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diff --git a/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/assoc_performance_tests.html b/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/assoc_performance_tests.html new file mode 100644 index 000000000..642f84809 --- /dev/null +++ b/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/assoc_performance_tests.html @@ -0,0 +1,345 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" + "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.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>Associative-Container Performance Tests</title> +<meta http-equiv="Content-Type" content="text/html; charset=us-ascii" /> +</head> +<body> +<div id="page"> +<h1><a name="assoc" id="assoc">Associative-Container + Performance Tests</a></h1> +<h2><a name="settings" id="settings">Settings</a></h2> +<p>This section describes performance tests and their results. + In the following, <a href="#gcc"><u>g++</u></a>, <a href="#msvc"><u>msvc++</u></a>, and <a href="#local"><u>local</u></a> (the build used for generating this + documentation) stand for three different builds:</p> +<div id="gcc_settings_div"> +<div class="c1"> +<h3><a name="gcc" id="gcc"><u>g++</u></a></h3> +<ul> +<li>CPU speed - cpu MHz : 2660.644</li> +<li>Memory - MemTotal: 484412 kB</li> +<li>Platform - + Linux-2.6.12-9-386-i686-with-debian-testing-unstable</li> +<li>Compiler - g++ (GCC) 4.0.2 20050808 (prerelease) + (Ubuntu 4.0.1-4ubuntu9) Copyright (C) 2005 Free Software + Foundation, Inc. This is free software; see the source + for copying conditions. There is NO warranty; not even + for MERCHANTABILITY or FITNESS FOR A PARTICULAR + PURPOSE.</li> +</ul> +</div> +<div class="c2"></div> +</div> +<div id="msvc_settings_div"> +<div class="c1"> +<h3><a name="msvc" id="msvc"><u>msvc++</u></a></h3> +<ul> +<li>CPU speed - cpu MHz : 2660.554</li> +<li>Memory - MemTotal: 484412 kB</li> +<li>Platform - Windows XP Pro</li> +<li>Compiler - Microsoft (R) 32-bit C/C++ Optimizing + Compiler Version 13.10.3077 for 80x86 Copyright (C) + Microsoft Corporation 1984-2002. All rights + reserved.</li> +</ul> +</div> +<div class="c2"></div> +</div> +<div id="local_settings_div"><div style = "border-style: dotted; border-width: 1px; border-color: lightgray"><h3><a name = "local"><u>local</u></a></h3><ul> +<li>CPU speed - cpu MHz : 2250.000</li> +<li>Memory - MemTotal: 2076248 kB</li> +<li>Platform - Linux-2.6.16-1.2133_FC5-i686-with-redhat-5-Bordeaux</li> +<li>Compiler - g++ (GCC) 4.1.1 20060525 (Red Hat 4.1.1-1) +Copyright (C) 2006 Free Software Foundation, Inc. +This is free software; see the source for copying conditions. There is NO +warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +</li> +</ul> +</div><div style = "width: 100%; height: 20px"></div></div> +<h2><a name="assoc_tests" id="assoc_tests">Tests</a></h2> +<h3><a name="hash_based" id="hash_based">Hash-Based + Containers</a></h3> +<ol> +<li><a href="hash_text_find_find_timing_test.html">Hash-Based + Text <tt>find</tt> Find Timing Test</a></li> +<li><a href="hash_random_int_find_find_timing_test.html">Hash-Based + Random-Integer <tt>find</tt> Find Timing Test</a></li> +<li><a href="hash_random_int_subscript_find_timing_test.html">Hash-Based + Random-Integer Subscript Find Timing Test</a></li> +<li><a href="hash_random_int_subscript_insert_timing_test.html">Hash-Based + Random-Integer Subscript Insert Timing Test</a></li> +<li><a href="hash_zlob_random_int_find_find_timing_test.html">Hash-Based + Skewed-Distribution Random-Integer <tt>find</tt> Find Timing + Test</a></li> +<li><a href="hash_random_int_erase_mem_usage_test.html">Hash-Based Erase + Memory Use Test</a></li> +</ol> +<h3><a name="tree_like_based" id="tree_like_based">Tree-Like-Based Containers</a></h3> +<ol> +<li><a href="tree_text_insert_timing_test.html">Tree-Based + and Trie-Based Text Insert Timing Test</a></li> +<li><a href="tree_text_find_find_timing_test.html">Tree-Based + and Trie-Based Text <tt>find</tt> Find Timing Test</a></li> +<li><a href="tree_text_lor_find_find_timing_test.html">Tree-Based + Locality-of-Reference Text <tt>find</tt> Find Timing + Test</a></li> +<li><a href="tree_random_int_find_find_timing_test.html">Tree-Based + Random-Integer <tt>find</tt> Find Timing Test</a></li> +<li><a href="tree_split_join_timing_test.html">Tree Split and + Join Timing Test</a></li> +<li><a href="tree_order_statistics_timing_test.html">Tree + Order-Statistics Timing Test</a></li> +</ol> +<h3><a name="multimaps" id="multimaps">Multimaps</a></h3> +<ol> +<li><a href="multimap_text_find_timing_test_small.html">"Multimap" + Text Find Timing Test with <u>Small</u> Average Secondary-Key + to Primary-Key Ratio</a></li> +<li><a href="multimap_text_find_timing_test_large.html">"Multimap" + Text Find Timing Test with <u>Large</u> Average Secondary-Key + to Primary-Key Ratio</a></li> +<li><a