~peter-pearse/ubuntu/natty/mawk/prop001

% $Log: array.w,v $
% Revision 1.4  1996/09/18 00:37:25  mike
% 1) Fix stupid bozo in A[expr], expr is numeric and not integer.
% 2) Add static for non-ansi compilers.
% 3) Minor tweaks to documentation.
%
% Revision 1.3  1996/07/28 21:55:32  mike
% trivial change -- add extra {}
%
% Revision 1.2  1996/02/25  23:42:25  mike
% Fix zfree bug in array_clear.
% Clean up documentation.
%

%\hi -- hang item
\def\hi{\smallskip\hangindent\parindent\indent\ignorespaces}
\def\expr{{\it expr}}
\def\Null{{\it null}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

<<"array.h">>=
<<array.h notice>>
#ifndef ARRAY_H
#define ARRAY_H 1
<<array typedefs and [[#defines]]>>
<<interface prototypes>>
#endif /* ARRAY_H */

<<"array.c">>=
<<array.c notice>>
#include "mawk.h"
#include "symtype.h"
#include "memory.h"
#include "field.h"
#include "bi_vars.h"
<<local constants, defs and prototypes>>
<<interface functions>>
<<local functions>>

@ Array Structure
The type [[ARRAY]] is a pointer to a [[struct array]].
The [[size]] field is the number of elements in the table.
The meaning of the other fields depends on the [[type]] field.

<<array typedefs and [[#defines]]>>=
typedef struct array {
   PTR ptr ;  /* What this points to depends on the type */
   unsigned size ; /* number of elts in the table */
   unsigned limit ; /* Meaning depends on type */
   unsigned hmask ; /* bitwise and with hash value to get table index */
   short type ;  /* values in AY_NULL .. AY_SPLIT */
} *ARRAY ;

@
There are three types of arrays and these are distinguished by the
[[type]] field in the structure.  The types are:

\hi [[AY_NULL]]\quad The array is empty and the [[size]] field is always
zero.  The other fields have no meaning.

\hi [[AY_SPLIT]]\quad The array was created by the [[AWK]] built-in
[[split]].  The return value from [[split]] is stored in the [[size]]
field.  The [[ptr]] field points at a vector of [[CELLs]].  The number
of [[CELLs]] is the [[limit]] field. It is always true that
${\it size}\leq{\it limit}$.  The address of [[A[i]]] is [[(CELL*)A->ptr+i-1]]
for $1\leq i\leq{\it size}$.  The [[hmask]] field has no meaning.

\hi {\bf Hash Table}\quad The array is a hash table.  If the [[AY_STR]] bit
in the [[type]] field is set, then the table is keyed on strings.
If the [[AY_INT]] bit in the [[type]] field is set, then the table is
keyed on integers.  Both bits can be set, and then the two keys are
consistent, i.e., look up of [[A[-14]]] and [[A["-14"]]] will
return identical [[CELL]] pointers although the look up methods will
be different.  In this case, the [[size]] field is the number of hash nodes
in the table.  When insertion of a new element would cause [[size]] to
exceed [[limit]], the table grows by doubling the number of hash chains.
The invariant, 
$({\it hmask}+1){\it max\_ave\_list\_length}={\it limit}$, is always true.
{\it Max\_ave\_list\_length} is a tunable constant.


<<array typedefs and [[#defines]]>>=
#define AY_NULL		0
#define AY_INT		1
#define AY_STR		2
#define AY_SPLIT	4

@ Hash Tables
The hash tables are linked lists of nodes, called [[ANODEs]].
The number of lists is [[hmask+1]] which is always a power of two.
The [[ptr]] field points at a vector of list heads.  Since there are
potentially two types of lists, integer lists and strings lists,
each list head is a structure, [[DUAL_LINK]].

<<local constants, defs and prototypes>>=
struct anode ;
typedef struct {struct anode *slink, *ilink ;} DUAL_LINK ;

@
The string lists are chains connected by [[slinks]] and the integer
lists are chains connected by [[ilinks]].  We sometimes refer to these
lists as slists and ilists, respectively.
The elements on the lists are [[ANODEs]].
The fields of an [[ANODE]] are:

\hi [[slink]]\quad The link field for slists.
\hi [[ilink]]\quad The link field for ilists.
\hi [[sval]]\quad If non-null, then [[sval]] is a pointer to a string
key.  For a given table, if the [[AY_STR]] bit is set then every
[[ANODE]] has a non-null [[sval]] field and conversely, if [[AY_STR]]
is not set, then every [[sval]] field is null.

\hi [[hval]]\quad The hash value of [[sval]].  This field has no
meaning if [[sval]] is null.
\hi [[ival]]\quad The integer key.  The field has no meaning if set
to the constant, [[NOT_AN_IVALUE]].  If the [[AY_STR]] bit is off,
then every [[ANODE]] will have a valid [[ival]] field.  If the
[[AY_STR]] bit is on, then the [[ival]] field may or may not be
valid.

\hi [[cell]]\quad The data field in the hash table.

