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      1 /*
      2 -------------------------------------------------------------------------------
      3 lookup3.c, by Bob Jenkins, May 2006, Public Domain.
      4 
      5 These are functions for producing 32-bit hashes for hash table lookup.
      6 hashword(), hashlittle(), hashlittle2(), hashbig(), mix(), and final()
      7 are externally useful functions.  Routines to test the hash are included
      8 if SELF_TEST is defined.  You can use this free for any purpose.  It's in
      9 the public domain.  It has no warranty.
     10 
     11 You probably want to use hashlittle().  hashlittle() and hashbig()
     12 hash byte arrays.  hashlittle() is is faster than hashbig() on
     13 little-endian machines.  Intel and AMD are little-endian machines.
     14 On second thought, you probably want hashlittle2(), which is identical to
     15 hashlittle() except it returns two 32-bit hashes for the price of one.
     16 You could implement hashbig2() if you wanted but I haven't bothered here.
     17 
     18 If you want to find a hash of, say, exactly 7 integers, do
     19   a = i1;  b = i2;  c = i3;
     20   mix(a,b,c);
     21   a += i4; b += i5; c += i6;
     22   mix(a,b,c);
     23   a += i7;
     24   final(a,b,c);
     25 then use c as the hash value.  If you have a variable length array of
     26 4-byte integers to hash, use hashword().  If you have a byte array (like
     27 a character string), use hashlittle().  If you have several byte arrays, or
     28 a mix of things, see the comments above hashlittle().
     29 
     30 Why is this so big?  I read 12 bytes at a time into 3 4-byte integers,
     31 then mix those integers.  This is fast (you can do a lot more thorough
     32 mixing with 12*3 instructions on 3 integers than you can with 3 instructions
     33 on 1 byte), but shoehorning those bytes into integers efficiently is messy.
     34 -------------------------------------------------------------------------------
     35 */
     36 #define SELF_TEST 1
     37 #undef SELF_TEST
     38 
     39 #include <stdio.h>      /* defines printf for tests */
     40 #include <time.h>       /* defines time_t for timings in the test */
     41 #include <stdint.h>     /* defines uint32_t etc */
     42 #include <sys/param.h>  /* attempt to define endianness */
     43 #ifdef linux
     44 # include <endian.h>    /* attempt to define endianness */
     45 #endif
     46 
     47 /*
     48  * My best guess at if you are big-endian or little-endian.  This may
     49  * need adjustment.
     50  */
     51 #if (defined(__BYTE_ORDER) && defined(__LITTLE_ENDIAN) && \
     52      __BYTE_ORDER == __LITTLE_ENDIAN) || \
     53     (defined(i386) || defined(__i386__) || defined(__i486__) || \
     54      defined(__i586__) || defined(__i686__) || defined(vax) || defined(MIPSEL))
     55 # define HASH_LITTLE_ENDIAN 1
     56 # define HASH_BIG_ENDIAN 0
     57 #elif (defined(__BYTE_ORDER) && defined(__BIG_ENDIAN) && \
     58        __BYTE_ORDER == __BIG_ENDIAN) || \
     59       (defined(sparc) || defined(POWERPC) || defined(mc68000) || defined(sel))
     60 # define HASH_LITTLE_ENDIAN 0
     61 # define HASH_BIG_ENDIAN 1
     62 #else
     63 # define HASH_LITTLE_ENDIAN 0
     64 # define HASH_BIG_ENDIAN 0
     65 #endif
     66 
     67 #define hashsize(n) ((uint32_t)1<<(n))
     68 #define hashmask(n) (hashsize(n)-1)
     69 #define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k))))
     70 
     71 /*
     72 -------------------------------------------------------------------------------
     73 mix -- mix 3 32-bit values reversibly.
     74 
     75 This is reversible, so any information in (a,b,c) before mix() is
     76 still in (a,b,c) after mix().
     77 
     78 If four pairs of (a,b,c) inputs are run through mix(), or through
     79 mix() in reverse, there are at least 32 bits of the output that
     80 are sometimes the same for one pair and different for another pair.
     81 This was tested for:
     82 * pairs that differed by one bit, by two bits, in any combination
     83   of top bits of (a,b,c), or in any combination of bottom bits of
     84   (a,b,c).
     85 * "differ" is defined as +, -, ^, or ~^.  For + and -, I transformed
     86   the output delta to a Gray code (a^(a>>1)) so a string of 1's (as
     87   is commonly produced by subtraction) look like a single 1-bit
     88   difference.
     89 * the base values were pseudorandom, all zero but one bit set, or
     90   all zero plus a counter that starts at zero.
     91 
     92 Some k values for my "a-=c; a^=rot(c,k); c+=b;" arrangement that
     93 satisfy this are
     94     4  6  8 16 19  4
     95     9 15  3 18 27 15
     96    14  9  3  7 17  3
     97 Well, "9 15 3 18 27 15" didn't quite get 32 bits diffing
     98 for "differ" defined as + with a one-bit base and a two-bit delta.  I
     99 used http://burtleburtle.net/bob/hash/avalanche.html to choose
    100 the operations, constants, and arrangements of the variables.
    101 
    102 This does not achieve avalanche.  There are input bits of (a,b,c)
    103 that fail to affect some output bits of (a,b,c), especially of a.  The
    104 most thoroughly mixed value is c, but it doesn't really even achieve
    105 avalanche in c.
    106 
    107 This allows some parallelism.  Read-after-writes are good at doubling
    108 the number of bits affected, so the goal of mixing pulls in the opposite
    109 direction as the goal of parallelism.  I did what I could.  Rotates
    110 seem to cost as much as shifts on every machine I could lay my hands
    111 on, and rotates are much kinder to the top and bottom bits, so I used
    112 rotates.
