Speed up software CRC-32 computation by a factor of 1.5 to 3.

Use the interleaved method of Kadatch and Jenkins in order to make
use of pipelined instructions through multiple ALUs in a single
core. This also speeds up and simplifies the combination of CRCs,
and updates the functions to pre-calculate and use an operator for
CRC combination.

1 files changed, 733 insertions, 337 deletions

diff --git a/crc32.c b/crc32.c
index 2d213b3..f41dc6d 100644
--- a/crc32.c
+++ b/crc32.c
@@ -2,11 +2,9 @@
  * 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
- * CRC methods: exclusive-oring 32 bits of data at a time, and pre-computing
- * tables for updating the shift register in one step with three exclusive-ors
- * instead of four steps with four exclusive-ors.  This results in about a
- * factor of two increase in speed on a Power PC G4 (PPC7455) using gcc -O3.
+ * This interleaved implementation of a CRC makes use of pipelined multiple
+ * arithmetic-logic units, commonly found in modern CPU cores. It is due to
+ * Kadatch and Jenkins (2010). See doc/crc-doc.1.0.pdf in this distribution.
  */
 
 /* @(#) $Id$ */
@@ -14,13 +12,12 @@
 /*
   Note on the use of DYNAMIC_CRC_TABLE: there is no mutex or semaphore
   protection on the static variables used to control the first-use generation
-  of the crc tables.  Therefore, if you #define DYNAMIC_CRC_TABLE, you should
+  of the crc tables. Therefore, if you #define DYNAMIC_CRC_TABLE, you should
   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. A main()
-  routine is also produced, so that this one source file can be compiled to an
-  executable.
+  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
@@ -30,161 +27,164 @@
 #  endif /* !DYNAMIC_CRC_TABLE */
 #endif /* MAKECRCH */
 
-#include "zutil.h"      /* for STDC and FAR definitions */
+#include "zutil.h"      /* for Z_U4, Z_U8, z_crc_t, and FAR definitions */
+
+ /*
+  A CRC of a message is computed on N braids of words in the message, where
+  each word consists of W bytes (4 or 8). If N is 3, for example, then three
+  running sparse CRCs are calculated respectively on each braid, at these
+  indices in the array of words: 0, 3, 6, ..., 1, 4, 7, ..., and 2, 5, 8, ...
+  This is done starting at a word boundary, and continues until as many blocks
+  of N * W bytes as are available have been processed. The results are combined
+  into a single CRC at the end. For this code, N must be in the range 1..6 and
+  W must be 4 or 8. The upper limit on N can be increased if desired by adding
+  more #if blocks, extending the patterns apparent in the code. In addition,
+  crc32.h would need to be regenerated, if the maximum N value is increased.
+
+  N and W are chosen empirically by benchmarking the execution time on a given
+  processor. The choices for N and W below were based on testing on Intel Kaby
+  Lake i7, AMD Ryzen 7, ARM Cortex-A57, Sparc64-VII, PowerPC POWER9, and MIPS64
+  Octeon II processors. The Intel, AMD, and ARM processors were all fastest
+  with N=5, W=8. The Sparc, PowerPC, and MIPS64 were all fastest at N=5, W=4.
+  They were all tested with either gcc or clang, all using the -O3 optimization
+  level. Your mileage may vary.
+ */
 
-/* Definitions for doing the crc four data bytes at a time. */
-#if !defined(NOBYFOUR) && defined(Z_U4)
-#  define BYFOUR
-#endif
-#ifdef BYFOUR
-   local unsigned long crc32_little OF((unsigned long,
-                        const unsigned char FAR *, z_size_t));
-   local unsigned long crc32_big OF((unsigned long,
-                        const unsigned char FAR *, z_size_t));
-#  define TBLS 8
+/* Define N */
+#ifdef Z_TESTN
+#  define N Z_TESTN
 #else
-#  define TBLS 1
-#endif /* BYFOUR */
+#  define N 5
+#endif
+#if N < 1 || N > 6
+#  error N must be in 1..6
+#endif
 
-/* Local functions for crc concatenation */
-#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 void crc32_combine_gen_ OF((z_crc_t *op, z_off64_t len2));
+/*
+  z_crc_t must be at least 32 bits. z_word_t must be at least as long as
+  z_crc_t. It is assumed here that z_word_t is either 32 bits or 64 bits, and
+  that bytes are eight bits.
+ */
 
