# Arithmetic coding/As a generalized change of radix

Arithmetic coding/As a generalized change of radix is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Arithmetic coding is a form of entropy encoding used in lossless data compression. Normally, a string of characters such as the words "hello there" is represented using a fixed number of bits per character, as in the ASCII code. When a string is converted to arithmetic encoding, frequently used characters will be stored with fewer bits and not-so-frequently occurring characters will be stored with more bits, resulting in fewer bits used in total. Arithmetic coding differs from other forms of entropy encoding, such as Huffman coding, in that rather than separating the input into component symbols and replacing each with a code, arithmetic coding encodes the entire message into a single number.

Create a program which implements the arithmetic coding as a generalized change of radix.

Show the results, in base 10, for all the following strings:

• "DABDDB"
• "DABDDBBDDBA"
• "TOBEORNOTTOBEORTOBEORNOT"

Verify the implementation by decoding the results back into strings and checking for equality with the given strings.

## C#

Translation of: Java
`using System;using System.Collections.Generic;using System.Linq;using System.Numerics;using System.Text; namespace AruthmeticCoding {    using Freq = Dictionary<char, long>;    using Triple = Tuple<BigInteger, int, Dictionary<char, long>>;     class Program {        static Freq CumulativeFreq(Freq freq) {            long total = 0;            Freq cf = new Freq();            for (int i = 0; i < 256; i++) {                char c = (char)i;                if (freq.ContainsKey(c)) {                    long v = freq[c];                    cf[c] = total;                    total += v;                }            }            return cf;        }         static Triple ArithmeticCoding(string str, long radix) {            // The frequency of characters            Freq freq = new Freq();            foreach (char c in str) {                if (freq.ContainsKey(c)) {                    freq[c] += 1;                } else {                    freq[c] = 1;                }            }             // The cumulative frequency            Freq cf = CumulativeFreq(freq);             // Base            BigInteger @base = str.Length;             // Lower bound            BigInteger lower = 0;             // Product of all frequencies            BigInteger pf = 1;             // Each term is multiplied by the product of the            // frequencies of all previously occuring symbols            foreach (char c in str) {                BigInteger x = cf[c];                lower = lower * @base + x * pf;                pf = pf * freq[c];            }             // Upper bound            BigInteger upper = lower + pf;             int powr = 0;            BigInteger bigRadix = radix;             while (true) {                pf = pf / bigRadix;                if (pf == 0) break;                powr++;            }             BigInteger diff = (upper - 1) / (BigInteger.Pow(bigRadix, powr));            return new Triple(diff, powr, freq);        }         static string ArithmeticDecoding(BigInteger num, long radix, int pwr, Freq freq) {            BigInteger powr = radix;            BigInteger enc = num * BigInteger.Pow(powr, pwr);            long @base = freq.Values.Sum();             // Create the cumulative frequency table            Freq cf = CumulativeFreq(freq);             // Create the dictionary            Dictionary<long, char> dict = new Dictionary<long, char>();            foreach (char key in cf.Keys) {                long value = cf[key];                dict[value] = key;            }             // Fill the gaps in the dictionary            long lchar = -1;            for (long i = 0; i < @base; i++) {                if (dict.ContainsKey(i)) {                    lchar = dict[i];                } else if (lchar != -1) {                    dict[i] = (char)lchar;                }            }             // Decode the input number            StringBuilder decoded = new StringBuilder((int)@base);            BigInteger bigBase = @base;            for (long i = @base - 1; i >= 0; --i) {                BigInteger pow = BigInteger.Pow(bigBase, (int)i);                BigInteger div = enc / pow;                char c = dict[(long)div];                