Ian H. Witten、Radford M. Neal和John G. Cleary在1987年發表了一篇啟發性的論文。論文中描述了一種基于整數運算的通用算術編碼器，而且還給出了由計算錯誤導致的效率低下的分析。以下源代碼來自于這篇論文：《基于算術編碼的數據壓縮》（Arithmetic Coding For Data Compression）。該論文的下載地址：http://www.sachingarg.com/compression/entropy_coding/acm87_arithmetic_coding.pdf

　　編碼函數和解碼函數的偽代碼：

/* ARITHMETIC ENCODING ALGORITHM. */

/* Call encode_symbol repeatedly for each symbol in the message.?????????? */
/* Ensure that a distinguished "terminator" symbol is encoded last, then?? */
/* transmit any value in the range [low, high).??????????????????????????? */

encode_symbol(symbo1, cum_freq)
??? range = high - low
??? high = low + range*cum_freq[symbol-1]
??? low?? = low + range*cum-freq[symbol]

/* ARITHMETIC DECODING ALGORITHM. */

/* "Value" is the number that has been received.?????????????????????????? */
/* Continue calling decode-symbol until the terminator symbol is returned. */

decode_symbol(cum_freq)
??? find symbol such that
??????? cum_freq[symbol] <= (value-low)/(high-low) < cum_freq[symbol-1]
??????????????????????????? /* This ensures that value lies within the new */
??????????????????????????? /* [low, high) range that will be calculated by */
??????????????????????????? /* the following lines of code.???????????????? */

??? range = high - low
??? high = low + range*cum_freq[symbol-1]
??? low?? = low + range*cum_freq[symbol]
??? return symbol

　　算術編碼器和解碼器的C語言實現：

arithmetic_coding.h
─────────────────────────────────────────
/* DECLARATIONS USED FOR ARITHMETIC ENCODING AND DECODING */

/* SIZE OF ARITHMETIC CODE VALUES. */

#define Code_value_bits 16????????????? /* Number of bits in a code value?? */
typedef long code_value;??????????????? /* Type of an arithmetic code value */

#define Top_value (((long)1<<Code_value_bits)-1)????? /* Largest code value */

/* HALF AND QUARTER POINTS IN THE CODE VALUE RANGE. */

#define First_qtr (Top_value/4+1)?????? /* Point after first quarter??????? */
#define Half????? (2*First_qtr)???????? /* Point after first half?????????? */
#define Third_qtr (3*First_qtr)???????? /* Point after third quarter??????? */
─────────────────────────────────────────

model.h
─────────────────────────────────────────
/* INTERFACE TO THE MODEL. */

/* THE SET OF SYMBOLS THAT MAY BE ENCODED. */

#define No_of_chars 256???????????????? /* Number of character symbols????? */
#define EOF_symbol (No_of_chars+1)????? /* Index of EOF symbol????????????? */

#define No_of_symbols (No_of_chars+1)?? /* Total number of symbols????????? */

/* TRANSLATION TABLES BETWEEN CHARACTERS AND SYMBOL INDEXES. */

int char_to_index[No_of_chars];???????? /* To index from character????????? */
unsigned char index_to_char[No_of_symbols+1]; /* To character from index??? */

/* CUMULATIVE FREQUENCY TABLE. */

#define Max_frequency 16383???????????? /* Maximum allowed frequency count */
??????????????????????????????????????? /*?? 2^14 - 1?????????????????????? */
int cum_freq[No_of_symbols+1];????????? /* Cumulative symbol frequencies??? */
─────────────────────────────────────────

encode.c
─────────────────────────────────────────
/* MAIN PROGRAM FOR ENCODING. */

