lua

ltable.c (41761B)

---

 /*
 ** $Id: ltable.c $
 ** Lua tables (hash)
 ** See Copyright Notice in lua.h
 */
 
 #define ltable_c
 #define LUA_CORE
 
 #include "lprefix.h"
 
 
 /*
 ** Implementation of tables (aka arrays, objects, or hash tables).
 ** Tables keep its elements in two parts: an array part and a hash part.
 ** Non-negative integer keys are all candidates to be kept in the array
 ** part. The actual size of the array is the largest 'n' such that
 ** more than half the slots between 1 and n are in use.
 ** Hash uses a mix of chained scatter table with Brent's variation.
 ** A main invariant of these tables is that, if an element is not
 ** in its main position (i.e. the 'original' position that its hash gives
 ** to it), then the colliding element is in its own main position.
 ** Hence even when the load factor reaches 100%, performance remains good.
 */
 
 #include <math.h>
 #include <limits.h>
 #include <string.h>
 
 #include "lua.h"
 
 #include "ldebug.h"
 #include "ldo.h"
 #include "lgc.h"
 #include "lmem.h"
 #include "lobject.h"
 #include "lstate.h"
 #include "lstring.h"
 #include "ltable.h"
 #include "lvm.h"
 
 
 /*
 ** Only hash parts with at least 2^LIMFORLAST have a 'lastfree' field
 ** that optimizes finding a free slot. That field is stored just before
 ** the array of nodes, in the same block. Smaller tables do a complete
 ** search when looking for a free slot.
 */
 #define LIMFORLAST    3  /* log2 of real limit (8) */
 
 /*
 ** The union 'Limbox' stores 'lastfree' and ensures that what follows it
 ** is properly aligned to store a Node.
 */
 typedef struct { Node *dummy; Node follows_pNode; } Limbox_aux;
 
 typedef union {
   Node *lastfree;
   char padding[offsetof(Limbox_aux, follows_pNode)];
 } Limbox;
 
 #define haslastfree(t)     ((t)->lsizenode >= LIMFORLAST)
 #define getlastfree(t)     ((cast(Limbox *, (t)->node) - 1)->lastfree)
 
 
 /*
 ** MAXABITS is the largest integer such that 2^MAXABITS fits in an
 ** unsigned int.
 */
 #define MAXABITS	cast_int(sizeof(int) * CHAR_BIT - 1)
 
 
 /*
 ** MAXASIZEB is the maximum number of elements in the array part such
 ** that the size of the array fits in 'size_t'.
 */
 #define MAXASIZEB	(MAX_SIZET/(sizeof(Value) + 1))
 
 
 /*
 ** MAXASIZE is the maximum size of the array part. It is the minimum
 ** between 2^MAXABITS and MAXASIZEB.
 */
 #define MAXASIZE  \
     (((1u << MAXABITS) < MAXASIZEB) ? (1u << MAXABITS) : cast_uint(MAXASIZEB))
 
 /*
 ** MAXHBITS is the largest integer such that 2^MAXHBITS fits in a
 ** signed int.
 */
 #define MAXHBITS	(MAXABITS - 1)
 
 
 /*
 ** MAXHSIZE is the maximum size of the hash part. It is the minimum
 ** between 2^MAXHBITS and the maximum size such that, measured in bytes,
 ** it fits in a 'size_t'.
 */
 #define MAXHSIZE	luaM_limitN(1 << MAXHBITS, Node)
 
 
 /*
 ** When the original hash value is good, hashing by a power of 2
 ** avoids the cost of '%'.
 */
 #define hashpow2(t,n)		(gnode(t, lmod((n), sizenode(t))))
 
 /*
 ** for other types, it is better to avoid modulo by power of 2, as
 ** they can have many 2 factors.
 */
 #define hashmod(t,n)	(gnode(t, ((n) % ((sizenode(t)-1u)|1u))))
 
 
 #define hashstr(t,str)		hashpow2(t, (str)->hash)
 #define hashboolean(t,p)	hashpow2(t, p)
 
 
 #define hashpointer(t,p)	hashmod(t, point2uint(p))
 
 
 #define dummynode		(&dummynode_)
 
 /*
 ** Common hash part for tables with empty hash parts. That allows all
 ** tables to have a hash part, avoiding an extra check ("is there a hash
 ** part?") when indexing. Its sole node has an empty value and a key
 ** (DEADKEY, NULL) that is different from any valid TValue.
 */
 static const Node dummynode_ = {
   {{NULL}, LUA_VEMPTY,  /* value's value and type */
    LUA_TDEADKEY, 0, {NULL}}  /* key type, next, and key value */
 };
 
 
 static const TValue absentkey = {ABSTKEYCONSTANT};
 
 
 /*
 ** Hash for integers. To allow a good hash, use the remainder operator
 ** ('%'). If integer fits as a non-negative int, compute an int
 ** remainder, which is faster. Otherwise, use an unsigned-integer
 ** remainder, which uses all bits and ensures a non-negative result.
 */
 static Node *hashint (const Table *t, lua_Integer i) {
   lua_Unsigned ui = l_castS2U(i);
   if (ui <= cast_uint(INT_MAX))
     return gnode(t, cast_int(ui) % cast_int((sizenode(t)-1) | 1));
   else
     return hashmod(t, ui);
 }
 
 
 /*
 ** Hash for floating-point numbers.
 ** The main computation should be just
 **     n = frexp(n, &i); return (n * INT_MAX) + i
 ** but there are some numerical subtleties.
 ** In a two-complement representation, INT_MAX does not has an exact
 ** representation as a float, but INT_MIN does; because the absolute
 ** value of 'frexp' is smaller than 1 (unless 'n' is inf/NaN), the
 ** absolute value of the product 'frexp * -INT_MIN' is smaller or equal
 ** to INT_MAX. Next, the use of 'unsigned int' avoids overflows when
 ** adding 'i'; the use of '~u' (instead of '-u') avoids problems with
 ** INT_MIN.
 */
 #if !defined(l_hashfloat)
 static unsigned l_hashfloat (lua_Number n) {
   int i;
   lua_Integer ni;
   n = l_mathop(frexp)(n, &i) * -cast_num(INT_MIN);
   if (!lua_numbertointeger(n, &ni)) {  /* is 'n' inf/-inf/NaN? */
     lua_assert(luai_numisnan(n) || l_mathop(fabs)(n) == cast_num(HUGE_VAL));
     return 0;
   }
   else {  /* normal case */
     unsigned int u = cast_uint(i) + cast_uint(ni);
     return (u <= cast_uint(INT_MAX) ? u : ~u);
   }
 }
 #endif
 
 
 /*
 ** returns the 'main' position of an element in a table (that is,
 ** the index of its hash value).
 */
 static Node *mainpositionTV (const Table *t, const TValue *key) {
   switch (ttypetag(key)) {
     case LUA_VNUMINT: {
       lua_Integer i = ivalue(key);
       return hashint(t, i);
     }
     case LUA_VNUMFLT: {
       lua_Number n = fltvalue(key);
       return hashmod(t, l_hashfloat(n));
     }
     case LUA_VSHRSTR: {
       TString *ts = tsvalue(key);
       return hashstr(t, ts);
     }
     case LUA_VLNGSTR: {
       TString *ts = tsvalue(key);
       return hashpow2(t, luaS_hashlongstr(ts));
     }
     case LUA_VFALSE:
       return hashboolean(t, 0);
     case LUA_VTRUE:
       return hashboolean(t, 1);
     case LUA_VLIGHTUSERDATA: {
       void *p = pvalue(key);
       return hashpointer(t, p);
     }
     case LUA_VLCF: {
       lua_CFunction f = fvalue(key);
       return hashpointer(t, f);
     }
     default: {
       GCObject *o = gcvalue(key);
       return hashpointer(t, o);
     }
   }
 }
 
 
 l_sinline Node *mainpositionfromnode (const Table *t, Node *nd) {
   TValue key;
   getnodekey(cast(lua_State *, NULL), &key, nd);
   return mainpositionTV(t, &key);
 }
 
 
 /*
 ** Check whether key 'k1' is equal to the key in node 'n2'. This
 ** equality is raw, so there are no metamethods. Floats with integer
 ** values have been normalized, so integers cannot be equal to
 ** floats. It is assumed that 'eqshrstr' is simply pointer equality, so
 ** that short strings are handled in the default case.
 ** A true 'deadok' means to accept dead keys as equal to their original
 ** values. All dead keys are compared in the default case, by pointer
 ** identity. (Only collectable objects can produce dead keys.) Note that
 ** dead long strings are also compared by identity.
 ** Once a key is dead, its corresponding value may be collected, and
 ** then another value can be created with the same address. If this
 ** other value is given to 'next', 'equalkey' will signal a false
 ** positive. In a regular traversal, this situation should never happen,
 ** as all keys given to 'next' came from the table itself, and therefore
 ** could not have been collected. Outside a regular traversal, we
 ** have garbage in, garbage out. What is relevant is that this false
 ** positive does not break anything.  (In particular, 'next' will return
 ** some other valid item on the table or nil.)
 */
 static int equalkey (const TValue *k1, const Node *n2, int deadok) {
   if ((rawtt(k1) != keytt(n2)) &&  /* not the same variants? */
        !(deadok && keyisdead(n2) && iscollectable(k1)))
    return 0;  /* cannot be same key */
   switch (keytt(n2)) {
     case LUA_VNIL: case LUA_VFALSE: case LUA_VTRUE:
       return 1;
     case LUA_VNUMINT:
       return (ivalue(k1) == keyival(n2));
     case LUA_VNUMFLT:
       return luai_numeq(fltvalue(k1), fltvalueraw(keyval(n2)));
     case LUA_VLIGHTUSERDATA:
       return pvalue(k1) == pvalueraw(keyval(n2));
     case LUA_VLCF:
       return fvalue(k1) == fvalueraw(keyval(n2));
     case ctb(LUA_VLNGSTR):
       return luaS_eqlngstr(tsvalue(k1), keystrval(n2));
     default:
       return gcvalue(k1) == gcvalueraw(keyval(n2));
   }
 }
 
 
 /*
 ** "Generic" get version. (Not that generic: not valid for integers,
 ** which may be in array part, nor for floats with integral values.)
 ** See explanation about 'deadok' in function 'equalkey'.
 */
 static const TValue *getgeneric (Table *t, const TValue *key, int deadok) {
   Node *n = mainpositionTV(t, key);
   for (;;) {  /* check whether 'key' is somewhere in the chain */
     if (equalkey(key, n, deadok))
       return gval(n);  /* that's it */
     else {
       int nx = gnext(n);
       if (nx == 0)
         return &absentkey;  /* not found */
       n += nx;
     }
   }
 }
 
 
 /*
 ** Return the index 'k' (converted to an unsigned) if it is inside
 ** the range [1, limit].
 */
 static unsigned checkrange (lua_Integer k, unsigned limit) {
   return (l_castS2U(k) - 1u < limit) ? cast_uint(k) : 0;
 }
 
 
 /*
 ** Return the index 'k' if 'k' is an appropriate key to live in the
 ** array part of a table, 0 otherwise.
 */
 #define arrayindex(k)	checkrange(k, MAXASIZE)
 
 
 /*
 ** Check whether an integer key is in the array part of a table and
 ** return its index there, or zero.
 */
 #define ikeyinarray(t,k)	checkrange(k, t->asize)
 
 
 /*
 ** Check whether a key is in the array part of a table and return its
 ** index there, or zero.
 */
 static unsigned keyinarray (Table *t, const TValue *key) {
   return (ttisinteger(key)) ? ikeyinarray(t, ivalue(key)) : 0;
 }
 
