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diff --git a/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/hash_based_containers.html b/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/hash_based_containers.html deleted file mode 100644 index 21d092a76..000000000 --- a/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/hash_based_containers.html +++ /dev/null @@ -1,835 +0,0 @@ -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" - "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - -<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> -<head> - <meta name="generator" content= - "HTML Tidy for Linux/x86 (vers 12 April 2005), see www.w3.org" /> - - <title>Hash-Based Containers</title> - <meta http-equiv="Content-Type" content= - "text/html; charset=us-ascii" /> - </head> - -<body> - <div id="page"> - <h1>Hash Table Design</h1> - - <h2><a name="overview" id="overview">Overview</a></h2> - - <p>The collision-chaining hash-based container has the - following declaration.</p> - <pre> -<b>template</b>< - <b>typename</b> Key, - <b>typename</b> Mapped, - <b>typename</b> Hash_Fn = std::hash<Key>, - <b>typename</b> Eq_Fn = std::equal_to<Key>, - <b>typename</b> Comb_Hash_Fn = <a href= -"direct_mask_range_hashing.html">direct_mask_range_hashing</a><> - <b>typename</b> Resize_Policy = <i>default explained below.</i> - <b>bool</b> Store_Hash = <b>false</b>, - <b>typename</b> Allocator = std::allocator<<b>char</b>> > -<b>class</b> <a href= -"cc_hash_table.html">cc_hash_table</a>; -</pre> - - <p>The parameters have the following meaning:</p> - - <ol> - <li><tt>Key</tt> is the key type.</li> - - <li><tt>Mapped</tt> is the mapped-policy, and is explained in - <a href="tutorial.html#assoc_ms">Tutorial::Associative - Containers::Associative Containers Others than Maps</a>.</li> - - <li><tt>Hash_Fn</tt> is a key hashing functor.</li> - - <li><tt>Eq_Fn</tt> is a key equivalence functor.</li> - - <li><tt>Comb_Hash_Fn</tt> is a <i>range-hashing_functor</i>; - it describes how to translate hash values into positions - within the table. This is described in <a href= - "#hash_policies">Hash Policies</a>.</li> - - <li><tt>Resize_Policy</tt> describes how a container object - should change its internal size. This is described in - <a href="#resize_policies">Resize Policies</a>.</li> - - <li><tt>Store_Hash</tt> indicates whether the hash value - should be stored with each entry. This is described in - <a href="#policy_interaction">Policy Interaction</a>.</li> - - <li><tt>Allocator</tt> is an allocator - type.</li> - </ol> - - <p>The probing hash-based container has the following - declaration.</p> - <pre> -<b>template</b>< - <b>typename</b> Key, - <b>typename</b> Mapped, - <b>typename</b> Hash_Fn = std::hash<Key>, - <b>typename</b> Eq_Fn = std::equal_to<Key>, - <b>typename</b> Comb_Probe_Fn = <a href= -"direct_mask_range_hashing.html">direct_mask_range_hashing</a><> - <b>typename</b> Probe_Fn = <i>default explained below.</i> - <b>typename</b> Resize_Policy = <i>default explained below.</i> - <b>bool</b> Store_Hash = <b>false</b>, - <b>typename</b> Allocator = std::allocator<<b>char</b>> > -<b>class</b> <a href= -"gp_hash_table.html">gp_hash_table</a>; -</pre> - - <p>The parameters are identical to those of the - collision-chaining container, except for the following.</p> - - <ol> - <li><tt>Comb_Probe_Fn</tt> describes how to transform a probe - sequence into a sequence of positions within the table.</li> - - <li><tt>Probe_Fn</tt> describes a probe sequence policy.</li> - </ol> - - <p>Some of the default template values depend on the values of - other parameters, and are explained in <a href= - "#policy_interaction">Policy Interaction</a>.</p> - - <h2><a name="hash_policies" id="hash_policies">Hash - Policies</a></h2> - - <h3><a name="general_terms" id="general_terms">General - Terms</a></h3> - - <p>Following is an explanation of some functions which hashing - involves. Figure <a href= - "#hash_ranged_hash_range_hashing_fns">Hash functions, - ranged-hash functions, and range-hashing functions</a>) - illustrates the discussion.