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crc32.c (31747B)


      1 /* crc32.c -- compute the CRC-32 of a data stream
      2 * Copyright (C) 1995-2022 Mark Adler
      3 * For conditions of distribution and use, see copyright notice in zlib.h
      4 *
      5 * This interleaved implementation of a CRC makes use of pipelined multiple
      6 * arithmetic-logic units, commonly found in modern CPU cores. It is due to
      7 * Kadatch and Jenkins (2010). See doc/crc-doc.1.0.pdf in this distribution.
      8 */
      9 
     10 /* @(#) $Id$ */
     11 
     12 /*
     13  Note on the use of DYNAMIC_CRC_TABLE: there is no mutex or semaphore
     14  protection on the static variables used to control the first-use generation
     15  of the crc tables. Therefore, if you #define DYNAMIC_CRC_TABLE, you should
     16  first call get_crc_table() to initialize the tables before allowing more than
     17  one thread to use crc32().
     18 
     19  MAKECRCH can be #defined to write out crc32.h. A main() routine is also
     20  produced, so that this one source file can be compiled to an executable.
     21 */
     22 
     23 #ifdef MAKECRCH
     24 #  include <stdio.h>
     25 #  ifndef DYNAMIC_CRC_TABLE
     26 #    define DYNAMIC_CRC_TABLE
     27 #  endif /* !DYNAMIC_CRC_TABLE */
     28 #endif /* MAKECRCH */
     29 
     30 #include "zutil.h"      /* for Z_U4, Z_U8, z_crc_t, and FAR definitions */
     31 
     32 /*
     33  A CRC of a message is computed on N braids of words in the message, where
     34  each word consists of W bytes (4 or 8). If N is 3, for example, then three
     35  running sparse CRCs are calculated respectively on each braid, at these
     36  indices in the array of words: 0, 3, 6, ..., 1, 4, 7, ..., and 2, 5, 8, ...
     37  This is done starting at a word boundary, and continues until as many blocks
     38  of N * W bytes as are available have been processed. The results are combined
     39  into a single CRC at the end. For this code, N must be in the range 1..6 and
     40  W must be 4 or 8. The upper limit on N can be increased if desired by adding
     41  more #if blocks, extending the patterns apparent in the code. In addition,
     42  crc32.h would need to be regenerated, if the maximum N value is increased.
     43 
     44  N and W are chosen empirically by benchmarking the execution time on a given
     45  processor. The choices for N and W below were based on testing on Intel Kaby
     46  Lake i7, AMD Ryzen 7, ARM Cortex-A57, Sparc64-VII, PowerPC POWER9, and MIPS64
     47  Octeon II processors. The Intel, AMD, and ARM processors were all fastest
     48  with N=5, W=8. The Sparc, PowerPC, and MIPS64 were all fastest at N=5, W=4.
     49  They were all tested with either gcc or clang, all using the -O3 optimization
     50  level. Your mileage may vary.
     51 */
     52 
     53 /* Define N */
     54 #ifdef Z_TESTN
     55 #  define N Z_TESTN
     56 #else
     57 #  define N 5
     58 #endif
     59 #if N < 1 || N > 6
     60 #  error N must be in 1..6
     61 #endif
     62 
     63 /*
     64  z_crc_t must be at least 32 bits. z_word_t must be at least as long as
     65  z_crc_t. It is assumed here that z_word_t is either 32 bits or 64 bits, and
     66  that bytes are eight bits.
     67 */
     68 
     69 /*
     70  Define W and the associated z_word_t type. If W is not defined, then a
     71  braided calculation is not used, and the associated tables and code are not
     72  compiled.
     73 */
     74 #ifdef Z_TESTW
     75 #  if Z_TESTW-1 != -1
     76 #    define W Z_TESTW
     77 #  endif
     78 #else
     79 #  ifdef MAKECRCH
     80 #    define W 8         /* required for MAKECRCH */
     81 #  else
     82 #    if defined(__x86_64__) || defined(__aarch64__)
     83 #      define W 8
     84 #    else
     85 #      define W 4
     86 #    endif
     87 #  endif
     88 #endif
     89 #ifdef W
     90 #  if W == 8 && defined(Z_U8)
     91     typedef Z_U8 z_word_t;
     92 #  elif defined(Z_U4)
     93 #    undef W
     94 #    define W 4
     95     typedef Z_U4 z_word_t;
     96 #  else
     97 #    undef W
     98 #  endif
     99 #endif
    100 
    101 /* If available, use the ARM processor CRC32 instruction. */
    102 #if defined(__aarch64__) && defined(__ARM_FEATURE_CRC32) && W == 8
    103 #  define ARMCRC32
    104 #endif
    105 
    106 #if defined(W) && (!defined(ARMCRC32) || defined(DYNAMIC_CRC_TABLE))
    107 /*
    108  Swap the bytes in a z_word_t to convert between little and big endian. Any
    109  self-respecting compiler will optimize this to a single machine byte-swap
    110  instruction, if one is available. This assumes that word_t is either 32 bits
    111  or 64 bits.
