bdlb_hashutil.h

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/// @file bdlb_hashutil.h
///
/// The content of this file has been pre-processed for Doxygen.
///
 
 
// bdlb_hashutil.h                                                    -*-C++-*-
#ifndef INCLUDED_BDLB_HASHUTIL
#define INCLUDED_BDLB_HASHUTIL
 
#include <bsls_ident.h>
BSLS_IDENT("$Id: $")
 
/// @defgroup bdlb_hashutil bdlb_hashutil
/// @brief  Provide a utility of hash functions.
/// @addtogroup bdl
/// @{
/// @addtogroup bdlb
/// @{
/// @addtogroup bdlb_hashutil
/// @{
///
/// <h1> Outline </h1>
/// * <a href="#bdlb_hashutil-purpose"> Purpose</a>
/// * <a href="#bdlb_hashutil-classes"> Classes </a>
/// * <a href="#bdlb_hashutil-description"> Description </a>
///   * <a href="#bdlb_hashutil-hashing-fundamental-types"> Hashing Fundamental Types </a>
///   * <a href="#bdlb_hashutil-hashing-user-defined-types"> Hashing User-defined Types </a>
///   * <a href="#bdlb_hashutil-definitions-and-formal-statement-of-no-funneling-property"> Definitions and Formal Statement of No-Funneling Property </a>
///   * <a href="#bdlb_hashutil-usage"> Usage </a>
///     * <a href="#bdlb_hashutil-examples-introduction"> Examples Introduction </a>
///     * <a href="#bdlb_hashutil-example-1-using-chaining"> Example 1: Using Chaining </a>
///     * <a href="#bdlb_hashutil-example-2-using-double-hashing"> Example 2: Using Double-Hashing </a>
///     * <a href="#bdlb_hashutil-example-3-creating-a-generator-of-sequential-integers"> Example 3: Creating a Generator of Sequential Integers </a>
///     * <a href="#bdlb_hashutil-example-4-creating-a-character-string-generator"> Example 4: Creating a Character String Generator </a>
///     * <a href="#bdlb_hashutil-example-5-creating-a-multiple-field-keys-generator"> Example 5: Creating a Multiple-Field Keys Generator </a>
///     * <a href="#bdlb_hashutil-example-6-experimental-results"> Example 6: Experimental Results </a>
///
/// # Purpose {#bdlb_hashutil-purpose}
/// Provide a utility of hash functions.
///
/// # Classes {#bdlb_hashutil-classes}
///
/// -  bdlb::HashUtil: utility for hash functions
///
/// @see  bdlc_hashtable2, bdeimp_inthash, bdeimp_strhash, bdlde_crc32
///
/// # Description {#bdlb_hashutil-description}
/// This component defines a utility `struct`, `bdlb::HashUtil`,
/// that provides two hash functions, `hash1` and `hash2`.  These hash functions
/// have a good funneling property, which can be formalized as documented below
/// (see {Definitions and Formal Statement of No-Funneling Property}).  In
/// short, these hashes have the property that even if two inputs differ in only
/// a few bits, they have a negligible probability of producing collisions.  In
/// addition, these two hash functions produce full 32-bit results and allow
/// hash table sizes to be a power of two.  They are fast and reliable.  They
/// should work equally well on all types of keys.
///
/// The two hash functions `hash1` and `hash2` have similar characteristics.
/// `hash2` is a bit faster than `hash1`, especially for longer keys; it also
/// does not produce many collisions as determined experimentally for the key
/// types given in the example below.  On the other hand, it does not have the
/// formal no-funnel guarantees of `hash1` which is reasonably fast and provably
/// achieves low collision probability.
///
/// Furthermore, this component provides a third hash function `hash0` that
/// performs a simple hash by taking the modulus of a user specified size on the
/// input key.  This hash function has a poor distribution, as the function
/// exhibits a clustering effect when the input keys only differ slightly.
/// However, `hash0` is about 6 to 8 times faster than `hash1` and `hash2`.
///
/// In general, use `hash0` when speed matters, and `hash1` or `hash2` when a
/// more thorough hash is needed (e.g., keys exhibit a pattern that results in
/// many collision when using `bdeimp`, or cost of collision is high but hashing
/// is not a bottleneck).
///
/// ## Hashing Fundamental Types {#bdlb_hashutil-hashing-fundamental-types}
///
///
/// In order to facilitate hashing user-defined types (see next section), this
/// component supports hashing fundamental types in a manner that is both
/// seemingly random (i.e., the hash is good) but predictable (i.e., identical
/// on all platforms, irrespective of endianness).  Note that the following
/// expressions for some `key` of a fundamental integral type:
/// @code
/// bdlb::HashUtil::hash1((const char *)&key, sizeof(key));  // not recommended
/// bdlb::HashUtil::hash2((const char *)&key, sizeof(key));  // not recommended
/// @endcode
/// return values that differ on big- and little-endian platforms if the key
/// size is more than one byte.  Instead, the recommended way to hash this `key`
/// is simply to:
/// @code
/// bdlb::HashUtil::hash1(key);
/// bdlb::HashUtil::hash2(key);
/// @endcode
/// This works if `key` is of one of the following fundamental types:
/// @code
/// char, signed char, unsigned char,
/// short, unsigned short,
/// int, unsigned int,
/// long, unsigned long,
/// bsls::Types::Int64, bsls::Types::Uint64,
/// float, double,
/// const void *
/// @endcode
///
/// ## Hashing User-defined Types {#bdlb_hashutil-hashing-user-defined-types}
///
///
/// This component can be used for hashing a user-defined type as well.  The
/// recommended way to do this is to provide a `hash` class method for the type,