</p> - - <h6 class="c1"><a name="hash_ranged_hash_range_hashing_fns" id= - "hash_ranged_hash_range_hashing_fns"><img src= - "hash_ranged_hash_range_hashing_fns.png" alt= - "no image" /></a></h6> - - <h6 class="c1">Hash functions, ranged-hash functions, and - range-hashing functions.</h6> - - <p>Let <i>U</i> be a domain (<i>e.g.</i>, the integers, or the - strings of 3 characters). A hash-table algorithm needs to map - elements of <i>U</i> "uniformly" into the range <i>[0,..., m - - 1]</i> (where <i>m</i> is a non-negative integral value, and - is, in general, time varying). <i>I.e.</i>, the algorithm needs - a <i>ranged-hash</i> function</p> - - <p><i>f : U × Z<sub>+</sub> → Z<sub>+</sub></i> - ,</p> - - <p>such that for any <i>u</i> in <i>U</i> ,</p> - - <p><i>0 ≤ f(u, m) ≤ m - 1</i> ,</p> - - <p>and which has "good uniformity" properties [<a href= - "references.html#knuth98sorting">knuth98sorting</a>]. One - common solution is to use the composition of the hash - function</p> - - <p><i>h : U → Z<sub>+</sub></i> ,</p> - - <p>which maps elements of <i>U</i> into the non-negative - integrals, and</p> - - <p class="c2">g : Z<sub>+</sub> × Z<sub>+</sub> → - Z<sub>+</sub>,</p> - - <p>which maps a non-negative hash value, and a non-negative - range upper-bound into a non-negative integral in the range - between 0 (inclusive) and the range upper bound (exclusive), - <i>i.e.</i>, for any <i>r</i> in <i>Z<sub>+</sub></i>,</p> - - <p><i>0 ≤ g(r, m) ≤ m - 1</i> .</p> - - <p>The resulting ranged-hash function, is</p> - - <p><i><a name="ranged_hash_composed_of_hash_and_range_hashing" - id="ranged_hash_composed_of_hash_and_range_hashing">f(u , m) = - g(h(u), m)</a></i> (1) .</p> - - <p>From the above, it is obvious that given <i>g</i> and - <i>h</i>, <i>f</i> can always be composed (however the converse - is not true). The STL's hash-based containers allow specifying - a hash function, and use a hard-wired range-hashing function; - the ranged-hash function is implicitly composed.</p> - - <p>The above describes the case where a key is to be mapped - into a <i>single position</i> within a hash table, <i>e.g.</i>, - in a collision-chaining table. In other cases, a key is to be - mapped into a <i>sequence of positions</i> within a table, - <i>e.g.</i>, in a probing table. Similar terms apply in this - case: the table requires a <i>ranged probe</i> function, - mapping a key into a sequence of positions withing the table. - This is typically achieved by composing a <i>hash function</i> - mapping the key into a non-negative integral type, a - <i>probe</i> function transforming the hash value into a - sequence of hash values, and a <i>range-hashing</i> function - transforming the sequence of hash values into a sequence of - positions.</p> - - <h3><a name="range_hashing_fns" id= - "range_hashing_fns">Range-Hashing Functions</a></h3> - - <p>Some common choices for range-hashing functions are the - division, multiplication, and middle-square methods [<a href= - "references.html#knuth98sorting">knuth98sorting</a>], defined - as</p> - - <p><i><a name="division_method" id="division_method">g(r, m) = - r mod m</a></i> (2) ,</p> - - <p><i>g(r, m) = ⌈ u/v ( a r mod v ) ⌉</i> ,</p> - - <p>and</p> - - <p><i>g(r, m) = ⌈ u/v ( r<sup>2</sup> mod v ) ⌉</i> - ,</p> - - <p>respectively, for some positive integrals <i>u</i> and - <i>v</i> (typically powers of 2), and some <i>a</i>. Each of - these range-hashing functions works best for some different - setting.</p> - - <p>The division method <a href="#division_method">(2)</a> is a - very common choice. However, even this single method can be - implemented in two very different ways. It is possible to - implement <a href="#division_method">(2)</a> using the low - level <i>%</i> (modulo) operation (for any <i>m</i>), or the - low level <i>&</i> (bit-mask) operation (for the case where - <i>m</i> is a power of 2), <i>i.e.</i>,</p> - - <p><i><a name="division_method_prime_mod" id= - "division_method_prime_mod">g(r, m) = r % m</a></i> (3) ,</p> - - <p>and</p> - - <p><i><a name="division_method_bit_mask" id= - "division_method_bit_mask">g(r, m) = r & m - 1, (m = - 2<sup>k</sup>)</a></i> for some <i>k)</i> (4),</p> - - <p>respectively.