-/* ========================================================================= */
-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;
-}
+/*
+  Define W and the associated z_word_t type. If W is not defined, then a
+  braided calculation is not used, and the associated tables and code are not
+  compiled.
+ */
+#ifdef Z_TESTW
+#  if Z_TESTW-1 != -1
+#    define W Z_TESTW
+#  endif
+#else
+#  ifdef MAKECRCH
+#    define W 8         /* required for MAKECRCH */
+#  else
+#    if defined(__x86_64__) || defined(__aarch64__)
+#      define W 8
+#    else
+#      define W 4
+#    endif
+#  endif
+#endif
+#ifdef W
+#  if W == 8 && defined(Z_U8)
+     typedef Z_U8 z_word_t;
+#  elif defined(Z_U4)
+#    undef W
+#    define W 4
+     typedef Z_U4 z_word_t;
+#  else
+#    undef W
+#  endif
+#endif
+
+/* Local functions. */
+local z_crc_t multmodp OF((z_crc_t a, z_crc_t b));
+local z_crc_t x2nmodp OF((z_off64_t n, unsigned k));
+#ifdef W
+   local z_word_t byte_swap OF((z_word_t word));
+   local z_crc_t crc_word OF((z_word_t data));
+   local z_word_t crc_word_big OF((z_word_t data));
+#endif /* W */
 
+/* CRC polynomial. */
+#define POLY 0xedb88320         /* p(x) reflected, with x^32 implied */
 
 #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 z_crc_t FAR crc_table[256];
+local z_crc_t FAR x2n_table[32];
 local void make_crc_table OF((void));
-local void gf2_matrix_square OF((z_crc_t *square, const z_crc_t *mat));
+#ifdef W
+   local z_word_t FAR crc_big_table[256];
+   local z_crc_t FAR crc_braid_table[W][256];
+   local z_word_t FAR crc_braid_big_table[W][256];
+   local void braid OF((z_crc_t [][256], z_word_t [][256], int, int));
+#endif
 #ifdef MAKECRCH
    local void write_table OF((FILE *, const z_crc_t FAR *, int));
+   local void write_table32hi OF((FILE *, const z_word_t FAR *, int));
+   local void write_table64 OF((FILE *, const z_word_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.
 
   Polynomials over GF(2) are represented in binary, one bit per coefficient,
-  with the lowest powers in the most significant bit.  Then adding polynomials
+  with the lowest powers in the most significant bit. Then adding polynomials
   is just exclusive-or, and multiplying a polynomial by x is a right shift by
-  one.  If we call the above polynomial p, and represent a byte as the
+  one. If we call the above polynomial p, and represent a byte as the
   polynomial q, also with the lowest power in the most significant bit (so the
   byte 0xb1 is the polynomial x^7+x^3+x+1), then the CRC is (q*x^32) mod p,
   where a mod b means the remainder after dividing a by b.
 
   This calculation is done using the shift-register method of multiplying and
-  taking the remainder.  The register is initialized to zero, and for each
+  taking the remainder. The register is initialized to zero, and for each
   incoming bit, x^32 is added mod p to the register if the bit is a one (where
-  x^32 mod p is p+x^32 = x^26+...+1), and the register is multiplied mod p by
-  x (which is shifting right by one and adding x^32 mod p if the bit shifted
-  out is a one).  We start with the highest power (least significant bit) of
-  q and repeat for all eight bits of q.
-
-  The first table is simply the CRC of all possible eight bit values.  This is
-  all the information needed to generate CRCs on data a byte at a time for all
-  combinations of CRC register values and incoming bytes.  The remaining tables
-  allow for word-at-a-time CRC calculation for both big-endian and little-
-  endian machines, where a word is four bytes.
-*/
+  x^32 mod p is p+x^32 = x^26+...+1), and the register is multiplied mod p by x
+  (which is shifting right by one and adding x^32 mod p if the bit shifted out
+  is a one). We start with the highest power (least significant bit) of q and
+  repeat for all eight bits of q.
+
+  The table is simply the CRC of all possible eight bit values. This is all the
+  information needed to generate CRCs on data a byte at a time for all
+  combinations of CRC register values and incoming bytes.
+ */
+
 local void make_crc_table()
 {
-    z_crc_t c;
-    int n, k;
-    z_crc_t poly;                       /* polynomial exclusive-or pattern */
-    /* terms of polynomial defining this crc (except x^32): */
+    z_crc_t p;
     static volatile int first = 1;      /* flag to limit concurrent making */
-    static const unsigned char p[] = {0,1,2,4,5,7,8,10,11,12,16,22,23,26};
 
     /* See if another task is already doing this (not thread-safe, but better
        than nothing -- significantly reduces duration of vulnerability in
        case the advice about DYNAMIC_CRC_TABLE is ignored) */
     if (first) {
+        unsigned i, j, n;
         first = 0;
 
-        /* make exclusive-or pattern from polynomial (0xedb88320UL) */
-        poly = 0;
-        for (n = 0; n < (int)(sizeof(p)/sizeof(unsigned char)); n++)
-            poly |= (z_crc_t)1 << (31 - p[n]);
-
-        /* generate a crc for every 8-bit value */
-        for (n = 0; n < 256; n++) {
-            c = (z_crc_t)n;
-            for (k = 0; k < 8; k++)
-                c = c & 1 ? poly ^ (c >> 1) : c >> 1;
-            crc_table[0][n] = c;
-        }
-
-#ifdef BYFOUR
-        /* generate crc for each value followed by one, two, and three zeros,
-           and then the byte reversal of those as well as the first table */
-        for (n = 0; n < 256; n++) {
-            c = crc_table[0][n];
-            crc_table[4][n] = ZSWAP32(c);
-            for (k = 1; k < 4; k++) {
-                c = crc_table[0][c & 0xff] ^ (c >> 8);
-                crc_table[k][n] = c;
-                crc_table[k + 4][n] = ZSWAP32(c);
-            }
-        }
-#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;
+        /* initialize the CRC of bytes tables */
+        for (i = 0; i < 256; i++) {
+            p = i;
+            for (j = 0; j < 8; j++)
+                p = p & 1 ? (p >> 1) ^ POLY : p >> 1;
+            crc_table[i] = p;
+#ifdef W
+            crc_big_table[i] = byte_swap(p);
+#endif
         }
 
