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    1 /*
    2 ** $Id: ltable.c $
    3 ** Lua tables (hash)
    4 ** See Copyright Notice in lua.h
    5 */
    6 
    7 #define ltable_c
    8 #define LUA_CORE
    9 
   10 #include "lprefix.h"
   11 
   12 
   13 /*
   14 ** Implementation of tables (aka arrays, objects, or hash tables).
   15 ** Tables keep its elements in two parts: an array part and a hash part.
   16 ** Non-negative integer keys are all candidates to be kept in the array
   17 ** part. The actual size of the array is the largest 'n' such that
   18 ** more than half the slots between 1 and n are in use.
   19 ** Hash uses a mix of chained scatter table with Brent's variation.
   20 ** A main invariant of these tables is that, if an element is not
   21 ** in its main position (i.e. the 'original' position that its hash gives
   22 ** to it), then the colliding element is in its own main position.
   23 ** Hence even when the load factor reaches 100%, performance remains good.
   24 */
   25 
   26 #include <math.h>
   27 #include <limits.h>
   28 
   29 #include "lua.h"
   30 
   31 #include "ldebug.h"
   32 #include "ldo.h"
   33 #include "lgc.h"
   34 #include "lmem.h"
   35 #include "lobject.h"
   36 #include "lstate.h"
   37 #include "lstring.h"
   38 #include "ltable.h"
   39 #include "lvm.h"
   40 
   41 
   42 /*
   43 ** MAXABITS is the largest integer such that MAXASIZE fits in an
   44 ** unsigned int.
   45 */
   46 #define MAXABITS    cast_int(sizeof(int) * CHAR_BIT - 1)
   47 
   48 
   49 /*
   50 ** MAXASIZE is the maximum size of the array part. It is the minimum
   51 ** between 2^MAXABITS and the maximum size that, measured in bytes,
   52 ** fits in a 'size_t'.
   53 */
   54 #define MAXASIZE    luaM_limitN(1u << MAXABITS, TValue)
   55 
   56 /*
   57 ** MAXHBITS is the largest integer such that 2^MAXHBITS fits in a
   58 ** signed int.
   59 */
   60 #define MAXHBITS    (MAXABITS - 1)
   61 
   62 
   63 /*
   64 ** MAXHSIZE is the maximum size of the hash part. It is the minimum
   65 ** between 2^MAXHBITS and the maximum size such that, measured in bytes,
   66 ** it fits in a 'size_t'.
   67 */
   68 #define MAXHSIZE    luaM_limitN(1u << MAXHBITS, Node)
   69 
   70 
   71 /*
   72 ** When the original hash value is good, hashing by a power of 2
   73 ** avoids the cost of '%'.
   74 */
   75 #define hashpow2(t,n)       (gnode(t, lmod((n), sizenode(t))))
   76 
   77 /*
   78 ** for other types, it is better to avoid modulo by power of 2, as
   79 ** they can have many 2 factors.
   80 */
   81 #define hashmod(t,n)    (gnode(t, ((n) % ((sizenode(t)-1)|1))))
   82 
   83 
   84 #define hashstr(t,str)      hashpow2(t, (str)->hash)
   85 #define hashboolean(t,p)    hashpow2(t, p)
   86 
   87 #define hashint(t,i)        hashpow2(t, i)
   88 
   89 
   90 #define hashpointer(t,p)    hashmod(t, point2uint(p))
   91 
   92 
   93 #define dummynode       (&dummynode_)
   94 
   95 static const Node dummynode_ = {
   96   {{NULL}, LUA_VEMPTY,  /* value's value and type */
   97    LUA_VNIL, 0, {NULL}}  /* key type, next, and key value */
   98 };
   99 
  100 
  101 static const TValue absentkey = {ABSTKEYCONSTANT};
  102 
  103 
  104 
  105 /*
  106 ** Hash for floating-point numbers.
  107 ** The main computation should be just
  108 **     n = frexp(n, &i); return (n * INT_MAX) + i
  109 ** but there are some numerical subtleties.
  110 ** In a two-complement representation, INT_MAX does not has an exact
  111 ** representation as a float, but INT_MIN does; because the absolute
  112 ** value of 'frexp' is smaller than 1 (unless 'n' is inf/NaN), the
  113 ** absolute value of the product 'frexp * -INT_MIN' is smaller or equal
  114 ** to INT_MAX. Next, the use of 'unsigned int' avoids overflows when
  115 ** adding 'i'; the use of '~u' (instead of '-u') avoids problems with
  116 ** INT_MIN.
  117 */
  118 #if !defined(l_hashfloat)
  119 static int l_hashfloat (lua_Number n) {
  120   int i;
  121   lua_Integer ni;
  122   n = l_mathop(frexp)(n, &i) * -cast_num(INT_MIN);
  123   if (!lua_numbertointeger(n, &ni)) {  /* is 'n' inf/-inf/NaN? */
  124     lua_assert(luai_numisnan(n) || l_mathop(fabs)(n) == cast_num(HUGE_VAL));
  125     return 0;
  126   }
  127   else {  /* normal case */
  128     unsigned int u = cast_uint(i) + cast_uint(ni);
  129     return cast_int(u <= cast_uint(INT_MAX) ? u : ~u);
  130   }
  131 }
  132 #endif
  133 
  134 
  135 /*
  136 ** returns the 'main' position of an element in a table (that is,
  137 ** the index of its hash value). The key comes broken (tag in 'ktt'
  138 ** and value in 'vkl') so that we can call it on keys inserted into
  139 ** nodes.