    113 -------------------------------------------------------------------------------
    114 */
    115 #define mix(a,b,c) \
    116 { \
    117   a -= c;  a ^= rot(c, 4);  c += b; \
    118   b -= a;  b ^= rot(a, 6);  a += c; \
    119   c -= b;  c ^= rot(b, 8);  b += a; \
    120   a -= c;  a ^= rot(c,16);  c += b; \
    121   b -= a;  b ^= rot(a,19);  a += c; \
    122   c -= b;  c ^= rot(b, 4);  b += a; \
    123 }
    124 
    125 /*
    126 -------------------------------------------------------------------------------
    127 final -- final mixing of 3 32-bit values (a,b,c) into c
    128 
    129 Pairs of (a,b,c) values differing in only a few bits will usually
    130 produce values of c that look totally different.  This was tested for
    131 * pairs that differed by one bit, by two bits, in any combination
    132   of top bits of (a,b,c), or in any combination of bottom bits of
    133   (a,b,c).
    134 * "differ" is defined as +, -, ^, or ~^.  For + and -, I transformed
    135   the output delta to a Gray code (a^(a>>1)) so a string of 1's (as
    136   is commonly produced by subtraction) look like a single 1-bit
    137   difference.
    138 * the base values were pseudorandom, all zero but one bit set, or
    139   all zero plus a counter that starts at zero.
    140 
    141 These constants passed:
    142  14 11 25 16 4 14 24
    143  12 14 25 16 4 14 24
    144 and these came close:
    145   4  8 15 26 3 22 24
    146  10  8 15 26 3 22 24
    147  11  8 15 26 3 22 24
    148 -------------------------------------------------------------------------------
    149 */
    150 #define final(a,b,c) \
    151 { \
    152   c ^= b; c -= rot(b,14); \
    153   a ^= c; a -= rot(c,11); \
    154   b ^= a; b -= rot(a,25); \
    155   c ^= b; c -= rot(b,16); \
    156   a ^= c; a -= rot(c,4);  \
    157   b ^= a; b -= rot(a,14); \
    158   c ^= b; c -= rot(b,24); \
    159 }
    160 
    161 /*
    162 --------------------------------------------------------------------
    163  This works on all machines.  To be useful, it requires
    164  -- that the key be an array of uint32_t's, and
    165  -- that the length be the number of uint32_t's in the key
    166 
    167  The function hashword() is identical to hashlittle() on little-endian
    168  machines, and identical to hashbig() on big-endian machines,
    169  except that the length has to be measured in uint32_ts rather than in
    170  bytes.  hashlittle() is more complicated than hashword() only because
    171  hashlittle() has to dance around fitting the key bytes into registers.
    172 --------------------------------------------------------------------
    173 */
    174 uint32_t hashword(
    175 const uint32_t *k,                   /* the key, an array of uint32_t values */
    176 size_t          length,               /* the length of the key, in uint32_ts */
    177 uint32_t        initval)         /* the previous hash, or an arbitrary value */
    178 {
    179   uint32_t a,b,c;
    180 
    181   /* Set up the internal state */
    182   a = b = c = 0xdeadbeef + (((uint32_t)length)<<2) + initval;
    183 
    184   /*------------------------------------------------- handle most of the key */
    185   while (length > 3)
    186   {
    187     a += k[0];
    188     b += k[1];
    189     c += k[2];
    190     mix(a,b,c);
    191     length -= 3;
    192     k += 3;
    193   }
    194 
    195   /*------------------------------------------- handle the last 3 uint32_t's */
    196   switch(length)                     /* all the case statements fall through */
    197   {
    198   case 3 : c+=k[2];
    199   case 2 : b+=k[1];
    200   case 1 : a+=k[0];
    201     final(a,b,c);
    202   case 0:     /* case 0: nothing left to add */
    203     break;
    204   }
    205   /*------------------------------------------------------ report the result */
    206   return c;
    207 }
    208 
    209 
    210 /*
    211 --------------------------------------------------------------------
    212 hashword2() -- same as hashword(), but take two seeds and return two
    213 32-bit values.  pc and pb must both be nonnull, and *pc and *pb must
    214 both be initialized with seeds.  If you pass in (*pb)==0, the output
    215 (*pc) will be the same as the return value from hashword().
    216 --------------------------------------------------------------------
    217 */
    218 void hashword2 (
    219 const uint32_t *k,                   /* the key, an array of uint32_t values */
    220 size_t          length,               /* the length of the key, in uint32_ts */
    221 uint32_t       *pc,                      /* IN: seed OUT: primary hash value */
    222 uint32_t       *pb)               /* IN: more seed OUT: secondary hash value */
    223 {
    224   uint32_t a,b,c;
    225 
    226   /* Set up the internal state */
    227   a = b = c = 0xdeadbeef + ((uint32_t)(length<<2)) + *pc;
    228   c += *pb;
    229 
    230   /*------------------------------------------------- handle most of the key */
    231   while (length > 3)
    232   {
    233     a += k[0];
    234     b += k[1];
    235     c += k[2];
    236     mix(a,b,c);
    237     length -= 3;
    238     k += 3;
    239   }
    240 
    241   /*------------------------------------------- handle the last 3 uint32_t's */
    242   switch(length)                     /* all the case statements fall through */
    243   {
    244   case 3 : c+=k[2];
    245   case 2 : b+=k[1];
    246   case 1 : a+=k[0];
    247     final(a,b,c);
    248   case 0:     /* case 0: nothing left to add */
    249     break;
    250   }
    251   /*------------------------------------------------------ report the result */
    252   *pc=c; *pb=b;
    253 }
    254 
    255 
    256 /*
    257 -------------------------------------------------------------------------------
    258 hashlittle() -- hash a variable-length key into a 32-bit value
    259   k       : the key (the unaligned variable-length array of bytes)
    260   length  : the length of the key, counting by bytes
    261   initval : can be any 4-byte value
    262 Returns a 32-bit value.  Every bit of the key affects every bit of
    263 the return value.  Two keys differing by one or two bits will have
    264 totally different hash values.
