Merge remote-tracking branch 'upstream/master'

9 files changed, 522 insertions, 199 deletions

diff --git a/utils/Makefile.am b/utils/Makefile.am
index a22b6727..341fd80b 100644
--- a/utils/Makefile.am
+++ b/utils/Makefile.am
@@ -27,6 +27,7 @@ libutils_a_SOURCES = \
   citycrc.h \
   corpus_tools.h \
   dict.h \
+  exp_semiring.h \
   fast_sparse_vector.h \
   fdict.h \
   feature_vector.h \
@@ -38,7 +39,8 @@ libutils_a_SOURCES = \
   kernel_string_subseq.h \
   logval.h \
   m.h \
-  murmur_hash.h \
+  murmur_hash3.h \
+  murmur_hash3.cc \
   named_enum.h \
   null_deleter.h \
   null_traits.h \
@@ -49,6 +51,7 @@ libutils_a_SOURCES = \
   show.h \
   small_vector.h \
   sparse_vector.h \
+  star.h \
   static_utoa.h \
   stringlib.h \
   tdict.h \
diff --git a/utils/exp_semiring.h b/utils/exp_semiring.h
new file mode 100644
index 00000000..26a22071
--- /dev/null
+++ b/utils/exp_semiring.h
@@ -0,0 +1,64 @@
+#ifndef _EXP_SEMIRING_H_
+#define _EXP_SEMIRING_H_
+
+#include <iostream>
+#include "star.h"
+
+// this file implements the first-order expectation semiring described
+// in Li & Eisner (EMNLP 2009)
+
+// requirements:
+//   RType * RType ==> RType
+//   PType * PType ==> PType
+//   RType * PType ==> RType
+// good examples:
+//   PType scalar, RType vector
+// BAD examples:
+//   PType vector, RType scalar
+template <class PType, class RType>
+struct PRPair {
+  PRPair() : p(), r() {}
+  // Inside algorithm requires that T(0) and T(1)
+  // return the 0 and 1 values of the semiring
+  explicit PRPair(double x) : p(x), r() {}
+  PRPair(const PType& p, const RType& r) : p(p), r(r) {}
+  PRPair& operator+=(const PRPair& o) {
+    p += o.p;
+    r += o.r;
+    return *this;
+  }
+  PRPair& operator*=(const PRPair& o) {
+    r = (o.r * p) + (o.p * r);
+    p *= o.p;
+    return *this;
+  }
+  PType p;
+  RType r;
+};
+
+template <class P, class R>
+std::ostream& operator<<(std::ostream& o, const PRPair<P,R>& x) {
+  return o << '<' << x.p << ", " << x.r << '>';
+}
+
+template <class P, class R>
+const PRPair<P,R> operator+(const PRPair<P,R>& a, const PRPair<P,R>& b) {
+  PRPair<P,R> result = a;
+  result += b;
+  return result;
+}
+
+template <class P, class R>
+const PRPair<P,R> operator*(const PRPair<P,R>& a, const PRPair<P,R>& b) {
+  PRPair<P,R> result = a;
+  result *= b;
+  return result;
+}
+
+template <class P, class R>
+inline const PRPair<P,R> star(const PRPair<P,R>& x) {
+  const P pstar = star(x.p);
+  return PRPair<P,R>(pstar, pstar * x.r * pstar);
+}
+
+#endif
diff --git a/utils/fast_sparse_vector.h b/utils/fast_sparse_vector.h
index 590a60c4..6e2a77cd 100644
--- a/utils/fast_sparse_vector.h
+++ b/utils/fast_sparse_vector.h
@@ -384,13 +384,21 @@ class FastSparseVector {
   T dot(const std::vector<T>& v) const {
     T res = T();
     for (const_iterator it = begin(), e = end(); it != e; ++it)
+#if FP_FAST_FMA
+      if (static_cast<unsigned>(it->first) < v.size()) res = std::fma(it->second, v[it->first], res);
+#else
       if (static_cast<unsigned>(it->first) < v.size()) res += it->second * v[it->first];
+#endif
     return res;
   }
   T dot(const FastSparseVector<T>& other) const {
     T res = T();
     for (const_iterator it = begin(), e = end(); it != e; ++it)
+#if FP_FAST_FMA
+      res = std::fma(other.value(it->first), it->second, res);
+#else
       res += other.value(it->first) * it->second;
+#endif
     return res;
   }
   bool operator==(const FastSparseVector<T>& other) const {
diff --git a/utils/hash.h b/utils/hash.h
index e1426ffb..24d2b6ad 100644
--- a/utils/hash.h
+++ b/utils/hash.h
@@ -3,7 +3,7 @@
 
 #include <boost/functional/hash.hpp>
 
-#include "murmur_hash.h"
+#include "murmur_hash3.h"
 
 #ifdef HAVE_CONFIG_H
 #include "config.h"
@@ -44,23 +44,21 @@ const unsigned GOLDEN_MEAN_FRACTION=2654435769U;
 
 // assumes C is POD
 template <class C>
-struct murmur_hash
-{
-  typedef MurmurInt result_type;
+struct murmur_hash {
+  typedef size_t result_type;
   typedef C /*const&*/ argument_type;
   result_type operator()(argument_type const& c) const {
-    return MurmurHash((void*)&c,sizeof(c));
+    return cdec::MurmurHash3_64((void*)&c, sizeof(c), GOLDEN_MEAN_FRACTION);
   }
 };
 
 // murmur_hash_array isn't std guaranteed safe (you need to use string::data())
 template <>
-struct murmur_hash<std::string>
-{
-  typedef MurmurInt result_type;
+struct murmur_hash<std::string> {
+  typedef size_t result_type;
   typedef std::string /*const&*/ argument_type;
   result_type operator()(argument_type const& c) const {
-    return MurmurHash(c.data(),c.size());
+    return cdec::MurmurHash3_64(c.data(), c.size(), GOLDEN_MEAN_FRACTION);
   }
 };
 
@@ -68,10 +66,10 @@ struct murmur_hash<std::string>
 template <class C>
 struct murmur_hash_array
 {
-  typedef MurmurInt result_type;
+  typedef size_t result_type;
   typedef C /*const&*/ argument_type;
   result_type operator()(argument_type const& c) const {
-    return MurmurHash(&*c.begin(),c.size()*sizeof(*c.begin()));
+    return cdec::MurmurHash3_64(&*c.begin(), c.size()*sizeof(*c.begin()), GOLDEN_MEAN_FRACTION);
   }
 };
 
@@ -95,7 +93,6 @@ typename H::mapped_type & get_or_construct(H &ht,K const& k,C0 const& c0) {
   }
 }
 
-
 // get_or_call (0 arg)
 template <class H,class K,class F>
 typename H::mapped_type & get_or_call(H &ht,K const& k,F const& f) {
diff --git a/utils/logval.h b/utils/logval.h
index ec1f6acd..0c9ee982 100644
--- a/utils/logval.h
+++ b/utils/logval.h
@@ -11,6 +11,7 @@
 #include <cassert>
 #include "semiring.h"
 #include "show.h"
+#include "star.h"
 
 //TODO: template for supporting negation or not - most uses are for nonnegative "probs" only; probably some 10-20% speedup available
 template <class T>
@@ -242,4 +243,15 @@ bool operator>=(const LogVal<T>& lhs, const LogVal<T>& rhs) {
 template <class T>
 std::size_t hash_value(const LogVal<T>& x) { return x.hash_impl(); }
 
+template <class T>
+inline LogVal<T> star(LogVal<T> x) {
