c-strcasestr: avoid quadratic time consumption

[Bruno Haible]

Like c_strstr, here is a patch for c_strcasestr that avoids quadratic
asymptotic complexity.

2007-02-11  Bruno Haible  <address@hidden>

        Ensure O(n) worst-case complexity of c_strcasestr.
        * lib/c-strcasestr.c: Include stdbool.h, string.h.
        (knuth_morris_pratt): New function.
        (c_strcasestr): Add some bookkeeping. Invoke knuth_morris_pratt when
        the bookkeeping indicates that it's worth it.
        * modules/c-strcasestr (Depends-on): Add stdbool, strnlen.

        * modules/c-strcasestr-tests: New file.
        * tests/test-c-strcasestr.c: New file.

*** lib/c-strcasestr.c  14 Sep 2006 14:18:36 -0000      1.2
--- lib/c-strcasestr.c  11 Feb 2007 15:00:17 -0000
***************
*** 21,30 ****
--- 21,121 ----
  /* Specification.  */
  #include "c-strcasestr.h"
  
+ #include <stdbool.h>
  #include <stddef.h>
+ #include <string.h>
  
  #include "c-ctype.h"
  
+ /* Knuth-Morris-Pratt algorithm.
+    See http://en.wikipedia.org/wiki/Knuth-Morris-Pratt_algorithm
+    Return a boolean indicating success.  */
+ static bool
+ knuth_morris_pratt (const char *haystack, const char *needle,
+                   const char **resultp)
+ {
+   size_t m = strlen (needle);
+ 
+   /* Allocate the table.  */
+   size_t *table = (size_t *) malloc (m * sizeof (size_t));
+   if (table == NULL)
+     return false;
+   /* Fill the table.
+      For 0 < i < m:
+        0 < table[i] <= i is defined such that
+        rhaystack[0..i-1] == needle[0..i-1] and rhaystack[i] != needle[i]
+        implies
+        forall 0 <= x < table[i]: rhaystack[x..x+m-1] != needle[0..m-1],
+        and table[i] is as large as possible with this property.
+      table[0] remains uninitialized.  */
+   {
+     size_t i, j;
+ 
+     table[1] = 1;
+     j = 0;
+     for (i = 2; i < m; i++)
+       {
+       unsigned char b = c_tolower ((unsigned char) needle[i - 1]);
+ 
+       for (;;)
+         {
+           if (b == c_tolower ((unsigned char) needle[j]))
+             {
+               table[i] = i - ++j;
+               break;
+             }
+           if (j == 0)
+             {
+               table[i] = i;
+               break;
+             }
+           j = j - table[j];
+         }
+       }
+   }
+ 
+   /* Search, using the table to accelerate the processing.  */
+   {
+     size_t j;
+     const char *rhaystack;
+     const char *phaystack;
+ 
+     *resultp = NULL;
+     j = 0;
+     rhaystack = haystack;
+     phaystack = haystack;
+     /* Invariant: phaystack = rhaystack + j.  */
+     while (*phaystack != '\0')
+       if (c_tolower ((unsigned char) needle[j])
+         == c_tolower ((unsigned char) *phaystack))
+       {
+         j++;
+         phaystack++;
+         if (j == m)
+           {
+             /* The entire needle has been found.  */
+             *resultp = rhaystack;
+             break;
+           }
+       }
+       else if (j > 0)
+       {
+         /* Found a match of needle[0..j-1], mismatch at needle[j].  */
+         rhaystack += table[j];
+         j -= table[j];
+       }
+       else
+       {
+         /* Found a mismatch at needle[0] already.  */
+         rhaystack++;
+         phaystack++;
+       }
+   }
+ 
+   free (table);
+   return true;
+ }
+ 
  /* Find the first occurrence of NEEDLE in HAYSTACK, using case-insensitive
     comparison.
     Note: This function may, in multibyte locales, return success even if
***************
*** 39,44 ****
--- 130,155 ----
           needle may be found in haystack.  */
    if (*needle != '\0')
      {
+       /* Minimizing the worst-case complexity:
+        Let n = strlen(haystack), m = strlen(needle).
+        The naïve algorithm is O(n*m) worst-case.
+        The Knuth-Morris-Pratt algorithm is O(n) worst-case but it needs a
+        memory allocation.
+        To achieve linear complexity and yet amortize the cost of the memory
+        allocation, we activate the Knuth-Morris-Pratt algorithm only once
+        the naïve algorithm has already run for some time; more precisely,
+        when
+          - the outer loop count is >= 10,
+          - the average number of comparisons per outer loop is >= 5,
+          - the total number of comparisons is >= m.
+        But we try it only once.  If the memory allocation attempt failed,
+        we don't retry it.  */
+       bool try_kmp = true;
+       size_t outer_loop_count = 0;
+       size_t comparison_count = 0;
+       size_t last_ccount = 0;                 /* last comparison count */
+       const char *needle_last_ccount = needle;        /* = needle + 
last_ccount */
+ 
        /* Speed up the following searches of needle by caching its first
         character.  */
        unsigned char b = c_tolower ((unsigned char) *needle);
***************
*** 49,54 ****
--- 160,196 ----
          if (*haystack == '\0')
            /* No match.  */
            return NULL;
+ 
+         /* See whether it's advisable to use an asymptotically faster
+            algorithm.  */
+         if (try_kmp
+             && outer_loop_count >= 10
+             && comparison_count >= 5 * outer_loop_count)
+           {
+             /* See if needle + comparison_count now reaches the end of
+                needle.  */
+             if (needle_last_ccount != NULL)
+               {
+                 needle_last_ccount +=
+                   strnlen (needle_last_ccount, comparison_count - 
last_ccount);
+                 if (*needle_last_ccount == '\0')
+                   needle_last_ccount = NULL;
+                 last_ccount = comparison_count;
+               }
+             if (needle_last_ccount == NULL)
+               {
+                 /* Try the Knuth-Morris-Pratt algorithm.  */
+                 const char *result;
+                 bool success =
+                   knuth_morris_pratt (haystack, needle - 1, &result);
+                 if (success)
+                   return (char *) result;
+                 try_kmp = false;
+               }
+           }
+ 
+         outer_loop_count++;
+         comparison_count++;
          if (c_tolower ((unsigned char) *haystack) == b)
            /* The first character matches.  */
            {
***************
*** 63,68 ****
--- 205,211 ----
                  if (*rhaystack == '\0')
                    /* No match.  */
                    return NULL;
+                 comparison_count++;
                  if (c_tolower ((unsigned char) *rhaystack)
                      != c_tolower ((unsigned char) *rneedle))
                    /* Nothing in this round.  */
*** modules/c-strcasestr        11 Oct 2005 18:50:36 -0000      1.1
--- modules/c-strcasestr        11 Feb 2007 15:00:17 -0000
***************
*** 7,12 ****
--- 7,14 ----
  
  Depends-on:
  c-ctype
+ stdbool
+ strnlen
  
  configure.ac: