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Author image Michael Robinton


Math::Base::Convert - very fast base to base conversion


As a function

  use Math::Base::Convert qw( :all )
  use Math::Base::Convert qw( 


                        # comments
        bin             base 2 0,1
        dna             base 4 lower case dna
        DNA             base 4 upper case DNA
        oct             base 8 octal
        dec             base 10 decimal
        hex             base 16 lower case hex
        HEX             base 16 upper case HEX
        b62             base 62
        b64             base 64 month:C:12 day:V:31
        m64             base 64 0-63 from MIME::Base64
        iru             base 64 P10 protocol - IRCu daemon
        url             base 64 url with no %2B %2F expansion of + - /
        rex             base 64 regular expression variant
        id0             base 64 IDentifier style 0
        id1             base 64 IDentifier style 1
        xnt             base 64 XML Name Tokens (Nmtoken)
        xid             base 64 XML identifiers (Name)
        b85             base 85 RFC 1924 for IPv6 addresses
        ascii           base 96 7 bit printible 0x20 - 0x7F

  my $converted = cnv($number,optionalFROM,optionalTO);
  my $basemap = basmap(base);

As a method:

  use Math::Base::Convert;
  use Math::Base::Convert qw(:base);

  my $bc = new Math::Base::Convert(optionalFROM,optionalTO);
  my $converted = $bc->cnv($number);
  my $basemap = $bc->basemap(base);


This module provides fast functions and methods to convert between arbitrary number bases from 2 (binary) thru 65535.

This module is pure Perl, has no external dependencies, and is backward compatible with old versions of Perl 5.


Setting up the conversion parameters, context and error checking consume a significant portion of the execution time of a single base conversion. These operations are performed each time cnv is called as a function.

Using method calls eliminates a large portion of this overhead and will improve performance for repetitive conversions. See the benchmarks sub-directory in this distribution.


Number set variants courtesy of the authors of Math::Base:Cnv and Math::BaseConvert.

The functions below return a reference to an array

  $arrayref     = function;

  bin => ['0', '1']                               # binary
  dna => ['a','t','c','g']                        # lc dna
  DNA => ['A','T','C','G'],     {default}         # uc DNA
  oct => ['0'..'7']                               # octal
  dec => ['0'..'9']                               # decimal
  hex => ['0'..'9', 'a'..'f']                     # lc hex
  HEX => ['0'..'9', 'A'..'F']   {default}         # uc HEX
  b62 => ['0'..'9', 'a'..'z', 'A'..'Z']           # base 62
  b64 => ['0'..'9', 'A'..'Z', 'a'..'z', '.', '_'] # m:C:12 d:V:31
  m64 => ['A'..'Z', 'a'..'z', '0'..'9', '+', '/'] # MIMI::Base64
  iru => ['A'..'Z', 'a'..'z', '0'..'9', '[', ']'] # P10 - IRCu
  url => ['A'..'Z', 'a'..'z', '0'..'9', '*', '-'] # url no %2B %2F
  rex => ['A'..'Z', 'a'..'z', '0'..'9', '!', '-'] # regex variant
  id0 => ['A'..'Z', 'a'..'z', '0'..'9', '_', '-'] # ID 0
  id1 => ['A'..'Z', 'a'..'z', '0'..'9', '.', '_'] # ID 1
  xnt => ['A'..'Z', 'a'..'z', '0'..'9', '.', '-'] # XML (Nmtoken)
  xid => ['A'..'Z', 'a'..'z', '0'..'9', '_', ':'] # XML (Name)
  b85 => ['0'..'9', 'A'..'Z', 'a'..'z', '!', '#', # RFC 1924
          '$', '%', '&', '(', ')', '*', '+', '-', 
          ';', '<', '=', '>', '?', '@', '^', '_', 
          '', '{', '|', '}', '~']
  An arbitrary base 96 composed of printable 7 bit ascii
  from 0x20 (space) through 0x7F (tilde ~)
  ascii => [
        ' ','!','"','#','$','%','&',"'",'(',')',

  NOTE: Clean text with =~ s/\s+/ /; before applying to ascii


  • $converted = cnv($number,[from],[to])

    SCALAR context: array context covered later in this document.

    To preserve similarity to other similar base conversion modules, cnv returns the converted number string with SIGN if both the input and output base strings are in known signed set of bases in this module.

    In the case of binary, octal, hex, all leading base designator strings such as '0b','0', '0x' are automatically stripped from the input. Base designator strings are NOT applied to the output.

    The context of base FROM and TO is optional and flexible.

    Unconditional conversion from decimal to HEX [upper case]

            $converted = cnv($number);

    Example conversion from octal to default HEX [upper case] with different context for the 'octal' designator.

      base as a number
            $converted = cnv($number,8);
      base as a function    (imported)
            $converted = cnv($number,oct);
      base as text
            $converted = convbase($number,'oct');

    Conversion to/from arbitrary bases i.e.

      $converted = cnv($number); # dec -> hex (default)
      $converted = cnv($number,oct);        # oct to HEX
      $converted = cnv($number,10,HEX);     # dec to uc HEX
      $converted = cnv($number,10,hex);     # dec to lc hex
      $converted = cnv($number,dec,hex);#    same
            pointer notation
      $converted = cnv($number, oct => dec);
      $converted = cnv($number,10 => 23); # dec to base23
      $converted = cnv($number,23 => 5);  # b23 to base5
  • $bc = new Math::Base::Convert([from],[to]);

    This method has the same usage and syntax for FROM and TO as cnv above.

    Setup for unconditional conversion from HEX to decimal

            $bc = new Math::Base::Convert();

    Example conversion from octal to decimal

      base number
            $bc = new Math::Base::Convert(8);
      base function (imported)
            $bc = new Math::Base::Convert(oct);
      base text
            $bc = new Math::Base::Convert('oct')

    The number conversion for any of the above:

    NOTE: iterative conversions using a method pointer are ALWAYS faster than calling cnv as a function.

            $converted = $bc->cnv($number);
  • $converted = cnvpre($number,[from],[to])

    Same as cnv except that base descriptor PREfixes are applied to binary, octal, and hexadecimal output strings.

  • $converted = cnvabs($number,[from],[to])

    Same as cnv except that the ABSolute value of the number string is returned without SIGN is returned. i.e. just the raw string.

  • ($sign,$prefix,$string) = cnv($number,[$from,[$to]])

  • ($sign,$prefix,$string) = cnv($number,[$from,[$to]])

  • ($sign,$prefix,$string) = cnv($number,[$from,[$to]])

    ARRAY context:

    All three functions return the same items in array context.

      sign          the sign of the input number string
      prefix        the prefix which would be applied to output
      string        the raw output string
  • $basemap = basemap(base);

  • $basemap = $bc->basemap(base);

    This function / method returns a pointer to a hash that maps the keys of a base to its numeric value for base conversion. It accepts base in any of the forms described for cnv.

    The return basemap includes upper and lower case variants of the the number base in cases such as hex where upper and lower case a..f, A..F map to the same numeric value for base conversion.

      i.e. $hex_ptr = {
            0  => 0,
            1  => 1,
            2  => 2,
            3  => 3,
            4  => 4,
            5  => 5,
            6  => 6,
            7  => 7,
            8  => 8,
            9  => 9,
            A  => 10,
            B  => 11,
            C  => 12,
            D  => 13,
            E  => 14,
            F  => 15,
            a  => 10,
            b  => 11,
            c  => 12,
            d  => 13,
            e  => 14,
            f  => 15


Math::Base::Convert includes 2 development and one real world benchmark sequences included in the test suite. Benchmark results for a 500mhz system can be found in the 'benchmarks' source directory.

  make test BENCHMARK=1

Provides comparison data for bi-directional conversion of an ascending series of number strings in all base powers. The test sequence contains number strings that go from a a single 32 bit register to several. Tested bases are: (note: b32, b128, b256 not useful and are for testing only)

    base 2    4    8    16   32   64   85   128   256
        bin, dna, oct, hex, b32, b64, b85, b128, b256

Conversions are performed FROM all bases TO decimal and are repeated in the opposing direction FROM decimal TO all bases.

Benchmark 1 results indicate the Math::Base::Convert typically runs significantly faster ( 10x to 100x) than Math::BigInt based implementations used in similar modules.

  make test BENCHMARK=2

Provides comparison data for the frontend and backend converters in Math::Base::Convert's CalcPP and Shortcuts packages, and Math::Bigint conversions if it is present on the system under test.

  make test BENCHMARK=3

Checks the relative timing of short and long number string conversions. FROM a base number to n*32 bit register and TO a base number from an n*32 bit register set.

i.e. strings that convert to and from 1, 2, 3... etc.. 32 bit registers



        Math::BigInt is conditionally used in
        the test suite but is not a requirement


Conditional EXPORT functions



Conditional EXPORT function groups

        :all    => all of above
        :base   => all except 'cnv,cnvabs,cnvpre'


This module was inspired by Math::BaseConvert maintained by Shane Warden <chromatic@cpan.org> and forked from Math::BaseCnv, both authored by Pip Stuart <Pip@CPAN.Org>


Michael Robinton, <miker@cpan.org>


Copyright 2012-2015, Michael Robinton

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

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.