+  if (x.is_0()) return x;
+  if (x.v_ >= 0) {
+    x.v_ = std::numeric_limits<T>::infinity();
+  } else {
+    x.v_ = -log1p(-x.as_float());
+  }
+  return x;
+}
+
 #endif
diff --git a/utils/murmur_hash.h b/utils/murmur_hash.h
deleted file mode 100644
index 6063d524..00000000
--- a/utils/murmur_hash.h
+++ /dev/null
@@ -1,186 +0,0 @@
-#ifndef _MURMUR_HASH_H_
-#define _MURMUR_HASH_H_
-
-//NOTE: quite fast, nice collision properties, but endian dependent hash values
-
-#include "have_64_bits.h"
-typedef uintptr_t MurmurInt;
-
-// MurmurHash2, by Austin Appleby
-
-static const uint32_t DEFAULT_SEED=2654435769U;
-
-#if HAVE_64_BITS
-//MurmurInt MurmurHash(void const *key, int len, uint32_t seed=DEFAULT_SEED);
-
-inline uint64_t MurmurHash64( const void * key, int len, unsigned int seed=DEFAULT_SEED )
-{
-  const uint64_t m = 0xc6a4a7935bd1e995ULL;
-  const int r = 47;
-
-  uint64_t h = seed ^ (len * m);
-
-  const uint64_t * data = (const uint64_t *)key;
-  const uint64_t * end = data + (len/8);
-
-  while(data != end)
-  {
-    uint64_t k = *data++;
-
-    k *= m;
-    k ^= k >> r;
-    k *= m;
-
-    h ^= k;
-    h *= m;
-  }
-
-  const unsigned char * data2 = (const unsigned char*)data;
-
-  switch(len & 7)
-  {
-  case 7: h ^= uint64_t(data2[6]) << 48;
-  case 6: h ^= uint64_t(data2[5]) << 40;
-  case 5: h ^= uint64_t(data2[4]) << 32;
-  case 4: h ^= uint64_t(data2[3]) << 24;
-  case 3: h ^= uint64_t(data2[2]) << 16;
-  case 2: h ^= uint64_t(data2[1]) << 8;
-  case 1: h ^= uint64_t(data2[0]);
-    h *= m;
-  };
-
-  h ^= h >> r;
-  h *= m;
-  h ^= h >> r;
-
-  return h;
-}
-
-inline uint32_t MurmurHash32(void const *key, int len, uint32_t seed=DEFAULT_SEED)
-{
-  return (uint32_t) MurmurHash64(key,len,seed);
-}
-
-inline MurmurInt MurmurHash(void const *key, int len, uint32_t seed=DEFAULT_SEED)
-{
-  return MurmurHash64(key,len,seed);
-}
-
-#else
-// 32-bit
-
-// Note - This code makes a few assumptions about how your machine behaves -
-// 1. We can read a 4-byte value from any address without crashing
-// 2. sizeof(int) == 4
-inline uint32_t MurmurHash32 ( const void * key, int len, uint32_t seed=DEFAULT_SEED)
-{
-  // 'm' and 'r' are mixing constants generated offline.
-  // They're not really 'magic', they just happen to work well.
-
-  const uint32_t m = 0x5bd1e995;
-  const int r = 24;
-
-  // Initialize the hash to a 'random' value
-
-  uint32_t h = seed ^ len;
-
-  // Mix 4 bytes at a time into the hash
-
-  const unsigned char * data = (const unsigned char *)key;
-
-  while(len >= 4)
-  {
-    uint32_t k = *(uint32_t *)data;
-
-    k *= m;
-    k ^= k >> r;
-    k *= m;
-
-    h *= m;
-    h ^= k;
-
-    data += 4;
-    len -= 4;
-  }
-
-  // Handle the last few bytes of the input array
-
-  switch(len)
-  {
-  case 3: h ^= data[2] << 16;
-  case 2: h ^= data[1] << 8;
-  case 1: h ^= data[0];
-    h *= m;
-  };
-
-  // Do a few final mixes of the hash to ensure the last few
-  // bytes are well-incorporated.
