string/str-two-way.h - native_client/nacl-glibc - Git at Google

 /* Byte-wise substring search, using the Two-Way algorithm.
    Copyright (C) 2008 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Written by Eric Blake <ebb9@byu.net>, 2008.

    The GNU C Library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
    License as published by the Free Software Foundation; either
    version 2.1 of the License, or (at your option) any later version.

    The GNU C Library 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
    Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public
    License along with the GNU C Library; if not, write to the Free
    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
    02111-1307 USA.  */

 /* Before including this file, you need to include <string.h> (and
    <config.h> before that, if not part of libc), and define:
      RESULT_TYPE             A macro that expands to the return type.
      AVAILABLE(h, h_l, j, n_l)
 			     A macro that returns nonzero if there are
 			     at least N_L bytes left starting at H[J].
 			     H is 'unsigned char *', H_L, J, and N_L
 			     are 'size_t'; H_L is an lvalue.  For
 			     NUL-terminated searches, H_L can be
 			     modified each iteration to avoid having
 			     to compute the end of H up front.

   For case-insensitivity, you may optionally define:
      CMP_FUNC(p1, p2, l)     A macro that returns 0 iff the first L
 			     characters of P1 and P2 are equal.
      CANON_ELEMENT(c)        A macro that canonicalizes an element right after
 			     it has been fetched from one of the two strings.
 			     The argument is an 'unsigned char'; the result
 			     must be an 'unsigned char' as well.

   This file undefines the macros documented above, and defines
   LONG_NEEDLE_THRESHOLD.
 */

 #include <limits.h>
 #include <stdint.h>

 /* We use the Two-Way string matching algorithm, which guarantees
    linear complexity with constant space.  Additionally, for long
    needles, we also use a bad character shift table similar to the
    Boyer-Moore algorithm to achieve improved (potentially sub-linear)
    performance.

    See http://www-igm.univ-mlv.fr/~lecroq/string/node26.html#SECTION00260
    and http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm
 */

 /* Point at which computing a bad-byte shift table is likely to be
    worthwhile.  Small needles should not compute a table, since it
    adds (1 << CHAR_BIT) + NEEDLE_LEN computations of preparation for a
    speedup no greater than a factor of NEEDLE_LEN.  The larger the
    needle, the better the potential performance gain.  On the other
    hand, on non-POSIX systems with CHAR_BIT larger than eight, the
    memory required for the table is prohibitive.  */
 #if CHAR_BIT < 10
 # define LONG_NEEDLE_THRESHOLD 32U
 #else
 # define LONG_NEEDLE_THRESHOLD SIZE_MAX
 #endif

 #ifndef MAX
 # define MAX(a, b) ((a < b) ? (b) : (a))
 #endif

 #ifndef CANON_ELEMENT
 # define CANON_ELEMENT(c) c
 #endif
 #ifndef CMP_FUNC
 # define CMP_FUNC memcmp
 #endif

 /* Perform a critical factorization of NEEDLE, of length NEEDLE_LEN.
    Return the index of the first byte in the right half, and set
    *PERIOD to the global period of the right half.

    The global period of a string is the smallest index (possibly its
    length) at which all remaining bytes in the string are repetitions
    of the prefix (the last repetition may be a subset of the prefix).

    When NEEDLE is factored into two halves, a local period is the
    length of the smallest word that shares a suffix with the left half
    and shares a prefix with the right half.  All factorizations of a
    non-empty NEEDLE have a local period of at least 1 and no greater
    than NEEDLE_LEN.

    A critical factorization has the property that the local period
    equals the global period.  All strings have at least one critical
    factorization with the left half smaller than the global period.

    Given an ordered alphabet, a critical factorization can be computed
    in linear time, with 2 * NEEDLE_LEN comparisons, by computing the
    larger of two ordered maximal suffixes.  The ordered maximal
    suffixes are determined by lexicographic comparison of
    periodicity.  */
 static size_t
 critical_factorization (const unsigned char *needle, size_t needle_len,
 			size_t *period)
 {
   /* Index of last byte of left half, or SIZE_MAX.  */
   size_t max_suffix, max_suffix_rev;
   size_t j; /* Index into NEEDLE for current candidate suffix.  */
   size_t k; /* Offset into current period.  */
   size_t p; /* Intermediate period.  */
   unsigned char a, b; /* Current comparison bytes.  */

   /* Invariants:
      0 <= j < NEEDLE_LEN - 1
      -1 <= max_suffix{,_rev} < j (treating SIZE_MAX as if it were signed)
      min(max_suffix, max_suffix_rev) < global period of NEEDLE
      1 <= p <= global period of NEEDLE
      p == global period of the substring NEEDLE[max_suffix{,_rev}+1...j]
      1 <= k <= p
   */

   /* Perform lexicographic search.  */
   max_suffix = SIZE_MAX;
   j = 0;
   k = p = 1;
   while (j + k < needle_len)
     {
       a = CANON_ELEMENT (needle[j + k]);
       b = CANON_ELEMENT (needle[max_suffix + k]);
       if (a < b)
 	{
 	  /* Suffix is smaller, period is entire prefix so far.  */
 	  j += k;
 	  k = 1;
 	  p = j - max_suffix;
 	}
       else if (a == b)
 	{
 	  /* Advance through repetition of the current period.  */
 	  if (k != p)
 	    ++k;
 	  else
 	    {
 	      j += p;
 	      k = 1;
 	    }
 	}
       else /* b < a */
 	{
 	  /* Suffix is larger, start over from current location.  */
 	  max_suffix = j++;
 	  k = p = 1;
 	}
     }
   *period = p;

   /* Perform reverse lexicographic search.  */
   max_suffix_rev = SIZE_MAX;
   j = 0;
   k = p = 1;
   while (j + k < needle_len)
     {
       a = CANON_ELEMENT (needle[j + k]);
       b = CANON_ELEMENT (needle[max_suffix_rev + k]);
       if (b < a)
 	{
 	  /* Suffix is smaller, period is entire prefix so far.  */
 	  j += k;
 	  k = 1;
 	  p = j - max_suffix_rev;
 	}
       else if (a == b)
 	{
 	  /* Advance through repetition of the current period.  */
 	  if (k != p)
 	    ++k;
 	  else
 	    {
 	      j += p;
 	      k = 1;
 	    }
 	}
       else /* a < b */
 	{
 	  /* Suffix is larger, start over from current location.  */
 	  max_suffix_rev = j++;
 	  k = p = 1;
 	}
     }

   /* Choose the longer suffix.  Return the first byte of the right
      half, rather than the last byte of the left half.  */
   if (max_suffix_rev + 1 < max_suffix + 1)
     return max_suffix + 1;
   *period = p;
   return max_suffix_rev + 1;
 }

 /* Return the first location of non-empty NEEDLE within HAYSTACK, or
    NULL.  HAYSTACK_LEN is the minimum known length of HAYSTACK.  This
    method is optimized for NEEDLE_LEN < LONG_NEEDLE_THRESHOLD.
    Performance is guaranteed to be linear, with an initialization cost
    of 2 * NEEDLE_LEN comparisons.

    If AVAILABLE does not modify HAYSTACK_LEN (as in memmem), then at
    most 2 * HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching.
    If AVAILABLE modifies HAYSTACK_LEN (as in strstr), then at most 3 *
    HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching.  */
 static RETURN_TYPE
 two_way_short_needle (const unsigned char *haystack, size_t haystack_len,
 		      const unsigned char *needle, size_t needle_len)
 {
   size_t i; /* Index into current byte of NEEDLE.  */
   size_t j; /* Index into current window of HAYSTACK.  */
   size_t period; /* The period of the right half of needle.  */
   size_t suffix; /* The index of the right half of needle.  */

