Annotation of embedaddon/rsync/hashtable.c, revision 1.1.1.4

1.1       misho       1: /*
                      2:  * Routines to provide a memory-efficient hashtable.
                      3:  *
1.1.1.4 ! misho       4:  * Copyright (C) 2007-2020 Wayne Davison
1.1       misho       5:  *
                      6:  * This program is free software; you can redistribute it and/or modify
                      7:  * it under the terms of the GNU General Public License as published by
                      8:  * the Free Software Foundation; either version 3 of the License, or
                      9:  * (at your option) any later version.
                     10:  *
                     11:  * This program is distributed in the hope that it will be useful,
                     12:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
                     13:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
                     14:  * GNU General Public License for more details.
                     15:  *
                     16:  * You should have received a copy of the GNU General Public License along
                     17:  * with this program; if not, visit the http://fsf.org website.
                     18:  */
                     19: 
                     20: #include "rsync.h"
                     21: 
                     22: #define HASH_LOAD_LIMIT(size) ((size)*3/4)
                     23: 
                     24: struct hashtable *hashtable_create(int size, int key64)
                     25: {
1.1.1.2   misho      26:        int req = size;
1.1       misho      27:        struct hashtable *tbl;
                     28:        int node_size = key64 ? sizeof (struct ht_int64_node)
                     29:                              : sizeof (struct ht_int32_node);
                     30: 
                     31:        /* Pick a power of 2 that can hold the requested size. */
                     32:        if (size & (size-1) || size < 16) {
                     33:                size = 16;
                     34:                while (size < req)
                     35:                        size *= 2;
                     36:        }
                     37: 
1.1.1.4 ! misho      38:        tbl = new(struct hashtable);
        !            39:        tbl->nodes = new_array0(char, size * node_size);
1.1       misho      40:        tbl->size = size;
                     41:        tbl->entries = 0;
                     42:        tbl->node_size = node_size;
                     43:        tbl->key64 = key64 ? 1 : 0;
                     44: 
1.1.1.2   misho      45:        if (DEBUG_GTE(HASH, 1)) {
                     46:                char buf[32];
                     47:                if (req != size)
                     48:                        snprintf(buf, sizeof buf, "req: %d, ", req);
                     49:                else
                     50:                        *buf = '\0';
                     51:                rprintf(FINFO, "[%s] created hashtable %lx (%ssize: %d, keys: %d-bit)\n",
                     52:                        who_am_i(), (long)tbl, buf, size, key64 ? 64 : 32);
                     53:        }
                     54: 
1.1       misho      55:        return tbl;
                     56: }
                     57: 
                     58: void hashtable_destroy(struct hashtable *tbl)
                     59: {
1.1.1.2   misho      60:        if (DEBUG_GTE(HASH, 1)) {
                     61:                rprintf(FINFO, "[%s] destroyed hashtable %lx (size: %d, keys: %d-bit)\n",
                     62:                        who_am_i(), (long)tbl, tbl->size, tbl->key64 ? 64 : 32);
                     63:        }
1.1       misho      64:        free(tbl->nodes);
                     65:        free(tbl);
                     66: }
                     67: 
1.1.1.4 ! misho      68: /* Returns the node that holds the indicated key if it exists. When it does not
        !            69:  * exist, it returns either NULL (when data_when_new is NULL), or it returns a
        !            70:  * new node with its node->data set to the indicated value.
        !            71:  *
        !            72:  * If your code doesn't know the data value for a new node in advance (usually
        !            73:  * because it doesn't know if a node is new or not) you should pass in a unique
        !            74:  * (non-0) value that you can use to check if the returned node is new. You can
        !            75:  * then overwrite the data with any value you want (even 0) since it only needs
        !            76:  * to be different than whatever data_when_new value you use later on.