#include <stdio.h>
#include "model.h"

main()
{?? start_model();???????????????????????????? /* Set up other modules.???? */
??? start_outputing_bits();
??? start_encoding();
??? for (;;) {???????????????????????????????? /* Loop through characters. */
??????? int ch; int symbol;
??????? ch = getc(stdin);????????????????????? /* Read the next character. */
??????? if (ch==EOF) break;??????????????????? /* Exit loop on end-of-file. */
??????? symbol = char_to_index[ch];??????????? /* Translate to an index.??? */
??????? encode_symbol(symbol,cum_freq);??????? /* Encode that symbol.?????? */
??????? update_model(symbol);????????????????? /* Update the model.???????? */
??? }
??? encode_symbol(EOF_symbol,cum_freq);??????? /* Encode the EOF symbol.??? */
??? done_encoding();?????????????????????????? /* Send the last few bits.?? */
??? done_outputing_bits();
??? exit(0);
}
─────────────────────────────────────────

arithmetic_encode.c
─────────────────────────────────────────
/* ARITHMETIC ENCODING ALGORITHM. */

#include "arithmetic_coding.h"

static void bit_plus_follow();?? /* Routine that follows??????????????????? */

/* CURRENT STATE OF THE ENCODING. */

static code_value low, high;??? /* Ends of the current code region????????? */
static long bits_to_follow;???? /* Number of opposite bits to output after */
??????????????????????????????? /* the next bit.??????????????????????????? */

/* START ENCODING A STREAM OF SYMBOLS. */

start_encoding()
{?? low = 0;??????????????????????????? /* Full code range.???????????????? */
??? high = Top_value;
??? bits_to_follow = 0;???????????????? /* No bits to follow next.????????? */
}

/* ENCODE A SYMBOL. */

encode_symbol(symbol,cum_freq)
??? int symbol;???????????????? /* Symbol to encode???????????????????????? */
??? int cum_freq[];???????????? /* Cumulative symbol frequencies??????????? */
{?? long range;???????????????? /* Size of the current code region????????? */
??? range = (long)(high-low)+1;
??? high = low +??????????????????????????????? /* Narrow the code region?? */
????? (range*cum_freq[symbol-1])/cum_freq[0]-1; /* to that allotted to this */
??? low = low +???????????????????????????????? /* symbol.????????????????? */
????? (range*cum_freq[symbol])/cum_freq[0];
??? for (;;) {????????????????????????????????? /* Loop to output bits.???? */
??????? if (high<Half) {
??????????? bit_plus_follow(0);???????????????? /* Output 0 if in low half. */
??????? }
??????? else if (low>=Half) {?????????????????? /* Output 1 if in high half.*/
??????????? bit_plus_follow(1);
??????????? low -= Half;
??????????? high -= Half;?????????????????????? /* Subtract offset to top. */
??????? }
??????? else if (low>=First_qtr???????????????? /* Output an opposite bit?? */
????????????? && high<Third_qtr) {????????????? /* later if in middle half. */
??????????? bits_to_follow += 1;
??????????? low -= First_qtr;?????????????????? /* Subtract offset to middle*/
??????????? high -= First_qtr;
??????? }
??????? else break;???????????????????????????? /* Otherwise exit loop.???? */
??????? low = 2*low;
??????? high = 2*high+1;??????????????????????? /* Scale up code range.???? */
??? }
}

/* FINISH ENCODING THE STREAM. */

done_encoding()
{?? bits_to_follow += 1;?????????????????????? /* Output two bits that????? */
??? if (low<First_qtr) bit_plus_follow(0);???? /* select the quarter that?? */
??? else bit_plus_follow(1);?????????????????? /* the current code range??? */
}????????????????????????????????????????????? /* contains.???????????????? */

/* OUTPUT BITS PLUS FOLLOWING OPPOSITE BITS. */

static void bit_plus_follow(bit)
??? int bit;
{?? output_bit(bit);?????????????????????????? /* Output the bit.?????????? */
??? while (bits_to_follow>0) {
??????? output_bit(!bit);????????????????????? /* Output bits_to_follow???? */
??????? bits_to_follow -= 1;?????????????????? /* opposite bits. Set??????? */
??? }????????????????????????????????????????? /* bits_to_follow to zero.?? */
}
─────────────────────────────────────────

decode.c
─────────────────────────────────────────
/* MAIN PROGPAM FOR DECODING. */