  140 */
  141 static Node *mainposition (const Table *t, int ktt, const Value *kvl) {
  142   switch (withvariant(ktt)) {
  143     case LUA_VNUMINT: {
  144       lua_Integer key = ivalueraw(*kvl);
  145       return hashint(t, key);
  146     }
  147     case LUA_VNUMFLT: {
  148       lua_Number n = fltvalueraw(*kvl);
  149       return hashmod(t, l_hashfloat(n));
  150     }
  151     case LUA_VSHRSTR: {
  152       TString *ts = tsvalueraw(*kvl);
  153       return hashstr(t, ts);
  154     }
  155     case LUA_VLNGSTR: {
  156       TString *ts = tsvalueraw(*kvl);
  157       return hashpow2(t, luaS_hashlongstr(ts));
  158     }
  159     case LUA_VFALSE:
  160       return hashboolean(t, 0);
  161     case LUA_VTRUE:
  162       return hashboolean(t, 1);
  163     case LUA_VLIGHTUSERDATA: {
  164       void *p = pvalueraw(*kvl);
  165       return hashpointer(t, p);
  166     }
  167     case LUA_VLCF: {
  168       lua_CFunction f = fvalueraw(*kvl);
  169       return hashpointer(t, f);
  170     }
  171     default: {
  172       GCObject *o = gcvalueraw(*kvl);
  173       return hashpointer(t, o);
  174     }
  175   }
  176 }
  177 
  178 
  179 /*
  180 ** Returns the main position of an element given as a 'TValue'
  181 */
  182 static Node *mainpositionTV (const Table *t, const TValue *key) {
  183   return mainposition(t, rawtt(key), valraw(key));
  184 }
  185 
  186 
  187 /*
  188 ** Check whether key 'k1' is equal to the key in node 'n2'. This
  189 ** equality is raw, so there are no metamethods. Floats with integer
  190 ** values have been normalized, so integers cannot be equal to
  191 ** floats. It is assumed that 'eqshrstr' is simply pointer equality, so
  192 ** that short strings are handled in the default case.
  193 ** A true 'deadok' means to accept dead keys as equal to their original
  194 ** values. All dead keys are compared in the default case, by pointer
  195 ** identity. (Only collectable objects can produce dead keys.) Note that
  196 ** dead long strings are also compared by identity.
  197 ** Once a key is dead, its corresponding value may be collected, and
  198 ** then another value can be created with the same address. If this
  199 ** other value is given to 'next', 'equalkey' will signal a false
  200 ** positive. In a regular traversal, this situation should never happen,
  201 ** as all keys given to 'next' came from the table itself, and therefore
  202 ** could not have been collected. Outside a regular traversal, we
  203 ** have garbage in, garbage out. What is relevant is that this false
  204 ** positive does not break anything.  (In particular, 'next' will return
  205 ** some other valid item on the table or nil.)
  206 */
  207 static int equalkey (const TValue *k1, const Node *n2, int deadok) {
  208   if ((rawtt(k1) != keytt(n2)) &&  /* not the same variants? */
  209        !(deadok && keyisdead(n2) && iscollectable(k1)))
  210    return 0;  /* cannot be same key */
  211   switch (keytt(n2)) {
  212     case LUA_VNIL: case LUA_VFALSE: case LUA_VTRUE:
  213       return 1;
  214     case LUA_VNUMINT:
  215       return (ivalue(k1) == keyival(n2));
  216     case LUA_VNUMFLT:
  217       return luai_numeq(fltvalue(k1), fltvalueraw(keyval(n2)));
  218     case LUA_VLIGHTUSERDATA:
  219       return pvalue(k1) == pvalueraw(keyval(n2));
  220     case LUA_VLCF:
  221       return fvalue(k1) == fvalueraw(keyval(n2));
  222     case ctb(LUA_VLNGSTR):
  223       return luaS_eqlngstr(tsvalue(k1), keystrval(n2));
  224     default:
  225       return gcvalue(k1) == gcvalueraw(keyval(n2));
  226   }
  227 }
  228 
  229 
  230 /*
  231 ** True if value of 'alimit' is equal to the real size of the array
  232 ** part of table 't'. (Otherwise, the array part must be larger than
  233 ** 'alimit'.)