/// that takes an instance of the class and a size.  For instance, let us
/// consider the following class (the meaning and implementation are irrelevant
/// here) with the following private data members:
/// @code
/// /// This class is an aggregate.
/// class UserDefinedTickerType {
///
///     enum { CUSIP_LENGTH = 10 };
///
///     // PRIVATE DATA MEMBERS
///     bool      d_isConstant;          // not recommended, because of padding
///     char      d_cusip[CUSIP_LENGTH];
///     int       d_value;
/// @endcode
/// A hash class method can be provided and documented as follows:
/// @code
///   public:
///     // CLASS METHODS
///
///     // Return a hash value calculated from the specified `object` using
///     // the specified `size` as the number of slots.  The hash value
///     // is guaranteed to be in the range [0, size).
///     static int hash(const UserDefinedTickerType& object, int size);
///
///     // Rest of the class definition omitted...
/// };
/// @endcode
/// The implementation of `hash` can be very simple, depending on the semantics
/// of the class.  Here we assume that `d_isConstant` is an implementation
/// detail and that data members `d_cusip` and `d_value` should participate in
/// the hash and that the character string should be hashed by value.  The
/// implementation follows:
/// @code
/// int UserDefinedTickerType::hash(const UserDefinedTickerType& object,
///                                 int                          size)
/// {
///     return (bdlb::HashUtil::hash1(object.d_cusip, CUSIP_LENGTH) +
///                              bdlb::HashUtil::hash1(object.d_value)) % size;
/// }
/// @endcode
/// Note that more intricate combinations of the individual hashes in the
/// aggregate can be appropriate if the individual members in the aggregate my
/// exhibit a pattern.
///
/// CAVEAT: When hashing user-defined classes, because of the potential padding
/// in the class footprint, the simple-minded hashes
/// @code
/// const UserDefinedTickerType& key;
/// bdlb::HashUtil::hash1((const char *)&key, sizeof(key)); // wrong, because
/// bdlb::HashUtil::hash2((const char *)&key, sizeof(key)); // of padding
/// @endcode
/// may actually *not* produce the same hash values for copies of the same
/// object.
///
/// ## Definitions and Formal Statement of No-Funneling Property {#bdlb_hashutil-definitions-and-formal-statement-of-no-funneling-property}
///
///
/// Let us say a given bit in the input affects a given bit in the output (which
/// has `v` bits) if two keys differing only at that input bit will differ at
/// the given output bit about half the time.  We define a hash to be a
/// funneling hash if there is some subset of size `t` of all the input bits
/// that can affect only a subset of size `u` of bits in the output, and `t > u`
/// and `v > u`, and we say that the hash function has a funnel of those `t`
/// input bits into those `u` bits.  In that case, then `u` of those `t` bits
/// can cancel out the effects of the other `t - u`, and so the set of keys
/// differing only in the input bits of the funnel can produce no more than half
/// that number of hash values.  (Those `2^t` keys can produce no more than
/// `2^u` out of `2^v` hash values.)  Differing in only a few bits is a common
/// pattern in human and computer keys, so a funneling hash is seriously flawed.
///
/// This component offers a hash function (`hash1`) that has no funnels, except
/// for a funnel of 32 bits into 31 bits, which is a negligible vulnerability.
/// The `hash2` does not have known no-funneling properties, but operates on the
/// same principle and is just as good (and faster) in experiments with chaining
/// as in the usage below.  In addition, these two hash functions produce full
/// 32-bit results and allow hash table sizes to be a power of two.
///
/// For further details and references, the interested reader is invited to
/// consult `http://burtleburtle.net/bob/hash/evahash.html`.
///
/// ## Usage {#bdlb_hashutil-usage}
///
///
/// This section illustrates intended use of this component.
///
/// ### Examples Introduction {#bdlb_hashutil-examples-introduction}
///
///
/// We illustrate the usage of this component by some experiments (code and
/// results) on the number of collision expected for various usage.  For
/// returning the results of an experiment, we will use the following structure:
/// @code
/// struct ExperimentalResult {
///
///     // DATA MEMBERS
///     int    d_max;     // maximum length of a chain
///     double d_average; // average length of a chain
///     double d_sigma;   // standard deviation
///
///     // CREATORS
///
///     /// Create an experimental result reporting the optionally specified
///     /// `max`, `avg`, and `sigma` values.
///     explicit
///     ExperimentalResult(int max = 0, double avg = 0, double sigma = 0)
///     : d_max(max), d_average(avg), d_sigma(sigma)
///     {}
/// };
/// @endcode
/// For generating the data, we use a parameterized `GENERATOR` of which we give
/// three implementations below (sequential integers, character strings, and
/// multiple-field keys).  This template parameter needs to validate the
/// following syntactic expressions, which we call in this usage example our
/// `GeneratorConcept`.  In those requirements, `generator` is an instance of
/// `GENERATOR`.
/// @code
/// const char *data   = generator.data();   // address of storage of current
