<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">NAME
    Number::AnyBase - Converts decimals to and from any alphabet of any size
    (for shortening IDs, URLs etc.)

VERSION
    version 1.50001

SYNOPSIS
        use strict;
        use warnings;
    
        use Number::AnyBase;
    
        # 62 symbols alphabet
        my @alphabet = (0..9, 'A'..'Z', 'a'..'z');
        my $conv = Number::AnyBase-&gt;new(\@alphabet);
        my $base62_num = $conv-&gt;to_base(123456);     # W7E
        my $dec_num    = $conv-&gt;to_dec($base62_num); # back to 123456
    
        use feature 'say';
    
        # URI unreserved characters alphabet
        my $uri_conv = Number::AnyBase-&gt;new_urisafe;
        say $uri_conv-&gt;to_base(1234567890); # ~2Bn4
        say $uri_conv-&gt;to_dec( '~2Bn4' );   # 1234567890
    
        # ASCII printable characters alphabet
        my $ascii_conv = Number::AnyBase-&gt;new_ascii;
        say $ascii_conv-&gt;to_base(199_000_000_000); # &gt;Z8X&lt;8
        say $ascii_conv-&gt;to_dec( '&gt;Z8X&lt;8' );       # 199000000000
    
        # Hexadecimal base
        my $hex_conv = Number::AnyBase-&gt;new( 0..9, 'A'..'F' );
        say $hex_conv-&gt;to_base(2047);   # 7FF
        say $hex_conv-&gt;to_dec( '7FF' ); # 2047
    
        # Morse-like alphabet :-)
        my $morse_conv = Number::AnyBase-&gt;new( '_.' );
        say $morse_conv-&gt;to_base(99);         # ..___..
        say $morse_conv-&gt;to_dec( '..___..' ); # 99
    
        {
            # Unicode alphabet (webdings font);
            use utf8;
            binmode STDOUT, ':utf8';
            my $webdings_conv = Number::AnyBase-&gt;new(
                '笙｣笙､笙･笙ｦ笘ｭ笘ｹ笘ｺ笘ｻ笨遺悴笨ｫ笨ｭ笨ｰ笨ｵ笨ｶ笨ｻ笶問勦笙ｧ笙ｪ笙ｫ笙ｬ笞凪囃笵披愍笨ｾ笶≫揩笶�揣笶岩仭笞｡笞｢笞｣笞､笞･笞ｦ笵笵≫屹笵ｨ'
            );
            say $webdings_conv-&gt;to_base(1000000000); # 笘ｺ笞｢笙ｬ笙ｬ笞･笵ｦ
            say $webdings_conv-&gt;to_dec( '笘ｺ笞｢笙ｬ笙ｬ笞･笵ｦ' ); # 1000000000
        }
    
        # Fast native unary increment/decrement
        my $sequence = Number::AnyBase-&gt;fastnew(['A'..'Z']);
        say $sequence-&gt;next('ZZZ');  # BAAA
        say $sequence-&gt;prev('BAAA'); # ZZZ

DESCRIPTION
    First the intended usage scenario: this module has been conceived to
    shorten ids, URLs etc., like the URL shortening services do (then it can
    be extended to some other mildly interesting uses: please see the
    "COOKBOOK" section below).

    Then a bit of theory: an id is (or can anyway be mapped to) just a
    number, therefore it can be represented in any base. The longer is the
    alphabet of the base, the shorter the number representation will be (in
    terms of symbols of the said alphabet). This module converts any
    non-negative decimal integer (including Math::BigInt-compatible objects)
    to any given base/alphabet and vice versa, thus giving the shortest
    possible representation for the original number/id (provided that we are
    dealing with a *collision-free* transformation of random, non-skewed
    data).

    The suggested workflow to shorten your ids is therefore the following:

    1   when storing an item in your data store, generate a decimal id for
        it (for example through the SEQUENCE field type offered by many
        DBMSs);

    2   shorten the said decimal id through the "to_base" method explained
        below;

    3   publish the shortened id rather than the (longer) original decimal
        id.