-        /* 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]);
+        /* initialize the x^2^n mod p(x) table */
+        p = (z_crc_t)1 << 30;         /* x^1 */
+        x2n_table[0] = p;
+        for (n = 1; n < 32; n++)
+            x2n_table[n] = p = multmodp(p, p);
+#ifdef W
+        /* initialize the braiding tables -- needs x2n_table[] */
+        braid(crc_braid_table, crc_braid_big_table, N, W);
+#endif
 
         /* mark tables as complete, in case someone else is waiting */
         crc_table_empty = 0;
@@ -196,42 +196,145 @@ local void make_crc_table()
     }
 #ifdef MAKECRCH
     {
+        /*
+          The crc32.h header file contains tables for both 32-bit and 64-bit
+          z_word_t's, and so requires a 64-bit type be available. In that case,
+          z_word_t must be defined to be 64-bits. This code then also generates
+          and writes out the tables for the case that z_word_t is 32 bits.
+         */
+#if !defined(W) || W != 8
+#  error Need a 64-bit integer type in order to generate crc32.h.
+#endif
         FILE *out;
+        int k, n;
+        z_crc_t ltl[8][256];
+        z_word_t big[8][256];
 
         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[%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], 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);
+        /* write out little-endian CRC table to crc32.h */
+        fprintf(out,
+            "/* crc32.h -- tables for rapid CRC calculation\n"
+            " * Generated automatically by crc32.c\n */\n"
+            "\n"
+            "local const z_crc_t FAR crc_table[] = {\n"
+            "    ");
+        write_table(out, crc_table, 256);
+        fprintf(out,
+            "};\n");
+
+        /* write out big-endian CRC table for 64-bit z_word_t to crc32.h */
+        fprintf(out,
+            "\n"
+            "#ifdef W\n"
+            "\n"
+            "#if W == 8\n"
+            "\n"
+            "local const z_word_t FAR crc_big_table[] = {\n"
+            "    ");
+        write_table64(out, crc_big_table, 256);
+        fprintf(out,
+            "};\n");
+
+        /* write out big-endian CRC table for 32-bit z_word_t to crc32.h */
+        fprintf(out,
+            "\n"
+            "#else /* W == 4 */\n"
+            "\n"
+            "local const z_word_t FAR crc_big_table[] = {\n"
+            "    ");
+        write_table32hi(out, crc_big_table, 256);
+        fprintf(out,
+            "};\n"
+            "\n"
+            "#endif\n");
+
+        /* write out braid tables for each value of N */
+        for (n = 1; n <= 6; n++) {
+            fprintf(out,
+            "\n"
+            "#if N == %d\n", n);
+
+            /* compute braid tables for this N and 64-bit word_t */
+            braid(ltl, big, n, 8);
+
+            /* write out braid tables for 64-bit z_word_t to crc32.h */
+            fprintf(out,
+            "\n"
+            "#if W == 8\n"
+            "\n"
+            "local const z_crc_t FAR crc_braid_table[][256] = {\n");
+            for (k = 0; k < 8; k++) {
+                fprintf(out, "   {");
+                write_table(out, ltl[k], 256);
+                fprintf(out, "}%s", k < 7 ? ",\n" : "");
+            }
+            fprintf(out,
+            "};\n"
+            "\n"
+            "local const z_word_t FAR crc_braid_big_table[][256] = {\n");
+            for (k = 0; k < 8; k++) {
+                fprintf(out, "   {");
+                write_table64(out, big[k], 256);
+                fprintf(out, "}%s", k < 7 ? ",\n" : "");
+            }
+            fprintf(out,
+            "};\n");
+
+            /* compute braid tables for this N and 32-bit word_t */
+            braid(ltl, big, n, 4);
+
+            /* write out braid tables for 32-bit z_word_t to crc32.h */
+            fprintf(out,
+            "\n"
+            "#else /* W == 4 */\n"
+            "\n"
+            "local const z_crc_t FAR crc_braid_table[][256] = {\n");
+            for (k = 0; k < 4; k++) {
+                fprintf(out, "   {");
+                write_table(out, ltl[k], 256);
+                fprintf(out, "}%s", k < 3 ? ",\n" : "");
+            }
+            fprintf(out,
+            "};\n"
+            "\n"
+            "local const z_word_t FAR crc_braid_big_table[][256] = {\n");
+            for (k = 0; k < 4; k++) {
+                fprintf(out, "   {");
+                write_table32hi(out, big[k], 256);
+                fprintf(out, "}%s", k < 3 ? ",\n" : "");
+            }
+            fprintf(out,
+            "};\n"
+            "\n"
+            "#endif\n"
+            "\n"
+            "#endif\n");
         }
-        fprintf(out, "  }\n};\n");
+        fprintf(out,
+            "\n"
+            "#endif\n");
+
+        /* write out zeros operator table to crc32.h */
+        fprintf(out,
+            "\n"
+            "local const z_crc_t FAR x2n_table[] = {\n"
+            "    ");
+        write_table(out, x2n_table, 32);
+        fprintf(out,
+            "};\n");
         fclose(out);
     }
 #endif /* MAKECRCH */
 }
 