</p> - - <p>The <i>%</i> (modulo) implementation <a href= - "#division_method_prime_mod">(3)</a> has the advantage that for - <i>m</i> a prime far from a power of 2, <i>g(r, m)</i> is - affected by all the bits of <i>r</i> (minimizing the chance of - collision). It has the disadvantage of using the costly modulo - operation. This method is hard-wired into SGI's implementation - [<a href="references.html#sgi_stl">sgi_stl</a>].</p> - - <p>The <i>&</i> (bit-mask) implementation <a href= - "#division_method_bit_mask">(4)</a> has the advantage of - relying on the fast bit-wise and operation. It has the - disadvantage that for <i>g(r, m)</i> is affected only by the - low order bits of <i>r</i>. This method is hard-wired into - Dinkumware's implementation [<a href= - "references.html#dinkumware_stl">dinkumware_stl</a>].</p> - - <h3><a name="hash_policies_ranged_hash_policies" id= - "hash_policies_ranged_hash_policies">Ranged-Hash - Functions</a></h3> - - <p>In cases it is beneficial to allow the - client to directly specify a ranged-hash hash function. It is - true, that the writer of the ranged-hash function cannot rely - on the values of <i>m</i> having specific numerical properties - suitable for hashing (in the sense used in [<a href= - "references.html#knuth98sorting">knuth98sorting</a>]), since - the values of <i>m</i> are determined by a resize policy with - possibly orthogonal considerations.</p> - - <p>There are two cases where a ranged-hash function can be - superior. The firs is when using perfect hashing [<a href= - "references.html#knuth98sorting">knuth98sorting</a>]; the - second is when the values of <i>m</i> can be used to estimate - the "general" number of distinct values required. This is - described in the following.</p> - - <p>Let</p> - - <p class="c2">s = [ s<sub>0</sub>,..., s<sub>t - 1</sub>]</p> - - <p>be a string of <i>t</i> characters, each of which is from - domain <i>S</i>. Consider the following ranged-hash - function:</p> - - <p><a name="total_string_dna_hash" id= - "total_string_dna_hash"><i>f<sub>1</sub>(s, m) = ∑ <sub>i = - 0</sub><sup>t - 1</sup> s<sub>i</sub> a<sup>i</sup></i> mod - <i>m</i></a> (5) ,</p> - - <p>where <i>a</i> is some non-negative integral value. This is - the standard string-hashing function used in SGI's - implementation (with <i>a = 5</i>) [<a href= - "references.html#sgi_stl">sgi_stl</a>]. Its advantage is that - it takes into account all of the characters of the string.</p> - - <p>Now assume that <i>s</i> is the string representation of a - of a long DNA sequence (and so <i>S = {'A', 'C', 'G', - 'T'}</i>). In this case, scanning the entire string might be - prohibitively expensive. A possible alternative might be to use - only the first <i>k</i> characters of the string, where</p> - - <p>|S|<sup>k</sup> ≥ m ,</p> - - <p><i>i.e.</i>, using the hash function</p> - - <p><a name="only_k_string_dna_hash" id= - "only_k_string_dna_hash"><i>f<sub>2</sub>(s, m) = ∑ <sub>i - = 0</sub><sup>k - 1</sup> s<sub>i</sub> a<sup>i</sup></i> mod - <i>m</i></a> , (6)</p> - - <p>requiring scanning over only</p> - - <p><i>k =</i> log<i><sub>4</sub>( m )</i></p> - - <p>characters.</p> - - <p>Other more elaborate hash-functions might scan <i>k</i> - characters starting at a random position (determined at each - resize), or scanning <i>k</i> random positions (determined at - each resize), <i>i.e.</i>, using</p> - - <p><i>f<sub>3</sub>(s, m) = ∑ <sub>i = - r</sub>0</i><sup>r<sub>0</sub> + k - 1</sup> s<sub>i</sub> - a<sup>i</sup> mod <i>m</i> ,</p> - - <p>or</p> - - <p><i>f<sub>4</sub>(s, m) = ∑ <sub>i = 0</sub><sup>k - - 1</sup> s<sub>r</sub>i</i> a<sup>r<sub>i</sub></sup> mod - <i>m</i> ,</p> - - <p>respectively, for <i>r<sub>0</sub>,..., r<sub>k-1</sub></i> - each in the (inclusive) range <i>[0,...,t-1]</i>.</p> - - <p>It should be noted that the above functions cannot be - decomposed as <a href= - "#ranged_hash_composed_of_hash_and_range_hashing">(1)</a> .</p> - - <h3><a name="pb_ds_imp" id="pb_ds_imp">Implementation</a></h3> - - <p>This sub-subsection describes the implementation of the - above in <tt>pb_ds</tt>. It first explains range-hashing - functions in collision-chaining tables, then ranged-hash - functions in collision-chaining tables, then probing-based - tables, and, finally, lists the relevant classes in - <tt>pb_ds</tt>.