL, 0x44629f4fUL, 0x88c53e9eUL, 0xcafb7b7dUL,
+    0x4e87f0bbUL, 0x9d0fe176UL, 0xe16ec4adUL, 0x19ac8f1bUL, 0x33591e36UL,
+    0x66b23c6cUL, 0xcd6478d8UL, 0x41b9f7f1UL, 0x8373efe2UL, 0xdd96d985UL,
+    0x605cb54bUL, 0xc0b96a96UL, 0x5a03d36dUL, 0xb407a6daUL, 0xb37e4bf5UL,
+    0xbd8d91abUL, 0xa06a2517UL
+  },
+  {
+    0xf1da05aaUL, 0x38c50d15UL, 0x718a1a2aUL, 0xe3143454UL, 0x1d596ee9UL,
+    0x3ab2ddd2UL, 0x7565bba4UL, 0xeacb7748UL, 0x0ee7e8d1UL, 0x1dcfd1a2UL,
+    0x3b9fa344UL, 0x773f4688UL, 0xee7e8d10UL, 0x078c1c61UL, 0x0f1838c2UL,
+    0x1e307184UL, 0x3c60e308UL, 0x78c1c610UL, 0xf1838c20UL, 0x38761e01UL,
+    0x70ec3c02UL, 0xe1d87804UL, 0x18c1f649UL, 0x3183ec92UL, 0x6307d924UL,
+    0xc60fb248UL, 0x576e62d1UL, 0xaedcc5a2UL, 0x86c88d05UL, 0xd6e01c4bUL,
+    0x76b13ed7UL, 0xed627daeUL
+  },
+  {
+    0x8f352d95UL, 0xc51b5d6bUL, 0x5147bc97UL, 0xa28f792eUL, 0x9e6ff41dUL,
+    0xe7aeee7bUL, 0x142cdab7UL, 0x2859b56eUL, 0x50b36adcUL, 0xa166d5b8UL,
+    0x99bcad31UL, 0xe8085c23UL, 0x0b61be07UL, 0x16c37c0eUL, 0x2d86f81cUL,
+    0x5b0df038UL, 0xb61be070UL, 0xb746c6a1UL, 0xb5fc8b03UL, 0xb0881047UL,
+    0xba6126cfUL, 0xafb34bdfUL, 0x841791ffUL, 0xd35e25bfUL, 0x7dcd4d3fUL,
+    0xfb9a9a7eUL, 0x2c4432bdUL, 0x5888657aUL, 0xb110caf4UL, 0xb95093a9UL,
+    0xa9d02113UL, 0x88d14467UL
+  },
+  {
+    0x33fff533UL, 0x67ffea66UL, 0xcfffd4ccUL, 0x448eafd9UL, 0x891d5fb2UL,
+    0xc94bb925UL, 0x49e6740bUL, 0x93cce816UL, 0xfce8d66dUL, 0x22a0aa9bUL,
+    0x45415536UL, 0x8a82aa6cUL, 0xce745299UL, 0x4799a373UL, 0x8f3346e6UL,
+    0xc5178b8dUL, 0x515e115bUL, 0xa2bc22b6UL, 0x9e09432dUL, 0xe763801bUL,
+    0x15b60677UL, 0x2b6c0ceeUL, 0x56d819dcUL, 0xadb033b8UL, 0x80116131UL,
+    0xdb53c423UL, 0x6dd68e07UL, 0xdbad1c0eUL, 0x6c2b3e5dUL, 0xd8567cbaUL,
+    0x6bddff35UL, 0xd7bbfe6aUL
+  },
+  {
+    0xce3371cbUL, 0x4717e5d7UL, 0x8e2fcbaeUL, 0xc72e911dUL, 0x552c247bUL,
+    0xaa5848f6UL, 0x8fc197adUL, 0xc4f2291bUL, 0x52955477UL, 0xa52aa8eeUL,
+    0x9124579dUL, 0xf939a97bUL, 0x290254b7UL, 0x5204a96eUL, 0xa40952dcUL,
+    0x9363a3f9UL, 0xfdb641b3UL, 0x201d8527UL, 0x403b0a4eUL, 0x8076149cUL,
+    0xdb9d2f79UL, 0x6c4b58b3UL, 0xd896b166UL, 0x6a5c648dUL, 0xd4b8c91aUL,
+    0x72009475UL, 0xe40128eaUL, 0x13735795UL, 0x26e6af2aUL, 0x4dcd5e54UL,
+    0x9b9abca8UL, 0xec447f11UL