 #ifdef MAKECRCH
+
+/*
+   Write the 32-bit values in table[0..k-1] to out, five per line in
+   hexadecimal separated by commas.
+ */
 local void write_table(out, table, k)
     FILE *out;
     const z_crc_t FAR *table;
@@ -240,26 +343,194 @@ local void write_table(out, table, k)
     int n;
 
     for (n = 0; n < k; n++)
-        fprintf(out, "%s0x%08lxUL%s", n % 5 ? "" : "    ",
+        fprintf(out, "%s0x%08lx%s", n == 0 || n % 5 ? "" : "    ",
                 (unsigned long)(table[n]),
-                n == k - 1 ? "\n" : (n % 5 == 4 ? ",\n" : ", "));
+                n == k - 1 ? "" : (n % 5 == 4 ? ",\n" : ", "));
+}
+
+/*
+   Write the high 32-bits of each value in table[0..k-1] to out, five per line
+   in hexadecimal separated by commas.
+ */
+local void write_table32hi(out, table, k)
+FILE *out;
+const z_word_t FAR *table;
+int k;
+{
+    int n;
+
+    for (n = 0; n < k; n++)
+        fprintf(out, "%s0x%08lx%s", n == 0 || n % 5 ? "" : "    ",
+                (unsigned long)(table[n] >> 32),
+                n == k - 1 ? "" : (n % 5 == 4 ? ",\n" : ", "));
 }
 
+/*
+  Write the 64-bit values in table[0..k-1] to out, three per line in
+  hexadecimal separated by commas. This assumes that if there is a 64-bit
+  type, then there is also a long long integer type, and it is at least 64
+  bits. If not, then the type cast and format string can be adjusted
+  accordingly.
+ */
+local void write_table64(out, table, k)
+    FILE *out;
+    const z_word_t FAR *table;
+    int k;
+{
+    int n;
+
+    for (n = 0; n < k; n++)
+        fprintf(out, "%s0x%016llx%s", n == 0 || n % 3 ? "" : "    ",
+                (unsigned long long)(table[n]),
+                n == k - 1 ? "" : (n % 3 == 2 ? ",\n" : ", "));
+}
+
+/* Actually do the deed. */
 int main()
 {
     make_crc_table();
     return 0;
 }
+
 #endif /* MAKECRCH */
 
+#ifdef W
+/*
+  Generate the little and big-endian braid tables for the given n and z_word_t
+  size w. Each array must have room for w blocks of 256 elements.
+ */
+local void braid(ltl, big, n, w)
+    z_crc_t ltl[][256];
+    z_word_t big[][256];
+    int n;
+    int w;
+{
+    int k;
+    z_crc_t i, p, q;
+    for (k = 0; k < w; k++) {
+        p = x2nmodp((n * w + 3 - k) << 3, 0);
+        ltl[k][0] = 0;
+        big[w - 1 - k][0] = 0;
+        for (i = 1; i < 256; i++) {
+            ltl[k][i] = q = multmodp(i << 24, p);
+            big[w - 1 - k][i] = byte_swap(q);
+        }
+    }
+}
+#endif
+
 #else /* !DYNAMIC_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().
+ * Tables for byte-wise and braided CRC-32 calculations, and a table of powers
+ * of x for combining CRC-32s, all made by make_crc_table().
  */
 #include "crc32.h"
 #endif /* DYNAMIC_CRC_TABLE */
 