    112 */
    113 local z_word_t byte_swap(z_word_t word) {
    114 #  if W == 8
    115    return
    116        (word & 0xff00000000000000) >> 56 |
    117        (word & 0xff000000000000) >> 40 |
    118        (word & 0xff0000000000) >> 24 |
    119        (word & 0xff00000000) >> 8 |
    120        (word & 0xff000000) << 8 |
    121        (word & 0xff0000) << 24 |
    122        (word & 0xff00) << 40 |
    123        (word & 0xff) << 56;
    124 #  else   /* W == 4 */
    125    return
    126        (word & 0xff000000) >> 24 |
    127        (word & 0xff0000) >> 8 |
    128        (word & 0xff00) << 8 |
    129        (word & 0xff) << 24;
    130 #  endif
    131 }
    132 #endif
    133 
    134 #ifdef DYNAMIC_CRC_TABLE
    135 /* =========================================================================
    136 * Table of powers of x for combining CRC-32s, filled in by make_crc_table()
    137 * below.
    138 */
    139   local z_crc_t FAR x2n_table[32];
    140 #else
    141 /* =========================================================================
    142 * Tables for byte-wise and braided CRC-32 calculations, and a table of powers
    143 * of x for combining CRC-32s, all made by make_crc_table().
    144 */
    145 #  include "crc32.h"
    146 #endif
    147 
    148 /* CRC polynomial. */
    149 #define POLY 0xedb88320         /* p(x) reflected, with x^32 implied */
    150 
    151 #ifndef Z_FREETYPE
    152 
    153 /*
    154  Return a(x) multiplied by b(x) modulo p(x), where p(x) is the CRC polynomial,
    155  reflected. For speed, this requires that a not be zero.
    156 */
    157 local z_crc_t multmodp(z_crc_t a, z_crc_t b) {
    158    z_crc_t m, p;
    159 
    160    m = (z_crc_t)1 << 31;
    161    p = 0;
    162    for (;;) {
    163        if (a & m) {
    164            p ^= b;
    165            if ((a & (m - 1)) == 0)
    166                break;
    167        }
    168        m >>= 1;
    169        b = b & 1 ? (b >> 1) ^ POLY : b >> 1;
    170    }
    171    return p;
    172 }
    173 
    174 /*
    175  Return x^(n * 2^k) modulo p(x). Requires that x2n_table[] has been
    176  initialized.
    177 */
    178 local z_crc_t x2nmodp(z_off64_t n, unsigned k) {
    179    z_crc_t p;
    180 
    181    p = (z_crc_t)1 << 31;           /* x^0 == 1 */
    182    while (n) {
    183        if (n & 1)
    184            p = multmodp(x2n_table[k & 31], p);
    185        n >>= 1;
    186        k++;
    187    }
    188    return p;
    189 }
    190 
    191 #endif  /* !Z_FREETYPE */
    192 
    193 #ifdef DYNAMIC_CRC_TABLE
    194 /* =========================================================================
    195 * Build the tables for byte-wise and braided CRC-32 calculations, and a table
    196 * of powers of x for combining CRC-32s.
    197 */
    198 local z_crc_t FAR crc_table[256];
    199 #ifdef W
    200   local z_word_t FAR crc_big_table[256];
    201   local z_crc_t FAR crc_braid_table[W][256];
    202   local z_word_t FAR crc_braid_big_table[W][256];
    203   local void braid(z_crc_t [][256], z_word_t [][256], int, int);
    204 #endif
    205 #ifdef MAKECRCH
    206   local void write_table(FILE *, const z_crc_t FAR *, int);
    207   local void write_table32hi(FILE *, const z_word_t FAR *, int);
    208   local void write_table64(FILE *, const z_word_t FAR *, int);
    209 #endif /* MAKECRCH */
    210 
    211 /*
    212  Define a once() function depending on the availability of atomics. If this is
    213  compiled with DYNAMIC_CRC_TABLE defined, and if CRCs will be computed in
    214  multiple threads, and if atomics are not available, then get_crc_table() must
    215  be called to initialize the tables and must return before any threads are
    216  allowed to compute or combine CRCs.
    217 */
    218 
    219 /* Definition of once functionality. */
    220 typedef struct once_s once_t;
    221 
    222 /* Check for the availability of atomics. */
    223 #if defined(__STDC__) && __STDC_VERSION__ >= 201112L && \
    224    !defined(__STDC_NO_ATOMICS__)
    225 
    226 #include <stdatomic.h>
    227 
    228 /* Structure for once(), which must be initialized with ONCE_INIT. */
    229 struct once_s {
    230    atomic_flag begun;
    231    atomic_int done;
    232 };