</p> - - <h4>Range-Hashing and Ranged-Hashes in Collision-Chaining - Tables</h4> - - <p><a href= - "cc_hash_table.html"><tt>cc_hash_table</tt></a> is - parametrized by <tt>Hash_Fn</tt> and <tt>Comb_Hash_Fn</tt>, a - hash functor and a combining hash functor, respectively.</p> - - <p>In general, <tt>Comb_Hash_Fn</tt> is considered a - range-hashing functor. <a href= - "cc_hash_table.html"><tt>cc_hash_table</tt></a> - synthesizes a ranged-hash function from <tt>Hash_Fn</tt> and - <tt>Comb_Hash_Fn</tt> (see <a href= - "#ranged_hash_composed_of_hash_and_range_hashing">(1)</a> - above). Figure <a href="#hash_range_hashing_seq_diagram">Insert - hash sequence diagram</a> shows an <tt>insert</tt> sequence - diagram for this case. The user inserts an element (point A), - the container transforms the key into a non-negative integral - using the hash functor (points B and C), and transforms the - result into a position using the combining functor (points D - and E).</p> - - <h6 class="c1"><a name="hash_range_hashing_seq_diagram" id= - "hash_range_hashing_seq_diagram"><img src= - "hash_range_hashing_seq_diagram.png" alt="no image" /></a></h6> - - <h6 class="c1">Insert hash sequence diagram.</h6> - - <p>If <a href= - "cc_hash_table.html"><tt>cc_hash_table</tt></a>'s - hash-functor, <tt>Hash_Fn</tt> is instantiated by <a href= - "null_hash_fn.html"><tt>null_hash_fn</tt></a> (see <a href= - "concepts.html#concepts_null_policies">Interface::Concepts::Null - Policy Classes</a>), then <tt>Comb_Hash_Fn</tt> is taken to be - a ranged-hash function. Figure <a href= - "#hash_range_hashing_seq_diagram2">Insert hash sequence diagram - with a null hash policy</a> shows an <tt>insert</tt> sequence - diagram. The user inserts an element (point A), the container - transforms the key into a position using the combining functor - (points B and C).</p> - - <h6 class="c1"><a name="hash_range_hashing_seq_diagram2" id= - "hash_range_hashing_seq_diagram2"><img src= - "hash_range_hashing_seq_diagram2.png" alt= - "no image" /></a></h6> - - <h6 class="c1">Insert hash sequence diagram with a null hash - policy.</h6> - - <h4>Probing Tables</h4> - - <p><a href= - "gp_hash_table.html"></a><tt>gp_hash_table</tt> is - parametrized by <tt>Hash_Fn</tt>, <tt>Probe_Fn</tt>, and - <tt>Comb_Probe_Fn</tt>. As before, if <tt>Hash_Fn</tt> and - <tt>Probe_Fn</tt> are, respectively, <a href= - "null_hash_fn.html"><tt>null_hash_fn</tt></a> and <a href= - "null_probe_fn.html"><tt>null_probe_fn</tt></a>, then - <tt>Comb_Probe_Fn</tt> is a ranged-probe functor. Otherwise, - <tt>Hash_Fn</tt> is a hash functor, <tt>Probe_Fn</tt> is a - functor for offsets from a hash value, and - <tt>Comb_Probe_Fn</tt> transforms a probe sequence into a - sequence of positions within the table.</p> - - <h4>Pre-Defined Policies</h4> - - <p><tt>pb_ds</tt> contains some pre-defined classes - implementing range-hashing and probing functions:</p> - - <ol> - <li><a href= - "direct_mask_range_hashing.html"><tt>direct_mask_range_hashing</tt></a> - and <a href= - "direct_mod_range_hashing.html"><tt>direct_mod_range_hashing</tt></a> - are range-hashing functions based on a bit-mask and a modulo - operation, respectively.</li> - - <li><a href= - "linear_probe_fn.html"><tt>linear_probe_fn</tt></a>, and - <a href= - "quadratic_probe_fn.html"><tt>quadratic_probe_fn</tt></a> are - a linear probe and a quadratic probe function, - respectively.</li> - </ol>Figure <a href="#hash_policy_cd">Hash policy class - diagram</a> shows a class diagram. - - <h6 class="c1"><a name="hash_policy_cd" id= - "hash_policy_cd"><img src="hash_policy_cd.png" alt= - "no image" /></a></h6> - - <h6 class="c1">Hash policy class diagram.</h6> - - <h2><a name="resize_policies" id="resize_policies">Resize - Policies</a></h2> - - <h3><a name="general" id="general">General Terms</a></h3> - - <p>Hash-tables, as opposed to trees, do not naturally grow or - shrink. It is necessary to specify policies to determine how - and when a hash table should change its size. Usually, resize - policies can be decomposed into orthogonal policies:</p> - - <ol> - <li>A <i>size policy</i> indicating <i>how</i> a hash table - should grow (<i>e.g.,</i> it should multiply by powers of - 2).