  234 */
  235 #define limitequalsasize(t) (isrealasize(t) || ispow2((t)->alimit))
  236 
  237 
  238 /*
  239 ** Returns the real size of the 'array' array
  240 */
  241 LUAI_FUNC unsigned int luaH_realasize (const Table *t) {
  242   if (limitequalsasize(t))
  243     return t->alimit;  /* this is the size */
  244   else {
  245     unsigned int size = t->alimit;
  246     /* compute the smallest power of 2 not smaller than 'n' */
  247     size |= (size >> 1);
  248     size |= (size >> 2);
  249     size |= (size >> 4);
  250     size |= (size >> 8);
  251     size |= (size >> 16);
  252 #if (UINT_MAX >> 30) > 3
  253     size |= (size >> 32);  /* unsigned int has more than 32 bits */
  254 #endif
  255     size++;
  256     lua_assert(ispow2(size) && size/2 < t->alimit && t->alimit < size);
  257     return size;
  258   }
  259 }
  260 
  261 
  262 /*
  263 ** Check whether real size of the array is a power of 2.
  264 ** (If it is not, 'alimit' cannot be changed to any other value
  265 ** without changing the real size.)
  266 */
  267 static int ispow2realasize (const Table *t) {
  268   return (!isrealasize(t) || ispow2(t->alimit));
  269 }
  270 
  271 
  272 static unsigned int setlimittosize (Table *t) {
  273   t->alimit = luaH_realasize(t);
  274   setrealasize(t);
  275   return t->alimit;
  276 }
  277 
  278 
  279 #define limitasasize(t) check_exp(isrealasize(t), t->alimit)
  280 
  281 
  282 
  283 /*
  284 ** "Generic" get version. (Not that generic: not valid for integers,
  285 ** which may be in array part, nor for floats with integral values.)
  286 ** See explanation about 'deadok' in function 'equalkey'.
  287 */
  288 static const TValue *getgeneric (Table *t, const TValue *key, int deadok) {
  289   Node *n = mainpositionTV(t, key);
  290   for (;;) {  /* check whether 'key' is somewhere in the chain */
  291     if (equalkey(key, n, deadok))
  292       return gval(n);  /* that's it */
  293     else {
  294       int nx = gnext(n);
  295       if (nx == 0)
  296         return &absentkey;  /* not found */
  297       n += nx;
  298     }
  299   }
  300 }
  301 
  302 
  303 /*
  304 ** returns the index for 'k' if 'k' is an appropriate key to live in
  305 ** the array part of a table, 0 otherwise.
  306 */
  307 static unsigned int arrayindex (lua_Integer k) {
  308   if (l_castS2U(k) - 1u < MAXASIZE)  /* 'k' in [1, MAXASIZE]? */
  309     return cast_uint(k);  /* 'key' is an appropriate array index */
  310   else
  311     return 0;
  312 }
  313 
  314 
  315 /*
  316 ** returns the index of a 'key' for table traversals. First goes all
  317 ** elements in the array part, then elements in the hash part. The
  318 ** beginning of a traversal is signaled by 0.
  319 */
  320 static unsigned int findindex (lua_State *L, Table *t, TValue *key,
  321                                unsigned int asize) {
  322   unsigned int i;
  323   if (ttisnil(key)) return 0;  /* first iteration */
  324   i = ttisinteger(key) ? arrayindex(ivalue(key)) : 0;
  325   if (i - 1u < asize)  /* is 'key' inside array part? */
  326     return i;  /* yes; that's the index */
  327   else {
  328     const TValue *n = getgeneric(t, key, 1);
  329     if (l_unlikely(isabstkey(n)))
  330       luaG_runerror(L, "invalid key to 'next'");  /* key not found */
  331     i = cast_int(nodefromval(n) - gnode(t, 0));  /* key index in hash table */
  332     /* hash elements are numbered after array ones */
  333     return (i + 1) + asize;
  334   }
  335 }
  336 
  337 
  338 int luaH_next (lua_State *L, Table *t, StkId key) {
  339   unsigned int asize = luaH_realasize(t);
  340   unsigned int i = findindex(L, t, s2v(key), asize);  /* find original key */
  341   for (; i < asize; i++) {  /* try first array part */
  342     if (!isempty(&t->array[i])) {  /* a non-empty entry? */
  343       setivalue(s2v(key), i + 1);
  344       setobj2s(L, key + 1, &t->array[i]);
  345       return 1;
  346     }
  347   }
  348   for (i -= asize; cast_int(i) < sizenode(t); i++) {  /* hash part */
  349     if (!isempty(gval(gnode(t, i)))) {  /* a non-empty entry? */
  350       Node *n = gnode(t, i);
  351       getnodekey(L, s2v(key), n);
  352       setobj2s(L, key + 1, gval(n));
  353       return 1;
  354     }
  355   }
  356   return 0;  /* no more elements */
  357 }
  358 
  359 
  360 static void freehash (lua_State *L, Table *t) {
  361   if (!isdummy(t))
  362     luaM_freearray(L, t->node, cast_sizet(sizenode(t)));
  363 }
  364 
  365 
  366 /*
  367 ** {=============================================================
  368 ** Rehash
  369 ** ==============================================================
  370 */
  371 
  372 /*
  373 ** Compute the optimal size for the array part of table 't'. 'nums' is a
  374 ** "count array" where 'nums[i]' is the number of integers in the table
  375 ** between 2^(i - 1) + 1 and 2^i. 'pna' enters with the total number of
  376 ** integer keys in the table and leaves with the number of keys that
  377 ** will go to the array part; return the optimal size.  (The condition
  378 ** 'twotoi > 0' in the for loop stops the loop if 'twotoi' overflows.)