-
-  h ^= h >> 13;
-  h *= m;
-  h ^= h >> 15;
-
-  return h;
-}
-
-inline MurmurInt MurmurHash ( const void * key, int len, uint32_t seed=DEFAULT_SEED) {
-  return MurmurHash32(key,len,seed);
-}
-
-// 64-bit hash for 32-bit platforms
-
-inline uint64_t MurmurHash64 ( const void * key, int len, uint32_t seed=DEFAULT_SEED)
-{
-  const uint32_t m = 0x5bd1e995;
-  const int r = 24;
-
-  uint32_t h1 = seed ^ len;
-  uint32_t h2 = 0;
-
-  const uint32_t * data = (const uint32_t *)key;
-
-  while(len >= 8)
-  {
-    uint32_t k1 = *data++;
-    k1 *= m; k1 ^= k1 >> r; k1 *= m;
-    h1 *= m; h1 ^= k1;
-    len -= 4;
-
-    uint32_t k2 = *data++;
-    k2 *= m; k2 ^= k2 >> r; k2 *= m;
-    h2 *= m; h2 ^= k2;
-    len -= 4;
-  }
-
-  if(len >= 4)
-  {
-    uint32_t k1 = *data++;
-    k1 *= m; k1 ^= k1 >> r; k1 *= m;
-    h1 *= m; h1 ^= k1;
-    len -= 4;
-  }
-
-  switch(len)
-  {
-  case 3: h2 ^= ((unsigned char*)data)[2] << 16;
-  case 2: h2 ^= ((unsigned char*)data)[1] << 8;
-  case 1: h2 ^= ((unsigned char*)data)[0];
-    h2 *= m;
-  };
-
-  h1 ^= h2 >> 18; h1 *= m;
-  h2 ^= h1 >> 22; h2 *= m;
-  h1 ^= h2 >> 17; h1 *= m;
-  h2 ^= h1 >> 19; h2 *= m;
-
-  uint64_t h = h1;
-
-  h = (h << 32) | h2;
-
-  return h;
-}
-
-#endif
-//32bit
-
-#endif
diff --git a/utils/murmur_hash3.cc b/utils/murmur_hash3.cc
new file mode 100644
index 00000000..68a71d02
--- /dev/null
+++ b/utils/murmur_hash3.cc
@@ -0,0 +1,340 @@
+//-----------------------------------------------------------------------------
+// MurmurHash3 was written by Austin Appleby, and is placed in the public
+// domain. The author hereby disclaims copyright to this source code.
+
+// Note - The x86 and x64 versions do _not_ produce the same results, as the
+// algorithms are optimized for their respective platforms. You can still
+// compile and run any of them on any platform, but your performance with the
+// non-native version will be less than optimal.
+
+#include "murmur_hash3.h"
+
+//-----------------------------------------------------------------------------
+// Platform-specific functions and macros
+
+// Microsoft Visual Studio
+
+#if defined(_MSC_VER)
+
+#define FORCE_INLINE    __forceinline
+
+#include <stdlib.h>
+
+#define ROTL32(x,y)     _rotl(x,y)
+#define ROTL64(x,y)     _rotl64(x,y)
+
+#define BIG_CONSTANT(x) (x)
+
+// Other compilers
+
+#else   // defined(_MSC_VER)
+
+#define FORCE_INLINE inline __attribute__((always_inline))
+
+namespace cdec {
+
+inline uint32_t rotl32 ( uint32_t x, int8_t r )
+{
+  return (x << r) | (x >> (32 - r));
+}
+
+inline uint64_t rotl64 ( uint64_t x, int8_t r )
+{
+  return (x << r) | (x >> (64 - r));
+}
+
+#define ROTL32(x,y)     rotl32(x,y)
+#define ROTL64(x,y)     rotl64(x,y)
+
+#define BIG_CONSTANT(x) (x##LLU)
+
+#endif // !defined(_MSC_VER)
+
+//-----------------------------------------------------------------------------
+// Block read - if your platform needs to do endian-swapping or can only
+// handle aligned reads, do the conversion here
+
+FORCE_INLINE uint32_t getblock32 ( const uint32_t * p, int i )
+{
+  return p[i];
+}
+
+FORCE_INLINE uint64_t getblock64 ( const uint64_t * p, int i )
