xref: /dragonfly/contrib/grep/lib/str-kmp.h (revision 31524921)
1 /* Substring search in a NUL terminated string of UNIT elements,
2    using the Knuth-Morris-Pratt algorithm.
3    Copyright (C) 2005-2015 Free Software Foundation, Inc.
4    Written by Bruno Haible <bruno@clisp.org>, 2005.
5 
6    This program is free software; you can redistribute it and/or modify
7    it under the terms of the GNU General Public License as published by
8    the Free Software Foundation; either version 3, or (at your option)
9    any later version.
10 
11    This program is distributed in the hope that it will be useful,
12    but WITHOUT ANY WARRANTY; without even the implied warranty of
13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
14    GNU General Public License for more details.
15 
16    You should have received a copy of the GNU General Public License
17    along with this program; if not, see <http://www.gnu.org/licenses/>.  */
18 
19 /* Before including this file, you need to define:
20      UNIT                    The element type of the needle and haystack.
21      CANON_ELEMENT(c)        A macro that canonicalizes an element right after
22                              it has been fetched from needle or haystack.
23                              The argument is of type UNIT; the result must be
24                              of type UNIT as well.  */
25 
26 /* Knuth-Morris-Pratt algorithm.
27    See http://en.wikipedia.org/wiki/Knuth-Morris-Pratt_algorithm
28    HAYSTACK is the NUL terminated string in which to search for.
29    NEEDLE is the string to search for in HAYSTACK, consisting of NEEDLE_LEN
30    units.
31    Return a boolean indicating success:
32    Return true and set *RESULTP if the search was completed.
33    Return false if it was aborted because not enough memory was available.  */
34 static bool
35 knuth_morris_pratt (const UNIT *haystack,
36                     const UNIT *needle, size_t needle_len,
37                     const UNIT **resultp)
38 {
39   size_t m = needle_len;
40 
41   /* Allocate the table.  */
42   size_t *table = (size_t *) nmalloca (m, sizeof (size_t));
43   if (table == NULL)
44     return false;
45   /* Fill the table.
46      For 0 < i < m:
47        0 < table[i] <= i is defined such that
48        forall 0 < x < table[i]: needle[x..i-1] != needle[0..i-1-x],
49        and table[i] is as large as possible with this property.
50      This implies:
51      1) For 0 < i < m:
52           If table[i] < i,
53           needle[table[i]..i-1] = needle[0..i-1-table[i]].
54      2) For 0 < i < m:
55           rhaystack[0..i-1] == needle[0..i-1]
56           and exists h, i <= h < m: rhaystack[h] != needle[h]
57           implies
58           forall 0 <= x < table[i]: rhaystack[x..x+m-1] != needle[0..m-1].
59      table[0] remains uninitialized.  */
60   {
61     size_t i, j;
62 
63     /* i = 1: Nothing to verify for x = 0.  */
64     table[1] = 1;
65     j = 0;
66 
67     for (i = 2; i < m; i++)
68       {
69         /* Here: j = i-1 - table[i-1].
70            The inequality needle[x..i-1] != needle[0..i-1-x] is known to hold
71            for x < table[i-1], by induction.
72            Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1].  */
73         UNIT b = CANON_ELEMENT (needle[i - 1]);
74 
75         for (;;)
76           {
77             /* Invariants: The inequality needle[x..i-1] != needle[0..i-1-x]
78                is known to hold for x < i-1-j.
79                Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1].  */
80             if (b == CANON_ELEMENT (needle[j]))
81               {
82                 /* Set table[i] := i-1-j.  */
83                 table[i] = i - ++j;
84                 break;
85               }
86             /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
87                for x = i-1-j, because
88                  needle[i-1] != needle[j] = needle[i-1-x].  */
89             if (j == 0)
90               {
91                 /* The inequality holds for all possible x.  */
92                 table[i] = i;
93                 break;
94               }
95             /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
96                for i-1-j < x < i-1-j+table[j], because for these x:
97                  needle[x..i-2]
98                  = needle[x-(i-1-j)..j-1]
99                  != needle[0..j-1-(x-(i-1-j))]  (by definition of table[j])
100                     = needle[0..i-2-x],
101                hence needle[x..i-1] != needle[0..i-1-x].
102                Furthermore
103                  needle[i-1-j+table[j]..i-2]
104                  = needle[table[j]..j-1]
105                  = needle[0..j-1-table[j]]  (by definition of table[j]).  */
106             j = j - table[j];
107           }
108         /* Here: j = i - table[i].  */
109       }
110   }
111 
112   /* Search, using the table to accelerate the processing.  */
113   {
114     size_t j;
115     const UNIT *rhaystack;
116     const UNIT *phaystack;
117 
118     *resultp = NULL;
119     j = 0;
120     rhaystack = haystack;
121     phaystack = haystack;
122     /* Invariant: phaystack = rhaystack + j.  */
123     while (*phaystack != 0)
124       if (CANON_ELEMENT (needle[j]) == CANON_ELEMENT (*phaystack))
125         {
126           j++;
127           phaystack++;
128           if (j == m)
129             {
130               /* The entire needle has been found.  */
131               *resultp = rhaystack;
132               break;
133             }
134         }
135       else if (j > 0)
136         {
137           /* Found a match of needle[0..j-1], mismatch at needle[j].  */
138           rhaystack += table[j];
139           j -= table[j];
140         }
141       else
142         {
143           /* Found a mismatch at needle[0] already.  */
144           rhaystack++;
145           phaystack++;
146         }
147   }
148 
149   freea (table);
150   return true;
151 }
152 
153 #undef CANON_ELEMENT
154