1 /* Substring search in a NUL terminated string of UNIT elements,
2 using the Knuth-Morris-Pratt algorithm.
3 Copyright (C) 2005-2021 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 <https://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 https://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