 
 /*
 ** returns the index of a 'key' for table traversals. First goes all
 ** elements in the array part, then elements in the hash part. The
 ** beginning of a traversal is signaled by 0.
 */
 static unsigned findindex (lua_State *L, Table *t, TValue *key,
                                unsigned asize) {
   unsigned int i;
   if (ttisnil(key)) return 0;  /* first iteration */
   i = keyinarray(t, key);
   if (i != 0)  /* is 'key' inside array part? */
     return i;  /* yes; that's the index */
   else {
     const TValue *n = getgeneric(t, key, 1);
     if (l_unlikely(isabstkey(n)))
       luaG_runerror(L, "invalid key to 'next'");  /* key not found */
     i = cast_uint(nodefromval(n) - gnode(t, 0));  /* key index in hash table */
     /* hash elements are numbered after array ones */
     return (i + 1) + asize;
   }
 }
 
 
 int luaH_next (lua_State *L, Table *t, StkId key) {
   unsigned int asize = t->asize;
   unsigned int i = findindex(L, t, s2v(key), asize);  /* find original key */
   for (; i < asize; i++) {  /* try first array part */
     lu_byte tag = *getArrTag(t, i);
     if (!tagisempty(tag)) {  /* a non-empty entry? */
       setivalue(s2v(key), cast_int(i) + 1);
       farr2val(t, i, tag, s2v(key + 1));
       return 1;
     }
   }
   for (i -= asize; i < sizenode(t); i++) {  /* hash part */
     if (!isempty(gval(gnode(t, i)))) {  /* a non-empty entry? */
       Node *n = gnode(t, i);
       getnodekey(L, s2v(key), n);
       setobj2s(L, key + 1, gval(n));
       return 1;
     }
   }
   return 0;  /* no more elements */
 }
 
 
 /* Extra space in Node array if it has a lastfree entry */
 #define extraLastfree(t)	(haslastfree(t) ? sizeof(Limbox) : 0)
 
 /* 'node' size in bytes */
 static size_t sizehash (Table *t) {
   return cast_sizet(sizenode(t)) * sizeof(Node) + extraLastfree(t);
 }
 
 
 static void freehash (lua_State *L, Table *t) {
   if (!isdummy(t)) {
     /* get pointer to the beginning of Node array */
     char *arr = cast_charp(t->node) - extraLastfree(t);
     luaM_freearray(L, arr, sizehash(t));
   }
 }
 
 
 /*
 ** {=============================================================
 ** Rehash
 ** ==============================================================
 */
 
 static int insertkey (Table *t, const TValue *key, TValue *value);
 static void newcheckedkey (Table *t, const TValue *key, TValue *value);
 
 
 /*
 ** Structure to count the keys in a table.
 ** 'total' is the total number of keys in the table.
 ** 'na' is the number of *array indices* in the table (see 'arrayindex').
 ** 'deleted' is true if there are deleted nodes in the hash part.
 ** 'nums' is a "count array" where 'nums[i]' is the number of integer
 ** keys between 2^(i - 1) + 1 and 2^i. Note that 'na' is the summation
 ** of 'nums'.
 */
 typedef struct {
   unsigned total;
   unsigned na;
   int deleted;
   unsigned nums[MAXABITS + 1];
 } Counters;
 
 
 /*
 ** Check whether it is worth to use 'na' array entries instead of 'nh'
 ** hash nodes. (A hash node uses ~3 times more memory than an array
 ** entry: Two values plus 'next' versus one value.) Evaluate with size_t
 ** to avoid overflows.
 */
 #define arrayXhash(na,nh)	(cast_sizet(na) <= cast_sizet(nh) * 3)
 
 /*
 ** Compute the optimal size for the array part of table 't'.
 ** This size maximizes the number of elements going to the array part
 ** while satisfying the condition 'arrayXhash' with the use of memory if
 ** all those elements went to the hash part.
 ** 'ct->na' enters with the total number of array indices in the table
 ** and leaves with the number of keys that will go to the array part;
 ** return the optimal size for the array part.
 */
 static unsigned computesizes (Counters *ct) {
   int i;
   unsigned int twotoi;  /* 2^i (candidate for optimal size) */
   unsigned int a = 0;  /* number of elements smaller than 2^i */
   unsigned int na = 0;  /* number of elements to go to array part */
   unsigned int optimal = 0;  /* optimal size for array part */
   /* traverse slices while 'twotoi' does not overflow and total of array
      indices still can satisfy 'arrayXhash' against the array size */
   for (i = 0, twotoi = 1;
        twotoi > 0 && arrayXhash(twotoi, ct->na);
        i++, twotoi *= 2) {
     unsigned nums = ct->nums[i];
     a += nums;
     if (nums > 0 &&  /* grows array only if it gets more elements... */
         arrayXhash(twotoi, a)) {  /* ...while using "less memory" */
       optimal = twotoi;  /* optimal size (till now) */
       na = a;  /* all elements up to 'optimal' will go to array part */
     }
   }
   ct->na = na;
   return optimal;
 }
 
 
 static void countint (lua_Integer key, Counters *ct) {
   unsigned int k = arrayindex(key);
   if (k != 0) {  /* is 'key' an array index? */
     ct->nums[luaO_ceillog2(k)]++;  /* count as such */
     ct->na++;
   }
 }
 
 
 l_sinline int arraykeyisempty (const Table *t, unsigned key) {
   int tag = *getArrTag(t, key - 1);
   return tagisempty(tag);
 }
 
 
 /*
 ** Count keys in array part of table 't'.
 */
 static void numusearray (const Table *t, Counters *ct) {
   int lg;
   unsigned int ttlg;  /* 2^lg */
   unsigned int ause = 0;  /* summation of 'nums' */
   unsigned int i = 1;  /* index to traverse all array keys */
   unsigned int asize = t->asize;
   /* traverse each slice */
   for (lg = 0, ttlg = 1; lg <= MAXABITS; lg++, ttlg *= 2) {
     unsigned int lc = 0;  /* counter */
     unsigned int lim = ttlg;
     if (lim > asize) {
       lim = asize;  /* adjust upper limit */
       if (i > lim)
         break;  /* no more elements to count */
     }
     /* count elements in range (2^(lg - 1), 2^lg] */
     for (; i <= lim; i++) {
       if (!arraykeyisempty(t, i))
         lc++;
     }
     ct->nums[lg] += lc;
     ause += lc;
   }
   ct->total += ause;
   ct->na += ause;
 }
 