        !            77:  *
        !            78:  * This return is a void* just because it might be pointing at a ht_int32_node
        !            79:  * or a ht_int64_node, and that makes the caller's assignment a little easier. */
        !            80: void *hashtable_find(struct hashtable *tbl, int64 key, void *data_when_new)
1.1       misho      81: {
                     82:        int key64 = tbl->key64;
                     83:        struct ht_int32_node *node;
                     84:        uint32 ndx;
                     85: 
                     86:        if (key64 ? key == 0 : (int32)key == 0) {
                     87:                rprintf(FERROR, "Internal hashtable error: illegal key supplied!\n");
                     88:                exit_cleanup(RERR_MESSAGEIO);
                     89:        }
                     90: 
1.1.1.4 ! misho      91:        if (data_when_new && tbl->entries > HASH_LOAD_LIMIT(tbl->size)) {
1.1       misho      92:                void *old_nodes = tbl->nodes;
                     93:                int size = tbl->size * 2;
                     94:                int i;
                     95: 
1.1.1.4 ! misho      96:                tbl->nodes = new_array0(char, size * tbl->node_size);
1.1       misho      97:                tbl->size = size;
                     98:                tbl->entries = 0;
                     99: 
1.1.1.2   misho     100:                if (DEBUG_GTE(HASH, 1)) {
                    101:                        rprintf(FINFO, "[%s] growing hashtable %lx (size: %d, keys: %d-bit)\n",
                    102:                                who_am_i(), (long)tbl, size, key64 ? 64 : 32);
                    103:                }
                    104: 
1.1       misho     105:                for (i = size / 2; i-- > 0; ) {
                    106:                        struct ht_int32_node *move_node = HT_NODE(tbl, old_nodes, i);
                    107:                        int64 move_key = HT_KEY(move_node, key64);
                    108:                        if (move_key == 0)
                    109:                                continue;
1.1.1.4 ! misho     110:                        if (move_node->data)
        !           111:                                hashtable_find(tbl, move_key, move_node->data);
        !           112:                        else {
        !           113:                                node = hashtable_find(tbl, move_key, "");
        !           114:                                node->data = 0;
        !           115:                        }
1.1       misho     116:                }
                    117: 
                    118:                free(old_nodes);
                    119:        }
                    120: 
                    121:        if (!key64) {
                    122:                /* Based on Jenkins One-at-a-time hash. */
                    123:                uchar buf[4], *keyp = buf;
                    124:                int i;
                    125: 
                    126:                SIVALu(buf, 0, key);
                    127:                for (ndx = 0, i = 0; i < 4; i++) {
                    128:                        ndx += keyp[i];
                    129:                        ndx += (ndx << 10);
                    130:                        ndx ^= (ndx >> 6);
                    131:                }
                    132:                ndx += (ndx << 3);
                    133:                ndx ^= (ndx >> 11);
                    134:                ndx += (ndx << 15);
                    135:        } else {
                    136:                /* Based on Jenkins hashword() from lookup3.c. */
                    137:                uint32 a, b, c;
                    138: 
                    139:                /* Set up the internal state */
                    140:                a = b = c = 0xdeadbeef + (8 << 2);
                    141: 
                    142: #define rot(x,k) (((x)<<(k)) ^ ((x)>>(32-(k))))
                    143: #if SIZEOF_INT64 >= 8
                    144:                b += (uint32)(key >> 32);
                    145: #endif
                    146:                a += (uint32)key;
                    147:                c ^= b; c -= rot(b, 14);
                    148:                a ^= c; a -= rot(c, 11);
                    149:                b ^= a; b -= rot(a, 25);
                    150:                c ^= b; c -= rot(b, 16);
                    151:                a ^= c; a -= rot(c, 4);
                    152:                b ^= a; b -= rot(a, 14);
                    153:                c ^= b; c -= rot(b, 24);
                    154: #undef rot
                    155:                ndx = c;
                    156:        }
                    157: 
                    158:        /* If it already exists, return the node.  If we're not
                    159:         * allocating, return NULL if the key is not found. */
                    160:        while (1) {
                    161:                int64 nkey;
                    162: 
                    163:                ndx &= tbl->size - 1;
                    164:                node = HT_NODE(tbl, tbl->nodes, ndx);
                    165:                nkey = HT_KEY(node, key64);
                    166: 
                    167:                if (nkey == key)
                    168:                        return node;
                    169:                if (nkey == 0) {
1.1.1.4 ! misho     170:                        if (!data_when_new)
1.1       misho     171:                                return NULL;
                    172:                        break;
                    173:                }
                    174:                ndx++;
                    175:        }
                    176: 
                    177:        /* Take over this empty spot and then return the node. */
                    178:        if (key64)
                    179:                ((struct ht_int64_node*)node)->key = key;
                    180:        else
                    181:                node->key = (int32)key;
1.1.1.4 ! misho     182:        node->data = data_when_new;
1.1       misho     183:        tbl->entries++;
                    184:        return node;
                    185: }
1.1.1.4 ! misho     186: 
        !           187: #ifndef WORDS_BIGENDIAN
        !           188: # define HASH_LITTLE_ENDIAN 1
        !           189: # define HASH_BIG_ENDIAN 0
        !           190: #else
        !           191: # define HASH_LITTLE_ENDIAN 0
        !           192: # define HASH_BIG_ENDIAN 1
        !           193: #endif
        !           194: 
        !           195: /*
        !           196:  -------------------------------------------------------------------------------
        !           197:  lookup3.c, by Bob Jenkins, May 2006, Public Domain.