    233 #define ONCE_INIT {ATOMIC_FLAG_INIT, 0}
    234 
    235 /*
    236  Run the provided init() function exactly once, even if multiple threads
    237  invoke once() at the same time. The state must be a once_t initialized with
    238  ONCE_INIT.
    239 */
    240 local void once(once_t *state, void (*init)(void)) {
    241    if (!atomic_load(&state->done)) {
    242        if (atomic_flag_test_and_set(&state->begun))
    243            while (!atomic_load(&state->done))
    244                ;
    245        else {
    246            init();
    247            atomic_store(&state->done, 1);
    248        }
    249    }
    250 }
    251 
    252 #else   /* no atomics */
    253 
    254 /* Structure for once(), which must be initialized with ONCE_INIT. */
    255 struct once_s {
    256    volatile int begun;
    257    volatile int done;
    258 };
    259 #define ONCE_INIT {0, 0}
    260 
    261 /* Test and set. Alas, not atomic, but tries to minimize the period of
    262   vulnerability. */
    263 local int test_and_set(int volatile *flag) {
    264    int was;
    265 
    266    was = *flag;
    267    *flag = 1;
    268    return was;
    269 }
    270 
    271 /* Run the provided init() function once. This is not thread-safe. */
    272 local void once(once_t *state, void (*init)(void)) {
    273    if (!state->done) {
    274        if (test_and_set(&state->begun))
    275            while (!state->done)
    276                ;
    277        else {
    278            init();
    279            state->done = 1;
    280        }
    281    }
    282 }
    283 
    284 #endif
    285 
    286 /* State for once(). */
    287 local once_t made = ONCE_INIT;
    288 
    289 /*
    290  Generate tables for a byte-wise 32-bit CRC calculation on the polynomial:
    291  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.
    292 
    293  Polynomials over GF(2) are represented in binary, one bit per coefficient,
    294  with the lowest powers in the most significant bit. Then adding polynomials
    295  is just exclusive-or, and multiplying a polynomial by x is a right shift by
    296  one. If we call the above polynomial p, and represent a byte as the
    297  polynomial q, also with the lowest power in the most significant bit (so the
    298  byte 0xb1 is the polynomial x^7+x^3+x^2+1), then the CRC is (q*x^32) mod p,
    299  where a mod b means the remainder after dividing a by b.
    300 
    301  This calculation is done using the shift-register method of multiplying and
    302  taking the remainder. The register is initialized to zero, and for each
    303  incoming bit, x^32 is added mod p to the register if the bit is a one (where
    304  x^32 mod p is p+x^32 = x^26+...+1), and the register is multiplied mod p by x
    305  (which is shifting right by one and adding x^32 mod p if the bit shifted out
    306  is a one). We start with the highest power (least significant bit) of q and
    307  repeat for all eight bits of q.
    308 
    309  The table is simply the CRC of all possible eight bit values. This is all the
    310  information needed to generate CRCs on data a byte at a time for all
    311  combinations of CRC register values and incoming bytes.
    312 */
    313 
    314 local void make_crc_table(void) {
    315    unsigned i, j, n;
    316    z_crc_t p;
    317 
    318    /* initialize the CRC of bytes tables */
    319    for (i = 0; i < 256; i++) {
    320        p = i;
    321        for (j = 0; j < 8; j++)
    322            p = p & 1 ? (p >> 1) ^ POLY : p >> 1;
    323        crc_table[i] = p;
    324 #ifdef W
    325        crc_big_table[i] = byte_swap(p);
    326 #endif
    327    }
    328 
    329    /* initialize the x^2^n mod p(x) table */
    330    p = (z_crc_t)1 << 30;         /* x^1 */
    331    x2n_table[0] = p;
    332    for (n = 1; n < 32; n++)
    333        x2n_table[n] = p = multmodp(p, p);
    334 
    335 #ifdef W
    336    /* initialize the braiding tables -- needs x2n_table[] */
    337    braid(crc_braid_table, crc_braid_big_table, N, W);
    338 #endif
    339 
    340 #ifdef MAKECRCH
    341    {
    342        /*
    343          The crc32.h header file contains tables for both 32-bit and 64-bit
    344          z_word_t's, and so requires a 64-bit type be available. In that case,
    345          z_word_t must be defined to be 64-bits. This code then also generates
    346          and writes out the tables for the case that z_word_t is 32 bits.
    347         */
    348 #if !defined(W) || W != 8
    349 #  error Need a 64-bit integer type in order to generate crc32.h.