\smallskip\noindent
So the value of $A[\expr]$ is stored in the [[cell]] field, and if
\expr{} is an integer, then \expr{} is stored in [[ival]], else it
is stored in [[sval]].


<<local constants, defs and prototypes>>=
typedef struct anode {
   struct anode *slink ;
   struct anode  *ilink ;
   STRING *sval ;
   unsigned hval ;
   Int     ival ;
   CELL    cell ;
} ANODE ;


@ Interface Functions
The interface functions are:

\nobreak
\hi [[CELL* array_find(ARRAY A, CELL *cp, int create_flag)]] returns a
pointer to $A[\expr]$ where [[cp]] is a pointer to the [[CELL]]
holding \expr\/.  If the [[create_flag]] is on and \expr\/ is not
an element of [[A]], then the element is created with value \Null\/.

\hi [[void array_delete(ARRAY A, CELL *cp)]] removes an element
$A[\expr]$ from the array $A$.  [[cp]] points at the [[CELL]] holding
\expr\/.

\hi [[void array_load(ARRAY A, int cnt)]] builds a split array.  The
values $A[1..{\it cnt}]$ are copied from the array 
${\it split\_buff}[0..{\it cnt}-1]$.

\hi [[void array_clear(ARRAY A)]] removes all elements of $A$.  The
type of $A$ is then [[AY_NULL]].

\hi [[STRING** array_loop_vector(ARRAY A, unsigned *sizep)]] 
returns a pointer
to a linear vector that holds all the strings that are indices of $A$.
The size of the the vector is returned indirectly in [[*sizep]].
If [[A->size==0]], a \Null{} pointer is returned.

\hi [[CELL* array_cat(CELL *sp, int cnt)]] concatenates the elements
of ${\it sp}[1-cnt..0]$, with each element separated by [[SUBSEP]], to
compute an array index.  For example, on a reference to $A[i,j]$,
[[array_cat]] computes $i\circ{\it SUBSEP}\circ j$ where 
$\circ$ denotes concatenation.


<<interface prototypes>>=
CELL* PROTO(array_find, (ARRAY,CELL*,int)) ;
void  PROTO(array_delete, (ARRAY,CELL*)) ;
void  PROTO(array_load, (ARRAY,int)) ;
void  PROTO(array_clear, (ARRAY)) ;
STRING** PROTO(array_loop_vector, (ARRAY,unsigned*)) ;
CELL* PROTO(array_cat, (CELL*,int)) ;

@ Array Find
Any reference to $A[\expr]$ creates a call to 
[[array_find(A,cp,CREATE)]] where [[cp]] points at the cell holding
\expr\/.  The test, $\expr \hbox{ in } A$, creates a call to
[[array_find(A,cp,NO_CREATE)]].

<<array typedefs and [[#defines]]>>=
#define NO_CREATE  0
#define CREATE     1

@
[[Array_find]] is hash-table lookup that breaks into two cases:

\hi 1)\quad If [[*cp]] is numeric and integer valued, then lookup by
integer value using [[find_by_ival]].  If [[*cp]] is numeric, but not
integer valued, then convert to string with [[sprintf(CONVFMT,...)]] and
go to case~2.

\hi 2)\quad if [[*cp]] is string valued, then lookup by string value
using [[find_by_sval]].

<<interface functions>>=
CELL* array_find(A, cp, create_flag)
   ARRAY A ;
   CELL *cp ;
   int create_flag ;
{
   ANODE *ap ;
   if (A->size == 0 && !create_flag) 
      /* eliminating this trivial case early avoids unnecessary conversions later */
      return (CELL*) 0 ;
   switch (cp->type) {
      case C_DOUBLE:
	 <<if the [[*cp]] is an integer, find by integer value else find by string value>>
	 break ;
      case C_NOINIT:
	 ap = find_by_sval(A, &null_str, create_flag) ;
	 break ;
      default:
	 ap = find_by_sval(A, string(cp), create_flag) ;
	 break ;
   }
   return ap ? &ap->cell : (CELL *) 0 ;
}

@
To test whether [[cp->dval]] is integer, we convert to the nearest
integer by rounding towards zero (done by [[do_to_I]]) and then cast
back to double.  If we get the same number we started with, then
[[cp->dval]] is integer valued.  

<<if the [[*cp]] is an integer, find by integer value else find by string value>>=
{
   double d = cp->dval ;
   Int ival = d_to_I(d) ;
   if ((double)ival == d) {
      if (A->type == AY_SPLIT) {
         if (ival >= 1 && ival <= A->size) 
            return (CELL*)A->ptr+(ival-1) ;
         if (!create_flag) return (CELL*) 0 ;
         convert_split_array_to_table(A) ;
      }
      else if (A->type == AY_NULL) make_empty_table(A, AY_INT) ;
      ap = find_by_ival(A, ival, create_flag) ;
   }
   else {
      /* convert to string */
      char buff[260] ;
      STRING *sval ;
      sprintf(buff, string(CONVFMT)->str, d) ;
      sval = new_STRING(buff) ;
      ap = find_by_sval(A,sval,create_flag) ;
      free_STRING(sval) ;
   }
}

@
When we get to the function [[find_by_ival]], the search has been reduced
to lookup in a hash table by integer value.