///                                          // value
/// int         length = generator.length(); // length of storage of current
///                                          // value
///
/// generator.next();                        // advance to next value
/// @endcode
///
/// ### Example 1: Using Chaining {#bdlb_hashutil-example-1-using-chaining}
///
///
/// The following code will check the number of collisions for a chaining-based
/// hash table given a certain distribution of keys:
/// @code
/// /// Simulate insertion of the specified `numElements` generated by the
/// /// specified `input` generator into a hash table of the specified
/// /// `size` using chaining as the mechanism to resolve collisions.
/// /// Return the results (maximum and average length of a chain, with
/// /// standard deviation).  `GENERATOR` must be a model of the
/// /// `GeneratorConcept`.  For the good functioning of this function, it
/// /// is required that `input` never be default nor repeat itself.
/// template <class GENERATOR>
/// ExperimentalResult computeChainingCollisions(int       numElements,
///                                              int       size,
///                                              GENERATOR input)
/// {
///     bsl::vector<int> table(size);   // all counters are init'ed to 0
///
///     for (int i = 0; i < numElements; ++i, input.next()) {
///         unsigned int hash = Util::hash1(input.data(),
///                                                  input.length());
///         ++table[hash % size];
///     }
///
///     double avgLength    = 0; // average number of collisions
///     double sigmaLength  = 0; // standard deviation from average
///     int    maxLength    = 0; // maximum length of a chain
///
///     for (int k = 0; k < size; ++k) {
///         avgLength   += table[k];
///         sigmaLength += table[k] * table[k];
///         maxLength    = bsl::max(maxLength, table[k]);
///     }
///     avgLength   /= size;
///     sigmaLength  = bsl::sqrt(sigmaLength / size - avgLength * avgLength);
///
///     return ExperimentalResult(maxLength, avgLength, sigmaLength);
/// }
/// @endcode
///
/// ### Example 2: Using Double-Hashing {#bdlb_hashutil-example-2-using-double-hashing}
///
///
/// The following code will check the number of collisions for a double-hashing
/// based hash table (such as @ref bdlc_hashtable2 ) given a certain distribution
/// of keys:
/// @code
/// /// Simulate insertion of the specified `numElements` generated by the
/// /// specified `input` generator into a hash table of the specified
/// /// `size` using double hashing as the mechanism to resolve collisions.
/// /// Return the results (maximum and average length of a chain, with
/// /// standard deviation).  `GENERATOR` must be a model of the
/// /// `GeneratorConcept`.  For the good functioning of this function, it
/// /// is required that `input` never be default nor repeat itself.
/// template <class GENERATOR>
/// ExperimentalResult computeDoubleHashingCollisions(int       numElements,
///                                                   int       size,
///                                                   GENERATOR input)
/// {
///     typedef typename GENERATOR::ResultType  ResultType;
///     bsl::vector<ResultType> table(size); // all counters are default-ct'ed
///
///     double avgLength    = 0; // average number of collisions
///     double sigmaLength  = 0; // standard deviation from average
///     int    maxLength    = 0; // maximum length of a chain
///
///     for (int i = 0; i < numElements; ++i, input.next()) {
///         unsigned int hash1 = Util::hash1(input.data(),
///                                                   input.length());
///
///         int chainLength = 0;
///         int bucket      = hash1 % size;
///         if (ResultType() == table[bucket]) {
///             table[bucket] = input.current();
///         } else {
///             unsigned int hash2 = Util::hash2(input.data(),
///                                                       input.length());
///             hash2 = 1 + hash2 % (size - 1);
///
///             while (++chainLength < size) {
///                 bucket = (bucket + hash2) % size;
///
///                 if (ResultType() == table[bucket]) {
///                     table[bucket] = input.current();
///                     break; // while loop
///                 }
///             }
///         }
///
///         if (chainLength == size) {
///             bsl::cerr << "\tCould not insert in doubly-hashed table\n";
///             avgLength   = bsl::numeric_limits<double>::infinity();
///             sigmaLength = bsl::numeric_limits<double>::infinity();
///             maxLength   = static_cast<int>(
///                                   bsl::numeric_limits<double>::infinity());
///             return ExperimentalResult(maxLength, avgLength, sigmaLength);
///                                                                   // RETURN
///         }
///
///         avgLength   += chainLength;
///         sigmaLength += chainLength * chainLength;
///         maxLength    = bsl::max(maxLength, chainLength);
///     }
///     avgLength   /= numElements;
///     sigmaLength  = bsl::sqrt(sigmaLength / numElements
///                            -   avgLength * avgLength);
///
///     return ExperimentalResult(maxLength, avgLength, sigmaLength);
/// }
/// @endcode