 
 /*
 ** Count keys in hash part of table 't'. As this only happens during
 ** a rehash, all nodes have been used. A node can have a nil value only
 ** if it was deleted after being created.
 */
 static void numusehash (const Table *t, Counters *ct) {
   unsigned i = sizenode(t);
   unsigned total = 0;
   while (i--) {
     Node *n = &t->node[i];
     if (isempty(gval(n))) {
       lua_assert(!keyisnil(n));  /* entry was deleted; key cannot be nil */
       ct->deleted = 1;
     }
     else {
       total++;
       if (keyisinteger(n))
         countint(keyival(n), ct);
     }
   }
   ct->total += total;
 }
 
 
 /*
 ** Convert an "abstract size" (number of slots in an array) to
 ** "concrete size" (number of bytes in the array).
 */
 static size_t concretesize (unsigned int size) {
   if (size == 0)
     return 0;
   else  /* space for the two arrays plus an unsigned in between */
     return size * (sizeof(Value) + 1) + sizeof(unsigned);
 }
 
 
 /*
 ** Resize the array part of a table. If new size is equal to the old,
 ** do nothing. Else, if new size is zero, free the old array. (It must
 ** be present, as the sizes are different.) Otherwise, allocate a new
 ** array, move the common elements to new proper position, and then
 ** frees the old array.
 ** We could reallocate the array, but we still would need to move the
 ** elements to their new position, so the copy implicit in realloc is a
 ** waste. Moreover, most allocators will move the array anyway when the
 ** new size is double the old one (the most common case).
 */
 static Value *resizearray (lua_State *L , Table *t,
                                unsigned oldasize,
                                unsigned newasize) {
   if (oldasize == newasize)
     return t->array;  /* nothing to be done */
   else if (newasize == 0) {  /* erasing array? */
     Value *op = t->array - oldasize;  /* original array's real address */
     luaM_freemem(L, op, concretesize(oldasize));  /* free it */
     return NULL;
   }
   else {
     size_t newasizeb = concretesize(newasize);
     Value *np = cast(Value *,
                   luaM_reallocvector(L, NULL, 0, newasizeb, lu_byte));
     if (np == NULL)  /* allocation error? */
       return NULL;
     np += newasize;  /* shift pointer to the end of value segment */
     if (oldasize > 0) {
       /* move common elements to new position */
       size_t oldasizeb = concretesize(oldasize);
       Value *op = t->array;  /* original array */
       unsigned tomove = (oldasize < newasize) ? oldasize : newasize;
       size_t tomoveb = (oldasize < newasize) ? oldasizeb : newasizeb;
       lua_assert(tomoveb > 0);
       memcpy(np - tomove, op - tomove, tomoveb);
       luaM_freemem(L, op - oldasize, oldasizeb);  /* free old block */
     }
     return np;
   }
 }
 
 
 /*
 ** Creates an array for the hash part of a table with the given
 ** size, or reuses the dummy node if size is zero.
 ** The computation for size overflow is in two steps: the first
 ** comparison ensures that the shift in the second one does not
 ** overflow.
 */
 static void setnodevector (lua_State *L, Table *t, unsigned size) {
   if (size == 0) {  /* no elements to hash part? */
     t->node = cast(Node *, dummynode);  /* use common 'dummynode' */
     t->lsizenode = 0;
     setdummy(t);  /* signal that it is using dummy node */
   }
   else {
     int i;
     int lsize = luaO_ceillog2(size);
     if (lsize > MAXHBITS || (1 << lsize) > MAXHSIZE)
       luaG_runerror(L, "table overflow");
     size = twoto(lsize);
     if (lsize < LIMFORLAST)  /* no 'lastfree' field? */
       t->node = luaM_newvector(L, size, Node);
     else {
       size_t bsize = size * sizeof(Node) + sizeof(Limbox);
       char *node = luaM_newblock(L, bsize);
       t->node = cast(Node *, node + sizeof(Limbox));
       getlastfree(t) = gnode(t, size);  /* all positions are free */
     }
     t->lsizenode = cast_byte(lsize);
     setnodummy(t);
     for (i = 0; i < cast_int(size); i++) {
       Node *n = gnode(t, i);
       gnext(n) = 0;
       setnilkey(n);
       setempty(gval(n));
     }
   }
 }
 
 
 /*
 ** (Re)insert all elements from the hash part of 'ot' into table 't'.
 */
 static void reinserthash (lua_State *L, Table *ot, Table *t) {
   unsigned j;
   unsigned size = sizenode(ot);
   for (j = 0; j < size; j++) {
     Node *old = gnode(ot, j);
     if (!isempty(gval(old))) {
       /* doesn't need barrier/invalidate cache, as entry was
          already present in the table */
       TValue k;
       getnodekey(L, &k, old);
       newcheckedkey(t, &k, gval(old));
     }
   }
 }
 
 
 /*
 ** Exchange the hash part of 't1' and 't2'. (In 'flags', only the
 ** dummy bit must be exchanged: The 'isrealasize' is not related
 ** to the hash part, and the metamethod bits do not change during
 ** a resize, so the "real" table can keep their values.)
 */
 static void exchangehashpart (Table *t1, Table *t2) {
   lu_byte lsizenode = t1->lsizenode;
   Node *node = t1->node;
   int bitdummy1 = t1->flags & BITDUMMY;
   t1->lsizenode = t2->lsizenode;
   t1->node = t2->node;
   t1->flags = cast_byte((t1->flags & NOTBITDUMMY) | (t2->flags & BITDUMMY));
   t2->lsizenode = lsizenode;
   t2->node = node;
   t2->flags = cast_byte((t2->flags & NOTBITDUMMY) | bitdummy1);
 }
 