+/* ========================================================================
+ * Routines used for CRC calculation. Some are also required for the table
+ * generation above.
+ */
+
+/*
+  Return a(x) multiplied by b(x) modulo p(x), where p(x) is the CRC polynomial,
+  reflected. For speed, this requires that a not be zero.
+ */
+local z_crc_t multmodp(a, b)
+    z_crc_t a;
+    z_crc_t b;
+{
+    z_crc_t m, p;
+
+    m = (z_crc_t)1 << 31;
+    p = 0;
+    for (;;) {
+        if (a & m) {
+            p ^= b;
+            if ((a & (m - 1)) == 0)
+                break;
+        }
+        m >>= 1;
+        b = b & 1 ? (b >> 1) ^ POLY : b >> 1;
+    }
+    return p;
+}
+
+/*
+  Return x^(n+k) modulo p(x). Requires that x2n_table[] has been initialized.
+ */
+local z_crc_t x2nmodp(n, k)
+    z_off64_t n;
+    unsigned k;
+{
+    z_crc_t p;
+
+    p = (z_crc_t)1 << 31;           /* x^0 == 1 */
+    while (n) {
+        if (n & 1)
+            p = multmodp(x2n_table[k & 31], p);
+        n >>= 1;
+        k++;
+    }
+    return p;
+}
+
+#ifdef W
+
+/*
+  Swap the bytes in a z_word_t to convert between little and big endian. Any
+  self-respecting compiler will optimize this to a single machine byte-swap
+  instruction, if one is available. This assumes that word_t is either 32 bits
+  or 64 bits.
+ */
+local z_word_t byte_swap(word)
+    z_word_t word;
+{
+#if W == 8
+    return
+        (word & 0xff00000000000000) >> 56 |
+        (word & 0xff000000000000) >> 40 |
+        (word & 0xff0000000000) >> 24 |
+        (word & 0xff00000000) >> 8 |
+        (word & 0xff000000) << 8 |
+        (word & 0xff0000) << 24 |
+        (word & 0xff00) << 40 |
+        (word & 0xff) << 56;
+#else   /* W == 4 */
+    return
+        (word & 0xff000000) >> 24 |
+        (word & 0xff0000) >> 8 |
+        (word & 0xff00) << 8 |
+        (word & 0xff) << 24;
+#endif
+}
+
+/*
+  Return the CRC of the W bytes in the word_t data, taking the
+  least-significant byte of the word as the first byte of data, without any pre
+  or post conditioning. This is used to combine the CRCs of each braid.
+ */
+local z_crc_t crc_word(data)
+    z_word_t data;
+{
+    int k;
+    for (k = 0; k < W; k++)
+        data = (data >> 8) ^ crc_table[data & 0xff];
+    return (z_crc_t)data;
+}
+
+local z_word_t crc_word_big(data)
+    z_word_t data;
+{
+    int k;
+    for (k = 0; k < W; k++)
+        data = (data << 8) ^
+            crc_big_table[(data >> ((W - 1) << 3)) & 0xff];
+    return data;
+}
+
+#endif /* W */
+
 /* =========================================================================
  * This function can be used by asm versions of crc32()
  */
@@ -273,168 +544,348 @@ const z_crc_t FAR * ZEXPORT get_crc_table()
 }
 
 /* ========================================================================= */
-#define DO1 crc = crc_table[0][((int)crc ^ (*buf++)) & 0xff] ^ (crc >> 8)
-#define DO8 DO1; DO1; DO1; DO1; DO1; DO1; DO1; DO1
-
-/* ========================================================================= */
 unsigned long ZEXPORT crc32_z(crc, buf, len)
     unsigned long crc;
     const unsigned char FAR *buf;
     z_size_t len;
 {
-    if (buf == Z_NULL) return 0UL;
+    /* Return initial CRC, if requested. */
+    if (buf == Z_NULL) return 0;
 
 #ifdef DYNAMIC_CRC_TABLE
     if (crc_table_empty)
         make_crc_table();
 #endif /* DYNAMIC_CRC_TABLE */
 
-#ifdef BYFOUR
-    if (sizeof(void *) == sizeof(z_size_t)) {
-        z_crc_t endian;
+    /* Pre-condition the CRC */
+    crc ^= 0xffffffff;
+
+#ifdef W
+
+    /* If provided enough bytes, do a braided CRC calculation. */
+    if (len >= N * W + W - 1) {
+        z_size_t blks;
+        z_word_t const *words;
+        unsigned endian;
+        int k;
+
+        /* Compute the CRC up to a z_word_t boundary. */
+        while (len && ((z_size_t)buf & (W - 1)) != 0) {
+            len--;
+            crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
+        }
+
+        /* Compute the CRC on as many N z_word_t blocks as are available. */
+        blks = len / (N * W);
+        len -= blks * N * W;
+        words = (z_word_t const *)buf;
 
+        /* Do endian check at execution time instead of compile time, since ARM
+           processors can change the endianess at execution time. If the
+           compiler knows what the endianess will be, it can optimize out the
+           check and the unused branch. */
         endian = 1;
-        if (*((unsigned char *)(&endian)))
-            return crc32_little(crc, buf, len);
-        else
-            return crc32_big(crc, buf, len);
-    }
-#endif /* BYFOUR */
-    crc = crc ^ 0xffffffffUL;
-    while (len >= 8) {
-        DO8;
-        len -= 8;
-    }
-    if (len) do {
-        DO1;
-    } while (--len);
-    return crc ^ 0xffffffffUL;
-}
+        if (*(unsigned char *)&endian) {
+            /* Little endian. */
+
+            z_crc_t crc0;
+            z_word_t word0;
+#if N > 1
+            z_crc_t crc1;
+            z_word_t word1;
+#if N > 2
+            z_crc_t crc2;
+            z_word_t word2;
+#if N > 3
+            z_crc_t crc3;
+            z_word_t word3;
+#if N > 4
+            z_crc_t crc4;
+            z_word_t word4;
+#if N > 5
+            z_crc_t crc5;
+            z_word_t word5;
+#endif
+#endif
+#endif
+#endif
+#endif
 