    265 
    266 The best hash table sizes are powers of 2.  There is no need to do
    267 mod a prime (mod is sooo slow!).  If you need less than 32 bits,
    268 use a bitmask.  For example, if you need only 10 bits, do
    269   h = (h & hashmask(10));
    270 In which case, the hash table should have hashsize(10) elements.
    271 
    272 If you are hashing n strings (uint8_t **)k, do it like this:
    273   for (i=0, h=0; i<n; ++i) h = hashlittle( k[i], len[i], h);
    274 
    275 By Bob Jenkins, 2006.  bob_jenkins (at) burtleburtle.net.  You may use this
    276 code any way you wish, private, educational, or commercial.  It's free.
    277 
    278 Use for hash table lookup, or anything where one collision in 2^^32 is
    279 acceptable.  Do NOT use for cryptographic purposes.
    280 -------------------------------------------------------------------------------
    281 */
    282 
    283 uint32_t hashlittle( const void *key, size_t length, uint32_t initval)
    284 {
    285   uint32_t a,b,c;                                          /* internal state */
    286   union { const void *ptr; size_t i; } u;     /* needed for Mac Powerbook G4 */
    287 
    288   /* Set up the internal state */
    289   a = b = c = 0xdeadbeef + ((uint32_t)length) + initval;
    290 
    291   u.ptr = key;
    292   if (HASH_LITTLE_ENDIAN && ((u.i & 0x3) == 0)) {
    293     const uint32_t *k = (const uint32_t *)key;         /* read 32-bit chunks */
    294     const uint8_t  *k8;
    295 
    296     /*------ all but last block: aligned reads and affect 32 bits of (a,b,c) */
    297     while (length > 12)
    298     {
    299       a += k[0];
    300       b += k[1];
    301       c += k[2];
    302       mix(a,b,c);
    303       length -= 12;
    304       k += 3;
    305     }
    306 
    307     /*----------------------------- handle the last (probably partial) block */
    308     /*
    309      * "k[2]&0xffffff" actually reads beyond the end of the string, but
    310      * then masks off the part it's not allowed to read.  Because the
    311      * string is aligned, the masked-off tail is in the same word as the
    312      * rest of the string.  Every machine with memory protection I've seen
    313      * does it on word boundaries, so is OK with this.  But VALGRIND will
    314      * still catch it and complain.  The masking trick does make the hash
    315      * noticably faster for short strings (like English words).
    316      */
    317 #ifndef VALGRIND
    318 
    319     switch(length)
    320     {
    321     case 12: c+=k[2]; b+=k[1]; a+=k[0]; break;
    322     case 11: c+=k[2]&0xffffff; b+=k[1]; a+=k[0]; break;
    323     case 10: c+=k[2]&0xffff; b+=k[1]; a+=k[0]; break;
    324     case 9 : c+=k[2]&0xff; b+=k[1]; a+=k[0]; break;
    325     case 8 : b+=k[1]; a+=k[0]; break;
    326     case 7 : b+=k[1]&0xffffff; a+=k[0]; break;
    327     case 6 : b+=k[1]&0xffff; a+=k[0]; break;
    328     case 5 : b+=k[1]&0xff; a+=k[0]; break;
    329     case 4 : a+=k[0]; break;
    330     case 3 : a+=k[0]&0xffffff; break;
    331     case 2 : a+=k[0]&0xffff; break;
    332     case 1 : a+=k[0]&0xff; break;
    333     case 0 : return c;              /* zero length strings require no mixing */
    334     }
    335 
    336 #else /* make valgrind happy */
    337 
    338     k8 = (const uint8_t *)k;
    339     switch(length)
    340     {
    341     case 12: c+=k[2]; b+=k[1]; a+=k[0]; break;
    342     case 11: c+=((uint32_t)k8[10])<<16;  /* fall through */
    343     case 10: c+=((uint32_t)k8[9])<<8;    /* fall through */
    344     case 9 : c+=k8[8];                   /* fall through */
    345     case 8 : b+=k[1]; a+=k[0]; break;
    346     case 7 : b+=((uint32_t)k8[6])<<16;   /* fall through */
    347     case 6 : b+=((uint32_t)k8[5])<<8;    /* fall through */
    348     case 5 : b+=k8[4];                   /* fall through */
    349     case 4 : a+=k[0]; break;
    350     case 3 : a+=((uint32_t)k8[2])<<16;   /* fall through */
    351     case 2 : a+=((uint32_t)k8[1])<<8;    /* fall through */
    352     case 1 : a+=k8[0]; break;
    353     case 0 : return c;
    354     }
    355 
    356 #endif /* !valgrind */
    357 
    358   } else if (HASH_LITTLE_ENDIAN && ((u.i & 0x1) == 0)) {
    359     const uint16_t *k = (const uint16_t *)key;         /* read 16-bit chunks */
    360     const uint8_t  *k8;
    361 
    362     /*--------------- all but last block: aligned reads and different mixing */
    363     while (length > 12)
    364     {
    365       a += k[0] + (((uint32_t)k[1])<<16);
    366       b += k[2] + (((uint32_t)k[3])<<16);
    367       c += k[4] + (((uint32_t)k[5])<<16);
    368       mix(a,b,c);
    369       length -= 12;
    370       k += 6;
    371     }
    372 
    373     /*----------------------------- handle the last (probably partial) block */
    374     k8 = (const uint8_t *)k;
    375     switch(length)
    376     {
    377     case 12: c+=k[4]+(((uint32_t)k[5])<<16);
    378              b+=k[2]+(((uint32_t)k[3])<<16);
    379              a+=k[0]+(((uint32_t)k[1])<<16);
