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#
!/usr/bin/perl
#
Daniel "Trizen" Șuteu
#
Date: 07 May 2015
#
https://github.com/trizen
#
The binary arithmetic coding algorithm.
#
See also:
#
https://en.wikipedia.org/wiki/Arithmetic_coding
use
5.010;
use
strict;
use
warnings;
use
Math::BigInt (
try
=>
'
GMP
'
);
use
Math::BigRat (
try
=>
'
GMP
'
);
sub
asciibet
{
map
{
chr
} 0 .. 255;
}
sub
cumulative_freq
{
my
(
$freq
,
$sum
) =
@_
;
my
%cf
;
my
$total
= 0;
foreach
my
$c
(asciibet()) {
if
(
exists
$freq
->
{
$c
}) {
$cf
{
$c
} =
$total
;
$total
+=
$freq
->
{
$c
};
}
}
return
%cf
;
}
sub
mass_function
{
my
(
$freq
,
$sum
) =
@_
;
my
%p
;
$p
{
$_
} = Math::BigRat
->
new(
$freq
->
{
$_
}) /
$sum
for
keys
%{
$freq
};
return
%p
;
}
sub
arithmethic_coding
{
my
(
$str
) =
@_
;
my
@chars
=
split
(
//
,
$str
);
my
%freq
;
$freq
{
$_
}++
for
@chars
;
my
$len
=
@chars
;
my
%p
= mass_function(\
%freq
,
$len
);
my
%cf
= cumulative_freq(\
%p
,
$len
);
my
$pf
= Math::BigRat
->
new(1);
my
$L
= Math::BigRat
->
new(0);
foreach
my
$c
(
@chars
) {
$L
->
badd(
$pf
*
$cf
{
$c
});
$pf
->
bmul(
$p
{
$c
});
}
my
$U
=
$L
+
$pf
;
my
$big_two
= Math::BigInt
->
new(2);
my
$two_pow
= Math::BigInt
->
new(1);
my
$n
= Math::BigRat
->
new(0);
my
$bin
=
'
'
;
for
(
my
$i
= Math::BigInt
->
new(1) ; (
$n
<
$L
||
$n
>=
$U
) ;
$i
->
binc) {
my
$m
= Math::BigRat
->
new(1)
->
bdiv(
$two_pow
->
bmul(
$big_two
));
if
(
$n
+
$m
<
$U
) {
$n
+=
$m
;
$bin
.=
'
1
'
;
}
else
{
$bin
.=
'
0
'
;
}
}
return
(
$bin
,
$len
, \
%freq
);
}
sub
arithmethic_decoding
{
my
(
$enc
,
$len
,
$freq
) =
@_
;
my
$two_pow
= Math::BigInt
->
new(1);
my
$big_two
= Math::BigInt
->
new(2);
my
$line
= Math::BigRat
->
new(0);
my
@bin
=
split
(
//
,
$enc
);
foreach
my
$i
(0 ..
$#bin
) {
$line
->
badd(
scalar
Math::BigRat
->
new(
$bin
[
$i
])
->
bdiv(
$two_pow
->
bmul(
$big_two
)));
}
my
%p
= mass_function(
$freq
,
$len
);
my
%cf
= cumulative_freq(\
%p
,
$len
);
my
%df
;
foreach
my
$k
(
keys
%p
) {
$df
{
$k
} =
$cf
{
$k
} +
$p
{
$k
};
}
my
$L
= 0;
my
$U
= 1;
my
$decoded
=
'
'
;
my
@chars
=
sort
{
$p
{
$a
}
<=>
$p
{
$b
}
or
$a
cmp
$b
}
keys
%p
;
my
$i
= 0;
while
(1) {
foreach
my
$c
(
@chars
) {
my
$w
=
$U
-
$L
;
my
$low
=
$L
+
$w
*
$cf
{
$c
};
my
$high
=
$L
+
$w
*
$df
{
$c
};
if
(
$low
<=
$line
and
$line
<
$high
) {
(
$L
,
$U
) = (
$low
,
$high
);
$decoded
.=
$c
;
if
(++
$i
==
$len
) {
return
$decoded
;
}
}
}
}
}
#
#
# Run some tests
#
foreach
my
$str
(
'
this is a message for you to encode and to decode correctly!
'
,
join
(
'
'
,
'
a
'
..
'
z
'
, 0 .. 9,
'
A
'
..
'
Z
'
, 0 .. 9),
qw(
DABDDB DABDDBBDDBA ABBDDD ABRACADABRA CoMpReSSeD Sidef Trizen google TOBEORNOTTOBEORTOBEORNOT
)
,
'
In a positional numeral system the radix, or base, is numerically equal to a number of different symbols
'
.
'
used to express the number. For example, in the decimal system the number of symbols is 10, namely 0, 1, 2,
'
.
'
3, 4, 5, 6, 7, 8, and 9. The radix is used to express any finite integer in a presumed multiplier in polynomial
'
.
'
form. For example, the number 457 is actually 4×102 + 5×101 + 7×100, where base 10 is presumed but not shown explicitly.
'
) {
my
(
$enc
,
$len
,
$freq
) = arithmethic_coding(
$str
);
my
$dec
= arithmethic_decoding(
$enc
,
$len
,
$freq
);
say
"
Encoded:
$enc
"
;
say
"
Decoded:
$dec
"
;
if
(
$str
ne
$dec
) {
die
"
\t
However that is incorrect!
"
;
}
say
"
-
"
x
80
;
}
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