jdarith.c

/*
 * jdarith.c
 *
 * This file was part of the Independent JPEG Group's software:
 * Developed 1997-2015 by Guido Vollbeding.
 * libjpeg-turbo Modifications:
 * Copyright (C) 2015-2020, 2022, D. R. Commander.
 * For conditions of distribution and use, see the accompanying README.ijg
 * file.
 *
 * This file contains portable arithmetic entropy encoding routines for JPEG
 * (implementing Recommendation ITU-T T.81 | ISO/IEC 10918-1).
 *
 * Both sequential and progressive modes are supported in this single module.
 *
 * Suspension is not currently supported in this module.
 *
 * NOTE: All referenced figures are from
 * Recommendation ITU-T T.81 (1992) | ISO/IEC 10918-1:1994.
 */

#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"


#define NEG_1  ((unsigned int)-1)


/* Expanded entropy decoder object for arithmetic decoding. */

typedef struct {
  struct jpeg_entropy_decoder pub; /* public fields */

  JLONG c;       /* C register, base of coding interval + input bit buffer */
  JLONG a;               /* A register, normalized size of coding interval */
  int ct;     /* bit shift counter, # of bits left in bit buffer part of C */
                                                         /* init: ct = -16 */
                                                         /* run: ct = 0..7 */
                                                         /* error: ct = -1 */
  int last_dc_val[MAX_COMPS_IN_SCAN]; /* last DC coef for each component */
  int dc_context[MAX_COMPS_IN_SCAN]; /* context index for DC conditioning */

  unsigned int restarts_to_go;  /* MCUs left in this restart interval */

  /* Pointers to statistics areas (these workspaces have image lifespan) */
  unsigned char *dc_stats[NUM_ARITH_TBLS];
  unsigned char *ac_stats[NUM_ARITH_TBLS];

  /* Statistics bin for coding with fixed probability 0.5 */
  unsigned char fixed_bin[4];
} arith_entropy_decoder;

typedef arith_entropy_decoder *arith_entropy_ptr;

/* The following two definitions specify the allocation chunk size
 * for the statistics area.
 * According to sections F.1.4.4.1.3 and F.1.4.4.2, we need at least
 * 49 statistics bins for DC, and 245 statistics bins for AC coding.
 *
 * We use a compact representation with 1 byte per statistics bin,
 * thus the numbers directly represent byte sizes.
 * This 1 byte per statistics bin contains the meaning of the MPS
 * (more probable symbol) in the highest bit (mask 0x80), and the
 * index into the probability estimation state machine table
 * in the lower bits (mask 0x7F).
 */

#define DC_STAT_BINS  64
#define AC_STAT_BINS  256


LOCAL(int)
get_byte(j_decompress_ptr cinfo)
/* Read next input byte; we do not support suspension in this module. */
{
  struct jpeg_source_mgr *src = cinfo->src;

  if (src->bytes_in_buffer == 0)
    if (!(*src->fill_input_buffer) (cinfo))
      ERREXIT(cinfo, JERR_CANT_SUSPEND);
  src->bytes_in_buffer--;
  return *src->next_input_byte++;
}


/*
 * The core arithmetic decoding routine (common in JPEG and JBIG).
 * This needs to go as fast as possible.
 * Machine-dependent optimization facilities
 * are not utilized in this portable implementation.
 * However, this code should be fairly efficient and
 * may be a good base for further optimizations anyway.
 *
 * Return value is 0 or 1 (binary decision).
 *
 * Note: I've changed the handling of the code base & bit
 * buffer register C compared to other implementations
 * based on the standards layout & procedures.
 * While it also contains both the actual base of the
 * coding interval (16 bits) and the next-bits buffer,
 * the cut-point between these two parts is floating
 * (instead of fixed) with the bit shift counter CT.
 * Thus, we also need only one (variable instead of
 * fixed size) shift for the LPS/MPS decision, and
 * we can do away with any renormalization update
 * of C (except for new data insertion, of course).
 *
 * I've also introduced a new scheme for accessing
 * the probability estimation state machine table,
 * derived from Markus Kuhn's JBIG implementation.
 */

LOCAL(int)
arith_decode(j_decompress_ptr cinfo, unsigned char *st)
{
  register arith_entropy_ptr e = (arith_entropy_ptr)cinfo->entropy;
  register unsigned char nl, nm;
  register JLONG qe, temp;
  register int sv, data;