   /* Factor the needle into two halves, such that the left half is
      smaller than the global period, and the right half is
      periodic (with a period as large as NEEDLE_LEN - suffix).  */
   suffix = critical_factorization (needle, needle_len, &period);

   /* Perform the search.  Each iteration compares the right half
      first.  */
   if (CMP_FUNC (needle, needle + period, suffix) == 0)
     {
       /* Entire needle is periodic; a mismatch can only advance by the
 	 period, so use memory to avoid rescanning known occurrences
 	 of the period.  */
       size_t memory = 0;
       j = 0;
       while (AVAILABLE (haystack, haystack_len, j, needle_len))
 	{
 	  /* Scan for matches in right half.  */
 	  i = MAX (suffix, memory);
 	  while (i < needle_len && (CANON_ELEMENT (needle[i])
 				    == CANON_ELEMENT (haystack[i + j])))
 	    ++i;
 	  if (needle_len <= i)
 	    {
 	      /* Scan for matches in left half.  */
 	      i = suffix - 1;
 	      while (memory < i + 1 && (CANON_ELEMENT (needle[i])
 					== CANON_ELEMENT (haystack[i + j])))
 		--i;
 	      if (i + 1 < memory + 1)
 		return (RETURN_TYPE) (haystack + j);
 	      /* No match, so remember how many repetitions of period
 		 on the right half were scanned.  */
 	      j += period;
 	      memory = needle_len - period;
 	    }
 	  else
 	    {
 	      j += i - suffix + 1;
 	      memory = 0;
 	    }
 	}
     }
   else
     {
       /* The two halves of needle are distinct; no extra memory is
 	 required, and any mismatch results in a maximal shift.  */
       period = MAX (suffix, needle_len - suffix) + 1;
       j = 0;
       while (AVAILABLE (haystack, haystack_len, j, needle_len))
 	{
 	  /* Scan for matches in right half.  */
 	  i = suffix;
 	  while (i < needle_len && (CANON_ELEMENT (needle[i])
 				    == CANON_ELEMENT (haystack[i + j])))
 	    ++i;
 	  if (needle_len <= i)
 	    {
 	      /* Scan for matches in left half.  */
 	      i = suffix - 1;
 	      while (i != SIZE_MAX && (CANON_ELEMENT (needle[i])
 				       == CANON_ELEMENT (haystack[i + j])))
 		--i;
 	      if (i == SIZE_MAX)
 		return (RETURN_TYPE) (haystack + j);
 	      j += period;
 	    }
 	  else
 	    j += i - suffix + 1;
 	}
     }
   return NULL;
 }

 /* Return the first location of non-empty NEEDLE within HAYSTACK, or
    NULL.  HAYSTACK_LEN is the minimum known length of HAYSTACK.  This
    method is optimized for LONG_NEEDLE_THRESHOLD <= NEEDLE_LEN.
    Performance is guaranteed to be linear, with an initialization cost
    of 3 * NEEDLE_LEN + (1 << CHAR_BIT) operations.

    If AVAILABLE does not modify HAYSTACK_LEN (as in memmem), then at
    most 2 * HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching,
    and sublinear performance O(HAYSTACK_LEN / NEEDLE_LEN) is possible.
    If AVAILABLE modifies HAYSTACK_LEN (as in strstr), then at most 3 *
    HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching, and
    sublinear performance is not possible.  */
 static RETURN_TYPE
 two_way_long_needle (const unsigned char *haystack, size_t haystack_len,
 		     const unsigned char *needle, size_t needle_len)
 {
   size_t i; /* Index into current byte of NEEDLE.  */
   size_t j; /* Index into current window of HAYSTACK.  */
   size_t period; /* The period of the right half of needle.  */
   size_t suffix; /* The index of the right half of needle.  */
   size_t shift_table[1U << CHAR_BIT]; /* See below.  */