+{
+  return p[i];
+}
+
+//-----------------------------------------------------------------------------
+// Finalization mix - force all bits of a hash block to avalanche
+
+FORCE_INLINE uint32_t fmix32 ( uint32_t h )
+{
+  h ^= h >> 16;
+  h *= 0x85ebca6b;
+  h ^= h >> 13;
+  h *= 0xc2b2ae35;
+  h ^= h >> 16;
+
+  return h;
+}
+
+//----------
+
+FORCE_INLINE uint64_t fmix64 ( uint64_t k )
+{
+  k ^= k >> 33;
+  k *= BIG_CONSTANT(0xff51afd7ed558ccd);
+  k ^= k >> 33;
+  k *= BIG_CONSTANT(0xc4ceb9fe1a85ec53);
+  k ^= k >> 33;
+
+  return k;
+}
+
+//-----------------------------------------------------------------------------
+
+void MurmurHash3_x86_32 ( const void * key, int len,
+                          uint32_t seed, void * out )
+{
+  const uint8_t * data = (const uint8_t*)key;
+  const int nblocks = len / 4;
+
+  uint32_t h1 = seed;
+
+  const uint32_t c1 = 0xcc9e2d51;
+  const uint32_t c2 = 0x1b873593;
+
+  //----------
+  // body
+
+  const uint32_t * blocks = (const uint32_t *)(data + nblocks*4);
+
+  for(int i = -nblocks; i; i++)
+  {
+    uint32_t k1 = getblock32(blocks,i);
+
+    k1 *= c1;
+    k1 = ROTL32(k1,15);
+    k1 *= c2;
+    
+    h1 ^= k1;
+    h1 = ROTL32(h1,13); 
+    h1 = h1*5+0xe6546b64;
+  }
+
+  //----------
+  // tail
+
+  const uint8_t * tail = (const uint8_t*)(data + nblocks*4);
+
+  uint32_t k1 = 0;
+
+  switch(len & 3)
+  {
+  case 3: k1 ^= tail[2] << 16;
+  case 2: k1 ^= tail[1] << 8;
+  case 1: k1 ^= tail[0];
+          k1 *= c1; k1 = ROTL32(k1,15); k1 *= c2; h1 ^= k1;
+  };
+
+  //----------
+  // finalization
+
+  h1 ^= len;
+
+  h1 = fmix32(h1);
+
+  *(uint32_t*)out = h1;
+} 
+
+//-----------------------------------------------------------------------------
+
+void MurmurHash3_x86_128 ( const void * key, const int len,
+                           uint32_t seed, void * out )
+{
+  const uint8_t * data = (const uint8_t*)key;
+  const int nblocks = len / 16;
+
+  uint32_t h1 = seed;
+  uint32_t h2 = seed;
+  uint32_t h3 = seed;
+  uint32_t h4 = seed;
+
+  const uint32_t c1 = 0x239b961b; 
+  const uint32_t c2 = 0xab0e9789;
+  const uint32_t c3 = 0x38b34ae5; 
+  const uint32_t c4 = 0xa1e38b93;
+
+  //----------
+  // body
+
+  const uint32_t * blocks = (const uint32_t *)(data + nblocks*16);
+
+  for(int i = -nblocks; i; i++)
+  {
+    uint32_t k1 = getblock32(blocks,i*4+0);
+    uint32_t k2 = getblock32(blocks,i*4+1);
+    uint32_t k3 = getblock32(blocks,i*4+2);
+    uint32_t k4 = getblock32(blocks,i*4+3);
+
+    k1 *= c1; k1  = ROTL32(k1,15); k1 *= c2; h1 ^= k1;
+
+    h1 = ROTL32(h1,19); h1 += h2; h1 = h1*5+0x561ccd1b;
+
+    k2 *= c2; k2  = ROTL32(k2,16); k2 *= c3; h2 ^= k2;
+
+    h2 = ROTL32(h2,17); h2 += h3; h2 = h2*5+0x0bcaa747;
+
+    k3 *= c3; k3  = ROTL32(k3,17); k3 *= c4; h3 ^= k3;
+
+    h3 = ROTL32(h3,15); h3 += h4; h3 = h3*5+0x96cd1c35;
+
+    k4 *= c4; k4  = ROTL32(k4,18); k4 *= c1; h4 ^= k4;
+
+    h4 = ROTL32(h4,13); h4 += h1; h4 = h4*5+0x32ac3b17;
+  }
+
+  //----------
+  // tail
+
+  const uint8_t * tail = (const uint8_t*)(data + nblocks*16);
+
+  uint32_t k1 = 0;
+  uint32_t k2 = 0;