<<local functions>>=
static ANODE* find_by_ival(A, ival, create_flag)
   ARRAY A ;
   Int ival ;
   int create_flag ;
{
   DUAL_LINK *table = (DUAL_LINK*) A->ptr ;
   unsigned index = ival & A->hmask ;
   ANODE *p = table[index].ilink ; /* walks ilist */
   ANODE *q = (ANODE*) 0 ; /* trails p */
   while(1) {
      if (!p) {
	  /* search failed */
	  <<search by string value if needed and create if needed>>
	  break ;
      }
      else if (p->ival == ival) { 
	 /* found it, now move to the front */
	 if (!q) /* already at the front */
	    return p ;
	 /* delete for insertion at the front */
	 q->ilink = p->ilink ;
	 break ;
      }
      q = p ; p = q->ilink ;
   }
   /* insert at the front */
   p->ilink = table[index].ilink ;
   table[index].ilink = p ;
   return p ;
}

@
When a search by integer value fails, we have to check by string
value to correctly
handle the case insertion by [[A["123"]]] and later search as 
[[A[123]]].  This string search is necessary if and only if the
[[AY_STR]] bit is set.  An important point is that all [[ANODEs]] get
created with a valid [[sval]] if [[AY_STR]] is set, because then creation
of new nodes always occurs in a call to [[find_by_sval]].

<<search by string value if needed and create if needed>>=
if (A->type & AY_STR) {
   /* need to search by string */
   char buff[256] ;
   STRING *sval ;
   sprintf(buff, INT_FMT, ival) ;
   sval = new_STRING(buff) ;
   p = find_by_sval(A, sval, create_flag) ;
   free_STRING(sval) ;
   if (!p) return (ANODE*) 0 ;
}
else if (create_flag) {
   p = ZMALLOC(ANODE) ;
   p->sval = (STRING*) 0 ;
   p->cell.type = C_NOINIT ;
   if (++A->size > A->limit) {
      double_the_hash_table(A) ; /* changes table, may change index */
      table = (DUAL_LINK*) A->ptr ;
      index = A->hmask & ival ;
   }
}
else return (ANODE*) 0 ;
p->ival = ival ;
A->type |= AY_INT ;

@
Searching by string value is easier because [[AWK]] arrays are really
string associations.  If the array does not have the [[AY_STR]] bit set,
then we have to convert the array to a dual hash table with strings
which is done by the function [[add_string_associations]].

<<local functions>>=
static ANODE* find_by_sval(A, sval, create_flag)
   ARRAY A ;
   STRING *sval ;
   int create_flag ;
{
   unsigned hval = ahash(sval) ;
   char *str = sval->str ;
   DUAL_LINK *table ;
   int index ;
   ANODE *p ;  /* walks list */
   ANODE *q = (ANODE*) 0 ; /* trails p */
   if (! (A->type & AY_STR)) add_string_associations(A) ;
   table = (DUAL_LINK*) A->ptr ;
   index = hval & A->hmask ;
   p = table[index].slink ;
   while(1) {
      if (!p)  {
         if (create_flag) {
	    <<create a new anode for [[sval]]>>
	    break ;
	 }
	 else return (ANODE*) 0 ;
      }
      else if (p->hval == hval && strcmp(p->sval->str,str) == 0 ) {
	 /* found */
	 if (!q) /* already at the front */
	    return p ;
	 else { /* delete for move to the front */
	    q->slink = p->slink ;
	    break ;
	 }
      }
      q = p ; p = q->slink ;
   }
   p->slink = table[index].slink ;
   table[index].slink = p ;
   return p ;
}

@
One [[Int]] value is reserved to show that the [[ival]] field is invalid.
This works because [[d_to_I]] returns a value in [[[-Max_Int, Max_Int]]].

<<local constants, defs and prototypes>>=
#define NOT_AN_IVALUE (-Max_Int-1)  /* usually 0x80000000 */

<<create a new anode for [[sval]]>>=
{
   p = ZMALLOC(ANODE) ;
   p->sval = sval ;
   sval->ref_cnt++ ;
   p->ival = NOT_AN_IVALUE ;
   p->hval = hval ;
   p->cell.type = C_NOINIT ;
   if (++A->size > A->limit) {
      double_the_hash_table(A) ; /* changes table, may change index */
      table = (DUAL_LINK*) A->ptr ;
      index = hval & A->hmask ;
   }
}

@
On entry to [[add_string_associations]], we know that the [[AY_STR]] bit
is not set. We convert to a dual hash table, then walk all the integer
lists and put each [[ANODE]] on a string list.