BigInteger fv = freq[c];                BigInteger cv = cf[c];                BigInteger diff = enc - pow * cv;                enc = diff / fv;                decoded.Append(c);            }             // Return the decoded output            return decoded.ToString();        }         static void Main(string[] args) {            long radix = 10;            string[] strings = { "DABDDB", "DABDDBBDDBA", "ABRACADABRA", "TOBEORNOTTOBEORTOBEORNOT" };            foreach (string str in strings) {                Triple encoded = ArithmeticCoding(str, radix);                string dec = ArithmeticDecoding(encoded.Item1, radix, encoded.Item2, encoded.Item3);                Console.WriteLine("{0,-25}=> {1,19} * {2}^{3}", str, encoded.Item1, radix, encoded.Item2);                if (str != dec) {                    throw new Exception("\tHowever that is incorrect!");                }            }        }    }}`
Output:
```DABDDB                   =>                 251 * 10^2
DABDDBBDDBA              =>              167351 * 10^6
TOBEORNOTTOBEORTOBEORNOT => 1150764267498783364 * 10^15```

## D

Translation of: Go
`import std.array;import std.bigint;import std.stdio;import std.typecons; BigInt bigPow(BigInt b, BigInt e) {    if (e == 0) {        return BigInt(1);    }     BigInt result = 1;    while (e > 1) {        if (e % 2 == 0) {            b *= b;            e /= 2;        } else {            result *= b;            b *= b;            e = (e - 1) / 2;        }    }     return b * result;} long[byte] cumulative_freq(long[byte] freq) {    long[byte] cf;    long total;    foreach (i; 0..256) {        byte b = cast(byte) i;        if (b in freq) {            cf[b] = total;            total += freq[b];        }    }    return cf;} Tuple!(BigInt, BigInt, long[byte]) arithmethic_coding(string str, long radix) {    // Convert the string into a slice of bytes    auto chars = cast(byte[]) str;     // The frequency characters    long[byte] freq;    foreach (c; chars) {        freq[c]++;    }     // The cumulative frequency    auto cf = cumulative_freq(freq);     // Base    BigInt base = chars.length;     // Lower bound    BigInt lower = 0;     // Product of all frequencies    BigInt pf = 1;     // Each term is multiplied by the product of the    // frequencies of all previously occurring symbols    foreach (c; chars) {        BigInt x = cf[c];         lower = lower*base + x*pf;        pf = pf*freq[c];    }     // Upper bound    auto upper = lower + pf;     BigInt tmp = pf;    auto powr = BigInt("0");     while (true) {        tmp = tmp / radix;        if (tmp == 0) {            break;        }        powr++;    }     auto diff = (upper-1) / bigPow(BigInt(radix), powr);     return tuple(diff, powr, freq);} string arithmethic_decoding(BigInt num, long radix, BigInt pow, long[byte] freq) {    BigInt powr = radix;     BigInt enc = num * bigPow(powr, pow);     BigInt base = 0;    foreach (v; freq) {        base += v;    }     // Create the cumulative frequency table    auto cf = cumulative_freq(freq);     // Create the dictionary    byte[long] dict;    foreach (k,v; cf) {        dict[v] = k;    }     // Fill the gaps in the dictionary    long lchar = -1;    for (long i=0; i<base; i++) {        if (i in dict) {            lchar = dict[i];        } else if (lchar != -1) {            dict[i] = cast(byte) lchar;        }    }     // Decode the input number    auto decoded = appender!string;    for (BigInt i=base-1; i>=0; i--) {        pow = bigPow(base, i);         auto div = enc / pow;         auto c = dict[div.toLong];        auto fv = freq[c];        auto cv = cf[c];         auto prod = pow * cv;        auto diff = enc - prod;        enc = diff / fv;         decoded.put(c);    }     // Return the decoded output    return decoded.data;} void main() {    long radix = 10;     foreach (str; ["DABDDB", "DABDDBBDDBA", "ABRACADABRA", "TOBEORNOTTOBEORTOBEORNOT"]) {        auto output = arithmethic_coding(str, radix);        auto dec = arithmethic_decoding(output[0], radix, output[1], output[2]);        writefln("%-25s=> %19s * %s^%s", str, output[0], radix, output[1]);         if (str != dec) {            throw new Exception("\tHowever that is incorrect!");        }    }}`
Output:
```DABDDB                   =>                 251 * 10^2
DABDDBBDDBA              =>              167351 * 10^6
TOBEORNOTTOBEORTOBEORNOT => 1150764267498783364 * 10^15```

