Emanuele Zeppieri >
Number-AnyBase-1.00000 >
Number::AnyBase

Module Version: 1.00000
Number::AnyBase - Converts decimals to and from any alphabet of any size (for shortening IDs, URLs etc.)

version 1.00000

use strict; use warnings; use Number::AnyBase; # 62 symbols alphabet my @alphabet = (0..9, 'A'..'Z', 'a'..'z'); my $conv = Number::AnyBase->new(\@alphabet); my $base62_num = $conv->to_base(123456); # W7E my $dec_num = $conv->to_dec($base62_num); # back to 123456 use feature 'say'; # URI unreserved characters alphabet my $uri_conv = Number::AnyBase->new_urisafe; say $uri_conv->to_base(1234567890); # ~2Bn4 say $uri_conv->to_dec( '~2Bn4' ); # 1234567890 # ASCII printable characters alphabet my $ascii_conv = Number::AnyBase->new_ascii; say $ascii_conv->to_base(199_000_000_000); # >Z8X<8 say $ascii_conv->to_dec( '>Z8X<8' ); # 199000000000 # Hexadecimal base my $hex_conv = Number::AnyBase->new( 0..9, 'A'..'F' ); say $hex_conv->to_base(2047); # 7FF say $hex_conv->to_dec( '7FF' ); # 2047 # Morse-like alphabet :-) my $morse_conv = Number::AnyBase->new( '_.' ); say $morse_conv->to_base(99); # ..___.. say $morse_conv->to_dec( '..___..' ); # 99 { # Unicode alphabet (webdings font); use utf8; binmode STDOUT, ':utf8'; my $webdings_conv = Number::AnyBase->new( '♣♤♥♦☭☹☺☻✈✪✫✭✰✵✶✻❖♩♧♪♫♬⚓⚒⛔✼✾❁❂❄❅❊☿⚡⚢⚣⚤⚥⚦⛀⛁⛦⛨' ); say $webdings_conv->to_base(1000000000); # ☺⚢♬♬⚥⛦ say $webdings_conv->to_dec( '☺⚢♬♬⚥⛦' ); # 1000000000 } # Fast native unary increment/decrement my $sequence = Number::AnyBase->fastnew(['A'..'Z']); say $sequence->next('ZZZ'); # BAAA say $sequence->prev('BAAA'); # ZZZ

First the intended usage scenario: this module has been conceived to shorten ids, URLs etc., like the most popular URL shortening services do (think of TinyURL and similar).

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 (at least for a *collision-free* transformation).

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

- 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);
- shorten the said decimal id through the "to_base" method explained below;
- 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:

- obtain the corresponding original decimal id through the "to_dec" method explained below;
- retrieve the requested item in your data store through its original decimal id you've obtained at the previous step;
- 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.

`new`

`Number::AnyBase->new( @alphabet )`

`Number::AnyBase->new( \@alphabet )`

`Number::AnyBase->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->new( '0'..'9', 'a'..'z' ); # Same as above $conv = Number::AnyBase->new( ['0'..'9', 'a'..'z'] ); # The same through a string $conv = Number::AnyBase->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->new( 'a'..'z', '0'..'9' ); # Exactly the same as above $conv = Number::AnyBase->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->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->new( qw/z z z aa/ ); # This is instead correct since the alphabet will be: 'z', 'a' Number::AnyBase->new( 'zzzaa' );

`fastnew`

`Number::AnyBase->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.

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. More precisely, it is the same as:

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

`new_base36`

The same as:

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

`new_base62`

The same as:

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

`new_base64`

The same as:

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

`new_base64url`

The same as:

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

`new_bin`

It builds a binary converter. The same as:

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

`new_oct`

It builds an octal converter. The same as:

Number::AnyBase->fastnew( ['0'..'7'] )

`new_hex`

It builds an hexadecimal converter. The same as:

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

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

`to_base`

`$string = $converter->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->accuracy(60); # For example my $bignum = Math::BigInt->new( '123456789012345678901234567890123456789012345678901234567890' ); # Or Math::GMP->new(...) my $conv = Number::AnyBase->new_base62; my $base_num = $conv->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.

`to_dec`

`$decimal_number = $converter->to_base( $base_num )`

`$decimal_bignumber = $converter->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 harm anyway).

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

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

`next`

`$string = $converter->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 = $converter->next($base_num);

It is over 2x faster than the conversion roundtrip:

$next_base_num = $converter->to_base( $converter->to_dec($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 = $converter->prev($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 = $converter->prev($base_num);

It is over 2x faster than the conversion roundtrip:

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

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

.

`alphabet`

`$listref = $converter->alphabet`

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

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.

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.

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).

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 => 10_000; my $conv = Number::AnyBase->new( 0..9, 'A'..'Z', 'a'..'z' ); my (@seq1, @seq2); my $base_num = 'zzzzzz'; # @seq1 construction through native increment: my $next = $base_num; push @seq1, $next = $conv->next($next) for 1..SEQ_LENGTH; # @seq2 construction through to_base is marginally faster than @seq1: my $dec_num = $conv->to_dec($base_num); push @seq2, $conv->to_base( $dec_num + $_ ) for 1..SEQ_LENGTH;

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

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 coversion speed gaps tend to increase with the numbers size.

- vs
`Math::BaseCalc`

- Pros
`Number::AnyBase`

is faster: decimal->base conversion is about 2x (100%) faster, base->decimal conversion is about the same,`fastnew`

is about 20% faster than`Math::BaseCalc::new`

.- Base->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`

).

- Pros
- vs
`Math::BaseConvert`

- Pros
- With native perl integers,
`Number::AnyBase`

is hugely faster: something like 200x faster in decimal->base conversion and 130x faster in base->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->base conversion and base->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 anyway be given.`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.

- With native perl integers,
- 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 call.`Math::BaseConvert`

converts also negative integers.

- Pros
- vs
`Math::Base::Convert`

- Pros
- With native perl integers,
`Number::AnyBase`

is largely faster: something like over 15x faster in decimal->base conversion and over 22x faster in base->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->base conversion and about 100% faster in base->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 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.

- With native perl integers,
- Cons
`Math::Base::Convert`

manages big numbers transparently and natively, i.e. without resorting to`Math::BigInt`

or similar modules (but, though not as pathologically 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->base conversion and about 6x in in base->decimal conversion (as already said,`Number::AnyBase`

can however use`Math::GMP`

and be faster even with big integers). `Math::Base::Convert`

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

converts also negative integers.

- Pros

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 even on big numbers without any external module.

No known bugs.

Please report any bugs or feature requests to `bug-number-AnyBase at rt.cpan.org`

, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Number-AnyBase. I will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

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)
- GitHub issues (you can also report bugs here)
- AnnoCPAN: Annotated CPAN documentation
- CPAN Ratings
- Search CPAN

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

Emanuele Zeppieri <emazep@cpan.org>

This software is copyright (c) 2012 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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