+  },
+  {
+    0x1072db28UL, 0x20e5b650UL, 0x41cb6ca0UL, 0x8396d940UL, 0xdc5cb4c1UL,
+    0x63c86fc3UL, 0xc790df86UL, 0x5450b94dUL, 0xa8a1729aUL, 0x8a33e375UL,
+    0xcf16c0abUL, 0x455c8717UL, 0x8ab90e2eUL, 0xce031a1dUL, 0x4777327bUL,
+    0x8eee64f6UL, 0xc6adcfadUL, 0x562a991bUL, 0xac553236UL, 0x83db622dUL,
+    0xdcc7c21bUL, 0x62fe8277UL, 0xc5fd04eeUL, 0x508b0f9dUL, 0xa1161f3aUL,
+    0x995d3835UL, 0xe9cb762bUL, 0x08e7ea17UL, 0x11cfd42eUL, 0x239fa85cUL,
+    0x473f50b8UL, 0x8e7ea170UL
+  },
+  {
+    0xf891f16fUL, 0x2a52e49fUL, 0x54a5c93eUL, 0xa94b927cUL, 0x89e622b9UL,
+    0xc8bd4333UL, 0x4a0b8027UL, 0x9417004eUL, 0xf35f06ddUL, 0x3dcf0bfbUL,
+    0x7b9e17f6UL, 0xf73c2fecUL, 0x35095999UL, 0x6a12b332UL, 0xd4256664UL,
+    0x733bca89UL, 0xe6779512UL, 0x179e2c65UL, 0x2f3c58caUL, 0x5e78b194UL,
+    0xbcf16328UL, 0xa293c011UL, 0x9e568663UL, 0xe7dc0a87UL, 0x14c9134fUL,
+    0x2992269eUL, 0x53244d3cUL, 0xa6489a78UL, 0x97e032b1UL, 0xf4b16323UL,
+    0x3213c007UL, 0x6427800eUL
+  },
+  {
+    0x88b6ba63UL, 0xca1c7287UL, 0x4f49e34fUL, 0x9e93c69eUL, 0xe6568b7dUL,
+    0x17dc10bbUL, 0x2fb82176UL, 0x5f7042ecUL, 0xbee085d8UL, 0xa6b00df1UL,
+    0x96111da3UL, 0xf7533d07UL, 0x35d77c4fUL, 0x6baef89eUL, 0xd75df13cUL,
+    0x75cae439UL, 0xeb95c872UL, 0x0c5a96a5UL, 0x18b52d4aUL, 0x316a5a94UL,
+    0x62d4b528UL, 0xc5a96a50UL, 0x5023d2e1UL, 0xa047a5c2UL, 0x9bfe4dc5UL,
+    0xec8d9dcbUL, 0x026a3dd7UL, 0x04d47baeUL, 0x09a8f75cUL, 0x1351eeb8UL,
+    0x26a3dd70UL, 0x4d47bae0UL
+  },
+  {
+    0x5ad8a92cUL, 0xb5b15258UL, 0xb013a2f1UL, 0xbb5643a3UL, 0xaddd8107UL,
+    0x80ca044fUL, 0xdae50edfUL, 0x6ebb1bffUL, 0xdd7637feUL, 0x619d69bdUL,
+    0xc33ad37aUL, 0x5d04a0b5UL, 0xba09416aUL, 0xaf638495UL, 0x85b60f6bUL,
+    0xd01d1897UL, 0x7b4b376fUL, 0xf6966edeUL, 0x365ddbfdUL, 0x6cbbb7faUL,
+    0xd9776ff4UL, 0x699fd9a9UL, 0xd33fb352UL, 0x7d0e60e5UL, 0xfa1cc1caUL,
+    0x2f4885d5UL, 0x5e910baaUL, 0xbd221754UL, 0xa13528e9UL, 0x991b5793UL,
+    0xe947a967UL, 0x09fe548fUL
+  },
+  {
+    0xb566f6e2UL, 0xb1bceb85UL, 0xb808d14bUL, 0xab60a4d7UL, 0x8db04fefUL,
+    0xc011999fUL, 0x5b52357fUL, 0xb6a46afeUL, 0xb639d3bdUL, 0xb702a13bUL,
+    0xb5744437UL, 0xb1998e2fUL, 0xb8421a1fUL, 0xabf5327fUL, 0x8c9b62bfUL,
+    0xc247c33fUL, 0x5ffe803fUL, 0xbffd007eUL, 0xa48b06bdUL, 0x92670b3bUL,