## Go

`package main import (    "fmt"    "math/big") func cumulative_freq(freq map[byte]int64) map[byte]int64 {    total := int64(0)    cf := make(map[byte]int64)    for i := 0; i < 256; i++ {        b := byte(i)        if v, ok := freq[b]; ok {            cf[b] = total            total += v        }    }    return cf} func arithmethic_coding(str string, radix int64) (*big.Int,                                *big.Int, map[byte]int64) {     // Convert the string into a slice of bytes    chars := []byte(str)     // The frequency characters    freq := make(map[byte]int64)    for _, c := range chars {        freq[c] += 1    }     // The cumulative frequency    cf := cumulative_freq(freq)     // Base    base := len(chars)     // Lower bound    L := big.NewInt(0)     // Product of all frequencies    pf := big.NewInt(1)     // Each term is multiplied by the product of the    // frequencies of all previously occurring symbols    bigBase := big.NewInt(int64(base))     for _, c := range chars {        x := big.NewInt(cf[c])         L.Mul(L, bigBase)        L.Add(L, x.Mul(x, pf))        pf.Mul(pf, big.NewInt(freq[c]))    }     // Upper bound    U := big.NewInt(0)    U.Set(L)    U.Add(U, pf)     bigOne := big.NewInt(1)    bigZero := big.NewInt(0)    bigRadix := big.NewInt(radix)     tmp := big.NewInt(0).Set(pf)    powr := big.NewInt(0)     for {        tmp.Div(tmp, bigRadix)        if tmp.Cmp(bigZero) == 0 {            break        }        powr.Add(powr, bigOne)    }     diff := big.NewInt(0)    diff.Sub(U, bigOne)    diff.Div(diff, big.NewInt(0).Exp(bigRadix, powr, nil))     return diff, powr, freq} func arithmethic_decoding(num *big.Int, radix int64,          pow *big.Int, freq map[byte]int64) string {     powr := big.NewInt(radix)     enc := big.NewInt(0).Set(num)    enc.Mul(enc, powr.Exp(powr, pow, nil))     base := int64(0)    for _, v := range freq {        base += v    }     // Create the cumulative frequency table    cf := cumulative_freq(freq)     // Create the dictionary    dict := make(map[int64]byte)    for k, v := range cf {        dict[v] = k    }     // Fill the gaps in the dictionary    lchar := -1    for i := int64(0); i < base; i++ {        if v, ok := dict[i]; ok {            lchar = int(v)        } else if lchar != -1 {            dict[i] = byte(lchar)        }    }     // Decode the input number    decoded := make([]byte, base)    bigBase := big.NewInt(base)     for i := base - 1; i >= 0; i-- {         pow := big.NewInt(0)        pow.Exp(bigBase, big.NewInt(i), nil)         div := big.NewInt(0)        div.Div(enc, pow)         c := dict[div.Int64()]        fv := freq[c]        cv := cf[c]         prod := big.NewInt(0).Mul(pow, big.NewInt(cv))        diff := big.NewInt(0).Sub(enc, prod)        enc.Div(diff, big.NewInt(fv))         decoded[base-i-1] = c    }     // Return the decoded output    return string(decoded)} func main() {     var radix = int64(10)     strSlice := []string{        `DABDDB`,        `DABDDBBDDBA`,        `ABRACADABRA`,        `TOBEORNOTTOBEORTOBEORNOT`,    }     for _, str := range strSlice {        enc, pow, freq := arithmethic_coding(str, radix)        dec := arithmethic_decoding(enc, radix, pow, freq)        fmt.Printf("%-25s=> %19s * %d^%s\n", str, enc, radix, pow)         if str != dec {            panic("\tHowever that is incorrect!")        }    }}`
Output:
```DABDDB                   =>                 251 * 10^2
DABDDBBDDBA              =>              167351 * 10^6
TOBEORNOTTOBEORTOBEORNOT => 1150764267498783364 * 10^15
```

## J

Implementation:

`NB. generate a frequency dictionary from a reference stringaekDict=:verb define  d=. ~.y            NB. dictionary lists unique characters  o=. /:d            NB. in canonical order  f=. (#/.~%&x:#)y   NB. and their relative frequencies  (o{d);o{f) NB. encode a string against a reference dictaekEnc=:verb define  NB. use string to generate a dict if none provided  (aekDict y) aekEnc y:  'u F'=.x                   NB. unpack dictionary  b=. x:#y                   NB. numeric base  f=. b*F                    NB. absolute frequencies  i=. u i.y                  NB. character indices  c=. +/\0,}:f               NB. cumulative frequencies  L=. b #. (i{c)**/\1,}:i{f  NB. lower bound  p=. */i{f                  NB. product of character frequencies  e=. x:<.10^.p              NB. number of decimal positions to drop  e,~<.(L+p)%10^e) aekDec=:adverb define:  'u F'=. x                  NB. unpack dictionary  f=. m*F                    NB. frequencies of characters  c=.+/\0,}:f                NB. cumulative frequencies  C=.<:}.c,m                 NB. id lookup table  N=. (* 10&^)/y             NB. remainder being decoded  r=. ''                     NB. result of decode   for_d. m^x:i.-m do.        NB. positional values   id=. <.N%d                NB. character id   i=.C I.id                 NB. character index   N=.<.(N -(i{c)*d)%i{f     NB. corrected remainder    r=.r,u{~i                 NB. accumulated result  end.) NB. task demo utility:aek=:verb define  dict=. aekDict y  echo 'Dictionary:'  echo ' ',.(0{::dict),.' ',.":,.1{::dict  echo 'Length:'  echo ' ',":#y  echo 'Encoded:'  echo ' ',":dict aekEnc y  echo 'Decoded:'  echo ' ',":dict (#y) aekDec aekEnc y)`

Example use:

`   aek 'DABDDB'Dictionary: A 1r6 B 1r3 D 1r2Length: 6Encoded: 251 2Decoded: DABDDB    aek 'DABDDBBDDBA'Dictionary: A 2r11 B 4r11 D 5r11Length: 11Encoded: 167351 6Decoded: DABDDBBDDBA    aek 'ABRACADABRA'Dictionary: A 5r11 B 2r11 C 1r11 D 1r11 R 2r11Length: 11Encoded: 7954170 4Decoded: ABRACADABRA    aek 'TOBEORNOTTOBEORTOBEORNOT'Dictionary: B  1r8 E  1r8 N 1r12 O  1r3 R  1r8 T 5r24Length: 24Encoded: 1150764267498783364 15Decoded: TOBEORNOTTOBEORTOBEORNOT`

Note that for this task we use our plaintext to generate our dictionary for decoding. Also note that we use rational numbers, rather than floating point, for our dictionary, because floating point tends to be inexact.

