vpx/aom_dsp/entenc.c

/*Daala video codec
Copyright (c) 2001-2013 Daala project contributors.  All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

- Redistributions of source code must retain the above copyright notice, this
  list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above copyright notice,
  this list of conditions and the following disclaimer in the documentation
  and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.*/

#ifdef HAVE_CONFIG_H
#include "./config.h"
#endif

#include <stdlib.h>
#include <string.h>
#include "aom_dsp/entenc.h"

/*A range encoder.
  See entdec.c and the references for implementation details \cite{Mar79,MNW98}.

  @INPROCEEDINGS{Mar79,
   author="Martin, G.N.N.",
   title="Range encoding: an algorithm for removing redundancy from a digitised
    message",
   booktitle="Video \& Data Recording Conference",
   year=1979,
   address="Southampton",
   month=Jul,
   URL="http://www.compressconsult.com/rangecoder/rngcod.pdf.gz"
  }
  @ARTICLE{MNW98,
   author="Alistair Moffat and Radford Neal and Ian H. Witten",
   title="Arithmetic Coding Revisited",
   journal="{ACM} Transactions on Information Systems",
   year=1998,
   volume=16,
   number=3,
   pages="256--294",
   month=Jul,
   URL="http://researchcommons.waikato.ac.nz/bitstream/handle/10289/78/content.pdf"
  }*/

/*Takes updated low and range values, renormalizes them so that
   32768 <= rng < 65536 (flushing bytes from low to the pre-carry buffer if
   necessary), and stores them back in the encoder context.
  low: The new value of low.
  rng: The new value of the range.*/
static void od_ec_enc_normalize(od_ec_enc *enc, od_ec_window low,
                                unsigned rng) {
  int d;
  int c;
  int s;
  c = enc->cnt;
  OD_ASSERT(rng <= 65535U);
  d = 16 - OD_ILOG_NZ(rng);
  s = c + d;
  /*TODO: Right now we flush every time we have at least one byte available.
    Instead we should use an od_ec_window and flush right before we're about to
     shift bits off the end of the window.
    For a 32-bit window this is about the same amount of work, but for a 64-bit
     window it should be a fair win.*/
  if (s >= 0) {
    uint16_t *buf;
    uint32_t storage;
    uint32_t offs;
    unsigned m;
    buf = enc->precarry_buf;
    storage = enc->precarry_storage;
    offs = enc->offs;
    if (offs + 2 > storage) {
      storage = 2 * storage + 2;
      buf = (uint16_t *)realloc(buf, sizeof(*buf) * storage);
      if (buf == NULL) {
        enc->error = -1;
        enc->offs = 0;
        return;
      }
      enc->precarry_buf = buf;
      enc->precarry_storage = storage;
    }
    c += 16;
    m = (1 << c) - 1;
    if (s >= 8) {
      OD_ASSERT(offs < storage);
      buf[offs++] = (uint16_t)(low >> c);
      low &= m;
      c -= 8;
      m >>= 8;
    }
    OD_ASSERT(offs < storage);
    buf[offs++] = (uint16_t)(low >> c);
    s = c + d - 24;
    low &= m;
    enc->offs = offs;
  }
  enc->low = low << d;
  enc->rng = rng << d;
  enc->cnt = s;
}

/*Initializes the encoder.
  size: The initial size of the buffer, in bytes.*/
void od_ec_enc_init(od_ec_enc *enc, uint32_t size) {
  od_ec_enc_reset(enc);
  enc->buf = (unsigned char *)malloc(sizeof(*enc->buf) * size);
  enc->storage = size;
  if (size > 0 && enc->buf == NULL) {
    enc->storage = 0;
    enc->error = -1;
  }
  enc->precarry_buf = (uint16_t *)malloc(sizeof(*enc->precarry_buf) * size);
  enc->precarry_storage = size;
  if (size > 0 && enc->precarry_buf == NULL) {
    enc->precarry_storage = 0;
    enc->error = -1;
  }
}