    When receiving a request for a certain item through its corresponding
    shortened id you've published:

    1   obtain the corresponding original decimal id through the "to_dec"
        method explained below;

    2   retrieve the requested item in your data store through its original
        decimal id you've obtained at the previous step;

    3   serve the requested item.

    Of course one can also save the shortened id along with the item in the
    data store, thus saving the "to_dec" conversion at the step 1 above
    (using the shortened id rather than the decimal one in the subsequent
    step 2).

    Through the fast native unary increment/decrement offered by the "next"
    and "prev" methods, it is even possible to skip the decimal ids
    generation and the conversion steps altogether.

    A couple of similar modules were already present on CPAN, but for one
    reason or another I did not find them completely satisfactory: for a
    detailed explanation, please see the "COMPARISON" section below.

METHODS
  Constructors
   "new"
    *   "Number::AnyBase-&gt;new( @alphabet )"

    *   "Number::AnyBase-&gt;new( \@alphabet )"

    *   "Number::AnyBase-&gt;new( $alphabet )"

    This is the constructor method, which initializes and returns the
    *converter* object. It requires an *alphabet*, that is the set of
    symbols to represent the converted numbers (the size of the base is the
    number of symbols of the provided alphabet).

    An exception is thrown if no alphabet is passed to "new".

    The alphabet can be passed as a list or as a listref of characters, or
    packed into a string (in which case the alphabet is obtained by
    splitting the string into its individual characters).

    For example the following three invocations return exactly the same
    object:

        $conv = Number::AnyBase-&gt;new( '0'..'9', 'a'..'z' );
    
        # Same as above
        $conv = Number::AnyBase-&gt;new( ['0'..'9', 'a'..'z'] );
    
        # The same through a string
        $conv = Number::AnyBase-&gt;new( '0123456789abcdefghijklmnopqrstuvwxyz' );

    An alphabet must have at least two symbols (that is, at least two
    distinct characters), otherwise an excpetion is thrown. Any duplicate
    character is automatically removed, so for example:

        $conv = Number::AnyBase-&gt;new( 'a'..'z', '0'..'9' );
    
        # Exactly the same as above
        $conv = Number::AnyBase-&gt;new( 'a'..'z', '0'..'9', qw/a b c d z z z/ );
    
        # Error: an alphabet with a single symbol has been passed
        $conv = Number::AnyBase-&gt;new( 'aaaaaaaaaaaaaaaa' );

    As a single symbol alphabet is not admissible, when "new" is called with
    a single (string) parameter, it is interpreted as a string containing
    the whole alphabet and not as a list containing a single (multichar)
    symbol. In other words, if you want to pass the alphabet as a list, it
    must contain at least two elements.

    The alphabet can't contain symbols longer than one character, otherwise
    an exception is thrown. Note that this can happen only when the alphabet
    is passed as a list or a listref, since when a (single) string is given
    to "new", the alphabet is obtained by splitting the string into its
    individual characters (and the possible duplicate characters are
    removed), so no multichar symbols are ever created in this case:

        # Error: the last symbol in the provided alphabet (as a list) is two characters long
        Number::AnyBase-&gt;new( qw/z z z aa/ );
    
        # This is instead correct since the alphabet will be: 'z', 'a'
        Number::AnyBase-&gt;new( 'zzzaa' );

   "fastnew"
    *   "Number::AnyBase-&gt;fastnew( \@alphabet )"

    This is an alternative, faster constructor, which skips all of the
    checks performed by "new" (if an illegal alphabet is passed, the
    behavior is currently indeterminate).

    It only accepts a listref.

   Specialized Constructors
    Several constructors with ready-made alphabets are offered as well.

   "new_urisafe"
    It builds and returns a converter to/from an alphabet made by the
    *unreserved URI characters*, as per the RFC3986
    &lt;http://www.ietf.org/rfc/rfc3986.txt&gt;. More precisely, it is the same
    as:

        Number::AnyBase-&gt;fastnew( ['-', '.', '0'..'9', 'A'..'Z', '_', 'a'..'z', '~'] );

   "new_base36"
    The same as:

        Number::AnyBase-&gt;fastnew( ['0'..'9', 'A'..'Z'] );

   "new_base62"
    The same as:

