/* Substring search in a NUL terminated string of UNIT elements,

   using the Knuth-Morris-Pratt algorithm.

   Copyright (C) 2005-2018 Free Software Foundation, Inc.

   Written by Bruno Haible <bruno@clisp.org>, 2005.

   This program is free software; you can redistribute it and/or modify

   it under the terms of the GNU General Public License as published by

   the Free Software Foundation; either version 3, or (at your option)

   any later version.

   This program is distributed in the hope that it will be useful,

   but WITHOUT ANY WARRANTY; without even the implied warranty of

   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License

   along with this program; if not, see <https://www.gnu.org/licenses/>.  */

/* Before including this file, you need to define:

     UNIT                    The element type of the needle and haystack.

     CANON_ELEMENT(c)        A macro that canonicalizes an element right after

                             it has been fetched from needle or haystack.

                             The argument is of type UNIT; the result must be

                             of type UNIT as well.  */

/* Knuth-Morris-Pratt algorithm.

   See https://en.wikipedia.org/wiki/Knuth-Morris-Pratt_algorithm

   HAYSTACK is the NUL terminated string in which to search for.

   NEEDLE is the string to search for in HAYSTACK, consisting of NEEDLE_LEN

   units.

   Return a boolean indicating success:

   Return true and set *RESULTP if the search was completed.

   Return false if it was aborted because not enough memory was available.  */

static bool

knuth_morris_pratt (const UNIT *haystack,

                    const UNIT *needle, size_t needle_len,

                    const UNIT **resultp)

{

  size_t m = needle_len;

  /* Allocate the table.  */

  size_t *table = (size_t *) nmalloca (m, sizeof (size_t));

  if (table == NULL)

    return false;

  /* Fill the table.

     For 0 < i < m:

       0 < table[i] <= i is defined such that

       forall 0 < x < table[i]: needle[x..i-1] != needle[0..i-1-x],

       and table[i] is as large as possible with this property.

     This implies:

     1) For 0 < i < m:

          If table[i] < i,

          needle[table[i]..i-1] = needle[0..i-1-table[i]].

     2) For 0 < i < m:

          rhaystack[0..i-1] == needle[0..i-1]

          and exists h, i <= h < m: rhaystack[h] != needle[h]

          implies

          forall 0 <= x < table[i]: rhaystack[x..x+m-1] != needle[0..m-1].

     table[0] remains uninitialized.  */

  {

    size_t i, j;

    /* i = 1: Nothing to verify for x = 0.  */

    table[1] = 1;

    j = 0;

    for (i = 2; i < m; i++)

      {

        /* Here: j = i-1 - table[i-1].

           The inequality needle[x..i-1] != needle[0..i-1-x] is known to hold

           for x < table[i-1], by induction.

           Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1].  */

        UNIT b = CANON_ELEMENT (needle[i - 1]);

        for (;;)

          {

            /* Invariants: The inequality needle[x..i-1] != needle[0..i-1-x]

               is known to hold for x < i-1-j.

               Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1].  */

            if (b == CANON_ELEMENT (needle[j]))

              {

                /* Set table[i] := i-1-j.  */

                table[i] = i - ++j;

                break;

              }

            /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds

               for x = i-1-j, because

                 needle[i-1] != needle[j] = needle[i-1-x].  */

            if (j == 0)

              {

                /* The inequality holds for all possible x.  */

                table[i] = i;

                break;

              }

            /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds

               for i-1-j < x < i-1-j+table[j], because for these x:

                 needle[x..i-2]

                 = needle[x-(i-1-j)..j-1]

                 != needle[0..j-1-(x-(i-1-j))]  (by definition of table[j])

                    = needle[0..i-2-x],

               hence needle[x..i-1] != needle[0..i-1-x].

               Furthermore

                 needle[i-1-j+table[j]..i-2]

                 = needle[table[j]..j-1]

                 = needle[0..j-1-table[j]]  (by definition of table[j]).  */

            j = j - table[j];

          }

        /* Here: j = i - table[i].  */

      }

  }

  /* Search, using the table to accelerate the processing.  */

  {

    size_t j;

    const UNIT *rhaystack;

    const UNIT *phaystack;

    *resultp = NULL;

    j = 0;

    rhaystack = haystack;

    phaystack = haystack;

    /* Invariant: phaystack = rhaystack + j.  */

    while (*phaystack != 0)

      if (CANON_ELEMENT (needle[j]) == CANON_ELEMENT (*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++;

        }

  }

  freea (table);

  return true;

}

#undef CANON_ELEMENT