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Math-BigInt-Random-OO-0.05
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/ Math::BigInt::Random::OO

NAME

Math::BigInt::Random::OO - generate uniformly distributed Math::BigInt objects

SYNOPSIS

  use Math::BigInt::Random::OO;

  # Random numbers between 1e20 and 2e30:

  $gen = Math::BigInt::Random::OO -> new(min => "1e20",
                                         min => "2e30");
  $x = $gen -> generate();      # one number
  $x = $gen -> generate(1);     # ditto
  @x = $gen -> generate(100);   # 100 numbers

  # Random numbers with size fitting 20 hexadecimal digits:

  $gen = Math::BigInt::Random::OO -> new(length => 20,
                                         base => 16);
  @x = $gen -> generate(100);

ABSTRACT

Math::BigInt::Random::OO is a module for generating arbitrarily large random integers from a discrete, uniform distribution. The numbers are returned as Math::BigInt objects.

DESCRIPTION

Math::BigInt::Random::OO is a module for generating arbitrarily large random integers from a discrete, uniform distribution. The numbers are returned as Math::BigInt objects.

CONSTRUCTORS

CLASS -> new ( ... )

Returns a new Math::BigInt::Random::OO random number generator object. The arguments are given in the "hash style", as shown in the following example which constructs a generator for random numbers in the range from -2 to 3, inclusive.

  my $gen = Math::BigInt::Random::OO -> new(min => -2,
                                            max =>  3);

The following parameters are recognized.

min => NUM

Specifies the minimum possible output value, i.e., the lower bound. If `max' is given, but `min' is not, then `min' is set to zero.

max => NUM

Specifies the maximum possible output value, i.e., the upper bound. If `max' is given, but `min' is not, then `max' must be non-negative.

length => NUM

Specifies the length of the output value, i.e., the number of digits. This parameter, possibly used together with `base', is more convenient than `min' and `max' when you want all random numbers have the same number of digits. If the base is not given explicitly with the `base' option, then a base of 10 is used. The following two constructors are equivalent

  $gen1 = Math::BigInt::Random::OO -> new(length => $n, base => $b);

  $min  = Math::BigInt -> new($b) -> bpow($n - 1);
  $max  = Math::BigInt -> new($b) -> bpow($n) -> bsub(1));
  $gen2 = Math::BigInt::Random::OO -> new(min => $min, max => $max);

For instance, if the length is 4 and the base is 10, the random numbers will be in the range from 1000 to 9999, inclusive. If the length is 3 and the base is 16, the random numbers will be in the range from 256 to 4095, which is 100 to fff hexadecimal.

This option is ignored if the `max' option is present.

base => NUM

Sets the base to be used with the `length' option. See also the description for the `length' option.

length_bin => NUM

This option is only for compatibility with Math::BigInt::Random. The following two cases are equivalent

  $class -> new(length_bin => $n);
  $class -> new(length => $n, base => 2);
length_hex => NUM

This option is only for compatibility with Math::BigInt::Random. The following two cases are equivalent

  $class -> new(length_hex => $n);
  $class -> new(length => $n, base => 16);
OBJECT -> generate ( COUNT )
OBJECT -> generate ( )

Generates the given number of random numbers, or one number, if no input argument is given.

  # Generate ten random numbers:

  my @num = $gen -> generate(10);

TODO

  • Add a way to change the core uniform random number generator. Currently, CORE::rand() is used, but it would be nice to be able to switch to, e.g., Math::Random::random_uniform_integer().

  • Add functionality similar to the use_internet parameter argument in Math::BigInt::Random::random_bigint(). This could be implemented using, e.g., Net::Random.

  • Add more tests.

NOTES

The task is to generate a random integer X satisfying X_min <= X <= X_max. This is equivalent to generating a random integer U satisfying 0 <= U < U_max, where U_max = X_max - X_min + 1, and then returning X, where X = U + X_min.

  • Find the smallest integer N so that U_max <= 2**N.

  • Generate uniformly distributed random integers U in the range 0 <= U < 2**N until we have the first U < U_max. Then return X, where X = U + X_min.

The random integer U, where 0 <= U < 2**N is generated as a sequence of random bytes, except for the N % 8 most significant bits, if any. For example, if N = 21 = 5 + 8 + 8, then the 5 most significand bits are generated first, followed by two 8 bit bytes.

    |    top bits   |    first whole byte    |    second whole byte   |
      0  0  0  0  0   1  1  1  1  1  1  1  1   2  2  2  2  2  2  2  2
  int(rand(1 << 5))     int(rand(1 << 8))         int(rand(1 << 8))

Problems with Math::BigInt::Random

I wrote this module partly since Math::BigInt::Random v0.04 is buggy, and in many cases slower, and partly because I prefer an object-oriented interface. The bugs in Math::BigInt::Random v0.04 are

  • When the range (the maximum value minus the minimum value) is smaller than 1048575 (fffff hexadecimal), the maximum value will never be returned.

  • When the range is not a power of two, certain values are more likely to occur than others.

The core of this last problem is the use of int(rand(X)), which only returns uniformly distributed numbers when X is a power of two no larger than RANDBITS.

In addition, the function Math::BigInt::Random::random_bigint() generates only one random integer at a time, and in doing so, there is some overhead. In Math::BigInt::Random::OO, this overhead is placed in the new() constructor, so it is done only once, independently of how many random numbers are generated by the generator() method.

CAVEATS

  • Some versions of CORE::rand() behave poorly, so the quality of the random numbers generated depend on the quality of the random number returned by int(rand(256)).

BUGS

Please report any bugs or feature requests to bug-math-bigint-random-oo at rt.cpan.org, or through the web interface at http://rt.cpan.org/Public/Bug/Report.html?Queue=Math-BigInt-Random-OO I will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

SUPPORT

You can find documentation for this module with the perldoc command.

    perldoc Math::BigInt::Random::OO

You can also look for information at:

SEE ALSO

Math::BigInt::Random(3), Math::Random(3), Net::Random(3).

AUTHOR

Peter John Acklam <pjacklam (at) gmail.com>.

COPYRIGHT & LICENSE

Copyright 2010,2020,2023 Peter John Acklam.

This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself.