1 /* An expandable hash tables datatype.
2 Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004
3 Free Software Foundation, Inc.
4 Contributed by Vladimir Makarov (vmakarov@cygnus.com).
6 This file is part of the libiberty library.
7 Libiberty is free software; you can redistribute it and/or
8 modify it under the terms of the GNU Library General Public
9 License as published by the Free Software Foundation; either
10 version 2 of the License, or (at your option) any later version.
12 Libiberty is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 Library General Public License for more details.
17 You should have received a copy of the GNU Library General Public
18 License along with libiberty; see the file COPYING.LIB. If
19 not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
20 Boston, MA 02111-1307, USA. */
22 /* This package implements basic hash table functionality. It is possible
23 to search for an entry, create an entry and destroy an entry.
25 Elements in the table are generic pointers.
27 The size of the table is not fixed; if the occupancy of the table
28 grows too high the hash table will be expanded.
30 The abstract data implementation is based on generalized Algorithm D
31 from Knuth's book "The art of computer programming". Hash table is
32 expanded by creation of new hash table and transferring elements from
33 the old table to the new table. */
39 #include <sys/types.h>
59 #include "libiberty.h"
67 /* This macro defines reserved value for empty table entry. */
69 #define EMPTY_ENTRY ((PTR) 0)
71 /* This macro defines reserved value for table entry which contained
74 #define DELETED_ENTRY ((PTR) 1)
76 static unsigned int higher_prime_index PARAMS ((unsigned long));
77 static hashval_t htab_mod_1 PARAMS ((hashval_t, hashval_t, hashval_t, int));
78 static hashval_t htab_mod PARAMS ((hashval_t, htab_t));
79 static hashval_t htab_mod_m2 PARAMS ((hashval_t, htab_t));
80 static hashval_t hash_pointer PARAMS ((const void *));
81 static int eq_pointer PARAMS ((const void *, const void *));
82 static int htab_expand PARAMS ((htab_t));
83 static PTR *find_empty_slot_for_expand PARAMS ((htab_t, hashval_t));
85 /* At some point, we could make these be NULL, and modify the
86 hash-table routines to handle NULL specially; that would avoid
87 function-call overhead for the common case of hashing pointers. */
88 htab_hash htab_hash_pointer = hash_pointer;
89 htab_eq htab_eq_pointer = eq_pointer;
91 /* Table of primes and multiplicative inverses.
93 Note that these are not minimally reduced inverses. Unlike when generating
94 code to divide by a constant, we want to be able to use the same algorithm
95 all the time. All of these inverses (are implied to) have bit 32 set.
97 For the record, here's the function that computed the table; it's a
98 vastly simplified version of the function of the same name from gcc. */
102 ceil_log2 (unsigned int x)
105 for (i = 31; i >= 0 ; --i)
112 choose_multiplier (unsigned int d, unsigned int *mlp, unsigned char *shiftp)
114 unsigned long long mhigh;
116 int lgup, post_shift;
118 int n = 32, precision = 32;
120 lgup = ceil_log2 (d);
122 pow2 = n + lgup - precision;
124 nx = ldexp (1.0, pow) + ldexp (1.0, pow2);
137 hashval_t inv_m2; /* inverse of prime-2 */