    350 #endif
    351        FILE *out;
    352        int k, n;
    353        z_crc_t ltl[8][256];
    354        z_word_t big[8][256];
    355 
    356        out = fopen("crc32.h", "w");
    357        if (out == NULL) return;
    358 
    359        /* write out little-endian CRC table to crc32.h */
    360        fprintf(out,
    361            "/* crc32.h -- tables for rapid CRC calculation\n"
    362            " * Generated automatically by crc32.c\n */\n"
    363            "\n"
    364            "local const z_crc_t FAR crc_table[] = {\n"
    365            "    ");
    366        write_table(out, crc_table, 256);
    367        fprintf(out,
    368            "};\n");
    369 
    370        /* write out big-endian CRC table for 64-bit z_word_t to crc32.h */
    371        fprintf(out,
    372            "\n"
    373            "#ifdef W\n"
    374            "\n"
    375            "#if W == 8\n"
    376            "\n"
    377            "local const z_word_t FAR crc_big_table[] = {\n"
    378            "    ");
    379        write_table64(out, crc_big_table, 256);
    380        fprintf(out,
    381            "};\n");
    382 
    383        /* write out big-endian CRC table for 32-bit z_word_t to crc32.h */
    384        fprintf(out,
    385            "\n"
    386            "#else /* W == 4 */\n"
    387            "\n"
    388            "local const z_word_t FAR crc_big_table[] = {\n"
    389            "    ");
    390        write_table32hi(out, crc_big_table, 256);
    391        fprintf(out,
    392            "};\n"
    393            "\n"
    394            "#endif\n");
    395 
    396        /* write out braid tables for each value of N */
    397        for (n = 1; n <= 6; n++) {
    398            fprintf(out,
    399            "\n"
    400            "#if N == %d\n", n);
    401 
    402            /* compute braid tables for this N and 64-bit word_t */
    403            braid(ltl, big, n, 8);
    404 
    405            /* write out braid tables for 64-bit z_word_t to crc32.h */
    406            fprintf(out,
    407            "\n"
    408            "#if W == 8\n"
    409            "\n"
    410            "local const z_crc_t FAR crc_braid_table[][256] = {\n");
    411            for (k = 0; k < 8; k++) {
    412                fprintf(out, "   {");
    413                write_table(out, ltl[k], 256);
    414                fprintf(out, "}%s", k < 7 ? ",\n" : "");
    415            }
    416            fprintf(out,
    417            "};\n"
    418            "\n"
    419            "local const z_word_t FAR crc_braid_big_table[][256] = {\n");
    420            for (k = 0; k < 8; k++) {
    421                fprintf(out, "   {");
    422                write_table64(out, big[k], 256);
    423                fprintf(out, "}%s", k < 7 ? ",\n" : "");
    424            }
    425            fprintf(out,
    426            "};\n");
    427 
    428            /* compute braid tables for this N and 32-bit word_t */
    429            braid(ltl, big, n, 4);
    430 
    431            /* write out braid tables for 32-bit z_word_t to crc32.h */
    432            fprintf(out,
    433            "\n"
    434            "#else /* W == 4 */\n"
    435            "\n"
    436            "local const z_crc_t FAR crc_braid_table[][256] = {\n");
    437            for (k = 0; k < 4; k++) {
    438                fprintf(out, "   {");
    439                write_table(out, ltl[k], 256);
    440                fprintf(out, "}%s", k < 3 ? ",\n" : "");
    441            }
    442            fprintf(out,
    443            "};\n"
    444            "\n"
    445            "local const z_word_t FAR crc_braid_big_table[][256] = {\n");
    446            for (k = 0; k < 4; k++) {
    447                fprintf(out, "   {");
    448                write_table32hi(out, big[k], 256);
    449                fprintf(out, "}%s", k < 3 ? ",\n" : "");
    450            }
    451            fprintf(out,
    452            "};\n"
    453            "\n"
    454            "#endif\n"
    455            "\n"
    456            "#endif\n");
    457        }
    458        fprintf(out,
    459            "\n"
    460            "#endif\n");
    461 
    462        /* write out zeros operator table to crc32.h */
    463        fprintf(out,
    464            "\n"
    465            "local const z_crc_t FAR x2n_table[] = {\n"
    466            "    ");
    467        write_table(out, x2n_table, 32);
    468        fprintf(out,
    469            "};\n");
    470        fclose(out);
    471    }
    472 #endif /* MAKECRCH */
    473 }
    474 
    475 #ifdef MAKECRCH
    476 
    477 /*
    478   Write the 32-bit values in table[0..k-1] to out, five per line in
    479   hexadecimal separated by commas.
    480 */
    481 local void write_table(FILE *out, const z_crc_t FAR *table, int k) {
    482    int n;
    483 
    484    for (n = 0; n < k; n++)
    485        fprintf(out, "%s0x%08lx%s", n == 0 || n % 5 ? "" : "    ",
    486                (unsigned long)(table[n]),
    487                n == k - 1 ? "" : (n % 5 == 4 ? ",\n" : ", "));
    488 }
    489 
    490 /*
    491   Write the high 32-bits of each value in table[0..k-1] to out, five per line
    492   in hexadecimal separated by commas.
    493 */
    494 local void write_table32hi(FILE *out, const z_word_t FAR *table, int k) {
    495    int n;
    496 
    497    for (n = 0; n < k; n++)
    498        fprintf(out, "%s0x%08lx%s", n == 0 || n % 5 ? "" : "    ",
    499                (unsigned long)(table[n] >> 32),
    500                n == k - 1 ? "" : (n % 5 == 4 ? ",\n" : ", "));
    501 }
    502 
    503 /*
    504  Write the 64-bit values in table[0..k-1] to out, three per line in
    505  hexadecimal separated by commas. This assumes that if there is a 64-bit
    506  type, then there is also a long long integer type, and it is at least 64
    507  bits. If not, then the type cast and format string can be adjusted
    508  accordingly.
    509 */
    510 local void write_table64(FILE *out, const z_word_t FAR *table, int k) {
    511    int n;
    512 
    513    for (n = 0; n < k; n++)
    514        fprintf(out, "%s0x%016llx%s", n == 0 || n % 3 ? "" : "    ",
    515                (unsigned long long)(table[n]),
    516                n == k - 1 ? "" : (n % 3 == 2 ? ",\n" : ", "));
    517 }
    518 
    519 /* Actually do the deed. */
    520 int main(void) {
    521    make_crc_table();
    522    return 0;
    523 }
    524 
    525 #endif /* MAKECRCH */
    526 
    527 #ifdef W
    528 /*
    529  Generate the little and big-endian braid tables for the given n and z_word_t
    530  size w. Each array must have room for w blocks of 256 elements.