  379 */
  380 static unsigned int computesizes (unsigned int nums[], unsigned int *pna) {
  381   int i;
  382   unsigned int twotoi;  /* 2^i (candidate for optimal size) */
  383   unsigned int a = 0;  /* number of elements smaller than 2^i */
  384   unsigned int na = 0;  /* number of elements to go to array part */
  385   unsigned int optimal = 0;  /* optimal size for array part */
  386   /* loop while keys can fill more than half of total size */
  387   for (i = 0, twotoi = 1;
  388        twotoi > 0 && *pna > twotoi / 2;
  389        i++, twotoi *= 2) {
  390     a += nums[i];
  391     if (a > twotoi/2) {  /* more than half elements present? */
  392       optimal = twotoi;  /* optimal size (till now) */
  393       na = a;  /* all elements up to 'optimal' will go to array part */
  394     }
  395   }
  396   lua_assert((optimal == 0 || optimal / 2 < na) && na <= optimal);
  397   *pna = na;
  398   return optimal;
  399 }
  400 
  401 
  402 static int countint (lua_Integer key, unsigned int *nums) {
  403   unsigned int k = arrayindex(key);
  404   if (k != 0) {  /* is 'key' an appropriate array index? */
  405     nums[luaO_ceillog2(k)]++;  /* count as such */
  406     return 1;
  407   }
  408   else
  409     return 0;
  410 }
  411 
  412 
  413 /*
  414 ** Count keys in array part of table 't': Fill 'nums[i]' with
  415 ** number of keys that will go into corresponding slice and return
  416 ** total number of non-nil keys.
  417 */
  418 static unsigned int numusearray (const Table *t, unsigned int *nums) {
  419   int lg;
  420   unsigned int ttlg;  /* 2^lg */
  421   unsigned int ause = 0;  /* summation of 'nums' */
  422   unsigned int i = 1;  /* count to traverse all array keys */
  423   unsigned int asize = limitasasize(t);  /* real array size */
  424   /* traverse each slice */
  425   for (lg = 0, ttlg = 1; lg <= MAXABITS; lg++, ttlg *= 2) {
  426     unsigned int lc = 0;  /* counter */
  427     unsigned int lim = ttlg;
  428     if (lim > asize) {
  429       lim = asize;  /* adjust upper limit */
  430       if (i > lim)
  431         break;  /* no more elements to count */
  432     }
  433     /* count elements in range (2^(lg - 1), 2^lg] */
  434     for (; i <= lim; i++) {
  435       if (!isempty(&t->array[i-1]))
  436         lc++;
  437     }
  438     nums[lg] += lc;
  439     ause += lc;
  440   }
  441   return ause;
  442 }
  443 
  444 
  445 static int numusehash (const Table *t, unsigned int *nums, unsigned int *pna) {
  446   int totaluse = 0;  /* total number of elements */
  447   int ause = 0;  /* elements added to 'nums' (can go to array part) */
  448   int i = sizenode(t);
  449   while (i--) {
  450     Node *n = &t->node[i];
  451     if (!isempty(gval(n))) {
  452       if (keyisinteger(n))
  453         ause += countint(keyival(n), nums);
  454       totaluse++;
  455     }
  456   }
  457   *pna += ause;
  458   return totaluse;
  459 }
  460 
  461 
  462 /*
  463 ** Creates an array for the hash part of a table with the given
  464 ** size, or reuses the dummy node if size is zero.
  465 ** The computation for size overflow is in two steps: the first
  466 ** comparison ensures that the shift in the second one does not
  467 ** overflow.
  468 */
  469 static void setnodevector (lua_State *L, Table *t, unsigned int size) {
  470   if (size == 0) {  /* no elements to hash part? */
  471     t->node = cast(Node *, dummynode);  /* use common 'dummynode' */
  472     t->lsizenode = 0;
  473     t->lastfree = NULL;  /* signal that it is using dummy node */
  474   }
  475   else {
  476     int i;
  477     int lsize = luaO_ceillog2(size);
  478     if (lsize > MAXHBITS || (1u << lsize) > MAXHSIZE)
  479       luaG_runerror(L, "table overflow");
  480     size = twoto(lsize);
  481     t->node = luaM_newvector(L, size, Node);
  482     for (i = 0; i < (int)size; i++) {
  483       Node *n = gnode(t, i);
  484       gnext(n) = 0;
  485       setnilkey(n);
  486       setempty(gval(n));
  487     }
  488     t->lsizenode = cast_byte(lsize);
  489     t->lastfree = gnode(t, size);  /* all positions are free */
  490   }
  491 }
  492 
  493 
  494 /*
  495 ** (Re)insert all elements from the hash part of 'ot' into table 't'.
  496 */
  497 static void reinsert (lua_State *L, Table *ot, Table *t) {
  498   int j;
  499   int size = sizenode(ot);
  500   for (j = 0; j < size; j++) {
  501     Node *old = gnode(ot, j);
  502     if (!isempty(gval(old))) {
  503       /* doesn't need barrier/invalidate cache, as entry was
  504          already present in the table */
  505       TValue k;
  506       getnodekey(L, &k, old);
  507       luaH_set(L, t, &k, gval(old));
  508     }
  509   }
  510 }
  511 
  512 
  513 /*
  514 ** Exchange the hash part of 't1' and 't2'.
  515 */
  516 static void exchangehashpart (Table *t1, Table *t2) {
  517   lu_byte lsizenode = t1->lsizenode;
  518   Node *node = t1->node;
  519   Node *lastfree = t1->lastfree;
  520   t1->lsizenode = t2->lsizenode;
  521   t1->node = t2->node;
  522   t1->lastfree = t2->lastfree;
  523   t2->lsizenode = lsizenode;
  524   t2->node = node;
  525   t2->lastfree = lastfree;
  526 }
  527 
  528 
  529 /*
  530 ** Resize table 't' for the new given sizes. Both allocations (for
  531 ** the hash part and for the array part) can fail, which creates some
  532 ** subtleties. If the first allocation, for the hash part, fails, an
  533 ** error is raised and that is it. Otherwise, it copies the elements from
  534 ** the shrinking part of the array (if it is shrinking) into the new
  535 ** hash. Then it reallocates the array part.  If that fails, the table
  536 ** is in its original state; the function frees the new hash part and then
  537 ** raises the allocation error. Otherwise, it sets the new hash part
  538 ** into the table, initializes the new part of the array (if any) with
  539 ** nils and reinserts the elements of the old hash back into the new
  540 ** parts of the table.
  541 */
  542 void luaH_resize (lua_State *L, Table *t, unsigned int newasize,
  543                                           unsigned int nhsize) {
  544   unsigned int i;
  545   Table newt;  /* to keep the new hash part */
  546   unsigned int oldasize = setlimittosize(t);
  547   TValue *newarray;
  548   /* create new hash part with appropriate size into 'newt' */
  549   setnodevector(L, &newt, nhsize);
  550   if (newasize < oldasize) {  /* will array shrink? */
  551     t->alimit = newasize;  /* pretend array has new size... */
  552     exchangehashpart(t, &newt);  /* and new hash */
  553     /* re-insert into the new hash the elements from vanishing slice */
  554     for (i = newasize; i < oldasize; i++) {
  555       if (!isempty(&t->array[i]))
  556         luaH_setint(L, t, i + 1, &t->array[i]);
  557     }
  558     t->alimit = oldasize;  /* restore current size... */
  559     exchangehashpart(t, &newt);  /* and hash (in case of errors) */
  560   }
  561   /* allocate new array */
  562   newarray = luaM_reallocvector(L, t->array, oldasize, newasize, TValue);
  563   if (l_unlikely(newarray == NULL && newasize > 0)) {  /* allocation failed? */
  564     freehash(L, &newt);  /* release new hash part */
  565     luaM_error(L);  /* raise error (with array unchanged) */
  566   }
  567   /* allocation ok; initialize new part of the array */
  568   exchangehashpart(t, &newt);  /* 't' has the new hash ('newt' has the old) */
  569   t->array = newarray;  /* set new array part */
  570   t->alimit = newasize;
  571   for (i = oldasize; i < newasize; i++)  /* clear new slice of the array */
  572      setempty(&t->array[i]);
  573   /* re-insert elements from old hash part into new parts */
  574   reinsert(L, &newt, t);  /* 'newt' now has the old hash */
  575   freehash(L, &newt);  /* free old hash part */
  576 }
  577 
  578 
  579 void luaH_resizearray (lua_State *L, Table *t, unsigned int nasize) {
  580   int nsize = allocsizenode(t);
  581   luaH_resize(L, t, nasize, nsize);
  582 }
  583 
  584 /*
  585 ** nums[i] = number of keys 'k' where 2^(i - 1) < k <= 2^i
  586 */
  587 static void rehash (lua_State *L, Table *t, const TValue *ek) {
  588   unsigned int asize;  /* optimal size for array part */
  589   unsigned int na;  /* number of keys in the array part */
  590   unsigned int nums[MAXABITS + 1];
  591   int i;
  592   int totaluse;
  593   for (i = 0; i <= MAXABITS; i++) nums[i] = 0;  /* reset counts */
  594   setlimittosize(t);
  595   na = numusearray(t, nums);  /* count keys in array part */
  596   totaluse = na;  /* all those keys are integer keys */
  597   totaluse += numusehash(t, nums, &na);  /* count keys in hash part */
  598   /* count extra key */
  599   if (ttisinteger(ek))
  600     na += countint(ivalue(ek), nums);
  601   totaluse++;
  602   /* compute new size for array part */
  603   asize = computesizes(nums, &na);
  604   /* resize the table to new computed sizes */
  605   luaH_resize(L, t, asize, totaluse - na);
  606 }
  607 
  608 
  609 
  610 /*
  611 ** }=============================================================
  612 */
  613 
  614 
  615 Table *luaH_new (lua_State *L) {
  616   GCObject *o = luaC_newobj(L, LUA_VTABLE, sizeof(Table));
  617   Table *t = gco2t(o);
  618   t->metatable = NULL;
  619   t->flags = cast_byte(maskflags);  /* table has no metamethod fields */
  620   t->array = NULL;
  621   t->alimit = 0;
  622   setnodevector(L, t, 0);
  623   return t;
  624 }
  625 
  626 
  627 void luaH_free (lua_State *L, Table *t) {
  628   freehash(L, t);
  629   luaM_freearray(L, t->array, luaH_realasize(t));
  630   luaM_free(L, t);
  631 }
  632 
  633 
  634 static Node *getfreepos (Table *t) {
  635   if (!isdummy(t)) {
  636     while (t->lastfree > t->node) {
  637       t->lastfree--;
  638       if (keyisnil(t->lastfree))
  639         return t->lastfree;
  640     }
  641   }
  642   return NULL;  /* could not find a free place */
  643 }
  644 
  645 
  646 
  647 /*
  648 ** inserts a new key into a hash table; first, check whether key's main
  649 ** position is free. If not, check whether colliding node is in its main
  650 ** position or not: if it is not, move colliding node to an empty place and
  651 ** put new key in its main position; otherwise (colliding node is in its main
  652 ** position), new key goes to an empty position.