        !           198: 
        !           199:  These are functions for producing 32-bit hashes for hash table lookup.
        !           200:  hash_word(), hashlittle(), hashlittle2(), hashbig(), mix(), and final()
        !           201:  are externally useful functions.  Routines to test the hash are included
        !           202:  if SELF_TEST is defined.  You can use this free for any purpose.  It's in
        !           203:  the public domain.  It has no warranty.
        !           204: 
        !           205:  You probably want to use hashlittle().  hashlittle() and hashbig()
        !           206:  hash byte arrays.  hashlittle() is is faster than hashbig() on
        !           207:  little-endian machines.  Intel and AMD are little-endian machines.
        !           208:  On second thought, you probably want hashlittle2(), which is identical to
        !           209:  hashlittle() except it returns two 32-bit hashes for the price of one.
        !           210:  You could implement hashbig2() if you wanted but I haven't bothered here.
        !           211: 
        !           212:  If you want to find a hash of, say, exactly 7 integers, do
        !           213:    a = i1;  b = i2;  c = i3;
        !           214:    mix(a,b,c);
        !           215:    a += i4; b += i5; c += i6;
        !           216:    mix(a,b,c);
        !           217:    a += i7;
        !           218:    final(a,b,c);
        !           219:  then use c as the hash value.  If you have a variable length array of
        !           220:  4-byte integers to hash, use hash_word().  If you have a byte array (like
        !           221:  a character string), use hashlittle().  If you have several byte arrays, or
        !           222:  a mix of things, see the comments above hashlittle().
        !           223: 
        !           224:  Why is this so big?  I read 12 bytes at a time into 3 4-byte integers,
        !           225:  then mix those integers.  This is fast (you can do a lot more thorough
        !           226:  mixing with 12*3 instructions on 3 integers than you can with 3 instructions
        !           227:  on 1 byte), but shoehorning those bytes into integers efficiently is messy.
        !           228: */
        !           229: 
        !           230: #define hashsize(n) ((uint32_t)1<<(n))
        !           231: #define hashmask(n) (hashsize(n)-1)
        !           232: #define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k))))
        !           233: 
        !           234: /*
        !           235:  -------------------------------------------------------------------------------
        !           236:  mix -- mix 3 32-bit values reversibly.
        !           237: 
        !           238:  This is reversible, so any information in (a,b,c) before mix() is
        !           239:  still in (a,b,c) after mix().
        !           240: 
        !           241:  If four pairs of (a,b,c) inputs are run through mix(), or through
        !           242:  mix() in reverse, there are at least 32 bits of the output that
        !           243:  are sometimes the same for one pair and different for another pair.
        !           244:  This was tested for:
        !           245:  * pairs that differed by one bit, by two bits, in any combination
        !           246:    of top bits of (a,b,c), or in any combination of bottom bits of
        !           247:    (a,b,c).
        !           248:  * "differ" is defined as +, -, ^, or ~^.  For + and -, I transformed
        !           249:    the output delta to a Gray code (a^(a>>1)) so a string of 1's (as
        !           250:    is commonly produced by subtraction) look like a single 1-bit
        !           251:    difference.
        !           252:  * the base values were pseudorandom, all zero but one bit set, or
        !           253:    all zero plus a counter that starts at zero.
