replace modulus with FastMod

Replaces the slow modulo operation with a much faster 32bit multiplication & shift. This works
because the hash should be uniformly distributed between 0 and 2^32-1. This speeds up the benchmark
by a factor of about 1.3:

RollingBloom, 5, 1500000, 3.73733, 4.97569e-07, 4.99002e-07, 4.98372e-07 # before
RollingBloom, 5, 1500000, 2.86842, 3.81630e-07, 3.83730e-07, 3.82473e-07 # FastMod

Be aware that this changes the position of the bits that are toggled, so this should probably
not be used for CBloomFilter which is serialized.

Author: martinus

src/bloom.cpp

@@ -245,6 +245,14 @@ static inline uint32_t RollingBloomHash(unsigned int nHashNum, uint32_t nTweak,
     return MurmurHash3(nHashNum * 0xFBA4C795 + nTweak, vDataToHash);
 }
 
+
+// A replacement for x % n. This assumes that x and n are 32bit integers, and x is a uniformly random distributed 32bit value
+// which should be the case for a good hash.
+// See https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
+static inline uint32_t FastMod(uint32_t x, size_t n) {
+    return ((uint64_t)x * (uint64_t)n) >> 32;
+}
+
 void CRollingBloomFilter::insert(const std::vector<unsigned char>& vKey)
 {
     if (nEntriesThisGeneration == nEntriesPerGeneration) {
@@ -268,7 +276,8 @@ void CRollingBloomFilter::insert(const std::vector<unsigned char>& vKey)
     for (int n = 0; n < nHashFuncs; n++) {
         uint32_t h = RollingBloomHash(n, nTweak, vKey);
         int bit = h & 0x3F;
-        uint32_t pos = (h >> 6) % data.size();
+        /* FastMod works with the upper bits of h, so it is safe to ignore that the lower bits of h are already used for bit. */
+        uint32_t pos = FastMod(h, data.size());
         /* The lowest bit of pos is ignored, and set to zero for the first bit, and to one for the second. */
         data[pos & ~1] = (data[pos & ~1] & ~(((uint64_t)1) << bit)) | ((uint64_t)(nGeneration & 1)) << bit;
         data[pos | 1] = (data[pos | 1] & ~(((uint64_t)1) << bit)) | ((uint64_t)(nGeneration >> 1)) << bit;
@@ -286,7 +295,7 @@ bool CRollingBloomFilter::contains(const std::vector<unsigned char>& vKey) const
     for (int n = 0; n < nHashFuncs; n++) {
         uint32_t h = RollingBloomHash(n, nTweak, vKey);
         int bit = h & 0x3F;
-        uint32_t pos = (h >> 6) % data.size();
+        uint32_t pos = FastMod(h, data.size());
         /* If the relevant bit is not set in either data[pos & ~1] or data[pos | 1], the filter does not contain vKey */
         if (!(((data[pos & ~1] | data[pos | 1]) >> bit) & 1)) {
             return false;