1Data::Entropy::AlgorithUmsse(r3)Contributed Perl DocumenDtaattai:o:nEntropy::Algorithms(3)
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6 Data::Entropy::Algorithms - basic entropy-using algorithms
7
9 use Data::Entropy::Algorithms
10 qw(rand_bits rand_int rand_prob);
11 $str = rand_bits(17);
13 $i = rand_int(12345);
14 $i = rand_int(Math::BigInt->new("1000000000000"));
15 $j = rand_prob(1, 2, 3);
16 $j = rand_prob([ 1, 2, 3 ]);
17 use Data::Entropy::Algorithms qw(rand_fix rand rand_flt);
19 $x = rand_fix(48);
21 $x = rand(7);
22 $x = rand_flt(0.0, 7.0);
23 use Data::Entropy::Algorithms
25 qw(pick pick_r choose choose_r shuffle shuffle_r);
26 $item = pick($item0, $item1, $item2);
28 $item = pick_r(\@items);
29 @chosen = choose(3, $item0, $item1, $item2, $item3, $item4);
30 $chosen = choose_r(3, \@items);
31 @shuffled = shuffle($item0, $item1, $item2, $item3, $item4);
32 $shuffled = shuffle_r(\@items);
33
35 This module contains a collection of fundamental algorithms that use
36 entropy. They all use the entropy source mechanism described in
37 Data::Entropy.
38
40 All of these functions use entropy. The entropy source is not an
41 explicit input in any case. All functions use the current entropy
42 source maintained by the "Data::Entropy" module. To select an entropy
43 source use the "with_entropy_source" function in that module, or
44 alternatively do nothing to use the default source.
45 Fundamental entropy extraction
47 rand_bits(NBITS)
48 Returns NBITS bits of entropy, as a string of octets. If NBITS is
49 not a multiple of eight then the last octet in the string has its
50 most significant bits set to zero.
51 rand_int(LIMIT)
53 LIMIT must be a positive integer. Returns a uniformly-distributed
54 random integer in the range [0, LIMIT). LIMIT may be either a
55 native integer, a "Math::BigInt" object, or an integer-valued
56 "Math::BigRat" object; the returned number is of the same type.
57 rand_prob(PROB ...)
59 rand_prob(PROBS)
60 Returns a random integer selected with non-uniform probability.
61 The relative probabilities are supplied as a list of non-negative
62 integers (multiple PROB arguments) or a reference to an array of
63 integers (the PROBS argument). The relative probabilities may be
64 native integers, "Math::BigInt" objects, or integer-valued
65 "Math::BigRat" objects; they must all be of the same type. At
66 least one probability value must be positive.
67 The first relative probability value (the first PROB or the first
69 element of PROBS) is the relative probability of returning 0. The
70 absolute probability of returning 0 is this value divided by the
71 total of all the relative probability values. Similarly the second
72 value controls the probability of returning 1, and so on.
73 Numbers
75 rand_fix(NBITS)
76 Returns a uniformly-distributed random NBITS-bit fixed-point
77 fraction in the range [0, 1). That is, the result is a randomly-
78 chosen multiple of 2^-NBITS, the multiplier being a random integer
79 in the range [0, 2^NBITS). The value is returned in the form of a
80 native floating point number, so NBITS can be at most one greater
81 than the number of bits of significand in the floating point
82 format.
83 With NBITS = 48 the range of output values is the same as that of
85 the Unix "drand48" function.
86 rand([LIMIT])
88 Generates a random fixed-point fraction by "rand_fix" and then
89 multiplies it by LIMIT, returning the result. LIMIT defaults to 1,
90 and if it is 0 then that is also treated as 1. The length of the
91 fixed-point fraction is 48 bits, unless that can't be represented
92 in the native floating point type, in which case the longest
93 possible fraction will be generated instead.
94 This is a drop-in replacement for "CORE::rand": it produces exactly
96 the same range of output values, but using the current entropy
97 source instead of a sucky PRNG with linear relationships between
98 successive outputs. ("CORE::rand" does the type of calculation
99 described, but using the PRNG "drand48" to generate the fixed-point
100 fraction.) The details of behaviour may change in the future if
101 the behaviour of "CORE::rand" changes, to maintain the match.