+  uint32_t k3 = 0;
+  uint32_t k4 = 0;
+
+  switch(len & 15)
+  {
+  case 15: k4 ^= tail[14] << 16;
+  case 14: k4 ^= tail[13] << 8;
+  case 13: k4 ^= tail[12] << 0;
+           k4 *= c4; k4  = ROTL32(k4,18); k4 *= c1; h4 ^= k4;
+
+  case 12: k3 ^= tail[11] << 24;
+  case 11: k3 ^= tail[10] << 16;
+  case 10: k3 ^= tail[ 9] << 8;
+  case  9: k3 ^= tail[ 8] << 0;
+           k3 *= c3; k3  = ROTL32(k3,17); k3 *= c4; h3 ^= k3;
+
+  case  8: k2 ^= tail[ 7] << 24;
+  case  7: k2 ^= tail[ 6] << 16;
+  case  6: k2 ^= tail[ 5] << 8;
+  case  5: k2 ^= tail[ 4] << 0;
+           k2 *= c2; k2  = ROTL32(k2,16); k2 *= c3; h2 ^= k2;
+
+  case  4: k1 ^= tail[ 3] << 24;
+  case  3: k1 ^= tail[ 2] << 16;
+  case  2: k1 ^= tail[ 1] << 8;
+  case  1: k1 ^= tail[ 0] << 0;
+           k1 *= c1; k1  = ROTL32(k1,15); k1 *= c2; h1 ^= k1;
+  };
+
+  //----------
+  // finalization
+
+  h1 ^= len; h2 ^= len; h3 ^= len; h4 ^= len;
+
+  h1 += h2; h1 += h3; h1 += h4;
+  h2 += h1; h3 += h1; h4 += h1;
+
+  h1 = fmix32(h1);
+  h2 = fmix32(h2);
+  h3 = fmix32(h3);
+  h4 = fmix32(h4);
+
+  h1 += h2; h1 += h3; h1 += h4;
+  h2 += h1; h3 += h1; h4 += h1;
+
+  ((uint32_t*)out)[0] = h1;
+  ((uint32_t*)out)[1] = h2;
+  ((uint32_t*)out)[2] = h3;
+  ((uint32_t*)out)[3] = h4;
+}
+
+//-----------------------------------------------------------------------------
+
+void MurmurHash3_x64_128 ( const void * key, const int len,
+                           const uint32_t seed, void * out )
+{
+  const uint8_t * data = (const uint8_t*)key;
+  const int nblocks = len / 16;
+
+  uint64_t h1 = seed;
+  uint64_t h2 = seed;
+
+  const uint64_t c1 = BIG_CONSTANT(0x87c37b91114253d5);
+  const uint64_t c2 = BIG_CONSTANT(0x4cf5ad432745937f);
+
+  //----------
+  // body
+
+  const uint64_t * blocks = (const uint64_t *)(data);
+
+  for(int i = 0; i < nblocks; i++)
+  {
+    uint64_t k1 = getblock64(blocks,i*2+0);
+    uint64_t k2 = getblock64(blocks,i*2+1);
+
+    k1 *= c1; k1  = ROTL64(k1,31); k1 *= c2; h1 ^= k1;
+
+    h1 = ROTL64(h1,27); h1 += h2; h1 = h1*5+0x52dce729;
+
+    k2 *= c2; k2  = ROTL64(k2,33); k2 *= c1; h2 ^= k2;
+
+    h2 = ROTL64(h2,31); h2 += h1; h2 = h2*5+0x38495ab5;
+  }
+
+  //----------
+  // tail
+
+  const uint8_t * tail = (const uint8_t*)(data + nblocks*16);
+
+  uint64_t k1 = 0;
+  uint64_t k2 = 0;
+
+  switch(len & 15)
+  {
+  case 15: k2 ^= ((uint64_t)tail[14]) << 48;
+  case 14: k2 ^= ((uint64_t)tail[13]) << 40;
+  case 13: k2 ^= ((uint64_t)tail[12]) << 32;
+  case 12: k2 ^= ((uint64_t)tail[11]) << 24;
+  case 11: k2 ^= ((uint64_t)tail[10]) << 16;
+  case 10: k2 ^= ((uint64_t)tail[ 9]) << 8;
+  case  9: k2 ^= ((uint64_t)tail[ 8]) << 0;
+           k2 *= c2; k2  = ROTL64(k2,33); k2 *= c1; h2 ^= k2;
+
+  case  8: k1 ^= ((uint64_t)tail[ 7]) << 56;
+  case  7: k1 ^= ((uint64_t)tail[ 6]) << 48;
+  case  6: k1 ^= ((uint64_t)tail[ 5]) << 40;
+  case  5: k1 ^= ((uint64_t)tail[ 4]) << 32;
+  case  4: k1 ^= ((uint64_t)tail[ 3]) << 24;
+  case  3: k1 ^= ((uint64_t)tail[ 2]) << 16;
+  case  2: k1 ^= ((uint64_t)tail[ 1]) << 8;
+  case  1: k1 ^= ((uint64_t)tail[ 0]) << 0;
+           k1 *= c1; k1  = ROTL64(k1,31); k1 *= c2; h1 ^= k1;