  653 */
  654 void luaH_newkey (lua_State *L, Table *t, const TValue *key, TValue *value) {
  655   Node *mp;
  656   TValue aux;
  657   if (l_unlikely(ttisnil(key)))
  658     luaG_runerror(L, "table index is nil");
  659   else if (ttisfloat(key)) {
  660     lua_Number f = fltvalue(key);
  661     lua_Integer k;
  662     if (luaV_flttointeger(f, &k, F2Ieq)) {  /* does key fit in an integer? */
  663       setivalue(&aux, k);
  664       key = &aux;  /* insert it as an integer */
  665     }
  666     else if (l_unlikely(luai_numisnan(f)))
  667       luaG_runerror(L, "table index is NaN");
  668   }
  669   if (ttisnil(value))
  670     return;  /* do not insert nil values */
  671   mp = mainpositionTV(t, key);
  672   if (!isempty(gval(mp)) || isdummy(t)) {  /* main position is taken? */
  673     Node *othern;
  674     Node *f = getfreepos(t);  /* get a free place */
  675     if (f == NULL) {  /* cannot find a free place? */
  676       rehash(L, t, key);  /* grow table */
  677       /* whatever called 'newkey' takes care of TM cache */
  678       luaH_set(L, t, key, value);  /* insert key into grown table */
  679       return;
  680     }
  681     lua_assert(!isdummy(t));
  682     othern = mainposition(t, keytt(mp), &keyval(mp));
  683     if (othern != mp) {  /* is colliding node out of its main position? */
  684       /* yes; move colliding node into free position */
  685       while (othern + gnext(othern) != mp)  /* find previous */
  686         othern += gnext(othern);
  687       gnext(othern) = cast_int(f - othern);  /* rechain to point to 'f' */
  688       *f = *mp;  /* copy colliding node into free pos. (mp->next also goes) */
  689       if (gnext(mp) != 0) {
  690         gnext(f) += cast_int(mp - f);  /* correct 'next' */
  691         gnext(mp) = 0;  /* now 'mp' is free */
  692       }
  693       setempty(gval(mp));
  694     }
  695     else {  /* colliding node is in its own main position */
  696       /* new node will go into free position */
  697       if (gnext(mp) != 0)
  698         gnext(f) = cast_int((mp + gnext(mp)) - f);  /* chain new position */
  699       else lua_assert(gnext(f) == 0);
  700       gnext(mp) = cast_int(f - mp);
  701       mp = f;
  702     }
  703   }
  704   setnodekey(L, mp, key);
  705   luaC_barrierback(L, obj2gco(t), key);
  706   lua_assert(isempty(gval(mp)));
  707   setobj2t(L, gval(mp), value);
  708 }
  709 
  710 
  711 /*
  712 ** Search function for integers. If integer is inside 'alimit', get it
  713 ** directly from the array part. Otherwise, if 'alimit' is not equal to
  714 ** the real size of the array, key still can be in the array part. In
  715 ** this case, try to avoid a call to 'luaH_realasize' when key is just
  716 ** one more than the limit (so that it can be incremented without
  717 ** changing the real size of the array).