  /* Renormalization & data input per section D.2.6 */
  while (e->a < 0x8000L) {
    if (--e->ct < 0) {
      /* Need to fetch next data byte */
      if (cinfo->unread_marker)
        data = 0;               /* stuff zero data */
      else {
        data = get_byte(cinfo); /* read next input byte */
        if (data == 0xFF) {     /* zero stuff or marker code */
          do data = get_byte(cinfo);
          while (data == 0xFF); /* swallow extra 0xFF bytes */
          if (data == 0)
            data = 0xFF;        /* discard stuffed zero byte */
          else {
            /* Note: Different from the Huffman decoder, hitting
             * a marker while processing the compressed data
             * segment is legal in arithmetic coding.
             * The convention is to supply zero data
             * then until decoding is complete.
             */
            cinfo->unread_marker = data;
            data = 0;
          }
        }
      }
      e->c = (e->c << 8) | data; /* insert data into C register */
      if ((e->ct += 8) < 0)      /* update bit shift counter */
        /* Need more initial bytes */
        if (++e->ct == 0)
          /* Got 2 initial bytes -> re-init A and exit loop */
          e->a = 0x8000L; /* => e->a = 0x10000L after loop exit */
    }
    e->a <<= 1;
  }

  /* Fetch values from our compact representation of Table D.2:
   * Qe values and probability estimation state machine
   */
  sv = *st;
  qe = jpeg_aritab[sv & 0x7F];  /* => Qe_Value */
  nl = qe & 0xFF;  qe >>= 8;    /* Next_Index_LPS + Switch_MPS */
  nm = qe & 0xFF;  qe >>= 8;    /* Next_Index_MPS */

  /* Decode & estimation procedures per sections D.2.4 & D.2.5 */
  temp = e->a - qe;
  e->a = temp;
  temp <<= e->ct;
  if (e->c >= temp) {
    e->c -= temp;
    /* Conditional LPS (less probable symbol) exchange */
    if (e->a < qe) {
      e->a = qe;
      *st = (sv & 0x80) ^ nm;   /* Estimate_after_MPS */
    } else {
      e->a = qe;
      *st = (sv & 0x80) ^ nl;   /* Estimate_after_LPS */
      sv ^= 0x80;               /* Exchange LPS/MPS */
    }
  } else if (e->a < 0x8000L) {
    /* Conditional MPS (more probable symbol) exchange */
    if (e->a < qe) {
      *st = (sv & 0x80) ^ nl;   /* Estimate_after_LPS */
      sv ^= 0x80;               /* Exchange LPS/MPS */
    } else {
      *st = (sv & 0x80) ^ nm;   /* Estimate_after_MPS */
    }
  }

  return sv >> 7;
}


/*
 * Check for a restart marker & resynchronize decoder.
 */

LOCAL(void)
process_restart(j_decompress_ptr cinfo)
{
  arith_entropy_ptr entropy = (arith_entropy_ptr)cinfo->entropy;
  int ci;
  jpeg_component_info *compptr;

  /* Advance past the RSTn marker */
  if (!(*cinfo->marker->read_restart_marker) (cinfo))
    ERREXIT(cinfo, JERR_CANT_SUSPEND);

  /* Re-initialize statistics areas */
  for (ci = 0; ci < cinfo->comps_in_scan; ci++) {
    compptr = cinfo->cur_comp_info[ci];
    if (!cinfo->progressive_mode || (cinfo->Ss == 0 && cinfo->Ah == 0)) {
      memset(entropy->dc_stats[compptr->dc_tbl_no], 0, DC_STAT_BINS);
      /* Reset DC predictions to 0 */
      entropy->last_dc_val[ci] = 0;
      entropy->dc_context[ci] = 0;
    }
    if (!cinfo->progressive_mode || cinfo->Ss) {
      memset(entropy->ac_stats[compptr->ac_tbl_no], 0, AC_STAT_BINS);
    }
  }

  /* Reset arithmetic decoding variables */
  entropy->c = 0;
  entropy->a = 0;
  entropy->ct = -16;    /* force reading 2 initial bytes to fill C */

  /* Reset restart counter */
  entropy->restarts_to_go = cinfo->restart_interval;
}


/*
 * Arithmetic MCU decoding.
 * Each of these routines decodes and returns one MCU's worth of
 * arithmetic-compressed coefficients.
 * The coefficients are reordered from zigzag order into natural array order,
 * but are not dequantized.
 *
 * The i'th block of the MCU is stored into the block pointed to by
 * MCU_data[i].  WE ASSUME THIS AREA IS INITIALLY ZEROED BY THE CALLER.
 */