    380              break;
    381     case 11: c+=((uint32_t)k8[10])<<16;     /* fall through */
    382     case 10: c+=k[4];
    383              b+=k[2]+(((uint32_t)k[3])<<16);
    384              a+=k[0]+(((uint32_t)k[1])<<16);
    385              break;
    386     case 9 : c+=k8[8];                      /* fall through */
    387     case 8 : b+=k[2]+(((uint32_t)k[3])<<16);
    388              a+=k[0]+(((uint32_t)k[1])<<16);
    389              break;
    390     case 7 : b+=((uint32_t)k8[6])<<16;      /* fall through */
    391     case 6 : b+=k[2];
    392              a+=k[0]+(((uint32_t)k[1])<<16);
    393              break;
    394     case 5 : b+=k8[4];                      /* fall through */
    395     case 4 : a+=k[0]+(((uint32_t)k[1])<<16);
    396              break;
    397     case 3 : a+=((uint32_t)k8[2])<<16;      /* fall through */
    398     case 2 : a+=k[0];
    399              break;
    400     case 1 : a+=k8[0];
    401              break;
    402     case 0 : return c;                     /* zero length requires no mixing */
    403     }
    404 
    405   } else {                        /* need to read the key one byte at a time */
    406     const uint8_t *k = (const uint8_t *)key;
    407 
    408     /*--------------- all but the last block: affect some 32 bits of (a,b,c) */
    409     while (length > 12)
    410     {
    411       a += k[0];
    412       a += ((uint32_t)k[1])<<8;
    413       a += ((uint32_t)k[2])<<16;
    414       a += ((uint32_t)k[3])<<24;
    415       b += k[4];
    416       b += ((uint32_t)k[5])<<8;
    417       b += ((uint32_t)k[6])<<16;
    418       b += ((uint32_t)k[7])<<24;
    419       c += k[8];
    420       c += ((uint32_t)k[9])<<8;
    421       c += ((uint32_t)k[10])<<16;
    422       c += ((uint32_t)k[11])<<24;
    423       mix(a,b,c);
    424       length -= 12;
    425       k += 12;
    426     }
    427 
    428     /*-------------------------------- last block: affect all 32 bits of (c) */
    429     switch(length)                   /* all the case statements fall through */
    430     {
    431     case 12: c+=((uint32_t)k[11])<<24;
    432     case 11: c+=((uint32_t)k[10])<<16;
    433     case 10: c+=((uint32_t)k[9])<<8;
    434     case 9 : c+=k[8];
    435     case 8 : b+=((uint32_t)k[7])<<24;
    436     case 7 : b+=((uint32_t)k[6])<<16;
    437     case 6 : b+=((uint32_t)k[5])<<8;
    438     case 5 : b+=k[4];
    439     case 4 : a+=((uint32_t)k[3])<<24;
    440     case 3 : a+=((uint32_t)k[2])<<16;
    441     case 2 : a+=((uint32_t)k[1])<<8;
    442     case 1 : a+=k[0];
    443              break;
    444     case 0 : return c;
    445     }
    446   }
    447 
    448   final(a,b,c);
    449   return c;
    450 }
    451 
    452 
    453 /*
    454  * hashlittle2: return 2 32-bit hash values
    455  *
    456  * This is identical to hashlittle(), except it returns two 32-bit hash
    457  * values instead of just one.  This is good enough for hash table
    458  * lookup with 2^^64 buckets, or if you want a second hash if you're not
    459  * happy with the first, or if you want a probably-unique 64-bit ID for
    460  * the key.  *pc is better mixed than *pb, so use *pc first.  If you want
    461  * a 64-bit value do something like "*pc + (((uint64_t)*pb)<<32)".
    462  */
    463 void hashlittle2(
    464   const void *key,       /* the key to hash */
    465   size_t      length,    /* length of the key */
    466   uint32_t   *pc,        /* IN: primary initval, OUT: primary hash */
    467   uint32_t   *pb)        /* IN: secondary initval, OUT: secondary hash */
    468 {
    469   uint32_t a,b,c;                                          /* internal state */
    470   union { const void *ptr; size_t i; } u;     /* needed for Mac Powerbook G4 */
    471 
    472   /* Set up the internal state */
    473   a = b = c = 0xdeadbeef + ((uint32_t)length) + *pc;
    474   c += *pb;
    475 
    476   u.ptr = key;
    477   if (HASH_LITTLE_ENDIAN && ((u.i & 0x3) == 0)) {
    478     const uint32_t *k = (const uint32_t *)key;         /* read 32-bit chunks */
    479     const uint8_t  *k8;
    480 
    481     /*------ all but last block: aligned reads and affect 32 bits of (a,b,c) */
    482     while (length > 12)
    483     {
    484       a += k[0];
    485       b += k[1];
    486       c += k[2];
    487       mix(a,b,c);
    488       length -= 12;
    489       k += 3;
    490     }
    491 
    492     /*----------------------------- handle the last (probably partial) block */
    493     /*
    494      * "k[2]&0xffffff" actually reads beyond the end of the string, but
    495      * then masks off the part it's not allowed to read.  Because the
    496      * string is aligned, the masked-off tail is in the same word as the
    497      * rest of the string.  Every machine with memory protection I've seen
    498      * does it on word boundaries, so is OK with this.  But VALGRIND will
    499      * still catch it and complain.  The masking trick does make the hash
    500      * noticably faster for short strings (like English words).