///
/// ### Example 3: Creating a Generator of Sequential Integers {#bdlb_hashutil-example-3-creating-a-generator-of-sequential-integers}
///
///
/// Here is a simple generator that returns a sequence of integers.  This
/// generator has a period of `INT_MAX / gcd(increment, INT_MAX+1)`.
/// @code
/// class SequentialIntegers {
///     int d_current;
///     int d_inc;
///
///   public:
///     // TYPES
///     typedef int ResultType;
///         // Type returned by this generator.
///
///     // CREATORS
///
///     // Create a generator returning integers in a sequence starting at
///     // the optionally specified `first` integer, with the optionally
///     // specified `increment`.
///     explicit SequentialIntegers(int first = 1, int increment = 1)
///         : d_current(first), d_inc(increment) {}
///
///     // MANIPULATORS
///
///     /// Advance to the next element.
///     void next()
///     {
///         d_current += d_inc;
///     }
///
///     // ACCESSORS
///
///     /// Return current element.
///     ResultType current() const
///     {
///         return d_current;
///     }
///
///     /// Return data buffer of result type.
///     const char *data() const
///     {
///         return reinterpret_cast<const char*>(&d_current);
///     }
///
///     /// Return length of result type (in bytes).
///     int length() const
///     {
///         return sizeof(ResultType);
///     }
/// };
/// @endcode
///
/// ### Example 4: Creating a Character String Generator {#bdlb_hashutil-example-4-creating-a-character-string-generator}
///
///
/// Here is a simple generator that returns a sequence of strings that are a
/// permutation of an initial string.  This generator has a period of
/// `factorial(initial.length())` where `factorial(N)` returns the number of
/// permutations of `N` distinct elements.
/// @code
/// class SequentialStrings {
///     size_t      d_length;
///     bsl::string d_current;
///
///   public:
///     // TYPES
///     typedef bsl::string ResultType;
///         // Type returned by this generator.
///
///     // CREATORS
///
///     /// Create a generator returning strings in a sequence starting at
///     /// the specified `initial` string (sorted by characters) and
///     /// looping through all permutations of `str`.  The behavior is
///     /// undefined unless all the characters of the `initial` string are
///     /// distinct.
///     explicit SequentialStrings(bsl::string const& initial)
///         : d_length(initial.length()), d_current(initial)
///     {
///         bsl::sort(d_current.begin(), d_current.end());
///         assert(bsl::unique(d_current.begin(), d_current.end()) ==
///                                                           d_current.end());
///     }
///
///     // MANIPULATORS
///
///     /// Advance to the next element.
///     void next()
///     {
///         bsl::next_permutation(d_current.begin(), d_current.end());
///     }
///
///     // ACCESSORS
///
///     /// Return current element.
///     ResultType current() const
///     {
///         return d_current;
///     }
///
///     /// Return data buffer of result type.
///     const char *data() const
///     {
///         return d_current.data();
///     }
///
///     /// Return length of result type (in bytes).
///     size_t length() const
///     {
///         return d_current.length();
///     }
/// };
/// @endcode
///
/// ### Example 5: Creating a Multiple-Field Keys Generator {#bdlb_hashutil-example-5-creating-a-multiple-field-keys-generator}
///
///
/// It is not uncommon for keys to consist of concatenated keys in multiple
/// combinations.  We simulate this by a character string in which each
/// character loops through a specified number of values.  The period of this
/// generator is the product of the length of each character range.
/// @code
/// struct SequentialVector {
///     bsl::vector<char> d_ranges;
///     size_t            d_length;
///     bsl::string       d_current;
///
///   public:
///     // TYPES
///     typedef bsl::string ResultType;
///         // Type returned by this generator.
///
///     // CREATORS
///
///     /// Create a generator returning strings having the same length as
///     /// the specified `ranges` (i.e., `ranges.size()`) in a sequence
///     /// starting at the string with all null characters and looping
///     /// through all the strings with each character at position `i` in
///     /// the specified range from 0 until `ranges[i]` (excluded).  The
///     /// behavior is undefined unless `ranges` does not contain zero
///     /// entries.
///     explicit SequentialVector(bsl::vector<char> const& ranges)
///     : d_ranges(ranges)
///     , d_length(ranges.size())
///     , d_current(d_length, (char)0)
///     {
///     }
///
///     // MANIPULATORS
///
///     /// Advance to the next element.
///     void next()
///     {
///         for (size_t i = 0;
///              i < d_length && ++d_current[i] == d_ranges[i]; ++i) {
///             d_current[i] = 0;
///         }
///     }
///
///     // ACCESSORS
///
///     /// Return current element.
///     ResultType current() const
///     {
///         return d_current;
///     }
///
///     /// Return data buffer of current value.
///     const char *data() const
///     {
///         return d_current.data();
///     }
///
///     /// Return length of current value (in bytes).
///     size_t length() const
