Make strstr and strcasestr O(n), not O(n^2); add memmem.

* libc/string/str-two-way.h: New file.
* libc/string/memmem.c (memmem): New file.
* libc/include/string.h (memmem): Declare for all platforms.
* libc/string/strstr.c (strstr): Provide O(n) implementation when
not optimizing for space.
* libc/string/strcasestr.c (strcasestr): Likewise.
* libc/string/Makefile.am (ELIX_SOURCES): Rename to...
(ELIX_2_SOURCES): ...this.
(ELIX_4_SOURCES): New category, for memmem.
(lib_a_SOURCES, libstring_la_SOURCES): Build new file.
(CHEWOUT_FILES): Build documentation for memmem.
* libc/string/strings.tex: Include new docs.

1 files changed, 415 insertions, 0 deletions

diff --git a/newlib/libc/string/str-two-way.h b/newlib/libc/string/str-two-way.h
new file mode 100644
index 000000000..ad71a2595
--- /dev/null
+++ b/newlib/libc/string/str-two-way.h
@@ -0,0 +1,415 @@
+/* Byte-wise substring search, using the Two-Way algorithm.
+ * Copyright (C) 2008 Eric Blake
+ * Permission to use, copy, modify, and distribute this software
+ * is freely granted, provided that this notice is preserved.
+ */
+
+
+/* Before including this file, you need to include <string.h>, 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
+
+#define MAX(a, b) ((a < b) ? (b) : (a))
+
+#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