  718 */
  719 const TValue *luaH_getint (Table *t, lua_Integer key) {
  720   if (l_castS2U(key) - 1u < t->alimit)  /* 'key' in [1, t->alimit]? */
  721     return &t->array[key - 1];
  722   else if (!limitequalsasize(t) &&  /* key still may be in the array part? */
  723            (l_castS2U(key) == t->alimit + 1 ||
  724             l_castS2U(key) - 1u < luaH_realasize(t))) {
  725     t->alimit = cast_uint(key);  /* probably '#t' is here now */
  726     return &t->array[key - 1];
  727   }
  728   else {
  729     Node *n = hashint(t, key);
  730     for (;;) {  /* check whether 'key' is somewhere in the chain */
  731       if (keyisinteger(n) && keyival(n) == key)
  732         return gval(n);  /* that's it */
  733       else {
  734         int nx = gnext(n);
  735         if (nx == 0) break;
  736         n += nx;
  737       }
  738     }
  739     return &absentkey;
  740   }
  741 }
  742 
  743 
  744 /*
  745 ** search function for short strings
  746 */
  747 const TValue *luaH_getshortstr (Table *t, TString *key) {
  748   Node *n = hashstr(t, key);
  749   lua_assert(key->tt == LUA_VSHRSTR);
  750   for (;;) {  /* check whether 'key' is somewhere in the chain */
  751     if (keyisshrstr(n) && eqshrstr(keystrval(n), key))
  752       return gval(n);  /* that's it */
  753     else {
  754       int nx = gnext(n);
  755       if (nx == 0)
  756         return &absentkey;  /* not found */
  757       n += nx;
  758     }
  759   }
  760 }
  761 
  762 
  763 const TValue *luaH_getstr (Table *t, TString *key) {
  764   if (key->tt == LUA_VSHRSTR)
  765     return luaH_getshortstr(t, key);
  766   else {  /* for long strings, use generic case */
  767     TValue ko;
  768     setsvalue(cast(lua_State *, NULL), &ko, key);
  769     return getgeneric(t, &ko, 0);
  770   }
  771 }
  772 
  773 
  774 /*
  775 ** main search function
  776 */
  777 const TValue *luaH_get (Table *t, const TValue *key) {
  778   switch (ttypetag(key)) {
  779     case LUA_VSHRSTR: return luaH_getshortstr(t, tsvalue(key));
  780     case LUA_VNUMINT: return luaH_getint(t, ivalue(key));
  781     case LUA_VNIL: return &absentkey;
  782     case LUA_VNUMFLT: {
  783       lua_Integer k;
  784       if (luaV_flttointeger(fltvalue(key), &k, F2Ieq)) /* integral index? */
  785         return luaH_getint(t, k);  /* use specialized version */
  786       /* else... */
  787     }  /* FALLTHROUGH */
  788     default:
  789       return getgeneric(t, key, 0);
  790   }
  791 }
  792 
  793 
  794 /*
  795 ** Finish a raw "set table" operation, where 'slot' is where the value
  796 ** should have been (the result of a previous "get table").
  797 ** Beware: when using this function you probably need to check a GC
  798 ** barrier and invalidate the TM cache.
  799 */
  800 void luaH_finishset (lua_State *L, Table *t, const TValue *key,
  801                                    const TValue *slot, TValue *value) {
  802   if (isabstkey(slot))
  803     luaH_newkey(L, t, key, value);
  804   else
  805     setobj2t(L, cast(TValue *, slot), value);
  806 }
  807 
  808 
  809 /*
  810 ** beware: when using this function you probably need to check a GC
  811 ** barrier and invalidate the TM cache.
  812 */
  813 void luaH_set (lua_State *L, Table *t, const TValue *key, TValue *value) {
  814   const TValue *slot = luaH_get(t, key);
  815   luaH_finishset(L, t, key, slot, value);
  816 }
  817 
  818 
  819 void luaH_setint (lua_State *L, Table *t, lua_Integer key, TValue *value) {
  820   const TValue *p = luaH_getint(t, key);
  821   if (isabstkey(p)) {
  822     TValue k;
  823     setivalue(&k, key);
  824     luaH_newkey(L, t, &k, value);
  825   }
  826   else
  827     setobj2t(L, cast(TValue *, p), value);
  828 }
  829 
  830 
  831 /*
  832 ** Try to find a boundary in the hash part of table 't'. From the
  833 ** caller, we know that 'j' is zero or present and that 'j + 1' is
  834 ** present. We want to find a larger key that is absent from the
  835 ** table, so that we can do a binary search between the two keys to
  836 ** find a boundary. We keep doubling 'j' until we get an absent index.
  837 ** If the doubling would overflow, we try LUA_MAXINTEGER. If it is
  838 ** absent, we are ready for the binary search. ('j', being max integer,
  839 ** is larger or equal to 'i', but it cannot be equal because it is
  840 ** absent while 'i' is present; so 'j > i'.) Otherwise, 'j' is a
  841 ** boundary. ('j + 1' cannot be a present integer key because it is
  842 ** not a valid integer in Lua.)
  843 */
  844 static lua_Unsigned hash_search (Table *t, lua_Unsigned j) {
  845   lua_Unsigned i;
  846   if (j == 0) j++;  /* the caller ensures 'j + 1' is present */
  847   do {
  848     i = j;  /* 'i' is a present index */
  849     if (j <= l_castS2U(LUA_MAXINTEGER) / 2)
  850       j *= 2;
  851     else {
  852       j = LUA_MAXINTEGER;
  853       if (isempty(luaH_getint(t, j)))  /* t[j] not present? */
  854         break;  /* 'j' now is an absent index */
  855       else  /* weird case */
  856         return j;  /* well, max integer is a boundary... */
  857     }
  858   } while (!isempty(luaH_getint(t, j)));  /* repeat until an absent t[j] */
  859   /* i < j  &&  t[i] present  &&  t[j] absent */
  860   while (j - i > 1u) {  /* do a binary search between them */
  861     lua_Unsigned m = (i + j) / 2;
  862     if (isempty(luaH_getint(t, m))) j = m;
  863     else i = m;
  864   }
  865   return i;
  866 }
  867 
  868 
  869 static unsigned int binsearch (const TValue *array, unsigned int i,
  870                                                     unsigned int j) {
  871   while (j - i > 1u) {  /* binary search */
  872     unsigned int m = (i + j) / 2;
  873     if (isempty(&array[m - 1])) j = m;
  874     else i = m;
  875   }
  876   return i;
  877 }
  878 
  879 
  880 /*
  881 ** Try to find a boundary in table 't'. (A 'boundary' is an integer index
  882 ** such that t[i] is present and t[i+1] is absent, or 0 if t[1] is absent
  883 ** and 'maxinteger' if t[maxinteger] is present.)