## Java

Translation of: Kotlin
`import java.math.BigInteger;import java.util.HashMap;import java.util.Map;import java.util.Objects; public class ArithmeticCoding {    private static class Triple<A, B, C> {        A a;        B b;        C c;         Triple(A a, B b, C c) {            this.a = a;            this.b = b;            this.c = c;        }    }     private static class Freq extends HashMap<Character, Long> {        //"type alias"    }     private static Freq cumulativeFreq(Freq freq) {        long total = 0;        Freq cf = new Freq();        for (int i = 0; i < 256; ++i) {            char c = (char) i;            Long v = freq.get(c);            if (v != null) {                cf.put(c, total);                total += v;            }        }        return cf;    }     private static Triple<BigInteger, Integer, Freq> arithmeticCoding(String str, Long radix) {        // Convert the string into a char array        char[] chars = str.toCharArray();         // The frequency characters        Freq freq = new Freq();        for (char c : chars) {            if (!freq.containsKey(c))                freq.put(c, 1L);            else                freq.put(c, freq.get(c) + 1);        }         // The cumulative frequency        Freq cf = cumulativeFreq(freq);         // Base        BigInteger base = BigInteger.valueOf(chars.length);         // LowerBound        BigInteger lower = BigInteger.ZERO;         // Product of all frequencies        BigInteger pf = BigInteger.ONE;         // Each term is multiplied by the product of the        // frequencies of all previously occurring symbols        for (char c : chars) {            BigInteger x = BigInteger.valueOf(cf.get(c));            lower = lower.multiply(base).add(x.multiply(pf));            pf = pf.multiply(BigInteger.valueOf(freq.get(c)));        }         // Upper bound        BigInteger upper = lower.add(pf);         int powr = 0;        BigInteger bigRadix = BigInteger.valueOf(radix);         while (true) {            pf = pf.divide(bigRadix);            if (pf.equals(BigInteger.ZERO)) break;            powr++;        }         BigInteger diff = upper.subtract(BigInteger.ONE).divide(bigRadix.pow(powr));        return new Triple<>(diff, powr, freq);    }     private static String arithmeticDecoding(BigInteger num, long radix, int pwr, Freq freq) {        BigInteger powr = BigInteger.valueOf(radix);        BigInteger enc = num.multiply(powr.pow(pwr));        long base = 0;        for (Long v : freq.values()) base += v;         // Create the cumulative frequency table        Freq cf = cumulativeFreq(freq);         // Create the dictionary        Map<Long, Character> dict = new HashMap<>();        for (Map.Entry<Character, Long> entry : cf.entrySet()) dict.put(entry.getValue(), entry.getKey());         // Fill the gaps in the dictionary        long lchar = -1;        for (long i = 0; i < base; ++i) {            Character v = dict.get(i);            if (v != null) {                lchar = v;            } else if (lchar != -1) {                dict.put(i, (char) lchar);            }        }         // Decode the input number        StringBuilder decoded = new StringBuilder((int) base);        BigInteger bigBase = BigInteger.valueOf(base);        for (long i = base - 1; i >= 0; --i) {            BigInteger pow = bigBase.pow((int) i);            BigInteger div = enc.divide(pow);            Character c = dict.get(div.longValue());            BigInteger fv = BigInteger.valueOf(freq.get(c));            BigInteger cv = BigInteger.valueOf(cf.get(c));            BigInteger diff = enc.subtract(pow.multiply(cv));            enc = diff.divide(fv);            decoded.append(c);        }        // Return the decoded output        return decoded.toString();    }     public static void main(String[] args) {        long radix = 10;        String[] strings = {"DABDDB", "DABDDBBDDBA", "ABRACADABRA", "TOBEORNOTTOBEORTOBEORNOT"};        String fmt = "%-25s=> %19s * %d^%s\n";        for (String str : strings) {            Triple<BigInteger, Integer, Freq> encoded = arithmeticCoding(str, radix);            String dec = arithmeticDecoding(encoded.a, radix, encoded.b, encoded.c);            System.out.printf(fmt, str, encoded.a, radix, encoded.b);            if (!Objects.equals(str, dec)) throw new RuntimeException("\tHowever that is incorrect!");        }    }}`
Output:
```DABDDB                   =>                 251 * 10^2