        !           254: 
        !           255:  Some k values for my "a-=c; a^=rot(c,k); c+=b;" arrangement that
        !           256:  satisfy this are
        !           257:      4  6  8 16 19  4
        !           258:      9 15  3 18 27 15
        !           259:     14  9  3  7 17  3
        !           260:  Well, "9 15 3 18 27 15" didn't quite get 32 bits diffing
        !           261:  for "differ" defined as + with a one-bit base and a two-bit delta.  I
        !           262:  used http://burtleburtle.net/bob/hash/avalanche.html to choose
        !           263:  the operations, constants, and arrangements of the variables.
        !           264: 
        !           265:  This does not achieve avalanche.  There are input bits of (a,b,c)
        !           266:  that fail to affect some output bits of (a,b,c), especially of a.  The
        !           267:  most thoroughly mixed value is c, but it doesn't really even achieve
        !           268:  avalanche in c.
        !           269: 
        !           270:  This allows some parallelism.  Read-after-writes are good at doubling
        !           271:  the number of bits affected, so the goal of mixing pulls in the opposite
        !           272:  direction as the goal of parallelism.  I did what I could.  Rotates
        !           273:  seem to cost as much as shifts on every machine I could lay my hands
        !           274:  on, and rotates are much kinder to the top and bottom bits, so I used
        !           275:  rotates.
        !           276:  -------------------------------------------------------------------------------
        !           277: */
        !           278: #define mix(a,b,c) \
        !           279: { \
        !           280:   a -= c;  a ^= rot(c, 4);  c += b; \
        !           281:   b -= a;  b ^= rot(a, 6);  a += c; \
        !           282:   c -= b;  c ^= rot(b, 8);  b += a; \
        !           283:   a -= c;  a ^= rot(c,16);  c += b; \
        !           284:   b -= a;  b ^= rot(a,19);  a += c; \
        !           285:   c -= b;  c ^= rot(b, 4);  b += a; \
        !           286: }
        !           287: 
        !           288: /*
        !           289:  -------------------------------------------------------------------------------
        !           290:  final -- final mixing of 3 32-bit values (a,b,c) into c
        !           291: 
        !           292:  Pairs of (a,b,c) values differing in only a few bits will usually
        !           293:  produce values of c that look totally different.  This was tested for
        !           294:  * pairs that differed by one bit, by two bits, in any combination
        !           295:    of top bits of (a,b,c), or in any combination of bottom bits of
        !           296:    (a,b,c).
        !           297:  * "differ" is defined as +, -, ^, or ~^.  For + and -, I transformed
        !           298:    the output delta to a Gray code (a^(a>>1)) so a string of 1's (as
        !           299:    is commonly produced by subtraction) look like a single 1-bit
        !           300:    difference.
        !           301:  * the base values were pseudorandom, all zero but one bit set, or
        !           302:    all zero plus a counter that starts at zero.
        !           303: 
        !           304:  These constants passed:
        !           305:   14 11 25 16 4 14 24
        !           306:   12 14 25 16 4 14 24
        !           307:  and these came close:
        !           308:    4  8 15 26 3 22 24
        !           309:   10  8 15 26 3 22 24
        !           310:   11  8 15 26 3 22 24
        !           311:  -------------------------------------------------------------------------------
        !           312: */
        !           313: #define final(a,b,c) \
        !           314: { \
        !           315:   c ^= b; c -= rot(b,14); \
        !           316:   a ^= c; a -= rot(c,11); \
        !           317:   b ^= a; b -= rot(a,25); \
        !           318:   c ^= b; c -= rot(b,16); \
        !           319:   a ^= c; a -= rot(c,4);  \
        !           320:   b ^= a; b -= rot(a,14); \
        !           321:   c ^= b; c -= rot(b,24); \
        !           322: }
        !           323: 
        !           324: 
        !           325: /*
        !           326:  -------------------------------------------------------------------------------
        !           327:  hashlittle() -- hash a variable-length key into a 32-bit value
        !           328:    k       : the key (the unaligned variable-length array of bytes)
        !           329:    length  : the length of the key, counting by bytes
        !           330:    val2    : IN: can be any 4-byte value OUT: second 32 bit hash.
        !           331:  Returns a 32-bit value.  Every bit of the key affects every bit of
        !           332:  the return value.  Two keys differing by one or two bits will have
        !           333:  totally different hash values.  Note that the return value is better
        !           334:  mixed than val2, so use that first.