/*Reinitializes the encoder.*/
void od_ec_enc_reset(od_ec_enc *enc) {
  enc->end_offs = 0;
  enc->end_window = 0;
  enc->nend_bits = 0;
  enc->offs = 0;
  enc->low = 0;
  enc->rng = 0x8000;
  /*This is initialized to -9 so that it crosses zero after we've accumulated
     one byte + one carry bit.*/
  enc->cnt = -9;
  enc->error = 0;
#if OD_MEASURE_EC_OVERHEAD
  enc->entropy = 0;
  enc->nb_symbols = 0;
#endif
}

/*Frees the buffers used by the encoder.*/
void od_ec_enc_clear(od_ec_enc *enc) {
  free(enc->precarry_buf);
  free(enc->buf);
}

/*Encodes a symbol given its scaled frequency information.
  The frequency information must be discernable by the decoder, assuming it
   has read only the previous symbols from the stream.
  You can change the frequency information, or even the entire source alphabet,
   so long as the decoder can tell from the context of the previously encoded
   information that it is supposed to do so as well.
  fl: The cumulative frequency of all symbols that come before the one to be
       encoded.
  fh: The cumulative frequency of all symbols up to and including the one to
       be encoded.
      Together with fl, this defines the range [fl, fh) in which the decoded
       value will fall.
  ft: The sum of the frequencies of all the symbols.
      This must be at least 16384, and no more than 32768.*/
static void od_ec_encode(od_ec_enc *enc, unsigned fl, unsigned fh,
                         unsigned ft) {
  od_ec_window l;
  unsigned r;
  int s;
  unsigned d;
  unsigned u;
  unsigned v;
  OD_ASSERT(fl < fh);
  OD_ASSERT(fh <= ft);
  OD_ASSERT(16384 <= ft);
  OD_ASSERT(ft <= 32768U);
  l = enc->low;
  r = enc->rng;
  OD_ASSERT(ft <= r);
  s = r - ft >= ft;
  ft <<= s;
  fl <<= s;
  fh <<= s;
  d = r - ft;
  OD_ASSERT(d < ft);
#if OD_EC_REDUCED_OVERHEAD
  {
    unsigned e;
    e = OD_SUBSATU(2 * d, ft);
    u = fl + OD_MINI(fl, e) + OD_MINI(OD_SUBSATU(fl, e) >> 1, d);
    v = fh + OD_MINI(fh, e) + OD_MINI(OD_SUBSATU(fh, e) >> 1, d);
  }
#else
  u = fl + OD_MINI(fl, d);
  v = fh + OD_MINI(fh, d);
#endif
  r = v - u;
  l += u;
  od_ec_enc_normalize(enc, l, r);
#if OD_MEASURE_EC_OVERHEAD
  enc->entropy -= OD_LOG2((double)(fh - fl) / ft);
  enc->nb_symbols++;
#endif
}

/*Encodes a symbol given its frequency in Q15.
  This is like od_ec_encode() when ft == 32768, but is simpler and has lower
   overhead.
  Symbols encoded with this function cannot be properly decoded with
   od_ec_decode(), and must be decoded with one of the equivalent _q15()
   functions instead.
  fl: The cumulative frequency of all symbols that come before the one to be
       encoded.
  fh: The cumulative frequency of all symbols up to and including the one to
       be encoded.*/
static void od_ec_encode_q15(od_ec_enc *enc, unsigned fl, unsigned fh) {
  od_ec_window l;
  unsigned r;
  unsigned u;
  unsigned v;
  OD_ASSERT(fl < fh);
  OD_ASSERT(fh <= 32768U);
  l = enc->low;
  r = enc->rng;
  OD_ASSERT(32768U <= r);
  u = fl * (uint32_t)r >> 15;
  v = fh * (uint32_t)r >> 15;
  r = v - u;
  l += u;
  od_ec_enc_normalize(enc, l, r);
#if OD_MEASURE_EC_OVERHEAD
  enc->entropy -= OD_LOG2((double)(fh - fl) / 32768.);
  enc->nb_symbols++;
#endif
}