    501      */
    502 #ifndef VALGRIND
    503 
    504     switch(length)
    505     {
    506     case 12: c+=k[2]; b+=k[1]; a+=k[0]; break;
    507     case 11: c+=k[2]&0xffffff; b+=k[1]; a+=k[0]; break;
    508     case 10: c+=k[2]&0xffff; b+=k[1]; a+=k[0]; break;
    509     case 9 : c+=k[2]&0xff; b+=k[1]; a+=k[0]; break;
    510     case 8 : b+=k[1]; a+=k[0]; break;
    511     case 7 : b+=k[1]&0xffffff; a+=k[0]; break;
    512     case 6 : b+=k[1]&0xffff; a+=k[0]; break;
    513     case 5 : b+=k[1]&0xff; a+=k[0]; break;
    514     case 4 : a+=k[0]; break;
    515     case 3 : a+=k[0]&0xffffff; break;
    516     case 2 : a+=k[0]&0xffff; break;
    517     case 1 : a+=k[0]&0xff; break;
    518     case 0 : *pc=c; *pb=b; return;  /* zero length strings require no mixing */
    519     }
    520 
    521 #else /* make valgrind happy */
    522 
    523     k8 = (const uint8_t *)k;
    524     switch(length)
    525     {
    526     case 12: c+=k[2]; b+=k[1]; a+=k[0]; break;
    527     case 11: c+=((uint32_t)k8[10])<<16;  /* fall through */
    528     case 10: c+=((uint32_t)k8[9])<<8;    /* fall through */
    529     case 9 : c+=k8[8];                   /* fall through */
    530     case 8 : b+=k[1]; a+=k[0]; break;
    531     case 7 : b+=((uint32_t)k8[6])<<16;   /* fall through */
    532     case 6 : b+=((uint32_t)k8[5])<<8;    /* fall through */
    533     case 5 : b+=k8[4];                   /* fall through */
    534     case 4 : a+=k[0]; break;
    535     case 3 : a+=((uint32_t)k8[2])<<16;   /* fall through */
    536     case 2 : a+=((uint32_t)k8[1])<<8;    /* fall through */
    537     case 1 : a+=k8[0]; break;
    538     case 0 : *pc=c; *pb=b; return;  /* zero length strings require no mixing */
    539     }
    540 
    541 #endif /* !valgrind */
    542 
    543   } else if (HASH_LITTLE_ENDIAN && ((u.i & 0x1) == 0)) {
    544     const uint16_t *k = (const uint16_t *)key;         /* read 16-bit chunks */
    545     const uint8_t  *k8;
    546 
    547     /*--------------- all but last block: aligned reads and different mixing */
    548     while (length > 12)
    549     {
    550       a += k[0] + (((uint32_t)k[1])<<16);
    551       b += k[2] + (((uint32_t)k[3])<<16);
    552       c += k[4] + (((uint32_t)k[5])<<16);
    553       mix(a,b,c);
    554       length -= 12;
    555       k += 6;
    556     }
    557 
    558     /*----------------------------- handle the last (probably partial) block */
    559     k8 = (const uint8_t *)k;
    560     switch(length)
    561     {
    562     case 12: c+=k[4]+(((uint32_t)k[5])<<16);
    563              b+=k[2]+(((uint32_t)k[3])<<16);
    564              a+=k[0]+(((uint32_t)k[1])<<16);
    565              break;
    566     case 11: c+=((uint32_t)k8[10])<<16;     /* fall through */
    567     case 10: c+=k[4];
    568              b+=k[2]+(((uint32_t)k[3])<<16);
    569              a+=k[0]+(((uint32_t)k[1])<<16);
    570              break;
    571     case 9 : c+=k8[8];                      /* fall through */
    572     case 8 : b+=k[2]+(((uint32_t)k[3])<<16);
    573              a+=k[0]+(((uint32_t)k[1])<<16);
    574              break;
    575     case 7 : b+=((uint32_t)k8[6])<<16;      /* fall through */
    576     case 6 : b+=k[2];
    577              a+=k[0]+(((uint32_t)k[1])<<16);
    578              break;
    579     case 5 : b+=k8[4];                      /* fall through */
    580     case 4 : a+=k[0]+(((uint32_t)k[1])<<16);
    581              break;
    582     case 3 : a+=((uint32_t)k8[2])<<16;      /* fall through */
    583     case 2 : a+=k[0];
    584              break;
    585     case 1 : a+=k8[0];
    586              break;
    587     case 0 : *pc=c; *pb=b; return;  /* zero length strings require no mixing */
    588     }
    589 
    590   } else {                        /* need to read the key one byte at a time */
    591     const uint8_t *k = (const uint8_t *)key;
    592 
    593     /*--------------- all but the last block: affect some 32 bits of (a,b,c) */
    594     while (length > 12)
    595     {
    596       a += k[0];
    597       a += ((uint32_t)k[1])<<8;
    598       a += ((uint32_t)k[2])<<16;
    599       a += ((uint32_t)k[3])<<24;
    600       b += k[4];
    601       b += ((uint32_t)k[5])<<8;
    602       b += ((uint32_t)k[6])<<16;
    603       b += ((uint32_t)k[7])<<24;
    604       c += k[8];
    605       c += ((uint32_t)k[9])<<8;
    606       c += ((uint32_t)k[10])<<16;
    607       c += ((uint32_t)k[11])<<24;
    608       mix(a,b,c);
    609       length -= 12;
    610       k += 12;
    611     }
    612 
    613     /*-------------------------------- last block: affect all 32 bits of (c) */
    614     switch(length)                   /* all the case statements fall through */
    615     {
    616     case 12: c+=((uint32_t)k[11])<<24;
    617     case 11: c+=((uint32_t)k[10])<<16;
    618     case 10: c+=((uint32_t)k[9])<<8;
    619     case 9 : c+=k[8];
    620     case 8 : b+=((uint32_t)k[7])<<24;
    621     case 7 : b+=((uint32_t)k[6])<<16;
    622     case 6 : b+=((uint32_t)k[5])<<8;
    623     case 5 : b+=k[4];
    624     case 4 : a+=((uint32_t)k[3])<<24;
    625     case 3 : a+=((uint32_t)k[2])<<16;
    626     case 2 : a+=((uint32_t)k[1])<<8;
    627     case 1 : a+=k[0];
    628              break;
    629     case 0 : *pc=c; *pb=b; return;  /* zero length strings require no mixing */
    630     }
    631   }
    632 
    633   final(a,b,c);
    634   *pc=c; *pb=b;
    635 }
    636 
    637 
    638 
    639 /*
    640  * hashbig():
    641  * This is the same as hashword() on big-endian machines.  It is different
    642  * from hashlittle() on all machines.  hashbig() takes advantage of
    643  * big-endian byte ordering.