   /* Factor the needle into two halves, such that the left half is
      smaller than the global period, and the right half is
      periodic (with a period as large as NEEDLE_LEN - suffix).  */
   suffix = critical_factorization (needle, needle_len, &period);

   /* Populate shift_table.  For each possible byte value c,
      shift_table[c] is the distance from the last occurrence of c to
      the end of NEEDLE, or NEEDLE_LEN if c is absent from the NEEDLE.
      shift_table[NEEDLE[NEEDLE_LEN - 1]] contains the only 0.  */
   for (i = 0; i < 1U << CHAR_BIT; i++)
     shift_table[i] = needle_len;
   for (i = 0; i < needle_len; i++)
     shift_table[CANON_ELEMENT (needle[i])] = needle_len - i - 1;

   /* Perform the search.  Each iteration compares the right half
      first.  */
   if (CMP_FUNC (needle, needle + period, suffix) == 0)
     {
       /* Entire needle is periodic; a mismatch can only advance by the
 	 period, so use memory to avoid rescanning known occurrences
 	 of the period.  */
       size_t memory = 0;
       size_t shift;
       j = 0;
       while (AVAILABLE (haystack, haystack_len, j, needle_len))
 	{
 	  /* Check the last byte first; if it does not match, then
 	     shift to the next possible match location.  */
 	  shift = shift_table[CANON_ELEMENT (haystack[j + needle_len - 1])];
 	  if (0 < shift)
 	    {
 	      if (memory && shift < period)
 		{
 		  /* Since needle is periodic, but the last period has
 		     a byte out of place, there can be no match until
 		     after the mismatch.  */
 		  shift = needle_len - period;
 		  memory = 0;
 		}
 	      j += shift;
 	      continue;
 	    }
 	  /* Scan for matches in right half.  The last byte has
 	     already been matched, by virtue of the shift table.  */
 	  i = MAX (suffix, memory);
 	  while (i < needle_len - 1 && (CANON_ELEMENT (needle[i])
 					== CANON_ELEMENT (haystack[i + j])))
 	    ++i;
 	  if (needle_len - 1 <= i)
 	    {
 	      /* Scan for matches in left half.  */
 	      i = suffix - 1;
 	      while (memory < i + 1 && (CANON_ELEMENT (needle[i])
 					== CANON_ELEMENT (haystack[i + j])))
 		--i;
 	      if (i + 1 < memory + 1)
 		return (RETURN_TYPE) (haystack + j);
 	      /* No match, so remember how many repetitions of period
 		 on the right half were scanned.  */
 	      j += period;
 	      memory = needle_len - period;
 	    }
 	  else
 	    {
 	      j += i - suffix + 1;
 	      memory = 0;
 	    }
 	}
     }
   else
     {
       /* The two halves of needle are distinct; no extra memory is
 	 required, and any mismatch results in a maximal shift.  */
       size_t shift;
       period = MAX (suffix, needle_len - suffix) + 1;
       j = 0;
       while (AVAILABLE (haystack, haystack_len, j, needle_len))
 	{
 	  /* Check the last byte first; if it does not match, then
 	     shift to the next possible match location.  */
 	  shift = shift_table[CANON_ELEMENT (haystack[j + needle_len - 1])];
 	  if (0 < shift)
 	    {
 	      j += shift;
 	      continue;
 	    }
 	  /* Scan for matches in right half.  The last byte has
 	     already been matched, by virtue of the shift table.  */
 	  i = suffix;
 	  while (i < needle_len - 1 && (CANON_ELEMENT (needle[i])
 					== CANON_ELEMENT (haystack[i + j])))
 	    ++i;
 	  if (needle_len - 1 <= i)
 	    {
 	      /* Scan for matches in left half.  */
 	      i = suffix - 1;
 	      while (i != SIZE_MAX && (CANON_ELEMENT (needle[i])
 				       == CANON_ELEMENT (haystack[i + j])))
 		--i;
 	      if (i == SIZE_MAX)
 		return (RETURN_TYPE) (haystack + j);
 	      j += period;
 	    }
 	  else
 	    j += i - suffix + 1;
 	}
     }
   return NULL;
 }