        Number::AnyBase-&gt;fastnew( ['0'..'9', 'A'..'Z', 'a'..'z'] );

   "new_base64"
    The same as:

        Number::AnyBase-&gt;fastnew( ['A'..'Z', 'a'..'z', '0'..'9', '+', '/'] );

   "new_base64url"
    The same as:

        Number::AnyBase-&gt;fastnew( ['A'..'Z', 'a'..'z', '0'..'9', '-', '_'] );

   "new_bin"
    It builds a binary converter. The same as:

        Number::AnyBase-&gt;fastnew( ['0', '1'] );

   "new_oct"
    It builds an octal converter. The same as:

        Number::AnyBase-&gt;fastnew( ['0'..'7'] )

   "new_hex"
    It builds an hexadecimal converter. The same as:

        Number::AnyBase-&gt;fastnew( ['0'..'9', 'A'..'F'] );

   "new_hex_lc"
    The same as above, except that the alphabet is lower-cased:

        Number::AnyBase-&gt;fastnew( ['0'..'9', 'a'..'f'] );

   "new_dna"
    It builds a converter for DNA sequences. The same as:

        Number::AnyBase-&gt;fastnew( ['A', 'C', 'G', 'T'] );

   "new_dna_lc"
    The same as above, except that the alphabet is lower-cased:

        Number::AnyBase-&gt;fastnew( ['a', 'c', 'g', 't'] );

   "new_ascii"
    It builds and returns a converter to/from an alphabet composed of all
    the printable ASCII characters except the space. More precisely, it is
    the same as:

        Number::AnyBase-&gt;fastnew([
            '!', '"' , '#', '$', '%', '&amp;', "'", '(', ')', '*', '+', '-', '.', '/',
            '0'..'9' , ':', ';', '&lt;', '=', '&gt;', '?', '@', 'A'..'Z',
            '[', '\\', ']', '^', '_', '`', 'a'..'z', '{', '|', '}', '~'
        ]);

   "new_bytes"
    It builds a converter to/from an alphabet which includes all the binary
    octets from 0x0 to 0xFF. The same as:

        Number::AnyBase-&gt;fastnew( [ map {chr} 0..255 ] );

    It is useful to convert from/to binary data (for an example, please see
    the "DNA Compression" or the "Binary-to-text Encoding" recipes in the
    "COOKBOOK" section below).

  "to_base"
    *   "$string = $converter-&gt;to_base( $decimal )"

    This is the method which transforms the given decimal number into its
    representation in the new base, as shown in the "SYNOPSIS" above.

    It works only on decimal non-negative integers (including 0). For speed
    reasons, no check is performed on the given number: in case it is
    illegal, the behavior is currently indeterminate.

    It works transparently also on Math::BigInt-compatible objects (that is,
    any object which overloads the arithmetic operators like Math::BigInt
    does): just pass any such *big number* and you will get the correct
    result:

        use Math::BigInt; # Or use Math::GMP;
        Math::BigInt-&gt;accuracy(60); # For example
    
        my $bignum = Math::BigInt-&gt;new( '123456789012345678901234567890123456789012345678901234567890' ); # Or Math::GMP-&gt;new(...)
    
        my $conv = Number::AnyBase-&gt;new_base62;
    
        my $base_num = $conv-&gt;to_base( $bignum ); # sK0FUywPQsEhMwNhdPBZJcA9KumP0WpD0

    This permits to freely choose any Math::BigInt *option* (the *accuracy*,
    as shown above, or the *backend library* etc.), or to use any other
    compatible class, such as, for example, Math::GMP or Math::Int128 (in
    this latter case, if the number size permits its use).

  "to_dec"
    *   "$decimal_number = $converter-&gt;to_base( $base_num )"

    *   "$decimal_bignumber = $converter-&gt;to_base( $base_num, $bigint_obj )"

    This is the method which converts the transformed *number* (or rather
    *string*) back to its decimal representation, as exemplified in the
    "SYNOPSIS" above.

    For speed reasons, no check is performed on the given string, which
    could be inconsistent (for example because it contains characters not
    present in the current alphabet): in this case the behavior is currently
    indeterminate.