<<local functions>>=
static void add_string_associations(A)
   ARRAY A ;
{
   if (A->type == AY_NULL) make_empty_table(A, AY_STR) ;
   else {
      DUAL_LINK *table ;
      int i ; /* walks table */
      ANODE *p ; /* walks ilist */
      char buff[256] ;
      if (A->type == AY_SPLIT) convert_split_array_to_table(A) ;
      table = (DUAL_LINK*) A->ptr ;
      for(i=0;i <= A->hmask; i++) {
	 p = table[i].ilink ;
	 while(p) {
	    sprintf(buff, INT_FMT, p->ival) ;
	    p->sval = new_STRING(buff) ;
	    p->hval = ahash(p->sval) ;
	    p->slink = table[A->hmask&p->hval].slink ;
	    table[A->hmask&p->hval].slink = p ;
	    p = p->ilink ;
	 }
      }
      A->type |= AY_STR ;
   }
}

@ Array Delete
The execution of the statement, $\hbox{\it delete }A[\expr]$, creates a
call to [[array_delete(ARRAY A, CELL *cp)]].  Depending on the
type of [[*cp]], the call is routed to [[find_by_sval]] or [[find_by_ival]].
Each of these functions leaves its return value on the front of an
slist or ilist, respectively, and then it is deleted from the front of
the list.  The case where $A[\expr]$ is on two lists, e.g., 
[[A[12]]] and [[A["12"]]] is checked by examining the [[sval]] and
[[ival]] fields of the returned [[ANODE*]].

<<interface functions>>=
void array_delete(A, cp)
   ARRAY A ;
   CELL *cp ;
{
   ANODE *ap ;
   if (A->size == 0) return ; 
   switch(cp->type) {
      case C_DOUBLE :
	 {
	    double d = cp->dval ;
	    Int ival = d_to_I(d) ;
	    if ((double)ival == d) <<delete by integer value and return>>
	    else { /* get the string value */
	       char buff[260] ;
	       STRING *sval ;
	       sprintf(buff, string(CONVFMT)->str, d) ;
	       sval = new_STRING(buff) ;
	       ap = find_by_sval(A, sval, NO_CREATE) ;
	       free_STRING(sval) ;
	    }
	 }
	 break ;
      case C_NOINIT :
	 ap = find_by_sval(A, &null_str, NO_CREATE) ;
	 break ;
      default :
	 ap = find_by_sval(A, string(cp), NO_CREATE) ;
	 break ;
   }
   if (ap) { /* remove from the front of the slist */
      DUAL_LINK *table = (DUAL_LINK*) A->ptr ;
      table[ap->hval&A->hmask].slink = ap->slink ;
      <<if [[ival]] is valid, remove [[ap]] from its ilist>>
      free_STRING(ap->sval) ;
      cell_destroy(&ap->cell) ;
      ZFREE(ap) ;
      <<decrement [[A->size]]>>
   }
}

<<delete by integer value and return>>=
{
   if (A->type == AY_SPLIT)
      if (ival >=1 && ival <= A->size) convert_split_array_to_table(A) ;
      else return ; /* ival not in range */
   ap = find_by_ival(A, ival, NO_CREATE) ;
   if (ap) { /* remove from the front of the ilist */
      DUAL_LINK *table = (DUAL_LINK*) A->ptr ;
      table[ap->ival & A->hmask].ilink = ap->ilink ;
      <<if [[sval]] is valid, remove [[ap]] from its slist>>
      cell_destroy(&ap->cell) ;
      ZFREE(ap) ;
      <<decrement [[A->size]]>>
   }
   return ;
}

@
Even though we found a node by searching an ilist it might also
be on an slist and vice-versa.

<<if [[sval]] is valid, remove [[ap]] from its slist>>=
if (ap->sval) {
   ANODE *p, *q = 0 ;
   int index = ap->hval & A->hmask ;
   p = table[index].slink ;
   while(p != ap) { q = p ; p = q->slink ; }
   if (q) q->slink = p->slink ;
   else table[index].slink = p->slink ;
   free_STRING(ap->sval) ;
}

<<if [[ival]] is valid, remove [[ap]] from its ilist>>=
if (ap->ival != NOT_AN_IVALUE) {
   ANODE *p, *q = 0 ;
   int index = ap->ival & A->hmask ;
   p = table[index].ilink ;
   while(p != ap) { q = p ; p = q->ilink ; }
   if (q) q->ilink = p->ilink ;
   else table[index].ilink = p->ilink ;
}

@
When the size of a hash table drops below a certain value, it might
be profitable to shrink the hash table.  Currently we don't do this,
because our guess is that it would be a waste of time for most
[[AWK]] applications.  However, we do convert an array to [[AY_NULL]]
when the size goes to zero which would resize a large hash table 
that had been completely cleared by successive deletions.

<<decrement [[A->size]]>>=
if (--A->size == 0) array_clear(A) ;


@ Building an Array with Split
A simple operation is to create an array with the [[AWK]]
primitive [[split]].  The code that performs [[split]] puts the
pieces in the global buffer [[split_buff]].  The call
[[array_load(A, cnt)]] moves the [[cnt]] elements from [[split_buff]] to
[[A]].  This is the only way an array of type [[AY_SPLIT]] is 
created.

<<interface functions>>=
void array_load(A, cnt)
   ARRAY A ;
   int cnt ;
{
   CELL *cells ; /* storage for A[1..cnt] */
   int i ;  /* index into cells[] */
   <<clean up the existing array and prepare an empty split array>>
   cells = (CELL*) A->ptr ;
   A->size = cnt ;
   <<if [[cnt]] exceeds [[MAX_SPLIT]], load from overflow list and adjust [[cnt]]>>
   for(i=0;i < cnt; i++) {
      cells[i].type = C_MBSTRN ;
      cells[i].ptr = split_buff[i] ;
   }
}

@
When [[cnt > MAX_SPLIT]], [[split_buff]] was not big enough to hold
everything so the overflow went on the [[split_ov_list]].  
The elements from [[MAX_SPLIT+1]] to [[cnt]] get loaded into
[[cells[MAX_SPLIT..cnt-1]]] from this list.

<<if [[cnt]] exceeds [[MAX_SPLIT]], load from overflow list and adjust [[cnt]]>>=
if (cnt > MAX_SPLIT) {
   SPLIT_OV *p = split_ov_list ;
   SPLIT_OV *q ;
   split_ov_list = (SPLIT_OV*) 0 ;
   i = MAX_SPLIT ;  
   while( p ) {
      cells[i].type = C_MBSTRN ;
      cells[i].ptr = (PTR) p->sval ;
      q = p ; p = q->link ; ZFREE(q) ;
      i++ ;
   }
   cnt = MAX_SPLIT ;
}

@
If the array [[A]] is a split array and big enough then we reuse it,
otherwise we need to allocate a new split array.
When we allocate a block of [[CELLs]] for a split array, we round up
to a multiple of 4.

<<clean up the existing array and prepare an empty split array>>=
if (A->type != AY_SPLIT || A->limit < cnt) {
   array_clear(A) ;
   A->limit = (cnt&~3)+4 ;
   A->ptr = zmalloc(A->limit*sizeof(CELL)) ;
   A->type = AY_SPLIT ;
}
else
   for(i=0;i < A->size; i++)  cell_destroy((CELL*)A->ptr+i) ;

@ Array Clear
The function [[array_clear(ARRAY A)]] converts [[A]] to type [[AY_NULL]]
and frees all storage used by [[A]] except for the [[struct array]] 
itself.  This function gets called in two contexts:
(1)~when an array local to a user function goes out of scope and
(2)~execution of the [[AWK]] statement, [[delete A]].

<<interface functions>>=
void array_clear(A)
   ARRAY A ;
{
   int i ;
   ANODE *p, *q ;
   if (A->type == AY_SPLIT) {
      for(i=0;i < A->size; i++) cell_destroy((CELL*)A->ptr+i) ;
      zfree(A->ptr, A->limit * sizeof(CELL)) ;
   }
   else if (A->type & AY_STR) {
      DUAL_LINK *table = (DUAL_LINK*) A->ptr ;
      for(i=0;i <= A->hmask; i++) {
	 p = table[i].slink ;
	 while(p) {
	    q = p ; p = q->slink ;
	    free_STRING(q->sval) ;
	    cell_destroy(&q->cell) ;
	    ZFREE(q) ;
	 }
      }
      zfree(A->ptr, (A->hmask+1)*sizeof(DUAL_LINK)) ;
   }
   else if (A->type & AY_INT) {
      DUAL_LINK *table = (DUAL_LINK*) A->ptr ;
      for(i=0;i <= A->hmask; i++) {
	 p = table[i].ilink ;
	 while(p) {
	    q = p ; p = q->ilink ;
	    cell_destroy(&q->cell) ;
	    ZFREE(q) ;
	 }
      }
      zfree(A->ptr, (A->hmask+1)*sizeof(DUAL_LINK)) ;
   }
   memset(A, 0, sizeof(*A)) ;
}



@ Constructor and Conversions
Arrays are always created as empty arrays of type [[AY_NULL]].
Global arrays are never destroyed although they can go empty or have
their type change by conversion.  The only constructor function is
a macro.

<<array typedefs and [[#defines]]>>=
#define new_ARRAY()  ((ARRAY)memset(ZMALLOC(struct array),0,sizeof(struct array)))

@
Hash tables only get constructed by conversion.  This happens in two
ways.
The function [[make_empty_table]] converts an empty array of type
[[AY_NULL]] to an empty hash table.  The number of lists in the table
is a power of 2 determined by the constant [[STARTING_HMASK]].
The limit size of the table is determined by the constant
[[MAX_AVE_LIST_LENGTH]] which is the largest average size of the hash
lists that we are willing to tolerate before enlarging the table.
When [[A->size]] exceeds [[A->limit]],
the hash table grows in size by doubling the number of lists.
[[A->limit]] is then reset to [[MAX_AVE_LIST_LENGTH]] times
[[A->hmask+1]]. 