        !           335: 
        !           336:  The best hash table sizes are powers of 2.  There is no need to do
        !           337:  mod a prime (mod is sooo slow!).  If you need less than 32 bits,
        !           338:  use a bitmask.  For example, if you need only 10 bits, do
        !           339:    h = (h & hashmask(10));
        !           340:  In which case, the hash table should have hashsize(10) elements.
        !           341: 
        !           342:  If you are hashing n strings (uint8_t **)k, do it like this:
        !           343:    for (i=0, h=0; i<n; ++i) h = hashlittle( k[i], len[i], h);
        !           344: 
        !           345:  By Bob Jenkins, 2006.  bob_jenkins@burtleburtle.net.  You may use this
        !           346:  code any way you wish, private, educational, or commercial.  It's free.
        !           347: 
        !           348:  Use for hash table lookup, or anything where one collision in 2^^32 is
        !           349:  acceptable.  Do NOT use for cryptographic purposes.
        !           350:  -------------------------------------------------------------------------------
        !           351: */
        !           352: 
        !           353: uint32_t hashlittle(const void *key, size_t length)
        !           354: {
        !           355:   uint32_t a,b,c;                                          /* internal state */
        !           356:   union { const void *ptr; size_t i; } u;     /* needed for Mac Powerbook G4 */
        !           357: 
        !           358:   /* Set up the internal state */
        !           359:   a = b = c = 0xdeadbeef + ((uint32_t)length);
        !           360: 
        !           361:   u.ptr = key;
        !           362:   if (HASH_LITTLE_ENDIAN && ((u.i & 0x3) == 0)) {
        !           363:     const uint32_t *k = (const uint32_t *)key;         /* read 32-bit chunks */
        !           364:     const uint8_t  *k8;
        !           365: 
        !           366:     /*------ all but last block: aligned reads and affect 32 bits of (a,b,c) */
        !           367:     while (length > 12)
        !           368:     {
        !           369:       a += k[0];
        !           370:       b += k[1];
        !           371:       c += k[2];
        !           372:       mix(a,b,c);
        !           373:       length -= 12;
        !           374:       k += 3;
        !           375:     }
        !           376: 
        !           377:     /*----------------------------- handle the last (probably partial) block */
        !           378:     k8 = (const uint8_t *)k;
        !           379:     switch(length)
        !           380:     {
        !           381:     case 12: c+=k[2]; b+=k[1]; a+=k[0]; break;
        !           382:     case 11: c+=((uint32_t)k8[10])<<16;  /* fall through */
        !           383:     case 10: c+=((uint32_t)k8[9])<<8;    /* fall through */
        !           384:     case 9 : c+=k8[8];                   /* fall through */
        !           385:     case 8 : b+=k[1]; a+=k[0]; break;
        !           386:     case 7 : b+=((uint32_t)k8[6])<<16;   /* fall through */
        !           387:     case 6 : b+=((uint32_t)k8[5])<<8;    /* fall through */
        !           388:     case 5 : b+=k8[4];                   /* fall through */
        !           389:     case 4 : a+=k[0]; break;
        !           390:     case 3 : a+=((uint32_t)k8[2])<<16;   /* fall through */
        !           391:     case 2 : a+=((uint32_t)k8[1])<<8;    /* fall through */
        !           392:     case 1 : a+=k8[0]; break;
        !           393:     case 0 : return c;
        !           394:     }
        !           395:   } else if (HASH_LITTLE_ENDIAN && ((u.i & 0x1) == 0)) {
        !           396:     const uint16_t *k = (const uint16_t *)key;         /* read 16-bit chunks */
        !           397:     const uint8_t  *k8;
        !           398: 
        !           399:     /*--------------- all but last block: aligned reads and different mixing */
        !           400:     while (length > 12)
        !           401:     {
        !           402:       a += k[0] + (((uint32_t)k[1])<<16);
        !           403:       b += k[2] + (((uint32_t)k[3])<<16);
        !           404:       c += k[4] + (((uint32_t)k[5])<<16);
        !           405:       mix(a,b,c);
        !           406:       length -= 12;
        !           407:       k += 6;
        !           408:     }
        !           409: 
        !           410:     /*----------------------------- handle the last (probably partial) block */
        !           411:     k8 = (const uint8_t *)k;
        !           412:     switch(length)
        !           413:     {