</li> - - <li>A <i>trigger policy</i> indicating <i>when</i> a hash - table should grow (<i>e.g.,</i> a load factor is - exceeded).</li> - </ol> - - <h3><a name="size_policies" id="size_policies">Size - Policies</a></h3> - - <p>Size policies determine how a hash table changes size. These - policies are simple, and there are relatively few sensible - options. An exponential-size policy (with the initial size and - growth factors both powers of 2) works well with a mask-based - range-hashing function (see <a href= - "#hash_policies">Range-Hashing Policies</a>), and is the - hard-wired policy used by Dinkumware [<a href= - "references.html#dinkumware_stl">dinkumware_stl</a>]. A - prime-list based policy works well with a modulo-prime range - hashing function (see <a href="#hash_policies">Range-Hashing - Policies</a>), and is the hard-wired policy used by SGI's - implementation [<a href= - "references.html#sgi_stl">sgi_stl</a>].</p> - - <h3><a name="trigger_policies" id="trigger_policies">Trigger - Policies</a></h3> - - <p>Trigger policies determine when a hash table changes size. - Following is a description of two policies: <i>load-check</i> - policies, and collision-check policies.</p> - - <p>Load-check policies are straightforward. The user specifies - two factors, <i>α<sub>min</sub></i> and - <i>α<sub>max</sub></i>, and the hash table maintains the - invariant that</p> - - <p><i><a name="load_factor_min_max" id= - "load_factor_min_max">α<sub>min</sub> ≤ (number of - stored elements) / (hash-table size) ≤ - α<sub>max</sub></a></i> (1) .</p> - - <p>Collision-check policies work in the opposite direction of - load-check policies. They focus on keeping the number of - collisions moderate and hoping that the size of the table will - not grow very large, instead of keeping a moderate load-factor - and hoping that the number of collisions will be small. A - maximal collision-check policy resizes when the longest - probe-sequence grows too large.</p> - - <p>Consider Figure <a href="#balls_and_bins">Balls and - bins</a>. Let the size of the hash table be denoted by - <i>m</i>, the length of a probe sequence be denoted by - <i>k</i>, and some load factor be denoted by α. We would - like to calculate the minimal length of <i>k</i>, such that if - there were <i>α m</i> elements in the hash table, a probe - sequence of length <i>k</i> would be found with probability at - most <i>1/m</i>.</p> - - <h6 class="c1"><a name="balls_and_bins" id= - "balls_and_bins"><img src="balls_and_bins.png" alt= - "no image" /></a></h6> - - <h6 class="c1">Balls and bins.</h6> - - <p>Denote the probability that a probe sequence of length - <i>k</i> appears in bin <i>i</i> by <i>p<sub>i</sub></i>, the - length of the probe sequence of bin <i>i</i> by - <i>l<sub>i</sub></i>, and assume uniform distribution. Then</p> - - <p><a name="prob_of_p1" id= - "prob_of_p1"><i>p<sub>1</sub></i></a> = (3)</p> - - <p class="c2"><b>P</b>(l<sub>1</sub> ≥ k) =</p> - - <p><i><b>P</b>(l<sub>1</sub> ≥ α ( 1 + k / α - 1 - ) ≤</i> (a)</p> - - <p><i>e ^ ( - ( α ( k / α - 1 )<sup>2</sup> ) /2 - )</i> ,</p> - - <p>where (a) follows from the Chernoff bound [<a href= - "references.html#motwani95random">motwani95random</a>]. To - calculate the probability that <i>some</i> bin contains a probe - sequence greater than <i>k</i>, we note that the - <i>l<sub>i</sub></i> are negatively-dependent [<a href= - "references.html#dubhashi98neg">dubhashi98neg</a>]. Let - <i><b>I</b>(.)</i> denote the indicator function. Then</p> - - <p><a name="at_least_k_i_n_some_bin" id= - "at_least_k_i_n_some_bin"><i><b>P</b>( exists<sub>i</sub> - l<sub>i</sub> ≥ k ) =</i> (3)</a></p> - - <p class="c2"><b>P</b> ( ∑ <sub>i = 1</sub><sup>m</sup> - <b>I</b>(l<sub>i</sub> ≥ k) ≥ 1 ) =</p> - - <p><i><b>P</b> ( ∑ <sub>i = 1</sub><sup>m</sup> <b>I</b> ( - l<sub>i</sub> ≥ k ) ≥ m p<sub>1</sub> ( 1 + 1 / (m - p<sub>1</sub>) - 1 ) ) ≤</i> (a)</p> - - <p class="c2">e ^ ( ( - m p<sub>1</sub> ( 1 / (m p<sub>1</sub>) - - 1 ) <sup>2</sup> ) / 2 ) ,</p> - - <p>where (a) follows from the fact that the Chernoff bound can - be applied to negatively-dependent variables [<a href= - "references.html#dubhashi98neg">dubhashi98neg</a>]. Inserting - <a href="#prob_of_p1">(2)</a> into <a href= - "#at_least_k_i_n_some_bin">(3)</a>, and equating with - <i>1/m</i>, we obtain</p> - - <p><i>k ~ √ ( 2 α</i> ln <i>2 m</i> ln<i>(m) ) - )</i> .