1 /* Substring search in a NUL terminated string of UNIT elements,
2 using the Knuth-Morris-Pratt algorithm.
3 Copyright (C) 2005-2023 Free Software Foundation, Inc.
4 Written by Bruno Haible <bruno@clisp.org>, 2005.
5
6 This file is free software.
7 It is dual-licensed under "the GNU LGPLv3+ or the GNU GPLv2+".
8 You can redistribute it and/or modify it under either
9 - the terms of the GNU Lesser General Public License as published
10 by the Free Software Foundation, either version 3, or (at your
11 option) any later version, or
12 - the terms of the GNU General Public License as published by the
13 Free Software Foundation; either version 2, or (at your option)
14 any later version, or
15 - the same dual license "the GNU LGPLv3+ or the GNU GPLv2+".
16
17 This file is distributed in the hope that it will be useful,
18 but WITHOUT ANY WARRANTY; without even the implied warranty of
19 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
20 Lesser General Public License and the GNU General Public License
21 for more details.
22
23 You should have received a copy of the GNU Lesser General Public
24 License and of the GNU General Public License along with this
25 program. If not, see <https://www.gnu.org/licenses/>. */
26
27 /* Before including this file, you need to define:
28 UNIT The element type of the needle and haystack.
29 CANON_ELEMENT(c) A macro that canonicalizes an element right after
30 it has been fetched from needle or haystack.
31 The argument is of type UNIT; the result must be
32 of type UNIT as well. */
33
34 /* Knuth-Morris-Pratt algorithm.
35 See https://en.wikipedia.org/wiki/Knuth-Morris-Pratt_algorithm
36 HAYSTACK is the NUL terminated string in which to search for.
37 NEEDLE is the string to search for in HAYSTACK, consisting of NEEDLE_LEN
38 units.
39 Return a boolean indicating success:
40 Return true and set *RESULTP if the search was completed.
41 Return false if it was aborted because not enough memory was available. */
42 static bool
43 knuth_morris_pratt (const UNIT *haystack,
44 const UNIT *needle, size_t needle_len,
45 const UNIT **resultp)
46 {
47 size_t m = needle_len;
48
49 /* Allocate the table. */
50 size_t *table = (size_t *) nmalloca (m, sizeof (size_t));
51 if (table == NULL)
52 return false;
53 /* Fill the table.
54 For 0 < i < m:
55 0 < table[i] <= i is defined such that
56 forall 0 < x < table[i]: needle[x..i-1] != needle[0..i-1-x],
57 and table[i] is as large as possible with this property.
58 This implies:
59 1) For 0 < i < m:
60 If table[i] < i,
61 needle[table[i]..i-1] = needle[0..i-1-table[i]].
62 2) For 0 < i < m:
63 rhaystack[0..i-1] == needle[0..i-1]
64 and exists h, i <= h < m: rhaystack[h] != needle[h]
65 implies
66 forall 0 <= x < table[i]: rhaystack[x..x+m-1] != needle[0..m-1].
67 table[0] remains uninitialized. */
68 {
69 size_t i, j;
70
71 /* i = 1: Nothing to verify for x = 0. */
72 table[1] = 1;
73 j = 0;
74
75 for (i = 2; i < m; i++)
76 {
77 /* Here: j = i-1 - table[i-1].
78 The inequality needle[x..i-1] != needle[0..i-1-x] is known to hold
79 for x < table[i-1], by induction.
80 Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1]. */
81 UNIT b = CANON_ELEMENT (needle[i - 1]);
82
83 for (;;)
84 {
85 /* Invariants: The inequality needle[x..i-1] != needle[0..i-1-x]
86 is known to hold for x < i-1-j.
87 Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1]. */
88 if (b == CANON_ELEMENT (needle[j]))
89 {
90 /* Set table[i] := i-1-j. */
91 table[i] = i - ++j;
92 break;
93 }
94 /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
95 for x = i-1-j, because
96 needle[i-1] != needle[j] = needle[i-1-x]. */
97 if (j == 0)
98 {
99 /* The inequality holds for all possible x. */
100 table[i] = i;
101 break;
102 }
103 /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
104 for i-1-j < x < i-1-j+table[j], because for these x:
105 needle[x..i-2]
106 = needle[x-(i-1-j)..j-1]
107 != needle[0..j-1-(x-(i-1-j))] (by definition of table[j])
108 = needle[0..i-2-x],
109 hence needle[x..i-1] != needle[0..i-1-x].
110 Furthermore
111 needle[i-1-j+table[j]..i-2]
112 = needle[table[j]..j-1]
113 = needle[0..j-1-table[j]] (by definition of table[j]). */
114 j = j - table[j];
115 }
116 /* Here: j = i - table[i]. */
117 }
118 }
119
120 /* Search, using the table to accelerate the processing. */
121 {
122 size_t j;
123 const UNIT *rhaystack;
124 const UNIT *phaystack;
125
126 *resultp = NULL;
127 j = 0;
128 rhaystack = haystack;
129 phaystack = haystack;
130 /* Invariant: phaystack = rhaystack + j. */
131 while (*phaystack != 0)
132 if (CANON_ELEMENT (needle[j]) == CANON_ELEMENT (*phaystack))
133 {
134 j++;
135 phaystack++;
136 if (j == m)
137 {
138 /* The entire needle has been found. */
139 *resultp = rhaystack;
140 break;
141 }
142 }
143 else if (j > 0)
144 {
145 /* Found a match of needle[0..j-1], mismatch at needle[j]. */
146 rhaystack += table[j];
147 j -= table[j];
148 }
149 else
150 {
151 /* Found a mismatch at needle[0] already. */
152 rhaystack++;
153 phaystack++;
154 }
155 }
156
157 freea (table);
158 return true;
159 }
160
161 #undef CANON_ELEMENT