 
 /*
 ** Re-insert into the new hash part of a table the elements from the
 ** vanishing slice of the array part.
 */
 static void reinsertOldSlice (Table *t, unsigned oldasize,
                                         unsigned newasize) {
   unsigned i;
   for (i = newasize; i < oldasize; i++) {  /* traverse vanishing slice */
     lu_byte tag = *getArrTag(t, i);
     if (!tagisempty(tag)) {  /* a non-empty entry? */
       TValue key, aux;
       setivalue(&key, l_castU2S(i) + 1);  /* make the key */
       farr2val(t, i, tag, &aux);  /* copy value into 'aux' */
       insertkey(t, &key, &aux);  /* insert entry into the hash part */
     }
   }
 }
 
 
 /*
 ** Clear new slice of the array.
 */
 static void clearNewSlice (Table *t, unsigned oldasize, unsigned newasize) {
   for (; oldasize < newasize; oldasize++)
     *getArrTag(t, oldasize) = LUA_VEMPTY;
 }
 
 
 /*
 ** Resize table 't' for the new given sizes. Both allocations (for
 ** the hash part and for the array part) can fail, which creates some
 ** subtleties. If the first allocation, for the hash part, fails, an
 ** error is raised and that is it. Otherwise, it copies the elements from
 ** the shrinking part of the array (if it is shrinking) into the new
 ** hash. Then it reallocates the array part.  If that fails, the table
 ** is in its original state; the function frees the new hash part and then
 ** raises the allocation error. Otherwise, it sets the new hash part
 ** into the table, initializes the new part of the array (if any) with
 ** nils and reinserts the elements of the old hash back into the new
 ** parts of the table.
 ** Note that if the new size for the array part ('newasize') is equal to
 ** the old one ('oldasize'), this function will do nothing with that
 ** part.
 */
 void luaH_resize (lua_State *L, Table *t, unsigned newasize,
                                           unsigned nhsize) {
   Table newt;  /* to keep the new hash part */
   unsigned oldasize = t->asize;
   Value *newarray;
   if (newasize > MAXASIZE)
     luaG_runerror(L, "table overflow");
   /* create new hash part with appropriate size into 'newt' */
   newt.flags = 0;
   setnodevector(L, &newt, nhsize);
   if (newasize < oldasize) {  /* will array shrink? */
     /* re-insert into the new hash the elements from vanishing slice */
     exchangehashpart(t, &newt);  /* pretend table has new hash */
     reinsertOldSlice(t, oldasize, newasize);
     exchangehashpart(t, &newt);  /* restore old hash (in case of errors) */
   }
   /* allocate new array */
   newarray = resizearray(L, t, oldasize, newasize);
   if (l_unlikely(newarray == NULL && newasize > 0)) {  /* allocation failed? */
     freehash(L, &newt);  /* release new hash part */
     luaM_error(L);  /* raise error (with array unchanged) */
   }
   /* allocation ok; initialize new part of the array */
   exchangehashpart(t, &newt);  /* 't' has the new hash ('newt' has the old) */
   t->array = newarray;  /* set new array part */
   t->asize = newasize;
   if (newarray != NULL)
     *lenhint(t) = newasize / 2u;  /* set an initial hint */
   clearNewSlice(t, oldasize, newasize);
   /* re-insert elements from old hash part into new parts */
   reinserthash(L, &newt, t);  /* 'newt' now has the old hash */
   freehash(L, &newt);  /* free old hash part */
 }
 
 
 void luaH_resizearray (lua_State *L, Table *t, unsigned int nasize) {
   unsigned nsize = allocsizenode(t);
   luaH_resize(L, t, nasize, nsize);
 }
 
 
 /*
 ** Rehash a table. First, count its keys. If there are array indices
 ** outside the array part, compute the new best size for that part.
 ** Then, resize the table.
 */
 static void rehash (lua_State *L, Table *t, const TValue *ek) {
   unsigned asize;  /* optimal size for array part */
   Counters ct;
   unsigned i;
   unsigned nsize;  /* size for the hash part */
   /* reset counts */
   for (i = 0; i <= MAXABITS; i++) ct.nums[i] = 0;
   ct.na = 0;
   ct.deleted = 0;
   ct.total = 1;  /* count extra key */
   if (ttisinteger(ek))
     countint(ivalue(ek), &ct);  /* extra key may go to array */
   numusehash(t, &ct);  /* count keys in hash part */
   if (ct.na == 0) {
     /* no new keys to enter array part; keep it with the same size */
     asize = t->asize;
   }
   else {  /* compute best size for array part */
     numusearray(t, &ct);  /* count keys in array part */
     asize = computesizes(&ct);  /* compute new size for array part */
   }
   /* all keys not in the array part go to the hash part */
   nsize = ct.total - ct.na;
   if (ct.deleted) {  /* table has deleted entries? */
     /* insertion-deletion-insertion: give hash some extra size to
        avoid repeated resizings */
     nsize += nsize >> 2;
   }
   /* resize the table to new computed sizes */
   luaH_resize(L, t, asize, nsize);
 }
 
 /*
 ** }=============================================================
 */
 
 
 Table *luaH_new (lua_State *L) {
   GCObject *o = luaC_newobj(L, LUA_VTABLE, sizeof(Table));
   Table *t = gco2t(o);
   t->metatable = NULL;
   t->flags = maskflags;  /* table has no metamethod fields */
   t->array = NULL;
   t->asize = 0;
   setnodevector(L, t, 0);
   return t;
 }
 
 
 lu_mem luaH_size (Table *t) {
   lu_mem sz = cast(lu_mem, sizeof(Table)) + concretesize(t->asize);
   if (!isdummy(t))
     sz += sizehash(t);
   return sz;
 }
 
 
 /*
 ** Frees a table.
 */
 void luaH_free (lua_State *L, Table *t) {
   freehash(L, t);
   resizearray(L, t, t->asize, 0);
   luaM_free(L, t);
 }
 
 
 static Node *getfreepos (Table *t) {
   if (haslastfree(t)) {  /* does it have 'lastfree' information? */
     /* look for a spot before 'lastfree', updating 'lastfree' */
     while (getlastfree(t) > t->node) {
       Node *free = --getlastfree(t);
       if (keyisnil(free))
         return free;
     }
   }
   else {  /* no 'lastfree' information */
     unsigned i = sizenode(t);
     while (i--) {  /* do a linear search */
       Node *free = gnode(t, i);
       if (keyisnil(free))
         return free;
     }
   }
   return NULL;  /* could not find a free place */
 }
 
