diff --git a/src/Makefile.am b/src/Makefile.am
index b946a325c9c..0b177480c8f 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -240,6 +240,7 @@ BITCOIN_CORE_H = \
   util/check.h \
   util/epochguard.h \
   util/error.h \
+  util/fastrange.h \
   util/fees.h \
   util/getuniquepath.h \
   util/golombrice.h \
diff --git a/src/blockfilter.cpp b/src/blockfilter.cpp
index 566254d8399..63a9ba498f5 100644
--- a/src/blockfilter.cpp
+++ b/src/blockfilter.cpp
@@ -29,7 +29,7 @@ uint64_t GCSFilter::HashToRange(const Element& element) const
     uint64_t hash = CSipHasher(m_params.m_siphash_k0, m_params.m_siphash_k1)
         .Write(element.data(), element.size())
         .Finalize();
-    return MapIntoRange(hash, m_F);
+    return FastRange64(hash, m_F);
 }
 
 std::vector<uint64_t> GCSFilter::BuildHashedSet(const ElementSet& elements) const
diff --git a/src/common/bloom.cpp b/src/common/bloom.cpp
index c3603b5d2aa..0bb72dbcbb6 100644
--- a/src/common/bloom.cpp
+++ b/src/common/bloom.cpp
@@ -11,6 +11,7 @@
 #include <script/standard.h>
 #include <span.h>
 #include <streams.h>
+#include <util/fastrange.h>
 
 #include <algorithm>
 #include <cmath>
@@ -191,14 +192,6 @@ 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(Span<const unsigned char> vKey)
 {
     if (nEntriesThisGeneration == nEntriesPerGeneration) {
@@ -223,7 +216,7 @@ void CRollingBloomFilter::insert(Span<const unsigned char> vKey)
         uint32_t h = RollingBloomHash(n, nTweak, vKey);
         int bit = h & 0x3F;
         /* 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());
+        uint32_t pos = FastRange32(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;
@@ -235,7 +228,7 @@ bool CRollingBloomFilter::contains(Span<const 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 = FastMod(h, data.size());
+        uint32_t pos = FastRange32(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;
diff --git a/src/cuckoocache.h b/src/cuckoocache.h
index 15cb55c3ce9..d0dc61c7e62 100644
--- a/src/cuckoocache.h
+++ b/src/cuckoocache.h
@@ -5,6 +5,8 @@
 #ifndef BITCOIN_CUCKOOCACHE_H
 #define BITCOIN_CUCKOOCACHE_H
 
+#include <util/fastrange.h>
+
 #include <algorithm> // std::find
 #include <array>
 #include <atomic>
@@ -219,13 +221,8 @@ private:
      * One option would be to implement the same trick the compiler uses and compute the
      *  constants for exact division based on the size, as described in "{N}-bit Unsigned
      *  Division via {N}-bit Multiply-Add" by Arch D. Robison in 2005. But that code is
-     *  somewhat complicated and the result is still slower than other options:
-     *
-     * Instead we treat the 32-bit random number as a Q32 fixed-point number in the range
-     *  [0, 1) and simply multiply it by the size. Then we just shift the result down by
-     *  32-bits to get our bucket number. The result has non-uniformity the same as a
-     *  mod, but it is much faster to compute. More about this technique can be found at
-     *  https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/ .
+     *  somewhat complicated and the result is still slower than an even simpler option:
+     *  see the FastRange32 function in util/fastrange.h.
      *
      * The resulting non-uniformity is also more equally distributed which would be
      *  advantageous for something like linear probing, though it shouldn't matter
@@ -241,14 +238,14 @@ private:
      */
     inline std::array<uint32_t, 8> compute_hashes(const Element& e) const
     {
-        return {{(uint32_t)(((uint64_t)hash_function.template operator()<0>(e) * (uint64_t)size) >> 32),
-                 (uint32_t)(((uint64_t)hash_function.template operator()<1>(e) * (uint64_t)size) >> 32),
-                 (uint32_t)(((uint64_t)hash_function.template operator()<2>(e) * (uint64_t)size) >> 32),
-                 (uint32_t)(((uint64_t)hash_function.template operator()<3>(e) * (uint64_t)size) >> 32),
-                 (uint32_t)(((uint64_t)hash_function.template operator()<4>(e) * (uint64_t)size) >> 32),
-                 (uint32_t)(((uint64_t)hash_function.template operator()<5>(e) * (uint64_t)size) >> 32),
-                 (uint32_t)(((uint64_t)hash_function.template operator()<6>(e) * (uint64_t)size) >> 32),
-                 (uint32_t)(((uint64_t)hash_function.template operator()<7>(e) * (uint64_t)size) >> 32)}};
+        return {{FastRange32(hash_function.template operator()<0>(e), size),
+                 FastRange32(hash_function.template operator()<1>(e), size),
+                 FastRange32(hash_function.template operator()<2>(e), size),
+                 FastRange32(hash_function.template operator()<3>(e), size),
+                 FastRange32(hash_function.template operator()<4>(e), size),
+                 FastRange32(hash_function.template operator()<5>(e), size),
+                 FastRange32(hash_function.template operator()<6>(e), size),
+                 FastRange32(hash_function.template operator()<7>(e), size)}};
     }
 