#include <stdio.h>
#include "model.h"

main ()
{?? start_model();????????????????????????????? /* Set up other modules.??? */
??? start_inputing_bits();
??? start_decoding();
??? for (;;) {????????????????????????????????? /* Loop through characters. */
??????? int ch; int symbol;
??????? symbol = decode_symbol(cum_freq);?????? /* Decode next symbol.????? */
??????? if (symbol==EOF_symbol) break;????????? /* Exit loop if EOF symbol. */
??????? ch = index_to_char[symbol];???????????? /* Translate to a character.*/
??????? putc(ch,stdout);??????????????????????? /* Write that character.??? */
??????? update_model(symbol);?????????????????? /* Update the model.??????? */
??? }
??? exit(0);
}
─────────────────────────────────────────

arithmetic_decode.c
─────────────────────────────────────────
/* ARITHMETIC DECODING ALGORITHM. */

#include "arithmetic_coding.h"

/* CURRENT STATE OF THE DECODING. */

static code_value value;??????? /* Currently-seen code value??????????????? */
static code_value low, high;??? /* Ends of current code repion????????????? */

/* START DECODING A STREAM OF SYMBOLS. */

start_decoding()
{?? int i;
??? value = 0;????????????????????????????????? /* Input bits to fill the?? */
??? for (i = 1; i<=Code_value_bits; i++) {????? /* code value.????????????? */
??????? value = 2*value+input_bit();
??? }
??? low = 0;??????????????????????????????????? /* Full code range.???????? */
??? high = Top_value;
}

/* DECODE THE NEXT SYMBOL. */

int decode_symbol(cum_freq)
??? int cum_freq[];???????????? /* Cumulative symbol frequencies??????????? */
{?? long range;???????????????? /* Size of current code region????????????? */
??? int cum;??????????????????? /* Cumulative frequency calculated????????? */
??? int symbol;???????????????? /* Symbol decoded */
??? range = (long)(high-low)+1;
??? cum =?????????????????????????????????????? /* Find cum freq for value. */
????? (((long)(value-low)+1)*cum_freq[0]-1)/range;
??? for (symbol = 1; cum_freq[symbol]>cum; symbol++) ; /* Then find symbol. */
??? high = low +??????????????????????????????? /* Narrow the code region?? */
????? (range*cum_freq[symbol-1])/cum_freq[0]-1; /* to that allotted to this */
??? low = low +???????????????????????????????? /* symbol.????????????????? */
????? (range*cum_freq[symbol])/cum_freq[0];
??? for (;;) {????????????????????????????????? /* Loop to get rid of bits. */
??????? if (high<Half) {
??????????? /* nothing */?????????????????????? /* Expand low half.???????? */
??????? }
??????? else if (low>=Half) {?????????????????? /* Expand high half.??????? */
??????????? value -= Half;
??????????? low -= Half;??????????????????????? /* Subtract offset to top. */
??????????? high -= Half;
??????? }
??????? else if (low>=First_qtr???????????????? /* Expand middle half.????? */
????????????? && high<Third_qtr) {
??????????? value -= First_qtr;
??????????? low -= First_qtr;?????????????????? /* Subtract offset to middle*/
??????????? high -= First_qtr;
??????? }
??????? else break;???????????????????????????? /* Otherwise exit loop.???? */
??????? low = 2*low;
??????? high = 2*high+1;??????????????????????? /* Scale up code range.???? */
??????? value = 2*value+input_bit();??????????? /* Move in next input blt. */
??? }
??? return symbol;
}

bit_input.c
─────────────────────────────────────────
/* BIT INPUT ROUTINES. */

#include <stdio.h>
#include "arithmetic_coding.h"

/* THE BIT BUFFER. */

static int buffer;????????????? /* Bits waiting to be input???????????????? */
static int bits_to_go;????????? /* Number of bits still in buffer?????????? */
static int garbage_bits;??????? /* Number of bits past end-of-file????????? */

/* INITIALIZE BIT INPUT. */

start_inputing_bits()
{?? bits_to_go = 0;???????????????????????????? /* Buffer starts out with?? */
??? garbage_bits = 0;?????????????????????????? /* no bits in it.?????????? */
}