 
 
 /*
 ** Inserts a new key into a hash table; first, check whether key's main
 ** position is free. If not, check whether colliding node is in its main
 ** position or not: if it is not, move colliding node to an empty place
 ** and put new key in its main position; otherwise (colliding node is in
 ** its main position), new key goes to an empty position. Return 0 if
 ** could not insert key (could not find a free space).
 */
 static int insertkey (Table *t, const TValue *key, TValue *value) {
   Node *mp = mainpositionTV(t, key);
   /* table cannot already contain the key */
   lua_assert(isabstkey(getgeneric(t, key, 0)));
   if (!isempty(gval(mp)) || isdummy(t)) {  /* main position is taken? */
     Node *othern;
     Node *f = getfreepos(t);  /* get a free place */
     if (f == NULL)  /* cannot find a free place? */
       return 0;
     lua_assert(!isdummy(t));
     othern = mainpositionfromnode(t, mp);
     if (othern != mp) {  /* is colliding node out of its main position? */
       /* yes; move colliding node into free position */
       while (othern + gnext(othern) != mp)  /* find previous */
         othern += gnext(othern);
       gnext(othern) = cast_int(f - othern);  /* rechain to point to 'f' */
       *f = *mp;  /* copy colliding node into free pos. (mp->next also goes) */
       if (gnext(mp) != 0) {
         gnext(f) += cast_int(mp - f);  /* correct 'next' */
         gnext(mp) = 0;  /* now 'mp' is free */
       }
       setempty(gval(mp));
     }
     else {  /* colliding node is in its own main position */
       /* new node will go into free position */
       if (gnext(mp) != 0)
         gnext(f) = cast_int((mp + gnext(mp)) - f);  /* chain new position */
       else lua_assert(gnext(f) == 0);
       gnext(mp) = cast_int(f - mp);
       mp = f;
     }
   }
   setnodekey(mp, key);
   lua_assert(isempty(gval(mp)));
   setobj2t(cast(lua_State *, 0), gval(mp), value);
   return 1;
 }
 
 
 /*
 ** Insert a key in a table where there is space for that key, the
 ** key is valid, and the value is not nil.
 */
 static void newcheckedkey (Table *t, const TValue *key, TValue *value) {
   unsigned i = keyinarray(t, key);
   if (i > 0)  /* is key in the array part? */
     obj2arr(t, i - 1, value);  /* set value in the array */
   else {
     int done = insertkey(t, key, value);  /* insert key in the hash part */
     lua_assert(done);  /* it cannot fail */
     cast(void, done);  /* to avoid warnings */
   }
 }
 
 
 static void luaH_newkey (lua_State *L, Table *t, const TValue *key,
                                                  TValue *value) {
   if (!ttisnil(value)) {  /* do not insert nil values */
     int done = insertkey(t, key, value);
     if (!done) {  /* could not find a free place? */
       rehash(L, t, key);  /* grow table */
       newcheckedkey(t, key, value);  /* insert key in grown table */
     }
     luaC_barrierback(L, obj2gco(t), key);
     /* for debugging only: any new key may force an emergency collection */
     condchangemem(L, (void)0, (void)0, 1);
   }
 }
 
 
 static const TValue *getintfromhash (Table *t, lua_Integer key) {
   Node *n = hashint(t, key);
   lua_assert(!ikeyinarray(t, key));
   for (;;) {  /* check whether 'key' is somewhere in the chain */
     if (keyisinteger(n) && keyival(n) == key)
       return gval(n);  /* that's it */
     else {
       int nx = gnext(n);
       if (nx == 0) break;
       n += nx;
     }
   }
   return &absentkey;
 }
 
 
 static int hashkeyisempty (Table *t, lua_Unsigned key) {
   const TValue *val = getintfromhash(t, l_castU2S(key));
   return isempty(val);
 }
 
 
 static lu_byte finishnodeget (const TValue *val, TValue *res) {
   if (!ttisnil(val)) {
     setobj(((lua_State*)NULL), res, val);
   }
   return ttypetag(val);
 }
 
 
 lu_byte luaH_getint (Table *t, lua_Integer key, TValue *res) {
   unsigned k = ikeyinarray(t, key);
   if (k > 0) {
     lu_byte tag = *getArrTag(t, k - 1);
     if (!tagisempty(tag))
       farr2val(t, k - 1, tag, res);
     return tag;
   }
   else
     return finishnodeget(getintfromhash(t, key), res);
 }
 
 
 /*
 ** search function for short strings
 */
 const TValue *luaH_Hgetshortstr (Table *t, TString *key) {
   Node *n = hashstr(t, key);
   lua_assert(strisshr(key));
   for (;;) {  /* check whether 'key' is somewhere in the chain */
     if (keyisshrstr(n) && eqshrstr(keystrval(n), key))
       return gval(n);  /* that's it */
     else {
       int nx = gnext(n);
       if (nx == 0)
         return &absentkey;  /* not found */
       n += nx;
     }
   }
 }
 
 
 lu_byte luaH_getshortstr (Table *t, TString *key, TValue *res) {
   return finishnodeget(luaH_Hgetshortstr(t, key), res);
 }
 
 
 static const TValue *Hgetlongstr (Table *t, TString *key) {
   TValue ko;
   lua_assert(!strisshr(key));
   setsvalue(cast(lua_State *, NULL), &ko, key);
   return getgeneric(t, &ko, 0);  /* for long strings, use generic case */
 }
 
 
 static const TValue *Hgetstr (Table *t, TString *key) {
   if (strisshr(key))
     return luaH_Hgetshortstr(t, key);
   else
     return Hgetlongstr(t, key);
 }
 
 
 lu_byte luaH_getstr (Table *t, TString *key, TValue *res) {
   return finishnodeget(Hgetstr(t, key), res);
 }
 