-/* ========================================================================= */
-unsigned long ZEXPORT crc32(crc, buf, len)
-    unsigned long crc;
-    const unsigned char FAR *buf;
-    uInt len;
-{
-    return crc32_z(crc, buf, len);
-}
+            /* Initialize the CRC for each braid. */
+            crc0 = crc;
+#if N > 1
+            crc1 = 0;
+#if N > 2
+            crc2 = 0;
+#if N > 3
+            crc3 = 0;
+#if N > 4
+            crc4 = 0;
+#if N > 5
+            crc5 = 0;
+#endif
+#endif
+#endif
+#endif
+#endif
 
-#ifdef BYFOUR
+            /*
+              Process the first blks-1 blocks, computing the CRCs on each braid
+              independently.
+             */
+            while (--blks) {
+                /* Load the word for each braid into registers. */
+                word0 = crc0 ^ words[0];
+#if N > 1
+                word1 = crc1 ^ words[1];
+#if N > 2
+                word2 = crc2 ^ words[2];
+#if N > 3
+                word3 = crc3 ^ words[3];
+#if N > 4
+                word4 = crc4 ^ words[4];
+#if N > 5
+                word5 = crc5 ^ words[5];
+#endif
+#endif
+#endif
+#endif
+#endif
+                words += N;
+
+                /* Compute and update the CRC for each word. The loop should
+                   get unrolled. */
+                crc0 = crc_braid_table[0][word0 & 0xff];
+#if N > 1
+                crc1 = crc_braid_table[0][word1 & 0xff];
+#if N > 2
+                crc2 = crc_braid_table[0][word2 & 0xff];
+#if N > 3
+                crc3 = crc_braid_table[0][word3 & 0xff];
+#if N > 4
+                crc4 = crc_braid_table[0][word4 & 0xff];
+#if N > 5
+                crc5 = crc_braid_table[0][word5 & 0xff];
+#endif
+#endif
+#endif
+#endif
+#endif
+                for (k = 1; k < W; k++) {
+                    crc0 ^= crc_braid_table[k][(word0 >> (k << 3)) & 0xff];
+#if N > 1
+                    crc1 ^= crc_braid_table[k][(word1 >> (k << 3)) & 0xff];
+#if N > 2
+                    crc2 ^= crc_braid_table[k][(word2 >> (k << 3)) & 0xff];
+#if N > 3
+                    crc3 ^= crc_braid_table[k][(word3 >> (k << 3)) & 0xff];
+#if N > 4
+                    crc4 ^= crc_braid_table[k][(word4 >> (k << 3)) & 0xff];
+#if N > 5
+                    crc5 ^= crc_braid_table[k][(word5 >> (k << 3)) & 0xff];
+#endif
+#endif
+#endif
+#endif
+#endif
+                }
+            }
 
-/*
-   This BYFOUR code accesses the passed unsigned char * buffer with a 32-bit
-   integer pointer type. This violates the strict aliasing rule, where a
-   compiler can assume, for optimization purposes, that two pointers to
-   fundamentally different types won't ever point to the same memory. This can
-   manifest as a problem only if one of the pointers is written to. This code
-   only reads from those pointers. So long as this code remains isolated in
-   this compilation unit, there won't be a problem. For this reason, this code
-   should not be copied and pasted into a compilation unit in which other code
-   writes to the buffer that is passed to these routines.
- */
+            /*
+              Process the last block, combining the CRCs of the N braids at the
+              same time.
+             */
+            crc = crc_word(crc0 ^ words[0]);
+#if N > 1
+            crc = crc_word(crc1 ^ words[1] ^ crc);
+#if N > 2
+            crc = crc_word(crc2 ^ words[2] ^ crc);
+#if N > 3
+            crc = crc_word(crc3 ^ words[3] ^ crc);
+#if N > 4
+            crc = crc_word(crc4 ^ words[4] ^ crc);
+#if N > 5
+            crc = crc_word(crc5 ^ words[5] ^ crc);
+#endif
+#endif
+#endif
+#endif
+#endif
+            words += N;
+        }
+        else {
+            /* Big endian. */
+
+            z_word_t crc0, word0, comb;
+#if N > 1
+            z_word_t crc1, word1;
+#if N > 2
+            z_word_t crc2, word2;
+#if N > 3
+            z_word_t crc3, word3;
+#if N > 4
+            z_word_t crc4, word4;
+#if N > 5
+            z_word_t crc5, word5;
+#endif
+#endif
+#endif
+#endif
+#endif
 
-/* ========================================================================= */
-#define DOLIT4 c ^= *buf4++; \
-        c = crc_table[3][c & 0xff] ^ crc_table[2][(c >> 8) & 0xff] ^ \
-            crc_table[1][(c >> 16) & 0xff] ^ crc_table[0][c >> 24]
-#define DOLIT32 DOLIT4; DOLIT4; DOLIT4; DOLIT4; DOLIT4; DOLIT4; DOLIT4; DOLIT4
+            /* Initialize the CRC for each braid. */
+            crc0 = byte_swap(crc);
+#if N > 1
+            crc1 = 0;
+#if N > 2
+            crc2 = 0;
+#if N > 3
+            crc3 = 0;
+#if N > 4
+            crc4 = 0;
+#if N > 5
+            crc5 = 0;
+#endif
+#endif
+#endif
+#endif
+#endif
 
-/* ========================================================================= */
-local unsigned long crc32_little(crc, buf, len)
-    unsigned long crc;
-    const unsigned char FAR *buf;
-    z_size_t len;
-{
-    register z_crc_t c;
-    register const z_crc_t FAR *buf4;
+            /*
+              Process the first blks-1 blocks, computing the CRCs on each braid
+              independently.
+             */
+            while (--blks) {
+                /* Load the word for each braid into registers. */
+                word0 = crc0 ^ words[0];
+#if N > 1
+                word1 = crc1 ^ words[1];
+#if N > 2
+                word2 = crc2 ^ words[2];
+#if N > 3
+                word3 = crc3 ^ words[3];
+#if N > 4
+                word4 = crc4 ^ words[4];
+#if N > 5
+                word5 = crc5 ^ words[5];
+#endif
+#endif
+#endif
+#endif
+#endif
+                words += N;
+
+                /* Compute and update the CRC for each word. The loop should
+                   get unrolled. */
+                crc0 = crc_braid_big_table[0][word0 & 0xff];
+#if N > 1
+                crc1 = crc_braid_big_table[0][word1 & 0xff];
+#if N > 2
+                crc2 = crc_braid_big_table[0][word2 & 0xff];
+#if N > 3
+                crc3 = crc_braid_big_table[0][word3 & 0xff];
+#if N > 4
+                crc4 = crc_braid_big_table[0][word4 & 0xff];
+#if N > 5
+                crc5 = crc_braid_big_table[0][word5 & 0xff];
+#endif
+#endif
+#endif
+#endif
+#endif
+                for (k = 1; k < W; k++) {
+                    crc0 ^= crc_braid_big_table[k][(word0 >> (k << 3)) & 0xff];
+#if N > 1
+                    crc1 ^= crc_braid_big_table[k][(word1 >> (k << 3)) & 0xff];
+#if N > 2
+                    crc2 ^= crc_braid_big_table[k][(word2 >> (k << 3)) & 0xff];
+#if N > 3
+                    crc3 ^= crc_braid_big_table[k][(word3 >> (k << 3)) & 0xff];
+#if N > 4
+                    crc4 ^= crc_braid_big_table[k][(word4 >> (k << 3)) & 0xff];
+#if N > 5
+                    crc5 ^= crc_braid_big_table[k][(word5 >> (k << 3)) & 0xff];
+#endif
+#endif
+#endif
+#endif
+#endif
+                }
+            }
 
-    c = (z_crc_t)crc;
-    c = ~c;
-    while (len && ((z_size_t)buf & 3)) {
-        c = crc_table[0][(c ^ *buf++) & 0xff] ^ (c >> 8);
-        len--;
+            /*
+              Process the last block, combining the CRCs of the N braids at the
+              same time.
+             */
+            comb = crc_word_big(crc0 ^ words[0]);
+#if N > 1
+            comb = crc_word_big(crc1 ^ words[1] ^ comb);
+#if N > 2
+            comb = crc_word_big(crc2 ^ words[2] ^ comb);
+#if N > 3
+            comb = crc_word_big(crc3 ^ words[3] ^ comb);
+#if N > 4
+            comb = crc_word_big(crc4 ^ words[4] ^ comb);
+#if N > 5
+            comb = crc_word_big(crc5 ^ words[5] ^ comb);
+#endif
+#endif
+#endif
+#endif
+#endif
+            words += N;
+            crc = byte_swap(comb);
+        }
+
+        /*
+          Update the pointer to the remaining bytes to process.
+         */
+        buf = (unsigned char const *)words;
     }
 
-    buf4 = (const z_crc_t FAR *)(const void FAR *)buf;
-    while (len >= 32) {
-        DOLIT32;
-        len -= 32;
+#endif /* W */
+
+    /* Complete the computation of the CRC on any remaining bytes. */
+    while (len >= 8) {
+        len -= 8;
+        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
+        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
+        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
+        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
+        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
+        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
+        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
+        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
     }
-    while (len >= 4) {
-        DOLIT4;
-        len -= 4;
+    while (len) {
+        len--;
+        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
     }
-    buf = (const unsigned char FAR *)buf4;
 
-    if (len) do {
-        c = crc_table[0][(c ^ *buf++) & 0xff] ^ (c >> 8);
-    } while (--len);
-    c = ~c;
-    return (unsigned long)c;
+    /* Return the CRC, post-conditioned. */
+    return crc ^ 0xffffffff;
 }
 