/*
 * MCU decoding for DC initial scan (either spectral selection,
 * or first pass of successive approximation).
 */

METHODDEF(boolean)
decode_mcu_DC_first(j_decompress_ptr cinfo, JBLOCKROW *MCU_data)
{
  arith_entropy_ptr entropy = (arith_entropy_ptr)cinfo->entropy;
  JBLOCKROW block;
  unsigned char *st;
  int blkn, ci, tbl, sign;
  int v, m;

  /* Process restart marker if needed */
  if (cinfo->restart_interval) {
    if (entropy->restarts_to_go == 0)
      process_restart(cinfo);
    entropy->restarts_to_go--;
  }

  if (entropy->ct == -1) return TRUE;   /* if error do nothing */

  /* Outer loop handles each block in the MCU */

  for (blkn = 0; blkn < cinfo->blocks_in_MCU; blkn++) {
    block = MCU_data[blkn];
    ci = cinfo->MCU_membership[blkn];
    tbl = cinfo->cur_comp_info[ci]->dc_tbl_no;

    /* Sections F.2.4.1 & F.1.4.4.1: Decoding of DC coefficients */

    /* Table F.4: Point to statistics bin S0 for DC coefficient coding */
    st = entropy->dc_stats[tbl] + entropy->dc_context[ci];

    /* Figure F.19: Decode_DC_DIFF */
    if (arith_decode(cinfo, st) == 0)
      entropy->dc_context[ci] = 0;
    else {
      /* Figure F.21: Decoding nonzero value v */
      /* Figure F.22: Decoding the sign of v */
      sign = arith_decode(cinfo, st + 1);
      st += 2;  st += sign;
      /* Figure F.23: Decoding the magnitude category of v */
      if ((m = arith_decode(cinfo, st)) != 0) {
        st = entropy->dc_stats[tbl] + 20;       /* Table F.4: X1 = 20 */
        while (arith_decode(cinfo, st)) {
          if ((m <<= 1) == 0x8000) {
            WARNMS(cinfo, JWRN_ARITH_BAD_CODE);
            entropy->ct = -1;                   /* magnitude overflow */
            return TRUE;
          }
          st += 1;
        }
      }
      /* Section F.1.4.4.1.2: Establish dc_context conditioning category */
      if (m < (int)((1L << cinfo->arith_dc_L[tbl]) >> 1))
        entropy->dc_context[ci] = 0;               /* zero diff category */
      else if (m > (int)((1L << cinfo->arith_dc_U[tbl]) >> 1))
        entropy->dc_context[ci] = 12 + (sign * 4); /* large diff category */
      else
        entropy->dc_context[ci] = 4 + (sign * 4);  /* small diff category */
      v = m;
      /* Figure F.24: Decoding the magnitude bit pattern of v */
      st += 14;
      while (m >>= 1)
        if (arith_decode(cinfo, st)) v |= m;
      v += 1;  if (sign) v = -v;
      entropy->last_dc_val[ci] = (entropy->last_dc_val[ci] + v) & 0xffff;
    }

    /* Scale and output the DC coefficient (assumes jpeg_natural_order[0]=0) */
    (*block)[0] = (JCOEF)LEFT_SHIFT(entropy->last_dc_val[ci], cinfo->Al);
  }

  return TRUE;
}


/*
 * MCU decoding for AC initial scan (either spectral selection,
 * or first pass of successive approximation).
 */

METHODDEF(boolean)
decode_mcu_AC_first(j_decompress_ptr cinfo, JBLOCKROW *MCU_data)
{
  arith_entropy_ptr entropy = (arith_entropy_ptr)cinfo->entropy;
  JBLOCKROW block;
  unsigned char *st;
  int tbl, sign, k;
  int v, m;

  /* Process restart marker if needed */
  if (cinfo->restart_interval) {
    if (entropy->restarts_to_go == 0)
      process_restart(cinfo);
    entropy->restarts_to_go--;
  }

  if (entropy->ct == -1) return TRUE;   /* if error do nothing */

  /* There is always only one block per MCU */
  block = MCU_data[0];
  tbl = cinfo->cur_comp_info[0]->ac_tbl_no;