+    0xffbf1037UL, 0x240f262fUL, 0x481e4c5eUL, 0x903c98bcUL, 0xfb083739UL,
+    0x2d616833UL, 0x5ac2d066UL, 0xb585a0ccUL, 0xb07a47d9UL, 0xbb8589f3UL,
+    0xac7a15a7UL, 0x83852d0fUL
+  },
+  {
+    0x9d9129bfUL, 0xe053553fUL, 0x1bd7ac3fUL, 0x37af587eUL, 0x6f5eb0fcUL,
+    0xdebd61f8UL, 0x660bc5b1UL, 0xcc178b62UL, 0x435e1085UL, 0x86bc210aUL,
+    0xd6094455UL, 0x77638eebUL, 0xeec71dd6UL, 0x06ff3dedUL, 0x0dfe7bdaUL,
+    0x1bfcf7b4UL, 0x37f9ef68UL, 0x6ff3ded0UL, 0xdfe7bda0UL, 0x64be7d01UL,
+    0xc97cfa02UL, 0x4988f245UL, 0x9311e48aUL, 0xfd52cf55UL, 0x21d498ebUL,
+    0x43a931d6UL, 0x875263acUL, 0xd5d5c119UL, 0x70da8473UL, 0xe1b508e6UL,
+    0x181b178dUL, 0x30362f1aUL
+  },
+  {
+    0x2ee43a2cUL, 0x5dc87458UL, 0xbb90e8b0UL, 0xac50d721UL, 0x83d0a803UL,
+    0xdcd05647UL, 0x62d1aacfUL, 0xc5a3559eUL, 0x5037ad7dUL, 0xa06f5afaUL,
+    0x9bafb3b5UL, 0xec2e612bUL, 0x032dc417UL, 0x065b882eUL, 0x0cb7105cUL,
+    0x196e20b8UL, 0x32dc4170UL, 0x65b882e0UL, 0xcb7105c0UL, 0x4d930dc1UL,
+    0x9b261b82UL, 0xed3d3145UL, 0x010b64cbUL, 0x0216c996UL, 0x042d932cUL,
+    0x085b2658UL, 0x10b64cb0UL, 0x216c9960UL, 0x42d932c0UL, 0x85b26580UL,
+    0xd015cd41UL, 0x7b5a9cc3UL
+  },
+  {
+    0x1b4511eeUL, 0x368a23dcUL, 0x6d1447b8UL, 0xda288f70UL, 0x6f2018a1UL,
+    0xde403142UL, 0x67f164c5UL, 0xcfe2c98aUL, 0x44b49555UL, 0x89692aaaUL,
+    0xc9a35315UL, 0x4837a06bUL, 0x906f40d6UL, 0xfbaf87edUL, 0x2c2e099bUL,
+    0x585c1336UL, 0xb0b8266cUL, 0xba014a99UL, 0xaf739373UL, 0x859620a7UL,
+    0xd05d470fUL, 0x7bcb885fUL, 0xf79710beUL, 0x345f273dUL, 0x68be4e7aUL,
+    0xd17c9cf4UL, 0x79883fa9UL, 0xf3107f52UL, 0x3d51f8e5UL, 0x7aa3f1caUL,
+    0xf547e394UL, 0x31fec169UL
+  },
+  {
+    0xbce15202UL, 0xa2b3a245UL, 0x9e1642cbUL, 0xe75d83d7UL, 0x15ca01efUL,
+    0x2b9403deUL, 0x572807bcUL, 0xae500f78UL, 0x87d118b1UL, 0xd4d33723UL,
+    0x72d76807UL, 0xe5aed00eUL, 0x102ca65dUL, 0x20594cbaUL, 0x40b29974UL,
+    0x816532e8UL, 0xd9bb6391UL, 0x6807c163UL, 0xd00f82c6UL, 0x7b6e03cdUL,
+    0xf6dc079aUL, 0x36c90975UL, 0x6d9212eaUL, 0xdb2425d4UL, 0x6d394de9UL,
+    0xda729bd2UL, 0x6f9431e5UL, 0xdf2863caUL, 0x6521c1d5UL, 0xca4383aaUL,
+    0x4ff60115UL, 0x9fec022aUL
+  },
+  {
+    0xff08e5efUL, 0x2560cd9fUL, 0x4ac19b3eUL, 0x9583367cUL, 0xf0776ab9UL,
+    0x3b9fd333UL, 0x773fa666UL, 0xee7f4cccUL, 0x078f9fd9UL, 0x0f1f3fb2UL,
+    0x1e3e7f64UL, 0x3c7cfec8UL, 0x78f9fd90UL, 0xf1f3fb20UL, 0x3896f001UL,
+    0x712de002UL, 0xe25bc004UL, 0x1fc68649UL, 0x3f8d0c92UL, 0x7f1a1924UL,
+    0xfe343248UL, 0x271962d1UL, 0x4e32c5a2UL, 0x9c658b44UL, 0xe3ba10c9UL,
+    0x1c0527d3UL, 0x380a4fa6UL, 0x70149f4cUL, 0xe0293e98UL, 0x1b237b71UL,
+    0x3646f6e2UL, 0x6c8dedc4UL
+  },
+  {
+    0x6f76172eUL, 0xdeec2e5cUL, 0x66a95af9UL, 0xcd52b5f2UL, 0x41d46da5UL,
+    0x83a8db4aUL, 0xdc20b0d5UL, 0x633067ebUL, 0xc660cfd6UL, 0x57b099edUL,
+    0xaf6133daUL, 0x85b361f5UL, 0xd017c5abUL, 0x7b5e8d17UL, 0xf6bd1a2eUL,
+    0x360b321dUL, 0x6c16643aUL, 0xd82cc874UL, 0x6b2896a9UL, 0xd6512d52UL,
+    0x77d35ce5UL, 0xefa6b9caUL, 0x043c75d5UL, 0x0878ebaaUL, 0x10f1d754UL,
+    0x21e3aea8UL, 0x43c75d50UL, 0x878ebaa0UL, 0xd46c7301UL, 0x73a9e043UL,
+    0xe753c086UL, 0x15d6874dUL
+  },
+  {
+    0x56f5cab9UL, 0xadeb9572UL, 0x80a62ca5UL, 0xda3d5f0bUL, 0x6f0bb857UL,
+    0xde1770aeUL, 0x675fe71dUL, 0xcebfce3aUL, 0x460e9a35UL, 0x8c1d346aUL,
+    0xc34b6e95UL, 0x5de7db6bUL, 0xbbcfb6d6UL, 0xacee6bedUL, 0x82add19bUL,
+    0xde2aa577UL, 0x67244cafUL, 0xce48995eUL, 0x47e034fdUL, 0x8fc069faUL,
+    0xc4f1d5b5UL, 0x5292ad2bUL, 0xa5255a56UL, 0x913bb2edUL, 0xf906639bUL,
+    0x297dc177UL, 0x52fb82eeUL, 0xa5f705dcUL, 0x909f0df9UL, 0xfa4f1db3UL,
+    0x2fef3d27UL, 0x5fde7a4eUL
+  },
+  {
+    0x385993acUL, 0x70b32758UL, 0xe1664eb0UL, 0x19bd9b21UL, 0x337b3642UL,
+    0x66f66c84UL, 0xcdecd908UL, 0x40a8b451UL, 0x815168a2UL, 0xd9d3d705UL,
+    0x68d6a84bUL, 0xd1ad5096UL, 0x782ba76dUL, 0xf0574edaUL, 0x3bdf9bf5UL,
+    0x77bf37eaUL, 0xef7e6fd4UL, 0x058dd9e9UL, 0x0b1bb3d2UL, 0x163767a4UL,
+    0x2c6ecf48UL, 0x58dd9e90UL, 0xb1bb3d20UL, 0xb8077c01UL, 0xab7ffe43UL,
+    0x8d8efac7UL, 0xc06cf3cfUL, 0x5ba8e1dfUL, 0xb751c3beUL, 0xb5d2813dUL,
+    0xb0d4043bUL, 0xbad90e37UL
+  },
+  {
+    0xb4247b20UL, 0xb339f001UL, 0xbd02e643UL, 0xa174cac7UL, 0x999893cfUL,
+    0xe84021dfUL, 0x0bf145ffUL, 0x17e28bfeUL, 0x2fc517fcUL, 0x5f8a2ff8UL,
+    0xbf145ff0UL, 0xa559b9a1UL, 0x91c27503UL, 0xf8f5ec47UL, 0x2a9adecfUL,
+    0x5535bd9eUL, 0xaa6b7b3cUL, 0x8fa7f039UL, 0xc43ee633UL, 0x530cca27UL,
+    0xa619944eUL, 0x97422eddUL, 0xf5f55bfbUL, 0x309bb1b7UL, 0x6137636eUL,