href="multimap_text_insert_timing_test_small.html">"Multimap" + Text Insert Timing Test with <u>Small</u> Average + Secondary-Key to Primary-Key Ratio</a></li> +<li><a href="multimap_text_insert_timing_test_large.html">"Multimap" + Text Insert Timing Test with <u>Large</u> Average + Secondary-Key to Primary-Key Ratio</a></li> +<li><a href="multimap_text_insert_mem_usage_test_small.html">"Multimap" + Text Insert Memory-Use Test with <u>Small</u> Average + Secondary-Key to Primary-Key Ratio</a></li> +<li><a href="multimap_text_insert_mem_usage_test_large.html">"Multimap" + Text Insert Memory-Use Test with <u>Large</u> Average + Secondary-Key to Primary-Key Ratio</a></li> +</ol> +<h2><a name="assoc_observations" id="assoc_observations">Observations</a></h2> +<h3><a name="dss_family_choice" id="dss_family_choice">Underlying Data-Structure Families</a></h3> +<p>In general, hash-based containers (see <a href="hash_based_containers.html">Design::Associative + Containers::Hash-Based Containers</a>) have better timing + performance than containers based on different underlying-data + structures. The main reason to choose a tree-based (see + <a href="tree_based_containers.html">Design::Associative + Containers::Tree-Based Containers</a>) or trie-based container + (see <a href="trie_based_containers.html">Design::Associative + Containers::Trie-Based Containers</a>) is if a byproduct of the + tree-like structure is required: either order-preservation, or + the ability to utilize node invariants (see <a href="tree_based_containers.html#invariants">Design::Associative + Containers::Tree-Based Containers::Node Invariants</a> and + <a href="trie_based_containers.html#invariants">Design::Associative + Containers::Trie-Based Containers::Node Invariants</a>). If + memory-use is the major factor, an ordered-vector tree (see + <a href="tree_based_containers.html">Design::Associative + Containers::Tree-Based Containers</a>) gives optimal results + (albeit with high modificiation costs), and a list-based + container (see <a href="lu_based_containers.html">Design::Associative + Containers::List-Based Containers</a>) gives reasonable + results.</p> +<h3><a name="hash_based_types" id="hash_based_types">Hash-Based + Container Types</a></h3> +<p>Hash-based containers are typically either collision + chaining or probing (see <a href="hash_based_containers.html">Design::Associative + Containers::Hash-Based Containers</a>). Collision-chaining + containers are more flexible internally, and so offer better + timing performance. Probing containers, if used for simple + value-types, manage memory more efficiently (they perform far + fewer allocation-related calls). In general, therefore, a + collision-chaining table should be used. A probing container, + conversely, might be used efficiently for operations such as + eliminating duplicates in a sequence, or counting the number of + occurrences within a sequence. Probing containers might be more + useful also in multithreaded applications where each thread + manipulates a hash-based container: in the STL, allocators have + class-wise semantics (see [<a href="references.html#meyers96more">meyers96more</a>] - Item 10); a + probing container might incur less contention in this case.</p> +<h3><a name="hash_based_policies" id="hash_based_policies">Hash-Based Containers' Policies</a></h3> +<p>In hash-based containers, the range-hashing scheme (see + <a href="hash_based_containers.html#hash_policies">Design::Associative + Containers::Hash-Based Containers::Hash Policies</a>) seems to + affect performance more than other considerations. In most + settings, a mask-based scheme works well (or can be made to + work well). If the key-distribution can be estimated a-priori, + a simple hash function can produce nearly uniform hash-value + distribution. In many other cases (<i>e.g.</i>, text hashing, + floating-point hashing), the hash function is powerful enough + to generate hash values with good uniformity properties + [<a href="references.html#knuth98sorting">knuth98sorting</a>]; + a modulo-based scheme, taking into account all bits of the hash + value, appears to overlap the hash function in its effort.</p> +<p>The range-hashing scheme determines many of the other + policies (see <a href="hash_based_containers.html#policy_interaction">Design::Hash-Based + Containers::Policy Interaction</a>). A mask-based scheme works + well with an exponential-size policy (see <a href="hash_based_containers.html#resize_policies">Design::Associative + Containers::Hash-Based Containers::Resize Policies</a>) ; for + probing-based containers, it goes well with a linear-probe + function (see <a href="hash_based_containers.html#hash_policies">Design::Associative + Containers::Hash-Based Containers::Hash Policies</a>).</p> +<p>An orthogonal consideration is the trigger policy (see + <a href="hash_based_containers.html#resize_policies">Design::Associative + Containers::Hash-Based Containers::Resize Policies</a>). This + presents difficult tradeoffs. <i>E.g.