        !           414:     case 12: c+=k[4]+(((uint32_t)k[5])<<16);
        !           415:              b+=k[2]+(((uint32_t)k[3])<<16);
        !           416:              a+=k[0]+(((uint32_t)k[1])<<16);
        !           417:              break;
        !           418:     case 11: c+=((uint32_t)k8[10])<<16;     /* fall through */
        !           419:     case 10: c+=k[4];
        !           420:              b+=k[2]+(((uint32_t)k[3])<<16);
        !           421:              a+=k[0]+(((uint32_t)k[1])<<16);
        !           422:              break;
        !           423:     case 9 : c+=k8[8];                      /* fall through */
        !           424:     case 8 : b+=k[2]+(((uint32_t)k[3])<<16);
        !           425:              a+=k[0]+(((uint32_t)k[1])<<16);
        !           426:              break;
        !           427:     case 7 : b+=((uint32_t)k8[6])<<16;      /* fall through */
        !           428:     case 6 : b+=k[2];
        !           429:              a+=k[0]+(((uint32_t)k[1])<<16);
        !           430:              break;
        !           431:     case 5 : b+=k8[4];                      /* fall through */
        !           432:     case 4 : a+=k[0]+(((uint32_t)k[1])<<16);
        !           433:              break;
        !           434:     case 3 : a+=((uint32_t)k8[2])<<16;      /* fall through */
        !           435:     case 2 : a+=k[0];
        !           436:              break;
        !           437:     case 1 : a+=k8[0];
        !           438:              break;
        !           439:     case 0 : return c;                     /* zero length requires no mixing */
        !           440:     }
        !           441: 
        !           442:   } else {                        /* need to read the key one byte at a time */
        !           443:     const uint8_t *k = (const uint8_t *)key;
        !           444: 
        !           445:     /*--------------- all but the last block: affect some 32 bits of (a,b,c) */
        !           446:     while (length > 12)
        !           447:     {
        !           448:       a += k[0];
        !           449:       a += ((uint32_t)k[1])<<8;
        !           450:       a += ((uint32_t)k[2])<<16;
        !           451:       a += ((uint32_t)k[3])<<24;
        !           452:       b += k[4];
        !           453:       b += ((uint32_t)k[5])<<8;
        !           454:       b += ((uint32_t)k[6])<<16;
        !           455:       b += ((uint32_t)k[7])<<24;
        !           456:       c += k[8];
        !           457:       c += ((uint32_t)k[9])<<8;
        !           458:       c += ((uint32_t)k[10])<<16;
        !           459:       c += ((uint32_t)k[11])<<24;
        !           460:       mix(a,b,c);
        !           461:       length -= 12;
        !           462:       k += 12;
        !           463:     }
        !           464: 
        !           465:     /*-------------------------------- last block: affect all 32 bits of (c) */
        !           466:     switch(length)                   /* all the case statements fall through */
        !           467:     {
        !           468:     case 12: c+=((uint32_t)k[11])<<24;
        !           469:             /* FALLTHROUGH */
        !           470:     case 11: c+=((uint32_t)k[10])<<16;
        !           471:             /* FALLTHROUGH */
        !           472:     case 10: c+=((uint32_t)k[9])<<8;
        !           473:             /* FALLTHROUGH */
        !           474:     case 9 : c+=k[8];
        !           475:             /* FALLTHROUGH */
        !           476:     case 8 : b+=((uint32_t)k[7])<<24;
        !           477:             /* FALLTHROUGH */
        !           478:     case 7 : b+=((uint32_t)k[6])<<16;
        !           479:             /* FALLTHROUGH */
        !           480:     case 6 : b+=((uint32_t)k[5])<<8;
        !           481:             /* FALLTHROUGH */
        !           482:     case 5 : b+=k[4];
        !           483:             /* FALLTHROUGH */
        !           484:     case 4 : a+=((uint32_t)k[3])<<24;
        !           485:             /* FALLTHROUGH */
        !           486:     case 3 : a+=((uint32_t)k[2])<<16;
        !           487:             /* FALLTHROUGH */
        !           488:     case 2 : a+=((uint32_t)k[1])<<8;
        !           489:             /* FALLTHROUGH */
        !           490:     case 1 : a+=k[0];
        !           491:              break;
        !           492:     case 0 : return c;
        !           493:     }
        !           494:   }
        !           495: 
        !           496:   final(a,b,c);
        !           497:   return c;
        !           498: }

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