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* Copyright (c) 2001-2016, Alliance for Open Media. All rights reserved
* This source code is subject to the terms of the BSD 2 Clause License and
* the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
* was not distributed with this source code in the LICENSE file, you can
* obtain it at If the Alliance for Open
* Media Patent License 1.0 was not distributed with this source code in the
* PATENTS file, you can obtain it at
#include <assert.h>
#include "aom_dsp/entdec.h"
#include "aom_dsp/prob.h"
/*A range decoder.
This is an entropy decoder based upon \cite{Mar79}, which is itself a
rediscovery of the FIFO arithmetic code introduced by \cite{Pas76}.
It is very similar to arithmetic encoding, except that encoding is done with
digits in any base, instead of with bits, and so it is faster when using
larger bases (i.e.: a byte).
The author claims an average waste of $\frac{1}{2}\log_b(2b)$ bits, where $b$
is the base, longer than the theoretical optimum, but to my knowledge there
is no published justification for this claim.
This only seems true when using near-infinite precision arithmetic so that
the process is carried out with no rounding errors.
An excellent description of implementation details is available at
A recent work \cite{MNW98} which proposes several changes to arithmetic
encoding for efficiency actually re-discovers many of the principles
behind range encoding, and presents a good theoretical analysis of them.
End of stream is handled by writing out the smallest number of bits that
ensures that the stream will be correctly decoded regardless of the value of
any subsequent bits.
od_ec_dec_tell() can be used to determine how many bits were needed to decode
all the symbols thus far; other data can be packed in the remaining bits of
the input buffer.
author="Richard Clark Pasco",
title="Source coding algorithms for fast data compression",
school="Dept. of Electrical Engineering, Stanford University",
address="Stanford, CA",
author="Martin, G.N.N.",
title="Range encoding: an algorithm for removing redundancy from a digitised
booktitle="Video & Data Recording Conference",
author="Alistair Moffat and Radford Neal and Ian H. Witten",
title="Arithmetic Coding Revisited",
journal="{ACM} Transactions on Information Systems",
/*This is meant to be a large, positive constant that can still be efficiently
loaded as an immediate (on platforms like ARM, for example).
Even relatively modest values like 100 would work fine.*/
#define OD_EC_LOTS_OF_BITS (0x4000)
/*The return value of od_ec_dec_tell does not change across an od_ec_dec_refill
static void od_ec_dec_refill(od_ec_dec *dec) {
int s;
od_ec_window dif;
int16_t cnt;
const unsigned char *bptr;
const unsigned char *end;
dif = dec->dif;
cnt = dec->cnt;
bptr = dec->bptr;
end = dec->end;
s = OD_EC_WINDOW_SIZE - 9 - (cnt + 15);
for (; s >= 0 && bptr < end; s -= 8, bptr++) {
/*Each time a byte is inserted into the window (dif), bptr advances and cnt
is incremented by 8, so the total number of consumed bits (the return
value of od_ec_dec_tell) does not change.*/
assert(s <= OD_EC_WINDOW_SIZE - 8);
dif ^= (od_ec_window)bptr[0] << s;
cnt += 8;
if (bptr >= end) {
/*We've reached the end of the buffer. It is perfectly valid for us to need
to fill the window with additional bits past the end of the buffer (and
this happens in normal operation). These bits should all just be taken
as zero. But we cannot increment bptr past 'end' (this is undefined
behavior), so we start to increment dec->tell_offs. We also don't want
to keep testing bptr against 'end', so we set cnt to OD_EC_LOTS_OF_BITS
and adjust dec->tell_offs so that the total number of unconsumed bits in
the window (dec->cnt - dec->tell_offs) does not change. This effectively
puts lots of zero bits into the window, and means we won't try to refill
it from the buffer for a very long time (at which point we'll put lots
of zero bits into the window again).*/
dec->tell_offs += OD_EC_LOTS_OF_BITS - cnt;
dec->dif = dif;
dec->cnt = cnt;
dec->bptr = bptr;
/*Takes updated dif and range values, renormalizes them so that
32768 <= rng < 65536 (reading more bytes from the stream into dif if
necessary), and stores them back in the decoder context.
dif: The new value of dif.
rng: The new value of the range.
ret: The value to return.
Return: ret.