</i>, different load + factors in a load-check trigger policy yield a + space/amortized-cost tradeoff.</p> +<h3><a name="tree_like_based_types" id="tree_like_based_types">Tree-Like-Based Container + Types</a></h3> +<p>In general, there are several families of tree-based + underlying data structures: balanced node-based trees + (<i>e.g.</i>, red-black or AVL trees), high-probability + balanced node-based trees (<i>e.g.</i>, random treaps or + skip-lists), competitive node-based trees (<i>e.g.</i>, splay + trees), vector-based "trees", and tries. (Additionally, there + are disk-residing or network-residing trees, such as B-Trees + and their numerous variants. An interface for this would have + to deal with the execution model and ACID guarantees; this is + out of the scope of this library.) Following are some + observations on their application to different settings.</p> +<p>Of the balanced node-based trees, this library includes a + red-black tree (see <a href="tree_based_containers.html">Design::Associative + Containers::Tree-Based Containers</a>), as does STL (in + practice). This type of tree is the "workhorse" of tree-based + containers: it offers both reasonable modification and + reasonable lookup time. Unfortunately, this data structure + stores a huge amount of metadata. Each node must contain, + besides a value, three pointers and a boolean. This type might + be avoided if space is at a premium [<a href="references.html#austern00noset">austern00noset</a>].</p> +<p>High-probability balanced node-based trees suffer the + drawbacks of deterministic balanced trees. Although they are + fascinating data structures, preliminary tests with them showed + their performance was worse than red-black trees. The library + does not contain any such trees, therefore.</p> +<p>Competitive node-based trees have two drawbacks. They are + usually somewhat unbalanced, and they perform a large number of + comparisons. Balanced trees perform one comparison per each + node they encounter on a search path; a splay tree performs two + comparisons. If the keys are complex objects, <i>e.g.</i>, + <tt>std::string</tt>, this can increase the running time. + Conversely, such trees do well when there is much locality of + reference. It is difficult to determine in which case to prefer + such trees over balanced trees. This library includes a splay + tree (see <a href="tree_based_containers.html">Design::Associative + Containers::Tree-Based Containers</a>).</p> +<p>Ordered-vector trees (see <a href="tree_based_containers.html">Design::Associative + Containers::Tree-Based Containers</a>) use very little space + [<a href="references.html#austern00noset">austern00noset</a>]. + They do not have any other advantages (at least in this + implementation).</p> +<p>Large-fan-out PATRICIA tries (see <a href="trie_based_containers.html">Design::Associative + Containers::Trie-Based Containers</a>) have excellent lookup + performance, but they do so through maintaining, for each node, + a miniature "hash-table". Their space efficiency is low, and + their modification performance is bad. These tries might be + used for semi-static settings, where order preservation is + important. Alternatively, red-black trees cross-referenced with + hash tables can be used. [<a href="references.html#okasaki98mereable">okasaki98mereable</a>] + discusses small-fan-out PATRICIA tries for integers, but the + cited results seem to indicate that the amortized cost of + maintaining such trees is higher than that of balanced trees. + Moderate-fan-out trees might be useful for sequences where each + element has a limited number of choices, <i>e.g.</i>, DNA + strings (see <a href="assoc_examples.html#trie_based">Examples::Associative + Containers::Trie-Based Containers</a>).</p> +<h3><a name="msc" id="msc">Mapping-Semantics + Considerations</a></h3> +<p>Different mapping semantics were discussed in <a href="motivation.html#assoc_mapping_semantics">Motivation::Associative + Containers::Alternative to Multiple Equivalent Keys</a> and + <a href="tutorial.html#assoc_ms">Tutorial::Associative + Containers::Associative Containers Others than Maps</a>. We + will focus here on the case where a keys can be composed into + primary keys and secondary keys. (In the case where some keys + are completely identical, it is trivial that one should use an + associative container mapping values to size types.) In this + case there are (at least) five possibilities:</p> +<ol> +<li>Use an associative container that allows equivalent-key + values (such as <tt>std::multimap</tt>)</li> +<li>Use a unique-key value associative container that maps + each primary key to some complex associative container of + secondary keys, say a tree-based or hash-based container (see + <a href="tree_based_containers.html">Design::Associative + Containers::Tree-Based Containers</a> and <a href="hash_based_containers.html">Design::Associative + Containers::Hash-Based Containers</a>)</li> +<li>Use a unique-key value associative container that maps + each primary key to some simple associative container of + secondary keys, say a list-based container (see <a href="lu_based_containers.html">Design::Associative + Containers::List-Based Containers</a>)</li> +<li>Use a unique-key value associative container that maps + each primary key to some non-associative container + (<i>e.g.