[PATCH] memmem: slight optimization

[Eric Blake]

For any needle, the factorization 0/n has a local period of 1, so it
is a critical factorization iff the entire needle consists only of a
single repeated byte, in which case 1/n-1 would also be critical.
Starting with a comparison of x[0] and x[1] in the maximal suffix
check will either find the 0/n case or move on to something else, so
we can optimize and start with the x[1] vs. x[2] case to begin with.

To avoid out-of-bounds references, we must then special case needles
of length two or less.  However, for these cases, we can determine a
critical factorization without any probes of the needle (we already
require a non-empty needle; a 1-byte needle can factor as either 0/1
or 1/0 but the rest of our code assumes a non-empty suffix; and of the
two 2-byte needle patterns, "aa" can factor as either 0/2 or 1/1 but
with best performance for 1/1, and "ab" must be factored as 1/1).

* lib/str-two-way.h (critical_factorization): Update comments.
Reduce work during factorization phase.
Reported by Carlos Bueno.

Signed-off-by: Eric Blake <address@hidden>
---
 ChangeLog         |    7 ++++++
 lib/str-two-way.h |   59 +++++++++++++++++++++++++++++++++++-----------------
 2 files changed, 47 insertions(+), 19 deletions(-)

diff --git a/ChangeLog b/ChangeLog
index 4b72933..0361c60 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,10 @@
+2010-06-21  Eric Blake  <address@hidden>
+
+       memmem: slight optimization
+       * lib/str-two-way.h (critical_factorization): Update comments.
+       Reduce work during factorization phase.
+       Reported by Carlos Bueno <address@hidden>.
+
 2010-02-17  Eric Blake  <address@hidden>

        manywarnings: add more warnings
diff --git a/lib/str-two-way.h b/lib/str-two-way.h
index 3f67741..dbc2f88 100644
--- a/lib/str-two-way.h
+++ b/lib/str-two-way.h
@@ -95,26 +95,37 @@
    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
-   larger of two ordered maximal suffixes.  The ordered maximal
-   suffixes are determined by lexicographic comparison of
+   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.  */
+  /* Index of last byte of left half.  */
   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)
+     1 <= j < NEEDLE_LEN - 1
+     0 <= max_suffix{,_rev} < j
      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]
@@ -122,9 +133,8 @@ critical_factorization (const unsigned char *needle, size_t 
needle_len,
   */

   /* Perform lexicographic search.  */
-  max_suffix = SIZE_MAX;
-  j = 0;
-  k = p = 1;
+  max_suffix = 0;
+  j = k = p = 1;
   while (j + k < needle_len)
     {
       a = CANON_ELEMENT (needle[j + k]);
@@ -157,9 +167,8 @@ critical_factorization (const unsigned char *needle, size_t 
needle_len,
   *period = p;

   /* Perform reverse lexicographic search.  */
-  max_suffix_rev = SIZE_MAX;
-  j = 0;
-  k = p = 1;
+  max_suffix_rev = 0;
+  j = k = p = 1;
   while (j + k < needle_len)
     {
       a = CANON_ELEMENT (needle[j + k]);
@@ -190,8 +199,20 @@ critical_factorization (const unsigned char *needle, 
size_t needle_len,
         }
     }

-  /* Choose the longer suffix.  Return the first byte of the right
-     half, rather than the last byte of the left half.  */
+  /* 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;
@@ -226,9 +247,9 @@ two_way_short_needle (const unsigned char *haystack, size_t 
haystack_len,
      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.  */
+      /* 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))
@@ -330,9 +351,9 @@ two_way_long_needle (const unsigned char *haystack, size_t 
haystack_len,
      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.  */
+      /* 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;
-- 
1.7.0.1