    531 */
    532 local void braid(z_crc_t ltl[][256], z_word_t big[][256], int n, int w) {
    533    int k;
    534    z_crc_t i, p, q;
    535    for (k = 0; k < w; k++) {
    536        p = x2nmodp((n * w + 3 - k) << 3, 0);
    537        ltl[k][0] = 0;
    538        big[w - 1 - k][0] = 0;
    539        for (i = 1; i < 256; i++) {
    540            ltl[k][i] = q = multmodp(i << 24, p);
    541            big[w - 1 - k][i] = byte_swap(q);
    542        }
    543    }
    544 }
    545 #endif
    546 
    547 #endif /* DYNAMIC_CRC_TABLE */
    548 
    549 #ifndef Z_FREETYPE
    550 
    551 /* =========================================================================
    552 * This function can be used by asm versions of crc32(), and to force the
    553 * generation of the CRC tables in a threaded application.
    554 */
    555 const z_crc_t FAR * ZEXPORT get_crc_table(void) {
    556 #ifdef DYNAMIC_CRC_TABLE
    557    once(&made, make_crc_table);
    558 #endif /* DYNAMIC_CRC_TABLE */
    559    return (const z_crc_t FAR *)crc_table;
    560 }
    561 
    562 #endif   /* !Z_FREETYPE */
    563 
    564 /* =========================================================================
    565 * Use ARM machine instructions if available. This will compute the CRC about
    566 * ten times faster than the braided calculation. This code does not check for
    567 * the presence of the CRC instruction at run time. __ARM_FEATURE_CRC32 will
    568 * only be defined if the compilation specifies an ARM processor architecture
    569 * that has the instructions. For example, compiling with -march=armv8.1-a or
    570 * -march=armv8-a+crc, or -march=native if the compile machine has the crc32
    571 * instructions.
    572 */
    573 #ifdef ARMCRC32
    574 
    575 /*
    576   Constants empirically determined to maximize speed. These values are from
    577   measurements on a Cortex-A57. Your mileage may vary.
    578 */
    579 #define Z_BATCH 3990                /* number of words in a batch */
    580 #define Z_BATCH_ZEROS 0xa10d3d0c    /* computed from Z_BATCH = 3990 */
    581 #define Z_BATCH_MIN 800             /* fewest words in a final batch */
    582 
    583 unsigned long ZEXPORT crc32_z(unsigned long crc, const unsigned char FAR *buf,
    584                              z_size_t len) {
    585    z_crc_t val;
    586    z_word_t crc1, crc2;
    587    const z_word_t *word;
    588    z_word_t val0, val1, val2;
    589    z_size_t last, last2, i;
    590    z_size_t num;
    591 
    592    /* Return initial CRC, if requested. */
    593    if (buf == Z_NULL) return 0;
    594 
    595 #ifdef DYNAMIC_CRC_TABLE
    596    once(&made, make_crc_table);
    597 #endif /* DYNAMIC_CRC_TABLE */
    598 
    599    /* Pre-condition the CRC */
    600    crc = (~crc) & 0xffffffff;
    601 
    602    /* Compute the CRC up to a word boundary. */
    603    while (len && ((z_size_t)buf & 7) != 0) {
    604        len--;
    605        val = *buf++;
    606        __asm__ volatile("crc32b %w0, %w0, %w1" : "+r"(crc) : "r"(val));
    607    }
    608 
    609    /* Prepare to compute the CRC on full 64-bit words word[0..num-1]. */
    610    word = (z_word_t const *)buf;
    611    num = len >> 3;
    612    len &= 7;
    613 
    614    /* Do three interleaved CRCs to realize the throughput of one crc32x
    615       instruction per cycle. Each CRC is calculated on Z_BATCH words. The
    616       three CRCs are combined into a single CRC after each set of batches. */
    617    while (num >= 3 * Z_BATCH) {
    618        crc1 = 0;
    619        crc2 = 0;
    620        for (i = 0; i < Z_BATCH; i++) {
    621            val0 = word[i];
    622            val1 = word[i + Z_BATCH];
    623            val2 = word[i + 2 * Z_BATCH];
    624            __asm__ volatile("crc32x %w0, %w0, %x1" : "+r"(crc) : "r"(val0));
    625            __asm__ volatile("crc32x %w0, %w0, %x1" : "+r"(crc1) : "r"(val1));
    626            __asm__ volatile("crc32x %w0, %w0, %x1" : "+r"(crc2) : "r"(val2));
    627        }
    628        word += 3 * Z_BATCH;
    629        num -= 3 * Z_BATCH;
    630        crc = multmodp(Z_BATCH_ZEROS, crc) ^ crc1;
    631        crc = multmodp(Z_BATCH_ZEROS, crc) ^ crc2;
    632    }
    633 
    634    /* Do one last smaller batch with the remaining words, if there are enough
    635       to pay for the combination of CRCs. */
    636    last = num / 3;
    637    if (last >= Z_BATCH_MIN) {
    638        last2 = last << 1;
    639        crc1 = 0;
    640        crc2 = 0;
    641        for (i = 0; i < last; i++) {
    642            val0 = word[i];
    643            val1 = word[i + last];
    644            val2 = word[i + last2];