    It accepts a second optional parameter, which should be a
    Math::BigInt-compatible object (it does not matter if it is initialized
    or not), which tells "to_base" that a *bignum* result is requested. It
    is necessary only when the result is too large to be held by a native
    perl integer (though, other than slowing down the conversion, it does
    not cause any harm, so in case of doubt it can be used anyway).

    The passed bignum object is then used for the internal calculations so,
    though unusual, this interface permits to have the maximum flexibility,
    as it completely decouples the *bignum* library, allowing the user to
    freely choose any Math::BigInt *option* as well as any (faster)
    Math::BigInt-compatible alternative (such as Math::GMP, or Math::Int128
    when permitted by the number size):

        use Math::BigInt; # Or use Math::GMP;
        Math::BigInt-&gt;accuracy(60); # For example
    
        my $conv = Number::AnyBase-&gt;new_base62;
    
        my $big_dec_num = $conv-&gt;to_dec( 'sK0FUywPQsEhMwNhdPBZJcA9KumP0WpD0', Math::BigInt-&gt;new ); # Or Math::GMP-&gt;new
        # $big_dec_num is now a Math::BigInt object which stringifies to:
        # 123456789012345678901234567890123456789012345678901234567890

  "next"
    *   "$string = $converter-&gt;next( $base_num )"

    This method performs an optimized *native* unary increment on the given
    converted number/string, returning the next number/string in the current
    base (see also the "SYNOPSYS" above):

        $next_base_num = $converter-&gt;next($base_num);

    It is over 2x faster than the conversion roundtrip:

        $next_base_num = $converter-&gt;to_base( $converter-&gt;to_dec($base_num) + 1 );

    (see the benchmark/native_sequence.pl benchmark included in the
    distribution). It therefore offers an efficient way to get the next id
    from the last (converted) id stored in a db, for example.

  "prev"
    *   "$string = $converter-&gt;prev( $base_num )"

    This method performs an optimized *native* unary decrement on the given
    converted number/string, returning the previous number/string in the
    current base (see also the "SYNOPSYS" above):

        $prev_base_num = $converter-&gt;prev($base_num);

    It is over 2x faster than the conversion roundtrip:

        $prev_base_num = $converter-&gt;to_base( $converter-&gt;to_dec($base_num) - 1 );

    When called on the *zero* of the base, it returns "undef".

  "alphabet"
    *   "$listref = $converter-&gt;alphabet"

    Read-only method which returns the alphabet of the current *target*
    base, as a listref.

COOKBOOK
    This section contains some general advices, together with some examples
    of *creative* uses, if a bit extravagant :-)

  DNA Compression
    This example shows how the *bytes* alphabet can be used to effectively
    compress random data, when expressed in a shorter alphabet (the *DNA
    alphabet* in this case).

    If the data are sufficiently randomized (i.e. not skewed), this
    technique easily beats most general purpose compression algorithms.

    As shown below, the conversion to the bytes alphabet produces about a
    40% better compression than zip (with default options). Even the
    conversions to the *urisafe* and to the printable ascii alphabets offer
    a better compression, and they have the additional advantage that the
    produced string has only *safe* characters.

        use strict;
        use warnings;
    
        use feature 'say';
    
        use Number::AnyBase;
        use Math::BigInt; # Or use Math::GMP for speed
    
        # For comparison
        use IO::Compress::Zip qw(zip);
    
        $| = 1;
    
        ( my $dnastring = do { local $/; &lt;DATA&gt; } ) =~ tr/\n//d;
    
        # dna string in decimal form (itself a compression)
        my $dnastring_dec = Number::AnyBase-&gt;new_dna-&gt;to_dec($dnastring, Math::BigInt-&gt;new);
    
        # Let's try several compressions
        my $dnastring_urisafe = Number::AnyBase-&gt;new_urisafe-&gt;to_base($dnastring_dec);
        my $dnastring_ascii   = Number::AnyBase-&gt;new_ascii-&gt;to_base($dnastring_dec);
        my $dnastring_bytes   = Number::AnyBase-&gt;new_bytes-&gt;to_base($dnastring_dec);
    