 #undef AVAILABLE
 #undef CANON_ELEMENT
 #undef CMP_FUNC
 #undef MAX
 #undef RETURN_TYPE
	/* Byte-wise substring search, using the Two-Way algorithm.
	Copyright (C) 2008 Free Software Foundation, Inc.
	This file is part of the GNU C Library.
	Written by Eric Blake <ebb9@byu.net>, 2008.

	The GNU C Library is free software; you can redistribute it and/or
	modify it under the terms of the GNU Lesser General Public
	License as published by the Free Software Foundation; either
	version 2.1 of the License, or (at your option) any later version.

	The GNU C Library 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
	Lesser General Public License for more details.

	You should have received a copy of the GNU Lesser General Public
	License along with the GNU C Library; if not, write to the Free
	Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
	02111-1307 USA. */

	/* Before including this file, you need to include <string.h> (and
	<config.h> before that, if not part of libc), and define:
	RESULT_TYPE A macro that expands to the return type.
	AVAILABLE(h, h_l, j, n_l)
	A macro that returns nonzero if there are
	at least N_L bytes left starting at H[J].
	H is 'unsigned char *', H_L, J, and N_L
	are 'size_t'; H_L is an lvalue. For
	NUL-terminated searches, H_L can be
	modified each iteration to avoid having
	to compute the end of H up front.

	For case-insensitivity, you may optionally define:
	CMP_FUNC(p1, p2, l) A macro that returns 0 iff the first L
	characters of P1 and P2 are equal.
	CANON_ELEMENT(c) A macro that canonicalizes an element right after
	it has been fetched from one of the two strings.
	The argument is an 'unsigned char'; the result
	must be an 'unsigned char' as well.

	This file undefines the macros documented above, and defines
	LONG_NEEDLE_THRESHOLD.
	*/

	#include <limits.h>
	#include <stdint.h>

	/* We use the Two-Way string matching algorithm, which guarantees
	linear complexity with constant space. Additionally, for long
	needles, we also use a bad character shift table similar to the
	Boyer-Moore algorithm to achieve improved (potentially sub-linear)
	performance.

	See http://www-igm.univ-mlv.fr/~lecroq/string/node26.html#SECTION00260
	and http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm
	*/

	/* Point at which computing a bad-byte shift table is likely to be
	worthwhile. Small needles should not compute a table, since it
	adds (1 << CHAR_BIT) + NEEDLE_LEN computations of preparation for a
	speedup no greater than a factor of NEEDLE_LEN. The larger the
	needle, the better the potential performance gain. On the other
	hand, on non-POSIX systems with CHAR_BIT larger than eight, the
	memory required for the table is prohibitive. */
	#if CHAR_BIT < 10
	# define LONG_NEEDLE_THRESHOLD 32U
	#else
	# define LONG_NEEDLE_THRESHOLD SIZE_MAX
	#endif

	#ifndef MAX
	# define MAX(a, b) ((a < b) ? (b) : (a))
	#endif

	#ifndef CANON_ELEMENT
	# define CANON_ELEMENT(c) c
	#endif
	#ifndef CMP_FUNC
	# define CMP_FUNC memcmp
	#endif

	/* Perform a critical factorization of NEEDLE, of length NEEDLE_LEN.
	Return the index of the first byte in the right half, and set
	*PERIOD to the global period of the right half.

	The global period of a string is the smallest index (possibly its
	length) at which all remaining bytes in the string are repetitions
	of the prefix (the last repetition may be a subset of the prefix).

	When NEEDLE is factored into two halves, a local period is the
	length of the smallest word that shares a suffix with the left half
	and shares a prefix with the right half. All factorizations of a
	non-empty NEEDLE have a local period of at least 1 and no greater
	than NEEDLE_LEN.