 /* ========================================================================= */
-#define DOBIG4 c ^= *buf4++; \
-        c = crc_table[4][c & 0xff] ^ crc_table[5][(c >> 8) & 0xff] ^ \
-            crc_table[6][(c >> 16) & 0xff] ^ crc_table[7][c >> 24]
-#define DOBIG32 DOBIG4; DOBIG4; DOBIG4; DOBIG4; DOBIG4; DOBIG4; DOBIG4; DOBIG4
-
-/* ========================================================================= */
-local unsigned long crc32_big(crc, buf, len)
+unsigned long ZEXPORT crc32(crc, buf, len)
     unsigned long crc;
     const unsigned char FAR *buf;
-    z_size_t len;
+    uInt len;
 {
-    register z_crc_t c;
-    register const z_crc_t FAR *buf4;
-
-    c = ZSWAP32((z_crc_t)crc);
-    c = ~c;
-    while (len && ((z_size_t)buf & 3)) {
-        c = crc_table[4][(c >> 24) ^ *buf++] ^ (c << 8);
-        len--;
-    }
-
-    buf4 = (const z_crc_t FAR *)(const void FAR *)buf;
-    while (len >= 32) {
-        DOBIG32;
-        len -= 32;
-    }
-    while (len >= 4) {
-        DOBIG4;
-        len -= 4;
-    }
-    buf = (const unsigned char FAR *)buf4;
-
-    if (len) do {
-        c = crc_table[4][(c >> 24) ^ *buf++] ^ (c << 8);
-    } while (--len);
-    c = ~c;
-    return (unsigned long)(ZSWAP32(c));
+    return crc32_z(crc, buf, len);
 }
 
-#endif /* BYFOUR */
-
 /* ========================================================================= */
-local uLong crc32_combine_(crc1, crc2, len2)
+uLong ZEXPORT crc32_combine64(crc1, crc2, len2)
     uLong crc1;
     uLong crc2;
     z_off64_t len2;
 {
-    int n;
-
 #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;
+    return multmodp(x2nmodp(len2, 3), crc1) ^ crc2;
 }
 
 /* ========================================================================= */
@@ -443,87 +894,32 @@ uLong ZEXPORT crc32_combine(crc1, crc2, len2)
     uLong crc2;
     z_off_t len2;
 {
-    return crc32_combine_(crc1, crc2, len2);
-}
-
-uLong ZEXPORT crc32_combine64(crc1, crc2, len2)
-    uLong crc1;
-    uLong crc2;
-    z_off64_t len2;
-{
-    return crc32_combine_(crc1, crc2, len2);
+    return crc32_combine64(crc1, crc2, len2);
 }
 
 /* ========================================================================= */
-local void crc32_combine_gen_(op, len2)
-    z_crc_t *op;
+uLong ZEXPORT crc32_combine_gen64(len2)
     z_off64_t len2;
 {
-    z_crc_t row;
-    int j;
-    unsigned i;
-
 #ifdef DYNAMIC_CRC_TABLE
     if (crc_table_empty)
         make_crc_table();
 #endif /* DYNAMIC_CRC_TABLE */
-
-    /* if len2 is zero or negative, return the identity matrix */
-    if (len2 <= 0) {
-        row = 1;
-        for (j = 0; j < GF2_DIM; j++) {
-            op[j] = row;
-            row <<= 1;
-        }
-        return;
-    }
-
-    /* at least one bit in len2 is set -- find it, and copy the operator
-       corresponding to that position into op */
-    i = 0;
-    for (;;) {
-        if (len2 & 1) {
-            for (j = 0; j < GF2_DIM; j++)
-                op[j] = crc_comb[i][j];
-            break;
-        }
-        len2 >>= 1;
-        i = (i + 1) % GF2_DIM;
-    }
-
-    /* for each remaining bit set in len2 (if any), multiply op by the operator
-       corresponding to that position */
-    for (;;) {
-        len2 >>= 1;
-        i = (i + 1) % GF2_DIM;
-        if (len2 == 0)
-            break;
-        if (len2 & 1)
-            for (j = 0; j < GF2_DIM; j++)
-                op[j] = gf2_matrix_times(crc_comb[i], op[j]);
-    }
+    return x2nmodp(len2, 3);
 }
 
 /* ========================================================================= */
-void ZEXPORT crc32_combine_gen(op, len2)
-    z_crc_t *op;
+uLong ZEXPORT crc32_combine_gen(len2)
     z_off_t len2;
 {
-    crc32_combine_gen_(op, len2);
-}
-
-void ZEXPORT crc32_combine_gen64(op, len2)
-    z_crc_t *op;
-    z_off64_t len2;
-{
-    crc32_combine_gen_(op, len2);
+    return crc32_combine_gen64(len2);
 }
 
 /* ========================================================================= */
 uLong crc32_combine_op(crc1, crc2, op)
     uLong crc1;
     uLong crc2;
-    const z_crc_t *op;
+    uLong op;
 {
-    return gf2_matrix_times(op, crc1) ^ crc2;
+    return multmodp(op, crc1) ^ crc2;
 }