  884 ** (In the next explanation, we use Lua indices, that is, with base 1.
  885 ** The code itself uses base 0 when indexing the array part of the table.)
  886 ** The code starts with 'limit = t->alimit', a position in the array
  887 ** part that may be a boundary.
  888 **
  889 ** (1) If 't[limit]' is empty, there must be a boundary before it.
  890 ** As a common case (e.g., after 't[#t]=nil'), check whether 'limit-1'
  891 ** is present. If so, it is a boundary. Otherwise, do a binary search
  892 ** between 0 and limit to find a boundary. In both cases, try to
  893 ** use this boundary as the new 'alimit', as a hint for the next call.
  894 **
  895 ** (2) If 't[limit]' is not empty and the array has more elements
  896 ** after 'limit', try to find a boundary there. Again, try first
  897 ** the special case (which should be quite frequent) where 'limit+1'
  898 ** is empty, so that 'limit' is a boundary. Otherwise, check the
  899 ** last element of the array part. If it is empty, there must be a
  900 ** boundary between the old limit (present) and the last element
  901 ** (absent), which is found with a binary search. (This boundary always
  902 ** can be a new limit.)
  903 **
  904 ** (3) The last case is when there are no elements in the array part
  905 ** (limit == 0) or its last element (the new limit) is present.
  906 ** In this case, must check the hash part. If there is no hash part
  907 ** or 'limit+1' is absent, 'limit' is a boundary.  Otherwise, call
  908 ** 'hash_search' to find a boundary in the hash part of the table.
  909 ** (In those cases, the boundary is not inside the array part, and
  910 ** therefore cannot be used as a new limit.)
  911 */
  912 lua_Unsigned luaH_getn (Table *t) {
  913   unsigned int limit = t->alimit;
  914   if (limit > 0 && isempty(&t->array[limit - 1])) {  /* (1)? */
  915     /* there must be a boundary before 'limit' */
  916     if (limit >= 2 && !isempty(&t->array[limit - 2])) {
  917       /* 'limit - 1' is a boundary; can it be a new limit? */
  918       if (ispow2realasize(t) && !ispow2(limit - 1)) {
  919         t->alimit = limit - 1;
  920         setnorealasize(t);  /* now 'alimit' is not the real size */
  921       }
  922       return limit - 1;
  923     }
  924     else {  /* must search for a boundary in [0, limit] */
  925       unsigned int boundary = binsearch(t->array, 0, limit);
  926       /* can this boundary represent the real size of the array? */
  927       if (ispow2realasize(t) && boundary > luaH_realasize(t) / 2) {
  928         t->alimit = boundary;  /* use it as the new limit */
  929         setnorealasize(t);
  930       }
  931       return boundary;
  932     }
  933   }
  934   /* 'limit' is zero or present in table */
  935   if (!limitequalsasize(t)) {  /* (2)? */
  936     /* 'limit' > 0 and array has more elements after 'limit' */
  937     if (isempty(&t->array[limit]))  /* 'limit + 1' is empty? */
  938       return limit;  /* this is the boundary */
  939     /* else, try last element in the array */
  940     limit = luaH_realasize(t);
  941     if (isempty(&t->array[limit - 1])) {  /* empty? */
  942       /* there must be a boundary in the array after old limit,
  943          and it must be a valid new limit */
  944       unsigned int boundary = binsearch(t->array, t->alimit, limit);
  945       t->alimit = boundary;
  946       return boundary;
  947     }
  948     /* else, new limit is present in the table; check the hash part */
  949   }
  950   /* (3) 'limit' is the last element and either is zero or present in table */
  951   lua_assert(limit == luaH_realasize(t) &&
  952              (limit == 0 || !isempty(&t->array[limit - 1])));
  953   if (isdummy(t) || isempty(luaH_getint(t, cast(lua_Integer, limit + 1))))
  954     return limit;  /* 'limit + 1' is absent */
  955   else  /* 'limit + 1' is also present */
  956     return hash_search(t, limit);
  957 }
  958 
  959 
  960 
  961 #if defined(LUA_DEBUG)
  962 
  963 /* export these functions for the test library */
  964 
  965 Node *luaH_mainposition (const Table *t, const TValue *key) {
  966   return mainpositionTV(t, key);
  967 }
  968 
  969 int luaH_isdummy (const Table *t) { return isdummy(t); }
  970 
  971 #endif