/*Encodes a symbol given its frequency information with an arbitrary scale.
  This operates just like od_ec_encode(), but does not require that ft be at
   least 16384.
  fl: The cumulative frequency of all symbols that come before the one to be
       encoded.
  fh: The cumulative frequency of all symbols up to and including the one to
       be encoded.
  ft: The sum of the frequencies of all the symbols.
      This must be at least 2 and no more than 32768.*/
static void od_ec_encode_unscaled(od_ec_enc *enc, unsigned fl, unsigned fh,
                                  unsigned ft) {
  int s;
  OD_ASSERT(fl < fh);
  OD_ASSERT(fh <= ft);
  OD_ASSERT(2 <= ft);
  OD_ASSERT(ft <= 32768U);
  s = 15 - OD_ILOG_NZ(ft - 1);
  od_ec_encode(enc, fl << s, fh << s, ft << s);
}

/*Encode a bit that has an fz/ft probability of being a zero.
  val: The value to encode (0 or 1).
  fz: The probability that val is zero, scaled by ft.
  ft: The total probability.
      This must be at least 16384 and no more than 32768.*/
void od_ec_encode_bool(od_ec_enc *enc, int val, unsigned fz, unsigned ft) {
  od_ec_window l;
  unsigned r;
  int s;
  unsigned v;
  OD_ASSERT(0 < fz);
  OD_ASSERT(fz < ft);
  OD_ASSERT(16384 <= ft);
  OD_ASSERT(ft <= 32768U);
  l = enc->low;
  r = enc->rng;
  OD_ASSERT(ft <= r);
  s = r - ft >= ft;
  ft <<= s;
  fz <<= s;
  OD_ASSERT(r - ft < ft);
#if OD_EC_REDUCED_OVERHEAD
  {
    unsigned d;
    unsigned e;
    d = r - ft;
    e = OD_SUBSATU(2 * d, ft);
    v = fz + OD_MINI(fz, e) + OD_MINI(OD_SUBSATU(fz, e) >> 1, d);
  }
#else
  v = fz + OD_MINI(fz, r - ft);
#endif
  if (val) l += v;
  r = val ? r - v : v;
  od_ec_enc_normalize(enc, l, r);
#if OD_MEASURE_EC_OVERHEAD
  enc->entropy -= OD_LOG2((double)(val ? ft - fz : fz) / ft);
  enc->nb_symbols++;
#endif
}

/*Encode a bit that has an fz probability of being a zero in Q15.
  This is a simpler, lower overhead version of od_ec_encode_bool() for use when
   ft == 32768.
  Symbols encoded with this function cannot be properly decoded with
   od_ec_decode(), and must be decoded with one of the equivalent _q15()
   functions instead.
  val: The value to encode (0 or 1).
  fz: The probability that val is zero, scaled by 32768.*/
void od_ec_encode_bool_q15(od_ec_enc *enc, int val, unsigned fz) {
  od_ec_window l;
  unsigned r;
  unsigned v;
  OD_ASSERT(0 < fz);
  OD_ASSERT(fz < 32768U);
  l = enc->low;
  r = enc->rng;
  OD_ASSERT(32768U <= r);
  v = fz * (uint32_t)r >> 15;
  if (val) l += v;
  r = val ? r - v : v;
  od_ec_enc_normalize(enc, l, r);
#if OD_MEASURE_EC_OVERHEAD
  enc->entropy -= OD_LOG2((double)(val ? 32768 - fz : fz) / 32768.);
  enc->nb_symbols++;
#endif
}

