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diff --git a/REORG.TODO/manual/search.texi b/REORG.TODO/manual/search.texi new file mode 100644 index 0000000000..1d9628d6e3 --- /dev/null +++ b/REORG.TODO/manual/search.texi @@ -0,0 +1,637 @@ +@node Searching and Sorting, Pattern Matching, Message Translation, Top +@c %MENU% General searching and sorting functions +@chapter Searching and Sorting + +This chapter describes functions for searching and sorting arrays of +arbitrary objects. You pass the appropriate comparison function to be +applied as an argument, along with the size of the objects in the array +and the total number of elements. + +@menu +* Comparison Functions:: Defining how to compare two objects. + Since the sort and search facilities + are general, you have to specify the + ordering. +* Array Search Function:: The @code{bsearch} function. +* Array Sort Function:: The @code{qsort} function. +* Search/Sort Example:: An example program. +* Hash Search Function:: The @code{hsearch} function. +* Tree Search Function:: The @code{tsearch} function. +@end menu + +@node Comparison Functions +@section Defining the Comparison Function +@cindex Comparison Function + +In order to use the sorted array library functions, you have to describe +how to compare the elements of the array. + +To do this, you supply a comparison function to compare two elements of +the array. The library will call this function, passing as arguments +pointers to two array elements to be compared. Your comparison function +should return a value the way @code{strcmp} (@pxref{String/Array +Comparison}) does: negative if the first argument is ``less'' than the +second, zero if they are ``equal'', and positive if the first argument +is ``greater''. + +Here is an example of a comparison function which works with an array of +numbers of type @code{double}: + +@smallexample +int +compare_doubles (const void *a, const void *b) +@{ + const double *da = (const double *) a; + const double *db = (const double *) b; + + return (*da > *db) - (*da < *db); +@} +@end smallexample + +The header file @file{stdlib.h} defines a name for the data type of +comparison functions. This type is a GNU extension. + +@comment stdlib.h +@comment GNU +@tindex comparison_fn_t +@smallexample +int comparison_fn_t (const void *, const void *); +@end smallexample + +@node Array Search Function +@section Array Search Function +@cindex search function (for arrays) +@cindex binary search function (for arrays) +@cindex array search function + +Generally searching for a specific element in an array means that +potentially all elements must be checked. @Theglibc{} contains +functions to perform linear search. The prototypes for the following +two functions can be found in @file{search.h}. + +@comment search.h +@comment SVID +@deftypefun {void *} lfind (const void *@var{key}, const void *@var{base}, size_t *@var{nmemb}, size_t @var{size}, comparison_fn_t @var{compar}) +@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}} +The @code{lfind} function searches in the array with @code{*@var{nmemb}} +elements of @var{size} bytes pointed to by @var{base} for an element +which matches the one pointed to by @var{key}. The function pointed to +by @var{compar} is used to decide whether two elements match. + +The return value is a pointer to the matching element in the array +starting at @var{base} if it is found. If no matching element is +available @code{NULL} is returned. + +The mean runtime of this function is @code{*@var{nmemb}}/2. This +function should only be used if elements often get added to or deleted from +the array in which case it might not be useful to sort the array before +searching. +@end deftypefun + +@comment search.h +@comment SVID +@deftypefun {void *} lsearch (const void *@var{key}, void *@var{base}, size_t *@var{nmemb}, size_t @var{size}, comparison_fn_t @var{compar}) +@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}} +@c A signal handler that interrupted an insertion and performed an +@c insertion itself would leave the array in a corrupt state (e.g. one +@c new element initialized twice, with parts of both initializations +@c prevailing, and another uninitialized element), but this is just a +@c special case of races on user-controlled objects, that have to be +@c avoided by users. + +@c In case of cancellation, we know the array won't be left in a corrupt +@c state; the new element is initialized before the element count is +@c incremented, and the compiler can't reorder these operations because +@c it can't know that they don't alias. So, we'll either cancel after +@c the increment and the initialization are both complete, or the +@c increment won't have taken place, and so how far the initialization +@c got doesn't matter. +The @code{lsearch} function is similar to