<<local constants, defs and prototypes>>=
#define STARTING_HMASK    63  /* 2^6-1, must have form 2^n-1 */
#define MAX_AVE_LIST_LENGTH   12
#define hmask_to_limit(x) (((x)+1)*MAX_AVE_LIST_LENGTH)

<<local functions>>=
static void make_empty_table(A, type)
   ARRAY A ;
   int type ; /* AY_INT or AY_STR */
{
   size_t sz = (STARTING_HMASK+1)*sizeof(DUAL_LINK) ;
   A->type = type ;
   A->hmask = STARTING_HMASK ;
   A->limit = hmask_to_limit(STARTING_HMASK) ;
   A->ptr = memset(zmalloc(sz), 0, sz) ;
}

@
The other way a hash table gets constructed is when a split array is
converted to a hash table of type [[AY_INT]].

<<local functions>>=
static void convert_split_array_to_table(A)
   ARRAY A ;
{
   CELL *cells = (CELL*) A->ptr ;
   int i ; /* walks cells */
   DUAL_LINK *table ;
   int j ; /* walks table */
   unsigned entry_limit = A->limit ;
   <<determine the size of the hash table and allocate>>
   /* insert each cells[i] in the new hash table on an ilist */
   for(i=0, j=1 ;i < A->size; i++) {
      ANODE *p = ZMALLOC(ANODE) ;
      p->sval = (STRING*) 0 ;
      p->ival = i+1 ;
      p->cell = cells[i] ;
      p->ilink = table[j].ilink ;
      table[j].ilink = p ;
      j++ ; j &= A->hmask ;
   }
   A->type = AY_INT ;
   zfree(cells, entry_limit*sizeof(CELL)) ;
}

@
To determine the size of the table, we set the initial size to
[[STARTING_HMASK+1]] and then double the size until
[[A->size <= A->limit]].

<<determine the size of the hash table and allocate>>=
A->hmask = STARTING_HMASK ;
A->limit = hmask_to_limit(STARTING_HMASK) ;
while(A->size > A->limit) {
   A->hmask = (A->hmask<<1) + 1 ; /* double the size */
   A->limit = hmask_to_limit(A->hmask) ;
}
{
   size_t sz = (A->hmask+1)*sizeof(DUAL_LINK) ;
   A->ptr = memset(zmalloc(sz), 0, sz) ;
   table = (DUAL_LINK*) A->ptr ;
}


@ Doubling the Size of a Hash Table
The whole point of making the table size a power of two is to
facilitate resizing the table.  If the table size is $2^n$ and
$h$ is the hash key, then $h\bmod 2^n$ is the hash chain index
which can be calculated with bit-wise and, 
{\mathchardef~="2026 $h ~ (2^n-1)$}.
When the table size doubles, the new bit-mask has one more bit
turned on.  Elements of an old hash chain whose hash value have this bit
turned on get moved to a new chain. Elements with this bit turned off
stay on the same chain.  On average only half the old chain moves to the
new chain.  If the old chain is at ${\it table}[i],\ 0\le i < 2^n$,
then the elements that move, all move to the new chain at
${\it table}[i+2^n]$.

<<local functions>>=
static void double_the_hash_table(A)
   ARRAY A ;
{
   unsigned old_hmask = A->hmask ;
   unsigned new_hmask = (old_hmask<<1)+1 ;
   DUAL_LINK *table ;
   <<allocate the new hash table>>
   <<if the old table has string lists, move about half the string nodes>>
   <<if the old table has integer lists, move about half the integer nodes>>
   A->hmask = new_hmask ;
   A->limit = hmask_to_limit(new_hmask) ;
}


<<allocate the new hash table>>=
A->ptr = zrealloc(A->ptr, (old_hmask+1)*sizeof(DUAL_LINK),
			  (new_hmask+1)*sizeof(DUAL_LINK)) ;
table = (DUAL_LINK*) A->ptr ;
/* zero out the new part which is the back half */
memset(&table[old_hmask+1], 0, (old_hmask+1)*sizeof(DUAL_LINK)) ;

<<if the old table has string lists, move about half the string nodes>>=
if (A->type & AY_STR) {
   int i ; /* index to old lists */
   int j ; /* index to new lists */
   ANODE *p ; /* walks an old list */
   ANODE *q ; /* trails p for deletion */
   ANODE *tail ; /* builds new list from the back */
   ANODE dummy0, dummy1 ;
   for(i=0, j=old_hmask+1;i <= old_hmask; i++, j++) 
      <<walk one old string list, creating one new string list>>
}

@
As we walk an old string list with pointer [[p]], the expression
[[p->hval & new_hmask]] takes one of two values.  If it is equal
to [[p->hval & old_hmask]] (which equals [[i]]), 
then the node stays otherwise it gets moved
to a new string list at [[j]].  The new string list preserves order so that
the positions of the move-to-the-front heuristic are preserved.
Nodes moving to the new list are appended at pointer [[tail]].
The [[ANODEs]], [[dummy0]]~and [[dummy1]], are sentinels that remove
special handling of boundary conditions.

<<walk one old string list, creating one new string list>>=
{
   q = &dummy0 ;
   q->slink = p = table[i].slink ;
   tail = &dummy1 ;
   while (p) {
      if ((p->hval&new_hmask) != i) { /* move it */
	 q->slink = p->slink ;
	 tail = tail->slink = p ;
      }
      else q = p ;
      p = q->slink ;
   }
   table[i].slink = dummy0.slink ;
   tail->slink = (ANODE*) 0 ;
   table[j].slink = dummy1.slink ;
}

@
The doubling of the integer lists is exactly the same except that
[[slink]] is replaced by [[ilink]] and [[hval]] is replaced by [[ival]].