///     {
///         return d_current.length();
///     }
/// };
/// @endcode
///
/// ### Example 6: Experimental Results {#bdlb_hashutil-example-6-experimental-results}
///
///
/// Checking the above distributions is done in a straightforward manner.  We do
/// this at various load factors (the load factor is the percentage of the table
/// that actually holds data; it is defined as `N / SIZE` where `N` is the
/// number of elements and `SIZE` is the size of the hash table).  Note that
/// chaining accommodates arbitrary load factors, while double hashing requires
/// that the load factor be strictly less than 1.
/// @code
/// int usageExample(int verbose, int veryVerbose, int /* veryVeryVerbose */) {
///     const int SIZE = 10000;
///     const int INC  = SIZE / 5; // load factors for every 20% percentile
///     const int COLS = (4*SIZE)/INC;
///
///     {
///         ExperimentalResult results[3][COLS];
///         bsls::Stopwatch    timer;
///
///         if (verbose) cout << "\nUsing chaining"
///                           << "\n--------------" << endl;
///
///         if (verbose) cout << "Sequential Integers\n";
///         timer.start();
///         for (int n = INC, i = 0; n < 4*SIZE; n += INC, ++i) {
///             if (veryVerbose)
///                 cout << "\tWith load factor " <<
///                                      static_cast<double>(n) / SIZE << "\n";
///
///             results[0][i] = computeChainingCollisions(
///                                                      n,
///                                                      SIZE,
///                                                      SequentialIntegers());
///             assert(results[0][i].d_average < 1.5 * n / SIZE);
///         }
///         if (verbose) cout << "\t... in " << timer.elapsedTime() << "\n";
///         timer.reset();
///
///         if (verbose) cout << "Sequential Strings\n";
///         timer.start();
///         for (int n = INC, i = 0; n < 4*SIZE; n += INC, ++i) {
///             if (veryVerbose)
///                 cout << "\tWith load factor " <<
///                                      static_cast<double>(n) / SIZE << "\n";
///
///             bsl::string initial("abcdefghij"); // period = 10! = 3628800
///             results[1][i] = computeChainingCollisions(
///                                                n,
///                                                SIZE,
///                                                SequentialStrings(initial));
///             assert(results[1][i].d_average < 1.5 * n / SIZE);
///         }
///         if (verbose) cout << "\t... in " << timer.elapsedTime() << "\n";
///         timer.reset();
///
///         if (verbose) cout << "Sequential Vector\n";
///         timer.start();
///         for (int n = INC, i = 0; n < 4*SIZE; n += INC, ++i) {
///             if (veryVerbose)
///                 cout << "\tWith load factor " <<
///                                      static_cast<double>(n) / SIZE << "\n";
///
///             bsl::vector<char> ranges(6, static_cast<char>(4));
///                                                      // period = 4^6 = 4096
///             results[2][i] = computeChainingCollisions(
///                                                  n,
///                                                  SIZE,
///                                                  SequentialVector(ranges));
///             assert(results[2][i].d_average < 1.5 * n / SIZE);
///         }
///         if (verbose) cout << "\t... in " << timer.elapsedTime() << "\n";
///         timer.reset();
///
///         if (verbose) {
///             cout << "\nDisplaying average (max) for chaining:";
///             cout << "\n--------------------------------------n";
///             const char *ROW_LABELS[] = { "\nIntegers:",
///                                          "\nStrings :",
///                                          "\nVector  :",
///                                          "\nLoad factor:",
///             };
///             const int   NUM_ROWS     = sizeof  ROW_LABELS
///                                      / sizeof *ROW_LABELS - 1;
///
///             cout << ROW_LABELS[NUM_ROWS] << bsl::setprecision(2);
///             for (int n = INC; n < 4*SIZE; n += INC) {
///                 cout << "\t" << static_cast<double>(n) / SIZE;
///             }
///             for (int j = 0; j < NUM_ROWS; ++j) {
///                 cout << ROW_LABELS[j];
///                 for (int i = 0; i < COLS; ++i) {
///                     cout << "\t" << results[j][i].d_average;
///                     cout << "(" << results[j][i].d_max << ")";
///                 }
///                 cout << "\n";
///             }
///         }
///     }
/// @endcode
/// We repeat the same steps with double hashing, except that due to the nature
/// of the collision-resolution mechanism, the tolerance for the average must be
/// slightly increased to 2.5 times the load factor, when the load factor is
/// high.
/// @code
///     {
///         // const int SIZE = 1000003;   // must be a prime number
///         const int SIZE = 10007;     // must be a prime number
///         const int INC  = SIZE / 5; // load factors for every 20% percentile
///         const int COLS = SIZE/INC;
///
///         ExperimentalResult results[3][COLS];
///         bsls::Stopwatch    timer;
///
///         if (verbose) cout << "\nUsing double hashing"