  /* Sections F.2.4.2 & F.1.4.4.2: Decoding of AC coefficients */

  /* Figure F.20: Decode_AC_coefficients */
  for (k = cinfo->Ss; k <= cinfo->Se; k++) {
    st = entropy->ac_stats[tbl] + 3 * (k - 1);
    if (arith_decode(cinfo, st)) break;         /* EOB flag */
    while (arith_decode(cinfo, st + 1) == 0) {
      st += 3;  k++;
      if (k > cinfo->Se) {
        WARNMS(cinfo, JWRN_ARITH_BAD_CODE);
        entropy->ct = -1;                       /* spectral overflow */
        return TRUE;
      }
    }
    /* Figure F.21: Decoding nonzero value v */
    /* Figure F.22: Decoding the sign of v */
    sign = arith_decode(cinfo, entropy->fixed_bin);
    st += 2;
    /* Figure F.23: Decoding the magnitude category of v */
    if ((m = arith_decode(cinfo, st)) != 0) {
      if (arith_decode(cinfo, st)) {
        m <<= 1;
        st = entropy->ac_stats[tbl] +
             (k <= cinfo->arith_ac_K[tbl] ? 189 : 217);
        while (arith_decode(cinfo, st)) {
          if ((m <<= 1) == 0x8000) {
            WARNMS(cinfo, JWRN_ARITH_BAD_CODE);
            entropy->ct = -1;                   /* magnitude overflow */
            return TRUE;
          }
          st += 1;
        }
      }
    }
    v = m;
    /* Figure F.24: Decoding the magnitude bit pattern of v */
    st += 14;
    while (m >>= 1)
      if (arith_decode(cinfo, st)) v |= m;
    v += 1;  if (sign) v = -v;
    /* Scale and output coefficient in natural (dezigzagged) order */
    (*block)[jpeg_natural_order[k]] = (JCOEF)((unsigned)v << cinfo->Al);
  }

  return TRUE;
}


/*
 * MCU decoding for DC successive approximation refinement scan.
 */

METHODDEF(boolean)
decode_mcu_DC_refine(j_decompress_ptr cinfo, JBLOCKROW *MCU_data)
{
  arith_entropy_ptr entropy = (arith_entropy_ptr)cinfo->entropy;
  unsigned char *st;
  int p1, blkn;

  /* Process restart marker if needed */
  if (cinfo->restart_interval) {
    if (entropy->restarts_to_go == 0)
      process_restart(cinfo);
    entropy->restarts_to_go--;
  }

  st = entropy->fixed_bin;      /* use fixed probability estimation */
  p1 = 1 << cinfo->Al;          /* 1 in the bit position being coded */

  /* Outer loop handles each block in the MCU */

  for (blkn = 0; blkn < cinfo->blocks_in_MCU; blkn++) {
    /* Encoded data is simply the next bit of the two's-complement DC value */
    if (arith_decode(cinfo, st))
      MCU_data[blkn][0][0] |= p1;
  }

  return TRUE;
}


/*
 * MCU decoding for AC successive approximation refinement scan.
 */

METHODDEF(boolean)
decode_mcu_AC_refine(j_decompress_ptr cinfo, JBLOCKROW *MCU_data)
{
  arith_entropy_ptr entropy = (arith_entropy_ptr)cinfo->entropy;
  JBLOCKROW block;
  JCOEFPTR thiscoef;
  unsigned char *st;
  int tbl, k, kex;
  int p1, m1;

  /* Process restart marker if needed */
  if (cinfo->restart_interval) {
    if (entropy->restarts_to_go == 0)
      process_restart(cinfo);
    entropy->restarts_to_go--;
  }

  if (entropy->ct == -1) return TRUE;   /* if error do nothing */

  /* There is always only one block per MCU */
  block = MCU_data[0];
  tbl = cinfo->cur_comp_info[0]->ac_tbl_no;

  p1 = 1 << cinfo->Al;          /* 1 in the bit position being coded */
  m1 = (NEG_1) << cinfo->Al;    /* -1 in the bit position being coded */

  /* Establish EOBx (previous stage end-of-block) index */
  for (kex = cinfo->Se; kex > 0; kex--)
    if ((*block)[jpeg_natural_order[kex]]) break;

  for (k = cinfo->Ss; k <= cinfo->Se; k++) {
    st = entropy->ac_stats[tbl] + 3 * (k - 1);
    if (k > kex)
      if (arith_decode(cinfo, st)) break;       /* EOB flag */
    for (;;) {
      thiscoef = *block + jpeg_natural_order[k];
      if (*thiscoef) {                          /* previously nonzero coef */
        if (arith_decode(cinfo, st + 2)) {
          if (*thiscoef < 0)
            *thiscoef += (JCOEF)m1;
          else
            *thiscoef += (JCOEF)p1;
        }
        break;
      }
      if (arith_decode(cinfo, st + 1)) {        /* newly nonzero coef */
        if (arith_decode(cinfo, entropy->fixed_bin))
          *thiscoef = (JCOEF)m1;
        else
          *thiscoef = (JCOEF)p1;
        break;
      }
      st += 3;  k++;
      if (k > cinfo->Se) {
        WARNMS(cinfo, JWRN_ARITH_BAD_CODE);
        entropy->ct = -1;                       /* spectral overflow */
        return TRUE;
      }
    }
  }

  return TRUE;
}


/*
 * Decode one MCU's worth of arithmetic-compressed coefficients.
 */

METHODDEF(boolean)
decode_mcu(j_decompress_ptr cinfo, JBLOCKROW *MCU_data)
{
  arith_entropy_ptr entropy = (arith_entropy_ptr)cinfo->entropy;
  jpeg_component_info *compptr;
  JBLOCKROW block;
  unsigned char *st;
  int blkn, ci, tbl, sign, k;
  int v, m;

  /* Process restart marker if needed */
  if (cinfo->restart_interval) {
    if (entropy->restarts_to_go == 0)
      process_restart(cinfo);
    entropy->restarts_to_go--;
  }

  if (entropy->ct == -1) return TRUE;   /* if error do nothing */

  /* Outer loop handles each block in the MCU */

  for (blkn = 0; blkn < cinfo->blocks_in_MCU; blkn++) {
    block = MCU_data ? MCU_data[blkn] : NULL;
    ci = cinfo->MCU_membership[blkn];
    compptr = cinfo->cur_comp_info[ci];

    /* Sections F.2.4.1 & F.1.4.4.1: Decoding of DC coefficients */

    tbl = compptr->dc_tbl_no;

    /* Table F.4: Point to statistics bin S0 for DC coefficient coding */
    st = entropy->dc_stats[tbl] + entropy->dc_context[ci];

    /* Figure F.19: Decode_DC_DIFF */
    if (arith_decode(cinfo, st) == 0)
      entropy->dc_context[ci] = 0;
    else {
      /* Figure F.21: Decoding nonzero value v */
      /* Figure F.22: Decoding the sign of v */
      sign = arith_decode(cinfo, st + 1);
      st += 2;  st += sign;
      /* Figure F.23: Decoding the magnitude category of v */
      if ((m = arith_decode(cinfo, st)) != 0) {
        st = entropy->dc_stats[tbl] + 20;       /* Table F.4: X1 = 20 */
        while (arith_decode(cinfo, st)) {
          if ((m <<= 1) == 0x8000) {
            WARNMS(cinfo, JWRN_ARITH_BAD_CODE);
            entropy->ct = -1;                   /* magnitude overflow */
            return TRUE;
          }
          st += 1;
        }
      }
      /* Section F.1.4.4.1.2: Establish dc_context conditioning category */
      if (m < (int)((1L << cinfo->arith_dc_L[tbl]) >> 1))
        entropy->dc_context[ci] = 0;               /* zero diff category */
      else if (m > (int)((1L << cinfo->arith_dc_U[tbl]) >> 1))
        entropy->dc_context[ci] = 12 + (sign * 4); /* large diff category */
      else
        entropy->dc_context[ci] = 4 + (sign * 4);  /* small diff category */
      v = m;
      /* Figure F.24: Decoding the magnitude bit pattern of v */
      st += 14;
      while (m >>= 1)
        if (arith_decode(cinfo, st)) v |= m;
      v += 1;  if (sign) v = -v;
      entropy->last_dc_val[ci] = (entropy->last_dc_val[ci] + v) & 0xffff;
    }

    if (block)
      (*block)[0] = (JCOEF)entropy->last_dc_val[ci];

    /* Sections F.2.4.2 & F.1.4.4.2: Decoding of AC coefficients */

    tbl = compptr->ac_tbl_no;