        # zip with default options for comparison
        zip \$dnastring, \my $dnastring_zipped;
    
        # Check the length
        say length $dnastring;         # 1231 (original length)
        say length $dnastring_dec;     #  741
        say length $dnastring_urisafe; #  408
        say length $dnastring_ascii;   #  377
        say length $dnastring_bytes;   #  308
    
        say length $dnastring_zipped;  #  515
    
        # Real human gene for bone gla protein (BGP)
        __DATA__
        GGCAGATTCCCCCTAGACCCGCCCGCACCATGGTCAGGCATGCCCCTCCTCATCGCTGGGCACAGCCCAGAGGGT
        ATAAACAGTGCTGGAGGCTGGCGGGGCAGGCCAGCTGAGTCCTGAGCAGCAGCCCAGCGCAGCCACCGAGACACC
        ATGAGAGCCCTCACACTCCTCGCCCTATTGGCCCTGGCCGCACTTTGCATCGCTGGCCAGGCAGGTGAGTGCCCC
        CACCTCCCCTCAGGCCGCATTGCAGTGGGGGCTGAGAGGAGGAAGCACCATGGCCCACCTCTTCTCACCCCTTTG
        GCTGGCAGTCCCTTTGCAGTCTAACCACCTTGTTGCAGGCTCAATCCATTTGCCCCAGCTCTGCCCTTGCAGAGG
        GAGAGGAGGGAAGAGCAAGCTGCCCGAGACGCAGGGGAAGGAGGATGAGGGCCCTGGGGATGAGCTGGGGTGAAC
        CAGGCTCCCTTTCCTTTGCAGGTGCGAAGCCCAGCGGTGCAGAGTCCAGCAAAGGTGCAGGTATGAGGATGGACC
        TGATGGGTTCCTGGACCCTCCCCTCTCACCCTGGTCCCTCAGTCTCATTCCCCCACTCCTGCCACCTCCTGTCTG
        GCCATCAGGAAGGCCAGCCTGCTCCCCACCTGATCCTCCCAAACCCAGAGCCACCTGATGCCTGCCCCTCTGCTC
        CACAGCCTTTGTGTCCAAGCAGGAGGGCAGCGAGGTAGTGAAGAGACCCAGGCGCTACCTGTATCAATGGCTGGG
        GTGAGAGAAAAGGCAGAGCTGGGCCAAGGCCCTGCCTCTCCGGGATGGTCTGTGGGGGAGCTGCAGCAGGGAGTG
        GCCTCTCTGGGTTGTGGTGGGGGTACAGGCAGCCTGCCCTGGTGGGCACCCTGGAGCCCCATGTGTAGGGAGAGG
        AGGGATGGGCATTTTGCACGGGGGCTGATGCCACCACGTCGGGTGTCTCAGAGCCCCAGTCCCCTACCCGGATCC
        CCTGGAGCCCAGGAGGGAGGTGTGTGAGCTCAATCCGGACTGTGACGAGTTGGCTGACCACATCGGCTTTCAGGA
        GGCCTATCGGCGCTTCTACGGCCCGGTCTAGGGTGTCGCTCTGCTGGCCTGGCCGGCAACCCCAGTTCTGCTCCT
        CTCCAGGCACCCTTCTTTCCTCTTCCCCTTGCCCTTGCCCTGACCTCCCAGCCCTATGGATGTGGGGTCCCCATC
        ATCCCAGCTGCTCCCAAATAAACTCCAGAAG

    Of course there is nothing magic here: this technique simply leads to a
    2-bit representation for the original symbols (being them just 4). For
    truly random data, this is the best that can be done however
    (compression algorithms specifically tailored for DNA sequences there
    exist, but they still leverage on some data pattern repetitions to get
    better results).

  Binary-to-text Encoding
    In a sense, this example is the opposite of the previous one: this time
    the target alphabet is shorter than the source one, therefore the
    resulting string is longer than the original one. There is an advantage
    however: the resulting string contains only *safe* characters (while the
    original string is in general binary), and it can therefore be
    trasmitted/embedded where binary data would have caused problems.