    645            __asm__ volatile("crc32x %w0, %w0, %x1" : "+r"(crc) : "r"(val0));
    646            __asm__ volatile("crc32x %w0, %w0, %x1" : "+r"(crc1) : "r"(val1));
    647            __asm__ volatile("crc32x %w0, %w0, %x1" : "+r"(crc2) : "r"(val2));
    648        }
    649        word += 3 * last;
    650        num -= 3 * last;
    651        val = x2nmodp(last, 6);
    652        crc = multmodp(val, crc) ^ crc1;
    653        crc = multmodp(val, crc) ^ crc2;
    654    }
    655 
    656    /* Compute the CRC on any remaining words. */
    657    for (i = 0; i < num; i++) {
    658        val0 = word[i];
    659        __asm__ volatile("crc32x %w0, %w0, %x1" : "+r"(crc) : "r"(val0));
    660    }
    661    word += num;
    662 
    663    /* Complete the CRC on any remaining bytes. */
    664    buf = (const unsigned char FAR *)word;
    665    while (len) {
    666        len--;
    667        val = *buf++;
    668        __asm__ volatile("crc32b %w0, %w0, %w1" : "+r"(crc) : "r"(val));
    669    }
    670 
    671    /* Return the CRC, post-conditioned. */
    672    return crc ^ 0xffffffff;
    673 }
    674 
    675 #else
    676 
    677 #ifdef W
    678 
    679 /*
    680  Return the CRC of the W bytes in the word_t data, taking the
    681  least-significant byte of the word as the first byte of data, without any pre
    682  or post conditioning. This is used to combine the CRCs of each braid.
    683 */
    684 local z_crc_t crc_word(z_word_t data) {
    685    int k;
    686    for (k = 0; k < W; k++)
    687        data = (data >> 8) ^ crc_table[data & 0xff];
    688    return (z_crc_t)data;
    689 }
    690 
    691 local z_word_t crc_word_big(z_word_t data) {
    692    int k;
    693    for (k = 0; k < W; k++)
    694        data = (data << 8) ^
    695            crc_big_table[(data >> ((W - 1) << 3)) & 0xff];
    696    return data;
    697 }
    698 
    699 #endif
    700 
    701 /* ========================================================================= */
    702 unsigned long ZEXPORT crc32_z(unsigned long crc, const unsigned char FAR *buf,
    703                              z_size_t len) {
    704    /* Return initial CRC, if requested. */
    705    if (buf == Z_NULL) return 0;
    706 
    707 #ifdef DYNAMIC_CRC_TABLE
    708    once(&made, make_crc_table);
    709 #endif /* DYNAMIC_CRC_TABLE */
    710 
    711    /* Pre-condition the CRC */
    712    crc = (~crc) & 0xffffffff;
    713 
    714 #ifdef W
    715 
    716    /* If provided enough bytes, do a braided CRC calculation. */
    717    if (len >= N * W + W - 1) {
    718        z_size_t blks;
    719        z_word_t const *words;
    720        unsigned endian;
    721        int k;
    722 
    723        /* Compute the CRC up to a z_word_t boundary. */
    724        while (len && ((z_size_t)buf & (W - 1)) != 0) {
    725            len--;
    726            crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
    727        }
    728 
    729        /* Compute the CRC on as many N z_word_t blocks as are available. */
    730        blks = len / (N * W);
    731        len -= blks * N * W;
    732        words = (z_word_t const *)buf;
    733 
    734        /* Do endian check at execution time instead of compile time, since ARM
    735           processors can change the endianness at execution time. If the
    736           compiler knows what the endianness will be, it can optimize out the
    737           check and the unused branch. */
    738        endian = 1;
    739        if (*(unsigned char *)&endian) {
    740            /* Little endian. */
    741 
    742            z_crc_t crc0;
    743            z_word_t word0;
    744 #if N > 1
    745            z_crc_t crc1;
    746            z_word_t word1;
    747 #if N > 2
    748            z_crc_t crc2;
    749            z_word_t word2;
    750 #if N > 3
    751            z_crc_t crc3;
    752            z_word_t word3;
    753 #if N > 4
    754            z_crc_t crc4;
    755            z_word_t word4;
    756 #if N > 5
    757            z_crc_t crc5;
    758            z_word_t word5;
    759 #endif
    760 #endif
    761 #endif
    762 #endif
    763 #endif
    764 
    765            /* Initialize the CRC for each braid. */
    766            crc0 = crc;
    767 #if N > 1
    768            crc1 = 0;
    769 #if N > 2
    770            crc2 = 0;
    771 #if N > 3
    772            crc3 = 0;
    773 #if N > 4
    774            crc4 = 0;
    775 #if N > 5
    776            crc5 = 0;
    777 #endif
    778 #endif
    779 #endif
    780 #endif
    781 #endif
    782 
    783            /*
    784              Process the first blks-1 blocks, computing the CRCs on each braid
    785              independently.