+  };
+
+  //----------
+  // finalization
+
+  h1 ^= len; h2 ^= len;
+
+  h1 += h2;
+  h2 += h1;
+
+  h1 = fmix64(h1);
+  h2 = fmix64(h2);
+
+  h1 += h2;
+  h2 += h1;
+
+  ((uint64_t*)out)[0] = h1;
+  ((uint64_t*)out)[1] = h2;
+}
+
+//-----------------------------------------------------------------------------
+
+} // namespace cdec
+
+
diff --git a/utils/murmur_hash3.h b/utils/murmur_hash3.h
new file mode 100644
index 00000000..a125d775
--- /dev/null
+++ b/utils/murmur_hash3.h
@@ -0,0 +1,67 @@
+//-----------------------------------------------------------------------------
+// MurmurHash3 was written by Austin Appleby, and is placed in the public
+// domain. The author hereby disclaims copyright to this source code.
+
+#ifndef _MURMURHASH3_H_
+#define _MURMURHASH3_H_
+
+//-----------------------------------------------------------------------------
+// Platform-specific functions and macros
+
+// Microsoft Visual Studio
+
+#if defined(_MSC_VER) && (_MSC_VER < 1600)
+
+typedef unsigned char uint8_t;
+typedef unsigned int uint32_t;
+typedef unsigned __int64 uint64_t;
+
+// Other compilers
+
+#else   // defined(_MSC_VER)
+
+#include <stdint.h>
+
+#endif // !defined(_MSC_VER)
+
+//-----------------------------------------------------------------------------
+
+namespace cdec {
+
+void MurmurHash3_x86_32  ( const void * key, int len, uint32_t seed, void * out );
+
+void MurmurHash3_x86_128 ( const void * key, int len, uint32_t seed, void * out );
+
+void MurmurHash3_x64_128 ( const void * key, int len, uint32_t seed, void * out );
+
+namespace {
+  #ifdef __clang__
+  #pragma clang diagnostic push
+  #pragma clang diagnostic ignored "-Wunused-function"
+  #endif
+  template <unsigned L> inline void cdecMurmurHashNativeBackend(const void * key, int len, uint32_t seed, void * out) {
+    MurmurHash3_x86_128(key, len, seed, out);
+  }
+  template <> inline void cdecMurmurHashNativeBackend<4>(const void * key, int len, uint32_t seed, void * out) {
+    MurmurHash3_x64_128(key, len, seed, out);
+  }
+  #ifdef __clang__
+  #pragma clang diagnostic pop
+  #endif
+} // namespace
+
+inline uint64_t MurmurHash3_64(const void * key, int len, uint32_t seed) {
+  uint64_t out[2];
+  cdecMurmurHashNativeBackend<sizeof(void*)>(key, len, seed, &out);
+  return out[0];
+}
+
+inline void MurmurHash3_128(const void * key, int len, uint32_t seed, void * out) {
+  cdecMurmurHashNativeBackend<sizeof(void*)>(key, len, seed, out);
+}
+
+}
+
+//-----------------------------------------------------------------------------
+
+#endif // _MURMURHASH3_H_
diff --git a/utils/star.h b/utils/star.h
new file mode 100644
index 00000000..21977dc9
--- /dev/null
+++ b/utils/star.h
@@ -0,0 +1,18 @@
+#ifndef _STAR_H_
+#define _STAR_H_
+
+// star(x) computes the infinite sum x^0 + x^1 + x^2 + ...
+
+template <typename T>
+inline T star(const T& x) {
+  if (!x) return T();
+  if (x > T(1)) return std::numeric_limits<T>::infinity();
+  if (x < -T(1)) return -std::numeric_limits<T>::infinity();
+  return T(1) / (T(1) - x);
+}
+
+inline bool star(bool x) {
+  return x;
+}
+
+#endif