    Working on the whole original string rather than on blocks, the
    technique shown below easily beats any binary-to-text standard algorithm
    (the efficiency of which is measured by the shortness of the overhead
    added to the original data), such as Base64
    &lt;http://en.wikipedia.org/wiki/Base64&gt; or Ascii85
    &lt;http://en.wikipedia.org/wiki/Ascii85&gt;, even with the optimizations
    offered by default by the Convert::Ascii85 CPAN module used here for
    comparison (to be fair, the "Number::AnyBase" ascii alphabet has also
    more than 85 symbols, but that's an "Number::AnyBase" merit :-)

    Also note how, in order to maximize the efficiency, "Number::AnyBase"
    lets freely choose the bignum library (in this case the excellent
    "Math::GMP"), even when converting (to decimals) from arbitrary
    alphabets.

        use strict;
        use warnings;
    
        use feature 'say';
    
        use Number::AnyBase;
        use Math::GMP; # For speed
    
        # For Comparison
        use MIME::Base64;
        use Convert::Ascii85 qw(ascii85_encode);
    
        $| = 1;
    
        # Generic binary data
        my $bytes = '';
        $bytes .= chr int(256 * rand) for 1..1024;
    
        # byte string in decimal form
        my $bytes_dec = Number::AnyBase-&gt;new_bytes-&gt;to_dec($bytes, Math::GMP-&gt;new);
    
        my $bites_base64 = Number::AnyBase-&gt;new_base64-&gt;to_base($bytes_dec);
        my $bites_ascii  = Number::AnyBase-&gt;new_ascii-&gt;to_base($bytes_dec);
    
        say length $bytes; # Original length
    
        say length $bites_base64;
        say length encode_base64($bytes); # Longer than $bites_base64
    
        say length $bites_ascii;
        say length ascii85_encode($bytes); # Longer than $bites_ascii

    The downside is that this technique becomes impractical (both in time
    and space efficiency) when the string to convert grows. It can however
    be applied block-by-block, say up to blocks of (few) tens of Kbytes,
    still producing the best results.

  UUIDs compression
    This example is a mix of the previous two: using a longer alphabet, it
    compresses the original (hexadecimal) UUID, but it keeps also the UUID
    textual.

    Once again it is shown how, in order to maximize the efficiency,
    "Number::AnyBase" can freely choose the bignum library to use: in this
    case the excellent "Math::Int128" (which fits perfectly, being an UUID
    exactly 128-bit long).

        use strict;
        use warnings;
    
        use feature 'say';
    
        use Math::Int128 qw(string_to_uint128); # For maximum speed
        use Data::UUID;
        use Number::AnyBase;
    
        $| = 1;
    
        my $uuid = Data::UUID-&gt;new-&gt;create_hex;
        my $dec_uuid = string_to_uint128($uuid);
    
        # Let's try several compressions
        my $base64url_uuid = Number::AnyBase-&gt;new_base64url-&gt;to_base($dec_uuid);
        my $urisafe_uuid   = Number::AnyBase-&gt;new_urisafe-&gt;to_base($dec_uuid);
        my $ascii_uuid     = Number::AnyBase-&gt;new_ascii-&gt;to_base($dec_uuid);
    
        # Check the length
        say length($uuid) - 2;      # Original length (32)
        say length $base64url_uuid; # Max. 22, better than standard Base64
        say length $urisafe_uuid;   # Max. 22, sometimes better than the previous
        say length $ascii_uuid;     # Max. 20, better than standard Base85

  Security
    This module focuses only on converting numbers from decimals to any
    base/alphabet and vice versa, therefore it has nothing to do with
    security, that is, given a number/string and the alphabet it is
    represented on, the next (through an unary increment) number/string is
    guessable. If you want your (converted) id sequence not to be guessable,
    the solution is however simple: just randomize your decimal numbers
    upfront, leaving large random gaps in the set. Then feed the randomized
    decimals to this module to have them shortened.

  Sorting
    Characters ordering in the given alphabet does matter: if it is
    desidered that converting a sorted sequence of decimals produces a
    sorted sequence of strings (when properly padded of course), the
    characters in the provided alphabet must be sorted as well.

    An alphabet with unsorted characters can be used to make the converted
    numbers somewhat harder to guess.

    Note that the predefined constructors always use sorted alphabets.