    786             */
    787            while (--blks) {
    788                /* Load the word for each braid into registers. */
    789                word0 = crc0 ^ words[0];
    790 #if N > 1
    791                word1 = crc1 ^ words[1];
    792 #if N > 2
    793                word2 = crc2 ^ words[2];
    794 #if N > 3
    795                word3 = crc3 ^ words[3];
    796 #if N > 4
    797                word4 = crc4 ^ words[4];
    798 #if N > 5
    799                word5 = crc5 ^ words[5];
    800 #endif
    801 #endif
    802 #endif
    803 #endif
    804 #endif
    805                words += N;
    806 
    807                /* Compute and update the CRC for each word. The loop should
    808                   get unrolled. */
    809                crc0 = crc_braid_table[0][word0 & 0xff];
    810 #if N > 1
    811                crc1 = crc_braid_table[0][word1 & 0xff];
    812 #if N > 2
    813                crc2 = crc_braid_table[0][word2 & 0xff];
    814 #if N > 3
    815                crc3 = crc_braid_table[0][word3 & 0xff];
    816 #if N > 4
    817                crc4 = crc_braid_table[0][word4 & 0xff];
    818 #if N > 5
    819                crc5 = crc_braid_table[0][word5 & 0xff];
    820 #endif
    821 #endif
    822 #endif
    823 #endif
    824 #endif
    825                for (k = 1; k < W; k++) {
    826                    crc0 ^= crc_braid_table[k][(word0 >> (k << 3)) & 0xff];
    827 #if N > 1
    828                    crc1 ^= crc_braid_table[k][(word1 >> (k << 3)) & 0xff];
    829 #if N > 2
    830                    crc2 ^= crc_braid_table[k][(word2 >> (k << 3)) & 0xff];
    831 #if N > 3
    832                    crc3 ^= crc_braid_table[k][(word3 >> (k << 3)) & 0xff];
    833 #if N > 4
    834                    crc4 ^= crc_braid_table[k][(word4 >> (k << 3)) & 0xff];
    835 #if N > 5
    836                    crc5 ^= crc_braid_table[k][(word5 >> (k << 3)) & 0xff];
    837 #endif
    838 #endif
    839 #endif
    840 #endif
    841 #endif
    842                }
    843            }
    844 
    845            /*
    846              Process the last block, combining the CRCs of the N braids at the
    847              same time.
    848             */
    849            crc = crc_word(crc0 ^ words[0]);
    850 #if N > 1
    851            crc = crc_word(crc1 ^ words[1] ^ crc);
    852 #if N > 2
    853            crc = crc_word(crc2 ^ words[2] ^ crc);
    854 #if N > 3
    855            crc = crc_word(crc3 ^ words[3] ^ crc);
    856 #if N > 4
    857            crc = crc_word(crc4 ^ words[4] ^ crc);
    858 #if N > 5
    859            crc = crc_word(crc5 ^ words[5] ^ crc);
    860 #endif
    861 #endif
    862 #endif
    863 #endif
    864 #endif
    865            words += N;
    866        }
    867        else {
    868            /* Big endian. */
    869 
    870            z_word_t crc0, word0, comb;
    871 #if N > 1
    872            z_word_t crc1, word1;
    873 #if N > 2
    874            z_word_t crc2, word2;
    875 #if N > 3
    876            z_word_t crc3, word3;
    877 #if N > 4
    878            z_word_t crc4, word4;
    879 #if N > 5
    880            z_word_t crc5, word5;
    881 #endif
    882 #endif
    883 #endif
    884 #endif
    885 #endif
    886 
    887            /* Initialize the CRC for each braid. */
    888            crc0 = byte_swap(crc);
    889 #if N > 1
    890            crc1 = 0;
    891 #if N > 2
    892            crc2 = 0;
    893 #if N > 3
    894            crc3 = 0;
    895 #if N > 4
    896            crc4 = 0;
    897 #if N > 5
    898            crc5 = 0;
    899 #endif
    900 #endif
    901 #endif
    902 #endif
    903 #endif
    904 
    905            /*
    906              Process the first blks-1 blocks, computing the CRCs on each braid
    907              independently.