/* INPUT A BIT. */

int input_bit()
{?? int t;
??? if (bits_to_go==0) {??????????????????????? /* Read the next byte if no */
??????? buffer = getc(stdin);?????????????????? /* bits are left in buffer. */
??????? if (buffer==EOF) {
??????????? garbage_bits += 1;????????????????????? /* Return arbitrary bits*/
??????????? if (garbage_bits>Code_value_bits-2) {?? /* after eof, but check */
??????????????? fprintf(stderr,"Bad input file/n"); /* for too many such.?? */
??????????????? exit(-1);
??????????? }
??????? }
??????? bits_to_go = 8;
??? }
??? t = buffer&1;?????????????????????????????? /* Return the next bit from */
??? buffer >>= 1;?????????????????????????????? /* the bottom of the byte. */
??? bits_to_go -= 1;
??? return t;
}
─────────────────────────────────────────

bit_output.c
─────────────────────────────────────────
/* BIT OUTPUT ROUTINES. */

#include <stdio.h>

/* THE BIT BUFFER. */

static int buffer;?????????????? /* Bits buffered for output??????????????? */
static int bits_to_go;?????????? /* Number of bits free in buffer?????????? */

/* INITIALIZE FOR BIT OUTPUT. */

start_outputing_bits()
{?? buffer = 0;???????????????????????????????? /* Buffer is empty to start */
??? bits_to_go = 8;???????????????????????????? /* with.??????????????????? */
}

/* OUTPUT A BIT. */

output_bit(bit)
??? int bit;
{?? buffer >>= 1;?????????????????????????????? /* Put bit in top of buffer.*/
??? if (bit) buffer |= 0x80;
??? bits_to_go -= 1;
??? if (bits_to_go==0) {??????????????????????? /* Output buffer if it is?? */
??????? putc(buffer,stdout);??????????????????? /* now full.??????????????? */
??????? bits_to_go = 8;
??? }
}

/* FLUSH OUT THE LAST BITS. */

done_outputing_bits()
{?? putc(buffer>>bits_to_go,stdout);
}
─────────────────────────────────────────

　　靜態模型和自適應模型的程序調用：

fixed_model.c
─────────────────────────────────────────
/* THE FIXED SOURCE MODEL */

#include "model.h"

int freq[No_of_symbols+1] = (
?? 0,
?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1, 124,?? 1,?? 1,?? 1,?? 1,?? 1,
?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,

/*????? !??? "??? #??? $??? %??? &??? '??? (??? )??? *??? +??? ,??? -??? .??? / */
1236,?? 1, 21,?? 9,?? 3,?? 1, 25, 15,?? 2,?? 2,?? 2,?? 1, 79, 19, 60,?? 1,

/* 0??? 1??? 2??? 3??? 4??? 5??? 6??? 7??? 8??? 9??? :??? ;??? <??? =??? >??? ? */
15, 15,?? 8,?? 5,?? 4,?? 7,?? 5,?? 4,?? 4,?? 6,?? 3,?? 2,?? 1,?? 1,?? 1,?? 1,

/* @??? A??? B??? C??? D??? E??? F??? G??? H??? I??? J??? K??? L??? M??? N??? O */
?? 1, 24, 15, 22, 12, 15, 10,?? 9, 16, 16,?? 8,?? 6, 12, 23, 13, 11,

/* P??? Q??? R??? S??? T??? U??? V??? W??? X??? Y??? Z??? [??? /??? ]??? ^??? _ */
14,?? 1, 14, 28, 29,?? 6,?? 3, 11,?? 1,?? 3,?? 1,?? 1,?? 1,?? 1,?? 1,?? 3,

/* '??? a??? b??? c??? d??? e??? f??? g??? h??? i??? j??? k??? l??? m??? n??? o */
?? 1, 491, 85, 173, 232, 744, 127, 110, 293, 418,?? 6, 39, 250, 139, 429, 446,

/* p??? q??? r??? s??? t??? u??? v??? w??? x??? y??? z??? {??? |??? }??? ~????? */
111,?? 5, 388, 375, 531, 152, 57, 97, 12, 101,?? 5,?? 2,?? 1,?? 2,?? 3,?? 1,