  Speed
    For maximum speed, as a constructor use "fastnew" or any of the
    predefined constructors, resorting to "new" only when it is necessary to
    perform the extra checks.

    Conversion speed maximization does not require any trick: as long as
    *big numbers* are not used, the calculations are performed at the full
    perl native integers speed.

    Big numbers of course slow down the conversions but, as shown above,
    performances can be fine-tuned, for example by properly setting the
    Math::BigInt precision and accuracy, by choosing a faster back-end
    library, or by using Math::GMP directly in place of Math::BigInt
    (advised). If permitted by the number size, Math::Int128 is an even
    faster alternative.

    As already said, the optimized native unary increment [decrement]
    provided by "next" ["prev"] is over 2x faster than the
    "to_dec"/"to_base" conversion rountrip. However, if a sequence of
    converted numbers must be generated, and such sequence is large enough
    so that the first "to_dec()" call can be amortized, using "to_base()"
    (only) is marginally faster than using "next":

        use Number::AnyBase;
    
        use constant SEQ_LENGTH =&gt; 10_000;
    
        my $conv = Number::AnyBase-&gt;new( 0..9, 'A'..'Z', 'a'..'z' );
        my (@seq1, @seq2); # They will contain the same sequence, through different methods
        my $base_num = 'zzzzzz';
    
        # @seq1 construction through native increment
        my $next = $base_num;
        push @seq1, $next = $conv-&gt;next($next) for 1..SEQ_LENGTH;
    
        # @seq2 construction through to_base; marginally faster than @seq1
        my $dec_num = $conv-&gt;to_dec($base_num);
        push @seq2, $conv-&gt;to_base( $dec_num + $_ ) for 1..SEQ_LENGTH;

    See the benchmark/native_sequence.pl benchmark script included in the
    distribution.

COMPARISON
    Here is a brief and completely biased comparison with Math::BaseCalc,
    Math::BaseConvert and Math::Base::Convert, which are similar CPAN
    modules.

    For the performance claims, please see the
    benchmark/other_cpan_modules.pl benchmark script included in the
    distribution. Also note that the conversion speed gaps tend to increase
    with the numbers size.

    *   vs "Math::BaseCalc"

        *   Pros

            *   "Number::AnyBase" is faster: decimal-&gt;base conversion is
                about 2x (100%) faster, base-&gt;decimal conversion is about on
                par, "fastnew" is about 20% faster than
                "Math::BaseCalc::new".

            *   Base-&gt;decimal conversion in "Number::AnyBase" can return
                "Math::BigInt" (or *similar*) objects upon request, while
                "Math::BaseCalc" only returns native perl integers, thus
                producing wrong results when the decimal number is too
                large.

            *   "Math::BaseCalc" lacks the fast native unary
                increment/decrement offered by "Number::Anybase", which
                permits an additional 2x speedup.

        *   Cons

            *   "Math::BaseCalc::new" converts also negative integers, while
                "Number::AnyBase" only converts non-negative integers (this
                feature has been considered not particularly important and
                therefore traded for speed in "Number::AnyBase").

    *   vs "Math::BaseConvert"

        *   Pros

            *   With native perl integers, "Number::AnyBase" is hugely
                faster: something like 200x faster in decimal-&gt;base
                conversion and 130x faster in base-&gt;decimal conversion
                (using "Math::BaseConvert::cnv").

            *   With big integers (60 digits), "Number::AnyBase" (using
                "Math::GMP") is still faster: over 13x faster in both
                decimal-&gt;base conversion and base-&gt;decimal conversion;
                though much less, it's faster even using "Math::BigInt" with
                its pure-perl backend.

            *   "Math::BaseConvert" has a weird API: first it has a
                functional interface, which is not ideal for code which has
                to maintain its internal state. Then, though a custom
                alphabet can be set (through a state-changing function
                called "dig"), every time "cnv" is called, the *target*
                alphabet size must be passed anyway.

            *   "Math::BaseConvert" doesn't permit to use a bignum library
                other than "Math::BigInt", nor it permits to set any
                "Math::BigInt" option.

            *   "Math::BaseConvert" lacks the fast native unary
                increment/decrement offered by "Number::Anybase", which
                permits an additional 2x speedup.