/*Encodes a symbol given a cumulative distribution function (CDF) table.
  s: The index of the symbol to encode.
  cdf: The CDF, such that symbol s falls in the range
        [s > 0 ? cdf[s - 1] : 0, cdf[s]).
       The values must be monotonically non-decreasing, and the last value
        must be at least 16384, and no more than 32768.
  nsyms: The number of symbols in the alphabet.
         This should be at most 16.*/
void od_ec_encode_cdf(od_ec_enc *enc, int s, const uint16_t *cdf, int nsyms) {
  OD_ASSERT(s >= 0);
  OD_ASSERT(s < nsyms);
  od_ec_encode(enc, s > 0 ? cdf[s - 1] : 0, cdf[s], cdf[nsyms - 1]);
}

/*Encodes a symbol given a cumulative distribution function (CDF) table in Q15.
  This is a simpler, lower overhead version of od_ec_encode_cdf() for use when
   cdf[nsyms - 1] == 32768.
  Symbols encoded with this function cannot be properly decoded with
   od_ec_decode(), and must be decoded with one of the equivalent _q15()
   functions instead.
  s: The index of the symbol to encode.
  cdf: The CDF, such that symbol s falls in the range
        [s > 0 ? cdf[s - 1] : 0, cdf[s]).
       The values must be monotonically non-decreasing, and the last value
        must be exactly 32768.
  nsyms: The number of symbols in the alphabet.
         This should be at most 16.*/
void od_ec_encode_cdf_q15(od_ec_enc *enc, int s, const uint16_t *cdf,
                          int nsyms) {
  (void)nsyms;
  OD_ASSERT(s >= 0);
  OD_ASSERT(s < nsyms);
  OD_ASSERT(cdf[nsyms - 1] == 32768U);
  od_ec_encode_q15(enc, s > 0 ? cdf[s - 1] : 0, cdf[s]);
}

/*Encodes a symbol given a cumulative distribution function (CDF) table.
  s: The index of the symbol to encode.
  cdf: The CDF, such that symbol s falls in the range
        [s > 0 ? cdf[s - 1] : 0, cdf[s]).
       The values must be monotonically non-decreasing, and the last value
        must be at least 2, and no more than 32768.
  nsyms: The number of symbols in the alphabet.
         This should be at most 16.*/
void od_ec_encode_cdf_unscaled(od_ec_enc *enc, int s, const uint16_t *cdf,
                               int nsyms) {
  OD_ASSERT(s >= 0);
  OD_ASSERT(s < nsyms);
  od_ec_encode_unscaled(enc, s > 0 ? cdf[s - 1] : 0, cdf[s], cdf[nsyms - 1]);
}

/*Equivalent to od_ec_encode_cdf_q15() with the cdf scaled by
   (1 << (15 - ftb)).
  s: The index of the symbol to encode.
  cdf: The CDF, such that symbol s falls in the range
        [s > 0 ? cdf[s - 1] : 0, cdf[s]).
       The values must be monotonically non-decreasing, and the last value
        must be exactly 1 << ftb.
  nsyms: The number of symbols in the alphabet.
         This should be at most 16.
  ftb: The number of bits of precision in the cumulative distribution.
       This must be no more than 15.*/
void od_ec_encode_cdf_unscaled_dyadic(od_ec_enc *enc, int s,
                                      const uint16_t *cdf, int nsyms,
                                      unsigned ftb) {
  (void)nsyms;
  OD_ASSERT(s >= 0);
  OD_ASSERT(s < nsyms);
  OD_ASSERT(ftb <= 15);
  OD_ASSERT(cdf[nsyms - 1] == 1U << ftb);
  od_ec_encode_q15(enc, s > 0 ? cdf[s - 1] << (15 - ftb) : 0,
                   cdf[s] << (15 - ftb));
}