	A critical factorization has the property that the local period
	equals the global period. All strings have at least one critical
	factorization with the left half smaller than the global period.

	Given an ordered alphabet, a critical factorization can be computed
	in linear time, with 2 * NEEDLE_LEN comparisons, by computing the
	larger of two ordered maximal suffixes. The ordered maximal
	suffixes are determined by lexicographic comparison of
	periodicity. */
	static size_t
	critical_factorization (const unsigned char *needle, size_t needle_len,
	size_t *period)
	{
	/* Index of last byte of left half, or SIZE_MAX. */
	size_t max_suffix, max_suffix_rev;
	size_t j; /* Index into NEEDLE for current candidate suffix. */
	size_t k; /* Offset into current period. */
	size_t p; /* Intermediate period. */
	unsigned char a, b; /* Current comparison bytes. */

	/* Invariants:
	0 <= j < NEEDLE_LEN - 1
	-1 <= max_suffix{,_rev} < j (treating SIZE_MAX as if it were signed)
	min(max_suffix, max_suffix_rev) < global period of NEEDLE
	1 <= p <= global period of NEEDLE
	p == global period of the substring NEEDLE[max_suffix{,_rev}+1...j]
	1 <= k <= p
	*/

	/* Perform lexicographic search. */
	max_suffix = SIZE_MAX;
	j = 0;
	k = p = 1;
	while (j + k < needle_len)
	{
	a = CANON_ELEMENT (needle[j + k]);
	b = CANON_ELEMENT (needle[max_suffix + k]);
	if (a < b)
	{
	/* Suffix is smaller, period is entire prefix so far. */
	j += k;
	k = 1;
	p = j - max_suffix;
	}
	else if (a == b)
	{
	/* Advance through repetition of the current period. */
	if (k != p)
	++k;
	else
	{
	j += p;
	k = 1;
	}
	}
	else /* b < a */
	{
	/* Suffix is larger, start over from current location. */
	max_suffix = j++;
	k = p = 1;
	}
	}
	*period = p;

	/* Perform reverse lexicographic search. */
	max_suffix_rev = SIZE_MAX;
	j = 0;
	k = p = 1;
	while (j + k < needle_len)
	{
	a = CANON_ELEMENT (needle[j + k]);
	b = CANON_ELEMENT (needle[max_suffix_rev + k]);
	if (b < a)
	{
	/* Suffix is smaller, period is entire prefix so far. */
	j += k;
	k = 1;
	p = j - max_suffix_rev;
	}
	else if (a == b)
	{
	/* Advance through repetition of the current period. */
	if (k != p)
	++k;
	else
	{
	j += p;
	k = 1;
	}
	}
	else /* a < b */
	{
	/* Suffix is larger, start over from current location. */
	max_suffix_rev = j++;
	k = p = 1;
	}
	}

	/* Choose the longer suffix. Return the first byte of the right
	half, rather than the last byte of the left half. */
	if (max_suffix_rev + 1 < max_suffix + 1)
	return max_suffix + 1;
	*period = p;
	return max_suffix_rev + 1;
	}

	/* Return the first location of non-empty NEEDLE within HAYSTACK, or
	NULL. HAYSTACK_LEN is the minimum known length of HAYSTACK. This
	method is optimized for NEEDLE_LEN < LONG_NEEDLE_THRESHOLD.
	Performance is guaranteed to be linear, with an initialization cost
	of 2 * NEEDLE_LEN comparisons.