141 static struct prime_ent const prime_tab[] = {
142 { 7, 0x24924925, 0x9999999b, 2 },
143 { 13, 0x3b13b13c, 0x745d1747, 3 },
144 { 31, 0x08421085, 0x1a7b9612, 4 },
145 { 61, 0x0c9714fc, 0x15b1e5f8, 5 },
146 { 127, 0x02040811, 0x0624dd30, 6 },
147 { 251, 0x05197f7e, 0x073260a5, 7 },
148 { 509, 0x01824366, 0x02864fc8, 8 },
149 { 1021, 0x00c0906d, 0x014191f7, 9 },
150 { 2039, 0x0121456f, 0x0161e69e, 10 },
151 { 4093, 0x00300902, 0x00501908, 11 },
152 { 8191, 0x00080041, 0x00180241, 12 },
153 { 16381, 0x000c0091, 0x00140191, 13 },
154 { 32749, 0x002605a5, 0x002a06e6, 14 },
155 { 65521, 0x000f00e2, 0x00110122, 15 },
156 { 131071, 0x00008001, 0x00018003, 16 },
157 { 262139, 0x00014002, 0x0001c004, 17 },
158 { 524287, 0x00002001, 0x00006001, 18 },
159 { 1048573, 0x00003001, 0x00005001, 19 },
160 { 2097143, 0x00004801, 0x00005801, 20 },
161 { 4194301, 0x00000c01, 0x00001401, 21 },
162 { 8388593, 0x00001e01, 0x00002201, 22 },
163 { 16777213, 0x00000301, 0x00000501, 23 },
164 { 33554393, 0x00001381, 0x00001481, 24 },
165 { 67108859, 0x00000141, 0x000001c1, 25 },
166 { 134217689, 0x000004e1, 0x00000521, 26 },
167 { 268435399, 0x00000391, 0x000003b1, 27 },
168 { 536870909, 0x00000019, 0x00000029, 28 },
169 { 1073741789, 0x0000008d, 0x00000095, 29 },
170 { 2147483647, 0x00000003, 0x00000007, 30 },
171 /* Avoid "decimal constant so large it is unsigned" for 4294967291. */
172 { 0xfffffffb, 0x00000006, 0x00000008, 31 }
175 /* The following function returns an index into the above table of the
176 nearest prime number which is greater than N, and near a power of two. */
179 higher_prime_index (n)
182 unsigned int low = 0;
183 unsigned int high = sizeof(prime_tab) / sizeof(prime_tab[0]);
187 unsigned int mid = low + (high - low) / 2;
188 if (n > prime_tab[mid].prime)
194 /* If we've run out of primes, abort. */
195 if (n > prime_tab[low].prime)
197 fprintf (stderr, "Cannot find prime bigger than %lu\n", n);
204 /* Returns a hash code for P. */
210 return (hashval_t) ((long)p >> 3);
213 /* Returns non-zero if P1 and P2 are equal. */
223 /* Return the current size of given hash table. */
232 /* Return the current number of elements in given hash table. */
238 return htab->n_elements - htab->n_deleted;
243 static inline hashval_t
244 htab_mod_1 (x, y, inv, shift)
248 /* The multiplicative inverses computed above are for 32-bit types, and
249 requires that we be able to compute a highpart multiply. */
250 #ifdef UNSIGNED_64BIT_TYPE
251 __extension__ typedef UNSIGNED_64BIT_TYPE ull;
252 if (sizeof (hashval_t) * CHAR_BIT <= 32)
254 hashval_t t1, t2, t3, t4, q, r;
256 t1 = ((ull)x * inv) >> 32;
267 /* Otherwise just use the native division routines. */
271 /* Compute the primary hash for HASH given HTAB's current size. */
273 static inline hashval_t
274 htab_mod (hash, htab)
278 const struct prime_ent *p = &prime_tab[htab->size_prime_index];
279 return htab_mod_1 (hash, p->prime, p->inv, p->shift);
282 /* Compute the secondary hash for HASH given HTAB's current size. */
284 static inline hashval_t
285 htab_mod_m2 (hash, htab)
289 const struct prime_ent *p = &prime_tab[htab->size_prime_index];
290 return 1 + htab_mod_1 (hash, p->prime - 2, p->inv_m2, p->shift);