<<if the old table has integer lists, move about half the integer nodes>>=
if (A->type & AY_INT) {
   int i ; /* index to old lists */
   int j ; /* index to new lists */
   ANODE *p ; /* walks an old list */
   ANODE *q ; /* trails p for deletion */
   ANODE *tail ; /* builds new list from the back */
   ANODE dummy0, dummy1 ;
   for(i=0, j=old_hmask+1;i <= old_hmask; i++, j++) 
      <<walk one old integer list, creating one new integer list>>
}

<<walk one old integer list, creating one new integer list>>=
{
   q = &dummy0 ;
   q->ilink = p = table[i].ilink ;
   tail = &dummy1 ;
   while (p) {
      if ((p->ival&new_hmask) != i) { /* move it */
	 q->ilink = p->ilink ;
	 tail = tail->ilink = p ;
      }
      else q = p ;
      p = q->ilink ;
   }
   table[i].ilink = dummy0.ilink ;
   tail->ilink = (ANODE*) 0 ;
   table[j].ilink = dummy1.ilink ;
}

@ Initializing Array Loops
Our mechanism for dealing with execution of the statement,
\medskip
\centerline{[[for(i in A) {]] {\it statements} [[}]]}
\medskip
\noindent 
is simple. We allocate a vector of [[STRING*]] of size,
[[A->size]].  Each element of the vector is a string key for~[[A]].
Note that if the [[AY_STR]] bit of [[A]] is not set, then [[A]]
has to be converted to a string hash table, because the index
[[i]] walks string indices.

To execute the loop, the only state that needs to be saved is the
address of [[i]] and an index into the vector of string keys.  Since
nothing about [[A]] is saved as state, the user
program can do anything to [[A]] inside the body of
the loop, even [[delete A]], and the loop
still works.  Essentially, we have traded data space (the string vector)
in exchange for implementation simplicity.  On a 32-bit system, each
[[ANODE]] is 36 bytes, so the extra memory needed for the array loop is
11\% more than the memory consumed by the [[ANODEs]] of the array.
Note that the large size of the [[ANODEs]] is indicative of our whole
design which pays data space for integer lookup speed and algorithm
simplicity.

The only aspect of array loops that occurs in [[array.c]] is construction
of the string vector.  The rest of the implementation
is in the file [[execute.c]].

<<interface functions>>=
STRING** array_loop_vector(A, sizep)
   ARRAY A ;
   unsigned *sizep ;
{
   STRING** ret ;
   *sizep = A->size ;
   if (A->size > 0) {
      if (!(A->type & AY_STR)) add_string_associations(A) ;
      ret = (STRING**) zmalloc(A->size*sizeof(STRING*)) ;
      <<for each [[ANODE]] in [[A]], put one string in [[ret]]>>
      return ret ;
   }
   else return (STRING**) 0 ;
}

@
As we walk over the hash table [[ANODEs]], putting each [[sval]] in
[[ret]], we need to increment each reference count.  The user of the
return value is responsible for these new reference counts.

<<for each [[ANODE]] in [[A]], put one string in [[ret]]>>=
{
   int r = 0 ; /* indexes ret */
   DUAL_LINK* table = (DUAL_LINK*) A->ptr ;
   int i ; /* indexes table */
   ANODE *p ; /* walks slists */
   for(i=0;i <= A->hmask; i++) {
      for(p = table[i].slink; p ; p = p->slink) {
	 ret[r++] = p->sval ;
	 p->sval->ref_cnt++ ;
      }
   }
}

@ The Hash Function
Since a hash value is turned into a table index via bit-wise and with
\hbox{[[A->hmask]]}, it is important that the hash function does a good job
of scrambling the low-order bits of the returned hash value.
Empirical tests indicate the following function does an adequate job.
Note that for strings with length greater than 10, we only hash on 
the first five characters, the last five character and the length.

<<local functions>>=
static unsigned ahash(sval)
   STRING* sval ;
{
   unsigned sum1 = sval->len ;
   unsigned sum2 = sum1 ;
   unsigned char *p , *q ;
   if (sum1 <= 10) {
      for(p=(unsigned char*)sval->str; *p ; p++) {
	 sum1 += sum1 + *p ;
	 sum2 += sum1 ;
      }
   }
   else {
      int cnt = 5 ;
      p = (unsigned char*)sval->str ; /* p starts at the front */
      q = (unsigned char*)sval->str + (sum1-1) ; /* q starts at the back */
      while( cnt ) {
	 cnt-- ;
	 sum1 += sum1 + *p ;
	 sum2 += sum1 ;
	 sum1 += sum1 + *q ;
	 sum2 += sum1 ;
	 p++ ; q-- ;
      }
   }
   return sum2 ;
}


@ Concatenating Array Indices
In [[AWK]], an array expression [[A[i,j]]] is equivalent to the
expression [[A[i SUBSEP j]]], i.e., the index is the
concatenation of the three
elements [[i]], [[SUBSEP]] and [[j]].  This is performed by the
function [[array_cat]].  On entry, [[sp]] points at the top of a
stack of [[CELLs]].
[[Cnt]] cells are popped off the stack and concatenated together 
separated by [[SUBSEP]] and the result is pushed back on the stack.
On entry, the first multi-index is in [[sp[1-cnt]]] and the last is
in [[sp[0]]].  The return value is the new stack top.
(The stack is the run-time evaluation stack.
This operation really has nothing to do with array structure, so
logically this code belongs in [[execute.c]], but remains here for 
historical reasons.)