	If AVAILABLE does not modify HAYSTACK_LEN (as in memmem), then at
	most 2 * HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching.
	If AVAILABLE modifies HAYSTACK_LEN (as in strstr), then at most 3 *
	HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching. */
	static RETURN_TYPE
	two_way_short_needle (const unsigned char *haystack, size_t haystack_len,
	const unsigned char *needle, size_t needle_len)
	{
	size_t i; /* Index into current byte of NEEDLE. */
	size_t j; /* Index into current window of HAYSTACK. */
	size_t period; /* The period of the right half of needle. */
	size_t suffix; /* The index of the right half of needle. */

	/* Factor the needle into two halves, such that the left half is
	smaller than the global period, and the right half is
	periodic (with a period as large as NEEDLE_LEN - suffix). */
	suffix = critical_factorization (needle, needle_len, &period);

	/* Perform the search. Each iteration compares the right half
	first. */
	if (CMP_FUNC (needle, needle + period, suffix) == 0)
	{
	/* Entire needle is periodic; a mismatch can only advance by the
	period, so use memory to avoid rescanning known occurrences
	of the period. */
	size_t memory = 0;
	j = 0;
	while (AVAILABLE (haystack, haystack_len, j, needle_len))
	{
	/* Scan for matches in right half. */
	i = MAX (suffix, memory);
	while (i < needle_len && (CANON_ELEMENT (needle[i])
	== CANON_ELEMENT (haystack[i + j])))
	++i;
	if (needle_len <= i)
	{
	/* Scan for matches in left half. */
	i = suffix - 1;
	while (memory < i + 1 && (CANON_ELEMENT (needle[i])
	== CANON_ELEMENT (haystack[i + j])))
	--i;
	if (i + 1 < memory + 1)
	return (RETURN_TYPE) (haystack + j);
	/* No match, so remember how many repetitions of period
	on the right half were scanned. */
	j += period;
	memory = needle_len - period;
	}
	else
	{
	j += i - suffix + 1;
	memory = 0;
	}
	}
	}
	else
	{
	/* The two halves of needle are distinct; no extra memory is
	required, and any mismatch results in a maximal shift. */
	period = MAX (suffix, needle_len - suffix) + 1;
	j = 0;
	while (AVAILABLE (haystack, haystack_len, j, needle_len))
	{
	/* Scan for matches in right half. */
	i = suffix;
	while (i < needle_len && (CANON_ELEMENT (needle[i])
	== CANON_ELEMENT (haystack[i + j])))
	++i;
	if (needle_len <= i)
	{
	/* Scan for matches in left half. */
	i = suffix - 1;
	while (i != SIZE_MAX && (CANON_ELEMENT (needle[i])
	== CANON_ELEMENT (haystack[i + j])))
	--i;
	if (i == SIZE_MAX)
	return (RETURN_TYPE) (haystack + j);
	j += period;
	}
	else
	j += i - suffix + 1;
	}
	}
	return NULL;
	}

	/* Return the first location of non-empty NEEDLE within HAYSTACK, or
	NULL. HAYSTACK_LEN is the minimum known length of HAYSTACK. This
	method is optimized for LONG_NEEDLE_THRESHOLD <= NEEDLE_LEN.
	Performance is guaranteed to be linear, with an initialization cost
	of 3 * NEEDLE_LEN + (1 << CHAR_BIT) operations.

	If AVAILABLE does not modify HAYSTACK_LEN (as in memmem), then at
	most 2 * HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching,
	and sublinear performance O(HAYSTACK_LEN / NEEDLE_LEN) is possible.
	If AVAILABLE modifies HAYSTACK_LEN (as in strstr), then at most 3 *
	HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching, and
	sublinear performance is not possible. */
	static RETURN_TYPE
	two_way_long_needle (const unsigned char *haystack, size_t haystack_len,
	const unsigned char *needle, size_t needle_len)
	{
	size_t i; /* Index into current byte of NEEDLE. */
	size_t j; /* Index into current window of HAYSTACK. */
	size_t period; /* The period of the right half of needle. */
	size_t suffix; /* The index of the right half of needle. */
	size_t shift_table[1U << CHAR_BIT]; /* See below. */