DABDDBBDDBA              =>              167351 * 10^6
TOBEORNOTTOBEORTOBEORNOT => 1150764267498783364 * 10^15```

## Kotlin

Translation of: Go
`// version 1.2.10 import java.math.BigInteger typealias Freq = Map<Char, Long> val bigZero = BigInteger.ZEROval bigOne  = BigInteger.ONE fun cumulativeFreq(freq: Freq): Freq {    var total = 0L    val cf = mutableMapOf<Char, Long>()    for (i in 0..255) {        val c = i.toChar()        val v = freq[c]        if (v != null) {            cf[c] = total            total += v        }    }    return cf} fun arithmeticCoding(str: String, radix: Long): Triple<BigInteger, Int, Freq> {    // Convert the string into a char array    val chars = str.toCharArray()     // The frequency characters    val freq = mutableMapOf<Char, Long>()    for (c in chars) {        if (c !in freq)            freq[c] = 1L        else            freq[c] = freq[c]!! + 1    }     // The cumulative frequency    val cf = cumulativeFreq(freq)     // Base    val base = chars.size.toBigInteger()     // LowerBound    var lower = bigZero     // Product of all frequencies    var pf = BigInteger.ONE     // Each term is multiplied by the product of the    // frequencies of all previously occurring symbols    for (c in chars) {        val x = cf[c]!!.toBigInteger()        lower  = lower * base + x * pf        pf *= freq[c]!!.toBigInteger()    }     // Upper bound    val upper = lower + pf     var powr = 0    val bigRadix = radix.toBigInteger()     while (true) {        pf /= bigRadix        if (pf == bigZero) break        powr++    }     val diff = (upper - bigOne) / bigRadix.pow(powr)    return Triple(diff, powr, freq)} fun arithmeticDecoding(num: BigInteger, radix: Long, pwr: Int, freq: Freq): String {    val powr = radix.toBigInteger()    var enc = num * powr.pow(pwr)    var base = 0L    for ((_, v) in freq) base += v     // Create the cumulative frequency table    val cf = cumulativeFreq(freq)     // Create the dictionary    val dict = mutableMapOf<Long, Char>()    for ((k, v) in cf) dict[v] = k     // Fill the gaps in the dictionary    var lchar = -1    for (i in 0L until base) {        val v = dict[i]        if (v != null) {            lchar = v.toInt()        }        else if(lchar != -1) {            dict[i] = lchar.toChar()        }    }     // Decode the input number    val decoded = StringBuilder(base.toInt())    val bigBase = base.toBigInteger()    for (i in base - 1L downTo 0L) {        val pow = bigBase.pow(i.toInt())        val div = enc / pow        val c = dict[div.toLong()]        val fv = freq[c]!!.toBigInteger()        val cv = cf[c]!!.toBigInteger()        val diff = enc - pow * cv        enc = diff / fv        decoded.append(c)    }    // Return the decoded output    return decoded.toString()} fun main(args: Array<String>) {    val radix = 10L    val strings = listOf(        "DABDDB", "DABDDBBDDBA", "ABRACADABRA", "TOBEORNOTTOBEORTOBEORNOT"    )    val fmt = "%-25s=> %19s * %d^%s"    for (str in strings) {        val (enc, pow, freq) = arithmeticCoding(str, radix)        val dec = arithmeticDecoding(enc, radix, pow, freq)        println(fmt.format(str, enc, radix, pow))        if (str != dec) throw Exception("\tHowever that is incorrect!")    }}`
Output:
```DABDDB                   =>                 251 * 10^2
DABDDBBDDBA              =>              167351 * 10^6
TOBEORNOTTOBEORTOBEORNOT => 1150764267498783364 * 10^15
```

## Perl

`use Math::BigInt (try => 'GMP'); sub cumulative_freq {    my (\$freq) = @_;     my %cf;    my \$total = Math::BigInt->new(0);    foreach my \$c (sort keys %\$freq) {        \$cf{\$c} = \$total;        \$total += \$freq->{\$c};    }     return %cf;} sub arithmethic_coding {    my (\$str, \$radix) = @_;    my @chars = split(//, \$str);     # The frequency characters    my %freq;    \$freq{\$_}++ for @chars;     # The cumulative frequency table    my %cf = cumulative_freq(\%freq);     # Base    my \$base = Math::BigInt->new(scalar @chars);     # Lower bound    my \$L = Math::BigInt->new(0);     # Product of all frequencies    my \$pf = Math::BigInt->new(1);     # Each term is multiplied by the product of the    # frequencies of all previously occurring symbols    foreach my \$c (@chars) {        \$L->bmuladd(\$base, \$cf{\$c} * \$pf);        \$pf->bmul(\$freq{\$c});    }     # Upper bound    my \$U = \$L + \$pf;     my \$pow = Math::BigInt->new(\$pf)->blog(\$radix);    my \$enc = (\$U - 1)->bdiv(Math::BigInt->new(\$radix)->bpow(\$pow));     return (\$enc, \$pow, \%freq);} sub arithmethic_decoding {    my (\$enc, \$radix, \$pow, \$freq) = @_;     # Multiply enc by radix^pow    \$enc *= \$radix**\$pow;     # Base    my \$base = Math::BigInt->new(0);    \$base += \$_ for values %{\$freq};     # Create the cumulative frequency table    my %cf = cumulative_freq(\$freq);     # Create the dictionary    my %dict;    while (my (\$k, \$v) = each %cf) {        \$dict{\$v} = \$k;    }     # Fill the gaps in the dictionary    my \$lchar;    foreach my \$i (0 .. \$base - 1) {        if (exists \$dict{\$i}) {            \$lchar = \$dict{\$i};        }        elsif (defined \$lchar) {            \$dict{\$i} = \$lchar;        }    }     # Decode the input number    my \$decoded = '';    for (my \$pow = \$base**(\$base - 1) ; \$pow > 0 ; \$pow /= \$base) {        my \$div = \$enc / \$pow;         my \$c  = \$dict{\$div};        my \$fv = \$freq->{\$c};        my \$cv = \$cf{\$c};         \$enc = (\$enc - \$pow * \$cv) / \$fv;        \$decoded .= \$c;    }     # Return the decoded output    return \$decoded;} my \$radix = 10;    # can be any integer greater or equal with 2 foreach my \$str (qw(DABDDB DABDDBBDDBA ABRACADABRA TOBEORNOTTOBEORTOBEORNOT)) {    my (\$enc, \$pow, \$freq) = arithmethic_coding(\$str, \$radix);    my \$dec = arithmethic_decoding(\$enc, \$radix, \$pow, \$freq);     printf("%-25s=> %19s * %d^%s\n", \$str, \$enc, \$radix, \$pow);     if (\$str ne \$dec) {        die "\tHowever that is incorrect!";    }}`
Output:
```DABDDB                   =>                 251 * 10^2
DABDDBBDDBA              =>              167351 * 10^6
TOBEORNOTTOBEORTOBEORNOT => 1150764267498783364 * 10^15
```

## Perl 6

`sub cumulative_freq(%freq) {    my %cf;    my \$total = 0;    for %freq.keys.sort -> \$c {        %cf{\$c} = \$total;        \$total += %freq{\$c};    }    return %cf;} sub arithmethic_coding(\$str, \$radix) {    my @chars = \$str.comb;     # The frequency characters    my %freq;    %freq{\$_}++ for @chars;     # The cumulative frequency table    my %cf = cumulative_freq(%freq);     # Base    my \$base = @chars.elems;     # Lower bound    my \$L = 0;     # Product of all frequencies    my \$pf = 1;     # Each term is multiplied by the product of the    # frequencies of all previously occurring symbols    for @chars -> \$c {        \$L = \$L*\$base + %cf{\$c}*\$pf;        \$pf *= %freq{\$c};    }     # Upper bound    my \$U = \$L + \$pf;     my \$pow = 0;    loop {        \$pf div= \$radix;        last if \$pf == 0;        ++\$pow;    }     my \$enc = (\$U - 1) div (\$radix ** \$pow);    (\$enc, \$pow, %freq);} sub arithmethic_decoding(\$encoding, \$radix, \$pow, %freq) {     # Multiply encoding by radix^pow    my \$enc = \$encoding * \$radix**\$pow;     # Base    my \$base = [+] %freq.values;     # Create the cumulative frequency table    my %cf = cumulative_freq(%freq);     # Create the dictionary    my %dict;    for %cf.kv -> \$k,\$v {        %dict{\$v} = \$k;    }     # Fill the gaps in the dictionary    my \$lchar;    for ^\$base -> \$i {        if (%dict{\$i}:exists) {            \$lchar = %dict{\$i};        }        elsif (defined \$lchar) {            %dict{\$i} = \$lchar;        }    }     # Decode the input number    my \$decoded = '';    for reverse(^\$base) -> \$i {         my \$pow = \$base**\$i;        my \$div = \$enc div \$pow;         my \$c  = %dict{\$div};        my \$fv = %freq{\$c};        my \$cv = %cf{\$c};         my \$rem = (\$enc - \$pow*\$cv) div \$fv;         \$enc = \$rem;        \$decoded ~= \$c;    }     # Return the decoded output    return \$decoded;} my \$radix = 10;    # can be any integer greater or equal with 2 for <DABDDB DABDDBBDDBA ABRACADABRA TOBEORNOTTOBEORTOBEORNOT> -> \$str {    my (\$enc, \$pow, %freq) = arithmethic_coding(\$str, \$radix);    my \$dec = arithmethic_decoding(\$enc, \$radix, \$pow, %freq);     printf("%-25s=> %19s * %d^%s\n", \$str, \$enc, \$radix, \$pow);     if (\$str ne \$dec) {        die "\tHowever that is incorrect!";    }}`
Output:
```DABDDB                   =>                 251 * 10^2
DABDDBBDDBA              =>              167351 * 10^6
TOBEORNOTTOBEORTOBEORNOT => 1150764267498783364 * 10^15
```

## Python

Works with: Python version 3.1+