the @code{lfind} function. It +searches the given array for an element and returns it if found. The +difference is that if no matching element is found the @code{lsearch} +function adds the object pointed to by @var{key} (with a size of +@var{size} bytes) at the end of the array and it increments the value of +@code{*@var{nmemb}} to reflect this addition. + +This means for the caller that if it is not sure that the array contains +the element one is searching for the memory allocated for the array +starting at @var{base} must have room for at least @var{size} more +bytes. If one is sure the element is in the array it is better to use +@code{lfind} so having more room in the array is always necessary when +calling @code{lsearch}. +@end deftypefun + +To search a sorted array for an element matching the key, use the +@code{bsearch} function. The prototype for this function is in +the header file @file{stdlib.h}. +@pindex stdlib.h + +@comment stdlib.h +@comment ISO +@deftypefun {void *} bsearch (const void *@var{key}, const void *@var{array}, size_t @var{count}, size_t @var{size}, comparison_fn_t @var{compare}) +@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}} +The @code{bsearch} function searches the sorted array @var{array} for an object +that is equivalent to @var{key}. The array contains @var{count} elements, +each of which is of size @var{size} bytes. + +The @var{compare} function is used to perform the comparison. This +function is called with two pointer arguments and should return an +integer less than, equal to, or greater than zero corresponding to +whether its first argument is considered less than, equal to, or greater +than its second argument. The elements of the @var{array} must already +be sorted in ascending order according to this comparison function. + +The return value is a pointer to the matching array element, or a null +pointer if no match is found. If the array contains more than one element +that matches, the one that is returned is unspecified. + +This function derives its name from the fact that it is implemented +using the binary search algorithm. +@end deftypefun + +@node Array Sort Function +@section Array Sort Function +@cindex sort function (for arrays) +@cindex quick sort function (for arrays) +@cindex array sort function + +To sort an array using an arbitrary comparison function, use the +@code{qsort} function. The prototype for this function is in +@file{stdlib.h}. +@pindex stdlib.h + +@comment stdlib.h +@comment ISO +@deftypefun void qsort (void *@var{array}, size_t @var{count}, size_t @var{size}, comparison_fn_t @var{compare}) +@safety{@prelim{}@mtsafe{}@assafe{}@acunsafe{@acucorrupt{}}} +The @code{qsort} function sorts the array @var{array}. The array +contains @var{count} elements, each of which is of size @var{size}. + +The @var{compare} function is used to perform the comparison on the +array elements. This function is called with two pointer arguments and +should return an integer less than, equal to, or greater than zero +corresponding to whether its first argument is considered less than, +equal to, or greater than its second argument. + +@cindex stable sorting +@strong{Warning:} If two objects compare as equal, their order after +sorting is unpredictable. That is to say, the sorting is not stable. +This can make a difference when the comparison considers only part of +the elements. Two elements with the same sort key may differ in other +respects. + +Although the object addresses passed to the comparison function lie +within the array, they need not correspond with the original locations +of those objects because the sorting algorithm may swap around objects +in the array before making some comparisons. The only way to perform +a stable sort with @code{qsort} is to first augment the objects with a +monotonic counter of some kind. + +Here is a simple example of sorting an array of doubles in numerical +order, using the comparison function defined above (@pxref{Comparison +Functions}): + +@smallexample +@{ + double *array; + int size; + @dots{} + qsort (array, size, sizeof (double), compare_doubles); +@} +@end smallexample + +The @code{qsort} function derives its name from the fact that it was +originally implemented using the ``quick sort'' algorithm. + +The implementation of @code{qsort} in this library might not be an +in-place sort and might thereby use an extra amount of memory to store +the array. +@end deftypefun + +@node Search/Sort Example +@section Searching and Sorting Example + +Here is an example showing the use of @code{qsort} and @code{bsearch} +with an array of structures. The objects in the array are sorted +by comparing their @code{name} fields with the @code{strcmp} function. +Then, we can look up individual objects based on their names. + +@comment This example is dedicated to the memory of Jim Henson. RIP. +@smallexample +@include search.c.texi +@end smallexample + +@cindex Kermit the frog +The output from this program looks like: + +@smallexample +Kermit, the frog +Piggy, the pig +Gonzo, the whatever +Fozzie, the bear +Sam, the eagle +Robin, the frog +Animal, the animal +Camilla, the chicken +Sweetums, the monster +Dr. Strangepork, the pig +Link Hogthrob, the pig +Zoot, the human +Dr. Bunsen Honeydew, the human +Beaker, the human +Swedish Chef, the human + +Animal, the animal +Beaker, the human +Camilla, the chicken +Dr. Bunsen Honeydew, the human +Dr. Strangepork, the pig +Fozzie, the bear +Gonzo, the whatever +Kermit, the frog +Link Hogthrob, the pig +Piggy, the pig +Robin, the frog +Sam, the eagle +Swedish Chef, the human +Sweetums, the monster +Zoot, the human + +Kermit, the frog +Gonzo, the whatever +Couldn't find Janice. +@end smallexample + + +@node Hash Search Function +@section The @code{hsearch} function. + +The functions mentioned so far in this chapter are for searching in a sorted +or unsorted array. There are other methods to organize information +which later should be searched. The costs of insert, delete and search +differ. One possible implementation is using hashing tables. +The following functions are declared in the header file @file{search.h}. + +@comment search.h +@comment SVID +@deftypefun int hcreate (size_t @var{nel}) +@safety{@prelim{}@mtunsafe{@mtasurace{:hsearch}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}} +@c hcreate @mtasurace:hsearch @ascuheap @acucorrupt @acsmem +@c hcreate_r dup @mtsrace:htab @ascuheap @acucorrupt @acsmem +The @code{hcreate} function creates a hashing table which can contain at +least @var{nel} elements. There is no possibility to grow this table so +it is necessary to choose the value for @var{nel} wisely. The method +used to implement this function might make it necessary to make the +number of elements in the hashing table larger than the expected maximal +number of elements. Hashing tables usually work inefficiently if they are +filled 80% or more. The constant access time guaranteed by hashing can +only be achieved if few collisions exist. See Knuth's ``The Art of +Computer Programming, Part 3: Searching and Sorting'' for more +information. + +The weakest aspect of this function is that there can be at most one +hashing table used through the whole program. The table is allocated +in local memory out of control of the programmer. As an extension @theglibc{} +provides an additional set of functions with a reentrant +interface which provides a similar interface but which allows keeping +arbitrarily many hashing tables. + +It is possible to use more than one hashing table in the program run if +the former table is first destroyed by a call to @code{hdestroy}. + +The function returns a non-zero value if successful. If it returns zero, +something went wrong. This could either mean there is already a hashing +table in use or the program ran out of memory. +@end deftypefun + +@comment search.h +@comment SVID +@deftypefun void hdestroy (void) +@safety{@prelim{}@mtunsafe{@mtasurace{:hsearch}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}} +@c hdestroy @mtasurace:hsearch @ascuheap @acucorrupt @acsmem +@c hdestroy_r dup @mtsrace:htab @ascuheap @acucorrupt @acsmem +The @code{hdestroy} function can be used to free all the resources +allocated in a previous call of @code{hcreate}. After a call to this +function it is again possible to call @code{hcreate} and allocate a new +table with possibly different size. + +It is important to remember that the elements contained in the hashing +table at the time @code{hdestroy} is called are @emph{not} freed by this +function. It is the responsibility of the program code to free those +strings (if necessary at all). Freeing all the element memory is not +possible without extra, separately kept information since there is no +function to iterate through all available elements in the hashing table. +If it is really necessary to free a table and all elements the +programmer has to keep a list of all table elements and before calling +@code{hdestroy} s/he has to free all element's data using this list. +This is a very unpleasant mechanism and it also shows that this kind of +hashing table is mainly meant for tables which are created once and +used until the end of the program run. +@end deftypefun + +Entries of the hashing table and keys for the search are defined using +this type: + +@deftp {Data type} {struct ENTRY} +Both elements of this structure are pointers to zero-terminated strings. +This is a limiting restriction of the functionality of the +@code{hsearch} functions. They can only be used for data sets which use +the NUL character always and solely to terminate the records. It is not +possible to handle general binary data. + +@table @code +@item char *key +Pointer to a zero-terminated string of characters describing the key for +the search or the element in the hashing table. +@item char *data +Pointer to a zero-terminated string of characters describing the data. +If the functions will be called only for searching an existing entry +this element might stay undefined since it is not used. +@end table +@end deftp + +@comment search.h +@comment SVID +@deftypefun {ENTRY *} hsearch (ENTRY @var{item}, ACTION @var{action}) +@safety{@prelim{}@mtunsafe{@mtasurace{:hsearch}}@asunsafe{}@acunsafe{@acucorrupt{/action==ENTER}}} +@c hsearch @mtasurace:hsearch @acucorrupt/action==ENTER +@c hsearch_r dup @mtsrace:htab @acucorrupt/action==ENTER +To search in a hashing table created using @code{hcreate} the +@code{hsearch} function must be used. This function can perform a simple +search for an element (if @var{action} has the value @code{FIND}) or it can +alternatively insert the key element into the hashing table. Entries +are never replaced. + +The key is denoted by a pointer to an object of type @code{ENTRY}. For +locating the corresponding position in the hashing table only the +@code{key} element of the structure is used. + +If an entry with a matching key is found the @var{action} parameter is +irrelevant. The found entry is returned. If no matching entry is found +and the @var{action} parameter has the value @code{FIND} the function +returns a @code{NULL} pointer. If no entry is found and the +@var{action} parameter has the value @code{ENTER} a new entry is added +to the hashing table which is initialized with the parameter @var{item}. +A pointer to the newly added entry is returned. +@end deftypefun + +As mentioned before, the hashing table used by the functions described so +far is global and there can be at any time at most one hashing table in +the program. A solution is to use the following functions which are a +GNU extension. All have in common that they operate on a hashing table +which is described by the content of an object of the type @code{struct +hsearch_data}. This type should be treated as opaque, none of its +members should be changed directly. + +@comment search.h +@comment GNU +@deftypefun int hcreate_r (size_t @var{nel}, struct hsearch_data *@var{htab}) +@safety{@prelim{}@mtsafe{@mtsrace{:htab}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}} +@c Unlike the lsearch array, the htab is (at least in part) opaque, so +@c let's make it absolutely clear that ensuring exclusive access is a +@c caller responsibility. + +@c Cancellation is unlikely to leave the htab in a corrupt state: the +@c last field to be initialized is the one that tells whether the entire +@c data structure was initialized, and there's a function call (calloc) +@c in between that will often ensure all other fields are written before +@c the table. However, should this call be inlined (say with LTO), this +@c assumption may not hold. The calloc call doesn't cross our library +@c interface barrier, so let's consider this could happen and mark this +@c with @acucorrupt. It's no safety loss, since we already have +@c @ascuheap anyway... + +@c hcreate_r @mtsrace:htab @ascuheap @acucorrupt @acsmem +@c isprime ok +@c calloc dup @ascuheap @acsmem +The @code{hcreate_r} function initializes the object pointed to by +@var{htab} to contain a hashing table with at least @var{nel} elements. +So this function is equivalent to the @code{hcreate} function except +that the initialized data structure is controlled by the user. + +This allows having more than one hashing table at one time. The memory +necessary for the @code{struct hsearch_data} object can be allocated +dynamically. It must be initialized with zero before calling this +function. + +The return value is non-zero if the operation was successful. If the +return value is zero, something went wrong, which probably means the +program ran out of memory. +@end deftypefun + +@comment search.h +@comment GNU +@deftypefun void hdestroy_r (struct hsearch_data *@var{htab}) +@safety{@prelim{}@mtsafe{@mtsrace{:htab}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}} +@c The table is released while the table pointer still points to it. +@c Async cancellation is thus unsafe, but it already was because we call +@c free(). Using the table in a handler while it's being released would +@c also be dangerous, but calling free() already makes it unsafe, and +@c the requirement on the caller to ensure exclusive access already +@c guarantees this doesn't happen, so we don't get @asucorrupt. + +@c hdestroy_r @mtsrace:htab @ascuheap @acucorrupt @acsmem +@c free dup @ascuheap @acsmem +The @code{hdestroy_r} function frees all resources allocated by the +@code{hcreate_r} function for this very same object @var{htab}. As for +@code{hdestroy} it is the program's responsibility to free the strings +for the elements of the table. +@end deftypefun + +@comment search.h +@comment GNU +@deftypefun int hsearch_r (ENTRY @var{item}, ACTION @var{action}, ENTRY **@var{retval}, struct hsearch_data *@var{htab}) +@safety{@prelim{}@mtsafe{@mtsrace{:htab}}@assafe{}@acunsafe{@acucorrupt{/action==ENTER}}} +@c Callers have to ensure mutual exclusion; insertion, if cancelled, +@c leaves the table in a corrupt state. + +@c hsearch_r @mtsrace:htab @acucorrupt/action==ENTER +@c strlen dup ok +@c strcmp dup ok +The @code{hsearch_r} function is equivalent to @code{hsearch}. The +meaning of the first two arguments is identical. But instead of +operating on a single global hashing table the function works on the +table described by the object pointed to by @var{htab} (which is +initialized by a call to @code{hcreate_r}). + +Another difference to @code{hcreate} is that the pointer to the found +entry in the table is not the return value of the function. It is +returned by storing it in a pointer variable pointed to by the +@var{retval} parameter. The return value of the function is an integer +value indicating success if it is non-zero and failure if it is zero. +In the latter case the global variable @var{errno} signals the reason for +the failure. + +@table @code +@item ENOMEM +The table is filled and @code{hsearch_r} was called with a so far +unknown key and @var{action} set to @code{ENTER}. +@item ESRCH +The @var{action} parameter is @code{FIND} and no corresponding element +is found in the table. +@end table +@end deftypefun + + +@node Tree Search Function +@section The @code{tsearch} function. + +Another common form to organize data for efficient search is to use +trees. The @code{tsearch} function family provides a nice interface to +functions to organize possibly large amounts of data by providing a mean +access time proportional to the logarithm of the number of elements. +@Theglibc{} implementation even guarantees that this bound is +never exceeded even for input data which cause problems for simple +binary tree implementations. + +The functions described in the chapter are all described in the @w{System +V} and X/Open specifications and are therefore quite portable. + +In contrast to the @code{hsearch} functions the @code{tsearch} functions +can be used with arbitrary data and not only zero-terminated strings. + +The @code{tsearch} functions have the advantage that no function to +initialize data structures is necessary. A simple pointer of type +@code{void *} initialized to @code{NULL} is a valid tree and can be +extended or searched. The prototypes for these functions can be found +in the header file @file{search.h}. + +@comment search.h +@comment SVID +@deftypefun {void *} tsearch (const void *@var{key}, void **@var{rootp}, comparison_fn_t @var{compar}) +@safety{@prelim{}@mtsafe{@mtsrace{:rootp}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}} +@c The tree is not modified in a thread-safe manner, and rotations may +@c leave the tree in an inconsistent state that could be observed in an +@c asynchronous signal handler (except for the caller-synchronization +@c requirement) or after asynchronous cancellation of the thread +@c performing the rotation or the insertion. +The @code{tsearch} function searches in the tree pointed to by +@code{*@var{rootp}} for an element matching @var{key}. The function +pointed to by @var{compar} is used to determine whether two elements +match. @xref{Comparison Functions}, for a specification of the functions +which can be used for the @var{compar} parameter. + +If the tree does not contain a matching entry the @var{key} value will +be added to the tree. @code{tsearch} does not make a copy of the object +pointed to by @var{key} (how could it since the size is unknown). +Instead it adds a reference to this object which means the object must +be available as long as the tree data structure is used. + +The tree is represented by a pointer to a pointer since it is sometimes +necessary to change the root node of the tree. So it must not be +assumed that the variable pointed to by @var{rootp} has the same value +after the call. This also shows that it is not safe to call the +@code{tsearch} function more than once at the same time using the same +tree. It is no problem to run it more than once at a time on different +trees. + +The return value is a pointer to the matching element in the tree. If a +new element was created the pointer points to the new data (which is in +fact @var{key}). If an entry had to be created and the program ran out +of space @code{NULL} is returned. +@end deftypefun + +@comment search.h +@comment SVID +@deftypefun {void *} tfind (const void *@var{key}, void *const *@var{rootp}, comparison_fn_t @var{compar}) +@safety{@prelim{}@mtsafe{@mtsrace{:rootp}}@assafe{}@acsafe{}} +The @code{tfind} function is similar to the @code{tsearch} function. It +locates an element matching the one pointed to by @var{key} and returns +a pointer to this element. But if no matching element is available no +new element is entered (note that the @var{rootp} parameter points to a +constant pointer). Instead the function returns @code{NULL}. +@end deftypefun + +Another advantage of the @code{tsearch} functions in contrast to the +@code{hsearch} functions is that there is an easy way to remove +elements. + +@comment search.h +@comment SVID +@deftypefun {void *} tdelete (const void *@var{key}, void **@var{rootp}, comparison_fn_t @var{compar}) +@safety{@prelim{}@mtsafe{@mtsrace{:rootp}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}} +To remove a specific element matching @var{key} from the tree +@code{tdelete} can be used. It locates the matching element using the +same method as @code{tfind}. The corresponding element is then removed +and a pointer to the parent of the deleted node is returned by the +function. If there is no matching entry in the tree nothing can be +deleted and the function returns @code{NULL}. If the root of the tree +is deleted @code{tdelete} returns some unspecified value not equal to +@code{NULL}. +@end deftypefun + +@comment search.h +@comment GNU +@deftypefun void tdestroy (void *@var{vroot}, __free_fn_t @var{freefct}) +@safety{@prelim{}@mtsafe{}@asunsafe{@ascuheap{}}@acunsafe{@acsmem{}}} +If the complete search tree has to be removed one can use +@code{tdestroy}. It frees all resources allocated by the @code{tsearch} +functions to generate the tree pointed to by @var{vroot}. + +For the data in each tree node the function @var{freefct} is called. +The pointer to the data is passed as the argument to the function. If +no such work is necessary @var{freefct} must point to a function doing +nothing. It is called in any case. + +This function is a GNU extension and not covered by the @w{System V} or +X/Open specifications. +@end deftypefun + +In addition to the functions to create and destroy the tree data +structure, there is another function which allows you to apply a +function to all elements of the tree. The function must have this type: + +@smallexample +void __action_fn_t (const void *nodep, VISIT value, int level); +@end smallexample + +The @var{nodep} is the data value of the current node (once given as the +@var{key} argument to @code{tsearch}). @var{level} is a numeric value +which corresponds to the depth of the current node in the tree. The +root node has the depth @math{0} and its children have a depth of +@math{1} and so on. The @code{VISIT} type is an enumeration type. + +@deftp {Data Type} VISIT +The @code{VISIT} value indicates the status of the current node in the +tree and how the function is called. The status of a node is either +`leaf' or `internal node'. For each leaf node the function is called +exactly once, for each internal node it is called three times: before +the first child is processed, after the first child is processed and +after both children are processed. This makes it possible to handle all +three methods of tree traversal (or even a combination of them). + +@vtable @code +@item preorder +The current node is an internal node and the function is called before +the first child was processed. +@item postorder +The current node is an internal node and the function is called after +the first child was processed. +@item endorder +The current node is an internal node and the function is called after +the second child was processed. +@item leaf +The current node is a leaf. +@end vtable +@end deftp + +@comment search.h +@comment SVID +@deftypefun void twalk (const void *@var{root}, __action_fn_t @var{action}) +@safety{@prelim{}@mtsafe{@mtsrace{:root}}@assafe{}@acsafe{}} +For each node in the tree with a node pointed to by @var{root}, the +@code{twalk} function calls the function provided by the parameter +@var{action}. For leaf nodes the function is called exactly once with +@var{value} set to @code{leaf}. For internal nodes the function is +called three times, setting the @var{value} parameter or @var{action} to +the appropriate value. The @var{level} argument for the @var{action} +function is computed while descending the tree by increasing the value +by one for each descent to a child, starting with the value @math{0} for +the root node. + +Since the functions used for the @var{action} parameter to @code{twalk} +must not modify the tree data, it is safe to run @code{twalk} in more +than one thread at the same time, working on the same tree. It is also +safe to call @code{tfind} in parallel. Functions which modify the tree +must not be used, otherwise the behavior is undefined. +@end deftypefun |