</p> - - <h3><a name="imp_pb_ds" id="imp_pb_ds">Implementation</a></h3> - - <p>This sub-subsection describes the implementation of the - above in <tt>pb_ds</tt>. It first describes resize policies and - their decomposition into trigger and size policies, then - describes pre-defined classes, and finally discusses controlled - access the policies' internals.</p> - - <h4>Resize Policies and Their Decomposition</h4> - - <p>Each hash-based container is parametrized by a - <tt>Resize_Policy</tt> parameter; the container derives - <tt><b>public</b></tt>ly from <tt>Resize_Policy</tt>. For - example:</p> - <pre> -<a href="cc_hash_table.html">cc_hash_table</a>< - <b>typename</b> Key, - <b>typename</b> Mapped, - ... - <b>typename</b> Resize_Policy - ...> : - <b>public</b> Resize_Policy -</pre> - - <p>As a container object is modified, it continuously notifies - its <tt>Resize_Policy</tt> base of internal changes - (<i>e.g.</i>, collisions encountered and elements being - inserted). It queries its <tt>Resize_Policy</tt> base whether - it needs to be resized, and if so, to what size.</p> - - <p>Figure <a href="#insert_resize_sequence_diagram1">Insert - resize sequence diagram</a> shows a (possible) sequence diagram - of an insert operation. The user inserts an element; the hash - table notifies its resize policy that a search has started - (point A); in this case, a single collision is encountered - - the table notifies its resize policy of this (point B); the - container finally notifies its resize policy that the search - has ended (point C); it then queries its resize policy whether - a resize is needed, and if so, what is the new size (points D - to G); following the resize, it notifies the policy that a - resize has completed (point H); finally, the element is - inserted, and the policy notified (point I).</p> - - <h6 class="c1"><a name="insert_resize_sequence_diagram1" id= - "insert_resize_sequence_diagram1"><img src= - "insert_resize_sequence_diagram1.png" alt= - "no image" /></a></h6> - - <h6 class="c1">Insert resize sequence diagram.</h6> - - <p>In practice, a resize policy can be usually orthogonally - decomposed to a size policy and a trigger policy. Consequently, - the library contains a single class for instantiating a resize - policy: <a href= - "hash_standard_resize_policy.html"><tt>hash_standard_resize_policy</tt></a> - is parametrized by <tt>Size_Policy</tt> and - <tt>Trigger_Policy</tt>, derives <tt><b>public</b></tt>ly from - both, and acts as a standard delegate [<a href= - "references.html#gamma95designpatterns">gamma95designpatterns</a>] - to these policies.</p> - - <p>Figures <a href="#insert_resize_sequence_diagram2">Standard - resize policy trigger sequence diagram</a> and <a href= - "#insert_resize_sequence_diagram3">Standard resize policy size - sequence diagram</a> show sequence diagrams illustrating the - interaction between the standard resize policy and its trigger - and size policies, respectively.</p> - - <h6 class="c1"><a name="insert_resize_sequence_diagram2" id= - "insert_resize_sequence_diagram2"><img src= - "insert_resize_sequence_diagram2.png" alt= - "no image" /></a></h6> - - <h6 class="c1">Standard resize policy trigger sequence - diagram.</h6> - - <h6 class="c1"><a name="insert_resize_sequence_diagram3" id= - "insert_resize_sequence_diagram3"><img src= - "insert_resize_sequence_diagram3.png" alt= - "no image" /></a></h6> - - <h6 class="c1">Standard resize policy size sequence - diagram.</h6> - - <h4>Pre-Defined Policies</h4> - - <p>The library includes the following - instantiations of size and trigger policies:</p> - - <ol> - <li><a href= - "hash_load_check_resize_trigger.html"><tt>hash_load_check_resize_trigger</tt></a> - implements a load check trigger policy.</li> - - <li><a href= - "cc_hash_max_collision_check_resize_trigger.html"><tt>cc_hash_max_collision_check_resize_trigger</tt></a> - implements a collision check trigger policy.