	/* Factor the needle into two halves, such that the left half is
	smaller than the global period, and the right half is
	periodic (with a period as large as NEEDLE_LEN - suffix). */
	suffix = critical_factorization (needle, needle_len, &period);

	/* Populate shift_table. For each possible byte value c,
	shift_table[c] is the distance from the last occurrence of c to
	the end of NEEDLE, or NEEDLE_LEN if c is absent from the NEEDLE.
	shift_table[NEEDLE[NEEDLE_LEN - 1]] contains the only 0. */
	for (i = 0; i < 1U << CHAR_BIT; i++)
	shift_table[i] = needle_len;
	for (i = 0; i < needle_len; i++)
	shift_table[CANON_ELEMENT (needle[i])] = needle_len - i - 1;

	/* Perform the search. Each iteration compares the right half
	first. */
	if (CMP_FUNC (needle, needle + period, suffix) == 0)
	{
	/* Entire needle is periodic; a mismatch can only advance by the
	period, so use memory to avoid rescanning known occurrences
	of the period. */
	size_t memory = 0;
	size_t shift;
	j = 0;
	while (AVAILABLE (haystack, haystack_len, j, needle_len))
	{
	/* Check the last byte first; if it does not match, then
	shift to the next possible match location. */
	shift = shift_table[CANON_ELEMENT (haystack[j + needle_len - 1])];
	if (0 < shift)
	{
	if (memory && shift < period)
	{
	/* Since needle is periodic, but the last period has
	a byte out of place, there can be no match until
	after the mismatch. */
	shift = needle_len - period;
	memory = 0;
	}
	j += shift;
	continue;
	}
	/* Scan for matches in right half. The last byte has
	already been matched, by virtue of the shift table. */
	i = MAX (suffix, memory);
	while (i < needle_len - 1 && (CANON_ELEMENT (needle[i])
	== CANON_ELEMENT (haystack[i + j])))
	++i;
	if (needle_len - 1 <= i)
	{
	/* Scan for matches in left half. */
	i = suffix - 1;
	while (memory < i + 1 && (CANON_ELEMENT (needle[i])
	== CANON_ELEMENT (haystack[i + j])))
	--i;
	if (i + 1 < memory + 1)
	return (RETURN_TYPE) (haystack + j);
	/* No match, so remember how many repetitions of period
	on the right half were scanned. */
	j += period;
	memory = needle_len - period;
	}
	else
	{
	j += i - suffix + 1;
	memory = 0;
	}
	}
	}
	else
	{
	/* The two halves of needle are distinct; no extra memory is
	required, and any mismatch results in a maximal shift. */
	size_t shift;
	period = MAX (suffix, needle_len - suffix) + 1;
	j = 0;
	while (AVAILABLE (haystack, haystack_len, j, needle_len))
	{
	/* Check the last byte first; if it does not match, then
	shift to the next possible match location. */
	shift = shift_table[CANON_ELEMENT (haystack[j + needle_len - 1])];
	if (0 < shift)
	{
	j += shift;
	continue;
	}
	/* Scan for matches in right half. The last byte has
	already been matched, by virtue of the shift table. */
	i = suffix;
	while (i < needle_len - 1 && (CANON_ELEMENT (needle[i])
	== CANON_ELEMENT (haystack[i + j])))
	++i;
	if (needle_len - 1 <= i)
	{
	/* Scan for matches in left half. */
	i = suffix - 1;
	while (i != SIZE_MAX && (CANON_ELEMENT (needle[i])
	== CANON_ELEMENT (haystack[i + j])))
	--i;
	if (i == SIZE_MAX)
	return (RETURN_TYPE) (haystack + j);
	j += period;
	}
	else
	j += i - suffix + 1;
	}
	}
	return NULL;
	}

	#undef AVAILABLE
	#undef CANON_ELEMENT
	#undef CMP_FUNC
	#undef MAX
	#undef RETURN_TYPE