Replace bit shift with deruijn in hyperloglog

src/hyperloglog.c

@@ -186,6 +186,7 @@ struct hllhdr {
 
 static char *invalid_hll_err = "-INVALIDOBJ Corrupted HLL object detected";
 
+
 /* =========================== Low level bit macros ========================= */
 
 /* Macros to access the dense representation.
@@ -425,11 +426,19 @@ uint64_t MurmurHash64A (const void * key, int len, unsigned int seed) {
     return h;
 }
 
+static int hll_de_bruijn_64_lookup[64] = {
+    0,  1,  56, 2,  57, 49, 28, 3,  61, 58, 42, 50, 38, 29, 17, 4,
+    62, 47, 59, 36, 45, 43, 51, 22, 53, 39, 33, 30, 24, 18, 12, 5,
+    63, 55, 48, 27, 60, 41, 37, 16, 46, 35, 44, 21, 52, 32, 23, 11,
+    54, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9,  13, 8,  7,  6,
+};
+
+
 /* Given a string element to add to the HyperLogLog, returns the length
  * of the pattern 000..1 of the element hash. As a side effect 'regp' is
  * set to the register index this element hashes to. */
 int hllPatLen(unsigned char *ele, size_t elesize, long *regp) {
-    uint64_t hash, bit, index;
+    uint64_t hash, index;
     int count;
 
     /* Count the number of zeroes starting from bit HLL_REGISTERS
@@ -448,12 +457,24 @@ int hllPatLen(unsigned char *ele, size_t elesize, long *regp) {
     hash >>= HLL_P; /* Remove bits used to address the register. */
     hash |= ((uint64_t)1<<HLL_Q); /* Make sure the loop terminates
                                      and count will be <= Q+1. */
-    bit = 1;
-    count = 1; /* Initialized to 1 since we count the "00000...1" pattern. */
-    while((hash & bit) == 0) {
-        count++;
-        bit <<= 1;
-    }
+
+
+    /* x & -x leaves only the right-most bit set in the word.
+     *
+     * Let k be the index of that bit. Since only a single bit is set, the value
+     * is two to the power of k. Multiplying by a power of two is equivalent to
+     * left shifting, in this case by k bits. The de Bruijn (64 bit) constant is
+     * such that all six bit, consecutive substrings are distinct. Therefore, if
+     * we have a left shifted version of this constant we can find by how many
+     * bits it was shifted by looking at which six bit substring ended up at the
+     * top of the word. (Knuth, volume 4, section 7.3.1)
+     */
+    hash &= -hash;
+	hash *= 0x03f79d71b4ca8b09;
+	hash >>= 58;
+	/* Initialized to 1 since we count the "00000...1" pattern. */
+	count = hll_de_bruijn_64_lookup[hash] + 1;
+
     *regp = (int) index;
     return count;
 }