</li> - - <li><a href= - "hash_exponential_size_policy.html"><tt>hash_exponential_size_policy</tt></a> - implements an exponential-size policy (which should be used - with mask range hashing).</li> - - <li><a href= - "hash_prime_size_policy.html"><tt>hash_prime_size_policy</tt></a> - implementing a size policy based on a sequence of primes - [<a href="references.html#sgi_stl">sgi_stl</a>] (which should - be used with mod range hashing</li> - </ol> - - <p>Figure <a href="#resize_policy_cd">Resize policy class - diagram</a> gives an overall picture of the resize-related - classes. <a href= - "basic_hash_table.html"><tt>basic_hash_table</tt></a> - is parametrized by <tt>Resize_Policy</tt>, which it subclasses - publicly. This class is currently instantiated only by <a href= - "hash_standard_resize_policy.html"><tt>hash_standard_resize_policy</tt></a>. - <a href= - "hash_standard_resize_policy.html"><tt>hash_standard_resize_policy</tt></a> - itself is parametrized by <tt>Trigger_Policy</tt> and - <tt>Size_Policy</tt>. Currently, <tt>Trigger_Policy</tt> is - instantiated by <a href= - "hash_load_check_resize_trigger.html"><tt>hash_load_check_resize_trigger</tt></a>, - or <a href= - "cc_hash_max_collision_check_resize_trigger.html"><tt>cc_hash_max_collision_check_resize_trigger</tt></a>; - <tt>Size_Policy</tt> is instantiated by <a href= - "hash_exponential_size_policy.html"><tt>hash_exponential_size_policy</tt></a>, - or <a href= - "hash_prime_size_policy.html"><tt>hash_prime_size_policy</tt></a>.</p> - - <h6 class="c1"><a name="resize_policy_cd" id= - "resize_policy_cd"><img src="resize_policy_cd.png" alt= - "no image" /></a></h6> - - <h6 class="c1">Resize policy class diagram.</h6> - - <h4>Controlled Access to Policies' Internals</h4> - - <p>There are cases where (controlled) access to resize - policies' internals is beneficial. <i>E.g.</i>, it is sometimes - useful to query a hash-table for the table's actual size (as - opposed to its <tt>size()</tt> - the number of values it - currently holds); it is sometimes useful to set a table's - initial size, externally resize it, or change load factors.</p> - - <p>Clearly, supporting such methods both decreases the - encapsulation of hash-based containers, and increases the - diversity between different associative-containers' interfaces. - Conversely, omitting such methods can decrease containers' - flexibility.</p> - - <p>In order to avoid, to the extent possible, the above - conflict, the hash-based containers themselves do not address - any of these questions; this is deferred to the resize policies, - which are easier to change or replace. Thus, for example, - neither <a href= - "cc_hash_table.html"><tt>cc_hash_table</tt></a> nor - <a href= - "gp_hash_table.html"><tt>gp_hash_table</tt></a> - contain methods for querying the actual size of the table; this - is deferred to <a href= - "hash_standard_resize_policy.html"><tt>hash_standard_resize_policy</tt></a>.</p> - - <p>Furthermore, the policies themselves are parametrized by - template arguments that determine the methods they support - ([<a href= - "references.html#alexandrescu01modern">alexandrescu01modern</a>] - shows techniques for doing so). <a href= - "hash_standard_resize_policy.html"><tt>hash_standard_resize_policy</tt></a> - is parametrized by <tt>External_Size_Access</tt> that - determines whether it supports methods for querying the actual - size of the table or resizing it. <a href= - "hash_load_check_resize_trigger.html"><tt>hash_load_check_resize_trigger</tt></a> - is parametrized by <tt>External_Load_Access</tt> that - determines whether it supports methods for querying or - modifying the loads. <a href= - "cc_hash_max_collision_check_resize_trigger.html"><tt>cc_hash_max_collision_check_resize_trigger</tt></a> - is parametrized by <tt>External_Load_Access</tt> that - determines whether it supports methods for querying the - load.