File: str-two-way.h

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/* Byte-wise substring search, using the Two-Way algorithm.
   Copyright (C) 2008-2020 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Written by Eric Blake <ebb9@byu.net>, 2008.

   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 include <config.h> and
   <string.h>, and define:
     RETURN_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 (also known as
   Chrochemore-Perrin), 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 https://www-igm.univ-mlv.fr/~lecroq/string/node26.html#SECTION00260,
   https://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm,
   https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.34.6641&rep=rep1&type=pdf
*/

/* 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.
   And while some strings have more than one critical factorization,
   it is provable that with an ordered alphabet, at least one of the
   critical factorizations corresponds to a maximal suffix.

   Given an ordered alphabet, a critical factorization can be computed
   in linear time, with 2 * NEEDLE_LEN comparisons, by computing the
   shorter of two ordered maximal suffixes.  The ordered maximal
   suffixes are determined by lexicographic comparison while tracking
   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.  */

  /* Special case NEEDLE_LEN of 1 or 2 (all callers already filtered
     out 0-length needles.  */
  if (needle_len < 3)
    {
      *period = 1;
      return needle_len - 1;
    }

  /* 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 shorter suffix.  Return the index of the first byte of
     the right half, rather than the last byte of the left half.

     For some examples, 'banana' has two critical factorizations, both
     exposed by the two lexicographic extreme suffixes of 'anana' and
     'nana', where both suffixes have a period of 2.  On the other
     hand, with 'aab' and 'bba', both strings have a single critical
     factorization of the last byte, with the suffix having a period
     of 1.  While the maximal lexicographic suffix of 'aab' is 'b',
     the maximal lexicographic suffix of 'bba' is 'ba', which is not a
     critical factorization.  Conversely, the maximal reverse
     lexicographic suffix of 'a' works for 'bba', but not 'ab' for
     'aab'.  The shorter suffix of the two will always be a critical
     factorization.  */
  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 in the left half can
         only advance by the period, so use memory to avoid rescanning
         known occurrences of the period in the right half.  */
      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 in the left half can
         only advance by the period, so use memory to avoid rescanning
         known occurrences of the period in the right half.  */
      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