    /* Figure F.20: Decode_AC_coefficients */
    for (k = 1; k <= DCTSIZE2 - 1; k++) {
      st = entropy->ac_stats[tbl] + 3 * (k - 1);
      if (arith_decode(cinfo, st)) break;       /* EOB flag */
      while (arith_decode(cinfo, st + 1) == 0) {
        st += 3;  k++;
        if (k > DCTSIZE2 - 1) {
          WARNMS(cinfo, JWRN_ARITH_BAD_CODE);
          entropy->ct = -1;                     /* spectral overflow */
          return TRUE;
        }
      }
      /* Figure F.21: Decoding nonzero value v */
      /* Figure F.22: Decoding the sign of v */
      sign = arith_decode(cinfo, entropy->fixed_bin);
      st += 2;
      /* Figure F.23: Decoding the magnitude category of v */
      if ((m = arith_decode(cinfo, st)) != 0) {
        if (arith_decode(cinfo, st)) {
          m <<= 1;
          st = entropy->ac_stats[tbl] +
               (k <= cinfo->arith_ac_K[tbl] ? 189 : 217);
          while (arith_decode(cinfo, st)) {
            if ((m <<= 1) == 0x8000) {
              WARNMS(cinfo, JWRN_ARITH_BAD_CODE);
              entropy->ct = -1;                 /* magnitude overflow */
              return TRUE;
            }
            st += 1;
          }
        }
      }
      v = m;
      /* Figure F.24: Decoding the magnitude bit pattern of v */
      st += 14;
      while (m >>= 1)
        if (arith_decode(cinfo, st)) v |= m;
      v += 1;  if (sign) v = -v;
      if (block)
        (*block)[jpeg_natural_order[k]] = (JCOEF)v;
    }
  }

  return TRUE;
}


/*
 * Initialize for an arithmetic-compressed scan.
 */

METHODDEF(void)
start_pass(j_decompress_ptr cinfo)
{
  arith_entropy_ptr entropy = (arith_entropy_ptr)cinfo->entropy;
  int ci, tbl;
  jpeg_component_info *compptr;

  if (cinfo->progressive_mode) {
    /* Validate progressive scan parameters */
    if (cinfo->Ss == 0) {
      if (cinfo->Se != 0)
        goto bad;
    } else {
      /* need not check Ss/Se < 0 since they came from unsigned bytes */
      if (cinfo->Se < cinfo->Ss || cinfo->Se > DCTSIZE2 - 1)
        goto bad;
      /* AC scans may have only one component */
      if (cinfo->comps_in_scan != 1)
        goto bad;
    }
    if (cinfo->Ah != 0) {
      /* Successive approximation refinement scan: must have Al = Ah-1. */
      if (cinfo->Ah - 1 != cinfo->Al)
        goto bad;
    }
    if (cinfo->Al > 13) {       /* need not check for < 0 */
bad:
      ERREXIT4(cinfo, JERR_BAD_PROGRESSION,
               cinfo->Ss, cinfo->Se, cinfo->Ah, cinfo->Al);
    }
    /* Update progression status, and verify that scan order is legal.
     * Note that inter-scan inconsistencies are treated as warnings
     * not fatal errors ... not clear if this is right way to behave.
     */
    for (ci = 0; ci < cinfo->comps_in_scan; ci++) {
      int coefi, cindex = cinfo->cur_comp_info[ci]->component_index;
      int *coef_bit_ptr = &cinfo->coef_bits[cindex][0];
      int *prev_coef_bit_ptr =
        &cinfo->coef_bits[cindex + cinfo->num_components][0];
      if (cinfo->Ss && coef_bit_ptr[0] < 0) /* AC without prior DC scan */
        WARNMS2(cinfo, JWRN_BOGUS_PROGRESSION, cindex, 0);
      for (coefi = MIN(cinfo->Ss, 1); coefi <= MAX(cinfo->Se, 9); coefi++) {
        if (cinfo->input_scan_number > 1)
          prev_coef_bit_ptr[coefi] = coef_bit_ptr[coefi];
        else
          prev_coef_bit_ptr[coefi] = 0;
      }
      for (coefi = cinfo->Ss; coefi <= cinfo->Se; coefi++) {
        int expected = (coef_bit_ptr[coefi] < 0) ? 0 : coef_bit_ptr[coefi];
        if (cinfo->Ah != expected)
          WARNMS2(cinfo, JWRN_BOGUS_PROGRESSION, cindex, coefi);
        coef_bit_ptr[coefi] = cinfo->Al;
      }
    }
    /* Select MCU decoding routine */
    if (cinfo->Ah == 0) {
      if (cinfo->Ss == 0)
        entropy->pub.decode_mcu = decode_mcu_DC_first;
      else
        entropy->pub.decode_mcu = decode_mcu_AC_first;
    } else {
      if (cinfo->Ss == 0)
        entropy->pub.decode_mcu = decode_mcu_DC_refine;
      else
        entropy->pub.decode_mcu = decode_mcu_AC_refine;
    }
  } else {
    /* Check that the scan parameters Ss, Se, Ah/Al are OK for sequential JPEG.
     * This ought to be an error condition, but we make it a warning.
     */
    if (cinfo->Ss != 0 || cinfo->Se != DCTSIZE2 - 1 ||
        cinfo->Ah != 0 || cinfo->Al != 0)
      WARNMS(cinfo, JWRN_NOT_SEQUENTIAL);
    /* Select MCU decoding routine */
    entropy->pub.decode_mcu = decode_mcu;
  }