293 /* This function creates table with length slightly longer than given
294 source length. Created hash table is initiated as empty (all the
295 hash table entries are EMPTY_ENTRY). The function returns the
296 created hash table, or NULL if memory allocation fails. */
299 htab_create_alloc (size, hash_f, eq_f, del_f, alloc_f, free_f)
308 unsigned int size_prime_index;
310 size_prime_index = higher_prime_index (size);
311 size = prime_tab[size_prime_index].prime;
313 result = (htab_t) (*alloc_f) (1, sizeof (struct htab));
316 result->entries = (PTR *) (*alloc_f) (size, sizeof (PTR));
317 if (result->entries == NULL)
324 result->size_prime_index = size_prime_index;
325 result->hash_f = hash_f;
327 result->del_f = del_f;
328 result->alloc_f = alloc_f;
329 result->free_f = free_f;
333 /* As above, but use the variants of alloc_f and free_f which accept
334 an extra argument. */
337 htab_create_alloc_ex (size, hash_f, eq_f, del_f, alloc_arg, alloc_f,
344 htab_alloc_with_arg alloc_f;
345 htab_free_with_arg free_f;
348 unsigned int size_prime_index;
350 size_prime_index = higher_prime_index (size);
351 size = prime_tab[size_prime_index].prime;
353 result = (htab_t) (*alloc_f) (alloc_arg, 1, sizeof (struct htab));
356 result->entries = (PTR *) (*alloc_f) (alloc_arg, size, sizeof (PTR));
357 if (result->entries == NULL)
360 (*free_f) (alloc_arg, result);
364 result->size_prime_index = size_prime_index;
365 result->hash_f = hash_f;
367 result->del_f = del_f;
368 result->alloc_arg = alloc_arg;
369 result->alloc_with_arg_f = alloc_f;
370 result->free_with_arg_f = free_f;
374 /* Update the function pointers and allocation parameter in the htab_t. */
377 htab_set_functions_ex (htab, hash_f, eq_f, del_f, alloc_arg, alloc_f, free_f)
383 htab_alloc_with_arg alloc_f;
384 htab_free_with_arg free_f;
386 htab->hash_f = hash_f;
389 htab->alloc_arg = alloc_arg;
390 htab->alloc_with_arg_f = alloc_f;
391 htab->free_with_arg_f = free_f;
394 /* These functions exist solely for backward compatibility. */
398 htab_create (size, hash_f, eq_f, del_f)
404 return htab_create_alloc (size, hash_f, eq_f, del_f, xcalloc, free);
408 htab_try_create (size, hash_f, eq_f, del_f)
414 return htab_create_alloc (size, hash_f, eq_f, del_f, calloc, free);
417 /* This function frees all memory allocated for given hash table.
418 Naturally the hash table must already exist. */
424 size_t size = htab_size (htab);
425 PTR *entries = htab->entries;
429 for (i = size - 1; i >= 0; i--)
430 if (entries[i] != EMPTY_ENTRY && entries[i] != DELETED_ENTRY)
431 (*htab->del_f) (entries[i]);
433 if (htab->free_f != NULL)
435 (*htab->free_f) (entries);
436 (*htab->free_f) (htab);
438 else if (htab->free_with_arg_f != NULL)
440 (*htab->free_with_arg_f) (htab->alloc_arg, entries);
441 (*htab->free_with_arg_f) (htab->alloc_arg, htab);
445 /* This function clears all entries in the given hash table. */
451 size_t size = htab_size (htab);
452 PTR *entries = htab->entries;
456 for (i = size - 1; i >= 0; i--)
457 if (entries[i] != EMPTY_ENTRY && entries[i] != DELETED_ENTRY)
458 (*htab->del_f) (entries[i]);
460 memset (entries, 0, size * sizeof (PTR));
463 /* Similar to htab_find_slot, but without several unwanted side effects:
464 - Does not call htab->eq_f when it finds an existing entry.