 
 /*
 ** main search function
 */
 lu_byte luaH_get (Table *t, const TValue *key, TValue *res) {
   const TValue *slot;
   switch (ttypetag(key)) {
     case LUA_VSHRSTR:
       slot = luaH_Hgetshortstr(t, tsvalue(key));
       break;
     case LUA_VNUMINT:
       return luaH_getint(t, ivalue(key), res);
     case LUA_VNIL:
       slot = &absentkey;
       break;
     case LUA_VNUMFLT: {
       lua_Integer k;
       if (luaV_flttointeger(fltvalue(key), &k, F2Ieq)) /* integral index? */
         return luaH_getint(t, k, res);  /* use specialized version */
       /* else... */
     }  /* FALLTHROUGH */
     default:
       slot = getgeneric(t, key, 0);
       break;
   }
   return finishnodeget(slot, res);
 }
 
 
 /*
 ** When a 'pset' cannot be completed, this function returns an encoding
 ** of its result, to be used by 'luaH_finishset'.
 */
 static int retpsetcode (Table *t, const TValue *slot) {
   if (isabstkey(slot))
     return HNOTFOUND;  /* no slot with that key */
   else  /* return node encoded */
     return cast_int((cast(Node*, slot) - t->node)) + HFIRSTNODE;
 }
 
 
 static int finishnodeset (Table *t, const TValue *slot, TValue *val) {
   if (!ttisnil(slot)) {
     setobj(((lua_State*)NULL), cast(TValue*, slot), val);
     return HOK;  /* success */
   }
   else
     return retpsetcode(t, slot);
 }
 
 
 static int rawfinishnodeset (const TValue *slot, TValue *val) {
   if (isabstkey(slot))
     return 0;  /* no slot with that key */
   else {
     setobj(((lua_State*)NULL), cast(TValue*, slot), val);
     return 1;  /* success */
   }
 }
 
 
 int luaH_psetint (Table *t, lua_Integer key, TValue *val) {
   lua_assert(!ikeyinarray(t, key));
   return finishnodeset(t, getintfromhash(t, key), val);
 }
 
 
 static int psetint (Table *t, lua_Integer key, TValue *val) {
   int hres;
   luaH_fastseti(t, key, val, hres);
   return hres;
 }
 
 
 /*
 ** This function could be just this:
 **    return finishnodeset(t, luaH_Hgetshortstr(t, key), val);
 ** However, it optimizes the common case created by constructors (e.g.,
 ** {x=1, y=2}), which creates a key in a table that has no metatable,
 ** it is not old/black, and it already has space for the key.
 */
 
 int luaH_psetshortstr (Table *t, TString *key, TValue *val) {
   const TValue *slot = luaH_Hgetshortstr(t, key);
   if (!ttisnil(slot)) {  /* key already has a value? (all too common) */
     setobj(((lua_State*)NULL), cast(TValue*, slot), val);  /* update it */
     return HOK;  /* done */
   }
   else if (checknoTM(t->metatable, TM_NEWINDEX)) {  /* no metamethod? */
     if (ttisnil(val))  /* new value is nil? */
       return HOK;  /* done (value is already nil/absent) */
     if (isabstkey(slot) &&  /* key is absent? */
        !(isblack(t) && iswhite(key))) {  /* and don't need barrier? */
       TValue tk;  /* key as a TValue */
       setsvalue(cast(lua_State *, NULL), &tk, key);
       if (insertkey(t, &tk, val)) {  /* insert key, if there is space */
         invalidateTMcache(t);
         return HOK;
       }
     }
   }
   /* Else, either table has new-index metamethod, or it needs barrier,
      or it needs to rehash for the new key. In any of these cases, the
      operation cannot be completed here. Return a code for the caller. */
   return retpsetcode(t, slot);
 }
 
 
 int luaH_psetstr (Table *t, TString *key, TValue *val) {
   if (strisshr(key))
     return luaH_psetshortstr(t, key, val);
   else
     return finishnodeset(t, Hgetlongstr(t, key), val);
 }
 
 
 int luaH_pset (Table *t, const TValue *key, TValue *val) {
   switch (ttypetag(key)) {
     case LUA_VSHRSTR: return luaH_psetshortstr(t, tsvalue(key), val);
     case LUA_VNUMINT: return psetint(t, ivalue(key), val);
     case LUA_VNIL: return HNOTFOUND;
     case LUA_VNUMFLT: {
       lua_Integer k;
       if (luaV_flttointeger(fltvalue(key), &k, F2Ieq)) /* integral index? */
         return psetint(t, k, val);  /* use specialized version */
       /* else... */
     }  /* FALLTHROUGH */
     default:
       return finishnodeset(t, getgeneric(t, key, 0), val);
   }
 }
 
 /*
 ** Finish a raw "set table" operation, where 'hres' encodes where the
 ** value should have been (the result of a previous 'pset' operation).
 ** Beware: when using this function the caller probably need to check a
 ** GC barrier and invalidate the TM cache.
 */
 void luaH_finishset (lua_State *L, Table *t, const TValue *key,
                                     TValue *value, int hres) {
   lua_assert(hres != HOK);
   if (hres == HNOTFOUND) {
     TValue aux;
     if (l_unlikely(ttisnil(key)))
       luaG_runerror(L, "table index is nil");
     else if (ttisfloat(key)) {
       lua_Number f = fltvalue(key);
       lua_Integer k;
       if (luaV_flttointeger(f, &k, F2Ieq)) {
         setivalue(&aux, k);  /* key is equal to an integer */
         key = &aux;  /* insert it as an integer */
       }
       else if (l_unlikely(luai_numisnan(f)))
         luaG_runerror(L, "table index is NaN");
     }
     luaH_newkey(L, t, key, value);
   }
   else if (hres > 0) {  /* regular Node? */
     setobj2t(L, gval(gnode(t, hres - HFIRSTNODE)), value);
   }
   else {  /* array entry */
     hres = ~hres;  /* real index */
     obj2arr(t, cast_uint(hres), value);
   }
 }
 