?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,
?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,
?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,
?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,
?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,
?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,
?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,
?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,?? 1,
?? 1
};

/* INITIALIZE THE MODEL. */

start_model()
{?? int 1;
??? for (i = 0; i<No_of_chars; i++) {?????????? /* Set up tables that?????? */
??????? char_to_index[i] = i+1;???????????????? /* translate between symbol */
??????? index_to_char[i+1] = i;???????????????? /* indexes and characters. */
??? }
??? cum_freq[No_of_symbols] = 0;
??? for (i = No_of_symbols; i>0; i--) {??????? /* Set up cumulative??????? */
??????? cum_freq[i-1] = cum_freq[i] + freq[i]; /* frequency counts.??????? */
??? }
??? if (cum_freq[0] > Max_frequency) abort();?? /* Check counts within limit*/
}

/* UPDATE THE MODEL TO ACCOUNT FOR A NEW SYMBOL. */

update_model(symbol)
??? int symbol;
{?????????????????????????????????????????????? /* Do nothing. */
}
─────────────────────────────────────────

adaptive_model.c
─────────────────────────────────────────
/* THE ADAPTIVE SOURCE MODEL */

#include "modol.h"

int freq[No_of_symbols+1];?????? /* symbol frequencies????????????????????? */

/* INITIALIZE THE MODEL. */

start_model()
{?? int i;
??? for (i = 0; i<No_of_chars; i++) {?????????? /* Set up tables that?????? */
??????? char_to_index[i] = i+1;???????????????? /* translate between symbol */
??????? index_to_char[i+1] = i;???????????????? /* indexes and characters. */
??? }
??? for (i = 0; i<=No_of_symbols; i++) {??????? /* Set up initial frequency */
??????? freq[i] = 1;??????????????????????????? /* counts to be one for all */
??????? cum_freq[i] = No_of_symbols-i;????????? /* symbols.???????????????? */
??? }
??? freq[0] = 0;??????????????????????????????? /* Freq[0] must not be the */
}?????????????????????????????????????????????? /* same as freq[1].???????? */

/* UPDATE THE MODEL TO ACCOUNT FOR A NEW SYMBOL. */

update_model(symbol)
??? int symbol;???????????????? /* Index of new symbol????????????????????? */
{?? int i;????????????????????? /* New index for symbol???????????????????? */
??? if (cum_freq[0]==Max_frequency) {?????????? /* See if frequency counts */
??????? int cum;??????????????????????????????? /* are at their maximum.??? */
??????? cum = 0;
??????? for (i = No_of_symbols; i>=0; i--) {??? /* If so, halve all the???? */
??????????? freq[i] = (freq[i]+1)/2;??????????? /* counts (keeping them???? */
??????????? cum_freq[i] = cum;????????????????? /* non-zero).?????????????? */
??????????? cum += freq[i];
??????? }
??? }
??? for (i = symbol; freq[i]==freq[i-1]; i--) ; /* Find symbol's new index. */
??? if (i<symbol) {
??????? int ch_i, ch_symbol;
??????? ch_i = index_to_char[i];??????????????? /* Update the translation?? */
??????? ch_symbol = index_to_char[symbol];????? /* tables if the symbol has */
??????? index_to_char[i] = ch_symbol;?????????? /* moved.?????????????????? */
??????? index_to_char[symbol] = ch_i;
??????? char_to_index[ch_i] = symbol;
??????? char_to_index[ch_symbol] = i;
??? }
??? freq[i] += 1;
??? while (i>0) {?????????????????????????????? /* Increment the frequency */
??????? i -= 1;???????????????????????????????? /* count for the symbol and */
??????? cum_freq[i] += 1;?????????????????????? /* update the cumulative??? */
??? }?????????????????????????????????????????? /* frequencies.???????????? */
}

?

?

?

?

?

?

?

總結

以上是生活随笔為你收集整理的算术编码（Arithmetic Coding）源代码的全部內容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網站內容還不錯，歡迎將生活随笔推薦給好友。