    644  */
    645 uint32_t hashbig( const void *key, size_t length, uint32_t initval)
    646 {
    647   uint32_t a,b,c;
    648   union { const void *ptr; size_t i; } u; /* to cast key to (size_t) happily */
    649 
    650   /* Set up the internal state */
    651   a = b = c = 0xdeadbeef + ((uint32_t)length) + initval;
    652 
    653   u.ptr = key;
    654   if (HASH_BIG_ENDIAN && ((u.i & 0x3) == 0)) {
    655     const uint32_t *k = (const uint32_t *)key;         /* read 32-bit chunks */
    656     const uint8_t  *k8;
    657 
    658     /*------ all but last block: aligned reads and affect 32 bits of (a,b,c) */
    659     while (length > 12)
    660     {
    661       a += k[0];
    662       b += k[1];
    663       c += k[2];
    664       mix(a,b,c);
    665       length -= 12;
    666       k += 3;
    667     }
    668 
    669     /*----------------------------- handle the last (probably partial) block */
    670     /*
    671      * "k[2]<<8" actually reads beyond the end of the string, but
    672      * then shifts out the part it's not allowed to read.  Because the
    673      * string is aligned, the illegal read is in the same word as the
    674      * rest of the string.  Every machine with memory protection I've seen
    675      * does it on word boundaries, so is OK with this.  But VALGRIND will
    676      * still catch it and complain.  The masking trick does make the hash
    677      * noticably faster for short strings (like English words).
    678      */
    679 #ifndef VALGRIND
    680 
    681     switch(length)
    682     {
    683     case 12: c+=k[2]; b+=k[1]; a+=k[0]; break;
    684     case 11: c+=k[2]&0xffffff00; b+=k[1]; a+=k[0]; break;
    685     case 10: c+=k[2]&0xffff0000; b+=k[1]; a+=k[0]; break;
    686     case 9 : c+=k[2]&0xff000000; b+=k[1]; a+=k[0]; break;
    687     case 8 : b+=k[1]; a+=k[0]; break;
    688     case 7 : b+=k[1]&0xffffff00; a+=k[0]; break;
    689     case 6 : b+=k[1]&0xffff0000; a+=k[0]; break;
    690     case 5 : b+=k[1]&0xff000000; a+=k[0]; break;
    691     case 4 : a+=k[0]; break;
    692     case 3 : a+=k[0]&0xffffff00; break;
    693     case 2 : a+=k[0]&0xffff0000; break;
    694     case 1 : a+=k[0]&0xff000000; break;
    695     case 0 : return c;              /* zero length strings require no mixing */
    696     }
    697 
    698 #else  /* make valgrind happy */
    699 
    700     k8 = (const uint8_t *)k;
    701     switch(length)                   /* all the case statements fall through */
    702     {
    703     case 12: c+=k[2]; b+=k[1]; a+=k[0]; break;
    704     case 11: c+=((uint32_t)k8[10])<<8;  /* fall through */
    705     case 10: c+=((uint32_t)k8[9])<<16;  /* fall through */
    706     case 9 : c+=((uint32_t)k8[8])<<24;  /* fall through */
    707     case 8 : b+=k[1]; a+=k[0]; break;
    708     case 7 : b+=((uint32_t)k8[6])<<8;   /* fall through */
    709     case 6 : b+=((uint32_t)k8[5])<<16;  /* fall through */
    710     case 5 : b+=((uint32_t)k8[4])<<24;  /* fall through */
    711     case 4 : a+=k[0]; break;
    712     case 3 : a+=((uint32_t)k8[2])<<8;   /* fall through */
    713     case 2 : a+=((uint32_t)k8[1])<<16;  /* fall through */
    714     case 1 : a+=((uint32_t)k8[0])<<24; break;
    715     case 0 : return c;
    716     }
    717 
    718 #endif /* !VALGRIND */
    719 
    720   } else {                        /* need to read the key one byte at a time */
    721     const uint8_t *k = (const uint8_t *)key;
    722 
    723     /*--------------- all but the last block: affect some 32 bits of (a,b,c) */
    724     while (length > 12)
    725     {
    726       a += ((uint32_t)k[0])<<24;
    727       a += ((uint32_t)k[1])<<16;
    728       a += ((uint32_t)k[2])<<8;
    729       a += ((uint32_t)k[3]);
    730       b += ((uint32_t)k[4])<<24;
    731       b += ((uint32_t)k[5])<<16;
    732       b += ((uint32_t)k[6])<<8;
    733       b += ((uint32_t)k[7]);
    734       c += ((uint32_t)k[8])<<24;
    735       c += ((uint32_t)k[9])<<16;
    736       c += ((uint32_t)k[10])<<8;
    737       c += ((uint32_t)k[11]);
    738       mix(a,b,c);
    739       length -= 12;
    740       k += 12;
    741     }
    742 
    743     /*-------------------------------- last block: affect all 32 bits of (c) */
    744     switch(length)                   /* all the case statements fall through */
    745     {
    746     case 12: c+=k[11];
    747     case 11: c+=((uint32_t)k[10])<<8;
    748     case 10: c+=((uint32_t)k[9])<<16;
    749     case 9 : c+=((uint32_t)k[8])<<24;
    750     case 8 : b+=k[7];
    751     case 7 : b+=((uint32_t)k[6])<<8;
    752     case 6 : b+=((uint32_t)k[5])<<16;
    753     case 5 : b+=((uint32_t)k[4])<<24;
    754     case 4 : a+=k[3];
    755     case 3 : a+=((uint32_t)k[2])<<8;
    756     case 2 : a+=((uint32_t)k[1])<<16;
    757     case 1 : a+=((uint32_t)k[0])<<24;
    758              break;
    759     case 0 : return c;
    760     }
    761   }
    762 
    763   final(a,b,c);
    764   return c;
    765 }
    766 