    908             */
    909            while (--blks) {
    910                /* Load the word for each braid into registers. */
    911                word0 = crc0 ^ words[0];
    912 #if N > 1
    913                word1 = crc1 ^ words[1];
    914 #if N > 2
    915                word2 = crc2 ^ words[2];
    916 #if N > 3
    917                word3 = crc3 ^ words[3];
    918 #if N > 4
    919                word4 = crc4 ^ words[4];
    920 #if N > 5
    921                word5 = crc5 ^ words[5];
    922 #endif
    923 #endif
    924 #endif
    925 #endif
    926 #endif
    927                words += N;
    928 
    929                /* Compute and update the CRC for each word. The loop should
    930                   get unrolled. */
    931                crc0 = crc_braid_big_table[0][word0 & 0xff];
    932 #if N > 1
    933                crc1 = crc_braid_big_table[0][word1 & 0xff];
    934 #if N > 2
    935                crc2 = crc_braid_big_table[0][word2 & 0xff];
    936 #if N > 3
    937                crc3 = crc_braid_big_table[0][word3 & 0xff];
    938 #if N > 4
    939                crc4 = crc_braid_big_table[0][word4 & 0xff];
    940 #if N > 5
    941                crc5 = crc_braid_big_table[0][word5 & 0xff];
    942 #endif
    943 #endif
    944 #endif
    945 #endif
    946 #endif
    947                for (k = 1; k < W; k++) {
    948                    crc0 ^= crc_braid_big_table[k][(word0 >> (k << 3)) & 0xff];
    949 #if N > 1
    950                    crc1 ^= crc_braid_big_table[k][(word1 >> (k << 3)) & 0xff];
    951 #if N > 2
    952                    crc2 ^= crc_braid_big_table[k][(word2 >> (k << 3)) & 0xff];
    953 #if N > 3
    954                    crc3 ^= crc_braid_big_table[k][(word3 >> (k << 3)) & 0xff];
    955 #if N > 4
    956                    crc4 ^= crc_braid_big_table[k][(word4 >> (k << 3)) & 0xff];
    957 #if N > 5
    958                    crc5 ^= crc_braid_big_table[k][(word5 >> (k << 3)) & 0xff];
    959 #endif
    960 #endif
    961 #endif
    962 #endif
    963 #endif
    964                }
    965            }
    966 
    967            /*
    968              Process the last block, combining the CRCs of the N braids at the
    969              same time.
    970             */
    971            comb = crc_word_big(crc0 ^ words[0]);
    972 #if N > 1
    973            comb = crc_word_big(crc1 ^ words[1] ^ comb);
    974 #if N > 2
    975            comb = crc_word_big(crc2 ^ words[2] ^ comb);
    976 #if N > 3
    977            comb = crc_word_big(crc3 ^ words[3] ^ comb);
    978 #if N > 4
    979            comb = crc_word_big(crc4 ^ words[4] ^ comb);
    980 #if N > 5
    981            comb = crc_word_big(crc5 ^ words[5] ^ comb);
    982 #endif
    983 #endif
    984 #endif
    985 #endif
    986 #endif
    987            words += N;
    988            crc = byte_swap(comb);
    989        }
    990 
    991        /*
    992          Update the pointer to the remaining bytes to process.
    993         */
    994        buf = (unsigned char const *)words;
    995    }
    996 
    997 #endif /* W */
    998 
    999    /* Complete the computation of the CRC on any remaining bytes. */
   1000    while (len >= 8) {
   1001        len -= 8;
   1002        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
   1003        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
   1004        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
   1005        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
   1006        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
   1007        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
   1008        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
   1009        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
   1010    }
   1011    while (len) {
   1012        len--;
   1013        crc = (crc >> 8) ^ crc_table[(crc ^ *buf++) & 0xff];
   1014    }
   1015 
   1016    /* Return the CRC, post-conditioned. */
   1017    return crc ^ 0xffffffff;
   1018 }
   1019 
   1020 #endif
   1021 
   1022 /* ========================================================================= */
   1023 unsigned long ZEXPORT crc32(unsigned long crc, const unsigned char FAR *buf,
   1024                            uInt len) {
   1025    return crc32_z(crc, buf, len);
   1026 }
   1027 
   1028 #ifndef Z_FREETYPE
   1029 
   1030 /* ========================================================================= */
   1031 uLong ZEXPORT crc32_combine64(uLong crc1, uLong crc2, z_off64_t len2) {
   1032 #ifdef DYNAMIC_CRC_TABLE
   1033    once(&made, make_crc_table);
   1034 #endif /* DYNAMIC_CRC_TABLE */
   1035    return multmodp(x2nmodp(len2, 3), crc1) ^ (crc2 & 0xffffffff);
   1036 }
   1037 
   1038 /* ========================================================================= */
   1039 uLong ZEXPORT crc32_combine(uLong crc1, uLong crc2, z_off_t len2) {
   1040    return crc32_combine64(crc1, crc2, (z_off64_t)len2);
   1041 }
   1042 
   1043 /* ========================================================================= */
   1044 uLong ZEXPORT crc32_combine_gen64(z_off64_t len2) {
   1045 #ifdef DYNAMIC_CRC_TABLE
   1046    once(&made, make_crc_table);
   1047 #endif /* DYNAMIC_CRC_TABLE */
   1048    return x2nmodp(len2, 3);
   1049 }
   1050 
   1051 /* ========================================================================= */
   1052 uLong ZEXPORT crc32_combine_gen(z_off_t len2) {
   1053    return crc32_combine_gen64((z_off64_t)len2);
   1054 }
   1055 
   1056 /* ========================================================================= */
   1057 uLong ZEXPORT crc32_combine_op(uLong crc1, uLong crc2, uLong op) {
   1058    return multmodp(op, crc1) ^ (crc2 & 0xffffffff);
   1059 }
   1060 
   1061 #endif  /* !Z_FREETYPE */