+    0xc26ec6dcUL, 0x5fac8bf9UL, 0xbf5917f2UL, 0xa5c329a5UL, 0x90f7550bUL,
+    0xfa9fac57UL, 0x2e4e5eefUL
+  },
+  {
+    0x695186a7UL, 0xd2a30d4eUL, 0x7e371cddUL, 0xfc6e39baUL, 0x23ad7535UL,
+    0x475aea6aUL, 0x8eb5d4d4UL, 0xc61aafe9UL, 0x57445993UL, 0xae88b326UL,
+    0x8660600dUL, 0xd7b1c65bUL, 0x74128af7UL, 0xe82515eeUL, 0x0b3b2d9dUL,
+    0x16765b3aUL, 0x2cecb674UL, 0x59d96ce8UL, 0xb3b2d9d0UL, 0xbc14b5e1UL,
+    0xa3586d83UL, 0x9dc1dd47UL, 0xe0f2bccfUL, 0x1a947fdfUL, 0x3528ffbeUL,
+    0x6a51ff7cUL, 0xd4a3fef8UL, 0x7236fbb1UL, 0xe46df762UL, 0x13aae885UL,
+    0x2755d10aUL, 0x4eaba214UL
+  },
+  {
+    0x66bc001eUL, 0xcd78003cUL, 0x41810639UL, 0x83020c72UL, 0xdd751ea5UL,
+    0x619b3b0bUL, 0xc3367616UL, 0x5d1dea6dUL, 0xba3bd4daUL, 0xaf06aff5UL,
+    0x857c59abUL, 0xd189b517UL, 0x78626c6fUL, 0xf0c4d8deUL, 0x3af8b7fdUL,
+    0x75f16ffaUL, 0xebe2dff4UL, 0x0cb4b9a9UL, 0x19697352UL, 0x32d2e6a4UL,
+    0x65a5cd48UL, 0xcb4b9a90UL, 0x4de63361UL, 0x9bcc66c2UL, 0xece9cbc5UL,
+    0x02a291cbUL, 0x05452396UL, 0x0a8a472cUL, 0x15148e58UL, 0x2a291cb0UL,
+    0x54523960UL, 0xa8a472c0UL
+  },
+  {
+    0xb58b27b3UL, 0xb0674927UL, 0xbbbf940fUL, 0xac0e2e5fUL, 0x836d5affUL,
+    0xddabb3bfUL, 0x6026613fUL, 0xc04cc27eUL, 0x5be882bdUL, 0xb7d1057aUL,
+    0xb4d30cb5UL, 0xb2d71f2bUL, 0xbedf3817UL, 0xa6cf766fUL, 0x96efea9fUL,
+    0xf6aed37fUL, 0x362ca0bfUL, 0x6c59417eUL, 0xd8b282fcUL, 0x6a1403b9UL,
+    0xd4280772UL, 0x732108a5UL, 0xe642114aUL, 0x17f524d5UL, 0x2fea49aaUL,
+    0x5fd49354UL, 0xbfa926a8UL, 0xa4234b11UL, 0x93379063UL, 0xfd1e2687UL,
+    0x214d4b4fUL, 0x429a969eUL
+  },
+  {
+    0xfe273162UL, 0x273f6485UL, 0x4e7ec90aUL, 0x9cfd9214UL, 0xe28a2269UL,
+    0x1e654293UL, 0x3cca8526UL, 0x79950a4cUL, 0xf32a1498UL, 0x3d252f71UL,
+    0x7a4a5ee2UL, 0xf494bdc4UL, 0x32587dc9UL, 0x64b0fb92UL, 0xc961f724UL,
+    0x49b2e809UL, 0x9365d012UL, 0xfdbaa665UL, 0x20044a8bUL, 0x40089516UL,
+    0x80112a2cUL, 0xdb535219UL, 0x6dd7a273UL, 0xdbaf44e6UL, 0x6c2f8f8dUL,
+    0xd85f1f1aUL, 0x6bcf3875UL, 0xd79e70eaUL, 0x744de795UL, 0xe89bcf2aUL,
+    0x0a469815UL, 0x148d302aUL
+  },
+  {
+    0xd3c98813UL, 0x7ce21667UL, 0xf9c42cceUL, 0x28f95fddUL, 0x51f2bfbaUL,
+    0xa3e57f74UL, 0x9cbbf8a9UL, 0xe206f713UL, 0x1f7ce867UL, 0x3ef9d0ceUL,
+    0x7df3a19cUL, 0xfbe74338UL, 0x2cbf8031UL, 0x597f0062UL, 0xb2fe00c4UL,