102 Where the source of a module can't be readily modified, it can be
104 made to use this "rand" by an incantation such as
105 *Foreign::Module::rand = \&Data::Entropy::Algorithms::rand;
107 This must be done before the module is loaded, most likely in a
109 "BEGIN" block. It is also possible to override "CORE::rand" for
110 all modules, by performing this similarly early:
111 *CORE::GLOBAL::rand = \&Data::Entropy::Algorithms::rand;
113 This function should not be used in any new code, because the kind
115 of output supplied by "rand" is hardly ever the right thing to use.
116 The "int(rand($n))" idiom to generate a random integer has non-
117 uniform probabilities of generating each possible value, except
118 when $n is a power of two. For floating point numbers, "rand"
119 can't generate most representable numbers in its output range, and
120 the output is biased towards zero. In new code use "rand_int" to
121 generate integers and "rand_flt" to generate floating point
122 numbers.
123 rand_flt(MIN, MAX)
125 Selects a uniformly-distributed real number (with infinite
126 precision) in the range [MIN, MAX] and then rounds this number to
127 the nearest representable floating point value, which it returns.
128 (Actually it is only as if the function worked this way: in fact it
129 never generates the number with infinite precision. It selects
130 between the representable floating point values with the
131 probabilities implied by this process.)
132 This can return absolutely any floating point value in the range
134 [MIN, MAX]; both MIN and MAX themselves are possible return values.
135 All bits of the floating point type are filled randomly, so the
136 range of values that can be returned depends on the details of the
137 floating point format. (See Data::Float for low-level floating
138 point utilities.)
139 The function "die"s if MIN and MAX are not both finite. If MIN is
141 greater than MAX then their roles are swapped: the order of the
142 limit parameters actually doesn't matter. If the limits are
143 identical then that value is always returned. As a special case,
144 if the limits are positive zero and negative zero then a zero will
145 be returned with a randomly-chosen sign.
146 Combinatorics
148 pick(ITEM ...)
149 Randomly selects and returns one of the ITEMs. Each ITEM has equal
150 probability of being selected.
151 pick_r(ITEMS)
153 ITEMS must be a reference to an array. Randomly selects and
154 returns one of the elements of the array. Each element has equal
155 probability of being selected.
156 This is the same operation as that performed by "pick", but using
158 references to avoid expensive copying of arrays.
159 choose(NCHOOSE, ITEM ...)
161 Randomly selects NCHOOSE of the ITEMs. Each ITEM has equal
162 probability of being selected. The chosen items are returned in a
163 list in the same order in which they appeared in the argument list.
164 choose_r(NCHOOSE, ITEMS)
166 ITEMS must be a reference to an array. Randomly selects NCHOOSE of
167 the elements in the array. Each element has equal probability of
168 being selected. Returns a reference to an array containing the
169 chosen items in the same order in which they appeared in the input
170 array.
171 This is the same operation as that performed by "choose", but using
173 references to avoid expensive copying of arrays.
174 shuffle(ITEM ...)
176 Reorders the ITEMs randomly, and returns them in a list in random
177 order. Each possible order has equal probability.
178 shuffle_r(ITEMS)
180 ITEMS must be a reference to an array. Reorders the elements of
181 the array randomly. Each possible order has equal probability.
182 Returns a reference to an array containing the elements in random
183 order.
184 This is the same operation as that performed by "shuffle", but
186 using references to avoid expensive copying of arrays.
187
189 Data::Entropy, Data::Entropy::Source
190
192 Andrew Main (Zefram) <zefram@fysh.org>
193
195 Copyright (C) 2006, 2007, 2009, 2011 Andrew Main (Zefram)
196 <zefram@fysh.org>
197
199 This module is free software; you can redistribute it and/or modify it
200 under the same terms as Perl itself.
201perl v5.32.1 2021-01-27 Data::Entropy::Algorithms(3)