  /* Allocate & initialize requested statistics areas */
  for (ci = 0; ci < cinfo->comps_in_scan; ci++) {
    compptr = cinfo->cur_comp_info[ci];
    if (!cinfo->progressive_mode || (cinfo->Ss == 0 && cinfo->Ah == 0)) {
      tbl = compptr->dc_tbl_no;
      if (tbl < 0 || tbl >= NUM_ARITH_TBLS)
        ERREXIT1(cinfo, JERR_NO_ARITH_TABLE, tbl);
      if (entropy->dc_stats[tbl] == NULL)
        entropy->dc_stats[tbl] = (unsigned char *)(*cinfo->mem->alloc_small)
          ((j_common_ptr)cinfo, JPOOL_IMAGE, DC_STAT_BINS);
      memset(entropy->dc_stats[tbl], 0, DC_STAT_BINS);
      /* Initialize DC predictions to 0 */
      entropy->last_dc_val[ci] = 0;
      entropy->dc_context[ci] = 0;
    }
    if (!cinfo->progressive_mode || cinfo->Ss) {
      tbl = compptr->ac_tbl_no;
      if (tbl < 0 || tbl >= NUM_ARITH_TBLS)
        ERREXIT1(cinfo, JERR_NO_ARITH_TABLE, tbl);
      if (entropy->ac_stats[tbl] == NULL)
        entropy->ac_stats[tbl] = (unsigned char *)(*cinfo->mem->alloc_small)
          ((j_common_ptr)cinfo, JPOOL_IMAGE, AC_STAT_BINS);
      memset(entropy->ac_stats[tbl], 0, AC_STAT_BINS);
    }
  }

  /* Initialize arithmetic decoding variables */
  entropy->c = 0;
  entropy->a = 0;
  entropy->ct = -16;    /* force reading 2 initial bytes to fill C */
  entropy->pub.insufficient_data = FALSE;

  /* Initialize restart counter */
  entropy->restarts_to_go = cinfo->restart_interval;
}


/*
 * Module initialization routine for arithmetic entropy decoding.
 */

GLOBAL(void)
jinit_arith_decoder(j_decompress_ptr cinfo)
{
  arith_entropy_ptr entropy;
  int i;

  entropy = (arith_entropy_ptr)
    (*cinfo->mem->alloc_small) ((j_common_ptr)cinfo, JPOOL_IMAGE,
                                sizeof(arith_entropy_decoder));
  cinfo->entropy = (struct jpeg_entropy_decoder *)entropy;
  entropy->pub.start_pass = start_pass;

  /* Mark tables unallocated */
  for (i = 0; i < NUM_ARITH_TBLS; i++) {
    entropy->dc_stats[i] = NULL;
    entropy->ac_stats[i] = NULL;
  }

  /* Initialize index for fixed probability estimation */
  entropy->fixed_bin[0] = 113;

  if (cinfo->progressive_mode) {
    /* Create progression status table */
    int *coef_bit_ptr, ci;
    cinfo->coef_bits = (int (*)[DCTSIZE2])
      (*cinfo->mem->alloc_small) ((j_common_ptr)cinfo, JPOOL_IMAGE,
                                  cinfo->num_components * 2 * DCTSIZE2 *
                                  sizeof(int));
    coef_bit_ptr = &cinfo->coef_bits[0][0];
    for (ci = 0; ci < cinfo->num_components; ci++)
      for (i = 0; i < DCTSIZE2; i++)
        *coef_bit_ptr++ = -1;
  }
}