    767 
    768 #ifdef SELF_TEST
    769 
    770 /* used for timings */
    771 void driver1()
    772 {
    773   uint8_t buf[256];
    774   uint32_t i;
    775   uint32_t h=0;
    776   time_t a,z;
    777 
    778   time(&a);
    779   for (i=0; i<256; ++i) buf[i] = 'x';
    780   for (i=0; i<1; ++i)
    781   {
    782     h = hashlittle(&buf[0],1,h);
    783   }
    784   time(&z);
    785   if (z-a > 0) printf("time %d %.8x\n", z-a, h);
    786 }
    787 
    788 /* check that every input bit changes every output bit half the time */
    789 #define HASHSTATE 1
    790 #define HASHLEN   1
    791 #define MAXPAIR 60
    792 #define MAXLEN  70
    793 void driver2()
    794 {
    795   uint8_t qa[MAXLEN+1], qb[MAXLEN+2], *a = &qa[0], *b = &qb[1];
    796   uint32_t c[HASHSTATE], d[HASHSTATE], i=0, j=0, k, l, m=0, z;
    797   uint32_t e[HASHSTATE],f[HASHSTATE],g[HASHSTATE],h[HASHSTATE];
    798   uint32_t x[HASHSTATE],y[HASHSTATE];
    799   uint32_t hlen;
    800 
    801   printf("No more than %d trials should ever be needed \n",MAXPAIR/2);
    802   for (hlen=0; hlen < MAXLEN; ++hlen)
    803   {
    804     z=0;
    805     for (i=0; i<hlen; ++i)  /*----------------------- for each input byte, */
    806     {
    807       for (j=0; j<8; ++j)   /*------------------------ for each input bit, */
    808       {
    809 	for (m=1; m<8; ++m) /*------------ for serveral possible initvals, */
    810 	{
    811 	  for (l=0; l<HASHSTATE; ++l)
    812 	    e[l]=f[l]=g[l]=h[l]=x[l]=y[l]=~((uint32_t)0);
    813 
    814       	  /*---- check that every output bit is affected by that input bit */
    815 	  for (k=0; k<MAXPAIR; k+=2)
    816 	  {
    817 	    uint32_t finished=1;
    818 	    /* keys have one bit different */
    819 	    for (l=0; l<hlen+1; ++l) {a[l] = b[l] = (uint8_t)0;}
    820 	    /* have a and b be two keys differing in only one bit */
    821 	    a[i] ^= (k<<j);
    822 	    a[i] ^= (k>>(8-j));
    823 	     c[0] = hashlittle(a, hlen, m);
    824 	    b[i] ^= ((k+1)<<j);
    825 	    b[i] ^= ((k+1)>>(8-j));
    826 	     d[0] = hashlittle(b, hlen, m);
    827 	    /* check every bit is 1, 0, set, and not set at least once */
    828 	    for (l=0; l<HASHSTATE; ++l)
    829 	    {
    830 	      e[l] &= (c[l]^d[l]);
    831 	      f[l] &= ~(c[l]^d[l]);
    832 	      g[l] &= c[l];
    833 	      h[l] &= ~c[l];
    834 	      x[l] &= d[l];
    835 	      y[l] &= ~d[l];
    836 	      if (e[l]|f[l]|g[l]|h[l]|x[l]|y[l]) finished=0;
    837 	    }
    838 	    if (finished) break;
    839 	  }
    840 	  if (k>z) z=k;
    841 	  if (k==MAXPAIR)
    842 	  {
    843 	     printf("Some bit didn't change: ");
    844 	     printf("%.8x %.8x %.8x %.8x %.8x %.8x  ",
    845 	            e[0],f[0],g[0],h[0],x[0],y[0]);
    846 	     printf("i %d j %d m %d len %d\n", i, j, m, hlen);
    847 	  }
    848 	  if (z==MAXPAIR) goto done;
    849 	}
    850       }
    851     }
    852    done:
    853     if (z < MAXPAIR)
    854     {
    855       printf("Mix success  %2d bytes  %2d initvals  ",i,m);
    856       printf("required  %d  trials\n", z/2);
    857     }
    858   }
    859   printf("\n");
    860 }
    861 
    862 /* Check for reading beyond the end of the buffer and alignment problems */
    863 void driver3()
    864 {
    865   uint8_t buf[MAXLEN+20], *b;
    866   uint32_t len;
    867   uint8_t q[] = "This is the time for all good men to come to the aid of their country...";
    868   uint32_t h;
    869   uint8_t qq[] = "xThis is the time for all good men to come to the aid of their country...";
    870   uint32_t i;
    871   uint8_t qqq[] = "xxThis is the time for all good men to come to the aid of their country...";
    872   uint32_t j;
    873   uint8_t qqqq[] = "xxxThis is the time for all good men to come to the aid of their country...";
    874   uint32_t ref,x,y;
    875   uint8_t *p;
    876 
    877   printf("Endianness.  These lines should all be the same (for values filled in):\n");
    878   printf("%.8x                            %.8x                            %.8x\n",
    879          hashword((const uint32_t *)q, (sizeof(q)-1)/4, 13),
    880          hashword((const uint32_t *)q, (sizeof(q)-5)/4, 13),
    881          hashword((const uint32_t *)q, (sizeof(q)-9)/4, 13));
    882   p = q;
    883   printf("%.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x\n",
    884          hashlittle(p, sizeof(q)-1, 13), hashlittle(p, sizeof(q)-2, 13),
    885          hashlittle(p, sizeof(q)-3, 13), hashlittle(p, sizeof(q)-4, 13),
    886          hashlittle(p, sizeof(q)-5, 13), hashlittle(p, sizeof(q)-6, 13),
    887          hashlittle(p, sizeof(q)-7, 13), hashlittle(p, sizeof(q)-8, 13),
    888          hashlittle(p, sizeof(q)-9, 13), hashlittle(p, sizeof(q)-10, 13),
    889          hashlittle(p, sizeof(q)-11, 13), hashlittle(p, sizeof(q)-12, 13));
    890   p = &qq[1];
    891   printf("%.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x\n",
    892          hashlittle(p, sizeof(q)-1, 13), hashlittle(p, sizeof(q)-2, 13),
