MAWK-ARRAYS(7)

NAME
mawk-arrays - design notes for mawk's array implementation

SYNOPSIS
This is the documentation for the mawk implementation of awk arrays. Arrays in awk are associations of strings to awk scalar values. The mawk implementation stores the associations in hash tables. The hash table scheme was influenced by and is similar to the design presented in Griswold and Townsend, The Design and Implementation of Dynamic Hashing Sets and Tables in Icon, Software Practice and Experience, 23, 351-367, 1993.

DATA STRUCTURES

  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.

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

AY_NULL
    The array is empty and the size field is always zero. The other fields have no meaning.

AY_SPLIT
    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 size ≤ limit. The address of A[i] is (CELL*)A->ptr+i-1 for 1≤ i ≤ size. The hmask field has no meaning.

Hash Table
    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, (hmask+1)max_ave_list_length=limit is always true. Max_ave_list_length is a tunable constant.

  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.

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:

slink The link field for slists. ilink The link field for ilists. sval 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.

hval The hash value of sval. This field has no meaning if sval is null.

ival 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.

cell The data field in the hash table. \ndhitems

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.

ARRAY OPERATIONS
The functions that operate on arrays are,

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.

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

void array_load(ARRAY A, size_t cnt)
    builds a split array. The values A[1..cnt] are moved into A from an anonymous buffer with transfer_to_array() which is declared in split.h.

void array_clear(ARRAY A) removes all elements of A.
    The type of A is then AY_NULL.

STRING** array_loop_vector(ARRAY A, size_t *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.

CELL* array_cat(CELL *sp, int cnt)
    concatenates the elements of 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 ○ SUBSEP ○ j where ○ denotes concatenation.

  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 in A, creates a call to array_find(A,cp,NO_CREATE).

Array_find is a hash-table lookup function that handles two cases:

1.  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.

2.  If *cp is string valued, then lookup by string value using find_by_sval. \ndlist

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.

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

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.

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.

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].

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.

  Array Delete
The execution of the statement, 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*.

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

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.

  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 an anonymous buffer. array_load(A, cnt) moves the cnt elements from the anonymous buffer into A. This is the only way an array of type AY_SPLIT is created.

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.

  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 three contexts:

(1) when an array local to a user function goes out of scope,

(2) execution of the AWK statement, delete A and

(3) when an existing changes type or size from split().

  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.

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.

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

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.

  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 and h is the hash key, then h mod is the hash chain index which can be calculated with bit-wise and, h & 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 table[i], 0 ≤ i < then the elements that move, all move to the new chain at table[i +

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.

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

  Array Loops
Our mechanism for dealing with execution of the statement,

    for (i in A) { statements }

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.

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.

  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.)

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

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

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

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