This allows the compiler to jump to this function via a tail-call.*/
static int od_ec_dec_normalize(od_ec_dec *dec, od_ec_window dif, unsigned rng,
int ret) {
int d;
assert(rng <= 65535U);
/*The number of leading zeros in the 16-bit binary representation of rng.*/
d = 16 - OD_ILOG_NZ(rng);
/*d bits in dec->dif are consumed.*/
dec->cnt -= d;
/*This is equivalent to shifting in 1's instead of 0's.*/
dec->dif = ((dif + 1) << d) - 1;
dec->rng = rng << d;
if (dec->cnt < 0) od_ec_dec_refill(dec);
return ret;
/*Initializes the decoder.
buf: The input buffer to use.
storage: The size in bytes of the input buffer.*/
void od_ec_dec_init(od_ec_dec *dec, const unsigned char *buf,
uint32_t storage) {
dec->buf = buf;
dec->tell_offs = 10 - (OD_EC_WINDOW_SIZE - 8);
dec->end = buf + storage;
dec->bptr = buf;
dec->dif = ((od_ec_window)1 << (OD_EC_WINDOW_SIZE - 1)) - 1;
dec->rng = 0x8000;
dec->cnt = -15;
/*Decode a single binary value.
f: The probability that the bit is one, scaled by 32768.
Return: The value decoded (0 or 1).*/
int od_ec_decode_bool_q15(od_ec_dec *dec, unsigned f) {
od_ec_window dif;
od_ec_window vw;
unsigned r;
unsigned r_new;
unsigned v;
int ret;
assert(0 < f);
assert(f < 32768U);
dif = dec->dif;
r = dec->rng;
assert(dif >> (OD_EC_WINDOW_SIZE - 16) < r);
assert(32768U <= r);
v = ((r >> 8) * (uint32_t)(f >> EC_PROB_SHIFT) >> (7 - EC_PROB_SHIFT));
vw = (od_ec_window)v << (OD_EC_WINDOW_SIZE - 16);
ret = 1;
r_new = v;
if (dif >= vw) {
r_new = r - v;
dif -= vw;
ret = 0;
return od_ec_dec_normalize(dec, dif, r_new, ret);
/*Decodes a symbol given an inverse cumulative distribution function (CDF)
table in Q15.
icdf: CDF_PROB_TOP minus the CDF, such that symbol s falls in the range
[s > 0 ? (CDF_PROB_TOP - icdf[s - 1]) : 0, CDF_PROB_TOP - icdf[s]).
The values must be monotonically non-increasing, and icdf[nsyms - 1]
must be 0.
nsyms: The number of symbols in the alphabet.
This should be at most 16.
Return: The decoded symbol s.*/
int od_ec_decode_cdf_q15(od_ec_dec *dec, const uint16_t *icdf, int nsyms) {
od_ec_window dif;
unsigned r;
unsigned c;
unsigned u;
unsigned v;
int ret;
dif = dec->dif;
r = dec->rng;
const int N = nsyms - 1;
assert(dif >> (OD_EC_WINDOW_SIZE - 16) < r);
assert(icdf[nsyms - 1] == OD_ICDF(CDF_PROB_TOP));
assert(32768U <= r);
assert(7 - EC_PROB_SHIFT - CDF_SHIFT >= 0);
c = (unsigned)(dif >> (OD_EC_WINDOW_SIZE - 16));
v = r;
ret = -1;
do {
u = v;
v = ((r >> 8) * (uint32_t)(icdf[++ret] >> EC_PROB_SHIFT) >>
v += EC_MIN_PROB * (N - ret);
} while (c < v);
assert(v < u);
assert(u <= r);
r = u - v;
dif -= (od_ec_window)v << (OD_EC_WINDOW_SIZE - 16);
return od_ec_dec_normalize(dec, dif, r, ret);
/*Returns the number of bits "used" by the decoded symbols so far.
This same number can be computed in either the encoder or the decoder, and is
suitable for making coding decisions.
Return: The number of bits.
This will always be slightly larger than the exact value (e.g., all
rounding error is in the positive direction).*/
int od_ec_dec_tell(const od_ec_dec *dec) {
/*There is a window of bits stored in dec->dif. The difference
(dec->bptr - dec->buf) tells us how many bytes have been read into this
window. The difference (dec->cnt - dec->tell_offs) tells us how many of
the bits in that window remain unconsumed.*/
return (int)((dec->bptr - dec->buf) * 8 - dec->cnt + dec->tell_offs);
/*Returns the number of bits "used" by the decoded symbols so far.
This same number can be computed in either the encoder or the decoder, and is
suitable for making coding decisions.
Return: The number of bits scaled by 2**OD_BITRES.
This will always be slightly larger than the exact value (e.g., all
rounding error is in the positive direction).*/
uint32_t od_ec_dec_tell_frac(const od_ec_dec *dec) {
return od_ec_tell_frac(od_ec_dec_tell(dec), dec->rng);