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This is a simple implementation of the CHD perfect hash algorithm. CHD can generate perfect hash functions for very large key sets--on the order of millions of keys--in a very short time. On my circa 2012 desktop and using the default parameters (hash load factor of 80% and average displacement map bucket load of 4.0 keys) this implementation can generate a hash function for 1,000 keys in less than 1/100th of a second, and 1,000,000 keys in less than a second.

For more information about the algorithm, see


  • No runtime dependencies.
  • Requires a modern C++ compiler to build.
  • The included build requires GNU Make.


Make Macros

The typical GNU macros can be used control the build.


Note that the modules for Lua 5.1, 5.2, and 5.3 can be built simultaneously.

  • CXX: C++ compiler path.
  • CXXFLAGS: C++ compiler flags.
  • CPPFLAGS: C preprocessor flags. Necessary if Lua API cannot be discovered automatically. You can specify multiple include paths if building more than one Lua module.
  • LDFLAGS: Linker flags. Not normally needed.
  • SOFLAGS: Flags needed to build dynamic library.
  • LOFLAGS: Flags needed to build loadable module. Normally should be the same as SOFLAGS, except on OS X.
  • LIBS: Library dependencies. Normally empty, but see the section Avoiding C++ Dependencies.

Avoiding C++ Dependencies

Defining the preprocessor macro PHF_NO_LIBCXX to 1 will prevent usage of C++ interfaces such as std::string that would require a dependency on libc++ or libstdc++. This allows using platform-dependent flags in CXXFLAGS, LDFLAGS, and SOFLAGS to prevent a dependency on the system C++ library.

For example, on OS X you can do:

CXXFLAGS="-std=c++11 -fno-rtti -fno-exceptions -O3 -march=native" \
LDFLAGS="-nostdlib" \


  • prefix
  • includedir
  • libdir
  • luacpath: Lua C module install path. Can be used for one-shot installation of a particular Lua version module.
  • lua51cpath: Lua 5.1 C module install path.
  • lua52cpath: Same as above, for 5.2.
  • lua53cpath: Same as above, for 5.3.

Make Targets

  • phf: Builds command-line utility (development)
  • Builds dynamic library for non-OS X
  • libphf.dylib: Builds dynamic library for OS X
  • lua5.1: Builds Lua 5.1 module at 5.1/ Lua 5.1 headers should be specified using CPPFLAGS if not in normal locations.
  • lua5.2: Same as above, for Lua 5.2.
  • lua5.3: Same as above, for Lua 5.3.



API[, lambda][, alpha][, seed][, nodiv])

  • keys: array of keys in order from 1..#keys. They should be all numbers or all strings.

  • lambda: number of keys per bucket when generating the g() function mapping.

  • alpha: output hash space loading factor as percentage from 1..100. 100% generates a minimal perfect hash function. But note that the implementation does not implement the necessary optimizations to ensure timely generation of minimal perfect hash functions. Normally you want a loading factor of 80% to 90% for large key sets.

  • seed: random integer seed.

  • nodiv: if true rounds r and m to powers of 2, and performs modular reduction using bitwise AND. Otherwise, r and m are rounded up to the nearest primes and modulo division used when indexing tables. Note that the rounding occurs after calculation of the intermediate and output hash table loading.

    This is more important when building small hash tables with the C interface. The optimization is substantial when the compiler can inline the code, but isn't substantial from Lua.

Returns a callable object.


  • Returns an integer hash in the range 1..phf:m(). The returned integer will be unique for all keys in the original set. Otherwise the result is unspecified.


local phf = require"phf"

local lambda = 4 -- how many keys per intermediate bucket
local alpha = 80 -- output hash space loading in percentage.

local keys = { "apple", "banana", "cherry", "date", "eggplant", "fig",
               "guava", "honeydew", "jackfruit", "kiwi", "lemon", "mango" }

local F =, lambda, alpha)

for i=1,#keys do
	print(keys[i], F(keys[i]))



PHF::uniq(T k[], size_t n);

Similar to the shell command sort | uniq. Sorts, deduplicates, and shifts down the keys in the array k. Returns the number of unique keys, which will have been moved to the beginning of the array. If necessary do this before calling PHF::init, as PHF::init does not tolerate duplicate keys.

int PHF::init<T, nodiv>(struct phf *f, const T k[], size_t n, size_t l, size_t a, phf_seed_t s);

Generate a perfect hash function for the n keys in array k and store the results in f. Returns a system error number on failure, or 0 on success. f is unmodified on failure.

void PHF::destroy(struct phf *);

Deallocates internal tables, but not the struct object itself.

void PHF::compact<T, nodiv>(struct phf *);

By default the displacement map is an array of uint32_t integers. This function will select the smallest type necessary to hold the largest displacement value and update the internal state accordingly. For a loading factor of 80% (0.8) in the output hash space, and displacement map loading factor of 4 (400%), the smallest primitive type will often be uint8_t.

phf_hash_t PHF::hash(struct phf *f, T k);

Returns an integer hash value, h, where 0 <= h < f->m. h will be unique for each unique key provided when generating the function. f->m will be larger than the number of unique keys and is based on the specified loading factor (alpha), rounded up to the nearest prime or nearest power of 2, depending on the mode of modular reduction selected. For example, for a loading factor of 80% m will be 127: 100 is 80% of 125, and 127 is the closest prime greater than or equal to 125. With the nodiv option, m would be 128: 100 is 80% of 125, and 128 is the closest power of 2 greater than or equal to 125.


The C API is nearly identical to the C++ API, except the prefix is phf_ instead of PHF::. phf_uniq, phf_init, and phf_hash are macros which utilize C11's _Generic or GCC's __builtin_types_compatible_p interfaces to overload the interfaces by key type. The explicit suffixes _uint32, _uint64, and _string may be used directly.


Tiny perfect hash library for C, C++, and Lua







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