</p> - - <p>Some operations, for example, resizing a container at - run time, or changing the load factors of a load-check trigger - policy, require the container itself to resize. As mentioned - above, the hash-based containers themselves do not contain - these types of methods, only their resize policies. - Consequently, there must be some mechanism for a resize policy - to manipulate the hash-based container. As the hash-based - container is a subclass of the resize policy, this is done - through virtual methods. Each hash-based container has a - <tt><b>private</b></tt> <tt><b>virtual</b></tt> method:</p> - <pre> -<b>virtual void</b> - do_resize - (size_type new_size); -</pre> - - <p>which resizes the container. Implementations of - <tt>Resize_Policy</tt> can export public methods for resizing - the container externally; these methods internally call - <tt>do_resize</tt> to resize the table.</p> - - <h2><a name="policy_interaction" id="policy_interaction">Policy - Interaction</a></h2> - - <p>Hash-tables are unfortunately especially susceptible to - choice of policies. One of the more complicated aspects of this - is that poor combinations of good policies can form a poor - container. Following are some considerations.</p> - - <h3><a name="policy_interaction_probe_size_trigger" id= - "policy_interaction_probe_size_trigger">Probe Policies, Size - Policies, and Trigger Policies</a></h3> - - <p>Some combinations do not work well for probing containers. - For example, combining a quadratic probe policy with an - exponential size policy can yield a poor container: when an - element is inserted, a trigger policy might decide that there - is no need to resize, as the table still contains unused - entries; the probe sequence, however, might never reach any of - the unused entries.</p> - - <p>Unfortunately, <tt>pb_ds</tt> cannot detect such problems at - compilation (they are halting reducible). It therefore defines - an exception class <a href= - "insert_error.html"><tt>insert_error</tt></a> to throw an - exception in this case.</p> - - <h3><a name="policy_interaction_hash_trigger" id= - "policy_interaction_hash_trigger">Hash Policies and Trigger - Policies</a></h3> - - <p>Some trigger policies are especially susceptible to poor - hash functions. Suppose, as an extreme case, that the hash - function transforms each key to the same hash value. After some - inserts, a collision detecting policy will always indicate that - the container needs to grow.</p> - - <p>The library, therefore, by design, limits each operation to - one resize. For each <tt>insert</tt>, for example, it queries - only once whether a resize is needed.</p> - - <h3><a name="policy_interaction_eq_sth_hash" id= - "policy_interaction_eq_sth_hash">Equivalence Functors, Storing - Hash Values, and Hash Functions</a></h3> - - <p><a href= - "cc_hash_table.html"><tt>cc_hash_table</tt></a> and - <a href= - "gp_hash_table.html"><tt>gp_hash_table</tt></a> are - parametrized by an equivalence functor and by a - <tt>Store_Hash</tt> parameter. If the latter parameter is - <tt><b>true</b></tt>, then the container stores with each entry - a hash value, and uses this value in case of collisions to - determine whether to apply a hash value. This can lower the - cost of collision for some types, but increase the cost of - collisions for other types.</p> - - <p>If a ranged-hash function or ranged probe function is - directly supplied, however, then it makes no sense to store the - hash value with each entry. <tt>pb_ds</tt>'s container will - fail at compilation, by design, if this is attempted.</p> - - <h3><a name="policy_interaction_size_load_check" id= - "policy_interaction_size_load_check">Size Policies and - Load-Check Trigger Policies</a></h3> - - <p>Assume a size policy issues an increasing sequence of sizes - <i>a, a q, a q<sup>1</sup>, a q<sup>2</sup>, ...</i> For - example, an exponential size policy might issue the sequence of - sizes <i>8, 16, 32, 64, ...</i></p> - - <p>If a load-check trigger policy is used, with loads - <i>α<sub>min</sub></i> and <i>α<sub>max</sub></i>, - respectively, then it is a good idea to have:</p> - - <ol> - <li><i>α<sub>max</sub> ~ 1 / q</i></li> - - <li><i>α<sub>min</sub> < 1 / (2 q)</i></li> - </ol> - - <p>This will ensure that the amortized hash cost of each - modifying operation is at most approximately 3.</p> - - <p><i>α<sub>min</sub> ~ α<sub>max</sub></i> is, in - any case, a bad choice, and <i>α<sub>min</sub> > - α<sub>max</sub></i> is horrendous.</p> - </div> -</body> -</html> |