///                           << "\n--------------------" << endl;
///
///         if (verbose) cout << "Sequential Integers\n";
///         timer.start();
///         for (int n = INC/2, i = 0; n < SIZE; n += INC, ++i) {
///             if (veryVerbose)
///                 cout << "\tWith load factor " <<
///                                      static_cast<double>(n) / SIZE << "\n";
///
///             results[0][i] = computeDoubleHashingCollisions(
///                                                      n,
///                                                      SIZE,
///                                                      SequentialIntegers());
///             assert(results[0][i].d_average < 2.5 * n / SIZE);
///         }
///         if (verbose) cout << "\t... in " << timer.elapsedTime() << "\n";
///         timer.reset();
///
///         if (verbose) cout << "Sequential Strings\n";
///         timer.start();
///         for (int n = INC/2, i = 0; n < SIZE; n += INC, ++i) {
///             if (veryVerbose)
///                 cout << "\tWith load factor " <<
///                                      static_cast<double>(n) / SIZE << "\n";
///
///             bsl::string initial("abcdefghij"); // period = 10! = 3628800
///             results[1][i] = computeDoubleHashingCollisions(
///                                                n,
///                                                SIZE,
///                                                SequentialStrings(initial));
///             assert(results[1][i].d_average < 2.5 * n / SIZE);
///         }
///         if (verbose) cout << "\t... in " << timer.elapsedTime() << "\n";
///         timer.reset();
///
///         if (verbose) cout << "Sequential Vector\n";
///         timer.start();
///         for (int n = INC/2, i = 0; n < SIZE; n += INC, ++i) {
///             if (veryVerbose)
///                 cout << "\tWith load factor " <<
///                                      static_cast<double>(n) / SIZE << "\n";
///
///             bsl::vector<char> ranges(7, static_cast<char>(8));
///                                                   // period = 8^7 = 2097152
///             results[2][i] = computeDoubleHashingCollisions(
///                                                  n,
///                                                  SIZE,
///                                                  SequentialVector(ranges));
///             assert(results[2][i].d_average < 2.5 * n / SIZE);
///         }
///         if (verbose) cout << "\t... in " << timer.elapsedTime() << "\n";
///         timer.reset();
///
///         if (verbose) {
///             cout << "\nDisplaying average (max) for double-hashing:";
///             cout << "\n--------------------------------------------\n";
///             const char *ROW_LABELS[] = { "\nIntegers:",
///                                          "\nStrings :",
///                                          "\nVector  :",
///                                          "\nLoad factor:",
///             };
///             const int   NUM_ROWS     = sizeof  ROW_LABELS
///                                      / sizeof *ROW_LABELS -1;
///
///             cout << ROW_LABELS[NUM_ROWS] << bsl::setprecision(2);
///             for (int n = INC/2; n < SIZE; n += INC) {
///                 cout << "\t" << static_cast<double>(n) / SIZE;
///             }
///             for (int j = 0; j < NUM_ROWS; ++j) {
///                 cout << ROW_LABELS[j];
///                 for (int i = 0; i < COLS; ++i) {
///                     cout << "\t" << results[j][i].d_average;
///                     cout << "(" << results[j][i].d_max << ")";
///                 }
///                 cout << "\n";
///             }
///         }
///     }
///
///     return 0;
/// }
/// @endcode
/// The above code produces the following results.  The results for chaining are
/// identical for `hash1` (used in the code above) or `hash2` (code identical
/// except `hash2` is used in place of `hash1` in `computeChainingCollisions`).
/// @code
/// Displaying average(max) for chaining:
/// ---------------------------------------------------------------------------
/// Load factor:    0.2     0.4     0.6     0.8     1       1.2     1.4
/// Integers:       0.2(3)  0.4(5)  0.6(6)  0.8(6)  1(7)    1.2(7)  1.4(8)
/// Strings :       0.2(4)  0.4(4)  0.6(5)  0.8(7)  1(7)    1.2(7)  1.4(7)
/// Vector  :       0.2(5)  0.4(5)  0.6(10) 0.8(10) 1(15)   1.2(15) 1.4(20)
///
/// Load factor:    1.6     1.8     2       2.2     2.4     2.6     2.8
/// Integers:       1.6(9)  1.8(9)  2(10)   2.2(10) 2.4(10) 2.6(10) 2.8(11)
/// Strings :       1.6(7)  1.8(8)  2(9)    2.2(11) 2.4(11) 2.6(11) 2.8(11)
/// Vector  :       1.6(20) 1.8(24) 2(25)   2.2(29) 2.4(30) 2.6(34) 2.8(35)
///
/// Load factor:    3       3.2     3.4     3.6     3.8
/// Integers:       3(11)   3.2(11) 3.4(12) 3.6(12) 3.8(13)
/// Strings :       3(12)   3.2(12) 3.4(13) 3.6(13) 3.8(13)
/// Vector  :       3(39)   3.2(40) 3.4(42) 3.6(45) 3.8(46)
///
/// Displaying average(max) for double-hashing:
/// ---------------------------------------------------------------------------
/// Load factor:    0.1      0.3     0.5      0.7      0.9
/// Integers:       0.046(2) 0.20(4) 0.37(10) 0.71(15) 1.6(59)
/// Strings :       0.064(2) 0.20(6) 0.40(12) 0.75(18) 1.6(50)
/// Vector  :       0.05(2)  0.19(5) 0.58(9)  1.20(15) 2.4(64)
/// @endcode
/// @}
/** @} */
/** @} */
 
/** @addtogroup bdl
 * @{
 */
/** @addtogroup bdlb
 * @{
 */
/** @addtogroup bdlb_hashutil
 * @{
 */
 
#include <bdlscm_version.h>
 
#include <bsls_assert.h>
#include <bsls_review.h>
#include <bsls_types.h>
 
 
namespace bdlb {
                              // ===============
                              // struct HashUtil
                              // ===============
 
/// This `struct` provides a namespace for hash functions.
struct HashUtil {
 
    // CLASS METHODS
 
    static unsigned int hash0(char                 key, int modulus);
    static unsigned int hash0(signed char          key, int modulus);
    static unsigned int hash0(unsigned char        key, int modulus);
    static unsigned int hash0(short                key, int modulus);
    static unsigned int hash0(unsigned short       key, int modulus);
    static unsigned int hash0(int                  key, int modulus);
    static unsigned int hash0(unsigned int         key, int modulus);
    static unsigned int hash0(long                 key, int modulus);
    static unsigned int hash0(unsigned long        key, int modulus);
    static unsigned int hash0(bsls::Types::Int64   key, int modulus);
    static unsigned int hash0(bsls::Types::Uint64  key, int modulus);
    static unsigned int hash0(float                key, int modulus);
    static unsigned int hash0(double               key, int modulus);
    /// Return an unsigned integer hash value in the range from zero to one
    /// less than the specified `modulus` corresponding to the specified
    /// `key`.  The behavior is undefined unless `0 < modulus < 2^31`.  Note
    /// that `modulus` is expected to be a prime not close to an integral
    /// power of 2.  Also note that specifying a `modulus` of 1 will cause 0
    /// to be returned for every `value`.
    static unsigned int hash0(const void          *key, int modulus);
 
    /// Return a pseudo-random unsigned integer in the range from zero to
    /// one less than the specified `modulus` corresponding to the specified
    /// null-terminated `string`.  The behavior is undefined unless
    /// `0 < modulus < 2^31`.  Note that `modulus` is expected to be a prime
    /// not close to an integral power of 2.  Also note that specifying a
    /// `modulus` of 1 will cause 0 to be returned for every `string`.
    static unsigned int hash0(const char *string, int modulus);
 
    static unsigned int hash0(const char *string,
                              int         stringLength,
                              int         modulus);
    /// Return a pseudo-random unsigned integer in the range from zero to
    /// one less than the specified `modulus` corresponding to the specified
    /// `string` having the specified `stringLength`.  `string` need not be
    /// null-terminated and may contain embedded null characters.  The
    /// behavior is undefined unless `0 <= stringLength` and
    /// `0 < modulus < 2^31`.  Note that `modulus` is expected to be a prime
    /// not close to an integral power of 2.  Also note that specifying a
    /// `modulus` of 1 will cause 0 to be returned for every `string`.
 
    static unsigned int hash1(const char *data, int length);
 
    /// Return an unsigned integer hash value corresponding to the specified
    /// `data` of the specified `length` (in bytes).  The behavior is
    /// undefined unless `0 <= length`.  Note that if `data` is 0, then
    /// `length` also must be 0.  Also note that every byte in `data` is
    /// significant; that is, it is not appropriate to cast a `struct`
    /// address to a `char *` unless the `struct` is packed (no padding).
    ///
    /// Both `hash1` and `hash2` return a hash, but both hashes can be
    /// assumed to be independent (i.e., there are no known correlations
    /// between the results of the two hash functions given the same input
    /// data).
    static unsigned int hash2(const char *data, int length);
 
    static unsigned int hash1(char                 key);
    static unsigned int hash1(signed char          key);
    static unsigned int hash1(unsigned char        key);
    static unsigned int hash1(short                key);
    static unsigned int hash1(unsigned short       key);
    static unsigned int hash1(int                  key);
    static unsigned int hash1(unsigned int         key);
    static unsigned int hash1(long                 key);
    static unsigned int hash1(unsigned long        key);
    static unsigned int hash1(bsls::Types::Int64   key);
    static unsigned int hash1(bsls::Types::Uint64  key);
    static unsigned int hash1(float                key);
    static unsigned int hash1(double               key);
    /// Return an unsigned integer hash value corresponding to the specified
    /// `key`.  Note that the return value is seemingly random (i.e., the
    /// hash is good) but identical on all platforms (irrespective of
    /// endianness).  Both functions `hash1` and `hash2` return a hash, but
    /// both hashes can be assumed to be independent (i.e., there are no
    /// known correlations between the results of both hash functions given
    /// the same input data).
    static unsigned int hash1(const void          *key);
 