465 - Does not change the count of elements/searches/collisions in the
467 This function also assumes there are no deleted entries in the table.
468 HASH is the hash value for the element to be inserted. */
471 find_empty_slot_for_expand (htab, hash)
475 hashval_t index = htab_mod (hash, htab);
476 size_t size = htab_size (htab);
477 PTR *slot = htab->entries + index;
480 if (*slot == EMPTY_ENTRY)
482 else if (*slot == DELETED_ENTRY)
485 hash2 = htab_mod_m2 (hash, htab);
492 slot = htab->entries + index;
493 if (*slot == EMPTY_ENTRY)
495 else if (*slot == DELETED_ENTRY)
500 /* The following function changes size of memory allocated for the
501 entries and repeatedly inserts the table elements. The occupancy
502 of the table after the call will be about 50%. Naturally the hash
503 table must already exist. Remember also that the place of the
504 table entries is changed. If memory allocation failures are allowed,
505 this function will return zero, indicating that the table could not be
506 expanded. If all goes well, it will return a non-zero value. */
516 size_t nsize, osize, elts;
517 unsigned int oindex, nindex;
519 oentries = htab->entries;
520 oindex = htab->size_prime_index;
522 olimit = oentries + osize;
523 elts = htab_elements (htab);
525 /* Resize only when table after removal of unused elements is either
526 too full or too empty. */
527 if (elts * 2 > osize || (elts * 8 < osize && osize > 32))
529 nindex = higher_prime_index (elts * 2);
530 nsize = prime_tab[nindex].prime;
538 if (htab->alloc_with_arg_f != NULL)
539 nentries = (PTR *) (*htab->alloc_with_arg_f) (htab->alloc_arg, nsize,
542 nentries = (PTR *) (*htab->alloc_f) (nsize, sizeof (PTR *));
543 if (nentries == NULL)
545 htab->entries = nentries;
547 htab->size_prime_index = nindex;
548 htab->n_elements -= htab->n_deleted;
556 if (x != EMPTY_ENTRY && x != DELETED_ENTRY)
558 PTR *q = find_empty_slot_for_expand (htab, (*htab->hash_f) (x));
567 if (htab->free_f != NULL)
568 (*htab->free_f) (oentries);
569 else if (htab->free_with_arg_f != NULL)
570 (*htab->free_with_arg_f) (htab->alloc_arg, oentries);
574 /* This function searches for a hash table entry equal to the given
575 element. It cannot be used to insert or delete an element. */
578 htab_find_with_hash (htab, element, hash)
583 hashval_t index, hash2;
588 size = htab_size (htab);
589 index = htab_mod (hash, htab);
591 entry = htab->entries[index];
592 if (entry == EMPTY_ENTRY
593 || (entry != DELETED_ENTRY && (*htab->eq_f) (entry, element)))
596 hash2 = htab_mod_m2 (hash, htab);
604 entry = htab->entries[index];
605 if (entry == EMPTY_ENTRY
606 || (entry != DELETED_ENTRY && (*htab->eq_f) (entry, element)))
611 /* Like htab_find_slot_with_hash, but compute the hash value from the
615 htab_find (htab, element)
619 return htab_find_with_hash (htab, element, (*htab->hash_f) (element));
622 /* This function searches for a hash table slot containing an entry
623 equal to the given element. To delete an entry, call this with
624 insert=NO_INSERT, then call htab_clear_slot on the slot returned
625 (possibly after doing some checks). To insert an entry, call this
626 with insert=INSERT, then write the value you want into the returned
627 slot. When inserting an entry, NULL may be returned if memory
631 htab_find_slot_with_hash (htab, element, hash, insert)
635 enum insert_option insert;
637 PTR *first_deleted_slot;
638 hashval_t index, hash2;
642 size = htab_size (htab);
643 if (insert == INSERT && size * 3 <= htab->n_elements * 4)
645 if (htab_expand (htab) == 0)
647 size = htab_size (htab);
650 index = htab_mod (hash, htab);
653 first_deleted_slot = NULL;
655 entry = htab->entries[index];
656 if (entry == EMPTY_ENTRY)
658 else if (entry == DELETED_ENTRY)
659 first_deleted_slot = &htab->entries[index];
660 else if ((*htab->eq_f) (entry, element))
661 return &htab->entries[index];
663 hash2 = htab_mod_m2 (hash, htab);
671 entry = htab->entries[index];
672 if (entry == EMPTY_ENTRY)
674 else if (entry == DELETED_ENTRY)
676 if (!first_deleted_slot)
677 first_deleted_slot = &htab->entries[index];
679 else if ((*htab->eq_f) (entry, element))
680 return &htab->entries[index];
684 if (insert == NO_INSERT)
687 if (first_deleted_slot)
690 *first_deleted_slot = EMPTY_ENTRY;
691 return first_deleted_slot;
695 return &htab->entries[index];
698 /* Like htab_find_slot_with_hash, but compute the hash value from the
702 htab_find_slot (htab, element, insert)
705 enum insert_option insert;
707 return htab_find_slot_with_hash (htab, element, (*htab->hash_f) (element),
711 /* This function deletes an element with the given value from hash