 
 /*
 ** beware: when using this function you probably need to check a GC
 ** barrier and invalidate the TM cache.
 */
 void luaH_set (lua_State *L, Table *t, const TValue *key, TValue *value) {
   int hres = luaH_pset(t, key, value);
   if (hres != HOK)
     luaH_finishset(L, t, key, value, hres);
 }
 
 
 /*
 ** Ditto for a GC barrier. (No need to invalidate the TM cache, as
 ** integers cannot be keys to metamethods.)
 */
 void luaH_setint (lua_State *L, Table *t, lua_Integer key, TValue *value) {
   unsigned ik = ikeyinarray(t, key);
   if (ik > 0)
     obj2arr(t, ik - 1, value);
   else {
     int ok = rawfinishnodeset(getintfromhash(t, key), value);
     if (!ok) {
       TValue k;
       setivalue(&k, key);
       luaH_newkey(L, t, &k, value);
     }
   }
 }
 
 
 /*
 ** Try to find a boundary in the hash part of table 't'. From the
 ** caller, we know that 'j' is zero or present and that 'j + 1' is
 ** present. We want to find a larger key that is absent from the
 ** table, so that we can do a binary search between the two keys to
 ** find a boundary. We keep doubling 'j' until we get an absent index.
 ** If the doubling would overflow, we try LUA_MAXINTEGER. If it is
 ** absent, we are ready for the binary search. ('j', being max integer,
 ** is larger or equal to 'i', but it cannot be equal because it is
 ** absent while 'i' is present; so 'j > i'.) Otherwise, 'j' is a
 ** boundary. ('j + 1' cannot be a present integer key because it is
 ** not a valid integer in Lua.)
 */
 static lua_Unsigned hash_search (Table *t, lua_Unsigned j) {
   lua_Unsigned i;
   if (j == 0) j++;  /* the caller ensures 'j + 1' is present */
   do {
     i = j;  /* 'i' is a present index */
     if (j <= l_castS2U(LUA_MAXINTEGER) / 2)
       j *= 2;
     else {
       j = LUA_MAXINTEGER;
       if (hashkeyisempty(t, j))  /* t[j] not present? */
         break;  /* 'j' now is an absent index */
       else  /* weird case */
         return j;  /* well, max integer is a boundary... */
     }
   } while (!hashkeyisempty(t, j));  /* repeat until an absent t[j] */
   /* i < j  &&  t[i] present  &&  t[j] absent */
   while (j - i > 1u) {  /* do a binary search between them */
     lua_Unsigned m = (i + j) / 2;
     if (hashkeyisempty(t, m)) j = m;
     else i = m;
   }
   return i;
 }
 
 
 static unsigned int binsearch (Table *array, unsigned int i, unsigned int j) {
   lua_assert(i <= j);
   while (j - i > 1u) {  /* binary search */
     unsigned int m = (i + j) / 2;
     if (arraykeyisempty(array, m)) j = m;
     else i = m;
   }
   return i;
 }
 
 
 /* return a border, saving it as a hint for next call */
 static lua_Unsigned newhint (Table *t, unsigned hint) {
   lua_assert(hint <= t->asize);
   *lenhint(t) = hint;
   return hint;
 }
 
 
 /*
 ** Try to find a border in table 't'. (A 'border' is an integer index
 ** such that t[i] is present and t[i+1] is absent, or 0 if t[1] is absent,
 ** or 'maxinteger' if t[maxinteger] is present.)
 ** If there is an array part, try to find a border there. First try
 ** to find it in the vicinity of the previous result (hint), to handle
 ** cases like 't[#t + 1] = val' or 't[#t] = nil', that move the border
 ** by one entry. Otherwise, do a binary search to find the border.
 ** If there is no array part, or its last element is non empty, the
 ** border may be in the hash part.
 */
 lua_Unsigned luaH_getn (Table *t) {
   unsigned asize = t->asize;
   if (asize > 0) {  /* is there an array part? */
     const unsigned maxvicinity = 4;
     unsigned limit = *lenhint(t);  /* start with the hint */
     if (limit == 0)
       limit = 1;  /* make limit a valid index in the array */
     if (arraykeyisempty(t, limit)) {  /* t[limit] empty? */
       /* there must be a border before 'limit' */
       unsigned i;
       /* look for a border in the vicinity of the hint */
       for (i = 0; i < maxvicinity && limit > 1; i++) {
         limit--;
         if (!arraykeyisempty(t, limit))
           return newhint(t, limit);  /* 'limit' is a border */
       }
       /* t[limit] still empty; search for a border in [0, limit) */
       return newhint(t, binsearch(t, 0, limit));
     }
     else {  /* 'limit' is present in table; look for a border after it */
       unsigned i;
       /* look for a border in the vicinity of the hint */
       for (i = 0; i < maxvicinity && limit < asize; i++) {
         limit++;
         if (arraykeyisempty(t, limit))
           return newhint(t, limit - 1);  /* 'limit - 1' is a border */
       }
       if (arraykeyisempty(t, asize)) {  /* last element empty? */
         /* t[limit] not empty; search for a border in [limit, asize) */
         return newhint(t, binsearch(t, limit, asize));
       }
     }
     /* last element non empty; set a hint to speed up finding that again */
     /* (keys in the hash part cannot be hints) */
     *lenhint(t) = asize;
   }
   /* no array part or t[asize] is not empty; check the hash part */
   lua_assert(asize == 0 || !arraykeyisempty(t, asize));
   if (isdummy(t) || hashkeyisempty(t, asize + 1))
     return asize;  /* 'asize + 1' is empty */
   else  /* 'asize + 1' is also non empty */
     return hash_search(t, asize);
 }
 
 
 
 #if defined(LUA_DEBUG)
 
 /* export this function for the test library */
 
 Node *luaH_mainposition (const Table *t, const TValue *key) {
   return mainpositionTV(t, key);
 }
 
 #endif