`from collections import Counter def cumulative_freq(freq):    cf = {}    total = 0    for b in range(256):        if b in freq:            cf[b] = total            total += freq[b]    return cf def arithmethic_coding(bytes, radix):     # The frequency characters    freq = Counter(bytes)     # The cumulative frequency table    cf = cumulative_freq(freq)     # Base    base = len(bytes)     # Lower bound    lower = 0     # Product of all frequencies    pf = 1     # Each term is multiplied by the product of the    # frequencies of all previously occurring symbols    for b in bytes:        lower = lower*base + cf[b]*pf        pf *= freq[b]     # Upper bound    upper = lower+pf     pow = 0    while True:        pf //= radix        if pf==0: break        pow += 1     enc = (upper-1) // radix**pow    return enc, pow, freq def arithmethic_decoding(enc, radix, pow, freq):     # Multiply enc by radix^pow    enc *= radix**pow;     # Base    base = sum(freq.values())     # Create the cumulative frequency table    cf = cumulative_freq(freq)     # Create the dictionary    dict = {}    for k,v in cf.items():        dict[v] = k     # Fill the gaps in the dictionary    lchar = None    for i in range(base):        if i in dict:            lchar = dict[i]        elif lchar is not None:            dict[i] = lchar     # Decode the input number    decoded = bytearray()    for i in range(base-1, -1, -1):        pow = base**i        div = enc//pow         c  = dict[div]        fv = freq[c]        cv = cf[c]         rem = (enc - pow*cv) // fv         enc = rem        decoded.append(c)     # Return the decoded output    return bytes(decoded) radix = 10      # can be any integer greater or equal with 2 for str in b'DABDDB DABDDBBDDBA ABRACADABRA TOBEORNOTTOBEORTOBEORNOT'.split():    enc, pow, freq = arithmethic_coding(str, radix)    dec = arithmethic_decoding(enc, radix, pow, freq)     print("%-25s=> %19s * %d^%s" % (str, enc, radix, pow))     if str != dec:    	raise Exception("\tHowever that is incorrect!")`
Output:
```DABDDB                   =>                 251 * 10^2
DABDDBBDDBA              =>              167351 * 10^6
TOBEORNOTTOBEORTOBEORNOT => 1150764267498783364 * 10^15
```

## Ruby

`def cumulative_freq(freq)  cf = {}  total = 0  freq.keys.sort.each do |b|    cf[b] = total    total += freq[b]  end  return cfend def arithmethic_coding(bytes, radix)   # The frequency characters  freq = Hash.new(0)  bytes.each { |b| freq[b] += 1 }   # The cumulative frequency table  cf = cumulative_freq(freq)   # Base  base = bytes.size   # Lower bound  lower = 0   # Product of all frequencies  pf = 1   # Each term is multiplied by the product of the  # frequencies of all previously occurring symbols  bytes.each do |b|    lower = lower*base + cf[b]*pf    pf *= freq[b]  end   # Upper bound  upper = lower+pf   pow = 0  loop do    pf /= radix    break if pf==0    pow += 1  end   enc = ((upper-1) / radix**pow)  [enc, pow, freq]end def arithmethic_decoding(enc, radix, pow, freq)   # Multiply enc by radix^pow  enc *= radix**pow;   # Base  base = freq.values.reduce(:+)   # Create the cumulative frequency table  cf = cumulative_freq(freq)   # Create the dictionary  dict = {}  cf.each_pair do |k,v|    dict[v] = k  end   # Fill the gaps in the dictionary  lchar = nil  (0...base).each do |i|    if dict.has_key?(i)      lchar = dict[i]    elsif lchar != nil      dict[i] = lchar    end  end   # Decode the input number  decoded = []  (0...base).reverse_each do |i|    pow = base**i    div = enc/pow     c  = dict[div]    fv = freq[c]    cv = cf[c]     rem = ((enc - pow*cv) / fv)     enc = rem    decoded << c  end   # Return the decoded output  return decodedend radix = 10      # can be any integer greater or equal with 2 %w(DABDDB DABDDBBDDBA ABRACADABRA TOBEORNOTTOBEORTOBEORNOT).each do |str|   enc, pow, freq = arithmethic_coding(str.bytes, radix)  dec = arithmethic_decoding(enc, radix, pow, freq).map{|b| b.chr }.join   printf("%-25s=> %19s * %d^%s\n", str, enc, radix, pow)   if str != dec    raise "\tHowever that is incorrect!"  endend`
Output:
```DABDDB                   =>                 251 * 10^2
DABDDBBDDBA              =>              167351 * 10^6
TOBEORNOTTOBEORTOBEORNOT => 1150764267498783364 * 10^15
```