<<interface functions>>=
CELL *array_cat(sp, cnt)
   CELL *sp ;
   int cnt ;
{
   CELL *p ;  /* walks the eval stack */
   CELL subsep ;  /* local copy of SUBSEP */
   <<subsep parts>>
   unsigned total_len ;  /* length of cat'ed expression */
   CELL *top ;   /* value of sp at entry */
   char *target ;  /* build cat'ed char* here */
   STRING *sval ;  /* build cat'ed STRING here */
   <<get subsep and compute parts>>
   <<set [[top]] and return value of [[sp]]>>
   <<cast cells to string and compute [[total_len]]>>
   <<build the cat'ed [[STRING]] in [[sval]]>>
   <<cleanup, set [[sp]] and return>>
}

@
We make a copy of [[SUBSEP]] which we can cast to string in the
unlikely event the user has assigned a number to [[SUBSEP]].  

<<subsep parts>>=
unsigned subsep_len ; /* string length of subsep_str */
char *subsep_str ;   

<<get subsep and compute parts>>=
cellcpy(&subsep, SUBSEP) ;
if ( subsep.type < C_STRING ) cast1_to_s(&subsep) ;
subsep_len = string(&subsep)->len ;
subsep_str = string(&subsep)->str ;

@
Set [[sp]] and [[top]] so the cells to concatenate are inclusively
between [[sp]] and [[top]].

<<set [[top]] and return value of [[sp]]>>=
top = sp ; sp -= (cnt-1) ;

@
The [[total_len]] is the sum of the lengths of the [[cnt]] 
strings and the [[cnt-1]] copies of [[subsep]].

<<cast cells to string and compute [[total_len]]>>=
total_len = (cnt-1)*subsep_len ;
for(p = sp ; p <= top ; p++) {
   if ( p->type < C_STRING ) cast1_to_s(p) ;
   total_len += string(p)->len ;
}

<<build the cat'ed [[STRING]] in [[sval]]>>=
sval = new_STRING0(total_len) ;
target = sval->str ;
for(p = sp ; p < top ; p++) {
   memcpy(target, string(p)->str, string(p)->len) ;
   target += string(p)->len ;
   memcpy(target, subsep_str, subsep_len) ;
   target += subsep_len ;
}
/* now p == top */
memcpy(target, string(p)->str, string(p)->len) ;

@
The return value is [[sp]] and it is already set correctly.  We
just need to free the strings and set the contents of [[sp]].

<<cleanup, set [[sp]] and return>>=
for(p = sp; p <= top ; p++) free_STRING(string(p)) ;
free_STRING(string(&subsep)) ;
/* set contents of sp , sp->type > C_STRING is possible so reset */
sp->type = C_STRING ; 
sp->ptr = (PTR) sval ;
return sp ;

@ Loose Ends 
Here are some things we want to make sure end up in the [[.c]] and
[[.h]] files.
The compiler needs prototypes for the local functions, and we will
put a copyright and links to the source file, [[array.w]], in each
output file.

<<local constants, defs and prototypes>>=
static ANODE* PROTO(find_by_ival,(ARRAY, Int, int)) ;
static ANODE* PROTO(find_by_sval,(ARRAY, STRING*, int)) ;
static void PROTO(add_string_associations,(ARRAY)) ;
static void PROTO(make_empty_table,(ARRAY, int)) ;
static void PROTO(convert_split_array_to_table,(ARRAY)) ;
static void PROTO(double_the_hash_table,(ARRAY)) ;
static unsigned PROTO(ahash, (STRING*)) ;


<<array.c notice>>=
/*
array.c 
<<mawk blurb>>
*/

/*
This file was generated with the command

   notangle -R'"array.c"' array.w > array.c

<<notangle blurb>>
*/

<<notangle blurb>>=
Notangle is part of Norman Ramsey's noweb literate programming package
available from CTAN(ftp.shsu.edu).

It's easiest to read or modify this file by working with array.w.
<<array.h notice>>=
/*
array.h 
<<mawk blurb>>
*/

/*
This file was generated with the command

   notangle -R'"array.h"' array.w > array.h

<<notangle blurb>>
*/

<<mawk blurb>>=
copyright 1991-96, Michael D. Brennan

This is a source file for mawk, an implementation of
the AWK programming language.

Mawk is distributed without warranty under the terms of
the GNU General Public License, version 2, 1991.