        *   Cons

            *   "Math::BaseConvert" manages big numbers transparently (but
                this makes it extremely slow and does not permit to use a
                library other than "Math::BigInt", as already said).

            *   "Math::BaseConvert" can convert numbers between two
                arbitrary bases with a single function call.

            *   "Math::BaseConvert" converts also negative integers.

    *   vs "Math::Base::Convert"

        *   Pros

            *   With native perl integers, "Number::AnyBase" is largely
                faster: something like over 15x faster in decimal-&gt;base
                conversion and over 22x faster in base-&gt;decimal conversion
                (using the "Math::Base::Convert" object API, which is the
                recommended one for speed); "fastnew" is over 70% faster
                than "Math::Base::Convert::new".

            *   With big integers (60 digits), "Number::AnyBase" (using
                "Math::GMP") is still faster: about 15% faster in
                decimal-&gt;base conversion and about 100% faster in
                base-&gt;decimal conversion.

            *   Though generally better, "Math::Base::Convert" preserves
                some of the "Math::BaseConvert" API shortcomings: to convert
                numbers bidirectionally between base 10 to/from another
                given base, two different objects must be istantiated (or
                the bases must be passed each time through the functional
                API).

            *   "Math::Base::Convert" lacks the fast native unary
                increment/decrement offered by "Number::Anybase", which
                permits an additional 2x speedup.

            *   Possible minor glitch: some of the predefined alphabets
                offered by "Math::Base::Convert" are not sorted.

        *   Cons

            *   "Math::Base::Convert" manages big numbers transparently and
                natively, i.e. without resorting to "Math::BigInt" or
                similar modules (but, though not as slow as
                "Math::BaseConvert", this makes "Math::Base::Convert"
                massively slow as well, when native perl integers can be
                used).

            *   On big integers, if "Number::AnyBase" uses "Math::BigInt"
                with its pure-perl engine, "Math::Base::Convert" is faster:
                about 11x in decimal-&gt;base conversion and about 6x in in
                base-&gt;decimal conversion (as already said, "Number::AnyBase"
                can however use "Math::GMP" and be faster even with big
                numbers).

            *   "Math::Base::Convert" can convert numbers between two
                arbitrary bases with a single function call.

            *   "Math::Base::Convert" converts also negative integers.

    All of the reviewed modules are *pure-perled*, though the "Math::GMP"
    module that "Number::AnyBase" can (optionally) use to maximize its speed
    with big numbers it's not. Note however that the "Number::AnyBase" fast
    native unary increment/decrement work on arbitrarily big numbers without
    any external module.

SEE ALSO
    *   Math::BaseCalc

    *   Math::BaseConvert

    *   Math::Base::Convert

    *   Math::BigInt

    *   Math::GMP

    *   Math::Int128

BUGS
    No known bugs.

    Please report any bugs or feature requests to "bug-number-AnyBase at
    rt.cpan.org", or through the web interface at
    &lt;http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Number-AnyBase&gt;. 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 Number::AnyBase

    You can also look for information at:

    *   RT: CPAN's request tracker (report bugs here)

        &lt;http://rt.cpan.org/NoAuth/Bugs.html?Dist=Number-AnyBase&gt;

    *   GitHub issues (you can also report bugs here)

        &lt;https://github.com/emazep/Number-AnyBase/issues&gt;

    *   AnnoCPAN: Annotated CPAN documentation

        &lt;http://annocpan.org/dist/Number-AnyBase&gt;

    *   CPAN Ratings

        &lt;http://cpanratings.perl.org/d/Number-AnyBase&gt;

    *   Search CPAN

        &lt;http://search.cpan.org/dist/Number-AnyBase/&gt;

ACKNOWLEDGEMENTS
    Many thanks to the IPW (Italian Perl Workshop) organizers, sponsors and
    speakers: they run a fascinating an inspiring event.

AUTHOR
    Emanuele Zeppieri &lt;emazep@cpan.org&gt;

COPYRIGHT AND LICENSE
    This software is copyright (c) 2013 by Emanuele Zeppieri.

    This is free software; you can redistribute it and/or modify it under
    the same terms as the Perl 5 programming language system itself.

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