712 table (the hash is computed from the element). If there is no matching
713 element in the hash table, this function does nothing. */
716 htab_remove_elt (htab, element)
720 htab_remove_elt_with_hash (htab, element, (*htab->hash_f) (element));
724 /* This function deletes an element with the given value from hash
725 table. If there is no matching element in the hash table, this
726 function does nothing. */
729 htab_remove_elt_with_hash (htab, element, hash)
736 slot = htab_find_slot_with_hash (htab, element, hash, NO_INSERT);
737 if (*slot == EMPTY_ENTRY)
741 (*htab->del_f) (*slot);
743 *slot = DELETED_ENTRY;
747 /* This function clears a specified slot in a hash table. It is
748 useful when you've already done the lookup and don't want to do it
752 htab_clear_slot (htab, slot)
756 if (slot < htab->entries || slot >= htab->entries + htab_size (htab)
757 || *slot == EMPTY_ENTRY || *slot == DELETED_ENTRY)
761 (*htab->del_f) (*slot);
763 *slot = DELETED_ENTRY;
767 /* This function scans over the entire hash table calling
768 CALLBACK for each live entry. If CALLBACK returns false,
769 the iteration stops. INFO is passed as CALLBACK's second
773 htab_traverse_noresize (htab, callback, info)
781 slot = htab->entries;
782 limit = slot + htab_size (htab);
788 if (x != EMPTY_ENTRY && x != DELETED_ENTRY)
789 if (!(*callback) (slot, info))
792 while (++slot < limit);
795 /* Like htab_traverse_noresize, but does resize the table when it is
796 too empty to improve effectivity of subsequent calls. */
799 htab_traverse (htab, callback, info)
804 if (htab_elements (htab) * 8 < htab_size (htab))
807 htab_traverse_noresize (htab, callback, info);
810 /* Return the fraction of fixed collisions during all work with given
814 htab_collisions (htab)
817 if (htab->searches == 0)
820 return (double) htab->collisions / (double) htab->searches;
823 /* Hash P as a null-terminated string.
825 Copied from gcc/hashtable.c. Zack had the following to say with respect
826 to applicability, though note that unlike hashtable.c, this hash table
827 implementation re-hashes rather than chain buckets.
829 http://gcc.gnu.org/ml/gcc-patches/2001-08/msg01021.html
830 From: Zack Weinberg <zackw@panix.com>
831 Date: Fri, 17 Aug 2001 02:15:56 -0400
833 I got it by extracting all the identifiers from all the source code
834 I had lying around in mid-1999, and testing many recurrences of
835 the form "H_n = H_{n-1} * K + c_n * L + M" where K, L, M were either
836 prime numbers or the appropriate identity. This was the best one.
837 I don't remember exactly what constituted "best", except I was
838 looking at bucket-length distributions mostly.
840 So it should be very good at hashing identifiers, but might not be
841 as good at arbitrary strings.
843 I'll add that it thoroughly trounces the hash functions recommended
844 for this use at http://burtleburtle.net/bob/hash/index.html, both
845 on speed and bucket distribution. I haven't tried it against the
846 function they just started using for Perl's hashes. */
852 const unsigned char *str = (const unsigned char *) p;
856 while ((c = *str++) != 0)
857 r = r * 67 + c - 113;
863 --------------------------------------------------------------------
864 lookup2.c, by Bob Jenkins, December 1996, Public Domain.
865 hash(), hash2(), hash3, and mix() are externally useful functions.
866 Routines to test the hash are included if SELF_TEST is defined.
867 You can use this free for any purpose. It has no warranty.
868 --------------------------------------------------------------------
872 --------------------------------------------------------------------
873 mix -- mix 3 32-bit values reversibly.
874 For every delta with one or two bit set, and the deltas of all three
875 high bits or all three low bits, whether the original value of a,b,c
876 is almost all zero or is uniformly distributed,
877 * If mix() is run forward or backward, at least 32 bits in a,b,c
878 have at least 1/4 probability of changing.
879 * If mix() is run forward, every bit of c will change between 1/3 and
880 2/3 of the time. (Well, 22/100 and 78/100 for some 2-bit deltas.)
881 mix() was built out of 36 single-cycle latency instructions in a
882 structure that could supported 2x parallelism, like so:
890 Unfortunately, superscalar Pentiums and Sparcs can't take advantage
891 of that parallelism. They've also turned some of those single-cycle
892 latency instructions into multi-cycle latency instructions. Still,
893 this is the fastest good hash I could find. There were about 2^^68
894 to choose from. I only looked at a billion or so.