     /** invalid returns a special index that can never be inserted to
diff --git a/src/test/fuzz/golomb_rice.cpp b/src/test/fuzz/golomb_rice.cpp
index 2d0b29953c6..b4bb4c6dc64 100644
--- a/src/test/fuzz/golomb_rice.cpp
+++ b/src/test/fuzz/golomb_rice.cpp
@@ -25,7 +25,7 @@ uint64_t HashToRange(const std::vector<uint8_t>& element, const uint64_t f)
     const uint64_t hash = CSipHasher(0x0706050403020100ULL, 0x0F0E0D0C0B0A0908ULL)
                               .Write(element.data(), element.size())
                               .Finalize();
-    return MapIntoRange(hash, f);
+    return FastRange64(hash, f);
 }
 
 std::vector<uint64_t> BuildHashedSet(const std::unordered_set<std::vector<uint8_t>, ByteVectorHash>& elements, const uint64_t f)
diff --git a/src/util/fastrange.h b/src/util/fastrange.h
new file mode 100644
index 00000000000..77cb883ce0e
--- /dev/null
+++ b/src/util/fastrange.h
@@ -0,0 +1,51 @@
+// Copyright (c) 2018-2020 The Bitcoin Core developers
+// Distributed under the MIT software license, see the accompanying
+// file COPYING or http://www.opensource.org/licenses/mit-license.php.
+
+#ifndef BITCOIN_UTIL_FASTRANGE_H
+#define BITCOIN_UTIL_FASTRANGE_H
+
+#include <cstdint>
+
+/* This file offers implementations of the fast range reduction technique described
+ * in https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
+ *
+ * In short, they take an integer x and a range n, and return the upper bits of
+ * (x * n). If x is uniformly distributed over its domain, the result is as close to
+ * uniformly distributed over [0, n) as (x mod n) would be, but significantly faster.
+ */
+
+/** Fast range reduction with 32-bit input and 32-bit range. */
+static inline uint32_t FastRange32(uint32_t x, uint32_t n)
+{
+    return (uint64_t{x} * n) >> 32;
+}
+
+/** Fast range reduction with 64-bit input and 64-bit range. */
+static inline uint64_t FastRange64(uint64_t x, uint64_t n)
+{
+#ifdef __SIZEOF_INT128__
+    return (static_cast<unsigned __int128>(x) * static_cast<unsigned __int128>(n)) >> 64;
+#else
+    // To perform the calculation on 64-bit numbers without losing the
+    // result to overflow, split the numbers into the most significant and
+    // least significant 32 bits and perform multiplication piece-wise.
+    //
+    // See: https://stackoverflow.com/a/26855440
+    const uint64_t x_hi = x >> 32;
+    const uint64_t x_lo = x & 0xFFFFFFFF;
+    const uint64_t n_hi = n >> 32;
+    const uint64_t n_lo = n & 0xFFFFFFFF;
+
+    const uint64_t ac = x_hi * n_hi;
+    const uint64_t ad = x_hi * n_lo;
+    const uint64_t bc = x_lo * n_hi;
+    const uint64_t bd = x_lo * n_lo;
+
+    const uint64_t mid34 = (bd >> 32) + (bc & 0xFFFFFFFF) + (ad & 0xFFFFFFFF);
+    const uint64_t upper64 = ac + (bc >> 32) + (ad >> 32) + (mid34 >> 32);
+    return upper64;
+#endif
+}
+
+#endif // BITCOIN_UTIL_FASTRANGE_H
diff --git a/src/util/golombrice.h b/src/util/golombrice.h
index f14cb594db7..4ff4f6d7e59 100644
--- a/src/util/golombrice.h
+++ b/src/util/golombrice.h
@@ -5,6 +5,8 @@
 #ifndef BITCOIN_UTIL_GOLOMBRICE_H
 #define BITCOIN_UTIL_GOLOMBRICE_H
 
+#include <util/fastrange.h>
+
 #include <streams.h>
 
 #include <cstdint>
@@ -40,35 +42,4 @@ uint64_t GolombRiceDecode(BitStreamReader<IStream>& bitreader, uint8_t P)
     return (q << P) + r;
 }
 
-// Map a value x that is uniformly distributed in the range [0, 2^64) to a
-// value uniformly distributed in [0, n) by returning the upper 64 bits of
-// x * n.
-//
-// See: https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
-static inline uint64_t MapIntoRange(uint64_t x, uint64_t n)
-{
-#ifdef __SIZEOF_INT128__
-    return (static_cast<unsigned __int128>(x) * static_cast<unsigned __int128>(n)) >> 64;
-#else
-    // To perform the calculation on 64-bit numbers without losing the
-    // result to overflow, split the numbers into the most significant and
-    // least significant 32 bits and perform multiplication piece-wise.
-    //
-    // See: https://stackoverflow.com/a/26855440
-    const uint64_t x_hi = x >> 32;
-    const uint64_t x_lo = x & 0xFFFFFFFF;
-    const uint64_t n_hi = n >> 32;
-    const uint64_t n_lo = n & 0xFFFFFFFF;
-
-    const uint64_t ac = x_hi * n_hi;
-    const uint64_t ad = x_hi * n_lo;
-    const uint64_t bc = x_lo * n_hi;
-    const uint64_t bd = x_lo * n_lo;
-
-    const uint64_t mid34 = (bd >> 32) + (bc & 0xFFFFFFFF) + (ad & 0xFFFFFFFF);
-    const uint64_t upper64 = ac + (bc >> 32) + (ad >> 32) + (mid34 >> 32);
-    return upper64;
-#endif
-}
-
 #endif // BITCOIN_UTIL_GOLOMBRICE_H