/*Encodes a raw unsigned integer in the stream.
  fl: The integer to encode.
  ft: The number of integers that can be encoded (one more than the max).
      This must be at least 2, and no more than 2**29.*/
void od_ec_enc_uint(od_ec_enc *enc, uint32_t fl, uint32_t ft) {
  OD_ASSERT(ft >= 2);
  OD_ASSERT(fl < ft);
  OD_ASSERT(ft <= (uint32_t)1 << (25 + OD_EC_UINT_BITS));
  if (ft > 1U << OD_EC_UINT_BITS) {
    int ft1;
    int ftb;
    ft--;
    ftb = OD_ILOG_NZ(ft) - OD_EC_UINT_BITS;
    ft1 = (int)(ft >> ftb) + 1;
    od_ec_encode_cdf_q15(enc, (int)(fl >> ftb), OD_UNIFORM_CDF_Q15(ft1), ft1);
    od_ec_enc_bits(enc, fl & (((uint32_t)1 << ftb) - 1), ftb);
  } else {
    od_ec_encode_cdf_q15(enc, (int)fl, OD_UNIFORM_CDF_Q15(ft), (int)ft);
  }
}

/*Encodes a sequence of raw bits in the stream.
  fl: The bits to encode.
  ftb: The number of bits to encode.
       This must be between 0 and 25, inclusive.*/
void od_ec_enc_bits(od_ec_enc *enc, uint32_t fl, unsigned ftb) {
  od_ec_window end_window;
  int nend_bits;
  OD_ASSERT(ftb <= 25);
  OD_ASSERT(fl < (uint32_t)1 << ftb);
#if OD_MEASURE_EC_OVERHEAD
  enc->entropy += ftb;
#endif
  end_window = enc->end_window;
  nend_bits = enc->nend_bits;
  if (nend_bits + ftb > OD_EC_WINDOW_SIZE) {
    unsigned char *buf;
    uint32_t storage;
    uint32_t end_offs;
    buf = enc->buf;
    storage = enc->storage;
    end_offs = enc->end_offs;
    if (end_offs + (OD_EC_WINDOW_SIZE >> 3) >= storage) {
      unsigned char *new_buf;
      uint32_t new_storage;
      new_storage = 2 * storage + (OD_EC_WINDOW_SIZE >> 3);
      new_buf = (unsigned char *)malloc(sizeof(*new_buf) * new_storage);
      if (new_buf == NULL) {
        enc->error = -1;
        enc->end_offs = 0;
        return;
      }
      OD_COPY(new_buf + new_storage - end_offs, buf + storage - end_offs,
              end_offs);
      storage = new_storage;
      free(buf);
      enc->buf = buf = new_buf;
      enc->storage = storage;
    }
    do {
      OD_ASSERT(end_offs < storage);
      buf[storage - ++end_offs] = (unsigned char)end_window;
      end_window >>= 8;
      nend_bits -= 8;
    } while (nend_bits >= 8);
    enc->end_offs = end_offs;
  }
  OD_ASSERT(nend_bits + ftb <= OD_EC_WINDOW_SIZE);
  end_window |= (od_ec_window)fl << nend_bits;
  nend_bits += ftb;
  enc->end_window = end_window;
  enc->nend_bits = nend_bits;
}

/*Overwrites a few bits at the very start of an existing stream, after they
   have already been encoded.
  This makes it possible to have a few flags up front, where it is easy for
   decoders to access them without parsing the whole stream, even if their
   values are not determined until late in the encoding process, without having
   to buffer all the intermediate symbols in the encoder.
  In order for this to work, at least nbits bits must have already been encoded
   using probabilities that are an exact power of two.
  The encoder can verify the number of encoded bits is sufficient, but cannot
   check this latter condition.
  val: The bits to encode (in the least nbits significant bits).
       They will be decoded in order from most-significant to least.
  nbits: The number of bits to overwrite.
         This must be no more than 8.*/
void od_ec_enc_patch_initial_bits(od_ec_enc *enc, unsigned val, int nbits) {
  int shift;
  unsigned mask;
  OD_ASSERT(nbits >= 0);
  OD_ASSERT(nbits <= 8);
  OD_ASSERT(val < 1U << nbits);
  shift = 8 - nbits;
  mask = ((1U << nbits) - 1) << shift;
  if (enc->offs > 0) {
    /*The first byte has been finalized.*/
    enc->precarry_buf[0] =
        (uint16_t)((enc->precarry_buf[0] & ~mask) | val << shift);
  } else if (9 + enc->cnt + (enc->rng == 0x8000) > nbits) {
    /*The first byte has yet to be output.*/
    enc->low = (enc->low & ~((od_ec_window)mask << (16 + enc->cnt))) |
               (od_ec_window)val << (16 + enc->cnt + shift);
  } else {
    /*The encoder hasn't even encoded _nbits of data yet.*/
    enc->error = -1;
  }
}