    893          hashlittle(p, sizeof(q)-3, 13), hashlittle(p, sizeof(q)-4, 13),
    894          hashlittle(p, sizeof(q)-5, 13), hashlittle(p, sizeof(q)-6, 13),
    895          hashlittle(p, sizeof(q)-7, 13), hashlittle(p, sizeof(q)-8, 13),
    896          hashlittle(p, sizeof(q)-9, 13), hashlittle(p, sizeof(q)-10, 13),
    897          hashlittle(p, sizeof(q)-11, 13), hashlittle(p, sizeof(q)-12, 13));
    898   p = &qqq[2];
    899   printf("%.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x\n",
    900          hashlittle(p, sizeof(q)-1, 13), hashlittle(p, sizeof(q)-2, 13),
    901          hashlittle(p, sizeof(q)-3, 13), hashlittle(p, sizeof(q)-4, 13),
    902          hashlittle(p, sizeof(q)-5, 13), hashlittle(p, sizeof(q)-6, 13),
    903          hashlittle(p, sizeof(q)-7, 13), hashlittle(p, sizeof(q)-8, 13),
    904          hashlittle(p, sizeof(q)-9, 13), hashlittle(p, sizeof(q)-10, 13),
    905          hashlittle(p, sizeof(q)-11, 13), hashlittle(p, sizeof(q)-12, 13));
    906   p = &qqqq[3];
    907   printf("%.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x %.8x\n",
    908          hashlittle(p, sizeof(q)-1, 13), hashlittle(p, sizeof(q)-2, 13),
    909          hashlittle(p, sizeof(q)-3, 13), hashlittle(p, sizeof(q)-4, 13),
    910          hashlittle(p, sizeof(q)-5, 13), hashlittle(p, sizeof(q)-6, 13),
    911          hashlittle(p, sizeof(q)-7, 13), hashlittle(p, sizeof(q)-8, 13),
    912          hashlittle(p, sizeof(q)-9, 13), hashlittle(p, sizeof(q)-10, 13),
    913          hashlittle(p, sizeof(q)-11, 13), hashlittle(p, sizeof(q)-12, 13));
    914   printf("\n");
    915 
    916   /* check that hashlittle2 and hashlittle produce the same results */
    917   i=47; j=0;
    918   hashlittle2(q, sizeof(q), &i, &j);
    919   if (hashlittle(q, sizeof(q), 47) != i)
    920     printf("hashlittle2 and hashlittle mismatch\n");
    921 
    922   /* check that hashword2 and hashword produce the same results */
    923   len = 0xdeadbeef;
    924   i=47, j=0;
    925   hashword2(&len, 1, &i, &j);
    926   if (hashword(&len, 1, 47) != i)
    927     printf("hashword2 and hashword mismatch %x %x\n",
    928 	   i, hashword(&len, 1, 47));
    929 
    930   /* check hashlittle doesn't read before or after the ends of the string */
    931   for (h=0, b=buf+1; h<8; ++h, ++b)
    932   {
    933     for (i=0; i<MAXLEN; ++i)
    934     {
    935       len = i;
    936       for (j=0; j<i; ++j) *(b+j)=0;
    937 
    938       /* these should all be equal */
    939       ref = hashlittle(b, len, (uint32_t)1);
    940       *(b+i)=(uint8_t)~0;
    941       *(b-1)=(uint8_t)~0;
    942       x = hashlittle(b, len, (uint32_t)1);
    943       y = hashlittle(b, len, (uint32_t)1);
    944       if ((ref != x) || (ref != y))
    945       {
    946 	printf("alignment error: %.8x %.8x %.8x %d %d\n",ref,x,y,
    947                h, i);
    948       }
    949     }
    950   }
    951 }
    952 
    953 /* check for problems with nulls */
    954  void driver4()
    955 {
    956   uint8_t buf[1];
    957   uint32_t h,i,state[HASHSTATE];
    958 
    959 
    960   buf[0] = ~0;
    961   for (i=0; i<HASHSTATE; ++i) state[i] = 1;
    962   printf("These should all be different\n");
    963   for (i=0, h=0; i<8; ++i)
    964   {
    965     h = hashlittle(buf, 0, h);
    966     printf("%2ld  0-byte strings, hash is  %.8x\n", i, h);
    967   }
    968 }
    969 
    970 void driver5()
    971 {
    972   uint32_t b,c;
    973   b=0, c=0, hashlittle2("", 0, &c, &b);
    974   printf("hash is %.8lx %.8lx\n", c, b);   /* deadbeef deadbeef */
    975   b=0xdeadbeef, c=0, hashlittle2("", 0, &c, &b);
    976   printf("hash is %.8lx %.8lx\n", c, b);   /* bd5b7dde deadbeef */
    977   b=0xdeadbeef, c=0xdeadbeef, hashlittle2("", 0, &c, &b);
    978   printf("hash is %.8lx %.8lx\n", c, b);   /* 9c093ccd bd5b7dde */
    979   b=0, c=0, hashlittle2("Four score and seven years ago", 30, &c, &b);
    980   printf("hash is %.8lx %.8lx\n", c, b);   /* 17770551 ce7226e6 */
    981   b=1, c=0, hashlittle2("Four score and seven years ago", 30, &c, &b);
    982   printf("hash is %.8lx %.8lx\n", c, b);   /* e3607cae bd371de4 */
    983   b=0, c=1, hashlittle2("Four score and seven years ago", 30, &c, &b);
    984   printf("hash is %.8lx %.8lx\n", c, b);   /* cd628161 6cbea4b3 */
    985   c = hashlittle("Four score and seven years ago", 30, 0);
    986   printf("hash is %.8lx\n", c);   /* 17770551 */
    987   c = hashlittle("Four score and seven years ago", 30, 1);
    988   printf("hash is %.8lx\n", c);   /* cd628161 */
    989 }
    990 
    991 
    992 int main()
    993 {
    994   driver1();   /* test that the key is hashed: used for timings */
    995   driver2();   /* test that whole key is hashed thoroughly */
    996   driver3();   /* test that nothing but the key is hashed */
    997   driver4();   /* test hashing multiple buffers (all buffers are null) */
    998   driver5();   /* test the hash against known vectors */
    999   return 1;
   1000 }
   1001 
   1002 #endif  /* SELF_TEST */
   1003