    static unsigned int hash2(char                 key);
    static unsigned int hash2(signed char          key);
    static unsigned int hash2(unsigned char        key);
    static unsigned int hash2(short                key);
    static unsigned int hash2(unsigned short       key);
    static unsigned int hash2(int                  key);
    static unsigned int hash2(unsigned int         key);
    static unsigned int hash2(long                 key);
    static unsigned int hash2(unsigned long        key);
    static unsigned int hash2(bsls::Types::Int64   key);
    static unsigned int hash2(bsls::Types::Uint64  key);
    static unsigned int hash2(float                key);
    static unsigned int hash2(double               key);
    /// Return an unsigned integer hash value corresponding to the specified
    /// `key`.  Note that the return value is seemingly random (i.e., the
    /// hash is good) but identical on all platforms (irrespective of
    /// endianness).  Both functions `hash1` and `hash2` return a hash, but
    /// both hashes can be assumed to be independent (i.e., there are no
    /// known correlations between the results of both hash functions given
    /// the same input data).
    static unsigned int hash2(const void          *key);
};
 
// ============================================================================
//                            INLINE DEFINITIONS
// ============================================================================
 
                              // ---------------
                              // struct HashUtil
                              // ---------------
 
// CLASS METHODS
inline
unsigned int HashUtil::hash0(int key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    if (4 == sizeof(int)) {
        return static_cast<unsigned int>(key)
             % static_cast<unsigned int>(modulus);                    // RETURN
    }
 
    return (static_cast<unsigned int>(key) & 0xFFFFFFFF)
          % static_cast<unsigned int>(modulus);
}
 
inline
unsigned int HashUtil::hash0(bsls::Types::Int64 key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    return ((static_cast<unsigned int>((key >> 32) & 0xFFFFFFFF)
           % static_cast<unsigned int>(modulus))
           ^ static_cast<unsigned int>(key         & 0xFFFFFFFF))
           % static_cast<unsigned int>(modulus);
}
 
inline
unsigned int HashUtil::hash0(char key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    return HashUtil::hash0(static_cast<int>(static_cast<unsigned char>(key)),
                           modulus);
}
 
inline
unsigned int HashUtil::hash0(signed char key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    return HashUtil::hash0(static_cast<int>(static_cast<unsigned char>(key)),
                           modulus);
}
 
inline
unsigned int HashUtil::hash0(unsigned char key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    return HashUtil::hash0(static_cast<int>(key), modulus);
}
 
inline
unsigned int HashUtil::hash0(short key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    return HashUtil::hash0(static_cast<int>(static_cast<unsigned short>(key)),
                           modulus);
}
 
inline
unsigned int HashUtil::hash0(unsigned short key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    return HashUtil::hash0(static_cast<int>(key), modulus);
}
 
inline
unsigned int HashUtil::hash0(unsigned int key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    return HashUtil::hash0(static_cast<int>(key), modulus);
}
 
inline
unsigned int HashUtil::hash0(long key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    if (4 == sizeof(long)) {
        return HashUtil::hash0(
                             static_cast<int>(static_cast<unsigned long>(key)),
                             modulus);                                // RETURN
    }
    else {
        return HashUtil::hash0(
              static_cast<bsls::Types::Int64>(static_cast<unsigned long>(key)),
              modulus);                                               // RETURN
    }
}
 
inline
unsigned int HashUtil::hash0(unsigned long key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    if (4 == sizeof(unsigned long)) {
        return HashUtil::hash0(static_cast<int>(key), modulus);       // RETURN
    }
    else {
        return HashUtil::hash0(static_cast<bsls::Types::Int64>(key), modulus);
                                                                      // RETURN
    }
}
 
inline
unsigned int HashUtil::hash0(bsls::Types::Uint64 key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    return HashUtil::hash0(static_cast<bsls::Types::Int64>(key), modulus);
}
 
inline
unsigned int HashUtil::hash0(double key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    bsls::Types::Int64 *v = reinterpret_cast<bsls::Types::Int64 *>(&key);
    return HashUtil::hash0(*v, modulus);
}
 
inline
unsigned int HashUtil::hash0(float key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    return HashUtil::hash0(static_cast<double>(key), modulus);
}
 
inline
unsigned int HashUtil::hash0(const void *key, int modulus)
{
    BSLS_ASSERT(0 < modulus);
 
    if (4 == sizeof(void *)) {
        const int *v = reinterpret_cast<const int *>(&key);
        return HashUtil::hash0(*v, modulus);                          // RETURN
    }
    else {
        const bsls::Types::Int64 *v = static_cast<const bsls::Types::Int64 *>(
                                              static_cast<const void *>(&key));
        return HashUtil::hash0(*v, modulus);                          // RETURN
    }
}
 
}  // close package namespace
 
 
#endif
 
// ----------------------------------------------------------------------------
// Copyright 2015 Bloomberg Finance L.P.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// ----------------------------- END-OF-FILE ----------------------------------
 
/** @} */
/** @} */
/** @} */