#if OD_MEASURE_EC_OVERHEAD
#include <stdio.h>
#endif

/*Indicates that there are no more symbols to encode.
  All remaining output bytes are flushed to the output buffer.
  od_ec_enc_reset() should be called before using the encoder again.
  bytes: Returns the size of the encoded data in the returned buffer.
  Return: A pointer to the start of the final buffer, or NULL if there was an
           encoding error.*/
unsigned char *od_ec_enc_done(od_ec_enc *enc, uint32_t *nbytes) {
  unsigned char *out;
  uint32_t storage;
  uint16_t *buf;
  uint32_t offs;
  uint32_t end_offs;
  int nend_bits;
  od_ec_window m;
  od_ec_window e;
  od_ec_window l;
  unsigned r;
  int c;
  int s;
  if (enc->error) return NULL;
#if OD_MEASURE_EC_OVERHEAD
  {
    uint32_t tell;
    /* Don't count the 1 bit we lose to raw bits as overhead. */
    tell = od_ec_enc_tell(enc) - 1;
    fprintf(stderr, "overhead: %f%%\n",
            100 * (tell - enc->entropy) / enc->entropy);
    fprintf(stderr, "efficiency: %f bits/symbol\n",
            (double)tell / enc->nb_symbols);
  }
#endif
  /*We output the minimum number of bits that ensures that the symbols encoded
     thus far will be decoded correctly regardless of the bits that follow.*/
  l = enc->low;
  r = enc->rng;
  c = enc->cnt;
  s = 9;
  m = 0x7FFF;
  e = (l + m) & ~m;
  while ((e | m) >= l + r) {
    s++;
    m >>= 1;
    e = (l + m) & ~m;
  }
  s += c;
  offs = enc->offs;
  buf = enc->precarry_buf;
  if (s > 0) {
    unsigned n;
    storage = enc->precarry_storage;
    if (offs + ((s + 7) >> 3) > storage) {
      storage = storage * 2 + ((s + 7) >> 3);
      buf = (uint16_t *)realloc(buf, sizeof(*buf) * storage);
      if (buf == NULL) {
        enc->error = -1;
        return NULL;
      }
      enc->precarry_buf = buf;
      enc->precarry_storage = storage;
    }
    n = (1 << (c + 16)) - 1;
    do {
      OD_ASSERT(offs < storage);
      buf[offs++] = (uint16_t)(e >> (c + 16));
      e &= n;
      s -= 8;
      c -= 8;
      n >>= 8;
    } while (s > 0);
  }
  /*Make sure there's enough room for the entropy-coded bits and the raw
     bits.*/
  out = enc->buf;
  storage = enc->storage;
  end_offs = enc->end_offs;
  e = enc->end_window;
  nend_bits = enc->nend_bits;
  s = -s;
  c = OD_MAXI((nend_bits - s + 7) >> 3, 0);
  if (offs + end_offs + c > storage) {
    storage = offs + end_offs + c;
    out = (unsigned char *)realloc(out, sizeof(*out) * storage);
    if (out == NULL) {
      enc->error = -1;
      return NULL;
    }
    OD_MOVE(out + storage - end_offs, out + enc->storage - end_offs, end_offs);
    enc->buf = out;
    enc->storage = storage;
  }
  /*If we have buffered raw bits, flush them as well.*/
  while (nend_bits > s) {
    OD_ASSERT(end_offs < storage);
    out[storage - ++end_offs] = (unsigned char)e;
    e >>= 8;
    nend_bits -= 8;
  }
  *nbytes = offs + end_offs;
  /*Perform carry propagation.*/
  OD_ASSERT(offs + end_offs <= storage);
  out = out + storage - (offs + end_offs);
  c = 0;
  end_offs = offs;
  while (offs-- > 0) {
    c = buf[offs] + c;
    out[offs] = (unsigned char)c;
    c >>= 8;
  }
  /*Add any remaining raw bits to the last byte.
    There is guaranteed to be enough room, because nend_bits <= s.*/
  OD_ASSERT(nend_bits <= 0 || end_offs > 0);
  if (nend_bits > 0) out[end_offs - 1] |= (unsigned char)e;
  /*Note: Unless there's an allocation error, if you keep encoding into the
     current buffer and call this function again later, everything will work
     just fine (you won't get a new packet out, but you will get a single
     buffer with the new data appended to the old).
    However, this function is O(N) where N is the amount of data coded so far,
     so calling it more than once for a given packet is a bad idea.*/
  return out;
}