+    0xbe8d07c9UL, 0xa66b09d3UL, 0x97a715e7UL, 0xf43f2d8fUL, 0x330f5d5fUL,
+    0x661ebabeUL, 0xcc3d757cUL, 0x430becb9UL, 0x8617d972UL, 0xd75eb4a5UL,
+    0x75cc6f0bUL, 0xeb98de16UL, 0x0c40ba6dUL, 0x188174daUL, 0x3102e9b4UL,
+    0x6205d368UL, 0xc40ba6d0UL
+  },
+  {
+    0xf7d6deb4UL, 0x34dcbb29UL, 0x69b97652UL, 0xd372eca4UL, 0x7d94df09UL,
+    0xfb29be12UL, 0x2d227a65UL, 0x5a44f4caUL, 0xb489e994UL, 0xb262d569UL,
+    0xbfb4ac93UL, 0xa4185f67UL, 0x9341b88fUL, 0xfdf2775fUL, 0x2095e8ffUL,
+    0x412bd1feUL, 0x8257a3fcUL, 0xdfde41b9UL, 0x64cd8533UL, 0xc99b0a66UL,
+    0x4847128dUL, 0x908e251aUL, 0xfa6d4c75UL, 0x2fab9eabUL, 0x5f573d56UL,
+    0xbeae7aacUL, 0xa62df319UL, 0x972ae073UL, 0xf524c6a7UL, 0x31388b0fUL,
+    0x6271161eUL, 0xc4e22c3cUL
+  },
+  {
+    0xedb88320UL, 0x00000001UL, 0x00000002UL, 0x00000004UL, 0x00000008UL,
+    0x00000010UL, 0x00000020UL, 0x00000040UL, 0x00000080UL, 0x00000100UL,
+    0x00000200UL, 0x00000400UL, 0x00000800UL, 0x00001000UL, 0x00002000UL,
+    0x00004000UL, 0x00008000UL, 0x00010000UL, 0x00020000UL, 0x00040000UL,
+    0x00080000UL, 0x00100000UL, 0x00200000UL, 0x00400000UL, 0x00800000UL,
+    0x01000000UL, 0x02000000UL, 0x04000000UL, 0x08000000UL, 0x10000000UL,
+    0x20000000UL, 0x40000000UL
+  },
+  {
+    0x76dc4190UL, 0xedb88320UL, 0x00000001UL, 0x00000002UL, 0x00000004UL,
+    0x00000008UL, 0x00000010UL, 0x00000020UL, 0x00000040UL, 0x00000080UL,
+    0x00000100UL, 0x00000200UL, 0x00000400UL, 0x00000800UL, 0x00001000UL,
+    0x00002000UL, 0x00004000UL, 0x00008000UL, 0x00010000UL, 0x00020000UL,
+    0x00040000UL, 0x00080000UL, 0x00100000UL, 0x00200000UL, 0x00400000UL,
+    0x00800000UL, 0x01000000UL, 0x02000000UL, 0x04000000UL, 0x08000000UL,
+    0x10000000UL, 0x20000000UL
+  },
+  {
+    0x1db71064UL, 0x3b6e20c8UL, 0x76dc4190UL, 0xedb88320UL, 0x00000001UL,
+    0x00000002UL, 0x00000004UL, 0x00000008UL, 0x00000010UL, 0x00000020UL,
+    0x00000040UL, 0x00000080UL, 0x00000100UL, 0x00000200UL, 0x00000400UL,
+    0x00000800UL, 0x00001000UL, 0x00002000UL, 0x00004000UL, 0x00008000UL,
+    0x00010000UL, 0x00020000UL, 0x00040000UL, 0x00080000UL, 0x00100000UL,
+    0x00200000UL, 0x00400000UL, 0x00800000UL, 0x01000000UL, 0x02000000UL,
+    0x04000000UL, 0x08000000UL
+  }
+};