</i>, <tt>std::vector</tt>)</li> +<li>Use a unique-key value associative container that takes + into account both primary and secondary keys.</li> +</ol> +<p>We do not think there is a simple answer for this (excluding + option 1, which we think should be avoided in all cases).</p> +<p>If the expected ratio of secondary keys to primary keys is + small, then 3 and 4 seem reasonable. Both types of secondary + containers are relatively lightweight (in terms of memory use + and construction time), and so creating an entire container + object for each primary key is not too expensive. Option 4 + might be preferable to option 3 if changing the secondary key + of some primary key is frequent - one cannot modify an + associative container's key, and the only possibility, + therefore, is erasing the secondary key and inserting another + one instead; a non-associative container, conversely, can + support in-place modification. The actual cost of erasing a + secondary key and inserting another one depends also on the + allocator used for secondary associative-containers (The tests + above used the standard allocator, but in practice one might + choose to use, <i>e.g.</i>, [<a href="references.html#boost_pool">boost_pool</a>]). Option 2 is + definitely an overkill in this case. Option 1 loses out either + immediately (when there is one secondary key per primary key) + or almost immediately after that. Option 5 has the same + drawbacks as option 2, but it has the additional drawback that + finding all values whose primary key is equivalent to some key, + might be linear in the total number of values stored (for + example, if using a hash-based container).</p> +<p>If the expected ratio of secondary keys to primary keys is + large, then the answer is more complicated. It depends on the + distribution of secondary keys to primary keys, the + distribution of accesses according to primary keys, and the + types of operations most frequent.</p> +<p>To be more precise, assume there are <i>m</i> primary keys, + primary key <i>i</i> is mapped to <i>n<sub>i</sub></i> + secondary keys, and each primary key is mapped, on average, to + <i>n</i> secondary keys (<i>i.e.</i>, + <i><b>E</b>(n<sub>i</sub>) = n</i>).</p> +<p>Suppose one wants to find a specific pair of primary and + secondary keys. Using 1 with a tree based container + (<tt>std::multimap</tt>), the expected cost is + <i><b>E</b>(Θ(log(m) + n<sub>i</sub>)) = Θ(log(m) + + n)</i>; using 1 with a hash-based container + (<tt>std::tr1::unordered_multimap</tt>), the expected cost is + <i>Θ(n)</i>. Using 2 with a primary hash-based container + and secondary hash-based containers, the expected cost is + <i>O(1)</i>; using 2 with a primary tree-based container and + secondary tree-based containers, the expected cost is (using + the Jensen inequality [<a href="references.html#motwani95random">motwani95random</a>]) + <i><b>E</b>(O(log(m) + log(n<sub>i</sub>)) = O(log(m)) + + <b>E</b>(O(log(n<sub>i</sub>)) = O(log(m)) + O(log(n))</i>, + assuming that primary keys are accessed equiprobably. 3 and 4 + are similar to 1, but with lower constants. Using 5 with a + hash-based container, the expected cost is <i>O(1)</i>; using 5 + with a tree based container, the cost is + <i><b>E</b>(Θ(log(mn))) = Θ(log(m) + + log(n))</i>.</p> +<p>Suppose one needs the values whose primary key matches some + given key. Using 1 with a hash-based container, the expected + cost is <i>Θ(n)</i>, but the values will not be ordered + by secondary keys (which may or may not be required); using 1 + with a tree-based container, the expected cost is + <i>Θ(log(m) + n)</i>, but with high constants; again the + values will not be ordered by secondary keys. 2, 3, and 4 are + similar to 1, but typically with lower constants (and, + additionally, if one uses a tree-based container for secondary + keys, they will be ordered). Using 5 with a hash-based + container, the cost is <i>Θ(mn)</i>.</p> +<p>Suppose one wants to assign to a primary key all secondary + keys assigned to a different primary key. Using 1 with a + hash-based container, the expected cost is <i>Θ(n)</i>, + but with very high constants; using 1 with a tree-based + container, the cost is <i>Θ(nlog(mn))</i>. Using 2, 3, + and 4, the expected cost is <i>Θ(n)</i>, but typically + with far lower costs than 1. 5 is similar to 1.</p> +</div> +</body> +</html> |