895 --------------------------------------------------------------------
897 /* same, but slower, works on systems that might have 8 byte hashval_t's */
900 a -= b; a -= c; a ^= (c>>13); \
901 b -= c; b -= a; b ^= (a<< 8); \
902 c -= a; c -= b; c ^= ((b&0xffffffff)>>13); \
903 a -= b; a -= c; a ^= ((c&0xffffffff)>>12); \
904 b -= c; b -= a; b = (b ^ (a<<16)) & 0xffffffff; \
905 c -= a; c -= b; c = (c ^ (b>> 5)) & 0xffffffff; \
906 a -= b; a -= c; a = (a ^ (c>> 3)) & 0xffffffff; \
907 b -= c; b -= a; b = (b ^ (a<<10)) & 0xffffffff; \
908 c -= a; c -= b; c = (c ^ (b>>15)) & 0xffffffff; \
912 --------------------------------------------------------------------
913 hash() -- hash a variable-length key into a 32-bit value
914 k : the key (the unaligned variable-length array of bytes)
915 len : the length of the key, counting by bytes
916 level : can be any 4-byte value
917 Returns a 32-bit value. Every bit of the key affects every bit of
918 the return value. Every 1-bit and 2-bit delta achieves avalanche.
919 About 36+6len instructions.
921 The best hash table sizes are powers of 2. There is no need to do
922 mod a prime (mod is sooo slow!). If you need less than 32 bits,
923 use a bitmask. For example, if you need only 10 bits, do
924 h = (h & hashmask(10));
925 In which case, the hash table should have hashsize(10) elements.
927 If you are hashing n strings (ub1 **)k, do it like this:
928 for (i=0, h=0; i<n; ++i) h = hash( k[i], len[i], h);
930 By Bob Jenkins, 1996. bob_jenkins@burtleburtle.net. You may use this
931 code any way you wish, private, educational, or commercial. It's free.
933 See http://burtleburtle.net/bob/hash/evahash.html
934 Use for hash table lookup, or anything where one collision in 2^32 is
935 acceptable. Do NOT use for cryptographic purposes.
936 --------------------------------------------------------------------
939 hashval_t iterative_hash (k_in, length, initval)
940 const PTR k_in; /* the key */
941 register size_t length; /* the length of the key */
942 register hashval_t initval; /* the previous hash, or an arbitrary value */
944 register const unsigned char *k = (const unsigned char *)k_in;
945 register hashval_t a,b,c,len;
947 /* Set up the internal state */
949 a = b = 0x9e3779b9; /* the golden ratio; an arbitrary value */
950 c = initval; /* the previous hash value */
952 /*---------------------------------------- handle most of the key */
953 #ifndef WORDS_BIGENDIAN
954 /* On a little-endian machine, if the data is 4-byte aligned we can hash
955 by word for better speed. This gives nondeterministic results on
956 big-endian machines. */
957 if (sizeof (hashval_t) == 4 && (((size_t)k)&3) == 0)
958 while (len >= 12) /* aligned */
960 a += *(hashval_t *)(k+0);
961 b += *(hashval_t *)(k+4);
962 c += *(hashval_t *)(k+8);
970 a += (k[0] +((hashval_t)k[1]<<8) +((hashval_t)k[2]<<16) +((hashval_t)k[3]<<24));
971 b += (k[4] +((hashval_t)k[5]<<8) +((hashval_t)k[6]<<16) +((hashval_t)k[7]<<24));
972 c += (k[8] +((hashval_t)k[9]<<8) +((hashval_t)k[10]<<16)+((hashval_t)k[11]<<24));
977 /*------------------------------------- handle the last 11 bytes */
979 switch(len) /* all the case statements fall through */
981 case 11: c+=((hashval_t)k[10]<<24);
982 case 10: c+=((hashval_t)k[9]<<16);
983 case 9 : c+=((hashval_t)k[8]<<8);
984 /* the first byte of c is reserved for the length */
985 case 8 : b+=((hashval_t)k[7]<<24);
986 case 7 : b+=((hashval_t)k[6]<<16);
987 case 6 : b+=((hashval_t)k[5]<<8);
989 case 4 : a+=((hashval_t)k[3]<<24);
990 case 3 : a+=((hashval_t)k[2]<<16);
991 case 2 : a+=((hashval_t)k[1]<<8);
993 /* case 0: nothing left to add */
996 /*-------------------------------------------- report the result */