/*Returns the number of bits "used" by the encoded symbols so far.
  This same number can be computed in either the encoder or the decoder, and is
   suitable for making coding decisions.
  Warning: The value returned by this function can decrease compared to an
   earlier call, even after encoding more data, if there is an encoding error
   (i.e., a failure to allocate enough space for the output buffer).
  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_enc_tell(const od_ec_enc *enc) {
  /*The 10 here counteracts the offset of -9 baked into cnt, and adds 1 extra
     bit, which we reserve for terminating the stream.*/
  return (enc->offs + enc->end_offs) * 8 + enc->cnt + enc->nend_bits + 10;
}

/*Returns the number of bits "used" by the encoded symbols so far.
  This same number can be computed in either the encoder or the decoder, and is
   suitable for making coding decisions.
  Warning: The value returned by this function can decrease compared to an
   earlier call, even after encoding more data, if there is an encoding error
   (i.e., a failure to allocate enough space for the output buffer).
  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_enc_tell_frac(const od_ec_enc *enc) {
  return od_ec_tell_frac(od_ec_enc_tell(enc), enc->rng);
}

/*Saves a entropy coder checkpoint to dst.
  This allows an encoder to reverse a series of entropy coder
   decisions if it decides that the information would have been
   better coded some other way.*/
void od_ec_enc_checkpoint(od_ec_enc *dst, const od_ec_enc *src) {
  OD_COPY(dst, src, 1);
}

/*Restores an entropy coder checkpoint saved by od_ec_enc_checkpoint.
  This can only be used to restore from checkpoints earlier in the target
   state's history: you can not switch backwards and forwards or otherwise
   switch to a state which isn't a casual ancestor of the current state.
  Restore is also incompatible with patching the initial bits, as the
   changes will remain in the restored version.*/
void od_ec_enc_rollback(od_ec_enc *dst, const od_ec_enc *src) {
  unsigned char *buf;
  uint32_t storage;
  uint16_t *precarry_buf;
  uint32_t precarry_storage;
  OD_ASSERT(dst->storage >= src->storage);
  OD_ASSERT(dst->precarry_storage >= src->precarry_storage);
  buf = dst->buf;
  storage = dst->storage;
  precarry_buf = dst->precarry_buf;
  precarry_storage = dst->precarry_storage;
  OD_COPY(dst, src, 1);
  dst->buf = buf;
  dst->storage = storage;
  dst->precarry_buf = precarry_buf;
  dst->precarry_storage = precarry_storage;
}