## Sidef

`func cumulative_freq(freq) {    var cf = Hash()    var total = 0    256.range.each { |b|        if (freq.contains(b)) {            cf{b} = total            total += freq{b}        }    }    return cf} func arithmethic_coding(bytes, radix=10) {     # The frequency characters    var freq = Hash()    bytes.each { |b| freq{b} := 0 ++ }     # The cumulative frequency table    var cf = cumulative_freq(freq)     # Base    var base = bytes.len     # Lower bound    var L = 0     # Product of all frequencies    var pf = 1     # Each term is multiplied by the product of the    # frequencies of all previously occurring symbols    bytes.each { |b|        L = (L*base + cf{b}*pf)        pf *= freq{b}    }     # Upper bound    var U = L+pf     var pow = pf.log(radix).int    var enc = ((U-1) // radix**pow)     return (enc, pow, freq)} func arithmethic_decoding(enc, radix, pow, freq) {     # Multiply enc by radix^pow    enc *= radix**pow;     # Base    var base = freq.values.sum     # Create the cumulative frequency table    var cf = cumulative_freq(freq);     # Create the dictionary    var dict = Hash()    cf.each_kv { |k,v|        dict{v} = k    }     # Fill the gaps in the dictionary    var lchar = ''    base.range.each { |i|        if (dict.contains(i)) {            lchar = dict{i}        }        elsif (!lchar.is_empty) {            dict{i} = lchar        }    }     # Decode the input number    var decoded = []    base.range.reverse.each { |i|         var pow = base**i;        var div = enc//pow         var c  = dict{div}        var fv = freq{c}        var cv = cf{c}         var rem = ((enc - pow*cv) // fv)         enc = rem        decoded << c    }     # Return the decoded output    return decoded} var radix = 10;      # can be any integer greater or equal with 2 %w(DABDDB DABDDBBDDBA ABRACADABRA TOBEORNOTTOBEORTOBEORNOT).each { |str|     var (enc, pow, freq) = arithmethic_coding(str.bytes, radix)    var dec = arithmethic_decoding(enc, radix, pow, freq).join_bytes('UTF-8')     printf("%-25s=> %19s * %d^%s\n", str, enc, radix, pow);     if (str != dec) {        die "\tHowever that is incorrect!"    }}`
Output:
```DABDDB                   =>                 251 * 10^2
DABDDBBDDBA              =>              167351 * 10^6
TOBEORNOTTOBEORTOBEORNOT => 1150764267498783364 * 10^15
```

## zkl

Uses libGMP (GNU MP Bignum Library)

`var [const] BN=Import("zklBigNum");  // libGMP fcn cumulativeFreq(freqHash){   total,cf := 0,Dictionary();   foreach b in (256){ if(v:=freqHash.find(b)){ cf[b]=total; total+=v; } }   cf} fcn arithmethicCoding(str, radix){   bytes   :=str.split("").apply("toAsc");   // string to bytes: "0"-->0x31   freqHash:=Dictionary(); bytes.pump(Void,freqHash.incV); // frequency chars   cf      :=cumulativeFreq(freqHash);		// The cumulative frequency    base,lower:=bytes.len(), BN(0);	// Lower bound   pf:=BN(1);				// Product of all frequencies    // Each term is multiplied by the product of the   // frequencies of all previously occurring symbols   foreach b in (bytes){      lower.mul(base).add(pf*cf[b]);  // gets quite large      pf.mul(freqHash[b]);	      // gets big   }    upper,powr := lower + pf, 0;   while(1){      pf.div(radix);	// in place BigInt math, no garbage      if(pf==0) break;      powr+=1;   }   enc:=(upper - 1)/BN(radix).pow(powr);    return(enc,powr,freqHash);}`
`fcn arithmethicDecoding(enc, radix, powr, freqHash){   enc*=radix.pow(powr);   base:=freqHash.values.sum(0);   cf  :=cumulativeFreq(freqHash);   // Create the cumulative frequency table   dict:=cf.pump(Dictionary(),   // Invert/transpose cumulative table, keys are strings		fcn(kv){ kv.reverse().apply("toInt") });   // Fill the gaps in the dictionary   lchar:=Void;   foreach b in (base){      if(v:=dict.find(b)) lchar=v;      else if(lchar)      dict[b]=lchar;   }    // Decode the input number   decoded:=Data();	// byte bucket   foreach n in ([base-1..0, -1]){      pow:=BN(base).pow(n);	// a big number      div:=(enc/pow).toInt();	// a small number, convert from BigInt      c,fv,cv := dict[div],freqHash[c],cf[c];      decoded.append(c.toChar());      enc.sub(pow*cv).div(fv);	// in place BigInt math, no garbage   }   decoded.text    // Return the decoded output}`
`radix:=10;testStrings:=T(        "DABDDB",        "DABDDBBDDBA",        "ABRACADABRA",        "TOBEORNOTTOBEORTOBEORNOT",); foreach  str in (testStrings){    enc,pow,freq := arithmethicCoding(str,radix);    dec:=arithmethicDecoding(enc, radix, pow, freq);    print("%-25s=> %19s * %d^%s\n".fmt(str,enc,radix,pow));     if(str!=dec) println("\tHowever that is incorrect!");}`
Output:
```DABDDB                   =>                 251 * 10^2
DABDDBBDDBA              =>              167351 * 10^6